?gbsv

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 3/31/2023

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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

call sgbsv( n, kl, ku, nrhs, ab, ldab, ipiv, b, ldb, info )

call dgbsv( n, kl, ku, nrhs, ab, ldab, ipiv, b, ldb, info )

call cgbsv( n, kl, ku, nrhs, ab, ldab, ipiv, b, ldb, info )

call zgbsv( n, kl, ku, nrhs, ab, ldab, ipiv, b, ldb, info )

call gbsv( ab, b [,kl] [,ipiv] [,info] )

Include Files

mkl.fi, lapack.f90

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

n	INTEGER. The order of `A`. The number of rows in `B`; `n`≥ 0.
kl	INTEGER. The number of subdiagonals within the band of `A`; `kl`≥ 0.
ku	INTEGER. The number of superdiagonals within the band of `A`; `ku`≥ 0.
nrhs	INTEGER. The number of right-hand sides. The number of columns in `B`; `nrhs`≥ 0.
ab, b	REAL for sgbsv DOUBLE PRECISION for dgbsv COMPLEX for cgbsv DOUBLE COMPLEX for zgbsv. Arrays: `ab`(size `ldab` by ), `b`(size `ldb` by ). The array `ab` contains the matrix `A` in band storage (see Matrix Storage Schemes). The second dimension of `ab` must be at least `max(1, n)`. The array `b` contains the matrix `B` whose columns are the right-hand sides for the systems of equations. The second dimension of `b` must be at least `max(1,nrhs)`.
ldab	INTEGER. The leading dimension of the array `ab`. (`ldab`≥ 2`kl` + `ku` +1)
ldb	INTEGER. The leading dimension of `b`; `ldb≥ max(1, n)`.

Output Parameters

ab	Overwritten by `L` and `U`. The diagonal and `kl` + `ku` superdiagonals of `U` are stored in the first 1 + `kl` + `ku` rows of `ab`. The multipliers used to form `L` are stored in the next `kl` rows.
b	Overwritten by the solution matrix `X`.
ipiv	INTEGER. Array, size at least `max(1, n)`. The pivot indices: row `i` was interchanged with row `ipiv(i)`.
info	INTEGER. If `info = 0`, the execution is successful. If `info = -i`, the `i`-th parameter 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

Routines in Fortran 95 interface have fewer arguments in the calling sequence than their FORTRAN 77 counterparts. For general conventions applied to skip redundant or reconstructible arguments, see LAPACK 95 Interface Conventions.

Specific details for the routine gbsv interface are as follows:

ab	Holds the array `A` of size (`2*kl+ku+1,n`).
b	Holds the matrix `B` of size (`n,nrhs`).
ipiv	Holds the vector of length `n`.
kl	If omitted, assumed `kl = ku`.
ku	Restored as `ku = lda-2*kl-1`.

Parent topic: LAPACK Linear Equation Driver Routines

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