IRIX Base Documentation 2001 May/SGI IRIX Base Documentation 2001 May.iso/usr/share/catman/p_man/cat3/libblas/syr2k.z/syr2k

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

____SSSSYYYYRRRR2222KKKK((((3333FFFF))))                                                          ____SSSSYYYYRRRR2222KKKK((((3333FFFF))))



NNNNAAAAMMMMEEEE
     dsyr2k, ssyr2k, zsyr2k, csyr2k - BLAS level three  Symmetric Rank 2K
     Update.


FFFFOOOORRRRTTTTRRRRAAAANNNN 77777777 SSSSYYYYNNNNOOOOPPPPSSSSIIIISSSS
     ssssuuuubbbbrrrroooouuuuttttiiiinnnneeee ddddssssyyyyrrrr2222kkkk((((uuuupppplllloooo,,,,ttttrrrraaaannnnssss,,,,nnnn,,,,kkkk,,,,aaaallllpppphhhhaaaa,,,,aaaa,,,,llllddddaaaa,,,,bbbb,,,,llllddddbbbb,,,,bbbbeeeettttaaaa,,,,cccc,,,,llllddddcccc))))
           cccchhhhaaaarrrraaaacccctttteeeerrrr****1111        uuuupppplllloooo,,,, ttttrrrraaaannnnssss
           iiiinnnntttteeeeggggeeeerrrr            nnnn,,,, kkkk,,,, llllddddaaaa,,,, llllddddbbbb,,,, llllddddcccc
           ddddoooouuuubbbblllleeee pppprrrreeeecccciiiissssiiiioooonnnn   aaaallllpppphhhhaaaa,,,, bbbbeeeettttaaaa
           ddddoooouuuubbbblllleeee pppprrrreeeecccciiiissssiiiioooonnnn   aaaa(((( llllddddaaaa,,,,****)))),,,, bbbb(((( llllddddbbbb,,,,****)))),,,, cccc((((llllddddcccc,,,,****))))

     ssssuuuubbbbrrrroooouuuuttttiiiinnnneeee ssssssssyyyyrrrr2222kkkk((((uuuupppplllloooo,,,,ttttrrrraaaannnnssss,,,,nnnn,,,,kkkk,,,,aaaallllpppphhhhaaaa,,,,aaaa,,,,llllddddaaaa,,,,bbbb,,,,llllddddbbbb,,,,bbbbeeeettttaaaa,,,,cccc,,,,llllddddcccc))))
           cccchhhhaaaarrrraaaacccctttteeeerrrr****1111        uuuupppplllloooo,,,, ttttrrrraaaannnnssss
           iiiinnnntttteeeeggggeeeerrrr            nnnn,,,, kkkk,,,, llllddddaaaa,,,, llllddddbbbb,,,, llllddddcccc
           rrrreeeeaaaallll               aaaallllpppphhhhaaaa,,,, bbbbeeeettttaaaa
           rrrreeeeaaaallll               aaaa(((( llllddddaaaa,,,,****)))),,,, bbbb(((( llllddddbbbb,,,,****)))),,,, cccc((((llllddddcccc,,,,****))))

     ssssuuuubbbbrrrroooouuuuttttiiiinnnneeee zzzzssssyyyyrrrr2222kkkk((((uuuupppplllloooo,,,,ttttrrrraaaannnnssss,,,,nnnn,,,,kkkk,,,,aaaallllpppphhhhaaaa,,,,aaaa,,,,llllddddaaaa,,,,bbbb,,,,llllddddbbbb,,,,bbbbeeeettttaaaa,,,,cccc,,,,llllddddcccc))))
           cccchhhhaaaarrrraaaacccctttteeeerrrr****1111        uuuupppplllloooo,,,, ttttrrrraaaannnnssss
           iiiinnnntttteeeeggggeeeerrrr            nnnn,,,, kkkk,,,, llllddddaaaa,,,, llllddddbbbb,,,, llllddddcccc
           ddddoooouuuubbbblllleeee ccccoooommmmpppplllleeeexxxx     aaaallllpppphhhhaaaa,,,, bbbbeeeettttaaaa
           ddddoooouuuubbbblllleeee ccccoooommmmpppplllleeeexxxx     aaaa(((( llllddddaaaa,,,,****)))),,,, bbbb(((( llllddddbbbb,,,,****)))),,,, cccc((((llllddddcccc,,,,****))))

     ssssuuuubbbbrrrroooouuuuttttiiiinnnneeee ccccssssyyyyrrrr2222kkkk((((uuuupppplllloooo,,,,ttttrrrraaaannnnssss,,,,nnnn,,,,kkkk,,,,aaaallllpppphhhhaaaa,,,,aaaa,,,,llllddddaaaa,,,,bbbb,,,,llllddddbbbb,,,,bbbbeeeettttaaaa,,,,cccc,,,,llllddddcccc))))
           cccchhhhaaaarrrraaaacccctttteeeerrrr****1111        uuuupppplllloooo,,,, ttttrrrraaaannnnssss
           iiiinnnntttteeeeggggeeeerrrr            nnnn,,,, kkkk,,,, llllddddaaaa,,,, llllddddbbbb,,,, llllddddcccc
           ccccoooommmmpppplllleeeexxxx            aaaallllpppphhhhaaaa,,,, bbbbeeeettttaaaa
           ccccoooommmmpppplllleeeexxxx            aaaa(((( llllddddaaaa,,,,****)))),,,, bbbb(((( llllddddbbbb,,,,****)))),,,, cccc((((llllddddcccc,,,,****))))



CCCC SSSSYYYYNNNNOOOOPPPPSSSSIIIISSSS
     vvvvooooiiiidddd ddddssssyyyyrrrr2222kkkk((((uuuupppplllloooo,,,,ttttrrrraaaannnnssss,,,,nnnn,,,,kkkk,,,,aaaallllpppphhhhaaaa,,,,aaaa,,,,llllddddaaaa,,,,bbbb,,,,llllddddbbbb,,,,bbbbeeeettttaaaa,,,,cccc,,,,llllddddcccc))))
           MMMMaaaattttrrrriiiixxxxTTTTrrrriiiiaaaannnngggglllleeee     uuuupppplllloooo;;;;
           MMMMaaaattttrrrriiiixxxxTTTTrrrraaaannnnssssppppoooosssseeee    ttttrrrraaaannnnssss;;;;
           IIIInnnntttteeeeggggeeeerrrr            nnnn,,,, kkkk,,,, llllddddaaaa,,,, llllddddbbbb,,,, llllddddcccc;;;;
           ddddoooouuuubbbblllleeee             aaaallllpppphhhhaaaa,,,, bbbbeeeettttaaaa;;;;
           ddddoooouuuubbbblllleeee             ((((****aaaa))))[[[[llllddddaaaa****kkkk]]]],,,, ((((****bbbb))))[[[[llllddddaaaa****kkkk]]]],,,, ((((****cccc))))[[[[llllddddaaaa****nnnn]]]];;;;

     vvvvooooiiiidddd ssssssssyyyyrrrr2222kkkk((((uuuupppplllloooo,,,,ttttrrrraaaannnnssss,,,,nnnn,,,,kkkk,,,,aaaallllpppphhhhaaaa,,,,aaaa,,,,llllddddaaaa,,,,bbbb,,,,llllddddbbbb,,,,bbbbeeeettttaaaa,,,,cccc,,,,llllddddcccc))))
           MMMMaaaattttrrrriiiixxxxTTTTrrrriiiiaaaannnngggglllleeee     uuuupppplllloooo;;;;
           MMMMaaaattttrrrriiiixxxxTTTTrrrraaaannnnssssppppoooosssseeee    ttttrrrraaaannnnssss;;;;
           IIIInnnntttteeeeggggeeeerrrr            nnnn,,,, kkkk,,,, llllddddaaaa,,,, llllddddbbbb,,,, llllddddcccc;;;;
           ffffllllooooaaaatttt              aaaallllpppphhhhaaaa,,,, bbbbeeeettttaaaa;;;;
           ffffllllooooaaaatttt              ((((****aaaa))))[[[[llllddddaaaa****kkkk]]]],,,, ((((****bbbb))))[[[[llllddddaaaa****kkkk]]]],,,, ((((****cccc))))[[[[llllddddaaaa****nnnn]]]];;;;

     vvvvooooiiiidddd zzzzssssyyyyrrrr2222kkkk((((uuuupppplllloooo,,,,ttttrrrraaaannnnssss,,,,nnnn,,,,kkkk,,,,aaaallllpppphhhhaaaa,,,,aaaa,,,,llllddddaaaa,,,,bbbb,,,,llllddddbbbb,,,,bbbbeeeettttaaaa,,,,cccc,,,,llllddddcccc))))
           MMMMaaaattttrrrriiiixxxxTTTTrrrriiiiaaaannnngggglllleeee     uuuupppplllloooo;;;;
           MMMMaaaattttrrrriiiixxxxTTTTrrrraaaannnnssssppppoooosssseeee    ttttrrrraaaannnnssss;;;;
           IIIInnnntttteeeeggggeeeerrrr            nnnn,,,, kkkk,,,, llllddddaaaa,,,, llllddddbbbb,,,, llllddddcccc;;;;
           ZZZZoooommmmpppplllleeeexxxx            aaaallllpppphhhhaaaa,,,, bbbbeeeettttaaaa;;;;



                                                                        PPPPaaaaggggeeee 1111






____SSSSYYYYRRRR2222KKKK((((3333FFFF))))                                                          ____SSSSYYYYRRRR2222KKKK((((3333FFFF))))



           ZZZZoooommmmpppplllleeeexxxx            ((((****aaaa))))[[[[llllddddaaaa****kkkk]]]],,,, ((((****bbbb))))[[[[llllddddaaaa****kkkk]]]],,,, ((((****cccc))))[[[[llllddddaaaa****nnnn]]]];;;;

     vvvvooooiiiidddd ccccssssyyyyrrrr2222kkkk((((uuuupppplllloooo,,,,ttttrrrraaaannnnssss,,,,nnnn,,,,kkkk,,,,aaaallllpppphhhhaaaa,,,,aaaa,,,,llllddddaaaa,,,,bbbb,,,,llllddddbbbb,,,,bbbbeeeettttaaaa,,,,cccc,,,,llllddddcccc))))
           MMMMaaaattttrrrriiiixxxxTTTTrrrriiiiaaaannnngggglllleeee     uuuupppplllloooo;;;;
           MMMMaaaattttrrrriiiixxxxTTTTrrrraaaannnnssssppppoooosssseeee    ttttrrrraaaannnnssss;;;;
           IIIInnnntttteeeeggggeeeerrrr            nnnn,,,, kkkk,,,, llllddddaaaa,,,, llllddddbbbb,,,, llllddddcccc;;;;
           CCCCoooommmmpppplllleeeexxxx            aaaallllpppphhhhaaaa,,,, bbbbeeeettttaaaa;;;;
           CCCCoooommmmpppplllleeeexxxx            ((((****aaaa))))[[[[llllddddaaaa****kkkk]]]],,,, ((((****bbbb))))[[[[llllddddaaaa****kkkk]]]],,,, ((((****cccc))))[[[[llllddddaaaa****nnnn]]]];;;;



DDDDEEEESSSSCCCCRRRRIIIIPPPPTTTTIIIIOOOONNNN
     ddddssssyyyyrrrr2222kkkk ,,,, ssssssssyyyyrrrr2222kkkk ,,,, zzzzssssyyyyrrrr2222kkkk and ccccssssyyyyrrrr2222kkkk perform one of the matrix-matrix
     operations

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

     or

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

     where alpha and beta are scalars, C is an n by n symmetric matrix and A
     and B are n by k matrices in the first case and k by n matrices in the
     second case.


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

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

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

             Unchanged on exit.

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

             FFFFOOOORRRRTTTTRRRRAAAANNNN
             trans = 'N' or 'n'       C := alpha*A*B' + alpha*B*A' + beta*C.
             trans = 'T' or 't'       C := alpha*A'*B + alpha*B'*A + beta*C.

             CCCC



                                                                        PPPPaaaaggggeeee 2222






____SSSSYYYYRRRR2222KKKK((((3333FFFF))))                                                          ____SSSSYYYYRRRR2222KKKK((((3333FFFF))))



             trans = NoTranspose      C := alpha*A*B' + alpha*B*A' + beta*C.
             trans = Transpose        C := alpha*A'*B + alpha*B'*A + beta*C.

             Unchanged on exit.

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

     kkkk       On entry with, trans = 'N' or 'n' or NoTranspose kkkk specifies the
             number of columns of the matrices A and B, and on entry with
             trans = 'T' or 't' or Transpose, kkkk specifies  the number of rows
             of the matries A and B.  K must be at least zero.
             Unchanged on exit.

     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 nnnn
             otherwise.  Before entry with trans = 'N' or 'n' or NoTranspose,
             the leading n by k part of the array aaaa must contain the matrix A,
             otherwise the leading  k by n 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, n ), otherwise lda
             must be at least  max( 1, k ).
             Unchanged on exit.

     bbbb       An array containing the matrix B.

             FFFFOOOORRRRTTTTRRRRAAAANNNN
             Array of dimension (lda, kb).

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

             kkkkbbbb is kkkk when transa = 'N' or 'n' or NoTranspose and is nnnn
             otherwise.  Before entry with trans = 'N' or 'n' or NoTranspose,



                                                                        PPPPaaaaggggeeee 3333






____SSSSYYYYRRRR2222KKKK((((3333FFFF))))                                                          ____SSSSYYYYRRRR2222KKKK((((3333FFFF))))



             the leading n by k part of the array bbbb must contain the matrix B,
             otherwise the leading  k by n 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  trans = 'N' or 'n' or
             NoTranspose, then ldb must be at least max( 1, n ), otherwise lda
             must be at least  max( 1, k ).
             Unchanged on exit.

     bbbbeeeettttaaaa    On entry, bbbbeeeettttaaaa specifies the scalar beta.
             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  with uplo = 'U' or 'u' or UpperTraingle, the
             leading  n by n triangular part  of the  symmetric matrix  and
             the strictly lower triangular part of C is not referenced.  On
             exit, the upper triangular part of the array  C is overwritten by
             the upper triangular part of the updated matrix.

             Before entry  with  uplo = 'L' or 'l',  the leading  n by n lower
             triangular part of the array C must contain the lower triangular
             part  of the  symmetric matrix  and the strictly upper triangular
             part of C is not referenced.  On exit, the lower triangular part
             of the array  C is overwritten by the lower triangular part of
             the 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, n ).

             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






____SSSSYYYYRRRR2222KKKK((((3333FFFF))))                                                          ____SSSSYYYYRRRR2222KKKK((((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.














































                                                                        PPPPaaaaggggeeee 5555