def apply_stiffness_matrix(modes, **kwargs):
"""
Generates and applies the stiffness matrix to the modal coefficients.
"""
from spyctral.wiener.matrices import weighted_wiener_stiffness_matrix as stiffmat
stiff = stiffmat(len(modes), **kwargs)
try:
from pymbolic.algorithm import csr_matrix_multiply as csr_mult
return csr_mult(stiff, modes)
except:
return stiff * mdoes
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)