scipy.linalg.lapack.sgesvx#

scipy.linalg.lapack.sgesvx(a, b, fact='E', trans='N', af=None, ipiv=None, equed='B', r=None, c=None, overwrite_a=0, overwrite_b=0) = <flapack function sgesvx>#

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

Parameters:

andarray: Square matrix of shape (n, n).
bndarray: Right-hand side(s) of shape (n, nrhs).
factstr, 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'.
transstr, optional: 'N', 'T' or 'C' for the system, its transpose, or its conjugate transpose. Default is 'N'.
afndarray, optional: Factorization to reuse when fact='F'; otherwise it is computed.
ipivndarray, optional: Pivot indices to reuse when fact='F', 0-based; otherwise computed.
equedstr, optional: Equilibration already applied when fact='F': 'N', 'R', 'C' or 'B'. Otherwise it is an output. Default is 'B'.
rndarray, optional: Row scale factors, used when fact='F' and equed is 'R' or 'B'.
cndarray, optional: Column scale factors, used when fact='F' and equed is 'C' or 'B'.
overwrite_aint, optional: If nonzero, a may be overwritten in place. Default is 0.
overwrite_bint, optional: If nonzero, b may be overwritten in place. Default is 0.

Returns:

as_ndarray: a, equilibrated if equed is not b'N'.
lundarray: LU factorization of the equilibrated matrix.
pivndarray: Pivot indices, 0-based: row i was interchanged with row piv[i].
equedbytes: Equilibration actually applied: b'N', b'R', b'C' or b'B'.
rsndarray: Row scale factors.
csndarray: Column scale factors.
bsndarray: b, scaled to match the equilibrated system.
xndarray: Solution of the system.
rcondfloat: Estimate of the reciprocal condition number of the equilibrated matrix.
ferrndarray: Estimated forward error bound for each solution vector.
berrndarray: Componentwise relative backward error of each solution vector.
infoint: 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.