NAME
ZTRSV - solve one of the systems of equations A*x = b, or A’*x = b,
or conjg( A’ )*x = b,
SYNOPSIS
SUBROUTINE ZTRSV ( UPLO, TRANS, DIAG, N, A, LDA, X, INCX )
INTEGER INCX, LDA, N
CHARACTER*1 DIAG, TRANS, UPLO
COMPLEX*16 A( LDA, * ), X( * )
PURPOSE
ZTRSV solves one of the systems of equations
where b and x are n element vectors and A is an n by n unit, or non-
unit, upper or lower triangular matrix.
No test for singularity or near-singularity is included in this
routine. Such tests must be performed before calling this routine.
PARAMETERS
UPLO - CHARACTER*1.
On entry, UPLO specifies whether the matrix is an upper or lower
triangular matrix as follows:
UPLO = ’U’ or ’u’ A is an upper triangular matrix.
UPLO = ’L’ or ’l’ A is a lower triangular matrix.
Unchanged on exit.
TRANS - CHARACTER*1.
On entry, TRANS specifies the equations to be solved as follows:
TRANS = ’N’ or ’n’ A*x = b.
TRANS = ’T’ or ’t’ A’*x = b.
TRANS = ’C’ or ’c’ conjg( A’ )*x = b.
Unchanged on exit.
DIAG - CHARACTER*1.
On entry, DIAG specifies whether or not A is unit triangular as
follows:
DIAG = ’U’ or ’u’ A is assumed to be unit triangular.
DIAG = ’N’ or ’n’ A is not assumed to be unit triangular.
Unchanged on exit.
N - INTEGER.
On entry, N specifies the order of the matrix A. N must be at
least zero. Unchanged on exit.
A - COMPLEX*16 array of DIMENSION ( LDA, n ).
Before entry with UPLO = ’U’ or ’u’, the leading n by n upper
triangular part of the array A must contain the upper triangular
matrix and the strictly lower triangular part of A is not
referenced. Before entry with UPLO = ’L’ or ’l’, the leading n
by n lower triangular part of the array A must contain the lower
triangular matrix and the strictly upper triangular part of A is
not referenced. Note that when DIAG = ’U’ or ’u’, the diagonal
elements of A are not referenced either, but are assumed to be
unity. Unchanged on exit.
LDA - INTEGER.
On entry, LDA specifies the first dimension of A as declared in
the calling (sub) program. LDA must be at least max( 1, n ).
Unchanged on exit.
X - COMPLEX*16 array of dimension at least
( 1 + ( n - 1 )*abs( INCX ) ). Before entry, the incremented
array X must contain the n element right-hand side vector b. On
exit, X is overwritten with the solution vector x.
INCX - INTEGER.
On entry, INCX specifies the increment for the elements of X.
INCX must not be zero. Unchanged on exit.
Level 2 Blas routine.
-- Written on 22-October-1986. Jack Dongarra, Argonne National
Lab. Jeremy Du Croz, Nag Central Office. Sven Hammarling, Nag
Central Office. Richard Hanson, Sandia National Labs.