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Developer Reference for Intel® oneAPI Math Kernel Library for C

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ID 766684

Date 12/16/2022

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Computes the solution to the system of linear equations with a tridiagonal coefficient matrix A and multiple right-hand sides.

Syntax

lapack_int LAPACKE_sgtsv (int matrix_layout , lapack_int n , lapack_int nrhs , float * dl , float * d , float * du , float * b , lapack_int ldb );

lapack_int LAPACKE_dgtsv (int matrix_layout , lapack_int n , lapack_int nrhs , double * dl , double * d , double * du , double * b , lapack_int ldb );

lapack_int LAPACKE_cgtsv (int matrix_layout , lapack_int n , lapack_int nrhs , lapack_complex_float * dl , lapack_complex_float * d , lapack_complex_float * du , lapack_complex_float * b , lapack_int ldb );

lapack_int LAPACKE_zgtsv (int matrix_layout , lapack_int n , lapack_int nrhs , lapack_complex_double * dl , lapack_complex_double * d , lapack_complex_double * du , lapack_complex_double * b , lapack_int ldb );

Include Files

mkl.h

Description

The routine solves for X the system of linear equations A*X = B, where A is an n-by-n tridiagonal matrix, the columns of matrix B are individual right-hand sides, and the columns of X are the corresponding solutions. The routine uses Gaussian elimination with partial pivoting.

Note that the equation A^T*X = B may be solved by interchanging the order of the arguments du and dl.

Input Parameters

matrix_layout	Specifies whether matrix storage layout is row major (LAPACK_ROW_MAJOR) or column major (LAPACK_COL_MAJOR).
n	The order of `A`, the number of rows in `B`; `n`≥ 0.
nrhs	The number of right-hand sides, the number of columns in `B; nrhs≥ 0`.
dl	The array `dl` (size `n` - 1) contains the `(n - 1)` subdiagonal elements of `A`.
d	The array `d` (size `n`) contains the diagonal elements of `A`.
du	The array `du` (size `n` - 1) contains the `(n - 1)` superdiagonal elements of `A`.
b	The array `b`of size max(1, ldbnrhs) for column major layout and max(1, ldbn) for row major layout 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 `ldb`≥nrhs for row major layout.

Output Parameters

dl	Overwritten by the `(n-2)` elements of the second superdiagonal of the upper triangular matrix `U` from the `LU` factorization of A. These elements are stored in `dl[0], ..., dl[n - 3]`.
d	Overwritten by the `n` diagonal elements of `U`.
du	Overwritten by the `(n-1)` elements of the first superdiagonal of `U`.
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, U_{i, i} is exactly zero, and the solution has not been computed. The factorization has not been completed unless i = n.

Parent topic: LAPACK Linear Equation Driver Routines

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Developer Reference for Intel® oneAPI Math Kernel Library for C

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