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/ IRIX Base Documentation 2001 May / SGI IRIX Base Documentation 2001 May.iso / usr / share / catman / p_man / cat3 / libblas / spr2.z / spr2
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Text File  |  1998-10-30  |  12.7 KB  |  199 lines
  1.  
  2.  
  3.  
  4. ____SSSSPPPPRRRR2222,,,,____HHHHPPPPRRRR2222((((3333FFFF))))                                                ____SSSSPPPPRRRR2222,,,,____HHHHPPPPRRRR2222((((3333FFFF))))
  5.  
  6.  
  7.  
  8. NNNNAAAAMMMMEEEE
  9.      dspr2, sspr2, zhpr2, chpr2 - BLAS Level Two   Symmetric Packed Matrix
  10.      Rank 2 Update
  11.  
  12.  
  13. FFFFOOOORRRRTTTTRRRRAAAANNNN 77777777 SSSSYYYYNNNNOOOOPPPPSSSSIIIISSSS
  14.      ssssuuuubbbbrrrroooouuuuttttiiiinnnneeee ddddsssspppprrrr2222(((( uuuupppplllloooo,,,, nnnn,,,, aaaallllpppphhhhaaaa,,,, nnnn,,,, iiiinnnnccccxxxx,,,, yyyy,,,, iiiinnnnccccyyyy,,,, aaaapppp ))))
  15.            cccchhhhaaaarrrraaaacccctttteeeerrrr****1111        uuuupppplllloooo
  16.            iiiinnnntttteeeeggggeeeerrrr            nnnn,,,, iiiinnnnccccxxxx,,,, iiiinnnnccccyyyy
  17.            ddddoooouuuubbbblllleeee pppprrrreeeecccciiiissssiiiioooonnnn   aaaallllpppphhhhaaaa
  18.            ddddoooouuuubbbblllleeee pppprrrreeeecccciiiissssiiiioooonnnn   aaaapppp((((****)))),,,, xxxx((((****)))),,,, yyyy((((****))))
  19.  
  20.      ssssuuuubbbbrrrroooouuuuttttiiiinnnneeee sssssssspppprrrr2222(((( uuuupppplllloooo,,,, nnnn,,,, aaaallllpppphhhhaaaa,,,, nnnn,,,,
  21.            cccchhhhaaaarrrraaaacccctttteeeerrrr****1111        uuuupppplllloooo
  22.            iiiinnnntttteeeeggggeeeerrrr            nnnn,,,, iiiinnnnccccxxxx,,,, iiiinnnnccccyyyy
  23.            rrrreeeeaaaallll               aaaallllpppphhhhaaaa
  24.            rrrreeeeaaaallll               aaaapppp((((****)))),,,, xxxx((((****)))),,,, yyyy((((****))))
  25.  
  26.      ssssuuuubbbbrrrroooouuuuttttiiiinnnneeee zzzzhhhhpppprrrr2222(((( uuuupppplllloooo,,,, nnnn,,,, aaaallllpppphhhhaaaa,,,, nnnn,,,, iiiinnnnccccxxxx,,,, yyyy,,,, iiiinnnnccccyyyy,,,, aaaapppp ))))
  27.            cccchhhhaaaarrrraaaacccctttteeeerrrr****1111        uuuupppplllloooo
  28.            iiiinnnntttteeeeggggeeeerrrr            nnnn,,,, iiiinnnnccccxxxx,,,, iiiinnnnccccyyyy
  29.            ccccoooommmmpppplllleeeexxxx****11116666         aaaallllpppphhhhaaaa
  30.            ccccoooommmmpppplllleeeexxxx****11116666         aaaapppp((((****)))),,,, xxxx((((****)))),,,, yyyy((((****))))
  31.  
  32.      ssssuuuubbbbrrrroooouuuuttttiiiinnnneeee cccchhhhpppprrrr2222(((( uuuupppplllloooo,,,, nnnn,,,, aaaallllpppphhhhaaaa,,,, nnnn,,,,
  33.            cccchhhhaaaarrrraaaacccctttteeeerrrr****1111        uuuupppplllloooo
  34.            iiiinnnntttteeeeggggeeeerrrr            nnnn,,,, iiiinnnnccccxxxx,,,, iiiinnnnccccyyyy
  35.            ccccoooommmmpppplllleeeexxxx            aaaallllpppphhhhaaaa
  36.            ccccoooommmmpppplllleeeexxxx            aaaapppp((((****)))),,,, xxxx((((****)))),,,, yyyy((((****))))
  37.  
  38.  
  39. CCCC SSSSYYYYNNNNOOOOPPPPSSSSIIIISSSS
  40.      vvvvooooiiiidddd ddddsssspppprrrr2222(((( uuuupppplllloooo,,,, nnnn,,,, aaaallllpppphhhhaaaa,,,, nnnn,,,, iiiinnnnccccxxxx,,,, yyyy,,,, iiiinnnnccccyyyy,,,, aaaapppp ))))
  41.            MMMMaaaattttrrrriiiixxxxTTTTrrrriiiiaaaannnngggglllleeee     uuuupppplllloooo;;;;
  42.            IIIInnnntttteeeeggggeeeerrrr            nnnn,,,, iiiinnnnccccxxxx,,,, iiiinnnnccccyyyy;;;;
  43.            ddddoooouuuubbbblllleeee             aaaallllpppphhhhaaaa;;;;
  44.            ddddoooouuuubbbblllleeee             ((((****aaaapppp))))[[[[ nnnn ]]]],,,, ((((****xxxx))))[[[[ nnnn ]]]],,,, ((((****yyyy))))[[[[ nnnn ]]]];;;;
  45.  
  46.      vvvvooooiiiidddd sssssssspppprrrr2222(((( uuuupppplllloooo,,,, nnnn,,,, aaaallllpppphhhhaaaa,,,, nnnn,,,, iiiinnnnccccxxxx,,,, yyyy,,,, iiiinnnnccccyyyy,,,, aaaapppp ))))
  47.            MMMMaaaattttrrrriiiixxxxTTTTrrrriiiiaaaannnngggglllleeee     uuuupppplllloooo;;;;
  48.            IIIInnnntttteeeeggggeeeerrrr            nnnn,,,, iiiinnnnccccxxxx,,,, iiiinnnnccccyyyy;;;;
  49.            ffffllllooooaaaatttt              aaaallllpppphhhhaaaa;;;;
  50.            ffffllllooooaaaatttt             ((((****aaaapppp))))[[[[ nnnn ]]]],,,, ((((****xxxx))))[[[[ nnnn ]]]],,,, ((((****yyyy))))[[[[ nnnn ]]]];;;;
  51.  
  52.      vvvvooooiiiidddd zzzzhhhhpppprrrr2222(((( uuuupppplllloooo,,,, nnnn,,,, aaaallllpppphhhhaaaa,,,, nnnn,,,, iiiinnnnccccxxxx,,,, yyyy,,,, iiiinnnnccccyyyy,,,, aaaapppp ))))
  53.            MMMMaaaattttrrrriiiixxxxTTTTrrrriiiiaaaannnngggglllleeee     uuuupppplllloooo;;;;
  54.            IIIInnnntttteeeeggggeeeerrrr            nnnn,,,, iiiinnnnccccxxxx,,,, iiiinnnnccccyyyy;;;;
  55.            ZZZZoooommmmpppplllleeeexxxx            aaaallllpppphhhhaaaa;;;;
  56.            ZZZZoooommmmpppplllleeeexxxx           ((((****aaaapppp))))[[[[ nnnn ]]]],,,, ((((****xxxx))))[[[[ nnnn ]]]],,,, ((((****yyyy))))[[[[ nnnn ]]]];;;;
  57.  
  58.      vvvvooooiiiidddd cccchhhhpppprrrr2222(((( uuuupppplllloooo,,,, nnnn,,,, aaaallllpppphhhhaaaa,,,, nnnn,,,, iiiinnnnccccxxxx,,,, yyyy,,,, iiiinnnnccccyyyy,,,, aaaapppp ))))
  59.            MMMMaaaattttrrrriiiixxxxTTTTrrrriiiiaaaannnngggglllleeee     uuuupppplllloooo;;;;
  60.  
  61.  
  62.  
  63.                                                                         PPPPaaaaggggeeee 1111
  64.  
  65.  
  66.  
  67.  
  68.  
  69.  
  70. ____SSSSPPPPRRRR2222,,,,____HHHHPPPPRRRR2222((((3333FFFF))))                                                ____SSSSPPPPRRRR2222,,,,____HHHHPPPPRRRR2222((((3333FFFF))))
  71.  
  72.  
  73.  
  74.            IIIInnnntttteeeeggggeeeerrrr            nnnn,,,, iiiinnnnccccxxxx,,,, iiiinnnnccccyyyy;;;;
  75.            CCCCoooommmmpppplllleeeexxxx            aaaallllpppphhhhaaaa;;;;
  76.            CCCCoooommmmpppplllleeeexxxx           ((((****aaaapppp))))[[[[ nnnn ]]]],,,, ((((****xxxx))))[[[[ nnnn ]]]],,,, ((((****yyyy))))[[[[ nnnn ]]]];;;;
  77.  
  78.  
  79.  
  80. DDDDEEEESSSSCCCCRRRRIIIIPPPPTTTTIIIIOOOONNNN
  81.      ddddsssspppprrrr2222 and sssssssspppprrrr2222 perform the symmetric rank 2 operation
  82.  
  83.           A := alpha*x*y' + alpha*y*x' + A,
  84.  
  85.      zzzzhhhhpppprrrr2222 and cccchhhhpppprrrr2222 perform the hermitian rank 2 operation
  86.  
  87.           A := alpha*x*conjg( y' ) + conjg( alpha )*y*conjg( x' ) + A,
  88.  
  89.      where alpha is a real/complex scalar, x is an n element vector and A is
  90.      an n by n symmetric/hermitian matrix, supplied in packed form.
  91.  
  92.  
  93. PPPPAAAARRRRAAAAMMMMEEEETTTTEEEERRRRSSSS
  94.      uuuupppplllloooo    On entry, uuuupppplllloooo specifies whether the upper or lower triangular
  95.              part of the matrix A is being supplied as follows:
  96.  
  97.  
  98.  
  99.              FFFFOOOORRRRTTTTRRRRAAAANNNN
  100.              uplo = 'U' or 'u'   Only the upper triangular part of A
  101.                                  is to be referenced.
  102.              uplo = 'L' or 'l'   Only the lower triangular part of A
  103.                                  is to be referenced.
  104.  
  105.              CCCC
  106.              uplo = UpperTriangle     Only the lower triangular part of A
  107.                                       is to be referenced.
  108.              uplo = LowerTriangle     Only the lower triangular part of A
  109.                                       is to be referenced.
  110.  
  111.              Unchanged on exit.
  112.  
  113.      nnnn       On entry, nnnn specifies the the order of the matrix A.  nnnn must be
  114.              at least zero.
  115.              Unchanged on exit.
  116.  
  117.      aaaallllpppphhhhaaaa   specifies the scalar alpha.
  118.              Unchanged on exit.
  119.  
  120.      xxxx       Array of size at least ( 1 + ( n - 1 )*abs( incx ) ). Before
  121.              entry, the incremented array xxxx must contain the n element vector
  122.              x.
  123.              Unchanged on exit.
  124.  
  125.  
  126.  
  127.  
  128.  
  129.                                                                         PPPPaaaaggggeeee 2222
  130.  
  131.  
  132.  
  133.  
  134.  
  135.  
  136. ____SSSSPPPPRRRR2222,,,,____HHHHPPPPRRRR2222((((3333FFFF))))                                                ____SSSSPPPPRRRR2222,,,,____HHHHPPPPRRRR2222((((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.      yyyy       Array of size at least ( 1 + ( n - 1 )*abs( incy ) ). Before
  145.              entry, the incremented array yyyy must contain the n element vector
  146.              y. On exit, Y is overwritten by the updated vector y.
  147.  
  148.      iiiinnnnccccyyyy    On entry, iiiinnnnccccyyyy specifies the increment for the elements of yyyy.
  149.              iiiinnnnccccyyyy must not be zero.
  150.              Unchanged on exit.
  151.  
  152.      aaaapppp      Array of size at least ( ( n*( n + 1 ) )/2 ).
  153.              Before entry with uuuupppplllloooo ==== ''''UUUU'''' oooorrrr ''''uuuu'''' oooorrrr the array aaaapppp must contain
  154.              the upper triangular part of the symmetric/hermitian matrix
  155.              packed sequentially, column by column, so that aaaapppp( 1 ) contains
  156.              A( 1, 1 ), aaaapppp( 2 ) and aaaapppp( 3 ) contain A( 1, 2 ) and A( 2, 2 )
  157.              respectively, and so on.
  158.  
  159.              Before entry with UUUUPPPPLLLLOOOO ==== ''''LLLL'''' oooorrrr ''''llll'''' oooorrrr , the array aaaapppp must
  160.              contain the lower triangular part of the symmetric/hermitian
  161.              matrix packed sequentially, column by column, so that aaaapppp( 1 )
  162.              contains A( 1, 1 ), aaaapppp( 2 ) and aaaapppp( 3 ) contain A( 2, 1 ) and A(
  163.              3, 1 ) respectively, and so on.
  164.  
  165.              Note that for the hermitian matrix the imaginary parts of the
  166.              diagonal elements need not be set, they are assumed to be zero,
  167.              and on exit they are set to zero.
  168.  
  169.              Unchanged on exit.
  170.  
  171.  
  172. AAAAUUUUTTTTHHHHOOOORRRRSSSS
  173.           Jack Dongarra, Argonne National Laboratory.
  174.           Iain Duff, AERE Harwell.
  175.           Jeremy Du Croz, Numerical Algorithms Group Ltd.
  176.           Sven Hammarling, Numerical Algorithms Group Ltd.
  177.  
  178.  
  179.  
  180.  
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  191.  
  192.  
  193.  
  194.  
  195.                                                                         PPPPaaaaggggeeee 3333
  196.  
  197.  
  198.  
  199.