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fracture3_pod.py
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Mon, Jun 10, 12:08

fracture3_pod.py
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import numpy as np
from mpl_toolkits.mplot3d import Axes3D
from matplotlib import pyplot as plt
from rrompy.hfengines.linear_problem.tridimensional import \
MembraneFractureEngine3 as MFE
from rrompy.reduction_methods.standard import RationalInterpolant as RI
from rrompy.reduction_methods.standard import ReducedBasis as RB
from rrompy.reduction_methods.pivoted import RationalInterpolantPivoted as RIP
from rrompy.reduction_methods.pivoted import ReducedBasisPivoted as RBP
from rrompy.parameter.parameter_sampling import (QuadratureSampler as QS,
QuadratureSamplerTotal as QST,
ManualSampler as MS,
RandomSampler as RS)
verb = 70
size = 4
show_sample = False
show_norm = False
clip = -1
#clip = .4
#clip = .6
Delta = 0
MN = 5
R = (MN + 3) * (MN + 2) * (MN + 1) // 6
S = [int(np.ceil(R ** (1. / 3.)))] * 3
PODTol = 1e-8
SPivot = [MN + 1, 5, 5]
MMarginal = SPivot[1] - 1
matchingWeight = 10.
samples = "centered"
samples = "standard"
#samples = "pivoted"
algo = "rational"
#algo = "RB"
sampling = "quadrature"
#sampling = "quadrature_total"
#sampling = "random"
samplingM = "quadrature"
samplingM = "quadrature_total"
#samplingM = "random"
polydegreetype = "TOTAL"
#polydegreetype = "FULL"
if samples == "standard":
radial = ""
# radial = "_gaussian"
# radial = "_thinplate"
# radial = "_multiquadric"
rW0 = 5.
radialWeight = [rW0] * 3
if samples == "pivoted":
radial = ""
# radial = "_gaussian"
# radial = "_thinplate"
# radial = "_multiquadric"
rW0 = 5.
radialWeight = [rW0]
radialM = ""
# radialM = "_gaussian"
# radialM = "_thinplate"
# radialM = "_multiquadric"
rMW0 = 2.
radialWeightM = [rMW0] * 2
assert Delta <= 0
if size == 1:
mu0 = [47.5 ** .5, .4, .05]
mutar = [50 ** .5, .45, .07]
murange = [[40 ** .5, .3, .025], [55 ** .5, .5, .075]]
if size == 2:
mu0 = [50 ** .5, .3, .02]
mutar = [55 ** .5, .4, .03]
murange = [[40 ** .5, .1, .005], [60 ** .5, .5, .035]]
if size == 3:
mu0 = [45 ** .5, .5, .05]
mutar = [47 ** .5, .4, .045]
murange = [[40 ** .5, .3, .04], [50 ** .5, .7, .06]]
if size == 4:
mu0 = [45 ** .5, .4, .05]
mutar = [47 ** .5, .45, .045]
murange = [[40 ** .5, .3, .04], [50 ** .5, .5, .06]]
if size == 5:
mu0 = [45 ** .5, .5, .05]
mutar = [47 ** .5, .45, .045]
murange = [[40 ** .5, .3, .04], [50 ** .5, .7, .06]]
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[0][2] + bEff*murange[1][2]],
[(aEff*murange[1][0]**2. + bEff*murange[0][0]**2.) ** .5,
aEff*murange[1][1] + bEff*murange[0][1],
aEff*murange[1][2] + bEff*murange[0][2]]]
H = 1.
L = .75
delta = .05
n = 50
solver = MFE(mu0 = mu0, H = H, L = L, delta = delta, n = n, verbosity = verb)
rescalingExp = [2., 1., 1.]
if algo == "rational":
params = {'N':MN, 'M':MN + Delta, 'S':S, 'POD':True,
'polydegreetype':polydegreetype}
if samples == "standard":
params['polybasis'] = "CHEBYSHEV" + radial
# params['polybasis'] = "LEGENDRE" + radial
# params['polybasis'] = "MONOMIAL" + radial
params['radialDirectionalWeights'] = radialWeight
method = RI
elif samples == "centered":
params['polybasis'] = "MONOMIAL"
params['S'] = R
method = RI
elif samples == "pivoted":
params['S'] = [SPivot[0]]
params['SMarginal'] = SPivot[1:]
params['MMarginal'] = MMarginal
params['polybasisPivot'] = "CHEBYSHEV" + radial
params['polybasisMarginal'] = "MONOMIAL" + radialM
params['matchingWeight'] = matchingWeight
params['radialDirectionalWeightsPivot'] = radialWeight
params['radialDirectionalWeightsMarginal'] = radialWeightM
method = RIP
else: #if algo == "RB":
params = {'R':(MN + 3 + Delta) * (MN + 2 + Delta) * (MN + 1 + Delta) // 6,
'S':S, 'POD':True, 'PODTolerance':PODTol}
if samples == "standard":
method = RB
elif samples == "centered":
params['S'] = R
method = RB
elif samples == "pivoted":
params['S'] = [SPivot[0]]
params['SMarginal'] = SPivot[1:]
params['MMarginal'] = MMarginal
params['polybasisMarginal'] = "MONOMIAL" + radialM
params['matchingWeight'] = matchingWeight
params['radialDirectionalWeightsMarginal'] = radialWeightM
method = RBP
if samples == "standard":
if sampling == "quadrature":
params['sampler'] = QS(murange, "CHEBYSHEV", scalingExp = rescalingExp)
# params['sampler'] = QS(murange, "GAUSSLEGENDRE",scalingExp = rescalingExp)
# params['sampler'] = QS(murange, "UNIFORM", scalingExp = rescalingExp)
params['S'] = [max(j, MN + 1) for j in params['S']]
elif sampling == "quadrature_total":
params['sampler'] = QST(murange, "CHEBYSHEV", scalingExp = rescalingExp)
params['S'] = R
else: # if sampling == "random":
params['sampler'] = RS(murange, "HALTON", scalingExp = rescalingExp)
params['S'] = R
elif samples == "centered":
params['sampler'] = MS(murange, points = [mu0], scalingExp = rescalingExp)
elif samples == "pivoted":
if sampling == "quadrature":
params['samplerPivot'] = QS([murange[0][0], murange[1][0]], "CHEBYSHEV")
# params['samplerPivot'] = QS([murange[0][0], murange[1][0]], "GAUSSLEGENDRE")
# params['samplerPivot'] = QS([murange[0][0], murange[1][0]], "UNIFORM")
elif sampling == "quadrature_total":
params['samplerPivot'] = QST([murange[0][0], murange[1][0]], "CHEBYSHEV")
params['S'] = MN + 1
else: # if sampling == "random":
params['samplerPivot'] = RS([murange[0][0], murange[1][0]], "HALTON")
params['S'] = MN + 1
if samplingM == "quadrature":
params['samplerMarginal'] = QS([murange[0][1:], murange[1][1:]], "UNIFORM")
elif samplingM == "quadrature_total":
params['samplerMarginal'] = QST([murange[0][1:], murange[1][1:]], "CHEBYSHEV")
params['SMarginal'] = (MMarginal + 2) * (MMarginal + 1) // 2
params['polybasisMarginal'] = "CHEBYSHEV" + radialM
else: # if samplingM == "random":
params['samplerMarginal'] = RS([murange[0][1:], murange[1][1:]], "HALTON")
params['SMarginal'] = (MMarginal + 2) * (MMarginal + 1) // 2
if samples != "pivoted":
approx = method(solver, mu0 = mu0, approxParameters = params,
verbosity = verb)
else:
approx = method(solver, mu0 = mu0, directionPivot = [0],
approxParameters = params, verbosity = verb)
if samples != "centered": approx.samplingEngine.allowRepeatedSamples = False
approx.setupApprox()
if show_sample:
from fracture3_warping import fracture3_warping
warps = fracture3_warping(solver.V.mesh(), L, mutar[1], delta, mutar[2])
approx.plotApprox(mutar, warps, name = 'u_app', what = "REAL")
approx.plotHF(mutar, warps, name = 'u_HF', what = "REAL")
approx.plotErr(mutar, warps, name = 'err', what = "REAL")
# approx.plotRes(mutar, warps, name = 'res', what = "REAL")
appErr = approx.normErr(mutar)
solNorm = approx.normHF(mutar)
resNorm = approx.normRes(mutar)
RHSNorm = approx.normRHS(mutar)
print(('SolNorm:\t{}\nErr:\t{}\nErrRel:\t{}').format(solNorm, appErr,
np.divide(appErr, solNorm)))
print(('RHSNorm:\t{}\nRes:\t{}\nResRel:\t{}').format(RHSNorm, resNorm,
np.divide(resNorm, RHSNorm)))
fig = plt.figure(figsize = (8, 6))
ax = Axes3D(fig)
ax.scatter(np.real(approx.mus(0) ** 2.), np.real(approx.mus(1)),
np.real(approx.mus(2)), '.')
plt.show()
plt.close()
approx.verbosity = 0
approx.trainedModel.verbosity = 0
from plot_zero_set_3 import plotZeroSet3
#muZeroVals, Qvals = plotZeroSet3(murange, murangeEff, approx, mu0, 200,
# [None, mu0[1], mu0[2]], [2., 1., 1.],
# clip = clip)
#muZeroVals, Qvals = plotZeroSet3(murange, murangeEff, approx, mu0, 200,
# [None, None, mu0[2]], [2., 1., 1.],
# clip = clip)
#muZeroVals, Qvals = plotZeroSet3(murange, murangeEff, approx, mu0, 200,
# [None, mu0[1], None], [2., 1., 1.],
# clip = clip)
muZeroScatter = plotZeroSet3(murange, murangeEff, approx, mu0, 50,
[None, None, None], [2., 1., 1.], clip = clip)
if show_norm:
solver._solveBatchSize = 25
from plot_inf_set_3 import plotInfSet3
muInfVals, normEx, normApp, normRes, normErr, beta = plotInfSet3(
murange, murangeEff, approx, mu0, 25,
[None, mu0[1], mu0[2]], [2., 1., 1.],
clip = clip, relative = False,
normalizeDen = True)
muInfVals, normEx, normApp, normRes, normErr, beta = plotInfSet3(
murange, murangeEff, approx, mu0, 25,
[None, None, mu0[2]], [2., 1., 1.],
clip = clip, relative = False,
normalizeDen = True)
muInfVals, normEx, normApp, normRes, normErr, beta = plotInfSet3(
murange, murangeEff, approx, mu0, 25,
[None, mu0[1], None], [2., 1., 1.],
clip = clip, relative = False,
normalizeDen = True)
print(approx.getPoles([None, .5, .05]) ** 2.)

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