def D1_eo(N, h):
"""
Compute the d1 matrix for mapping even functions to odd functions.
"""
DM = sincmats.deriv_mats(2 * N + 1, 1, h)
D1 = DM[:, :, 0]
# Reflect and add values appropriatey
return (D1[-N - 1:][:, -N - 1:] + hstack((zeros(
(N + 1, 1)), fliplr(D1[-N - 1:][:, 0:N]))))
def D2_e(N, h):
"""
Compute the d2 matrix for even functions.
"""
DM = sincmats.deriv_mats(2 * N + 1, 2, h)
D2 = DM[:, :, 1]
# Reflect and add values appropriatey
return (D2[-N - 1:][:, -N - 1:] + hstack((zeros(
(N + 1, 1)), fliplr(D2[-N - 1:][:, 0:N]))))
def D1_eo(N,h): """ Compute the d1 matrix for mapping even functions to odd functions. """ DM = sincmats.deriv_mats(2 * N + 1, 1, h) D1 = DM[:, :, 0] # Reflect and add values appropriatey return (D1[-N - 1:][:, -N - 1:] + hstack((zeros((N + 1, 1)), fliplr(D1[-N - 1:][:, 0:N]))))
def D2_e(N, h): """ Compute the d2 matrix for even functions. """ DM = sincmats.deriv_mats(2 * N + 1, 2, h) D2 = DM[:, :, 1] # Reflect and add values appropriatey return (D2[-N-1:][:,-N-1:] + hstack((zeros((N + 1, 1)), fliplr(D2[-N - 1:][:, 0:N]))))
def D1_x_e(N,h): """ Compute the (1/x)(d/dx) matrix for even functions. """ x = points(N, h) k = arange(1, N + 1) DM = sincmats.deriv_mats(2 * N + 1, 1, h) D1 = DM[:, :, 0] # This row needs to be specially constructed zero_row = hstack(([-pi**2 / (3 * h**2)], -4 * ((-1)**k) / ((h**2) * k**2))) # Reflect and add values appropriatey return vstack(( zero_row, ( dot(diag(1.0 / x[-N:]), D1[-N:][:,-N-1:]) + hstack(( zeros((N, 1)), fliplr(dot(diag(1.0 / x[-N:] ), D1[-N:][:, 0:N])) )) ) ))
def D1_x_e(N, h):
"""
Compute the (1/x)(d/dx) matrix for even functions.
"""
x = points(N, h)
k = arange(1, N + 1)
DM = sincmats.deriv_mats(2 * N + 1, 1, h)
D1 = DM[:, :, 0]
# This row needs to be specially constructed
zero_row = hstack(
([-pi**2 / (3 * h**2)], -4 * ((-1)**k) / ((h**2) * k**2)))
# Reflect and add values appropriatey
return vstack(
(zero_row, (dot(diag(1.0 / x[-N:]), D1[-N:][:, -N - 1:]) + hstack(
(zeros(
(N, 1)), fliplr(dot(diag(1.0 / x[-N:]), D1[-N:][:, 0:N])))))))
