# ?ppsv

Computes the solution to the system of linear equations with a symmetric (Hermitian) positive definite packed matrix A and multiple right-hand sides.

## Syntax

FORTRAN 77:

call sppsv( uplo, n, nrhs, ap, b, ldb, info )

call dppsv( uplo, n, nrhs, ap, b, ldb, info )

call cppsv( uplo, n, nrhs, ap, b, ldb, info )

call zppsv( uplo, n, nrhs, ap, b, ldb, info )

Fortran 95:

call ppsv( a, b [,uplo] [,info] )

## Description

This routine solves for X the real or complex system of linear equations `A*X = B`, where A is an n-by-n real symmetric/Hermitian positive-definite matrix stored in packed format, the columns of matrix B are individual right-hand sides, and the columns of X are the corresponding solutions.

The Cholesky decomposition is used to factor A as

`A = U`T*U (real flavors) and `A = U`H*U (complex flavors), if `uplo = 'U'`

or `A = L*LT` (real flavors) and `A = L*LH` (complex flavors), 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`.

## Input Parameters

uplo

  CHARACTER*1. Must be 'U' or 'L'.

  Indicates whether the upper or lower triangular part of A is stored:

  If `uplo = 'U'`, the upper triangle of A is stored.

  If `uplo = 'L'`, the lower triangle of A is stored.

n

  INTEGER. The order of matrix A; n ≥ 0.

nrhs

  INTEGER. The number of right-hand sides, the number of columns in `B; nrhs ≥ 0`.

ap, b

  REAL for sppsv

  DOUBLE PRECISION for dppsv

  COMPLEX for cppsv

  DOUBLE COMPLEX for zppsv.

  Arrays: `ap(*)`, `b(ldb,*)`. The array ap contains the upper or the lower triangular part of the matrix A (as specified by uplo) in packed storage (see Matrix Storage Schemes). The dimension of ap must be at least `max(1,n(n+1)/2)`.

  The array b contains the matrix B whose columns are the right-hand sides for the systems of equations. The second dimension of b must be at least `max(1,nrhs)`.

ldb

  INTEGER. The first dimension of b; `ldb ≥ max(1, n)`.

## Output Parameters

ap

  If info = 0, the upper or lower triangular part of A in packed storage is overwritten by the Cholesky factor U or L, as specified by uplo.

b

  Overwritten by the solution matrix X.

info

  INTEGER. If `info = 0`, the execution is successful.

  If `info = -i`, the i-th parameter had an illegal value.

  If `info = i`, the leading minor of order i (and therefore the matrix A itself) is not positive-definite, so the factorization could not be completed, and the solution has not been computed.

## Fortran 95 Interface Notes

Routines in Fortran 95 interface have fewer arguments in the calling sequence than their Fortran 77 counterparts. For general conventions applied to skip redundant or reconstructible arguments, see Fortran 95 Interface Conventions.

Specific details for the routine ppsv interface are as follows:

a

  Stands for argument ap in Fortan 77 interface. Holds the array A of size `(n*(n+1)/2)`.

b

  Holds the matrix B of size (`n,nrhs`).

uplo

  Must be 'U' or 'L'. The default value is 'U'.

Parent topic: Driver Routines