/usr/include/linbox/algorithms/smith-form-local2.inl is in liblinbox-dev 1.3.2-1.1build2.
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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 | /* linbox/algorithms/localsmith.h
* Copyright (C) LinBox
*
* Written by David Saunders
*
* ------------------------------------
*
*
* ========LICENCE========
* This file is part of the library LinBox.
*
* LinBox is free software: you can redistribute it and/or modify
* it under the terms of the GNU Lesser General Public
* License as published by the Free Software Foundation; either
* version 2.1 of the License, or (at your option) any later version.
*
* This library is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
* Lesser General Public License for more details.
*
* You should have received a copy of the GNU Lesser General Public
* License along with this library; if not, write to the Free Software
* Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
* ========LICENCE========
*.
*/
#ifndef __LINBOX_smith_form_local2_H
#define __LINBOX_smith_form_local2_H
#include <vector>
#include <list>
//#include <algorithm>
#include "linbox/field/local2_32.h"
namespace LinBox
{
/**
\brief Smith normal form (invariant factors) of a matrix over a local ring.
*/
template<class LocalRing>
class SmithFormLocal;
template <>
class SmithFormLocal<Local2_32>
{
public:
typedef Local2_32 LocalPIR;
typedef LocalPIR::Element Elt;
template<class Matrix>
std::list<Elt>& operator()(std::list<Elt>& L, Matrix& A, const LocalPIR& R)
{ Elt d; R.init(d, 1);
Elt *p = &(A[0][0]);
return smithStep(L, d, p, A.rowdim(), A.coldim(), A.getStride(), R);
}
std::list<Elt>&
smithStep(std::list<Elt>& L, Elt& d, Elt* Ap, size_t m, size_t n, size_t stride, const LocalPIR& R)
{
if ( m == 0 || n == 0 )
return L;
LocalPIR::Exponent g = LocalPIR::Exponent(32); //R.init(g, 0); // must change to 2^31 maybe.
size_t i, j, k;
/* Arguably this search order should be reversed to increase the likelyhood of no col swap,
assuming row swaps cheaper. Not so, however on my example. -bds 11Nov */
for ( i = 0; i != m; ++i)
{
for (j = 0; j != n; ++j)
{
R.gcdin(g, Ap[i*stride + j]);
if ( R.isUnit(g) ) break;
}
if ( R.isUnit(g) ) break;
}
if ( R.isZero(g) )
{
L.insert(L.end(), (m < n) ? m : n, 0);
return L;
}
if ( i != m ) // g is a unit and, because this is a local ring,
// value at which this first happened also is a unit.
{ // put pivot in 0,0 position
if ( i != 0 ) // swap rows
std::swap_ranges(Ap, Ap+n, Ap + i*stride);
if ( j != 0 ) // swap cols
for(k = 0; k != m; ++k)
std::swap(Ap[k*stride + 0], Ap[k*stride + j]);
// elimination step - crude and for dense only - fix later
// Want to use a block method or "left looking" elimination.
Elt f; R.inv(f, Ap[0*stride + 0] );
R.negin(f);
// normalize first row to -1, ...
for ( j = 0; j != n; ++j)
R.mulin(Ap[0*stride + j], f);
// eliminate in subsequent rows
for ( i = 1; i != m; ++i)
{
f = Ap[i*stride + 0];
for ( j = 0; j != n; ++j)
R.axpyin( Ap[i*stride +j], f, Ap[0*stride +j] );
}
L.push_back(d);
return smithStep(L, d, Ap + stride+1,m-1, n-1, stride, R);
}
else
{
for ( i = 0; i != m; ++i)
for ( j = 0; j != n; ++j)
{
R.divin(Ap[i*stride + j], g);
}
return smithStep(L, R.mulin(d, g), Ap, m, n, stride, R);
}
}
}; // end SmithFormLocal
} // end LinBox
#endif // __LINBOX_smith_form_local2_H
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