# dposv (l) - Linux Man Pages

## 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
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

U**T* U,  if UPLO aqUaq, or

L**T,  if UPLO aqLaq,
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
= aqUaq: Upper triangle of A is stored;
= aqLaq: 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 = aqUaq, 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 = aqLaq, 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.