`scipy.linalg._flapack:zgesvx`

Signature

def zgesvx(a, b, fact = E, trans = N, af = None, ipiv = None, equed = B, r = None, c = None, overwrite_a = 0, overwrite_b = 0)

Solve a @ x = b with equilibration, condition estimation and error bounds (LAPACK zgesvx).

a : ndarray: Square 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, ipiv, equed, r and c supplied. Default is 'E'.
trans : str, optional: 'N', 'T' or 'C' for the system, its transpose, or its conjugate transpose. Default is 'N'.
af : ndarray, optional: Factorization to reuse when fact='F'; otherwise it is computed.
ipiv : ndarray, optional: Pivot indices to reuse when fact='F', 0-based; otherwise computed.
equed : str, optional: Equilibration already applied when fact='F': 'N', 'R', 'C' or 'B'. Otherwise it is an output. Default is 'B'.
r : ndarray, optional: Row scale factors, used when fact='F' and equed is 'R' or 'B'.
c : ndarray, optional: Column scale factors, used when fact='F' and equed is 'C' or 'B'.
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.

as_ : ndarray: a, equilibrated if equed is not b'N'.
lu : ndarray: LU factorization of the equilibrated matrix.
piv : ndarray: Pivot indices, 0-based: row i was interchanged with row piv[i].
equed : bytes: Equilibration actually applied: b'N', b'R', b'C' or b'B'.
rs : ndarray: Row scale factors.
cs : ndarray: Column scale factors.
bs : 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, u[info-1, info-1] is exactly zero; if info = n+1, the matrix is singular to working precision and x may be inaccurate.