def custom_violin_stats(data, weights):
# Get weighted median and mean (using weighted module for median)
median = weighted.quantile_1D(data, weights, 0.5)
pcent_16 = weighted.quantile_1D(data, weights, 0.16)
pcent_84 = weighted.quantile_1D(data, weights, 0.84)
mean, sumw = np.ma.average(data, weights=list(weights), returned=True)
# Use matplotlib violin_stats, which expects a function that takes in data and coords
# which we get from closure above
results = violin_stats(data, vdensity_with_weights(weights))
# Update result dictionary with our updated info
results[0][u"mean"] = mean
results[0][u"median"] = median
results[0][u"pcent_16"] = pcent_16
results[0][u"pcent_84"] = pcent_84
# No need to do this, since it should be populated from violin_stats
# results[0][u"min"] = np.min(data)
# results[0][u"max"] = np.max(data)
return results
def weighted_quantiles(data, labels, weights, return_quantiles=False):
num_categories = len(labels)
breaks = linspace(0, 1, num_categories + 1)
quantiles = [
weighted.quantile_1D(data, weights, mybreak) for mybreak in breaks[1:]
]
ret = zeros(len(data))
for i in range(0, len(quantiles) - 1):
lower = quantiles[i]
upper = quantiles[i + 1]
ret[and_(data >= lower, data < upper)] = labels[i]
if return_quantiles:
return ret + 1, quantiles
else:
return ret + 1
def custom_violin_stats(data, weights):
"""Taken from https://colab.research.google.com/drive/1cSnJGKJEqbllkPbF2z0cnfdwT40sUKKR#scrollTo=RIcLIr5XJRmx"""
# Get weighted median and mean (using weighted module for median)
median = weighted.quantile_1D(data, weights, 0.5)
mean, sumw = np.ma.average(data, weights=list(weights), returned=True)
# Use matplotlib violin_stats, which expects a function that takes in data and coords
# which we get from closure above
results = violin_stats(data, vdensity_with_weights(weights))
# Update result dictionary with our updated info
results[0][u"mean"] = mean
results[0][u"median"] = median
# No need to do this, since it should be populated from violin_stats
# results[0][u"min"] = np.min(data)
# results[0][u"max"] = np.max(data)
return results
def test_weighted_median_1D_unsorted(self):
# Median of the unsorted array
self.assertEqual(quantile_1D(self.a1Du, self.a1Du_w, 0.5), 30)
self.assertEqual(quantile_1D(self.a1Du, np.ones_like(self.a1Du), 0.5), 27.5)
def analyzeResults(self):
self.matched = [] # for paired comparisons
for i, f in enumerate(self.pickles):
s = f.split(os.sep)[-1]
if not (fnmatch.filter(itertools.chain.from_iterable(self.matched),
"*" + s)):
self.matched.append(fnmatch.filter(self.pickles, "*" + s))
plotname = f.replace('.pkl', '.xplt')
print("\n... Analyzing results for {:s}".format(plotname))
results = febio.FebPlt(plotname)
stress = np.zeros((len(self.data[f]['elements']), 3, 3), float)
strain = np.copy(stress)
#material element volumes
mvolumes = np.zeros(len(self.data[f]['elements']), float)
#spatial element volumes
svolumes = np.copy(mvolumes)
nnodes = len(list(results.NodeData.keys()))
displacement = np.zeros((nnodes, 3))
for j, n in enumerate(self.data[f]['nodes']):
tmp = results.NodeData[j + 1]['displacement'][-1, :]
displacement[j, :] = [tmp[0], tmp[1], tmp[2]]
pstress = []
pstressdir = []
pstrain = []
pstraindir = []
for j, e in enumerate(self.data[f]['elements']):
tmp = results.ElementData[j + 1]['stress'][-1, :]
stress[j, :, :] = [[tmp[0], tmp[3], tmp[5]],
[tmp[3], tmp[1], tmp[4]],
[tmp[5], tmp[4], tmp[2]]]
#material coordinates
X = np.zeros((4, 3), float)
#spatial coordinates
x = np.zeros((4, 3), float)
for k in range(4):
X[k, :] = self.data[f]['nodes'][e[k] - 1]
x[k, :] = (X[k, :] +
results.NodeData[e[k]]['displacement'][-1, :])
#set up tangent space
W = np.zeros((6, 3), float)
w = np.zeros((6, 3), float)
for k, c in enumerate([(0, 1), (0, 2), (0, 3), (1, 3), (2, 3),
(1, 2)]):
W[k, :] = X[c[1], :] - X[c[0], :]
w[k, :] = x[c[1], :] - x[c[0], :]
dX = np.zeros((6, 6), float)
ds = np.zeros((6, 1), float)
for k in range(6):
for l in range(3):
dX[k, l] = 2 * W[k, l]**2
dX[k, 3] = 4 * W[k, 0] * W[k, 1]
dX[k, 4] = 4 * W[k, 1] * W[k, 2]
dX[k, 5] = 4 * W[k, 0] * W[k, 2]
ds[k, 0] = (np.linalg.norm(w[k, :])**2 -
np.linalg.norm(W[k, :])**2)
#solve for strain
E = np.linalg.solve(dX, ds)
#get volumes
mvolumes[j] = old_div(
np.abs(np.dot(W[0, :], np.cross(W[1, :], W[2, :]))), 6.0)
svolumes[j] = old_div(
np.abs(np.dot(w[0, :], np.cross(w[1, :], w[2, :]))), 6.0)
strain[j, :, :] = [[E[0], E[3], E[5]], [E[3], E[1], E[4]],
[E[5], E[4], E[2]]]
#eigenvalues and eigenvectors of stress and strain tensors
#eigenvectors are normalized
eigstrain, eigstraindir = np.linalg.eigh(strain[j, :, :])
order = np.argsort(eigstrain)
eigstrain = eigstrain[order]
eigstraindir /= np.linalg.norm(eigstraindir,
axis=0,
keepdims=True)
eigstraindir = eigstraindir[:, order]
pstrain.append(eigstrain)
pstraindir.append(eigstraindir)
eigstress, eigstressdir = np.linalg.eigh(stress[j, :, :])
order = np.argsort(eigstress)
eigstress = eigstress[order]
eigstressdir /= np.linalg.norm(eigstressdir,
axis=0,
keepdims=True)
eigstressdir = eigstressdir[:, order]
pstress.append(eigstress)
pstressdir.append(eigstressdir)
pstress = np.array(pstress)
pstressdir = np.array(pstressdir)
pstrain = np.array(pstrain)
pstraindir = np.array(pstraindir)
#save reference volumes
self.volumes.update({f: mvolumes})
self.results['Effective Strain (von Mises)'].update({
f:
np.sqrt(
old_div(((pstrain[:, 2] - pstrain[:, 1])**2 +
(pstrain[:, 1] - pstrain[:, 0])**2 +
(pstrain[:, 2] - pstrain[:, 0])**2), 2.0))
})
self.results['Maximum Compressive Strain'].update(
{f: np.outer(pstrain[:, 0], [1, 1, 1]) * pstraindir[:, :, 0]})
self.results['Maximum Tensile Strain'].update(
{f: np.outer(pstrain[:, 2], [1, 1, 1]) * pstraindir[:, :, 2]})
self.results['Maximum Shear Strain'].update(
{f: 0.5 * (pstrain[:, 2] - pstrain[:, 0])})
self.results['Volumetric Strain'].update(
{f: old_div(svolumes, mvolumes) - 1.0})
self.results['Effective Stress (von Mises)'].update({
f:
np.sqrt(
old_div(((pstress[:, 2] - pstress[:, 1])**2 +
(pstress[:, 1] - pstress[:, 0])**2 +
(pstress[:, 2] - pstress[:, 0])**2), 2.0))
})
self.results['Maximum Compressive Stress'].update(
{f: np.outer(pstress[:, 0], [1, 1, 1]) * pstressdir[:, :, 0]})
self.results['Maximum Tensile Stress'].update(
{f: np.outer(pstress[:, 2], [1, 1, 1]) * pstressdir[:, :, 2]})
self.results['Maximum Shear Stress'].update(
{f: 0.5 * (pstress[:, 2] - pstress[:, 0])})
self.results['Pressure'].update(
{f: old_div(np.sum(pstress, axis=1), 3.0)})
self.results['Displacement'].update({f: displacement})
for i, k in enumerate(self.outputs.keys()):
if self.outputs[k].get():
for m in self.matched:
weights = old_div(self.volumes[m[0]],
np.sum(self.volumes[m[0]]))
for j, f in enumerate(m):
if len(self.results[k][f].shape) > 1:
dat = np.ravel(
np.linalg.norm(self.results[k][f], axis=1))
else:
dat = np.ravel(self.results[k][f])
if self.analysis['Generate Histograms'].get():
IQR = np.subtract(*np.percentile(dat, [75, 25]))
nbins = (int(
old_div(
np.ptp(dat),
(2 * IQR * dat.size**(old_div(-1., 3.))))))
h = histogram(dat, numbins=nbins, weights=weights)
bins = np.linspace(h[1],
h[1] + h[2] * nbins,
nbins,
endpoint=False)
self.histograms[k][f] = {
'bins': bins,
'heights': h[0],
'width': h[2]
}
if self.analysis['Tukey Boxplots'].get():
quantiles = np.zeros(3, float)
for n, q in enumerate([0.25, 0.5, 0.75]):
quantiles[n] = quantile_1D(dat, weights, q)
self.boxwhiskers[k][f] = {
'quantiles': quantiles,
'data': dat
}
if self.analysis['Calculate Differences'].get():
for c in itertools.combinations(m, 2):
if len(self.results[k][c[0]].shape) > 1:
dat1 = np.ravel(
np.linalg.norm(self.results[k][c[0]],
axis=1))
dat2 = np.ravel(
np.linalg.norm(self.results[k][c[1]],
axis=1))
else:
dat1 = np.ravel(self.results[k][c[0]])
dat2 = np.ravel(self.results[k][c[1]])
difference = dat2 - dat1
wrms = np.sqrt(
np.average(difference**2, weights=weights))
self.differences[k][c[1] + "MINUS" + c[0]] = {
'difference': difference,
'weighted RMS': wrms
}
self.saveResults()
print("... ... Analysis Complete")
def test_weighted_median_1D_unsorted(self):
# Median of the unsorted array
self.assertEqual(quantile_1D(self.a1Du, self.a1Du_w, 0.5), 30)
self.assertEqual(quantile_1D(self.a1Du, np.ones_like(self.a1Du), 0.5),
27.5)
def analyzeResults(self):
self.matched = [] # for paired comparisons
for i, f in enumerate(self.pickles):
s = f.split(os.sep)[-1]
if not(fnmatch.filter(
itertools.chain.from_iterable(self.matched), "*" + s)):
self.matched.append(fnmatch.filter(self.pickles, "*" + s))
plotname = f.replace('.pkl', '.xplt')
print("\n... Analyzing results for {:s}".format(plotname))
results = febio.FebPlt(plotname)
stress = np.zeros((len(self.data[f]['elements']), 3, 3), float)
strain = np.copy(stress)
#material element volumes
mvolumes = np.zeros(len(self.data[f]['elements']), float)
#spatial element volumes
svolumes = np.copy(mvolumes)
nnodes = len(list(results.NodeData.keys()))
displacement = np.zeros((nnodes, 3))
for j, n in enumerate(self.data[f]['nodes']):
tmp = results.NodeData[j + 1]['displacement'][-1, :]
displacement[j, :] = [tmp[0], tmp[1], tmp[2]]
pstress = []
pstressdir = []
pstrain = []
pstraindir = []
for j, e in enumerate(self.data[f]['elements']):
tmp = results.ElementData[j + 1]['stress'][-1, :]
stress[j, :, :] = [[tmp[0], tmp[3], tmp[5]],
[tmp[3], tmp[1], tmp[4]],
[tmp[5], tmp[4], tmp[2]]]
#material coordinates
X = np.zeros((4, 3), float)
#spatial coordinates
x = np.zeros((4, 3), float)
for k in range(4):
X[k, :] = self.data[f]['nodes'][e[k] - 1]
x[k, :] = (X[k, :] +
results.NodeData[e[k]]['displacement'][-1, :])
#set up tangent space
W = np.zeros((6, 3), float)
w = np.zeros((6, 3), float)
for k, c in enumerate(
[(0, 1), (0, 2), (0, 3), (1, 3), (2, 3), (1, 2)]):
W[k, :] = X[c[1], :] - X[c[0], :]
w[k, :] = x[c[1], :] - x[c[0], :]
dX = np.zeros((6, 6), float)
ds = np.zeros((6, 1), float)
for k in range(6):
for l in range(3):
dX[k, l] = 2 * W[k, l] ** 2
dX[k, 3] = 4 * W[k, 0] * W[k, 1]
dX[k, 4] = 4 * W[k, 1] * W[k, 2]
dX[k, 5] = 4 * W[k, 0] * W[k, 2]
ds[k, 0] = (np.linalg.norm(w[k, :]) ** 2 -
np.linalg.norm(W[k, :]) ** 2)
#solve for strain
E = np.linalg.solve(dX, ds)
#get volumes
mvolumes[j] = old_div(np.abs(
np.dot(W[0, :], np.cross(W[1, :], W[2, :]))), 6.0)
svolumes[j] = old_div(np.abs(
np.dot(w[0, :], np.cross(w[1, :], w[2, :]))), 6.0)
strain[j, :, :] = [[E[0], E[3], E[5]],
[E[3], E[1], E[4]],
[E[5], E[4], E[2]]]
#eigenvalues and eigenvectors of stress and strain tensors
#eigenvectors are normalized
eigstrain, eigstraindir = np.linalg.eigh(strain[j, :, :])
order = np.argsort(eigstrain)
eigstrain = eigstrain[order]
eigstraindir /= np.linalg.norm(eigstraindir, axis=0, keepdims=True)
eigstraindir = eigstraindir[:, order]
pstrain.append(eigstrain)
pstraindir.append(eigstraindir)
eigstress, eigstressdir = np.linalg.eigh(stress[j, :, :])
order = np.argsort(eigstress)
eigstress = eigstress[order]
eigstressdir /= np.linalg.norm(eigstressdir, axis=0, keepdims=True)
eigstressdir = eigstressdir[:, order]
pstress.append(eigstress)
pstressdir.append(eigstressdir)
pstress = np.array(pstress)
pstressdir = np.array(pstressdir)
pstrain = np.array(pstrain)
pstraindir = np.array(pstraindir)
#save reference volumes
self.volumes.update({f: mvolumes})
self.results['Effective Strain (von Mises)'].update(
{f: np.sqrt(old_div(((pstrain[:, 2] - pstrain[:, 1]) ** 2 +
(pstrain[:, 1] - pstrain[:, 0]) ** 2 +
(pstrain[:, 2] - pstrain[:, 0]) ** 2),
2.0))})
self.results['Maximum Compressive Strain'].update(
{f: np.outer(pstrain[:, 0], [1 , 1, 1]) * pstraindir[:, :, 0]})
self.results['Maximum Tensile Strain'].update(
{f: np.outer(pstrain[:, 2], [1, 1, 1]) * pstraindir[:, :, 2]})
self.results['Maximum Shear Strain'].update(
{f: 0.5 * (pstrain[:, 2] - pstrain[:, 0])})
self.results['Volumetric Strain'].update(
{f: old_div(svolumes, mvolumes) - 1.0})
self.results['Effective Stress (von Mises)'].update(
{f: np.sqrt(old_div(((pstress[:, 2] - pstress[:, 1]) ** 2 +
(pstress[:, 1] - pstress[:, 0]) ** 2 +
(pstress[:, 2] - pstress[:, 0]) ** 2), 2.0))})
self.results['Maximum Compressive Stress'].update(
{f: np.outer(pstress[:, 0], [1 , 1, 1]) * pstressdir[:, :, 0]})
self.results['Maximum Tensile Stress'].update(
{f: np.outer(pstress[:, 2], [1, 1, 1]) * pstressdir[:, :, 2]})
self.results['Maximum Shear Stress'].update(
{f: 0.5 * (pstress[:, 2] - pstress[:, 0])})
self.results['Pressure'].update(
{f: old_div(np.sum(pstress, axis=1), 3.0)})
self.results['Displacement'].update({f: displacement})
for i, k in enumerate(self.outputs.keys()):
if self.outputs[k].get():
for m in self.matched:
weights = old_div(self.volumes[m[0]], np.sum(self.volumes[m[0]]))
for j, f in enumerate(m):
if len(self.results[k][f].shape) > 1:
dat = np.ravel(np.linalg.norm(self.results[k][f], axis=1))
else:
dat = np.ravel(self.results[k][f])
if self.analysis['Generate Histograms'].get():
IQR = np.subtract(*np.percentile(dat, [75, 25]))
nbins = (int(old_div(np.ptp(dat),
(2 * IQR * dat.size ** (old_div(-1., 3.))))))
h = histogram(dat, numbins=nbins, weights=weights)
bins = np.linspace(h[1], h[1] + h[2] * nbins,
nbins, endpoint=False)
self.histograms[k][f] = {'bins': bins,
'heights': h[0],
'width': h[2]}
if self.analysis['Tukey Boxplots'].get():
quantiles = np.zeros(3, float)
for n, q in enumerate([0.25, 0.5, 0.75]):
quantiles[n] = quantile_1D(dat, weights, q)
self.boxwhiskers[k][f] = {'quantiles': quantiles,
'data': dat}
if self.analysis['Calculate Differences'].get():
for c in itertools.combinations(m, 2):
if len(self.results[k][c[0]].shape) > 1:
dat1 = np.ravel(np.linalg.norm(self.results[k][c[0]], axis=1))
dat2 = np.ravel(np.linalg.norm(self.results[k][c[1]], axis=1))
else:
dat1 = np.ravel(self.results[k][c[0]])
dat2 = np.ravel(self.results[k][c[1]])
difference = dat2 - dat1
wrms = np.sqrt(np.average(difference ** 2,
weights=weights))
self.differences[k][c[1] + "MINUS" + c[0]] = {
'difference': difference, 'weighted RMS': wrms}
self.saveResults()
print("... ... Analysis Complete")