---
name: "dsposv"
section: "3lapack"
platform: "linux"
package: "liblapack-doc"
version: "3.2.1-8"
release: "Debian 6.0 (Squeeze)"
platforms: ["linux"]
url: "https://new.carta.tech/dsposv/3lapack"
---

# dsposv(3lapack)

computes the solution to a real system of linear equations A \* X = B,

## NAME

DSPOSV - computes the solution to a real system of linear equations  A \* X = B,

## SYNOPSIS

- SUBROUTINE DSPOSV(

  UPLO, N, NRHS, A, LDA, B, LDB, X, LDX, WORK,

- \+

  SWORK, ITER, INFO )

- CHARACTER

  UPLO

- INTEGER

  INFO, ITER, LDA, LDB, LDX, N, NRHS

- REAL

  SWORK( \* )

- DOUBLE

  PRECISION A( LDA, \* ), B( LDB, \* ), WORK( N, \* ),

- \+

  X( LDX, \* )

## PURPOSE

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 (see below). If the approach fails the method switches to a DOUBLE PRECISION factorization and solve.\
 The iterative refinement is not going to be a winning strategy if the ratio SINGLE PRECISION performance over DOUBLE PRECISION 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.\

## ARGUMENTS

- UPLO (input) CHARACTER

  \= 'U':  Upper triangle of A is stored;\
   \= 'L':  Lower triangle of A is stored.

- N (input) INTEGER

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

- NRHS (input) INTEGER

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

- A (input or input/ouptut) 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, and the strictly lower triangular part of A is not referenced.  If UPLO = 'L', the leading N-by-N lower triangular part of A contains the lower triangular part of the matrix A, and the strictly upper triangular part of A is not referenced. On exit, if iterative refinement has been successfully used (INFO.EQ.0 and ITER.GE.0, see description below), then A is unchanged, if double precision factorization has been used (INFO.EQ.0 and ITER.LT.0, see description below), then the array A contains the factor U or L from the Cholesky factorization A = U\*\*T\*U or A = L\*L\*\*T.

- LDA (input) INTEGER

  The leading dimension of the array A.  LDA \>= max(1,N).

- B (input) DOUBLE PRECISION array, dimension (LDB,NRHS)

  The N-by-NRHS right hand side matrix B.

- LDB (input) INTEGER

  The leading dimension of the array B.  LDB \>= max(1,N).

- X (output) DOUBLE PRECISION array, dimension (LDX,NRHS)

  If INFO = 0, the N-by-NRHS solution matrix X.

- LDX (input) INTEGER

  The leading dimension of the array X.  LDX \>= max(1,N).

- WORK (workspace) DOUBLE PRECISION array, dimension (N\*NRHS)

  This array is used to hold the residual vectors.

- SWORK (workspace) REAL 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.

- ITER (output) INTEGER

  \< 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 SPOTRF\
   \-31: stop the iterative refinement after the 30th iterations \> 0: iterative refinement has been sucessfully used. Returns the number of iterations

- INFO (output) INTEGER

  \= 0:  successful exit\
   \< 0:  if INFO = -i, the i-th argument had an illegal value\
   \> 0:  if INFO = i, the leading minor of order i of (DOUBLE PRECISION) A is not positive definite, so the factorization could not be completed, and the solution has not been computed. =========