dsposv#

Functions

void dsposv(
    const char*           uplo,
    const INT             n,
    const INT             nrhs,
          f64*   restrict A,
    const INT             lda,
    const f64*   restrict B,
    const INT             ldb,
          f64*   restrict X,
    const INT             ldx,
          f64*   restrict work,
          float* restrict swork,
          INT*            iter,
          INT*            info
);
void dsposv(const char *uplo, const INT n, const INT nrhs, f64 *restrict A, const INT lda, const f64 *restrict B, const INT ldb, f64 *restrict X, const INT ldx, f64 *restrict work, float *restrict swork, INT *iter, INT *info)#

DSPOSV computes the solution to a real system of linear equations A * X = B, where A is an N-by-N symmetric positive definite matrix and X and B are N-by-NRHS matrices.

DSPOSV first attempts to factorize the matrix in SINGLE PRECISION and use this factorization within an iterative refinement procedure to produce a solution with DOUBLE PRECISION normwise backward error quality. If the approach fails the method switches to a DOUBLE PRECISION 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
uplo

Specifies whether the upper or lower triangular part of the symmetric matrix A is stored. = ‘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

Double precision array, dimension (lda, n). On entry, the symmetric 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. On exit, if iterative refinement has been successfully used (info = 0 and iter >= 0) then A is unchanged. If f64 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**T*U or A = L*L**T.

in
lda

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

in
B

Double precision array, 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

Double precision array, 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

Double precision array, dimension (n, nrhs). This array is used to hold the residual vectors.

out
swork

Single precision array, dimension (n*(n+nrhs)). This array is used to use the single precision matrix and the right-hand sides or solutions in single precision.

out
iter

Iteration count:

  • < 0: iterative refinement has failed, f64 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 SPOTRF

    • -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, the i-th argument had an illegal value

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

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