# 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

Univ. of Colorado Denver

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