diff --git a/VERSION b/VERSION
index 840ca8c..400122e 100644
--- a/VERSION
+++ b/VERSION
@@ -1 +1 @@
-1.4
\ No newline at end of file
+1.5
\ No newline at end of file
diff --git a/examples/2d/base/square.py b/examples/2d/base/square.py
new file mode 100644
index 0000000..ae2428e
--- /dev/null
+++ b/examples/2d/base/square.py
@@ -0,0 +1,13 @@
+import numpy as np
+from rrompy.hfengines.linear_problem.bidimensional import \
+ HelmholtzSquareDomainProblemEngine as HSDPE
+verb = 100
+
+mu0 = [4 ** .5, 1.5 ** .5]
+solver = HSDPE(kappa = 2.5, theta = np.pi / 3, mu0 = mu0, n = 50,
+ verbosity = verb)
+uh = solver.solve(mu0)[0]
+solver.plotmesh()
+print(solver.norm(uh))
+solver.plot(uh)
+solver.plot(solver.residual(uh, mu0)[0], 'res')
diff --git a/examples/2d/pod/plot_zero_set.py b/examples/2d/pod/plot_zero_set.py
new file mode 100644
index 0000000..7281164
--- /dev/null
+++ b/examples/2d/pod/plot_zero_set.py
@@ -0,0 +1,49 @@
+import numpy as np
+from matplotlib import pyplot as plt
+
+def plotZeroSet(murange, murangeEff, approx, mu0, nSamples = 200,
+ exps = [2., 2.], clip = -1):
+ if hasattr(approx, "mus"):
+ mu2x, mu2y = approx.mus(0) ** exps[0], approx.mus(1) ** exps[1]
+ else:
+ mu2x, mu2y = mu0[0] ** exps[0], mu0[1] ** exps[1]
+ murangeExp = [[murange[0][0] ** exps[0], murange[0][1] ** exps[1]],
+ [murange[1][0] ** exps[0], murange[1][1] ** exps[1]]]
+ mu1 = np.linspace(murangeEff[0][0] ** exps[0], murangeEff[1][0] ** exps[0],
+ nSamples)
+ mu2 = np.linspace(murangeEff[0][1] ** exps[1], murangeEff[1][1] ** exps[1],
+ nSamples)
+ mu1s = np.power(mu1, 1. / exps[0])
+ mu2s = np.power(mu2, 1. / exps[1])
+ Mu1, Mu2 = np.meshgrid(np.real(mu1), np.real(mu2))
+ mus = [(m1, m2) for m2 in mu2s for m1 in mu1s]
+ Z = approx.trainedModel.getQVal(mus).reshape(Mu1.shape)
+ Zabs = np.log(np.abs(Z))
+ Zabsmin, Zabsmax = np.min(Zabs), np.max(Zabs)
+ if clip > 0:
+ Zabsmin += clip * (Zabsmax - Zabsmin)
+ cmap = plt.cm.bone_r
+ else:
+ cmap = plt.cm.jet
+ plt.figure(figsize = (15, 7))
+ plt.jet()
+ p = plt.contourf(Mu1, Mu2, Zabs, cmap = cmap,
+ levels = np.linspace(Zabsmin, Zabsmax, 50))
+ if clip > 0:
+ plt.contour(Mu1, Mu2, Zabs, [Zabsmin])
+ plt.contour(Mu1, Mu2, np.real(Z), [0.], linestyles = 'dashed')
+ plt.contour(Mu1, Mu2, np.imag(Z), [0.], linewidths = 1,
+ linestyles = 'dotted')
+ plt.plot(mu2x, mu2y, 'kx')
+ plt.plot([murangeExp[0][0]] * 2,
+ [murangeExp[0][1], murangeExp[1][1]], 'm:')
+ plt.plot([murangeExp[0][0], murangeExp[1][0]],
+ [murangeExp[1][1]] * 2, 'm:')
+ plt.plot([murangeExp[1][0]] * 2,
+ [murangeExp[1][1], murangeExp[0][1]], 'm:')
+ plt.plot([murangeExp[1][0], murangeExp[0][0]],
+ [murangeExp[0][1]] * 2, 'm:')
+ plt.colorbar(p)
+ plt.grid()
+ plt.show()
+
diff --git a/examples/2d/pod/square_pod.py b/examples/2d/pod/square_pod.py
new file mode 100644
index 0000000..56de10d
--- /dev/null
+++ b/examples/2d/pod/square_pod.py
@@ -0,0 +1,144 @@
+import numpy as np
+from rrompy.hfengines.linear_problem.bidimensional import \
+ HelmholtzSquareDomainProblemEngine as HSDPE
+from rrompy.reduction_methods.centered import RationalPade as RP
+from rrompy.reduction_methods.distributed import RationalInterpolant as RI
+from rrompy.reduction_methods.centered import RBCentered as RBC
+from rrompy.reduction_methods.distributed import RBDistributed as RBD
+from rrompy.parameter.parameter_sampling import (QuadratureSampler as QS,
+ QuadratureSamplerTotal as QST,
+ ManualSampler as MS,
+ RandomSampler as RS)
+
+verb = 5
+size = 1
+show_sample = False
+ignore_forcing = True
+ignore_forcing = False
+clip = -1
+#clip = .4
+#clip = .6
+
+MN = 6
+R = (MN + 2) * (MN + 1) // 2
+S = [int(np.ceil(R ** .5))] * 2
+
+samples = "centered"
+samples = "centered_fake"
+samples = "distributed"
+algo = "rational"
+#algo = "RB"
+sampling = "quadrature"
+sampling = "quadrature_total"
+#sampling = "random"
+
+if size == 1: # small
+ mu0 = [4 ** .5, 1.5 ** .5]
+ mutar = [5 ** .5, 1.75 ** .5]
+ murange = [[2 ** .5, 1. ** .5], [6 ** .5, 2. ** .5]]
+elif size == 2: # medium
+ mu0 = [4 ** .5, 1.75 ** .5]
+ mutar = [5 ** .5, 1.25 ** .5]
+ murange = [[1 ** .5, 1. ** .5], [7 ** .5, 2.5 ** .5]]
+elif size == 3: # fat
+ mu0 = [6 ** .5, 4 ** .5]
+ mutar = [2 ** .5, 2.5 ** .5]
+ murange = [[0 ** .5, 2 ** .5], [12 ** .5, 6 ** .5]]
+elif size == 4: # crowded
+ mu0 = [10 ** .5, 2 ** .5]
+ mutar = [9 ** .5, 2.25 ** .5]
+ murange = [[8 ** .5, 1.5 ** .5], [12 ** .5, 2.5 ** .5]]
+elif size == 5: # tall
+ mu0 = [11 ** .5, 2.25 ** .5]
+ mutar = [10.5 ** .5, 2.5 ** .5]
+ murange = [[10 ** .5, 1.5 ** .5], [12 ** .5, 3 ** .5]]
+elif size == 6: # taller
+ mu0 = [11 ** .5, 2.25 ** .5]
+ mutar = [10.5 ** .5, 2.5 ** .5]
+ murange = [[10 ** .5, 1.25 ** .5], [12 ** .5, 3.25 ** .5]]
+elif size == 7: # low
+ mu0 = [7 ** .5, .75 ** .5]
+ mutar = [6.5 ** .5, .9 ** .5]
+ murange = [[6 ** .5, .5 ** .5], [8 ** .5, 1. ** .5]]
+
+aEff = 1.25
+bEff = 1. - aEff
+murangeEff = [[(aEff*murange[0][0]**2. + bEff*murange[1][0]**2.) ** .5,
+ (aEff*murange[0][1]**2. + bEff*murange[1][1]**2.) ** .5],
+ [(aEff*murange[1][0]**2. + bEff*murange[0][0]**2.) ** .5,
+ (aEff*murange[1][1]**2. + bEff*murange[0][1]**2.) ** .5]]
+
+solver = HSDPE(kappa = 2.5, theta = np.pi / 3, mu0 = mu0, n = 20,
+ verbosity = verb)
+if ignore_forcing: solver.nbs = 1
+
+rescaling = [lambda x: np.power(x, 2.), lambda x: x]
+rescalingInv = [lambda x: np.power(x, .5), lambda x: x]
+if algo == "rational":
+ params = {'N':MN, 'M':MN, 'S':S, 'POD':True}
+ if samples == "distributed":
+ params['polybasis'] = "CHEBYSHEV"
+# params['polybasis'] = "LEGENDRE"
+# params['polybasis'] = "MONOMIAL"
+ params['E'] = MN
+ method = RI
+ elif samples == "centered_fake":
+ params['polybasis'] = "MONOMIAL"
+ params['S'] = R
+ method = RI
+ else:
+ params['S'] = R
+ method = RP
+else: #if algo == "RB":
+ params = {'R':R, 'S':S, 'POD':True}
+ if samples == "distributed":
+ method = RBD
+ elif samples == "centered_fake":
+ params['S'] = R
+ method = RBD
+ else:
+ params['S'] = R
+ method = RBC
+
+if samples == "distributed":
+ if sampling == "quadrature":
+ params['sampler'] = QS(murange, "CHEBYSHEV", scaling = rescaling,
+ scalingInv = rescalingInv)
+# params['sampler'] = QS(murange, "GAUSSLEGENDRE", scaling = rescaling,
+# scalingInv = rescalingInv)
+# params['sampler'] = QS(murange, "UNIFORM", scaling = rescaling,
+# scalingInv = rescalingInv)
+ params['S'] = [max(j, MN + 1) for j in params['S']]
+ elif sampling == "quadrature_total":
+ params['sampler'] = QST(murange, "CHEBYSHEV", scaling = rescaling,
+ scalingInv = rescalingInv)
+ params['S'] = R
+ else: # if sampling == "random":
+ params['sampler'] = RS(murange, "HALTON", scaling = rescaling,
+ scalingInv = rescalingInv)
+ params['S'] = R
+
+elif samples == "centered_fake":
+ params['sampler'] = MS(murange, points = [mu0], scaling = rescaling,
+ scalingInv = rescalingInv)
+
+approx = method(solver, mu0 = mu0, approxParameters = params,
+ verbosity = verb)
+
+approx.setupApprox()
+if show_sample:
+ approx.plotApprox(mutar, name = 'u_app')
+ approx.plotHF(mutar, name = 'u_HF')
+ approx.plotErr(mutar, name = 'err')
+ approx.plotRes(mutar, name = 'res')
+ appErr, solNorm = approx.normErr(mutar), approx.normHF(mutar)
+ resNorm, RHSNorm = approx.normRes(mutar), approx.normRHS(mutar)
+ print(('SolNorm:\t{}\nErr:\t{}\nErrRel:\t{}').format(solNorm, appErr,
+ np.divide(appErr, solNorm)))
+ print(('RHSNorm:\t{}\nRes:\t{}\nResRel:\t{}').format(RHSNorm, resNorm,
+ np.divide(resNorm, RHSNorm)))
+
+if algo == "rational":
+ from plot_zero_set import plotZeroSet
+ plotZeroSet(murange, murangeEff, approx, mu0,
+ 200, [2., 1.], clip = clip)
\ No newline at end of file
diff --git a/examples/2d/pod/square_simplified_pod_hermite.py b/examples/2d/pod/square_pod_hermite.py
similarity index 58%
copy from examples/2d/pod/square_simplified_pod_hermite.py
copy to examples/2d/pod/square_pod_hermite.py
index 453cf0c..9fc5401 100644
--- a/examples/2d/pod/square_simplified_pod_hermite.py
+++ b/examples/2d/pod/square_pod_hermite.py
@@ -1,107 +1,100 @@
import numpy as np
from rrompy.hfengines.linear_problem.bidimensional import \
- HelmholtzSquareSimplifiedDomainProblemEngine as HSSDPE
+ HelmholtzSquareDomainProblemEngine as HSDPE
from rrompy.reduction_methods.centered import RationalPade as RP
from rrompy.reduction_methods.distributed import RationalInterpolant as RI
from rrompy.reduction_methods.centered import RBCentered as RBC
from rrompy.reduction_methods.distributed import RBDistributed as RBD
from rrompy.parameter.parameter_sampling import (QuadratureSampler as QS,
RandomSampler as RS,
ManualSampler as MS)
verb = 0
-size = 2
+size = 1
+show_sample = False
MN = 4
R = (MN + 2) * (MN + 1) // 2
S0 = [3] * 2
S = [25]
assert R < np.prod(S)
samples = "centered"
samples = "distributed"
algo = "rational"
#algo = "RB"
sampling = "quadrature"
-#sampling = "random"
+sampling = "random"
if size == 1: # small
mu0 = [4 ** .5, 1.5 ** .5]
mutar = [5 ** .5, 1.75 ** .5]
murange = [[2 ** .5, 1. ** .5], [6 ** .5, 2. ** .5]]
elif size == 2: # medium
mu0 = [4 ** .5, 1.75 ** .5]
mutar = [4.5 ** .5, 1.25 ** .5]
murange = [[1 ** .5, 1. ** .5], [7 ** .5, 2.5 ** .5]]
elif size == 3: # large
mu0 = [6 ** .5, 4 ** .5]
mutar = [2 ** .5, 2.5 ** .5]
murange = [[0 ** .5, 2 ** .5], [12 ** .5, 6 ** .5]]
elif size == 4: # crowded
mu0 = [10 ** .5, 2 ** .5]
mutar = [9 ** .5, 2.25 ** .5]
murange = [[8 ** .5, 1.5 ** .5], [12 ** .5, 2.5 ** .5]]
-solver = HSSDPE(kappa = 2.5, theta = np.pi / 3, mu0 = mu0, n = 20,
- verbosity = verb)
+aEff = 1.25
+bEff = 1. - aEff
+murangeEff = [[(aEff*murange[0][0]**2. + bEff*murange[1][0]**2.) ** .5,
+ (aEff*murange[0][1]**2. + bEff*murange[1][1]**2.) ** .5],
+ [(aEff*murange[1][0]**2. + bEff*murange[0][0]**2.) ** .5,
+ (aEff*murange[1][1]**2. + bEff*murange[0][1]**2.) ** .5]]
+
+solver = HSDPE(kappa = 2.5, theta = np.pi / 3, mu0 = mu0, n = 20,
+ verbosity = verb)
-rescaling = [lambda x: np.power(x, 2.)] * 2
-rescalingInv = [lambda x: np.power(x, .5)] * 2
+rescaling = [lambda x: np.power(x, 2.), lambda x: x]
+rescalingInv = [lambda x: np.power(x, .5), lambda x: x]
if algo == "rational":
params = {'N':MN, 'M':MN, 'S':S, 'POD':True}
if samples == "distributed":
params['polybasis'] = "CHEBYSHEV"
method = RI
else:
method = RP
else: #if algo == "RB":
params = {'R':R, 'S':S, 'POD':True}
if samples == "distributed":
method = RBD
else:
method = RBC
if samples == "distributed":
if sampling == "quadrature":
sampler0 = QS(murange, "CHEBYSHEV", scaling = rescaling,
scalingInv = rescalingInv)
else: # if sampling == "random":
sampler0 = RS(murange, "SOBOL", scaling = rescaling,
scalingInv = rescalingInv)
S0 = np.prod(S0)
params['sampler'] = MS(murange, points = sampler0.generatePoints(S0))
approx = method(solver, mu0 = mu0, approxParameters = params,
verbosity = verb)
approx.setupApprox()
-approx.plotApprox(mutar, name = 'u_app')
-approx.plotHF(mutar, name = 'u_HF')
-approx.plotErr(mutar, name = 'err')
-approx.plotRes(mutar, name = 'res')
-appErr, solNorm = approx.normErr(mutar), approx.normHF(mutar)
-resNorm, RHSNorm = approx.normRes(mutar), approx.normRHS(mutar)
-print(('SolNorm:\t{}\nErr:\t{}\nErrRel:\t{}').format(solNorm, appErr,
- np.divide(appErr, solNorm)))
-print(('RHSNorm:\t{}\nRes:\t{}\nResRel:\t{}').format(RHSNorm, resNorm,
- np.divide(resNorm, RHSNorm)))
+if show_sample:
+ approx.plotApprox(mutar, name = 'u_app')
+ approx.plotHF(mutar, name = 'u_HF')
+ approx.plotErr(mutar, name = 'err')
+ approx.plotRes(mutar, name = 'res')
+ appErr, solNorm = approx.normErr(mutar), approx.normHF(mutar)
+ resNorm, RHSNorm = approx.normRes(mutar), approx.normRHS(mutar)
+ print(('SolNorm:\t{}\nErr:\t{}\nErrRel:\t{}').format(solNorm, appErr,
+ np.divide(appErr, solNorm)))
+ print(('RHSNorm:\t{}\nRes:\t{}\nResRel:\t{}').format(RHSNorm, resNorm,
+ np.divide(resNorm, RHSNorm)))
if algo == "rational":
- from matplotlib import pyplot as plt
- mu1 = np.linspace(murange[0][0]**2, murange[1][0]**2, 100)
- mu2 = np.linspace(murange[0][1]**2, murange[1][1]**2, 100)
- mu1s = np.power(mu1, .5)
- mu2s = np.power(mu2, .5)
- Mu1, Mu2 = np.meshgrid(mu1, mu2)
- mus = [(m1, m2) for m2 in mu2s for m1 in mu1s]
- Z = approx.trainedModel.getQVal(mus).reshape(Mu1.shape)
- plt.figure(figsize = (15, 7))
- p = plt.contourf(Mu1, Mu2, np.log(np.abs(Z)), 50)
- plt.contour(Mu1, Mu2, np.real(Z), [0.], linestyles = 'dashed')
- plt.contour(Mu1, Mu2, np.imag(Z), [0.], linewidths = 1,
- linestyles = 'dotted')
- plt.plot(approx.mus(0) ** 2, approx.mus(1) ** 2, 'kx')
- plt.colorbar(p)
- plt.grid()
- plt.show()
-
\ No newline at end of file
+ from plot_zero_set import plotZeroSet
+ plotZeroSet(murange, murangeEff, approx, mu0, 200, [2., 2.])
diff --git a/examples/2d/pod/square_simplified_pod.py b/examples/2d/pod/square_simplified_pod.py
index e8c47bf..bd0d439 100644
--- a/examples/2d/pod/square_simplified_pod.py
+++ b/examples/2d/pod/square_simplified_pod.py
@@ -1,106 +1,138 @@
import numpy as np
from rrompy.hfengines.linear_problem.bidimensional import \
HelmholtzSquareSimplifiedDomainProblemEngine as HSSDPE
from rrompy.reduction_methods.centered import RationalPade as RP
from rrompy.reduction_methods.distributed import RationalInterpolant as RI
from rrompy.reduction_methods.centered import RBCentered as RBC
from rrompy.reduction_methods.distributed import RBDistributed as RBD
from rrompy.parameter.parameter_sampling import (QuadratureSampler as QS,
+ QuadratureSamplerTotal as QST,
+ ManualSampler as MS,
RandomSampler as RS)
-verb = 0
-size = 2
+verb = 5
+size = 1
+show_sample = False
-MN = 4
+MN = 5
R = (MN + 2) * (MN + 1) // 2
-S = [5] * 2
-assert R < np.prod(S)
+S = [int(np.ceil(R ** .5))] * 2
samples = "centered"
+samples = "centered_fake"
samples = "distributed"
algo = "rational"
#algo = "RB"
sampling = "quadrature"
+sampling = "quadrature_total"
sampling = "random"
if size == 1: # small
mu0 = [4 ** .5, 1.5 ** .5]
mutar = [5 ** .5, 1.75 ** .5]
murange = [[2 ** .5, 1. ** .5], [6 ** .5, 2. ** .5]]
elif size == 2: # medium
mu0 = [4 ** .5, 1.75 ** .5]
mutar = [5 ** .5, 1.25 ** .5]
murange = [[1 ** .5, 1. ** .5], [7 ** .5, 2.5 ** .5]]
-elif size == 3: # large
+elif size == 3: # fat
mu0 = [6 ** .5, 4 ** .5]
mutar = [2 ** .5, 2.5 ** .5]
murange = [[0 ** .5, 2 ** .5], [12 ** .5, 6 ** .5]]
elif size == 4: # crowded
mu0 = [10 ** .5, 2 ** .5]
mutar = [9 ** .5, 2.25 ** .5]
murange = [[8 ** .5, 1.5 ** .5], [12 ** .5, 2.5 ** .5]]
+elif size == 5: # tall
+ mu0 = [11 ** .5, 2.25 ** .5]
+ mutar = [10.5 ** .5, 2.5 ** .5]
+ murange = [[10 ** .5, 1.5 ** .5], [12 ** .5, 3 ** .5]]
+elif size == 6: # taller
+ mu0 = [11 ** .5, 2.25 ** .5]
+ mutar = [10.5 ** .5, 2.5 ** .5]
+ murange = [[10 ** .5, 1.25 ** .5], [12 ** .5, 3.25 ** .5]]
+elif size == 7: # low
+ mu0 = [7 ** .5, .75 ** .5]
+ mutar = [8 ** .5, 1 ** .5]
+ murange = [[6 ** .5, .25 ** .5], [8 ** .5, 1.25 ** .5]]
+
+aEff = 1.25
+bEff = 1. - aEff
+murangeEff = [[(aEff*murange[0][0]**2. + bEff*murange[1][0]**2.) ** .5,
+ (aEff*murange[0][1]**2. + bEff*murange[1][1]**2.) ** .5],
+ [(aEff*murange[1][0]**2. + bEff*murange[0][0]**2.) ** .5,
+ (aEff*murange[1][1]**2. + bEff*murange[0][1]**2.) ** .5]]
solver = HSSDPE(kappa = 2.5, theta = np.pi / 3, mu0 = mu0, n = 20,
verbosity = verb)
rescaling = [lambda x: np.power(x, 2.)] * 2
rescalingInv = [lambda x: np.power(x, .5)] * 2
if algo == "rational":
params = {'N':MN, 'M':MN, 'S':S, 'POD':True}
if samples == "distributed":
params['polybasis'] = "CHEBYSHEV"
+ params['polybasis'] = "LEGENDRE"
+ params['polybasis'] = "MONOMIAL"
+ params['E'] = MN
+ method = RI
+ elif samples == "centered_fake":
+ params['polybasis'] = "MONOMIAL"
+ params['S'] = R
method = RI
else:
- params['S'] = np.prod(params['S'])
+ params['S'] = R
method = RP
else: #if algo == "RB":
params = {'R':R, 'S':S, 'POD':True}
if samples == "distributed":
method = RBD
+ elif samples == "centered_fake":
+ params['S'] = R
+ method = RBD
else:
- params['S'] = np.prod(params['S'])
+ params['S'] = R
method = RBC
if samples == "distributed":
if sampling == "quadrature":
params['sampler'] = QS(murange, "CHEBYSHEV", scaling = rescaling,
scalingInv = rescalingInv)
+# params['sampler'] = QS(murange, "GAUSSLEGENDRE", scaling = rescaling,
+# scalingInv = rescalingInv)
+# params['sampler'] = QS(murange, "UNIFORM", scaling = rescaling,
+# scalingInv = rescalingInv)
+ params['S'] = [max(j, MN + 1) for j in params['S']]
+ elif sampling == "quadrature_total":
+ params['sampler'] = QST(murange, "CHEBYSHEV", scaling = rescaling,
+ scalingInv = rescalingInv)
+ params['S'] = R
else: # if sampling == "random":
- params['sampler'] = RS(murange, "SOBOL", scaling = rescaling,
+ params['sampler'] = RS(murange, "HALTON", scaling = rescaling,
scalingInv = rescalingInv)
- params['S'] = np.prod(params['S'])
+ params['S'] = R
+
+elif samples == "centered_fake":
+ params['sampler'] = MS(murange, points = [mu0], scaling = rescaling,
+ scalingInv = rescalingInv)
approx = method(solver, mu0 = mu0, approxParameters = params,
verbosity = verb)
approx.setupApprox()
-approx.plotApprox(mutar, name = 'u_app')
-approx.plotHF(mutar, name = 'u_HF')
-approx.plotErr(mutar, name = 'err')
-approx.plotRes(mutar, name = 'res')
-appErr, solNorm = approx.normErr(mutar), approx.normHF(mutar)
-resNorm, RHSNorm = approx.normRes(mutar), approx.normRHS(mutar)
-print(('SolNorm:\t{}\nErr:\t{}\nErrRel:\t{}').format(solNorm, appErr,
- np.divide(appErr, solNorm)))
-print(('RHSNorm:\t{}\nRes:\t{}\nResRel:\t{}').format(RHSNorm, resNorm,
- np.divide(resNorm, RHSNorm)))
+if show_sample:
+ approx.plotApprox(mutar, name = 'u_app')
+ approx.plotHF(mutar, name = 'u_HF')
+ approx.plotErr(mutar, name = 'err')
+ approx.plotRes(mutar, name = 'res')
+ appErr, solNorm = approx.normErr(mutar), approx.normHF(mutar)
+ resNorm, RHSNorm = approx.normRes(mutar), approx.normRHS(mutar)
+ print(('SolNorm:\t{}\nErr:\t{}\nErrRel:\t{}').format(solNorm, appErr,
+ np.divide(appErr, solNorm)))
+ print(('RHSNorm:\t{}\nRes:\t{}\nResRel:\t{}').format(RHSNorm, resNorm,
+ np.divide(resNorm, RHSNorm)))
if algo == "rational":
- from matplotlib import pyplot as plt
- mu1 = np.linspace(murange[0][0]**2, murange[1][0]**2, 100)
- mu2 = np.linspace(murange[0][1]**2, murange[1][1]**2, 100)
- mu1s = np.power(mu1, .5)
- mu2s = np.power(mu2, .5)
- Mu1, Mu2 = np.meshgrid(mu1, mu2)
- mus = [(m1, m2) for m2 in mu2s for m1 in mu1s]
- Z = approx.trainedModel.getQVal(mus).reshape(Mu1.shape)
- plt.figure(figsize = (15, 7))
- p = plt.contourf(Mu1, Mu2, np.log(np.abs(Z)), 50)
- plt.contour(Mu1, Mu2, np.real(Z), [0.], linestyles = 'dashed')
- plt.contour(Mu1, Mu2, np.imag(Z), [0.], linewidths = 1,
- linestyles = 'dotted')
- plt.plot(approx.mus(0) ** 2, approx.mus(1) ** 2, 'kx')
- plt.colorbar(p)
- plt.grid()
- plt.show()
+ from plot_zero_set import plotZeroSet
+ plotZeroSet(murange, murangeEff, approx, mu0, 200, [2., 2.])
\ No newline at end of file
diff --git a/examples/2d/pod/square_simplified_pod_hermite.py b/examples/2d/pod/square_simplified_pod_hermite.py
index 453cf0c..ce63c07 100644
--- a/examples/2d/pod/square_simplified_pod_hermite.py
+++ b/examples/2d/pod/square_simplified_pod_hermite.py
@@ -1,107 +1,100 @@
import numpy as np
from rrompy.hfengines.linear_problem.bidimensional import \
HelmholtzSquareSimplifiedDomainProblemEngine as HSSDPE
from rrompy.reduction_methods.centered import RationalPade as RP
from rrompy.reduction_methods.distributed import RationalInterpolant as RI
from rrompy.reduction_methods.centered import RBCentered as RBC
from rrompy.reduction_methods.distributed import RBDistributed as RBD
from rrompy.parameter.parameter_sampling import (QuadratureSampler as QS,
RandomSampler as RS,
ManualSampler as MS)
verb = 0
-size = 2
+size = 1
+show_sample = False
MN = 4
R = (MN + 2) * (MN + 1) // 2
S0 = [3] * 2
S = [25]
assert R < np.prod(S)
samples = "centered"
samples = "distributed"
algo = "rational"
#algo = "RB"
sampling = "quadrature"
#sampling = "random"
if size == 1: # small
mu0 = [4 ** .5, 1.5 ** .5]
mutar = [5 ** .5, 1.75 ** .5]
murange = [[2 ** .5, 1. ** .5], [6 ** .5, 2. ** .5]]
elif size == 2: # medium
mu0 = [4 ** .5, 1.75 ** .5]
mutar = [4.5 ** .5, 1.25 ** .5]
murange = [[1 ** .5, 1. ** .5], [7 ** .5, 2.5 ** .5]]
elif size == 3: # large
mu0 = [6 ** .5, 4 ** .5]
mutar = [2 ** .5, 2.5 ** .5]
murange = [[0 ** .5, 2 ** .5], [12 ** .5, 6 ** .5]]
elif size == 4: # crowded
mu0 = [10 ** .5, 2 ** .5]
mutar = [9 ** .5, 2.25 ** .5]
murange = [[8 ** .5, 1.5 ** .5], [12 ** .5, 2.5 ** .5]]
+aEff = 1.25
+bEff = 1. - aEff
+murangeEff = [[(aEff*murange[0][0]**2. + bEff*murange[1][0]**2.) ** .5,
+ (aEff*murange[0][1]**2. + bEff*murange[1][1]**2.) ** .5],
+ [(aEff*murange[1][0]**2. + bEff*murange[0][0]**2.) ** .5,
+ (aEff*murange[1][1]**2. + bEff*murange[0][1]**2.) ** .5]]
+
solver = HSSDPE(kappa = 2.5, theta = np.pi / 3, mu0 = mu0, n = 20,
verbosity = verb)
rescaling = [lambda x: np.power(x, 2.)] * 2
rescalingInv = [lambda x: np.power(x, .5)] * 2
if algo == "rational":
params = {'N':MN, 'M':MN, 'S':S, 'POD':True}
if samples == "distributed":
params['polybasis'] = "CHEBYSHEV"
method = RI
else:
method = RP
else: #if algo == "RB":
params = {'R':R, 'S':S, 'POD':True}
if samples == "distributed":
method = RBD
else:
method = RBC
if samples == "distributed":
if sampling == "quadrature":
sampler0 = QS(murange, "CHEBYSHEV", scaling = rescaling,
scalingInv = rescalingInv)
else: # if sampling == "random":
sampler0 = RS(murange, "SOBOL", scaling = rescaling,
scalingInv = rescalingInv)
S0 = np.prod(S0)
params['sampler'] = MS(murange, points = sampler0.generatePoints(S0))
approx = method(solver, mu0 = mu0, approxParameters = params,
verbosity = verb)
approx.setupApprox()
-approx.plotApprox(mutar, name = 'u_app')
-approx.plotHF(mutar, name = 'u_HF')
-approx.plotErr(mutar, name = 'err')
-approx.plotRes(mutar, name = 'res')
-appErr, solNorm = approx.normErr(mutar), approx.normHF(mutar)
-resNorm, RHSNorm = approx.normRes(mutar), approx.normRHS(mutar)
-print(('SolNorm:\t{}\nErr:\t{}\nErrRel:\t{}').format(solNorm, appErr,
- np.divide(appErr, solNorm)))
-print(('RHSNorm:\t{}\nRes:\t{}\nResRel:\t{}').format(RHSNorm, resNorm,
- np.divide(resNorm, RHSNorm)))
+if show_sample:
+ approx.plotApprox(mutar, name = 'u_app')
+ approx.plotHF(mutar, name = 'u_HF')
+ approx.plotErr(mutar, name = 'err')
+ approx.plotRes(mutar, name = 'res')
+ appErr, solNorm = approx.normErr(mutar), approx.normHF(mutar)
+ resNorm, RHSNorm = approx.normRes(mutar), approx.normRHS(mutar)
+ print(('SolNorm:\t{}\nErr:\t{}\nErrRel:\t{}').format(solNorm, appErr,
+ np.divide(appErr, solNorm)))
+ print(('RHSNorm:\t{}\nRes:\t{}\nResRel:\t{}').format(RHSNorm, resNorm,
+ np.divide(resNorm, RHSNorm)))
if algo == "rational":
- from matplotlib import pyplot as plt
- mu1 = np.linspace(murange[0][0]**2, murange[1][0]**2, 100)
- mu2 = np.linspace(murange[0][1]**2, murange[1][1]**2, 100)
- mu1s = np.power(mu1, .5)
- mu2s = np.power(mu2, .5)
- Mu1, Mu2 = np.meshgrid(mu1, mu2)
- mus = [(m1, m2) for m2 in mu2s for m1 in mu1s]
- Z = approx.trainedModel.getQVal(mus).reshape(Mu1.shape)
- plt.figure(figsize = (15, 7))
- p = plt.contourf(Mu1, Mu2, np.log(np.abs(Z)), 50)
- plt.contour(Mu1, Mu2, np.real(Z), [0.], linestyles = 'dashed')
- plt.contour(Mu1, Mu2, np.imag(Z), [0.], linewidths = 1,
- linestyles = 'dotted')
- plt.plot(approx.mus(0) ** 2, approx.mus(1) ** 2, 'kx')
- plt.colorbar(p)
- plt.grid()
- plt.show()
-
\ No newline at end of file
+ from plot_zero_set import plotZeroSet
+ plotZeroSet(murange, murangeEff, approx, mu0, 200, [2., 2.])
diff --git a/rrompy/hfengines/base/matrix_engine_base.py b/rrompy/hfengines/base/matrix_engine_base.py
index cb3e2e6..664e74e 100644
--- a/rrompy/hfengines/base/matrix_engine_base.py
+++ b/rrompy/hfengines/base/matrix_engine_base.py
@@ -1,421 +1,441 @@
# Copyright (C) 2018 by the RROMPy authors
#
# This file is part of RROMPy.
#
# RROMPy is free software: you can redistribute it and/or modify
# it under the terms of the GNU Lesser General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# RROMPy is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU Lesser General Public License for more details.
#
# You should have received a copy of the GNU Lesser General Public License
# along with RROMPy. If not, see .
#
from abc import abstractmethod
import numpy as np
import scipy.sparse as scsp
from matplotlib import pyplot as plt
from copy import deepcopy as copy
from rrompy.utilities.base.types import (Np1D, Np2D, ScOp, strLst, Tuple, List,
DictAny, paramVal, paramList,
sampList)
from rrompy.utilities.base import (purgeList, getNewFilename, verbosityDepth,
multibinom)
from rrompy.utilities.poly_fitting.polynomial import (
hashDerivativeToIdx as hashD, hashIdxToDerivative as hashI)
from rrompy.utilities.exception_manager import RROMPyException, RROMPyAssert
from rrompy.parameter import checkParameter, checkParameterList
from rrompy.sampling import sampleList, emptySampleList
from rrompy.solver import setupSolver
__all__ = ['MatrixEngineBase']
class MatrixEngineBase:
"""
Generic solver for parametric matrix problems.
Attributes:
verbosity: Verbosity level.
As: Scipy sparse array representation (in CSC format) of As.
bs: Numpy array representation of bs.
bsH: Numpy array representation of homogeneized bs.
energyNormMatrix: Scipy sparse matrix representing inner product.
"""
- nAs, nbs = 1, 1
-
def __init__(self, verbosity : int = 10, timestamp : bool = True):
self.verbosity = verbosity
self.timestamp = timestamp
- self.resetAs()
- self.resetbs()
+ self.nAs, self.nbs = 1, 1
self.setSolver("SPSOLVE", {"use_umfpack" : False})
self.npar = 0
def name(self) -> str:
return self.__class__.__name__
def __str__(self) -> str:
return self.name()
def __repr__(self) -> str:
return self.__str__() + " at " + hex(id(self))
def __dir_base__(self):
return [x for x in self.__dir__() if x[:2] != "__"]
@property
def npar(self):
"""Value of npar."""
return self._npar
@npar.setter
def npar(self, npar):
nparOld = self._npar if hasattr(self, "_npar") else -1
if npar != nparOld:
self.rescalingExp = [1.] * npar
self._npar = npar
+ @property
+ def nAs(self):
+ """Value of nAs."""
+ return self._nAs
+ @nAs.setter
+ def nAs(self, nAs):
+ self._nAs = nAs
+ self.resetAs()
+
+ @property
+ def nbs(self):
+ """Value of nbs."""
+ return self._nbs
+ @nbs.setter
+ def nbs(self, nbs):
+ self._nbs = nbs
+ self.resetbs()
+
@property
def nbsH(self) -> int:
return max(self.nbs, self.nAs)
def spacedim(self):
return self.As[0].shape[1]
def checkParameter(self, mu:paramList):
return checkParameter(mu, self.npar)
def checkParameterList(self, mu:paramList):
return checkParameterList(mu, self.npar)
def buildEnergyNormForm(self): # eye
"""
Build sparse matrix (in CSR format) representative of scalar product.
"""
self.energyNormMatrix = np.eye(self.spacedim())
def innerProduct(self, u:Np2D, v:Np2D, onlyDiag : bool = False) -> Np2D:
"""Scalar product."""
if not hasattr(self, "energyNormMatrix"):
if self.verbosity >= 20:
verbosityDepth("INIT", "Assembling energy matrix.",
timestamp = self.timestamp)
self.buildEnergyNormForm()
if self.verbosity >= 20:
verbosityDepth("DEL", "Done assembling energy matrix.",
timestamp = self.timestamp)
if not isinstance(u, (np.ndarray,)): u = u.data
if not isinstance(v, (np.ndarray,)): v = v.data
if onlyDiag:
return np.sum(self.energyNormMatrix.dot(u) * v.conj(), axis = 0)
return v.T.conj().dot(self.energyNormMatrix.dot(u))
def norm(self, u:Np2D) -> Np1D:
return np.abs(self.innerProduct(u, u, onlyDiag = True)) ** .5
def checkAInBounds(self, derI : int = 0):
"""Check if derivative index is oob for operator of linear system."""
if derI < 0 or derI >= self.nAs:
d = self.spacedim()
return scsp.csr_matrix((np.zeros(0), np.zeros(0), np.zeros(d + 1)),
shape = (d, d), dtype = np.complex)
def checkbInBounds(self, derI : int = 0, homogeneized : bool = False):
"""Check if derivative index is oob for RHS of linear system."""
nbs = self.nbsH if homogeneized else self.nbs
if derI < 0 or derI >= nbs:
return np.zeros(self.spacedim(), dtype = np.complex)
def resetAs(self):
"""Reset (derivatives of) operator of linear system."""
- self.resetbsH()
self.setAs([None] * self.nAs)
+ if hasattr(self, "_nbs"): self.resetbsH()
def resetbs(self):
"""Reset (derivatives of) RHS of linear system."""
- self.resetbsH()
self.setbs([None] * self.nbs)
+ if hasattr(self, "_nAs"): self.resetbsH()
def resetbsH(self):
"""Reset (derivatives of) homogeneized RHS of linear system."""
self.setbsH([None] * self.nbsH)
def setAs(self, As:List[Np2D]):
"""Assign terms of operator of linear system."""
if len(As) != self.nAs:
raise RROMPyException(("Expected number {} of terms of As not "
"matching given list length {}.").format(self.nAs,
len(As)))
self.As = [copy(A) for A in As]
def setbs(self, bs:List[Np1D]):
"""Assign terms of RHS of linear system."""
if len(bs) != self.nbs:
raise RROMPyException(("Expected number {} of terms of bs not "
"matching given list length {}.").format(self.nbs,
len(bs)))
self.bs = [copy(b) for b in bs]
def setbsH(self, bsH:List[Np1D]):
"""Assign terms of homogeneized RHS of linear system."""
if len(bsH) != self.nbsH:
raise RROMPyException(("Expected number {} of terms of bsH not "
"matching given list length {}.").format(self.nbsH,
len(bsH)))
self.bsH = [copy(bH) for bH in bsH]
def _assembleA(self, mu : paramVal = [], der : List[int] = 0,
- derI : int = None) -> ScOp:
+ derI : int = None, muBase : paramVal = None) -> ScOp:
"""Assemble (derivative of) operator of linear system."""
mu = self.checkParameter(mu)
+ if muBase is None: muBase = [0.] * self.npar
+ muBase = self.checkParameter(muBase)
+ if self.npar > 0: mu, muBase = mu[0], muBase[0]
if not hasattr(der, "__len__"): der = [der] * self.npar
if derI is None: derI = hashD(der)
Anull = self.checkAInBounds(derI)
if Anull is not None: return Anull
- As0 = self.As[derI]
+ rExp = self.rescalingExp
+ A = copy(self.As[derI])
for j in range(derI + 1, self.nAs):
derIdx = hashI(j, self.npar)
diffIdx = [x - y for (x, y) in zip(derIdx, der)]
if np.all([x >= 0 for x in diffIdx]):
- coeff = multibinom(derIdx, diffIdx)
- for d in range(self.npar):
- coeff *= mu(0, d) ** (self.rescalingExp[d] * diffIdx[d])
- As0 = As0 + coeff * self.As[j]
- return As0
+ A = A + (np.prod((mu ** rExp - muBase ** rExp) ** diffIdx)
+ * multibinom(derIdx, diffIdx) * self.As[j])
+ return A
@abstractmethod
def A(self, mu : paramVal = [], der : List[int] = 0) -> ScOp:
"""
Assemble terms of operator of linear system and return it (or its
derivative) at a given parameter.
"""
if not hasattr(der, "__len__"): der = [der] * self.npar
derI = hashD(der)
for j in range(derI, self.nAs):
if self.As[j] is None: self.As[j] = 0.
return self._assembleA(mu, der, derI)
def affineLinearSystemA(self, mu : paramVal = []) -> List[Np2D]:
"""
Assemble affine blocks of operator of linear system (just linear
blocks).
"""
As = [None] * self.nAs
for j in range(self.nAs):
As[j] = self.A(mu, hashI(j, self.npar))
return As
def affineWeightsA(self, mu : paramVal = []) -> List[str]:
"""
Assemble affine blocks of operator of linear system (just affine
weights). Stored as strings for the sake of pickling.
"""
mu = self.checkParameter(mu)
lambdasA = ["1."]
mu0Eff = mu ** self.rescalingExp
for j in range(1, self.nAs):
lambdasA += ["np.prod((mu ** ({1}) - [{0}]) ** ({2}))".format(
','.join([str(x) for x in mu0Eff[0]]),
self.rescalingExp, hashI(j, self.npar))]
return lambdasA
def affineBlocksA(self, mu : paramVal = [])\
-> Tuple[List[Np2D], List[str]]:
"""Assemble affine blocks of operator of linear system."""
return self.affineLinearSystemA(mu), self.affineWeightsA(mu)
def _assembleb(self, mu : paramVal = [], der : List[int] = 0,
- derI : int = None, homogeneized : bool = False) -> ScOp:
+ derI : int = None, homogeneized : bool = False,
+ muBase : paramVal = None) -> ScOp:
"""Assemble (derivative of) (homogeneized) RHS of linear system."""
mu = self.checkParameter(mu)
+ if muBase is None: muBase = [0.] * self.npar
+ muBase = self.checkParameter(muBase)
+ if self.npar > 0: mu, muBase = mu[0], muBase[0]
if not hasattr(der, "__len__"): der = [der] * self.npar
if derI is None: derI = hashD(der)
- bnull = self.checkbInBounds(derI)
+ bnull = self.checkbInBounds(derI, homogeneized)
if bnull is not None: return bnull
bs = self.bsH if homogeneized else self.bs
- b = bs[derI]
+ rExp = self.rescalingExp
+ b = copy(bs[derI])
for j in range(derI + 1, len(bs)):
derIdx = hashI(j, self.npar)
diffIdx = [x - y for (x, y) in zip(derIdx, der)]
if np.all([x >= 0 for x in diffIdx]):
- coeff = multibinom(derIdx, diffIdx)
- for d in range(self.npar):
- coeff *= mu(0, d) ** (self.rescalingExp[d] * diffIdx[d])
- b = b + coeff * bs[j]
+ b = b + (np.prod((mu ** rExp - muBase ** rExp) ** diffIdx)
+ * multibinom(derIdx, diffIdx) * bs[j])
return b
@abstractmethod
def b(self, mu : paramVal = [], der : List[int] = 0,
homogeneized : bool = False) -> Np1D:
"""
Assemble terms of (homogeneized) RHS of linear system and return it (or
its derivative) at a given parameter.
"""
if not hasattr(der, "__len__"): der = [der] * self.npar
derI = hashD(der)
if homogeneized:
for j in range(derI, self.nbsH):
if self.bsH[j] is None: self.bsH[j] = 0.
else:
for j in range(derI, self.nbs):
if self.bs[j] is None: self.bs[j] = 0.
return self._assembleb(mu, der, derI, homogeneized)
def affineLinearSystemb(self, mu : paramVal = [],
homogeneized : bool = False) -> List[Np1D]:
"""
Assemble affine blocks of RHS of linear system (just linear blocks).
"""
nbs = self.nbsH if homogeneized else self.nbs
bs = [None] * nbs
for j in range(nbs):
bs[j] = self.b(mu, hashI(j, self.npar), homogeneized)
return bs
def affineWeightsb(self, mu : paramVal = [],
homogeneized : bool = False) -> List[str]:
"""
Assemble affine blocks of RHS of linear system (just affine weights).
Stored as strings for the sake of pickling.
"""
mu = self.checkParameter(mu)
nbs = self.nbsH if homogeneized else self.nbs
lambdasb = ["1."]
mu0Eff = mu ** self.rescalingExp
for j in range(1, nbs):
lambdasb += ["np.prod((mu ** ({1}) - [{0}]) ** ({2}))".format(
','.join([str(x) for x in mu0Eff[0]]),
self.rescalingExp, hashI(j, self.npar))]
return lambdasb
def affineBlocksb(self, mu : paramVal = [], homogeneized : bool = False)\
-> Tuple[List[Np1D], List[str]]:
"""Assemble affine blocks of RHS of linear system."""
return (self.affineLinearSystemb(mu, homogeneized),
self.affineWeightsb(mu, homogeneized))
def setSolver(self, solverType:str, solverArgs : DictAny = {}):
"""Choose solver type and parameters."""
self._solver, self._solverArgs = setupSolver(solverType, solverArgs)
def solve(self, mu : paramList = [], RHS : sampList = None,
homogeneized : bool = False) -> sampList:
"""
Find solution of linear system.
Args:
mu: parameter value.
RHS: RHS of linear system. If None, defaults to that of parametric
system. Defaults to None.
"""
mu, _ = self.checkParameterList(mu)
if mu.shape[0] == 0: mu.reset((1, self.npar), mu.dtype)
if RHS is None:
RHS = [self.b(m, homogeneized = homogeneized) for m in mu]
RHS = sampleList(RHS)
mult = 0 if len(RHS) == 1 else 1
RROMPyAssert(mult * (len(mu) - 1) + 1, len(RHS), "Sample size")
sol = emptySampleList()
for j in range(len(mu)):
u = self._solver(self.A(mu[j]), RHS[mult * j], self._solverArgs)
if j == 0:
sol.reset((len(u), len(mu)), dtype = u.dtype)
sol[j] = u
return sol
def residual(self, u:sampList, mu : paramList = [],
homogeneized : bool = False) -> sampList:
"""
Find residual of linear system for given approximate solution.
Args:
u: numpy complex array with function dofs. If None, set to 0.
mu: parameter value.
"""
mu, _ = self.checkParameterList(mu)
if mu.shape[0] == 0: mu.reset((1, self.npar), mu.dtype)
if u is not None:
u = sampleList(u)
mult = 0 if len(u) == 1 else 1
RROMPyAssert(mult * (len(mu) - 1) + 1, len(u), "Sample size")
res = emptySampleList()
for j in range(len(mu)):
b = self.b(mu[j], homogeneized = homogeneized)
if u is None:
r = b
else:
r = b - self.A(mu[j]).dot(u[mult * j])
if j == 0:
res.reset((len(r), len(mu)), dtype = r.dtype)
res[j] = r
return res
def plot(self, u:Np1D, name : str = "u", save : str = None,
what : strLst = 'all', saveFormat : str = "eps",
saveDPI : int = 100, show : bool = True, **figspecs):
"""
Do some nice plots of the complex-valued function with given dofs.
Args:
u: numpy complex array with function dofs.
name(optional): Name to be shown as title of the plots. Defaults to
'u'.
save(optional): Where to save plot(s). Defaults to None, i.e. no
saving.
what(optional): Which plots to do. If list, can contain 'ABS',
'PHASE', 'REAL', 'IMAG'. If str, same plus wildcard 'ALL'.
Defaults to 'ALL'.
saveFormat(optional): Format for saved plot(s). Defaults to "eps".
saveDPI(optional): DPI for saved plot(s). Defaults to 100.
show(optional): Whether to show figure. Defaults to True.
figspecs(optional key args): Optional arguments for matplotlib
figure creation.
"""
if isinstance(what, (str,)):
if what.upper() == 'ALL':
what = ['ABS', 'PHASE', 'REAL', 'IMAG']
else:
what = [what]
what = purgeList(what, ['ABS', 'PHASE', 'REAL', 'IMAG'],
listname = self.name() + ".what", baselevel = 1)
if len(what) == 0: return
if 'figsize' not in figspecs.keys():
figspecs['figsize'] = (13. * len(what) / 4, 3)
subplotcode = 100 + len(what) * 10
idxs = np.arange(self.spacedim())
plt.figure(**figspecs)
plt.jet()
if 'ABS' in what:
subplotcode = subplotcode + 1
plt.subplot(subplotcode)
plt.plot(idxs, np.abs(u))
plt.title("|{0}|".format(name))
if 'PHASE' in what:
subplotcode = subplotcode + 1
plt.subplot(subplotcode)
plt.plot(idxs, np.angle(u))
plt.title("phase({0})".format(name))
if 'REAL' in what:
subplotcode = subplotcode + 1
plt.subplot(subplotcode)
plt.plot(idxs, np.real(u))
plt.title("Re({0})".format(name))
if 'IMAG' in what:
subplotcode = subplotcode + 1
plt.subplot(subplotcode)
plt.plot(idxs, np.imag(u))
plt.title("Im({0})".format(name))
if save is not None:
save = save.strip()
plt.savefig(getNewFilename("{}_fig_".format(save), saveFormat),
format = saveFormat, dpi = saveDPI)
if show:
plt.show()
plt.close()
diff --git a/rrompy/hfengines/linear_problem/bidimensional/__init__.py b/rrompy/hfengines/linear_problem/bidimensional/__init__.py
index 03b8e69..8e2d377 100644
--- a/rrompy/hfengines/linear_problem/bidimensional/__init__.py
+++ b/rrompy/hfengines/linear_problem/bidimensional/__init__.py
@@ -1,29 +1,32 @@
# Copyright (C) 2018 by the RROMPy authors
#
# This file is part of RROMPy.
#
# RROMPy is free software: you can redistribute it and/or modify
# it under the terms of the GNU Lesser General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# RROMPy is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU Lesser General Public License for more details.
#
# You should have received a copy of the GNU Lesser General Public License
# along with RROMPy. If not, see .
#
from .laplace_disk_gaussian_2 import LaplaceDiskGaussian2
from .helmholtz_square_simplified_domain_problem_engine import \
HelmholtzSquareSimplifiedDomainProblemEngine
+from .helmholtz_square_domain_problem_engine import \
+ HelmholtzSquareDomainProblemEngine
__all__ = [
'LaplaceDiskGaussian2',
- 'HelmholtzSquareSimplifiedDomainProblemEngine'
+ 'HelmholtzSquareSimplifiedDomainProblemEngine',
+ 'HelmholtzSquareDomainProblemEngine'
]
diff --git a/rrompy/hfengines/linear_problem/bidimensional/helmholtz_square_domain_problem_engine.py b/rrompy/hfengines/linear_problem/bidimensional/helmholtz_square_domain_problem_engine.py
new file mode 100644
index 0000000..04a296b
--- /dev/null
+++ b/rrompy/hfengines/linear_problem/bidimensional/helmholtz_square_domain_problem_engine.py
@@ -0,0 +1,229 @@
+# Copyright (C) 2018 by the RROMPy authors
+#
+# This file is part of RROMPy.
+#
+# RROMPy is free software: you can redistribute it and/or modify
+# it under the terms of the GNU Lesser General Public License as published by
+# the Free Software Foundation, either version 3 of the License, or
+# (at your option) any later version.
+#
+# RROMPy is distributed in the hope that it will be useful,
+# but WITHOUT ANY WARRANTY; without even the implied warranty of
+# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+# GNU Lesser General Public License for more details.
+#
+# You should have received a copy of the GNU Lesser General Public License
+# along with RROMPy. If not, see .
+#
+
+import numpy as np
+import scipy.sparse as scsp
+from scipy.special import factorial as fact
+import fenics as fen
+from rrompy.utilities.base.types import (ScOp, List, Tuple, paramVal, Np1D,
+ FenExpr)
+from rrompy.solver.fenics import fenZERO, fenONE
+from rrompy.hfengines.linear_problem.helmholtz_problem_engine import (
+ HelmholtzProblemEngine)
+from rrompy.utilities.base import verbosityDepth
+from rrompy.utilities.poly_fitting.polynomial import (
+ hashDerivativeToIdx as hashD, hashIdxToDerivative as hashI)
+
+__all__ = ['HelmholtzSquareDomainProblemEngine']
+
+class HelmholtzSquareDomainProblemEngine(HelmholtzProblemEngine):
+ """
+ Solver for square Helmholtz problems with parametric laplacian.
+ - \dxx u - mu_2**2 \dyy u - mu_1**2 * u = f(mu_2) in \Omega = [0,\pi]^2
+ u = 0 on \partial\Omega
+ """
+
+ def __init__(self, kappa:float, theta:float, n:int,
+ mu0 : paramVal = [12. ** .5, 1.],
+ degree_threshold : int = np.inf, verbosity : int = 10,
+ timestamp : bool = True):
+ super().__init__(mu0 = mu0, degree_threshold = degree_threshold,
+ verbosity = verbosity, timestamp = timestamp)
+ self.nAs, self.nbs = 6, 11 * 12 // 2
+ self.npar = 2
+ self.rescalingExp = [2., 1.]
+ pi = np.pi
+ mesh = fen.RectangleMesh(fen.Point(0, 0), fen.Point(pi, pi),
+ 3 * n, 3 * n)
+ self.V = fen.FunctionSpace(mesh, "P", 1)
+
+ c, s = np.cos(theta), np.sin(theta)
+ x, y = fen.SpatialCoordinate(mesh)[:]
+ self.forcingTerm = [fen.cos(kappa * (c * x + s / self.mu0(0, 1) * y)),
+ fen.sin(kappa * (c * x + s / self.mu0(0, 1) * y))]
+ self.forcingTermDer = kappa * s * y
+
+ def getExtraFactorB(self, mu : paramVal = [],
+ derI : int = 0) -> Tuple[FenExpr, FenExpr]:
+ """Compute extra expression in RHS."""
+ mu = self.checkParameter(mu)
+ def getPowMinusj(x, power):
+ powR = x ** power
+ powI = fenZERO
+ if power % 2 == 1:
+ powR, powI = powI, powR
+ if power % 4 > 1:
+ powR, powI = - powR, - powI
+ return powR, powI
+ if self.verbosity >= 25:
+ verbosityDepth("INIT", ("Assembling auxiliary expression for "
+ "forcing term derivative."),
+ timestamp = self.timestamp)
+ if derI == 0: return fenONE, fenZERO
+ coeffs = np.zeros(derI + 1)
+ coeffs[1] = - 2.
+ for j in range(2, derI + 1):
+ coeffs[1 :] = (-2. / j * coeffs[1 :]
+ - (3 - (1 + 2 * np.arange(derI)) / j) * coeffs[: -1])
+ for j in range(derI):
+ powR, powI = getPowMinusj(self.forcingTermDer, derI - j)
+ mupBase = coeffs[j + 1] * mu(0, 1) ** (- 3 * derI + 2 * j)
+ mupR, mupI = np.real(mupBase), np.imag(mupBase)
+ if j == 0:
+ exprR = mupR * powR - mupI * powI
+ exprI = mupI * powR + mupR * powI
+ else:
+ exprR += mupR * powR - mupI * powI
+ exprI += mupI * powR + mupR * powI
+ if self.verbosity >= 25:
+ verbosityDepth("DEL", "Done assembling auxiliary expression.",
+ timestamp = self.timestamp)
+ return exprR, exprI
+
+ def A(self, mu : paramVal = [], der : List[int] = 0) -> ScOp:
+ """Assemble (derivative of) operator of linear system."""
+ mu = self.checkParameter(mu)
+ if not hasattr(der, "__len__"): der = [der] * self.npar
+ derI = hashD(der)
+ self.autoSetDS()
+ if derI <= 0 and self.As[0] is None:
+ if self.verbosity >= 20:
+ verbosityDepth("INIT", "Assembling operator term A0.",
+ timestamp = self.timestamp)
+ DirichletBC0 = fen.DirichletBC(self.V, fenZERO,
+ self.DirichletBoundary)
+ a0Re = fen.dot(self.u.dx(0), self.v.dx(0)) * fen.dx
+ A0Re = fen.assemble(a0Re)
+ DirichletBC0.apply(A0Re)
+ A0ReMat = fen.as_backend_type(A0Re).mat()
+ A0Rer, A0Rec, A0Rev = A0ReMat.getValuesCSR()
+ self.As[0] = scsp.csr_matrix((A0Rev, A0Rec, A0Rer),
+ shape = A0ReMat.size,
+ dtype = np.complex)
+ if self.verbosity >= 20:
+ verbosityDepth("DEL", "Done assembling operator term.",
+ timestamp = self.timestamp)
+ if derI <= 1 and self.As[1] is None:
+ if self.verbosity >= 20:
+ verbosityDepth("INIT", "Assembling operator term A1.",
+ timestamp = self.timestamp)
+ DirichletBC0 = fen.DirichletBC(self.V, fenZERO,
+ self.DirichletBoundary)
+ nRe, nIm = self.refractionIndex
+ n2Re, n2Im = nRe * nRe - nIm * nIm, 2 * nRe * nIm
+ parsRe = self.iterReduceQuadratureDegree(zip([n2Re],
+ ["refractionIndexSquaredReal"]))
+ parsIm = self.iterReduceQuadratureDegree(zip([n2Im],
+ ["refractionIndexSquaredImag"]))
+ a1Re = - n2Re * fen.dot(self.u, self.v) * fen.dx
+ a1Im = - n2Im * fen.dot(self.u, self.v) * fen.dx
+ A1Re = fen.assemble(a1Re, form_compiler_parameters = parsRe)
+ A1Im = fen.assemble(a1Im, form_compiler_parameters = parsIm)
+ DirichletBC0.zero(A1Re)
+ DirichletBC0.zero(A1Im)
+ A1ReMat = fen.as_backend_type(A1Re).mat()
+ A1ImMat = fen.as_backend_type(A1Im).mat()
+ A1Rer, A1Rec, A1Rev = A1ReMat.getValuesCSR()
+ A1Imr, A1Imc, A1Imv = A1ImMat.getValuesCSR()
+ self.As[1] = (scsp.csr_matrix((A1Rev, A1Rec, A1Rer),
+ shape = A1ReMat.size)
+ + 1.j * scsp.csr_matrix((A1Imv, A1Imc, A1Imr),
+ shape = A1ImMat.size))
+ if self.verbosity >= 20:
+ verbosityDepth("DEL", "Done assembling operator term.",
+ timestamp = self.timestamp)
+ if derI <= 2 and self.As[2] is None: self.As[2] = 0.
+ if derI <= 3 and self.As[3] is None: self.As[3] = 0.
+ if derI <= 4 and self.As[4] is None: self.As[4] = 0.
+ if derI <= 5 and self.As[5] is None:
+ if self.verbosity >= 20:
+ verbosityDepth("INIT", "Assembling operator term A5.",
+ timestamp = self.timestamp)
+ DirichletBC0 = fen.DirichletBC(self.V, fenZERO,
+ self.DirichletBoundary)
+ a5Re = fen.dot(self.u.dx(1), self.v.dx(1)) * fen.dx
+ A5Re = fen.assemble(a5Re)
+ DirichletBC0.zero(A5Re)
+ A5ReMat = fen.as_backend_type(A5Re).mat()
+ A5Rer, A5Rec, A5Rev = A5ReMat.getValuesCSR()
+ self.As[5] = scsp.csr_matrix((A5Rev, A5Rec, A5Rer),
+ shape = A5ReMat.size,
+ dtype = np.complex)
+ if self.verbosity >= 20:
+ verbosityDepth("DEL", "Done assembling operator term.",
+ timestamp = self.timestamp)
+ return self._assembleA(mu, der, derI)
+
+ def b(self, mu : paramVal = [], der : List[int] = 0,
+ homogeneized : bool = False) -> Np1D:
+ """Assemble (derivative of) RHS of linear system."""
+ mu = self.checkParameter(mu)
+ if not hasattr(der, "__len__"): der = [der] * self.npar
+ derI = hashD(der)
+ nbsTot = self.nbsH if homogeneized else self.nbs
+ bs = self.bsH if homogeneized else self.bs
+ if homogeneized and self.mu0 != self.mu0BC:
+ self.liftDirichletData(self.mu0)
+ for j in range(derI, nbsTot):
+ derH = hashI(j, self.npar)
+ if bs[j] is None:
+ if np.sum(derH) != derH[-1]:
+ if homogeneized:
+ self.bsH[j] = 0.
+ else:
+ self.bs[j] = 0.
+ continue
+ if self.verbosity >= 20:
+ verbosityDepth("INIT", ("Assembling forcing term "
+ "b{}.").format(j),
+ timestamp = self.timestamp)
+ if j == 0:
+ u0Re, u0Im = self.DirichletDatum
+ else:
+ u0Re, u0Im = fenZERO, fenZERO
+ if j < self.nbs:
+ fRe, fIm = self.forcingTerm
+ cRe, cIm = self.getExtraFactorB(self.mu0, derH[-1])
+ cfRe, cfIm = cRe * fRe - cIm * fIm, cRe * fIm + cIm * fRe
+ else:
+ cfRe, cfIm = fenZERO, fenZERO
+ parsRe = self.iterReduceQuadratureDegree(zip([cfRe],
+ ["forcingTermDer{}Real".format(j)]))
+ parsIm = self.iterReduceQuadratureDegree(zip([cfIm],
+ ["forcingTermDer{}Imag".format(j)]))
+ L0Re = fen.dot(cfRe, self.v) * fen.dx
+ L0Im = fen.dot(cfIm, self.v) * fen.dx
+ b0Re = fen.assemble(L0Re, form_compiler_parameters = parsRe)
+ b0Im = fen.assemble(L0Im, form_compiler_parameters = parsIm)
+ DBCR = fen.DirichletBC(self.V, u0Re, self.DirichletBoundary)
+ DBCI = fen.DirichletBC(self.V, u0Im, self.DirichletBoundary)
+ DBCR.apply(b0Re)
+ DBCI.apply(b0Im)
+ b = np.array(b0Re[:] + 1.j * b0Im[:], dtype = np.complex)
+ if homogeneized:
+ Ader = self.A(self.mu0, derH)
+ b -= Ader.dot(self.liftedDirichletDatum)
+ if homogeneized:
+ self.bsH[j] = b
+ else:
+ self.bs[j] = b
+ if self.verbosity >= 20:
+ verbosityDepth("DEL", "Done assembling forcing term.",
+ timestamp = self.timestamp)
+ return self._assembleb(mu, der, derI, homogeneized, self.mu0)
+
diff --git a/rrompy/hfengines/linear_problem/bidimensional/helmholtz_square_simplified_domain_problem_engine.py b/rrompy/hfengines/linear_problem/bidimensional/helmholtz_square_simplified_domain_problem_engine.py
index 026f3b4..d310906 100644
--- a/rrompy/hfengines/linear_problem/bidimensional/helmholtz_square_simplified_domain_problem_engine.py
+++ b/rrompy/hfengines/linear_problem/bidimensional/helmholtz_square_simplified_domain_problem_engine.py
@@ -1,133 +1,129 @@
# Copyright (C) 2018 by the RROMPy authors
#
# This file is part of RROMPy.
#
# RROMPy is free software: you can redistribute it and/or modify
# it under the terms of the GNU Lesser General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# RROMPy is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU Lesser General Public License for more details.
#
# You should have received a copy of the GNU Lesser General Public License
# along with RROMPy. If not, see .
#
import numpy as np
import scipy.sparse as scsp
import fenics as fen
from rrompy.utilities.base.types import ScOp, List, paramVal
from rrompy.solver.fenics import fenZERO
from rrompy.hfengines.linear_problem.helmholtz_problem_engine import (
HelmholtzProblemEngine)
from rrompy.utilities.base import verbosityDepth
from rrompy.utilities.poly_fitting.polynomial import (
hashDerivativeToIdx as hashD)
__all__ = ['HelmholtzSquareSimplifiedDomainProblemEngine']
class HelmholtzSquareSimplifiedDomainProblemEngine(HelmholtzProblemEngine):
"""
Solver for square Helmholtz problems with parametric laplacian.
- \dxx u - mu_2**2 \dyy u - mu_1**2 * u = f in \Omega_mu = [0,\pi]^2
u = 0 on \partial\Omega
"""
- nAs, nbs = 3, 1
-
def __init__(self, kappa:float, theta:float, n:int,
mu0 : paramVal = [12. ** .5, 1.],
degree_threshold : int = np.inf, verbosity : int = 10,
timestamp : bool = True):
super().__init__(mu0 = mu0, degree_threshold = degree_threshold,
verbosity = verbosity, timestamp = timestamp)
+ self.nAs = 3
self.npar = 2
self.rescalingExp = [2., 2.]
pi = np.pi
- mesh = fen.RectangleMesh(fen.Point(0, 0), fen.Point(pi, pi), n, n)
- self.V = fen.FunctionSpace(mesh, "P", 3)
+ mesh = fen.RectangleMesh(fen.Point(0, 0), fen.Point(pi, pi),
+ 3 * n, 3 * n)
+ self.V = fen.FunctionSpace(mesh, "P", 1)
c, s = np.cos(theta), np.sin(theta)
x, y = fen.SpatialCoordinate(mesh)[:]
C = 16. / pi ** 4.
- bR = C * 2 * (x * (pi - x) + y * (pi - y))
- bI = C * 2 * kappa * (c * (pi - 2 * x) * y * (pi - y)
- + s * x * (pi - x) * (pi - 2 * y))
- wR = fen.cos(kappa * (c * x + s * y))
- wI = fen.sin(kappa * (c * x + s * y))
- self.forcingTerm = [bR * wR + bI * wI, bI * wR - bR * wI]
+ self.forcingTerm = [fen.cos(kappa * (c * x + s * y)),
+ fen.sin(kappa * (c * x + s * y))]
def A(self, mu : paramVal = [], der : List[int] = 0) -> ScOp:
"""Assemble (derivative of) operator of linear system."""
mu = self.checkParameter(mu)
if not hasattr(der, "__len__"): der = [der] * self.npar
derI = hashD(der)
self.autoSetDS()
if derI <= 0 and self.As[0] is None:
if self.verbosity >= 20:
verbosityDepth("INIT", "Assembling operator term A0.",
timestamp = self.timestamp)
DirichletBC0 = fen.DirichletBC(self.V, fenZERO,
self.DirichletBoundary)
a0Re = fen.dot(self.u.dx(0), self.v.dx(0)) * fen.dx
A0Re = fen.assemble(a0Re)
DirichletBC0.apply(A0Re)
A0ReMat = fen.as_backend_type(A0Re).mat()
A0Rer, A0Rec, A0Rev = A0ReMat.getValuesCSR()
self.As[0] = scsp.csr_matrix((A0Rev, A0Rec, A0Rer),
shape = A0ReMat.size,
dtype = np.complex)
if self.verbosity >= 20:
verbosityDepth("DEL", "Done assembling operator term.",
timestamp = self.timestamp)
if derI <= 1 and self.As[1] is None:
if self.verbosity >= 20:
- verbosityDepth("INIT", "Assembling operator term A2.",
+ verbosityDepth("INIT", "Assembling operator term A1.",
timestamp = self.timestamp)
DirichletBC0 = fen.DirichletBC(self.V, fenZERO,
self.DirichletBoundary)
nRe, nIm = self.refractionIndex
n2Re, n2Im = nRe * nRe - nIm * nIm, 2 * nRe * nIm
parsRe = self.iterReduceQuadratureDegree(zip([n2Re],
["refractionIndexSquaredReal"]))
parsIm = self.iterReduceQuadratureDegree(zip([n2Im],
["refractionIndexSquaredImag"]))
- a2Re = - n2Re * fen.dot(self.u, self.v) * fen.dx
- a2Im = - n2Im * fen.dot(self.u, self.v) * fen.dx
- A2Re = fen.assemble(a2Re, form_compiler_parameters = parsRe)
- A2Im = fen.assemble(a2Im, form_compiler_parameters = parsIm)
- DirichletBC0.zero(A2Re)
- DirichletBC0.zero(A2Im)
- A2ReMat = fen.as_backend_type(A2Re).mat()
- A2ImMat = fen.as_backend_type(A2Im).mat()
- A2Rer, A2Rec, A2Rev = A2ReMat.getValuesCSR()
- A2Imr, A2Imc, A2Imv = A2ImMat.getValuesCSR()
- self.As[1] = (scsp.csr_matrix((A2Rev, A2Rec, A2Rer),
- shape = A2ReMat.size)
- + 1.j * scsp.csr_matrix((A2Imv, A2Imc, A2Imr),
- shape = A2ImMat.size))
+ a1Re = - n2Re * fen.dot(self.u, self.v) * fen.dx
+ a1Im = - n2Im * fen.dot(self.u, self.v) * fen.dx
+ A1Re = fen.assemble(a1Re, form_compiler_parameters = parsRe)
+ A1Im = fen.assemble(a1Im, form_compiler_parameters = parsIm)
+ DirichletBC0.zero(A1Re)
+ DirichletBC0.zero(A1Im)
+ A1ReMat = fen.as_backend_type(A1Re).mat()
+ A1ImMat = fen.as_backend_type(A1Im).mat()
+ A1Rer, A1Rec, A1Rev = A1ReMat.getValuesCSR()
+ A1Imr, A1Imc, A1Imv = A1ImMat.getValuesCSR()
+ self.As[1] = (scsp.csr_matrix((A1Rev, A1Rec, A1Rer),
+ shape = A1ReMat.size)
+ + 1.j * scsp.csr_matrix((A1Imv, A1Imc, A1Imr),
+ shape = A1ImMat.size))
if self.verbosity >= 20:
verbosityDepth("DEL", "Done assembling operator term.",
timestamp = self.timestamp)
if derI <= 2 and self.As[2] is None:
if self.verbosity >= 20:
verbosityDepth("INIT", "Assembling operator term A2.",
timestamp = self.timestamp)
DirichletBC0 = fen.DirichletBC(self.V, fenZERO,
self.DirichletBoundary)
a2Re = fen.dot(self.u.dx(1), self.v.dx(1)) * fen.dx
- A2Re = fen.assemble(a2Re, form_compiler_parameters = parsRe)
+ A2Re = fen.assemble(a2Re)
DirichletBC0.zero(A2Re)
A2ReMat = fen.as_backend_type(A2Re).mat()
A2Rer, A2Rec, A2Rev = A2ReMat.getValuesCSR()
self.As[2] = scsp.csr_matrix((A2Rev, A2Rec, A2Rer),
shape = A2ReMat.size,
dtype = np.complex)
if self.verbosity >= 20:
verbosityDepth("DEL", "Done assembling operator term.",
timestamp = self.timestamp)
return self._assembleA(mu, der, derI)
diff --git a/rrompy/hfengines/linear_problem/bidimensional/laplace_disk_gaussian_2.py b/rrompy/hfengines/linear_problem/bidimensional/laplace_disk_gaussian_2.py
index b27b96c..db0ed1d 100644
--- a/rrompy/hfengines/linear_problem/bidimensional/laplace_disk_gaussian_2.py
+++ b/rrompy/hfengines/linear_problem/bidimensional/laplace_disk_gaussian_2.py
@@ -1,128 +1,125 @@
# Copyright (C) 2018 by the RROMPy authors
#
# This file is part of RROMPy.
#
# RROMPy is free software: you can redistribute it and/or modify
# it under the terms of the GNU Lesser General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# RROMPy is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU Lesser General Public License for more details.
#
# You should have received a copy of the GNU Lesser General Public License
# along with RROMPy. If not, see .
#
import numpy as np
import fenics as fen
from rrompy.utilities.base.types import Np1D, Tuple, List, FenExpr, paramVal
from rrompy.hfengines.linear_problem.laplace_disk_gaussian import (
LaplaceDiskGaussian)
from rrompy.solver.fenics import fenZERO, fenONE
from rrompy.utilities.base import verbosityDepth
from rrompy.utilities.poly_fitting.polynomial import (
hashDerivativeToIdx as hashD, hashIdxToDerivative as hashI)
from rrompy.utilities.exception_manager import RROMPyException
__all__ = ['LaplaceDiskGaussian2']
class LaplaceDiskGaussian2(LaplaceDiskGaussian):
"""
Solver for disk Laplace problems with parametric forcing term center.
- \Delta u = C exp(-.5 * ||\cdot - (mu1, mu2)||^2) in \Omega = B(0, 5)
u = 0 on \partial\Omega.
"""
- nAs, nbs = 1, 1
-
def __init__(self, n:int, mu0 : paramVal = [0., 0.],
degree_threshold : int = np.inf, verbosity : int = 10,
timestamp : bool = True):
super().__init__(n = n, mu0 = mu0, degree_threshold = degree_threshold,
verbosity = verbosity, timestamp = timestamp)
+ self.nbs = 1
self.npar = 2
def getForcingTerm(self, mu : paramVal = []) -> Tuple[FenExpr, FenExpr]:
"""Compute forcing term."""
mu = self.checkParameter(mu)
if mu != self.forcingTermMu:
if self.verbosity >= 25:
verbosityDepth("INIT", ("Assembling base expression for "
"forcing term."),
timestamp = self.timestamp)
x, y = fen.SpatialCoordinate(self.V.mesh())[:]
C = np.exp(-.5 * (mu(0, 0) ** 2. + mu(0, 1) ** 2.))
CR, CI = np.real(C), np.imag(C)
f0 = (2 * np.pi) ** -.5 * fen.exp(-.5 * (x ** 2. + y ** 2.))
muxR, muxI = np.real(mu(0, 0)), np.imag(mu(0, 0))
muyR, muyI = np.real(mu(0, 1)), np.imag(mu(0, 1))
f1R = fen.exp(muxR * x + muyR * y) * fen.cos(muxI * x + muyI * y)
f1I = fen.exp(muxR * x + muyR * y) * fen.sin(muxI * x + muyI * y)
self.forcingTerm = [f0 * (CR * f1R - CI * f1I),
f0 * (CR * f1I + CI * f1R)]
self.forcingTermMu = mu
if self.verbosity >= 25:
verbosityDepth("DEL", "Done assembling base expression.",
timestamp = self.timestamp)
return self.forcingTerm
def computebsFactors(self):
pass
def getExtraFactorB(self, mu : paramVal = [],
derI : int = 0) -> Tuple[FenExpr, FenExpr]:
if derI == 0: return [fenONE, fenZERO]
raise RROMPyException("Not implemented.")
def b(self, mu : paramVal = [], der : List[int] = 0,
homogeneized : bool = False) -> Np1D:
"""Assemble (derivative of) RHS of linear system."""
mu = self.checkParameter(mu)
if not hasattr(der, "__len__"): der = [der] * self.npar
derI = hashD(der)
nbsTot = self.nbsH if homogeneized else self.nbs
bs = self.bsH if homogeneized else self.bs
if homogeneized and self.mu0 != self.mu0BC:
self.liftDirichletData(self.mu0)
for j in range(derI, nbsTot):
if True or bs[j] is None:
if self.verbosity >= 20:
verbosityDepth("INIT", ("Assembling forcing term "
"b{}.").format(j),
timestamp = self.timestamp)
if j < self.nbs:
fRe, fIm = self.getForcingTerm(mu)
cRe, cIm = self.getExtraFactorB(mu, j)
cfRe, cfIm = cRe * fRe - cIm * fIm, cRe * fIm + cIm * fRe
else:
cfRe, cfIm = fenZERO, fenZERO
parsRe = self.iterReduceQuadratureDegree(zip([cfRe],
["forcingTermDer{}Real".format(j)]))
parsIm = self.iterReduceQuadratureDegree(zip([cfIm],
["forcingTermDer{}Imag".format(j)]))
L0Re = fen.dot(cfRe, self.v) * fen.dx
L0Im = fen.dot(cfIm, self.v) * fen.dx
b0Re = fen.assemble(L0Re, form_compiler_parameters = parsRe)
b0Im = fen.assemble(L0Im, form_compiler_parameters = parsIm)
- if homogeneized:
- Ader = self.A(self.mu0, hashI(j))
- b0Re[:] -= np.real(Ader.dot(self.liftedDirichletDatum))
- b0Im[:] -= np.imag(Ader.dot(self.liftedDirichletDatum))
DirichletBC0 = fen.DirichletBC(self.V, fenZERO,
self.DirichletBoundary)
DirichletBC0.apply(b0Re)
DirichletBC0.apply(b0Im)
+ b = np.array(b0Re[:] + 1.j * b0Im[:], dtype = np.complex)
+ if homogeneized:
+ Ader = self.A(self.mu0, hashI(j, self.npar))
+ b -= Ader.dot(self.liftedDirichletDatum)
if homogeneized:
- self.bsH[j] = np.array(b0Re[:] + 1.j * b0Im[:],
- dtype = np.complex)
+ self.bsH[j] = b
else:
- self.bs[j] = np.array(b0Re[:] + 1.j * b0Im[:],
- dtype = np.complex)
+ self.bs[j] = b
if self.verbosity >= 20:
verbosityDepth("DEL", "Done assembling forcing term.",
timestamp = self.timestamp)
- return self._assembleb(mu - self.mu0, der, derI, homogeneized)
+ return self._assembleb(mu, der, derI, homogeneized, self.mu0)
diff --git a/rrompy/hfengines/linear_problem/helmholtz_box_scattering_problem_engine.py b/rrompy/hfengines/linear_problem/helmholtz_box_scattering_problem_engine.py
index 94dd364..20a0480 100644
--- a/rrompy/hfengines/linear_problem/helmholtz_box_scattering_problem_engine.py
+++ b/rrompy/hfengines/linear_problem/helmholtz_box_scattering_problem_engine.py
@@ -1,57 +1,58 @@
# Copyright (C) 2018 by the RROMPy authors
#
# This file is part of RROMPy.
#
# RROMPy is free software: you can redistribute it and/or modify
# it under the terms of the GNU Lesser General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# RROMPy is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU Lesser General Public License for more details.
#
# You should have received a copy of the GNU Lesser General Public License
# along with RROMPy. If not, see .
#
import numpy as np
import fenics as fen
from .scattering_problem_engine import ScatteringProblemEngine
__all__ = ['HelmholtzBoxScatteringProblemEngine']
class HelmholtzBoxScatteringProblemEngine(ScatteringProblemEngine):
"""
Solver for scattering problem outside a box with parametric wavenumber.
- \Delta u - omega^2 * n^2 * u = 0 in \Omega
u = 0 on \Gamma_D
\partial_nu - i k u = 0 on \Gamma_R
with exact solution a transmitted plane wave.
"""
def __init__(self, R:float, kappa:float, theta:float, n:int,
degree_threshold : int = np.inf, verbosity : int = 10,
timestamp : bool = True):
super().__init__(mu0 = [kappa], degree_threshold = degree_threshold,
verbosity = verbosity, timestamp = timestamp)
import mshr
scatterer = mshr.Polygon([fen.Point(-1, -.5), fen.Point(1, -.5),
fen.Point(1, .5), fen.Point(.8, .5),
fen.Point(.8, -.3), fen.Point(-.8, -.3),
fen.Point(-.8, .5), fen.Point(-1, .5),])
- mesh = mshr.generate_mesh(mshr.Circle(fen.Point(0, 0), R)-scatterer, n)
- self.V = fen.FunctionSpace(mesh, "P", 3)
+ mesh = mshr.generate_mesh(mshr.Circle(fen.Point(0, 0), R) - scatterer,
+ 3 * n)
+ self.V = fen.FunctionSpace(mesh, "P", 1)
self.DirichletBoundary = (lambda x, on_boundary:
on_boundary and (x[0]**2+x[1]**2)**.5 < .95 * R)
self.RobinBoundary = "REST"
c, s = np.cos(theta), np.sin(theta)
x, y = fen.SpatialCoordinate(mesh)[:]
u0R = - fen.cos(kappa * (c * x + s * y))
u0I = - fen.sin(kappa * (c * x + s * y))
self.DirichletDatum = [u0R, u0I]
diff --git a/rrompy/hfengines/linear_problem/helmholtz_cavity_scattering_problem_engine.py b/rrompy/hfengines/linear_problem/helmholtz_cavity_scattering_problem_engine.py
index 976eaa5..5efe8ec 100644
--- a/rrompy/hfengines/linear_problem/helmholtz_cavity_scattering_problem_engine.py
+++ b/rrompy/hfengines/linear_problem/helmholtz_cavity_scattering_problem_engine.py
@@ -1,58 +1,59 @@
# Copyright (C) 2018 by the RROMPy authors
#
# This file is part of RROMPy.
#
# RROMPy is free software: you can redistribute it and/or modify
# it under the terms of the GNU Lesser General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# RROMPy is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU Lesser General Public License for more details.
#
# You should have received a copy of the GNU Lesser General Public License
# along with RROMPy. If not, see .
#
import numpy as np
import fenics as fen
from .scattering_problem_engine import ScatteringProblemEngine
__all__ = ['HelmholtzCavityScatteringProblemEngine']
class HelmholtzCavityScatteringProblemEngine(ScatteringProblemEngine):
"""
Solver for scattering problem inside a cavity with parametric wavenumber.
- \Delta u - omega^2 * n^2 * u = 0 in \Omega
u = 0 on \Gamma_D
\partial_nu - i k u = 0 on \Gamma_R
with exact solution a transmitted plane wave.
"""
def __init__(self, kappa:float, n:int, gamma : float = 0.,
signR : int = -1, degree_threshold : int = np.inf,
verbosity : int = 10, timestamp : bool = True):
super().__init__(mu0 = [kappa], degree_threshold = degree_threshold,
verbosity = verbosity, timestamp = timestamp)
self.signR = signR
pi = np.pi
- mesh = fen.RectangleMesh(fen.Point(0, 0), fen.Point(pi, pi), n, n)
- self.V = fen.FunctionSpace(mesh, "P", 3)
+ mesh = fen.RectangleMesh(fen.Point(0, 0), fen.Point(pi, pi),
+ 3 * n, 3 * n)
+ self.V = fen.FunctionSpace(mesh, "P", 1)
self.RobinBoundary = (lambda x, on_boundary: on_boundary
and np.isclose(x[1], np.pi))
self.DirichletBoundary = "REST"
x, y = fen.SpatialCoordinate(mesh)[:]
C = 4. / pi ** 4.
bR = C * (2 * (x * (pi - x) + y * (2 * pi - y))
+ (kappa * gamma) ** 2. * x * (pi - x) * y * (2 * pi - y))
bI = C * signR * 2 * kappa * (gamma * (pi - 2 * x) * y * (pi - y)
+ 2 * x * (pi - x) * (pi - y))
wR = fen.cos(kappa * signR * (gamma * x + y))
wI = fen.sin(kappa * signR * (gamma * x + y))
self.forcingTerm = [bR * wR + bI * wI, bI * wR - bR * wI]
diff --git a/rrompy/hfengines/linear_problem/helmholtz_problem_engine.py b/rrompy/hfengines/linear_problem/helmholtz_problem_engine.py
index 1ceeba4..a77dd46 100644
--- a/rrompy/hfengines/linear_problem/helmholtz_problem_engine.py
+++ b/rrompy/hfengines/linear_problem/helmholtz_problem_engine.py
@@ -1,161 +1,160 @@
# Copyright (C) 2018 by the RROMPy authors
#
# This file is part of RROMPy.
#
# RROMPy is free software: you can redistribute it and/or modify
# it under the terms of the GNU Lesser General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# RROMPy is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU Lesser General Public License for more details.
#
# You should have received a copy of the GNU Lesser General Public License
# along with RROMPy. If not, see .
#
import numpy as np
import scipy.sparse as scsp
import fenics as fen
from .laplace_base_problem_engine import LaplaceBaseProblemEngine
from rrompy.utilities.base.types import List, ScOp, paramVal
from rrompy.solver.fenics import fenZERO, fenONE
from rrompy.utilities.base import verbosityDepth
from rrompy.utilities.poly_fitting.polynomial import (
hashDerivativeToIdx as hashD)
__all__ = ['HelmholtzProblemEngine']
class HelmholtzProblemEngine(LaplaceBaseProblemEngine):
"""
Solver for generic Helmholtz problems with parametric wavenumber.
- \nabla \cdot (a \nabla u) - omega^2 * n**2 * u = f in \Omega
u = u0 on \Gamma_D
\partial_nu = g1 on \Gamma_N
\partial_nu + h u = g2 on \Gamma_R
Attributes:
verbosity: Verbosity level.
BCManager: Boundary condition manager.
V: Real FE space.
u: Generic trial functions for variational form evaluation.
v: Generic test functions for variational form evaluation.
As: Scipy sparse array representation (in CSC format) of As.
bs: Numpy array representation of bs.
bsH: Numpy array representation of homogeneized bs.
energyNormMatrix: Scipy sparse matrix representing inner product over
V.
liftedDirichletDatum: Dofs of Dirichlet datum lifting.
mu0BC: Mu value of last Dirichlet datum lifting.
degree_threshold: Threshold for ufl expression interpolation degree.
omega: Value of omega.
diffusivity: Value of a.
refractionIndex: Value of n.
forcingTerm: Value of f.
DirichletDatum: Value of u0.
NeumannDatum: Value of g1.
RobinDatumG: Value of g2.
RobinDatumH: Value of h.
DirichletBoundary: Function handle to \Gamma_D.
NeumannBoundary: Function handle to \Gamma_N.
RobinBoundary: Function handle to \Gamma_R.
ds: Boundary measure 2-tuple (resp. for Neumann and Robin boundaries).
A0: Scipy sparse array representation (in CSC format) of A0.
A1: Scipy sparse array representation (in CSC format) of A1.
b0: Numpy array representation of b0.
dsToBeSet: Whether ds needs to be set.
"""
- nAs = 2
-
def __init__(self, mu0 : paramVal = [0.], degree_threshold : int = np.inf,
verbosity : int = 10, timestamp : bool = True):
super().__init__(mu0 = mu0, degree_threshold = degree_threshold,
verbosity = verbosity, timestamp = timestamp)
+ self.nAs = 2
self.rescalingExp = [2.]
self.refractionIndex = fenONE
@property
def refractionIndex(self):
"""Value of n."""
return self._refractionIndex
@refractionIndex.setter
def refractionIndex(self, refractionIndex):
self.resetAs()
if not isinstance(refractionIndex, (list, tuple,)):
refractionIndex = [refractionIndex, fenZERO]
self._refractionIndex = refractionIndex
def A(self, mu : paramVal = [], der : List[int] = 0) -> ScOp:
"""Assemble (derivative of) operator of linear system."""
mu = self.checkParameter(mu)
if not hasattr(der, "__len__"): der = [der] * self.npar
derI = hashD(der)
if derI <= 0 and self.As[0] is None:
self.autoSetDS()
if self.verbosity >= 20:
verbosityDepth("INIT", "Assembling operator term A0.",
timestamp = self.timestamp)
DirichletBC0 = fen.DirichletBC(self.V, fenZERO,
self.DirichletBoundary)
aRe, aIm = self.diffusivity
hRe, hIm = self.RobinDatumH
termNames = ["diffusivity", "RobinDatumH"]
parsRe = self.iterReduceQuadratureDegree(zip(
[aRe, hRe],
[x + "Real" for x in termNames]))
parsIm = self.iterReduceQuadratureDegree(zip(
[aIm, hIm],
[x + "Imag" for x in termNames]))
a0Re = (aRe * fen.dot(fen.grad(self.u), fen.grad(self.v)) * fen.dx
+ hRe * fen.dot(self.u, self.v) * self.ds(1))
a0Im = (aIm * fen.dot(fen.grad(self.u), fen.grad(self.v)) * fen.dx
+ hIm * fen.dot(self.u, self.v) * self.ds(1))
A0Re = fen.assemble(a0Re, form_compiler_parameters = parsRe)
A0Im = fen.assemble(a0Im, form_compiler_parameters = parsIm)
DirichletBC0.apply(A0Re)
DirichletBC0.zero(A0Im)
A0ReMat = fen.as_backend_type(A0Re).mat()
A0ImMat = fen.as_backend_type(A0Im).mat()
A0Rer, A0Rec, A0Rev = A0ReMat.getValuesCSR()
A0Imr, A0Imc, A0Imv = A0ImMat.getValuesCSR()
self.As[0] = (scsp.csr_matrix((A0Rev, A0Rec, A0Rer),
shape = A0ReMat.size)
+ 1.j * scsp.csr_matrix((A0Imv, A0Imc, A0Imr),
shape = A0ImMat.size))
if self.verbosity >= 20:
verbosityDepth("DEL", "Done assembling operator term.",
timestamp = self.timestamp)
if derI <= 1 and self.As[1] is None:
if self.verbosity >= 20:
verbosityDepth("INIT", "Assembling operator term A1.",
timestamp = self.timestamp)
DirichletBC0 = fen.DirichletBC(self.V, fenZERO,
self.DirichletBoundary)
nRe, nIm = self.refractionIndex
n2Re, n2Im = nRe * nRe - nIm * nIm, 2 * nRe * nIm
parsRe = self.iterReduceQuadratureDegree(zip([n2Re],
["refractionIndexSquaredReal"]))
parsIm = self.iterReduceQuadratureDegree(zip([n2Im],
["refractionIndexSquaredImag"]))
a1Re = - n2Re * fen.dot(self.u, self.v) * fen.dx
a1Im = - n2Im * fen.dot(self.u, self.v) * fen.dx
A1Re = fen.assemble(a1Re, form_compiler_parameters = parsRe)
A1Im = fen.assemble(a1Im, form_compiler_parameters = parsIm)
DirichletBC0.zero(A1Re)
DirichletBC0.zero(A1Im)
A1ReMat = fen.as_backend_type(A1Re).mat()
A1ImMat = fen.as_backend_type(A1Im).mat()
A1Rer, A1Rec, A1Rev = A1ReMat.getValuesCSR()
A1Imr, A1Imc, A1Imv = A1ImMat.getValuesCSR()
self.As[1] = (scsp.csr_matrix((A1Rev, A1Rec, A1Rer),
shape = A1ReMat.size)
+ 1.j * scsp.csr_matrix((A1Imv, A1Imc, A1Imr),
shape = A1ImMat.size))
if self.verbosity >= 20:
verbosityDepth("DEL", "Done assembling operator term.",
timestamp = self.timestamp)
return self._assembleA(mu, der, derI)
diff --git a/rrompy/hfengines/linear_problem/helmholtz_square_bubble_domain_problem_engine.py b/rrompy/hfengines/linear_problem/helmholtz_square_bubble_domain_problem_engine.py
index d8f039d..b29b809 100644
--- a/rrompy/hfengines/linear_problem/helmholtz_square_bubble_domain_problem_engine.py
+++ b/rrompy/hfengines/linear_problem/helmholtz_square_bubble_domain_problem_engine.py
@@ -1,245 +1,245 @@
# Copyright (C) 2018 by the RROMPy authors
#
# This file is part of RROMPy.
#
# RROMPy is free software: you can redistribute it and/or modify
# it under the terms of the GNU Lesser General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# RROMPy is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU Lesser General Public License for more details.
#
# You should have received a copy of the GNU Lesser General Public License
# along with RROMPy. If not, see .
#
import numpy as np
import scipy.sparse as scsp
import fenics as fen
from rrompy.utilities.base.types import (Np1D, ScOp, Tuple, List, FenExpr,
paramVal)
from rrompy.solver.fenics import fenZERO
from .helmholtz_problem_engine import HelmholtzProblemEngine
from rrompy.utilities.base import verbosityDepth
from rrompy.utilities.poly_fitting.polynomial import (
hashDerivativeToIdx as hashD, hashIdxToDerivative as hashI)
__all__ = ['HelmholtzSquareBubbleDomainProblemEngine']
class HelmholtzSquareBubbleDomainProblemEngine(HelmholtzProblemEngine):
"""
Solver for square bubble Helmholtz problems with parametric domain heigth.
- \Delta u - kappa^2 * u = f in \Omega_mu = [0,\pi] x [0,\mu\pi]
u = 0 on \Gamma_mu = \partial\Omega_mu
with exact solution square bubble times plane wave.
"""
- nAs, nbs = 3, 20
-
def __init__(self, kappa:float, theta:float, n:int, mu0 : paramVal = [1.],
degree_threshold : int = np.inf, verbosity : int = 10,
timestamp : bool = True):
super().__init__(mu0 = mu0, degree_threshold = degree_threshold,
verbosity = verbosity, timestamp = timestamp)
+ self.nAs, self.nbs = 3, 20
self.kappa = kappa
self.theta = theta
self.forcingTermMu = np.nan
- mesh = fen.RectangleMesh(fen.Point(0,0), fen.Point(np.pi,np.pi), n, n)
- self.V = fen.FunctionSpace(mesh, "P", 3)
+ mesh = fen.RectangleMesh(fen.Point(0, 0), fen.Point(np.pi, np.pi),
+ 3 * n, 3 * n)
+ self.V = fen.FunctionSpace(mesh, "P", 1)
self.rescalingExp = [1.]
def buildEnergyNormForm(self): # H1
"""
Build sparse matrix (in CSR format) representative of scalar product.
"""
mudxM = np.abs(self.mu0(0, 0)) * (fen.dot(self.u.dx(0), self.v.dx(0))
+ fen.dot(self.u, self.v))
imudy = 1. / np.abs(self.mu0(0, 0)) * fen.dot(self.u.dx(1),
self.v.dx(1))
normMatFen = fen.assemble((mudxM + imudy) * fen.dx)
normMat = fen.as_backend_type(normMatFen).mat()
self.energyNormMatrix = scsp.csr_matrix(normMat.getValuesCSR()[::-1],
shape = normMat.size)
def getForcingTerm(self, mu : paramVal = []) -> Tuple[FenExpr, FenExpr]:
"""Compute forcing term."""
mu = self.checkParameter(mu)
if mu != self.forcingTermMu:
if self.verbosity >= 25:
verbosityDepth("INIT", ("Assembling base expression for "
"forcing term."),
timestamp = self.timestamp)
pi = np.pi
c, s = np.cos(self.theta), np.sin(self.theta)
x, y = fen.SpatialCoordinate(self.V.mesh())[:]
muR, muI = np.real(mu(0, 0)), np.imag(mu(0, 0))
mu2R, mu2I = np.real(mu(0, 0) ** 2.), np.imag(mu(0, 0) ** 2.)
C = 16. / pi ** 4.
bR = C * (2 * (x * (pi - x) + y * (pi - y))
+ (self.kappa * s) ** 2. * (mu2R - 1.)
* x * (pi - x) * y * (pi - y))
bI = C * (2 * self.kappa * (c * (pi - 2 * x) * y * (pi - y)
+ s * x * (pi - x) * (pi - 2 * y))
+ (self.kappa * s) ** 2. * mu2I
* x * (pi - x) * y * (pi - y))
wR = (fen.cos(self.kappa * (c * x + s * muR * y))
* fen.exp(self.kappa * s * muI * y))
wI = (fen.sin(self.kappa * (c * x + s * muR * y))
* fen.exp(self.kappa * s * muI * y))
self.forcingTerm = [bR * wR + bI * wI, bI * wR - bR * wI]
self.forcingTermMu = mu
if self.verbosity >= 25:
verbosityDepth("DEL", "Done assembling base expression.",
timestamp = self.timestamp)
return self.forcingTerm
def getExtraFactorB(self, mu : paramVal = [],
derI : int = 0) -> Tuple[FenExpr, FenExpr]:
"""Compute extra expression in RHS."""
mu = self.checkParameter(mu)
def getPowMinusj(x, power):
powR = x ** power
powI = fenZERO
if power % 2 == 1:
powR, powI = powI, powR
if (power + 3) % 4 < 2:
powR, powI = - powR, - powI
return powR, powI
if self.verbosity >= 25:
verbosityDepth("INIT", ("Assembling auxiliary expression for "
"forcing term derivative."),
timestamp = self.timestamp)
from scipy.special import factorial as fact
y = fen.SpatialCoordinate(self.V.mesh())[1]
powR, powI = [(self.kappa * np.sin(self.theta)) ** derI * k\
for k in getPowMinusj(y, derI)]
mu2R, mu2I = np.real(mu(0, 0) ** 2.), np.imag(mu(0, 0) ** 2.)
exprR = mu2R * powR - mu2I * powI
exprI = mu2I * powR + mu2R * powI
if derI >= 1:
muR, muI = np.real(2. * mu(0, 0)), np.imag(2. * mu(0, 0))
powR, powI = [(self.kappa * np.sin(self.theta)) ** (derI - 1) * k\
* derI for k in getPowMinusj(y, derI - 1)]
exprR += muR * powR - muI * powI
exprI += muI * powR + muR * powI
if derI >= 2:
powR, powI = [(self.kappa * np.sin(self.theta)) ** (derI - 2) * k\
* derI * (derI - 1) for k in getPowMinusj(y, derI - 2)]
exprR += powR
exprI += powI
fac = fact(derI)
if self.verbosity >= 25:
verbosityDepth("DEL", "Done assembling auxiliary expression.",
timestamp = self.timestamp)
return [exprR / fac, exprI / fac]
def A(self, mu : paramVal = [], der : List[int] = 0) -> ScOp:
"""Assemble (derivative of) operator of linear system."""
mu = self.checkParameter(mu)
if not hasattr(der, "__len__"): der = [der] * self.npar
derI = hashD(der)
self.autoSetDS()
if derI <= 0 and self.As[0] is None:
if self.verbosity >= 20:
verbosityDepth("INIT", "Assembling operator term A0.",
timestamp = self.timestamp)
DirichletBC0 = fen.DirichletBC(self.V, fenZERO,
self.DirichletBoundary)
a0Re = fen.dot(self.u.dx(1), self.v.dx(1)) * fen.dx
A0Re = fen.assemble(a0Re)
DirichletBC0.apply(A0Re)
A0ReMat = fen.as_backend_type(A0Re).mat()
A0Rer, A0Rec, A0Rev = A0ReMat.getValuesCSR()
self.As[0] = scsp.csr_matrix((A0Rev, A0Rec, A0Rer),
shape = A0ReMat.size,
dtype = np.complex)
if self.verbosity >= 20:
verbosityDepth("DEL", "Done assembling operator term.",
timestamp = self.timestamp)
if derI <= 1 and self.As[1] is None: self.As[1] = 0.
if derI <= 2 and self.As[2] is None:
if self.verbosity >= 20:
verbosityDepth("INIT", "Assembling operator term A2.",
timestamp = self.timestamp)
DirichletBC0 = fen.DirichletBC(self.V, fenZERO,
self.DirichletBoundary)
nRe, nIm = self.refractionIndex
n2Re, n2Im = nRe * nRe - nIm * nIm, 2 * nRe * nIm
k2Re, k2Im = np.real(self.omega ** 2), np.imag(self.omega ** 2)
k2n2Re = k2Re * n2Re - k2Im * n2Im
k2n2Im = k2Re * n2Im + k2Im * n2Re
parsRe = self.iterReduceQuadratureDegree(zip([k2n2Re],
["kappaSquaredRefractionIndexSquaredReal"]))
parsIm = self.iterReduceQuadratureDegree(zip([k2n2Im],
["kappaSquaredRefractionIndexSquaredImag"]))
a2Re = (fen.dot(self.u.dx(0), self.v.dx(0))
- k2n2Re * fen.dot(self.u, self.v)) * fen.dx
a2Im = - k2n2Im * fen.dot(self.u, self.v) * fen.dx
A2Re = fen.assemble(a2Re, form_compiler_parameters = parsRe)
A2Im = fen.assemble(a2Im, form_compiler_parameters = parsIm)
DirichletBC0.zero(A2Re)
DirichletBC0.zero(A2Im)
A2ReMat = fen.as_backend_type(A2Re).mat()
A2ImMat = fen.as_backend_type(A2Im).mat()
A2Rer, A2Rec, A2Rev = A2ReMat.getValuesCSR()
A2Imr, A2Imc, A2Imv = A2ImMat.getValuesCSR()
self.As[2] = (scsp.csr_matrix((A2Rev, A2Rec, A2Rer),
shape = A2ReMat.size)
+ 1.j * scsp.csr_matrix((A2Imv, A2Imc, A2Imr),
shape = A2ImMat.size))
if self.verbosity >= 20:
verbosityDepth("DEL", "Done assembling operator term.",
timestamp = self.timestamp)
return self._assembleA(mu, der, derI)
def b(self, mu : paramVal = [], der : List[int] = 0,
homogeneized : bool = False) -> Np1D:
"""Assemble (derivative of) RHS of linear system."""
mu = self.checkParameter(mu)
if not hasattr(der, "__len__"): der = [der] * self.npar
derI = hashD(der)
nbsTot = self.nbsH if homogeneized else self.nbs
bs = self.bsH if homogeneized else self.bs
if homogeneized and self.mu0 != self.mu0BC:
self.liftDirichletData(self.mu0)
for j in range(derI, nbsTot):
if bs[j] is None:
if self.verbosity >= 20:
verbosityDepth("INIT", ("Assembling forcing term "
"b{}.").format(j),
timestamp = self.timestamp)
if j < self.nbs:
fRe, fIm = self.getForcingTerm(self.mu0)
cRe, cIm = self.getExtraFactorB(self.mu0, j)
cfRe, cfIm = cRe * fRe - cIm * fIm, cRe * fIm + cIm * fRe
else:
cfRe, cfIm = fenZERO, fenZERO
parsRe = self.iterReduceQuadratureDegree(zip([cfRe],
["forcingTermDer{}Real".format(j)]))
parsIm = self.iterReduceQuadratureDegree(zip([cfIm],
["forcingTermDer{}Imag".format(j)]))
L0Re = fen.dot(cfRe, self.v) * fen.dx
L0Im = fen.dot(cfIm, self.v) * fen.dx
b0Re = fen.assemble(L0Re, form_compiler_parameters = parsRe)
b0Im = fen.assemble(L0Im, form_compiler_parameters = parsIm)
- if homogeneized:
- Ader = self.A(self.mu0, hashI(j))
- b0Re[:] -= np.real(Ader.dot(self.liftedDirichletDatum))
- b0Im[:] -= np.imag(Ader.dot(self.liftedDirichletDatum))
+
DirichletBC0 = fen.DirichletBC(self.V, fenZERO,
self.DirichletBoundary)
DirichletBC0.apply(b0Re)
DirichletBC0.apply(b0Im)
+ b = np.array(b0Re[:] + 1.j * b0Im[:], dtype = np.complex)
if homogeneized:
- self.bsH[j] = np.array(b0Re[:] + 1.j * b0Im[:],
- dtype = np.complex)
+ Ader = self.A(self.mu0, hashI(j, self.npar))
+ b -= Ader.dot(self.liftedDirichletDatum)
+ if homogeneized:
+ self.bsH[j] = b
else:
- self.bs[j] = np.array(b0Re[:] + 1.j * b0Im[:],
- dtype = np.complex)
+ self.bs[j] = b
if self.verbosity >= 20:
verbosityDepth("DEL", "Done assembling forcing term.",
timestamp = self.timestamp)
- return self._assembleb(mu - self.mu0, der, derI, homogeneized)
+ return self._assembleb(mu, der, derI, homogeneized, self.mu0)
+
diff --git a/rrompy/hfengines/linear_problem/helmholtz_square_bubble_problem_engine.py b/rrompy/hfengines/linear_problem/helmholtz_square_bubble_problem_engine.py
index 1fc3ca8..59b81c1 100644
--- a/rrompy/hfengines/linear_problem/helmholtz_square_bubble_problem_engine.py
+++ b/rrompy/hfengines/linear_problem/helmholtz_square_bubble_problem_engine.py
@@ -1,52 +1,53 @@
# Copyright (C) 2018 by the RROMPy authors
#
# This file is part of RROMPy.
#
# RROMPy is free software: you can redistribute it and/or modify
# it under the terms of the GNU Lesser General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# RROMPy is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU Lesser General Public License for more details.
#
# You should have received a copy of the GNU Lesser General Public License
# along with RROMPy. If not, see .
#
import numpy as np
import fenics as fen
from .helmholtz_problem_engine import HelmholtzProblemEngine
__all__ = ['HelmholtzSquareBubbleProblemEngine']
class HelmholtzSquareBubbleProblemEngine(HelmholtzProblemEngine):
"""
Solver for square bubble Helmholtz problems with parametric wavenumber.
- \Delta u - omega^2 * u = f in \Omega
u = 0 on \Gamma_D
with exact solution square bubble times plane wave.
"""
def __init__(self, kappa:float, theta:float, n:int,
degree_threshold : int = np.inf, verbosity : int = 10,
timestamp : bool = True):
super().__init__(mu0 = [kappa], degree_threshold = degree_threshold,
verbosity = verbosity, timestamp = timestamp)
pi = np.pi
- mesh = fen.RectangleMesh(fen.Point(0, 0), fen.Point(pi, pi), n, n)
- self.V = fen.FunctionSpace(mesh, "P", 3)
+ mesh = fen.RectangleMesh(fen.Point(0, 0), fen.Point(pi, pi),
+ 3 * n, 3 * n)
+ self.V = fen.FunctionSpace(mesh, "P", 1)
c, s = np.cos(theta), np.sin(theta)
x, y = fen.SpatialCoordinate(mesh)[:]
C = 16. / pi ** 4.
bR = C * 2 * (x * (pi - x) + y * (pi - y))
bI = C * 2 * kappa * (c * (pi - 2 * x) * y * (pi - y)
+ s * x * (pi - x) * (pi - 2 * y))
wR = fen.cos(kappa * (c * x + s * y))
wI = fen.sin(kappa * (c * x + s * y))
self.forcingTerm = [bR * wR + bI * wI, bI * wR - bR * wI]
diff --git a/rrompy/hfengines/linear_problem/helmholtz_square_transmission_problem_engine.py b/rrompy/hfengines/linear_problem/helmholtz_square_transmission_problem_engine.py
index fbc05fc..5726350 100644
--- a/rrompy/hfengines/linear_problem/helmholtz_square_transmission_problem_engine.py
+++ b/rrompy/hfengines/linear_problem/helmholtz_square_transmission_problem_engine.py
@@ -1,74 +1,74 @@
# Copyright (C) 2018 by the RROMPy authors
#
# This file is part of RROMPy.
#
# RROMPy is free software: you can redistribute it and/or modify
# it under the terms of the GNU Lesser General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# RROMPy is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU Lesser General Public License for more details.
#
# You should have received a copy of the GNU Lesser General Public License
# along with RROMPy. If not, see .
#
import numpy as np
import fenics as fen
import ufl
from .helmholtz_problem_engine import HelmholtzProblemEngine
__all__ = ['HelmholtzSquareTransmissionProblemEngine']
class HelmholtzSquareTransmissionProblemEngine(HelmholtzProblemEngine):
"""
Solver for square transmission Helmholtz problems with parametric
wavenumber.
- \Delta u - omega^2 * n^2 * u = 0 in \Omega
u = 0 on \Gamma_D
with exact solution a transmitted plane wave.
"""
def __init__(self, nT:float, nB:float, kappa:float, theta:float, n:int,
degree_threshold : int = np.inf, verbosity : int = 10,
timestamp : bool = True):
super().__init__(mu0 = [kappa], degree_threshold = degree_threshold,
verbosity = verbosity, timestamp = timestamp)
mesh = fen.RectangleMesh(fen.Point(-np.pi/2, -np.pi/2),
- fen.Point(np.pi/2, np.pi/2), n, n)
- self.V = fen.FunctionSpace(mesh, "P", 3)
+ fen.Point(np.pi/2, np.pi/2), 3 * n, 3 * n)
+ self.V = fen.FunctionSpace(mesh, "P", 1)
dx, dy = np.cos(theta), np.sin(theta)
Kx = kappa * nB * dx
Ky = kappa * (nT**2. - (nB * dx)**2. + 0.j)**.5
T = 2 * kappa * nB * dy / (Ky + kappa * nB * dy)
x, y = fen.SpatialCoordinate(mesh)[:]
TR, TI = np.real(T), np.imag(T)
if np.isclose(np.imag(Ky), 0.):
u0RT = (TR * fen.cos(Kx * x + np.real(Ky) * y)
- TI * fen.sin(Kx * x + np.real(Ky) * y))
u0IT = (TR * fen.sin(Kx * x + np.real(Ky) * y)
+ TI * fen.cos(Kx * x + np.real(Ky) * y))
else:
u0RT = fen.exp(- np.imag(Ky) * y) * (TR * fen.cos(Kx * x)
- TI * fen.sin(Kx * x))
u0IT = fen.exp(- np.imag(Ky) * y) * (TR * fen.sin(Kx * x)
+ TI * fen.cos(Kx * x))
u0RB = (fen.cos(kappa * nB * (dx * x + dy * y))
+ (TR - 1) * fen.cos(kappa * nB * (dx*x - dy*y))
- TI * fen.sin(kappa * nB * (dx*x - dy*y)))
u0IB = (fen.sin(kappa * nB * (dx * x + dy * y))
+ (TR - 1) * fen.sin(kappa * nB * (dx*x - dy*y))
+ TI * fen.cos(kappa * nB * (dx*x - dy*y)))
u0R = ufl.conditional(ufl.ge(y, 0.), u0RT, u0RB)
u0I = ufl.conditional(ufl.ge(y, 0.), u0IT, u0IB)
self.refractionIndex = ufl.conditional(ufl.ge(y, 0.),
fen.Constant(nT),
fen.Constant(nB))
self.DirichletDatum = [u0R, u0I]
diff --git a/rrompy/hfengines/linear_problem/laplace_base_problem_engine.py b/rrompy/hfengines/linear_problem/laplace_base_problem_engine.py
index cbab415..b2bbe18 100644
--- a/rrompy/hfengines/linear_problem/laplace_base_problem_engine.py
+++ b/rrompy/hfengines/linear_problem/laplace_base_problem_engine.py
@@ -1,321 +1,320 @@
# Copyright (C) 2018 by the RROMPy authors
#
# This file is part of RROMPy.
#
# RROMPy is free software: you can redistribute it and/or modify
# it under the terms of the GNU Lesser General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# RROMPy is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU Lesser General Public License for more details.
#
# You should have received a copy of the GNU Lesser General Public License
# along with RROMPy. If not, see .
#
import numpy as np
import scipy.sparse as scsp
import fenics as fen
from rrompy.hfengines.base.problem_engine_base import ProblemEngineBase
from rrompy.utilities.base.types import Np1D, List, ScOp, paramVal, paramList
from rrompy.solver.fenics import fenZERO, fenONE, H1NormMatrix
from rrompy.utilities.base import verbosityDepth
from rrompy.utilities.poly_fitting.polynomial import (
- hashDerivativeToIdx as hashD)
+ hashDerivativeToIdx as hashD, hashIdxToDerivative as hashI)
from rrompy.parameter import checkParameter
__all__ = ['LaplaceBaseProblemEngine']
class LaplaceBaseProblemEngine(ProblemEngineBase):
"""
Solver for generic Laplace problems.
- \nabla \cdot (a \nabla u) = f in \Omega
u = u0 on \Gamma_D
\partial_nu = g1 on \Gamma_N
\partial_nu + h u = g2 on \Gamma_R
Attributes:
verbosity: Verbosity level.
BCManager: Boundary condition manager.
V: Real FE space.
u: Generic trial functions for variational form evaluation.
v: Generic test functions for variational form evaluation.
As: Scipy sparse array representation (in CSC format) of As.
bs: Numpy array representation of bs.
bsH: Numpy array representation of homogeneized bs.
energyNormMatrix: Scipy sparse matrix representing inner product over
V.
liftedDirichletDatum: Dofs of Dirichlet datum lifting.
mu0BC: Mu value of last Dirichlet datum lifting.
degree_threshold: Threshold for ufl expression interpolation degree.
omega: Value of omega.
diffusivity: Value of a.
forcingTerm: Value of f.
DirichletDatum: Value of u0.
NeumannDatum: Value of g1.
RobinDatumG: Value of g2.
RobinDatumH: Value of h.
DirichletBoundary: Function handle to \Gamma_D.
NeumannBoundary: Function handle to \Gamma_N.
RobinBoundary: Function handle to \Gamma_R.
ds: Boundary measure 2-tuple (resp. for Neumann and Robin boundaries).
A0: Scipy sparse array representation (in CSC format) of A0.
b0: Numpy array representation of b0.
dsToBeSet: Whether ds needs to be set.
"""
def __init__(self, mu0 : paramVal = [], degree_threshold : int = np.inf,
verbosity : int = 10, timestamp : bool = True):
super().__init__(degree_threshold = degree_threshold,
verbosity = verbosity, timestamp = timestamp)
self.mu0 = checkParameter(mu0)
self.npar = self.mu0.shape[1]
self.omega = np.abs(self.mu0(0, 0)) if self.npar > 0 else 0.
self.diffusivity = fenONE
self.forcingTerm = fenZERO
self.DirichletDatum = fenZERO
self.NeumannDatum = fenZERO
self.RobinDatumG = fenZERO
self.RobinDatumH = fenZERO
@property
def V(self):
"""Value of V."""
return self._V
@V.setter
def V(self, V):
ProblemEngineBase.V.fset(self, V)
self.dsToBeSet = True
@property
def diffusivity(self):
"""Value of a."""
return self._diffusivity
@diffusivity.setter
def diffusivity(self, diffusivity):
self.resetAs()
if not isinstance(diffusivity, (list, tuple,)):
diffusivity = [diffusivity, fenZERO]
self._diffusivity = diffusivity
@property
def forcingTerm(self):
"""Value of f."""
return self._forcingTerm
@forcingTerm.setter
def forcingTerm(self, forcingTerm):
self.resetbs()
if not isinstance(forcingTerm, (list, tuple,)):
forcingTerm = [forcingTerm, fenZERO]
self._forcingTerm = forcingTerm
@property
def DirichletDatum(self):
"""Value of u0."""
return self._DirichletDatum
@DirichletDatum.setter
def DirichletDatum(self, DirichletDatum):
self.resetbs()
if not isinstance(DirichletDatum, (list, tuple,)):
DirichletDatum = [DirichletDatum, fenZERO]
self._DirichletDatum = DirichletDatum
@property
def NeumannDatum(self):
"""Value of g1."""
return self._NeumannDatum
@NeumannDatum.setter
def NeumannDatum(self, NeumannDatum):
self.resetbs()
if not isinstance(NeumannDatum, (list, tuple,)):
NeumannDatum = [NeumannDatum, fenZERO]
self._NeumannDatum = NeumannDatum
@property
def RobinDatumG(self):
"""Value of g2."""
return self._RobinDatumG
@RobinDatumG.setter
def RobinDatumG(self, RobinDatumG):
self.resetbs()
if not isinstance(RobinDatumG, (list, tuple,)):
RobinDatumG = [RobinDatumG, fenZERO]
self._RobinDatumG = RobinDatumG
@property
def RobinDatumH(self):
"""Value of h."""
return self._RobinDatumH
@RobinDatumH.setter
def RobinDatumH(self, RobinDatumH):
self.resetAs()
if not isinstance(RobinDatumH, (list, tuple,)):
RobinDatumH = [RobinDatumH, fenZERO]
self._RobinDatumH = RobinDatumH
@property
def DirichletBoundary(self):
"""Function handle to DirichletBoundary."""
return self.BCManager.DirichletBoundary
@DirichletBoundary.setter
def DirichletBoundary(self, DirichletBoundary):
self.resetAs()
self.resetbs()
self.BCManager.DirichletBoundary = DirichletBoundary
@property
def NeumannBoundary(self):
"""Function handle to NeumannBoundary."""
return self.BCManager.NeumannBoundary
@NeumannBoundary.setter
def NeumannBoundary(self, NeumannBoundary):
self.resetAs()
self.resetbs()
self.dsToBeSet = True
self.BCManager.NeumannBoundary = NeumannBoundary
@property
def RobinBoundary(self):
"""Function handle to RobinBoundary."""
return self.BCManager.RobinBoundary
@RobinBoundary.setter
def RobinBoundary(self, RobinBoundary):
self.resetAs()
self.resetbs()
self.dsToBeSet = True
self.BCManager.RobinBoundary = RobinBoundary
def autoSetDS(self):
"""Set FEniCS boundary measure based on boundary function handles."""
if self.dsToBeSet:
if self.verbosity >= 20:
verbosityDepth("INIT", "Initializing boundary measures.",
timestamp = self.timestamp)
mesh = self.V.mesh()
NB = self.NeumannBoundary
RB = self.RobinBoundary
boundary_markers = fen.MeshFunction("size_t", mesh,
mesh.topology().dim() - 1)
NB.mark(boundary_markers, 0)
RB.mark(boundary_markers, 1)
self.ds = fen.Measure("ds", domain = mesh,
subdomain_data = boundary_markers)
self.dsToBeSet = False
if self.verbosity >= 20:
verbosityDepth("DEL", "Done initializing boundary measures.",
timestamp = self.timestamp)
def buildEnergyNormForm(self):
"""
Build sparse matrix (in CSR format) representative of scalar product.
"""
self.energyNormMatrix = H1NormMatrix(self.V, np.abs(self.omega)**2)
def A(self, mu : paramVal = [], der : List[int] = 0) -> ScOp:
"""Assemble (derivative of) operator of linear system."""
mu = self.checkParameter(mu)
if not hasattr(der, "__len__"): der = [der] * self.npar
derI = hashD(der)
if derI <= 0 and self.As[0] is None:
self.autoSetDS()
if self.verbosity >= 20:
verbosityDepth("INIT", "Assembling operator term A0.",
timestamp = self.timestamp)
DirichletBC0 = fen.DirichletBC(self.V, fenZERO,
self.DirichletBoundary)
aRe, aIm = self.diffusivity
hRe, hIm = self.RobinDatumH
termNames = ["diffusivity", "RobinDatumH"]
parsRe = self.iterReduceQuadratureDegree(zip([aRe, hRe],
[x + "Real" for x in termNames]))
parsIm = self.iterReduceQuadratureDegree(zip([aIm, hIm],
[x + "Imag" for x in termNames]))
a0Re = (aRe * fen.dot(fen.grad(self.u), fen.grad(self.v)) * fen.dx
+ hRe * fen.dot(self.u, self.v) * self.ds(1))
a0Im = (aIm * fen.dot(fen.grad(self.u), fen.grad(self.v)) * fen.dx
+ hIm * fen.dot(self.u, self.v) * self.ds(1))
A0Re = fen.assemble(a0Re, form_compiler_parameters = parsRe)
A0Im = fen.assemble(a0Im, form_compiler_parameters = parsIm)
DirichletBC0.apply(A0Re)
DirichletBC0.zero(A0Im)
A0ReMat = fen.as_backend_type(A0Re).mat()
A0ImMat = fen.as_backend_type(A0Im).mat()
A0Rer, A0Rec, A0Rev = A0ReMat.getValuesCSR()
A0Imr, A0Imc, A0Imv = A0ImMat.getValuesCSR()
self.As[0] = (scsp.csr_matrix((A0Rev, A0Rec, A0Rer),
shape = A0ReMat.size)
+ 1.j * scsp.csr_matrix((A0Imv, A0Imc, A0Imr),
shape = A0ImMat.size))
if self.verbosity >= 20:
verbosityDepth("DEL", "Done assembling operator term.",
timestamp = self.timestamp)
return self._assembleA(mu, der, derI)
def b(self, mu : paramVal = [], der : List[int] = 0,
homogeneized : bool = False) -> Np1D:
"""Assemble (derivative of) RHS of linear system."""
mu = self.checkParameter(mu)
if not hasattr(der, "__len__"): der = [der] * self.npar
derI = hashD(der)
nbsTot = self.nbsH if homogeneized else self.nbs
bs = self.bsH if homogeneized else self.bs
if homogeneized and self.mu0 != self.mu0BC:
self.liftDirichletData(self.mu0)
for j in range(derI, nbsTot):
if bs[j] is None:
self.autoSetDS()
if self.verbosity >= 20:
verbosityDepth("INIT", ("Assembling forcing term "
"b{}.").format(j),
timestamp = self.timestamp)
- if derI == 0:
+ termNames, terms = [], []
+ if j == 0:
+ u0Re, u0Im = self.DirichletDatum
fRe, fIm = self.forcingTerm
g1Re, g1Im = self.NeumannDatum
g2Re, g2Im = self.RobinDatumG
+ termNames += ["forcingTerm", "NeumannDatum", "RobinDatumG"]
+ terms += [[fRe, fIm], [g1Re, g1Im], [g2Re, g2Im]]
else:
+ u0Re, u0Im = fenZERO, fenZERO
fRe, fIm = fenZERO, fenZERO
g1Re, g1Im = fenZERO, fenZERO
g2Re, g2Im = fenZERO, fenZERO
- termNames = ["forcingTerm", "NeumannDatum", "RobinDatumG"]
- parsRe = self.iterReduceQuadratureDegree(zip(
- [fRe, g1Re, g2Re],
+ if len(termNames) > 0:
+ parsRe = self.iterReduceQuadratureDegree(zip(
+ [term[0] for term in terms],
[x + "Real" for x in termNames]))
- parsIm = self.iterReduceQuadratureDegree(zip(
- [fIm, g1Im, g2Im],
+ parsIm = self.iterReduceQuadratureDegree(zip(
+ [term[1] for term in terms],
[x + "Imag" for x in termNames]))
+ else:
+ parsRe, parsIm = {}, {}
L0Re = (fen.dot(fRe, self.v) * fen.dx
+ fen.dot(g1Re, self.v) * self.ds(0)
+ fen.dot(g2Re, self.v) * self.ds(1))
L0Im = (fen.dot(fIm, self.v) * fen.dx
+ fen.dot(g1Im, self.v) * self.ds(0)
+ fen.dot(g2Im, self.v) * self.ds(1))
b0Re = fen.assemble(L0Re, form_compiler_parameters = parsRe)
b0Im = fen.assemble(L0Im, form_compiler_parameters = parsIm)
- if homogeneized:
- Ader = self.A(self.mu0, der)
- b0Re[:] -= np.real(Ader.dot(self.liftedDirichletDatum))
- b0Im[:] -= np.imag(Ader.dot(self.liftedDirichletDatum))
- DBCR = fen.DirichletBC(self.V, fenZERO,
- self.DirichletBoundary)
- DBCI = fen.DirichletBC(self.V, fenZERO,
- self.DirichletBoundary)
- else:
- DBCR = fen.DirichletBC(self.V, self.DirichletDatum[0],
- self.DirichletBoundary)
- DBCI = fen.DirichletBC(self.V, self.DirichletDatum[1],
- self.DirichletBoundary)
+ DBCR = fen.DirichletBC(self.V, u0Re, self.DirichletBoundary)
+ DBCI = fen.DirichletBC(self.V, u0Im, self.DirichletBoundary)
DBCR.apply(b0Re)
DBCI.apply(b0Im)
b = np.array(b0Re[:] + 1.j * b0Im[:], dtype = np.complex)
+ if homogeneized:
+ Ader = self.A(self.mu0, hashI(j, self.npar))
+ b -= Ader.dot(self.liftedDirichletDatum)
if homogeneized:
self.bsH[j] = b
else:
self.bs[j] = b
if self.verbosity >= 20:
verbosityDepth("DEL", "Done assembling forcing term.",
timestamp = self.timestamp)
- return self._assembleb(mu - self.mu0, der, derI, homogeneized)
+ return self._assembleb(mu, der, derI, homogeneized, self.mu0)
diff --git a/rrompy/hfengines/linear_problem/laplace_disk_gaussian.py b/rrompy/hfengines/linear_problem/laplace_disk_gaussian.py
index cbd6187..4da30a2 100644
--- a/rrompy/hfengines/linear_problem/laplace_disk_gaussian.py
+++ b/rrompy/hfengines/linear_problem/laplace_disk_gaussian.py
@@ -1,163 +1,160 @@
# Copyright (C) 2018 by the RROMPy authors
#
# This file is part of RROMPy.
#
# RROMPy is free software: you can redistribute it and/or modify
# it under the terms of the GNU Lesser General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# RROMPy is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU Lesser General Public License for more details.
#
# You should have received a copy of the GNU Lesser General Public License
# along with RROMPy. If not, see .
#
import numpy as np
import fenics as fen
from rrompy.utilities.base.types import Np1D, Tuple, FenExpr, paramVal
from .laplace_base_problem_engine import LaplaceBaseProblemEngine
from rrompy.solver.fenics import fenZERO, fenONE
from rrompy.utilities.base import verbosityDepth
from rrompy.utilities.poly_fitting.polynomial import (
hashDerivativeToIdx as hashD, hashIdxToDerivative as hashI)
__all__ = ['LaplaceDiskGaussian']
class LaplaceDiskGaussian(LaplaceBaseProblemEngine):
"""
Solver for disk Laplace problems with parametric forcing term center.
- \Delta u = C exp(-.5 * ||\cdot - (mu, 0)||^2) in \Omega = B(0, 5)
u = 0 on \partial\Omega.
"""
- nbs = 20
-
def __init__(self, n:int, mu0 : paramVal = [0.], degree_threshold : int = np.inf,
verbosity : int = 10, timestamp : bool = True):
super().__init__(mu0 = mu0, degree_threshold = degree_threshold,
verbosity = verbosity, timestamp = timestamp)
+ self.nbs = 20
self.computebsFactors()
self.forcingTermMu = np.nan
import mshr
- mesh = mshr.generate_mesh(mshr.Circle(fen.Point(0., 0.), 5.), n)
- self.V = fen.FunctionSpace(mesh, "P", 3)
+ mesh = mshr.generate_mesh(mshr.Circle(fen.Point(0., 0.), 5.), 3 * n)
+ self.V = fen.FunctionSpace(mesh, "P", 1)
def getForcingTerm(self, mu : paramVal = []) -> Tuple[FenExpr, FenExpr]:
"""Compute forcing term."""
mu = self.checkParameter(mu)
if mu != self.forcingTermMu:
if self.verbosity >= 25:
verbosityDepth("INIT", ("Assembling base expression for "
"forcing term."),
timestamp = self.timestamp)
x, y = fen.SpatialCoordinate(self.V.mesh())[:]
C = np.exp(-.5 * mu(0, 0) ** 2.)
CR, CI = np.real(C), np.imag(C)
f0 = (2 * np.pi) ** -.5 * fen.exp(-.5 * (x ** 2. + y ** 2.))
muR, muI = np.real(mu(0, 0)), np.imag(mu(0, 0))
f1R = fen.exp(muR * x) * fen.cos(muI * x)
f1I = fen.exp(muR * x) * fen.sin(muI * x)
self.forcingTerm = [f0 * (CR * f1R - CI * f1I),
f0 * (CR * f1I + CI * f1R)]
self.forcingTermMu = mu
if self.verbosity >= 25:
verbosityDepth("DEL", "Done assembling base expression.",
timestamp = self.timestamp)
return self.forcingTerm
def computebsFactors(self):
self.bsFactors = np.zeros((self.nbs, self.nbs), dtype = float)
self.bsFactors[0, 0] = 1.
self.bsFactors[1, 1] = 1.
for j in range(2, self.nbs):
l = (j + 1) % 2 + 1
J = np.arange(l, j + 1, 2)
self.bsFactors[j, J] = self.bsFactors[j - 1, J - 1]
if l == 2:
l = 0
J = np.arange(l, j, 2)
self.bsFactors[j, J] += np.multiply(- 1 - J,
self.bsFactors[j - 1, J + 1])
self.bsFactors[j, l : j + 2 : 2] /= j
def getExtraFactorB(self, mu : paramVal = [],
derI : int = 0) -> Tuple[FenExpr, FenExpr]:
"""Compute extra expression in RHS."""
mu = self.checkParameter(mu)
if self.verbosity >= 25:
verbosityDepth("INIT", ("Assembling auxiliary expression for "
"forcing term derivative."),
timestamp = self.timestamp)
muR, muI = np.real(mu(0, 0)), np.imag(mu(0, 0))
x = fen.SpatialCoordinate(self.V.mesh())[0]
l = derI % 2
if l == 0:
powR, powI = fenONE, fenZERO
else:
powR, powI = x - muR, fen.Constant(muI)
exprR, exprI = [self.bsFactors[derI, l] * k for k in [powR, powI]]
for j in range(l + 2, derI + 1, 2):
for _ in range(2):
powR, powI = (powR * (x - muR) - powI * muI,
powR * muI + powI * (x - muR))
exprR += self.bsFactors[derI, j] * powR
exprI += self.bsFactors[derI, j] * powI
if self.verbosity >= 25:
verbosityDepth("DEL", "Done assembling auxiliary expression.",
timestamp = self.timestamp)
return[exprR, exprI]
def b(self, mu : paramVal = [], der : int = 0,
homogeneized : bool = False) -> Np1D:
"""Assemble (derivative of) RHS of linear system."""
mu = self.checkParameter(mu)
if not hasattr(der, "__len__"): der = [der] * self.npar
derI = hashD(der)
nbsTot = self.nbsH if homogeneized else self.nbs
bs = self.bsH if homogeneized else self.bs
if homogeneized and self.mu0 != self.mu0BC:
self.liftDirichletData(self.mu0)
for j in range(derI, nbsTot):
if bs[j] is None:
if self.verbosity >= 20:
verbosityDepth("INIT", ("Assembling forcing term "
"b{}.").format(j),
timestamp = self.timestamp)
if j < self.nbs:
fRe, fIm = self.getForcingTerm(self.mu0)
cRe, cIm = self.getExtraFactorB(self.mu0, j)
cfRe, cfIm = cRe * fRe - cIm * fIm, cRe * fIm + cIm * fRe
else:
cfRe, cfIm = fenZERO, fenZERO
parsRe = self.iterReduceQuadratureDegree(zip([cfRe],
["forcingTermDer{}Real".format(j)]))
parsIm = self.iterReduceQuadratureDegree(zip([cfIm],
["forcingTermDer{}Imag".format(j)]))
L0Re = fen.dot(cfRe, self.v) * fen.dx
L0Im = fen.dot(cfIm, self.v) * fen.dx
b0Re = fen.assemble(L0Re, form_compiler_parameters = parsRe)
b0Im = fen.assemble(L0Im, form_compiler_parameters = parsIm)
- if homogeneized:
- Ader = self.A(self.mu0, hashI(j))
- b0Re[:] -= np.real(Ader.dot(self.liftedDirichletDatum))
- b0Im[:] -= np.imag(Ader.dot(self.liftedDirichletDatum))
DirichletBC0 = fen.DirichletBC(self.V, fenZERO,
self.DirichletBoundary)
DirichletBC0.apply(b0Re)
DirichletBC0.apply(b0Im)
+ b = np.array(b0Re[:] + 1.j * b0Im[:], dtype = np.complex)
+ if homogeneized:
+ Ader = self.A(self.mu0, hashI(j, self.npar))
+ b -= Ader.dot(self.liftedDirichletDatum)
if homogeneized:
- self.bsH[j] = np.array(b0Re[:] + 1.j * b0Im[:],
- dtype = np.complex)
+ self.bsH[j] = b
else:
- self.bs[j] = np.array(b0Re[:] + 1.j * b0Im[:],
- dtype = np.complex)
+ self.bs[j] = b
if self.verbosity >= 20:
verbosityDepth("DEL", "Done assembling forcing term.",
timestamp = self.timestamp)
- return self._assembleb(mu - self.mu0, der, derI, homogeneized)
+ return self._assembleb(mu, der, derI, homogeneized, self.mu0)
diff --git a/rrompy/hfengines/linear_problem/scattering_problem_engine.py b/rrompy/hfengines/linear_problem/scattering_problem_engine.py
index 2a6b838..2b62cea 100644
--- a/rrompy/hfengines/linear_problem/scattering_problem_engine.py
+++ b/rrompy/hfengines/linear_problem/scattering_problem_engine.py
@@ -1,174 +1,174 @@
# Copyright (C) 2018 by the RROMPy authors
#
# This file is part of RROMPy.
#
# RROMPy is free software: you can redistribute it and/or modify
# it under the terms of the GNU Lesser General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# RROMPy is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU Lesser General Public License for more details.
#
# You should have received a copy of the GNU Lesser General Public License
# along with RROMPy. If not, see .
#
from numpy import inf
import scipy.sparse as scsp
import fenics as fen
from rrompy.utilities.base.types import List, ScOp, paramVal
from rrompy.solver.fenics import fenZERO
from rrompy.utilities.base import verbosityDepth
from .helmholtz_problem_engine import HelmholtzProblemEngine
from rrompy.utilities.poly_fitting.polynomial import (
hashDerivativeToIdx as hashD)
from rrompy.utilities.exception_manager import RROMPyWarning
__all__ = ['ScatteringProblemEngine']
class ScatteringProblemEngine(HelmholtzProblemEngine):
"""
Solver for scattering problems with parametric wavenumber.
- \nabla \cdot (a \nabla u) - omega^2 * n**2 * u = f in \Omega
u = u0 on \Gamma_D
\partial_nu = g1 on \Gamma_N
\partial_nu +- i omega u = g2 on \Gamma_R
Attributes:
verbosity: Verbosity level.
BCManager: Boundary condition manager.
V: Real FE space.
u: Generic trial functions for variational form evaluation.
v: Generic test functions for variational form evaluation.
As: Scipy sparse array representation (in CSC format) of As.
bs: Numpy array representation of bs.
bsH: Numpy array representation of homogeneized bs.
energyNormMatrix: Scipy sparse matrix representing inner product over
V.
liftedDirichletDatum: Dofs of Dirichlet datum lifting.
mu0BC: Mu value of last Dirichlet datum lifting.
degree_threshold: Threshold for ufl expression interpolation degree.
signR: Sign in ABC.
omega: Value of omega.
diffusivity: Value of a.
forcingTerm: Value of f.
DirichletDatum: Value of u0.
NeumannDatum: Value of g1.
RobinDatumG: Value of g2.
DirichletBoundary: Function handle to \Gamma_D.
NeumannBoundary: Function handle to \Gamma_N.
RobinBoundary: Function handle to \Gamma_R.
ds: Boundary measure 2-tuple (resp. for Neumann and Robin boundaries).
A0: Scipy sparse array representation (in CSC format) of A0.
A1: Scipy sparse array representation (in CSC format) of A1.
A2: Scipy sparse array representation (in CSC format) of A2.
b0: Numpy array representation of b0.
dsToBeSet: Whether ds needs to be set.
"""
- nAs = 3
signR = - 1.
def __init__(self, mu0 : paramVal = [0.], degree_threshold : int = inf,
verbosity : int = 10, timestamp : bool = True):
self.silenceWarnings = True
super().__init__(mu0 = mu0, degree_threshold = degree_threshold,
verbosity = verbosity, timestamp = timestamp)
del self.silenceWarnings
+ self.nAs = 3
self.rescalingExp = [1.]
@property
def RobinDatumH(self):
"""Value of h."""
return self.signR * self.omega
@RobinDatumH.setter
def RobinDatumH(self, RobinDatumH):
if not hasattr(self, "silenceWarnings"):
RROMPyWarning(("Scattering problems do not allow changes of h. "
"Ignoring assignment."))
return
def A(self, mu : paramVal = [], der : List[int] = 0) -> ScOp:
"""Assemble (derivative of) operator of linear system."""
mu = self.checkParameter(mu)
if not hasattr(der, "__len__"): der = [der] * self.npar
derI = hashD(der)
if derI <= 0 and self.As[0] is None:
if self.verbosity >= 20:
verbosityDepth("INIT", "Assembling operator term A0.",
timestamp = self.timestamp)
DirichletBC0 = fen.DirichletBC(self.V, fenZERO,
self.DirichletBoundary)
aRe, aIm = self.diffusivity
parsRe = self.iterReduceQuadratureDegree(zip([aRe],
["diffusivityReal"]))
parsIm = self.iterReduceQuadratureDegree(zip([aIm],
["diffusivityImag"]))
a0Re = aRe * fen.dot(fen.grad(self.u), fen.grad(self.v)) * fen.dx
a0Im = aIm * fen.dot(fen.grad(self.u), fen.grad(self.v)) * fen.dx
A0Re = fen.assemble(a0Re, form_compiler_parameters = parsRe)
A0Im = fen.assemble(a0Im, form_compiler_parameters = parsIm)
DirichletBC0.apply(A0Re)
DirichletBC0.zero(A0Im)
A0ReMat = fen.as_backend_type(A0Re).mat()
A0ImMat = fen.as_backend_type(A0Im).mat()
A0Rer, A0Rec, A0Rev = A0ReMat.getValuesCSR()
A0Imr, A0Imc, A0Imv = A0ImMat.getValuesCSR()
self.As[0] = (scsp.csr_matrix((A0Rev, A0Rec, A0Rer),
shape = A0ReMat.size)
+ 1.j * scsp.csr_matrix((A0Imv, A0Imc, A0Imr),
shape = A0ImMat.size))
if self.verbosity >= 20:
verbosityDepth("DEL", "Done assembling operator term.",
timestamp = self.timestamp)
if derI <= 1 and self.As[1] is None:
self.autoSetDS()
if self.verbosity >= 20:
verbosityDepth("INIT", "Assembling operator term A1.",
timestamp = self.timestamp)
DirichletBC0 = fen.DirichletBC(self.V, fenZERO,
self.DirichletBoundary)
a1 = fen.dot(self.u, self.v) * self.ds(1)
A1 = fen.assemble(a1)
DirichletBC0.zero(A1)
A1Mat = fen.as_backend_type(A1).mat()
A1r, A1c, A1v = A1Mat.getValuesCSR()
self.As[1] = self.signR * 1.j * scsp.csr_matrix((A1v, A1c, A1r),
shape = A1Mat.size)
if self.verbosity >= 20:
verbosityDepth("DEL", "Done assembling operator term.",
timestamp = self.timestamp)
if derI <= 2 and self.As[2] is None:
if self.verbosity >= 20:
verbosityDepth("INIT", "Assembling operator term A2.",
timestamp = self.timestamp)
DirichletBC0 = fen.DirichletBC(self.V, fenZERO,
self.DirichletBoundary)
nRe, nIm = self.refractionIndex
n2Re, n2Im = nRe * nRe - nIm * nIm, 2 * nRe * nIm
parsRe = self.iterReduceQuadratureDegree(zip([n2Re],
["refractionIndexSquaredReal"]))
parsIm = self.iterReduceQuadratureDegree(zip([n2Im],
["refractionIndexSquaredImag"]))
a2Re = - n2Re * fen.dot(self.u, self.v) * fen.dx
a2Im = - n2Im * fen.dot(self.u, self.v) * fen.dx
A2Re = fen.assemble(a2Re, form_compiler_parameters = parsRe)
A2Im = fen.assemble(a2Im, form_compiler_parameters = parsIm)
DirichletBC0.zero(A2Re)
DirichletBC0.zero(A2Im)
A2ReMat = fen.as_backend_type(A2Re).mat()
A2ImMat = fen.as_backend_type(A2Im).mat()
A2Rer, A2Rec, A2Rev = A2ReMat.getValuesCSR()
A2Imr, A2Imc, A2Imv = A2ImMat.getValuesCSR()
self.As[2] = (scsp.csr_matrix((A2Rev, A2Rec, A2Rer),
shape = A2ReMat.size)
+ 1.j * scsp.csr_matrix((A2Imv, A2Imc, A2Imr),
shape = A2ImMat.size))
if self.verbosity >= 20:
verbosityDepth("DEL", "Done assembling operator term.",
timestamp = self.timestamp)
return self._assembleA(mu, der, derI)
diff --git a/rrompy/hfengines/vector_linear_problem/bidimensional/linear_elasticity_beam_elasticity_constants.py b/rrompy/hfengines/vector_linear_problem/bidimensional/linear_elasticity_beam_elasticity_constants.py
index cd4023a..e43a097 100644
--- a/rrompy/hfengines/vector_linear_problem/bidimensional/linear_elasticity_beam_elasticity_constants.py
+++ b/rrompy/hfengines/vector_linear_problem/bidimensional/linear_elasticity_beam_elasticity_constants.py
@@ -1,150 +1,149 @@
# Copyright (C) 2018 by the RROMPy authors
#
# This file is part of RROMPy.
#
# RROMPy is free software: you can redistribute it and/or modify
# it under the terms of the GNU Lesser General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# RROMPy is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU Lesser General Public License for more details.
#
# You should have received a copy of the GNU Lesser General Public License
# along with RROMPy. If not, see .
#
import numpy as np
import scipy.sparse as scsp
import fenics as fen
from rrompy.hfengines.vector_linear_problem.\
linear_elasticity_beam_poisson_ratio import LinearElasticityBeamPoissonRatio
from rrompy.solver.fenics import fenZEROS
from rrompy.utilities.base.types import Np1D, List, ScOp, paramVal
from rrompy.utilities.base import verbosityDepth
from rrompy.utilities.exception_manager import RROMPyException
__all__ = ['LinearElasticityBeamElasticityConstants']
class LinearElasticityBeamElasticityConstants(
LinearElasticityBeamPoissonRatio):
"""
Solver for linear elasticity problem of a beam subject to its own weight,
with parametric Joung modulus and Poisson's ratio.
- div(lambda_ * div(u) * I + 2 * mu_ * epsilon(u)) = rho_ * g in \Omega
u = 0 on \Gamma_D
\partial_nu = 0 on \Gamma_N
"""
- nAs, nbs = 5, 4
-
def __init__(self, n:int, rho_:float, g:float, E0:float, nu0:float,
length:float, degree_threshold : int = np.inf,
verbosity : int = 10, timestamp : bool = True):
super().__init__(mu0 = [nu0, E0], degree_threshold = degree_threshold,
verbosity = verbosity, timestamp = timestamp)
+ self.nAs, self.nbs = 5, 4
mesh = fen.RectangleMesh(fen.Point(0., 0.), fen.Point(length, 1),
n, max(int(n / length), 1))
self.V = fen.VectorFunctionSpace(mesh, "P", 1)
self.forcingTerm = [fen.Constant((0., - rho_ * g)), fenZEROS(2)]
self.DirichletBoundary = lambda x, on_b: on_b and fen.near(x[0], 0.)
self.NeumannBoundary = "REST"
def A(self, mu : paramVal = [], der : List[int] = 0) -> ScOp:
"""Assemble (derivative of) operator of linear system."""
mu = self.checkParameter(mu)
if not hasattr(der, "__len__"): der = [der] * self.npar
derI = hashD(der)
self.autoSetDS()
if derI <= 0 and self.As[0] is None: self.As[0] = 0.
if derI <= 1 and self.As[1] is None: self.As[1] = 0.
if derI <= 4 and self.As[2] is None:
if self.verbosity >= 20:
verbosityDepth("INIT", "Assembling operator term A2.",
timestamp = self.timestamp)
DirichletBC0 = fen.DirichletBC(self.V, fenZEROS(2),
self.DirichletBoundary)
epsilon = lambda u: .5 * (fen.grad(u) + fen.nabla_grad(u))
a0Re = fen.inner(epsilon(self.u), epsilon(self.v)) * fen.dx
A0Re = fen.assemble(a0Re)
DirichletBC0.apply(A0Re)
A0ReMat = fen.as_backend_type(A0Re).mat()
A0Rer, A0Rec, A0Rev = A0ReMat.getValuesCSR()
self.As[2] = scsp.csr_matrix((A0Rev, A0Rec, A0Rer),
shape = A0ReMat.size,
dtype = np.complex)
if self.verbosity >= 20:
verbosityDepth("DEL", "Done assembling operator term.",
timestamp = self.timestamp)
if derI <= 3 and self.As[3] is None: self.As[3] = 0.
if derI <= 4 and self.As[4] is None:
if self.verbosity >= 20:
verbosityDepth("INIT", "Assembling operator term A4.",
timestamp = self.timestamp)
DirichletBC0 = fen.DirichletBC(self.V, fenZEROS(2),
self.DirichletBoundary)
a1Re = fen.div(self.u) * fen.div(self.v) * fen.dx
A1Re = fen.assemble(a1Re)
DirichletBC0.apply(A1Re)
A1ReMat = fen.as_backend_type(A1Re).mat()
A1Rer, A1Rec, A1Rev = A1ReMat.getValuesCSR()
self.As[4] = 2. * (scsp.csr_matrix((A1Rev, A1Rec, A1Rer),
shape = A1ReMat.size,
dtype = np.complex)
- self.As[2])
if self.verbosity >= 20:
verbosityDepth("DEL", "Done assembling operator term.",
timestamp = self.timestamp)
return self._assembleA(mu, der, derI)
def b(self, mu : paramVal = [], der : List[int] = 0,
homogeneized : bool = False) -> Np1D:
"""Assemble (derivative of) RHS of linear system."""
RROMPyAssert(homogeneized, False, "Homogeneized")
mu = self.checkParameter(mu)
if not hasattr(der, "__len__"): der = [der] * self.npar
derI = hashD(der)
if derI <= 3 and self.bs[0] is None:
self.autoSetDS()
if self.verbosity >= 20:
verbosityDepth("INIT", "Assembling forcing term b0.",
timestamp = self.timestamp)
fRe, fIm = self.forcingTerm
parsRe = self.iterReduceQuadratureDegree(zip([fRe],
["forcingTermReal"]))
parsIm = self.iterReduceQuadratureDegree(zip([fIm],
["forcingTermImag"]))
L0Re = fen.inner(fRe, self.v) * fen.dx
L0Im = fen.inner(fIm, self.v) * fen.dx
b0Re = fen.assemble(L0Re, form_compiler_parameters = parsRe)
b0Im = fen.assemble(L0Im, form_compiler_parameters = parsIm)
DBCR = fen.DirichletBC(self.V, self.DirichletDatum[0],
self.DirichletBoundary)
DBCI = fen.DirichletBC(self.V, self.DirichletDatum[1],
self.DirichletBoundary)
DBCR.apply(b0Re)
DBCI.apply(b0Im)
self.bs[0] = np.array(b0Re[:] + 1.j * b0Im[:], dtype = np.complex)
if derI <= 1 and self.bs[1] is None:
if self.verbosity >= 20:
verbosityDepth("INIT", "Assembling forcing term b1.",
timestamp = self.timestamp)
self.bs[1] = - self.bs[0]
if self.verbosity >= 20:
verbosityDepth("DEL", "Done assembling forcing term.",
timestamp = self.timestamp)
if derI <= 2 and self.bs[2] is None: self.bs[2] = 0.
if derI <= 3 and self.bs[3] is None:
if self.verbosity >= 20:
verbosityDepth("INIT", "Assembling forcing term b3.",
timestamp = self.timestamp)
self.bs[3] = - 2. * self.bs[0]
if self.verbosity >= 20:
verbosityDepth("DEL", "Done assembling forcing term.",
timestamp = self.timestamp)
return self._assembleb(mu, der, derI, homogeneized)
diff --git a/rrompy/hfengines/vector_linear_problem/linear_elasticity_beam_poisson_ratio.py b/rrompy/hfengines/vector_linear_problem/linear_elasticity_beam_poisson_ratio.py
index b6ffcc5..8b80487 100644
--- a/rrompy/hfengines/vector_linear_problem/linear_elasticity_beam_poisson_ratio.py
+++ b/rrompy/hfengines/vector_linear_problem/linear_elasticity_beam_poisson_ratio.py
@@ -1,149 +1,148 @@
# Copyright (C) 2018 by the RROMPy authors
#
# This file is part of RROMPy.
#
# RROMPy is free software: you can redistribute it and/or modify
# it under the terms of the GNU Lesser General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# RROMPy is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU Lesser General Public License for more details.
#
# You should have received a copy of the GNU Lesser General Public License
# along with RROMPy. If not, see .
#
import numpy as np
import scipy.sparse as scsp
import fenics as fen
from .linear_elasticity_problem_engine import LinearElasticityProblemEngine
from rrompy.solver.fenics import fenZEROS
from rrompy.utilities.base.types import Np1D, List, ScOp, paramVal
from rrompy.utilities.base import verbosityDepth
from rrompy.utilities.exception_manager import RROMPyAssert
from rrompy.utilities.poly_fitting.polynomial import (
hashDerivativeToIdx as hashD)
__all__ = ['LinearElasticityBeamPoissonRatio']
class LinearElasticityBeamPoissonRatio(LinearElasticityProblemEngine):
"""
Solver for linear elasticity problem of a beam subject to its own weight,
with parametric Poisson's ratio.
- div(lambda_ * div(u) * I + 2 * mu_ * epsilon(u)) = rho_ * g in \Omega
u = 0 on \Gamma_D
\partial_nu = 0 on \Gamma_N
"""
- nAs, nbs = 2, 3
-
def __init__(self, n:int, rho_:float, g:float, E:float, nu0:float,
length:float, degree_threshold : int = np.inf,
verbosity : int = 10, timestamp : bool = True):
super().__init__(mu0 = [nu0], degree_threshold = degree_threshold,
verbosity = verbosity, timestamp = timestamp)
+ self.nAs, self.nbs = 2, 3
self.E_ = E
mesh = fen.RectangleMesh(fen.Point(0., 0.), fen.Point(length, 1),
n, max(int(n / length), 1))
self.V = fen.VectorFunctionSpace(mesh, "P", 1)
self.forcingTerm = [fen.Constant((0., - rho_ * g / E)), fenZEROS(2)]
self.DirichletBoundary = lambda x, on_b: on_b and fen.near(x[0], 0.)
self.NeumannBoundary = "REST"
def A(self, mu : paramVal = [], der : List[int] = 0) -> ScOp:
"""Assemble (derivative of) operator of linear system."""
mu = self.checkParameter(mu)
if not hasattr(der, "__len__"): der = [der] * self.npar
derI = hashD(der)
self.autoSetDS()
if derI <= 1 and self.As[0] is None:
if self.verbosity >= 20:
verbosityDepth("INIT", "Assembling operator term A0.",
timestamp = self.timestamp)
DirichletBC0 = fen.DirichletBC(self.V, fenZEROS(2),
self.DirichletBoundary)
epsilon = lambda u: .5 * (fen.grad(u) + fen.nabla_grad(u))
a0Re = self.E_ * fen.inner(epsilon(self.u),
epsilon(self.v)) * fen.dx
A0Re = fen.assemble(a0Re)
DirichletBC0.apply(A0Re)
A0ReMat = fen.as_backend_type(A0Re).mat()
A0Rer, A0Rec, A0Rev = A0ReMat.getValuesCSR()
self.As[0] = scsp.csr_matrix((A0Rev, A0Rec, A0Rer),
shape = A0ReMat.size,
dtype = np.complex)
if self.verbosity >= 20:
verbosityDepth("DEL", "Done assembling operator term.",
timestamp = self.timestamp)
if derI <= 1 and self.As[1] is None:
if self.verbosity >= 20:
verbosityDepth("INIT", "Assembling operator term A1.",
timestamp = self.timestamp)
DirichletBC0 = fen.DirichletBC(self.V, fenZEROS(2),
self.DirichletBoundary)
a1Re = self.E_ * fen.div(self.u) * fen.div(self.v) * fen.dx
A1Re = fen.assemble(a1Re)
DirichletBC0.apply(A1Re)
A1ReMat = fen.as_backend_type(A1Re).mat()
A1Rer, A1Rec, A1Rev = A1ReMat.getValuesCSR()
self.As[1] = 2. * (scsp.csr_matrix((A1Rev, A1Rec, A1Rer),
shape = A1ReMat.size,
dtype = np.complex)
- self.As[0])
if self.verbosity >= 20:
verbosityDepth("DEL", "Done assembling operator term.",
timestamp = self.timestamp)
return self._assembleA(mu, der, derI)
def b(self, mu : paramVal = [], der : List[int] = 0,
homogeneized : bool = False) -> Np1D:
"""Assemble (derivative of) RHS of linear system."""
RROMPyAssert(homogeneized, False, "Homogeneized")
mu = self.checkParameter(mu)
if not hasattr(der, "__len__"): der = [der] * self.npar
derI = hashD(der)
if derI <= 2 and self.bs[0] is None:
self.autoSetDS()
if self.verbosity >= 20:
verbosityDepth("INIT", "Assembling forcing term b0.",
timestamp = self.timestamp)
fRe, fIm = self.forcingTerm
parsRe = self.iterReduceQuadratureDegree(zip([fRe],
["forcingTermReal"]))
parsIm = self.iterReduceQuadratureDegree(zip([fIm],
["forcingTermImag"]))
L0Re = fen.inner(fRe, self.v) * fen.dx
L0Im = fen.inner(fIm, self.v) * fen.dx
b0Re = fen.assemble(L0Re, form_compiler_parameters = parsRe)
b0Im = fen.assemble(L0Im, form_compiler_parameters = parsIm)
DBCR = fen.DirichletBC(self.V, self.DirichletDatum[0],
self.DirichletBoundary)
DBCI = fen.DirichletBC(self.V, self.DirichletDatum[1],
self.DirichletBoundary)
DBCR.apply(b0Re)
DBCI.apply(b0Im)
self.bs[0] = np.array(b0Re[:] + 1.j * b0Im[:], dtype = np.complex)
if derI <= 1 and self.bs[1] is None:
if self.verbosity >= 20:
verbosityDepth("INIT", "Assembling forcing term b1.",
timestamp = self.timestamp)
self.bs[1] = - self.bs[0]
if self.verbosity >= 20:
verbosityDepth("DEL", "Done assembling forcing term.",
timestamp = self.timestamp)
if derI <= 2 and self.bs[2] is None:
if self.verbosity >= 20:
verbosityDepth("INIT", "Assembling forcing term b2.",
timestamp = self.timestamp)
self.bs[2] = - 2. * self.bs[0]
if self.verbosity >= 20:
verbosityDepth("DEL", "Done assembling forcing term.",
timestamp = self.timestamp)
return self._assembleb(mu, der, derI, homogeneized)
diff --git a/rrompy/hfengines/vector_linear_problem/linear_elasticity_helmholtz_problem_engine.py b/rrompy/hfengines/vector_linear_problem/linear_elasticity_helmholtz_problem_engine.py
index fb278ff..0290795 100644
--- a/rrompy/hfengines/vector_linear_problem/linear_elasticity_helmholtz_problem_engine.py
+++ b/rrompy/hfengines/vector_linear_problem/linear_elasticity_helmholtz_problem_engine.py
@@ -1,181 +1,180 @@
# Copyright (C) 2018 by the RROMPy authors
#
# This file is part of RROMPy.
#
# RROMPy is free software: you can redistribute it and/or modify
# it under the terms of the GNU Lesser General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# RROMPy is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU Lesser General Public License for more details.
#
# You should have received a copy of the GNU Lesser General Public License
# along with RROMPy. If not, see .
#
import numpy as np
from scipy.sparse import csr_matrix
import fenics as fen
from .linear_elasticity_problem_engine import LinearElasticityProblemEngine
from rrompy.utilities.base.types import List, ScOp, paramVal
from rrompy.solver.fenics import fenZERO, fenZEROS, fenONE, elasticNormMatrix
from rrompy.utilities.base import verbosityDepth
from rrompy.utilities.poly_fitting.polynomial import (
hashDerivativeToIdx as hashD)
__all__ = ['LinearElasticityHelmholtzProblemEngine']
class LinearElasticityHelmholtzProblemEngine(LinearElasticityProblemEngine):
"""
Solver for generic linear elasticity Helmholtz problems with parametric
wavenumber.
- div(lambda_ * div(u) * I + 2 * mu_ * epsilon(u))
- rho_ * mu^2 * u = f in \Omega
u = u0 on \Gamma_D
\partial_nu = g1 on \Gamma_N
\partial_nu + h u = g2 on \Gamma_R
Attributes:
verbosity: Verbosity level.
BCManager: Boundary condition manager.
V: Real vector FE space.
u: Generic vector trial functions for variational form evaluation.
v: Generic vector test functions for variational form evaluation.
As: Scipy sparse array representation (in CSC format) of As.
bs: Numpy array representation of bs.
energyNormMatrix: Scipy sparse matrix representing inner product over
V.
liftedDirichletDatum: Dofs of Dirichlet datum lifting.
mu0BC: Mu value of last Dirichlet datum lifting.
degree_threshold: Threshold for ufl expression interpolation degree.
omega: Value of omega.
lambda_: Value of lambda_.
mu_: Value of mu_.
forcingTerm: Value of f.
DirichletDatum: Value of u0.
NeumannDatum: Value of g1.
RobinDatumG: Value of g2.
RobinDatumH: Value of h.
DirichletBoundary: Function handle to \Gamma_D.
NeumannBoundary: Function handle to \Gamma_N.
RobinBoundary: Function handle to \Gamma_R.
ds: Boundary measure 2-tuple (resp. for Neumann and Robin boundaries).
A0: Scipy sparse array representation (in CSC format) of A0.
A1: Scipy sparse array representation (in CSC format) of A1.
b0: Numpy array representation of b0.
dsToBeSet: Whether ds needs to be set.
"""
- nAs = 2
-
def __init__(self, mu0 : paramVal = [0.], degree_threshold : int = np.inf,
verbosity : int = 10, timestamp : bool = True):
super().__init__(mu0 = [mu0], degree_threshold = degree_threshold,
verbosity = verbosity, timestamp = timestamp)
+ self.nAs = 2
self.omega = np.abs(self.mu0(0, 0))
self.rho_ = fenONE
self.rescalingExp = [2.]
@property
def rho_(self):
"""Value of rho_."""
return self._rho_
@rho_.setter
def rho_(self, rho_):
self.resetAs()
if not isinstance(rho_, (list, tuple,)):
rho_ = [rho_, fenZERO]
self._rho_ = rho_
def buildEnergyNormForm(self): # energy + omega norm
"""
Build sparse matrix (in CSR format) representative of scalar product.
"""
lambda_Re, _ = self.lambda_
mu_Re, _ = self.mu_
r_Re, _ = self.rho_
self.energyNormMatrix = elasticNormMatrix(self.V, lambda_Re, mu_Re,
np.abs(self.omega)**2 * r_Re)
def A(self, mu : paramVal = [], der : List[int] = 0) -> ScOp:
"""Assemble (derivative of) operator of linear system."""
mu = self.checkParameter(mu)
if not hasattr(der, "__len__"): der = [der] * self.npar
derI = hashD(der)
self.autoSetDS()
if derI <= 0 and self.As[0] is None:
if self.verbosity >= 20:
verbosityDepth("INIT", "Assembling operator term A0.",
timestamp = self.timestamp)
DirichletBC0 = fen.DirichletBC(self.V,
fenZEROS(self.V.mesh().topology().dim()),
self.DirichletBoundary)
lambda_Re, lambda_Im = self.lambda_
mu_Re, mu_Im = self.mu_
hRe, hIm = self.RobinDatumH
termNames = ["lambda_", "mu_", "RobinDatumH"]
parsRe = self.iterReduceQuadratureDegree(zip(
[lambda_Re, mu_Re, hRe],
[x + "Real" for x in termNames]))
parsIm = self.iterReduceQuadratureDegree(zip(
[lambda_Im, mu_Re, hIm],
[x + "Imag" for x in termNames]))
epsilon = lambda u: 0.5 * (fen.grad(u) + fen.nabla_grad(u))
sigma = lambda u, l_, m_: (
l_ * fen.div(u) * fen.Identity(u.geometric_dimension())
+ 2. * m_ * epsilon(u))
a0Re = (fen.inner(sigma(self.u, lambda_Re, mu_Re),
epsilon(self.v)) * fen.dx
+ hRe * fen.inner(self.u, self.v) * self.ds(1))
a0Im = (fen.inner(sigma(self.u, lambda_Im, mu_Im),
epsilon(self.v)) * fen.dx
+ hIm * fen.inner(self.u, self.v) * self.ds(1))
A0Re = fen.assemble(a0Re, form_compiler_parameters = parsRe)
A0Im = fen.assemble(a0Im, form_compiler_parameters = parsIm)
DirichletBC0.apply(A0Re)
DirichletBC0.zero(A0Im)
A0ReMat = fen.as_backend_type(A0Re).mat()
A0ImMat = fen.as_backend_type(A0Im).mat()
A0Rer, A0Rec, A0Rev = A0ReMat.getValuesCSR()
A0Imr, A0Imc, A0Imv = A0ImMat.getValuesCSR()
self.As[0] = (csr_matrix((A0Rev, A0Rec, A0Rer),
shape = A0ReMat.size)
+ 1.j * csr_matrix((A0Imv, A0Imc, A0Imr),
shape = A0ImMat.size))
if self.verbosity >= 20:
verbosityDepth("DEL", "Done assembling operator term.",
timestamp = self.timestamp)
if derI <= 1 and self.As[1] is None:
if self.verbosity >= 20:
verbosityDepth("INIT", "Assembling operator term A1.",
timestamp = self.timestamp)
DirichletBC0 = fen.DirichletBC(self.V,
fenZEROS(self.V.mesh().topology().dim()),
self.DirichletBoundary)
rho_Re, rho_Im = self.rho_
parsRe = self.iterReduceQuadratureDegree(zip([rho_Re],
["rho_Real"]))
parsIm = self.iterReduceQuadratureDegree(zip([rho_Im],
["rho_Imag"]))
a1Re = - rho_Re * fen.inner(self.u, self.v) * fen.dx
a1Im = - rho_Im * fen.inner(self.u, self.v) * fen.dx
A1Re = fen.assemble(a1Re, form_compiler_parameters = parsRe)
A1Im = fen.assemble(a1Im, form_compiler_parameters = parsIm)
DirichletBC0.zero(A1Re)
DirichletBC0.zero(A1Im)
A1ReMat = fen.as_backend_type(A1Re).mat()
A1ImMat = fen.as_backend_type(A1Im).mat()
A1Rer, A1Rec, A1Rev = A1ReMat.getValuesCSR()
A1Imr, A1Imc, A1Imv = A1ImMat.getValuesCSR()
self.As[1] = (csr_matrix((A1Rev, A1Rec, A1Rer),
shape = A1ReMat.size)
+ 1.j * csr_matrix((A1Imv, A1Imc, A1Imr),
shape = A1ImMat.size))
if self.verbosity >= 20:
verbosityDepth("DEL", "Done assembling operator term.",
timestamp = self.timestamp)
return self._assembleA(mu, der, derI)
diff --git a/rrompy/hfengines/vector_linear_problem/linear_elasticity_helmholtz_problem_engine_damped.py b/rrompy/hfengines/vector_linear_problem/linear_elasticity_helmholtz_problem_engine_damped.py
index 035e321..898e32d 100644
--- a/rrompy/hfengines/vector_linear_problem/linear_elasticity_helmholtz_problem_engine_damped.py
+++ b/rrompy/hfengines/vector_linear_problem/linear_elasticity_helmholtz_problem_engine_damped.py
@@ -1,206 +1,205 @@
# Copyright (C) 2018 by the RROMPy authors
#
# This file is part of RROMPy.
#
# RROMPy is free software: you can redistribute it and/or modify
# it under the terms of the GNU Lesser General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# RROMPy is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU Lesser General Public License for more details.
#
# You should have received a copy of the GNU Lesser General Public License
# along with RROMPy. If not, see .
#
import numpy as np
from scipy.sparse import csr_matrix
import fenics as fen
from .linear_elasticity_helmholtz_problem_engine import \
LinearElasticityHelmholtzProblemEngine
from rrompy.utilities.base.types import List, ScOp, paramVal
from rrompy.solver.fenics import fenZERO, fenZEROS
from rrompy.utilities.base import verbosityDepth
from rrompy.utilities.poly_fitting.polynomial import (
hashDerivativeToIdx as hashD)
__all__ = ['LinearElasticityHelmholtzProblemEngineDamped']
class LinearElasticityHelmholtzProblemEngineDamped(
LinearElasticityHelmholtzProblemEngine):
"""
Solver for generic linear elasticity Helmholtz problems with parametric
wavenumber.
- div(lambda_ * div(u) * I + 2 * mu_ * epsilon(u))
- rho_ * (mu^2 - i * eta * mu) * u = f in \Omega
u = u0 on \Gamma_D
\partial_nu = g1 on \Gamma_N
\partial_nu + h u = g2 on \Gamma_R
Attributes:
verbosity: Verbosity level.
BCManager: Boundary condition manager.
V: Real vector FE space.
u: Generic vector trial functions for variational form evaluation.
v: Generic vector test functions for variational form evaluation.
As: Scipy sparse array representation (in CSC format) of As.
bs: Numpy array representation of bs.
energyNormMatrix: Scipy sparse matrix representing inner product over
V.
liftedDirichletDatum: Dofs of Dirichlet datum lifting.
mu0BC: Mu value of last Dirichlet datum lifting.
degree_threshold: Threshold for ufl expression interpolation degree.
omega: Value of omega.
lambda_: Value of lambda_.
mu_: Value of mu_.
eta: Value of eta.
forcingTerm: Value of f.
DirichletDatum: Value of u0.
NeumannDatum: Value of g1.
RobinDatumG: Value of g2.
RobinDatumH: Value of h.
DirichletBoundary: Function handle to \Gamma_D.
NeumannBoundary: Function handle to \Gamma_N.
RobinBoundary: Function handle to \Gamma_R.
ds: Boundary measure 2-tuple (resp. for Neumann and Robin boundaries).
A0: Scipy sparse array representation (in CSC format) of A0.
A1: Scipy sparse array representation (in CSC format) of A1.
b0: Numpy array representation of b0.
dsToBeSet: Whether ds needs to be set.
"""
- nAs = 3
-
def __init__(self, mu0 : paramVal = [0.], degree_threshold : int = np.inf,
verbosity : int = 10, timestamp : bool = True):
super().__init__(mu0 = [mu0], degree_threshold = degree_threshold,
verbosity = verbosity, timestamp = timestamp)
+ self.nAs = 3
self.eta = fenZERO
self.rescalingExp = [1.]
@property
def eta(self):
"""Value of eta."""
return self._eta
@eta.setter
def eta(self, eta):
self.resetAs()
if not isinstance(eta, (list, tuple,)):
eta = [eta, fenZERO]
self._eta = eta
def A(self, mu : paramVal = [], der : List[int] = 0) -> ScOp:
"""Assemble (derivative of) operator of linear system."""
mu = self.checkParameter(mu)
if not hasattr(der, "__len__"): der = [der] * self.npar
derI = hashD(der)
self.autoSetDS()
if derI <= 0 and self.As[0] is None:
if self.verbosity >= 20:
verbosityDepth("INIT", "Assembling operator term A0.",
timestamp = self.timestamp)
DirichletBC0 = fen.DirichletBC(self.V,
fenZEROS(self.V.mesh().topology().dim()),
self.DirichletBoundary)
lambda_Re, lambda_Im = self.lambda_
mu_Re, mu_Im = self.mu_
hRe, hIm = self.RobinDatumH
termNames = ["lambda_", "mu_", "RobinDatumH"]
parsRe = self.iterReduceQuadratureDegree(zip(
[lambda_Re, mu_Re, hRe],
[x + "Real" for x in termNames]))
parsIm = self.iterReduceQuadratureDegree(zip(
[lambda_Im, mu_Re, hIm],
[x + "Imag" for x in termNames]))
epsilon = lambda u: 0.5 * (fen.grad(u) + fen.nabla_grad(u))
sigma = lambda u, l_, m_: (
l_ * fen.div(u) * fen.Identity(u.geometric_dimension())
+ 2. * m_ * epsilon(u))
a0Re = (fen.inner(sigma(self.u, lambda_Re, mu_Re),
epsilon(self.v)) * fen.dx
+ hRe * fen.inner(self.u, self.v) * self.ds(1))
a0Im = (fen.inner(sigma(self.u, lambda_Im, mu_Im),
epsilon(self.v)) * fen.dx
+ hIm * fen.inner(self.u, self.v) * self.ds(1))
A0Re = fen.assemble(a0Re, form_compiler_parameters = parsRe)
A0Im = fen.assemble(a0Im, form_compiler_parameters = parsIm)
DirichletBC0.apply(A0Re)
DirichletBC0.zero(A0Im)
A0ReMat = fen.as_backend_type(A0Re).mat()
A0ImMat = fen.as_backend_type(A0Im).mat()
A0Rer, A0Rec, A0Rev = A0ReMat.getValuesCSR()
A0Imr, A0Imc, A0Imv = A0ImMat.getValuesCSR()
self.As[0] = (csr_matrix((A0Rev, A0Rec, A0Rer),
shape = A0ReMat.size)
+ 1.j * csr_matrix((A0Imv, A0Imc, A0Imr),
shape = A0ImMat.size))
if self.verbosity >= 20:
verbosityDepth("DEL", "Done assembling operator term.",
timestamp = self.timestamp)
if derI <= 1 and self.As[1] is None:
if self.verbosity >= 20:
verbosityDepth("INIT", "Assembling operator term A1.",
timestamp = self.timestamp)
DirichletBC0 = fen.DirichletBC(self.V,
fenZEROS(self.V.mesh().topology().dim()),
self.DirichletBoundary)
rho_Re, rho_Im = self.rho_
eta_Re, eta_Im = self.eta
termNames = ["rho_", "eta"]
parsRe = self.iterReduceQuadratureDegree(zip([rho_Re, eta_Re],
[x + "Real" for x in termNames]))
parsIm = self.iterReduceQuadratureDegree(zip([rho_Im, eta_Im],
[x + "Imag" for x in termNames]))
a1Re = - ((eta_Re * rho_Im + eta_Im * rho_Re)
* fen.inner(self.u, self.v)) * fen.dx
a1Im = ((eta_Re * rho_Re - eta_Im * rho_Im)
* fen.inner(self.u, self.v)) * fen.dx
A1Re = fen.assemble(a1Re, form_compiler_parameters = parsRe)
A1Im = fen.assemble(a1Im, form_compiler_parameters = parsIm)
DirichletBC0.zero(A1Re)
DirichletBC0.zero(A1Im)
A1ReMat = fen.as_backend_type(A1Re).mat()
A1ImMat = fen.as_backend_type(A1Im).mat()
A1Rer, A1Rec, A1Rev = A1ReMat.getValuesCSR()
A1Imr, A1Imc, A1Imv = A1ImMat.getValuesCSR()
self.As[1] = (csr_matrix((A1Rev, A1Rec, A1Rer),
shape = A1ReMat.size)
+ 1.j * csr_matrix((A1Imv, A1Imc, A1Imr),
shape = A1ImMat.size))
if self.verbosity >= 20:
verbosityDepth("DEL", "Done assembling operator term.",
timestamp = self.timestamp)
if derI <= 2 and self.As[2] is None:
if self.verbosity >= 20:
verbosityDepth("INIT", "Assembling operator term A2.",
timestamp = self.timestamp)
DirichletBC0 = fen.DirichletBC(self.V,
fenZEROS(self.V.mesh().topology().dim()),
self.DirichletBoundary)
rho_Re, rho_Im = self.rho_
parsRe = self.iterReduceQuadratureDegree(zip([rho_Re],
["rho_Real"]))
parsIm = self.iterReduceQuadratureDegree(zip([rho_Im],
["rho_Imag"]))
a2Re = - rho_Re * fen.inner(self.u, self.v) * fen.dx
a2Im = - rho_Im * fen.inner(self.u, self.v) * fen.dx
A2Re = fen.assemble(a2Re, form_compiler_parameters = parsRe)
A2Im = fen.assemble(a2Im, form_compiler_parameters = parsIm)
DirichletBC0.zero(A2Re)
DirichletBC0.zero(A2Im)
A2ReMat = fen.as_backend_type(A2Re).mat()
A2ImMat = fen.as_backend_type(A2Im).mat()
A2Rer, A2Rec, A2Rev = A2ReMat.getValuesCSR()
A2Imr, A2Imc, A2Imv = A2ImMat.getValuesCSR()
self.As[2] = (csr_matrix((A2Rev, A2Rec, A2Rer),
shape = A2ReMat.size)
+ 1.j * csr_matrix((A2Imv, A2Imc, A2Imr),
shape = A2ImMat.size))
if self.verbosity >= 20:
verbosityDepth("DEL", "Done assembling operator term.",
timestamp = self.timestamp)
return self._assembleA(mu, der, derI)
diff --git a/rrompy/hfengines/vector_linear_problem/linear_elasticity_problem_engine.py b/rrompy/hfengines/vector_linear_problem/linear_elasticity_problem_engine.py
index d99de76..5fe95b0 100644
--- a/rrompy/hfengines/vector_linear_problem/linear_elasticity_problem_engine.py
+++ b/rrompy/hfengines/vector_linear_problem/linear_elasticity_problem_engine.py
@@ -1,357 +1,346 @@
# Copyright (C) 2018 by the RROMPy authors
#
# This file is part of RROMPy.
#
# RROMPy is free software: you can redistribute it and/or modify
# it under the terms of the GNU Lesser General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# RROMPy is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU Lesser General Public License for more details.
#
# You should have received a copy of the GNU Lesser General Public License
# along with RROMPy. If not, see .
#
import numpy as np
from scipy.sparse import csr_matrix
import fenics as fen
from rrompy.hfengines.base.vector_problem_engine_base import \
VectorProblemEngineBase
from rrompy.utilities.base.types import Np1D, List, ScOp, paramVal
from rrompy.solver.fenics import fenZERO, fenZEROS, fenONE, elasticNormMatrix
from rrompy.utilities.base import verbosityDepth
from rrompy.utilities.poly_fitting.polynomial import (
hashDerivativeToIdx as hashD, hashIdxToDerivative as hashI)
from rrompy.parameter import checkParameter
__all__ = ['LinearElasticityProblemEngine']
class LinearElasticityProblemEngine(VectorProblemEngineBase):
"""
Solver for generic linear elasticity problems.
- div(lambda_ * div(u) * I + 2 * mu_ * epsilon(u)) = f in \Omega
u = u0 on \Gamma_D
\partial_nu = g1 on \Gamma_N
\partial_nu + h u = g2 on \Gamma_R
Attributes:
verbosity: Verbosity level.
BCManager: Boundary condition manager.
V: Real vector FE space.
u: Generic vector trial functions for variational form evaluation.
v: Generic vector test functions for variational form evaluation.
As: Scipy sparse array representation (in CSC format) of As.
bs: Numpy array representation of bs.
energyNormMatrix: Scipy sparse matrix representing inner product over
V.
liftedDirichletDatum: Dofs of Dirichlet datum lifting.
mu0BC: Mu value of last Dirichlet datum lifting.
degree_threshold: Threshold for ufl expression interpolation degree.
lambda_: Value of lambda_.
mu_: Value of mu_.
forcingTerm: Value of f.
DirichletDatum: Value of u0.
NeumannDatum: Value of g1.
RobinDatumG: Value of g2.
RobinDatumH: Value of h.
DirichletBoundary: Function handle to \Gamma_D.
NeumannBoundary: Function handle to \Gamma_N.
RobinBoundary: Function handle to \Gamma_R.
ds: Boundary measure 2-tuple (resp. for Neumann and Robin boundaries).
A0: Scipy sparse array representation (in CSC format) of A0.
b0: Numpy array representation of b0.
dsToBeSet: Whether ds needs to be set.
"""
def __init__(self, mu0 : paramVal = [], degree_threshold : int = np.inf,
verbosity : int = 10, timestamp : bool = True):
super().__init__(degree_threshold = degree_threshold,
verbosity = verbosity, timestamp = timestamp)
self.lambda_ = fenONE
self.mu_ = fenONE
self.mu0 = checkParameter(mu0)
self.npar = self.mu0.shape[1]
self.forcingTerm = fenZEROS(self.V.mesh().topology().dim())
self.DirichletDatum = fenZEROS(self.V.mesh().topology().dim())
self.NeumannDatum = fenZEROS(self.V.mesh().topology().dim())
self.RobinDatumG = fenZEROS(self.V.mesh().topology().dim())
self.RobinDatumH = fenZERO
@property
def V(self):
"""Value of V."""
return self._V
@V.setter
def V(self, V):
VectorProblemEngineBase.V.fset(self, V)
self.forcingTerm = fenZEROS(self.V.mesh().topology().dim())
self.DirichletDatum = fenZEROS(self.V.mesh().topology().dim())
self.NeumannDatum = fenZEROS(self.V.mesh().topology().dim())
self.RobinDatumG = fenZEROS(self.V.mesh().topology().dim())
self.dsToBeSet = True
@property
def lambda_(self):
"""Value of lambda_."""
return self._lambda_
@lambda_.setter
def lambda_(self, lambda_):
self.resetAs()
if not isinstance(lambda_, (list, tuple,)):
lambda_ = [lambda_, fenZERO]
self._lambda_ = lambda_
@property
def mu_(self):
"""Value of mu_."""
return self._mu_
@mu_.setter
def mu_(self, mu_):
self.resetAs()
if not isinstance(mu_, (list, tuple,)):
mu_ = [mu_, fenZERO]
self._mu_ = mu_
@property
def forcingTerm(self):
"""Value of f."""
return self._forcingTerm
@forcingTerm.setter
def forcingTerm(self, forcingTerm):
self.resetbs()
if not isinstance(forcingTerm, (list, tuple,)):
forcingTerm = [forcingTerm,
fenZEROS(self.V.mesh().topology().dim())]
self._forcingTerm = forcingTerm
@property
def DirichletDatum(self):
"""Value of u0."""
return self._DirichletDatum
@DirichletDatum.setter
def DirichletDatum(self, DirichletDatum):
self.resetbs()
if not isinstance(DirichletDatum, (list, tuple,)):
DirichletDatum = [DirichletDatum,
fenZEROS(self.V.mesh().topology().dim())]
self._DirichletDatum = DirichletDatum
@property
def NeumannDatum(self):
"""Value of g1."""
return self._NeumannDatum
@NeumannDatum.setter
def NeumannDatum(self, NeumannDatum):
self.resetbs()
if not isinstance(NeumannDatum, (list, tuple,)):
NeumannDatum = [NeumannDatum,
fenZEROS(self.V.mesh().topology().dim())]
self._NeumannDatum = NeumannDatum
@property
def RobinDatumG(self):
"""Value of g2."""
return self._RobinDatumG
@RobinDatumG.setter
def RobinDatumG(self, RobinDatumG):
self.resetbs()
if not isinstance(RobinDatumG, (list, tuple,)):
RobinDatumG = [RobinDatumG,
fenZEROS(self.V.mesh().topology().dim())]
self._RobinDatumG = RobinDatumG
@property
def RobinDatumH(self):
"""Value of h."""
return self._RobinDatumH
@RobinDatumH.setter
def RobinDatumH(self, RobinDatumH):
self.resetAs()
if not isinstance(RobinDatumH, (list, tuple,)):
RobinDatumH = [RobinDatumH, fenZERO]
self._RobinDatumH = RobinDatumH
@property
def DirichletBoundary(self):
"""Function handle to DirichletBoundary."""
return self.BCManager.DirichletBoundary
@DirichletBoundary.setter
def DirichletBoundary(self, DirichletBoundary):
self.resetAs()
self.resetbs()
self.BCManager.DirichletBoundary = DirichletBoundary
@property
def NeumannBoundary(self):
"""Function handle to NeumannBoundary."""
return self.BCManager.NeumannBoundary
@NeumannBoundary.setter
def NeumannBoundary(self, NeumannBoundary):
self.resetAs()
self.resetbs()
self.dsToBeSet = True
self.BCManager.NeumannBoundary = NeumannBoundary
@property
def RobinBoundary(self):
"""Function handle to RobinBoundary."""
return self.BCManager.RobinBoundary
@RobinBoundary.setter
def RobinBoundary(self, RobinBoundary):
self.resetAs()
self.resetbs()
self.dsToBeSet = True
self.BCManager.RobinBoundary = RobinBoundary
def autoSetDS(self):
"""Set FEniCS boundary measure based on boundary function handles."""
if self.dsToBeSet:
if self.verbosity >= 20:
verbosityDepth("INIT", "Initializing boundary measures.",
timestamp = self.timestamp)
NB = self.NeumannBoundary
RB = self.RobinBoundary
boundary_markers = fen.MeshFunction("size_t", self.V.mesh(),
self.V.mesh().topology().dim() - 1)
NB.mark(boundary_markers, 0)
RB.mark(boundary_markers, 1)
self.ds = fen.Measure("ds", domain = self.V.mesh(),
subdomain_data = boundary_markers)
self.dsToBeSet = False
if self.verbosity >= 20:
verbosityDepth("DEL", "Done initializing boundary measures.",
timestamp = self.timestamp)
def buildEnergyNormForm(self):
"""
Build sparse matrix (in CSR format) representative of scalar product.
"""
lambda_Re, _ = self.lambda_
mu_Re, _ = self.mu_
self.energyNormMatrix = elasticNormMatrix(self.V, lambda_Re, mu_Re)
def A(self, mu : paramVal = [], der : List[int] = 0) -> ScOp:
"""Assemble (derivative of) operator of linear system."""
mu = self.checkParameter(mu)
if not hasattr(der, "__len__"): der = [der] * self.npar
derI = hashD(der)
self.autoSetDS()
if derI <= 0 and self.As[0] is None:
if self.verbosity >= 20:
verbosityDepth("INIT", "Assembling operator term A0.",
timestamp = self.timestamp)
DirichletBC0 = fen.DirichletBC(self.V,
fenZEROS(self.V.mesh().topology().dim()),
self.DirichletBoundary)
lambda_Re, lambda_Im = self.lambda_
mu_Re, mu_Im = self.mu_
hRe, hIm = self.RobinDatumH
termNames = ["lambda_", "mu_", "RobinDatumH"]
parsRe = self.iterReduceQuadratureDegree(zip(
[lambda_Re, mu_Re, hRe],
[x + "Real" for x in termNames]))
parsIm = self.iterReduceQuadratureDegree(zip(
[lambda_Im, mu_Re, hIm],
[x + "Imag" for x in termNames]))
epsilon = lambda u: 0.5 * (fen.grad(u) + fen.nabla_grad(u))
sigma = lambda u, l_, m_: (
l_ * fen.div(u) * fen.Identity(u.geometric_dimension())
+ 2. * m_ * epsilon(u))
a0Re = (fen.inner(sigma(self.u, lambda_Re, mu_Re),
epsilon(self.v)) * fen.dx
+ hRe * fen.inner(self.u, self.v) * self.ds(1))
a0Im = (fen.inner(sigma(self.u, lambda_Im, mu_Im),
epsilon(self.v)) * fen.dx
+ hIm * fen.inner(self.u, self.v) * self.ds(1))
A0Re = fen.assemble(a0Re, form_compiler_parameters = parsRe)
A0Im = fen.assemble(a0Im, form_compiler_parameters = parsIm)
DirichletBC0.apply(A0Re)
DirichletBC0.zero(A0Im)
A0ReMat = fen.as_backend_type(A0Re).mat()
A0ImMat = fen.as_backend_type(A0Im).mat()
A0Rer, A0Rec, A0Rev = A0ReMat.getValuesCSR()
A0Imr, A0Imc, A0Imv = A0ImMat.getValuesCSR()
self.As[0] = (csr_matrix((A0Rev, A0Rec, A0Rer),
shape = A0ReMat.size)
+ 1.j * csr_matrix((A0Imv, A0Imc, A0Imr),
shape = A0ImMat.size))
if self.verbosity >= 20:
verbosityDepth("DEL", "Done assembling operator term.",
timestamp = self.timestamp)
return self._assembleA(mu, der, derI)
def b(self, mu : paramVal = [], der : List[int] = 0,
homogeneized : bool = False) -> Np1D:
"""Assemble (derivative of) RHS of linear system."""
mu = self.checkParameter(mu)
if not hasattr(der, "__len__"): der = [der] * self.npar
derI = hashD(der)
nbsTot = self.nbsH if homogeneized else self.nbs
bs = self.bsH if homogeneized else self.bs
if homogeneized and self.mu != self.mu0BC:
self.liftDirichletData(self.mu)
+ fenZEROSEff = fenZEROS(self.V.mesh().topology().dim())
for j in range(derI, nbsTot):
if bs[j] is None:
self.autoSetDS()
if self.verbosity >= 20:
verbosityDepth("INIT", ("Assembling forcing term "
"b{}.").format(j),
timestamp = self.timestamp)
if j == 0:
+ u0Re, u0Im = self.DirichletDatum
fRe, fIm = self.forcingTerm
g1Re, g1Im = self.NeumannDatum
g2Re, g2Im = self.RobinDatumG
else:
- fRe = fenZEROS(self.V.mesh().topology().dim())
- fIm = fenZEROS(self.V.mesh().topology().dim())
- g1Re = fenZEROS(self.V.mesh().topology().dim())
- g1Im = fenZEROS(self.V.mesh().topology().dim())
- g2Re = fenZEROS(self.V.mesh().topology().dim())
- g2Im = fenZEROS(self.V.mesh().topology().dim())
+ u0Re, u0Im = fenZEROSEff, fenZEROSEff
+ fRe, fIm = fenZEROSEff, fenZEROSEff
+ g1Re, g1Im = fenZEROSEff, fenZEROSEff
+ g2Re, g2Im = fenZEROSEff, fenZEROSEff
termNames = ["forcingTerm", "NeumannDatum", "RobinDatumG"]
parsRe = self.iterReduceQuadratureDegree(zip(
[fRe, g1Re, g2Re],
[x + "Real" for x in termNames]))
parsIm = self.iterReduceQuadratureDegree(zip(
[fIm, g1Im, g2Im],
[x + "Imag" for x in termNames]))
L0Re = (fen.inner(fRe, self.v) * fen.dx
+ fen.inner(g1Re, self.v) * self.ds(0)
+ fen.inner(g2Re, self.v) * self.ds(1))
L0Im = (fen.inner(fIm, self.v) * fen.dx
+ fen.inner(g1Im, self.v) * self.ds(0)
+ fen.inner(g2Im, self.v) * self.ds(1))
b0Re = fen.assemble(L0Re, form_compiler_parameters = parsRe)
b0Im = fen.assemble(L0Im, form_compiler_parameters = parsIm)
- if homogeneized:
- Ader = self.A(self.mu0, hashI(j))
- b0Re[:] -= np.real(Ader.dot(self.liftedDirichletDatum))
- b0Im[:] -= np.imag(Ader.dot(self.liftedDirichletDatum))
- DBCR = fen.DirichletBC(self.V,
- fenZEROS(self.V.mesh().topology().dim()),
- self.DirichletBoundary)
- DBCI = fen.DirichletBC(self.V,
- fenZEROS(self.V.mesh().topology().dim()),
- self.DirichletBoundary)
- else:
- DBCR = fen.DirichletBC(self.V, self.DirichletDatum[0],
- self.DirichletBoundary)
- DBCI = fen.DirichletBC(self.V, self.DirichletDatum[1],
- self.DirichletBoundary)
+ DBCR = fen.DirichletBC(self.V, u0Re, self.DirichletBoundary)
+ DBCI = fen.DirichletBC(self.V, u0Im, self.DirichletBoundary)
DBCR.apply(b0Re)
DBCI.apply(b0Im)
+ b = np.array(b0Re[:] + 1.j * b0Im[:], dtype = np.complex)
+ if homogeneized:
+ Ader = self.A(self.mu0, hashI(j, self.npar))
+ b -= Ader.dot(self.liftedDirichletDatum)
if homogeneized:
- self.bsH[j] = np.array(b0Re[:] + 1.j * b0Im[:],
- dtype = np.complex)
+ self.bsH[j] = b
else:
- self.bs[j] = np.array(b0Re[:] + 1.j * b0Im[:],
- dtype = np.complex)
+ self.bs[j] = b
if self.verbosity >= 20:
verbosityDepth("DEL", "Done assembling forcing term.",
timestamp = self.timestamp)
- return self._assembleb(mu - self.mu0, der, derI, homogeneized)
+ return self._assembleb(mu, der, derI, homogeneized, self.mu0)
diff --git a/rrompy/parameter/parameter_sampling/__init__.py b/rrompy/parameter/parameter_sampling/__init__.py
index 746a0ae..12e89ee 100644
--- a/rrompy/parameter/parameter_sampling/__init__.py
+++ b/rrompy/parameter/parameter_sampling/__init__.py
@@ -1,33 +1,35 @@
# Copyright (C) 2018 by the RROMPy authors
#
# This file is part of RROMPy.
#
# RROMPy is free software: you can redistribute it and/or modify
# it under the terms of the GNU Lesser General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# RROMPy is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU Lesser General Public License for more details.
#
# You should have received a copy of the GNU Lesser General Public License
# along with RROMPy. If not, see .
#
from .generic_sampler import GenericSampler
from .fft_sampler import FFTSampler
from .manual_sampler import ManualSampler
from .quadrature_sampler import QuadratureSampler
+from .quadrature_sampler_total import QuadratureSamplerTotal
from .random_sampler import RandomSampler
__all__ = [
'GenericSampler',
'FFTSampler',
'ManualSampler',
'QuadratureSampler',
+ 'QuadratureSamplerTotal',
'RandomSampler'
]
diff --git a/rrompy/parameter/parameter_sampling/fft_sampler.py b/rrompy/parameter/parameter_sampling/fft_sampler.py
index a41f44b..b59d4e0 100644
--- a/rrompy/parameter/parameter_sampling/fft_sampler.py
+++ b/rrompy/parameter/parameter_sampling/fft_sampler.py
@@ -1,51 +1,50 @@
# Copyright (C) 2018 by the RROMPy authors
#
# This file is part of RROMPy.
#
# RROMPy is free software: you can redistribute it and/or modify
# it under the terms of the GNU Lesser General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# RROMPy is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU Lesser General Public License for more details.
#
# You should have received a copy of the GNU Lesser General Public License
# along with RROMPy. If not, see .
#
import numpy as np
from .generic_sampler import GenericSampler
-from rrompy.utilities.base.types import Np1D, List, paramList
+from rrompy.utilities.base.types import List, paramList
from rrompy.utilities.base import lowDiscrepancy, kroneckerer
from rrompy.parameter import checkParameterList
__all__ = ['FFTSampler']
class FFTSampler(GenericSampler):
"""Generator of FFT-type sample points on scaled roots of unity."""
def generatePoints(self, n:List[int], reorder : bool = True) -> paramList:
"""Array of sample points."""
if not hasattr(n, "__len__"): n = [n]
super().generatePoints(n)
nleft, nright = 1, np.prod(n)
xmat = np.empty((nright, self.npar), dtype = np.complex)
for d in range(self.npar):
nright //= n[d]
a, b = self.lims(0, d), self.lims(1, d)
if self.scaling is not None:
a, b = self.scaling[d](a), self.scaling[d](b)
c, r = (a + b) / 2., np.abs(a - b) / 2.
xd = c + r * np.exp(1.j * np.linspace(0, 2 * np.pi, n[d] + 1)[:-1])
- if reorder:
- fejerOrdering = lowDiscrepancy(n[d])
- xd = xd[fejerOrdering]
if self.scalingInv is not None:
xd = self.scalingInv[d](xd)
xmat[:, d] = kroneckerer(xd, nleft, nright)
nleft *= n[d]
+ if reorder:
+ xmat = xmat[lowDiscrepancy(np.prod(n)), :]
x, _ = checkParameterList(xmat, self.npar)
return x
diff --git a/rrompy/parameter/parameter_sampling/generic_sampler.py b/rrompy/parameter/parameter_sampling/generic_sampler.py
index 8e8a0d7..52510f3 100644
--- a/rrompy/parameter/parameter_sampling/generic_sampler.py
+++ b/rrompy/parameter/parameter_sampling/generic_sampler.py
@@ -1,98 +1,98 @@
# Copyright (C) 2018 by the RROMPy authors
#
# This file is part of RROMPy.
#
# RROMPy is free software: you can redistribute it and/or modify
# it under the terms of the GNU Lesser General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# RROMPy is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU Lesser General Public License for more details.
#
# You should have received a copy of the GNU Lesser General Public License
# along with RROMPy. If not, see .
#
from abc import abstractmethod
-from rrompy.utilities.base.types import Np1D, List, paramList
+from rrompy.utilities.base.types import List, paramList
from rrompy.utilities.exception_manager import RROMPyException, RROMPyAssert
from rrompy.parameter import checkParameterList
__all__ = ['GenericSampler']
class GenericSampler:
"""ABSTRACT. Generic generator of sample points."""
def __init__(self, lims:paramList, scaling : List[callable] = None,
scalingInv : List[callable] = None):
self.lims = lims
self.scaling = scaling
self.scalingInv = scalingInv
def name(self) -> str:
return self.__class__.__name__
def __str__(self) -> str:
return "{}[{}_{}]".format(self.name(), self.lims[0], self.lims[1])
def __repr__(self) -> str:
return self.__str__() + " at " + hex(id(self))
def __eq__(self, other) -> bool:
return self.__dict__ == other.__dict__
@property
def npar(self):
"""Number of parameters."""
return self._lims.shape[1]
@property
def lims(self):
"""Value of lims."""
return self._lims
@lims.setter
def lims(self, lims):
lims, _ = checkParameterList(lims)
if len(lims) != 2:
raise RROMPyException("2 limits must be specified.")
self._lims = lims
@property
def scaling(self):
"""Value of scaling."""
return self._scaling
@scaling.setter
def scaling(self, scaling):
if scaling is not None:
if not hasattr(scaling, "__len__"): scaling = [scaling]
RROMPyAssert(self.npar, len(scaling), "Number of scaling terms")
if not all([callable(s) for s in scaling]):
raise RROMPyException(("Each value of scaling must be a "
"callable."))
self._scaling = scaling
@property
def scalingInv(self):
"""Value of scalingInv."""
return self._scalingInv
@scalingInv.setter
def scalingInv(self, scalingInv):
if scalingInv is not None:
if not hasattr(scalingInv, "__len__"): scalingInv = [scalingInv]
RROMPyAssert(self.npar, len(scalingInv),
"Number of scalingInv terms")
if not all([callable(sInv) for sInv in scalingInv]):
raise RROMPyException(("Each value of scalingInv must be a "
"callable."))
self._scalingInv = scalingInv
@abstractmethod
def generatePoints(self, n:List[int]) -> paramList:
"""Array of points."""
if not hasattr(n, "__len__"): n = [n]
RROMPyAssert(self.npar, len(n), "Point number")
pass
diff --git a/rrompy/parameter/parameter_sampling/manual_sampler.py b/rrompy/parameter/parameter_sampling/manual_sampler.py
index 60474b5..9a2c943 100644
--- a/rrompy/parameter/parameter_sampling/manual_sampler.py
+++ b/rrompy/parameter/parameter_sampling/manual_sampler.py
@@ -1,66 +1,63 @@
# Copyright (C) 2018 by the RROMPy authors
#
# This file is part of RROMPy.
#
# RROMPy is free software: you can redistribute it and/or modify
# it under the terms of the GNU Lesser General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# RROMPy is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU Lesser General Public License for more details.
#
# You should have received a copy of the GNU Lesser General Public License
# along with RROMPy. If not, see .
#
import numpy as np
from copy import deepcopy as copy
from .generic_sampler import GenericSampler
-from rrompy.utilities.base.types import Np1D, List, paramList
-from rrompy.utilities.exception_manager import RROMPyWarning, RROMPyAssert
+from rrompy.utilities.base.types import List, paramList
from rrompy.parameter import checkParameterList
__all__ = ['ManualSampler']
class ManualSampler(GenericSampler):
"""Manual generator of sample points."""
def __init__(self, lims:paramList, points:paramList,
scaling : List[callable] = None,
scalingInv : List[callable] = None):
super().__init__(lims = lims, scaling = scaling,
scalingInv = scalingInv)
self.points = points
@property
def points(self):
"""Value of points."""
return self._points
@points.setter
def points(self, points):
points, _ = checkParameterList(points, self.npar)
self._points = points
def __str__(self) -> str:
return "{}[{}]".format(self.name(), "_".join(map(str, self.points)))
def __repr__(self) -> str:
return self.__str__() + " at " + hex(id(self))
def generatePoints(self, n:int) -> paramList:
"""Array of sample points."""
if hasattr(n, "__len__"): n = n[0]
if n > len(self.points):
- RROMPyWarning(("Requested more points than given. Looping over "
- "first points."))
pts = copy(self.points)
- for j in range(np.int(np.ceil(n / len(self.points)))):
+ for j in range(int(np.ceil(n / len(self.points)))):
pts.append(self.points)
else:
pts = self.points
x, _ = checkParameterList(pts[list(range(n))], self.npar)
return x
diff --git a/rrompy/parameter/parameter_sampling/quadrature_sampler.py b/rrompy/parameter/parameter_sampling/quadrature_sampler.py
index 0900816..4ddfbcf 100644
--- a/rrompy/parameter/parameter_sampling/quadrature_sampler.py
+++ b/rrompy/parameter/parameter_sampling/quadrature_sampler.py
@@ -1,86 +1,87 @@
# Copyright (C) 2018 by the RROMPy authors
#
# This file is part of RROMPy.
#
# RROMPy is free software: you can redistribute it and/or modify
# it under the terms of the GNU Lesser General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# RROMPy is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU Lesser General Public License for more details.
#
# You should have received a copy of the GNU Lesser General Public License
# along with RROMPy. If not, see .
#
import numpy as np
from .generic_sampler import GenericSampler
-from rrompy.utilities.base.types import Np1D, List, paramList
+from rrompy.utilities.base.types import List, paramList
from rrompy.utilities.exception_manager import RROMPyException
from rrompy.utilities.base import lowDiscrepancy, kroneckerer
from rrompy.parameter import checkParameterList
__all__ = ['QuadratureSampler']
class QuadratureSampler(GenericSampler):
"""Generator of quadrature sample points."""
allowedKinds = ["UNIFORM", "CHEBYSHEV", "GAUSSLEGENDRE"]
def __init__(self, lims:paramList, kind : str = "UNIFORM",
scaling : List[callable] = None,
scalingInv : List[callable] = None):
super().__init__(lims = lims, scaling = scaling,
scalingInv = scalingInv)
self.kind = kind
def __str__(self) -> str:
return "{}_{}".format(super().__str__(), self.kind)
def __repr__(self) -> str:
return self.__str__() + " at " + hex(id(self))
@property
def kind(self):
"""Value of kind."""
return self._kind
@kind.setter
def kind(self, kind):
if kind.upper() not in self.allowedKinds:
raise RROMPyException("Generator kind not recognized.")
self._kind = kind.upper()
def generatePoints(self, n:List[int], reorder : bool = True) -> paramList:
"""Array of sample points."""
if not hasattr(n, "__len__"): n = [n]
super().generatePoints(n)
nleft, nright = 1, np.prod(n)
xmat = np.empty((nright, self.npar), dtype = self.lims.dtype)
for d in range(self.npar):
nright //= n[d]
a, b = self.lims(0, d), self.lims(1, d)
if self.scaling is not None:
a, b = self.scaling[d](a), self.scaling[d](b)
c, r = (a + b) / 2., (a - b) / 2.
dAbs = 2. * np.abs(r)
if self.kind == "UNIFORM":
xd = np.linspace(a, b, n[d])
elif self.kind == "CHEBYSHEV":
nodes, _ = np.polynomial.chebyshev.chebgauss(n[d])
xd = c + r * nodes
elif self.kind == "GAUSSLEGENDRE":
nodes, _ = np.polynomial.legendre.leggauss(n[d])
xd = c + r * nodes[::-1]
- if len(xd) > 1 and reorder:
- fejerOrdering = [n[d] - 1] + lowDiscrepancy(n[d] - 1)
- xd = xd[fejerOrdering]
if self.scalingInv is not None:
xd = self.scalingInv[d](xd)
xmat[:, d] = kroneckerer(xd, nleft, nright)
nleft *= n[d]
+ nright = np.prod(n)
+ if nright > 1 and reorder:
+ fejerOrdering = [nright - 1] + lowDiscrepancy(nright - 1)
+ xmat = xmat[fejerOrdering, :]
x, _ = checkParameterList(xmat, self.npar)
return x
diff --git a/rrompy/parameter/parameter_sampling/quadrature_sampler_total.py b/rrompy/parameter/parameter_sampling/quadrature_sampler_total.py
new file mode 100644
index 0000000..c08a94c
--- /dev/null
+++ b/rrompy/parameter/parameter_sampling/quadrature_sampler_total.py
@@ -0,0 +1,79 @@
+# Copyright (C) 2018 by the RROMPy authors
+#
+# This file is part of RROMPy.
+#
+# RROMPy is free software: you can redistribute it and/or modify
+# it under the terms of the GNU Lesser General Public License as published by
+# the Free Software Foundation, either version 3 of the License, or
+# (at your option) any later version.
+#
+# RROMPy is distributed in the hope that it will be useful,
+# but WITHOUT ANY WARRANTY; without even the implied warranty of
+# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+# GNU Lesser General Public License for more details.
+#
+# You should have received a copy of the GNU Lesser General Public License
+# along with RROMPy. If not, see .
+#
+
+import numpy as np
+from scipy.special import binom, factorial as fact
+from .quadrature_sampler import QuadratureSampler
+from rrompy.utilities.base.types import paramList
+from rrompy.utilities.base import lowDiscrepancy
+from rrompy.parameter import checkParameterList
+
+__all__ = ['QuadratureSamplerTotal']
+
+class QuadratureSamplerTotal(QuadratureSampler):
+ """
+ Generator of quadrature sample points for total degree polynomial
+ computations.
+ """
+
+ def generatePoints(self, n:int, reorder : bool = True) -> paramList:
+ """Array of sample points."""
+ if hasattr(n, "__len__"): n = n[0]
+ d = self.npar
+ n1d = int((fact(d) * n) ** (1. / d))
+ while binom(n1d + d - 1, d) > n: n1d -= 1
+
+ x = super().generatePoints([n1d] * d, reorder = False)
+ nTot = n1d ** d
+ indicesBase = np.zeros(nTot, dtype = int)
+ idxBase = [x + 1 for x in lowDiscrepancy(n1d - 1, inverse = True)]
+ linearIdxs = np.array(idxBase + [0])
+ nleft, nright = 1, nTot
+ for j in range(d):
+ nright //= n1d
+ kronIn = np.repeat(linearIdxs, nright)
+ indicesBase += np.tile(kronIn, nleft)
+ nleft *= n1d
+ keepIdxs = np.zeros(nTot, dtype = bool)
+ keepIdxs[indicesBase < n1d] = True
+ xmat = x.data[keepIdxs, :]
+ if reorder:
+ fejerTot = np.array([nTot - 1] + list(lowDiscrepancy(nTot - 1)))
+ xmat = xmat[np.argsort(np.argsort(fejerTot[keepIdxs])), :]
+ x, _ = checkParameterList(xmat, d)
+
+# x = super().generatePoints([n1d] * d, reorder = True)[list(range(n))]
+# if not reorder:
+# fejerOrderingInv = lowDiscrepancy(n, inverse = True)
+# xmat = x.data[fejerOrderingInv, :]
+# x, _ = checkParameterList(xmat, d)
+
+# x = super().generatePoints([n1d] * d, reorder = False)[list(range(n))]
+# nTot = n1d ** d
+# keepIdxs = np.ones(nTot, dtype = bool)
+# eps = nTot * 1e-10
+# gridPts = np.linspace(- eps, nTot - 1 + eps, 2 * (nTot - n) + 1)[1::2]
+# keepIdxs[np.round(gridPts).astype(int)] = False
+# xmat = x.data[keepIdxs, :]
+# if reorder:
+# fejerTot = np.array([nTot - 1] + list(lowDiscrepancy(nTot - 1)))
+# xmat = xmat[np.argsort(np.argsort(fejerTot[keepIdxs])), :]
+# x, _ = checkParameterList(xmat, d)
+
+ return x
+
diff --git a/rrompy/parameter/parameter_sampling/random_sampler.py b/rrompy/parameter/parameter_sampling/random_sampler.py
index cc68c21..4f51013 100644
--- a/rrompy/parameter/parameter_sampling/random_sampler.py
+++ b/rrompy/parameter/parameter_sampling/random_sampler.py
@@ -1,73 +1,77 @@
# Copyright (C) 2018 by the RROMPy authors
#
# This file is part of RROMPy.
#
# RROMPy is free software: you can redistribute it and/or modify
# it under the terms of the GNU Lesser General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# RROMPy is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU Lesser General Public License for more details.
#
# You should have received a copy of the GNU Lesser General Public License
# along with RROMPy. If not, see .
#
import numpy as np
from .generic_sampler import GenericSampler
+from rrompy.utilities.base.halton import haltonGenerate
from rrompy.utilities.base.sobol import sobolGenerate
-from rrompy.utilities.base.types import Np1D, List, paramList
+from rrompy.utilities.base.types import List, paramList
from rrompy.utilities.exception_manager import RROMPyException
from rrompy.parameter import checkParameterList
__all__ = ['RandomSampler']
class RandomSampler(GenericSampler):
"""Generator of quadrature sample points."""
- allowedKinds = ["UNIFORM", "SOBOL"]
+ allowedKinds = ["UNIFORM", "HALTON", "SOBOL"]
def __init__(self, lims:paramList, kind : str = "UNIFORM",
scaling : List[callable] = None,
- scalingInv : List[callable] = None):
+ scalingInv : List[callable] = None, seed : int = 42):
super().__init__(lims = lims, scaling = scaling,
scalingInv = scalingInv)
self.kind = kind
+ self.seed = seed
def __str__(self) -> str:
return "{}_{}".format(super().__str__(), self.kind)
def __repr__(self) -> str:
return self.__str__() + " at " + hex(id(self))
@property
def kind(self):
"""Value of kind."""
return self._kind
@kind.setter
def kind(self, kind):
if kind.upper() not in self.allowedKinds:
raise RROMPyException("Generator kind not recognized.")
self._kind = kind.upper()
- def generatePoints(self, n:int, seed : int = 420) -> paramList:
+ def generatePoints(self, n:int) -> paramList:
"""Array of quadrature points."""
if hasattr(n, "__len__"): n = n[0]
if self.kind == "UNIFORM":
- np.random.seed(seed)
+ np.random.seed(self.seed)
xmat = np.random.uniform(size = (n, self.npar))
+ elif self.kind == "HALTON":
+ xmat = haltonGenerate(self.npar, n, self.seed)
else:
- xmat = sobolGenerate(self.npar, n, seed)
+ xmat = sobolGenerate(self.npar, n, self.seed)
for d in range(self.npar):
a, b = self.lims(0, d), self.lims(1, d)
if self.scaling is not None:
a, b = self.scaling[d](a), self.scaling[d](b)
xmat[:, d] = a + (b - a) * xmat[:, d]
if self.scalingInv is not None:
xmat[:, d] = self.scalingInv[d](xmat[:, d])
x, _ = checkParameterList(xmat, self.npar)
return x
-
+
diff --git a/rrompy/reduction_methods/base/generic_approximant.py b/rrompy/reduction_methods/base/generic_approximant.py
index b6bbf9b..0a604b8 100644
--- a/rrompy/reduction_methods/base/generic_approximant.py
+++ b/rrompy/reduction_methods/base/generic_approximant.py
@@ -1,854 +1,909 @@
# Copyright (C) 2018 by the RROMPy authors
#
# This file is part of RROMPy.
#
# RROMPy is free software: you can redistribute it and/or modify
# it under the terms of the GNU Lesser General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# RROMPy is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU Lesser General Public License for more details.
#
# You should have received a copy of the GNU Lesser General Public License
# along with RROMPy. If not, see .
#
from abc import abstractmethod
import numpy as np
from itertools import product as iterprod
from copy import deepcopy as copy
from os import remove as osrm
from rrompy.sampling.linear_problem import (SamplingEngineLinear,
SamplingEngineLinearPOD)
-from rrompy.utilities.base.types import (Np1D, DictAny, HFEng, List, strLst,
- paramVal, paramList, sampList)
+from rrompy.utilities.base.types import (Np1D, DictAny, HFEng, List, ListAny,
+ strLst, paramVal, paramList, sampList)
from rrompy.utilities.base import purgeDict, verbosityDepth, getNewFilename
from rrompy.utilities.exception_manager import (RROMPyException, RROMPyAssert,
RROMPy_READY, RROMPy_FRAGILE)
from rrompy.utilities.base import pickleDump, pickleLoad
from rrompy.parameter import (emptyParameterList, checkParameter,
checkParameterList)
from rrompy.sampling import sampleList, emptySampleList
__all__ = ['GenericApproximant']
def addNormFieldToClass(self, fieldName):
def objFunc(self, mu:paramList, homogeneized : bool = False) -> float:
uV = getattr(self.__class__, "get" + fieldName)(self, mu, homogeneized)
val = self.HFEngine.norm(uV)
return val
setattr(self.__class__, "norm" + fieldName, objFunc)
def addPlotFieldToClass(self, fieldName):
def objFunc(self, mu:paramList, name : str = fieldName, save : str = None,
what : strLst = 'all', saveFormat : str = "eps",
saveDPI : int = 100, show : bool = True,
homogeneized : bool = False, **figspecs):
uV = getattr(self.__class__, "get" + fieldName)(self, mu, homogeneized)
for j, u in enumerate(uV):
self.HFEngine.plot(u, name = name + str(j), save = save,
what = what, saveFormat = saveFormat,
saveDPI = saveDPI, show = show, **figspecs)
setattr(self.__class__, "plot" + fieldName, objFunc)
def addOutParaviewFieldToClass(self, fieldName):
def objFunc(self, mu:paramVal, name : str = fieldName,
filename : str = "out", time : float = 0.,
what : strLst = 'all', forceNewFile : bool = True,
folder : bool = False, filePW = None,
homogeneized : bool = False):
if not hasattr(self.HFEngine, "outParaview"):
raise RROMPyException(("High fidelity engine cannot output to "
"Paraview."))
uV = getattr(self.__class__, "get" + fieldName)(self, mu, homogeneized)
for j, u in enumerate(uV):
self.HFEngine.outParaview(u, name = name + str(j),
filename = filename, time = time,
what = what, forceNewFile = forceNewFile,
folder = folder, filePW = filePW)
setattr(self.__class__, "outParaview" + fieldName, objFunc)
def addOutParaviewTimeDomainFieldToClass(self, fieldName):
def objFunc(self, mu:paramVal, omega : float = None,
timeFinal : float = None, periodResolution : int = 20,
name : str = fieldName, filename : str = "out",
forceNewFile : bool = True, folder : bool = False,
homogeneized : bool = False):
if not hasattr(self.HFEngine, "outParaviewTimeDomain"):
raise RROMPyException(("High fidelity engine cannot output to "
"Paraview."))
uV = getattr(self.__class__, "get" + fieldName)(self, mu, homogeneized)
if omega is None: omega = np.real(mu)
for j, u in enumerate(uV):
self.HFEngine.outParaviewTimeDomain(u, omega = omega,
timeFinal = timeFinal,
periodResolution = periodResolution,
name = name + str(j),
filename = filename,
forceNewFile = forceNewFile,
folder = folder)
setattr(self.__class__, "outParaviewTimeDomain" + fieldName, objFunc)
class GenericApproximant:
"""
ABSTRACT
ROM approximant computation for parametric problems.
Args:
HFEngine: HF problem solver.
mu0(optional): Default parameter. Defaults to 0.
approxParameters(optional): Dictionary containing values for main
parameters of approximant. Recognized keys are:
- 'POD': whether to compute POD of snapshots; defaults to True;
- 'S': total number of samples current approximant relies upon.
Defaults to empty dict.
homogeneized(optional): Whether to homogeneize Dirichlet BCs. Defaults
to False.
verbosity(optional): Verbosity level. Defaults to 10.
Attributes:
HFEngine: HF problem solver.
trainedModel: Trained model evaluator.
mu0: Default parameter.
homogeneized: Whether to homogeneize Dirichlet BCs.
approxParameters: Dictionary containing values for main parameters of
- approximant. Recognized keys are in parameterList.
- parameterList: Recognized keys of approximant parameters:
- - 'POD': whether to compute POD of snapshots;
+ approximant. Recognized keys are in parameterList{Soft,Critical}.
+ parameterListSoft: Recognized keys of soft approximant parameters:
+ - 'POD': whether to compute POD of snapshots.
+ parameterListCritical: Recognized keys of critical approximant
+ parameters:
- 'S': total number of samples current approximant relies upon.
verbosity: Verbosity level.
POD: Whether to compute POD of snapshots.
S: Number of solution snapshots over which current approximant is
based upon.
samplingEngine: Sampling engine.
uHF: High fidelity solution(s) with parameter(s) lastSolvedHF as
sampleList.
lastSolvedHF: Parameter(s) corresponding to last computed high fidelity
solution(s) as parameterList.
uAppReduced: Reduced approximate solution(s) with parameter(s)
lastSolvedApp as sampleList.
lastSolvedAppReduced: Parameter(s) corresponding to last computed
reduced approximate solution(s) as parameterList.
uApp: Approximate solution(s) with parameter(s) lastSolvedApp as
sampleList.
lastSolvedApp: Parameter(s) corresponding to last computed approximate
solution(s) as parameterList.
"""
__all__ += [ftype + dtype for ftype, dtype in iterprod(
["norm", "plot", "outParaview", "outParaviewTimeDomain"],
["HF", "RHS", "Approx", "Res", "Err"])]
def __init__(self, HFEngine:HFEng, mu0 : paramVal = None,
approxParameters : DictAny = {}, homogeneized : bool = False,
verbosity : int = 10, timestamp : bool = True):
self._preInit()
self._mode = RROMPy_READY
self.verbosity = verbosity
self.timestamp = timestamp
if self.verbosity >= 10:
verbosityDepth("INIT", ("Initializing approximant engine of "
"type {}.").format(self.name()),
timestamp = self.timestamp)
self._HFEngine = HFEngine
self.trainedModel = None
self.lastSolvedHF = emptyParameterList()
self.uHF = emptySampleList()
- self._addParametersToList(["POD", "S"])
+ self._addParametersToList(["POD"], [True], ["S"], [[1]])
if mu0 is None:
if hasattr(self.HFEngine, "mu0"):
self.mu0 = checkParameter(self.HFEngine.mu0)
else:
raise RROMPyException(("Center of approximation cannot be "
"inferred from HF engine. Parameter "
"required"))
else:
self.mu0 = checkParameter(mu0, self.HFEngine.npar)
+ self.resetSamples()
self.homogeneized = homogeneized
self.approxParameters = approxParameters
- self.resetSamples()
self._postInit()
### add norm{HF,RHS,Approx,Res,Err} methods
"""
Compute norm of * at arbitrary parameter.
Args:
mu: Target parameter.
homogeneized(optional): Whether to remove Dirichlet BC. Defaults to
False.
Returns:
Target norm of *.
"""
for objName in ["HF", "RHS", "Approx", "Res", "Err"]:
addNormFieldToClass(self, objName)
### add plot{HF,RHS,Approx,Res,Err} methods
"""
Do some nice plots of * at arbitrary parameter.
Args:
mu: Target parameter.
name(optional): Name to be shown as title of the plots. Defaults to
'u'.
what(optional): Which plots to do. If list, can contain 'ABS',
'PHASE', 'REAL', 'IMAG'. If str, same plus wildcard 'ALL'.
Defaults to 'ALL'.
save(optional): Where to save plot(s). Defaults to None, i.e. no
saving.
saveFormat(optional): Format for saved plot(s). Defaults to "eps".
saveDPI(optional): DPI for saved plot(s). Defaults to 100.
show(optional): Whether to show figure. Defaults to True.
homogeneized(optional): Whether to remove Dirichlet BC. Defaults to
False.
figspecs(optional key args): Optional arguments for matplotlib
figure creation.
"""
for objName in ["HF", "RHS", "Approx", "Res", "Err"]:
addPlotFieldToClass(self, objName)
### add outParaview{HF,RHS,Approx,Res,Err} methods
"""
Output * to ParaView file.
Args:
mu: Target parameter.
name(optional): Base name to be used for data output.
filename(optional): Name of output file.
time(optional): Timestamp.
what(optional): Which plots to do. If list, can contain 'MESH',
'ABS', 'PHASE', 'REAL', 'IMAG'. If str, same plus wildcard
'ALL'. Defaults to 'ALL'.
forceNewFile(optional): Whether to create new output file.
filePW(optional): Fenics File entity (for time series).
homogeneized(optional): Whether to remove Dirichlet BC. Defaults to
False.
"""
for objName in ["HF", "RHS", "Approx", "Res", "Err"]:
addOutParaviewFieldToClass(self, objName)
### add outParaviewTimeDomain{HF,RHS,Approx,Res,Err} methods
"""
Output * to ParaView file, converted to time domain.
Args:
mu: Target parameter.
omega(optional): frequency.
timeFinal(optional): final time of simulation.
periodResolution(optional): number of time steps per period.
name(optional): Base name to be used for data output.
filename(optional): Name of output file.
forceNewFile(optional): Whether to create new output file.
homogeneized(optional): Whether to remove Dirichlet BC. Defaults to
False.
"""
for objName in ["HF", "RHS", "Approx", "Res", "Err"]:
addOutParaviewTimeDomainFieldToClass(self, objName)
def _preInit(self):
if not hasattr(self, "depth"): self.depth = 0
else: self.depth += 1
- def _addParametersToList(self, what:strLst):
- if not hasattr(self, "parameterList"):
- self.parameterList = []
- self.parameterList += what
+ @property
+ def parameterList(self):
+ """Value of parameterListSoft + parameterListCritical."""
+ return self.parameterListSoft + self.parameterListCritical
+
+ def _addParametersToList(self, whatSoft:strLst, defaultSoft:ListAny,
+ whatCritical : strLst = [],
+ defaultCritical : ListAny = [],
+ toBeExcluded : strLst = []):
+ if not hasattr(self, "parameterToBeExcluded"):
+ self.parameterToBeExcluded = []
+ self.parameterToBeExcluded += toBeExcluded
+ if not hasattr(self, "parameterListSoft"):
+ self.parameterListSoft = []
+ if not hasattr(self, "parameterDefaultSoft"):
+ self.parameterDefaultSoft = {}
+ if not hasattr(self, "parameterListCritical"):
+ self.parameterListCritical = []
+ if not hasattr(self, "parameterDefaultCritical"):
+ self.parameterDefaultCritical = {}
+ for j, what in enumerate(whatSoft):
+ if what not in self.parameterToBeExcluded:
+ self.parameterListSoft += [what]
+ self.parameterDefaultSoft[what] = defaultSoft[j]
+ for j, what in enumerate(whatCritical):
+ if what not in self.parameterToBeExcluded:
+ self.parameterListCritical += [what]
+ self.parameterDefaultCritical[what] = defaultCritical[j]
def _postInit(self):
if self.depth == 0:
if self.verbosity >= 10:
verbosityDepth("DEL", "Done initializing.",
timestamp = self.timestamp)
del self.depth
else: self.depth -= 1
def name(self) -> str:
return self.__class__.__name__
def __str__(self) -> str:
return self.name()
def __repr__(self) -> str:
return self.__str__() + " at " + hex(id(self))
def setupSampling(self):
"""Setup sampling engine."""
RROMPyAssert(self._mode, message = "Cannot setup sampling engine.")
if not hasattr(self, "_POD") or self._POD is None: return
if self.POD:
SamplingEngine = SamplingEngineLinearPOD
else:
SamplingEngine = SamplingEngineLinear
self.samplingEngine = SamplingEngine(self.HFEngine,
verbosity = self.verbosity)
@property
def HFEngine(self):
"""Value of HFEngine."""
return self._HFEngine
@HFEngine.setter
def HFEngine(self, HFEngine):
raise RROMPyException("Cannot change HFEngine.")
@property
def mu0(self):
"""Value of mu0."""
return self._mu0
@mu0.setter
def mu0(self, mu0):
mu0 = checkParameter(mu0)
if not hasattr(self, "_mu0") or mu0 != self.mu0:
self.resetSamples()
self._mu0 = mu0
@property
def npar(self):
"""Number of parameters."""
return self.mu0.shape[1]
@property
def approxParameters(self):
"""Value of approximant parameters."""
return self._approxParameters
@approxParameters.setter
def approxParameters(self, approxParams):
if not hasattr(self, "approxParameters"):
self._approxParameters = {}
approxParameters = purgeDict(approxParams, self.parameterList,
dictname = self.name() + ".approxParameters",
baselevel = 1)
keyList = list(approxParameters.keys())
- if "POD" in keyList:
- self.POD = approxParameters["POD"]
- elif not hasattr(self, "_POD") or self._POD is None:
- self.POD = True
- if "S" in keyList:
- self.S = approxParameters["S"]
- elif hasattr(self, "_S") and self._S is not None:
- self.S = self.S
- else:
- raise RROMPyException("Must specify S.")
+ for key in self.parameterListCritical:
+ if key in keyList:
+ setattr(self, "_" + key, self.parameterDefaultCritical[key])
+ for key in self.parameterListSoft:
+ if key in keyList:
+ setattr(self, "_" + key, self.parameterDefaultSoft[key])
+ fragile = False
+ for key in self.parameterListCritical:
+ if key in keyList:
+ val = approxParameters[key]
+ else:
+ val = getattr(self, "_" + key, None)
+ if val is None:
+ val = self.parameterDefaultCritical[key]
+ getattr(self.__class__, key, None).fset(self, val)
+ fragile = fragile or val is None
+ for key in self.parameterListSoft:
+ if key in keyList:
+ val = approxParameters[key]
+ else:
+ val = getattr(self, "_" + key, None)
+ if val is None:
+ val = self.parameterDefaultSoft[key]
+ getattr(self.__class__, key, None).fset(self, val)
+ if fragile:
+ self._mode = RROMPy_FRAGILE
@property
def POD(self):
"""Value of POD."""
return self._POD
@POD.setter
def POD(self, POD):
if hasattr(self, "_POD"): PODold = self.POD
else: PODold = -1
self._POD = POD
self._approxParameters["POD"] = self.POD
if PODold != self.POD:
self.samplingEngine = None
self.resetSamples()
@property
def S(self):
"""Value of S."""
return self._S
@S.setter
def S(self, S):
if not hasattr(S, "__len__"): S = [S]
if any([s <= 0 for s in S]):
raise RROMPyException("S must be positive.")
if hasattr(self, "_S") and self._S is not None: Sold = tuple(self.S)
else: Sold = -1
self._S = S
self._approxParameters["S"] = self.S
if Sold != tuple(self.S):
self.resetSamples()
@property
def homogeneized(self):
"""Value of homogeneized."""
return self._homogeneized
@homogeneized.setter
def homogeneized(self, homogeneized):
if not hasattr(self, "_homogeneized"):
self._homogeneized = None
if homogeneized != self.homogeneized:
self._homogeneized = homogeneized
self.resetSamples()
@property
def trainedModel(self):
"""Value of trainedModel."""
return self._trainedModel
@trainedModel.setter
def trainedModel(self, trainedModel):
self._trainedModel = trainedModel
+ if self._trainedModel is not None:
+ self._trainedModel.lastSolvedAppReduced = emptyParameterList()
+ self._trainedModel.lastSolvedApp = emptyParameterList()
self.lastSolvedAppReduced = emptyParameterList()
self.lastSolvedApp = emptyParameterList()
self.uAppReduced = emptySampleList()
self.uApp = emptySampleList()
def resetSamples(self):
if hasattr(self, "samplingEngine") and self.samplingEngine is not None:
self.samplingEngine.resetHistory()
else:
self.setupSampling()
self._mode = RROMPy_READY
def plotSamples(self, name : str = "u", save : str = None,
what : strLst = 'all', saveFormat : str = "eps",
saveDPI : int = 100, **figspecs):
"""
Do some nice plots of the samples.
Args:
name(optional): Name to be shown as title of the plots. Defaults to
'u'.
what(optional): Which plots to do. If list, can contain 'ABS',
'PHASE', 'REAL', 'IMAG'. If str, same plus wildcard 'ALL'.
Defaults to 'ALL'.
save(optional): Where to save plot(s). Defaults to None, i.e. no
saving.
saveFormat(optional): Format for saved plot(s). Defaults to "eps".
saveDPI(optional): DPI for saved plot(s). Defaults to 100.
figspecs(optional key args): Optional arguments for matplotlib
figure creation.
"""
RROMPyAssert(self._mode, message = "Cannot plot samples.")
self.samplingEngine.plotSamples(name = name, save = save, what = what,
saveFormat = saveFormat,
saveDPI = saveDPI,
**figspecs)
def outParaviewSamples(self, name : str = "u", filename : str = "out",
times : Np1D = None, what : strLst = 'all',
forceNewFile : bool = True, folders : bool = False,
filePW = None):
"""
Output samples to ParaView file.
Args:
name(optional): Base name to be used for data output.
filename(optional): Name of output file.
times(optional): Timestamps.
what(optional): Which plots to do. If list, can contain 'MESH',
'ABS', 'PHASE', 'REAL', 'IMAG'. If str, same plus wildcard
'ALL'. Defaults to 'ALL'.
forceNewFile(optional): Whether to create new output file.
folders(optional): Whether to split output in folders.
filePW(optional): Fenics File entity (for time series).
"""
RROMPyAssert(self._mode, message = "Cannot output samples.")
self.samplingEngine.outParaviewSamples(name = name,
filename = filename,
times = times, what = what,
forceNewFile = forceNewFile,
folders = folders,
filePW = filePW)
def outParaviewTimeDomainSamples(self, omegas : Np1D = None,
timeFinal : Np1D = None,
periodResolution : int = 20,
name : str = "u",
filename : str = "out",
forceNewFile : bool = True,
folders : bool = False):
"""
Output samples to ParaView file, converted to time domain.
Args:
omegas(optional): frequencies.
timeFinal(optional): final time of simulation.
periodResolution(optional): number of time steps per period.
name(optional): Base name to be used for data output.
filename(optional): Name of output file.
forceNewFile(optional): Whether to create new output file.
folders(optional): Whether to split output in folders.
"""
RROMPyAssert(self._mode, message = "Cannot output samples.")
self.samplingEngine.outParaviewTimeDomainSamples(omegas = omegas,
timeFinal = timeFinal,
periodResolution = periodResolution,
name = name, filename = filename,
forceNewFile = forceNewFile,
folders = folders)
+ def setSamples(self, samplingEngine):
+ """Copy samplingEngine and samples."""
+ if self.verbosity >= 10:
+ verbosityDepth("INIT", "Transfering samples.",
+ timestamp = self.timestamp)
+ self.samplingEngine = samplingEngine
+ if self.verbosity >= 10:
+ verbosityDepth("DEL", "Done transfering samples.",
+ timestamp = self.timestamp)
+
def setTrainedModel(self, model):
"""Deepcopy approximation from trained model."""
if hasattr(model, "storeTrainedModel"):
verb = model.verbosity
model.verbosity = 0
fileOut = model.storeTrainedModel()
model.verbosity = verb
else:
try:
fileOut = getNewFilename("trained_model", "pkl")
pickleDump(model.data.__dict__, fileOut)
except:
raise RROMPyException(("Failed to store model data. Parameter "
"model must have either "
"storeTrainedModel or "
"data.__dict__ properties."))
self.loadTrainedModel(fileOut)
osrm(fileOut)
@abstractmethod
def setupApprox(self):
"""
Setup approximant. (ABSTRACT)
Any specialization should include something like
if self.checkComputedApprox():
return
RROMPyAssert(self._mode, message = "Cannot setup approximant.")
...
self.trainedModel = ...
self.trainedModel.data = ...
self.trainedModel.data.approxParameters = copy(
self.approxParameters)
"""
pass
def checkComputedApprox(self) -> bool:
"""
Check if setup of new approximant is not needed.
Returns:
True if new setup is not needed. False otherwise.
"""
return self._mode == RROMPy_FRAGILE or (self.trainedModel is not None
and self.trainedModel.data.approxParameters == self.approxParameters)
def setHF(self, muHF:paramList, uHF:sampleList,
append : bool = False) -> List[int]:
"""Assign high fidelity solution."""
newSolvedHF, _ = checkParameterList(muHF, self.npar)
newuHF = sampleList(uHF)
if append:
self.lastSolvedHF.append(newSolvedHF)
self.uHF.append(newuHF)
return list(range(len(self.uHF) - len(newuHF), len(self.uHF)))
self.lastSolvedHF, _ = checkParameterList(newSolvedHF, self.npar)
self.uHF = sampleList(newuHF)
return list(range(len(self.uHF)))
def evalHF(self, mu:paramList, append : bool = False,
prune : bool = True) -> List[int]:
"""
Find high fidelity solution with original parameters and arbitrary
parameter.
Args:
mu: Target parameter.
append(optional): Whether to append new HF solutions to old ones.
prune(optional): Whether to remove duplicates of already appearing
HF solutions.
"""
mu, _ = checkParameterList(mu, self.npar)
idx = np.empty(len(mu), dtype = np.int)
if prune:
jExtra = np.zeros(len(mu), dtype = bool)
muKeep = emptyParameterList()
muExtra = copy(muKeep)
for j in range(len(mu)):
jPos = self.lastSolvedHF.find(mu[j])
if jPos is not None:
idx[j] = jPos
muKeep.append(mu[j])
else:
jExtra[j] = True
muExtra.append(mu[j])
if len(muKeep) > 0 and not append:
idx[~jExtra] = self.setHF(muKeep, self.uHF[idx[~jExtra]],
append)
append = True
else:
jExtra = np.ones(len(mu), dtype = bool)
muExtra = mu
if len(muExtra) > 0:
newuHFs = self.samplingEngine.solveLS(muExtra,
homogeneized = self.homogeneized)
idx[jExtra] = self.setHF(muExtra, newuHFs, append)
return list(idx)
def setApproxReduced(self, muApp:paramList, uApp:sampleList,
append : bool = False) -> List[int]:
"""Assign high fidelity solution."""
newSolvedApp, _ = checkParameterList(muApp, self.npar)
newuApp = sampleList(uApp)
if append:
self.lastSolvedAppReduced.append(newSolvedApp)
self.uAppReduced.append(newuApp)
return list(range(len(self.uAppReduced) - len(newuApp),
len(self.uAppReduced)))
self.lastSolvedAppReduced, _ = checkParameterList(newSolvedApp,
self.npar)
self.uAppReduced = sampleList(newuApp)
return list(range(len(self.uAppReduced)))
def evalApproxReduced(self, mu:paramList, append : bool = False,
prune : bool = True) -> List[int]:
"""
Evaluate reduced representation of approximant at arbitrary parameter.
Args:
mu: Target parameter.
"""
self.setupApprox()
mu, _ = checkParameterList(mu, self.npar)
idx = np.empty(len(mu), dtype = np.int)
if prune:
jExtra = np.zeros(len(mu), dtype = bool)
muKeep = emptyParameterList()
muExtra = copy(muKeep)
for j in range(len(mu)):
jPos = self.lastSolvedAppReduced.find(mu[j])
if jPos is not None:
idx[j] = jPos
muKeep.append(mu[j])
else:
jExtra[j] = True
muExtra.append(mu[j])
if len(muKeep) > 0 and not append:
idx[~jExtra] = self.setApproxReduced(muKeep,
self.uAppReduced[idx[~jExtra]],
append)
append = True
else:
jExtra = np.ones(len(mu), dtype = bool)
muExtra = mu
if len(muExtra) > 0:
newuApps = self.trainedModel.getApproxReduced(muExtra)
idx[jExtra] = self.setApproxReduced(muExtra, newuApps, append)
return list(idx)
def setApprox(self, muApp:paramList, uApp:sampleList,
append : bool = False) -> List[int]:
"""Assign high fidelity solution."""
newSolvedApp, _ = checkParameterList(muApp, self.npar)
newuApp = sampleList(uApp)
if append:
self.lastSolvedApp.append(newSolvedApp)
self.uApp.append(newuApp)
return list(range(len(self.uApp) - len(newuApp), len(self.uApp)))
self.lastSolvedApp, _ = checkParameterList(newSolvedApp, self.npar)
self.uApp = sampleList(newuApp)
return list(range(len(self.uApp)))
def evalApprox(self, mu:paramList, append : bool = False,
prune : bool = True) -> List[int]:
"""
Evaluate approximant at arbitrary parameter.
Args:
mu: Target parameter.
"""
self.setupApprox()
mu, _ = checkParameterList(mu, self.npar)
idx = np.empty(len(mu), dtype = np.int)
if prune:
jExtra = np.zeros(len(mu), dtype = bool)
muKeep = emptyParameterList()
muExtra = copy(muKeep)
for j in range(len(mu)):
jPos = self.lastSolvedApp.find(mu[j])
if jPos is not None:
idx[j] = jPos
muKeep.append(mu[j])
else:
jExtra[j] = True
muExtra.append(mu[j])
if len(muKeep) > 0 and not append:
idx[~jExtra] = self.setApprox(muKeep, self.uApp[idx[~jExtra]],
append)
append = True
else:
jExtra = np.ones(len(mu), dtype = bool)
muExtra = mu
if len(muExtra) > 0:
newuApps = self.trainedModel.getApprox(muExtra)
idx[jExtra] = self.setApprox(muExtra, newuApps, append)
return list(idx)
def getHF(self, mu:paramList, homogeneized : bool = False,
append : bool = False, prune : bool = True) -> sampList:
"""
Get HF solution at arbitrary parameter.
Args:
mu: Target parameter.
homogeneized(optional): Whether to remove Dirichlet BC. Defaults to
False.
Returns:
HFsolution.
"""
mu, _ = checkParameterList(mu, self.npar)
idx = self.evalHF(mu, append = append, prune = prune)
uHFs = self.uHF(idx)
if self.homogeneized and not homogeneized:
for j, m in enumerate(mu):
uHFs[j] += self.HFEngine.liftDirichletData(m)
if not self.homogeneized and homogeneized:
for j, m in enumerate(mu):
uHFs[j] -= self.HFEngine.liftDirichletData(m)
return uHFs
def getRHS(self, mu:paramList, homogeneized : bool = False) -> sampList:
"""
Get linear system RHS at arbitrary parameter.
Args:
mu: Target parameter.
homogeneized(optional): Whether to remove Dirichlet BC. Defaults to
False.
Returns:
Linear system RHS.
"""
return self.HFEngine.residual(None, mu, homogeneized = homogeneized)
def getApproxReduced(self, mu:paramList, append : bool = False,
prune : bool = True) -> sampList:
"""
Get approximant at arbitrary parameter.
Args:
mu: Target parameter.
Returns:
Reduced approximant.
"""
mu, _ = checkParameterList(mu, self.npar)
idx = self.evalApproxReduced(mu, append = append, prune = prune)
uAppRs = self.uAppReduced(idx)
return uAppRs
def getApprox(self, mu:paramList, homogeneized : bool = False,
append : bool = False, prune : bool = True) -> sampList:
"""
Get approximant at arbitrary parameter.
Args:
mu: Target parameter.
homogeneized(optional): Whether to remove Dirichlet BC. Defaults to
False.
Returns:
Approximant.
"""
mu, _ = checkParameterList(mu, self.npar)
idx = self.evalApprox(mu, append = append, prune = prune)
uApps = self.uApp(idx)
if self.homogeneized and not homogeneized:
for j, m in enumerate(mu):
uApps[j] += self.HFEngine.liftDirichletData(m)
if not self.homogeneized and homogeneized:
for j, m in enumerate(mu):
uApps[j] -= self.HFEngine.liftDirichletData(m)
return uApps
def getRes(self, mu:paramList, homogeneized : bool = False) -> sampList:
"""
Get residual at arbitrary parameter.
Args:
mu: Target parameter.
homogeneized(optional): Whether to remove Dirichlet BC. Defaults to
False.
Returns:
Approximant residual.
"""
return self.HFEngine.residual(self.getApprox(mu, homogeneized), mu,
homogeneized = homogeneized)
def getErr(self, mu:paramList, homogeneized : bool = False) -> sampList:
"""
Get error at arbitrary parameter.
Args:
mu: Target parameter.
homogeneized(optional): Whether to remove Dirichlet BC. Defaults to
False.
Returns:
Approximant error.
"""
return self.getApprox(mu, homogeneized) - self.getHF(mu, homogeneized)
def getPoles(self) -> Np1D:
"""
Obtain approximant poles.
Returns:
Numpy complex vector of poles.
"""
self.setupApprox()
if self.verbosity >= 20:
verbosityDepth("INIT", "Computing poles of model.",
timestamp = self.timestamp)
poles = self.trainedModel.getPoles()
if self.verbosity >= 20:
verbosityDepth("DEL", "Done computing poles.",
timestamp = self.timestamp)
return poles
def storeTrainedModel(self, filenameBase : str = "trained_model",
forceNewFile : bool = True) -> str:
"""Store trained reduced model to file."""
self.setupApprox()
if self.verbosity >= 20:
verbosityDepth("INIT", "Storing trained model to file.",
timestamp = self.timestamp)
if forceNewFile:
filename = getNewFilename(filenameBase, "pkl")
else:
filename = "{}.pkl".format(filenameBase)
pickleDump(self.trainedModel.data.__dict__, filename)
if self.verbosity >= 20:
verbosityDepth("DEL", "Done storing trained model.",
timestamp = self.timestamp)
return filename
def loadTrainedModel(self, filename:str):
"""Load trained reduced model from file."""
if self.verbosity >= 20:
verbosityDepth("INIT", "Loading pre-trained model from file.",
timestamp = self.timestamp)
datadict = pickleLoad(filename)
name = datadict.pop("name")
if name == "TrainedModelPade":
from rrompy.reduction_methods.trained_model import \
TrainedModelPade as tModel
elif name == "TrainedModelRB":
from rrompy.reduction_methods.trained_model import \
TrainedModelRB as tModel
else:
raise RROMPyException(("Trained model name not recognized. "
"Loading failed."))
self.mu0 = datadict.pop("mu0")
from rrompy.reduction_methods.trained_model import TrainedModelData
trainedModel = tModel()
trainedModel.verbosity = self.verbosity
trainedModel.timestamp = self.timestamp
data = TrainedModelData(name, self.mu0, datadict.pop("projMat"),
datadict.pop("rescalingExp"))
if "mus" in datadict:
data.mus = datadict.pop("mus")
approxParameters = datadict.pop("approxParameters")
data.approxParameters = copy(approxParameters)
if "sampler" in approxParameters:
self._approxParameters["sampler"] = approxParameters.pop("sampler")
self.approxParameters = copy(approxParameters)
if "mus" in data.__dict__:
self.mus = copy(data.mus)
if name == "TrainedModelPade":
self.scaleFactor = datadict.pop("scaleFactor")
data.scaleFactor = self.scaleFactor
for key in datadict:
setattr(data, key, datadict[key])
trainedModel.data = data
self.trainedModel = trainedModel
self._mode = RROMPy_FRAGILE
if self.verbosity >= 20:
verbosityDepth("DEL", "Done loading pre-trained model.",
timestamp = self.timestamp)
diff --git a/rrompy/reduction_methods/base/rb_utils.py b/rrompy/reduction_methods/base/rb_utils.py
index 5286ac1..78b37cc 100644
--- a/rrompy/reduction_methods/base/rb_utils.py
+++ b/rrompy/reduction_methods/base/rb_utils.py
@@ -1,64 +1,62 @@
# Copyright (C) 2018 by the RROMPy authors
#
# This file is part of RROMPy.
#
# RROMPy is free software: you can redistribute it and/or modify
# it under the terms of the GNU Lesser General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# RROMPy is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU Lesser General Public License for more details.
#
# You should have received a copy of the GNU Lesser General Public License
# along with RROMPy. If not, see .
#
import numpy as np
-#from copy import deepcopy as copy
from rrompy.utilities.base.types import Np1D, Np2D, Tuple, List, sampList
from rrompy.utilities.exception_manager import RROMPyAssert
from rrompy.sampling import sampleList
__all__ = ['projectAffineDecomposition']
def projectAffineDecomposition(As:List[Np2D], bs:List[Np1D], pMat:sampList,
ARBsOld : List[Np2D] = None,
bRBsOld : List[Np1D] = None,
pMatOld : sampList = None)\
-> Tuple[List[Np2D], List[Np1D]]:
"""Project affine decomposition of linear system onto basis."""
RROMPyAssert((ARBsOld is None, bRBsOld is None),
(pMatOld is None, pMatOld is None),
"Old affine projected terms")
if isinstance(pMat, (sampleList,)): pMat = pMat.data
pMatH = pMat.T.conj()
ARBs = [None] * len(As)
bRBs = [None] * len(bs)
if pMatOld is None:
for j in range(len(As)):
ARBs[j] = pMatH.dot(As[j].dot(pMat))
for j in range(len(bs)):
bRBs[j] = pMatH.dot(bs[j])
else:
RROMPyAssert((len(ARBsOld), len(bRBsOld)), (len(As), len(bs)),
"Old affine projected terms")
if isinstance(pMatOld, (sampleList,)): pMatOld = pMatOld.data
pMatOldH = pMatOld.T.conj()
Sold = pMatOld.shape[1]
Snew = pMat.shape[1]
for j in range(len(As)):
ARBs[j] = np.empty((Sold + Snew, Sold + Snew), dtype = np.complex)
ARBs[j][: Sold, : Sold] = ARBsOld[j]
ARBs[j][: Sold, Sold :] = pMatOldH.dot(As[j].dot(pMat))
ARBs[j][Sold :, : Sold] = pMatH.dot(As[j].dot(pMatOld))
ARBs[j][Sold :, Sold :] = pMatH.dot(As[j].dot(pMat))
for j in range(len(bs)):
bRBs[j] = np.empty((Sold + Snew), dtype = np.complex)
bRBs[j][: Sold] = bRBsOld[j]
-# bRBs[j][: Sold] = copy(bRBsOld[j])
bRBs[j][Sold :] = pMatH.dot(bs[j])
return ARBs, bRBs
diff --git a/rrompy/reduction_methods/centered/generic_centered_approximant.py b/rrompy/reduction_methods/centered/generic_centered_approximant.py
index cf3b5db..48b9846 100644
--- a/rrompy/reduction_methods/centered/generic_centered_approximant.py
+++ b/rrompy/reduction_methods/centered/generic_centered_approximant.py
@@ -1,111 +1,113 @@
# Copyright (C) 2018 by the RROMPy authors
#
# This file is part of RROMPy.
#
# RROMPy is free software: you can redistribute it and/or modify
# it under the terms of the GNU Lesser General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# RROMPy is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU Lesser General Public License for more details.
#
# You should have received a copy of the GNU Lesser General Public License
# along with RROMPy. If not, see .
#
import numpy as np
from rrompy.reduction_methods.base.generic_approximant import (
GenericApproximant)
-from rrompy.utilities.base.types import DictAny, HFEng, paramVal
-from rrompy.utilities.base import purgeDict, verbosityDepth
-from rrompy.utilities.exception_manager import RROMPyException, RROMPyAssert
+from rrompy.utilities.base.types import paramList
+from rrompy.utilities.base import verbosityDepth
+from rrompy.utilities.exception_manager import RROMPyAssert
__all__ = ['GenericCenteredApproximant']
class GenericCenteredApproximant(GenericApproximant):
"""
ROM single-point approximant computation for parametric problems
(ABSTRACT).
Args:
HFEngine: HF problem solver.
mu0(optional): Default parameter. Defaults to 0.
approxParameters(optional): Dictionary containing values for main
parameters of approximant. Recognized keys are:
- 'POD': whether to compute POD of snapshots; defaults to True;
- 'S': total number of samples current approximant relies upon.
Defaults to empty dict.
homogeneized(optional): Whether to homogeneize Dirichlet BCs. Defaults
to False.
verbosity(optional): Verbosity level. Defaults to 10.
Attributes:
HFEngine: HF problem solver.
mu0: Default parameter.
homogeneized: Whether to homogeneize Dirichlet BCs.
approxParameters: Dictionary containing values for main parameters of
approximant. Recognized keys are in parameterList.
- parameterList: Recognized keys of approximant parameters:
- - 'POD': whether to compute POD of snapshots;
+ parameterListSoft: Recognized keys of soft approximant parameters:
+ - 'POD': whether to compute POD of snapshots.
+ parameterListCritical: Recognized keys of critical approximant
+ parameters:
- 'S': total number of samples current approximant relies upon.
POD: Whether to compute QR factorization of derivatives.
S: Number of solution snapshots over which current approximant is
based upon.
initialHFData: HF problem initial data.
samplingEngine: Sampling engine.
uHF: High fidelity solution(s) with parameter(s) lastSolvedHF as
sampleList.
lastSolvedHF: Parameter(s) corresponding to last computed high fidelity
solution(s) as parameterList.
uAppReduced: Reduced approximate solution(s) with parameter(s)
lastSolvedApp as sampleList.
lastSolvedAppReduced: Parameter(s) corresponding to last computed
reduced approximate solution(s) as parameterList.
uApp: Approximate solution(s) with parameter(s) lastSolvedApp as
sampleList.
lastSolvedApp: Parameter(s) corresponding to last computed approximate
solution(s) as parameterList.
"""
@property
def S(self):
"""Value of S."""
return self._S
@S.setter
def S(self, S):
GenericApproximant.S.fset(self, S)
RROMPyAssert(len(self.S), 1, "Length of S")
def computeDerivatives(self):
"""Compute derivatives of solution map starting from order 0."""
RROMPyAssert(self._mode,
message = "Cannot start derivative computation.")
- if self.samplingEngine.nsamples < np.prod(self.S):
+ if self.samplingEngine.nsamples != np.prod(self.S):
if self.verbosity >= 5:
verbosityDepth("INIT", "Starting computation of derivatives.",
timestamp = self.timestamp)
self.samplingEngine.iterSample([self.mu0[0]] * np.prod(self.S),
homogeneized = self.homogeneized)
if self.verbosity >= 5:
verbosityDepth("DEL", "Done computing derivatives.",
timestamp = self.timestamp)
- def normApprox(self, mu:complex, homogeneized : bool = False) -> float:
+ def normApprox(self, mu:paramList, homogeneized : bool = False) -> float:
"""
Compute norm of approximant at arbitrary parameter.
Args:
mu: Target parameter.
homogeneized(optional): Whether to remove Dirichlet BC. Defaults to
False.
Returns:
Target norm of approximant.
"""
if not self.POD or self.homogeneized != homogeneized:
return super().normApprox(mu, homogeneized)
return np.linalg.norm(self.getApproxReduced(mu), axis = 0)
diff --git a/rrompy/reduction_methods/centered/rational_pade.py b/rrompy/reduction_methods/centered/rational_pade.py
index e54de27..5356430 100644
--- a/rrompy/reduction_methods/centered/rational_pade.py
+++ b/rrompy/reduction_methods/centered/rational_pade.py
@@ -1,441 +1,440 @@
# Copyright (C) 2018 by the RROMPy authors
#
# This file is part of RROMPy.
#
# RROMPy is free software: you can redistribute it and/or modify
# it under the terms of the GNU Lesser General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# RROMPy is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU Lesser General Public License for more details.
#
# You should have received a copy of the GNU Lesser General Public License
# along with RROMPy. If not, see .
#
from copy import deepcopy as copy
import numpy as np
from rrompy.reduction_methods.base import checkRobustTolerance
from rrompy.reduction_methods.trained_model import (TrainedModelData,
TrainedModelPade as tModel)
from .generic_centered_approximant import GenericCenteredApproximant
from rrompy.utilities.base.types import (Np1D, Np2D, Tuple, DictAny, HFEng,
paramVal, paramList, sampList)
-from rrompy.utilities.base import verbosityDepth, purgeDict
+from rrompy.utilities.base import verbosityDepth
from rrompy.utilities.poly_fitting.polynomial import (nextDerivativeIndices,
hashDerivativeToIdx as hashD, hashIdxToDerivative as hashI)
from rrompy.utilities.exception_manager import (RROMPyException, RROMPyAssert,
RROMPyWarning)
__all__ = ['RationalPade']
class RationalPade(GenericCenteredApproximant):
"""
ROM single-point fast Pade' approximant computation for parametric
problems.
Args:
HFEngine: HF problem solver.
mu0(optional): Default parameter. Defaults to 0.
approxParameters(optional): Dictionary containing values for main
parameters of approximant. Recognized keys are:
- 'POD': whether to compute POD of snapshots; defaults to True;
- 'S': total number of samples current approximant relies upon;
+ - 'E': number of derivatives used to compute Pade'; defaults to 0;
- 'M': degree of Pade' approximant numerator; defaults to 0;
- 'N': degree of Pade' approximant denominator; defaults to 0;
- 'robustTol': tolerance for robust Pade' denominator management;
defaults to 0.
Defaults to empty dict.
homogeneized(optional): Whether to homogeneize Dirichlet BCs. Defaults
to False.
verbosity(optional): Verbosity level. Defaults to 10.
Attributes:
HFEngine: HF problem solver.
mu0: Default parameter.
homogeneized: Whether to homogeneize Dirichlet BCs.
approxParameters: Dictionary containing values for main parameters of
approximant. Recognized keys are in parameterList.
- parameterList: Recognized keys of approximant parameters:
- - 'POD': whether to compute POD of snapshots;
- - 'S': total number of samples current approximant relies upon;
+ parameterListSoft: Recognized keys of soft approximant parameters:
+ - 'POD': whether to compute POD of snapshots;
+ - 'E': number of derivatives used to compute Pade';
- 'M': degree of Pade' approximant numerator;
- 'N': degree of Pade' approximant denominator;
- 'robustTol': tolerance for robust Pade' denominator management.
+ parameterListCritical: Recognized keys of critical approximant
+ parameters:
+ - 'S': total number of samples current approximant relies upon.
POD: Whether to compute QR factorization of derivatives.
S: Number of solution snapshots over which current approximant is
based upon.
M: Numerator degree of approximant.
N: Denominator degree of approximant.
robustTol: Tolerance for robust Pade' denominator management.
E: Complete derivative depth level of S.
uHF: High fidelity solution(s) with parameter(s) lastSolvedHF as
sampleList.
lastSolvedHF: Parameter(s) corresponding to last computed high fidelity
solution(s) as parameterList.
uAppReduced: Reduced approximate solution(s) with parameter(s)
lastSolvedApp as sampleList.
lastSolvedAppReduced: Parameter(s) corresponding to last computed
reduced approximate solution(s) as parameterList.
uApp: Approximate solution(s) with parameter(s) lastSolvedApp as
sampleList.
lastSolvedApp: Parameter(s) corresponding to last computed approximate
solution(s) as parameterList.
G: Square Numpy 2D vector of size (N+1) corresponding to Pade'
denominator matrix (see paper).
"""
def __init__(self, HFEngine:HFEng, mu0 : paramVal = None,
approxParameters : DictAny = {}, homogeneized : bool = False,
verbosity : int = 10, timestamp : bool = True):
self._preInit()
- self._addParametersToList(["M", "N", "robustTol"])
+ self._addParametersToList(["E", "M", "N", "robustTol"], [-1, 0, 0, 0])
super().__init__(HFEngine = HFEngine, mu0 = mu0,
approxParameters = approxParameters,
homogeneized = homogeneized,
verbosity = verbosity, timestamp = timestamp)
self._postInit()
- @property
- def approxParameters(self):
- """Value of approximant parameters."""
- return self._approxParameters
- @approxParameters.setter
- def approxParameters(self, approxParams):
- approxParameters = purgeDict(approxParams, self.parameterList,
- dictname = self.name() + ".approxParameters",
- baselevel = 1)
- approxParametersCopy = purgeDict(approxParameters,
- ["M", "N", "robustTol"],
- True, True, baselevel = 1)
- keyList = list(approxParameters.keys())
- GenericCenteredApproximant.approxParameters.fset(self,
- approxParametersCopy)
- if "robustTol" in keyList:
- self.robustTol = approxParameters["robustTol"]
- elif not hasattr(self, "_robustTol") or self._robustTol is None:
- self.robustTol = 0
- if "M" in keyList:
- self.M = approxParameters["M"]
- elif hasattr(self, "_M") and self._M is not None:
- self.M = self.M
- else:
- self.M = 0
- if "N" in keyList:
- self.N = approxParameters["N"]
- elif hasattr(self, "_N") and self._N is not None:
- self.N = self.N
- else:
- self.N = 0
-
@property
def M(self):
"""Value of M.."""
return self._M
@M.setter
def M(self, M):
if M < 0: raise RROMPyException("M must be non-negative.")
self._M = M
self._approxParameters["M"] = self.M
- if hasattr(self, "E") and self.E < self.M:
- RROMPyWarning("Prescribed S is too small. Decreasing M.")
+ if hasattr(self, "_E") and self.E >= 0 and self.E < self.M:
+ RROMPyWarning("Prescribed E is too small. Decreasing M.")
self.M = self.E
@property
def N(self):
"""Value of N."""
return self._N
@N.setter
def N(self, N):
if N < 0: raise RROMPyException("N must be non-negative.")
self._N = N
self._approxParameters["N"] = self.N
- if hasattr(self, "E") and self.E < self.N:
- RROMPyWarning("Prescribed S is too small. Decreasing N.")
+ if hasattr(self, "_E") and self.E >= 0 and self.E < self.N:
+ RROMPyWarning("Prescribed E is too small. Decreasing N.")
self.N = self.E
+ @property
+ def E(self):
+ """Value of E."""
+ return self._E
+ @E.setter
+ def E(self, E):
+ if E < 0:
+ if not hasattr(self, "_S"):
+ raise RROMPyException(("Value of E must be positive if S is "
+ "not yet assigned."))
+ E = np.sum(hashI(np.prod(self.S), self.npar)) - 1
+ self._E = E
+ self._approxParameters["E"] = self.E
+ if (hasattr(self, "_S")
+ and self.E >= np.sum(hashI(np.prod(self.S), self.npar))):
+ RROMPyWarning("Prescribed S is too small. Decreasing E.")
+ self.E = -1
+ if hasattr(self, "_M"): self.M = self.M
+ if hasattr(self, "_N"): self.N = self.N
+
@property
def robustTol(self):
"""Value of tolerance for robust Pade' denominator management."""
return self._robustTol
@robustTol.setter
def robustTol(self, robustTol):
if robustTol < 0.:
RROMPyWarning(("Overriding prescribed negative robustness "
"tolerance to 0."))
robustTol = 0.
self._robustTol = robustTol
self._approxParameters["robustTol"] = self.robustTol
@property
def S(self):
"""Value of S."""
return self._S
@S.setter
def S(self, S):
GenericCenteredApproximant.S.fset(self, S)
- self.E = np.sum(hashI(np.prod(self.S), self.npar)) - 1
if hasattr(self, "_M"): self.M = self.M
if hasattr(self, "_N"): self.N = self.N
+ if hasattr(self, "_E"): self.E = self.E
def _setupDenominator(self):
"""Compute Pade' denominator."""
+ RROMPyAssert(self._mode, message = "Cannot setup denominator.")
if self.verbosity >= 7:
verbosityDepth("INIT", "Starting computation of denominator.",
timestamp = self.timestamp)
while self.N > 0:
if self.POD:
ev, eV = self.findeveVGQR()
else:
ev, eV = self.findeveVGExplicit()
newParameters = checkRobustTolerance(ev, self.N, self.robustTol)
if not newParameters:
break
self.approxParameters = newParameters
if self.N <= 0:
eV = np.ones((1, 1))
q = np.zeros(tuple([self.N + 1] * self.npar), dtype = np.complex)
for j in range(eV.shape[0]):
q[tuple(hashI(j, self.npar))] = eV[j, 0]
if self.verbosity >= 7:
verbosityDepth("DEL", "Done computing denominator.",
timestamp = self.timestamp)
return q
def _setupNumerator(self):
"""Compute Pade' numerator."""
+ RROMPyAssert(self._mode, message = "Cannot setup numerator.")
if self.verbosity >= 7:
verbosityDepth("INIT", "Starting computation of numerator.",
timestamp = self.timestamp)
- P = np.zeros((np.prod(self.S),) + tuple([self.M + 1] * self.npar),
+ P = np.zeros(tuple([self.M + 1] * self.npar) + (np.prod(self.S),),
dtype = np.complex)
mEnd = hashD([self.M + 1] + [0] * (self.npar - 1))
nEnd = hashD([self.N + 1] + [0] * (self.npar - 1))
mnIdxs = nextDerivativeIndices([], self.npar, max(mEnd, nEnd))
for j in range(mEnd):
mIdx = mnIdxs[j]
for n in range(nEnd):
diffIdx = [x - y for (x, y) in zip(mIdx, mnIdxs[n])]
if all([x >= 0 for x in diffIdx]):
- P[(hashD(diffIdx),) + (mIdx,)] = (
+ P[tuple(mIdx) + (hashD(diffIdx),)] = (
self.trainedModel.data.Q[tuple(mnIdxs[n])])
- return self.rescaleByParameter(P.T).T
+ if self.verbosity >= 7:
+ verbosityDepth("DEL", "Done computation numerator.",
+ timestamp = self.timestamp)
+ return self.rescaleByParameter(P).T
def setupApprox(self):
"""
Compute Pade' approximant. SVD-based robust eigenvalue management.
"""
if self.checkComputedApprox():
return
+ RROMPyAssert(self._mode, message = "Cannot setup approximant.")
if self.verbosity >= 5:
verbosityDepth("INIT", "Setting up {}.". format(self.name()),
timestamp = self.timestamp)
self.computeDerivatives()
if self.trainedModel is None:
self.trainedModel = tModel()
self.trainedModel.verbosity = self.verbosity
self.trainedModel.timestamp = self.timestamp
data = TrainedModelData(self.trainedModel.name(), self.mu0,
None, self.HFEngine.rescalingExp)
data.polytype = "MONOMIAL"
self.trainedModel.data = data
else:
self.trainedModel = self.trainedModel
if self.N > 0:
Q = self._setupDenominator()
else:
self.setScaleParameter()
Q = np.ones(1, dtype = np.complex)
self.trainedModel.data.Q = copy(Q)
self.trainedModel.data.scaleFactor = self.scaleFactor
self.trainedModel.data.projMat = copy(self.samplingEngine.samples(
list(range(np.prod(self.S)))))
P = self._setupNumerator()
if self.POD:
P = np.tensordot(self.samplingEngine.RPOD, P, axes = ([-1], [0]))
self.trainedModel.data.P = copy(P)
self.trainedModel.data.approxParameters = copy(self.approxParameters)
if self.verbosity >= 5:
verbosityDepth("DEL", "Done setting up approximant.",
timestamp = self.timestamp)
def setScaleParameter(self) -> Np2D:
"""Compute parameter for rescaling."""
RROMPyAssert(self._mode, message = "Cannot compute rescaling factor.")
self.computeDerivatives()
self.scaleFactor = [1.] * self.npar
for d in range(self.npar):
hashesd = [0]
for n in range(1, self.E + 1):
hashesd += [hashD([0] * (d - 1) + [n]
+ [0] * (self.npar - d - 1))]
if self.POD:
Rd = self.samplingEngine.RPOD[: hashesd[-1] + 1, hashesd]
Gd = np.diag(Rd.T.conj().dot(Rd))
else:
DerEd = self.samplingEngine.samples(hashesd)
Gd = self.HFEngine.norm(DerEd)
- scaleCoeffs = np.polyfit(np.arange(len(Gd)), np.log(Gd), 1)
- self.scaleFactor[d] = np.exp(- scaleCoeffs[0] / 2.)
+ if len(Gd) > 1:
+ scaleCoeffs = np.polyfit(np.arange(len(Gd)), np.log(Gd), 1)
+ self.scaleFactor[d] = np.exp(- scaleCoeffs[0] / 2.)
def rescaleByParameter(self, R:Np2D) -> Np2D:
"""
Rescale by scale parameter.
Args:
R: Matrix whose columns need rescaling.
Returns:
Rescaled matrix.
"""
RIdxs = nextDerivativeIndices([], self.npar, R.shape[-1])
Rscaled = copy(R)
for j, RIdx in enumerate(RIdxs):
Rscaled[..., j] *= np.prod([x ** y for (x, y) in
zip(self.scaleFactor, RIdx)])
return Rscaled
def buildG(self):
"""Assemble Pade' denominator matrix."""
RROMPyAssert(self._mode, message = "Cannot compute G matrix.")
self.computeDerivatives()
if self.verbosity >= 10:
verbosityDepth("INIT", "Building gramian matrix.",
timestamp = self.timestamp)
eStart = hashD([self.E] + [0] * (self.npar - 1))
eEnd = hashD([self.E + 1] + [0] * (self.npar - 1))
eIdxs = [hashI(e, self.npar) for e in range(eStart, eEnd)]
nEnd = hashD([self.N + 1] + [0] * (self.npar - 1))
nIdxs = nextDerivativeIndices([], self.npar, nEnd)
self.setScaleParameter()
if self.POD:
RPODE = self.rescaleByParameter(self.samplingEngine.RPOD[: eEnd,
: eEnd])
else:
DerE = self.rescaleByParameter(self.samplingEngine.samples(
list(range(eEnd))).data)
self.G = np.zeros((nEnd, nEnd), dtype = np.complex)
for eIdx in eIdxs:
nLoc = []
samplesIdxs = []
for n, nIdx in enumerate(nIdxs):
diffIdx = [x - y for (x, y) in zip(eIdx, nIdx)]
if all([x >= 0 for x in diffIdx]):
nLoc += [n]
samplesIdxs += [hashD(diffIdx)]
if self.POD:
RPODELoc = RPODE[: samplesIdxs[-1] + 1, samplesIdxs]
GLoc = RPODELoc.T.conj().dot(RPODELoc)
else:
DerELoc = DerE[:, samplesIdxs]
GLoc = self.HFEngine.innerProduct(DerELoc, DerELoc)
for j in range(len(nLoc)):
self.G[nLoc[j], nLoc] = self.G[nLoc[j], nLoc] + GLoc[j]
if self.verbosity >= 10:
verbosityDepth("DEL", "Done building gramian.",
timestamp = self.timestamp)
def findeveVGExplicit(self) -> Tuple[Np1D, Np2D]:
"""
Compute explicitly eigenvalues and eigenvectors of Pade' denominator
matrix.
"""
RROMPyAssert(self._mode, message = "Cannot solve eigenvalue problem.")
self.buildG()
if self.verbosity >= 7:
verbosityDepth("INIT",
"Solving eigenvalue problem for gramian matrix.",
timestamp = self.timestamp)
ev, eV = np.linalg.eigh(self.G)
if self.verbosity >= 5:
try: condev = ev[-1] / ev[0]
except: condev = np.inf
verbosityDepth("MAIN", ("Solved eigenvalue problem of size {} "
"with condition number {:.4e}.").format(
self.G.shape[0],
condev),
timestamp = self.timestamp)
if self.verbosity >= 7:
verbosityDepth("DEL", "Done solving eigenvalue problem.",
timestamp = self.timestamp)
return ev, eV
def findeveVGQR(self) -> Tuple[Np1D, Np2D]:
"""
Compute eigenvalues and eigenvectors of Pade' denominator matrix
through SVD of R factor.
Returns:
Eigenvalues in ascending order and corresponding eigenvector
matrix.
"""
RROMPyAssert(self._mode, message = "Cannot solve eigenvalue problem.")
RROMPyAssert(self.POD, True, "POD value")
self.computeDerivatives()
eStart = hashD([self.E] + [0] * (self.npar - 1))
eEnd = hashD([self.E + 1] + [0] * (self.npar - 1))
eIdxs = [hashI(e, self.npar) for e in range(eStart, eEnd)]
nEnd = hashD([self.N + 1] + [0] * (self.npar - 1))
nIdxs = nextDerivativeIndices([], self.npar, nEnd)
self.setScaleParameter()
RPODE = self.rescaleByParameter(self.samplingEngine.RPOD[: eEnd,
: eEnd])
Rstack = np.zeros((RPODE.shape[0] * (eEnd - eStart), nEnd),
dtype = np.complex)
for k, eIdx in enumerate(eIdxs):
nLoc = []
samplesIdxs = []
for n, nIdx in enumerate(nIdxs):
diffIdx = [x - y for (x, y) in zip(eIdx, nIdx)]
if all([x >= 0 for x in diffIdx]):
nLoc += [n]
samplesIdxs += [hashD(diffIdx)]
RPODELoc = RPODE[:, samplesIdxs]
for j in range(len(nLoc)):
Rstack[k * RPODE.shape[0] : (k + 1) * RPODE.shape[0],
nLoc[j]] = RPODELoc[:, j]
if self.verbosity >= 7:
verbosityDepth("INIT", ("Solving svd for square root of "
"gramian matrix."),
timestamp = self.timestamp)
sizeI = Rstack.shape
_, s, V = np.linalg.svd(Rstack, full_matrices = False)
eV = V[::-1, :].T.conj()
if self.verbosity >= 5:
try: condev = s[0] / s[-1]
except: condev = np.inf
verbosityDepth("MAIN", ("Solved svd problem of size {} x {} with "
"condition number {:.4e}.").format(*sizeI,
condev),
timestamp = self.timestamp)
if self.verbosity >= 7:
verbosityDepth("DEL", "Done solving eigenvalue problem.",
timestamp = self.timestamp)
return s[::-1], eV
def centerNormalize(self, mu : paramList = [],
mu0 : paramVal = None) -> paramList:
"""
Compute normalized parameter to be plugged into approximant.
Args:
mu: Parameter(s) 1.
mu0: Parameter(s) 2. If None, set to self.mu0.
Returns:
Normalized parameter.
"""
return self.trainedModel.centerNormalize(mu, mu0)
def getResidues(self) -> sampList:
"""
Obtain approximant residues.
Returns:
Matrix with residues as columns.
"""
return self.trainedModel.getResidues()
diff --git a/rrompy/reduction_methods/centered/rb_centered.py b/rrompy/reduction_methods/centered/rb_centered.py
index 9751b9b..c690b2a 100644
--- a/rrompy/reduction_methods/centered/rb_centered.py
+++ b/rrompy/reduction_methods/centered/rb_centered.py
@@ -1,203 +1,191 @@
# Copyright (C) 2018 by the RROMPy authors
#
# This file is part of RROMPy.
#
# RROMPy is free software: you can redistribute it and/or modify
# it under the terms of the GNU Lesser General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# RROMPy is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU Lesser General Public License for more details.
#
# You should have received a copy of the GNU Lesser General Public License
# along with RROMPy. If not, see .
#
from copy import deepcopy as copy
import numpy as np
from .generic_centered_approximant import GenericCenteredApproximant
from rrompy.reduction_methods.trained_model import TrainedModelRB as tModel
from rrompy.reduction_methods.trained_model import TrainedModelData
from rrompy.reduction_methods.base.rb_utils import projectAffineDecomposition
from rrompy.utilities.base.types import (Np1D, Np2D, Tuple, List, DictAny,
HFEng, paramVal, sampList)
-from rrompy.utilities.base import purgeDict, verbosityDepth
-from rrompy.utilities.exception_manager import RROMPyException, RROMPyWarning
+from rrompy.utilities.base import verbosityDepth
+from rrompy.utilities.exception_manager import (RROMPyException, RROMPyWarning,
+ RROMPyAssert)
__all__ = ['RBCentered']
class RBCentered(GenericCenteredApproximant):
"""
ROM single-point fast RB approximant computation for parametric problems
with polynomial dependence up to degree 2.
Args:
HFEngine: HF problem solver.
mu0(optional): Default parameter. Defaults to 0.
approxParameters(optional): Dictionary containing values for main
parameters of approximant. Recognized keys are:
- 'POD': whether to compute POD of snapshots; defaults to True;
- 'S': total number of samples current approximant relies upon;
- 'R': rank for Galerkin projection; defaults to prod(S).
Defaults to empty dict.
homogeneized(optional): Whether to homogeneize Dirichlet BCs. Defaults
to False.
verbosity(optional): Verbosity level. Defaults to 10.
Attributes:
HFEngine: HF problem solver.
mu0: Default parameter.
homogeneized: Whether to homogeneize Dirichlet BCs.
approxParameters: Dictionary containing values for main parameters of
approximant. Recognized keys are in parameterList.
- parameterList: Recognized keys of approximant parameters:
+ parameterListSoft: Recognized keys of soft approximant parameters:
- 'POD': whether to compute POD of snapshots;
- - 'S': total number of samples current approximant relies upon;
- 'R': rank for Galerkin projection.
+ parameterListCritical: Recognized keys of critical approximant
+ parameters:
+ - 'S': total number of samples current approximant relies upon.
POD: Whether to compute QR factorization of derivatives.
R: Rank for Galerkin projection.
S: Number of solution snapshots over which current approximant is
based upon.
uHF: High fidelity solution(s) with parameter(s) lastSolvedHF as
sampleList.
lastSolvedHF: Parameter(s) corresponding to last computed high fidelity
solution(s) as parameterList.
uAppReduced: Reduced approximate solution(s) with parameter(s)
lastSolvedApp as sampleList.
lastSolvedAppReduced: Parameter(s) corresponding to last computed
reduced approximate solution(s) as parameterList.
uApp: Approximate solution(s) with parameter(s) lastSolvedApp as
sampleList.
lastSolvedApp: Parameter(s) corresponding to last computed approximate
solution(s) as parameterList.
ARBs: List of sparse matrices (in CSC format) representing RB
coefficients of linear system matrix wrt mu.
bRBs: List of numpy vectors representing RB coefficients of linear
system RHS wrt mu.
"""
def __init__(self, HFEngine:HFEng, mu0 : paramVal = None,
approxParameters : DictAny = {}, homogeneized : bool = False,
verbosity : int = 10, timestamp : bool = True):
self._preInit()
- self._addParametersToList(["R"])
+ self._addParametersToList(["R"], [1])
super().__init__(HFEngine = HFEngine, mu0 = mu0,
approxParameters = approxParameters,
homogeneized = homogeneized,
verbosity = verbosity, timestamp = timestamp)
if self.verbosity >= 10:
verbosityDepth("INIT", "Computing affine blocks of system.",
timestamp = self.timestamp)
if self.verbosity >= 10:
verbosityDepth("DEL", "Done computing affine blocks.",
timestamp = self.timestamp)
self._postInit()
@property
- def approxParameters(self):
- """
- Value of approximant parameters. Its assignment may change M, N and S.
- """
- return self._approxParameters
- @approxParameters.setter
- def approxParameters(self, approxParams):
- approxParameters = purgeDict(approxParams, self.parameterList,
- dictname = self.name() + ".approxParameters",
- baselevel = 1)
- approxParametersCopy = purgeDict(approxParameters, ["R"],
- True, True, baselevel = 1)
- GenericCenteredApproximant.approxParameters.fset(self,
- approxParametersCopy)
- keyList = list(approxParameters.keys())
- if "R" in keyList:
- self.R = approxParameters["R"]
- else:
- self.R = np.prod(self.S)
+ def S(self):
+ """Value of S."""
+ return self._S
+ @S.setter
+ def S(self, S):
+ GenericCenteredApproximant.S.fset(self, S)
+ if not hasattr(self, "_R"): self._R = np.prod(self.S)
@property
def R(self):
"""Value of R. Its assignment may change S."""
return self._R
@R.setter
def R(self, R):
if R < 0: raise RROMPyException("R must be non-negative.")
self._R = R
self._approxParameters["R"] = self.R
if hasattr(self, "_S") and np.prod(self.S) < self.R:
RROMPyWarning("Prescribed S is too small. Reducing R.")
self.R = np.prod(self.S)
def setupApprox(self):
"""Setup RB system."""
if self.checkComputedApprox():
return
+ RROMPyAssert(self._mode, message = "Cannot setup approximant.")
if self.verbosity >= 5:
verbosityDepth("INIT", "Setting up {}.". format(self.name()),
timestamp = self.timestamp)
self.computeDerivatives()
if self.verbosity >= 7:
verbosityDepth("INIT", "Computing projection matrix.",
timestamp = self.timestamp)
if self.POD:
- U, _, _ = np.linalg.svd(self.samplingEngine.RPOD[: np.prod(self.S),
- : np.prod(self.S)])
- pMat = self.samplingEngine.samples(list(range(np.prod(self.S))))\
- .dot(U[:, : self.R])
+ Sprod = np.prod(self.S)
+ U, _, _ = np.linalg.svd(self.samplingEngine.RPOD[: Sprod,: Sprod])
+ pMat = self.samplingEngine.samples(list(range(Sprod))).dot(
+ U[:, : self.R])
else:
pMat = self.samplingEngine.samples(list(range(self.R)))
if self.trainedModel is None:
self.trainedModel = tModel()
self.trainedModel.verbosity = self.verbosity
self.trainedModel.timestamp = self.timestamp
data = TrainedModelData(self.trainedModel.name(), self.mu0,
pMat, self.HFEngine.rescalingExp)
data.thetaAs = self.HFEngine.affineWeightsA(self.mu0)
data.thetabs = self.HFEngine.affineWeightsb(self.mu0,
self.homogeneized)
- data.ARBs, data.bRBs = self.assembleReducedSystem(pMat)
self.trainedModel.data = data
else:
self.trainedModel = self.trainedModel
- pMatOld = self.trainedModel.data.projMat
- Sold = pMatOld.shape[1]
- ARBs, bRBs = self.assembleReducedSystem(
- pMat(list(range(Sold, pMat.shape[1]))), pMatOld)
- self.trainedModel.data.ARBs = ARBs
- self.trainedModel.data.bRBs = bRBs
self.trainedModel.data.projMat = copy(pMat)
+ ARBs, bRBs = self.assembleReducedSystem(pMat)
+ self.trainedModel.data.ARBs = ARBs
+ self.trainedModel.data.bRBs = bRBs
if self.verbosity >= 7:
verbosityDepth("DEL", "Done computing projection matrix.",
timestamp = self.timestamp)
self.trainedModel.data.approxParameters = copy(self.approxParameters)
if self.verbosity >= 5:
verbosityDepth("DEL", "Done setting up approximant.",
timestamp = self.timestamp)
def assembleReducedSystem(self, pMat : sampList = None,
pMatOld : sampList = None)\
-> Tuple[List[Np2D], List[Np1D]]:
"""Build affine blocks of RB linear system through projections."""
if pMat is None:
self.setupApprox()
ARBs = self.trainedModel.data.ARBs
bRBs = self.trainedModel.data.bRBs
else:
if self.verbosity >= 10:
verbosityDepth("INIT", "Projecting affine terms of HF model.",
timestamp = self.timestamp)
As = self.HFEngine.affineLinearSystemA(self.mu0)
bs = self.HFEngine.affineLinearSystemb(self.mu0, self.homogeneized)
ARBsOld = None if pMatOld is None else self.trainedModel.data.ARBs
bRBsOld = None if pMatOld is None else self.trainedModel.data.bRBs
ARBs, bRBs = projectAffineDecomposition(As, bs, pMat, ARBsOld,
bRBsOld, pMatOld)
if self.verbosity >= 10:
verbosityDepth("DEL", "Done projecting affine terms.",
timestamp = self.timestamp)
return ARBs, bRBs
diff --git a/rrompy/reduction_methods/distributed/generic_distributed_approximant.py b/rrompy/reduction_methods/distributed/generic_distributed_approximant.py
index b3859da..13ac033 100644
--- a/rrompy/reduction_methods/distributed/generic_distributed_approximant.py
+++ b/rrompy/reduction_methods/distributed/generic_distributed_approximant.py
@@ -1,196 +1,167 @@
# Copyright (C) 2018 by the RROMPy authors
#
# This file is part of RROMPy.
#
# RROMPy is free software: you can redistribute it and/or modify
# it under the terms of the GNU Lesser General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# RROMPy is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU Lesser General Public License for more details.
#
# You should have received a copy of the GNU Lesser General Public License
# along with RROMPy. If not, see .
#
import numpy as np
from copy import deepcopy as copy
from rrompy.reduction_methods.base.generic_approximant import (
GenericApproximant)
from rrompy.utilities.base.types import DictAny, HFEng, paramVal, paramList
-from rrompy.utilities.base import purgeDict, verbosityDepth
+from rrompy.utilities.base import verbosityDepth
from rrompy.utilities.exception_manager import RROMPyException, RROMPyAssert
from rrompy.parameter import checkParameterList
__all__ = ['GenericDistributedApproximant']
class GenericDistributedApproximant(GenericApproximant):
"""
ROM interpolant computation for parametric problems (ABSTRACT).
Args:
HFEngine: HF problem solver.
mu0(optional): Default parameter. Defaults to 0.
approxParameters(optional): Dictionary containing values for main
parameters of approximant. Recognized keys are:
- 'POD': whether to compute POD of snapshots; defaults to True;
- - 'muBounds': list of bounds for parameter values;
- 'S': total number of samples current approximant relies upon;
- - 'sampler': sample point generator; defaults to uniform sampler on
- muBounds.
+ - 'sampler': sample point generator.
Defaults to empty dict.
homogeneized(optional): Whether to homogeneize Dirichlet BCs. Defaults
to False.
verbosity(optional): Verbosity level. Defaults to 10.
Attributes:
HFEngine: HF problem solver.
mu0: Default parameter.
mus: Array of snapshot parameters.
homogeneized: Whether to homogeneize Dirichlet BCs.
approxParameters: Dictionary containing values for main parameters of
approximant. Recognized keys are in parameterList.
- parameterList: Recognized keys of approximant parameters:
- - 'POD': whether to compute POD of snapshots;
- - 'muBounds': list of bounds for parameter values;
+ parameterListSoft: Recognized keys of soft approximant parameters:
+ - 'POD': whether to compute POD of snapshots.
+ parameterListCritical: Recognized keys of critical approximant
+ parameters:
- 'S': total number of samples current approximant relies upon;
- 'sampler': sample point generator.
- extraApproxParameters: List of approxParameters keys in addition to
- mother class's.
POD: Whether to compute POD of snapshots.
- muBounds: list of bounds for parameter values.
S: Number of solution snapshots over which current approximant is
based upon.
sampler: Sample point generator.
+ muBounds: list of bounds for parameter values.
samplingEngine: Sampling engine.
uHF: High fidelity solution(s) with parameter(s) lastSolvedHF as
sampleList.
lastSolvedHF: Parameter(s) corresponding to last computed high fidelity
solution(s) as parameterList.
uAppReduced: Reduced approximate solution(s) with parameter(s)
lastSolvedApp as sampleList.
lastSolvedAppReduced: Parameter(s) corresponding to last computed
reduced approximate solution(s) as parameterList.
uApp: Approximate solution(s) with parameter(s) lastSolvedApp as
sampleList.
lastSolvedApp: Parameter(s) corresponding to last computed approximate
solution(s) as parameterList.
"""
def __init__(self, HFEngine:HFEng, mu0 : paramVal = None,
approxParameters : DictAny = {}, homogeneized : bool = False,
verbosity : int = 10, timestamp : bool = True):
self._preInit()
- self._addParametersToList(["muBounds", "sampler"])
+ from rrompy.parameter.parameter_sampling import QuadratureSampler as QS
+ self._addParametersToList([], [], ["sampler"],
+ [QS([[0], [1]], "UNIFORM")])
+ del QS
super().__init__(HFEngine = HFEngine, mu0 = mu0,
approxParameters = approxParameters,
homogeneized = homogeneized,
verbosity = verbosity, timestamp = timestamp)
self._postInit()
@property
def mus(self):
"""Value of mus. Its assignment may reset snapshots."""
return self._mus
@mus.setter
def mus(self, mus):
mus, _ = checkParameterList(mus, self.npar)
musOld = copy(self.mus) if hasattr(self, '_mus') else None
if (musOld is None or len(mus) != len(musOld) or not mus == musOld):
self.resetSamples()
self._mus = mus
- @property
- def approxParameters(self):
- """Value of approximant parameters. Its assignment may change S."""
- return self._approxParameters
- @approxParameters.setter
- def approxParameters(self, approxParams):
- approxParameters = purgeDict(approxParams, self.parameterList,
- dictname = self.name() + ".approxParameters",
- baselevel = 1)
- approxParametersCopy = purgeDict(approxParameters,
- ["muBounds", "sampler"],
- True, True, baselevel = 1)
- GenericApproximant.approxParameters.fset(self, approxParametersCopy)
- keyList = list(approxParameters.keys())
- if "muBounds" in keyList:
- self.muBounds = approxParameters["muBounds"]
- if "sampler" in keyList:
- self.sampler = approxParameters["sampler"]
- if ((not hasattr(self, "_muBounds") or self.muBounds is None)
- and (not hasattr(self, "_sampler") or self.sampler is None)):
- raise RROMPyException("Must specify either muBounds or sampler.")
- if not hasattr(self, "_sampler") or self.sampler is None:
- from rrompy.parameter.parameter_sampling import QuadratureSampler
- self.sampler = QuadratureSampler(self.muBounds, "UNIFORM")
- del QuadratureSampler
- if not hasattr(self, "_muBounds") or self.muBounds is None:
- self.muBounds = self.sampler.lims
-
@property
def muBounds(self):
"""Value of muBounds."""
- return self._muBounds
- @muBounds.setter
- def muBounds(self, muBounds):
- muBounds, _ = checkParameterList(muBounds, self.npar)
- if len(muBounds) != 2:
- raise RROMPyException("2 limits must be specified.")
- self._muBounds = muBounds
+ return self.sampler.lims
@property
def sampler(self):
"""Value of sampler."""
return self._sampler
@sampler.setter
def sampler(self, sampler):
if 'generatePoints' not in dir(sampler):
raise RROMPyException("Sampler type not recognized.")
if hasattr(self, '_sampler') and self._sampler is not None:
samplerOld = self.sampler
self._sampler = sampler
self._approxParameters["sampler"] = self.sampler.__str__()
if not 'samplerOld' in locals() or samplerOld != self.sampler:
self.resetSamples()
+ def setSamples(self, samplingEngine):
+ """Copy samplingEngine and samples."""
+ super().setSamples(samplingEngine)
+ self.mus = copy(self.samplingEngine.mus)
+
def computeSnapshots(self):
"""Compute snapshots of solution map."""
RROMPyAssert(self._mode,
message = "Cannot start snapshot computation.")
- if self.samplingEngine.nsamples == 0:
+ if self.samplingEngine.nsamples != np.prod(self.S):
if self.verbosity >= 5:
verbosityDepth("INIT", "Starting computation of snapshots.",
timestamp = self.timestamp)
self.mus = self.sampler.generatePoints(self.S)
self.samplingEngine.iterSample(self.mus,
homogeneized = self.homogeneized)
if self.verbosity >= 5:
verbosityDepth("DEL", "Done computing snapshots.",
timestamp = self.timestamp)
def normApprox(self, mu:paramList, homogeneized : bool = False) -> float:
"""
Compute norm of approximant at arbitrary parameter.
Args:
mu: Target parameter.
homogeneized(optional): Whether to remove Dirichlet BC. Defaults to
False.
Returns:
Target norm of approximant.
"""
if not self.POD or self.homogeneized != homogeneized:
return super().normApprox(mu, homogeneized)
return np.linalg.norm(self.getApproxReduced(mu), axis = 0)
def computeScaleFactor(self):
"""Compute parameter rescaling factor."""
RROMPyAssert(self._mode, message = "Cannot compute rescaling factor.")
self.scaleFactor = .5 * np.abs(
self.muBounds[0] ** self.HFEngine.rescalingExp
- self.muBounds[1] ** self.HFEngine.rescalingExp)
diff --git a/rrompy/reduction_methods/distributed/rational_interpolant.py b/rrompy/reduction_methods/distributed/rational_interpolant.py
index 7d3d7de..85a6af9 100644
--- a/rrompy/reduction_methods/distributed/rational_interpolant.py
+++ b/rrompy/reduction_methods/distributed/rational_interpolant.py
@@ -1,557 +1,540 @@
# Copyright (C) 2018 by the RROMPy authors
#
# This file is part of RROMPy.
#
# RROMPy is free software: you can redistribute it and/or modify
# it under the terms of the GNU Lesser General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# RROMPy is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU Lesser General Public License for more details.
#
# You should have received a copy of the GNU Lesser General Public License
# along with RROMPy. If not, see .
#
from copy import deepcopy as copy
import numpy as np
from rrompy.reduction_methods.base import checkRobustTolerance
from .generic_distributed_approximant import GenericDistributedApproximant
-from rrompy.utilities.poly_fitting import customFit
+from rrompy.utilities.poly_fitting import customFit, customPInv
from rrompy.utilities.poly_fitting.polynomial import (polybases, polyfitname,
nextDerivativeIndices,
hashDerivativeToIdx as hashD,
hashIdxToDerivative as hashI,
homogeneizedpolyvander)
from rrompy.reduction_methods.trained_model import TrainedModelPade as tModel
from rrompy.reduction_methods.trained_model import TrainedModelData
from rrompy.utilities.base.types import (Np1D, Np2D, HFEng, DictAny, Tuple,
List, paramVal, paramList, sampList)
-from rrompy.utilities.base import verbosityDepth, purgeDict, multifactorial
+from rrompy.utilities.base import verbosityDepth, multifactorial
from rrompy.utilities.exception_manager import (RROMPyException, RROMPyAssert,
RROMPyWarning)
__all__ = ['RationalInterpolant']
class RationalInterpolant(GenericDistributedApproximant):
"""
ROM rational interpolant computation for parametric problems.
Args:
HFEngine: HF problem solver.
mu0(optional): Default parameter. Defaults to 0.
approxParameters(optional): Dictionary containing values for main
parameters of approximant. Recognized keys are:
- 'POD': whether to compute POD of snapshots; defaults to True;
- - 'muBounds': list of bounds for parameter values;
- 'S': total number of samples current approximant relies upon;
- - 'sampler': sample point generator; defaults to uniform sampler on
- muBounds;
+ - 'sampler': sample point generator;
- 'polybasis': type of polynomial basis for interpolation; allowed
values include 'MONOMIAL', 'CHEBYSHEV' and 'LEGENDRE'; defaults
to 'MONOMIAL';
+ - 'E': number of derivatives used to compute interpolant; defaults
+ to 0;
- 'M': degree of Pade' interpolant numerator; defaults to 0;
- 'N': degree of Pade' interpolant denominator; defaults to 0;
- 'interpRcond': tolerance for interpolation; defaults to None;
- 'robustTol': tolerance for robust Pade' denominator management;
defaults to 0.
Defaults to empty dict.
homogeneized(optional): Whether to homogeneize Dirichlet BCs. Defaults
to False.
verbosity(optional): Verbosity level. Defaults to 10.
Attributes:
HFEngine: HF problem solver.
mu0: Default parameter.
mus: Array of snapshot parameters.
homogeneized: Whether to homogeneize Dirichlet BCs.
approxParameters: Dictionary containing values for main parameters of
approximant. Recognized keys are in parameterList.
- parameterList: Recognized keys of approximant parameters:
- - 'POD': whether to compute POD of snapshots;
- - 'muBounds': list of bounds for parameter values;
- - 'S': total number of samples current approximant relies upon;
- - 'sampler': sample point generator;
+ parameterListSoft: Recognized keys of soft approximant parameters:
+ - 'POD': whether to compute POD of snapshots;
- 'polybasis': type of polynomial basis for interpolation;
+ - 'E': number of derivatives used to compute interpolant;
- 'M': degree of Pade' interpolant numerator;
- 'N': degree of Pade' interpolant denominator;
- 'interpRcond': tolerance for interpolation via numpy.polyfit;
- 'robustTol': tolerance for robust Pade' denominator management.
- extraApproxParameters: List of approxParameters keys in addition to
- mother class's.
+ parameterListCritical: Recognized keys of critical approximant
+ parameters:
+ - 'S': total number of samples current approximant relies upon;
+ - 'sampler': sample point generator.
POD: Whether to compute POD of snapshots.
- muBounds: list of bounds for parameter values.
S: Number of solution snapshots over which current approximant is
based upon.
sampler: Sample point generator.
polybasis: type of polynomial basis for interpolation.
M: Numerator degree of approximant.
N: Denominator degree of approximant.
interpRcond: Tolerance for interpolation via numpy.polyfit.
robustTol: Tolerance for robust Pade' denominator management.
E: Complete derivative depth level of S.
+ muBounds: list of bounds for parameter values.
samplingEngine: Sampling engine.
uHF: High fidelity solution(s) with parameter(s) lastSolvedHF as
sampleList.
lastSolvedHF: Parameter(s) corresponding to last computed high fidelity
solution(s) as parameterList.
uAppReduced: Reduced approximate solution(s) with parameter(s)
lastSolvedApp as sampleList.
lastSolvedAppReduced: Parameter(s) corresponding to last computed
reduced approximate solution(s) as parameterList.
uApp: Approximate solution(s) with parameter(s) lastSolvedApp as
sampleList.
lastSolvedApp: Parameter(s) corresponding to last computed approximate
solution(s) as parameterList.
Q: Numpy 1D vector containing complex coefficients of approximant
denominator.
P: Numpy 2D vector whose columns are FE dofs of coefficients of
approximant numerator.
"""
def __init__(self, HFEngine:HFEng, mu0 : paramVal = None,
approxParameters : DictAny = {}, homogeneized : bool = False,
verbosity : int = 10, timestamp : bool = True):
self._preInit()
- self._addParametersToList(["polybasis", "M", "N", "interpRcond",
- "robustTol"])
+ self._addParametersToList(["polybasis", "E", "M", "N", "interpRcond",
+ "robustTol"], ["MONOMIAL", -1, 0, 0, -1, 0])
super().__init__(HFEngine = HFEngine, mu0 = mu0,
approxParameters = approxParameters,
homogeneized = homogeneized,
verbosity = verbosity, timestamp = timestamp)
self._postInit()
- @property
- def approxParameters(self):
- """
- Value of approximant parameters.
- """
- return self._approxParameters
- @approxParameters.setter
- def approxParameters(self, approxParams):
- approxParameters = purgeDict(approxParams, self.parameterList,
- dictname = self.name() + ".approxParameters",
- baselevel = 1)
- approxParametersCopy = purgeDict(approxParameters, ["polybasis",
- "M", "N",
- "interpRcond",
- "robustTol"],
- True, True, baselevel = 1)
- GenericDistributedApproximant.approxParameters.fset(self,
- approxParametersCopy)
- keyList = list(approxParameters.keys())
- if "polybasis" in keyList:
- self.polybasis = approxParameters["polybasis"]
- elif not hasattr(self, "_polybasis") or self._polybasis is None:
- self.polybasis = "MONOMIAL"
- if "interpRcond" in keyList:
- self.interpRcond = approxParameters["interpRcond"]
- elif not hasattr(self, "interpRcond") or self.interpRcond is None:
- self.interpRcond = None
- if "robustTol" in keyList:
- self.robustTol = approxParameters["robustTol"]
- elif not hasattr(self, "_robustTol") or self._robustTol is None:
- self.robustTol = 0
- if "M" in keyList:
- self.M = approxParameters["M"]
- elif hasattr(self, "_M") and self.M is not None:
- self.M = self.M
- else:
- self.M = 0
- if "N" in keyList:
- self.N = approxParameters["N"]
- elif hasattr(self, "_N") and self.N is not None:
- self.N = self.N
- else:
- self.N = 0
-
@property
def polybasis(self):
"""Value of polybasis."""
return self._polybasis
@polybasis.setter
def polybasis(self, polybasis):
try:
polybasis = polybasis.upper().strip().replace(" ","")
if polybasis not in polybases:
raise RROMPyException("Prescribed polybasis not recognized.")
self._polybasis = polybasis
except:
RROMPyWarning(("Prescribed polybasis not recognized. Overriding "
"to 'MONOMIAL'."))
self._polybasis = "MONOMIAL"
self._approxParameters["polybasis"] = self.polybasis
@property
def interpRcond(self):
"""Value of interpRcond."""
return self._interpRcond
@interpRcond.setter
def interpRcond(self, interpRcond):
self._interpRcond = interpRcond
self._approxParameters["interpRcond"] = self.interpRcond
@property
def M(self):
"""Value of M. Its assignment may change S."""
return self._M
@M.setter
def M(self, M):
if M < 0: raise RROMPyException("M must be non-negative.")
self._M = M
self._approxParameters["M"] = self.M
- if hasattr(self, "E") and self.E < self.M:
+ if hasattr(self, "_E") and self.E >= 0 and self.E < self.M:
RROMPyWarning("Prescribed S is too small. Decreasing M.")
self.M = self.E
@property
def N(self):
"""Value of N. Its assignment may change S."""
return self._N
@N.setter
def N(self, N):
if N < 0: raise RROMPyException("N must be non-negative.")
self._N = N
self._approxParameters["N"] = self.N
- if hasattr(self, "E") and self.E < self.N:
+ if hasattr(self, "_E") and self.E >= 0 and self.E < self.N:
RROMPyWarning("Prescribed S is too small. Decreasing N.")
self.N = self.E
+ @property
+ def E(self):
+ """Value of E."""
+ return self._E
+ @E.setter
+ def E(self, E):
+ if E < 0:
+ if not hasattr(self, "_S"):
+ raise RROMPyException(("Value of E must be positive if S is "
+ "not yet assigned."))
+ E = np.sum(hashI(np.prod(self.S), self.npar)) - 1
+ self._E = E
+ self._approxParameters["E"] = self.E
+ if (hasattr(self, "_S")
+ and self.E >= np.sum(hashI(np.prod(self.S), self.npar))):
+ RROMPyWarning("Prescribed S is too small. Decreasing E.")
+ self.E = -1
+ if hasattr(self, "_M"): self.M = self.M
+ if hasattr(self, "_N"): self.N = self.N
+
@property
def robustTol(self):
"""Value of tolerance for robust Pade' denominator management."""
return self._robustTol
@robustTol.setter
def robustTol(self, robustTol):
if robustTol < 0.:
RROMPyWarning(("Overriding prescribed negative robustness "
"tolerance to 0."))
robustTol = 0.
self._robustTol = robustTol
self._approxParameters["robustTol"] = self.robustTol
@property
def S(self):
"""Value of S."""
return self._S
@S.setter
def S(self, S):
GenericDistributedApproximant.S.fset(self, S)
- self.E = np.sum(hashI(np.prod(self.S), self.npar)) - 1
if hasattr(self, "_M"): self.M = self.M
if hasattr(self, "_N"): self.N = self.N
+ if hasattr(self, "_E"): self.E = self.E
def resetSamples(self):
"""Reset samples."""
super().resetSamples()
self._musUniqueCN = None
self._derIdxs = None
self._reorder = None
def _setupInterpolationIndices(self):
"""Setup parameters for polyvander."""
+ RROMPyAssert(self._mode,
+ message = "Cannot setup interpolation indices.")
if self._musUniqueCN is None or len(self._reorder) != len(self.mus):
self._musUniqueCN, musIdxsTo, musIdxs, musCount = (
self.centerNormalize(self.mus).unique(return_index = True,
return_inverse = True,
return_counts = True))
self._musUnique = self.mus[musIdxsTo]
self._derIdxs = [None] * len(self._musUniqueCN)
self._reorder = np.empty(len(musIdxs), dtype = int)
filled = 0
for j, cnt in enumerate(musCount):
self._derIdxs[j] = nextDerivativeIndices([], self.mus.shape[1],
cnt)
jIdx = np.nonzero(musIdxs == j)[0]
self._reorder[jIdx] = np.arange(filled, filled + cnt)
filled += cnt
def _setupDenominator(self):
"""Compute Pade' denominator."""
+ RROMPyAssert(self._mode, message = "Cannot setup denominator.")
if self.verbosity >= 7:
verbosityDepth("INIT", "Starting computation of denominator.",
timestamp = self.timestamp)
while self.N > 0:
invD = self._computeInterpolantInverseBlocks()
if self.POD:
ev, eV = self.findeveVGQR(self.samplingEngine.RPOD, invD)
else:
ev, eV = self.findeveVGExplicit(self.samplingEngine.samples,
invD)
newParams = checkRobustTolerance(ev, self.N, self.robustTol)
if not newParams:
break
self.approxParameters = newParams
if self.N <= 0:
self._N = 0
eV = np.ones((1, 1))
if self.verbosity >= 7:
verbosityDepth("DEL", "Done computing denominator.",
timestamp = self.timestamp)
q = np.zeros(tuple([self.N + 1] * self.npar), dtype = eV.dtype)
for j in range(eV.shape[0]):
q[tuple(hashI(j, self.npar))] = eV[j, 0]
return q
def _setupNumerator(self):
"""Compute Pade' numerator."""
+ RROMPyAssert(self._mode, message = "Cannot setup numerator.")
if self.verbosity >= 7:
verbosityDepth("INIT", "Starting computation of numerator.",
timestamp = self.timestamp)
Qevaldiag = np.zeros((len(self.mus), len(self.mus)),
dtype = np.complex)
verb = self.trainedModel.verbosity
self.trainedModel.verbosity = 0
self._setupInterpolationIndices()
idxGlob = 0
for j, derIdxs in enumerate(self._derIdxs):
nder = len(derIdxs)
idxLoc = np.arange(len(self.mus))[(self._reorder >= idxGlob)
* (self._reorder < idxGlob + nder)]
idxGlob += nder
Qval = [0] * nder
for der in range(nder):
derIdx = hashI(der, self.npar)
Qval[der] = (self.trainedModel.getQVal(
self._musUnique[j], derIdx,
scl = np.power(self.scaleFactor, -1.))
/ multifactorial(derIdx))
for derU, derUIdx in enumerate(derIdxs):
for derQ, derQIdx in enumerate(derIdxs):
diffIdx = [x - y for (x, y) in zip(derUIdx, derQIdx)]
if all([x >= 0 for x in diffIdx]):
diffj = hashD(diffIdx)
Qevaldiag[idxLoc[derU], idxLoc[derQ]] = Qval[diffj]
self.trainedModel.verbosity = verb
while self.M >= 0:
fitVander, _, argIdxs = homogeneizedpolyvander(self._musUniqueCN,
self.M, self.polybasis,
self._derIdxs, self._reorder,
scl = np.power(self.scaleFactor, -1.))
fitVander = fitVander[:, argIdxs]
fitOut = customFit(fitVander, Qevaldiag, full = True,
rcond = self.interpRcond)
if self.verbosity >= 5:
condfit = fitOut[1][2][0] / fitOut[1][2][-1]
verbosityDepth("MAIN", ("Fitting {} samples with degree {} "
"through {}... Conditioning of LS "
"system: {:.4e}.").format(
fitVander.shape[0], self.M,
polyfitname(self.polybasis),
condfit),
timestamp = self.timestamp)
if fitOut[1][1] == fitVander.shape[1]:
P = fitOut[0]
break
RROMPyWarning("Polyfit is poorly conditioned. Reducing M by 1.")
self.M -= 1
if self.M < 0:
raise RROMPyException(("Instability in computation of numerator. "
"Aborting."))
if self.verbosity >= 7:
verbosityDepth("DEL", "Done computing numerator.",
timestamp = self.timestamp)
p = np.zeros(tuple([self.M + 1] * self.npar) + (P.shape[1],),
dtype = P.dtype)
for j in range(P.shape[0]):
p[tuple(hashI(j, self.npar))] = P[j, :]
return p.T
def setupApprox(self):
"""
Compute Pade' interpolant.
SVD-based robust eigenvalue management.
"""
if self.checkComputedApprox():
return
RROMPyAssert(self._mode, message = "Cannot setup approximant.")
if self.verbosity >= 5:
verbosityDepth("INIT", "Setting up {}.". format(self.name()),
timestamp = self.timestamp)
self.computeScaleFactor()
self.computeSnapshots()
if self.trainedModel is None:
self.trainedModel = tModel()
self.trainedModel.verbosity = self.verbosity
self.trainedModel.timestamp = self.timestamp
data = TrainedModelData(self.trainedModel.name(), self.mu0,
self.samplingEngine.samples,
self.HFEngine.rescalingExp)
data.polytype = self.polybasis
data.scaleFactor = self.scaleFactor
data.mus = copy(self.mus)
self.trainedModel.data = data
else:
self.trainedModel = self.trainedModel
self.trainedModel.data.projMat = copy(self.samplingEngine.samples)
if self.N > 0:
Q = self._setupDenominator()
else:
Q = np.ones(1, dtype = np.complex)
self.trainedModel.data.Q = copy(Q)
P = self._setupNumerator()
if self.POD:
P = np.tensordot(self.samplingEngine.RPOD, P, axes = ([-1], [0]))
self.trainedModel.data.P = copy(P)
self.trainedModel.data.approxParameters = copy(self.approxParameters)
if self.verbosity >= 5:
verbosityDepth("DEL", "Done setting up approximant.",
timestamp = self.timestamp)
def _computeInterpolantInverseBlocks(self) -> List[Np2D]:
"""
Compute inverse factors for minimal interpolant target functional.
"""
RROMPyAssert(self._mode, message = "Cannot solve eigenvalue problem.")
self._setupInterpolationIndices()
- eStart = hashD([self.E] + [0] * (self.npar - 1))
- eEnd = hashD([self.E + 1] + [0] * (self.npar - 1))
- TE, _, argIdxs = homogeneizedpolyvander(self._musUniqueCN, self.E,
- self.polybasis, self._derIdxs, self._reorder,
- scl = np.power(self.scaleFactor, -1.))
- TE = TE[:, argIdxs].T
- RHS = np.zeros((TE.shape[0], eEnd - eStart))
- RHS[range(eStart, eEnd), range(eEnd - eStart)] = 1.
- fitOut = customFit(TE, RHS, full = True, rcond = self.interpRcond)
- if self.verbosity >= 5:
- condfit = fitOut[1][2][0] / fitOut[1][2][-1]
- verbosityDepth("MAIN", ("Fitting {} samples with degree {} "
- "through {}... Conditioning of LS "
- "system: {:.4e}.").format(
- TE.shape[1], self.E,
+ while self.E >= 0:
+ eWidth = (hashD([self.E + 1] + [0] * (self.npar - 1))
+ - hashD([self.E] + [0] * (self.npar - 1)))
+ TE, _, argIdxs = homogeneizedpolyvander(self._musUniqueCN,
+ self.E, self.polybasis,
+ self._derIdxs, self._reorder,
+ scl = np.power(self.scaleFactor, -1.))
+ fitOut = customPInv(TE[:, argIdxs], rcond = self.interpRcond,
+ full = True)
+ if self.verbosity >= 5:
+ condfit = fitOut[1][1][0] / fitOut[1][1][-1]
+ verbosityDepth("MAIN", ("Fitting {} samples with degree {} "
+ "through {}... Conditioning of "
+ "pseudoinverse system: {:.4e}.")\
+ .format(TE.shape[0], self.E,
polyfitname(self.polybasis),
condfit),
- timestamp = self.timestamp)
- self._fitinv = fitOut[0][:, -1]
+ timestamp = self.timestamp)
+ if fitOut[1][0] == len(argIdxs):
+ self._fitinv = fitOut[0][- eWidth : , :]
+ break
+ RROMPyWarning("Polyfit is poorly conditioned. Reducing E by 1.")
+ self.E -= 1
+ if self.E < 0:
+ raise RROMPyException(("Instability in computation of "
+ "denominator. Aborting."))
TN, _, argIdxs = homogeneizedpolyvander(self._musUniqueCN, self.N,
self.polybasis, self._derIdxs, self._reorder,
scl = np.power(self.scaleFactor, -1.))
TN = TN[:, argIdxs]
- invD = [None] * (eEnd - eStart)
- for k in range(eEnd - eStart):
- pseudoInv = np.diag(fitOut[0][:, k])
+ invD = [None] * (eWidth)
+ for k in range(eWidth):
+ pseudoInv = np.diag(self._fitinv[k, :])
idxGlob = 0
for j, derIdxs in enumerate(self._derIdxs):
nder = len(derIdxs)
idxGlob += nder
- idxLoc = np.arange(len(self.mus))[
- (self._reorder >= idxGlob - nder)
- * (self._reorder < idxGlob)]
if nder > 1:
- invLoc = fitOut[0][idxLoc, k]
+ idxLoc = np.arange(len(self.mus))[
+ (self._reorder >= idxGlob - nder)
+ * (self._reorder < idxGlob)]
+ invLoc = self._fitinv[k, idxLoc]
pseudoInv[np.ix_(idxLoc, idxLoc)] = 0.
for diffj, diffjIdx in enumerate(derIdxs):
for derQ, derQIdx in enumerate(derIdxs):
derUIdx = [x - y for (x, y) in
zip(diffjIdx, derQIdx)]
if all([x >= 0 for x in derUIdx]):
derU = hashD(derUIdx)
pseudoInv[idxLoc[derU], idxLoc[derQ]] = (
invLoc[diffj])
invD[k] = pseudoInv.dot(TN)
return invD
def findeveVGExplicit(self, sampleE:sampList,
invD:List[Np2D]) -> Tuple[Np1D, Np2D]:
"""
Compute explicitly eigenvalues and eigenvectors of Pade' denominator
matrix.
"""
RROMPyAssert(self._mode, message = "Cannot solve eigenvalue problem.")
nEnd = invD[0].shape[1]
- eStart = hashD([self.E] + [0] * (self.npar - 1))
- eEnd = hashD([self.E + 1] + [0] * (self.npar - 1))
+ eWidth = len(invD)
if self.verbosity >= 10:
verbosityDepth("INIT", "Building gramian matrix.",
timestamp = self.timestamp)
gramian = self.HFEngine.innerProduct(sampleE, sampleE)
G = np.zeros((nEnd, nEnd), dtype = np.complex)
- for k in range(eEnd - eStart):
+ for k in range(eWidth):
G += invD[k].T.conj().dot(gramian.dot(invD[k]))
if self.verbosity >= 10:
verbosityDepth("DEL", "Done building gramian.",
timestamp = self.timestamp)
if self.verbosity >= 7:
verbosityDepth("INIT", ("Solving eigenvalue problem for "
"gramian matrix."),
timestamp = self.timestamp)
ev, eV = np.linalg.eigh(G)
if self.verbosity >= 5:
try: condev = ev[-1] / ev[0]
except: condev = np.inf
verbosityDepth("MAIN", ("Solved eigenvalue problem of "
"size {} with condition number "
"{:.4e}.").format(nEnd, condev),
timestamp = self.timestamp)
if self.verbosity >= 7:
verbosityDepth("DEL", "Done solving eigenvalue problem.",
timestamp = self.timestamp)
return ev, eV
def findeveVGQR(self, RPODE:Np2D, invD:List[Np2D]) -> Tuple[Np1D, Np2D]:
"""
Compute eigenvalues and eigenvectors of Pade' denominator matrix
through SVD of R factor.
"""
RROMPyAssert(self._mode, message = "Cannot solve eigenvalue problem.")
nEnd = invD[0].shape[1]
- eStart = hashD([self.E] + [0] * (self.npar - 1))
- eEnd = hashD([self.E + 1] + [0] * (self.npar - 1))
+ S = RPODE.shape[0]
+ eWidth = len(invD)
if self.verbosity >= 10:
verbosityDepth("INIT", "Building half-gramian matrix stack.",
timestamp = self.timestamp)
- Rstack = np.zeros((RPODE.shape[0] * (eEnd - eStart), nEnd),
- dtype = np.complex)
- for k in range(eEnd - eStart):
- Rstack[k * RPODE.shape[0] : (k + 1) * RPODE.shape[0], :] =\
- RPODE.dot(invD[k])
+ Rstack = np.zeros((S * eWidth, nEnd), dtype = np.complex)
+ for k in range(eWidth):
+ Rstack[k * S : (k + 1) * S, :] = RPODE.dot(invD[k])
if self.verbosity >= 10:
verbosityDepth("DEL", "Done building half-gramian.",
timestamp = self.timestamp)
if self.verbosity >= 7:
verbosityDepth("INIT", ("Solving svd for square root of "
"gramian matrix."),
timestamp = self.timestamp)
_, s, eV = np.linalg.svd(Rstack, full_matrices = False)
ev = s[::-1]
eV = eV[::-1, :].T.conj()
if self.verbosity >= 5:
try: condev = s[0] / s[-1]
except: condev = np.inf
verbosityDepth("MAIN", ("Solved svd problem of size {} x "
"{} with condition number "
- "{:.4e}.").format(*Rstack.shape,
- condev),
+ "{:.4e}.").format(*Rstack.shape, condev),
timestamp = self.timestamp)
if self.verbosity >= 7:
verbosityDepth("DEL", "Done solving svd.",
timestamp = self.timestamp)
return ev, eV
def centerNormalize(self, mu : paramList = [],
mu0 : paramVal = None) -> paramList:
"""
Compute normalized parameter to be plugged into approximant.
Args:
mu: Parameter(s) 1.
mu0: Parameter(s) 2. If None, set to self.mu0.
Returns:
Normalized parameter.
"""
return self.trainedModel.centerNormalize(mu, mu0)
def getResidues(self) -> Np1D:
"""
Obtain approximant residues.
Returns:
Matrix with residues as columns.
"""
return self.trainedModel.getResidues()
diff --git a/rrompy/reduction_methods/distributed/rb_distributed.py b/rrompy/reduction_methods/distributed/rb_distributed.py
index 2c56a75..a7dfa03 100644
--- a/rrompy/reduction_methods/distributed/rb_distributed.py
+++ b/rrompy/reduction_methods/distributed/rb_distributed.py
@@ -1,223 +1,206 @@
# Copyright (C) 2018 by the RROMPy authors
#
# This file is part of RROMPy.
#
# RROMPy is free software: you can redistribute it and/or modify
# it under the terms of the GNU Lesser General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# RROMPy is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU Lesser General Public License for more details.
#
# You should have received a copy of the GNU Lesser General Public License
# along with RROMPy. If not, see .
#
from copy import deepcopy as copy
import numpy as np
from .generic_distributed_approximant import GenericDistributedApproximant
from rrompy.reduction_methods.trained_model import TrainedModelRB as tModel
from rrompy.reduction_methods.trained_model import TrainedModelData
from rrompy.reduction_methods.base.rb_utils import projectAffineDecomposition
from rrompy.utilities.base.types import (Np1D, Np2D, List, Tuple, DictAny,
HFEng, paramVal)
-from rrompy.utilities.base import purgeDict, verbosityDepth
-from rrompy.utilities.exception_manager import RROMPyWarning, RROMPyException
+from rrompy.utilities.base import verbosityDepth
+from rrompy.utilities.exception_manager import (RROMPyWarning, RROMPyException,
+ RROMPyAssert)
__all__ = ['RBDistributed']
class RBDistributed(GenericDistributedApproximant):
"""
ROM RB approximant computation for parametric problems.
Args:
HFEngine: HF problem solver.
mu0(optional): Default parameter. Defaults to 0.
approxParameters(optional): Dictionary containing values for main
parameters of approximant. Recognized keys are:
- - 'muBounds': list of bounds for parameter values; defaults to
- [0, 1];
+ - 'POD': whether to compute POD of snapshots; defaults to True;
- 'S': total number of samples current approximant relies upon;
- - 'sampler': sample point generator; defaults to uniform sampler on
- muBounds;
+ - 'sampler': sample point generator;
- 'R': rank for Galerkin projection; defaults to prod(S).
Defaults to empty dict.
homogeneized(optional): Whether to homogeneize Dirichlet BCs. Defaults
to False.
verbosity(optional): Verbosity level. Defaults to 10.
Attributes:
HFEngine: HF problem solver.
mu0: Default parameter.
mus: Array of snapshot parameters.
homogeneized: Whether to homogeneize Dirichlet BCs.
approxRadius: Dummy radius of approximant (i.e. distance from mu0 to
farthest sample point).
approxParameters: Dictionary containing values for main parameters of
approximant. Recognized keys are in parameterList.
- parameterList: Recognized keys of approximant parameters:
- - 'POD': whether to compute POD of snapshots;
- - 'muBounds': list of bounds for parameter values;
+ parameterListSoft: Recognized keys of soft approximant parameters:
+ - 'POD': whether to compute POD of snapshots.
+ - 'R': rank for Galerkin projection.
+ parameterListCritical: Recognized keys of critical approximant
+ parameters:
- 'S': total number of samples current approximant relies upon;
- 'sampler': sample point generator;
- - 'R': rank for Galerkin projection.
- extraApproxParameters: List of approxParameters keys in addition to
- mother class's.
POD: Whether to compute POD of snapshots.
- muBounds: list of bounds for parameter values.
S: Number of solution snapshots over which current approximant is
based upon.
sampler: Sample point generator.
R: Rank for Galerkin projection.
+ muBounds: list of bounds for parameter values.
samplingEngine: Sampling engine.
uHF: High fidelity solution(s) with parameter(s) lastSolvedHF as
sampleList.
lastSolvedHF: Parameter(s) corresponding to last computed high fidelity
solution(s) as parameterList.
uAppReduced: Reduced approximate solution(s) with parameter(s)
lastSolvedApp as sampleList.
lastSolvedAppReduced: Parameter(s) corresponding to last computed
reduced approximate solution(s) as parameterList.
uApp: Approximate solution(s) with parameter(s) lastSolvedApp as
sampleList.
lastSolvedApp: Parameter(s) corresponding to last computed approximate
solution(s) as parameterList.
As: List of sparse matrices (in CSC format) representing coefficients
of linear system matrix wrt theta(mu).
bs: List of numpy vectors representing coefficients of linear system
RHS wrt theta(mu).
thetaAs: List of callables representing coefficients of linear system
matrix wrt mu.
thetabs: List of callables representing coefficients of linear system
RHS wrt mu.
ARBs: List of sparse matrices (in CSC format) representing coefficients
of compressed linear system matrix wrt theta(mu).
bRBs: List of numpy vectors representing coefficients of compressed
linear system RHS wrt theta(mu).
"""
def __init__(self, HFEngine:HFEng, mu0 : paramVal = None,
approxParameters : DictAny = {}, homogeneized : bool = False,
verbosity : int = 10, timestamp : bool = True):
self._preInit()
- self._addParametersToList(["R"])
+ self._addParametersToList(["R"], [1])
super().__init__(HFEngine = HFEngine, mu0 = mu0,
approxParameters = approxParameters,
homogeneized = homogeneized,
verbosity = verbosity, timestamp = timestamp)
if self.verbosity >= 10:
verbosityDepth("INIT", "Computing affine blocks of system.",
timestamp = self.timestamp)
self.As = self.HFEngine.affineLinearSystemA(self.mu0)
self.bs = self.HFEngine.affineLinearSystemb(self.mu0,
self.homogeneized)
if self.verbosity >= 10:
verbosityDepth("DEL", "Done computing affine blocks.",
timestamp = self.timestamp)
self._postInit()
@property
- def approxParameters(self):
- """
- Value of approximant parameters. Its assignment may change M, N and S.
- """
- return self._approxParameters
- @approxParameters.setter
- def approxParameters(self, approxParams):
- approxParameters = purgeDict(approxParams, self.parameterList,
- dictname = self.name() + ".approxParameters",
- baselevel = 1)
- approxParametersCopy = purgeDict(approxParameters, ["R"], True, True,
- baselevel = 1)
- GenericDistributedApproximant.approxParameters.fset(self,
- approxParametersCopy)
- keyList = list(approxParameters.keys())
- if "R" in keyList:
- self.R = approxParameters["R"]
- elif hasattr(self, "_R") and self._R is not None:
- self.R = self.R
- else:
- self.R = np.prod(self.S)
+ def S(self):
+ """Value of S."""
+ return self._S
+ @S.setter
+ def S(self, S):
+ GenericDistributedApproximant.S.fset(self, S)
+ if not hasattr(self, "_R"): self._R = np.prod(self.S)
@property
def R(self):
"""Value of R. Its assignment may change S."""
return self._R
@R.setter
def R(self, R):
if R < 0: raise RROMPyException("R must be non-negative.")
self._R = R
self._approxParameters["R"] = self.R
if hasattr(self, "_S") and np.prod(self.S) < self.R:
RROMPyWarning("Prescribed S is too small. Decreasing R.")
self.R = np.prod(self.S)
def setupApprox(self):
"""Compute RB projection matrix."""
if self.checkComputedApprox():
return
+ RROMPyAssert(self._mode, message = "Cannot setup approximant.")
if self.verbosity >= 5:
verbosityDepth("INIT", "Setting up {}.". format(self.name()),
timestamp = self.timestamp)
self.computeSnapshots()
if self.verbosity >= 7:
verbosityDepth("INIT", "Computing projection matrix.",
timestamp = self.timestamp)
if self.POD:
U, _, _ = np.linalg.svd(self.samplingEngine.RPOD,
full_matrices = False)
pMat = self.samplingEngine.samples.dot(U[:, : self.R])
else:
pMat = self.samplingEngine.samples[: self.R]
if self.trainedModel is None:
self.trainedModel = tModel()
self.trainedModel.verbosity = self.verbosity
self.trainedModel.timestamp = self.timestamp
data = TrainedModelData(self.trainedModel.name(), self.mu0,
pMat, self.HFEngine.rescalingExp)
data.thetaAs = self.HFEngine.affineWeightsA(self.mu0)
data.thetabs = self.HFEngine.affineWeightsb(self.mu0,
self.homogeneized)
- data.ARBs, data.bRBs = self.assembleReducedSystem(pMat)
data.mus = copy(self.mus)
self.trainedModel.data = data
else:
self.trainedModel = self.trainedModel
- pMatOld = self.trainedModel.data.projMat
- Sold = pMatOld.shape[1]
- ARBs, bRBs = self.assembleReducedSystem(pMat[:, Sold :], pMatOld)
- self.trainedModel.data.ARBs = ARBs
- self.trainedModel.data.bRBs = bRBs
self.trainedModel.data.projMat = copy(pMat)
+ ARBs, bRBs = self.assembleReducedSystem(pMat)
+ self.trainedModel.data.ARBs = ARBs
+ self.trainedModel.data.bRBs = bRBs
+
if self.verbosity >= 7:
verbosityDepth("DEL", "Done computing projection matrix.",
timestamp = self.timestamp)
self.trainedModel.data.approxParameters = copy(self.approxParameters)
if self.verbosity >= 5:
verbosityDepth("DEL", "Done setting up approximant.",
timestamp = self.timestamp)
def assembleReducedSystem(self, pMat : Np2D = None, pMatOld : Np2D = None)\
-> Tuple[List[Np2D], List[Np1D]]:
"""Build affine blocks of RB linear system through projections."""
if pMat is None:
self.setupApprox()
ARBs = self.trainedModel.data.ARBs
bRBs = self.trainedModel.data.bRBs
else:
if self.verbosity >= 10:
verbosityDepth("INIT", "Projecting affine terms of HF model.",
timestamp = self.timestamp)
ARBsOld = None if pMatOld is None else self.trainedModel.data.ARBs
bRBsOld = None if pMatOld is None else self.trainedModel.data.bRBs
ARBs, bRBs = projectAffineDecomposition(self.As, self.bs, pMat,
ARBsOld, bRBsOld, pMatOld)
if self.verbosity >= 10:
verbosityDepth("DEL", "Done projecting affine terms.",
timestamp = self.timestamp)
return ARBs, bRBs
diff --git a/rrompy/reduction_methods/distributed_greedy/generic_distributed_greedy_approximant.py b/rrompy/reduction_methods/distributed_greedy/generic_distributed_greedy_approximant.py
index 6f0bf3a..f4c223c 100644
--- a/rrompy/reduction_methods/distributed_greedy/generic_distributed_greedy_approximant.py
+++ b/rrompy/reduction_methods/distributed_greedy/generic_distributed_greedy_approximant.py
@@ -1,654 +1,591 @@
# Copyright (C) 2018 by the RROMPy authors
#
# This file is part of RROMPy.
#
# RROMPy is free software: you can redistribute it and/or modify
# it under the terms of the GNU Lesser General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# RROMPy is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU Lesser General Public License for more details.
#
# You should have received a copy of the GNU Lesser General Public License
# along with RROMPy. If not, see .
#
from copy import deepcopy as copy
import numpy as np
from rrompy.reduction_methods.distributed.generic_distributed_approximant \
import GenericDistributedApproximant
from rrompy.utilities.base.types import (Np1D, Np2D, DictAny, HFEng, Tuple,
List, normEng, paramVal, paramList,
sampList)
-from rrompy.utilities.base import purgeDict, verbosityDepth
+from rrompy.utilities.base import verbosityDepth
from rrompy.solver import normEngine
from rrompy.utilities.exception_manager import (RROMPyException, RROMPyAssert,
RROMPyWarning)
from rrompy.parameter import checkParameterList, emptyParameterList
__all__ = ['GenericDistributedGreedyApproximant']
def pruneSamples(mus:paramList, badmus:paramList,
tol : float = 1e-8) -> paramList:
"""Remove from mus all the elements which are too close to badmus."""
if len(badmus) == 0: return mus
musNp = np.array(mus(0))
badmus = np.array(badmus(0))
proximity = np.min(np.abs(musNp.reshape(-1, 1)
- np.tile(badmus.reshape(1, -1), [len(mus), 1])),
axis = 1).flatten()
idxPop = np.arange(len(mus))[proximity <= tol]
for i, j in enumerate(idxPop):
mus.pop(j - i)
return mus
class GenericDistributedGreedyApproximant(GenericDistributedApproximant):
"""
ROM greedy interpolant computation for parametric problems
(ABSTRACT).
Args:
HFEngine: HF problem solver.
mu0(optional): Default parameter. Defaults to 0.
approxParameters(optional): Dictionary containing values for main
parameters of approximant. Recognized keys are:
- 'POD': whether to compute POD of snapshots; defaults to True;
- - 'muBounds': list of bounds for parameter values; defaults to
- [0, 1];
- - 'S': number of starting training points; defaults to 2;
- - 'sampler': sample point generator; defaults to uniform sampler on
- muBounds;
+ - 'S': number of starting training points;
+ - 'sampler': sample point generator;
- 'greedyTol': uniform error tolerance for greedy algorithm;
defaults to 1e-2;
- 'interactive': whether to interactively terminate greedy
algorithm; defaults to False;
- 'maxIter': maximum number of greedy steps; defaults to 1e2;
- 'refinementRatio': ratio of test points to be exhausted before
test set refinement; defaults to 0.2;
- - 'nTestPoints': number of test points; defaults to maxIter /
- refinementRatio;
- - 'trainSetGenerator': training sample points generator; defaults
- to Chebyshev sampler within muBounds.
+ - 'nTestPoints': number of test points; defaults to 5e2;
+ - 'trainSetGenerator': training sample points generator.
Defaults to empty dict.
homogeneized(optional): Whether to homogeneize Dirichlet BCs. Defaults
to False.
verbosity(optional): Verbosity level. Defaults to 10.
Attributes:
HFEngine: HF problem solver.
mu0: Default parameter.
mus: Array of snapshot parameters.
homogeneized: Whether to homogeneize Dirichlet BCs.
approxParameters: Dictionary containing values for main parameters of
approximant. Recognized keys are in parameterList.
- parameterList: Recognized keys of approximant parameters:
- - 'POD': whether to compute POD of snapshots;
- - 'muBounds': list of bounds for parameter values;
- - 'S': number of starting training points;
- - 'sampler': sample point generator;
+ parameterListSoft: Recognized keys of soft approximant parameters:
+ - 'POD': whether to compute POD of snapshots.
- 'greedyTol': uniform error tolerance for greedy algorithm;
- 'interactive': whether to interactively terminate greedy
algorithm;
- 'maxIter': maximum number of greedy steps;
- 'refinementRatio': ratio of test points to be exhausted before
test set refinement;
- - 'nTestPoints': number of test points;
+ - 'nTestPoints': number of test points.
+ parameterListCritical: Recognized keys of critical approximant
+ parameters:
+ - 'S': total number of samples current approximant relies upon;
+ - 'sampler': sample point generator;
- 'trainSetGenerator': training sample points generator.
- extraApproxParameters: List of approxParameters keys in addition to
- mother class's.
POD: whether to compute POD of snapshots.
- muBounds: list of bounds for parameter values.
S: number of test points.
sampler: Sample point generator.
greedyTol: uniform error tolerance for greedy algorithm.
+ interactive: whether to interactively terminate greedy algorithm.
maxIter: maximum number of greedy steps.
refinementRatio: ratio of training points to be exhausted before
training set refinement.
nTestPoints: number of starting training points.
trainSetGenerator: training sample points generator.
- robustTol: tolerance for robust Pade' denominator management.
+ muBounds: list of bounds for parameter values.
samplingEngine: Sampling engine.
estimatorNormEngine: Engine for estimator norm computation.
uHF: High fidelity solution(s) with parameter(s) lastSolvedHF as
sampleList.
lastSolvedHF: Parameter(s) corresponding to last computed high fidelity
solution(s) as parameterList.
uAppReduced: Reduced approximate solution(s) with parameter(s)
lastSolvedApp as sampleList.
lastSolvedAppReduced: Parameter(s) corresponding to last computed
reduced approximate solution(s) as parameterList.
uApp: Approximate solution(s) with parameter(s) lastSolvedApp as
sampleList.
lastSolvedApp: Parameter(s) corresponding to last computed approximate
solution(s) as parameterList.
"""
TOL_INSTABILITY = 1e-6
def __init__(self, HFEngine:HFEng, mu0 : paramVal = None,
approxParameters : DictAny = {}, homogeneized : bool = False,
verbosity : int = 10, timestamp : bool = True):
self._preInit()
+ from rrompy.parameter.parameter_sampling import QuadratureSampler as QS
self._addParametersToList(["greedyTol", "interactive", "maxIter",
- "refinementRatio", "nTestPoints",
- "trainSetGenerator"])
+ "refinementRatio", "nTestPoints"],
+ [1e-2, False, 1e2, .2, 5e2],
+ ["trainSetGenerator"],
+ [QS([[0], [1]], "UNIFORM")])
+ del QS
super().__init__(HFEngine = HFEngine, mu0 = mu0,
approxParameters = approxParameters,
homogeneized = homogeneized, verbosity = verbosity,
timestamp = timestamp)
RROMPyAssert(self.HFEngine.npar, 1, "Parameter dimension")
self._postInit()
- @property
- def approxParameters(self):
- """Value of approximant parameters. Its assignment may change S."""
- return self._approxParameters
- @approxParameters.setter
- def approxParameters(self, approxParams):
- approxParameters = purgeDict(approxParams, self.parameterList,
- dictname = self.name() + ".approxParameters",
- baselevel = 1)
- approxParametersCopy = purgeDict(approxParameters,
- ["greedyTol", "interactive",
- "maxIter", "refinementRatio",
- "nTestPoints", "trainSetGenerator"],
- True, True, baselevel = 1)
- GenericDistributedApproximant.approxParameters.fset(self,
- approxParametersCopy)
- keyList = list(approxParameters.keys())
- if "greedyTol" in keyList:
- self.greedyTol = approxParameters["greedyTol"]
- elif not hasattr(self, "_greedyTol") or self.greedyTol is None:
- self.greedyTol = 1e-2
- if "interactive" in keyList:
- self.interactive = approxParameters["interactive"]
- elif not hasattr(self, "interactive") or self.interactive is None:
- self.interactive = False
- if "maxIter" in keyList:
- self.maxIter = approxParameters["maxIter"]
- elif not hasattr(self, "_maxIter") or self.maxIter is None:
- self.maxIter = 1e2
- if "refinementRatio" in keyList:
- self.refinementRatio = approxParameters["refinementRatio"]
- elif (not hasattr(self, "_refinementRatio")
- or self.refinementRatio is None):
- self.refinementRatio = 0.2
- if "nTestPoints" in keyList:
- self.nTestPoints = approxParameters["nTestPoints"]
- elif (not hasattr(self, "_nTestPoints")
- or self.nTestPoints is None):
- self.nTestPoints = np.int(np.ceil(self.maxIter
- / self.refinementRatio))
- if "trainSetGenerator" in keyList:
- self.trainSetGenerator = approxParameters["trainSetGenerator"]
- elif (not hasattr(self, "_trainSetGenerator")
- or self.trainSetGenerator is None):
- from rrompy.parameter.parameter_sampling import QuadratureSampler
- self.trainSetGenerator = QuadratureSampler(self.muBounds,
- "CHEBYSHEV")
- del QuadratureSampler
-
@property
def greedyTol(self):
"""Value of greedyTol."""
return self._greedyTol
@greedyTol.setter
def greedyTol(self, greedyTol):
if greedyTol < 0:
raise RROMPyException("greedyTol must be non-negative.")
if hasattr(self, "_greedyTol") and self.greedyTol is not None:
greedyTolold = self.greedyTol
else:
greedyTolold = -1
self._greedyTol = greedyTol
self._approxParameters["greedyTol"] = self.greedyTol
if greedyTolold != self.greedyTol:
self.resetSamples()
+ @property
+ def interactive(self):
+ """Value of interactive."""
+ return self._interactive
+ @interactive.setter
+ def interactive(self, interactive):
+ self._interactive = interactive
+
@property
def maxIter(self):
"""Value of maxIter."""
return self._maxIter
@maxIter.setter
def maxIter(self, maxIter):
if maxIter <= 0: raise RROMPyException("maxIter must be positive.")
if hasattr(self, "_maxIter") and self.maxIter is not None:
maxIterold = self.maxIter
else:
maxIterold = -1
self._maxIter = maxIter
self._approxParameters["maxIter"] = self.maxIter
if maxIterold != self.maxIter:
self.resetSamples()
@property
def refinementRatio(self):
"""Value of refinementRatio."""
return self._refinementRatio
@refinementRatio.setter
def refinementRatio(self, refinementRatio):
if refinementRatio <= 0. or refinementRatio > 1.:
raise RROMPyException(("refinementRatio must be between 0 "
"(excluded) and 1."))
if (hasattr(self, "_refinementRatio")
and self.refinementRatio is not None):
refinementRatioold = self.refinementRatio
else:
refinementRatioold = -1
self._refinementRatio = refinementRatio
self._approxParameters["refinementRatio"] = self.refinementRatio
if refinementRatioold != self.refinementRatio:
self.resetSamples()
@property
def nTestPoints(self):
"""Value of nTestPoints."""
return self._nTestPoints
@nTestPoints.setter
def nTestPoints(self, nTestPoints):
if nTestPoints <= 0:
raise RROMPyException("nTestPoints must be positive.")
if not np.isclose(nTestPoints, np.int(nTestPoints)):
raise RROMPyException("nTestPoints must be an integer.")
nTestPoints = np.int(nTestPoints)
if hasattr(self, "_nTestPoints") and self.nTestPoints is not None:
nTestPointsold = self.nTestPoints
else:
nTestPointsold = -1
self._nTestPoints = nTestPoints
self._approxParameters["nTestPoints"] = self.nTestPoints
if nTestPointsold != self.nTestPoints:
self.resetSamples()
@property
def trainSetGenerator(self):
"""Value of trainSetGenerator."""
return self._trainSetGenerator
@trainSetGenerator.setter
def trainSetGenerator(self, trainSetGenerator):
if 'generatePoints' not in dir(trainSetGenerator):
raise RROMPyException("trainSetGenerator type not recognized.")
if (hasattr(self, '_trainSetGenerator')
and self.trainSetGenerator is not None):
trainSetGeneratorOld = self.trainSetGenerator
self._trainSetGenerator = trainSetGenerator
self._approxParameters["trainSetGenerator"] = self.trainSetGenerator
if (not 'trainSetGeneratorOld' in locals()
or trainSetGeneratorOld != self.trainSetGenerator):
self.resetSamples()
def resetSamples(self):
"""Reset samples."""
super().resetSamples()
self._mus = emptyParameterList()
def initEstimatorNormEngine(self, normEngn : normEng = None):
"""Initialize estimator norm engine."""
if (normEngn is not None or not hasattr(self, "estimatorNormEngine")
or self.estimatorNormEngine is None):
if normEngn is None:
if not hasattr(self.HFEngine, "energyNormMatrix"):
self.HFEngine.buildEnergyNormForm()
estimatorEnergyMatrix = self.HFEngine.energyNormMatrix
else:
if hasattr(normEngn, "buildEnergyNormForm"):
if not hasattr(normEngn, "energyNormMatrix"):
normEngn.buildEnergyNormForm()
estimatorEnergyMatrix = normEngn.energyNormMatrix
else:
estimatorEnergyMatrix = normEngn
self.estimatorNormEngine = normEngine(estimatorEnergyMatrix)
def errorEstimator(self, mus:paramList) -> List[complex]:
"""
Standard residual-based error estimator with explicit residual
computation.
"""
self.setupApprox()
if self.HFEngine.nbs == 1:
RHS = self.getRHS(mus[0], homogeneized = self.homogeneized)
RHSNorm = self.estimatorNormEngine.norm(RHS)
res = self.getRes(mus, homogeneized = self.homogeneized)
err = self.estimatorNormEngine.norm(res) / RHSNorm
else:
res = self.getRes(mus, homogeneized = self.homogeneized)
RHS = self.getRHS(mus, homogeneized = self.homogeneized)
err = (self.estimatorNormEngine.norm(res)
/ self.estimatorNormEngine.norm(RHS))
return np.abs(err)
def getMaxErrorEstimator(self, mus:paramList,
plot : bool = False) -> Tuple[Np1D, int, float]:
"""
Compute maximum of (and index of maximum of) error estimator over given
parameters.
"""
errorEstTest = self.errorEstimator(mus)
idxMaxEst = np.argmax(errorEstTest)
maxEst = errorEstTest[idxMaxEst]
if plot and not np.all(np.isinf(errorEstTest)):
musre = mus.re(0)
from matplotlib import pyplot as plt
plt.figure()
plt.semilogy(musre, errorEstTest, 'k')
plt.semilogy([musre[0], musre[-1]], [self.greedyTol] * 2, 'r--')
plt.semilogy(self.mus.re(0),
2. * self.greedyTol * np.ones(len(self.mus)), '*m')
plt.semilogy(musre[idxMaxEst], maxEst, 'xr')
plt.grid()
plt.show()
plt.close()
return errorEstTest, idxMaxEst, maxEst
def greedyNextSample(self, muidx:int, plotEst : bool = False)\
-> Tuple[Np1D, int, float, paramVal]:
"""Compute next greedy snapshot of solution map."""
RROMPyAssert(self._mode, message = "Cannot add greedy sample.")
mu = copy(self.muTest[muidx])
self.muTest.pop(muidx)
if self.verbosity >= 2:
verbosityDepth("MAIN", ("Adding {}-th sample point at {} to "
"training set.").format(
self.samplingEngine.nsamples + 1, mu),
timestamp = self.timestamp)
self.mus.append(mu)
self.samplingEngine.nextSample(mu, homogeneized = self.homogeneized)
errorEstTest, muidx, maxErrorEst = self.getMaxErrorEstimator(
self.muTest, plotEst)
return errorEstTest, muidx, maxErrorEst, self.muTest[muidx]
def _preliminaryTraining(self):
"""Initialize starting snapshots of solution map."""
RROMPyAssert(self._mode, message = "Cannot start greedy algorithm.")
self.computeScaleFactor()
if self.samplingEngine.nsamples > 0:
return
if self.verbosity >= 2:
verbosityDepth("INIT", "Starting computation of snapshots.",
timestamp = self.timestamp)
self.resetSamples()
self.mus = self.trainSetGenerator.generatePoints(self.S)
muLast = copy(self.mus[-1])
self.mus.pop()
muTestBase = self.sampler.generatePoints(self.nTestPoints)
if len(self.mus) > 0:
if self.verbosity >= 2:
verbosityDepth("MAIN",
("Adding first {} samples point at {} to "
"training set.").format(np.prod(self.S) - 1,
self.mus),
timestamp = self.timestamp)
self.samplingEngine.iterSample(self.mus,
homogeneized = self.homogeneized)
muTestBase = pruneSamples(muTestBase, self.mus,
1e-10 * self.scaleFactor[0]).sort()
self.muTest = emptyParameterList()
self.muTest.reset((len(muTestBase) + 1, self.mus.shape[1]))
self.muTest[: -1] = muTestBase
self.muTest[-1] = muLast
def _enrichTestSet(self, nTest:int):
"""Add extra elements to test set."""
-
+ RROMPyAssert(self._mode, message = "Cannot enrich test set.")
muTestExtra = self.sampler.generatePoints(2 * nTest)
muTotal = copy(self.mus)
muTotal.append(self.muTest)
muTestExtra = pruneSamples(muTestExtra, muTotal,
1e-10 * self.scaleFactor[0])
muTestNew = np.empty(len(self.muTest) + len(muTestExtra),
dtype = np.complex)
muTestNew[: len(self.muTest)] = self.muTest(0)
muTestNew[len(self.muTest) :] = muTestExtra(0)
self.muTest = checkParameterList(muTestNew.sort(), self.npar)
if self.verbosity >= 5:
verbosityDepth("MAIN", "Enriching test set by {} elements.".format(
len(muTestExtra)),
timestamp = self.timestamp)
def greedy(self, plotEst : bool = False):
"""Compute greedy snapshots of solution map."""
RROMPyAssert(self._mode, message = "Cannot start greedy algorithm.")
if self.samplingEngine.nsamples > 0:
return
self._preliminaryTraining()
nTest = self.nTestPoints
errorEstTest, muidx, maxErrorEst, mu = self.greedyNextSample(-1,
plotEst)
if self.verbosity >= 2:
verbosityDepth("MAIN", ("Uniform testing error estimate "
"{:.4e}.").format(maxErrorEst),
timestamp = self.timestamp)
trainedModelOld = copy(self.trainedModel)
while (self.samplingEngine.nsamples < self.maxIter
and maxErrorEst > self.greedyTol):
if (1. - self.refinementRatio) * nTest > len(self.muTest):
self._enrichTestSet(nTest)
nTest = len(self.muTest)
muTestOld, maxErrorEstOld = self.muTest, maxErrorEst
errorEstTest, muidx, maxErrorEst, mu = self.greedyNextSample(
muidx, plotEst)
if self.verbosity >= 2:
verbosityDepth("MAIN", ("Uniform testing error estimate "
"{:.4e}.").format(maxErrorEst),
timestamp = self.timestamp)
if (np.isnan(maxErrorEst) or np.isinf(maxErrorEst)
or maxErrorEstOld < maxErrorEst * self.TOL_INSTABILITY):
RROMPyWarning(("Instability in a posteriori estimator. "
"Starting preemptive greedy loop termination."))
maxErrorEst = maxErrorEstOld
self.muTest = muTestOld
self.mus = self.mus[:-1]
self.samplingEngine.popSample()
self.trainedModel.data = copy(trainedModelOld.data)
break
trainedModelOld.data = copy(self.trainedModel.data)
if (self.interactive and maxErrorEst <= self.greedyTol):
verbosityDepth("MAIN", ("Required tolerance {} achieved. Want "
"to decrease greedyTol and continue? "
"Y/N").format(self.greedyTol),
timestamp = self.timestamp, end = "")
increasemaxIter = input()
if increasemaxIter.upper() == "Y":
verbosityDepth("MAIN", "Reducing value of greedyTol...",
timestamp = self.timestamp)
while maxErrorEst <= self._greedyTol:
self._greedyTol *= .5
if (self.interactive
and self.samplingEngine.nsamples >= self.maxIter):
verbosityDepth("MAIN", ("Maximum number of iterations {} "
"reached. Want to increase maxIter "
"and continue? Y/N").format(
self.maxIter),
timestamp = self.timestamp, end = "")
increasemaxIter = input()
if increasemaxIter.upper() == "Y":
verbosityDepth("MAIN", "Doubling value of maxIter...",
timestamp = self.timestamp)
self._maxIter *= 2
if self.verbosity >= 2:
verbosityDepth("DEL", ("Done computing snapshots (final snapshot "
"count: {}).").format(
self.samplingEngine.nsamples),
timestamp = self.timestamp)
def checkComputedApprox(self) -> bool:
"""
Check if setup of new approximant is not needed.
Returns:
True if new setup is not needed. False otherwise.
"""
return (super().checkComputedApprox()
and len(self.mus) == self.trainedModel.data.projMat.shape[1])
def assembleReducedResidualGramian(self, pMat:sampList):
"""
Build residual gramian of reduced linear system through projections.
"""
self.initEstimatorNormEngine()
if (not hasattr(self.trainedModel.data, "gramian")
or self.trainedModel.data.gramian is None):
gramian = self.estimatorNormEngine.innerProduct(pMat, pMat)
else:
Sold = self.trainedModel.data.gramian.shape[0]
S = len(self.mus)
if Sold > S:
gramian = self.trainedModel.data.gramian[: S, : S]
else:
idxOld = list(range(Sold))
idxNew = list(range(Sold, S))
gramian = np.empty((S, S), dtype = np.complex)
gramian[: Sold, : Sold] = self.trainedModel.data.gramian
gramian[: Sold, Sold :] = (
self.estimatorNormEngine.innerProduct(pMat(idxNew),
pMat(idxOld)))
gramian[Sold :, : Sold] = gramian[: Sold, Sold :].T.conj()
gramian[Sold :, Sold :] = (
self.estimatorNormEngine.innerProduct(pMat(idxNew),
pMat(idxNew)))
self.trainedModel.data.gramian = gramian
def assembleReducedResidualBlocksbb(self, bs:List[Np1D],
scaling : float = 1.):
"""
Build blocks (of type bb) of reduced linear system through projections.
"""
self.initEstimatorNormEngine()
nbs = len(bs)
if (not hasattr(self.trainedModel.data, "resbb")
or self.trainedModel.data.resbb is None):
resbb = np.empty((nbs, nbs), dtype = np.complex)
for i in range(nbs):
Mbi = scaling ** i * bs[i]
resbb[i, i] = self.estimatorNormEngine.innerProduct(Mbi, Mbi)
for j in range(i):
Mbj = scaling ** j * bs[j]
resbb[i, j] = self.estimatorNormEngine.innerProduct(Mbj,
Mbi)
for i in range(nbs):
for j in range(i + 1, nbs):
resbb[i, j] = resbb[j, i].conj()
self.trainedModel.data.resbb = resbb
def assembleReducedResidualBlocksAb(self, As:List[Np2D], bs:List[Np1D],
pMat:sampList, scaling : float = 1.):
"""
Build blocks (of type Ab) of reduced linear system through projections.
"""
self.initEstimatorNormEngine()
nAs = len(As)
nbs = len(bs)
S = len(self.mus)
if (not hasattr(self.trainedModel.data, "resAb")
or self.trainedModel.data.resAb is None):
if not isinstance(pMat, (np.ndarray,)): pMat = pMat.data
resAb = np.empty((nbs, S, nAs), dtype = np.complex)
for j in range(nAs):
MAj = scaling ** (j + 1) * As[j].dot(pMat)
for i in range(nbs):
Mbi = scaling ** (i + 1) * bs[i]
resAb[i, :, j] = self.estimatorNormEngine.innerProduct(MAj,
Mbi)
else:
Sold = self.trainedModel.data.resAb.shape[1]
if Sold == S: return
if Sold > S:
resAb = self.trainedModel.data.resAb[:, : S, :]
else:
if not isinstance(pMat, (np.ndarray,)): pMat = pMat.data
resAb = np.empty((nbs, S, nAs), dtype = np.complex)
resAb[:, : Sold, :] = self.trainedModel.data.resAb
for j in range(nAs):
MAj = scaling ** (j + 1) * As[j].dot(pMat[:, Sold :])
for i in range(nbs):
Mbi = scaling ** (i + 1) * bs[i]
resAb[i, Sold :, j] = (
self.estimatorNormEngine.innerProduct(MAj, Mbi))
self.trainedModel.data.resAb = resAb
def assembleReducedResidualBlocksAA(self, As:List[Np2D], pMat:sampList,
- scaling : float = 1.,
- basic : bool = False):
+ scaling : float = 1.):
"""
Build blocks (of type AA) of reduced linear system through projections.
"""
self.initEstimatorNormEngine()
nAs = len(As)
S = len(self.mus)
if (not hasattr(self.trainedModel.data, "resAA")
or self.trainedModel.data.resAA is None):
if not isinstance(pMat, (np.ndarray,)): pMat = pMat.data
- if basic:
- MAEnd = scaling ** nAs * As[-1].dot(pMat)
- resAA = self.estimatorNormEngine.innerProduct(MAEnd, MAEnd)
- else:
- resAA = np.empty((S, nAs, S, nAs), dtype = np.complex)
- for i in range(nAs):
- MAi = scaling ** (i + 1) * As[i].dot(pMat)
- resAA[:, i, :, i] = (
+ resAA = np.empty((S, nAs, S, nAs), dtype = np.complex)
+ for i in range(nAs):
+ MAi = scaling ** (i + 1) * As[i].dot(pMat)
+ resAA[:, i, :, i] = (
self.estimatorNormEngine.innerProduct(MAi, MAi))
- for j in range(i):
- MAj = scaling ** (j + 1) * As[j].dot(pMat)
- resAA[:, i, :, j] = (
+ for j in range(i):
+ MAj = scaling ** (j + 1) * As[j].dot(pMat)
+ resAA[:, i, :, j] = (
self.estimatorNormEngine.innerProduct(MAj, MAi))
- for i in range(nAs):
- for j in range(i + 1, nAs):
- resAA[:, i, :, j] = resAA[:, j, :, i].T.conj()
+ for i in range(nAs):
+ for j in range(i + 1, nAs):
+ resAA[:, i, :, j] = resAA[:, j, :, i].T.conj()
else:
Sold = self.trainedModel.data.resAA.shape[0]
if Sold == S: return
if Sold > S:
- if basic:
- resAA = self.trainedModel.data.resAA[: S, : S]
- else:
- resAA = self.trainedModel.data.resAA[: S, :, : S, :]
+ resAA = self.trainedModel.data.resAA[: S, :, : S, :]
else:
if not isinstance(pMat, (np.ndarray,)): pMat = pMat.data
- if basic:
- resAA = np.empty((S, S), dtype = np.complex)
- resAA[: Sold, : Sold] = self.trainedModel.data.resAA
- MAi = scaling ** nAs * As[-1].dot(pMat)
- resAA[: Sold, Sold :] = (
- self.estimatorNormEngine.innerProduct(MAi[:, Sold :],
- MAi[:, : Sold]))
- resAA[Sold :, : Sold] = resAA[: Sold, Sold :].T.conj()
- resAA[Sold :, Sold :] = (
- self.estimatorNormEngine.innerProduct(MAi[:, Sold :],
- MAi[:, Sold :]))
- else:
- resAA = np.empty((S, nAs, S, nAs), dtype = np.complex)
- resAA[: Sold, :, : Sold, :] = self.trainedModel.data.resAA
- for i in range(nAs):
- MAi = scaling ** (i + 1) * As[i].dot(pMat)
- resAA[: Sold, i, Sold :, i] = (
+ resAA = np.empty((S, nAs, S, nAs), dtype = np.complex)
+ resAA[: Sold, :, : Sold, :] = self.trainedModel.data.resAA
+ for i in range(nAs):
+ MAi = scaling ** (i + 1) * As[i].dot(pMat)
+ resAA[: Sold, i, Sold :, i] = (
self.estimatorNormEngine.innerProduct(MAi[:, Sold :],
MAi[:, : Sold]))
- resAA[Sold :, i, : Sold, i] = resAA[: Sold, i,
- Sold :, i].T.conj()
- resAA[Sold :, i, Sold :, i] = (
+ resAA[Sold :, i, : Sold, i] = resAA[: Sold, i,
+ Sold :, i].T.conj()
+ resAA[Sold :, i, Sold :, i] = (
self.estimatorNormEngine.innerProduct(MAi[:, Sold :],
MAi[:, Sold :]))
- for j in range(i):
- MAj = scaling ** (j + 1) * As[j].dot(pMat)
- resAA[: Sold, i, Sold :, j] = (
+ for j in range(i):
+ MAj = scaling ** (j + 1) * As[j].dot(pMat)
+ resAA[: Sold, i, Sold :, j] = (
self.estimatorNormEngine.innerProduct(MAj[:, Sold :],
MAi[:, : Sold]))
- resAA[Sold :, i, : Sold, j] = (
+ resAA[Sold :, i, : Sold, j] = (
self.estimatorNormEngine.innerProduct(MAj[:, : Sold],
MAi[:, Sold :]))
- resAA[Sold :, i, Sold :, j] = (
+ resAA[Sold :, i, Sold :, j] = (
self.estimatorNormEngine.innerProduct(MAj[:, Sold :],
MAi[:, Sold :]))
- for i in range(nAs):
- for j in range(i + 1, nAs):
- resAA[: Sold, i, Sold :, j] = (
+ for i in range(nAs):
+ for j in range(i + 1, nAs):
+ resAA[: Sold, i, Sold :, j] = (
resAA[Sold :, j, : Sold, i].T.conj())
- resAA[Sold :, i, : Sold, j] = (
+ resAA[Sold :, i, : Sold, j] = (
resAA[: Sold, j, Sold :, i].T.conj())
- resAA[Sold :, i, Sold :, j] = (
+ resAA[Sold :, i, Sold :, j] = (
resAA[Sold :, j, Sold :, i].T.conj())
self.trainedModel.data.resAA = resAA
diff --git a/rrompy/reduction_methods/distributed_greedy/rational_interpolant_greedy.py b/rrompy/reduction_methods/distributed_greedy/rational_interpolant_greedy.py
index bbf14d2..0ec150b 100644
--- a/rrompy/reduction_methods/distributed_greedy/rational_interpolant_greedy.py
+++ b/rrompy/reduction_methods/distributed_greedy/rational_interpolant_greedy.py
@@ -1,456 +1,416 @@
# Copyright (C) 2018 by the RROMPy authors
#
# This file is part of RROMPy.
#
# RROMPy is free software: you can redistribute it and/or modify
# it under the terms of the GNU Lesser General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# RROMPy is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU Lesser General Public License for more details.
#
# You should have received a copy of the GNU Lesser General Public License
# along with RROMPy. If not, see .
#
from copy import deepcopy as copy
import numpy as np
from .generic_distributed_greedy_approximant import \
GenericDistributedGreedyApproximant
from rrompy.utilities.poly_fitting.polynomial import polybases, polydomcoeff
from rrompy.reduction_methods.distributed import RationalInterpolant
from rrompy.reduction_methods.trained_model import TrainedModelPade as tModel
from rrompy.reduction_methods.trained_model import TrainedModelData
from rrompy.utilities.base.types import Np1D, Np2D, DictAny, HFEng, paramVal
-from rrompy.utilities.base import purgeDict, verbosityDepth
+from rrompy.utilities.base import verbosityDepth
from rrompy.utilities.exception_manager import RROMPyWarning
from rrompy.utilities.exception_manager import RROMPyException, RROMPyAssert
__all__ = ['RationalInterpolantGreedy']
class RationalInterpolantGreedy(GenericDistributedGreedyApproximant,
RationalInterpolant):
"""
ROM greedy rational interpolant computation for parametric problems.
Args:
HFEngine: HF problem solver.
mu0(optional): Default parameter. Defaults to 0.
approxParameters(optional): Dictionary containing values for main
parameters of approximant. Recognized keys are:
- 'POD': whether to compute POD of snapshots; defaults to True;
- - 'muBounds': list of bounds for parameter values; defaults to
- [0, 1];
- 'S': number of starting training points;
- - 'sampler': sample point generator; defaults to uniform sampler on
- muBounds;
- - 'basis': type of basis for interpolation; allowed values include
- 'MONOMIAL', 'CHEBYSHEV' and 'LEGENDRE'; defaults to 'MONOMIAL';
- - 'Delta': difference between M and N in rational approximant;
- defaults to 0;
+ - 'sampler': sample point generator;
- 'greedyTol': uniform error tolerance for greedy algorithm;
defaults to 1e-2;
- - 'errorEstimatorKind': kind of error estimator; available values
- include 'EXACT', 'BASIC', and 'BARE'; defaults to 'EXACT';
+ - 'interactive': whether to interactively terminate greedy
+ algorithm; defaults to False;
- 'maxIter': maximum number of greedy steps; defaults to 1e2;
- 'refinementRatio': ratio of training points to be exhausted
before training set refinement; defaults to 0.2;
- - 'nTestPoints': number of test points; defaults to maxIter /
- refinementRatio;
+ - 'nTestPoints': number of test points; defaults to 5e2;
- 'trainSetGenerator': training sample points generator; defaults
to Chebyshev sampler within muBounds;
- - 'interpRcond': tolerance for interpolation via numpy.polyfit;
- defaults to None;
+ - 'polybasis': type of basis for interpolation; allowed values
+ include 'MONOMIAL', 'CHEBYSHEV' and 'LEGENDRE'; defaults to
+ 'MONOMIAL';
+ - 'Delta': difference between M and N in rational approximant;
+ defaults to 0;
+ - 'errorEstimatorKind': kind of error estimator; available values
+ include 'EXACT', 'BASIC', and 'BARE'; defaults to 'EXACT';
+ - 'interpRcond': tolerance for interpolation; defaults to None;
- 'robustTol': tolerance for robust Pade' denominator management;
defaults to 0.
Defaults to empty dict.
homogeneized(optional): Whether to homogeneize Dirichlet BCs. Defaults
to False.
verbosity(optional): Verbosity level. Defaults to 10.
Attributes:
HFEngine: HF problem solver.
mu0: Default parameter.
mus: Array of snapshot parameters.
homogeneized: Whether to homogeneize Dirichlet BCs.
approxParameters: Dictionary containing values for main parameters of
approximant. Recognized keys are in parameterList.
- parameterList: Recognized keys of approximant parameters:
- - 'POD': whether to compute POD of snapshots;
- - 'muBounds': list of bounds for parameter values;
- - 'S': number of starting training points;
- - 'sampler': sample point generator;
- - 'basis': type of basis for interpolation;
- - 'Delta': difference between M and N in rational approximant;
+ parameterListSoft: Recognized keys of soft approximant parameters:
+ - 'POD': whether to compute POD of snapshots.
- 'greedyTol': uniform error tolerance for greedy algorithm;
- - 'errorEstimatorKind': kind of error estimator;
+ - 'interactive': whether to interactively terminate greedy
+ algorithm;
- 'maxIter': maximum number of greedy steps;
- - 'refinementRatio': ratio of training points to be exhausted
- before training set refinement;
+ - 'refinementRatio': ratio of test points to be exhausted before
+ test set refinement;
- 'nTestPoints': number of test points;
- 'trainSetGenerator': training sample points generator;
- - 'interpRcond': tolerance for interpolation via numpy.polyfit;
+ - 'Delta': difference between M and N in rational approximant;
+ - 'errorEstimatorKind': kind of error estimator;
+ - 'interpRcond': tolerance for interpolation;
- 'robustTol': tolerance for robust Pade' denominator management.
- extraApproxParameters: List of approxParameters keys in addition to
- mother class's.
+ parameterListCritical: Recognized keys of critical approximant
+ parameters:
+ - 'S': total number of samples current approximant relies upon;
+ - 'sampler': sample point generator.
POD: whether to compute POD of snapshots.
- muBounds: list of bounds for parameter values.
- S: number of starting training points.
+ S: number of test points.
sampler: Sample point generator.
greedyTol: uniform error tolerance for greedy algorithm.
- errorEstimatorKind: kind of error estimator.
+ interactive: whether to interactively terminate greedy algorithm.
maxIter: maximum number of greedy steps.
refinementRatio: ratio of training points to be exhausted before
training set refinement.
nTestPoints: number of starting training points.
trainSetGenerator: training sample points generator.
- interpRcond: Tolerance for interpolation via numpy.polyfit.
- robustTol: Tolerance for robust Pade' denominator management.
+ robustTol: tolerance for robust Pade' denominator management.
+ Delta: difference between M and N in rational approximant.
+ errorEstimatorKind: kind of error estimator.
+ interpRcond: tolerance for interpolation.
+ robustTol: tolerance for robust Pade' denominator management.
+ muBounds: list of bounds for parameter values.
samplingEngine: Sampling engine.
estimatorNormEngine: Engine for estimator norm computation.
uHF: High fidelity solution(s) with parameter(s) lastSolvedHF as
sampleList.
lastSolvedHF: Parameter(s) corresponding to last computed high fidelity
solution(s) as parameterList.
uAppReduced: Reduced approximate solution(s) with parameter(s)
lastSolvedApp as sampleList.
lastSolvedAppReduced: Parameter(s) corresponding to last computed
reduced approximate solution(s) as parameterList.
uApp: Approximate solution(s) with parameter(s) lastSolvedApp as
sampleList.
lastSolvedApp: Parameter(s) corresponding to last computed approximate
solution(s) as parameterList.
"""
_allowedEstimatorKinds = ["EXACT", "BASIC", "BARE"]
def __init__(self, HFEngine:HFEng, mu0 : paramVal = None,
approxParameters : DictAny = {}, homogeneized : bool = False,
verbosity : int = 10, timestamp : bool = True):
self._preInit()
- self._addParametersToList(["polybasis", "Delta", "errorEstimatorKind",
- "interpRcond", "robustTol"])
+ self._addParametersToList(["Delta", "polybasis", "errorEstimatorKind",
+ "interpRcond", "robustTol"],
+ [0, "MONOMIAL", "EXACT", -1, 0],
+ toBeExcluded = ["E"])
super().__init__(HFEngine = HFEngine, mu0 = mu0,
approxParameters = approxParameters,
homogeneized = homogeneized,
verbosity = verbosity, timestamp = timestamp)
if self.verbosity >= 7:
verbosityDepth("INIT", "Computing Taylor blocks of system.",
timestamp = self.timestamp)
nAs = self.HFEngine.nAs - 1
nbs = max(self.HFEngine.nbs, (nAs + 1) * self.homogeneized)
self.As = [self.HFEngine.A(self.mu0, j + 1) for j in range(nAs)]
self.bs = [self.HFEngine.b(self.mu0, j, self.homogeneized)
for j in range(nbs)]
if self.verbosity >= 7:
verbosityDepth("DEL", "Done computing Taylor blocks.",
timestamp = self.timestamp)
self._postInit()
- @property
- def approxParameters(self):
- """
- Value of approximant parameters. Its assignment may change robustTol.
- """
- return self._approxParameters
- @approxParameters.setter
- def approxParameters(self, approxParams):
- approxParameters = purgeDict(approxParams, self.parameterList,
- dictname = self.name() + ".approxParameters",
- baselevel = 1)
- approxParametersCopy = purgeDict(approxParameters, ["polybasis",
- "Delta",
- "errorEstimatorKind",
- "interpRcond",
- "robustTol"],
- True, True, baselevel = 1)
- if "Delta" in list(approxParameters.keys()):
- self._Delta = approxParameters["Delta"]
- elif not hasattr(self, "_Delta") or self._Delta is None:
- self._Delta = 0
- GenericDistributedGreedyApproximant.approxParameters.fset(self,
- approxParametersCopy)
- keyList = list(approxParameters.keys())
- self.Delta = self.Delta
- if "polybasis" in keyList:
- self.polybasis = approxParameters["polybasis"]
- elif not hasattr(self, "_polybasis") or self._polybasis is None:
- self.polybasis = "MONOMIAL"
- if "errorEstimatorKind" in keyList:
- self.errorEstimatorKind = approxParameters["errorEstimatorKind"]
- elif (not hasattr(self, "_errorEstimatorKind")
- or self.errorEstimatorKind is None):
- self.errorEstimatorKind = "EXACT"
- if "interpRcond" in keyList:
- self.interpRcond = approxParameters["interpRcond"]
- elif not hasattr(self, "interpRcond") or self.interpRcond is None:
- self.interpRcond = None
- if "robustTol" in keyList:
- self.robustTol = approxParameters["robustTol"]
- elif not hasattr(self, "_robustTol") or self._robustTol is None:
- self.robustTol = 0
-
@property
def polybasis(self):
"""Value of polybasis."""
return self._polybasis
@polybasis.setter
def polybasis(self, polybasis):
try:
polybasis = polybasis.upper().strip().replace(" ","")
if polybasis not in polybases:
raise RROMPyException("Sample type not recognized.")
self._polybasis = polybasis
except:
RROMPyWarning(("Prescribed polybasis not recognized. Overriding "
"to 'MONOMIAL'."))
self._polybasis = "MONOMIAL"
self._approxParameters["polybasis"] = self.polybasis
@property
def Delta(self):
"""Value of Delta."""
return self._Delta
@Delta.setter
def Delta(self, Delta):
if not np.isclose(Delta, np.floor(Delta)):
raise RROMPyException("Delta must be an integer.")
if Delta < 0:
RROMPyWarning(("Error estimator unreliable for Delta < 0. "
"Overloading of errorEstimator is suggested."))
else:
Deltamin = (max(self.HFEngine.nbs,
self.HFEngine.nAs * self.homogeneized)
- 1 - 1 * (self.HFEngine.nAs > 1))
if Delta < Deltamin:
RROMPyWarning(("Method may be unreliable for selected Delta. "
"Suggested minimal value of Delta: {}.").format(
Deltamin))
self._Delta = Delta
self._approxParameters["Delta"] = self.Delta
@property
def errorEstimatorKind(self):
"""Value of errorEstimatorKind."""
return self._errorEstimatorKind
@errorEstimatorKind.setter
def errorEstimatorKind(self, errorEstimatorKind):
errorEstimatorKind = errorEstimatorKind.upper()
if errorEstimatorKind not in self._allowedEstimatorKinds:
RROMPyWarning(("Error estimator kind not recognized. Overriding "
"to 'EXACT'."))
errorEstimatorKind = "EXACT"
self._errorEstimatorKind = errorEstimatorKind
self._approxParameters["errorEstimatorKind"] = self.errorEstimatorKind
@property
def nTestPoints(self):
"""Value of nTestPoints."""
return self._nTestPoints
@nTestPoints.setter
def nTestPoints(self, nTestPoints):
if nTestPoints <= np.abs(self.Delta):
RROMPyWarning(("nTestPoints must be at least abs(Delta) + 1. "
"Increasing value to abs(Delta) + 1."))
nTestPoints = np.abs(self.Delta) + 1
if not np.isclose(nTestPoints, np.int(nTestPoints)):
raise RROMPyException("nTestPoints must be an integer.")
nTestPoints = np.int(nTestPoints)
if hasattr(self, "_nTestPoints") and self.nTestPoints is not None:
nTestPointsold = self.nTestPoints
else: nTestPointsold = -1
self._nTestPoints = nTestPoints
self._approxParameters["nTestPoints"] = self.nTestPoints
if nTestPointsold != self.nTestPoints:
self.resetSamples()
def _errorSamplingRatio(self, mus:Np1D, muRTest:Np1D,
muRTrain:Np1D) -> Np1D:
"""Scalar ratio in explicit error estimator."""
+ self.setupApprox()
testTile = np.tile(np.reshape(muRTest, (-1, 1)), [1, len(muRTrain)])
nodalVals = np.prod(testTile - np.reshape(muRTrain, (1, -1)), axis = 1)
denVals = self.trainedModel.getQVal(mus)
return np.abs(nodalVals / denVals)
def _RHSNorms(self, radiusb0:Np2D) -> Np1D:
"""High fidelity system RHS norms."""
+ self.assembleReducedResidualBlocks(full = False)
# 'ij,jk,ik->k', resbb, radiusb0, radiusb0.conj()
b0resb0 = np.sum(self.trainedModel.data.resbb.dot(radiusb0)
* radiusb0.conj(), axis = 0)
RHSnorms = np.power(np.abs(b0resb0), .5)
return RHSnorms
def _errorEstimatorBare(self) -> Np1D:
"""Bare residual-based error estimator."""
+ self.setupApprox()
self.assembleReducedResidualGramian(self.trainedModel.data.projMat)
pDom = self.trainedModel.data.P[:, -1]
LL = pDom.conj().dot(self.trainedModel.data.gramian.dot(pDom))
Adiag = self.As[0].diagonal()
LL = ((self.scaleFactor[0] * np.linalg.norm(Adiag)) ** 2. * LL
/ np.size(Adiag))
scalingDom = polydomcoeff(len(self.mus) - 1, self.polybasis)
return scalingDom * np.power(np.abs(LL), .5)
- def _errorEstimatorBasic(self, muTest:complex, ratioTest:complex) -> Np1D:
+ def _errorEstimatorBasic(self, muTest:paramVal, ratioTest:complex) -> Np1D:
"""Basic residual-based error estimator."""
resmu = self.HFEngine.residual(self.trainedModel.getApprox(muTest),
muTest, self.homogeneized)[0]
return np.abs(self.estimatorNormEngine.norm(resmu) / ratioTest)
def _errorEstimatorExact(self, muRTrain:Np1D, vanderBase:Np2D) -> Np1D:
"""Exact residual-based error estimator."""
+ self.setupApprox()
+ self.assembleReducedResidualBlocks(full = True)
nAs = self.HFEngine.nAs - 1
nbs = max(self.HFEngine.nbs - 1, nAs * self.homogeneized)
delta = len(self.mus) - len(self.trainedModel.data.Q)
nbsEff = max(0, nbs - delta)
momentQ = np.zeros(nbsEff, dtype = np.complex)
momentQu = np.zeros((len(self.mus), nAs), dtype = np.complex)
radiusbTen = np.zeros((nbsEff, nbsEff, vanderBase.shape[1]),
dtype = np.complex)
radiusATen = np.zeros((nAs, nAs, vanderBase.shape[1]),
dtype = np.complex)
if nbsEff > 0:
momentQ[0] = self.trainedModel.data.Q[-1]
radiusbTen[0, :, :] = vanderBase[: nbsEff, :]
momentQu[:, 0] = self.trainedModel.data.P[:, -1]
radiusATen[0, :, :] = vanderBase[: nAs, :]
Qvals = self.trainedModel.getQVal(self.mus)
for k in range(1, max(nAs, nbs * (nbsEff > 0))):
Qvals = Qvals * muRTrain
if k > delta and k < nbs:
momentQ[k - delta] = self._fitinv.dot(Qvals)
radiusbTen[k - delta, k :, :] = (
radiusbTen[0, : delta - k, :])
if k < nAs:
momentQu[:, k] = Qvals * self._fitinv
radiusATen[k, k :, :] = radiusATen[0, : - k, :]
if self.POD and nAs > 1:
momentQu[:, 1 :] = self.samplingEngine.RPOD.dot(
momentQu[:, 1 :])
radiusA = np.tensordot(momentQu, radiusATen, 1)
if nbsEff > 0:
radiusb = np.tensordot(momentQ, radiusbTen, 1)
# 'ij,jk,ik->k', resbb, radiusb, radiusb.conj()
ff = np.sum(self.trainedModel.data.resbb[delta + 1 :, delta + 1 :]\
.dot(radiusb) * radiusb.conj(), axis = 0)
# 'ijk,jkl,il->l', resAb, radiusA, radiusb.conj()
Lf = np.sum(np.tensordot(
self.trainedModel.data.resAb[delta :, :, :], radiusA, 2)
* radiusb.conj(), axis = 0)
else:
ff, Lf = 0., 0.
# 'ijkl,klt,ijt->t', resAA, radiusA, radiusA.conj()
LL = np.sum(np.tensordot(self.trainedModel.data.resAA, radiusA, 2)
* radiusA.conj(), axis = (0, 1))
scalingDom = polydomcoeff(len(self.mus) - 1, self.polybasis)
return scalingDom * np.power(np.abs(ff - 2. * np.real(Lf) + LL), .5)
def errorEstimator(self, mus:Np1D) -> Np1D:
"""Standard residual-based error estimator."""
self.setupApprox()
if (np.any(np.isnan(self.trainedModel.data.P[:, -1]))
or np.any(np.isinf(self.trainedModel.data.P[:, -1]))):
err = np.empty(len(mus))
err[:] = np.inf
return err
nAs = self.HFEngine.nAs - 1
nbs = max(self.HFEngine.nbs - 1, nAs * self.homogeneized)
muRTest = self.centerNormalize(mus)(0)
muRTrain = self.centerNormalize(self.mus)(0)
- self.assembleReducedResidualBlocks(kind = self.errorEstimatorKind)
samplingRatio = self._errorSamplingRatio(mus, muRTest, muRTrain)
vanderBase = np.polynomial.polynomial.polyvander(muRTest,
max(nAs, nbs)).T
RHSnorms = self._RHSNorms(vanderBase[: nbs + 1, :])
if self.errorEstimatorKind == "BARE":
jOpt = self._errorEstimatorBare()
elif self.errorEstimatorKind == "BASIC":
idx_muTestSample = np.argmax(samplingRatio)
- muTestSample = mus[idx_muTestSample]
- samplingRatioTestSample = samplingRatio[idx_muTestSample]
- jOpt = self._errorEstimatorBasic(muTestSample,
- samplingRatioTestSample)
+ jOpt = self._errorEstimatorBasic(mus[idx_muTestSample],
+ samplingRatio[idx_muTestSample])
else: #if self.errorEstimatorKind == "EXACT":
jOpt = self._errorEstimatorExact(muRTrain, vanderBase[: -1, :])
return jOpt * samplingRatio / RHSnorms
def setupApprox(self, plotEst : bool = False):
"""
Compute Pade' interpolant.
SVD-based robust eigenvalue management.
"""
if self.checkComputedApprox():
return
RROMPyAssert(self._mode, message = "Cannot setup approximant.")
if self.verbosity >= 5:
verbosityDepth("INIT", "Setting up {}.". format(self.name()),
timestamp = self.timestamp)
self.computeScaleFactor()
self.greedy(plotEst)
- self._N = len(self.mus) - 1
- self._M = copy(self._N)
- self.E = copy(self._N)
+ self._S = len(self.mus)
+ self._N, self._M, self._E = [self._S - 1] * 3
if self.Delta < 0:
self._M += self.Delta
else:
self._N -= self.Delta
if self.trainedModel is None:
self.trainedModel = tModel()
self.trainedModel.verbosity = self.verbosity
self.trainedModel.timestamp = self.timestamp
data = TrainedModelData(self.trainedModel.name(), self.mu0,
self.samplingEngine.samples,
self.HFEngine.rescalingExp)
data.polytype = self.polybasis
data.scaleFactor = self.scaleFactor
data.mus = copy(self.mus)
self.trainedModel.data = data
else:
self.trainedModel = self.trainedModel
self.trainedModel.data.projMat = copy(self.samplingEngine.samples)
self.trainedModel.data.mus = copy(self.mus)
if min(self.M, self.N) < 0:
if self.verbosity >= 5:
verbosityDepth("MAIN", "Minimal sample size not achieved.",
timestamp = self.timestamp)
Q = np.empty(max(self.N, 0) + 1, dtype = np.complex)
P = np.empty((len(self.mus), max(self.M, 0) + 1),
dtype = np.complex)
Q[:] = np.nan
P[:] = np.nan
self.trainedModel.data.Q = copy(Q)
self.trainedModel.data.P = copy(P)
self.trainedModel.data.approxParameters = copy(
self.approxParameters)
if self.verbosity >= 5:
verbosityDepth("DEL", "Aborting computation of approximant.",
timestamp = self.timestamp)
return
if self.N > 0:
Q = self._setupDenominator()
else:
Q = np.ones(1, dtype = np.complex)
self.trainedModel.data.Q = copy(Q)
P = self._setupNumerator()
if self.POD:
P = np.tensordot(self.samplingEngine.RPOD, P, axes = ([-1], [0]))
self.trainedModel.data.P = copy(P)
self.trainedModel.data.approxParameters = copy(self.approxParameters)
if self.verbosity >= 5:
verbosityDepth("DEL", "Done setting up approximant.",
timestamp = self.timestamp)
- def assembleReducedResidualBlocks(self, kind : str = "EXACT"):
+ def assembleReducedResidualBlocks(self, full : bool = False):
"""Build affine blocks of reduced linear system through projections."""
scaling = self.trainedModel.data.scaleFactor[0]
self.assembleReducedResidualBlocksbb(self.bs, scaling)
- if kind == "EXACT":
+ if full:
pMat = self.trainedModel.data.projMat
self.assembleReducedResidualBlocksAb(self.As, self.bs[1 :],
pMat, scaling)
- self.assembleReducedResidualBlocksAA(self.As, pMat, scaling,
- basic = (kind == "BASIC"))
+ self.assembleReducedResidualBlocksAA(self.As, pMat, scaling)
diff --git a/rrompy/reduction_methods/distributed_greedy/rb_distributed_greedy.py b/rrompy/reduction_methods/distributed_greedy/rb_distributed_greedy.py
index ab9d918..fc03fd1 100644
--- a/rrompy/reduction_methods/distributed_greedy/rb_distributed_greedy.py
+++ b/rrompy/reduction_methods/distributed_greedy/rb_distributed_greedy.py
@@ -1,262 +1,245 @@
# Copyright (C) 2018 by the RROMPy authors
#
# This file is part of RROMPy.
#
# RROMPy is free software: you can redistribute it and/or modify
# it under the terms of the GNU Lesser General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# RROMPy is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU Lesser General Public License for more details.
#
# You should have received a copy of the GNU Lesser General Public License
# along with RROMPy. If not, see .
#
import numpy as np
from copy import deepcopy as copy
from .generic_distributed_greedy_approximant import \
GenericDistributedGreedyApproximant
from rrompy.reduction_methods.distributed import RBDistributed
from rrompy.reduction_methods.trained_model import TrainedModelRB as tModel
from rrompy.reduction_methods.trained_model import TrainedModelData
from rrompy.utilities.base.types import Np1D, DictAny, HFEng, paramVal
from rrompy.utilities.base import verbosityDepth
-from rrompy.utilities.exception_manager import RROMPyException, RROMPyAssert
+from rrompy.utilities.exception_manager import RROMPyWarning, RROMPyAssert
from rrompy.parameter import checkParameterList
__all__ = ['RBDistributedGreedy']
class RBDistributedGreedy(GenericDistributedGreedyApproximant, RBDistributed):
"""
ROM greedy RB approximant computation for parametric problems.
Args:
HFEngine: HF problem solver.
mu0(optional): Default parameter. Defaults to 0.
approxParameters(optional): Dictionary containing values for main
parameters of approximant. Recognized keys are:
- 'POD': whether to compute POD of snapshots; defaults to True;
- - 'muBounds': list of bounds for parameter values; defaults to
- [0, 1];
- 'S': number of starting training points;
- - 'sampler': sample point generator; defaults to uniform sampler on
- muBounds;
+ - 'sampler': sample point generator;
- 'greedyTol': uniform error tolerance for greedy algorithm;
defaults to 1e-2;
+ - 'interactive': whether to interactively terminate greedy
+ algorithm; defaults to False;
- 'maxIter': maximum number of greedy steps; defaults to 1e2;
- - 'refinementRatio': ratio of training points to be exhausted
- before training set refinement; defaults to 0.2;
- - 'nTestPoints': number of test points; defaults to maxIter /
- refinementRatio;
+ - 'refinementRatio': ratio of test points to be exhausted before
+ test set refinement; defaults to 0.2;
+ - 'nTestPoints': number of test points; defaults to 5e2;
- 'trainSetGenerator': training sample points generator; defaults
to Chebyshev sampler within muBounds.
Defaults to empty dict.
homogeneized(optional): Whether to homogeneize Dirichlet BCs. Defaults
to False.
verbosity(optional): Verbosity level. Defaults to 10.
Attributes:
HFEngine: HF problem solver.
mu0: Default parameter.
mus: Array of snapshot parameters.
homogeneized: Whether to homogeneize Dirichlet BCs.
approxParameters: Dictionary containing values for main parameters of
approximant. Recognized keys are in parameterList.
- parameterList: Recognized keys of approximant parameters:
- - 'POD': whether to compute POD of snapshots;
- - 'muBounds': list of bounds for parameter values;
- - 'S': number of starting training points;
- - 'sampler': sample point generator;
+ parameterListSoft: Recognized keys of soft approximant parameters:
+ - 'POD': whether to compute POD of snapshots.
- 'greedyTol': uniform error tolerance for greedy algorithm;
+ - 'interactive': whether to interactively terminate greedy
+ algorithm;
- 'maxIter': maximum number of greedy steps;
- - 'refinementRatio': ratio of training points to be exhausted
- before training set refinement;
+ - 'refinementRatio': ratio of test points to be exhausted before
+ test set refinement;
- 'nTestPoints': number of test points;
- 'trainSetGenerator': training sample points generator.
- extraApproxParameters: List of approxParameters keys in addition to
- mother class's.
+ parameterListCritical: Recognized keys of critical approximant
+ parameters:
+ - 'S': total number of samples current approximant relies upon;
+ - 'sampler': sample point generator.
POD: whether to compute POD of snapshots.
- muBounds: list of bounds for parameter values.
S: number of test points.
sampler: Sample point generator.
greedyTol: uniform error tolerance for greedy algorithm.
+ interactive: whether to interactively terminate greedy algorithm.
maxIter: maximum number of greedy steps.
refinementRatio: ratio of training points to be exhausted before
training set refinement.
nTestPoints: number of starting training points.
trainSetGenerator: training sample points generator.
+ muBounds: list of bounds for parameter values.
samplingEngine: Sampling engine.
estimatorNormEngine: Engine for estimator norm computation.
uHF: High fidelity solution(s) with parameter(s) lastSolvedHF as
sampleList.
lastSolvedHF: Parameter(s) corresponding to last computed high fidelity
solution(s) as parameterList.
uAppReduced: Reduced approximate solution(s) with parameter(s)
lastSolvedApp as sampleList.
lastSolvedAppReduced: Parameter(s) corresponding to last computed
reduced approximate solution(s) as parameterList.
uApp: Approximate solution(s) with parameter(s) lastSolvedApp as
sampleList.
lastSolvedApp: Parameter(s) corresponding to last computed approximate
solution(s) as parameterList.
As: List of sparse matrices (in CSC format) representing coefficients
of linear system matrix wrt theta(mu).
bs: List of numpy vectors representing coefficients of linear system
RHS wrt theta(mu).
thetaAs: List of callables representing coefficients of linear system
matrix wrt mu.
thetabs: List of callables representing coefficients of linear system
RHS wrt mu.
ARBs: List of sparse matrices (in CSC format) representing coefficients
of compressed linear system matrix wrt theta(mu).
bRBs: List of numpy vectors representing coefficients of compressed
linear system RHS wrt theta(mu).
"""
def __init__(self, HFEngine:HFEng, mu0 : paramVal = None,
approxParameters : DictAny = {}, homogeneized : bool = False,
verbosity : int = 10, timestamp : bool = True):
self._preInit()
super().__init__(HFEngine = HFEngine, mu0 = mu0,
approxParameters = approxParameters,
homogeneized = homogeneized,
verbosity = verbosity, timestamp = timestamp)
if self.verbosity >= 10:
verbosityDepth("INIT", "Computing affine blocks of system.",
timestamp = self.timestamp)
self.As = self.HFEngine.affineLinearSystemA(self.mu0)
self.bs = self.HFEngine.affineLinearSystemb(self.mu0,
self.homogeneized)
if self.verbosity >= 10:
verbosityDepth("DEL", "Done computing affine blocks.",
timestamp = self.timestamp)
self._postInit()
@property
def R(self):
"""Value of R."""
- return self._S
+ self._R = np.prod(self._S)
+ return self._R
@R.setter
def R(self, R):
- raise RROMPyException(("R is used just to simplify inheritance, and "
- "its value cannot be changed from that of S."))
+ RROMPyWarning(("R is used just to simplify inheritance, and its value "
+ "cannot be changed from that of prod(S)."))
def errorEstimator(self, mus:Np1D) -> Np1D:
"""
Standard residual-based error estimator. Unreliable for unstable
problems (inf-sup constant is missing).
"""
self.setupApprox()
- self.assembleReducedResidualBlocks()
+ self.assembleReducedResidualBlocks(full = True)
nmus = len(mus)
nAs = self.trainedModel.data.resAA.shape[1]
nbs = self.trainedModel.data.resbb.shape[0]
thetaAs = self.trainedModel.data.thetaAs
thetabs = self.trainedModel.data.thetabs
radiusA = np.empty((len(self.mus), nAs, nmus), dtype = np.complex)
radiusb = np.empty((nbs, nmus), dtype = np.complex)
verb = self.trainedModel.verbosity
self.trainedModel.verbosity = 0
if verb >= 5:
mustr = mus
if nmus > 2:
mustr = "[{} ..({}).. {}]".format(mus[0], nmus - 2, mus[-1])
verbosityDepth("INIT", ("Computing RB solution at mu = "
"{}.").format(mustr),
timestamp = self.timestamp)
parmus, _ = checkParameterList(mus, self.npar)
uApps = self.getApproxReduced(parmus)
for j, muPL in enumerate(parmus):
mu = muPL[0]
uApp = uApps[j]
for i in range(nAs):
radiusA[:, i, j] = eval(thetaAs[i]) * uApp
for i in range(nbs):
radiusb[i, j] = eval(thetabs[i])
if verb >= 5:
verbosityDepth("DEL", "Done computing RB solution.",
timestamp = self.timestamp)
self.trainedModel.verbosity = verb
# 'ij,jk,ik->k', resbb, radiusb, radiusb.conj()
ff = np.sum(self.trainedModel.data.resbb.dot(radiusb) * radiusb.conj(),
axis = 0)
# 'ijk,jkl,il->l', resAb, radiusA, radiusb.conj()
Lf = np.sum(np.tensordot(self.trainedModel.data.resAb, radiusA, 2)
* radiusb.conj(), axis = 0)
# 'ijkl,klt,ijt->t', resAA, radiusA, radiusA.conj()
LL = np.sum(np.tensordot(self.trainedModel.data.resAA, radiusA, 2)
* radiusA.conj(), axis = (0, 1))
return np.abs((LL - 2. * np.real(Lf) + ff) / ff) ** .5
def setupApprox(self, plotEst : bool = False):
"""Compute RB projection matrix."""
if self.checkComputedApprox():
return
RROMPyAssert(self._mode, message = "Cannot setup approximant.")
if self.verbosity >= 5:
verbosityDepth("INIT", "Setting up {}.". format(self.name()),
timestamp = self.timestamp)
self.greedy(plotEst)
if self.verbosity >= 7:
verbosityDepth("INIT", "Computing projection matrix.",
timestamp = self.timestamp)
pMat = self.samplingEngine.samples
if self.trainedModel is None:
self.trainedModel = tModel()
self.trainedModel.verbosity = self.verbosity
self.trainedModel.timestamp = self.timestamp
data = TrainedModelData(self.trainedModel.name(), self.mu0,
pMat, self.HFEngine.rescalingExp)
data.thetaAs = self.HFEngine.affineWeightsA(self.mu0)
data.thetabs = self.HFEngine.affineWeightsb(self.mu0,
self.homogeneized)
- data.ARBs, data.bRBs = self.assembleReducedSystem(pMat)
- data.mus = copy(self.mus)
+ ARBs, bRBs = self.assembleReducedSystem(pMat)
self.trainedModel.data = data
else:
self.trainedModel = self.trainedModel
pMatOld = self.trainedModel.data.projMat
Sold = pMatOld.shape[1]
idxNew = list(range(Sold, pMat.shape[1]))
ARBs, bRBs = self.assembleReducedSystem(pMat(idxNew), pMatOld)
- self.trainedModel.data.ARBs = ARBs
- self.trainedModel.data.bRBs = bRBs
self.trainedModel.data.projMat = copy(pMat)
- self.trainedModel.data.mus = copy(self.mus)
+ self.trainedModel.data.mus = copy(self.mus)
+ self.trainedModel.data.ARBs = ARBs
+ self.trainedModel.data.bRBs = bRBs
if self.verbosity >= 7:
verbosityDepth("DEL", "Done computing projection matrix.",
timestamp = self.timestamp)
self.trainedModel.data.approxParameters = copy(self.approxParameters)
if self.verbosity >= 5:
verbosityDepth("DEL", "Done setting up approximant.",
timestamp = self.timestamp)
- def assembleReducedResidualBlocks(self):
+ def assembleReducedResidualBlocks(self, full : bool = False):
"""Build affine blocks of RB linear system through projections."""
- computeResbb = not hasattr(self.trainedModel.data, "resbb")
- computeResAb = (not hasattr(self.trainedModel.data, "resAb")
- or self.trainedModel.data.resAb.shape[1] != len(self.mus))
- computeResAA = (not hasattr(self.trainedModel.data, "resAA")
- or self.trainedModel.data.resAA.shape[0] != len(self.mus))
- if computeResbb or computeResAb or computeResAA:
- if self.verbosity >= 7:
- verbosityDepth("INIT", "Projecting affine terms of residual.",
- timestamp = self.timestamp)
- if computeResAb or computeResAA:
- pMat = self.trainedModel.data.projMat
- if computeResbb:
- self.assembleReducedResidualBlocksbb(self.bs)
- if computeResAb:
- self.assembleReducedResidualBlocksAb(self.As, self.bs, pMat)
- if computeResAA:
- self.assembleReducedResidualBlocksAA(self.As, pMat)
- if self.verbosity >= 7:
- verbosityDepth("DEL", ("Done setting up affine decomposition "
- "of residual."),
- timestamp = self.timestamp)
-
+ self.assembleReducedResidualBlocksbb(self.bs)
+ if full:
+ pMat = self.trainedModel.data.projMat
+ self.assembleReducedResidualBlocksAb(self.As, self.bs, pMat)
+ self.assembleReducedResidualBlocksAA(self.As, pMat)
diff --git a/rrompy/reduction_methods/trained_model/trained_model_pade.py b/rrompy/reduction_methods/trained_model/trained_model_pade.py
index cff94fd..5891875 100644
--- a/rrompy/reduction_methods/trained_model/trained_model_pade.py
+++ b/rrompy/reduction_methods/trained_model/trained_model_pade.py
@@ -1,145 +1,145 @@
# Copyright (C) 2018 by the RROMPy authors
#
# This file is part of RROMPy.
#
# RROMPy is free software: you can redistribute it and/or modify
# it under the terms of the GNU Lesser General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# RROMPy is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU Lesser General Public License for more details.
#
# You should have received a copy of the GNU Lesser General Public License
# along with RROMPy. If not, see .
#
import numpy as np
from . import TrainedModel
from rrompy.utilities.base.types import (Np1D, List, paramVal, paramList,
sampList)
from rrompy.utilities.base import verbosityDepth
from rrompy.utilities.poly_fitting.polynomial import polyval, polyroots
from rrompy.utilities.exception_manager import RROMPyAssert
from rrompy.parameter import checkParameterList
from rrompy.sampling import sampleList
__all__ = ['TrainedModelPade']
class TrainedModelPade(TrainedModel):
"""
ROM approximant evaluation for Pade' approximant.
Attributes:
Data: dictionary with all that can be pickled.
"""
def centerNormalize(self, mu : paramList = [],
mu0 : paramVal = None) -> paramList:
"""
Compute normalized parameter to be plugged into approximant.
Args:
mu: Parameter(s) 1.
mu0: Parameter(s) 2. If None, set to self.data.mu0.
Returns:
Normalized parameter.
"""
mu, _ = checkParameterList(mu, self.data.npar)
if mu0 is None: mu0 = self.data.mu0
rad = ((mu ** self.data.rescalingExp - mu0 ** self.data.rescalingExp)
/ self.data.scaleFactor)
return rad
def getPVal(self, mu : paramList = [], der : List[int] = None) -> sampList:
"""
Evaluate Pade' numerator at arbitrary parameter.
Args:
mu: Target parameter.
der(optional): Derivatives to take before evaluation.
"""
mu, _ = checkParameterList(mu, self.data.npar)
- if self.verbosity >= 10:
+ if self.verbosity >= 17:
verbosityDepth("INIT", ("Evaluating numerator at mu = "
"{}.").format(mu),
timestamp = self.timestamp)
muCenter = self.centerNormalize(mu)
p = sampleList(polyval(muCenter, self.data.P.T,
self.data.polytype, der))
- if self.verbosity >= 10:
+ if self.verbosity >= 17:
verbosityDepth("DEL", "Done evaluating numerator.",
timestamp = self.timestamp)
return p
def getQVal(self, mu:Np1D, der : List[int] = None,
scl : Np1D = None) -> Np1D:
"""
Evaluate Pade' denominator at arbitrary parameter.
Args:
mu: Target parameter.
der(optional): Derivatives to take before evaluation.
"""
mu, _ = checkParameterList(mu, self.data.npar)
- if self.verbosity >= 10:
+ if self.verbosity >= 17:
verbosityDepth("INIT", ("Evaluating denominator at mu = "
"{}.").format(mu),
timestamp = self.timestamp)
muCenter = self.centerNormalize(mu)
q = polyval(muCenter, self.data.Q, self.data.polytype, der, scl)
- if self.verbosity >= 10:
+ if self.verbosity >= 17:
verbosityDepth("DEL", "Done evaluating denominator.",
timestamp = self.timestamp)
return q
def getApproxReduced(self, mu : paramList = []) -> sampList:
"""
Evaluate reduced representation of approximant at arbitrary parameter.
Args:
mu: Target parameter.
"""
mu, _ = checkParameterList(mu, self.data.npar)
if (not hasattr(self, "lastSolvedAppReduced")
or self.lastSolvedAppReduced != mu):
- if self.verbosity >= 5:
+ if self.verbosity >= 12:
verbosityDepth("INIT", ("Evaluating approximant at mu = "
"{}.").format(mu),
timestamp = self.timestamp)
self.uAppReduced = self.getPVal(mu) / self.getQVal(mu)
- if self.verbosity >= 5:
+ if self.verbosity >= 12:
verbosityDepth("DEL", "Done evaluating approximant.",
timestamp = self.timestamp)
self.lastSolvedAppReduced = mu
return self.uAppReduced
def getPoles(self) -> Np1D:
"""
Obtain approximant poles.
Returns:
Numpy complex vector of poles.
"""
RROMPyAssert(self.data.npar, 1, "Number of parameters")
return np.power(self.data.mu0(0) ** self.data.rescalingExp[0]
+ self.data.scaleFactor
* polyroots(self.data.Q, self.data.polytype),
1. / self.data.rescalingExp[0])
def getResidues(self) -> Np1D:
"""
Obtain approximant residues.
Returns:
Numpy matrix with residues as columns.
"""
pls = self.getPoles()
poles, _ = checkParameterList(pls, 1)
res = (self.data.projMat.dot(self.getPVal(poles).data)
/ self.getQVal(poles, 1))
return pls, res
diff --git a/rrompy/reduction_methods/trained_model/trained_model_rb.py b/rrompy/reduction_methods/trained_model/trained_model_rb.py
index ce630fe..29bf5a9 100644
--- a/rrompy/reduction_methods/trained_model/trained_model_rb.py
+++ b/rrompy/reduction_methods/trained_model/trained_model_rb.py
@@ -1,113 +1,113 @@
# Copyright (C) 2018 by the RROMPy authors
#
# This file is part of RROMPy.
#
# RROMPy is free software: you can redistribute it and/or modify
# it under the terms of the GNU Lesser General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# RROMPy is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU Lesser General Public License for more details.
#
# You should have received a copy of the GNU Lesser General Public License
# along with RROMPy. If not, see .
#
import numpy as np
from scipy.linalg import eigvals
from .trained_model import TrainedModel
from rrompy.utilities.base.types import Np1D, paramList, sampList
from rrompy.utilities.base import verbosityDepth
from rrompy.utilities.exception_manager import RROMPyWarning, RROMPyAssert
from rrompy.parameter import checkParameterList
from rrompy.sampling import emptySampleList
__all__ = ['TrainedModelRB']
class TrainedModelRB(TrainedModel):
"""
ROM approximant evaluation for RB approximant.
Attributes:
Data: dictionary with all that can be pickled.
"""
def getApproxReduced(self, mu : paramList = []) -> sampList:
"""
Evaluate reduced representation of approximant at arbitrary parameter.
Args:
mu: Target parameter.
"""
mus, _ = checkParameterList(mu, self.data.npar)
if (not hasattr(self, "lastSolvedAppReduced")
or self.lastSolvedAppReduced != mus):
- if self.verbosity >= 5:
+ if self.verbosity >= 12:
verbosityDepth("INIT", ("Computing RB solution at mu = "
"{}.").format(mus),
timestamp = self.timestamp)
thetaAs, thetabs = self.data.thetaAs, self.data.thetabs
ARBs, bRBs = self.data.ARBs, self.data.bRBs
self.uAppReduced = emptySampleList()
self.uAppReduced.reset((ARBs[0].shape[0], len(mu)),
self.data.projMat.dtype)
for i, muPL in enumerate(mus):
mu = muPL[0]
- if self.verbosity >= 10:
+ if self.verbosity >= 17:
verbosityDepth("INIT", ("Assembling reduced model for mu "
"= {}.").format(mu),
timestamp = self.timestamp)
ARBmu = eval(thetaAs[0]) * ARBs[0]
bRBmu = eval(thetabs[0]) * bRBs[0]
for j in range(1, len(ARBs)):
ARBmu += eval(thetaAs[j]) * ARBs[j]
for j in range(1, len(bRBs)):
bRBmu += eval(thetabs[j]) * bRBs[j]
- if self.verbosity >= 10:
+ if self.verbosity >= 17:
verbosityDepth("DEL", "Done assembling reduced model.",
timestamp = self.timestamp)
- if self.verbosity >= 5:
+ if self.verbosity >= 15:
verbosityDepth("INIT", ("Solving reduced model for mu = "
"{}.").format(mu),
timestamp = self.timestamp)
self.uAppReduced[i] = np.linalg.solve(ARBmu, bRBmu)
- if self.verbosity >= 5:
+ if self.verbosity >= 15:
verbosityDepth("DEL", "Done solving reduced model.",
timestamp = self.timestamp)
- if self.verbosity >= 5:
+ if self.verbosity >= 12:
verbosityDepth("DEL", "Done computing RB solution.",
timestamp = self.timestamp)
self.lastSolvedAppReduced = mus
return self.uAppReduced
def getPoles(self) -> Np1D:
"""
Obtain approximant poles.
Returns:
Numpy complex vector of poles.
"""
RROMPyAssert(self.data.npar, 1, "Number of parameters")
RROMPyWarning(("Impossible to compute poles in general affine "
"parameter dependence. Results subject to "
"interpretation/rescaling, or possibly completely "
"wrong."))
ARBs = self.data.ARBs
R = ARBs[0].shape[0]
if len(ARBs) < 2:
return
A = np.eye(R * (len(ARBs) - 1), dtype = np.complex)
B = np.zeros_like(A)
A[: R, : R] = - ARBs[0]
for j in range(len(ARBs) - 1):
Aj = ARBs[j + 1]
B[: R, j * R : (j + 1) * R] = Aj
II = np.arange(R, R * (len(ARBs) - 1))
B[II, II - R] = 1.
return np.power(eigvals(A, B)
+ self.data.mu0(0, 0) ** self.data.rescalingExp[0],
1. / self.data.rescalingExp[0])
diff --git a/rrompy/sampling/base/sampling_engine_base.py b/rrompy/sampling/base/sampling_engine_base.py
index a18fcac..292204f 100644
--- a/rrompy/sampling/base/sampling_engine_base.py
+++ b/rrompy/sampling/base/sampling_engine_base.py
@@ -1,194 +1,194 @@
# Copyright (C) 2018 by the RROMPy authors
#
# This file is part of RROMPy.
#
# RROMPy is free software: you can redistribute it and/or modify
# it under the terms of the GNU Lesser General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# RROMPy is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU Lesser General Public License for more details.
#
# You should have received a copy of the GNU Lesser General Public License
# along with RROMPy. If not, see .
#
import numpy as np
from rrompy.utilities.base.types import (Np1D, HFEng, strLst, paramVal,
paramList, sampList)
from rrompy.utilities.base import verbosityDepth
from rrompy.utilities.exception_manager import RROMPyWarning
from rrompy.parameter import (emptyParameterList, checkParameter,
checkParameterList)
from rrompy.sampling import emptySampleList
__all__ = ['SamplingEngineBase']
class SamplingEngineBase:
"""HERE"""
def __init__(self, HFEngine:HFEng, verbosity : int = 10,
timestamp : bool = True):
self.verbosity = verbosity
self.timestamp = timestamp
if self.verbosity >= 10:
verbosityDepth("INIT",
"Initializing sampling engine of type {}.".format(
self.name()),
timestamp = self.timestamp)
self.HFEngine = HFEngine
if self.verbosity >= 10:
verbosityDepth("DEL", "Done initializing sampling engine.",
timestamp = self.timestamp)
def name(self) -> str:
return self.__class__.__name__
def __str__(self) -> str:
return self.name()
def __repr__(self) -> str:
return self.__str__() + " at " + hex(id(self))
def resetHistory(self):
self.samples = emptySampleList()
self.nsamples = 0
self.mus = emptyParameterList()
self._derIdxs = []
def popSample(self):
if hasattr(self, "nsamples") and self.nsamples > 1:
if self.samples.shape[1] > self.nsamples:
RROMPyWarning(("More than 'nsamples' memory allocated for "
"samples. Popping empty sample column."))
self.nsamples += 1
self.nsamples -= 1
self.samples.pop()
self.mus.pop()
else:
self.resetHistory()
def preallocateSamples(self, u:sampList, mu:paramVal, n:int):
self.samples.reset((u.shape[0], n), u.dtype)
self.samples[0] = u
mu = checkParameter(mu, self.HFEngine.npar)
self.mus.reset((n, self.HFEngine.npar))
self.mus[0] = mu[0]
@property
def HFEngine(self):
"""Value of HFEngine. Its assignment resets history."""
return self._HFEngine
@HFEngine.setter
def HFEngine(self, HFEngine):
self._HFEngine = HFEngine
self.resetHistory()
def solveLS(self, mu : paramList = [], RHS : sampList = None,
homogeneized : bool = False) -> sampList:
"""
Solve linear system.
Args:
mu: Parameter value.
Returns:
Solution of system.
"""
mu, _ = checkParameterList(mu, self.HFEngine.npar)
- if self.verbosity >= 5:
+ if self.verbosity >= 15:
verbosityDepth("INIT", "Solving HF model for mu = {}.".format(mu),
timestamp = self.timestamp)
u = self.HFEngine.solve(mu, RHS, homogeneized)
- if self.verbosity >= 5:
+ if self.verbosity >= 15:
verbosityDepth("DEL", "Done solving HF model.",
timestamp = self.timestamp)
return u
def plotSamples(self, name : str = "u", save : str = None,
what : strLst = 'all', saveFormat : str = "eps",
saveDPI : int = 100, show : bool = True, **figspecs):
"""
Do some nice plots of the samples.
Args:
name(optional): Name to be shown as title of the plots. Defaults to
'u'.
save(optional): Where to save plot(s). Defaults to None, i.e. no
saving.
what(optional): Which plots to do. If list, can contain 'ABS',
'PHASE', 'REAL', 'IMAG'. If str, same plus wildcard 'ALL'.
Defaults to 'ALL'.
saveFormat(optional): Format for saved plot(s). Defaults to "eps".
saveDPI(optional): DPI for saved plot(s). Defaults to 100.
show(optional): Whether to show figure. Defaults to True.
figspecs(optional key args): Optional arguments for matplotlib
figure creation.
"""
for j in range(self.nsamples):
self.HFEngine.plot(self.samples[j], name = "{}_{}".format(name, j),
save = save, what = what,
saveFormat = saveFormat, saveDPI = saveDPI,
show = show, **figspecs)
def outParaviewSamples(self, name : str = "u", folders : bool = True,
filename : str = "out", times : Np1D = None,
what : strLst = 'all', forceNewFile : bool = True,
filePW = None):
"""
Output samples to ParaView file.
Args:
name(optional): Base name to be used for data output.
folders(optional): Whether to split output in folders.
filename(optional): Name of output file.
times(optional): Timestamps.
what(optional): Which plots to do. If list, can contain 'MESH',
'ABS', 'PHASE', 'REAL', 'IMAG'. If str, same plus wildcard
'ALL'. Defaults to 'ALL'.
forceNewFile(optional): Whether to create new output file.
filePW(optional): Fenics File entity (for time series).
"""
if times is None: times = [0.] * self.nsamples
for j in range(self.nsamples):
self.HFEngine.outParaview(self.samples[j],
name = "{}_{}".format(name, j),
filename = "{}_{}".format(filename, j),
time = times[j], what = what,
forceNewFile = forceNewFile,
folder = folders, filePW = filePW)
def outParaviewTimeDomainSamples(self, omegas : Np1D = None,
timeFinal : Np1D = None,
periodResolution : int = 20,
name : str = "u", folders : bool = True,
filename : str = "out",
forceNewFile : bool = True):
"""
Output samples to ParaView file, converted to time domain.
Args:
omegas(optional): frequencies.
timeFinal(optional): final time of simulation.
periodResolution(optional): number of time steps per period.
name(optional): Base name to be used for data output.
folders(optional): Whether to split output in folders.
filename(optional): Name of output file.
forceNewFile(optional): Whether to create new output file.
"""
if omegas is None: omegas = np.real(self.mus)
if not isinstance(timeFinal, (list, tuple,)):
timeFinal = [timeFinal] * self.nsamples
for j in range(self.nsamples):
self.HFEngine.outParaviewTimeDomain(self.samples[j],
omega = omegas[j],
timeFinal = timeFinal[j],
periodResolution = periodResolution,
name = "{}_{}".format(name, j),
filename = "{}_{}".format(filename, j),
forceNewFile = forceNewFile,
folder = folders)
diff --git a/rrompy/sampling/linear_problem/sampling_engine_linear_pod.py b/rrompy/sampling/linear_problem/sampling_engine_linear_pod.py
index 9be02c5..2f4a100 100644
--- a/rrompy/sampling/linear_problem/sampling_engine_linear_pod.py
+++ b/rrompy/sampling/linear_problem/sampling_engine_linear_pod.py
@@ -1,84 +1,83 @@
# Copyright (C) 2018 by the RROMPy authors
#
# This file is part of RROMPy.
#
# RROMPy is free software: you can redistribute it and/or modify
# it under the terms of the GNU Lesser General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# RROMPy is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU Lesser General Public License for more details.
#
# You should have received a copy of the GNU Lesser General Public License
# along with RROMPy. If not, see .
#
import numpy as np
from rrompy.sampling.base.pod_engine import PODEngine
from .sampling_engine_linear import SamplingEngineLinear
from rrompy.utilities.base.types import Np1D, paramVal, sampList
from rrompy.utilities.base import verbosityDepth
__all__ = ['SamplingEngineLinearPOD']
class SamplingEngineLinearPOD(SamplingEngineLinear):
"""HERE"""
def resetHistory(self):
super().resetHistory()
self.RPOD = None
def popSample(self):
if hasattr(self, "nsamples") and self.nsamples > 1:
self.RPOD = self.RPOD[: -1, : -1]
super().popSample()
@property
def HFEngine(self):
"""Value of HFEngine. Its assignment resets history."""
return self._HFEngine
@HFEngine.setter
def HFEngine(self, HFEngine):
self._HFEngine = HFEngine
self.resetHistory()
self.PODEngine = PODEngine(self._HFEngine)
def preprocesssamples(self, idxs:Np1D) -> sampList:
idxMax = np.max(idxs) + 1
sampleBase = super().preprocesssamples(np.arange(idxMax))
- ##### maybe square brackets should be used below...
RPODBase = self.RPOD[: idxMax, idxs]
return sampleBase.dot(RPODBase)
def postprocessu(self, u:sampList, overwrite : bool = False) -> Np1D:
if self.verbosity >= 10:
verbosityDepth("INIT", "Starting orthogonalization.",
timestamp = self.timestamp)
ns = self.nsamples
if ns == 0:
u, r, _ = self.PODEngine.GS(u, np.empty((0, 0)))
r = r[0]
else:
u, r, _ = self.PODEngine.GS(u, self.samples(np.arange(ns)), ns)
if overwrite:
self.RPOD[: ns + 1, ns] = r
else:
if ns == 0:
self.RPOD = r.reshape((1, 1))
else:
self.RPOD=np.block([[ self.RPOD, r[:-1, None]],
[np.zeros((1, ns)), r[-1]]])
if self.verbosity >= 10:
verbosityDepth("DEL", "Done orthogonalizing.",
timestamp = self.timestamp)
return u
def preallocateSamples(self, u:Np1D, mu:paramVal, n:int):
super().preallocateSamples(u, mu, n)
r = self.RPOD
self.RPOD = np.zeros((n, n), dtype = u.dtype)
self.RPOD[0, 0] = r[0, 0]
diff --git a/rrompy/utilities/base/__init__.py b/rrompy/utilities/base/__init__.py
index c6c8528..6bcf126 100644
--- a/rrompy/utilities/base/__init__.py
+++ b/rrompy/utilities/base/__init__.py
@@ -1,53 +1,55 @@
# Copyright (C) 2018 by the RROMPy authors
#
# This file is part of RROMPy.
#
# RROMPy is free software: you can redistribute it and/or modify
# it under the terms of the GNU Lesser General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# RROMPy is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU Lesser General Public License for more details.
#
# You should have received a copy of the GNU Lesser General Public License
# along with RROMPy. If not, see .
#
from .find_dict_str_key import findDictStrKey
from .get_new_filename import getNewFilename
from .kroneckerer import kroneckerer
from .factorials import multibinom, multifactorial
from .pickle_utilities import pickleDump, pickleLoad
from .purge_dict import purgeDict
from .purge_list import purgeList
from .number_theory import (squareResonances, primeFactorize,
getLowestPrimeFactor)
+from .halton import haltonGenerate
from .sobol import sobolGenerate
from .low_discrepancy import vanderCorput, lowDiscrepancy
from . import types as Types
from .verbosity_depth import verbosityDepth
__all__ = [
'findDictStrKey',
'getNewFilename',
'kroneckerer',
'multibinom',
'multifactorial',
'pickleDump',
'pickleLoad',
'purgeDict',
'purgeList',
'squareResonances',
'primeFactorize',
'getLowestPrimeFactor',
+ 'haltonGenerate',
'sobolGenerate',
'vanderCorput',
'lowDiscrepancy',
'Types',
'verbosityDepth'
]
diff --git a/rrompy/utilities/base/halton.py b/rrompy/utilities/base/halton.py
new file mode 100644
index 0000000..509de0c
--- /dev/null
+++ b/rrompy/utilities/base/halton.py
@@ -0,0 +1,45 @@
+# Copyright (C) 2018 by the RROMPy authors
+#
+# This file is part of RROMPy.
+#
+# RROMPy is free software: you can redistribute it and/or modify
+# it under the terms of the GNU Lesser General Public License as published by
+# the Free Software Foundation, either version 3 of the License, or
+# (at your option) any later version.
+#
+# RROMPy is distributed in the hope that it will be useful,
+# but WITHOUT ANY WARRANTY; without even the implied warranty of
+# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+# GNU Lesser General Public License for more details.
+#
+# You should have received a copy of the GNU Lesser General Public License
+# along with RROMPy. If not, see .
+#
+
+import numpy as np
+
+__all__ = ['haltonGenerate']
+
+def haltonGenerate(dim, size, seed = 0, step = True):
+ seq = np.empty((size, dim), dtype = float)
+ primes = [2, 3]
+ for j in range(2, dim * (1 + 1 * step) + 1):
+ primeBase = primes[j - 1] + 2
+ while True:
+ for i in range(1, j):
+ if primeBase % primes[i] == 0: break
+ else:
+ break
+ primeBase += 2
+ primes += [primeBase]
+ base = np.array(primes[: dim])
+ stepSize = primes[dim * 2 - 1] if step else 1
+ seq = np.zeros((size, dim), dtype = float)
+ seqBase = np.tile((np.arange(seed, stepSize * size + seed, stepSize)
+ + 1).reshape(-1, 1), [1, dim])
+ powerB = 1
+ while seqBase[-1, 0] > 0:
+ seqBase, remainder = np.divmod(seqBase, base)
+ seq += remainder / np.power(base, powerB)
+ powerB += 1
+ return seq
diff --git a/rrompy/utilities/base/low_discrepancy.py b/rrompy/utilities/base/low_discrepancy.py
index 47f83ca..0dc73eb 100644
--- a/rrompy/utilities/base/low_discrepancy.py
+++ b/rrompy/utilities/base/low_discrepancy.py
@@ -1,46 +1,42 @@
# Copyright (C) 2018 by the RROMPy authors
#
# This file is part of RROMPy.
#
# RROMPy is free software: you can redistribute it and/or modify
# it under the terms of the GNU Lesser General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# RROMPy is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU Lesser General Public License for more details.
#
# You should have received a copy of the GNU Lesser General Public License
# along with RROMPy. If not, see .
#
import numpy as np
-from rrompy.utilities.base.types import Np1D
+from rrompy.utilities.base.types import List
from rrompy.utilities.exception_manager import RROMPyException
__all__ = ['vanderCorput', 'lowDiscrepancy']
-def vanderCorput(n:int) -> Np1D:
+def vanderCorput(n:int) -> List[int]:
if n <= 0:
raise RROMPyException("Only positive integers allowed.")
x = [0] * n
ln = int(np.ceil(np.log2(n)))
for j in range(n):
x[j] = int(np.binary_repr(j, width = ln)[::-1], 2)
return x
-def lowDiscrepancy(n:int) -> Np1D:
+def lowDiscrepancy(n:int, inverse : bool = False) -> List[int]:
if n <= 0:
raise RROMPyException("Only positive integers allowed.")
- x = [0] * n
- max2Pow = np.binary_repr(n)[::-1].find('1')
- max2Fac = 2 ** max2Pow
- res2 = n // max2Fac
- xBase = res2 * np.array(vanderCorput(max2Fac), dtype = np.int)
- stride = ((n - 1) // 2 - 1) * (max2Pow == 0) + 1
- for i in range(res2):
- x[i * max2Fac : (i + 1) * max2Fac] = (i * stride + xBase) % n
+ max2Fac = 2 ** int(np.ceil(np.log2(n)))
+ xBase = np.array(vanderCorput(max2Fac), dtype = np.int)
+ x = list(xBase[xBase < n])
+ if inverse: x = list(np.argsort(x))
return x
diff --git a/rrompy/utilities/poly_fitting/__init__.py b/rrompy/utilities/poly_fitting/__init__.py
index dc4d3ac..c9d4457 100644
--- a/rrompy/utilities/poly_fitting/__init__.py
+++ b/rrompy/utilities/poly_fitting/__init__.py
@@ -1,25 +1,27 @@
# Copyright (C) 2018 by the RROMPy authors
#
# This file is part of RROMPy.
#
# RROMPy is free software: you can redistribute it and/or modify
# it under the terms of the GNU Lesser General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# RROMPy is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU Lesser General Public License for more details.
#
# You should have received a copy of the GNU Lesser General Public License
# along with RROMPy. If not, see .
#
from .custom_fit import customFit
+from .custom_pinv import customPInv
__all__ = [
- 'customFit'
+ 'customFit',
+ 'customPInv'
]
diff --git a/rrompy/utilities/poly_fitting/custom_fit.py b/rrompy/utilities/poly_fitting/custom_fit.py
index f4164b7..79a9260 100644
--- a/rrompy/utilities/poly_fitting/custom_fit.py
+++ b/rrompy/utilities/poly_fitting/custom_fit.py
@@ -1,135 +1,135 @@
# Copyright (C) 2018 by the RROMPy authors
#
# This file is part of RROMPy.
#
# RROMPy is free software: you can redistribute it and/or modify
# it under the terms of the GNU Lesser General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# RROMPy is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU Lesser General Public License for more details.
#
# You should have received a copy of the GNU Lesser General Public License
# along with RROMPy. If not, see .
#
import numpy as np
import numpy.linalg as la
from rrompy.utilities.exception_manager import RROMPyException, RROMPyWarning
__all__ = ["customFit"]
-def customFit(van, y, rcond=None, full=False, w=None):
+def customFit(van, y, rcond=-1, full=False, w=None):
"""
Least-squares fit of a polynomial to data. Copied from
numpy.polynomial.polynomial.
Parameters
----------
va : array_like, shape (`M`,`deg` + 1)
Vandermonde-like matrix.
y : array_like, shape (`M`,) or (`M`, `K`)
y-coordinates of the sample points. Several sets of sample points
sharing the same x-coordinates can be (independently) fit with one
call to `polyfit` by passing in for `y` a 2-D array that contains
one data set per column.
rcond : float, optional
Relative condition number of the fit. Singular values smaller
than `rcond`, relative to the largest singular value, will be
ignored. The default value is ``len(van)*eps``, where `eps` is the
relative precision of the platform's float type, about 2e-16 in
most cases.
full : bool, optional
Switch determining the nature of the return value. When ``False``
(the default) just the coefficients are returned; when ``True``,
diagnostic information from the singular value decomposition (used
to solve the fit's matrix equation) is also returned.
w : array_like, shape (`M`,), optional
Weights. If not None, the contribution of each point
``(x[i],y[i])`` to the fit is weighted by `w[i]`. Ideally the
weights are chosen so that the errors of the products ``w[i]*y[i]``
all have the same variance. The default value is None.
Returns
-------
coef : ndarray, shape (`deg` + 1,) or (`deg` + 1, `K`)
Polynomial coefficients ordered from low to high. If `y` was 2-D,
the coefficients in column `k` of `coef` represent the polynomial
fit to the data in `y`'s `k`-th column.
[residuals, rank, singular_values, rcond] : list
These values are only returned if `full` = True
resid -- sum of squared residuals of the least squares fit
rank -- the numerical rank of the scaled Vandermonde matrix
sv -- singular values of the scaled Vandermonde matrix
rcond -- value of `rcond`.
For more details, see `linalg.lstsq`.
"""
van = np.asarray(van) + 0.0
y = np.asarray(y) + 0.0
# check arguments.
if van.ndim != 2:
raise RROMPyException("expected 2D vector for van")
if van.size == 0:
raise RROMPyException("expected non-empty vector for van")
if y.ndim < 1 or y.ndim > 2:
raise RROMPyException("expected 1D or 2D array for y")
if len(van) != len(y):
raise RROMPyException("expected van and y to have same length")
order = van.shape[1]
# set up the least squares matrices in transposed form
lhs = van.T
rhs = y.T
if isinstance(w, (str, )) and w.upper() == "AUTO":
# Determine the norms of the design matrix rows.
if issubclass(van.dtype.type, np.complexfloating):
w = np.sqrt((np.square(van.real) + np.square(van.imag)).sum(1))
else:
w = np.sqrt(np.square(van).sum(1))
w[w == 0] = 1
w = np.power(w, -1.)
if w is not None:
w = np.asarray(w) + 0.0
if w.ndim != 1:
raise RROMPyException("expected 1D vector for w")
if len(van) != len(w):
raise RROMPyException("expected van and w to have same length")
# apply weights. Don't use inplace operations as they
# can cause problems with NA.
lhs = lhs * w
rhs = rhs * w
# set rcond
- if rcond is None:
+ if rcond < 0:
rcond = len(van)*np.finfo(van.dtype).eps
# Determine the norms of the design matrix columns.
if issubclass(lhs.dtype.type, np.complexfloating):
scl = np.sqrt((np.square(lhs.real) + np.square(lhs.imag)).sum(1))
else:
scl = np.sqrt(np.square(lhs).sum(1))
scl[scl == 0] = 1
# Solve the least squares problem.
c, resids, rank, s = la.lstsq(lhs.T/scl, rhs.T, rcond)
c = (c.T/scl).T
# warn on rank reduction
if rank != order and not full:
RROMPyWarning("The fit may be poorly conditioned", stacklevel = 2)
if full:
return c, [resids, rank, s, rcond]
else:
return c
diff --git a/rrompy/hfengines/linear_problem/bidimensional/__init__.py b/rrompy/utilities/poly_fitting/custom_pinv.py
similarity index 50%
copy from rrompy/hfengines/linear_problem/bidimensional/__init__.py
copy to rrompy/utilities/poly_fitting/custom_pinv.py
index 03b8e69..45b5fbd 100644
--- a/rrompy/hfengines/linear_problem/bidimensional/__init__.py
+++ b/rrompy/utilities/poly_fitting/custom_pinv.py
@@ -1,29 +1,46 @@
# Copyright (C) 2018 by the RROMPy authors
#
# This file is part of RROMPy.
#
# RROMPy is free software: you can redistribute it and/or modify
# it under the terms of the GNU Lesser General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# RROMPy is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU Lesser General Public License for more details.
#
# You should have received a copy of the GNU Lesser General Public License
# along with RROMPy. If not, see .
#
-from .laplace_disk_gaussian_2 import LaplaceDiskGaussian2
-from .helmholtz_square_simplified_domain_problem_engine import \
- HelmholtzSquareSimplifiedDomainProblemEngine
-
-__all__ = [
- 'LaplaceDiskGaussian2',
- 'HelmholtzSquareSimplifiedDomainProblemEngine'
- ]
+from copy import deepcopy as copy
+import numpy as np
+__all__ = ["customPInv"]
+def customPInv(A, rcond=1e-15, full=False):
+ """
+ Compute the (Moore-Penrose) pseudo-inverse of a matrix.
+ Calculate the generalized inverse of a matrix using its
+ singular-value decomposition (SVD) and including all
+ *large* singular values.
+ """
+ A = A.conjugate()
+ u, s, vt = np.linalg.svd(A, full_matrices=False)
+ cutoff = rcond * np.amax(s)
+ large = s > cutoff
+
+ sinv = copy(s)
+ sinv = np.divide(1, s, where = large, out = sinv)
+ sinv[~large] = 0
+
+ res = (vt.T * sinv) @ u.T
+
+ if full:
+ return res, [np.sum(large), s, rcond]
+ else:
+ return res
diff --git a/rrompy/utilities/poly_fitting/polynomial/homogeneization.py b/rrompy/utilities/poly_fitting/polynomial/homogeneization.py
index e261241..f42d5e1 100644
--- a/rrompy/utilities/poly_fitting/polynomial/homogeneization.py
+++ b/rrompy/utilities/poly_fitting/polynomial/homogeneization.py
@@ -1,46 +1,55 @@
# Copyright (C) 2018 by the RROMPy authors
#
# This file is part of RROMPy.
#
# RROMPy is free software: you can redistribute it and/or modify
# it under the terms of the GNU Lesser General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# RROMPy is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU Lesser General Public License for more details.
#
# You should have received a copy of the GNU Lesser General Public License
# along with RROMPy. If not, see .
#
import numpy as np
from rrompy.utilities.base.types import Np1D, Np2D, Tuple, List, paramList
from rrompy.utilities.poly_fitting.polynomial import polyvander
from rrompy.parameter import checkParameterList
__all__ = ['homogeneizationMask', 'homogeneizedpolyvander']
def homogeneizationMask(degs:List[int]) -> Tuple[List[int], List[bool]]:
dim = len(degs)
N = np.prod([d + 1 for d in degs])
maskN = np.arange(N, dtype = int)
remN = np.zeros((N, dim), dtype = int)
for j in range(dim - 1, -1, -1):
remN[:, j] = maskN % (degs[j] + 1)
maskN //= degs[j] + 1
mask = np.sum(remN, axis = 1) <= min(degs)
return remN[mask], mask
def homogeneizedpolyvander(x:paramList, deg:int, basis:str,
derIdxs : List[List[List[int]]] = None,
reorder : List[int] = None, scl : Np1D = None)\
-> Tuple[Np2D, List[List[int]], List[int]]:
x, _ = checkParameterList(x)
degs = [deg] * x.shape[1]
VanBase = polyvander(x, degs, basis, derIdxs, reorder, scl)
derIdxs, mask = homogeneizationMask(degs)
- derDepth = [- np.sum(x) for x in derIdxs]
- return VanBase[:, mask], derIdxs, np.argsort(derDepth)[::-1]
+
+ ordIdxs = np.empty(len(derIdxs), dtype = int)
+ derTotal = np.array([np.sum(y) for y in derIdxs])
+ idxPrev = 0
+ rangeAux = np.arange(len(derIdxs))
+ for j in range(deg + 1):
+ idxLocal = rangeAux[derTotal == j][::-1]
+ idxPrev += len(idxLocal)
+ ordIdxs[idxPrev - len(idxLocal) : idxPrev] = idxLocal
+ return VanBase[:, mask], derIdxs, ordIdxs
+
diff --git a/setup.py b/setup.py
index fa46095..248956a 100644
--- a/setup.py
+++ b/setup.py
@@ -1,52 +1,52 @@
# Copyright (C) 2015-2018 by the RBniCS authors
#
# This file is part of RBniCS.
#
# RBniCS is free software: you can redistribute it and/or modify
# it under the terms of the GNU Lesser General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# RBniCS is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU Lesser General Public License for more details.
#
# You should have received a copy of the GNU Lesser General Public License
# along with RBniCS. If not, see .
#
import os
from setuptools import find_packages, setup
rrompy_directory = os.path.abspath(os.path.dirname(os.path.realpath(__file__)))
#rrompy_directory = os.path.join(rrompy_directory, 'rrompy')
setup(name="RROMPy",
description="Rational reduced order modelling in Python",
long_description="Rational reduced order modelling in Python",
author="Davide Pradovera",
author_email="davide.pradovera@epfl.ch",
- version="1.4",
+ version="1.5",
license="GNU Library or Lesser General Public License (LGPL)",
classifiers=[
"Development Status :: 1 - Planning"
"Intended Audience :: Developers",
"Intended Audience :: Science/Research",
"Programming Language :: Python :: 3",
"Programming Language :: Python :: 3.4",
"Programming Language :: Python :: 3.5",
"Programming Language :: Python :: 3.6",
"License :: OSI Approved :: GNU Library or Lesser General Public License (LGPL)",
"Topic :: Scientific/Engineering :: Mathematics",
"Topic :: Software Development :: Libraries :: Python Modules",
],
packages=find_packages(rrompy_directory),
setup_requires=[
"pytest-runner"
],
tests_require=[
"pytest"
],
zip_safe=False
)
diff --git a/tests/test_1_utilities/parameter_sampling.py b/tests/test_1_utilities/parameter_sampling.py
index 6e08e73..b94792e 100644
--- a/tests/test_1_utilities/parameter_sampling.py
+++ b/tests/test_1_utilities/parameter_sampling.py
@@ -1,60 +1,60 @@
# Copyright (C) 2018 by the RROMPy authors
#
# This file is part of RROMPy.
#
# RROMPy is free software: you can redistribute it and/or modify
# it under the terms of the GNU Lesser General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# RROMPy is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU Lesser General Public License for more details.
#
# You should have received a copy of the GNU Lesser General Public License
# along with RROMPy. If not, see .
#
import numpy as np
from rrompy.parameter.parameter_sampling import (ManualSampler,
QuadratureSampler, RandomSampler, FFTSampler)
from rrompy.parameter import checkParameter
def test_manual():
sampler = ManualSampler(lims = [0., 3.], points = np.linspace(0, 3, 101),
scaling = lambda x: np.power(x, 2.),
scalingInv = lambda x: np.power(x, .5))
assert sampler.name() == "ManualSampler"
x = sampler.generatePoints(10)
assert np.allclose(x(0), np.linspace(0, 3, 101)[:10], rtol = 1e-5)
def test_quadrature():
sampler = QuadratureSampler(lims = [0., 3.], kind = "CHEBYSHEV")
x = sampler.generatePoints(9)
assert np.isclose(x(0)[2], 1.5, rtol = 1e-5)
def test_random():
- sampler = RandomSampler(lims = [0., 3.], kind = "SOBOL")
- x = sampler.generatePoints(100, seed = 13432)
+ sampler = RandomSampler(lims = [0., 3.], kind = "SOBOL", seed = 13432)
+ x = sampler.generatePoints(100)
assert np.isclose(x(0)[47], 0.55609130859375, rtol = 1e-5)
def test_fft():
sampler = FFTSampler(lims = [-1., 1.])
x = sampler.generatePoints(100)
assert np.allclose(np.power(x(0), 100), 1., rtol = 1e-5)
def test_2D():
sampler = QuadratureSampler(lims = [(0., 0.), (3., 1.)],
kind = "GAUSSLEGENDRE")
x = sampler.generatePoints((9, 5))
assert sum(np.isclose(x(0), 1.5)) == 5
assert sum(np.isclose(x(1), .5)) == 9
def test_4D():
sampler = RandomSampler(lims = [tuple([0.] * 4), tuple([1.] * 4)],
- kind = "UNIFORM")
- x = sampler.generatePoints(10, seed = 1234)
+ kind = "UNIFORM", seed = 1234)
+ x = sampler.generatePoints(10)
assert x.shape[1] == 4
assert checkParameter([x[0]]) == checkParameter([(0.191519450378892,
0.622108771039832, 0.437727739007115, 0.785358583713769)])
diff --git a/tests/test_2_hfengines/helmholtz_external.py b/tests/test_2_hfengines/helmholtz_external.py
index 4dc418d..009ab89 100644
--- a/tests/test_2_hfengines/helmholtz_external.py
+++ b/tests/test_2_hfengines/helmholtz_external.py
@@ -1,64 +1,67 @@
# Copyright (C) 2018 by the RROMPy authors
#
# This file is part of RROMPy.
#
# RROMPy is free software: you can redistribute it and/or modify
# it under the terms of the GNU Lesser General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# RROMPy is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU Lesser General Public License for more details.
#
# You should have received a copy of the GNU Lesser General Public License
# along with RROMPy. If not, see .
#
+import pytest
import numpy as np
from rrompy.hfengines.linear_problem import (
HelmholtzCavityScatteringProblemEngine, HelmholtzBoxScatteringProblemEngine)
def test_helmholtz_square_scattering():
solver = HelmholtzCavityScatteringProblemEngine(kappa = 4, gamma = 2.,
n = 20, verbosity = 0)
mu = 5
uh = solver.solve(mu)[0]
- assert np.isclose(solver.norm(uh), 20.719752682674923, rtol = 1e-2)
+ assert np.isclose(solver.norm(uh), 19.9362, rtol = 1e-2)
assert np.isclose(solver.norm(solver.residual(uh, mu)[0]), 4.25056407e-13,
rtol = 1e-1)
def test_helmholtz_scattering_copy(capsys):
solver1 = HelmholtzCavityScatteringProblemEngine(kappa = 4, gamma = 2.,
n = 20, verbosity = 0)
mu = 5
uh1 = solver1.solve(mu)[0]
solver2 = HelmholtzCavityScatteringProblemEngine(kappa = 4, gamma = 2.,
n = 20, verbosity = 100)
assert solver1.As[0] is not None and solver1.bs[0] is not None
assert solver2.As[0] is None and solver2.bs[0] is None
solver2.setAs(solver1.As)
solver2.setbs(solver1.bs)
uh2 = solver2.solve(mu)[0]
assert np.allclose(uh1, uh2, rtol = 1e-8)
out, err = capsys.readouterr()
assert ("Assembling operator term" not in out
and "Assembling forcing term" not in out)
assert len(err) == 0
+@pytest.mark.xfail(raises = RuntimeError('Invalid DISPLAY variable'),
+ reason = "no graphical interface")
def test_helmholtz_box_scattering():
solver = HelmholtzBoxScatteringProblemEngine(R = 2, kappa = 10.,
theta = np.pi * 30 / 180, n = 20, verbosity = 0)
mu = 15
uh = solver.solve(mu)[0]
solver.plotmesh(show = False, figsize = (7, 7))
- assert np.isclose(solver.norm(uh), 63.98946657389119, rtol = 1e-2)
+ assert np.isclose(solver.norm(uh), 62.113, rtol = 1e-2)
assert np.isclose(solver.norm(solver.residual(uh, mu)[0]), 9.62989935e-13,
rtol = 1e-1)
from matplotlib import pyplot as plt
plt.close('all')
diff --git a/tests/test_2_hfengines/helmholtz_internal.py b/tests/test_2_hfengines/helmholtz_internal.py
index 998fa6f..00724bb 100644
--- a/tests/test_2_hfengines/helmholtz_internal.py
+++ b/tests/test_2_hfengines/helmholtz_internal.py
@@ -1,95 +1,98 @@
# Copyright (C) 2018 by the RROMPy authors
#
# This file is part of RROMPy.
#
# RROMPy is free software: you can redistribute it and/or modify
# it under the terms of the GNU Lesser General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# RROMPy is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU Lesser General Public License for more details.
#
# You should have received a copy of the GNU Lesser General Public License
# along with RROMPy. If not, see .
#
+import pytest
import os, shutil
import numpy as np
from rrompy.hfengines.linear_problem import (
HelmholtzSquareBubbleDomainProblemEngine, HelmholtzSquareBubbleProblemEngine,
HelmholtzSquareTransmissionProblemEngine)
def test_helmholtz_square_io():
solver = HelmholtzSquareBubbleProblemEngine(kappa = 4, theta = 1., n = 50,
verbosity = 0)
mu = 5
uh = solver.solve(mu)[0]
- assert np.isclose(solver.norm(uh), 70762597.99694124, rtol = 1e-3)
- assert np.isclose(solver.norm(solver.residual(uh, mu)[0]), 2.1855986e-06,
+ assert np.isclose(solver.norm(uh), 913.396, rtol = 1e-3)
+ assert np.isclose(solver.norm(solver.residual(uh, mu)[0]), 1.19934e-11,
rtol = 1e-1)
if not os.path.isdir("./.pytest_cache"): os.mkdir("./.pytest_cache")
filesOut = [x for x in os.listdir("./.pytest_cache") if
(x[-4:] == ".pvd" and x[:9] == "outSquare")]
filesOutData = [x for x in os.listdir("./.pytest_cache") if
(x[-4:] == ".vtu" and x[:9] == "outSquare")]
for fileOut in filesOut:
os.remove("./.pytest_cache/" + fileOut)
for fileOut in filesOutData:
os.remove("./.pytest_cache/" + fileOut)
solver.outParaview(uh, what = ["MESH", "ABS"],
filename = ".pytest_cache/outSquare",
forceNewFile = False)
filesOut = [x for x in os.listdir("./.pytest_cache") if
(x[-4:] == ".pvd" and x[:9] == "outSquare")]
filesOutData = [x for x in os.listdir("./.pytest_cache") if
(x[-4:] == ".vtu" and x[:9] == "outSquare")]
assert len(filesOut) == 1
assert len(filesOutData) == 1
os.remove("./.pytest_cache/" + filesOut[0])
os.remove("./.pytest_cache/" + filesOutData[0])
def test_helmholtz_transmission_io():
solver = HelmholtzSquareTransmissionProblemEngine(nT = 1, nB = 2,
theta = np.pi * 40 / 180, kappa = 4., n = 50, verbosity = 0)
mu = 5.
uh = solver.solve(mu)[0]
- assert np.isclose(solver.norm(uh), 46.4528217234862, rtol = 1e-5)
+ assert np.isclose(solver.norm(uh), 43.9268, rtol = 1e-2)
assert np.isclose(solver.norm(solver.residual(uh, mu)[0]), 3.7288565e-12,
rtol = 1e-1)
if not os.path.isdir("./.pytest_cache"): os.mkdir("./.pytest_cache")
solver.outParaviewTimeDomain(uh, omega = mu,
filename = ".pytest_cache/outTrans",
forceNewFile = False, folder = True)
filesOut = [x for x in os.listdir("./.pytest_cache/outTrans") if
(x[-4:] == ".pvd" and x[:8] == "outTrans")]
filesOutData = [x for x in os.listdir("./.pytest_cache/outTrans") if
(x[-4:] == ".vtu" and x[:8] == "outTrans")]
assert len(filesOut) == 1
assert len(filesOutData) == 20
shutil.rmtree("./.pytest_cache/outTrans")
+@pytest.mark.xfail(raises = RuntimeError('Invalid DISPLAY variable'),
+ reason = "no graphical interface")
def test_helmholtz_domain_io():
solver = HelmholtzSquareBubbleDomainProblemEngine(kappa = 4, theta = 1.,
- n = 20, mu0 = 1.5, verbosity = 0)
+ n = 10, mu0 = 1.5, verbosity = 0)
mu = 1.5
uh = solver.solve(mu)[0]
if not os.path.isdir("./.pytest_cache"): os.mkdir("./.pytest_cache")
solver.plot(uh, save = "./.pytest_cache/outDomain", show = False)
filesOut = [x for x in os.listdir("./.pytest_cache") if
(x[-4:] == ".eps" and x[:9] == "outDomain")]
assert len(filesOut) == 1
os.remove("./.pytest_cache/" + filesOut[0])
- assert np.isclose(solver.norm(uh), 9.408738562323533, rtol = 1e-2)
+ assert np.isclose(solver.norm(uh), 8.9947, rtol = 1e-2)
assert np.isclose(solver.norm(solver.residual(uh, mu)[0]), 6.14454989e-13,
rtol = 1e-1)
diff --git a/tests/test_3_reduction_methods_1D/rational_interpolant_1d.py b/tests/test_3_reduction_methods_1D/rational_interpolant_1d.py
index 908c8f7..5011114 100644
--- a/tests/test_3_reduction_methods_1D/rational_interpolant_1d.py
+++ b/tests/test_3_reduction_methods_1D/rational_interpolant_1d.py
@@ -1,69 +1,68 @@
# Copyright (C) 2018 by the RROMPy authors
#
# This file is part of RROMPy.
#
# RROMPy is free software: you can redistribute it and/or modify
# it under the terms of the GNU Lesser General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# RROMPy is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU Lesser General Public License for more details.
#
# You should have received a copy of the GNU Lesser General Public License
# along with RROMPy. If not, see .
#
import numpy as np
from matrix_fft import matrixFFT
from rrompy.reduction_methods.distributed import RationalInterpolant as RI
from rrompy.parameter.parameter_sampling import (QuadratureSampler as QS,
ManualSampler as MS)
from rrompy.parameter import checkParameterList
def test_monomials(capsys):
mu = 1.5
solver = matrixFFT()
params = {"POD": False, "M": 9, "N": 9, "S": 10, "robustTol": 1e-6,
"interpRcond": 1e-3, "polybasis": "MONOMIAL",
- "sampler": QS([1.5, 6.5], "UNIFORM"), "muBounds":[1.5, 6.5]}
+ "sampler": QS([1.5, 6.5], "UNIFORM")}
approx = RI(solver, 4., params, verbosity = 0)
approx.setupApprox()
out, err = capsys.readouterr()
- assert (("poorly conditioned. Reducing M " in out)
- and ("eigenvalues below tolerance. Reducing N " in out))
+ assert "poorly conditioned. Reducing E " in out
assert len(err) == 0
- assert np.isclose(approx.normErr(mu)[0], 8e-5, atol = 1e-4)
+ assert np.isclose(approx.normErr(mu)[0], 2.9051e-4, atol = 1e-4)
def test_well_cond():
mu = 1.5
solver = matrixFFT()
params = {"POD": True, "M": 9, "N": 9, "S": 10, "robustTol": 1e-14,
"interpRcond": 1e-10, "polybasis": "CHEBYSHEV",
"sampler": QS([1., 7.], "CHEBYSHEV")}
approx = RI(solver, 4., params, verbosity = 0)
approx.setupApprox()
poles = approx.getPoles()
for lambda_ in np.arange(1, 8):
assert np.isclose(np.min(np.abs(poles - lambda_)), 0., atol = 1e-4)
for mu in approx.mus:
assert np.isclose(approx.normErr(mu)[0], 0., atol = 1e-8)
def test_hermite():
mu = 1.5
solver = matrixFFT()
sampler0 = QS([1., 7.], "CHEBYSHEV")
points, _ = checkParameterList(np.tile(sampler0.generatePoints(4)(0), 3))
params = {"POD": True, "M": 11, "N": 11, "S": 12, "polybasis": "CHEBYSHEV",
"sampler": MS([1., 7.], points = points)}
approx = RI(solver, 4., params, verbosity = 0)
approx.setupApprox()
poles = approx.getPoles()
for lambda_ in np.arange(1, 8):
assert np.isclose(np.min(np.abs(poles - lambda_)), 0., atol = 1e-4)
for mu in approx.mus:
assert np.isclose(approx.normErr(mu)[0], 0., atol = 1e-8)
diff --git a/tests/test_3_reduction_methods_1D/rational_interpolant_greedy_1d.py b/tests/test_3_reduction_methods_1D/rational_interpolant_greedy_1d.py
index 78bbf2c..4ceb0ee 100644
--- a/tests/test_3_reduction_methods_1D/rational_interpolant_greedy_1d.py
+++ b/tests/test_3_reduction_methods_1D/rational_interpolant_greedy_1d.py
@@ -1,89 +1,94 @@
# Copyright (C) 2018 by the RROMPy authors
#
# This file is part of RROMPy.
#
# RROMPy is free software: you can redistribute it and/or modify
# it under the terms of the GNU Lesser General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# RROMPy is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU Lesser General Public License for more details.
#
# You should have received a copy of the GNU Lesser General Public License
# along with RROMPy. If not, see .
#
import numpy as np
from matrix_fft import matrixFFT
from rrompy.reduction_methods.distributed_greedy import \
RationalInterpolantGreedy as RIG
+from rrompy.parameter.parameter_sampling import QuadratureSampler as QS
def test_lax_tolerance(capsys):
mu = 2.25
solver = matrixFFT()
- params = {"POD": True, "muBounds": [1.5, 6.5], "S": 5,
+ params = {"POD": True, "sampler": QS([1.5, 6.5], "UNIFORM"), "S": 4,
"polybasis": "CHEBYSHEV", "greedyTol": 1e-2,
- "errorEstimatorKind": "bare"}
- approx = RIG(solver, 4., params, verbosity = 10)
+ "errorEstimatorKind": "bare",
+ "trainSetGenerator": QS([1.5, 6.5], "CHEBYSHEV")}
+ approx = RIG(solver, 4., params, verbosity = 100)
approx.greedy()
out, err = capsys.readouterr()
- assert "Done computing snapshots (final snapshot count: 16)." in out
+ assert "Done computing snapshots (final snapshot count: 10)." in out
assert len(err) == 0
- assert np.isclose(approx.normErr(mu)[0], 3.534746e-3, rtol = 1e-1)
+ assert np.isclose(approx.normErr(mu)[0], 2.169678e-4, rtol = 1e-1)
def test_samples_at_poles():
solver = matrixFFT()
- params = {"POD": True, "muBounds": [1.5, 6.5], "S": 4, "nTestPoints": 100,
- "polybasis": "CHEBYSHEV", "greedyTol": 1e-5,
- "errorEstimatorKind": "exact"}
+ params = {"POD": True, "sampler": QS([1.5, 6.5], "UNIFORM"), "S": 4,
+ "nTestPoints": 100, "polybasis": "CHEBYSHEV", "greedyTol": 1e-5,
+ "errorEstimatorKind": "exact",
+ "trainSetGenerator": QS([1.5, 6.5], "CHEBYSHEV")}
approx = RIG(solver, 4., params, verbosity = 0)
approx.greedy()
for mu in approx.mus:
assert np.isclose(approx.normErr(mu)[0] / (1e-15+approx.normHF(mu)[0]),
0., atol = 1e-4)
poles = approx.getPoles()
for lambda_ in range(2, 7):
assert np.isclose(np.min(np.abs(poles - lambda_)), 0., atol = 1e-3)
assert np.isclose(np.min(np.abs(np.array(approx.mus(0)) - lambda_)),
0., atol = 1e-1)
def test_maxIter():
solver = matrixFFT()
- params = {"POD": True, "muBounds": [1.5, 6.5], "S": 5, "nTestPoints": 500,
- "polybasis": "CHEBYSHEV", "greedyTol": 1e-6, "maxIter": 10,
- "errorEstimatorKind": "basic"}
+ params = {"POD": True, "sampler": QS([1.5, 6.5], "UNIFORM"),
+ "S": 5, "nTestPoints": 500, "polybasis": "CHEBYSHEV",
+ "greedyTol": 1e-6, "maxIter": 10, "errorEstimatorKind": "basic",
+ "trainSetGenerator": QS([1.5, 6.5], "CHEBYSHEV")}
approx = RIG(solver, 4., params, verbosity = 0)
approx.input = lambda: "N"
approx.greedy()
assert len(approx.mus) == 10
_, _, maxEst = approx.getMaxErrorEstimator(approx.muTest)
assert maxEst > 1e-6
def test_load_copy(capsys):
mu = 3.
solver = matrixFFT()
- params = {"POD": True, "muBounds": [1.5, 6.5], "S": 4, "nTestPoints": 100,
- "polybasis": "CHEBYSHEV", "greedyTol": 1e-5,
- "errorEstimatorKind": "exact"}
+ params = {"POD": True, "sampler": QS([1.5, 6.5], "UNIFORM"), "S": 4,
+ "nTestPoints": 100, "polybasis": "CHEBYSHEV",
+ "greedyTol": 1e-5, "errorEstimatorKind": "exact",
+ "trainSetGenerator": QS([1.5, 6.5], "CHEBYSHEV")}
approx1 = RIG(solver, 4., params, verbosity = 100)
approx1.greedy()
err1 = approx1.normErr(mu)[0]
out, err = capsys.readouterr()
assert "Solving HF model for mu =" in out
assert len(err) == 0
approx2 = RIG(solver, 4., params, verbosity = 100)
approx2.setTrainedModel(approx1)
approx2.setHF(mu, approx1.uHF)
err2 = approx2.normErr(mu)[0]
out, err = capsys.readouterr()
assert "Solving HF model for mu =" not in out
assert len(err) == 0
assert np.isclose(err1, err2, rtol = 1e-10)
diff --git a/tests/test_3_reduction_methods_1D/rational_pade_1d.py b/tests/test_3_reduction_methods_1D/rational_pade_1d.py
index 79e189f..99e9aaf 100644
--- a/tests/test_3_reduction_methods_1D/rational_pade_1d.py
+++ b/tests/test_3_reduction_methods_1D/rational_pade_1d.py
@@ -1,86 +1,86 @@
# Copyright (C) 2018 by the RROMPy authors
#
# This file is part of RROMPy.
#
# RROMPy is free software: you can redistribute it and/or modify
# it under the terms of the GNU Lesser General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# RROMPy is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU Lesser General Public License for more details.
#
# You should have received a copy of the GNU Lesser General Public License
# along with RROMPy. If not, see .
#
import os
import numpy as np
from matrix_fft import matrixFFT
from rrompy.reduction_methods.centered import RationalPade as RP
def test_rho():
mu = 1.5
mu0 = 2. + 1.j
solver = matrixFFT()
uh = solver.solve(mu)[0]
params = {"POD": False, "M": 9, "N": 10, "S": 11, "robustTol": 1e-6}
approx = RP(solver, mu0, params, verbosity = 0)
approx.setupApprox()
if not os.path.isdir("./.pytest_cache"): os.mkdir("./.pytest_cache")
filesOut = [x for x in os.listdir("./.pytest_cache") if
(x[-4:] == ".pkl" and x[:6] == "outPad")]
for fileOut in filesOut: os.remove("./.pytest_cache/" + fileOut)
fileStored = approx.storeTrainedModel(".pytest_cache/outPad")
filesOut = [x for x in os.listdir("./.pytest_cache") if
(x[-4:] == ".pkl" and x[:6] == "outPad")]
assert len(filesOut) == 1
assert filesOut[0] == fileStored[- len(filesOut[0]) :]
uhP1 = approx.getApprox(mu)[0]
errP = approx.getErr(mu)[0]
errNP = approx.normErr(mu)[0]
myerrP = uhP1 - uh
assert np.allclose(np.abs(errP - myerrP), 0., rtol = 1e-3)
assert np.isclose(solver.norm(errP), errNP, rtol = 1e-3)
resP = approx.getRes(mu)[0]
resNP = approx.normRes(mu)
assert np.isclose(solver.norm(resP), resNP, rtol = 1e-3)
assert np.allclose(np.abs(resP - (solver.b(mu) - solver.A(mu).dot(uhP1))),
0., rtol = 1e-3)
del approx
approx = RP(solver, mu0, {"S": 3}, verbosity = 0)
approx.loadTrainedModel(fileStored)
for fileOut in filesOut: os.remove("./.pytest_cache/" + fileOut)
uhP2 = approx.getApprox(mu)[0]
assert np.allclose(np.abs(uhP1 - uhP2), 0., rtol = 1e-3)
def test_E_warn(capsys):
mu = 1.5
mu0 = 2. + 1.j
solver = matrixFFT()
uh = solver.solve(mu)[0]
params = {"POD": True, "M": 14, "N": 15, "S": 10}
approx = RP(solver, mu0, params, verbosity = 0)
approx.setupApprox()
out, err = capsys.readouterr()
- assert "Prescribed S is too small. Decreasing M." in out
- assert "Prescribed S is too small. Decreasing N." in out
+ assert "Prescribed E is too small. Decreasing M." in out
+ assert "Prescribed E is too small. Decreasing N." in out
assert len(err) == 0
uhP = approx.getApprox(mu)[0]
errP = approx.getErr(mu)[0]
errNP = approx.normErr(mu)[0]
assert np.allclose(np.abs(errP - (uhP - uh)), 0., rtol = 1e-3)
assert np.isclose(errNP, 3.5197568e-07, rtol = 1e-1)
poles, ress = approx.getResidues()
condres = np.linalg.cond(solver.innerProduct(ress, ress))
assert np.isclose(condres, 192.1791778, rtol = 1e-3)
assert np.isclose(np.min(np.abs(poles - 2.)), 0., atol = 1e-3)
assert np.isclose(np.min(np.abs(poles - 1.)), 0., atol = 1e-2)
assert np.isclose(np.min(np.abs(poles - 3.)), 0., atol = 1e-2)
diff --git a/tests/test_3_reduction_methods_1D/rb_distributed_greedy_1d.py b/tests/test_3_reduction_methods_1D/rb_distributed_greedy_1d.py
index 52fb7a3..512a049 100644
--- a/tests/test_3_reduction_methods_1D/rb_distributed_greedy_1d.py
+++ b/tests/test_3_reduction_methods_1D/rb_distributed_greedy_1d.py
@@ -1,56 +1,60 @@
# Copyright (C) 2018 by the RROMPy authors
#
# This file is part of RROMPy.
#
# RROMPy is free software: you can redistribute it and/or modify
# it under the terms of the GNU Lesser General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# RROMPy is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU Lesser General Public License for more details.
#
# You should have received a copy of the GNU Lesser General Public License
# along with RROMPy. If not, see .
#
import numpy as np
from matrix_fft import matrixFFT
from rrompy.reduction_methods.distributed_greedy import RBDistributedGreedy \
as RBDG
+from rrompy.parameter.parameter_sampling import QuadratureSampler as QS
def test_lax_tolerance(capsys):
mu = 2.25
solver = matrixFFT()
- params = {"POD": True, "muBounds": [1.5, 6.5], "S": 4, "greedyTol": 1e-2}
+ params = {"POD": True, "sampler": QS([1.5, 6.5], "UNIFORM"),
+ "S": 4, "greedyTol": 1e-2,
+ "trainSetGenerator": QS([1.5, 6.5], "CHEBYSHEV")}
approx = RBDG(solver, 4., params, verbosity = 10)
approx.greedy()
out, err = capsys.readouterr()
assert "Done computing snapshots (final snapshot count: 10)." in out
assert len(err) == 0
assert len(approx.mus) == 10
_, _, maxEst = approx.getMaxErrorEstimator(approx.muTest)
assert maxEst < 1e-2
assert np.isclose(approx.normErr(mu)[0], 1.5056e-05, rtol = 1e-1)
def test_samples_at_poles():
solver = matrixFFT()
- params = {"POD": True, "muBounds": [1.5, 6.5], "S": 4, "nTestPoints": 100,
- "greedyTol": 1e-5}
+ params = {"POD": True, "sampler": QS([1.5, 6.5], "UNIFORM"),
+ "S": 4, "nTestPoints": 100, "greedyTol": 1e-5,
+ "trainSetGenerator": QS([1.5, 6.5], "CHEBYSHEV")}
approx = RBDG(solver, 4., params, verbosity = 0)
approx.greedy()
for mu in approx.mus:
assert np.isclose(approx.normErr(mu)[0] / (1e-15+approx.normHF(mu)[0]),
0., atol = 1e-4)
poles = approx.getPoles()
for lambda_ in range(2, 7):
assert np.isclose(np.min(np.abs(poles - lambda_)), 0., atol = 1e-3)
assert np.isclose(np.min(np.abs(np.array(approx.mus(0)) - lambda_)),
0., atol = 1e-1)
diff --git a/tests/test_4_reduction_methods_multiD/rational_interpolant_2d.py b/tests/test_4_reduction_methods_multiD/rational_interpolant_2d.py
index ed14275..fe75aa8 100644
--- a/tests/test_4_reduction_methods_multiD/rational_interpolant_2d.py
+++ b/tests/test_4_reduction_methods_multiD/rational_interpolant_2d.py
@@ -1,77 +1,79 @@
# Copyright (C) 2018 by the RROMPy authors
#
# This file is part of RROMPy.
#
# RROMPy is free software: you can redistribute it and/or modify
# it under the terms of the GNU Lesser General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# RROMPy is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU Lesser General Public License for more details.
#
# You should have received a copy of the GNU Lesser General Public License
# along with RROMPy. If not, see .
#
import numpy as np
from matrix_random import matrixRandom
from rrompy.reduction_methods.distributed import RationalInterpolant as RI
from rrompy.parameter.parameter_sampling import (QuadratureSampler as QS,
ManualSampler as MS)
def test_monomials(capsys):
mu = [5.05, 7.1]
mu0 = [5., 7.]
solver = matrixRandom()
uh = solver.solve(mu)[0]
params = {"POD": False, "M": 4, "N": 4, "S": [4, 4], "robustTol": 1e-6,
"interpRcond": 1e-3, "polybasis": "MONOMIAL",
"sampler": QS([[4.9, 6.85], [5.1, 7.15]], "UNIFORM")}
approx = RI(solver, mu0, params, verbosity = 0)
approx.setupApprox()
uhP1 = approx.getApprox(mu)[0]
errP = approx.getErr(mu)[0]
errNP = approx.normErr(mu)[0]
myerrP = uhP1 - uh
assert np.allclose(np.abs(errP - myerrP), 0., rtol = 1e-3)
assert np.isclose(solver.norm(errP), errNP, rtol = 1e-3)
resP = approx.getRes(mu)[0]
resNP = approx.normRes(mu)
assert np.isclose(solver.norm(resP), resNP, rtol = 1e-3)
assert np.allclose(np.abs(resP - (solver.b(mu) - solver.A(mu).dot(uhP1))),
0., rtol = 1e-3)
- assert np.isclose(errNP / solver.norm(uh), 7.537e-4, rtol = 1e-1)
+ assert np.isclose(errNP / solver.norm(uh), 5.2667e-05, rtol = 1e-1)
out, err = capsys.readouterr()
- assert ("poorly conditioned. Reducing M" in out)
+ print(out)
+ assert ("poorly conditioned. Reducing E" in out)
assert len(err) == 0
def test_well_cond():
mu = [5.05, 7.1]
mu0 = [5., 7.]
solver = matrixRandom()
params = {"POD": True, "M": 3, "N": 3, "S": [4, 4],
"interpRcond": 1e-10, "polybasis": "CHEBYSHEV",
"sampler": QS([[4.9, 6.85], [5.1, 7.15]], "UNIFORM")}
approx = RI(solver, mu0, params, verbosity = 0)
approx.setupApprox()
print(approx.normErr(mu)[0] / approx.normHF(mu)[0])
assert np.isclose(approx.normErr(mu)[0] / approx.normHF(mu)[0],
- 8.46624e-3, rtol = 1e-1)
+ 5.98695e-05, rtol = 1e-1)
def test_hermite():
mu = [5.05, 7.1]
mu0 = [5., 7.]
solver = matrixRandom()
sampler0 = QS([[4.9, 6.85], [5.1, 7.15]], "UNIFORM")
params = {"POD": True, "M": 3, "N": 3, "S": [25], "polybasis": "CHEBYSHEV",
"sampler": MS([[4.9, 6.85], [5.1, 7.15]],
points = sampler0.generatePoints([3, 3]))}
approx = RI(solver, mu0, params, verbosity = 0)
approx.setupApprox()
assert np.isclose(approx.normErr(mu)[0] / approx.normHF(mu)[0],
- 1.449341e-4, rtol = 1e-1)
+ 0.000236598, rtol = 1e-1)
+
diff --git a/tests/test_4_reduction_methods_multiD/rational_pade_2d.py b/tests/test_4_reduction_methods_multiD/rational_pade_2d.py
index 5dc7977..01ea5b7 100644
--- a/tests/test_4_reduction_methods_multiD/rational_pade_2d.py
+++ b/tests/test_4_reduction_methods_multiD/rational_pade_2d.py
@@ -1,64 +1,64 @@
# Copyright (C) 2018 by the RROMPy authors
#
# This file is part of RROMPy.
#
# RROMPy is free software: you can redistribute it and/or modify
# it under the terms of the GNU Lesser General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# RROMPy is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU Lesser General Public License for more details.
#
# You should have received a copy of the GNU Lesser General Public License
# along with RROMPy. If not, see .
#
import numpy as np
from matrix_random import matrixRandom
from rrompy.reduction_methods.centered import RationalPade as RP
def test_rho():
mu = [5.5, 7.5]
mu0 = [5., 7.]
solver = matrixRandom()
uh = solver.solve(mu)[0]
params = {"POD": False, "M": 3, "N": 3, "S": 10, "robustTol": 1e-6}
approx = RP(solver, mu0, params, verbosity = 0)
approx.setupApprox()
uhP1 = approx.getApprox(mu)[0]
errP = approx.getErr(mu)[0]
errNP = approx.normErr(mu)[0]
myerrP = uhP1 - uh
assert np.allclose(np.abs(errP - myerrP), 0., rtol = 1e-3)
assert np.isclose(solver.norm(errP), errNP, rtol = 1e-3)
resP = approx.getRes(mu)[0]
resNP = approx.normRes(mu)
assert np.isclose(solver.norm(resP), resNP, rtol = 1e-3)
assert np.allclose(np.abs(resP - (solver.b(mu) - solver.A(mu).dot(uhP1))),
0., rtol = 1e-3)
def test_E_warn(capsys):
mu = [5.5, 7.5]
mu0 = [5., 7.]
solver = matrixRandom()
uh = solver.solve(mu)[0]
params = {"POD": True, "M": 3, "N": 4, "S": 10}
approx = RP(solver, mu0, params, verbosity = 0)
approx.setupApprox()
out, err = capsys.readouterr()
- assert "Prescribed S is too small. Decreasing M" not in out
- assert "Prescribed S is too small. Decreasing N" in out
+ assert "Prescribed E is too small. Decreasing M" not in out
+ assert "Prescribed E is too small. Decreasing N" in out
assert len(err) == 0
uhP = approx.getApprox(mu)[0]
uhNP = approx.normApprox(mu)[0]
errP = approx.getErr(mu)[0]
errNP = approx.normErr(mu)[0]
assert np.allclose(np.abs(errP - (uhP - uh)), 0., rtol = 1e-3)
- assert np.isclose(errNP / uhNP, .9302, rtol = 1e-1)
+ assert np.isclose(errNP / uhNP, 1.41336e-2, rtol = 1e-1)