# Ubuntu Feisty 7.04 manual page repository

Ubuntu is a free computer operating system based on the Linux kernel. Many IT companies, like DeployIS is using it to provide an up-to-date, stable operating system.

Provided by: lapack3-doc_3.0.20000531a-6ubuntu3_all

` `

### NAME

```        ZGBSV  - compute the solution to a complex 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
```

### SYNOPSIS

```        SUBROUTINE ZGBSV( N, KL, KU, NRHS, AB, LDAB, IPIV, B, LDB, INFO )

INTEGER       INFO, KL, KU, LDAB, LDB, N, NRHS

INTEGER       IPIV( * )

COMPLEX*16    AB( LDAB, * ), B( LDB, * )
```

### PURPOSE

```        ZGBSV computes the solution to a complex 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 decomposi‐
tion 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 triangu‐
lar matrices with KL subdiagonals, and U is upper triangular with KL+KU
superdiagonals.   The factored form of A is then used to solve the sys‐
tem of equations A * X = B.
```

### ARGUMENTS

```        N       (input) INTEGER
The number of linear equations, i.e., the order of  the  matrix
A.  N >= 0.

KL      (input) INTEGER
The number of subdiagonals within the band of A.  KL >= 0.

KU      (input) INTEGER
The number of superdiagonals within the band of A.  KU >= 0.

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

AB      (input/output) 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(N,j+KL) On exit, details of the factorization: U is
stored as an upper triangular band matrix with KL+KU superdiag‐
onals 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    (input) INTEGER
The leading dimension of the array AB.  LDAB >= 2*KL+KU+1.

IPIV    (output) 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       (input/output) COMPLEX*16 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     (input) INTEGER
The leading dimension of the array B.  LDB >= max(1,N).

INFO    (output) 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.
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 ele‐
ments of U because of fill-in resulting from the row interchanges.

```
Sections

What does Ubuntu mean?
Ubuntu is an African word meaning 'Humanity to others', or 'I am what I am because of who we all are'. The Ubuntu distribution brings the spirit of Ubuntu to the software world.