---
name: "dgbtrs"
section: "3lapack"
platform: "linux"
package: "liblapack-doc"
version: "3.2.1-8"
release: "Debian 6.0 (Squeeze)"
platforms: ["linux"]
url: "https://new.carta.tech/dgbtrs/3lapack"
---

# dgbtrs(3lapack)

solves a system of linear equations A \* X = B or A' \* X = B with a general band matrix A using the LU factorization computed by DGBTRF

## NAME

DGBTRS - solves a system of linear equations  A \* X = B or A' \* 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' \* 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'\* X = B  (Transpose)\
   \= 'C':  A'\* 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