# cgbtrs.f - Man Page

SRC/cgbtrs.f

## Synopsis

### Functions/Subroutines

subroutine **cgbtrs** (trans, n, kl, ku, nrhs, ab, ldab, ipiv, b, ldb, info)**CGBTRS**

## Function/Subroutine Documentation

### subroutine cgbtrs (character trans, integer n, integer kl, integer ku, integer nrhs, complex, dimension( ldab, * ) ab, integer ldab, integer, dimension( * ) ipiv, complex, dimension( ldb, * ) b, integer ldb, integer info)

**CGBTRS**

**Purpose:**

CGBTRS 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 CGBTRF.

**Parameters***TRANS*TRANS is 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*N is INTEGER The order 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.

*NRHS*NRHS is INTEGER The number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0.

*AB*AB is COMPLEX array, dimension (LDAB,N) Details of the LU factorization of the band matrix A, as computed by CGBTRF. 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*LDAB is INTEGER The leading dimension of the array AB. LDAB >= 2*KL+KU+1.

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

*B*B is COMPLEX array, dimension (LDB,NRHS) On entry, the right hand side matrix B. On exit, the solution matrix X.

*LDB*LDB is INTEGER The leading dimension of the array B. LDB >= max(1,N).

*INFO*INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value

**Author**Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line **136** of file **cgbtrs.f**.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page cgbtrs(3) is an alias of cgbtrs.f(3).

Tue Nov 28 2023 12:08:41 Version 3.12.0 LAPACK