def get_A_GaNi(self, N, primaldual='primal', tensor=True):
"""
Returns stiffness matrix for a scheme with trapezoidal quadrature rule.
"""
coord = Grid.get_coordinates(N, self.Y)
A = self.evaluate(coord, tensor=tensor)
if primaldual is 'dual':
A = A.inv()
return A.shift()
def get_A_GaNi(self, N, primaldual='primal', tensor=True):
"""
Returns stiffness matrix for a scheme with trapezoidal quadrature rule.
"""
coord = Grid.get_coordinates(N, self.Y)
A = self.evaluate(coord, tensor=tensor)
if primaldual is 'dual':
A = A.inv()
return A.shift()
def savefig(self, fname='material.pdf', N=50*np.ones(2)):
import pylab as pl
pl.figure(num=None, figsize=(3,3), dpi=1000)
coord = Grid.get_coordinates(N, self.Y)
vals = self.evaluate(coord)[0, 0]
pl.pcolor(coord[0], coord[1], -vals)
pl.xlim([-self.Y[0]/2, self.Y[0]/2])
pl.ylim([-self.Y[1]/2, self.Y[1]/2])
pl.xlabel(r'coordinate $x_1$')
pl.ylabel(r'coordinate $x_2$')
pl.savefig(fname, pad_inches=0.02, bbox_inches='tight')
pl.close()
def savefig(self, fname='material.pdf', N=50 * np.ones(2)):
import pylab as pl
pl.figure(num=None, figsize=(3, 3), dpi=1000)
coord = Grid.get_coordinates(N, self.Y)
vals = self.evaluate(coord)[0, 0]
pl.pcolor(coord[0], coord[1], -vals)
pl.xlim([-self.Y[0] / 2, self.Y[0] / 2])
pl.ylim([-self.Y[1] / 2, self.Y[1] / 2])
pl.xlabel(r'coordinate $x_1$')
pl.ylabel(r'coordinate $x_2$')
pl.savefig(fname, pad_inches=0.02, bbox_inches='tight')
pl.close()
def plot(self, ind=slice(None), N=None, filen=None, ptype='imshow'):
if N is None:
N = self.N
from mpl_toolkits.mplot3d import axes3d
import matplotlib.pyplot as plt
from ffthompy.trigpol import Grid
coord = Grid.get_coordinates(N, self.Y)
Z = self.project(N)
Z = Z.val[ind]
if self.Fourier:
Z = np.abs(Z)
if Z.ndim != 2:
raise ValueError("The plotting is suited only for dim=2!")
fig = plt.figure()
if ptype in ['wireframe']:
ax = fig.add_subplot(111, projection='3d')
ax.plot_wireframe(coord[-2], coord[-1], Z)
elif ptype in ['surface']:
from matplotlib import cm
ax = fig.gca(projection='3d')
surf = ax.plot_surface(coord[-2],
coord[-1],
Z,
rstride=1,
cstride=1,
cmap=cm.coolwarm,
linewidth=0,
antialiased=False)
fig.colorbar(surf, shrink=0.5, aspect=5)
elif ptype in ['imshow']:
ax = plt.imshow(Z)
plt.colorbar(ax)
if filen is None:
plt.show()
else:
plt.savefig(filen)
def plot(self, ind=slice(None), N=None, filen=None, ptype='imshow'):
assert(not self.Fourier)
if N is None:
N = self.N
from mpl_toolkits.mplot3d import axes3d
import matplotlib.pyplot as plt
from ffthompy.trigpol import Grid
coord=Grid.get_coordinates(N, self.Y)
Z=self.project(N)
Z = Z.val[ind]
if Z.ndim != 2:
raise ValueError("The plotting is suited only for dim=2!")
fig = plt.figure()
if ptype in ['wireframe']:
ax = fig.add_subplot(111, projection='3d')
ax.plot_wireframe(coord[-2], coord[-1], Z)
elif ptype in ['surface']:
from matplotlib import cm
ax = fig.gca(projection='3d')
surf = ax.plot_surface(coord[-2], coord[-1], Z,
rstride=1, cstride=1, cmap=cm.coolwarm,
linewidth=0, antialiased=False)
fig.colorbar(surf, shrink=0.5, aspect=5)
elif ptype in ['imshow']:
ax = plt.imshow(Z)
plt.colorbar(ax)
if filen is None:
plt.show()
else:
plt.savefig(filen)
def plot(self, ind=0, N=None, filen=None, Y=None, ptype='surface'):
dim=self.N.size
if dim!=2:
raise ValueError("The plotting is suited only for dim=2!")
if Y is None:
Y=np.ones(dim)
if N is None:
N=self.N
from mpl_toolkits.mplot3d import axes3d
import matplotlib.pyplot as plt
from ffthompy.trigpol import Grid
fig=plt.figure()
coord=Grid.get_coordinates(N, Y)
if np.all(np.greater(N, self.N)):
Z=DFT.ifftnc(enlarge(DFT.fftnc(self.val[ind], self.N), N), N).real
elif np.all(np.less(N, self.N)):
Z=DFT.ifftnc(decrease(DFT.fftnc(self.val[ind], self.N), N), N).real
elif np.allclose(N, self.N):
Z=self.val[ind]
if ptype in ['wireframe']:
ax=fig.add_subplot(111, projection='3d')
ax.plot_wireframe(coord[0], coord[1], Z)
elif ptype in ['surface']:
from matplotlib import cm
ax=fig.gca(projection='3d')
surf=ax.plot_surface(coord[0], coord[1], Z,
rstride=1, cstride=1, cmap=cm.coolwarm,
linewidth=0, antialiased=False)
fig.colorbar(surf, shrink=0.5, aspect=5)
if filen is None:
plt.show()
else:
plt.savefig(filen)
def plot(self, ind=0, N=None, filen=None, Y=None, ptype='surface'):
dim=self.N.size
if dim!=2:
raise ValueError("The plotting is suited only for dim=2!")
if Y is None:
Y=np.ones(dim)
if N is None:
N=self.N
from mpl_toolkits.mplot3d import axes3d
import matplotlib.pyplot as plt
from ffthompy.trigpol import Grid
fig=plt.figure()
coord=Grid.get_coordinates(N, Y)
if np.all(np.greater(N, self.N)):
Z=DFT.ifftnc(enlarge(DFT.fftnc(self.val[ind], self.N), N), N).real
elif np.all(np.less(N, self.N)):
Z=DFT.ifftnc(decrease(DFT.fftnc(self.val[ind], self.N), N), N).real
elif np.allclose(N, self.N):
Z=self.val[ind]
if ptype in ['wireframe']:
ax=fig.add_subplot(111, projection='3d')
ax.plot_wireframe(coord[0], coord[1], Z)
elif ptype in ['surface']:
from matplotlib import cm
ax=fig.gca(projection='3d')
surf=ax.plot_surface(coord[0], coord[1], Z,
rstride=1, cstride=1, cmap=cm.coolwarm,
linewidth=0, antialiased=False)
fig.colorbar(surf, shrink=0.5, aspect=5)
if filen is None:
plt.show()
else:
plt.savefig(filen)
phi_fine = phi.project(M)
print(phi_fine)
print("""The procedure is provided by VecTri.enlarge(M) function, which consists of
a calculation of Fourier coefficients, putting zeros to Fourier coefficients
with high frequencies, and inverse FFT that evaluates the polynomial on
a fine grid.
""")
print("""In order to plot this polynomial, we also set a size of a cell
Y =""")
Y = np.ones(d) # size of a cell
print(Y)
print(""" and evaluate the coordinates of grid points, which are stored in
numpy.ndarray of following shape:
coord.shape =""")
coord = Grid.get_coordinates(M, Y)
print(coord.shape)
if __name__ == "__main__":
print("""
Now, the plot of fundamental trigonometric polynomial is shown:""")
from mpl_toolkits.mplot3d import axes3d
import matplotlib.pyplot as plt
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
ax.plot_wireframe(coord[0], coord[1], phi_fine.val)
plt.show()
print('END')
def get_A_Ga(self, Nbar, primaldual='primal', order=-1, P=None):
"""
Returns stiffness matrix for scheme with exact integration.
"""
if order == -1:
if 'order' in self.conf:
order = self.conf['order']
else:
raise ValueError('The material order is undefined!')
elif order not in [None, 'exact', 0, 1]:
raise ValueError('Wrong material order (%s)!' % str(order))
if order in [None, 'exact']: # inclusion-based composite
shape_funs = self.get_shape_functions(Nbar)
val = np.zeros(self.conf['vals'][0].shape + shape_funs[0].shape)
for ii in range(len(self.conf['inclusions'])):
if primaldual is 'primal':
Aincl = self.conf['vals'][ii]
elif primaldual is 'dual':
Aincl = np.linalg.inv(self.conf['vals'][ii])
val += np.einsum('ij...,k...->ijk...', Aincl, shape_funs[ii])
name = 'A_Ga'
else: # grid-based composite
if P is None and 'P' in self.conf:
P = self.conf['P']
coord = Grid.get_coordinates(P, self.Y)
vals = self.evaluate(coord)
if primaldual is 'dual':
vals = vals.inv()
h = self.Y/P
if order in [0, 'constant']:
Wraw = get_weights_con(h, Nbar, self.Y)
elif order in [1, 'bilinear']:
Wraw = get_weights_lin(h, Nbar, self.Y)
val = np.zeros(vals.shape+tuple(Nbar))
for m,n in itertools.product(*(range(d) for d in vals.shape)):
hAM0 = np.prod(P)*cfftnc(vals[m, n], P)
if np.allclose(P, Nbar):
hAM = hAM0
elif np.all(np.greater_equal(P, Nbar)):
hAM = decrease(hAM0, Nbar)
elif np.all(np.less(P, Nbar)):
factor = np.ceil(np.array(Nbar, dtype=np.float64) / P)
hAM0per = np.tile(hAM0,
2*np.array(factor, dtype=np.int)-1)
hAM = decrease(hAM0per, Nbar)
else:
msg = """This combination of double N (%s) and P (%s) "
implemented.""" % (str(Nbar), str(P))
raise NotImplementedError(msg)
val[m, n] = np.real(icfftnc(Wraw*hAM, Nbar))
name = 'A_Ga_o{0}_P{1}'.format(order, np.array(P).max())
return Tensor(name=name, val=val, N=Nbar, order=2, Y=self.Y, multype=21,
Fourier=False, origin='c').shift()
def get_A_Ga(self, Nbar, primaldual='primal', order=-1, P=None):
"""
Returns stiffness matrix for scheme with exact integration.
"""
if order == -1:
if 'order' in self.conf:
order = self.conf['order']
else:
raise ValueError('The material order is undefined!')
elif order not in [None, 'exact', 0, 1]:
raise ValueError('Wrong material order (%s)!' % str(order))
if order in [None, 'exact']: # inclusion-based composite
shape_funs = self.get_shape_functions(Nbar)
val = np.zeros(self.conf['vals'][0].shape + shape_funs[0].shape)
for ii in range(len(self.conf['inclusions'])):
if primaldual is 'primal':
Aincl = self.conf['vals'][ii]
elif primaldual is 'dual':
Aincl = np.linalg.inv(self.conf['vals'][ii])
val += np.einsum('ij...,k...->ijk...', Aincl, shape_funs[ii])
name = 'A_Ga'
else: # grid-based composite
if P is None and 'P' in self.conf:
P = self.conf['P']
coord = Grid.get_coordinates(P, self.Y)
vals = self.evaluate(coord)
if primaldual is 'dual':
vals = vals.inv()
h = self.Y / P
if order in [0, 'constant']:
Wraw = get_weights_con(h, Nbar, self.Y)
elif order in [1, 'bilinear']:
Wraw = get_weights_lin(h, Nbar, self.Y)
val = np.zeros(vals.shape + tuple(Nbar))
for m, n in itertools.product(*(list(range(d))
for d in vals.shape)):
hAM0 = np.prod(P) * cfftnc(vals[m, n], P)
if np.allclose(P, Nbar):
hAM = hAM0
elif np.all(np.greater_equal(P, Nbar)):
hAM = decrease(hAM0, Nbar)
elif np.all(np.less(P, Nbar)):
factor = np.ceil(np.array(Nbar, dtype=np.float64) / 2 / P)
hAM0per = np.tile(hAM0,
2 * np.array(factor, dtype=np.int) + 1)
hAM = decrease(hAM0per, Nbar)
else:
msg = """This combination of double N (%s) and P (%s) "
implemented.""" % (str(Nbar), str(P))
raise NotImplementedError(msg)
val[m, n] = np.real(icfftnc(Wraw * hAM, Nbar))
name = 'A_Ga_o{0}_P{1}'.format(order, np.array(P).max())
return Tensor(name=name,
val=val,
N=Nbar,
order=2,
Y=self.Y,
multype=21,
Fourier=False,
origin='c').shift()
phi_fine = phi.project(M)
print(phi_fine)
print(
"""The procedure is provided by VecTri.enlarge(M) function, which consists of
a calculation of Fourier coefficients, putting zeros to Fourier coefficients
with high frequencies, and inverse FFT that evaluates the polynomial on
a fine grid.
""")
print("""In order to plot this polynomial, we also set a size of a cell
Y =""")
Y = np.ones(d) # size of a cell
print(Y)
print(""" and evaluate the coordinates of grid points, which are stored in
numpy.ndarray of following shape:
coord.shape =""")
coord = Grid.get_coordinates(M, Y)
print(coord.shape)
if __name__ == "__main__":
print("""
Now, the plot of fundamental trigonometric polynomial is shown:""")
from mpl_toolkits.mplot3d import axes3d
import matplotlib.pyplot as plt
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
ax.plot_wireframe(coord[0], coord[1], phi_fine.val)
plt.show()
print('END')
