Developer Reference for Intel® oneAPI Math Kernel Library for C

ID 766684
Date 7/13/2023
Public

A newer version of this document is available. Customers should click here to go to the newest version.

Document Table of Contents

?pttrs

Solves a system of linear equations with a symmetric (Hermitian) positive-definite tridiagonal coefficient matrix using the factorization computed by ?pttrf.

Syntax

lapack_int LAPACKE_spttrs( int matrix_layout, lapack_int n, lapack_int nrhs, const float* d, const float* e, float* b, lapack_int ldb );

lapack_int LAPACKE_dpttrs( int matrix_layout, lapack_int n, lapack_int nrhs, const double* d, const double* e, double* b, lapack_int ldb );

lapack_int LAPACKE_cpttrs( int matrix_layout, char uplo, lapack_int n, lapack_int nrhs, const float* d, const lapack_complex_float* e, lapack_complex_float* b, lapack_int ldb );

lapack_int LAPACKE_zpttrs( int matrix_layout, char uplo, lapack_int n, lapack_int nrhs, const double* d, const lapack_complex_double* e, lapack_complex_double* b, lapack_int ldb );

Include Files

  • mkl.h

Description

The routine solves for X a system of linear equations A*X = B with a symmetric (Hermitian) positive-definite tridiagonal matrix A. Before calling this routine, call ?pttrf to compute the L*D*LT or UT*D*Ufor real data and the L*D*LH or UH*D*Ufactorization of A for complex data.

Input Parameters

matrix_layout

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

uplo

Used for cpttrs/zpttrs only. Must be 'U' or 'L'.

Specifies whether the superdiagonal or the subdiagonal of the tridiagonal matrix A is stored and how A is factored:

If uplo = 'U', the array e stores the conjugated values of the superdiagonal of U, and A is factored as UH*D*U.

If uplo = 'L', the array e stores the subdiagonal of L, and A is factored as L*D*LH.

n

The order of A; n 0.

nrhs

The number of right-hand sides, that is, the number of columns of the matrix B; nrhs 0.

d

Array, dimension (n). Contains the diagonal elements of the diagonal matrix D from the factorization computed by ?pttrf.

e

Array e is of size (n -1).

The array e contains the (n - 1) sub-diagonal elements of the unit bidiagonal factor L or the conjugated values of the superdiagonal of U from the factorization computed by ?pttrf (see uplo).

e, b

The array b contains the matrix B whose columns are the right-hand sides for the systems of equations.

The size of b is at least max(1, ldb*nrhs) for column major layout and max(1, ldb*n) for row major layout.

ldb

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

Output Parameters

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.