?pttrs

Developer Reference for Intel® oneAPI Math Kernel Library for C

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ID 766684

Date 11/07/2023

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?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*L^T or U^T*D*Ufor real data and the L*D*L^H or U^H*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 `U^HDU`. If `uplo = 'L'`, the array `e` stores the subdiagonal of `L`, and `A` is factored as `LDL^H`.
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, ldbnrhs) for column major layout and max(1, ldbn) for row major layout.
ldb	The leading dimension of `b`; `ldb`≥ max(1, n) for column major layout and `ldb`≥nrhs 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.

Parent topic: Solving Systems of Linear Equations: LAPACK Computational Routines

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Developer Reference for Intel® oneAPI Math Kernel Library for C

?pttrs

Syntax

Include Files

Description

Input Parameters

Output Parameters

Return Values

See Also