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

Text File | 1998-10-30 | 20.7 KB | 397 lines

____SSSSYYYYMMMMMMMM((((3333FFFF))))                                                            ____SSSSYYYYMMMMMMMM((((3333FFFF))))



NNNNAAAAMMMMEEEE
     dsymm, ssymm, zsymm, csymm - BLAS level three   Symmetric Matrix Product


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

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

     ssssuuuubbbbrrrroooouuuuttttiiiinnnneeee zzzzssssyyyymmmmmmmm(((( 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 ccccssssyyyymmmmmmmm(((( 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 ddddssssyyyymmmmmmmm(((( ssssiiiiddddeeee,,,,uuuupppplllloooo,,,,mmmm,,,,nnnn,,,,aaaallllpppphhhhaaaa,,,,aaaa,,,,llllddddaaaa,,,,bbbb,,,,llllddddbbbb,,,,bbbbeeeettttaaaa,,,,cccc,,,,llllddddcccc ))))
           OOOOppppeeeerrrraaaattttiiiioooonnnnSSSSiiiiddddeeee         ssssiiiiddddeeee;;;;
           MMMMaaaattttrrrriiiixxxxTTTTrrrriiiiaaaannnngggglllleeee        uuuupppplllloooo;;;;
           IIIInnnntttteeeeggggeeeerrrr               mmmm,,,, nnnn,,,, llllddddaaaa,,,, llllddddbbbb,,,, llllddddcccc;;;;
           ddddoooouuuubbbblllleeee                aaaallllpppphhhhaaaa,,,, bbbbeeeettttaaaa;;;;
           ddddoooouuuubbbblllleeee                ((((****aaaa))))[[[[llllddddaaaa****kkkkaaaa]]]],,,, ((((****bbbb))))[[[[llllddddaaaa****nnnn]]]],,,, ((((****cccc))))[[[[llllddddaaaa****nnnn]]]];;;;

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

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




                                                                        PPPPaaaaggggeeee 1111






____SSSSYYYYMMMMMMMM((((3333FFFF))))                                                            ____SSSSYYYYMMMMMMMM((((3333FFFF))))



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



DDDDEEEESSSSCCCCRRRRIIIIPPPPTTTTIIIIOOOONNNN
     ddddssssyyyymmmmmmmm, ssssssssyyyymmmmmmmm, zzzzssssyyyymmmmmmmm and ccccssssyyyymmmmmmmm

     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 a symmetric matrix and B and C are
     m by n matrices.


PPPPAAAARRRRAAAAMMMMEEEETTTTEEEERRRRSSSS
     ssssiiiiddddeeee    On entry, ssssiiiiddddeeee specifies whether op( A ) multiplies B from the
             left or right as follows:


                  FFFFOOOORRRRTTTTRRRRAAAANNNN
                  side = 'L' or 'l'   B := alpha*op( A )*B.
                  side = 'R' or 'r'   B := alpha*B*op( A ).

                  CCCC
                  side = LeftSide     B := alpha*op( A )*B.
                  side = RightSide    B := alpha*B*op( A ).

             Unchanged on exit.

     uuuupppplllloooo    On entry, uuuupppplllloooo specifies whether the matrix A is an upper or
             lower triangular matrix as follows:


                  FFFFOOOORRRRTTTTRRRRAAAANNNN
                  uplo = 'U' or 'u'   A is an upper triangular matrix.
                  uplo = 'L' or 'l'   A is a lower triangular matrix.

                  CCCC
                  uplo = UpperTriangle     A is an upper triangular matrix.
                  uplo = LowerTriangle     A is a lower triangular matrix.

             Unchanged on exit.






                                                                        PPPPaaaaggggeeee 2222






____SSSSYYYYMMMMMMMM((((3333FFFF))))                                                            ____SSSSYYYYMMMMMMMM((((3333FFFF))))



     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. When aaaallllpppphhhhaaaa is zero
             then aaaa is not referenced and bbbb need not be set before entry.













































                                                                        PPPPaaaaggggeeee 3333






____SSSSYYYYMMMMMMMM((((3333FFFF))))                                                            ____SSSSYYYYMMMMMMMM((((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 otherwise.

             Before entry  with ssssiiiiddddeeee ==== ''''LLLL'''' oooorrrr ''''llll'''' oooorrrr LLLLeeeeffffttttSSSSiiiiddddeeee, the array
             elements corresponding to the m by m part of the matrix A must
             contain the symmetric matrix, such that when:
             uuuupppplllloooo ==== ''''UUUU'''' oooorrrr ''''uuuu'''' oooorrrr UUUUppppppppeeeerrrrTTTTrrrriiiiaaaannnngggglllleeee, the array elements that
             correspond to the leading m by m upper triangular part of the
             matrix A must contain the upper triangular part of the symmetric
             matrix and the corresponding strictly lower triangular part of A
             is not referenced,
             and when uuuupppplllloooo ==== ''''LLLL'''' oooorrrr ''''llll'''' oooorrrr LLLLoooowwwweeeerrrrTTTTrrrriiiiaaaannnngggglllleeee, the array elements
             that correspond to the leading m by m lower triangular part of
             the matrix A must contain the lower triangular part of the
             symmetric matrix and the corresponding strictly upper triangular
             part of A is not referenced.

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

             Unchanged on exit.

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

     bbbb       An array containing the matrix B.

             FFFFOOOORRRRTTTTRRRRAAAANNNN



                                                                        PPPPaaaaggggeeee 4444






____SSSSYYYYMMMMMMMM((((3333FFFF))))                                                            ____SSSSYYYYMMMMMMMM((((3333FFFF))))



             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 array elements corresponding to the leading m
             by n part of the matrix B 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. llllddddbbbb 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 elements corresponding to the leading m by n
             part of the matrix C 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) ].


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




                                                                        PPPPaaaaggggeeee 5555






____SSSSYYYYMMMMMMMM((((3333FFFF))))                                                            ____SSSSYYYYMMMMMMMM((((3333FFFF))))



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





















































                                                                        PPPPaaaaggggeeee 6666