# dtbtrs.f - Man Page

SRC/dtbtrs.f

## Synopsis

### Functions/Subroutines

subroutine dtbtrs (uplo, trans, diag, n, kd, nrhs, ab, ldab, b, ldb, info)
DTBTRS

## Function/Subroutine Documentation

### subroutine dtbtrs (character uplo, character trans, character diag, integer n, integer kd, integer nrhs, double precision, dimension( ldab, * ) ab, integer ldab, double precision, dimension( ldb, * ) b, integer ldb, integer info)

DTBTRS

Purpose:

``` DTBTRS solves a triangular system of the form

A * X = B  or  A**T * X = B,

where A is a triangular band matrix of order N, and B is an
N-by NRHS matrix.  A check is made to verify that A is nonsingular.```
Parameters

UPLO

```          UPLO is CHARACTER*1
= 'U':  A is upper triangular;
= 'L':  A is lower triangular.```

TRANS

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

DIAG

```          DIAG is CHARACTER*1
= 'N':  A is non-unit triangular;
= 'U':  A is unit triangular.```

N

```          N is INTEGER
The order of the matrix A.  N >= 0.```

KD

```          KD is INTEGER
The number of superdiagonals or subdiagonals of the
triangular band matrix A.  KD >= 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 DOUBLE PRECISION array, dimension (LDAB,N)
The upper or lower triangular band matrix A, stored in the
first kd+1 rows of AB.  The j-th column of A is stored
in the j-th column of the array AB as follows:
if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+kd).
If DIAG = 'U', the diagonal elements of A are not referenced
and are assumed to be 1.```

LDAB

```          LDAB is INTEGER
The leading dimension of the array AB.  LDAB >= KD+1.```

B

```          B is DOUBLE PRECISION array, dimension (LDB,NRHS)
On entry, the right hand side matrix B.
On exit, if INFO = 0, 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
> 0:  if INFO = i, the i-th diagonal element of A is zero,
indicating that the matrix is singular and the
solutions X have not been computed.```
Author

Univ. of Tennessee

Univ. of California Berkeley

NAG Ltd.

Definition at line 144 of file dtbtrs.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

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

Tue Nov 28 2023 12:08:42 Version 3.12.0 LAPACK