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Text File  |  1998-10-30  |  13.9 KB  |  199 lines
  1.  
  2.  
  3.  
  4. ____SSSSPPPPMMMMVVVV,,,,____HHHHPPPPMMMMVVVV((((3333FFFF))))                                                ____SSSSPPPPMMMMVVVV,,,,____HHHHPPPPMMMMVVVV((((3333FFFF))))
  5.  
  6.  
  7.  
  8. NNNNAAAAMMMMEEEE
  9.      dspmv, sspmv, zhpmv, chpmv - BLAS Level Two   (Symmetric/Hermitian)
  10.      Packed Matrix - Vector Product
  11.  
  12.  
  13. FFFFOOOORRRRTTTTRRRRAAAANNNN 77777777 SSSSYYYYNNNNOOOOPPPPSSSSIIIISSSS
  14.      ssssuuuubbbbrrrroooouuuuttttiiiinnnneeee ddddssssppppmmmmvvvv(((( uuuupppplllloooo,,,,nnnn,,,,aaaallllpppphhhhaaaa,,,,aaaapppp,,,,xxxx,,,,iiiinnnnccccxxxx,,,,bbbbeeeettttaaaa,,,,yyyy,,,,iiiinnnnccccyyyy ))))
  15.            cccchhhhaaaarrrraaaacccctttteeeerrrr****1111        uuuupppplllloooo
  16.            iiiinnnntttteeeeggggeeeerrrr            nnnn,,,, iiiinnnnccccxxxx,,,, iiiinnnnccccyyyy
  17.            ddddoooouuuubbbblllleeee pppprrrreeeecccciiiissssiiiioooonnnn   aaaallllpppphhhhaaaa,,,, bbbbeeeettttaaaa
  18.            ddddoooouuuubbbblllleeee pppprrrreeeecccciiiissssiiiioooonnnn   aaaapppp((((****)))),,,, xxxx((((****)))),,,, yyyy((((****))))
  19.  
  20.      ssssuuuubbbbrrrroooouuuuttttiiiinnnneeee ssssssssppppmmmmvvvv(((( uuuupppplllloooo,,,,nnnn,,,,aaaallllpppphhhhaaaa,,,,aaaapppp,,,,xxxx,,,,iiiinnnnccccxxxx,,,,bbbbeeeettttaaaa,,,,yyyy,,,,iiiinnnnccccyyyy ))))
  21.            cccchhhhaaaarrrraaaacccctttteeeerrrr****1111        uuuupppplllloooo
  22.            iiiinnnntttteeeeggggeeeerrrr            nnnn,,,, iiiinnnnccccxxxx,,,, iiiinnnnccccyyyy
  23.            rrrreeeeaaaallll               aaaallllpppphhhhaaaa,,,, bbbbeeeettttaaaa
  24.            rrrreeeeaaaallll               aaaapppp((((****)))),,,, xxxx((((****)))),,,, yyyy((((****))))
  25.  
  26.      ssssuuuubbbbrrrroooouuuuttttiiiinnnneeee zzzzhhhhppppmmmmvvvv(((( uuuupppplllloooo,,,,nnnn,,,,aaaallllpppphhhhaaaa,,,,aaaapppp,,,,xxxx,,,,iiiinnnnccccxxxx,,,,bbbbeeeettttaaaa,,,,yyyy,,,,iiiinnnnccccyyyy ))))
  27.            cccchhhhaaaarrrraaaacccctttteeeerrrr****1111        uuuupppplllloooo
  28.            iiiinnnntttteeeeggggeeeerrrr            nnnn,,,, iiiinnnnccccxxxx,,,, iiiinnnnccccyyyy
  29.            ddddoooouuuubbbblllleeee ccccoooommmmpppplllleeeexxxx     aaaallllpppphhhhaaaa,,,, bbbbeeeettttaaaa
  30.            ddddoooouuuubbbblllleeee ccccoooommmmpppplllleeeexxxx     aaaapppp((((****)))),,,, xxxx((((****)))),,,, yyyy((((****))))
  31.  
  32.      ssssuuuubbbbrrrroooouuuuttttiiiinnnneeee cccchhhhppppmmmmvvvv(((( uuuupppplllloooo,,,,nnnn,,,,aaaallllpppphhhhaaaa,,,,aaaapppp,,,,xxxx,,,,iiiinnnnccccxxxx,,,,bbbbeeeettttaaaa,,,,yyyy,,,,iiiinnnnccccyyyy ))))
  33.            cccchhhhaaaarrrraaaacccctttteeeerrrr****1111        uuuupppplllloooo
  34.            iiiinnnntttteeeeggggeeeerrrr            nnnn,,,, iiiinnnnccccxxxx,,,, iiiinnnnccccyyyy
  35.            ccccoooommmmpppplllleeeexxxx            aaaallllpppphhhhaaaa,,,, bbbbeeeettttaaaa
  36.            ccccoooommmmpppplllleeeexxxx            aaaapppp((((****)))),,,, xxxx((((****)))),,,, yyyy((((****))))
  37.  
  38.  
  39. CCCC SSSSYYYYNNNNOOOOPPPPSSSSIIIISSSS
  40.      vvvvooooiiiidddd ddddssssppppmmmmvvvv(((( uuuupppplllloooo,,,,nnnn,,,,aaaallllpppphhhhaaaa,,,,aaaapppp,,,,xxxx,,,,iiiinnnnccccxxxx,,,,bbbbeeeettttaaaa,,,,yyyy,,,,iiiinnnnccccyyyy ))))
  41.            MMMMaaaattttrrrriiiixxxxTTTTrrrriiiiaaaannnngggglllleeee     uuuupppplllloooo;;;;
  42.            IIIInnnntttteeeeggggeeeerrrr            nnnn,,,, iiiinnnnccccxxxx,,,, iiiinnnnccccyyyy;;;;
  43.            ddddoooouuuubbbblllleeee             aaaallllpppphhhhaaaa,,,, bbbbeeeettttaaaa;;;;
  44.            ddddoooouuuubbbblllleeee             ((((****aaaapppp))))[[[[ nnnn****(((( nnnn ++++ 1111 )))) ))))////2222 ]]]],,,, ((((****xxxx))))[[[[ nnnn ]]]],,,, ((((****yyyy))))[[[[ nnnn ]]]];;;;
  45.  
  46.      vvvvooooiiiidddd ssssssssppppmmmmvvvv(((( uuuupppplllloooo,,,,nnnn,,,,aaaallllpppphhhhaaaa,,,,aaaapppp,,,,xxxx,,,,iiiinnnnccccxxxx,,,,bbbbeeeettttaaaa,,,,yyyy,,,,iiiinnnnccccyyyy ))))
  47.            MMMMaaaattttrrrriiiixxxxTTTTrrrriiiiaaaannnngggglllleeee     uuuupppplllloooo;;;;
  48.            IIIInnnntttteeeeggggeeeerrrr            nnnn,,,, iiiinnnnccccxxxx,,,, iiiinnnnccccyyyy;;;;
  49.            ffffllllooooaaaatttt              aaaallllpppphhhhaaaa,,,, bbbbeeeettttaaaa;;;;
  50.            ffffllllooooaaaatttt              ((((****aaaapppp))))[[[[ nnnn****(((( nnnn ++++ 1111 )))) ))))////2222 ]]]],,,, ((((****xxxx))))[[[[ nnnn ]]]],,,, ((((****yyyy))))[[[[ nnnn ]]]];;;;
  51.  
  52.      vvvvooooiiiidddd zzzzhhhhppppmmmmvvvv(((( uuuupppplllloooo,,,,nnnn,,,,aaaallllpppphhhhaaaa,,,,aaaapppp,,,,xxxx,,,,iiiinnnnccccxxxx,,,,bbbbeeeettttaaaa,,,,yyyy,,,,iiiinnnnccccyyyy ))))
  53.            MMMMaaaattttrrrriiiixxxxTTTTrrrriiiiaaaannnngggglllleeee     uuuupppplllloooo;;;;
  54.            IIIInnnntttteeeeggggeeeerrrr            nnnn,,,, iiiinnnnccccxxxx,,,, iiiinnnnccccyyyy;;;;
  55.            ZZZZoooommmmpppplllleeeexxxx            aaaallllpppphhhhaaaa,,,, bbbbeeeettttaaaa;;;;
  56.            ZZZZoooommmmpppplllleeeexxxx            ((((****aaaapppp))))[[[[ nnnn****(((( nnnn ++++ 1111 )))) ))))////2222 ]]]],,,, ((((****xxxx))))[[[[ nnnn ]]]],,,, ((((****yyyy))))[[[[ nnnn ]]]];;;;
  57.  
  58.      vvvvooooiiiidddd cccchhhhppppmmmmvvvv(((( uuuupppplllloooo,,,,nnnn,,,,aaaallllpppphhhhaaaa,,,,aaaapppp,,,,xxxx,,,,iiiinnnnccccxxxx,,,,bbbbeeeettttaaaa,,,,yyyy,,,,iiiinnnnccccyyyy ))))
  59.            MMMMaaaattttrrrriiiixxxxTTTTrrrriiiiaaaannnngggglllleeee     uuuupppplllloooo;;;;
  60.  
  61.  
  62.  
  63.                                                                         PPPPaaaaggggeeee 1111
  64.  
  65.  
  66.  
  67.  
  68.  
  69.  
  70. ____SSSSPPPPMMMMVVVV,,,,____HHHHPPPPMMMMVVVV((((3333FFFF))))                                                ____SSSSPPPPMMMMVVVV,,,,____HHHHPPPPMMMMVVVV((((3333FFFF))))
  71.  
  72.  
  73.  
  74.            IIIInnnntttteeeeggggeeeerrrr            nnnn,,,, iiiinnnnccccxxxx,,,, iiiinnnnccccyyyy;;;;
  75.            CCCCoooommmmpppplllleeeexxxx            aaaallllpppphhhhaaaa,,,, bbbbeeeettttaaaa;;;;
  76.            CCCCoooommmmpppplllleeeexxxx            ((((****aaaapppp))))[[[[ nnnn****(((( nnnn ++++ 1111 )))) ))))////2222 ]]]],,,, ((((****xxxx))))[[[[ nnnn ]]]],,,, ((((****yyyy))))[[[[ nnnn ]]]];;;;
  77.  
  78.  
  79. DDDDEEEESSSSCCCCRRRRIIIIPPPPTTTTIIIIOOOONNNN
  80.      ddddssssppppmmmmvvvv ,,,, ssssssssppppmmmmvvvv ,,,, ddddhhhhppppmmmmvvvv and cccchhhhppppmmmmvvvv perform matrix-vector operation
  81.  
  82.           y := alpha*A*x + beta*y,
  83.  
  84.      where alpha and beta are scalars, x and y are n element vectors and A is
  85.      an n by n symmetric/hermitian matrix, supplied in packed form.
  86.  
  87.  
  88. PPPPAAAARRRRAAAAMMMMEEEETTTTEEEERRRRSSSS
  89.      uuuupppplllloooo    On entry, uuuupppplllloooo specifies whether the upper or lower triangular
  90.              part of the matrix A is being supplied as follows:
  91.  
  92.  
  93.  
  94.              FFFFOOOORRRRTTTTRRRRAAAANNNN
  95.              uplo = 'U' or 'u'   The upper triangular part of A is
  96.                                  supplied in AP.
  97.              uplo = 'L' or 'l'   The lower triangular part of A is
  98.                                  supplied in AP.
  99.  
  100.              CCCC
  101.              uplo = UpperTriangle     The upper triangular part of A is
  102.                                       supplied in AP.
  103.              uplo = LowerTriangle     The lower triangular part of A is
  104.                                       supplied in AP.
  105.  
  106.              Unchanged on exit.
  107.  
  108.      nnnn       On entry, nnnn specifies the the order of the matrix A.  nnnn must be
  109.              at least zero.
  110.              Unchanged on exit.
  111.  
  112.      aaaallllpppphhhhaaaa   specifies the scalar alpha.
  113.              Unchanged on exit.
  114.  
  115.      aaaapppp      Array of size at least ( ( n*( n + 1 ) )/2 ).
  116.              Before entry with uuuupppplllloooo ==== ''''UUUU'''' oooorrrr ''''uuuu'''' oooorrrr the array aaaapppp must contain
  117.              the upper triangular part of the symmetric/hermitian matrix
  118.              packed sequentially, column by column, so that aaaapppp( 1 ) contains
  119.              A( 1, 1 ), aaaapppp( 2 ) and aaaapppp( 3 ) contain A( 1, 2 ) and A( 2, 2 )
  120.              respectively, and so on.
  121.  
  122.              Before entry with UUUUPPPPLLLLOOOO ==== ''''LLLL'''' oooorrrr ''''llll'''' oooorrrr , the array aaaapppp must
  123.              contain the lower triangular part of the symmetric/hermitian
  124.              matrix packed sequentially, column by column, so that aaaapppp( 1 )
  125.              contains A( 1, 1 ), aaaapppp( 2 ) and aaaapppp( 3 ) contain A( 2, 1 ) and A(
  126.  
  127.  
  128.  
  129.                                                                         PPPPaaaaggggeeee 2222
  130.  
  131.  
  132.  
  133.  
  134.  
  135.  
  136. ____SSSSPPPPMMMMVVVV,,,,____HHHHPPPPMMMMVVVV((((3333FFFF))))                                                ____SSSSPPPPMMMMVVVV,,,,____HHHHPPPPMMMMVVVV((((3333FFFF))))
  137.  
  138.  
  139.  
  140.              3, 1 ) respectively, and so on.
  141.  
  142.              Unchanged on exit.
  143.  
  144.      xxxx       Array of size at least ( 1 + ( n - 1 )*abs( incx ) ). Before
  145.              entry, the incremented array xxxx must contain the n element vector
  146.              x.
  147.              Unchanged on exit.
  148.  
  149.      iiiinnnnccccxxxx    On entry, iiiinnnnccccxxxx specifies the increment for the elements of xxxx.
  150.              iiiinnnnccccxxxx must not be zero.
  151.              Unchanged on exit.
  152.  
  153.      bbbbeeeettttaaaa    On entry, bbbbeeeettttaaaa specifies the scalar beta. When bbbbeeeettttaaaa is supplied
  154.              as zero then yyyy need not be set on input.
  155.              Unchanged on exit.
  156.  
  157.      yyyy       Array of size at least ( 1 + ( n - 1 )*abs( INCY ) ). Before
  158.              entry, the incremented array yyyy must contain the n element vector
  159.              y. On exit, yyyy is overwritten by the updated vector y.
  160.  
  161.      iiiinnnnccccyyyy    On entry, iiiinnnnccccyyyy specifies the increment for the elements of yyyy.
  162.              iiiinnnnccccyyyy must not be zero.
  163.              Unchanged on exit.
  164.  
  165.  
  166. AAAAUUUUTTTTHHHHOOOORRRRSSSS
  167.           Jack Dongarra, Argonne National Laboratory.
  168.           Iain Duff, AERE Harwell.
  169.           Jeremy Du Croz, Numerical Algorithms Group Ltd.
  170.           Sven Hammarling, Numerical Algorithms Group Ltd.
  171.  
  172.  
  173. TTTTUUUUNNNNIIIINNNNGGGG
  174.           DSPMV and SSPMV are optimized and parallelized for SGI R3000 and
  175.           R4x00 platforms.
  176.           ZHPMV and CHPMV are optimized and parallelized for SGI R3000, R4x00
  177.           and R8000 platforms.
  178.  
  179.  
  180.  
  181.  
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  183.  
  184.  
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  190.  
  191.  
  192.  
  193.  
  194.  
  195.                                                                         PPPPaaaaggggeeee 3333
  196.  
  197.  
  198.  
  199.