def apply_stiffness_matrix(self,modes):
from scipy.sparse.csr import csr_matrix
from numpy import ndarray, dot
if self.stiffness_matrix is None:
self.make_stiffness_matrix()
if isinstance(self.stiffness_matrix,csr_matrix):
try:
from pymbolic.algorithm import csr_matrix_multiply
return csr_matrix_multiply(self.stiffness_matrix,modes)
except:
return self.stiffness_matrix*modes
elif isinstance(self.stiffness_matrix,ndarray):
return dot(self.stiffness_matrix,modes)
else:
raise TypeError("Unrecognized type %s for stiffness matrix" % \
type(self.stiffness_matrix))
def test_sparse_multiply():
numpy = pytest.importorskip("numpy")
pytest.importorskip("scipy")
import scipy.sparse as ss
la = numpy.linalg
mat = numpy.random.randn(10, 10)
s_mat = ss.csr_matrix(mat)
vec = numpy.random.randn(10)
mat_vec = s_mat * vec
from pymbolic.algorithm import csr_matrix_multiply
mat_vec_2 = csr_matrix_multiply(s_mat, vec)
assert la.norm(mat_vec - mat_vec_2) < 1e-14
def test_sparse_multiply():
numpy = pytest.importorskip("numpy")
pytest.importorskip("scipy")
import scipy.sparse as ss
la = numpy.linalg
mat = numpy.random.randn(10, 10)
s_mat = ss.csr_matrix(mat)
vec = numpy.random.randn(10)
mat_vec = s_mat*vec
from pymbolic.algorithm import csr_matrix_multiply
mat_vec_2 = csr_matrix_multiply(s_mat, vec)
assert la.norm(mat_vec-mat_vec_2) < 1e-14
def fft_nodal_differentiation(fx, **kwargs):
"""Given the nodal function values, returns the nodal approximations to the
derivative computed using:
1.) the fft
2.) application of the sparse stiffness matrix to the nodes
3.) the ifft
s must be an integer for all this to work.
"""
from spyctral.wiener.matrices import weighted_wiener_stiffness_matrix as stiffmat
from spyctral.wiener.fft import fft_collocation as fft
from spyctral.wiener.fft import ifft_collocation as ifft
stiff = stiffmat(len(fx), **kwargs)
if fx.dtype == object:
from pymbolic.algorithm import csr_matrix_multiply
temp = fft(fx, **kwargs)
temp = csr_matrix_multiply(stiff, temp)
return ifft(temp, **kwargs)
else:
return ifft(stiff * fft(fx, **kwargs), **kwargs)