1CTRMV(1)                         BLAS routine                         CTRMV(1)
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NAME

6       CTRMV  -  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 CTRMV(UPLO,TRANS,DIAG,N,A,LDA,X,INCX)
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12           INTEGER                                      INCX,LDA,N
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14           CHARACTER                                    DIAG,TRANS,UPLO
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16           COMPLEX                                      A(LDA,*),X(*)
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PURPOSE

19       CTRMV  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.
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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       A      - COMPLEX          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.
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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.
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78       X      - COMPLEX          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.
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83       INCX   - INTEGER.
84              On  entry,  INCX  specifies the increment for the elements of X.
85              INCX must not be zero.  Unchanged on exit.
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FURTHER DETAILS

88       Level 2 Blas routine.
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90       -- Written on 22-October-1986.
91          Jack Dongarra, Argonne National Lab.
92          Jeremy Du Croz, Nag Central Office.
93          Sven Hammarling, Nag Central Office.
94          Richard Hanson, Sandia National Labs.
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99BLAS routine                     November 2008                        CTRMV(1)