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/ IRIX Base Documentation 2001 May / SGI IRIX Base Documentation 2001 May.iso / usr / share / catman / p_man / cat3 / libblas / tpmv.z / tpmv
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Text File  |  1998-10-30  |  17.3 KB  |  265 lines
  1.  
  2.  
  3.  
  4. ____TTTTPPPPMMMMVVVV,,,,____TTTTPPPPSSSSVVVV((((3333FFFF))))                                                ____TTTTPPPPMMMMVVVV,,,,____TTTTPPPPSSSSVVVV((((3333FFFF))))
  5.  
  6.  
  7.  
  8. NNNNAAAAMMMMEEEE
  9.      dtpmv, stpmv, ztpmv, ctpmv, dtpsv, stpsv, ztpsv, ctpsv - BLAS Level Two
  10.      Matrix-Vector Product  and  Solution of System of Equations
  11.  
  12.  
  13. FFFFOOOORRRRTTTTRRRRAAAANNNN 77777777 SSSSYYYYNNNNOOOOPPPPSSSSIIIISSSS
  14.      ssssuuuubbbbrrrroooouuuuttttiiiinnnneeee ddddttttppppmmmmvvvv(((( uuuupppplllloooo,,,, ttttrrrraaaannnnssss,,,, ddddiiiiaaaagggg,,,, nnnn,,,, aaaapppp,,,, xxxx,,,, iiiinnnnccccxxxx ))))
  15.      ssssuuuubbbbrrrroooouuuuttttiiiinnnneeee ddddttttppppssssvvvv(((( uuuupppplllloooo,,,, ttttrrrraaaannnnssss,,,, ddddiiiiaaaagggg,,,, nnnn,,,, aaaapppp,,,, xxxx,,,, iiiinnnnccccxxxx ))))
  16.            cccchhhhaaaarrrraaaacccctttteeeerrrr****1111        uuuupppplllloooo,,,, ttttrrrraaaannnnssss,,,, ddddiiiiaaaagggg
  17.            iiiinnnntttteeeeggggeeeerrrr            nnnn,,,, iiiinnnnccccxxxx
  18.            ddddoooouuuubbbblllleeee pppprrrreeeecccciiiissssiiiioooonnnn   aaaapppp((((****)))),,,, xxxx((((****))))
  19.  
  20.      ssssuuuubbbbrrrroooouuuuttttiiiinnnneeee ssssttttppppmmmmvvvv(((( uuuupppplllloooo,,,, ttttrrrraaaannnnssss,,,, ddddiiiiaaaagggg,,,, nnnn,,,, aaaapppp,,,, xxxx,,,, iiiinnnnccccxxxx ))))
  21.      ssssuuuubbbbrrrroooouuuuttttiiiinnnneeee ssssttttppppssssvvvv(((( uuuupppplllloooo,,,, ttttrrrraaaannnnssss,,,, ddddiiiiaaaagggg,,,, nnnn,,,, aaaapppp,,,, xxxx,,,, iiiinnnnccccxxxx ))))
  22.            cccchhhhaaaarrrraaaacccctttteeeerrrr****1111        uuuupppplllloooo,,,, ttttrrrraaaannnnssss,,,, ddddiiiiaaaagggg
  23.            iiiinnnntttteeeeggggeeeerrrr            nnnn,,,, iiiinnnnccccxxxx
  24.            rrrreeeeaaaallll               aaaapppp((((****)))),,,, xxxx((((****))))
  25.  
  26.      ssssuuuubbbbrrrroooouuuuttttiiiinnnneeee zzzzttttppppmmmmvvvv(((( uuuupppplllloooo,,,, ttttrrrraaaannnnssss,,,, ddddiiiiaaaagggg,,,, nnnn,,,, aaaapppp,,,, xxxx,,,, iiiinnnnccccxxxx ))))
  27.      ssssuuuubbbbrrrroooouuuuttttiiiinnnneeee zzzzttttppppssssvvvv(((( uuuupppplllloooo,,,, ttttrrrraaaannnnssss,,,, ddddiiiiaaaagggg,,,, nnnn,,,, aaaapppp,,,, xxxx,,,, iiiinnnnccccxxxx ))))
  28.            cccchhhhaaaarrrraaaacccctttteeeerrrr****1111        uuuupppplllloooo,,,, ttttrrrraaaannnnssss,,,, ddddiiiiaaaagggg
  29.            iiiinnnntttteeeeggggeeeerrrr            nnnn,,,, iiiinnnnccccxxxx
  30.            ddddoooouuuubbbblllleeee ccccoooommmmpppplllleeeexxxx     aaaapppp((((****)))),,,, xxxx((((****))))
  31.  
  32.      ssssuuuubbbbrrrroooouuuuttttiiiinnnneeee ccccttttppppmmmmvvvv(((( uuuupppplllloooo,,,, ttttrrrraaaannnnssss,,,, ddddiiiiaaaagggg,,,, nnnn,,,, aaaapppp,,,, xxxx,,,, iiiinnnnccccxxxx ))))
  33.      ssssuuuubbbbrrrroooouuuuttttiiiinnnneeee ccccttttppppssssvvvv(((( uuuupppplllloooo,,,, ttttrrrraaaannnnssss,,,, ddddiiiiaaaagggg,,,, nnnn,,,, aaaapppp,,,, xxxx,,,, iiiinnnnccccxxxx ))))
  34.            cccchhhhaaaarrrraaaacccctttteeeerrrr****1111        uuuupppplllloooo,,,, ttttrrrraaaannnnssss,,,, ddddiiiiaaaagggg
  35.            iiiinnnntttteeeeggggeeeerrrr            nnnn,,,, iiiinnnnccccxxxx
  36.            ccccoooommmmpppplllleeeexxxx            aaaapppp((((****)))),,,, xxxx((((****))))
  37.  
  38.  
  39. FFFFOOOORRRRTTTTRRRRAAAANNNN 77777777 SSSSYYYYNNNNOOOOPPPPSSSSIIIISSSS
  40.      vvvvooooiiiidddd ddddttttppppmmmmvvvv(((( uuuupppplllloooo,,,, ttttrrrraaaannnnssss,,,, ddddiiiiaaaagggg,,,, nnnn,,,, aaaapppp,,,, xxxx,,,, iiiinnnnccccxxxx ))))
  41.      vvvvooooiiiidddd ddddttttppppssssvvvv(((( uuuupppplllloooo,,,, ttttrrrraaaannnnssss,,,, ddddiiiiaaaagggg,,,, nnnn,,,, aaaapppp,,,, xxxx,,,, iiiinnnnccccxxxx ))))
  42.            MMMMaaaattttrrrriiiixxxxTTTTrrrriiiiaaaannnngggglllleeee        uuuupppplllloooo;;;;
  43.            MMMMaaaattttrrrriiiixxxxTTTTrrrraaaannnnssssppppoooosssseeee       ttttrrrraaaannnnssss;;;;
  44.            MMMMaaaattttrrrriiiixxxxUUUUnnnniiiittttTTTTrrrriiiiaaaannnngggguuuullllaaaarrrr  ddddiiiiaaaagggg;;;;
  45.            IIIInnnntttteeeeggggeeeerrrr               nnnn,,,, iiiinnnnccccxxxx;;;;
  46.            ddddoooouuuubbbblllleeee               ((((****aaaapppp[[[[ nnnn ]]]],,,, ((((****xxxx))))[[[[ nnnn ]]]];;;;
  47.  
  48.      vvvvooooiiiidddd ssssttttppppmmmmvvvv(((( uuuupppplllloooo,,,, ttttrrrraaaannnnssss,,,, ddddiiiiaaaagggg,,,, nnnn,,,, aaaapppp,,,, xxxx,,,, iiiinnnnccccxxxx ))))
  49.      vvvvooooiiiidddd ssssttttppppssssvvvv(((( uuuupppplllloooo,,,, ttttrrrraaaannnnssss,,,, ddddiiiiaaaagggg,,,, nnnn,,,, aaaapppp,,,, xxxx,,,, iiiinnnnccccxxxx ))))
  50.            MMMMaaaattttrrrriiiixxxxTTTTrrrriiiiaaaannnngggglllleeee        uuuupppplllloooo;;;;
  51.            MMMMaaaattttrrrriiiixxxxTTTTrrrraaaannnnssssppppoooosssseeee       ttttrrrraaaannnnssss;;;;
  52.            MMMMaaaattttrrrriiiixxxxUUUUnnnniiiittttTTTTrrrriiiiaaaannnngggguuuullllaaaarrrr  ddddiiiiaaaagggg;;;;
  53.            IIIInnnntttteeeeggggeeeerrrr               nnnn,,,, iiiinnnnccccxxxx;;;;
  54.            ffffllllooooaaaatttt                ((((****aaaapppp[[[[ nnnn ]]]],,,, ((((****xxxx))))[[[[ nnnn ]]]];;;;
  55.  
  56.      vvvvooooiiiidddd zzzzttttppppmmmmvvvv(((( uuuupppplllloooo,,,, ttttrrrraaaannnnssss,,,, ddddiiiiaaaagggg,,,, nnnn,,,, aaaapppp,,,, xxxx,,,, iiiinnnnccccxxxx ))))
  57.      vvvvooooiiiidddd zzzzttttppppssssvvvv(((( uuuupppplllloooo,,,, ttttrrrraaaannnnssss,,,, ddddiiiiaaaagggg,,,, nnnn,,,, aaaapppp,,,, xxxx,,,, iiiinnnnccccxxxx ))))
  58.            MMMMaaaattttrrrriiiixxxxTTTTrrrriiiiaaaannnngggglllleeee        uuuupppplllloooo;;;;
  59.            MMMMaaaattttrrrriiiixxxxTTTTrrrraaaannnnssssppppoooosssseeee       ttttrrrraaaannnnssss;;;;
  60.  
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  62.  
  63.                                                                         PPPPaaaaggggeeee 1111
  64.  
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  69.  
  70. ____TTTTPPPPMMMMVVVV,,,,____TTTTPPPPSSSSVVVV((((3333FFFF))))                                                ____TTTTPPPPMMMMVVVV,,,,____TTTTPPPPSSSSVVVV((((3333FFFF))))
  71.  
  72.  
  73.  
  74.            MMMMaaaattttrrrriiiixxxxUUUUnnnniiiittttTTTTrrrriiiiaaaannnngggguuuullllaaaarrrr  ddddiiiiaaaagggg;;;;
  75.            IIIInnnntttteeeeggggeeeerrrr               nnnn,,,, iiiinnnnccccxxxx;;;;
  76.            ZZZZoooommmmpppplllleeeexxxx               ((((****aaaapppp[[[[ nnnn ]]]],,,, ((((****xxxx))))[[[[ nnnn ]]]];;;;
  77.  
  78.      vvvvooooiiiidddd ccccttttppppmmmmvvvv(((( uuuupppplllloooo,,,, ttttrrrraaaannnnssss,,,, ddddiiiiaaaagggg,,,, nnnn,,,, aaaapppp,,,, xxxx,,,, iiiinnnnccccxxxx ))))
  79.      vvvvooooiiiidddd ccccttttppppssssvvvv(((( uuuupppplllloooo,,,, ttttrrrraaaannnnssss,,,, ddddiiiiaaaagggg,,,, nnnn,,,, aaaapppp,,,, xxxx,,,, iiiinnnnccccxxxx ))))
  80.            MMMMaaaattttrrrriiiixxxxTTTTrrrriiiiaaaannnngggglllleeee        uuuupppplllloooo;;;;
  81.            MMMMaaaattttrrrriiiixxxxTTTTrrrraaaannnnssssppppoooosssseeee       ttttrrrraaaannnnssss;;;;
  82.            MMMMaaaattttrrrriiiixxxxUUUUnnnniiiittttTTTTrrrriiiiaaaannnngggguuuullllaaaarrrr  ddddiiiiaaaagggg;;;;
  83.            IIIInnnntttteeeeggggeeeerrrr               nnnn,,,, iiiinnnnccccxxxx;;;;
  84.            CCCCoooommmmpppplllleeeexxxx               ((((****aaaapppp[[[[ nnnn ]]]],,,, ((((****xxxx))))[[[[ nnnn ]]]];;;;
  85.  
  86.  
  87.  
  88. DDDDEEEESSSSCCCCRRRRIIIIPPPPTTTTIIIIOOOONNNN
  89.      ddddttttppppmmmmvvvv, ssssttttppppmmmmvvvv, zzzzttttppppmmmmvvvv and ccccttttppppmmmmvvvv perform one of the matrix-vector operations
  90.  
  91.            x := A*x,   or   x := A'*x,   or   x := conjg( A' )*x,
  92.  
  93.      where x is an n element vector and A is an n by n unit, or non-unit,
  94.      upper or lower triangular matrix, supplied in packed form.
  95.  
  96.      ddddttttppppssssvvvv, ssssttttppppssssvvvv, zzzzttttppppssssvvvv and ccccttttppppssssvvvv solve one of the systems of equations
  97.  
  98.            A*x = b,   or   A'*x = b,   or   conjg( A' )*x = b,
  99.  
  100.      where b and x are n element vectors and A is an n by n unit, or non-unit,
  101.      upper or lower triangular matrix, supplied in packed form. No test for
  102.      singularity or near-singularity is included in this routine. Such tests
  103.      must be performed before calling this routine.
  104.  
  105.  
  106. PPPPAAAARRRRAAAAMMMMEEEETTTTEEEERRRRSSSS
  107.      uuuupppplllloooo    On entry, uuuupppplllloooo specifies whether the matrix is an upper or lower
  108.              triangular matrix as follows:
  109.  
  110.                   FFFFOOOORRRRTTTTRRRRAAAANNNN
  111.                   uplo = 'U' or 'u'        A is an upper triangular matrix.
  112.                   uplo = 'L' or 'l'        A is a lower triangular matrix.
  113.  
  114.                   CCCC
  115.                   uplo = UpperTriangle     A is an upper triangular matrix.
  116.                   uplo = LowerTriangle     A is a lower triangular matrix.
  117.  
  118.              Unchanged on exit.
  119.  
  120.      ttttrrrraaaannnnssss   On entry, ttttrrrraaaannnnssss ssssppppeeeecccciiiiffffiiiieeeessss tttthhhheeee ooooppppeeeerrrraaaattttiiiioooonnnn ttttoooo bbbbeeee
  121.  
  122.                   FFFFOOOORRRRTTTTRRRRAAAANNNN
  123.                   trans = 'N' or 'n'       x := A*x /  A*x = b.
  124.                   trans = 'T' or 't'       x := A'*x / A'*x = b.
  125.                   trans = 'C' or 'c'       x := conjg( A' )*x  /
  126.  
  127.  
  128.  
  129.                                                                         PPPPaaaaggggeeee 2222
  130.  
  131.  
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  133.  
  134.  
  135.  
  136. ____TTTTPPPPMMMMVVVV,,,,____TTTTPPPPSSSSVVVV((((3333FFFF))))                                                ____TTTTPPPPMMMMVVVV,,,,____TTTTPPPPSSSSVVVV((((3333FFFF))))
  137.  
  138.  
  139.  
  140.                                                 conjg( A' )*x = b.
  141.  
  142.                   CCCC
  143.                   trans = NoTranspose           x := A*x /  A*x = b.
  144.                   trans = Transpose             x := A'*x / A'*x = b.
  145.                   trans = ConjugateTranspose    x := conjg( A' )*x
  146.                                                 conjg( A' )*x = b.
  147.  
  148.              For real value matrices, ttttrrrraaaannnnssss='C' and ttttrrrraaaannnnssss='T' has the same
  149.              meaning.
  150.  
  151.              Unchanged on exit.
  152.  
  153.      ddddiiiiaaaagggg    On entry, ddddiiiiaaaagggg specifies whether or not A is unit triangular as
  154.              follows:
  155.  
  156.                   FFFFOOOORRRRTTTTRRRRAAAANNNN
  157.                   diag = 'U' or 'u'   A is assumed to be unit triangular.
  158.                   diag = 'N' or 'n'   A is not assumed to be unit triangular.
  159.  
  160.                   CCCC
  161.                   diag = UnitTriangular    A is assumed to be unit
  162.                                            triangular.
  163.                   diag = NotUnitTriangular A is not assumed to be unit
  164.                                            triangular.
  165.  
  166.              Unchanged on exit.
  167.  
  168.      nnnn       On entry, nnnn specifies the order of the matrix A. nnnn must be at
  169.              least zero.
  170.              Unchanged on exit.
  171.  
  172.      aaaapppp      Array of size at least ( ( n*( n + 1 ) )/2 ).
  173.              Before entry with uuuupppplllloooo ==== ''''UUUU'''' oooorrrr ''''uuuu'''' oooorrrr the array aaaapppp must contain
  174.              the upper triangular matrix packed sequentially, column by
  175.              column, so that aaaapppp( 1 ) contains A( 1, 1 ), aaaapppp( 2 ) and aaaapppp( 3 )
  176.              contain A( 1, 2 ) and A( 2, 2 ) respectively, and so on.
  177.  
  178.              Before entry with UUUUPPPPLLLLOOOO ==== ''''LLLL'''' oooorrrr ''''llll'''' oooorrrr , the array aaaapppp must
  179.              contain the lower triangular matrix packed sequentially, column
  180.              by column, so that aaaapppp( 1 ) contains A( 1, 1 ), aaaapppp( 2 ) and aaaapppp( 3
  181.              ) contain A( 2, 1 ) and A( 3, 1 ) respectively, and so on.
  182.  
  183.              Note that when ddddiiiiaaaagggg ==== ''''UUUU'''' oooorrrr ''''uuuu'''' oooorrrr , the elements of _a
  184.              corresponding to the diagonal elements of the matrix A are not
  185.              referenced either, but are assumed to be unity.
  186.  
  187.              Unchanged on exit.
  188.  
  189.      xxxx       Array of size at least ( 1 + ( n - 1 )*abs( incx ) ). Before
  190.              entry, the incremented array xxxx must contain the n element vector
  191.              x. On exit, xxxx is overwritten with the transformed/solution vector
  192.  
  193.  
  194.  
  195.                                                                         PPPPaaaaggggeeee 3333
  196.  
  197.  
  198.  
  199.  
  200.  
  201.  
  202. ____TTTTPPPPMMMMVVVV,,,,____TTTTPPPPSSSSVVVV((((3333FFFF))))                                                ____TTTTPPPPMMMMVVVV,,,,____TTTTPPPPSSSSVVVV((((3333FFFF))))
  203.  
  204.  
  205.  
  206.              x.
  207.  
  208.      iiiinnnnccccxxxx    On entry, iiiinnnnccccxxxx specifies the increment for the elements of xxxx.
  209.              iiiinnnnccccxxxx must not be zero.
  210.              Unchanged on exit.
  211.  
  212.  
  213. AAAAUUUUTTTTHHHHOOOORRRRSSSS
  214.           Jack Dongarra, Argonne National Laboratory.
  215.           Iain Duff, AERE Harwell.
  216.           Jeremy Du Croz, Numerical Algorithms Group Ltd.
  217.           Sven Hammarling, Numerical Algorithms Group Ltd.
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  260.  
  261.                                                                         PPPPaaaaggggeeee 4444
  262.  
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  265.