?ppsv

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 3/31/2023

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?ppsv

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

Syntax

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 )

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

Include Files

mkl.fi, lapack.f90

Description

The 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*L^T (real flavors) and A = L*L^H (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`(size ), `b`(size 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 leading dimension of `b`; `ldb≥ max(1, n)`.

Output Parameters

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.

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.

LAPACK 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 LAPACK 95 Interface Conventions.

Specific details for the routine ppsv interface are as follows:

ap	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: LAPACK Linear Equation Driver Routines

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