For the "adaptive" method, the matrix must be over the NTL_ZZ representation of the integers.
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.
This example was used during the design process of the adaptive algorithm.
#include <iostream>
#include <string>
#include <vector>
#include <list>
#include "linbox/field/modular-int32.h"
#include "linbox/blackbox/sparse.h"
#include "linbox/algorithms/smith-form-sparseelim-local.h"
#include "linbox/util/timer.h"
#include "linbox/field/unparametric.h"
#include "linbox/field/local2_32.h"
#include "linbox/field/ntl-ZZ.h"
#include "linbox/algorithms/smith-form-local.h"
#include "linbox/algorithms/smith-form-local2.h"
#include <linbox/algorithms/smith-form-iliopoulos.h>
#include "linbox/algorithms/smith-form-adaptive.h"
#include "linbox/blackbox/dense.h"
#include "linbox/field/PIR-modular-int32.h"
Functions | |
template<class PIR> void | Mat (DenseMatrix< PIR > &M, PIR &R, int n, string src, string file, string format) |
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Output matrix is determined by src which may be: "random-rough" This mat will have s, near sqrt(n), distinct invariant factors, each repeated twice), involving the s primes 101, 103, ... "random" This mat will have the same nontrivial invariant factors as diag(1,2,3,5,8, ... 999, 0, 1, 2, ...). "fib" 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. "file" (or any other string) mat read from named file with format "sparse" or "dense". Also "tref" and file with format "kdense" |