CGBTRF man page on Oracle

```cgbtrf.f(3)			    LAPACK			   cgbtrf.f(3)

NAME
cgbtrf.f -

SYNOPSIS
Functions/Subroutines
subroutine cgbtrf (M, N, KL, KU, AB, LDAB, IPIV, INFO)
CGBTRF

Function/Subroutine Documentation
subroutine cgbtrf (integerM, integerN, integerKL, integerKU, complex,
dimension( ldab, * )AB, integerLDAB, integer, dimension( * )IPIV,
integerINFO)
CGBTRF

Purpose:

CGBTRF computes an LU factorization of a complex m-by-n band matrix A
using partial pivoting with row interchanges.

This is the blocked version of the algorithm, calling Level 3 BLAS.

Parameters:
M

M is INTEGER
The number of rows of the matrix A.  M >= 0.

N

N is INTEGER
The number of columns 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.

AB

AB is COMPLEX 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(m,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 (min(M,N))
The pivot indices; for 1 <= i <= min(M,N), row i of the
matrix was interchanged with row IPIV(i).

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 division by zero will occur if it is used
to solve a system of equations.

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 145 of file cgbtrf.f.

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

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