def _typeset(self, val, dim, style='table', format='%f', step=None):
sym = (dim + 1) * dim / 2
mode = None
if val.ndim == 0:
mode = 'scalar'
elif val.ndim == 1:
if val.shape[0] == 1:
mode = 'scalar'
elif val.shape[0] == dim:
mode = 'vector'
elif val.shape[0] == sym:
mode = 'matrix_t1d'
elif val.ndim == 2:
if val.shape[0] == dim:
mode = 'matrix_2D'
elif val.shape[0] == sym:
mode = 'matrix_t2d'
out = ''
if mode == 'scalar':
out = format % val
elif mode == 'vector':
aux = ' \\\\\n'.join([
r'$_%d$ & %s' % (ir + 1, format % val[ir])
for ir in xrange(dim)
])
out = self._table_vector % aux
elif mode == 'matrix_t1d':
aux = ' \\\\\n'.join( [r'$_{%d%d}$ & %s' % (ir + 1, ic + 1,
format % val[ii])
for ii, (ir, ic) \
in enumerate( iter_sym( dim ) )] )
out = self._table_matrix_1 % aux
elif mode == 'matrix_2D':
aux = ' \\\\\n'.join([
r'$_{%d%d}$ & %s' % (ir + 1, ic + 1, format % val[ir, ic])
for ir in xrange(dim) for ic in xrange(dim)
])
out = self._table_matrix_1 % aux
elif mode == 'matrix_t2d':
aux = ' \\\\\n'.join( [r'$_{%d%d%d%d}$ & %s' % (irr + 1, irc + 1,
icr + 1, icc + 1,
format % val[ii,jj])
for ii, (irr, irc) \
in enumerate( iter_sym( dim ) )
for jj, (icr, icc) \
in enumerate( iter_sym( dim ) )] )
out = self._table_matrix_2 % aux
return out
def _typeset( self, val, dim, style = 'table', format = '%f',
step = None ):
sym = (dim + 1) * dim / 2
mode = None
if val.ndim == 0:
mode = 'scalar'
elif val.ndim == 1:
if val.shape[0] == 1:
mode = 'scalar'
elif val.shape[0] == dim:
mode = 'vector'
elif val.shape[0] == sym:
mode = 'matrix_t1d'
elif val.ndim == 2:
if val.shape[0] == dim:
mode = 'matrix_2D'
elif val.shape[0] == sym:
mode = 'matrix_t2d'
print mode
out = ''
if mode == 'scalar':
out = format % val
elif mode == 'vector':
aux = ' \\\\\n'.join( [r'$_%d$ & %s' % (ir + 1, format % val[ir])
for ir in xrange( dim )] )
out = self._table_vector % aux
elif mode == 'matrix_t1d':
aux = ' \\\\\n'.join( [r'$_{%d%d}$ & %s' % (ir + 1, ic + 1,
format % val[ii])
for ii, (ir, ic) \
in enumerate( iter_sym( dim ) )] )
out = self._table_matrix_1 % aux
elif mode == 'matrix_2D':
aux = ' \\\\\n'.join( [r'$_{%d%d}$ & %s' % (ir + 1, ic + 1,
format % val[ir,ic])
for ir in xrange( dim )
for ic in xrange( dim )] )
out = self._table_matrix_1 % aux
elif mode == 'matrix_t2d':
aux = ' \\\\\n'.join( [r'$_{%d%d%d%d}$ & %s' % (irr + 1, irc + 1,
icr + 1, icc + 1,
format % val[ii,jj])
for ii, (irr, irc) \
in enumerate( iter_sym( dim ) )
for jj, (icr, icc) \
in enumerate( iter_sym( dim ) )] )
out = self._table_matrix_2 % aux
return out
def fibre_function(out, pars, green_strain, fmode):
"""
Depending on `fmode`, compute fibre stress (0) or tangent modulus (!= 0).
"""
fmax, eps_opt, s, fdir, act = pars
eps = nm.zeros_like(fmax)
omega = nm.empty_like(green_strain)
for ii, (ir, ic) in enumerate(iter_sym(fdir.shape[2])):
omega[..., ii, 0] = fdir[..., ir, 0] * fdir[..., ic, 0]
eps[..., 0, 0] += omega[..., ii, 0] * green_strain[..., ii, 0]
tau = act * fmax * nm.exp(-((eps - eps_opt) / s)**2.0)
if fmode == 0:
out[:] = omega * tau
else:
for ir in range(omega.shape[2]):
for ic in range(omega.shape[2]):
out[..., ir, ic] = omega[..., ir, 0] * omega[..., ic, 0]
out[:] *= -2.0 * ((eps - eps_opt) / (s**2.0)) * tau
return out
def fibre_function(out, pars, green_strain, fmode):
"""
Depending on `fmode`, compute fibre stress (0) or tangent modulus (!= 0).
"""
fmax, eps_opt, s, fdir, act = pars
eps = nm.zeros_like(fmax)
omega = nm.empty_like(green_strain)
for ii, (ir, ic) in enumerate(iter_sym(fdir.shape[2])):
omega[..., ii, 0] = fdir[..., ir, 0] * fdir[..., ic, 0]
eps[..., 0, 0] += omega[..., ii, 0] * green_strain[..., ii, 0]
tau = act * fmax * nm.exp(-((eps - eps_opt) / s)**2.0)
if fmode == 0:
out[:] = omega * tau
else:
for ir in range(omega.shape[2]):
for ic in range(omega.shape[2]):
out[..., ir, ic] = omega[..., ir, 0] * omega[..., ic, 0]
out[:] *= -2.0 * ((eps - eps_opt) / (s**2.0)) * tau
return out
def compute_crt_data(self, family_data, mode, **kwargs):
pars = self.get_args(["material_1", "material_2", "material_3", "material_4", "material_5"], **kwargs)
fmax, eps_opt, s, fdir, act = pars
strainE = family_data[0]
eps = nm.zeros_like(fmax)
omega = nm.empty_like(strainE)
for ii, (ir, ic) in enumerate(iter_sym(fdir.shape[2])):
omega[..., ii, 0] = fdir[..., ir, 0] * fdir[..., ic, 0]
eps[..., 0, 0] += omega[..., ii, 0] * strainE[..., ii, 0]
tau = act * fmax * nm.exp(-((eps - eps_opt) / s) ** 2.0)
if mode == 0:
out = omega * tau
else:
shape = list(strainE.shape)
shape[-1] = shape[-2]
out = nm.empty(shape, dtype=nm.float64)
for ir in range(omega.shape[2]):
for ic in range(omega.shape[2]):
out[..., ir, ic] = omega[..., ir, 0] * omega[..., ic, 0]
out[:] *= -2.0 * ((eps - eps_opt) / (s ** 2.0)) * tau
return out
def get_fargs(self, mat1, mat2, virtual, mode=None, term_mode=None, diff_var=None, **kwargs):
vg, _ = self.get_mapping(virtual)
omega = nm.empty(mat1.shape[:3] + (1,), dtype=nm.float64)
for ii, (ir, ic) in enumerate(iter_sym(mat2.shape[2])):
omega[..., ii, 0] = mat2[..., ir, 0] * mat2[..., ic, 0]
return mat1, omega, vg
def get_fargs(self, mat1, mat2, virtual,
mode=None, term_mode=None, diff_var=None, **kwargs):
vg, _ = self.get_mapping(virtual)
omega = nm.empty(mat1.shape[:3] + (1,), dtype=nm.float64)
for ii, (ir, ic) in enumerate(iter_sym(mat2.shape[2])):
omega[..., ii, 0] = mat2[..., ir, 0] * mat2[..., ic, 0]
return mat1, omega, vg
def create_omega(fdir):
r"""
Create the fibre direction tensor :math:`\omega_{ij} = d_i d_j`.
"""
n_el, n_qp, dim, _ = fdir.shape
sym = dim2sym(dim)
omega = nm.empty((n_el, n_qp, sym, 1), dtype=nm.float64)
for ii, (ir, ic) in enumerate(iter_sym(dim)):
omega[..., ii, 0] = fdir[..., ir, 0] * fdir[..., ic, 0]
return omega
def create_omega(fdir):
r"""
Create the fibre direction tensor :math:`\omega_{ij} = d_i d_j`.
"""
n_el, n_qp, dim, _ = fdir.shape
sym = dim2sym(dim)
omega = nm.empty((n_el, n_qp, sym, 1), dtype=nm.float64)
for ii, (ir, ic) in enumerate(iter_sym(dim)):
omega[..., ii, 0] = fdir[..., ir, 0] * fdir[..., ic, 0]
return omega
