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Text File  |  1998-10-30  |  15.8 KB  |  265 lines
  1.  
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  4. ____SSSSYYYYMMMMVVVV,,,,____HHHHEEEEMMMMVVVV((((3333FFFF))))                                                ____SSSSYYYYMMMMVVVV,,,,____HHHHEEEEMMMMVVVV((((3333FFFF))))
  5.  
  6.  
  7.  
  8. NNNNAAAAMMMMEEEE
  9.      dsymv, ssymv, zhemv, chemv - BLAS Level Two   (Symmetric/Hermitian)Matrix
  10.      - Vector Product
  11.  
  12.  
  13. FFFFOOOORRRRTTTTRRRRAAAANNNN 77777777 SSSSYYYYNNNNOOOOPPPPSSSSIIIISSSS
  14.      ssssuuuubbbbrrrroooouuuuttttiiiinnnneeee ddddssssyyyymmmmvvvv(((( uuuupppplllloooo,,,,nnnn,,,,aaaallllpppphhhhaaaa,,,,aaaa,,,,llllddddaaaa,,,,xxxx,,,,iiiinnnnccccxxxx,,,,bbbbeeeettttaaaa,,,,yyyy,,,,iiiinnnnccccyyyy ))))
  15.            cccchhhhaaaarrrraaaacccctttteeeerrrr****1111        uuuupppplllloooo
  16.            iiiinnnntttteeeeggggeeeerrrr            nnnn,,,, llllddddaaaa,,,, iiiinnnnccccxxxx,,,, iiiinnnnccccyyyy
  17.            ddddoooouuuubbbblllleeee pppprrrreeeecccciiiissssiiiioooonnnn   aaaallllpppphhhhaaaa,,,, bbbbeeeettttaaaa
  18.            ddddoooouuuubbbblllleeee pppprrrreeeecccciiiissssiiiioooonnnn   aaaa(((( llllddddaaaa,,,,****)))),,,, xxxx((((****)))),,,, yyyy((((****))))
  19.  
  20.      ssssuuuubbbbrrrroooouuuuttttiiiinnnneeee ssssssssyyyymmmmvvvv(((( uuuupppplllloooo,,,,nnnn,,,,aaaallllpppphhhhaaaa,,,,aaaa,,,,llllddddaaaa,,,,xxxx,,,,iiiinnnnccccxxxx,,,,bbbbeeeettttaaaa,,,,yyyy,,,,iiiinnnnccccyyyy ))))
  21.            cccchhhhaaaarrrraaaacccctttteeeerrrr****1111        uuuupppplllloooo
  22.            iiiinnnntttteeeeggggeeeerrrr            nnnn,,,, llllddddaaaa,,,, iiiinnnnccccxxxx,,,, iiiinnnnccccyyyy
  23.            rrrreeeeaaaallll               aaaallllpppphhhhaaaa,,,, bbbbeeeettttaaaa
  24.            rrrreeeeaaaallll               aaaa(((( llllddddaaaa,,,,****)))),,,, xxxx((((****)))),,,, yyyy((((****))))
  25.  
  26.      ssssuuuubbbbrrrroooouuuuttttiiiinnnneeee zzzzhhhheeeemmmmvvvv(((( uuuupppplllloooo,,,,nnnn,,,,aaaallllpppphhhhaaaa,,,,aaaa,,,,llllddddaaaa,,,,xxxx,,,,iiiinnnnccccxxxx,,,,bbbbeeeettttaaaa,,,,yyyy,,,,iiiinnnnccccyyyy ))))
  27.            cccchhhhaaaarrrraaaacccctttteeeerrrr****1111        uuuupppplllloooo
  28.            iiiinnnntttteeeeggggeeeerrrr            nnnn,,,, llllddddaaaa,,,, iiiinnnnccccxxxx,,,, iiiinnnnccccyyyy
  29.            ddddoooouuuubbbblllleeee ccccoooommmmpppplllleeeexxxx     aaaallllpppphhhhaaaa,,,, bbbbeeeettttaaaa
  30.            ddddoooouuuubbbblllleeee ccccoooommmmpppplllleeeexxxx     aaaa(((( llllddddaaaa,,,,****)))),,,, xxxx((((****)))),,,, yyyy((((****))))
  31.  
  32.      ssssuuuubbbbrrrroooouuuuttttiiiinnnneeee cccchhhheeeemmmmvvvv(((( uuuupppplllloooo,,,,nnnn,,,,aaaallllpppphhhhaaaa,,,,aaaa,,,,llllddddaaaa,,,,xxxx,,,,iiiinnnnccccxxxx,,,,bbbbeeeettttaaaa,,,,yyyy,,,,iiiinnnnccccyyyy ))))
  33.            cccchhhhaaaarrrraaaacccctttteeeerrrr****1111        uuuupppplllloooo
  34.            iiiinnnntttteeeeggggeeeerrrr            nnnn,,,, llllddddaaaa,,,, iiiinnnnccccxxxx,,,, iiiinnnnccccyyyy
  35.            ccccoooommmmpppplllleeeexxxx            aaaallllpppphhhhaaaa,,,, bbbbeeeettttaaaa
  36.            ccccoooommmmpppplllleeeexxxx            aaaa(((( llllddddaaaa,,,,****)))),,,, xxxx((((****)))),,,, yyyy((((****))))
  37.  
  38.  
  39. CCCC SSSSYYYYNNNNOOOOPPPPSSSSIIIISSSS
  40.      vvvvooooiiiidddd ddddssssyyyymmmmvvvv(((( uuuupppplllloooo,,,,nnnn,,,,aaaallllpppphhhhaaaa,,,,aaaa,,,,llllddddaaaa,,,,xxxx,,,,iiiinnnnccccxxxx,,,,bbbbeeeettttaaaa,,,,yyyy,,,,iiiinnnnccccyyyy ))))
  41.            MMMMaaaattttrrrriiiixxxxTTTTrrrriiiiaaaannnngggglllleeee        uuuupppplllloooo;;;;
  42.            IIIInnnntttteeeeggggeeeerrrr            nnnn,,,, llllddddaaaa,,,, iiiinnnnccccxxxx,,,, iiiinnnnccccyyyy;;;;
  43.            ddddoooouuuubbbblllleeee             aaaallllpppphhhhaaaa,,,, bbbbeeeettttaaaa;;;;
  44.            ddddoooouuuubbbblllleeee             ((((****aaaa))))[[[[llllddddaaaa****nnnn]]]],,,, ((((****xxxx))))[[[[ nnnn ]]]],,,, ((((****yyyy))))[[[[ nnnn ]]]];;;;
  45.  
  46.      vvvvooooiiiidddd ssssssssyyyymmmmvvvv(((( uuuupppplllloooo,,,,nnnn,,,,aaaallllpppphhhhaaaa,,,,aaaa,,,,llllddddaaaa,,,,xxxx,,,,iiiinnnnccccxxxx,,,,bbbbeeeettttaaaa,,,,yyyy,,,,iiiinnnnccccyyyy ))))
  47.            MMMMaaaattttrrrriiiixxxxTTTTrrrriiiiaaaannnngggglllleeee        uuuupppplllloooo;;;;
  48.            IIIInnnntttteeeeggggeeeerrrr            nnnn,,,, llllddddaaaa,,,, iiiinnnnccccxxxx,,,, iiiinnnnccccyyyy;;;;
  49.            ffffllllooooaaaatttt              aaaallllpppphhhhaaaa,,,, bbbbeeeettttaaaa;;;;
  50.            ffffllllooooaaaatttt              ((((****aaaa))))[[[[llllddddaaaa****nnnn]]]],,,, ((((****xxxx))))[[[[ nnnn ]]]],,,, ((((****yyyy))))[[[[ nnnn ]]]];;;;
  51.  
  52.      vvvvooooiiiidddd zzzzhhhheeeemmmmvvvv(((( uuuupppplllloooo,,,,nnnn,,,,aaaallllpppphhhhaaaa,,,,aaaa,,,,llllddddaaaa,,,,xxxx,,,,iiiinnnnccccxxxx,,,,bbbbeeeettttaaaa,,,,yyyy,,,,iiiinnnnccccyyyy ))))
  53.            MMMMaaaattttrrrriiiixxxxTTTTrrrriiiiaaaannnngggglllleeee        uuuupppplllloooo;;;;
  54.            IIIInnnntttteeeeggggeeeerrrr            nnnn,,,, llllddddaaaa,,,, iiiinnnnccccxxxx,,,, iiiinnnnccccyyyy;;;;
  55.            ZZZZoooommmmpppplllleeeexxxx            aaaallllpppphhhhaaaa,,,, bbbbeeeettttaaaa;;;;
  56.            ZZZZoooommmmpppplllleeeexxxx           ((((****aaaa))))[[[[llllddddaaaa****nnnn]]]],,,, ((((****xxxx))))[[[[ nnnn ]]]],,,, ((((****yyyy))))[[[[ nnnn ]]]];;;;
  57.  
  58.      vvvvooooiiiidddd cccchhhheeeemmmmvvvv(((( uuuupppplllloooo,,,,nnnn,,,,aaaallllpppphhhhaaaa,,,,aaaa,,,,llllddddaaaa,,,,xxxx,,,,iiiinnnnccccxxxx,,,,bbbbeeeettttaaaa,,,,yyyy,,,,iiiinnnnccccyyyy ))))
  59.            MMMMaaaattttrrrriiiixxxxTTTTrrrriiiiaaaannnngggglllleeee        uuuupppplllloooo;;;;
  60.  
  61.  
  62.  
  63.                                                                         PPPPaaaaggggeeee 1111
  64.  
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  66.  
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  68.  
  69.  
  70. ____SSSSYYYYMMMMVVVV,,,,____HHHHEEEEMMMMVVVV((((3333FFFF))))                                                ____SSSSYYYYMMMMVVVV,,,,____HHHHEEEEMMMMVVVV((((3333FFFF))))
  71.  
  72.  
  73.  
  74.            IIIInnnntttteeeeggggeeeerrrr            nnnn,,,, llllddddaaaa,,,, iiiinnnnccccxxxx,,,, iiiinnnnccccyyyy;;;;
  75.            CCCCoooommmmpppplllleeeexxxx            aaaallllpppphhhhaaaa,,,, bbbbeeeettttaaaa;;;;
  76.            CCCCoooommmmpppplllleeeexxxx           ((((****aaaa))))[[[[llllddddaaaa****nnnn]]]],,,, ((((****xxxx))))[[[[ nnnn ]]]],,,, ((((****yyyy))))[[[[ nnnn ]]]];;;;
  77.  
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  79.  
  80.  
  81.  
  82. DDDDEEEESSSSCCCCRRRRIIIIPPPPTTTTIIIIOOOONNNN
  83.      ddddssssyyyymmmmvvvv ,,,, ssssssssyyyymmmmvvvv ,,,, ddddhhhheeeemmmmvvvv and cccchhhheeeemmmmvvvv perform the matrix-vector operation
  84.  
  85.            y := alpha*A*x + beta*y,
  86.  
  87.      where alpha and beta are scalars, x and y are n element vectors and A is
  88.      an n by n symmetric/hermitian matrix.
  89.  
  90.  
  91. PPPPAAAARRRRAAAAMMMMEEEETTTTEEEERRRRSSSS
  92.      uuuupppplllloooo    On entry, uuuupppplllloooo specifies whether the upper or lower triangular
  93.              part of the matrix A is being supplied as follows:
  94.  
  95.  
  96.  
  97.              FFFFOOOORRRRTTTTRRRRAAAANNNN
  98.              uplo = 'U' or 'u'   The upper triangular part of A is
  99.                                  being supplied.
  100.              uplo = 'L' or 'l'   The lower triangular part of A is
  101.                                  being supplied.
  102.  
  103.              CCCC
  104.              uplo = UpperTriangle     The upper triangular part of A is
  105.                                       being supplied.
  106.              uplo = LowerTriangle     The lower triangular part of A is
  107.                                       being supplied
  108.  
  109.              Unchanged on exit.
  110.  
  111.      nnnn       On entry, nnnn specifies the the order of the matrix A.  nnnn must be
  112.              at least zero.
  113.              Unchanged on exit.
  114.  
  115.      aaaallllpppphhhhaaaa   specifies the scalar alpha.
  116.              Unchanged on exit.
  117.  
  118.      aaaa       An array containing the matrix A.
  119.  
  120.              FFFFOOOORRRRTTTTRRRRAAAANNNN
  121.              Array of dimension ( lda, n ).
  122.  
  123.              CCCC
  124.              A pointer to an array of size lda*n.
  125.              See note below about array storage convention for C.
  126.  
  127.  
  128.  
  129.                                                                         PPPPaaaaggggeeee 2222
  130.  
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  133.  
  134.  
  135.  
  136. ____SSSSYYYYMMMMVVVV,,,,____HHHHEEEEMMMMVVVV((((3333FFFF))))                                                ____SSSSYYYYMMMMVVVV,,,,____HHHHEEEEMMMMVVVV((((3333FFFF))))
  137.  
  138.  
  139.  
  140.              Before entry with uuuupppplllloooo ==== ''''UUUU'''' oooorrrr ''''uuuu'''' oooorrrr , the array elements
  141.              corresponding to the leading n by n upper triangular part of the
  142.              matrix A must contain the corresponding upper triangular part of
  143.              the symmetric/hermitian matrix and the strictly lower triangular
  144.              part of A is not referenced.
  145.  
  146.              Before entry with uuuupppplllloooo ==== ''''LLLL'''' oooorrrr ''''llll'''' oooorrrr , the array elements
  147.              corresponding to the leading n by n lower triangular part of the
  148.              array A must contain the corresponding lower triangular part of
  149.              the symmetric/hermitian matrix and the strictly upper triangular
  150.              part of A is not referenced.
  151.  
  152.              Note that the imaginary parts of the diagonal elements need not
  153.              be set and are assumed to be zero.
  154.  
  155.              Unchanged on exit.
  156.  
  157.      llllddddaaaa     On entry, llllddddaaaa specifies the first dimension of A as declared in
  158.              the calling (sub) program. llllddddaaaa must be at least ( k + 1 ).
  159.              Unchanged on exit.
  160.  
  161.      xxxx       Array of size at least ( 1 + ( n - 1 )*abs( incx ) ). Before
  162.              entry, the incremented array xxxx must contain the vector x.
  163.              Unchanged on exit.
  164.  
  165.      iiiinnnnccccxxxx    On entry, iiiinnnnccccxxxx specifies the increment for the elements of xxxx.
  166.              iiiinnnnccccxxxx must not be zero.
  167.              Unchanged on exit.
  168.  
  169.      bbbbeeeettttaaaa    On entry, bbbbeeeettttaaaa specifies the scalar beta. When bbbbeeeettttaaaa is supplied
  170.              as zero then yyyy need not be set on input.
  171.              Unchanged on exit.
  172.  
  173.      yyyy       Array of size at least ( 1 + ( n - 1 )*abs( incy ) ). Before
  174.              entry, the incremented array yyyy must contain the n element vector
  175.              y. On exit, Y is overwritten by the updated vector y.
  176.  
  177.      iiiinnnnccccyyyy    On entry, iiiinnnnccccyyyy specifies the increment for the elements of yyyy.
  178.              iiiinnnnccccyyyy must not be zero.
  179.              Unchanged on exit.
  180.  
  181.  
  182. CCCC AAAARRRRRRRRAAAAYYYY SSSSTTTTOOOORRRRAAAAGGGGEEEE CCCCOOOONNNNVVVVEEEENNNNTTTTIIIIOOOONNNN
  183.        The matrices  are assumed  to be stored in a  oooonnnneeee ddddiiiimmmmeeeennnnssssiiiioooonnnnaaaallll CCCC aaaarrrrrrrraaaayyyy
  184.        in an analogous fashion as a Fortran array (column major). Therefore,
  185.        the element  A(i+1,j)  of matrix A  is stored  immediately  after the
  186.        element  A(i,j), while  A(i,j+1) is lda  elements apart from  A(i,j).
  187.        The element A(i,j) of the matrix can be accessed directly by reference
  188.        to  a[ (j-1)*lda + (i-1) ].
  189.  
  190.  
  191.  
  192.  
  193.  
  194.  
  195.                                                                         PPPPaaaaggggeeee 3333
  196.  
  197.  
  198.  
  199.  
  200.  
  201.  
  202. ____SSSSYYYYMMMMVVVV,,,,____HHHHEEEEMMMMVVVV((((3333FFFF))))                                                ____SSSSYYYYMMMMVVVV,,,,____HHHHEEEEMMMMVVVV((((3333FFFF))))
  203.  
  204.  
  205.  
  206. AAAAUUUUTTTTHHHHOOOORRRRSSSS
  207.           Jack Dongarra, Argonne National Laboratory.
  208.           Iain Duff, AERE Harwell.
  209.           Jeremy Du Croz, Numerical Algorithms Group Ltd.
  210.           Sven Hammarling, Numerical Algorithms Group Ltd.
  211.  
  212.  
  213. TTTTUUUUNNNNIIIINNNNGGGG
  214.           DSYMV and SSYMV are optimized and parallelized for SGI R3000 and
  215.           R4x00 platforms. For the R8000 it is optimized an parallelized
  216.           for the case when INCX = 1.
  217.           ZHEMV and CHEMV are optimized and parallelized for SGI R3000, R4x00
  218.           and R8000 platforms.
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  260.  
  261.                                                                         PPPPaaaaggggeeee 4444
  262.  
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  265.