---
name: "sgbtrs.f"
section: "3"
platform: "linux"
package: "lapack-doc"
version: "3.12.1-2"
release: "Arch Linux 2026-11-01"
platforms: ["linux"]
url: "https://new.carta.tech/sgbtrs.f"
---

# sgbtrs.f(3)

## NAME

SRC/sgbtrs.f

## SYNOPSIS

### Functions/Subroutines

subroutine **sgbtrs** (trans, n, kl, ku, nrhs, ab, ldab, ipiv, b, ldb, info)\
 **SGBTRS**

## Function/Subroutine Documentation

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

**SGBTRS**

**Purpose:**

```
!>
!> SGBTRS 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 SGBTRF.
!>
```

**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**T* X = B  (Conjugate transpose = 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 REAL array, dimension (LDAB,N)
!>          Details of the LU factorization of the band matrix A, as
!>          computed by SGBTRF.  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 REAL 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 **sgbtrs.f**.

## Author

Generated automatically by Doxygen for LAPACK from the source code.