def get_pred(sn, el, ns, set_id, step, compl):
"""read the file for euler angle, total strain and plastic strain fields"""
f = h5py.File("ref_%s%s_s%s.hdf5" % (ns, set_id, step), 'r')
print f.get('euler').shape
euler = f.get('euler')[sn, ...]
euler = euler.swapaxes(0, 1)
print euler.shape
et = np.zeros((el**3, 6))
ep = np.zeros((el**3, 6))
for ii in xrange(6):
comp = compl[ii]
tmp = f.get('r%s_epsilon_t' % comp)[sn, ...]
et[:, ii] = tmp.reshape(el**3)
tmp = f.get('r%s_epsilon_p' % comp)[sn, ...]
ep[:, ii] = tmp.reshape(el**3)
f.close()
epn_max = np.argmax(tensnorm(ep))
"""find the deviatoric strain tensor"""
print np.all(np.isclose(np.sum(et[:, 0:3]), np.zeros(el**3)))
et_ = np.zeros(et.shape)
et_[:,
0:3] = et[:,
0:3] - (1. / 3.) * np.expand_dims(np.sum(et[:, 0:3], 1), 1)
et_[:, 3:] = et[:, 3:]
print et_[epn_max, :]
print np.all(np.isclose(np.sum(et_[:, 0:3]), np.zeros(el**3)))
"""find the norm of the tensors"""
en = tensnorm(et_)
print "sn: %s" % sn
print "min(en): %s" % en.min()
print "max(en): %s" % en.max()
epn = tensnorm(ep)
orig = epn
"""normalize the deviatoric strain tensor"""
et_n = et_ / np.expand_dims(en, 1)
print np.all(np.isclose(tensnorm(et_n), np.ones(el**3)))
"""write the normalized deviatioric total strain and plastic strains
in matrix form"""
et_m = np.zeros((el**3, 3, 3))
et_m[:, 0, 0] = et_n[:, 0]
et_m[:, 1, 1] = et_n[:, 1]
et_m[:, 2, 2] = et_n[:, 2]
et_m[:, 0, 1] = et_n[:, 3]
et_m[:, 1, 0] = et_n[:, 3]
et_m[:, 0, 2] = et_n[:, 4]
et_m[:, 2, 0] = et_n[:, 4]
et_m[:, 1, 2] = et_n[:, 5]
et_m[:, 2, 1] = et_n[:, 5]
print epn[epn_max]
print euler[epn_max, ...]
print et[epn_max, ...]
print et_[epn_max, ...]
print et_n[epn_max, ...]
"""find the eigenvalues of the normalized tensor"""
eigval, g_p2s = LA.eigh(et_m)
del et_m
print eigval[:5, :]
"""find the deformation mode"""
theta = np.arccos(-np.sqrt(3. / 2.) * eigval[:, 0])
print "min(theta): %s" % np.str(theta.min() * 180. / np.pi)
print "mean(theta): %s" % np.str(theta.mean() * 180. / np.pi)
print "max(theta): %s" % np.str(theta.max() * 180. / np.pi)
"""find g_p2c = g_p2s*g_s2c"""
g_s2c = ef.bunge2g(euler[:, 0], euler[:, 1], euler[:, 2])
"""this application of einsum is validated vs loop with np.dot()"""
g_p2c = np.einsum('...ij,...jk', g_s2c, g_p2s)
phi1, phi, phi2 = ef.g2bunge(g_p2c)
# X = np.vstack([phi1, phi, phi2]).T
# X = np.array(ef.g2bunge(g_p2s.swapaxes(1, 2))).T
# X = np.array(ef.g2bunge(g_p2s)).T
# X = np.array(ef.g2bunge(g_s2c.swapaxes(1, 2))).T
# X = np.array(ef.g2bunge(g_s2c)).T
# X = np.array(ef.g2bunge(g_p2c.swapaxes(1, 2))).T
X = np.array(ef.g2bunge(g_s2c)).T
del phi1, phi, phi2
pred = rr.eval_func(theta, X, en).real
print "min(orig): %s" % orig.min()
print "min(pred): %s" % pred.min()
print "max(orig): %s" % orig.max()
print "max(pred): %s" % pred.max()
return orig, pred
n_sym = symop.shape[0]
print "number of symmetry operators: %s" % n_sym
euler_sym = np.zeros((n_sym, n_tot, 3))
g_orig = ef.bunge2g(euler[:, 0], euler[:, 1], euler[:, 2])
# find the symmetric equivalents to the euler angle within the FZ
for sym in xrange(n_sym):
op = symop[sym, ...]
# g_sym: array of orientation matrices transformed with a
# symmetry operator
g_sym = np.einsum('ik,...kj', op, g_orig)
tmp = np.array(ef.g2bunge(g_sym)).transpose()
if sym == 0:
print "g_sym shape: %s" % str(g_sym.shape)
print "tmp shape: %s" % str(tmp.shape)
del g_sym
euler_sym[sym, ...] = tmp
del tmp
# make sure all of the euler angles within the appropriate
# ranges (eg. not negative)
print "initial: euler angles less than zero: %s" % np.sum(euler_sym < 0)
lt = euler_sym < 0.0
euler_sym += 2 * np.pi * lt
print "final: euler angles less than zero: %s" % np.sum(euler_sym < 0)
def fip(sn, el, ns, set_id, step, typ, compl):
f = h5py.File("ref_%s%s_s%s.hdf5" % (ns, set_id, step), 'r')
euler = f.get('euler')[sn, ...].reshape(3, el**3)
euler = euler.swapaxes(0, 1)
et = np.zeros((el**3, 6))
for ii in xrange(6):
comp = compl[ii]
tmp = f.get('r%s_%s' % (comp, typ))[sn, ...]
et[:, ii] = tmp.reshape(el**3)
f.close()
""" find the deviatoric strain tensor """
et_ = et
et_[:, 0:3] = et_[:, 0:3] - (1./3.)*np.expand_dims(np.sum(et[:, 0:3], 1), 1)
# print np.all(np.isclose(np.sum(et[:, 0:3]), np.zeros(el**3)))
""" find the norm of the deviatoric strain tensor """
en = np.sqrt(np.sum(et_[:, 0:3]**2+2*et_[:, 3:]**2, 1))
print "sn: %s" % sn
print "min(en): %s" % en.min()
print "max(en): %s" % en.max()
""" normalize the deviatoric strain tensor """
et_n = et_/np.expand_dims(en, 1)
# print np.all(np.isclose(np.sqrt(np.sum(et_n[:, 0:3]**2+2*et_n[:, 3:]**2, 1)), np.ones(el**3)))
et_m = np.zeros((el**3, 3, 3))
et_m[:, 0, 0] = et_n[:, 0]
et_m[:, 1, 1] = et_n[:, 1]
et_m[:, 2, 2] = et_n[:, 2]
et_m[:, 0, 1] = et_n[:, 3]
et_m[:, 1, 0] = et_n[:, 3]
et_m[:, 0, 2] = et_n[:, 4]
et_m[:, 2, 0] = et_n[:, 4]
et_m[:, 1, 2] = et_n[:, 5]
et_m[:, 2, 1] = et_n[:, 5]
""" find the eigenvalues of the normalized tensor"""
eigval, g_s2p = LA.eigh(et_m)
# print eigval[:5, :]
# """ sort the principal strains in descending order """
# indx = np.argsort(eigval)
# indx = indx[::-1]
# eigval = eigval[indx]
""" find the deformation mode """
# theta1 = np.arccos(np.sqrt(3./2.)*eigval[:, 2])+(np.pi/3.)
# theta2 = np.arccos(np.sqrt(3./2.)*eigval[:, 1])-(np.pi/3.)
# theta3 = np.arccos(-np.sqrt(3./2.)*eigval[:, 0])
# print theta1[:10]*(180./np.pi)
# print theta2[:10]*(180./np.pi)
# print theta3[:10]*(180./np.pi)
theta = np.arccos(-np.sqrt(3./2.)*eigval[:, 0])
print "min(theta): %s" % theta.min()
print "max(theta): %s" % theta.max()
""" find g_p2c = g_p2s*g_s2c """
g_s2c = ef.bunge2g(euler[:, 0], euler[:, 1], euler[:, 2])
g_p2s = g_s2p.swapaxes(1, 2)
del g_s2p
g_p2c = np.einsum('...ik,...kj', g_p2s, g_s2c)
del g_s2c, g_p2s
phi1, phi, phi2 = ef.g2bunge(g_p2c)
X = np.vstack([phi1, phi, phi2]).T
del phi1, phi, phi2
fip = rr.eval_func(theta, X, en).real
print "min(FIP): %s" % fip.min()
print "max(FIP): %s" % fip.max()
return fip
def get_pred(sn, el, ns, set_id, step, compl):
"""read the file for euler angle, total strain and plastic strain fields"""
rcell = np.random.randint(0, el**3)
f = h5py.File("ref_%s%s_s%s.hdf5" % (ns, set_id, step), 'r')
print f.get('euler').shape
euler = f.get('euler')[sn, ...]
euler = euler.swapaxes(0, 1)
print euler.shape
"""check to make sure that the Euler manipulations are functioning"""
# ef.check_euler_op(euler)
"""load et and ep"""
et = np.zeros((el**3, 6))
ep = np.zeros((el**3, 6))
for ii in xrange(6):
comp = compl[ii]
tmp = f.get('r%s_epsilon_t' % comp)[sn, ...]
et[:, ii] = tmp.reshape(el**3)
tmp = f.get('r%s_epsilon_p' % comp)[sn, ...]
ep[:, ii] = tmp.reshape(el**3)
f.close()
"""write et and ep in matrix form"""
et = tens2mat(et)
ep = tens2mat(ep)
print "\net for cell #%s:" % rcell
print et[rcell, ...]
"""find the deviatoric strain tensor"""
isdev = np.all(np.abs(thydro(et)) < 1e-5)
print "\nis hydro(et) == 0?: %s" % isdev
et_ = np.zeros(et.shape)
Id = np.zeros(et.shape)
Id[:, 0, 0] = 1
Id[:, 1, 1] = 1
Id[:, 2, 2] = 1
et_ = et - thydro(et)[:, None, None]*Id
isdev = np.all(np.abs(thydro(et_)) < 1e-5)
print "is hydro(et_) == 0?: %s\n" % isdev
print "\net_ for cell #%s:" % rcell
print et_[rcell, ...]
"""find the norm of the tensors"""
en = tensnorm(et_)
print "\nen for cell #%s: %s" % (rcell, en[rcell])
print "min(en): %s" % en.min()
print "max(en): %s" % en.max()
"""normalize the deviatoric strain tensor"""
et_n = et_/en[:, None, None]
print "\net_n for cell #%s:" % rcell
print et_n[rcell, ...]
isnorm = np.all(np.isclose(tensnorm(et_n), np.ones(el**3)))
print "is norm(et_n) == 0?: %s\n" % isnorm
"""find the eigenvalues of the normalized tensor"""
eigval_, g_p2s_ = LA.eigh(et_n)
print "eigval_ (before sort) for cell #%s: %s" % (rcell, str(eigval_[rcell, :]))
print "g_p2s_ (before sort) for cell #%s:" % rcell
print g_p2s_[rcell, ...]
"""sort the eigenvalues/vectors by highest to lowest magnitude
eigenvalue"""
esort = np.argsort(np.abs(eigval_))[:, ::-1]
eigval = np.zeros(eigval_.shape)
g_p2s = np.zeros(g_p2s_.shape)
for ii in xrange(el**3):
eigval[ii, :] = eigval_[ii, esort[ii, :]]
for jj in xrange(3):
g_p2s[ii, jj, :] = g_p2s_[ii, jj, esort[ii, :]]
print "\neigval (after sort) for cell #%s: %s" % (rcell, str(eigval[rcell, :]))
print "g_p2s (after sort) for cell #%s:\n" % rcell
print g_p2s[rcell, ...]
"""show that the matrix of eigenvectors is g_p2s"""
print "use the backwards tensor transformation to " +\
"get et_n_prinicipal using g_p2s for cell# %s\n" % rcell +\
"(et_n_principal = g_p2s^t * et_n * g_p2s)"
tmp = np.dot(np.dot(g_p2s[rcell, ...].T, et_n[rcell, ...]),
g_p2s[rcell, ...])
print np.round(tmp, 6)
"""find the deformation mode"""
theta = np.arctan2(-2*eigval[:, 0]-eigval[:, 2], np.sqrt(3)*eigval[:, 2])
theta += np.pi*(theta < 0)
print "\nmin(theta): %s" % np.str(theta.min()*180./np.pi)
print "mean(theta): %s" % np.str(theta.mean()*180./np.pi)
print "max(theta): %s\n" % np.str(theta.max()*180./np.pi)
"""recover the principal values from the deformation mode"""
print "principal values of et_n recovered from theta for cell #%s:" % rcell
print theta2et_P(theta[rcell])
"""find g_p2c = g_p2s*g_s2c"""
g_s2c = ef.bunge2g(euler)
"""this application of einsum is validated vs loop with np.dot()"""
g_p2c = np.einsum('...ij,...jk', g_s2c, g_p2s)
tmp = ef.g2bunge(g_p2c)
euler_p2c = np.zeros((el**3, 3))
for ii in xrange(el**3):
euler_p2c[ii, :] = return2fz(tmp[ii, :])
"""try to reconstruct et_"""
g_p2c_ = ef.bunge2g(euler_p2c)
print "euler angles for cell#%s: %s" % (rcell, str(euler_p2c[rcell, ...]))
geq = np.all(np.isclose(g_p2c[rcell, ...], g_p2c_[rcell, ...]))
print "are g_p2c and g_p2c_ equal for cell #%s?: %s" % (rcell, geq)
is_equiv = is_equiv_g(g_p2c[rcell, ...], g_p2c_[rcell, ...])
print "are g_p2c and g_p2c_ equivalent for cell #%s?: %s\n" % (rcell, is_equiv)
et_n_P = theta2et_P(theta)
et_n_C = np.einsum('...ij,...jk,...lk', g_p2c_, et_n_P, g_p2c_)
g_c2s = g_s2c.swapaxes(1, 2)
et_n_S = np.einsum('...ij,...jk,...lk', g_c2s, et_n_C, g_c2s)
et_recon = et_n_S * en[:, None, None]
print "et_ for cell #%s:" % rcell
print et_[rcell, ...]
print "et_ reconstructed from theta, euler_p2c and en same cell:"
print et_recon[rcell, ...]
# X = np.vstack([phi1, phi, phi2]).T
# X = np.array(ef.g2bunge(g_p2c)).T
# X = np.array(ef.g2bunge(g_p2c.swapaxes(1, 2))).T
# X = np.array(ef.g2bunge(g_p2s)).T
# X = np.array(ef.g2bunge(g_p2s.swapaxes(1, 2))).T
# X = np.array(ef.g2bunge(g_s2c)).T
# X = np.array(ef.g2bunge(g_s2c.swapaxes(1, 2))).T
orig = tensnorm(ep)
pred = rr.eval_func(theta, euler_p2c, en).real
print "\nmin(orig): %s" % orig.min()
print "min(pred): %s" % pred.min()
print "max(orig): %s" % orig.max()
print "max(pred): %s" % pred.max()
return orig, pred
randloc = np.array([
2 * np.pi * np.random.rand(), 0.5 * np.pi * np.random.rand(),
(1. / 3.) * np.pi * np.random.rand()
])
randloc = randloc[:, np.newaxis]
g = ef.bunge2g(randloc[0], randloc[1], randloc[2])
tmp = np.zeros([12, 3])
for ii in xrange(12):
g_sym = np.dot(symhex[ii, :, :], g[0, ...])
g_sym = g_sym[np.newaxis, ...]
tmp[ii, :] = ef.g2bunge(g_sym)
euler = np.zeros([12, 3])
euler[:, 0] = tmp[:, 0]
ltz = euler[:, 0] < 0
euler[:, 0] = euler[:, 0] + 2 * np.pi * ltz
euler[:, 1] = tmp[:, 1]
ltz = euler[:, 1] < 0
euler[:, 1] = euler[:, 1] + 2 * np.pi * ltz
euler[:, 2] = tmp[:, 2]
ltz = euler[:, 2] < 0
euler[:, 2] = euler[:, 2] + 2 * np.pi * ltz
def get_pred(sn, el, ns, set_id, step, compl):
"""read the file for euler angle, total strain and plastic strain fields"""
f = h5py.File("ref_%s%s_s%s.hdf5" % (ns, set_id, step), 'r')
print f.get('euler').shape
euler = f.get('euler')[sn, ...]
euler = euler.swapaxes(0, 1)
print euler.shape
et = np.zeros((el**3, 6))
ep = np.zeros((el**3, 6))
for ii in xrange(6):
comp = compl[ii]
tmp = f.get('r%s_epsilon_t' % comp)[sn, ...]
et[:, ii] = tmp.reshape(el**3)
tmp = f.get('r%s_epsilon_p' % comp)[sn, ...]
ep[:, ii] = tmp.reshape(el**3)
f.close()
"""find the deviatoric strain tensor"""
isdev = np.all(np.isclose(np.sum(et[:, 0:3]), np.zeros(el**3)))
print "is trace(et) == 0?: %s" % isdev
et_ = np.zeros(et.shape)
et_[:,
0:3] = et[:,
0:3] - (1. / 3.) * np.expand_dims(np.sum(et[:, 0:3], 1), 1)
et_[:, 3:] = et[:, 3:]
isdev = np.all(np.isclose(np.sum(et_[:, 0:3]), np.zeros(el**3)))
print "is trace(et_) == 0?: %s" % isdev
"""find the norm of the tensors"""
en = tensnorm(et_)
print "sn: %s" % sn
print "min(en): %s" % en.min()
print "max(en): %s" % en.max()
"""normalize the deviatoric strain tensor"""
et_n = et_ / np.expand_dims(en, 1)
isnorm = np.all(np.isclose(tensnorm(et_n), np.ones(el**3)))
print "is norm(et_n) == 0?: %s" % isnorm
"""write the normalized deviatioric total strain and plastic strains
in matrix form"""
et_m = tens2mat(et_n)
epn = tensnorm(ep)
# epn_max = np.argmax(epn)
orig = epn
# print "max(norm(ep)): %s" % epn[epn_max]
# print "euler @ max(norm(ep)): %s" % str(euler[epn_max, ...])
# print et[epn_max, ...]
# print et_[epn_max, ...]
# print et_n[epn_max, ...]
"""find the eigenvalues of the normalized tensor"""
eigval_, g_p2s_ = LA.eigh(et_m)
del et_m
print "eigval_ example (before sort): %s" % str(eigval_[0, :])
print "g_p2s_ example (before sort):"
print g_p2s_[0, ...]
"""sort the eigenvalues/vectors by highest to lowest magnitude
eigenvalue"""
esort = np.argsort(np.abs(eigval_))[:, ::-1]
eigval = np.zeros(eigval_.shape)
g_p2s = np.zeros(g_p2s_.shape)
for ii in xrange(el**3):
eigval[ii, :] = eigval_[ii, esort[ii, :]]
for jj in xrange(3):
g_p2s[ii, jj, :] = g_p2s_[ii, jj, esort[ii, :]]
print "eigval example (after sort): %s" % str(eigval[0, :])
print "g_p2s example (after sort):"
print g_p2s[0, ...]
"""find the deformation mode"""
theta = np.arctan2(-2 * eigval[:, 0] - eigval[:, 2],
np.sqrt(3) * eigval[:, 2])
theta += np.pi * (theta < 0)
print "min(theta): %s" % np.str(theta.min() * 180. / np.pi)
print "mean(theta): %s" % np.str(theta.mean() * 180. / np.pi)
print "max(theta): %s" % np.str(theta.max() * 180. / np.pi)
"""find g_p2c = g_p2s*g_s2c"""
g_s2c = ef.bunge2g(euler[:, 0], euler[:, 1], euler[:, 2])
"""this application of einsum is validated vs loop with np.dot()"""
g_p2c = np.einsum('...ij,...jk', g_s2c, g_p2s)
phi1, phi, phi2 = ef.g2bunge(g_p2c)
X = np.vstack([phi1, phi, phi2]).T
# X = np.array(ef.g2bunge(g_p2c)).T
# X = np.array(ef.g2bunge(g_p2c.swapaxes(1, 2))).T
# X = np.array(ef.g2bunge(g_p2s)).T
# X = np.array(ef.g2bunge(g_p2s.swapaxes(1, 2))).T
# X = np.array(ef.g2bunge(g_s2c)).T
# X = np.array(ef.g2bunge(g_s2c.swapaxes(1, 2))).T
del phi1, phi, phi2
pred = rr.eval_func(theta, X, en).real
print "min(orig): %s" % orig.min()
print "min(pred): %s" % pred.min()
print "max(orig): %s" % orig.max()
print "max(pred): %s" % pred.max()
return orig, pred