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

# dposv(3lapack)

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

## NAME

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

## SYNOPSIS

- SUBROUTINE DPOSV(

  UPLO, N, NRHS, A, LDA, B, LDB, INFO )

- CHARACTER

  UPLO

- INTEGER

  INFO, LDA, LDB, N, NRHS

- DOUBLE

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

## PURPOSE

DPOSV 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.\
 The Cholesky decomposition is used to factor A as\
\
    A = U\*\*T\* U,  if UPLO = 'U', or\
\
    A = L \* L\*\*T,  if UPLO = 'L',\
 where U is an upper triangular matrix and L is a lower triangular matrix.  The factored form of A is then used to solve the system of equations A \* X = B.\

## ARGUMENTS

- UPLO (input) CHARACTER\*1

  \= '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/output) 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 INFO = 0, 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/output) DOUBLE PRECISION array, dimension (LDB,NRHS)

  On entry, the N-by-NRHS right hand side matrix B. On exit, if INFO = 0, the N-by-NRHS solution matrix X.

- LDB (input) INTEGER

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

- 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 A is not positive definite, so the factorization could not be completed, and the solution has not been computed.