Provided by: liblapack-doc_3.3.1-1_all

#### NAME

```       LAPACK-3  -  solves a system of linear equations  A * X = B or A**T * X = B with a general
band matrix A using the LU factorization computed by DGBTRF

```

#### SYNOPSIS

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

CHARACTER      TRANS

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

INTEGER        IPIV( * )

DOUBLE         PRECISION AB( LDAB, * ), B( LDB, * )

```

#### PURPOSE

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

```

#### 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**T* X = B  (Conjugate transpose = 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) DOUBLE PRECISION array, dimension (LDAB,N)
Details of the LU factorization of the band matrix A, as
computed by DGBTRF.  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) DOUBLE PRECISION 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

LAPACK routine (version 3.2)               April 2011                            DGBTRS(3lapack)
```