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 trian
gular.
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 con
tain 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 con
tain 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 ele
ments 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.
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