def qr(a: ndarray,
mode: str = 'reduced',
overwrite: bool = False) \
-> tp.Union[tp.Tuple[ndarray, ndarray, ndarray], ndarray]:
"""
Compute QR decomposition of a matrix.
"""
if overwrite:
return ndarray(af.qr_inplace(a._af_array))
else:
(Q, R, T) = af.qr(a._af_array)
return ndarray(Q), ndarray(R), ndarray(T)
def simple_lapack(verbose=False):
display_func = _util.display_func(verbose)
print_func = _util.print_func(verbose)
a = af.randu(5, 5)
l, u, p = af.lu(a)
display_func(l)
display_func(u)
display_func(p)
p = af.lu_inplace(a, "full")
display_func(a)
display_func(p)
a = af.randu(5, 3)
q, r, t = af.qr(a)
display_func(q)
display_func(r)
display_func(t)
af.qr_inplace(a)
display_func(a)
a = af.randu(5, 5)
a = af.matmulTN(a, a.copy()) + 10 * af.identity(5, 5)
R, info = af.cholesky(a)
display_func(R)
print_func(info)
af.cholesky_inplace(a)
display_func(a)
a = af.randu(5, 5)
ai = af.inverse(a)
display_func(a)
display_func(ai)
x0 = af.randu(5, 3)
b = af.matmul(a, x0)
x1 = af.solve(a, b)
display_func(x0)
display_func(x1)
p = af.lu_inplace(a)
x2 = af.solve_lu(a, p, b)
display_func(x2)
print_func(af.rank(a))
print_func(af.det(a))
print_func(af.norm(a, af.NORM.EUCLID))
print_func(af.norm(a, af.NORM.MATRIX_1))
print_func(af.norm(a, af.NORM.MATRIX_INF))
print_func(af.norm(a, af.NORM.MATRIX_L_PQ, 1, 1))
a = af.randu(10, 10)
display_func(a)
u, s, vt = af.svd(a)
display_func(af.matmul(af.matmul(u, af.diag(s, 0, False)), vt))
u, s, vt = af.svd_inplace(a)
display_func(af.matmul(af.matmul(u, af.diag(s, 0, False)), vt))
def simple_lapack(verbose=False):
display_func = _util.display_func(verbose)
print_func = _util.print_func(verbose)
a = af.randu(5,5)
l,u,p = af.lu(a)
display_func(l)
display_func(u)
display_func(p)
p = af.lu_inplace(a, "full")
display_func(a)
display_func(p)
a = af.randu(5,3)
q,r,t = af.qr(a)
display_func(q)
display_func(r)
display_func(t)
af.qr_inplace(a)
display_func(a)
a = af.randu(5, 5)
a = af.matmulTN(a, a) + 10 * af.identity(5,5)
R,info = af.cholesky(a)
display_func(R)
print_func(info)
af.cholesky_inplace(a)
display_func(a)
a = af.randu(5,5)
ai = af.inverse(a)
display_func(a)
display_func(ai)
x0 = af.randu(5, 3)
b = af.matmul(a, x0)
x1 = af.solve(a, b)
display_func(x0)
display_func(x1)
p = af.lu_inplace(a)
x2 = af.solve_lu(a, p, b)
display_func(x2)
print_func(af.rank(a))
print_func(af.det(a))
print_func(af.norm(a, af.NORM.EUCLID))
print_func(af.norm(a, af.NORM.MATRIX_1))
print_func(af.norm(a, af.NORM.MATRIX_INF))
print_func(af.norm(a, af.NORM.MATRIX_L_PQ, 1, 1))
a = af.randu(5, 5) l, u, p = af.lu(a) af.display(l) af.display(u) af.display(p) p = af.lu_inplace(a, "full") af.display(a) af.display(p) a = af.randu(5, 3) q, r, t = af.qr(a) af.display(q) af.display(r) af.display(t) af.qr_inplace(a) af.display(a) a = af.randu(5, 5) a = af.matmulTN(a, a) + 10 * af.identity(5, 5) R, info = af.cholesky(a) af.display(R) print(info)
