?pttrs

Developer Reference for Intel® oneAPI Math Kernel Library for C

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ID 766684

Date 10/15/2026

Version

Public

?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 (Computes the factorization of a symmetric (Hermitian) positive-definite tridiagonal matrix.) to compute the \(L*D*L^{T}\) or \(U^{T}*D*U\) for real data and the \(L*D*L^{H}\) or \(U^{H}*D*U\) factorization 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 \(U^{H}*D*U\) .

If uplo = 'L' , the array e stores the subdiagonal of \(L\) , and \(A\) is factored as \(L*D*L^{H}\) .

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 (Computes the factorization of a symmetric (Hermitian) positive-definite tridiagonal matrix.) .

e , b

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 (Computes the factorization of a symmetric (Hermitian) positive-definite tridiagonal matrix.) (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)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.

LAPACK 95 Interface Notes

There exist FORTRAN 77 and FORTRAN 95 interfaces for this routine. See the Intel® oneMKL Fortran Developer Reference for details.

NOTE:

Matrix Storage Schemes

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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

LAPACK 95 Interface Notes