1CTPMV(1)                         BLAS routine                         CTPMV(1)
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NAME

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

10       SUBROUTINE CTPMV(UPLO,TRANS,DIAG,N,AP,X,INCX)
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12           INTEGER                                   INCX,N
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14           CHARACTER                                 DIAG,TRANS,UPLO
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16           COMPLEX                                   AP(*),X(*)
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PURPOSE

19       CTPMV  performs one of the matrix-vector operations
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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.
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ARGUMENTS

26       UPLO   - CHARACTER*1.
27              On entry, UPLO specifies whether the matrix is an upper or lower
28              triangular matrix as follows:
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30              UPLO = 'U' or 'u'   A is an upper triangular matrix.
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32              UPLO = 'L' or 'l'   A is a lower triangular matrix.
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34              Unchanged on exit.
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36       TRANS  - CHARACTER*1.
37              On entry, TRANS specifies the operation to be performed as  fol‐
38              lows:
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40              TRANS = 'N' or 'n'   x := A*x.
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42              TRANS = 'T' or 't'   x := A'*x.
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44              TRANS = 'C' or 'c'   x := conjg( A' )*x.
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46              Unchanged on exit.
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48       DIAG   - CHARACTER*1.
49              On  entry, DIAG specifies whether or not A is unit triangular as
50              follows:
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52              DIAG = 'U' or 'u'   A is assumed to be unit triangular.
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54              DIAG = 'N' or 'n'   A is not assumed to be unit triangular.
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56              Unchanged on exit.
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58       N      - INTEGER.
59              On entry, N specifies the order of the matrix A.  N must  be  at
60              least zero.  Unchanged on exit.
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62       AP     - COMPLEX          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.
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75       X      - COMPLEX          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.
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80       INCX   - INTEGER.
81              On  entry,  INCX  specifies the increment for the elements of X.
82              INCX must not be zero.  Unchanged on exit.
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FURTHER DETAILS

85       Level 2 Blas routine.
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87       -- Written on 22-October-1986.
88          Jack Dongarra, Argonne National Lab.
89          Jeremy Du Croz, Nag Central Office.
90          Sven Hammarling, Nag Central Office.
91          Richard Hanson, Sandia National Labs.
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96BLAS routine                     November 2008                        CTPMV(1)