def test_LDLsolve():
A = Matrix([[2,3,5],
[3,6,2],
[8,3,6]])
x = Matrix(3,1,[3,7,5])
b = A*x
soln = A.LDLsolve(b)
assert soln == x
A = Matrix([[0,-1,2],
[5,10,7],
[8,3,4]])
x = Matrix(3,1,[-1,2,5])
b = A*x
soln = A.LDLsolve(b)
assert soln == x
def _mat_inv_mul(A, B):
"""
Computes A^-1 * B symbolically w/ substitution, where B is not
necessarily a vector, but can be a matrix.
"""
r1, c1 = A.shape
r2, c2 = B.shape
temp1 = Matrix(r1, c1, lambda i, j: Symbol('x' + str(j) + str(r1 * i)))
temp2 = Matrix(r2, c2, lambda i, j: Symbol('y' + str(j) + str(r2 * i)))
for i in range(len(temp1)):
if A[i] == 0:
temp1[i] = 0
for i in range(len(temp2)):
if B[i] == 0:
temp2[i] = 0
temp3 = []
for i in range(c2):
temp3.append(temp1.LDLsolve(temp2[:, i]))
temp3 = Matrix([i.T for i in temp3]).T
return temp3.subs(dict(list(zip(temp1, A)))).subs(dict(list(zip(temp2, B))))
