zcgesv#

Functions

void zcgesv(
    const INT            n,
    const INT            nrhs,
          c128* restrict A,
    const INT            lda,
          INT*  restrict ipiv,
    const c128* restrict B,
    const INT            ldb,
          c128* restrict X,
    const INT            ldx,
          c128* restrict work,
          c64*  restrict swork,
          f64*  restrict rwork,
          INT*           iter,
          INT*           info
);
void zcgesv(const INT n, const INT nrhs, c128 *restrict A, const INT lda, INT *restrict ipiv, const c128 *restrict B, const INT ldb, c128 *restrict X, const INT ldx, c128 *restrict work, c64 *restrict swork, f64 *restrict rwork, INT *iter, INT *info)#

ZCGESV computes the solution to a complex system of linear equations A * X = B, where A is an N-by-N matrix and X and B are N-by-NRHS matrices.

ZCGESV first attempts to factorize the matrix in COMPLEX and use this factorization within an iterative refinement procedure to produce a solution with COMPLEX*16 normwise backward error quality (see below). If the approach fails the method switches to a COMPLEX*16 factorization and solve.

The iterative refinement process is stopped if ITER > ITERMAX or for all the RHS we have: RNRM < SQRT(N)*XNRM*ANRM*EPS*BWDMAX where o ITER is the number of the current iteration in the iterative refinement process o RNRM is the infinity-norm of the residual o XNRM is the infinity-norm of the solution o ANRM is the infinity-operator-norm of the matrix A o EPS is the machine epsilon returned by DLAMCH(‘Epsilon’) The value ITERMAX and BWDMAX are fixed to 30 and 1.0D+00 respectively.

Parameters

in
n

The number of linear equations, i.e., the order of A. n >= 0.

in
nrhs

The number of right hand sides. nrhs >= 0.

inout
A

On entry, the N-by-N coefficient matrix A. On exit, if iterative refinement succeeded (iter >= 0), A is unchanged. If COMPLEX*16 factorization was used (iter < 0), A contains the factors L and U from A = P*L*U. Array of dimension (lda, n).

in
lda

The leading dimension of A. lda >= max(1, n).

out
ipiv

The pivot indices. Array of dimension n, 0-based.

in
B

The N-by-NRHS right hand side matrix B. Array of dimension (ldb, nrhs).

in
ldb

The leading dimension of B. ldb >= max(1, n).

out
X

If info = 0, the N-by-NRHS solution matrix X. Array of dimension (ldx, nrhs).

in
ldx

The leading dimension of X. ldx >= max(1, n).

out
work

Complex*16 workspace for residual vectors. Array of dimension (n, nrhs).

out
swork

Complex (single precision) workspace for matrix and solutions. Array of dimension n*(n+nrhs).

out
rwork

Double precision array, dimension (n).

out
iter

Iteration count:

  • < 0: iterative refinement has failed, COMPLEX*16 factorization has been performed

    • -1 : the routine fell back to full precision for implementation- or machine-specific reasons

    • -2 : narrowing the precision induced an overflow, the routine fell back to full precision

    • -3 : failure of CGETRF

    • -31: stop the iterative refinement after the 30th iterations

  • > 0: iterative refinement has been successfully used. Returns the number of iterations

out
info

Exit status:

  • = 0: successful exit

  • < 0: if info = -i, argument i had an illegal value

  • > 0: if info = i, U(i-1,i-1) is exactly zero

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