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

Text File | 1998-10-30 | 19.1 KB | 331 lines

____GGGGEEEEMMMMMMMM((((3333FFFF))))                                                            ____GGGGEEEEMMMMMMMM((((3333FFFF))))



NNNNAAAAMMMMEEEE
     dgemm, sgemm, zgemm, cgemm - BLAS level three Matrix Product


FFFFOOOORRRRTTTTRRRRAAAANNNN 77777777 SSSSYYYYNNNNOOOOPPPPSSSSIIIISSSS
     ssssuuuubbbbrrrroooouuuuttttiiiinnnneeee ddddggggeeeemmmmmmmm(((( ttttrrrraaaannnnssssaaaa,,,,ttttrrrraaaannnnssssbbbb,,,,mmmm,,,,nnnn,,,,kkkk,,,,aaaallllpppphhhhaaaa,,,,aaaa,,,,llllddddaaaa,,,,bbbb,,,,llllddddbbbb,,,,bbbbeeeettttaaaa,,,,cccc,,,,llllddddcccc ))))
           cccchhhhaaaarrrraaaacccctttteeeerrrr****1111        ttttrrrraaaannnnssssaaaa,,,, ttttrrrraaaannnnssssbbbb
           iiiinnnntttteeeeggggeeeerrrr            mmmm,,,, nnnn,,,, kkkk,,,, llllddddaaaa,,,, llllddddbbbb,,,, llllddddcccc
           ddddoooouuuubbbblllleeee pppprrrreeeecccciiiissssiiiioooonnnn   aaaallllpppphhhhaaaa,,,, bbbbeeeettttaaaa
           ddddoooouuuubbbblllleeee pppprrrreeeecccciiiissssiiiioooonnnn   aaaa(((( llllddddaaaa,,,,****)))),,,, bbbb((((llllddddbbbb,,,,****)))),,,, cccc((((llllddddcccc,,,,****))))

     ssssuuuubbbbrrrroooouuuuttttiiiinnnneeee ssssggggeeeemmmmmmmm(((( ttttrrrraaaannnnssssaaaa,,,,ttttrrrraaaannnnssssbbbb,,,,mmmm,,,,nnnn,,,,kkkk,,,,aaaallllpppphhhhaaaa,,,,aaaa,,,,llllddddaaaa,,,,bbbb,,,,llllddddbbbb,,,,bbbbeeeettttaaaa,,,,cccc,,,,llllddddcccc ))))
           cccchhhhaaaarrrraaaacccctttteeeerrrr****1111        ttttrrrraaaannnnssssaaaa,,,, ttttrrrraaaannnnssssbbbb
           iiiinnnntttteeeeggggeeeerrrr            mmmm,,,, nnnn,,,, kkkk,,,, llllddddaaaa,,,, llllddddbbbb,,,, llllddddcccc
           rrrreeeeaaaallll               aaaallllpppphhhhaaaa,,,, bbbbeeeettttaaaa
           rrrreeeeaaaallll               aaaa(((( llllddddaaaa,,,,****)))),,,, bbbb((((llllddddbbbb,,,,****)))),,,, cccc((((llllddddcccc,,,,****))))

     ssssuuuubbbbrrrroooouuuuttttiiiinnnneeee zzzzggggeeeemmmmmmmm(((( ttttrrrraaaannnnssssaaaa,,,,ttttrrrraaaannnnssssbbbb,,,,mmmm,,,,nnnn,,,,kkkk,,,,aaaallllpppphhhhaaaa,,,,aaaa,,,,llllddddaaaa,,,,bbbb,,,,llllddddbbbb,,,,bbbbeeeettttaaaa,,,,cccc,,,,llllddddcccc ))))
           cccchhhhaaaarrrraaaacccctttteeeerrrr****1111        ttttrrrraaaannnnssssaaaa,,,, ttttrrrraaaannnnssssbbbb
           iiiinnnntttteeeeggggeeeerrrr            mmmm,,,, nnnn,,,, kkkk,,,, llllddddaaaa,,,, llllddddbbbb,,,, llllddddcccc
           ddddoooouuuubbbblllleeee ccccoooommmmpppplllleeeexxxx     aaaallllpppphhhhaaaa,,,, bbbbeeeettttaaaa
           ddddoooouuuubbbblllleeee ccccoooommmmpppplllleeeexxxx     aaaa(((( llllddddaaaa,,,,****)))),,,, bbbb((((llllddddbbbb,,,,****)))),,,, cccc((((llllddddcccc,,,,****))))

     ssssuuuubbbbrrrroooouuuuttttiiiinnnneeee ccccggggeeeemmmmmmmm(((( ttttrrrraaaannnnssssaaaa,,,,ttttrrrraaaannnnssssbbbb,,,,mmmm,,,,nnnn,,,,kkkk,,,,aaaallllpppphhhhaaaa,,,,aaaa,,,,llllddddaaaa,,,,bbbb,,,,llllddddbbbb,,,,bbbbeeeettttaaaa,,,,cccc,,,,llllddddcccc ))))
           cccchhhhaaaarrrraaaacccctttteeeerrrr****1111        ttttrrrraaaannnnssssaaaa,,,, ttttrrrraaaannnnssssbbbb
           iiiinnnntttteeeeggggeeeerrrr            mmmm,,,, nnnn,,,, kkkk,,,, llllddddaaaa,,,, llllddddbbbb,,,, llllddddcccc
           ccccoooommmmpppplllleeeexxxx            aaaallllpppphhhhaaaa,,,, bbbbeeeettttaaaa
           ccccoooommmmpppplllleeeexxxx            aaaa(((( llllddddaaaa,,,,****)))),,,, bbbb((((llllddddbbbb,,,,****)))),,,, cccc((((llllddddcccc,,,,****))))


CCCC SSSSYYYYNNNNOOOOPPPPSSSSIIIISSSS
     vvvvooooiiiidddd ddddggggeeeemmmmmmmm(((( ttttrrrraaaannnnssssaaaa,,,,ttttrrrraaaannnnssssbbbb,,,,mmmm,,,,nnnn,,,,kkkk,,,,aaaallllpppphhhhaaaa,,,,aaaa,,,,llllddddaaaa,,,,bbbb,,,,llllddddbbbb,,,,bbbbeeeettttaaaa,,,,cccc,,,,llllddddcccc ))))
           MMMMaaaattttrrrriiiixxxxTTTTrrrraaaannnnssssppppoooosssseeee       ttttrrrraaaannnnssssaaaa,,,, ttttrrrraaaannnnssssbbbb;;;;
           IIIInnnntttteeeeggggeeeerrrr               mmmm,,,, nnnn,,,, kkkk,,,, llllddddaaaa,,,, llllddddbbbb,,,, llllddddcccc;;;;
           ddddoooouuuubbbblllleeee                aaaallllpppphhhhaaaa,,,, bbbbeeeettttaaaa;;;;
           ddddoooouuuubbbblllleeee                ((((****aaaa))))[[[[llllddddaaaa****kkkkaaaa]]]],,,, ((((****bbbb))))[[[[llllddddaaaa****nnnn]]]],,,, ((((****cccc))))[[[[llllddddaaaa****kkkkbbbb]]]];;;;

     vvvvooooiiiidddd ssssggggeeeemmmmmmmm(((( ttttrrrraaaannnnssssaaaa,,,,ttttrrrraaaannnnssssbbbb,,,,mmmm,,,,nnnn,,,,kkkk,,,,aaaallllpppphhhhaaaa,,,,aaaa,,,,llllddddaaaa,,,,bbbb,,,,llllddddbbbb,,,,bbbbeeeettttaaaa,,,,cccc,,,,llllddddcccc ))))
           MMMMaaaattttrrrriiiixxxxTTTTrrrraaaannnnssssppppoooosssseeee       ttttrrrraaaannnnssssaaaa,,,, ttttrrrraaaannnnssssbbbb;;;;
           IIIInnnntttteeeeggggeeeerrrr               mmmm,,,, nnnn,,,, kkkk,,,, llllddddaaaa,,,, llllddddbbbb,,,, llllddddcccc;;;;
           ffffllllooooaaaatttt                 aaaallllpppphhhhaaaa,,,, bbbbeeeettttaaaa;;;;
           ffffllllooooaaaatttt                 ((((****aaaa))))[[[[llllddddaaaa****kkkkaaaa]]]],,,, ((((****bbbb))))[[[[llllddddaaaa****nnnn]]]],,,, ((((****cccc))))[[[[llllddddaaaa****kkkkbbbb]]]];;;;

     vvvvooooiiiidddd zzzzggggeeeemmmmmmmm(((( ttttrrrraaaannnnssssaaaa,,,,ttttrrrraaaannnnssssbbbb,,,,mmmm,,,,nnnn,,,,kkkk,,,,aaaallllpppphhhhaaaa,,,,aaaa,,,,llllddddaaaa,,,,bbbb,,,,llllddddbbbb,,,,bbbbeeeettttaaaa,,,,cccc,,,,llllddddcccc ))))
           MMMMaaaattttrrrriiiixxxxTTTTrrrraaaannnnssssppppoooosssseeee       ttttrrrraaaannnnssssaaaa,,,, ttttrrrraaaannnnssssbbbb;;;;
           IIIInnnntttteeeeggggeeeerrrr               mmmm,,,, nnnn,,,, kkkk,,,, llllddddaaaa,,,, llllddddbbbb,,,, llllddddcccc;;;;
           ZZZZoooommmmpppplllleeeexxxx               aaaallllpppphhhhaaaa,,,, bbbbeeeettttaaaa;;;;
           ZZZZoooommmmpppplllleeeexxxx               ((((****aaaa))))[[[[llllddddaaaa****kkkkaaaa]]]],,,, ((((****bbbb))))[[[[llllddddaaaa****nnnn]]]],,,, ((((****cccc))))[[[[llllddddaaaa****kkkkbbbb]]]];;;;

     vvvvooooiiiidddd ccccggggeeeemmmmmmmm(((( ttttrrrraaaannnnssssaaaa,,,,ttttrrrraaaannnnssssbbbb,,,,mmmm,,,,nnnn,,,,kkkk,,,,aaaallllpppphhhhaaaa,,,,aaaa,,,,llllddddaaaa,,,,bbbb,,,,llllddddbbbb,,,,bbbbeeeettttaaaa,,,,cccc,,,,llllddddcccc ))))
           MMMMaaaattttrrrriiiixxxxTTTTrrrraaaannnnssssppppoooosssseeee       ttttrrrraaaannnnssssaaaa,,,, ttttrrrraaaannnnssssbbbb;;;;
           IIIInnnntttteeeeggggeeeerrrr               mmmm,,,, nnnn,,,, kkkk,,,, llllddddaaaa,,,, llllddddbbbb,,,, llllddddcccc;;;;



                                                                        PPPPaaaaggggeeee 1111






____GGGGEEEEMMMMMMMM((((3333FFFF))))                                                            ____GGGGEEEEMMMMMMMM((((3333FFFF))))



           CCCCoooommmmpppplllleeeexxxx               aaaallllpppphhhhaaaa,,,, bbbbeeeettttaaaa;;;;
           CCCCoooommmmpppplllleeeexxxx               ((((****aaaa))))[[[[llllddddaaaa****kkkkaaaa]]]],,,, ((((****bbbb))))[[[[llllddddaaaa****nnnn]]]],,,, ((((****cccc))))[[[[llllddddaaaa****kkkkbbbb]]]];;;;




DDDDEEEESSSSCCCCRRRRIIIIPPPPTTTTIIIIOOOONNNN
     ddddggggeeeemmmmmmmm, ssssggggeeeemmmmmmmm, zzzzggggeeeemmmmmmmm and ccccggggeeeemmmmmmmm perform one of the matrix-matrix operations

                    C := alpha*op( A )*op( B ) + beta*C,

     where  op( X ) is one of

                    op( X ) = X   or   op( X ) = X',

     alpha and beta are scalars, and A, B and C are matrices, with op( A ) an
     m by k matrix, op( B ) a k by n matrix and C an m by n matrix.


PPPPAAAARRRRAAAAMMMMEEEETTTTEEEERRRRSSSS
     ttttrrrraaaannnnssssaaaa  On entry, ttttrrrraaaannnnssssaaaa specifies the form of op( A ) to be used in the
             matrix multiplication as follows:

                  FFFFOOOORRRRTTTTRRRRAAAANNNN
                  transa = 'N' or 'n',     op( A ) = A.
                  transa = 'T' or 't',     op( A ) = A'.
                  transa = 'C' or 'c',     op( A ) = conjg( A').

                  CCCC
                  transa = NoTranspose          op( A ) = A.
                  transa = Transpose            op( A ) = A'.
                  transa = ConjugateTranspose   op( A ) = conjg( A').

             Unchanged on exit.

     ttttrrrraaaannnnssssbbbb  On entry, ttttrrrraaaannnnssssbbbb specifies the form of op( B ) to be used in the
             matrix multiplication as follows:

                  FFFFOOOORRRRTTTTRRRRAAAANNNN
                  transb = 'N' or 'n',     op( B ) = B.
                  transb = 'T' or 't',     op( B ) = B'.
                  transb = 'C' or 'c',     op( B ) = conjg( B' ).

                  CCCC
                  transb = NoTranspose          op( B ) = B.
                  transb = Transpose            op( B ) = B'.
                  transb = ConjugateTranspose   op( B ) = conjg( B' ).

             Unchanged on exit.






                                                                        PPPPaaaaggggeeee 2222






____GGGGEEEEMMMMMMMM((((3333FFFF))))                                                            ____GGGGEEEEMMMMMMMM((((3333FFFF))))



     mmmm       On entry, mmmm specifies the number of rows of the matrix op( A )
             and 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 op( B )
             and the number of columns of the matrix C. nnnn must be at least
             zero.
             Unchanged on exit.

     kkkk       On entry, kkkk specifies the number of columns of the matrix op( A )
             and the number of rows of the matrix op( B ).  kkkk must be at least
             zero.
             Unchanged on exit.

     aaaallllpppphhhhaaaa   On entry, aaaallllpppphhhhaaaa specifies the scalar alpha.
             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 kkkk when transa = 'N' or 'n' or NoTranspose and is mmmm
             otherwise.  Before entry with transa = 'N' or 'n' or NoTranspose,
             the leading m by k part of the array aaaa must contain the matrix A,
             otherwise the leading  k by m  part of the array aaaa must contain
             the matrix A.

             Unchanged on exit.

     llllddddaaaa     On entry, llllddddaaaa specifies the first dimension of aaaa as declared in
             the calling (sub) program. When  transa = 'N' or 'n' or
             NoTranspose, then lda must be at least max( 1, m ), otherwise lda
             must be at least  max( 1, k ).
             Unchanged on exit.

     bbbb       An array containing the matrix B.

             FFFFOOOORRRRTTTTRRRRAAAANNNN
             An array of dimension ( ldb, kb ).

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

             kkkkbbbb is nnnn when transb = 'N' or 'n' or NoTranspose, and is k
             otherwise. Before entry with transb = 'N' or 'n' or NoTranspose,
             the leading k by n part of the array bbbb must contain the matrix B,



                                                                        PPPPaaaaggggeeee 3333






____GGGGEEEEMMMMMMMM((((3333FFFF))))                                                            ____GGGGEEEEMMMMMMMM((((3333FFFF))))



             otherwise the leading n by k part of the array bbbb must contain the
             matrix B.

             Unchanged on exit.

     llllddddbbbb     On entry, llllddddbbbb specifies the first dimension of bbbb as declared in
             the calling (sub)program. When  transb = 'N' or 'n' or
             NoTranspose then ldb must be at least  max( 1, k ), otherwise ldb
             must be at least  max( 1, n ).
             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 matrix

                       ( alpha*op( A )*op( B ) + beta*C ).

     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) ].


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






____GGGGEEEEMMMMMMMM((((3333FFFF))))                                                            ____GGGGEEEEMMMMMMMM((((3333FFFF))))



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





















































                                                                        PPPPaaaaggggeeee 5555