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Developer Reference for Intel® oneAPI Math Kernel Library for C

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ID 766684

Date 3/31/2023

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

Syntax

lapack_int LAPACKE_spbsv (int matrix_layout , char uplo , lapack_int n , lapack_int kd , lapack_int nrhs , float * ab , lapack_int ldab , float * b , lapack_int ldb );

lapack_int LAPACKE_dpbsv (int matrix_layout , char uplo , lapack_int n , lapack_int kd , lapack_int nrhs , double * ab , lapack_int ldab , double * b , lapack_int ldb );

lapack_int LAPACKE_cpbsv (int matrix_layout , char uplo , lapack_int n , lapack_int kd , lapack_int nrhs , lapack_complex_float * ab , lapack_int ldab , lapack_complex_float * b , lapack_int ldb );

lapack_int LAPACKE_zpbsv (int matrix_layout , char uplo , lapack_int n , lapack_int kd , lapack_int nrhs , lapack_complex_double * ab , lapack_int ldab , 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 symmetric/Hermitian positive definite band matrix, the columns of matrix B are individual right-hand sides, and the columns of X are the corresponding solutions.

The Cholesky decomposition is used to factor A as

A = U^T*U (real flavors) and A = U^H*U (complex flavors), if uplo = 'U'

or A = L*L^T (real flavors) and A = L*L^H (complex flavors), if uplo = 'L',

where U is an upper triangular band matrix and L is a lower triangular band matrix, with the same number of superdiagonals or subdiagonals as A. 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).
`uplo`	Must be 'U' or 'L'. Indicates whether the upper or lower triangular part of `A` is stored: If `uplo = 'U'`, the upper triangle of `A` is stored. If `uplo = 'L'`, the lower triangle of `A` is stored.
n	The order of matrix `A`; `n`≥ 0.
kd	The number of superdiagonals of the matrix `A` if `uplo = 'U'`, or the number of subdiagonals if `uplo = 'L';kd`≥ 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 upper or the lower triangular part of the matrix `A` (as specified by `uplo`) 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`≥`kd` +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	The upper or lower triangular part of `A` (in band storage) is overwritten by the Cholesky factor `U` or `L`, as specified by `uplo`, in the same storage format as `A`.
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, the leading minor of order i (and therefore the matrix A itself) is not positive-definite, so the factorization could not be completed, and the solution has not been computed.

Parent topic: LAPACK Linear Equation Driver Routines

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