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

Text File | 1998-10-30 | 20.0 KB | 331 lines

____TTTTRRRRSSSSMMMM((((3333FFFF))))                                                            ____TTTTRRRRSSSSMMMM((((3333FFFF))))



NNNNAAAAMMMMEEEE
     dtrsm, strsm, ztrsm, ctrsm - BLAS level three Solution of Systems of
     Equations


FFFFOOOORRRRTTTTRRRRAAAANNNN 77777777 SSSSYYYYNNNNOOOOPPPPSSSSIIIISSSS
     ssssuuuubbbbrrrroooouuuuttttiiiinnnneeee ddddttttrrrrssssmmmm(((( ssssiiiiddddeeee,,,, uuuupppplllloooo,,,, ttttrrrraaaannnnssssaaaa,,,, ddddiiiiaaaagggg,,,, mmmm,,,, nnnn,,,, aaaallllpppphhhhaaaa,,,, aaaa,,,, llllddddaaaa,,,, bbbb,,,, llllddddbbbb ))))
           cccchhhhaaaarrrraaaacccctttteeeerrrr****1111        ssssiiiiddddeeee,,,,uuuupppplllloooo,,,,ttttrrrraaaannnnssssaaaa,,,,ddddiiiiaaaagggg
           iiiinnnntttteeeeggggeeeerrrr            mmmm,,,, nnnn,,,, llllddddaaaa,,,, llllddddbbbb
           ddddoooouuuubbbblllleeee pppprrrreeeecccciiiissssiiiioooonnnn   aaaallllpppphhhhaaaa
           ddddoooouuuubbbblllleeee pppprrrreeeecccciiiissssiiiioooonnnn   aaaa(((( llllddddaaaa,,,,****)))),,,, bbbb((((llllddddbbbb,,,,****))))

     ssssuuuubbbbrrrroooouuuuttttiiiinnnneeee ssssttttrrrrssssmmmm(((( ssssiiiiddddeeee,,,, uuuupppplllloooo,,,, ttttrrrraaaannnnssssaaaa,,,, ddddiiiiaaaagggg,,,, mmmm,,,, nnnn,,,, aaaallllpppphhhhaaaa,,,, aaaa,,,, llllddddaaaa,,,, bbbb,,,, llllddddbbbb ))))
           cccchhhhaaaarrrraaaacccctttteeeerrrr****1111        ssssiiiiddddeeee,,,,uuuupppplllloooo,,,,ttttrrrraaaannnnssssaaaa,,,,ddddiiiiaaaagggg
           iiiinnnntttteeeeggggeeeerrrr            mmmm,,,, nnnn,,,, llllddddaaaa,,,, llllddddbbbb
           rrrreeeeaaaallll               aaaallllpppphhhhaaaa
           rrrreeeeaaaallll               aaaa(((( llllddddaaaa,,,,****)))),,,, bbbb((((llllddddbbbb,,,,****))))

     ssssuuuubbbbrrrroooouuuuttttiiiinnnneeee zzzzttttrrrrssssmmmm(((( ssssiiiiddddeeee,,,, uuuupppplllloooo,,,, ttttrrrraaaannnnssssaaaa,,,, ddddiiiiaaaagggg,,,, mmmm,,,, nnnn,,,, aaaallllpppphhhhaaaa,,,, aaaa,,,, llllddddaaaa,,,, bbbb,,,, llllddddbbbb ))))
           cccchhhhaaaarrrraaaacccctttteeeerrrr****1111        ssssiiiiddddeeee,,,,uuuupppplllloooo,,,,ttttrrrraaaannnnssssaaaa,,,,ddddiiiiaaaagggg
           iiiinnnntttteeeeggggeeeerrrr            mmmm,,,, nnnn,,,, llllddddaaaa,,,, llllddddbbbb
           ddddoooouuuubbbblllleeee ccccoooommmmpppplllleeeexxxx     aaaallllpppphhhhaaaa
           ddddoooouuuubbbblllleeee ccccoooommmmpppplllleeeexxxx     aaaa(((( llllddddaaaa,,,,****)))),,,, bbbb((((llllddddbbbb,,,,****))))

     ssssuuuubbbbrrrroooouuuuttttiiiinnnneeee ccccttttrrrrssssmmmm(((( ssssiiiiddddeeee,,,, uuuupppplllloooo,,,, ttttrrrraaaannnnssssaaaa,,,, ddddiiiiaaaagggg,,,, mmmm,,,, nnnn,,,, aaaallllpppphhhhaaaa,,,, aaaa,,,, llllddddaaaa,,,, bbbb,,,, llllddddbbbb ))))
           cccchhhhaaaarrrraaaacccctttteeeerrrr****1111        ssssiiiiddddeeee,,,,uuuupppplllloooo,,,,ttttrrrraaaannnnssssaaaa,,,,ddddiiiiaaaagggg
           iiiinnnntttteeeeggggeeeerrrr            mmmm,,,, nnnn,,,, llllddddaaaa,,,, llllddddbbbb
           ccccoooommmmpppplllleeeexxxx            aaaallllpppphhhhaaaa
           ccccoooommmmpppplllleeeexxxx            aaaa(((( llllddddaaaa,,,,****)))),,,, bbbb((((llllddddbbbb,,,,****))))


CCCC SSSSYYYYNNNNOOOOPPPPSSSSIIIISSSS
     vvvvooooiiiidddd ddddttttrrrrssssmmmm(((( ssssiiiiddddeeee,,,, uuuupppplllloooo,,,, ttttrrrraaaannnnssssaaaa,,,, ddddiiiiaaaagggg,,,, mmmm,,,, nnnn,,,, aaaallllpppphhhhaaaa,,,, aaaa,,,, llllddddaaaa,,,, bbbb,,,, llllddddbbbb ))))
           OOOOppppeeeerrrraaaattttiiiioooonnnnSSSSiiiiddddeeee         ssssiiiiddddeeee;;;;
           MMMMaaaattttrrrriiiixxxxTTTTrrrriiiiaaaannnngggglllleeee        uuuupppplllloooo;;;;
           MMMMaaaattttrrrriiiixxxxTTTTrrrraaaannnnssssppppoooosssseeee       ttttrrrraaaannnnssssaaaa;;;;
           MMMMaaaattttrrrriiiixxxxUUUUnnnniiiittttTTTTrrrriiiiaaaannnngggguuuullllaaaarrrr  ddddiiiiaaaagggg;;;;
           IIIInnnntttteeeeggggeeeerrrr               mmmm,,,, nnnn,,,, ttttddddaaaa,,,, ttttddddbbbb;;;;
           ddddoooouuuubbbblllleeee                aaaallllpppphhhhaaaa;;;;
           ddddoooouuuubbbblllleeee                ((((****aaaa))))[[[[llllddddaaaa****kkkk]]]],,,, ((((****bbbb))))[[[[llllddddaaaa****nnnn]]]];;;;

     vvvvooooiiiidddd ssssttttrrrrssssmmmm(((( ssssiiiiddddeeee,,,, uuuupppplllloooo,,,, ttttrrrraaaannnnssssaaaa,,,, ddddiiiiaaaagggg,,,, mmmm,,,, nnnn,,,, aaaallllpppphhhhaaaa,,,, aaaa,,,, llllddddaaaa,,,, bbbb,,,, llllddddbbbb ))))
           OOOOppppeeeerrrraaaattttiiiioooonnnnSSSSiiiiddddeeee         ssssiiiiddddeeee;;;;
           MMMMaaaattttrrrriiiixxxxTTTTrrrriiiiaaaannnngggglllleeee        uuuupppplllloooo;;;;
           MMMMaaaattttrrrriiiixxxxTTTTrrrraaaannnnssssppppoooosssseeee       ttttrrrraaaannnnssssaaaa;;;;
           MMMMaaaattttrrrriiiixxxxUUUUnnnniiiittttTTTTrrrriiiiaaaannnngggguuuullllaaaarrrr  ddddiiiiaaaagggg;;;;
           IIIInnnntttteeeeggggeeeerrrr               mmmm,,,, nnnn,,,, llllddddaaaa,,,, llllddddbbbb;;;;
           ffffllllooooaaaatttt                 aaaallllpppphhhhaaaa;;;;
           ffffllllooooaaaatttt                 ((((****aaaa))))[[[[llllddddaaaa****kkkk]]]],,,, ((((****bbbb))))[[[[llllddddaaaa****nnnn]]]];;;;

     vvvvooooiiiidddd zzzzttttrrrrssssmmmm(((( ssssiiiiddddeeee,,,, uuuupppplllloooo,,,, ttttrrrraaaannnnssssaaaa,,,, ddddiiiiaaaagggg,,,, mmmm,,,, nnnn,,,, aaaallllpppphhhhaaaa,,,, aaaa,,,, llllddddaaaa,,,, bbbb,,,, llllddddbbbb ))))
           OOOOppppeeeerrrraaaattttiiiioooonnnnSSSSiiiiddddeeee         ssssiiiiddddeeee;;;;



                                                                        PPPPaaaaggggeeee 1111






____TTTTRRRRSSSSMMMM((((3333FFFF))))                                                            ____TTTTRRRRSSSSMMMM((((3333FFFF))))



           MMMMaaaattttrrrriiiixxxxTTTTrrrriiiiaaaannnngggglllleeee        uuuupppplllloooo;;;;
           MMMMaaaattttrrrriiiixxxxTTTTrrrraaaannnnssssppppoooosssseeee       ttttrrrraaaannnnssssaaaa;;;;
           MMMMaaaattttrrrriiiixxxxUUUUnnnniiiittttTTTTrrrriiiiaaaannnngggguuuullllaaaarrrr  ddddiiiiaaaagggg;;;;
           IIIInnnntttteeeeggggeeeerrrr               mmmm,,,, nnnn,,,, llllddddaaaa,,,, llllddddbbbb;;;;
           ZZZZoooommmmpppplllleeeexxxx               aaaallllpppphhhhaaaa;;;;
           ZZZZoooommmmpppplllleeeexxxx               ((((****aaaa))))[[[[llllddddaaaa****kkkk]]]],,,, ((((****bbbb))))[[[[llllddddaaaa****nnnn]]]];;;;

     vvvvooooiiiidddd ccccttttrrrrssssmmmm(((( ssssiiiiddddeeee,,,, uuuupppplllloooo,,,, ttttrrrraaaannnnssssaaaa,,,, ddddiiiiaaaagggg,,,, mmmm,,,, nnnn,,,, aaaallllpppphhhhaaaa,,,, aaaa,,,, llllddddaaaa,,,, bbbb,,,, llllddddbbbb ))))
           OOOOppppeeeerrrraaaattttiiiioooonnnnSSSSiiiiddddeeee         ssssiiiiddddeeee;;;;
           MMMMaaaattttrrrriiiixxxxTTTTrrrriiiiaaaannnngggglllleeee        uuuupppplllloooo;;;;
           MMMMaaaattttrrrriiiixxxxTTTTrrrraaaannnnssssppppoooosssseeee       ttttrrrraaaannnnssssaaaa;;;;
           MMMMaaaattttrrrriiiixxxxUUUUnnnniiiittttTTTTrrrriiiiaaaannnngggguuuullllaaaarrrr  ddddiiiiaaaagggg;;;;
           IIIInnnntttteeeeggggeeeerrrr               mmmm,,,, nnnn,,,, llllddddaaaa,,,, llllddddbbbb;;;;
           CCCCoooommmmpppplllleeeexxxx               aaaallllpppphhhhaaaa;;;;
           CCCCoooommmmpppplllleeeexxxx               ((((****aaaa))))[[[[llllddddaaaa****kkkk]]]],,,, ((((****bbbb))))[[[[llllddddaaaa****nnnn]]]];;;;



DDDDEEEESSSSCCCCRRRRIIIIPPPPTTTTIIIIOOOONNNN
     ddddttttrrrrssssmmmm, ssssttttrrrrssssmmmm, zzzzttttrrrrssssmmmm and ccccttttrrrrssssmmmm solve one of the matrix equations

           op( A )*X = alpha*B,   or   X*op( A ) = alpha*B,

     where alpha is a scalar, X and B are m by n matrices, A is a unit, or
     non-unit,  upper or lower triangular matrix  and  op( A )  is one  of

           op( A ) = A   or   op( A ) = A'   or   op( A ) = conjg( A' ).

     The matrix X is overwritten on B.


PPPPAAAARRRRAAAAMMMMEEEETTTTEEEERRRRSSSS
     ssssiiiiddddeeee    On entry, ssssiiiiddddeeee specifies whether op( A ) appears on the left or
             right of X as follows:


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

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

             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.



                                                                        PPPPaaaaggggeeee 2222






____TTTTRRRRSSSSMMMM((((3333FFFF))))                                                            ____TTTTRRRRSSSSMMMM((((3333FFFF))))



                     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.

     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.

     ddddiiiiaaaagggg    On entry, ddddiiiiaaaagggg specifies whether or not A is unit triangular as
             follows:

                  FFFFOOOORRRRTTTTRRRRAAAANNNN
                  diag = 'U' or 'u'   A is assumed to be unit
                                      triangular.
                  diag = 'N' or 'n'   A is not assumed to be unit
                                      triangular.

                  CCCC
                  diag = UnitTriangular    A is assumed to be unit
                                           triangular.
                  diag = NotUnitTriangular A is not assumed to be unit
                                           triangular.

             Unchanged on exit.

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

     nnnn       On entry, nnnn specifies the number of columns of B.  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.
             Unchanged on exit.




                                                                        PPPPaaaaggggeeee 3333






____TTTTRRRRSSSSMMMM((((3333FFFF))))                                                            ____TTTTRRRRSSSSMMMM((((3333FFFF))))



     aaaa       An array containing the matrix A.

             FFFFOOOORRRRTTTTRRRRAAAANNNN
             Array of dimension (lda, k).

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

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

             Before entry with uuuupppplllloooo ==== ''''UUUU'''' oooorrrr ''''uuuu'''' oooorrrr , the elements
             corresponding to the leading  k by k upper triangular elements of
             the matrix A must contain the upper triangular matrix and the
             corresponding strictly lower triangular part of the matrix A is
             not referenced.

             Before entry with uuuupppplllloooo ==== ''''LLLL'''' oooorrrr ''''llll'''' oooorrrr , the elements
             corresponding to the leading k by k lower triangular elements of
             the matrix A  must contain the lower triangular matrix and the
             corresponding strictly upper triangular part of the matrix A is
             not referenced.

             Note that when ddddiiiiaaaagggg ==== ''''UUUU'''' oooorrrr ''''uuuu'''' oooorrrr , the elements corresponding
             to the diagonal elements of the matrix A are not referenced
             either, but are assumed to be unity.

             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' then lda must
             be at least max( 1, m ), when side = 'R' or 'r' then lda must be
             at least max( 1, n ).
             Unchanged on exit.

     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 it should contain the elements corresponding to the
             m by n matrix B.  On exit it overwritten by the transformed
             matrix.







                                                                        PPPPaaaaggggeeee 4444






____TTTTRRRRSSSSMMMM((((3333FFFF))))                                                            ____TTTTRRRRSSSSMMMM((((3333FFFF))))



     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.


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.


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
































                                                                        PPPPaaaaggggeeee 5555