Developer Reference for Intel® oneAPI Math Kernel Library for C

ID 766684
Date 3/22/2024
Public

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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

lapack_int LAPACKE_sppsv (int matrix_layout , char uplo , lapack_int n , lapack_int nrhs , float * ap , float * b , lapack_int ldb );

lapack_int LAPACKE_dppsv (int matrix_layout , char uplo , lapack_int n , lapack_int nrhs , double * ap , double * b , lapack_int ldb );

lapack_int LAPACKE_cppsv (int matrix_layout , char uplo , lapack_int n , lapack_int nrhs , lapack_complex_float * ap , lapack_complex_float * b , lapack_int ldb );

lapack_int LAPACKE_zppsv (int matrix_layout , char uplo , lapack_int n , lapack_int nrhs , lapack_complex_double * ap , lapack_complex_double * b , lapack_int ldb );

Include Files

  • mkl.h

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 = UT*U (real flavors) and A = UH*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

matrix_layout

Specifies whether matrix storage layout is row major (LAPACK_ROW_MAJOR) or column major (LAPACK_COL_MAJOR).

uplo

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

The order of matrix A; n 0.

nrhs

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

ap, b

Arrays: ap (size max(1,n*(n+1)/2), b, size max(ldb*nrhs) for column major layout and max(ldb*n) for row major layout,. 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 array b contains the matrix B whose columns are the right-hand sides for the systems of equations.

ldb

The leading dimension of b; ldb max(1, n) for column major layout and ldbnrhs for row major layout.

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.

Return Values

This function returns a value info.

If info = 0, the execution is successful.

If info = -i, parameter i 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.