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Text File  |  1998-10-30  |  11.5 KB  |  199 lines
  1.  
  2.  
  3.  
  4. ____SSSSPPPPRRRR,,,,____HHHHPPPPRRRR((((3333FFFF))))                                                    ____SSSSPPPPRRRR,,,,____HHHHPPPPRRRR((((3333FFFF))))
  5.  
  6.  
  7.  
  8. NNNNAAAAMMMMEEEE
  9.      dspr, sspr, zhpr, chpr - BLAS Level Two   Symmetric Packed Matrix Rank 1
  10.      Update
  11.  
  12.  
  13. FFFFOOOORRRRTTTTRRRRAAAANNNN 77777777 SSSSYYYYNNNNOOOOPPPPSSSSIIIISSSS
  14.      ssssuuuubbbbrrrroooouuuuttttiiiinnnneeee ddddsssspppprrrr(((( uuuupppplllloooo,,,, nnnn,,,, aaaallllpppphhhhaaaa,,,, xxxx,,,, iiiinnnnccccxxxx,,,, aaaapppp ))))
  15.            cccchhhhaaaarrrraaaacccctttteeeerrrr****1111        uuuupppplllloooo
  16.            iiiinnnntttteeeeggggeeeerrrr            nnnn,,,, iiiinnnnccccxxxx
  17.            ddddoooouuuubbbblllleeee pppprrrreeeecccciiiissssiiiioooonnnn   aaaallllpppphhhhaaaa
  18.            ddddoooouuuubbbblllleeee pppprrrreeeecccciiiissssiiiioooonnnn   aaaapppp((((****)))),,,, xxxx((((****))))
  19.  
  20.      ssssuuuubbbbrrrroooouuuuttttiiiinnnneeee sssssssspppprrrr(((( uuuupppplllloooo,,,, nnnn,,,, aaaallllpppphhhhaaaa,,,, xxxx,,,, iiiinnnnccccxxxx,,,, aaaapppp ))))
  21.            cccchhhhaaaarrrraaaacccctttteeeerrrr****1111        uuuupppplllloooo
  22.            iiiinnnntttteeeeggggeeeerrrr            nnnn,,,, iiiinnnnccccxxxx
  23.            rrrreeeeaaaallll               aaaallllpppphhhhaaaa
  24.            rrrreeeeaaaallll               aaaapppp((((****)))),,,, xxxx((((****))))
  25.  
  26.      ssssuuuubbbbrrrroooouuuuttttiiiinnnneeee zzzzhhhhpppprrrr(((( uuuupppplllloooo,,,, nnnn,,,, aaaallllpppphhhhaaaa,,,, xxxx,,,, iiiinnnnccccxxxx,,,, aaaapppp ))))
  27.            cccchhhhaaaarrrraaaacccctttteeeerrrr****1111        uuuupppplllloooo
  28.            iiiinnnntttteeeeggggeeeerrrr            nnnn,,,, iiiinnnnccccxxxx
  29.            ccccoooommmmpppplllleeeexxxx****11116666         aaaallllpppphhhhaaaa
  30.            ccccoooommmmpppplllleeeexxxx****11116666         aaaapppp((((****)))),,,, xxxx((((****))))
  31.  
  32.      ssssuuuubbbbrrrroooouuuuttttiiiinnnneeee cccchhhhpppprrrr(((( uuuupppplllloooo,,,, nnnn,,,, aaaallllpppphhhhaaaa,,,, xxxx,,,, iiiinnnnccccxxxx,,,, aaaapppp ))))
  33.            cccchhhhaaaarrrraaaacccctttteeeerrrr****1111        uuuupppplllloooo
  34.            iiiinnnntttteeeeggggeeeerrrr            nnnn,,,, iiiinnnnccccxxxx
  35.            ccccoooommmmpppplllleeeexxxx            aaaallllpppphhhhaaaa
  36.            ccccoooommmmpppplllleeeexxxx            aaaapppp((((****)))),,,, xxxx((((****))))
  37.  
  38.  
  39. CCCC SSSSYYYYNNNNOOOOPPPPSSSSIIIISSSS
  40.      vvvvooooiiiidddd ddddsssspppprrrr(((( uuuupppplllloooo,,,, nnnn,,,, aaaallllpppphhhhaaaa,,,, xxxx,,,, iiiinnnnccccxxxx,,,, aaaapppp ))))
  41.            MMMMaaaattttrrrriiiixxxxTTTTrrrriiiiaaaannnngggglllleeee     uuuupppplllloooo;;;;
  42.            IIIInnnntttteeeeggggeeeerrrr            nnnn,,,, iiiinnnnccccxxxx;;;;
  43.            ddddoooouuuubbbblllleeee             aaaallllpppphhhhaaaa;;;;
  44.            ddddoooouuuubbbblllleeee             ((((****aaaapppp))))[[[[ nnnn****(((( nnnn ++++ 1111 )))) ))))////2222 ]]]],,,, ((((****xxxx))))[[[[ nnnn ]]]];;;;
  45.  
  46.      vvvvooooiiiidddd sssssssspppprrrr(((( uuuupppplllloooo,,,, nnnn,,,, aaaallllpppphhhhaaaa,,,, xxxx,,,, iiiinnnnccccxxxx,,,, aaaapppp ))))
  47.            MMMMaaaattttrrrriiiixxxxTTTTrrrriiiiaaaannnngggglllleeee     uuuupppplllloooo;;;;
  48.            IIIInnnntttteeeeggggeeeerrrr            nnnn,,,, iiiinnnnccccxxxx;;;;
  49.            ffffllllooooaaaatttt              aaaallllpppphhhhaaaa;;;;
  50.            ffffllllooooaaaatttt              ((((****aaaapppp))))[[[[ nnnn****(((( nnnn ++++ 1111 )))) ))))////2222 ]]]],,,, ((((****xxxx))))[[[[ nnnn ]]]];;;;
  51.  
  52.      vvvvooooiiiidddd zzzzhhhhpppprrrr(((( uuuupppplllloooo,,,, nnnn,,,, aaaallllpppphhhhaaaa,,,, xxxx,,,, iiiinnnnccccxxxx,,,, aaaapppp ))))
  53.            MMMMaaaattttrrrriiiixxxxTTTTrrrriiiiaaaannnngggglllleeee     uuuupppplllloooo;;;;
  54.            IIIInnnntttteeeeggggeeeerrrr            nnnn,,,, iiiinnnnccccxxxx;;;;
  55.            ZZZZoooommmmpppplllleeeexxxx            aaaallllpppphhhhaaaa;;;;
  56.            ZZZZoooommmmpppplllleeeexxxx            ((((****aaaapppp))))[[[[ nnnn****(((( nnnn ++++ 1111 )))) ))))////2222 ]]]],,,, ((((****xxxx))))[[[[ nnnn ]]]];;;;
  57.  
  58.      vvvvooooiiiidddd cccchhhhpppprrrr(((( uuuupppplllloooo,,,, nnnn,,,, aaaallllpppphhhhaaaa,,,, xxxx,,,, iiiinnnnccccxxxx,,,, aaaapppp ))))
  59.            MMMMaaaattttrrrriiiixxxxTTTTrrrriiiiaaaannnngggglllleeee     uuuupppplllloooo;;;;
  60.  
  61.  
  62.  
  63.                                                                         PPPPaaaaggggeeee 1111
  64.  
  65.  
  66.  
  67.  
  68.  
  69.  
  70. ____SSSSPPPPRRRR,,,,____HHHHPPPPRRRR((((3333FFFF))))                                                    ____SSSSPPPPRRRR,,,,____HHHHPPPPRRRR((((3333FFFF))))
  71.  
  72.  
  73.  
  74.            IIIInnnntttteeeeggggeeeerrrr            nnnn,,,, iiiinnnnccccxxxx;;;;
  75.            CCCCoooommmmpppplllleeeexxxx            aaaallllpppphhhhaaaa;;;;
  76.            CCCCoooommmmpppplllleeeexxxx            ((((****aaaapppp))))[[[[ nnnn****(((( nnnn ++++ 1111 )))) ))))////2222 ]]]],,,, ((((****xxxx))))[[[[ nnnn ]]]];;;;
  77.  
  78.  
  79. DDDDEEEESSSSCCCCRRRRIIIIPPPPTTTTIIIIOOOONNNN
  80.      ddddsssspppprrrr and sssssssspppprrrr perform the symmetric rank 1 operation
  81.  
  82.            A := alpha*x*x' + A,
  83.  
  84.      zzzzhhhhpppprrrr and cccchhhhpppprrrr perform the hermitian rank 1 operation
  85.  
  86.            A := alpha*x*conjg( x' ) + A,
  87.  
  88.      where alpha is a real/complex scalar, x is an n element vector and A is
  89.      an n by n symmetric/hermitian matrix, supplied in packed form.
  90.  
  91.  
  92. PPPPAAAARRRRAAAAMMMMEEEETTTTEEEERRRRSSSS
  93.      uuuupppplllloooo    On entry, uuuupppplllloooo specifies whether the upper or lower triangular
  94.              part of the array A is to be referenced a follows:
  95.  
  96.  
  97.  
  98.              FFFFOOOORRRRTTTTRRRRAAAANNNN
  99.              uplo = 'U' or 'u'   Only the upper triangular part of A
  100.                                  is to be referenced.
  101.              uplo = 'L' or 'l'   Only the lower triangular part of A
  102.                                  is to be referenced.
  103.  
  104.              CCCC
  105.              uplo = UpperTriangle     Only the lower triangular part of A
  106.                                       is to be referenced.
  107.              uplo = LowerTriangle     Only the lower triangular part of A
  108.                                       is to be referenced.
  109.  
  110.              Unchanged on exit.
  111.  
  112.      nnnn       On entry, nnnn specifies the the order of the matrix A.  nnnn must be
  113.              at least zero.
  114.              Unchanged on exit.
  115.  
  116.      aaaallllpppphhhhaaaa   specifies the scalar alpha.
  117.              Unchanged on exit.
  118.  
  119.      xxxx       Array of size at least ( 1 + ( n - 1 )*abs( incx ) ). Before
  120.              entry, the incremented array xxxx must contain the n element vector
  121.              x.
  122.              Unchanged on exit.
  123.  
  124.  
  125.  
  126.  
  127.  
  128.  
  129.                                                                         PPPPaaaaggggeeee 2222
  130.  
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  133.  
  134.  
  135.  
  136. ____SSSSPPPPRRRR,,,,____HHHHPPPPRRRR((((3333FFFF))))                                                    ____SSSSPPPPRRRR,,,,____HHHHPPPPRRRR((((3333FFFF))))
  137.  
  138.  
  139.  
  140.      iiiinnnnccccxxxx    On entry, iiiinnnnccccxxxx specifies the increment for the elements of xxxx.
  141.              iiiinnnnccccxxxx must not be zero.
  142.              Unchanged on exit.
  143.  
  144.      aaaapppp      Array of size at least ( ( n*( n + 1 ) )/2 ).
  145.              Before entry with uuuupppplllloooo ==== ''''UUUU'''' oooorrrr ''''uuuu'''' oooorrrr the array aaaapppp must contain
  146.              the upper triangular part of the symmetric/hermitian matrix
  147.              packed sequentially, column by column, so that aaaapppp( 1 ) contains
  148.              A( 1, 1 ), aaaapppp( 2 ) and aaaapppp( 3 ) contain A( 1, 2 ) and A( 2, 2 )
  149.              respectively, and so on.
  150.  
  151.              Before entry with UUUUPPPPLLLLOOOO ==== ''''LLLL'''' oooorrrr ''''llll'''' oooorrrr , the array aaaapppp must
  152.              contain the lower triangular part of the symmetric/hermitian
  153.              matrix packed sequentially, column by column, so that aaaapppp( 1 )
  154.              contains A( 1, 1 ), aaaapppp( 2 ) and aaaapppp( 3 ) contain A( 2, 1 ) and A(
  155.              3, 1 ) respectively, and so on.
  156.  
  157.              Note that for the hermitian matrix the imaginary parts of the
  158.              diagonal elements need not be set, they are assumed to be zero,
  159.              and on exit they are set to zero.
  160.  
  161.              Unchanged on exit.
  162.  
  163.  
  164. AAAAUUUUTTTTHHHHOOOORRRRSSSS
  165.           Jack Dongarra, Argonne National Laboratory.
  166.           Iain Duff, AERE Harwell.
  167.           Jeremy Du Croz, Numerical Algorithms Group Ltd.
  168.           Sven Hammarling, Numerical Algorithms Group Ltd.
  169.  
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  194.  
  195.                                                                         PPPPaaaaggggeeee 3333
  196.  
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  199.