def __call__(self, out_mesh):
from scipy.linalg import inv
out_mesh = mesh.coordify(out_mesh)
dimension = len(out_mesh[0])
self.C = self.eval_BF(out_mesh, out_mesh)
A = self.eval_BF(self.in_mesh, out_mesh)
V = np.zeros([len(self.in_mesh), dimension + 1])
V[:, 0] = 1
V[:, 1:] = self.in_mesh
Q = np.zeros([len(out_mesh), dimension + 1])
Q[:, 0] = 1
Q[:, 1:] = out_mesh
# Q, V = V, Q # Swap
f_xi = self.in_vals
QQ, QR = scipy.linalg.qr(Q, mode="economic")
epsilon = V.T @ f_xi
eta = A.T @ f_xi
mu = np.linalg.solve(self.C, eta)
tau = Q.T @ mu - epsilon
sigma = (QQ @ inv(QR).T) @ tau
output = mu - sigma
# output = sigma
# ST = inv(P).T @ Pt.T - (QQ @ inv(QR).T) @ (Q.T @ inv(P).T @ Pt.T + V.T)
return output
def __call__(self, out_mesh):
out_mesh = mesh.coordify(out_mesh)
dimension = len(out_mesh[0])
polyparams = dimension + 1
# polyparams = 0
C = np.zeros([len(out_mesh) + polyparams, len(out_mesh) + polyparams])
C[0, polyparams:] = 1
C[1:polyparams, polyparams:] = out_mesh.T
C[polyparams:, 0] = 1
C[polyparams:, 1:polyparams] = out_mesh
C[polyparams:, polyparams:] = self.eval_BF(out_mesh, out_mesh)
A = np.zeros([len(self.in_mesh), len(out_mesh) + polyparams])
A[:, 0] = 1
A[:, 1:polyparams] = self.in_mesh
A[:, polyparams:] = self.eval_BF(self.in_mesh, out_mesh)
au = A.T @ self.in_vals
out_vals = np.linalg.solve(C, au)[polyparams:]
if self.rescale:
au_rescaled = self.eval_BF(self.in_mesh,
out_mesh).T @ np.ones_like(self.in_vals)
out_vals = out_vals / np.linalg.solve(
self.eval_BF(out_mesh, out_mesh), au_rescaled)
return out_vals
def __call__(self, out_mesh):
out_mesh = mesh.coordify(out_mesh)
A = self.eval_BF(out_mesh, self.in_mesh)
V = np.zeros([out_mesh.shape[0], out_mesh.shape[1] + 1])
V[:, 0] = 1
V[:, 1:] = out_mesh
out_vals = A @ self.gamma
if self.rescaled:
out_vals = out_vals / (A @ self.gamma_rescaled)
return out_vals + V @ self.beta
def __init__(self, basisfunction, in_mesh, in_vals, rescale=False):
in_mesh = mesh.coordify(in_mesh)
self.in_mesh, self.basisfunction = in_mesh, basisfunction
Q = np.zeros([in_mesh.shape[0], in_mesh.shape[1] + 1])
Q[:, 0] = 1
Q[:, 1:] = in_mesh
lsqrRes = scipy.sparse.linalg.lsqr(Q, in_vals)
self.beta = lsqrRes[0]
self.C = self.eval_BF(in_mesh, in_mesh)
rhs = in_vals - Q @ self.beta
self.gamma = np.linalg.solve(self.C, rhs)
self.rescaled = rescale
if rescale:
self.gamma_rescaled = np.linalg.solve(self.C,
np.ones_like(self.gamma))
def __init__(self, basisfunction, in_mesh, in_vals):
self.basisfunction, self.in_vals = basisfunction, in_vals
self.in_mesh = mesh.coordify(in_mesh)
def __init__(self, basisfunction, in_mesh, in_vals, rescale=False):
self.basisfunction, self.in_vals, self.rescale = basisfunction, in_vals, rescale
self.in_mesh = mesh.coordify(in_mesh)