NAME

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

SYNOPSIS

SUBROUTINE CTRTRS(
UPLO, TRANS, DIAG, N, NRHS, A, LDA, B, LDB, INFO )

CHARACTER DIAG, TRANS, UPLO

INTEGER INFO, LDA, LDB, N, NRHS

COMPLEX A( LDA, ∗ ), B( LDB, ∗ )

PURPOSE

CTRTRS solves a triangular system of the form
 
where A is a triangular 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.

NRHS    (input) INTEGER
The number of right hand sides, i.e., the number of columns of the matrix B.  NRHS >= 0.

A       (input) COMPLEX array, dimension (LDA,N)
The triangular matrix A.  If UPLO = ’U’, the leading N-by-N upper triangular part of the array A contains the upper triangular matrix, and the strictly lower triangular part of A is not referenced.  If UPLO = ’L’, the leading N-by-N lower triangular part of the array A contains the lower triangular matrix, and the strictly upper triangular part of A is not referenced.  If DIAG = ’U’, the diagonal elements of A are also not referenced and are assumed to be 1.

LDA     (input) INTEGER
The leading dimension of the array A.  LDA >= max(1,N).

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.

  —  LAPACK version 2.0  —  08 October 1994