# ctbtrs.f

Section: LAPACK (3)
Updated: Tue Nov 14 2017
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ctbtrs.f

## SYNOPSIS

### Functions/Subroutines

subroutine ctbtrs (UPLO, TRANS, DIAG, N, KD, NRHS, AB, LDAB, B, LDB, INFO)
CTBTRS

## Function/Subroutine Documentation

### subroutine ctbtrs (character UPLO, character TRANS, character DIAG, integer N, integer KD, integer NRHS, complex, dimension( ldab, * ) AB, integer LDAB, complex, dimension( ldb, * ) B, integer LDB, integer INFO)

CTBTRS

Purpose:

``` CTBTRS solves a triangular system of the form

A * X = B,  A**T * X = B,  or  A**H * 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 of the system of equations:
= 'N':  A * X = B     (No transpose)
= 'T':  A**T * X = B  (Transpose)
= 'C':  A**H * X = B  (Conjugate 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 COMPLEX 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 COMPLEX 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