def cholesky(a: ndarray, overwrite: bool = False, is_upper: bool = False) -> ndarray: """ Compute the Cholesky decomposition of a matrix. """ if overwrite: info = af.cholesky_inplace(a._af_array, is_upper=is_upper) if info == 0: return a else: raise np.linalg.LinAlgError(f"cholesky decomposition failed at " f"rank {info}") else: R, info = af.cholesky(a._af_array, is_upper=is_upper) if info == 0: return ndarray(R) else: raise np.linalg.LinAlgError(f"cholesky decomposition failed at " f"rank {info}")
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, 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) af.cholesky_inplace(a) af.display(a) a = af.randu(5, 5) ai = af.inverse(a) af.display(a) af.display(ai) x0 = af.randu(5, 3) b = af.matmul(a, x0) x1 = af.solve(a, b)