def get_backward_mapping_inverse(self):
inverse_mapping = identity_mapping(self.backward_vector_fields.shape)
v = -0.5 * (self.backward_vector_fields[-2::-1] +
self.backward_vector_fields[:0:-1])
for i in xrange(self.n_step_half):
inverse_mapping = inverse_mapping - np.einsum(
'ij...,j...->i...', jacobian_matrix(inverse_mapping),
v[i]) / self.n_step
return inverse_mapping
def get_backward_mapping_inverse(self):
inverse_mapping = identity_mapping(self.backward_vector_fields.shape)
v = - 0.5 * (self.backward_vector_fields[-2::-1]
+ self.backward_vector_fields[:0:-1])
for i in xrange(self.n_step_half):
inverse_mapping = inverse_mapping - np.einsum(
'ij...,j...->i...',
jacobian_matrix(inverse_mapping),
v[i]) / self.n_step
return inverse_mapping
def set_operator(self, shape, resolution=1):
dx_sqinv = 1. / resolution ** 2
A = self.norm_penalty * np.ones(shape)
grid = identity_mapping(shape)
for frequencies, length in zip(grid, shape):
A += 2 * self.convexity_penalty * (
1 - np.cos(2 * np.pi * frequencies / length)) * dx_sqinv
# Since this is biharmonic, the exponent is 2.
self.operator = 1 / (A ** 2)
