?gbsv

Developer Reference for Intel® oneAPI Math Kernel Library for C

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ID 766684

Date 12/16/2022

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?gbsv

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

Syntax

lapack_int LAPACKE_sgbsv (int matrix_layout , lapack_int n , lapack_int kl , lapack_int ku , lapack_int nrhs , float * ab , lapack_int ldab , lapack_int * ipiv , float * b , lapack_int ldb );

lapack_int LAPACKE_dgbsv (int matrix_layout , lapack_int n , lapack_int kl , lapack_int ku , lapack_int nrhs , double * ab , lapack_int ldab , lapack_int * ipiv , double * b , lapack_int ldb );

lapack_int LAPACKE_cgbsv (int matrix_layout , lapack_int n , lapack_int kl , lapack_int ku , lapack_int nrhs , lapack_complex_float * ab , lapack_int ldab , lapack_int * ipiv , lapack_complex_float * b , lapack_int ldb );

lapack_int LAPACKE_zgbsv (int matrix_layout , lapack_int n , lapack_int kl , lapack_int ku , lapack_int nrhs , lapack_complex_double * ab , lapack_int ldab , lapack_int * ipiv , 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 band matrix with kl subdiagonals and ku superdiagonals, the columns of matrix B are individual right-hand sides, and the columns of X are the corresponding solutions.

The LU decomposition with partial pivoting and row interchanges is used to factor A as A = L*U, where L is a product of permutation and unit lower triangular matrices with kl subdiagonals, and U is upper triangular with kl+ku superdiagonals. 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).
n	The order of `A`. The number of rows in `B`; `n`≥ 0.
kl	The number of subdiagonals within the band of `A`; `kl`≥ 0.
ku	The number of superdiagonals within the band of `A`; `ku`≥ 0.
nrhs	The number of right-hand sides. The number of columns in `B`; `nrhs`≥ 0.
ab, b	Arrays: `ab`(size max(1, ldabn)), `b`of size max(1, ldbnrhs) for column major layout and max(1, ldb*n) for row major layout. The array `ab` contains the matrix `A` in band storage (see Matrix Storage Schemes). The array `b` contains the matrix `B` whose columns are the right-hand sides for the systems of equations.
ldab	The leading dimension of the array `ab`. (`ldab`≥ 2`kl` + `ku` +1)
ldb	The leading dimension of `b`; `ldb`≥ max(1, n) for column major layout and `ldb`≥nrhs for row major layout.

Output Parameters

ab	Overwritten by `L` and `U`. `U` is stored as an upper triangular band matrix with `kl` + `ku` superdiagonals and `L` is stored as a lower triangular band matrix with `kl` subdiagonals. See Matrix Storage Schemes.
b	Overwritten by the solution matrix `X`.
ipiv	Array, size at least `max(1, n)`. The pivot indices: row `i` was interchanged with row `ipiv[i-1]`.

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. The factorization has been completed, but the factor U is exactly singular, so the solution could not be computed.

Parent topic: LAPACK Linear Equation Driver Routines

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