IRIX Base Documentation 2001 May/SGI IRIX Base Documentation 2001 May.iso/usr/share/catman/p_man/cat3/libblas/hemm.z/hemm

Text File | 1998-10-30 | 15.6 KB | 331 lines

____HHHHEEEEMMMMMMMM((((3333FFFF))))                                                            ____HHHHEEEEMMMMMMMM((((3333FFFF))))



NNNNAAAAMMMMEEEE
     zhemm, chemm - BLAS level three   Hermitian Matrix Product


FFFFOOOORRRRTTTTRRRRAAAANNNN 77777777 SSSSYYYYNNNNOOOOPPPPSSSSIIIISSSS
     ssssuuuubbbbrrrroooouuuuttttiiiinnnneeee zzzzhhhheeeemmmmmmmm(((( ssssiiiiddddeeee,,,,uuuupppplllloooo,,,,mmmm,,,,nnnn,,,,aaaallllpppphhhhaaaa,,,,aaaa,,,,llllddddaaaa,,,,bbbb,,,,llllddddbbbb,,,,bbbbeeeettttaaaa,,,,cccc,,,,llllddddcccc ))))
           cccchhhhaaaarrrraaaacccctttteeeerrrr****1111        ssssiiiiddddeeee,,,,uuuupppplllloooo
           iiiinnnntttteeeeggggeeeerrrr            mmmm,,,, nnnn,,,, llllddddaaaa,,,, llllddddbbbb,,,, llllddddcccc
           ddddoooouuuubbbblllleeee ccccoooommmmpppplllleeeexxxx     aaaallllpppphhhhaaaa,,,, bbbbeeeettttaaaa
           ddddoooouuuubbbblllleeee ccccoooommmmpppplllleeeexxxx     aaaa(((( llllddddaaaa,,,,****)))),,,, bbbb((((llllddddbbbb,,,,****)))),,,, cccc((((llllddddcccc,,,,****))))

     ssssuuuubbbbrrrroooouuuuttttiiiinnnneeee cccchhhheeeemmmmmmmm(((( ssssiiiiddddeeee,,,,uuuupppplllloooo,,,,mmmm,,,,nnnn,,,,aaaallllpppphhhhaaaa,,,,aaaa,,,,llllddddaaaa,,,,bbbb,,,,llllddddbbbb,,,,bbbbeeeettttaaaa,,,,cccc,,,,llllddddcccc ))))
           cccchhhhaaaarrrraaaacccctttteeeerrrr****1111        ssssiiiiddddeeee,,,,uuuupppplllloooo
           iiiinnnntttteeeeggggeeeerrrr            mmmm,,,, nnnn,,,, llllddddaaaa,,,, llllddddbbbb,,,, llllddddcccc
           ccccoooommmmpppplllleeeexxxx            aaaallllpppphhhhaaaa,,,, bbbbeeeettttaaaa
           ccccoooommmmpppplllleeeexxxx            aaaa(((( llllddddaaaa,,,,****)))),,,, bbbb((((llllddddbbbb,,,,****)))),,,, cccc((((llllddddcccc,,,,****))))


CCCC SSSSYYYYNNNNOOOOPPPPSSSSIIIISSSS
     vvvvooooiiiidddd zzzzhhhheeeemmmmmmmm(((( ssssiiiiddddeeee,,,,uuuupppplllloooo,,,,mmmm,,,,nnnn,,,,aaaallllpppphhhhaaaa,,,,aaaa,,,,llllddddaaaa,,,,bbbb,,,,llllddddbbbb,,,,bbbbeeeettttaaaa,,,,cccc,,,,llllddddcccc ))))
           OOOOppppeeeerrrraaaattttiiiioooonnnnSSSSiiiiddddeeee         ssssiiiiddddeeee;;;;
           MMMMaaaattttrrrriiiixxxxTTTTrrrriiiiaaaannnngggglllleeee        uuuupppplllloooo;;;;
           IIIInnnntttteeeeggggeeeerrrr               mmmm,,,, nnnn,,,, llllddddaaaa,,,, llllddddbbbb,,,, llllddddcccc;;;;
           ZZZZoooommmmpppplllleeeexxxx               ((((****aaaa))))[[[[llllddddaaaa****kkkkaaaa]]]],,,, ((((****bbbb))))[[[[llllddddaaaa****nnnn]]]],,,, ((((****cccc))))[[[[llllddddaaaa****kkkkbbbb]]]];;;;

     vvvvooooiiiidddd cccchhhheeeemmmmmmmm(((( ssssiiiiddddeeee,,,,uuuupppplllloooo,,,,mmmm,,,,nnnn,,,,aaaallllpppphhhhaaaa,,,,aaaa,,,,llllddddaaaa,,,,bbbb,,,,llllddddbbbb,,,,bbbbeeeettttaaaa,,,,cccc,,,,llllddddcccc ))))
           OOOOppppeeeerrrraaaattttiiiioooonnnnSSSSiiiiddddeeee         ssssiiiiddddeeee;;;;
           MMMMaaaattttrrrriiiixxxxTTTTrrrriiiiaaaannnngggglllleeee        uuuupppplllloooo;;;;
           IIIInnnntttteeeeggggeeeerrrr               mmmm,,,, nnnn,,,, llllddddaaaa,,,, llllddddbbbb,,,, llllddddcccc;;;;
           CCCCoooommmmpppplllleeeexxxx               ((((****aaaa))))[[[[llllddddaaaa****kkkkaaaa]]]],,,, ((((****bbbb))))[[[[llllddddaaaa****nnnn]]]],,,, ((((****cccc))))[[[[llllddddaaaa****kkkkbbbb]]]];;;;


DDDDEEEESSSSCCCCRRRRIIIIPPPPTTTTIIIIOOOONNNN
     zzzzhhhheeeemmmmmmmm and cccchhhheeeemmmmmmmm perform one of the matrix-matrix operations

               C := alpha*A*B + beta*C, or

               C := alpha*B*A + beta*C,

     where alpha and beta are scalars, A is an hermitian matrix and B and C
     are m by n matrices.


PPPPAAAARRRRAAAAMMMMEEEETTTTEEEERRRRSSSS
     ssssiiiiddddeeee    specifies whether the hermitian matrix A appears on the left or
             right in the operation as follows:


                  FFFFOOOORRRRTTTTRRRRAAAANNNN
                  side = 'L' or 'l'        C := alpha*A*B + beta*C
                  side = 'R' or 'r'        C := alpha*B*A + beta*C




                                                                        PPPPaaaaggggeeee 1111






____HHHHEEEEMMMMMMMM((((3333FFFF))))                                                            ____HHHHEEEEMMMMMMMM((((3333FFFF))))



                 CCCC
                  side = LeftSide          C := alpha*A*B + beta*C
                  side = RightSide         C := alpha*B*A + beta*C

             Unchanged on exit.

     uuuupppplllloooo    On  entry, uuuupppplllloooo specifies whether the upper or lower triangular
             part of the hermitian matrix A is to be referenced as follows:


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

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

             Unchanged on exit.

     mmmm       On entry, mmmm specifies the number of rows of the matrix C. mmmm must
             be at least zero.
             Unchanged on exit.

     nnnn       On entry, nnnn specifies the number of columns of the matrix C. nnnn
             must be at least zero.
             Unchanged on exit.

     aaaallllpppphhhhaaaa   On entry, aaaallllpppphhhhaaaa specifies the scalar alpha.






















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____HHHHEEEEMMMMMMMM((((3333FFFF))))                                                            ____HHHHEEEEMMMMMMMM((((3333FFFF))))



             Unchanged on exit.

     aaaa       An array containing the matrix A.

             FFFFOOOORRRRTTTTRRRRAAAANNNN
             Array of dimension (lda, ka).

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

             kkkkaaaa is mmmm when side = 'L' or 'l' or LeftSide and is nnnn when side =
             'R' or 'r' or RightSide.

             Before entry with uuuupppplllloooo ==== ''''LLLL'''' oooorrrr ''''llll'''' oooorrrr LLLLoooowwwweeeerrrrTTTTrrrriiiiaaaannnngggglllleeee , the
             elements of the array aaaa corresponding to the m by m matrix A must
             contain the hermitian matrix, such that when uuuupppplllloooo ==== ''''UUUU'''' oooorrrr ''''uuuu'''' oooorrrr
             UUUUppppppppeeeerrrrTTTTrrrriiiiaaaannnngggglllleeee , the elements of the array aaaa corresponding to the
             leading m by m upper triangular part of the matrix A must contain
             the upper triangular part of the hermitian matrix and the
             elements corresponding to the strictly lower triangular part of A
             are not referenced. When uuuupppplllloooo ==== ''''LLLL'''' oooorrrr ''''llll'''' oooorrrr LLLLoooowwwweeeerrrrTTTTrrrriiiiaaaannnngggglllleeee , the
             elements of the array aaaa corresponding to the leading m by m lower
             triangular part of the matrix A must contain the lower triangular
             part of the hermitian matrix and the elements corresponding to
             the strictly upper triangular part of A are not referenced.

             Before entry with ssssiiiiddddeeee ==== ''''RRRR'''' oooorrrr ''''rrrr'''' oooorrrr RRRRiiiigggghhhhttttSSSSiiiiddddeeee , the elements
             of the array aaaa corresponding to the n by n matrix A must contain
             the hermitian matrix, such that when uuuupppplllloooo ==== ''''UUUU'''' oooorrrr ''''uuuu'''' oooorrrr
             UUUUppppppppeeeerrrrTTTTrrrriiiiaaaannnngggglllleeee , the elements of the array aaaa corresponding to the
             leading n by n upper triangular part of the matrix A must contain
             the upper triangular part of the hermitian matrix and the
             elements corresponding to the strictly lower triangular part of A
             are not referenced. When uuuupppplllloooo ==== ''''LLLL'''' oooorrrr ''''llll'''' oooorrrr LLLLoooowwwweeeerrrrTTTTrrrriiiiaaaannnngggglllleeee , the
             elements of the array aaaa corresponding to the leading n by n lower
             triangular part of the matrix A must contain the lower triangular
             part of the hermitian matrix and the elements corresponding to
             the strictly upper triangular part of A are not referenced.

             Note that the imaginary parts corresponding to the diagonal
             elements need not be set, they are assumed to be zero.

             Unchanged on exit.

     llllddddaaaa     On entry, llllddddaaaa specifies the first dimension of A as declared in
             the calling (sub) program. When side = 'L' or 'l' or LeftSide,
             then lda must be at least max( 1, m ). When side = 'R' or 'r' or
             RightSide, then lda must be at least max( 1, n ).
             Unchanged on exit.





                                                                        PPPPaaaaggggeeee 3333






____HHHHEEEEMMMMMMMM((((3333FFFF))))                                                            ____HHHHEEEEMMMMMMMM((((3333FFFF))))



     BBBB       An array containing the matrix B.

             FFFFOOOORRRRTTTTRRRRAAAANNNN
             An array of dimension ( ldb, n ).

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

             Before entry, the elements of bbbb that correspond to the leading m
             by n part of the matrix B should contain the elements
             corresponding to the m by n matrix B.

             Unchanged on exit.

     llllddddbbbb     On entry, llllddddbbbb specifies the first dimension of B as declared in
             the calling (sub)program. ldb
              must be at least max( 1, m ).
             Unchanged on exit.

     bbbbeeeettttaaaa    On entry, bbbbeeeettttaaaa specifies the scalar beta.  When bbbbeeeettttaaaa is supplied
             as zero then cccc need not be set on input.
             Unchanged on exit.

     cccc       An array containing the matrix C.

             FFFFOOOORRRRTTTTRRRRAAAANNNN
             An array of dimension ( ldc, n ).

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

             Before entry, the leading m by n part of the array cccc must contain
             the matrix C, except when beta is zero, in which case cccc need not
             be set on entry.

             On exit, the array cccc is overwritten by the m by n updated matrix.

     llllddddcccc     On entry, llllddddcccc specifies the first dimension of cccc as declared in
             the calling (sub) program. llllddddcccc must be at least max( 1, m ).
             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).
       The element A(i,j) of the matrix can be accessed directly by reference
       to  a[ (j-1)*lda + (i-1) ].




                                                                        PPPPaaaaggggeeee 4444






____HHHHEEEEMMMMMMMM((((3333FFFF))))                                                            ____HHHHEEEEMMMMMMMM((((3333FFFF))))



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


TTTTUUUUNNNNIIIINNNNGGGG
          Optimized and parallelized for SGI R3000, R4x00 and R8000 platforms.














































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