NAME¶

ZTRTRS - solves a triangular system of the form A * X = B, A**T * X = B, or A**H * X = B,

SYNOPSIS¶

SUBROUTINE ZTRTRS(

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

CHARACTER DIAG, TRANS, UPLO INTEGER INFO, LDA, LDB, N, NRHS COMPLEX*16 A( LDA, * ), B( LDB, * )

PURPOSE¶

ZTRTRS 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*16 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*16 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.