zcposv#

Functions

void zcposv(
    const char*          uplo,
    const INT            n,
    const INT            nrhs,
          c128* restrict A,
    const INT            lda,
    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 zcposv(const char *uplo, const INT n, const INT nrhs, c128 *restrict A, const INT lda, 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)#

ZCPOSV computes the solution to a complex system of linear equations. 

A * X = B

where A is an n-by-n Hermitian positive definite matrix and X and B are n-by-nrhs matrices.

ZCPOSV 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 is not going to be a winning strategy if the ratio COMPLEX performance over COMPLEX*16 performance is too small. A reasonable strategy should take the number of right-hand sides and the size of the matrix into account. This might be done with a call to ILAENV in the future. Up to now, we always try iterative refinement.

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
uplo

  • 'U': Upper triangle of A is stored

  • 'L': Lower triangle of A is stored

in
n

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

in
nrhs

The number of right hand sides, i.e., the number of columns of the matrix B. nrhs>=0.

inout
A

Array of dimension (lda, n). On entry, the Hermitian matrix A. If uplo='U', the leading n-by-n upper triangular part of A contains the upper triangular part of the matrix A. If uplo='L', the leading n-by-n lower triangular part of A contains the lower triangular part of the matrix A. Note that the imaginary parts of the diagonal elements need not be set and are assumed to be zero. On exit, if iterative refinement has been successfully used (info=0 and iter>=0) then A is unchanged. If double precision factorization has been used (info=0 and iter<0) then the array A contains the factor U or L from the Cholesky factorization A = U**H*U or A = L*L**H.

in
lda

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

in
B

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

in
ldb

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

out
X

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

in
ldx

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

out
work

Complex double precision workspace for residual vectors. Array of dimension (n, nrhs).

out
swork

Complex single precision workspace for the matrix and the right-hand sides or solutions in single precision. Array of dimension n*(n+nrhs).

out
rwork

Array of dimension n.

out
iter

Iteration count:

  • iter<0: iterative refinement has failed, double precision 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 CPOTRF

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

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

out
info

  • info=0: successful exit

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

  • info>0: if info=i, the leading principal minor of order i of (COMPLEX*16) A is not positive, so the factorization could not be completed, and the solution has not been computed.

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