# CGBTRF (3) - Linux Man Pages

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

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