diff --git a/examples/2d/base/fracture.py b/examples/2d/base/fracture.py
index 235b454..74d18b9 100644
--- a/examples/2d/base/fracture.py
+++ b/examples/2d/base/fracture.py
@@ -1,38 +1,47 @@
+import numpy as np
+import ufl
+import fenics as fen
from rrompy.hfengines.linear_problem.bidimensional import \
MembraneFractureEngine as MFE
+from rrompy.solver.fenics import affine_warping
+
verb = 100
mu0 = [45. ** .5, .6]
+
H = 1.
L = .75
delta = .05
n = 50
-solver = MFE(mu0 = mu0, H = H, L = L, delta = delta, n = n, verbosity = verb)
+solver = MFE(mu0 = mu0, H = H, L = L, delta = delta,
+ n = n, verbosity = verb)
+u0 = solver.liftDirichletData(mu0)
uh = solver.solve(mu0)[0]
-solver.plotmesh(figsize = (7.5, 4.5))
+#solver.plotmesh(figsize = (7.5, 4.5))
+#solver.plot(u0, what = 'REAL', figsize = (8, 5))
print(solver.norm(uh))
-solver.plot(uh, what = 'REAL', figsize = (8, 5))
-solver.plot(solver.residual(uh, mu0)[0], name = 'res',
- what = 'REAL', figsize = (8, 5))
-solver.outParaviewTimeDomain(uh, mu0[0], filename = 'out/out', folder = True)
+#solver.plot(uh, what = 'REAL', figsize = (8, 5))
+#solver.plot(solver.residual(uh, mu0)[0], name = 'res',
+# what = 'REAL', figsize = (8, 5))
+#solver.outParaviewTimeDomain(uh, mu0[0], filename = 'out', folder = True,
+# forceNewFile = False)
-##
-import numpy as np
-import ufl
-import fenics as fen
-from rrompy.solver.fenics import affine_warping
L = mu0[1]
y = fen.SpatialCoordinate(solver.V.mesh())[1]
-warp1, warpI1 = affine_warping(solver.V.mesh(), np.array([[1, 0], [0, 2. * L]]))
-warp2, warpI2 = affine_warping(solver.V.mesh(), np.array([[1, 0], [0, 2. - 2. * L]]))
+warp1, warpI1 = affine_warping(solver.V.mesh(),
+ np.array([[1, 0], [0, 2. * L]]))
+warp2, warpI2 = affine_warping(solver.V.mesh(),
+ np.array([[1, 0], [0, 2. - 2. * L]]))
warp = ufl.conditional(ufl.ge(y, 0.), warp1, warp2)
warpI = ufl.conditional(ufl.ge(y, 0.), warpI1, warpI2)
-solver.plotmesh([warp, warpI], figsize = (7.5, 4.5))
+#solver.plotmesh([warp, warpI], figsize = (7.5, 4.5))
+#solver.plot(u0, [warp, warpI], what = 'REAL', figsize = (8, 5))
solver.plot(uh, [warp, warpI], what = 'REAL', figsize = (8, 5))
-solver.plot(solver.residual(uh, mu0)[0], [warp, warpI], name = 'res',
- what = 'REAL', figsize = (8, 5))
-solver.outParaviewTimeDomain(uh, mu0[0], [warp, warpI],
- filename = 'out/outW', folder = True)
+#solver.plot(solver.residual(uh, mu0)[0], [warp, warpI], name = 'res',
+# what = 'REAL', figsize = (8, 5))
+#solver.outParaviewTimeDomain(uh, mu0[0], [warp, warpI],
+# filename = 'outW', folder = True,
+# forceNewFile = False)
diff --git a/examples/2d/base/fracture_nodomain.py b/examples/2d/base/fracture_nodomain.py
index a0d0438..7be9125 100644
--- a/examples/2d/base/fracture_nodomain.py
+++ b/examples/2d/base/fracture_nodomain.py
@@ -1,20 +1,47 @@
+import numpy as np
+import ufl
+import fenics as fen
from rrompy.hfengines.linear_problem import MembraneFractureEngineNoDomain \
as MFEND
-verb = 10
+from rrompy.solver.fenics import affine_warping
+
+verb = 100
mu0Aug = [45. ** .5, .6]
+mu0Aug = [45. ** .5, .1]
mu0 = mu0Aug[0]
H = 1.
L = .75
delta = .05
n = 50
-solver = MFEND(mu0 = mu0Aug, H = H, L = L, delta = delta, n = n,
- verbosity = verb)
+solver = MFEND(mu0 = mu0Aug, H = H, L = L, delta = delta,
+ n = n, verbosity = verb)
+u0 = solver.liftDirichletData(mu0)
uh = solver.solve(mu0)[0]
solver.plotmesh(figsize = (7.5, 4.5))
+solver.plot(u0, what = 'REAL', figsize = (8, 5))
print(solver.norm(uh))
solver.plot(uh, what = 'REAL', figsize = (8, 5))
-solver.plot(solver.residual(uh, mu0)[0], 'res',
+solver.plot(solver.residual(uh, mu0)[0], name = 'res',
what = 'REAL', figsize = (8, 5))
+solver.outParaviewTimeDomain(uh, mu0, filename = 'outND', folder = True)
+
+##
+L = mu0Aug[1]
+y = fen.SpatialCoordinate(solver.V.mesh())[1]
+warp1, warpI1 = affine_warping(solver.V.mesh(),
+ np.array([[1, 0], [0, 2. * L]]))
+warp2, warpI2 = affine_warping(solver.V.mesh(),
+ np.array([[1, 0], [0, 2. - 2. * L]]))
+warp = ufl.conditional(ufl.ge(y, 0.), warp1, warp2)
+warpI = ufl.conditional(ufl.ge(y, 0.), warpI1, warpI2)
+
+solver.plotmesh([warp, warpI], figsize = (7.5, 4.5))
+solver.plot(u0, [warp, warpI], what = 'REAL', figsize = (8, 5))
+solver.plot(uh, [warp, warpI], what = 'REAL', figsize = (8, 5))
+solver.plot(solver.residual(uh, mu0)[0], [warp, warpI], name = 'res',
+ what = 'REAL', figsize = (8, 5))
+solver.outParaviewTimeDomain(uh, mu0, [warp, warpI],
+ filename = 'outNDW', folder = True)
diff --git a/examples/2d/pod/fracture_pod.py b/examples/2d/pod/fracture_pod.py
index 6dc7a35..b494062 100644
--- a/examples/2d/pod/fracture_pod.py
+++ b/examples/2d/pod/fracture_pod.py
@@ -1,145 +1,177 @@
import numpy as np
from rrompy.hfengines.linear_problem.bidimensional import \
MembraneFractureEngine as MFE
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 = 3
+size = 100
show_sample = False
show_norm = True
ignore_forcing = True
ignore_forcing = False
clip = -1
#clip = .4
#clip = .6
homogeneize = False
#homogeneize = True
-MN = 11
+MN = 1
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"
+sampling = "random"
if size == 1: # below
mu0 = [40 ** .5, .4]
mutar = [45 ** .5, .4]
murange = [[30 ** .5, .3], [50 ** .5, .5]]
elif size == 2: # top
mu0 = [40 ** .5, .6]
mutar = [45 ** .5, .6]
murange = [[30 ** .5, .5], [50 ** .5, .7]]
elif size == 3: # interesting
mu0 = [40 ** .5, .5]
mutar = [45 ** .5, .5]
murange = [[30 ** .5, .3], [50 ** .5, .7]]
+elif size == 4: # wide_low
+ mu0 = [40 ** .5, .2]
+ mutar = [45 ** .5, .2]
+ murange = [[10 ** .5, .1], [70 ** .5, .3]]
+elif size == 5: # wide_hi
+ mu0 = [40 ** .5, .8]
+ mutar = [45 ** .5, .8]
+ murange = [[10 ** .5, .7], [70 ** .5, .9]]
+elif size == 6: # top_zoom
+ mu0 = [50 ** .5, .8]
+ mutar = [55 ** .5, .8]
+ murange = [[40 ** .5, .7], [60 ** .5, .9]]
+elif size == 100: # tiny
+ mu0 = [32.5 ** .5, .5]
+ mutar = [34 ** .5, .5]
+ murange = [[30 ** .5, .3], [35 ** .5, .7]]
aEff = 1.#25
bEff = 1. - aEff
murangeEff = [[(aEff*murange[0][0]**2. + bEff*murange[1][0]**2.) ** .5,
aEff*murange[0][1] + bEff*murange[1][1]],
[(aEff*murange[1][0]**2. + bEff*murange[0][0]**2.) ** .5,
aEff*murange[1][1] + bEff*murange[0][1]]]
H = 1.
L = .75
delta = .05
n = 25
solver = MFE(mu0 = mu0, H = H, L = L, delta = delta, n = n, verbosity = verb)
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, homogeneized = homogeneize)
if samples == "distributed": approx.samplingEngine.allowRepeatedSamples = False
approx.setupApprox()
if show_sample:
- approx.plotApprox(mutar, name = 'u_app', homogeneized = False,
- what = "REAL")
- approx.plotHF(mutar, name = 'u_HF', homogeneized = False, what = "REAL")
- approx.plotErr(mutar, name = 'err', homogeneized = False, what = "REAL")
-# approx.plotRes(mutar, name = 'res', homogeneized = False, what = "REAL")
+ import ufl
+ import fenics as fen
+ from rrompy.solver.fenics import affine_warping
+ L = mutar[1]
+ y = fen.SpatialCoordinate(solver.V.mesh())[1]
+ warp1, warpI1 = affine_warping(solver.V.mesh(),
+ np.array([[1, 0], [0, 2. * L]]))
+ warp2, warpI2 = affine_warping(solver.V.mesh(),
+ np.array([[1, 0], [0, 2. - 2. * L]]))
+ warp = ufl.conditional(ufl.ge(y, 0.), warp1, warp2)
+ warpI = ufl.conditional(ufl.ge(y, 0.), warpI1, warpI2)
+
+ approx.plotApprox(mutar, [warp, warpI], name = 'u_app',
+ homogeneized = False, what = "REAL")
+ approx.plotHF(mutar, [warp, warpI], name = 'u_HF',
+ homogeneized = False, what = "REAL")
+ approx.plotErr(mutar, [warp, warpI], name = 'err',
+ homogeneized = False, what = "REAL")
+# approx.plotRes(mutar, [warp, warpI], name = 'res',
+# homogeneized = False, what = "REAL")
appErr = approx.normErr(mutar, homogeneized = homogeneize)
solNorm = approx.normHF(mutar, homogeneized = homogeneize)
resNorm = approx.normRes(mutar, homogeneized = homogeneize)
RHSNorm = approx.normRHS(mutar, homogeneized = homogeneize)
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":
+if algo == "rational" and approx.N > 0:
from plot_zero_set import plotZeroSet2
muZeroVals, Qvals = plotZeroSet2(murange, murangeEff, approx, mu0,
200, [2., 1.], clip = clip)
if show_norm:
+ solver._solveBatchSize = 100
from plot_inf_set import plotInfSet2
muInfVals, normEx, normApp, normErr = plotInfSet2(murange, murangeEff,
- approx, mu0, 20,
+ approx, mu0, 50,
[2., 1.], clip = clip)
diff --git a/examples/2d/pod/fracture_pod_nodomain.py b/examples/2d/pod/fracture_pod_nodomain.py
index b89699e..428aaa4 100644
--- a/examples/2d/pod/fracture_pod_nodomain.py
+++ b/examples/2d/pod/fracture_pod_nodomain.py
@@ -1,144 +1,176 @@
import numpy as np
from rrompy.hfengines.linear_problem import MembraneFractureEngineNoDomain \
as MFEND
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
+size = 4
show_sample = True
show_norm = True
ignore_forcing = True
ignore_forcing = False
clip = -1
#clip = .4
#clip = .6
homogeneize = False
#homogeneize = True
MN = 8
R = MN + 1
S = R
samples = "centered"
samples = "centered_fake"
samples = "distributed"
algo = "rational"
#algo = "RB"
sampling = "quadrature"
sampling = "quadrature_total"
sampling = "random"
if size == 1: # below
mu0Aug = [40 ** .5, .4]
mu0 = mu0Aug[0]
mutar = 45 ** .5
murange = [[30 ** .5], [50 ** .5]]
elif size == 2: # top
mu0Aug = [40 ** .5, .6]
mu0 = mu0Aug[0]
mutar = 45 ** .5
murange = [[30 ** .5], [50 ** .5]]
elif size == 3: # interesting
mu0Aug = [40 ** .5, .5]
mu0 = mu0Aug[0]
mutar = 45 ** .5
murange = [[30 ** .5], [50 ** .5]]
+elif size == 4: # wide_low
+ mu0Aug = [40 ** .5, .2]
+ mu0 = mu0Aug[0]
+ mutar = 45 ** .5
+ murange = [[10 ** .5], [70 ** .5]]
+elif size == 5: # wide_hi
+ mu0Aug = [40 ** .5, .8]
+ mu0 = mu0Aug[0]
+ mutar = 45 ** .5
+ murange = [[10 ** .5], [70 ** .5]]
+elif size == 6: # top_zoom
+ mu0Aug = [50 ** .5, .8]
+ mu0 = mu0Aug[0]
+ mutar = 55 ** .5
+ murange = [[40 ** .5], [60 ** .5]]
-aEff = 1.25
+aEff = 1.#25
bEff = 1. - aEff
murangeEff = [[(aEff*murange[0][0]**2. + bEff*murange[1][0]**2.) ** .5],
[(aEff*murange[1][0]**2. + bEff*murange[0][0]**2.) ** .5]]
H = 1.
L = .75
delta = .05
n = 50
solver = MFEND(mu0 = mu0Aug, H = H, L = L, delta = delta, n = n,
verbosity = verb)
rescaling = lambda x: np.power(x, 2.)
rescalingInv = lambda x: np.power(x, .5)
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, homogeneized = homogeneize)
+if samples == "distributed": approx.samplingEngine.allowRepeatedSamples = False
approx.setupApprox()
if show_sample:
- approx.plotApprox(mutar, name = 'u_app', homogeneized = False,
- what = "REAL")
- approx.plotHF(mutar, name = 'u_HF', homogeneized = False, what = "REAL")
- approx.plotErr(mutar, name = 'err', homogeneized = False, what = "REAL")
-# approx.plotRes(mutar, name = 'res', homogeneized = False, what = "REAL")
+ import ufl
+ import fenics as fen
+ from rrompy.solver.fenics import affine_warping
+ L = solver.lFrac
+ y = fen.SpatialCoordinate(solver.V.mesh())[1]
+ warp1, warpI1 = affine_warping(solver.V.mesh(),
+ np.array([[1, 0], [0, 2. * L]]))
+ warp2, warpI2 = affine_warping(solver.V.mesh(),
+ np.array([[1, 0], [0, 2. - 2. * L]]))
+ warp = ufl.conditional(ufl.ge(y, 0.), warp1, warp2)
+ warpI = ufl.conditional(ufl.ge(y, 0.), warpI1, warpI2)
+
+ approx.plotApprox(mutar, [warp, warpI], name = 'u_app',
+ homogeneized = False, what = "REAL")
+ approx.plotHF(mutar, [warp, warpI], name = 'u_HF',
+ homogeneized = False, what = "REAL")
+ approx.plotErr(mutar, [warp, warpI], name = 'err',
+ homogeneized = False, what = "REAL")
+# approx.plotRes(mutar, [warp, warpI], name = 'res',
+# homogeneized = False, what = "REAL")
appErr = approx.normErr(mutar, homogeneized = homogeneize)
solNorm = approx.normHF(mutar, homogeneized = homogeneize)
resNorm = approx.normRes(mutar, homogeneized = homogeneize)
RHSNorm = approx.normRHS(mutar, homogeneized = homogeneize)
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 plotZeroSet1
muZeroVals, Qvals = plotZeroSet1(murange, murangeEff, approx, mu0,
- 1500, 2.)
+ 1000, 2.)
if show_norm:
+ solver._solveBatchSize = 100
from plot_inf_set import plotInfSet1
muInfVals, normEx, normApp, normErr = plotInfSet1(murange, murangeEff,
approx, mu0, 250, 2.)
diff --git a/examples/2d/pod/plot_inf_set.py b/examples/2d/pod/plot_inf_set.py
index b1555e8..05a3ddc 100644
--- a/examples/2d/pod/plot_inf_set.py
+++ b/examples/2d/pod/plot_inf_set.py
@@ -1,148 +1,148 @@
import warnings
import numpy as np
from matplotlib import pyplot as plt
def plotInfSet1FromData(mus, Z, T, E, murange, approx, mu0, exp = 2.):
if hasattr(approx, "mus"):
mu2x = approx.mus(0) ** exp
else:
mu2x = mu0[0] ** exp
murangeExp = [[murange[0][0] ** exp], [murange[1][0] ** exp]]
- mu1 = np.power(mus, exp)
+ mu1 = np.real(np.power(mus, exp))
ZTmin, ZTmax = min(np.min(Z), np.min(T)), max(np.max(Z), np.max(T))
Emin, Emax = np.min(E), np.max(E)
plt.figure(figsize = (15, 7))
plt.jet()
plt.semilogy(mu1, Z)
plt.semilogy(mu1, T, '--')
for l_ in approx.trainedModel.getPoles():
plt.plot([np.real(l_ ** exp)] * 2, [ZTmin, ZTmax], 'b:')
plt.plot(mu2x, [ZTmin] * len(mu2x), 'kx')
plt.plot([murangeExp[0][0]] * 2, [ZTmin, ZTmax], 'm:')
plt.plot([murangeExp[1][0]] * 2, [ZTmin, ZTmax], 'm:')
plt.xlim(mu1[0], mu1[-1])
plt.title("|u(mu)|, |u_app(mu)|")
plt.grid()
plt.show()
plt.figure(figsize = (15, 7))
plt.jet()
plt.semilogy(mu1, E)
for l_ in approx.trainedModel.getPoles():
plt.plot([np.real(l_ ** exp)] * 2, [Emin, Emax], 'b:')
plt.plot(mu2x, [Emax] * len(mu2x), 'kx')
plt.plot([murangeExp[0][0]] * 2, [Emin, Emax], 'm:')
plt.plot([murangeExp[1][0]] * 2, [Emin, Emax], 'm:')
plt.xlim(mu1[0], mu1[-1])
plt.title("|err(mu)|")
plt.grid()
plt.show()
def plotInfSet1(murange, murangeEff, approx, mu0, nSamples = 20, exp = 2.):
mu1 = np.linspace(murangeEff[0][0] ** exp, murangeEff[1][0] ** exp,
nSamples)
mus = np.power(mu1, 1. / exp)
Z = approx.normHF(mus)
T = approx.normApprox(mus)
E = approx.normErr(mus) / Z
plotInfSet1FromData(mus, Z, T, E, murange, approx, mu0, exp)
return mus, Z, T, E
def plotInfSet2FromData(mus, Ze, Te, Ee, murange, approx, mu0,
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]]]
mu1s = np.unique([m[0] for m in mus])
mu2s = np.unique([m[1] for m in mus])
mu1 = np.power(mu1s, exps[0])
mu2 = np.power(mu2s, exps[1])
Mu1, Mu2 = np.meshgrid(np.real(mu1), np.real(mu2))
Z = np.log(Ze)
T = np.log(Te)
E = np.log(Ee)
ZTmin, ZTmax = min(np.min(Z), np.min(T)), max(np.max(Z), np.max(T))
Emin, Emax = np.min(E), np.max(E)
if clip > 0:
ZTmax -= clip * (ZTmax - ZTmin)
cmap = plt.cm.bone
else:
cmap = plt.cm.jet
warnings.simplefilter("ignore", category = UserWarning)
plt.figure(figsize = (15, 7))
plt.jet()
p = plt.contourf(Mu1, Mu2, Z, cmap = cmap,
levels = np.linspace(ZTmin, ZTmax, 50))
if clip > 0:
plt.contour(Mu1, Mu2, Z, [ZTmin])
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.title("log|u(mu)|")
plt.grid()
plt.show()
plt.figure(figsize = (15, 7))
plt.jet()
p = plt.contourf(Mu1, Mu2, T, cmap = cmap,
levels = np.linspace(ZTmin, ZTmax, 50))
if clip > 0:
plt.contour(Mu1, Mu2, T, [ZTmin])
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.title("log|u_app(mu)|")
plt.colorbar(p)
plt.grid()
plt.show()
plt.figure(figsize = (15, 7))
plt.jet()
p = plt.contourf(Mu1, Mu2, E, levels = np.linspace(Emin, Emax, 50))
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.title("log|err(mu)|")
plt.colorbar(p)
plt.grid()
plt.show()
def plotInfSet2(murange, murangeEff, approx, mu0, nSamples = 200,
exps = [2., 2.], clip = -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])
mus = [(m1, m2) for m2 in mu2s for m1 in mu1s]
Ze = approx.normHF(mus).reshape((nSamples, nSamples))
Te = approx.normApprox(mus).reshape((nSamples, nSamples))
Ee = approx.normErr(mus).reshape((nSamples, nSamples)) / Ze
plotInfSet2FromData(mus, Ze, Te, Ee, murange, approx, mu0, exps, clip)
return mus, Ze, Te, Ee
diff --git a/examples/2d/pod/plot_zero_set.py b/examples/2d/pod/plot_zero_set.py
index 9d891cc..0b0f622 100644
--- a/examples/2d/pod/plot_zero_set.py
+++ b/examples/2d/pod/plot_zero_set.py
@@ -1,79 +1,80 @@
import warnings
import numpy as np
from matplotlib import pyplot as plt
def plotZeroSet1(murange, murangeEff, approx, mu0, nSamples = 200, exp = 2.):
if hasattr(approx, "mus"):
mu2x = approx.mus(0) ** exp
else:
mu2x = mu0[0] ** exp
murangeExp = [[murange[0][0] ** exp], [murange[1][0] ** exp]]
mu1 = np.linspace(murangeEff[0][0] ** exp, murangeEff[1][0] ** exp,
nSamples)
mus = np.power(mu1, 1. / exp)
+ mu1 = np.real(mu1)
Z = approx.trainedModel.getQVal(mus)
Zabs = np.abs(Z)
Zmin, Zmax = np.min(Zabs), np.max(Zabs)
plt.figure(figsize = (15, 7))
plt.jet()
plt.semilogy(mu1, Zabs)
for l_ in approx.trainedModel.getPoles():
plt.plot([np.real(l_ ** exp)] * 2, [Zmin, Zmax], 'b--')
plt.plot(mu2x, [Zmax] * len(mu2x), 'kx')
plt.plot([murangeExp[0][0]] * 2, [Zmin, Zmax], 'm:')
plt.plot([murangeExp[1][0]] * 2, [Zmin, Zmax], 'm:')
plt.xlim(mu1[0], mu1[-1])
plt.title("|Q(mu)|")
plt.grid()
plt.show()
return mus, Z
def plotZeroSet2(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
warnings.simplefilter("ignore", category = UserWarning)
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.title("log|Q(mu)|")
plt.grid()
plt.show()
return mus, Z
diff --git a/rrompy/hfengines/base/matrix_engine_base.py b/rrompy/hfengines/base/matrix_engine_base.py
index dbd7308..65f9fa7 100644
--- a/rrompy/hfengines/base/matrix_engine_base.py
+++ b/rrompy/hfengines/base/matrix_engine_base.py
@@ -1,446 +1,460 @@
# 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, copy as softcopy
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
+from rrompy.solver.scipy import tensorizeLS, detensorizeLS
__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.
"""
+
+ _solveBatchSize = 1
def __init__(self, verbosity : int = 10, timestamp : bool = True):
self.verbosity = verbosity
self.timestamp = timestamp
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] != "__"]
def __deepcopy__(self, memo):
return softcopy(self)
@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.setAs([None] * self.nAs)
if hasattr(self, "_nbs"): self.resetbsH()
def resetbs(self):
"""Reset (derivatives of) RHS of linear system."""
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, 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
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]):
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] = self.checkAInBounds(-1)
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,
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, homogeneized)
if bnull is not None: return bnull
bs = self.bsH if homogeneized else self.bs
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]):
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] = self.checkbInBounds(-1)
else:
for j in range(derI, self.nbs):
if self.bs[j] is None: self.bs[j] = self.checkbInBounds(-1)
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)
sol = emptySampleList()
if len(mu) > 0:
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")
u = self._solver(self.A(mu[0]), RHS[0], self._solverArgs)
sol.reset((len(u), len(mu)), dtype = u.dtype)
sol[0] = u
- for j in range(1, len(mu)):
- sol[j] = self._solver(self.A(mu[j]), RHS[mult * j],
- self._solverArgs)
+ for j in range(1, len(mu), self._solveBatchSize):
+ if self._solveBatchSize != 1:
+ iRange = list(range(j, min(j + self._solveBatchSize,
+ len(mu))))
+ As = [self.A(mu[i]) for i in iRange]
+ bs = [RHS[mult * i] for i in iRange]
+ A, b = tensorizeLS(As, bs)
+ else:
+ A, b = self.A(mu[j]), RHS[mult * j]
+ solStack = self._solver(A, b, self._solverArgs)
+ if self._solveBatchSize != 1:
+ sol[iRange] = detensorizeLS(solStack, len(iRange))
+ else:
+ sol[j] = solStack
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/membrane_fracture_engine.py b/rrompy/hfengines/linear_problem/bidimensional/membrane_fracture_engine.py
index df38d23..6e03ad0 100644
--- a/rrompy/hfengines/linear_problem/bidimensional/membrane_fracture_engine.py
+++ b/rrompy/hfengines/linear_problem/bidimensional/membrane_fracture_engine.py
@@ -1,289 +1,248 @@
# 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
import mshr, ufl
-from rrompy.utilities.base.types import ScOp, List, paramVal, Np1D
+from rrompy.utilities.base.types import ScOp, List, paramVal
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)
+ hashDerivativeToIdx as hashD)
__all__ = ['MembraneFractureEngine']
class MembraneFractureEngine(HelmholtzProblemEngine):
def __init__(self, mu0 : paramVal = [20. ** .5, .6], H : float = 1.,
L : float = .75, delta : float = .05, n : int = 50,
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 = 20, 1
+ self.nAs = 20
self.npar = 2
self.H = H
self.rescalingExp = [2., 1.]
- domain = mshr.Polygon([fen.Point(0., - H / 2.),
- fen.Point(2. * L + delta, - H / 2.),
- fen.Point(2. * L + delta, H / 2.),
- fen.Point(L + delta, H / 2.),
- fen.Point(L + delta, 0.),
- fen.Point(L, 0.),
- fen.Point(L, H / 2.),
- fen.Point(0., H / 2.),])
+ domain = (mshr.Rectangle(fen.Point(0., - H / 2.),
+ fen.Point(2. * L + delta, H / 2.))
+ - mshr.Rectangle(fen.Point(L, 0.),
+ fen.Point(L + delta, H / 2.)))
mesh = mshr.generate_mesh(domain, n)
self.V = fen.FunctionSpace(mesh, "P", 1)
self.NeumannBoundary = lambda x, on_b: (on_b and x[1] >= - H / 4.
and x[0] >= L
and x[0] <= L + delta)
self.DirichletBoundary = "REST"
x, y = fen.SpatialCoordinate(mesh)[:]
self._belowIndicator = ufl.conditional(ufl.le(y, 0.), fenONE, fenZERO)
self._aboveIndicator = fenONE - self._belowIndicator
self.DirichletDatum = [fen.exp(- 10. * (H / 2. + y) / H
- .5 * ((x - .6 * L) / (.1 * L)) ** 2.
) * self._belowIndicator, fenZERO]
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()
for j in [1, 3, 4, 6, 7, 10, 11, 12, 15, 16, 17, 18]:
if derI <= j and self.As[j] is None:
self.As[j] = self.checkAInBounds(-1)
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 = (self.H ** 4 / 4. * self._belowIndicator
+ a0Re = (self.H ** 4 / 4. * self._aboveIndicator
* 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 <= 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 = (- self.H ** 3 / 2. * self._belowIndicator
+ a2Re = (- self.H ** 3 / 2. * self._aboveIndicator
* fen.dot(self.u.dx(1), self.v.dx(1)) * fen.dx)
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)
if derI <= 5 and self.As[5] is None:
if self.verbosity >= 20:
verbosityDepth("INIT", "Assembling operator term A6.",
timestamp = self.timestamp)
DirichletBC0 = fen.DirichletBC(self.V, fenZERO,
self.DirichletBoundary)
a5Re = self.H ** 2 * (fen.dot(self.u.dx(0), self.v.dx(0))
+ .25 * 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)
if derI <= 8 and self.As[8] is None:
if self.verbosity >= 20:
verbosityDepth("INIT", "Assembling operator term A8.",
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"]))
a8Re = - self.H ** 2. * n2Re * fen.dot(self.u, self.v) * fen.dx
a8Im = - self.H ** 2. * n2Im * fen.dot(self.u, self.v) * fen.dx
A8Re = fen.assemble(a8Re, form_compiler_parameters = parsRe)
A8Im = fen.assemble(a8Im, form_compiler_parameters = parsIm)
DirichletBC0.zero(A8Re)
DirichletBC0.zero(A8Im)
A8ReMat = fen.as_backend_type(A8Re).mat()
A8ImMat = fen.as_backend_type(A8Im).mat()
A8Rer, A8Rec, A8Rev = A8ReMat.getValuesCSR()
A8Imr, A8Imc, A8Imv = A8ImMat.getValuesCSR()
self.As[8] = (scsp.csr_matrix((A8Rev, A8Rec, A8Rer),
shape = A8ReMat.size)
+ 1.j * scsp.csr_matrix((A8Imv, A8Imc, A8Imr),
shape = A8ImMat.size))
if self.verbosity >= 20:
verbosityDepth("DEL", "Done assembling operator term.",
timestamp = self.timestamp)
if derI <= 9 and self.As[9] is None:
if self.verbosity >= 20:
verbosityDepth("INIT", "Assembling operator term A9.",
timestamp = self.timestamp)
DirichletBC0 = fen.DirichletBC(self.V, fenZERO,
self.DirichletBoundary)
a9Re = - 2. * self.H * fen.dot(self.u.dx(0), self.v.dx(0)) * fen.dx
A9Re = fen.assemble(a9Re)
DirichletBC0.zero(A9Re)
A9ReMat = fen.as_backend_type(A9Re).mat()
A9Rer, A9Rec, A9Rev = A9ReMat.getValuesCSR()
self.As[9] = scsp.csr_matrix((A9Rev, A9Rec, A9Rer),
shape = A9ReMat.size,
dtype = np.complex)
if self.verbosity >= 20:
verbosityDepth("DEL", "Done assembling operator term.",
timestamp = self.timestamp)
if derI <= 13 and self.As[13] is None:
if self.verbosity >= 20:
verbosityDepth("INIT", "Assembling operator term A13.",
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"]))
a13Re = 2. * self.H * n2Re * fen.dot(self.u, self.v) * fen.dx
a13Im = 2. * self.H * n2Im * fen.dot(self.u, self.v) * fen.dx
A13Re = fen.assemble(a13Re, form_compiler_parameters = parsRe)
A13Im = fen.assemble(a13Im, form_compiler_parameters = parsIm)
DirichletBC0.zero(A13Re)
DirichletBC0.zero(A13Im)
A13ReMat = fen.as_backend_type(A13Re).mat()
A13ImMat = fen.as_backend_type(A13Im).mat()
A13Rer, A13Rec, A13Rev = A13ReMat.getValuesCSR()
A13Imr, A13Imc, A13Imv = A13ImMat.getValuesCSR()
self.As[13] = (scsp.csr_matrix((A13Rev, A13Rec, A13Rer),
shape = A13ReMat.size)
+ 1.j * scsp.csr_matrix((A13Imv, A13Imc, A13Imr),
shape = A13ImMat.size))
if self.verbosity >= 20:
verbosityDepth("DEL", "Done assembling operator term.",
timestamp = self.timestamp)
if derI <= 14 and self.As[14] is None:
if self.verbosity >= 20:
verbosityDepth("INIT", "Assembling operator term A14.",
timestamp = self.timestamp)
DirichletBC0 = fen.DirichletBC(self.V, fenZERO,
self.DirichletBoundary)
a14Re = fen.dot(self.u.dx(0), self.v.dx(0)) * fen.dx
A14Re = fen.assemble(a14Re)
DirichletBC0.zero(A14Re)
A14ReMat = fen.as_backend_type(A14Re).mat()
A14Rer, A14Rec, A14Rev = A14ReMat.getValuesCSR()
self.As[14] = scsp.csr_matrix((A14Rev, A14Rec, A14Rer),
shape = A14ReMat.size,
dtype = np.complex)
if self.verbosity >= 20:
verbosityDepth("DEL", "Done assembling operator term.",
timestamp = self.timestamp)
if derI <= 19 and self.As[19] is None:
if self.verbosity >= 20:
verbosityDepth("INIT", "Assembling operator term A19.",
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"]))
a19Re = - n2Re * fen.dot(self.u, self.v) * fen.dx
a19Im = - n2Im * fen.dot(self.u, self.v) * fen.dx
A19Re = fen.assemble(a19Re, form_compiler_parameters = parsRe)
A19Im = fen.assemble(a19Im, form_compiler_parameters = parsIm)
DirichletBC0.zero(A19Re)
DirichletBC0.zero(A19Im)
A19ReMat = fen.as_backend_type(A19Re).mat()
A19ImMat = fen.as_backend_type(A19Im).mat()
A19Rer, A19Rec, A19Rev = A19ReMat.getValuesCSR()
A19Imr, A19Imc, A19Imv = A19ImMat.getValuesCSR()
self.As[19] = (scsp.csr_matrix((A19Rev, A19Rec, A19Rer),
shape = A19ReMat.size)
+ 1.j * scsp.csr_matrix((A19Imv, A19Imc, A19Imr),
shape = A19ImMat.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):
- derH = hashI(j, self.npar)
- if bs[j] is None:
- if self.verbosity >= 20:
- verbosityDepth("INIT", ("Assembling forcing term "
- "b{}.").format(j),
- timestamp = self.timestamp)
- u0Re, u0Im = self.DirichletDatum
- b0Re = fen.assemble(fen.dot(fenZERO, self.v) * fen.dx)
- b0Im = fen.assemble(fen.dot(fenZERO, self.v) * fen.dx)
- 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/laplace_base_problem_engine.py b/rrompy/hfengines/linear_problem/laplace_base_problem_engine.py
index b2bbe18..1cecb1a 100644
--- a/rrompy/hfengines/linear_problem/laplace_base_problem_engine.py
+++ b/rrompy/hfengines/linear_problem/laplace_base_problem_engine.py
@@ -1,320 +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.utilities.base.types import Np1D, List, ScOp, paramVal
from rrompy.solver.fenics import fenZERO, fenONE, H1NormMatrix
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__ = ['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)
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
if len(termNames) > 0:
parsRe = self.iterReduceQuadratureDegree(zip(
[term[0] for term in terms],
[x + "Real" for x in termNames]))
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)
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, der, derI, homogeneized, self.mu0)
diff --git a/rrompy/hfengines/linear_problem/membrane_fracture_engine_nodomain.py b/rrompy/hfengines/linear_problem/membrane_fracture_engine_nodomain.py
index a92fca4..0586874 100644
--- a/rrompy/hfengines/linear_problem/membrane_fracture_engine_nodomain.py
+++ b/rrompy/hfengines/linear_problem/membrane_fracture_engine_nodomain.py
@@ -1,125 +1,120 @@
# 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
import mshr, ufl
from rrompy.utilities.base.types import ScOp, List, paramVal
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)
__all__ = ['MembraneFractureEngineNoDomain']
class MembraneFractureEngineNoDomain(HelmholtzProblemEngine):
def __init__(self, mu0 : paramVal = [20. ** .5, .6], H : float = 1.,
L : float = .75, delta : float = .05, n : int = 50,
degree_threshold : int = np.inf, verbosity : int = 10,
timestamp : bool = True):
super().__init__(mu0 = mu0[0], degree_threshold = degree_threshold,
verbosity = verbosity, timestamp = timestamp)
- self.nAs, self.nbs = 2, 1
self.npar = 1
self.lFrac = mu0[1]
self.H = H
self.rescalingExp = [2.]
- domain = mshr.Polygon([fen.Point(0., - H / 2.),
- fen.Point(2. * L + delta, - H / 2.),
- fen.Point(2. * L + delta, H / 2.),
- fen.Point(L + delta, H / 2.),
- fen.Point(L + delta, 0.),
- fen.Point(L, 0.),
- fen.Point(L, H / 2.),
- fen.Point(0., H / 2.),])
+ domain = (mshr.Rectangle(fen.Point(0., - H / 2.),
+ fen.Point(2. * L + delta, H / 2.))
+ - mshr.Rectangle(fen.Point(L, 0.),
+ fen.Point(L + delta, H / 2.)))
mesh = mshr.generate_mesh(domain, n)
self.V = fen.FunctionSpace(mesh, "P", 1)
self.NeumannBoundary = lambda x, on_b: (on_b and x[1] >= - H / 4.
and x[0] >= L
and x[0] <= L + delta)
self.DirichletBoundary = "REST"
x, y = fen.SpatialCoordinate(mesh)[:]
self._belowIndicator = ufl.conditional(ufl.le(y, 0.), fenONE, fenZERO)
self._aboveIndicator = fenONE - self._belowIndicator
self.DirichletDatum = [fen.exp(- 10. * (H / 2. + y) / H
- .5 * ((x - .6 * L) / (.1 * L)) ** 2.
) * self._belowIndicator, fenZERO]
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)
a0Re = (fen.dot(self.u.dx(0), self.v.dx(0))
- + self.H ** 4 / 4. * (self.lFrac ** -2. * self._belowIndicator
- + (self.H - self.lFrac) ** -2. * self._aboveIndicator)
+ + self.H ** 4 / 4. * (self.lFrac ** -2. * self._aboveIndicator
+ + (self.H - self.lFrac) ** -2. * self._belowIndicator)
* 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:
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/reduction_methods/base/generic_approximant.py b/rrompy/reduction_methods/base/generic_approximant.py
index 489b925..38bd141 100644
--- a/rrompy/reduction_methods/base/generic_approximant.py
+++ b/rrompy/reduction_methods/base/generic_approximant.py
@@ -1,903 +1,873 @@
# 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, ListAny,
- strLst, paramVal, paramList, sampList)
+from rrompy.utilities.base.types import (Np1D, DictAny, HFEng, List, Tuple,
+ 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) -> Np1D:
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, *args, homogeneized : bool = False,
**kwargs):
uV = getattr(self.__class__, "get" + fieldName)(self, mu, homogeneized)
kwargsCopy = copy(kwargs)
for j, u in enumerate(uV):
if "name" in kwargs.keys():
kwargsCopy["name"] = kwargs["name"] + str(j)
self.HFEngine.plot(u, *args, **kwargs)
setattr(self.__class__, "plot" + fieldName, objFunc)
def addOutParaviewFieldToClass(self, fieldName):
def objFunc(self, mu:paramVal, *args, homogeneized : bool = False,
**kwargs):
if not hasattr(self.HFEngine, "outParaview"):
raise RROMPyException(("High fidelity engine cannot output to "
"Paraview."))
uV = getattr(self.__class__, "get" + fieldName)(self, mu, homogeneized)
kwargsCopy = copy(kwargs)
for j, u in enumerate(uV):
if "name" in kwargs.keys():
kwargsCopy["name"] = kwargs["name"] + str(j)
self.HFEngine.outParaview(u, *args, **kwargsCopy)
setattr(self.__class__, "outParaview" + fieldName, objFunc)
def addOutParaviewTimeDomainFieldToClass(self, fieldName):
def objFunc(self, mu:paramVal, *args,
homogeneized : bool = False, **kwargs):
if not hasattr(self.HFEngine, "outParaviewTimeDomain"):
raise RROMPyException(("High fidelity engine cannot output to "
"Paraview."))
uV = getattr(self.__class__, "get" + fieldName)(self, mu, homogeneized)
omega = args.pop(0) if len(args) > 0 else np.real(mu)
kwargsCopy = copy(kwargs)
for j, u in enumerate(uV):
if "name" in kwargs.keys():
kwargsCopy["name"] = kwargs["name"] + str(j)
self.HFEngine.outParaviewTimeDomain(u, omega, *args,
**kwargsCopy)
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{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
+ uApproxReduced: Reduced approximate solution(s) with parameter(s)
+ lastSolvedApprox as sampleList.
+ lastSolvedApproxReduced: Parameter(s) corresponding to last computed
reduced approximate solution(s) as parameterList.
- uApp: Approximate solution(s) with parameter(s) lastSolvedApp as
+ uApprox: Approximate solution(s) with parameter(s) lastSolvedApprox as
sampleList.
- lastSolvedApp: Parameter(s) corresponding to last computed approximate
- solution(s) as parameterList.
+ lastSolvedApprox: 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"], [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._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", "Res", "Err"]:
addNormFieldToClass(self, objName)
if not hasattr(self, "normApprox"):
addNormFieldToClass(self, "Approx")
### 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
@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,
allowRepeatedSamples = True)
@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())
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()
+ self._trainedModel.lastSolvedApproxReduced = emptyParameterList()
+ self._trainedModel.lastSolvedApprox = emptyParameterList()
+ self.lastSolvedApproxReduced = emptyParameterList()
+ self.lastSolvedApprox = emptyParameterList()
+ self.uApproxReduced = emptySampleList()
+ self.uApprox = 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 = copy(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.
- """
+ def _pruneBeforeEval(self, mu:paramList, field:str, append:bool,
+ prune:bool) -> Tuple[paramList, Np1D, Np1D, bool]:
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)
+ muExtra = emptyParameterList()
+ lastSolvedMus = getattr(self, "lastSolved" + field)
+ if (len(mu) > 0 and len(mu) == len(lastSolvedMus)
+ and mu == lastSolvedMus):
+ idx = np.arange(len(mu), dtype = np.int)
+ return muExtra, jExtra, idx, True
+ muKeep = copy(muExtra)
for j in range(len(mu)):
- jPos = self.lastSolvedHF.find(mu[j])
+ jPos = lastSolvedMus.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)
+ lastSolvedu = getattr(self, "u" + field)
+ idx[~jExtra] = getattr(self.__class__, "set" + field)(self,
+ muKeep, lastSolvedu[idx[~jExtra]], append)
append = True
else:
jExtra = np.ones(len(mu), dtype = bool)
muExtra = mu
+ return muExtra, jExtra, idx, append
+
+ def _setObject(self, mu:paramList, field:str, object:sampList,
+ append:bool) -> List[int]:
+ newMus, _ = checkParameterList(mu, self.npar)
+ newObj = sampleList(object)
+ if append:
+ getattr(self, "lastSolved" + field).append(newMus)
+ getattr(self, "u" + field).append(newObj)
+ Ltot = len(getattr(self, "u" + field))
+ return list(range(Ltot - len(newObj), Ltot))
+ setattr(self, "lastSolved" + field, copy(newMus))
+ setattr(self, "u" + field, copy(newObj))
+ return list(range(len(getattr(self, "u" + field))))
+
+ def setHF(self, muHF:paramList, uHF:sampleList,
+ append : bool = False) -> List[int]:
+ """Assign high fidelity solution."""
+ return self._setObject(muHF, "HF", uHF, append)
+
+ 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.
+ """
+ muExtra, jExtra, idx, append = self._pruneBeforeEval(mu, "HF", append,
+ prune)
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,
+ def setApproxReduced(self, muApproxR:paramList, uApproxR: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)))
+ return self._setObject(muApproxR, "ApproxReduced", uApproxR, append)
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.
+ append(optional): Whether to append new HF solutions to old ones.
+ prune(optional): Whether to remove duplicates of already appearing
+ HF solutions.
"""
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
+ muExtra, jExtra, idx, append = self._pruneBeforeEval(mu,
+ "ApproxReduced",
+ append, prune)
if len(muExtra) > 0:
- newuApps = self.trainedModel.getApproxReduced(muExtra)
- idx[jExtra] = self.setApproxReduced(muExtra, newuApps, append)
+ newuApproxs = self.trainedModel.getApproxReduced(muExtra)
+ idx[jExtra] = self.setApproxReduced(muExtra, newuApproxs, append)
return list(idx)
- def setApprox(self, muApp:paramList, uApp:sampleList,
+ def setApprox(self, muApprox:paramList, uApprox: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)))
+ return self._setObject(muApprox, "Approx", uApprox, append)
def evalApprox(self, mu:paramList, append : bool = False,
prune : bool = True) -> List[int]:
"""
Evaluate approximant at 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.
"""
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
+ muExtra, jExtra, idx, append = self._pruneBeforeEval(mu, "Approx",
+ append, prune)
if len(muExtra) > 0:
- newuApps = self.trainedModel.getApprox(muExtra)
- idx[jExtra] = self.setApprox(muExtra, newuApps, append)
+ newuApproxs = self.trainedModel.getApprox(muExtra)
+ idx[jExtra] = self.setApprox(muExtra, newuApproxs, 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
+ uApproxRs = self.uApproxReduced(idx)
+ return uApproxRs
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)
+ uApproxs = self.uApprox(idx)
if self.homogeneized and not homogeneized:
for j, m in enumerate(mu):
- uApps[j] += self.HFEngine.liftDirichletData(m)
+ uApproxs[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
+ uApproxs[j] -= self.HFEngine.liftDirichletData(m)
+ return uApproxs
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:
+ def getErr(self, mu:paramList, homogeneized : bool = False,
+ append : bool = False, prune : bool = True) -> 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)
+ return (self.getApprox(mu, homogeneized, append = append, prune =prune)
+ - self.getHF(mu, homogeneized, append = append, prune = prune))
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/centered/generic_centered_approximant.py b/rrompy/reduction_methods/centered/generic_centered_approximant.py
index 5d3949f..aea1c71 100644
--- a/rrompy/reduction_methods/centered/generic_centered_approximant.py
+++ b/rrompy/reduction_methods/centered/generic_centered_approximant.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 rrompy.reduction_methods.base.generic_approximant import (
GenericApproximant)
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.
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
+ uApproxReduced: Reduced approximate solution(s) with parameter(s)
+ lastSolvedApprox as sampleList.
+ lastSolvedApproxReduced: Parameter(s) corresponding to last computed
reduced approximate solution(s) as parameterList.
- uApp: Approximate solution(s) with parameter(s) lastSolvedApp as
+ uApprox: Approximate solution(s) with parameter(s) lastSolvedApprox as
sampleList.
- lastSolvedApp: Parameter(s) corresponding to last computed approximate
- solution(s) as parameterList.
+ lastSolvedApprox: 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.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: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).data, axis = 0)
diff --git a/rrompy/reduction_methods/centered/rational_pade.py b/rrompy/reduction_methods/centered/rational_pade.py
index 5356430..04dcbf3 100644
--- a/rrompy/reduction_methods/centered/rational_pade.py
+++ b/rrompy/reduction_methods/centered/rational_pade.py
@@ -1,440 +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
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.
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
+ uApproxReduced: Reduced approximate solution(s) with parameter(s)
+ lastSolvedApprox as sampleList.
+ lastSolvedApproxReduced: Parameter(s) corresponding to last computed
reduced approximate solution(s) as parameterList.
- uApp: Approximate solution(s) with parameter(s) lastSolvedApp as
+ uApprox: Approximate solution(s) with parameter(s) lastSolvedApprox as
sampleList.
- lastSolvedApp: Parameter(s) corresponding to last computed approximate
- solution(s) as parameterList.
+ lastSolvedApprox: 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(["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 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 >= 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 >= 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)
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(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[tuple(mIdx) + (hashD(diffIdx),)] = (
self.trainedModel.data.Q[tuple(mnIdxs[n])])
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)
+ Q = np.ones(tuple([1] * self.npar), 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)
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 c690b2a..e8c8ac9 100644
--- a/rrompy/reduction_methods/centered/rb_centered.py
+++ b/rrompy/reduction_methods/centered/rb_centered.py
@@ -1,191 +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 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.
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.
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
+ uApproxReduced: Reduced approximate solution(s) with parameter(s)
+ lastSolvedApprox as sampleList.
+ lastSolvedApproxReduced: Parameter(s) corresponding to last computed
reduced approximate solution(s) as parameterList.
- uApp: Approximate solution(s) with parameter(s) lastSolvedApp as
+ uApprox: Approximate solution(s) with parameter(s) lastSolvedApprox as
sampleList.
- lastSolvedApp: Parameter(s) corresponding to last computed approximate
- solution(s) as parameterList.
+ lastSolvedApprox: 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"], [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 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:
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)
self.trainedModel.data = data
else:
self.trainedModel = self.trainedModel
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 6f12eea..11c620f 100644
--- a/rrompy/reduction_methods/distributed/generic_distributed_approximant.py
+++ b/rrompy/reduction_methods/distributed/generic_distributed_approximant.py
@@ -1,167 +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 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;
- 'S': total number of samples current approximant relies upon;
- '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.
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.
POD: Whether to compute POD of snapshots.
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
+ uApproxReduced: Reduced approximate solution(s) with parameter(s)
+ lastSolvedApprox as sampleList.
+ lastSolvedApproxReduced: Parameter(s) corresponding to last computed
reduced approximate solution(s) as parameterList.
- uApp: Approximate solution(s) with parameter(s) lastSolvedApp as
+ uApprox: Approximate solution(s) with parameter(s) lastSolvedApprox as
sampleList.
- lastSolvedApp: Parameter(s) corresponding to last computed approximate
- solution(s) as parameterList.
+ lastSolvedApprox: 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()
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 muBounds(self):
"""Value of 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 != 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).data, 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 85a6af9..765e1a5 100644
--- a/rrompy/reduction_methods/distributed/rational_interpolant.py
+++ b/rrompy/reduction_methods/distributed/rational_interpolant.py
@@ -1,540 +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, 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, 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;
- 'S': total number of samples current approximant relies upon;
- '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.
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.
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.
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
+ uApproxReduced: Reduced approximate solution(s) with parameter(s)
+ lastSolvedApprox as sampleList.
+ lastSolvedApproxReduced: Parameter(s) corresponding to last computed
reduced approximate solution(s) as parameterList.
- uApp: Approximate solution(s) with parameter(s) lastSolvedApp as
+ uApprox: Approximate solution(s) with parameter(s) lastSolvedApprox as
sampleList.
- lastSolvedApp: Parameter(s) corresponding to last computed approximate
- solution(s) as parameterList.
+ lastSolvedApprox: 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", "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 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 >= 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 >= 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)
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)
+ Q = np.ones(tuple([1] * self.npar), 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()
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)
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] * (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
if nder > 1:
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]
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(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]
S = RPODE.shape[0]
eWidth = len(invD)
if self.verbosity >= 10:
verbosityDepth("INIT", "Building half-gramian matrix stack.",
timestamp = self.timestamp)
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),
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 a7dfa03..fc5307a 100644
--- a/rrompy/reduction_methods/distributed/rb_distributed.py
+++ b/rrompy/reduction_methods/distributed/rb_distributed.py
@@ -1,206 +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 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:
- 'POD': whether to compute POD of snapshots; defaults to True;
- 'S': total number of samples current approximant relies upon;
- '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.
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;
POD: Whether to compute POD of snapshots.
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
+ uApproxReduced: Reduced approximate solution(s) with parameter(s)
+ lastSolvedApprox as sampleList.
+ lastSolvedApproxReduced: Parameter(s) corresponding to last computed
reduced approximate solution(s) as parameterList.
- uApp: Approximate solution(s) with parameter(s) lastSolvedApp as
+ uApprox: Approximate solution(s) with parameter(s) lastSolvedApprox as
sampleList.
- lastSolvedApp: Parameter(s) corresponding to last computed approximate
- solution(s) as parameterList.
+ lastSolvedApprox: 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"], [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 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.mus = copy(self.mus)
self.trainedModel.data = data
else:
self.trainedModel = self.trainedModel
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 f4c223c..63e51b1 100644
--- a/rrompy/reduction_methods/distributed_greedy/generic_distributed_greedy_approximant.py
+++ b/rrompy/reduction_methods/distributed_greedy/generic_distributed_greedy_approximant.py
@@ -1,591 +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 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;
- '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 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.
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.
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.
POD: whether to compute POD of snapshots.
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
+ uApproxReduced: Reduced approximate solution(s) with parameter(s)
+ lastSolvedApprox as sampleList.
+ lastSolvedApproxReduced: Parameter(s) corresponding to last computed
reduced approximate solution(s) as parameterList.
- uApp: Approximate solution(s) with parameter(s) lastSolvedApp as
+ uApprox: Approximate solution(s) with parameter(s) lastSolvedApprox as
sampleList.
- lastSolvedApp: Parameter(s) corresponding to last computed approximate
- solution(s) as parameterList.
+ lastSolvedApprox: 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"],
[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 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.):
"""
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
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] = (
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()
else:
Sold = self.trainedModel.data.resAA.shape[0]
if Sold == S: return
if Sold > S:
resAA = self.trainedModel.data.resAA[: S, :, : S, :]
else:
if not isinstance(pMat, (np.ndarray,)): pMat = pMat.data
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] = (
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] = (
self.estimatorNormEngine.innerProduct(MAj[:, Sold :],
MAi[:, : Sold]))
resAA[Sold :, i, : Sold, j] = (
self.estimatorNormEngine.innerProduct(MAj[:, : Sold],
MAi[:, Sold :]))
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] = (
resAA[Sold :, j, : Sold, i].T.conj())
resAA[Sold :, i, : Sold, j] = (
resAA[: Sold, j, Sold :, i].T.conj())
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 0ec150b..bedfeba 100644
--- a/rrompy/reduction_methods/distributed_greedy/rational_interpolant_greedy.py
+++ b/rrompy/reduction_methods/distributed_greedy/rational_interpolant_greedy.py
@@ -1,416 +1,418 @@
# 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 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;
- '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 training points to be exhausted
before training 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;
- '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.
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;
- 'trainSetGenerator': training sample points generator;
- '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.
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.
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.
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
+ uApproxReduced: Reduced approximate solution(s) with parameter(s)
+ lastSolvedApprox as sampleList.
+ lastSolvedApproxReduced: Parameter(s) corresponding to last computed
reduced approximate solution(s) as parameterList.
- uApp: Approximate solution(s) with parameter(s) lastSolvedApp as
+ uApprox: Approximate solution(s) with parameter(s) lastSolvedApprox as
sampleList.
- lastSolvedApp: Parameter(s) corresponding to last computed approximate
- solution(s) as parameterList.
+ lastSolvedApprox: 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(["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 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: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)
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)
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._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),
+ Q = np.empty(tuple([max(self.N, 0) + 1] * self.npar),
+ dtype = np.complex)
+ P = np.empty((len(self.mus),)
+ + tuple([max(self.M, 0) + 1] * self.npar),
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)
+ Q = np.ones(tuple([1] * self.npar), 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, full : bool = False):
"""Build affine blocks of reduced linear system through projections."""
scaling = self.trainedModel.data.scaleFactor[0]
self.assembleReducedResidualBlocksbb(self.bs, scaling)
if full:
pMat = self.trainedModel.data.projMat
self.assembleReducedResidualBlocksAb(self.As, self.bs[1 :],
pMat, scaling)
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 fc03fd1..061eb98 100644
--- a/rrompy/reduction_methods/distributed_greedy/rb_distributed_greedy.py
+++ b/rrompy/reduction_methods/distributed_greedy/rb_distributed_greedy.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
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 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;
- '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 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.
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;
- 'trainSetGenerator': training sample points generator.
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.
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
+ uApproxReduced: Reduced approximate solution(s) with parameter(s)
+ lastSolvedApprox as sampleList.
+ lastSolvedApproxReduced: Parameter(s) corresponding to last computed
reduced approximate solution(s) as parameterList.
- uApp: Approximate solution(s) with parameter(s) lastSolvedApp as
+ uApprox: Approximate solution(s) with parameter(s) lastSolvedApprox as
sampleList.
- lastSolvedApp: Parameter(s) corresponding to last computed approximate
- solution(s) as parameterList.
+ lastSolvedApprox: 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."""
self._R = np.prod(self._S)
return self._R
@R.setter
def R(self, R):
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(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)
+ uApproxRs = self.getApproxReduced(parmus)
for j, muPL in enumerate(parmus):
mu = muPL[0]
- uApp = uApps[j]
+ uApproxR = uApproxRs[j]
for i in range(nAs):
- radiusA[:, i, j] = eval(thetaAs[i]) * uApp
+ radiusA[:, i, j] = eval(thetaAs[i]) * uApproxR
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)
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.projMat = copy(pMat)
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, full : bool = False):
"""Build affine blocks of RB linear system through projections."""
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.py b/rrompy/reduction_methods/trained_model/trained_model.py
index eb310e9..9a2b190 100644
--- a/rrompy/reduction_methods/trained_model/trained_model.py
+++ b/rrompy/reduction_methods/trained_model/trained_model.py
@@ -1,87 +1,89 @@
# 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, paramList, sampList
from rrompy.parameter import checkParameterList
from rrompy.sampling import sampleList, emptySampleList
__all__ = ['TrainedModel']
class TrainedModel:
"""
ABSTRACT
ROM approximant evaluation.
Attributes:
Data: dictionary with all that can be pickled.
"""
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))
@abstractmethod
def getApproxReduced(self, mu : paramList = []) -> sampList:
"""
Evaluate reduced representation of approximant at arbitrary parameter.
(ABSTRACT)
Args:
mu: Target parameter.
"""
pass
def getApprox(self, mu : paramList = []) -> sampList:
"""
Evaluate approximant at arbitrary parameter.
Args:
mu: Target parameter.
"""
mu, _ = checkParameterList(mu, self.data.npar)
- if not hasattr(self, "lastSolvedApp") or self.lastSolvedApp != mu:
- uAppRed = self.getApproxReduced(mu)
- self.uApp = emptySampleList()
- self.uApp.reset((self.data.projMat.shape[0], len(mu)),
- self.data.projMat.dtype)
+ if (not hasattr(self, "lastSolvedApprox")
+ or self.lastSolvedApprox != mu):
+ uApproxR = self.getApproxReduced(mu)
+ self.uApprox = emptySampleList()
+ self.uApprox.reset((self.data.projMat.shape[0], len(mu)),
+ self.data.projMat.dtype)
for i in range(len(mu)):
if isinstance(self.data.projMat, (list, sampleList,)):
- self.uApp[i] = uAppRed[i][0] * self.data.projMat[0]
- for j in range(1, uAppRed.shape[0]):
- self.uApp[i] += uAppRed[i][j] * self.data.projMat[j]
+ self.uApprox[i] = uApproxR[i][0] * self.data.projMat[0]
+ for j in range(1, uApproxR.shape[0]):
+ self.uApprox[i] += (uApproxR[i][j]
+ * self.data.projMat[j])
else:
- self.uApp[i] = self.data.projMat.dot(uAppRed[i])
- self.lastSolvedApp = mu
- return self.uApp
+ self.uApprox[i] = self.data.projMat.dot(uApproxR[i])
+ self.lastSolvedApprox = mu
+ return self.uApprox
@abstractmethod
def getPoles(self) -> Np1D:
"""
Obtain approximant poles.
Returns:
Numpy complex vector of poles.
"""
pass
diff --git a/rrompy/reduction_methods/trained_model/trained_model_pade.py b/rrompy/reduction_methods/trained_model/trained_model_pade.py
index 5891875..146de0d 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 >= 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 >= 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 >= 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 >= 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 (not hasattr(self, "lastSolvedApproxReduced")
+ or self.lastSolvedApproxReduced != mu):
if self.verbosity >= 12:
verbosityDepth("INIT", ("Evaluating approximant at mu = "
"{}.").format(mu),
timestamp = self.timestamp)
- self.uAppReduced = self.getPVal(mu) / self.getQVal(mu)
+ self.uApproxReduced = self.getPVal(mu) / self.getQVal(mu)
if self.verbosity >= 12:
verbosityDepth("DEL", "Done evaluating approximant.",
timestamp = self.timestamp)
- self.lastSolvedAppReduced = mu
- return self.uAppReduced
+ self.lastSolvedApproxReduced = mu
+ return self.uApproxReduced
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 29bf5a9..9a7ae0b 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 (not hasattr(self, "lastSolvedApproxReduced")
+ or self.lastSolvedApproxReduced != mus):
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)
+ self.uApproxReduced = emptySampleList()
+ self.uApproxReduced.reset((ARBs[0].shape[0], len(mu)),
+ self.data.projMat.dtype)
for i, muPL in enumerate(mus):
mu = muPL[0]
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 >= 17:
verbosityDepth("DEL", "Done assembling reduced model.",
timestamp = self.timestamp)
if self.verbosity >= 15:
verbosityDepth("INIT", ("Solving reduced model for mu = "
"{}.").format(mu),
timestamp = self.timestamp)
- self.uAppReduced[i] = np.linalg.solve(ARBmu, bRBmu)
+ self.uApproxReduced[i] = np.linalg.solve(ARBmu, bRBmu)
if self.verbosity >= 15:
verbosityDepth("DEL", "Done solving reduced model.",
timestamp = self.timestamp)
if self.verbosity >= 12:
verbosityDepth("DEL", "Done computing RB solution.",
timestamp = self.timestamp)
- self.lastSolvedAppReduced = mus
- return self.uAppReduced
+ self.lastSolvedApproxReduced = mus
+ return self.uApproxReduced
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/solver/scipy/__init__.py b/rrompy/solver/scipy/__init__.py
new file mode 100644
index 0000000..c126e95
--- /dev/null
+++ b/rrompy/solver/scipy/__init__.py
@@ -0,0 +1,25 @@
+# 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 .scipy_tensorize import tensorizeLS, detensorizeLS
+
+__all__ = [
+ 'tensorizeLS',
+ 'detensorizeLS'
+ ]
+
diff --git a/rrompy/solver/scipy/scipy_tensorize.py b/rrompy/solver/scipy/scipy_tensorize.py
new file mode 100644
index 0000000..6abeb2e
--- /dev/null
+++ b/rrompy/solver/scipy/scipy_tensorize.py
@@ -0,0 +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 scipy.sparse as scsp
+from rrompy.utilities.base.types import Np1D, Np2D, List
+from rrompy.utilities.exception_manager import RROMPyException
+
+__all__ = ['tensorizeLS', 'detensorizeLS']
+
+def tensorizeLS(As : List[Np2D] = [], bs : List[Np1D] = [],
+ AFormat : str = "csr"):
+ if len(As) > 0:
+# A = scsp.block_diag(tuple(As), format = AFormat)
+ A = scsp.block_diag(As, format = AFormat)
+ else:
+ A = None
+ if len(bs) > 0:
+# b = np.concatenate(tuple(bs), axis = None)
+ b = np.concatenate(bs, axis = None)
+ else:
+ b = None
+ return A, b
+
+def detensorizeLS(x:Np1D, n : int = 0, sizes : List[int] = []):
+ if n > 0 and len(sizes) > 0 and n != len(sizes):
+ raise RROMPyException("Specified n and sizes are inconsistent.")
+ if n == 0 and len(sizes) == 0:
+ raise RROMPyException("Must specify either n or sizes.")
+ if len(sizes) == 0:
+ sizes = [len(x) // n] * n
+ if n * sizes[0] != len(x):
+ raise RROMPyException(("Number of chunks must divide vector "
+ "length."))
+ n = len(sizes)
+ sEnd = np.cumsum(sizes)
+ sStart = sEnd - sizes[0]
+ return [x[sStart[j] : sEnd[j]] for j in range(n)]
diff --git a/tests/test_1_utilities/scipy_tensorize.py b/tests/test_1_utilities/scipy_tensorize.py
new file mode 100644
index 0000000..037cdf5
--- /dev/null
+++ b/tests/test_1_utilities/scipy_tensorize.py
@@ -0,0 +1,57 @@
+# 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 rrompy.solver.scipy import tensorizeLS, detensorizeLS
+
+def test_dense():
+ N = 5
+ A1 = np.random.rand(N, N)
+ x1 = np.random.rand(N)
+ b1 = A1.dot(x1)
+ A2 = np.diag(np.arange(1, N + 1) * 2.)
+ x2 = np.ones(N)
+ b2 = A2.dot(x2)
+ A3 = np.eye(N)
+ x3 = np.ones(N)
+ b3 = A3.dot(x3)
+ A, b = tensorizeLS([A1, A2, A3], [b1, b2, b3])
+ assert np.allclose(A.shape, (3 * N, 3 * N))
+ assert np.allclose(b.shape, (3 * N,))
+ x = scsp.linalg.spsolve(A, b)
+ x1O, x2O, x3O = detensorizeLS(x, 3)
+ assert np.allclose(x1O, x1, rtol = 1e-8)
+ assert np.allclose(x2O, x2, rtol = 1e-8)
+ assert np.allclose(x3O, x3, rtol = 1e-8)
+
+def test_sparse():
+ N = 5
+ A1 = scsp.eye(N, format = "csr")
+ x1 = np.random.rand(N)
+ b1 = A1.dot(x1)
+ A2 = scsp.diags(np.arange(1, N + 1) * 2., 0, format = "csr")
+ x2 = np.ones(N)
+ b2 = A2.dot(x2)
+ A, b = tensorizeLS([A1, A2], [b1, b2])
+ assert np.allclose(A.shape, (2 * N, 2 * N))
+ assert np.allclose(b.shape, (2 * N,))
+ x = scsp.linalg.spsolve(A, b)
+ x1O, x2O = detensorizeLS(x, sizes = [5, 5])
+ assert np.allclose(x1O, x1, rtol = 1e-8)
+ assert np.allclose(x2O, x2, rtol = 1e-8)