1ZTRMV(1)                         BLAS routine                         ZTRMV(1)
2
3
4

NAME

6       ZTRMV  -  one of the matrix-vector operations   x := A*x, or x := A'*x,
7       or x := conjg( A' )*x,
8

SYNOPSIS

10       SUBROUTINE ZTRMV(UPLO,TRANS,DIAG,N,A,LDA,X,INCX)
11
12           INTEGER                                      INCX,LDA,N
13
14           CHARACTER                                    DIAG,TRANS,UPLO
15
16           DOUBLE                                       COMPLEX A(LDA,*),X(*)
17

PURPOSE

19       ZTRMV  performs one of the matrix-vector operations
20
21       where x is an n element vector and  A is an n by n unit,  or  non-unit,
22       upper or lower triangular matrix.
23
24

ARGUMENTS

26       UPLO   - CHARACTER*1.
27              On entry, UPLO specifies whether the matrix is an upper or lower
28              triangular matrix as follows:
29
30              UPLO = 'U' or 'u'   A is an upper triangular matrix.
31
32              UPLO = 'L' or 'l'   A is a lower triangular matrix.
33
34              Unchanged on exit.
35
36       TRANS  - CHARACTER*1.
37              On entry, TRANS specifies the operation to be performed as  fol‐
38              lows:
39
40              TRANS = 'N' or 'n'   x := A*x.
41
42              TRANS = 'T' or 't'   x := A'*x.
43
44              TRANS = 'C' or 'c'   x := conjg( A' )*x.
45
46              Unchanged on exit.
47
48       DIAG   - CHARACTER*1.
49              On  entry, DIAG specifies whether or not A is unit triangular as
50              follows:
51
52              DIAG = 'U' or 'u'   A is assumed to be unit triangular.
53
54              DIAG = 'N' or 'n'   A is not assumed to be unit triangular.
55
56              Unchanged on exit.
57
58       N      - INTEGER.
59              On entry, N specifies the order of the matrix A.  N must  be  at
60              least zero.  Unchanged on exit.
61
62       A      - COMPLEX*16       array of DIMENSION ( LDA, n ).
63              Before  entry  with  UPLO = 'U' or 'u', the leading n by n upper
64              triangular part of the array A must contain the upper triangular
65              matrix and the strictly lower triangular part of A is not refer‐
66              enced.  Before entry with UPLO = 'L' or 'l', the leading n by  n
67              lower triangular part of the array A must contain the lower tri‐
68              angular matrix and the strictly upper triangular part  of  A  is
69              not referenced.  Note that when  DIAG = 'U' or 'u', the diagonal
70              elements of A are not referenced either, but are assumed  to  be
71              unity.  Unchanged on exit.
72
73       LDA    - INTEGER.
74              On  entry, LDA specifies the first dimension of A as declared in
75              the calling (sub) program. LDA must be at least  max(  1,  n  ).
76              Unchanged on exit.
77
78       X      - COMPLEX*16       array of dimension at least
79              (  1  +  ( n - 1 )*abs( INCX ) ).  Before entry, the incremented
80              array X must contain the n element vector x. On exit, X is over‐
81              written with the tranformed vector x.
82
83       INCX   - INTEGER.
84              On  entry,  INCX  specifies the increment for the elements of X.
85              INCX must not be zero.  Unchanged on exit.
86
87              Level 2 Blas routine.
88
89              -- Written on 22-October-1986.  Jack Dongarra, Argonne  National
90              Lab.   Jeremy Du Croz, Nag Central Office.  Sven Hammarling, Nag
91              Central Office.  Richard Hanson, Sandia National Labs.
92
93
94
95BLAS routine                     November 2006                        ZTRMV(1)