# 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.

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### NAME

```        ZGBTRS - solve a system of linear equations A * X = B, A**T * X = B, or
A**H * X = B with a general band matrix A using  the  LU  factorization
computed by ZGBTRF
```

### SYNOPSIS

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

CHARACTER      TRANS

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

INTEGER        IPIV( * )

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

### PURPOSE

```        ZGBTRS solves a system of linear equations A * X = B, A**T * X = B,  or
A**H  *  X  = B with a general band matrix A using the LU factorization
computed by ZGBTRF.
```

### ARGUMENTS

```        TRANS   (input) CHARACTER*1
Specifies the form of the system of equations.  = ’N’:  A * X =
B     (No transpose)
= ’T’:  A**T * X = B  (Transpose)
= ’C’:  A**H * X = B  (Conjugate transpose)

N       (input) INTEGER
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) COMPLEX*16 array, dimension (LDAB,N)
Details of the LU factorization of the band matrix A,  as  com‐
puted  by  ZGBTRF.   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.

LDAB    (input) INTEGER
The leading dimension of the array AB.  LDAB >= 2*KL+KU+1.

IPIV    (input) INTEGER array, dimension (N)
The pivot indices; for 1 <= i <= N, row i  of  the  matrix  was
interchanged with row IPIV(i).

B       (input/output) COMPLEX*16 array, dimension (LDB,NRHS)
On  entry, the right hand side matrix B.  On exit, the 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

```
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