IRIX Base Documentation 1998 November/IRIX 6.5.2 Base Documentation November 1998.img/usr/share/catman/p_man/cat3/libblas/syr2.z/syr2

Text File | 1998-10-30 | 15KB | 265 lines

____SSSSYYYYRRRR2222,,,,____HHHHEEEERRRR2222((((3333FFFF))))                                                ____SSSSYYYYRRRR2222,,,,____HHHHEEEERRRR2222((((3333FFFF))))



NNNNAAAAMMMMEEEE
     dsyr2, ssyr2, zher2, cher2 - BLAS Level Two
     (Symmetric/Hermitian)Matrix Rank 2 Update


FFFFOOOORRRRTTTTRRRRAAAANNNN 77777777 SSSSYYYYNNNNOOOOPPPPSSSSIIIISSSS
     ssssuuuubbbbrrrroooouuuuttttiiiinnnneeee ddddssssyyyyrrrr2222(((( uuuupppplllloooo,,,, nnnn,,,, aaaallllpppphhhhaaaa,,,, xxxx,,,, iiiinnnnccccxxxx,,,, yyyy,,,, iiiinnnnccccyyyy,,,, aaaa,,,, llllddddaaaa ))))
           cccchhhhaaaarrrraaaacccctttteeeerrrr****1111        uuuupppplllloooo
           iiiinnnntttteeeeggggeeeerrrr            nnnn,,,, iiiinnnnccccxxxx,,,, iiiinnnnccccyyyy,,,, llllddddaaaa
           ddddoooouuuubbbblllleeee pppprrrreeeecccciiiissssiiiioooonnnn   aaaallllpppphhhhaaaa
           ddddoooouuuubbbblllleeee pppprrrreeeecccciiiissssiiiioooonnnn   aaaa(((( llllddddaaaa,,,,****)))),,,, xxxx((((****)))),,,, yyyy((((****))))

     ssssuuuubbbbrrrroooouuuuttttiiiinnnneeee ssssssssyyyyrrrr2222(((( uuuupppplllloooo,,,, nnnn,,,, aaaallllpppphhhhaaaa,,,, xxxx,,,, iiiinnnnccccxxxx,,,, yyyy,,,, iiiinnnnccccyyyy,,,, aaaa,,,, llllddddaaaa))))
           cccchhhhaaaarrrraaaacccctttteeeerrrr****1111        uuuupppplllloooo
           iiiinnnntttteeeeggggeeeerrrr            nnnn,,,, iiiinnnnccccxxxx,,,, iiiinnnnccccyyyy,,,, llllddddaaaa
           rrrreeeeaaaallll               aaaallllpppphhhhaaaa
           rrrreeeeaaaallll               aaaa(((( llllddddaaaa,,,,****)))),,,, xxxx((((****)))),,,, yyyy((((****))))

     ssssuuuubbbbrrrroooouuuuttttiiiinnnneeee zzzzhhhheeeerrrr2222(((( uuuupppplllloooo,,,, nnnn,,,, aaaallllpppphhhhaaaa,,,, xxxx,,,, iiiinnnnccccxxxx,,,, yyyy,,,, iiiinnnnccccyyyy,,,, aaaa,,,, llllddddaaaa))))
           cccchhhhaaaarrrraaaacccctttteeeerrrr****1111        uuuupppplllloooo
           iiiinnnntttteeeeggggeeeerrrr            nnnn,,,, iiiinnnnccccxxxx,,,, iiiinnnnccccyyyy,,,, llllddddaaaa
           ccccoooommmmpppplllleeeexxxx****11116666         aaaallllpppphhhhaaaa
           ccccoooommmmpppplllleeeexxxx****11116666         aaaa(((( llllddddaaaa,,,,****)))),,,, xxxx((((****)))),,,, yyyy((((****))))

     ssssuuuubbbbrrrroooouuuuttttiiiinnnneeee cccchhhheeeerrrr2222(((( uuuupppplllloooo,,,, nnnn,,,, aaaallllpppphhhhaaaa,,,, xxxx,,,, iiiinnnnccccxxxx,,,, yyyy,,,, iiiinnnnccccyyyy,,,, aaaa,,,, llllddddaaaa))))
           cccchhhhaaaarrrraaaacccctttteeeerrrr****1111        uuuupppplllloooo
           iiiinnnntttteeeeggggeeeerrrr            nnnn,,,, iiiinnnnccccxxxx,,,, iiiinnnnccccyyyy,,,, llllddddaaaa
           ccccoooommmmpppplllleeeexxxx            aaaallllpppphhhhaaaa
           ccccoooommmmpppplllleeeexxxx            aaaa(((( llllddddaaaa,,,,****)))),,,, xxxx((((****)))),,,, yyyy((((****))))



CCCC SSSSYYYYNNNNOOOOPPPPSSSSIIIISSSS
     vvvvooooiiiidddd ddddssssyyyyrrrr2222(((( uuuupppplllloooo,,,, nnnn,,,, aaaallllpppphhhhaaaa,,,, xxxx,,,, iiiinnnnccccxxxx,,,, yyyy,,,, iiiinnnnccccyyyy,,,, aaaa,,,, llllddddaaaa ))))
           MMMMaaaattttrrrriiiixxxxTTTTrrrriiiiaaaannnngggglllleeee     uuuupppplllloooo;;;;
           IIIInnnntttteeeeggggeeeerrrr            nnnn,,,, iiiinnnnccccxxxx,,,, iiiinnnnccccyyyy,,,, llllddddaaaa;;;;
           ddddoooouuuubbbblllleeee             aaaallllpppphhhhaaaa
           ddddoooouuuubbbblllleeee             ((((****aaaa))))[[[[llllddddaaaa****nnnn]]]],,,, ((((****xxxx))))[[[[ nnnn ]]]],,,, ((((****yyyy))))[[[[ nnnn ]]]];;;;

     vvvvooooiiiidddd ssssssssyyyyrrrr2222(((( uuuupppplllloooo,,,, nnnn,,,, aaaallllpppphhhhaaaa,,,, xxxx,,,, iiiinnnnccccxxxx,,,, yyyy,,,, iiiinnnnccccyyyy,,,, aaaa,,,, llllddddaaaa ))))
           MMMMaaaattttrrrriiiixxxxTTTTrrrriiiiaaaannnngggglllleeee     uuuupppplllloooo;;;;
           IIIInnnntttteeeeggggeeeerrrr            nnnn,,,, iiiinnnnccccxxxx,,,, iiiinnnnccccyyyy,,,, llllddddaaaa;;;;
           ffffllllooooaaaatttt              aaaallllpppphhhhaaaa
           ffffllllooooaaaatttt              ((((****aaaa))))[[[[llllddddaaaa****nnnn]]]],,,, ((((****xxxx))))[[[[ nnnn ]]]],,,, ((((****yyyy))))[[[[ nnnn ]]]];;;;

     vvvvooooiiiidddd zzzzhhhheeeerrrr2222(((( uuuupppplllloooo,,,, nnnn,,,, aaaallllpppphhhhaaaa,,,, xxxx,,,, iiiinnnnccccxxxx,,,, yyyy,,,, iiiinnnnccccyyyy,,,, aaaa,,,, llllddddaaaa ))))
           MMMMaaaattttrrrriiiixxxxTTTTrrrriiiiaaaannnngggglllleeee     uuuupppplllloooo;;;;
           IIIInnnntttteeeeggggeeeerrrr            nnnn,,,, iiiinnnnccccxxxx,,,, iiiinnnnccccyyyy,,,, llllddddaaaa;;;;
           ZZZZoooommmmpppplllleeeexxxx            aaaallllpppphhhhaaaa
           ZZZZoooommmmpppplllleeeexxxx            ((((****aaaa))))[[[[llllddddaaaa****nnnn]]]],,,, ((((****xxxx))))[[[[ nnnn ]]]],,,, ((((****yyyy))))[[[[ nnnn ]]]];;;;

     vvvvooooiiiidddd cccchhhheeeerrrr2222(((( uuuupppplllloooo,,,, nnnn,,,, aaaallllpppphhhhaaaa,,,, xxxx,,,, iiiinnnnccccxxxx,,,, yyyy,,,, iiiinnnnccccyyyy,,,, aaaa,,,, llllddddaaaa ))))



                                                                        PPPPaaaaggggeeee 1111






____SSSSYYYYRRRR2222,,,,____HHHHEEEERRRR2222((((3333FFFF))))                                                ____SSSSYYYYRRRR2222,,,,____HHHHEEEERRRR2222((((3333FFFF))))



           MMMMaaaattttrrrriiiixxxxTTTTrrrriiiiaaaannnngggglllleeee     uuuupppplllloooo;;;;
           IIIInnnntttteeeeggggeeeerrrr            nnnn,,,, iiiinnnnccccxxxx,,,, iiiinnnnccccyyyy,,,, llllddddaaaa;;;;
           CCCCoooommmmpppplllleeeexxxx            aaaallllpppphhhhaaaa
           CCCCoooommmmpppplllleeeexxxx            ((((****aaaa))))[[[[llllddddaaaa****nnnn]]]],,,, ((((****xxxx))))[[[[ nnnn ]]]],,,, ((((****yyyy))))[[[[ nnnn ]]]];;;;



DDDDEEEESSSSCCCCRRRRIIIIPPPPTTTTIIIIOOOONNNN
     ddddssssyyyyrrrr2222 and ssssssssyyyyrrrr2222 perform the symmetric rank 2 operation

           A := alpha*x*y' + alpha*y*x' + A,

     zzzzhhhheeeerrrr2222 and cccchhhheeeerrrr2222 perform the hermitian rank 2 operation

           A := alpha*x*conjg( y' ) + conjg( alpha )*y*conjg( x' ) + A,

     where alpha is a scalar, x and y are n element vectors and A is an n by n
     symmetric/hermitian matrix.


PPPPAAAARRRRAAAAMMMMEEEETTTTEEEERRRRSSSS
     uuuupppplllloooo    On entry, uuuupppplllloooo specifies whether the upper or lower triangular
             part of the array A is to be referenced a follows:



             FFFFOOOORRRRTTTTRRRRAAAANNNN
             uplo = 'U' or 'u'   Only the upper triangular part of A
                                 is to be referenced.
             uplo = 'L' or 'l'   Only the lower triangular part of A
                                 is to be referenced.

             CCCC
             uplo = UpperTriangle     Only the lower triangular part of A
                                      is to be referenced.
             uplo = LowerTriangle     Only the lower triangular part of A
                                      is to be referenced.

             Unchanged on exit.

     nnnn       On entry, nnnn specifies the the order of the matrix A.  nnnn must be
             at least zero.
             Unchanged on exit.

     aaaallllpppphhhhaaaa   specifies the scalar alpha.
             Unchanged on exit.

     xxxx       Array of size at least ( 1 + ( n - 1 )*abs( incx ) ). Before
             entry, the incremented array xxxx must contain the n element vector
             x.
             Unchanged on exit.




                                                                        PPPPaaaaggggeeee 2222






____SSSSYYYYRRRR2222,,,,____HHHHEEEERRRR2222((((3333FFFF))))                                                ____SSSSYYYYRRRR2222,,,,____HHHHEEEERRRR2222((((3333FFFF))))



     iiiinnnnccccxxxx    On entry, iiiinnnnccccxxxx specifies the increment for the elements of xxxx.
             iiiinnnnccccxxxx must not be zero.
             Unchanged on exit.

     yyyy       Array of size at least ( 1 + ( n - 1 )*abs( incy ) ). Before
             entry, the incremented array yyyy must contain the n element vector
             y. On exit, Y is overwritten by the updated vector y.

     iiiinnnnccccyyyy    On entry, iiiinnnnccccyyyy specifies the increment for the elements of yyyy.
             iiiinnnnccccyyyy must not be zero.
             Unchanged on exit.

     aaaa       An array containing the matrix A.

             FFFFOOOORRRRTTTTRRRRAAAANNNN
             Array of dimension ( lda, n ).

             CCCC
             A pointer to an array of size lda*n.
             See note below about array storage convention for C.

             Before entry with uuuupppplllloooo ==== ''''UUUU'''' oooorrrr ''''uuuu'''' oooorrrr , the array elements
             corresponding to the leading n by n upper triangular part of the
             matrix A must contain the uppertriangular part of the
             symmetric/hermitian matrix and the corresponding strictly lower
             triangular part of A is not referenced. On exit, the array
             elements corresponding to the upper triangular part of the matrix
             A is overwritten by the upper triangular part of the updated
             matrix.

             Before entry with uuuupppplllloooo ==== ''''LLLL'''' oooorrrr ''''llll'''' oooorrrr , the array elements
             corresponding to the leading n by n lower triangular part of the
             matrix A must contain the lower triangular part of the
             symmetric/hermitian matrix and the corresponding strictly upper
             triangular part of A is not referenced. On exit, the array
             elements corresponding to the lower triangular part of the matrix
             A is overwritten by the lower triangular part of the updated
             matrix.

             Note that the imaginary parts of the diagonal elements need not
             be set and are assumed to be zero.

     llllddddaaaa     On entry, llllddddaaaa specifies the first dimension of A as declared in
             the calling (sub) program. llllddddaaaa must be at least ( k + 1 ).
             Unchanged on exit.


CCCC AAAARRRRRRRRAAAAYYYY SSSSTTTTOOOORRRRAAAAGGGGEEEE CCCCOOOONNNNVVVVEEEENNNNTTTTIIIIOOOONNNN
       The matrices  are assumed  to be stored in a  oooonnnneeee ddddiiiimmmmeeeennnnssssiiiioooonnnnaaaallll CCCC aaaarrrrrrrraaaayyyy
       in an analogous fashion as a Fortran array (column major). Therefore,
       the element  A(i+1,j)  of matrix A  is stored  immediately  after the
       element  A(i,j), while  A(i,j+1) is lda  elements apart from  A(i,j).



                                                                        PPPPaaaaggggeeee 3333






____SSSSYYYYRRRR2222,,,,____HHHHEEEERRRR2222((((3333FFFF))))                                                ____SSSSYYYYRRRR2222,,,,____HHHHEEEERRRR2222((((3333FFFF))))



       The element A(i,j) of the matrix can be accessed directly by reference
       to  a[ (j-1)*lda + (i-1) ].


AAAAUUUUTTTTHHHHOOOORRRRSSSS
          Jack Dongarra, Argonne National Laboratory.
          Iain Duff, AERE Harwell.
          Jeremy Du Croz, Numerical Algorithms Group Ltd.
          Sven Hammarling, Numerical Algorithms Group Ltd.














































                                                                        PPPPaaaaggggeeee 4444