`scipy.linalg._flapack:dposvx`

Signature

def dposvx(a, b, fact = E, af = None, equed = Y, s = None, lower = 0, overwrite_a = 0, overwrite_b = 0)

Solve a @ x = b for a positive definite a with equilibration, condition estimation and error bounds (LAPACK dposvx).

a : ndarray: Symmetric or Hermitian positive definite matrix of shape (n, n).
b : ndarray: Right-hand side(s) of shape (n, nrhs).
fact : str, optional: 'E' to equilibrate then factorize, 'N' to factorize as given, 'F' to reuse the af, equed and s supplied. Default is 'E'.
af : ndarray, optional: Cholesky factor to reuse when fact='F'; otherwise it is computed.
equed : str, optional: Equilibration already applied when fact='F': 'N' or 'Y'. Otherwise it is an output. Default is 'Y'.
s : ndarray, optional: Scale factors, used when fact='F' and equed is 'Y'.
lower : int, optional: If nonzero, the lower triangle of a is referenced and the factor is lower triangular; otherwise the upper. Default is 0.
overwrite_a : int, optional: If nonzero, a may be overwritten in place. Default is 0.
overwrite_b : int, optional: If nonzero, b may be overwritten in place. Default is 0.

a_s : ndarray: a, equilibrated if equed is b'Y'.
lu : ndarray: Cholesky factor of the equilibrated matrix.
equed : bytes: Equilibration actually applied: b'N' or b'Y'.
s : ndarray: Scale factors.
b_s : ndarray: b, scaled to match the equilibrated system.
x : ndarray: Solution of the system.
rcond : float: Estimate of the reciprocal condition number of the equilibrated matrix.
ferr : ndarray: Estimated forward error bound for each solution vector.
berr : ndarray: Componentwise relative backward error of each solution vector.
info : int: 0 on success; if negative, the -info-th argument had an illegal value; if 0 < info <= n, the leading minor of order info is not positive definite; if info = n+1, the matrix is singular to working precision and x may be inaccurate.