1STPMV(1)                         BLAS routine                         STPMV(1)
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NAME

6       STPMV - one of the matrix-vector operations   x := A*x, or x := A'*x,
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SYNOPSIS

9       SUBROUTINE STPMV(UPLO,TRANS,DIAG,N,AP,X,INCX)
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11           INTEGER                                   INCX,N
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13           CHARACTER                                 DIAG,TRANS,UPLO
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15           REAL                                      AP(*),X(*)
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PURPOSE

18       STPMV  performs one of the matrix-vector operations
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20       where  x  is an n element vector and  A is an n by n unit, or non-unit,
21       upper or lower triangular matrix, supplied in packed form.
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ARGUMENTS

25       UPLO   - CHARACTER*1.
26              On entry, UPLO specifies whether the matrix is an upper or lower
27              triangular matrix as follows:
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29              UPLO = 'U' or 'u'   A is an upper triangular matrix.
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31              UPLO = 'L' or 'l'   A is a lower triangular matrix.
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33              Unchanged on exit.
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35       TRANS  - CHARACTER*1.
36              On  entry, TRANS specifies the operation to be performed as fol‐
37              lows:
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39              TRANS = 'N' or 'n'   x := A*x.
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41              TRANS = 'T' or 't'   x := A'*x.
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43              TRANS = 'C' or 'c'   x := A'*x.
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45              Unchanged on exit.
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47       DIAG   - CHARACTER*1.
48              On entry, DIAG specifies whether or not A is unit triangular  as
49              follows:
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51              DIAG = 'U' or 'u'   A is assumed to be unit triangular.
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53              DIAG = 'N' or 'n'   A is not assumed to be unit triangular.
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55              Unchanged on exit.
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57       N      - INTEGER.
58              On  entry,  N specifies the order of the matrix A.  N must be at
59              least zero.  Unchanged on exit.
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61       AP     - REAL             array of DIMENSION at least
62              ( ( n*( n + 1 ) )/2 ).  Before entry with  UPLO =  'U'  or  'u',
63              the  array  AP  must  contain the upper triangular matrix packed
64              sequentially, column by column, so that AP( 1 ) contains a( 1, 1
65              ),  AP(  2 ) and AP( 3 ) contain a( 1, 2 ) and a( 2, 2 ) respec‐
66              tively, and so on.  Before entry with UPLO =  'L'  or  'l',  the
67              array AP must contain the lower triangular matrix packed sequen‐
68              tially, column by column, so that AP( 1 ) contains a(  1,  1  ),
69              AP(  2  )  and  AP(  3 ) contain a( 2, 1 ) and a( 3, 1 ) respec‐
70              tively, and so on.  Note that when  DIAG = 'U' or 'u', the diag‐
71              onal  elements  of  A  are not referenced, but are assumed to be
72              unity.  Unchanged on exit.
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74       X      - REAL             array of dimension at least
75              ( 1 + ( n - 1 )*abs( INCX ) ).  Before  entry,  the  incremented
76              array X must contain the n element vector x. On exit, X is over‐
77              written with the tranformed vector x.
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79       INCX   - INTEGER.
80              On entry, INCX specifies the increment for the  elements  of  X.
81              INCX must not be zero.  Unchanged on exit.
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83              Level 2 Blas routine.
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85              --  Written on 22-October-1986.  Jack Dongarra, Argonne National
86              Lab.  Jeremy Du Croz, Nag Central Office.  Sven Hammarling,  Nag
87              Central Office.  Richard Hanson, Sandia National Labs.
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91BLAS routine                     November 2006                        STPMV(1)