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

Text File | 1998-10-30 | 15.2 KB | 265 lines

____GGGGEEEEMMMMVVVV((((3333FFFF))))                                                            ____GGGGEEEEMMMMVVVV((((3333FFFF))))



NNNNAAAAMMMMEEEE
     dgemv, sgemv, zgemv, cgemv - BLAS Level Two Matrix-Vector Product


FFFFOOOORRRRTTTTRRRRAAAANNNN 77777777 SSSSYYYYNNNNOOOOPPPPSSSSIIIISSSS
     ssssuuuubbbbrrrroooouuuuttttiiiinnnneeee ddddggggeeeemmmmvvvv(((( ttttrrrraaaannnnssss,,,,mmmm,,,,nnnn,,,,aaaallllpppphhhhaaaa,,,,aaaa,,,,llllddddaaaa,,,,xxxx,,,,iiiinnnnccccxxxx,,,,bbbbeeeettttaaaa,,,,yyyy,,,,iiiinnnnccccyyyy ))))
           cccchhhhaaaarrrraaaacccctttteeeerrrr****1111        ttttrrrraaaannnnssss
           iiiinnnntttteeeeggggeeeerrrr            nnnn,,,, mmmm,,,, llllddddaaaa,,,, iiiinnnnccccxxxx,,,, iiiinnnnccccyyyy
           ddddoooouuuubbbblllleeee pppprrrreeeecccciiiissssiiiioooonnnn   aaaallllpppphhhhaaaa,,,, bbbbeeeettttaaaa
           ddddoooouuuubbbblllleeee pppprrrreeeecccciiiissssiiiioooonnnn   aaaa(((( llllddddaaaa,,,,****)))),,,, xxxx((((****)))),,,, yyyy((((****))))

     ssssuuuubbbbrrrroooouuuuttttiiiinnnneeee ssssggggeeeemmmmvvvv(((( ttttrrrraaaannnnssss,,,,mmmm,,,,nnnn,,,,aaaallllpppphhhhaaaa,,,,aaaa,,,,llllddddaaaa,,,,xxxx,,,,iiiinnnnccccxxxx,,,,bbbbeeeettttaaaa,,,,yyyy,,,,iiiinnnnccccyyyy ))))
           cccchhhhaaaarrrraaaacccctttteeeerrrr****1111        ttttrrrraaaannnnssss
           iiiinnnntttteeeeggggeeeerrrr            nnnn,,,, mmmm,,,, llllddddaaaa,,,, iiiinnnnccccxxxx,,,, iiiinnnnccccyyyy
           rrrreeeeaaaallll               aaaallllpppphhhhaaaa,,,, bbbbeeeettttaaaa
           rrrreeeeaaaallll               aaaa(((( llllddddaaaa,,,,****)))),,,, xxxx((((****)))),,,, yyyy((((****))))

     ssssuuuubbbbrrrroooouuuuttttiiiinnnneeee zzzzggggeeeemmmmvvvv(((( ttttrrrraaaannnnssss,,,,mmmm,,,,nnnn,,,,aaaallllpppphhhhaaaa,,,,aaaa,,,,llllddddaaaa,,,,xxxx,,,,iiiinnnnccccxxxx,,,,bbbbeeeettttaaaa,,,,yyyy,,,,iiiinnnnccccyyyy ))))
           cccchhhhaaaarrrraaaacccctttteeeerrrr****1111        ttttrrrraaaannnnssss
           iiiinnnntttteeeeggggeeeerrrr            nnnn,,,, mmmm,,,, llllddddaaaa,,,, iiiinnnnccccxxxx,,,, iiiinnnnccccyyyy
           ddddoooouuuubbbblllleeee ccccoooommmmpppplllleeeexxxx     aaaallllpppphhhhaaaa,,,, bbbbeeeettttaaaa
           ddddoooouuuubbbblllleeee ccccoooommmmpppplllleeeexxxx     aaaa(((( llllddddaaaa,,,,****)))),,,, xxxx((((****)))),,,, yyyy((((****))))

     ssssuuuubbbbrrrroooouuuuttttiiiinnnneeee ccccggggeeeemmmmvvvv(((( ttttrrrraaaannnnssss,,,,mmmm,,,,nnnn,,,,aaaallllpppphhhhaaaa,,,,aaaa,,,,llllddddaaaa,,,,xxxx,,,,iiiinnnnccccxxxx,,,,bbbbeeeettttaaaa,,,,yyyy,,,,iiiinnnnccccyyyy ))))
           cccchhhhaaaarrrraaaacccctttteeeerrrr****1111        ttttrrrraaaannnnssss
           iiiinnnntttteeeeggggeeeerrrr            nnnn,,,, mmmm,,,, llllddddaaaa,,,, iiiinnnnccccxxxx,,,, iiiinnnnccccyyyy
           ccccoooommmmpppplllleeeexxxx            aaaallllpppphhhhaaaa,,,, bbbbeeeettttaaaa
           ccccoooommmmpppplllleeeexxxx            aaaa(((( llllddddaaaa,,,,****)))),,,, xxxx((((****)))),,,, yyyy((((****))))


CCCC SSSSYYYYNNNNOOOOPPPPSSSSIIIISSSS
     vvvvooooiiiidddd ddddggggeeeemmmmvvvv(((( ttttrrrraaaannnnssss,,,,mmmm,,,,nnnn,,,,aaaallllpppphhhhaaaa,,,,aaaa,,,,llllddddaaaa,,,,xxxx,,,,iiiinnnnccccxxxx,,,,bbbbeeeettttaaaa,,,,yyyy,,,,iiiinnnnccccyyyy ))))
           MMMMaaaattttrrrriiiixxxxTTTTrrrraaaannnnssssppppoooosssseeee    ttttrrrraaaannnnssss;;;;
           IIIInnnntttteeeeggggeeeerrrr            nnnn,,,, mmmm,,,, llllddddaaaa,,,, iiiinnnnccccxxxx,,,, iiiinnnnccccyyyy;;;;
           ddddoooouuuubbbblllleeee             aaaallllpppphhhhaaaa,,,, bbbbeeeettttaaaa;;;;
           ddddoooouuuubbbblllleeee            ((((****aaaa))))[[[[llllddddaaaa****nnnn]]]],,,, ((((****xxxx))))[[[[ nnnn ]]]],,,, ((((****yyyy))))[[[[ nnnn ]]]];;;;

     vvvvooooiiiidddd ssssggggeeeemmmmvvvv(((( ttttrrrraaaannnnssss,,,,mmmm,,,,nnnn,,,,aaaallllpppphhhhaaaa,,,,aaaa,,,,llllddddaaaa,,,,xxxx,,,,iiiinnnnccccxxxx,,,,bbbbeeeettttaaaa,,,,yyyy,,,,iiiinnnnccccyyyy ))))
           MMMMaaaattttrrrriiiixxxxTTTTrrrraaaannnnssssppppoooosssseeee    ttttrrrraaaannnnssss;;;;
           IIIInnnntttteeeeggggeeeerrrr            nnnn,,,, mmmm,,,, llllddddaaaa,,,, iiiinnnnccccxxxx,,,, iiiinnnnccccyyyy;;;;
           ffffllllooooaaaatttt              aaaallllpppphhhhaaaa,,,, bbbbeeeettttaaaa;;;;
           ffffllllooooaaaatttt             ((((****aaaa))))[[[[llllddddaaaa****nnnn]]]],,,, ((((****xxxx))))[[[[ nnnn ]]]],,,, ((((****yyyy))))[[[[ nnnn ]]]];;;;

     vvvvooooiiiidddd zzzzggggeeeemmmmvvvv(((( ttttrrrraaaannnnssss,,,,mmmm,,,,nnnn,,,,aaaallllpppphhhhaaaa,,,,aaaa,,,,llllddddaaaa,,,,xxxx,,,,iiiinnnnccccxxxx,,,,bbbbeeeettttaaaa,,,,yyyy,,,,iiiinnnnccccyyyy ))))
           MMMMaaaattttrrrriiiixxxxTTTTrrrraaaannnnssssppppoooosssseeee    ttttrrrraaaannnnssss;;;;
           IIIInnnntttteeeeggggeeeerrrr            nnnn,,,, mmmm,,,, llllddddaaaa,,,, iiiinnnnccccxxxx,,,, iiiinnnnccccyyyy;;;;
           ZZZZoooommmmpppplllleeeexxxx            aaaallllpppphhhhaaaa,,,, bbbbeeeettttaaaa;;;;
           ZZZZoooommmmpppplllleeeexxxx           ((((****aaaa))))[[[[llllddddaaaa****nnnn]]]],,,, ((((****xxxx))))[[[[ nnnn ]]]],,,, ((((****yyyy))))[[[[ nnnn ]]]];;;;

     vvvvooooiiiidddd ccccggggeeeemmmmvvvv(((( ttttrrrraaaannnnssss,,,,mmmm,,,,nnnn,,,,aaaallllpppphhhhaaaa,,,,aaaa,,,,llllddddaaaa,,,,xxxx,,,,iiiinnnnccccxxxx,,,,bbbbeeeettttaaaa,,,,yyyy,,,,iiiinnnnccccyyyy ))))
           MMMMaaaattttrrrriiiixxxxTTTTrrrraaaannnnssssppppoooosssseeee    ttttrrrraaaannnnssss;;;;
           IIIInnnntttteeeeggggeeeerrrr            nnnn,,,, mmmm,,,, llllddddaaaa,,,, iiiinnnnccccxxxx,,,, iiiinnnnccccyyyy;;;;



                                                                        PPPPaaaaggggeeee 1111






____GGGGEEEEMMMMVVVV((((3333FFFF))))                                                            ____GGGGEEEEMMMMVVVV((((3333FFFF))))



           CCCCoooommmmpppplllleeeexxxx            aaaallllpppphhhhaaaa,,,, bbbbeeeettttaaaa;;;;
           CCCCoooommmmpppplllleeeexxxx           ((((****aaaa))))[[[[llllddddaaaa****nnnn]]]],,,, ((((****xxxx))))[[[[ nnnn ]]]],,,, ((((****yyyy))))[[[[ nnnn ]]]];;;;


DDDDEEEESSSSCCCCRRRRIIIIPPPPTTTTIIIIOOOONNNN
     ddddggggeeeemmmmvvvv ,,,, ssssggggeeeemmmmvvvv ,,,, ddddggggeeeemmmmvvvv and ccccggggeeeemmmmvvvv perform one of the matrix-vector
     operations:

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

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

     where alpha and beta are scalars, x and y are vectors and A is an m by n
     matrix.


PPPPAAAARRRRAAAAMMMMEEEETTTTEEEERRRRSSSS
     ttttrrrraaaannnnssss   On entry, ttttrrrraaaannnnssss specifies the operation to be performed as
             follows:

             FFFFOOOORRRRTTTTRRRRAAAANNNN
             trans = 'N' or 'n'            y := alpha*A*x + beta*y.
             trans = 'T' or 't'            y := alpha*A'*x + beta*y.
             trans = 'C' or 'c'            y := alpha*conjg( A' )*x + beta*y.

             CCCC
             trans = NoTranspose           y := alpha*A*x + beta*y.
             trans = Transpose             y := alpha*A'*x + beta*y.
             trans = ConjugateTranspose    y := alpha*conjg( A' )*x + beta**y.

             Unchanged on exit.

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

     nnnn       On entry, nnnn specifies the order of the matrix A.  nnnn 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, n ).

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




                                                                        PPPPaaaaggggeeee 2222






____GGGGEEEEMMMMVVVV((((3333FFFF))))                                                            ____GGGGEEEEMMMMVVVV((((3333FFFF))))



             Before entry, the leading m by n part of the array A must contain
             the matrix of coefficients.
             Unchanged on exit.

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

     xxxx       Array of size at least ( 1 + ( n - 1 )*abs( incx ) ) when trans =
             'N' or 'n' or NoTranspose and at least ( 1 + ( m - 1 )*abs( incx
             ) ) otherwise. Before entry, the incremented array xxxx must contain
             the vector x.
             Unchanged on exit.

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

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

     yyyy       Array of size at least ( 1 + ( m - 1 )*abs( incy ) ) when trans =
             'N' or 'n' or NoTranspose and at least ( 1 + ( n - 1 )*abs( incy
             ) ) otherwise.

             Before entry with bbbbeeeettttaaaa non-zero, the incremented array yyyy must
             contain the vector y. On exit, yyyy 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.


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 3333






____GGGGEEEEMMMMVVVV((((3333FFFF))))                                                            ____GGGGEEEEMMMMVVVV((((3333FFFF))))



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





















































                                                                        PPPPaaaaggggeeee 4444