def computeKmsij(TInd, a, IPatch):
patch = lod_periodic.PatchPeriodic(world, k, TInd)
aPatch = lod_periodic.localizeCoefficient(patch, a, periodic=True)
correctorsList = lod.computeBasisCorrectors(patch, IPatch, aPatch)
csi = lod.computeBasisCoarseQuantities(patch, correctorsList, aPatch)
return patch, correctorsList, csi.Kmsij, csi
def computeIndicator(TInd):
aPatch = lambda: lod_periodic.localizeCoefficient(
patchT[TInd], aPert, periodic=True) # true coefficient
E_vh = lod.computeErrorIndicatorCoarseFromCoefficients(
patchT[TInd], muTPrimeRef, aRef, aPatch)
return E_vh
def UpdateCorrectors(TInd):
rPatch = lambda: lod_periodic.localizeCoefficient(
patchT[TInd], aPert, periodic=True)
correctorsList = lod.computeBasisCorrectors(patchT[TInd], IPatch,
rPatch)
csi = lod.computeBasisCoarseQuantities(patchT[TInd], correctorsList,
rPatch)
return patchT[TInd], correctorsList, csi.Kmsij
def compute_errorHarmT(TInd):
rPatch = lambda: lod_periodic.localizeCoefficient(
patchT[TInd], aPert, periodic=True)
alphaT = np.zeros(len(aHarmList))
NFineperEpsilon = world.NWorldFine // Nepsilon
alphaT[:len(alphaT) - 1] = (rPatch()[np.arange(len(aHarmList) - 1) *
np.prod(NFineperEpsilon)] -
alpha) / (beta - alpha)
alphaT[len(alphaT) - 1] = 1. - np.sum(alphaT[:len(alphaT) - 1])
aharmT_combined = np.dot(alphaT, aHarmList)
aharmT = computeAharm(TInd, aPert)
return np.abs(aharmT - aharmT_combined)
def computeAharm(TInd, a):
assert (dim == 1)
patch = lod_periodic.PatchPeriodic(world, 0, TInd)
aPatch = lod_periodic.localizeCoefficient(patch, a, periodic=True)
aPatchHarm = np.sum(1. / aPatch)
return world.NWorldFine / (world.NWorldCoarse * aPatchHarm)
def compute_combinedT(TInd):
rPatch = lambda: lod_periodic.localizeCoefficient(
patchT[TInd], aPert, periodic=True)
#direct determination of alpha without optimization
assert (model['name'] in [
'check', 'incl', 'inclvalue', 'inclfill', 'inclshift', 'inclLshape'
])
if model['name'] == 'check':
alphaT = np.zeros(len(aRefList))
alpha = model['alpha']
beta = model['beta']
NFineperEpsilon = world.NWorldFine // Nepsilon
NEpsilonperPatchCoarse = patchT[TInd].NPatchCoarse * (
Nepsilon // world.NWorldCoarse)
if dim == 2:
tmp_indx = np.array([
np.arange(len(aRefList) - 1) // NEpsilonperPatchCoarse[0],
np.arange(len(aRefList) - 1) % NEpsilonperPatchCoarse[0]
])
indx = tmp_indx[0] * NFineperEpsilon[1] * patchT[
TInd].NPatchFine[0] + tmp_indx[1] * NFineperEpsilon[0]
alphaT[:len(alphaT) -
1] = (rPatch()[indx] - alpha) / (beta - alpha)
elif dim == 1:
alphaT[:len(alphaT) -
1] = (rPatch()[np.arange(len(aRefList) - 1) *
np.prod(NFineperEpsilon)] -
alpha) / (beta - alpha)
alphaT[len(alphaT) - 1] = 1. - np.sum(alphaT[:len(alphaT) - 1])
elif model['name'] == 'incl':
alphaT = np.zeros(len(aRefList))
bgval = model['bgval']
inclval = model['inclval']
blx = model['left'][0]
bly = model['left'][1]
NFineperEpsilon = world.NWorldFine // Nepsilon
NEpsilonperPatchCoarse = patchT[TInd].NPatchCoarse * (
Nepsilon // world.NWorldCoarse)
tmp_indx = np.array([
np.arange(len(aRefList) - 1) // NEpsilonperPatchCoarse[0] +
blx,
np.arange(len(aRefList) - 1) % NEpsilonperPatchCoarse[0] + bly
])
indx = (tmp_indx[0] * NFineperEpsilon[1] * patchT[TInd].NPatchFine[0]).astype(int) \
+ (tmp_indx[1] * NFineperEpsilon[0]).astype(int)
alphaT[:len(alphaT) -
1] = (inclval - rPatch()[indx]) / (inclval - bgval)
alphaT[len(alphaT) - 1] = 1. - np.sum(alphaT[:len(alphaT) - 1])
elif model['name'] == 'inclvalue':
alphaT = np.zeros(len(aRefList))
defval = model['defval']
inclval = model['inclval']
blx = model['left'][0]
bly = model['left'][1]
NFineperEpsilon = world.NWorldFine // Nepsilon
NEpsilonperPatchCoarse = patchT[TInd].NPatchCoarse * (
Nepsilon // world.NWorldCoarse)
tmp_indx = np.array([
np.arange(len(aRefList) - 1) // NEpsilonperPatchCoarse[0] +
blx,
np.arange(len(aRefList) - 1) % NEpsilonperPatchCoarse[0] + bly
])
indx = (tmp_indx[0] * NFineperEpsilon[1] * patchT[TInd].NPatchFine[0]).astype(int) \
+ (tmp_indx[1] * NFineperEpsilon[0]).astype(int)
alphaT[:len(alphaT) -
1] = (inclval - rPatch()[indx]) / (inclval - defval)
alphaT[len(alphaT) - 1] = 1. - np.sum(alphaT[:len(alphaT) - 1])
elif model['name'] == 'inclfill':
alphaT = np.zeros(len(aRefList))
bgval = model['bgval']
inclval = model['inclval']
NFineperEpsilon = world.NWorldFine // Nepsilon
NEpsilonperPatchCoarse = patchT[TInd].NPatchCoarse * (
Nepsilon // world.NWorldCoarse)
tmp_indx = np.array([
np.arange(len(aRefList) - 1) // NEpsilonperPatchCoarse[0],
np.arange(len(aRefList) - 1) % NEpsilonperPatchCoarse[0]
])
indx = (tmp_indx[0] * NFineperEpsilon[1] * patchT[TInd].NPatchFine[0]).astype(int) \
+ (tmp_indx[1] * NFineperEpsilon[0]).astype(int)
alphaT[:len(alphaT) -
1] = (bgval - rPatch()[indx]) / (bgval - inclval)
alphaT[len(alphaT) - 1] = 1. - np.sum(alphaT[:len(alphaT) - 1])
elif model['name'] == 'inclshift':
alphaT = np.zeros(len(aRefList))
bgval = model['bgval']
inclval = model['inclval']
NFineperEpsilon = world.NWorldFine // Nepsilon
NEpsilonperPatchCoarse = patchT[TInd].NPatchCoarse * (
Nepsilon // world.NWorldCoarse)
assert (model['def_bl'][0] < model['left'][0]
or model['def_bl'][1] < model['left'][1]
or model['def_bl'][0] >= model['right'][0]
or model['def_bl'][1] >= model['right'][1])
# other cases not yet implemented
blx = model['def_bl'][0]
bly = model['def_bl'][1]
tmp_indx = np.array([
np.arange(len(aRefList) - 1) // NEpsilonperPatchCoarse[0] +
blx,
np.arange(len(aRefList) - 1) % NEpsilonperPatchCoarse[0] + bly
])
indx = (tmp_indx[0] * NFineperEpsilon[1] * patchT[TInd].NPatchFine[0]).astype(int) \
+ (tmp_indx[1] * NFineperEpsilon[0]).astype(int)
alphaT[:len(alphaT) -
1] = (bgval - rPatch()[indx]) / (bgval - inclval)
alphaT[len(alphaT) - 1] = 1. - np.sum(alphaT[:len(alphaT) - 1])
elif model['name'] == 'inclLshape':
alphaT = np.zeros(len(aRefList))
bgval = model['bgval']
inclval = model['inclval']
blx = model['def_bl'][0]
bly = model['def_bl'][1]
NFineperEpsilon = world.NWorldFine // Nepsilon
NEpsilonperPatchCoarse = patchT[TInd].NPatchCoarse * (
Nepsilon // world.NWorldCoarse)
tmp_indx = np.array([
np.arange(len(aRefList) - 1) // NEpsilonperPatchCoarse[0] +
blx,
np.arange(len(aRefList) - 1) % NEpsilonperPatchCoarse[0] + bly
])
indx = (tmp_indx[0] * NFineperEpsilon[1] * patchT[TInd].NPatchFine[0]).astype(int) \
+ (tmp_indx[1] * NFineperEpsilon[0]).astype(int)
alphaT[:len(alphaT) -
1] = (inclval - rPatch()[indx]) / (inclval - bgval)
alphaT[len(alphaT) - 1] = 1. - np.sum(alphaT[:len(alphaT) - 1])
if compute_indicator:
assert (correctorsList is not None)
indicatorValue = indicator.computeErrorIndicatorFineMultiple(
patchT[TInd], correctorsList, aRefList, alphaT)
defects = np.sum(alphaT[:len(alphaT) - 1])
indicatorT = [indicatorValue, defects]
else:
indicatorT = None
if compute_correc:
assert (correctorsList is not None)
correctorsT = np.einsum('i, ijk -> jk', alphaT, correctorsList)
else:
correctorsT = None
KmsijT = np.einsum('i, ijk -> jk', alphaT, KmsijList)
return KmsijT, indicatorT, correctorsT