home *** CD-ROM | disk | FTP | other *** search
/ IRIX Base Documentation 2001 May / SGI IRIX Base Documentation 2001 May.iso / usr / share / catman / p_man / cat3 / libblas / ger.z / ger
Encoding:
Text File  |  1998-10-30  |  15.5 KB  |  199 lines
  1.  
  2.  
  3.  
  4. ____GGGGEEEERRRR,,,,____GGGGEEEERRRRUUUU,,,,____GGGGEEEERRRRCCCC((((3333FFFF))))                                      ____GGGGEEEERRRR,,,,____GGGGEEEERRRRUUUU,,,,____GGGGEEEERRRRCCCC((((3333FFFF))))
  5.  
  6.  
  7.  
  8. NNNNAAAAMMMMEEEE
  9.      dger, sger, zgeru, cgeru, zgerc, cgerc - BLAS Level Two   Rank 1
  10.      Operation
  11.  
  12.  
  13. FFFFOOOORRRRTTTTRRRRAAAANNNN 77777777 SSSSYYYYNNNNOOOOPPPPSSSSIIIISSSS
  14.      ssssuuuubbbbrrrroooouuuuttttiiiinnnneeee ddddggggeeeerrrr(((( mmmm,,,, nnnn,,,, aaaallllpppphhhhaaaa,,,, xxxx,,,, iiiinnnnccccxxxx,,,, yyyy,,,, iiiinnnnccccyyyy,,,, aaaa,,,, llllddddaaaa ))))
  15.            iiiinnnntttteeeeggggeeeerrrr            mmmm,,,, nnnn,,,, llllddddaaaa,,,, iiiinnnnccccxxxx,,,, iiiinnnnccccyyyy
  16.            ddddoooouuuubbbblllleeee pppprrrreeeecccciiiissssiiiioooonnnn   aaaallllpppphhhhaaaa
  17.            ddddoooouuuubbbblllleeee pppprrrreeeecccciiiissssiiiioooonnnn   aaaa(((( llllddddaaaa,,,,****)))),,,, xxxx((((****)))),,,, yyyy((((****))))
  18.  
  19.      ssssuuuubbbbrrrroooouuuuttttiiiinnnneeee ssssggggeeeerrrr(((( mmmm,,,, nnnn,,,, aaaallllpppphhhhaaaa,,,, xxxx,,,, iiiinnnnccccxxxx,,,, yyyy,,,, iiiinnnnccccyyyy,,,, aaaa,,,, llllddddaaaa ))))
  20.            iiiinnnntttteeeeggggeeeerrrr            mmmm,,,, nnnn,,,, llllddddaaaa,,,, iiiinnnnccccxxxx,,,, iiiinnnnccccyyyy
  21.            rrrreeeeaaaallll               aaaallllpppphhhhaaaa
  22.            rrrreeeeaaaallll               aaaa(((( llllddddaaaa,,,,****)))),,,, xxxx((((****)))),,,, yyyy((((****))))
  23.  
  24.      ssssuuuubbbbrrrroooouuuuttttiiiinnnneeee zzzzggggeeeerrrruuuu(((( mmmm,,,, nnnn,,,, aaaallllpppphhhhaaaa,,,, xxxx,,,, iiiinnnnccccxxxx,,,, yyyy,,,, iiiinnnnccccyyyy,,,, aaaa,,,, llllddddaaaa ))))
  25.            iiiinnnntttteeeeggggeeeerrrr            mmmm,,,, nnnn,,,, llllddddaaaa,,,, iiiinnnnccccxxxx,,,, iiiinnnnccccyyyy
  26.            ccccoooommmmpppplllleeeexxxx****11116666         aaaallllpppphhhhaaaa
  27.            ccccoooommmmpppplllleeeexxxx****11116666         aaaa(((( llllddddaaaa,,,,****)))),,,, xxxx((((****)))),,,, yyyy((((****))))
  28.  
  29.      ssssuuuubbbbrrrroooouuuuttttiiiinnnneeee ccccggggeeeerrrruuuu(((( mmmm,,,, nnnn,,,, aaaallllpppphhhhaaaa,,,, xxxx,,,, iiiinnnnccccxxxx,,,, yyyy,,,, iiiinnnnccccyyyy,,,, aaaa,,,, llllddddaaaa ))))
  30.            iiiinnnntttteeeeggggeeeerrrr            mmmm,,,, nnnn,,,, llllddddaaaa,,,, iiiinnnnccccxxxx,,,, iiiinnnnccccyyyy
  31.            ccccoooommmmpppplllleeeexxxx            aaaallllpppphhhhaaaa
  32.            ccccoooommmmpppplllleeeexxxx            aaaa(((( llllddddaaaa,,,,****)))),,,, xxxx((((****)))),,,, yyyy((((****))))
  33.  
  34.      ssssuuuubbbbrrrroooouuuuttttiiiinnnneeee zzzzggggeeeerrrrcccc(((( mmmm,,,, nnnn,,,, aaaallllpppphhhhaaaa,,,, xxxx,,,, iiiinnnnccccxxxx,,,, yyyy,,,, iiiinnnnccccyyyy,,,, aaaa,,,, llllddddaaaa ))))
  35.            iiiinnnntttteeeeggggeeeerrrr            mmmm,,,, nnnn,,,, llllddddaaaa,,,, iiiinnnnccccxxxx,,,, iiiinnnnccccyyyy
  36.            ccccoooommmmpppplllleeeexxxx****11116666         aaaallllpppphhhhaaaa
  37.            ccccoooommmmpppplllleeeexxxx****11116666         aaaa(((( llllddddaaaa,,,,****)))),,,, xxxx((((****)))),,,, yyyy((((****))))
  38.  
  39.      ssssuuuubbbbrrrroooouuuuttttiiiinnnneeee ccccggggeeeerrrrcccc(((( mmmm,,,, nnnn,,,, aaaallllpppphhhhaaaa,,,, xxxx,,,, iiiinnnnccccxxxx,,,, yyyy,,,, iiiinnnnccccyyyy,,,, aaaa,,,, llllddddaaaa ))))
  40.            iiiinnnntttteeeeggggeeeerrrr            mmmm,,,, nnnn,,,, llllddddaaaa,,,, iiiinnnnccccxxxx,,,, iiiinnnnccccyyyy
  41.            ccccoooommmmpppplllleeeexxxx            aaaallllpppphhhhaaaa
  42.            ccccoooommmmpppplllleeeexxxx            aaaa(((( llllddddaaaa,,,,****)))),,,, xxxx((((****)))),,,, yyyy((((****))))
  43.  
  44.  
  45. CCCC SSSSYYYYNNNNOOOOPPPPSSSSIIIISSSS
  46.      vvvvooooiiiidddd ddddggggeeeerrrr(((( mmmm,,,, nnnn,,,, aaaallllpppphhhhaaaa,,,, xxxx,,,, iiiinnnnccccxxxx,,,, yyyy,,,, iiiinnnnccccyyyy,,,, aaaa,,,, llllddddaaaa ))))
  47.            IIIInnnntttteeeeggggeeeerrrr            mmmm,,,, nnnn,,,, llllddddaaaa,,,, iiiinnnnccccxxxx,,,, iiiinnnnccccyyyy;;;;
  48.            ddddoooouuuubbbblllleeee             aaaallllpppphhhhaaaa;;;;
  49.            ddddoooouuuubbbblllleeee             ((((****aaaa))))[[[[llllddddaaaa****nnnn]]]],,,, ((((****xxxx))))[[[[ nnnn ]]]],,,, ((((****yyyy))))[[[[ nnnn ]]]];;;;
  50.  
  51.      vvvvooooiiiidddd ssssggggeeeerrrr(((( mmmm,,,, nnnn,,,, aaaallllpppphhhhaaaa,,,, xxxx,,,, iiiinnnnccccxxxx,,,, yyyy,,,, iiiinnnnccccyyyy,,,, aaaa,,,, llllddddaaaa ))))
  52.            IIIInnnntttteeeeggggeeeerrrr            mmmm,,,, nnnn,,,, llllddddaaaa,,,, iiiinnnnccccxxxx,,,, iiiinnnnccccyyyy;;;;
  53.            ffffllllooooaaaatttt              aaaallllpppphhhhaaaa;;;;
  54.            ffffllllooooaaaatttt              ((((****aaaa))))[[[[llllddddaaaa****nnnn]]]],,,, ((((****xxxx))))[[[[ nnnn ]]]],,,, ((((****yyyy))))[[[[ nnnn ]]]];;;;
  55.  
  56.      vvvvooooiiiidddd zzzzggggeeeerrrruuuu(((( mmmm,,,, nnnn,,,, aaaallllpppphhhhaaaa,,,, xxxx,,,, iiiinnnnccccxxxx,,,, yyyy,,,, iiiinnnnccccyyyy,,,, aaaa,,,, llllddddaaaa ))))
  57.            IIIInnnntttteeeeggggeeeerrrr            mmmm,,,, nnnn,,,, llllddddaaaa,,,, iiiinnnnccccxxxx,,,, iiiinnnnccccyyyy;;;;
  58.            ZZZZoooommmmpppplllleeeexxxx            aaaallllpppphhhhaaaa;;;;
  59.            ZZZZoooommmmpppplllleeeexxxx            ((((****aaaa))))[[[[llllddddaaaa****nnnn]]]],,,, ((((****xxxx))))[[[[ nnnn ]]]],,,, ((((****yyyy))))[[[[ nnnn ]]]];;;;
  60.  
  61.  
  62.  
  63.                                                                         PPPPaaaaggggeeee 1111
  64.  
  65.  
  66.  
  67.  
  68.  
  69.  
  70. ____GGGGEEEERRRR,,,,____GGGGEEEERRRRUUUU,,,,____GGGGEEEERRRRCCCC((((3333FFFF))))                                      ____GGGGEEEERRRR,,,,____GGGGEEEERRRRUUUU,,,,____GGGGEEEERRRRCCCC((((3333FFFF))))
  71.  
  72.  
  73.  
  74.      vvvvooooiiiidddd ccccggggeeeerrrruuuu(((( mmmm,,,, nnnn,,,, aaaallllpppphhhhaaaa,,,, xxxx,,,, iiiinnnnccccxxxx,,,, yyyy,,,, iiiinnnnccccyyyy,,,, aaaa,,,, llllddddaaaa ))))
  75.            IIIInnnntttteeeeggggeeeerrrr            mmmm,,,, nnnn,,,, llllddddaaaa,,,, iiiinnnnccccxxxx,,,, iiiinnnnccccyyyy;;;;
  76.            CCCCoooommmmpppplllleeeexxxx            aaaallllpppphhhhaaaa;;;;
  77.            CCCCoooommmmpppplllleeeexxxx            ((((****aaaa))))[[[[llllddddaaaa****nnnn]]]],,,, ((((****xxxx))))[[[[ nnnn ]]]],,,, ((((****yyyy))))[[[[ nnnn ]]]];;;;
  78.  
  79.      vvvvooooiiiidddd zzzzhhhheeeerrrrcccc(((( mmmm,,,, nnnn,,,, aaaallllpppphhhhaaaa,,,, xxxx,,,, iiiinnnnccccxxxx,,,, yyyy,,,, iiiinnnnccccyyyy,,,, aaaa,,,, llllddddaaaa ))))
  80.            IIIInnnntttteeeeggggeeeerrrr            mmmm,,,, nnnn,,,, llllddddaaaa,,,, iiiinnnnccccxxxx,,,, iiiinnnnccccyyyy;;;;
  81.            ZZZZoooommmmpppplllleeeexxxx            aaaallllpppphhhhaaaa;;;;
  82.            ZZZZoooommmmpppplllleeeexxxx            ((((****aaaa))))[[[[llllddddaaaa****nnnn]]]],,,, ((((****xxxx))))[[[[ nnnn ]]]],,,, ((((****yyyy))))[[[[ nnnn ]]]];;;;
  83.  
  84.      vvvvooooiiiidddd ccccggggeeeerrrrcccc(((( mmmm,,,, nnnn,,,, aaaallllpppphhhhaaaa,,,, xxxx,,,, iiiinnnnccccxxxx,,,, yyyy,,,, iiiinnnnccccyyyy,,,, aaaa,,,, llllddddaaaa ))))
  85.            IIIInnnntttteeeeggggeeeerrrr            mmmm,,,, nnnn,,,, llllddddaaaa,,,, iiiinnnnccccxxxx,,,, iiiinnnnccccyyyy;;;;
  86.            CCCCoooommmmpppplllleeeexxxx            aaaallllpppphhhhaaaa;;;;
  87.            CCCCoooommmmpppplllleeeexxxx            ((((****aaaa))))[[[[llllddddaaaa****nnnn]]]],,,, ((((****xxxx))))[[[[ nnnn ]]]],,,, ((((****yyyy))))[[[[ nnnn ]]]];;;;
  88.  
  89.  
  90.  
  91. DDDDEEEESSSSCCCCRRRRIIIIPPPPTTTTIIIIOOOONNNN
  92.      ddddggggeeeerrrr ,,,, ssssggggeeeerrrr ,,,, zzzzhhhheeeerrrruuuu and ccccggggeeeerrrruuuu perform the rank 1 operation
  93.  
  94.            A := alpha*x*y' + A,
  95.  
  96.      zzzzggggeeeerrrrcccc and ccccggggeeeerrrrcccc perform the rank 1 operation
  97.  
  98.            A := alpha*x*conjg( y' ) + A,
  99.  
  100.      where alpha is a scalar, x is an m element vector, y is an n element
  101.      vector and A is an m by n matrix.
  102.  
  103.  
  104. PPPPAAAARRRRAAAAMMMMEEEETTTTEEEERRRRSSSS
  105.      mmmm       On entry, mmmm specifies the number of rows of the matrix A.  mmmm must
  106.              be at least zero.
  107.              Unchanged on exit.
  108.  
  109.      nnnn       On entry, nnnn specifies the number of columns of the matrix A.  nnnn
  110.              must be at least zero.
  111.              Unchanged on exit.
  112.  
  113.      aaaallllpppphhhhaaaa   On entry, aaaallllpppphhhhaaaa specifies the scalar alpha.
  114.              Unchanged on exit.
  115.  
  116.      xxxx       Array of size at least ( 1 + ( m - 1 )*abs( incx ) ). Before
  117.              entry, the incremented array xxxx must contain the m element vector
  118.              x.
  119.              Unchanged on exit.
  120.  
  121.      iiiinnnnccccxxxx    On entry, iiiinnnnccccxxxx specifies the increment for the elements of xxxx.
  122.              iiiinnnnccccxxxx must not be zero.
  123.              Unchanged on exit.
  124.  
  125.  
  126.  
  127.  
  128.  
  129.                                                                         PPPPaaaaggggeeee 2222
  130.  
  131.  
  132.  
  133.  
  134.  
  135.  
  136. ____GGGGEEEERRRR,,,,____GGGGEEEERRRRUUUU,,,,____GGGGEEEERRRRCCCC((((3333FFFF))))                                      ____GGGGEEEERRRR,,,,____GGGGEEEERRRRUUUU,,,,____GGGGEEEERRRRCCCC((((3333FFFF))))
  137.  
  138.  
  139.  
  140.      yyyy       Array of size at least ( 1 + ( n - 1 )*abs( incy ) ). Before
  141.              entry, the incremented array yyyy must contain the n element vector
  142.              y.
  143.              Unchanged on exit.
  144.  
  145.      iiiinnnnccccyyyy    On entry, iiiinnnnccccyyyy specifies the increment for the elements of yyyy.
  146.              iiiinnnnccccyyyy must not be zero.
  147.              Unchanged on exit.
  148.  
  149.      aaaa       An array containing the matrix A.
  150.  
  151.              FFFFOOOORRRRTTTTRRRRAAAANNNN
  152.              Array of dimension ( lda, n ).
  153.  
  154.              CCCC
  155.              A pointer to an array of size lda*n.
  156.              See note below about array storage convention for C.
  157.  
  158.              Before entry, the leading m by n part of the array A must contain
  159.              the matrix of coefficients.  On exit, A is overwritten by the
  160.              updated matrix.
  161.  
  162.      llllddddaaaa     On entry, llllddddaaaa specifies the first dimension of aaaa as declared in
  163.              the calling (sub) program.  llllddddaaaa must be at least max( 1, m ).
  164.              Unchanged on exit.
  165.  
  166.  
  167. CCCC AAAARRRRRRRRAAAAYYYY SSSSTTTTOOOORRRRAAAAGGGGEEEE CCCCOOOONNNNVVVVEEEENNNNTTTTIIIIOOOONNNN
  168.        The matrices  are assumed  to be stored in a  oooonnnneeee ddddiiiimmmmeeeennnnssssiiiioooonnnnaaaallll CCCC aaaarrrrrrrraaaayyyy
  169.        in an analogous fashion as a Fortran array (column major). Therefore,
  170.        the element  A(i+1,j)  of matrix A  is stored  immediately  after the
  171.        element  A(i,j), while  A(i,j+1) is lda  elements apart from  A(i,j).
  172.        The element A(i,j) of the matrix can be accessed directly by reference
  173.        to  a[ (j-1)*lda + (i-1) ].
  174.  
  175.  
  176. AAAAUUUUTTTTHHHHOOOORRRRSSSS
  177.           Jack Dongarra, Argonne National Laboratory.
  178.           Iain Duff, AERE Harwell.
  179.           Jeremy Du Croz, Numerical Algorithms Group Ltd.
  180.           Sven Hammarling, Numerical Algorithms Group Ltd.
  181.  
  182.  
  183. TTTTUUUUNNNNIIIINNNNGGGG
  184.           Optimized and parallelized for SGI R3000, R4x00 and R8000 platforms.
  185.  
  186.  
  187.  
  188.  
  189.  
  190.  
  191.  
  192.  
  193.  
  194.  
  195.                                                                         PPPPaaaaggggeeee 3333
  196.  
  197.  
  198.  
  199.