Provided by: liblapack-doc_3.3.1-1_all #### NAME

```       LAPACK-3 - solves a triangular system of the form   A * X = B or A**T * X = B,

```

#### SYNOPSIS

```       SUBROUTINE DTBTRS( UPLO, TRANS, DIAG, N, KD, NRHS, AB, LDAB, B, LDB, INFO )

CHARACTER      DIAG, TRANS, UPLO

INTEGER        INFO, KD, LDAB, LDB, N, NRHS

DOUBLE         PRECISION AB( LDAB, * ), B( LDB, * )

```

#### PURPOSE

```       DTBTRS solves a triangular system of the form
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.

```

#### ARGUMENTS

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

TRANS   (input) 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    (input) CHARACTER*1
= 'N':  A is non-unit triangular;
= 'U':  A is unit triangular.

N       (input) INTEGER
The order of the matrix A.  N >= 0.

KD      (input) INTEGER
The number of superdiagonals or subdiagonals of the
triangular band matrix A.  KD >= 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)
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    (input) INTEGER
The leading dimension of the array AB.  LDAB >= KD+1.

B       (input/output) DOUBLE PRECISION array, dimension (LDB,NRHS)
On entry, the right hand side matrix B.
On exit, if INFO = 0, 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
> 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.

LAPACK routine (version 3.2)               April 2011                            DTBTRS(3lapack)
```