?gbsv

Developer Reference for Intel® oneAPI Math Kernel Library for C

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ID 766684

Date 10/15/2026

Version

Public

?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, ldab * n )) , b of size max(1, ldb * nrhs ) 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)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)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.

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

?gbsv

Syntax

Include Files

Description

Input Parameters

Output Parameters

Return Values

LAPACK 95 Interface Notes