scipy.linalg.lapack.zposvx#

scipy.linalg.lapack.zposvx(a, b, fact='E', af=None, equed='Y', s=None, lower=0, overwrite_a=0, overwrite_b=0) = <flapack function zposvx>#

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

Parameters:

andarray: Symmetric or Hermitian positive definite 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, equed and s supplied. Default is 'E'.
afndarray, optional: Cholesky factor to reuse when fact='F'; otherwise it is computed.
equedstr, optional: Equilibration already applied when fact='F': 'N' or 'Y'. Otherwise it is an output. Default is 'Y'.
sndarray, optional: Scale factors, used when fact='F' and equed is 'Y'.
lowerint, optional: If nonzero, the lower triangle of a is referenced and the factor is lower triangular; otherwise the upper. Default is 0.
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:

a_sndarray: a, equilibrated if equed is b'Y'.
lundarray: Cholesky factor of the equilibrated matrix.
equedbytes: Equilibration actually applied: b'N' or b'Y'.
sndarray: Scale factors.
b_sndarray: 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, 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.