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# dgbsv.f(3) [centos man page]

```dgbsv.f(3)							      LAPACK								dgbsv.f(3)

NAME
dgbsv.f -

SYNOPSIS
Functions/Subroutines
subroutine dgbsv (N, KL, KU, NRHS, AB, LDAB, IPIV, B, LDB, INFO)
DGBSV computes the solution to system of linear equations A * X = B for GB matrices (simple driver)

Function/Subroutine Documentation
subroutine dgbsv (integerN, integerKL, integerKU, integerNRHS, double precision, dimension( ldab, * )AB, integerLDAB, integer, dimension( *
)IPIV, double precision, dimension( ldb, * )B, integerLDB, integerINFO)
DGBSV computes the solution to system of linear equations A * X = B for GB matrices (simple driver)

Purpose:

DGBSV 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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

NAG Ltd.

Date:
November 2011

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 163 of file dgbsv.f.

Author
Generated automatically by Doxygen for LAPACK from the source code.

Version 3.4.2							  Tue Sep 25 2012							dgbsv.f(3)```