NAME

ctbtrs - solve a triangular system of the form   A ∗ X = B, A∗∗T ∗ X = B, or A∗∗H ∗ X = B,

SYNOPSIS

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

CHARACTER DIAG, TRANS, UPLO

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

COMPLEX AB( LDAB, ∗ ), B( LDB, ∗ )

#include <sunperf.h>

void ctbtrs(char uplo, char trans, char diag, int n, int kd, int nrhs, complex ∗cab, int ldab, complex ∗cb, int ldb, int ∗info) ;

PURPOSE

CTBTRS 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 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 (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) 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 (input) INTEGER
The leading dimension of the array AB.  LDAB >= KD+1.

B (input/output) COMPLEX 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.

SunOS 5.0  —  Last change: 10 Dec 1998