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

NAME

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

SYNOPSIS

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

PURPOSE

19       ZTPMV  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, supplied in packed form.
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       AP     - COMPLEX*16       array of DIMENSION at least
63              (  (  n*(  n + 1 ) )/2 ).  Before entry with  UPLO = 'U' or 'u',
64              the array AP must contain the  upper  triangular  matrix  packed
65              sequentially, column by column, so that AP( 1 ) contains a( 1, 1
66              ), AP( 2 ) and AP( 3 ) contain a( 1, 2 ) and a( 2, 2  )  respec‐
67              tively,  and  so  on.   Before entry with UPLO = 'L' or 'l', the
68              array AP must contain the lower triangular matrix packed sequen‐
69              tially,  column  by  column, so that AP( 1 ) contains a( 1, 1 ),
70              AP( 2 ) and AP( 3 ) contain a( 2, 1 ) and  a(  3,  1  )  respec‐
71              tively, and so on.  Note that when  DIAG = 'U' or 'u', the diag‐
72              onal elements of A are not referenced, but  are  assumed  to  be
73              unity.  Unchanged on exit.
74
75       X      - COMPLEX*16       array of dimension at least
76              (  1  +  ( n - 1 )*abs( INCX ) ).  Before entry, the incremented
77              array X must contain the n element vector x. On exit, X is over‐
78              written with the tranformed vector x.
79
80       INCX   - INTEGER.
81              On  entry,  INCX  specifies the increment for the elements of X.
82              INCX must not be zero.  Unchanged on exit.
83
84              Level 2 Blas routine.
85
86              -- Written on 22-October-1986.  Jack Dongarra, Argonne  National
87              Lab.   Jeremy Du Croz, Nag Central Office.  Sven Hammarling, Nag
88              Central Office.  Richard Hanson, Sandia National Labs.
89
90
91
92BLAS routine                     November 2006                        ZTPMV(1)