def test_sparse():
J = Nested([[1, 0], [1, 0, 2], [1, 2]], dtype=int32)
A = array([-1, 2, 2, -1, -1, -1, 2], dtype=geode.real)
M = SparseMatrix(J, A)
assert M.rows() == M.columns() == 3
assert all(M.J.offsets == J.offsets)
assert all(M.J.flat == [0, 1, 0, 1, 2, 1, 2])
assert all(M.A.flat == A)
print M.J, M.A
b = array([pi, 3, e], dtype=geode.real)
C = M.incomplete_cholesky_factorization(0, 0)
t = empty_like(b)
C.solve_forward_substitution(b, t)
x = empty_like(b)
C.solve_backward_substitution(t, x)
b2 = empty_like(b)
M.multiply(x, b2)
print b, b2
assert all(abs(b - b2) < 1e-6)
b3 = 2 * x - [x[1], x[0] + x[2], x[1]]
assert all(abs(b2 - b3) < 1e-6)
def test_sparse(): J=Nested([[1,0],[1,0,2],[1,2]],dtype=int32) A=array([-1,2,2,-1,-1,-1,2],dtype=geode.real) M=SparseMatrix(J,A) assert M.rows()==M.columns()==3 assert all(M.J.offsets==J.offsets) assert all(M.J.flat==[0,1,0,1,2,1,2]) assert all(M.A.flat==A) print M.J,M.A b=array([pi,3,e],dtype=geode.real) C=M.incomplete_cholesky_factorization(0,0) t=empty_like(b) C.solve_forward_substitution(b,t) x=empty_like(b) C.solve_backward_substitution(t,x) b2=empty_like(b) M.multiply(x,b2) print b,b2 assert all(abs(b-b2)<1e-6) b3=2*x-[x[1],x[0]+x[2],x[1]] assert all(abs(b2-b3)<1e-6)
def test_matrix():
state = random.RandomState(221)
A = Matrix(state.rand(4, 3))
C = Matrix(state.rand(3, 4))
x = array(state.rand(3))
B = Matrix(state.rand(5, 2, 3))
D = Matrix(state.rand(5, 3, 2))
y = array(state.rand(5, 3))
check(B[-3], Matrix(array(B)[-3]))
check(A.T, Matrix(array(A).T))
check(B.T, Matrix([array(b).T for b in B]))
check(A * x, array(dot(A, x)))
check(A * C, Matrix(dot(A, C)))
check(B * x, array([b * x for b in B]))
check(A * y, array([A * v for v in y]))
check(B * y, array([b * v for b, v in zip(B, y)]))
check(A * D, Matrix([A * d for d in D]))
check(B * C, Matrix([b * C for b in B]))
check(B * D, Matrix([b * d for b, d in zip(B, D)]))
A = Matrix(state.rand(3, 3))
check(A.inverse(), Matrix(linalg.inv(A)))
def test_matrix(): state=random.RandomState(221) A=Matrix(state.rand(4,3)) C=Matrix(state.rand(3,4)) x=array(state.rand(3)) B=Matrix(state.rand(5,2,3)) D=Matrix(state.rand(5,3,2)) y=array(state.rand(5,3)) check(B[-3],Matrix(array(B)[-3])) check(A.T,Matrix(array(A).T)) check(B.T,Matrix([array(b).T for b in B])) check(A*x,array(dot(A,x))) check(A*C,Matrix(dot(A,C))) check(B*x,array([b*x for b in B])) check(A*y,array([A*v for v in y])) check(B*y,array([b*v for b,v in zip(B,y)])) check(A*D,Matrix([A*d for d in D])) check(B*C,Matrix([b*C for b in B])) check(B*D,Matrix([b*d for b,d in zip(B,D)])) A=Matrix(state.rand(3,3)) check(A.inverse(),Matrix(linalg.inv(A)))