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sgbsv.f(3) LAPACK sgbsv.f(3)

NAME

sgbsv.f

SYNOPSIS

Functions/Subroutines


subroutine sgbsv (N, KL, KU, NRHS, AB, LDAB, IPIV, B, LDB, INFO)
SGBSV computes the solution to system of linear equations A * X = B for GB matrices (simple driver)

Function/Subroutine Documentation

subroutine sgbsv (integer N, integer KL, integer KU, integer NRHS, real, dimension( ldab, * ) AB, integer LDAB, integer, dimension( * ) IPIV, real, dimension( ldb, * ) B, integer LDB, integer INFO)

SGBSV computes the solution to system of linear equations A * X = B for GB matrices (simple driver)

Purpose:


SGBSV computes the solution to a real system of linear equations
A * X = B, where A is a band matrix of order N with KL subdiagonals
and KU superdiagonals, and X and B are N-by-NRHS matrices.
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.

Parameters:

N


N is INTEGER
The number of linear equations, i.e., the order of the
matrix A. N >= 0.

KL


KL is INTEGER
The number of subdiagonals within the band of A. KL >= 0.

KU


KU is INTEGER
The number of superdiagonals within the band of A. KU >= 0.

NRHS


NRHS is INTEGER
The number of right hand sides, i.e., the number of columns
of the matrix B. NRHS >= 0.

AB


AB is REAL array, dimension (LDAB,N)
On entry, the matrix A in band storage, in rows KL+1 to
2*KL+KU+1; rows 1 to KL of the array need not be set.
The j-th column of A is stored in the j-th column of the
array AB as follows:
AB(KL+KU+1+i-j,j) = A(i,j) for max(1,j-KU)<=i<=min(N,j+KL)
On exit, details of the factorization: U is stored as an
upper triangular band matrix with KL+KU superdiagonals in
rows 1 to KL+KU+1, and the multipliers used during the
factorization are stored in rows KL+KU+2 to 2*KL+KU+1.
See below for further details.

LDAB


LDAB is INTEGER
The leading dimension of the array AB. LDAB >= 2*KL+KU+1.

IPIV


IPIV is INTEGER array, dimension (N)
The pivot indices that define the permutation matrix P;
row i of the matrix was interchanged with row IPIV(i).

B


B is REAL array, dimension (LDB,NRHS)
On entry, the N-by-NRHS right hand side matrix B.
On exit, if INFO = 0, the N-by-NRHS solution matrix X.

LDB


LDB is INTEGER
The leading dimension of the array B. LDB >= max(1,N).

INFO


INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: if INFO = i, U(i,i) is exactly zero. The factorization
has been completed, but the factor U is exactly
singular, and the solution has not been computed.

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

December 2016

Further Details:


The band storage scheme is illustrated by the following example, when
M = N = 6, KL = 2, KU = 1:
On entry: On exit:
* * * + + + * * * u14 u25 u36
* * + + + + * * u13 u24 u35 u46
* a12 a23 a34 a45 a56 * u12 u23 u34 u45 u56
a11 a22 a33 a44 a55 a66 u11 u22 u33 u44 u55 u66
a21 a32 a43 a54 a65 * m21 m32 m43 m54 m65 *
a31 a42 a53 a64 * * m31 m42 m53 m64 * *
Array elements marked * are not used by the routine; elements marked
+ need not be set on entry, but are required by the routine to store
elements of U because of fill-in resulting from the row interchanges.

Definition at line 164 of file sgbsv.f.

Author

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