linbox
examples/mats.C

example matrices that were chosen for Smith form testing.

Author
bds & zw

Various Smith form algorithms may be used for matrices over the integers or over Z_m. Moduli greater than 2^32 are not supported here. Several types of example matrices may be constructed or the matrix be read from a file. Run the program with no arguments for a synopsis of the command line parameters.

For the "adaptive" method, the matrix must be over the integers. This is expected to work best for large matrices.

For the "2local" method, the computation is done mod 2^32.

For the "local" method, the modulus must be a prime power.

For the "ilio" method, the modulus may be arbitrary composite. If the modulus is a multiple of the integer determinant, the integer Smith form is obtained.
Determinant plus ilio may be best for smaller matrices.

This example was used during the design process of the adaptive algorithm.

/*
* examples/mats.C
*
* Copyright (C) 2017 D. Saunders, Z. Wang, J-G Dumas
* ========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========
*/
#include <iostream>
#include <string>
using namespace std;
//#include <linbox/ring/modular.h>
//#include "givaro/zring.h"
//#include "linbox/integer.h"
// place A: Edit here and at place B for ring change
//#include <linbox/ring/pir-modular-int32.h>
//#include <linbox/ring/pir-ntl-zz_p.h>
#include <linbox/ring/pir-ntl-zz_p.h>
using namespace LinBox;
template <class PIR>
void Mat(DenseMatrix<PIR>& M, PIR& R, int & n, string src) ;
int main(int argc, char* argv[])
{
if (argc < 3 or argc > 4) {
cout << "usage: " << argv[0] << " type n [filename]" << endl;
cout << " type = `random', `random-rough', `tref', or `fib',"
<< " and n is the dimension" << endl;
cout << " If filename is present, matrix is written there, else to cout." << endl;
return 0;
}
string type = argv[1];
int n = atoi(argv[2]);
// place B: Edit here and at place A for ring change
//typedef PIRModular<int32_t> PIR;
typedef Givaro::ZRing<Integer> PIR;
PIR R;
Mat(M,R,n,type);
if (argc == 4) {
ofstream out(argv[3]);
M.write(out) << endl;
} else {
M.write(cout) << endl;
}
}// main
template < class Ring >
void scramble(DenseMatrix<Ring>& M)
{
Ring R = M.field();
int N,n = (int)M.rowdim(); // number of random basic row and col ops.
N = n;
for (int k = 0; k < N; ++k) {
int i = rand()%(int)M.rowdim();
int j = rand()%(int)M.coldim();
if (i == j) continue;
// M*i += alpha M*j and Mi* += beta Mj
//int a = rand()%2;
int a = 0;
for (size_t l = 0; l < M.rowdim(); ++l) {
if (a)
R.subin(M[(size_t)l][(size_t)i], M[(size_t)l][(size_t)j]);
else
R.addin(M[(size_t)l][(size_t)i], M[(size_t)l][(size_t)j]);
//K.axpy(c, M.getEntry(l, i), x, M.getEntry(l, j));
//M.setEntry(l, i, c);
}
//a = rand()%2;
for (size_t l = 0; l < M.coldim(); ++l) {
if (a)
R.subin(M[(size_t)i][l], M[(size_t)j][l]);
else
R.addin(M[(size_t)i][l], M[(size_t)j][l]);
}
}
}
// This mat will have s, near sqrt(n), distinct invariant factors,
// each repeated twice), involving the s primes 101, 103, ...
template <class PIR>
void RandomRoughMat(DenseMatrix<PIR>& M, PIR& R, int n) {
M.resize((size_t)n, (size_t)n, R.zero);
if (n > 10000) {cerr << "n too big" << endl; exit(-1);}
int jth_factor[130] =
{2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67,
71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149,
151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229,
233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313,
317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409,
419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499,
503, 509, 521, 523, 541, 547, 557, 563, 569, 571, 577, 587, 593, 599, 601,
607, 613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691,
701, 709, 719, 727, 733};
for (int j= 0, i = 0 ; i < n; ++j)
{
typename PIR::Element v; R.init(v, jth_factor[25+j]);
for (int k = j ; k > 0 && i < n ; --k)
{ M[(size_t)i][(size_t)i] = v; ++i;
if (i < n) {M[(size_t)i][(size_t)i] = v; ++i;}
}
}
scramble(M);
}
// This mat will have the same nontrivial invariant factors as
// diag(1,2,3,5,8, ... 999, 0, 1, 2, ...).
template <class PIR>
void RandomFromDiagMat(DenseMatrix<PIR>& M, PIR& R, int n) {
M.resize((size_t)n,(size_t) n, R.zero);
for (int i= 0 ; i < n; ++i)
R.init(M[(size_t)i][(size_t)i], i % 1000 + 1);
scramble(M);
}
// This mat will have the same nontrivial invariant factors as
// diag(1,2,3,5,8, ... fib(k)), where k is about sqrt(n).
// The basic matrix is block diagonal with i-th block of order i and
// being a tridiagonal {-1,0,1} matrix whose snf = diag(i-1 1's, fib(i)),
// where fib(1) = 1, fib(2) = 2. But note that, depending on n,
// the last block may be truncated, thus repeating an earlier fibonacci number.
template <class PIR>
void RandomFibMat(DenseMatrix<PIR>& M, PIR& R, int n) {
M.resize((size_t)n,(size_t) n, R.zero);
typename PIR::Element pmone; R.assign(pmone, R.one);
for (int i= 0 ; i < n; ++i) M[(size_t)i][(size_t)i] = R.one;
int j = 1, k = 0;
for (int i= 0 ; i < n-1; ++i) {
if ( i == k) {
M[(size_t)i][(size_t)i+1] = R.zero;
k += ++j;
}
else {
M[(size_t)i][(size_t)i+1] = pmone;
R.negin(pmone);
}
R.neg(M[(size_t)i+1][(size_t)i], M[(size_t)i][(size_t)i+1]);
}
scramble(M);
}
// special mats tref and krat
// Trefethen's challenge #7 mat (primes on diag, 1's on 2^e bands).
template <class PIR>
void TrefMat(DenseMatrix<PIR>& M, PIR& R, int n) {
M.resize((size_t)n, (size_t)n, R.zero);
std::vector<int> power2;
int i = 1;
do {
power2. push_back(i);
i *= 2;
} while (i < n);
std::ifstream in ("prime", std::ios::in);
for ( i = 0; i < n; ++ i)
in >> M[(size_t)i][(size_t)i];
std::vector<int>::iterator p;
for ( i = 0; i < n; ++ i) {
for ( p = power2. begin(); (p != power2. end()) && (*p <= i); ++ p)
M[(size_t)i][(size_t)(i - *p)] = 1;
for ( p = power2. begin(); (p != power2. end()) && (*p < n - i); ++ p)
M[(size_t)i][(size_t)(i + *p)] = 1;
}
}
struct pwrlist
{
vector<integer> m;
pwrlist(integer q)
{ m.push_back(1); m.push_back(q); //cout << "pwrlist " << m[0] << " " << m[1] << endl;
}
integer operator[](int e)
{
for (int i = (int)m.size(); i <= e; ++i) m.push_back(m[1]*m[(size_t)i-1]);
return m[(size_t)e];
}
};
// Read "1" or "q" or "q^e", for some (small) exponent e.
// Return value of the power of q at q = _q.
template <class num>
num& qread(num& Val, pwrlist& M, istream& in)
{
char c;
in >> c; // next nonwhitespace
if (c == '0') return Val = 0;
if (c == '1') return Val = 1;
if (c != 'p' && c != 'q') { cout << "exiting due to unknown char " << c << endl; exit(-1);}
in.get(c);
if (c !='^') {in.putback(c); return Val = M[1];}
else
{ int expt; in >> expt;
return Val = M[expt];
};
}
template <class PIR>
void KratMat(DenseMatrix<PIR>& M, PIR& R, int q)
{
pwrlist pwrs(q);
for (unsigned int i = 0; i < M.rowdim(); ++ i)
for ( unsigned int j = 0; j < M.coldim(); ++ j) {
int Val;
qread(Val, pwrs, cin);
R. init (M[(size_t)i][(size_t)j], Val);
}
}
template <class PIR>
void Mat(DenseMatrix<PIR>& M, PIR& R, int & n,
string src) {
if (src == "random-rough") RandomRoughMat(M, R, n);
else if (src == "random") RandomFromDiagMat(M, R, n);
else if (src == "fib") RandomFibMat(M, R, n);
else if (src == "tref") TrefMat(M, R, n);
else if (src == "krat") KratMat(M, R, n);
else { // from cin, mostly pointless, but may effect a file format change.
M.read(cin);
n = M.rowdim();
}
} // Mat
LinBox::BlasMatrix::rowdim
size_t rowdim() const
Get the number of rows in the matrix.
Definition: blas-matrix.inl:502
LinBox::BlasMatrix::resize
void resize(const size_t &m, const size_t &n, const Element &val=Element())
Resize the matrix to the given dimensions.
Definition: blas-matrix.inl:526
LinBox::BlasMatrix::read
std::istream & read(std::istream &file)
Read the matrix from an input stream.
Definition: blas-matrix.inl:423
LinBox::NTL_zz_pX
Ring (in fact, a unique factorization domain) of polynomial with coefficients in class NTL_zz_p (inte...
Definition: ntl-lzz_px.h:78
LinBox::BlasMatrix::field
const _Field & field() const
Retrieve a reference to a row.
Definition: blas-matrix.inl:1535
LinBox::integer
Givaro::Integer integer
Integers in LinBox.
Definition: integer.h:55
Mat
void Mat(DenseMatrix< PIR > &M, PIR &R, int n, string src, string file, string format)
Output matrix is determined by src which may be: "random-rough" This mat will have s,...
Definition: blackbox/smith.C:230
timer.h
LinBox
Namespace in which all linbox code resides.
Definition: alt-blackbox-block-container.h:4
LinBox::BlasMatrix::coldim
size_t coldim() const
Get the number of columns in the matrix.
Definition: blas-matrix.inl:508
linbox-config.h
linbox base configuration file
LinBox::BlasMatrix< _Field >
dense-matrix.h
NODOC.