dsgesv

Functions

void dsgesv(
    const INT             n,
    const INT             nrhs,
          f64*   restrict A,
    const INT             lda,
          INT*   restrict ipiv,
    const f64*   restrict B,
    const INT             ldb,
          f64*   restrict X,
    const INT             ldx,
          f64*   restrict work,
          float* restrict swork,
          INT*            iter,
          INT*            info
);

void dsgesv(const INT n, const INT nrhs, f64 *restrict A, const INT lda, INT *restrict ipiv, const f64 *restrict B, const INT ldb, f64 *restrict X, const INT ldx, f64 *restrict work, float *restrict swork, INT *iter, INT *info)

DSGESV computes the solution to a real system of linear equations.

A * X = B

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

DSGESV 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.

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

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

in

lda

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

out

ipiv

Array of dimension n. The pivot indices.

in

B

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

in

ldb

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

out

work

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

out

swork

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

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 SGETRF

  • -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, argument i had an illegal value

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