dposv.f

Section: LAPACK (3)
Updated: Tue Nov 14 2017
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dposv.f

SYNOPSIS

Functions/Subroutines

subroutine dposv (UPLO, N, NRHS, A, LDA, B, LDB, INFO)
DPOSV computes the solution to system of linear equations A * X = B for PO matrices

Function/Subroutine Documentation

subroutine dposv (character UPLO, integer N, integer NRHS, double precision, dimension( lda, * ) A, integer LDA, double precision, dimension( ldb, * ) B, integer LDB, integer INFO)

DPOSV computes the solution to system of linear equations A * X = B for PO matrices

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.
```

Parameters:

UPLO

```          UPLO is CHARACTER*1
= 'U':  Upper triangle of A is stored;
= 'L':  Lower triangle of A is stored.
```

N

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

NRHS

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

A

```          A is 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

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

B

```          B is 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

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

INFO

```          INFO is 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.
```

Author:

Univ. of Tennessee

Univ. of California Berkeley