def init(D, N, M):
# D-dimensional nodes for interval [-1,1]
nu = np.empty(M)
for k, nuk in enumerate(nu):
nuk = -math.cos((2 * k - 1) * math.pi / (2 * M))
# create a matrix that contains all possible length D product of nodes in each row
prod = itertools.product(nu, repeat=D)
X = np.empty(pow(M, D) * D)
X.shape = (pow(M, D), D)
for i, row in enumerate(prod):
X[i] = row
# create a matrix B, which contains vector of polynomials in each row
B = chebypol(N, nu)
# create a matrix T, where each row represents all possible tensor products
T = B
for i in range(D - 1):
T = np.kron(T, B)
return [X, T]
def approx(x,f,D,N,M,a,b):
theta = coef(f,D,N,M,a,b)
norm_x = - 1 + 2 * (x - a) / (b - a)
B = chebypol(N, x)
T = B
for i in range(D - 1):
T = np.kron(T, B)
p = np.dot(T, theta)
return p
def approx(x,f,D,N,M,a,b):
theta = coef(f,D,N,M,a,b)
norm_x = - 1 + 2 * (x - a) / (b - a)
B = chebypol(N, norm_x)
T = B
for i in range(D - 1):
T = np.kron(B, T)
if D == 1:
j = 1
else:
k = 1
A = []
while k <= D - 2:
A.append(k * pow(D, D - k - 1))
k = k + 1
j = sum(A) + D
t = T[j - 1]
p = np.dot(t, theta)
return p