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 zgbtf2.f(3) LAPACK zgbtf2.f(3)

zgbtf2.f -

# SYNOPSIS

## Functions/Subroutines

subroutine zgbtf2 (M, N, KL, KU, AB, LDAB, IPIV, INFO)

ZGBTF2 computes the LU factorization of a general band matrix using the unblocked version of the algorithm.

# Function/Subroutine Documentation

## subroutine zgbtf2 (integerM, integerN, integerKL, integerKU, complex*16, dimension( ldab, * )AB, integerLDAB, integer, dimension( * )IPIV, integerINFO)

ZGBTF2 computes the LU factorization of a general band matrix using the unblocked version of the algorithm.
Purpose:
``` ZGBTF2 computes an LU factorization of a complex m-by-n band matrix
A using partial pivoting with row interchanges.

This is the unblocked version of the algorithm, calling Level 2 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*16 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:
September 2012
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 146 of file zgbtf2.f.

# Author

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