def diag(self):
"""
Return a vector with the diagonal elements of the matrix.
"""
N = self.nrows
data = self.flat
return asvector([data.flat[i * N + i] for i in range(N)])
def solve_jacobi(self, b, tol=1e-3, x0=None, maxiter=1000):
"""
Solve a linear using Gauss-Jacobi method.
"""
b = asvector(b)
x = b * 0
D = self.from_diag([1.0 / x for x in self.diag()])
R = self.drop_diag()
for _ in range(maxiter):
x, old = D * (b - R * x), x
if (x - old).norm() < tol:
break
return x
def solve_triangular(self, b, lower=False):
"""
Solve a triangular system.
If lower=True, it assumes a lower triangular matrix, otherwise (default)
assumes an upper triangular matrix.
"""
N = self.nrows
x = [0] * N
if lower:
for i in range(N):
x[i] = (b[i] - self[i].dot(x)) / self[i, i]
else:
for i in range(N - 1, -1, -1):
x[i] = (b[i] - self[i].dot(x)) / self[i, i]
return asvector(x)
