void testTiming(Blackbox & A)
{
typedef typename Blackbox::MatrixDomain Dom;
typedef typename Dom::Block Block;
Dom MD = A.domain();
size_t m = A.rowdim(), n = A.coldim();
size_t k = (m + n)/2;
LinBox::UserTimer timer;
Block B(n,k), C(m,k), D(k,m), E(k,n), F(k,k);
MD.random(B); MD.random(D);
vector<typename Dom::Element> v1, v2(m);
typename Dom::RandIter r(MD);
typename Dom::Element x;
for(size_t i = 0; i != n; ++i){
r.random(x);
v1.push_back(x);
}
//Tests:
cout << "Timing tests:" << endl << endl;
timer.clear(); timer.start();
for(size_t j = 0; j != m; ++j) A.apply(v2,v1);
timer.stop();
cout << "apply using vectors time: " << timer << endl;
timer.clear(); timer.start();
A.applyTranspose(C,B);
timer.stop();
cout << "apply using row addin time: " << timer << endl;
timer.clear(); timer.start();
A.unpackingApplyTranspose(C,B);
timer.stop();
cout << "apply using block axpy time: " << timer << endl;
timer.clear(); timer.start();
MD.mul(F, D, C);
timer.stop();
cout << "Matrix Domain mul time: " << timer << endl;
cout << "End of timing tests" << endl << endl;
} // testTiming
void largeTest (Blackbox & A)
{
//Use for large blackboxes
typedef typename Blackbox::MatrixDomain Dom;
typedef typename Dom::Block Block;
Dom MD = A.domain();
size_t m = A.coldim();
size_t n = 2000;
LinBox::UserTimer timer;
Block B(m,n), C(m,n);
MD.random(B);
cout << "Test: " << A.rowdim() << "x" << m << "blackbox multiplied by " << m << "x" << n << "block\nblock size: 2048\n\n";
timer.clear(); timer.start();
A.unpackingApply(C,B,2048);
timer.stop();
cout << "unpacking apply time: " << timer << endl;
} //end largeTest
bool testAssociativity(Blackbox& A)
{
typedef typename Blackbox::MatrixDomain Dom;
Dom MD = A.domain();
size_t m = A.rowdim(), n = A.coldim() - 100;
size_t k = (m + n)/2;
typename Dom::Block B(A.field(),k,m), C(A.field(),m,n);
MD.random(B); MD.random(C);
typename Dom::Block D(A.field(),m,n), E(A.field(),k,n);
A.apply(D, C); // D = AC
MD.mul(E,B,D); // E = B(AC)
typename Dom::Block F(A.field(),k,m), G(A.field(),k,n);
A.unpackingApplyTranspose(F,B); // F = BA
MD.mul(G,F,C); // G = (BA)C
return MD.areEqual(E,G);
} // testAssociativity
static bool testTransposeBlackbox(Blackbox & A)
{
typedef typename Blackbox::Field Field;
commentator().start ("Testing Transpose", "testTranspose", 1);
Transpose<Blackbox> B(A);
bool ret = true, ret1;
size_t m = A.rowdim(), n = A.coldim();
const Field & F = A.field();
VectorDomain<Field> VD (F);
BlasVector<Field> x(F,n), y(F,m), z(F,n), w(F,m);
VD.random(x);
A.apply(y, x);
B.applyTranspose(w, x);
ret1 = VD.areEqual(y, w);
if (not ret1) commentator().report() << "A and B^T disagree, FAIL" << std::endl;
ret = ret and ret1;
VD.random(y);
A.applyTranspose(x, y);
B.apply(z, y);
ret1 = VD.areEqual(x, z);
if (not ret1) commentator().report() << "A^T and B disagree, FAIL" << std::endl;
ret = ret and ret1;
ret1 = testBlackboxNoRW(B);
if (not ret1) commentator().report() << "testBlackbox A^T FAIL" << std::endl;
ret = ret and ret1;
commentator().stop (MSG_STATUS (ret), (const char *) 0, "testTranspose");
return ret;
}
int main (int argc, char **argv)
{
// commentator().setMaxDetailLevel (-1);
// commentator().setMaxDepth (-1);
// commentator().setReportStream (std::cerr);
if (argc < 2 || argc > 4) {
std::cerr << "Usage: omp_smithvalence <matrix-file-in-supported-format> [-ata|-aat|valence] [coprime]" << std::endl;
std::cerr << " Optional parameters valence and coprime are integers." << std::endl;
std::cerr << " Prime factors of valence will be used for local computation." << std::endl;
std::cerr << " coprime will be used for overall rank computation." << std::endl;
return -1;
}
std::ifstream input (argv[1]);
if (!input) { std::cerr << "Error opening matrix file " << argv[1] << std::endl; return -1; }
Givaro::ZRing<Integer> ZZ;
MatrixStream< Givaro::ZRing<Integer> > ms( ZZ, input );
typedef SparseMatrix<Givaro::ZRing<Integer>> Blackbox;
Blackbox A (ms);
input.close();
std::cout << "A is " << A.rowdim() << " by " << A.coldim() << std::endl;
Givaro::ZRing<Integer>::Element val_A;
LinBox::Timer chrono; chrono.start();
if (argc >= 3) {
Transpose<Blackbox> T(&A);
if (strcmp(argv[2],"-ata") == 0) {
Compose< Transpose<Blackbox>, Blackbox > C (&T, &A);
std::cout << "A^T A is " << C.rowdim() << " by " << C.coldim() << std::endl;
valence(val_A, C);
}
else if (strcmp(argv[2],"-aat") == 0) {
Compose< Blackbox, Transpose<Blackbox> > C (&A, &T);
std::cout << "A A^T is " << C.rowdim() << " by " << C.coldim() << std::endl;
valence(val_A, C);
}
else {
std::cout << "Suppose primes are contained in " << argv[2] << std::endl;
val_A = LinBox::Integer(argv[2]);
}
}
else {
if (A.rowdim() != A.coldim()) {
std::cerr << "Valence works only on square matrices, try either to change the dimension in the matrix file, or to compute the valence of A A^T or A^T A, via the -aat or -ata options." << std::endl;
exit(0);
}
else
valence (val_A, A);
}
std::cout << "Valence is " << val_A << std::endl;
std::vector<Givaro::Integer> Moduli;
std::vector<size_t> exponents;
Givaro::IntFactorDom<> FTD;
typedef std::pair<Givaro::Integer,unsigned long> PairIntRk;
std::vector< PairIntRk > smith;
Givaro::Integer coprimeV=2;
if (argc >= 4) {
coprimeV =Givaro::Integer(argv[3]);
}
while ( gcd(val_A,coprimeV) > 1 ) {
FTD.nextprimein(coprimeV);
}
if (argc >= 4) {
std::cout << "Suppose " << argv[3] << " is coprime with Smith form" << std::endl;
}
std::cout << "Integer rank: " << std::endl;
unsigned long coprimeR; LRank(coprimeR, argv[1], coprimeV);
smith.push_back(PairIntRk(coprimeV, coprimeR));
// std::cerr << "Rank mod " << coprimeV << " is " << coprimeR << std::endl;
std::cout << "Some factors (50000 factoring loop bound): ";
FTD.set(Moduli, exponents, val_A, 50000);
std::vector<size_t>::const_iterator eit=exponents.begin();
for(std::vector<Givaro::Integer>::const_iterator mit=Moduli.begin();
mit != Moduli.end(); ++mit,++eit)
std::cout << *mit << '^' << *eit << ' ';
std::cout << std::endl;
std::vector<Givaro::Integer> SmithDiagonal(coprimeR,Givaro::Integer(1));
std::cout << "num procs: " << omp_get_num_procs() << std::endl;
std::cout << "max threads: " << omp_get_max_threads() << std::endl;
#pragma omp parallel for shared(SmithDiagonal, Moduli, coprimeR)
for(size_t j=0; j<Moduli.size(); ++j) {
unsigned long r; LRank(r, argv[1], Moduli[j]);
std::cerr << "Rank mod " << Moduli[j] << " is " << r << " on thread: " << omp_get_thread_num() << std::endl;
smith.push_back(PairIntRk( Moduli[j], r));
for(size_t i=r; i < coprimeR; ++i)
SmithDiagonal[i] *= Moduli[j];
}
/*
for(std::vector<Givaro::Integer>::const_iterator mit=Moduli.begin();
mit != Moduli.end(); ++mit) {
unsigned long r; LRank(r, argv[1], *mit);
std::cerr << "Rank mod " << *mit << " is " << r << std::endl;
smith.push_back(PairIntRk(*mit, r));
for(size_t i=r; i < coprimeR; ++i)
SmithDiagonal[i] *= *mit;
}
*/
eit=exponents.begin();
std::vector<PairIntRk>::const_iterator sit=smith.begin();
for( ++sit; sit != smith.end(); ++sit, ++eit) {
if (sit->second != coprimeR) {
std::vector<size_t> ranks;
ranks.push_back(sit->second);
size_t effexp;
if (*eit > 1) {
if (sit->first == 2)
PRankPowerOfTwo(ranks, effexp, argv[1], *eit, coprimeR);
else
PRank(ranks, effexp, argv[1], sit->first, *eit, coprimeR);
}
else {
// if (sit->first == 2)
PRank(ranks, effexp, argv[1], sit->first, 2, coprimeR);
// else
// PRank(ranks, effexp, argv[1], sit->first, 2, coprimeR);
}
if (ranks.size() == 1) ranks.push_back(coprimeR);
if (effexp < *eit) {
for(size_t expo = effexp<<1; ranks.back() < coprimeR; expo<<=1) {
if (sit->first == 2)
PRankIntegerPowerOfTwo(ranks, argv[1], expo, coprimeR);
else
PRankInteger(ranks, argv[1], sit->first, expo, coprimeR);
}
} else {
for(size_t expo = (*eit)<<1; ranks.back() < coprimeR; expo<<=1) {
if (sit->first == 2)
PRankPowerOfTwo(ranks, effexp, argv[1], expo, coprimeR);
else
PRank(ranks, effexp, argv[1], sit->first, expo, coprimeR);
if (ranks.size() < expo) {
std::cerr << "It seems we need a larger prime power, it will take longer ..." << std::endl;
// break;
if (sit->first == 2)
PRankIntegerPowerOfTwo(ranks, argv[1], expo, coprimeR);
else
PRankInteger(ranks, argv[1], sit->first, expo, coprimeR);
}
}
}
std::vector<size_t>::const_iterator rit=ranks.begin();
// unsigned long modrank = *rit;
for(++rit; rit!= ranks.end(); ++rit) {
if ((*rit)>= coprimeR) break;
for(size_t i=(*rit); i < coprimeR; ++i)
SmithDiagonal[i] *= sit->first;
// modrank = *rit;
}
}
}
Givaro::Integer si=1;
size_t num=0;
for( std::vector<Givaro::Integer>::const_iterator dit=SmithDiagonal.begin();
dit != SmithDiagonal.end(); ++dit) {
if (*dit == si) ++num;
else {
std::cerr << '[' << si << ',' << num << "] ";
num=1;
si = *dit;
}
}
std::cerr << '[' << si << ',' << num << "] " << std::endl;
chrono.stop();
std::cerr << chrono << std::endl;
return 0;
}
bool testQLUP(const Field &F, size_t n, unsigned int iterations, int rseed, double sparsity = 0.05)
{
bool res = true;
commentator().start ("Testing Sparse elimination qlup", "testQLUP", iterations);
size_t Ni = n;
size_t Nj = n;
integer card; F.cardinality(card);
typename Field::RandIter generator (F,card,rseed);
RandStream stream (F, generator, sparsity, n, n);
for (size_t i = 0; i < iterations; ++i) {
commentator().startIteration ((unsigned)i);
stream.reset();
Blackbox A (F, stream);
std::ostream & report = commentator().report (Commentator::LEVEL_UNIMPORTANT, INTERNAL_DESCRIPTION);
F.write( report ) << endl;
A.write( report,Tag::FileFormat::Maple ) << endl;
DenseVector<Field> u(F,Nj), v(F,Ni), w1(F,Nj), w2(F,Ni), w3(F,Ni), w(F,Ni);
for(auto it=u.begin();it!=u.end();++it)
generator.random (*it);
A.apply(v,u);
unsigned long rank;
Method::SparseElimination SE;
SE.strategy(Specifier::PIVOT_LINEAR);
GaussDomain<Field> GD ( F );
typename Field::Element determinant;
Blackbox L(F, A.rowdim(), A.coldim());
Permutation<Field> Q((int)A.rowdim(),F);
Permutation<Field> P((int)A.coldim(),F);
GD.QLUPin(rank, determinant,
Q, L, A, P,
A.rowdim(), A.coldim() );
Q.apply(w, L.apply(w3, A.apply(w2, P.apply(w1,u) ) ) );
bool error = false;
auto itv=v.begin();
auto itw=w.begin();
for( ; itw!=w.end();++itw,++itv) {
if (! F.areEqual(*itw,*itv) ) {
error = true;
}
}
if (error) {
res = false;
report << "ERROR : matrix(" << u.size() << ",1,[";
for(auto itu=u.begin(); itu!=u.end();++itu)
report << *itu << ',';
report << "]);\n[";
for(auto itv2=v.begin(); itv2!=v.end();++itv2)
report << *itv2 << ' ';
report << "] != [";
for(auto itw2=w.begin(); itw2!=w.end();++itw2)
report << *itw2 << ' ';
report << "]" << std::endl;
report << "w1: [";
for(auto itw2=w1.begin(); itw2!=w1.end();++itw2)
report << *itw2 << ' ';
report << "]" << std::endl;
report << "w2: [";
for(auto itw2=w2.begin(); itw2!=w2.end();++itw2)
report << *itw2 << ' ';
report << "]" << std::endl;
report << "w3: [";
for(auto itw2=w3.begin(); itw2!=w3.end();++itw2)
report << *itw2 << ' ';
report << "]" << std::endl;
}
commentator().stop ("done");
commentator().progress ();
}
commentator().stop (MSG_STATUS (res), (const char *) 0, "testQLUP");
return res;
}
bool testQLUPnullspace(const Field &F, size_t n, unsigned int iterations, int rseed, double sparsity = 0.05)
{
bool res = true;
commentator().start ("Testing Sparse elimination qlup nullspacebasis", "testQLUPnullspace", iterations);
size_t Ni = n;
size_t Nj = n;
integer card; F.cardinality(card);
typename Field::RandIter generator (F,card,rseed);
RandStream stream (F, generator, sparsity, n, n, rseed);
for (size_t i = 0; i < iterations; ++i) {
commentator().startIteration ((unsigned)i);
stream.reset();
Blackbox A (F, stream);
std::ostream & report = commentator().report (Commentator::LEVEL_UNIMPORTANT, INTERNAL_DESCRIPTION);
F.write( report ) << endl;
A.write( report, Tag::FileFormat::Maple ) << endl;
Method::SparseElimination SE;
SE.strategy(Specifier::PIVOT_LINEAR);
GaussDomain<Field> GD ( F );
Blackbox CopyA ( A );
Blackbox X(F, A.coldim(), A.coldim() );
GD.nullspacebasisin(X, CopyA );
size_t nullity = X.coldim();
DenseVector<Field> u(F,nullity);
for(auto it=u.begin();it!=u.end();++it)
generator.random (*it);
DenseVector<Field> v(F,Nj);
X.apply(v,u);
report << "Random combination of the rows of the NullSpace basis" << std::endl;
DenseVector<Field> w(F,Ni);
A.apply(w, v);
VectorDomain<Field> VD(F);
if (! VD.isZero(w)) {
res=false;
A.write( report, Tag::FileFormat::Maple ) << endl;
report << "ERROR u: matrix(" << u.size() << ",1,[";
for(auto itu=u.begin(); itu!=u.end();++itu)
report << *itu << ',';
report << "]);\n[";
report << "ERROR v: matrix(" << v.size() << ",1,[";
for(auto itu=v.begin(); itu!=v.end();++itu)
report << *itu << ',';
report << "]);\n[";
for(auto itv=w.begin(); itv!=w.end();++itv)
report << *itv << ' ';
report << "] != 0" << std::endl;
}
commentator().stop ("done");
commentator().progress ();
}
commentator().stop (MSG_STATUS (res), (const char *) 0, "testQLUPnullspace");
return res;
}