1DTPMV(1) BLAS routine DTPMV(1)
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6 DTPMV - one of the matrix-vector operations x := A*x, or x := A'*x,
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9 SUBROUTINE DTPMV(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 DOUBLE PRECISION AP(*),X(*)
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18 DTPMV 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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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
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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 - DOUBLE PRECISION 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 - DOUBLE PRECISION 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 DTPMV(1)