static bool testRandomLinearity (Field &F,
const char *text,
VectorStream<Row> &A_stream,
VectorStream<Vector> &stream1,
VectorStream<Vector> &stream2)
{
typedef SparseMatrix <Field, Row> Blackbox;
ostringstream str;
str << "Testing linearity (" << text << ")" << ends;
commentator().start (str.str ().c_str (), "testRandomLinearity", stream1.m ());
Blackbox A (F, A_stream);
A_stream.reset ();
ostream &report = commentator().report (Commentator::LEVEL_UNIMPORTANT, INTERNAL_DESCRIPTION);
report << "Input matrix:" << endl;
A.write (report, FORMAT_PRETTY);
bool ret = testLinearity (F, A, stream1, stream2);
stream1.reset ();
stream2.reset ();
commentator().stop (MSG_STATUS (ret), (const char *) 0, "testRandomLinearity");
return ret;
}
bool testRandomApply1 (Field &F, const char *text, unsigned int iterations, VectorStream<Row> &A_stream)
{
typedef SparseMatrix <Field, Row> Blackbox;
ostringstream str;
str << "Testing sparse random apply (1, " << text << ")" << ends;
commentator().start (str.str ().c_str (), "testRandomApply1", iterations);
bool ret = true;
bool iter_passed;
size_t i, k;
VectorDomain<Field> VD (F);
StandardBasisStream<Field, Vector> stream (F, A_stream.n ());
Vector e_j, w;
VectorWrapper::ensureDim (e_j, A_stream.n ());
VectorWrapper::ensureDim (w, A_stream.m ());
for (i = 0; i < iterations; i++) {
commentator().startIteration ((unsigned)i);
iter_passed = true;
Blackbox A (F, A_stream);
A_stream.reset ();
ostream &report = commentator().report (Commentator::LEVEL_UNIMPORTANT, INTERNAL_DESCRIPTION);
report << "Matrix:" << endl;
A.write (report, FORMAT_PRETTY);
stream.reset ();
while (stream) {
stream.next (e_j);
A.apply (w, e_j);
for (k = 0; k < A_stream.m (); k++)
if (!F.areEqual (A.getEntry (k, stream.j () - 1), VectorWrapper::constRef<Field> (w, k)))
ret = iter_passed = false;
report << "Output vector " << stream.j () << ": ";
VD.write (report, w) << endl;
}
if (!iter_passed)
commentator().report (Commentator::LEVEL_IMPORTANT, INTERNAL_ERROR)
<< "ERROR: Output vectors were incorrect" << endl;
commentator().stop ("done");
commentator().progress ();
}
commentator().stop (MSG_STATUS (ret), (const char *) 0, "testRandomApply1");
return ret;
}
static bool testIdentityApply (Field &F, const char *text, VectorStream<Vector> &stream)
{
typedef SparseMatrix <Field, Row> Blackbox;
ostringstream str;
str << "Testing identity apply (" << text << ")" << ends;
commentator().start (str.str ().c_str (), "testIdentityApply", stream.m ());
bool ret = true;
bool iter_passed = true;
VectorDomain<Field> VD (F);
StandardBasisStream<Field, Row> f1 (F, stream.n ());
Blackbox A (F, f1);
ostream &report = commentator().report (Commentator::LEVEL_UNIMPORTANT, INTERNAL_DESCRIPTION);
report << "Matrix:" << endl;
A.write (report, FORMAT_PRETTY);
Vector v, w;
VectorWrapper::ensureDim (v, stream.n ());
VectorWrapper::ensureDim (w, stream.n ());
while (stream) {
commentator().startIteration ((unsigned)stream.j ());
iter_passed = true;
stream.next (v);
ostream &Report = commentator().report (Commentator::LEVEL_UNIMPORTANT, INTERNAL_DESCRIPTION);
Report << "Input vector: ";
VD.write (Report, v);
Report << endl;
A.apply (w, v);
Report << "Output vector: ";
VD.write (Report, w);
Report << endl;
if (!VD.areEqual (v, w))
ret = iter_passed = false;
if (!iter_passed)
commentator().report (Commentator::LEVEL_IMPORTANT, INTERNAL_ERROR)
<< "ERROR: Vectors are not equal" << endl;
commentator().stop ("done");
commentator().progress ();
}
stream.reset ();
commentator().stop (MSG_STATUS (ret), (const char *) 0, "testIdentityApply");
return ret;
}
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;
}
bool testQLUPsolve(const Field &F, size_t n, unsigned int iterations, int rseed, double sparsity = 0.05)
{
bool res = true;
commentator().start ("Testing Sparse elimination qlup solve", "testQLUPsolve", 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);
GF2 F2;
GF2::RandIter bitgenerator(F2,2,rseed);
// GF2::Element randomsolve;
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), x(F,Nj), y(F,Ni);
for(auto it=u.begin();it!=u.end();++it)
generator.random (*it);
A.apply(v,u);
Method::SparseElimination SE;
SE.strategy(Specifier::PIVOT_LINEAR);
GaussDomain<Field> GD ( F );
Blackbox CopyA ( A );
GD.solvein(x, A, v /*, bitgenerator .random(randomsolve) */ );
// report << "Random solving: " << randomsolve << std::endl;
CopyA.apply(y, x);
VectorDomain<Field> VD(F);
if (! VD.areEqual(v,y)) {
res=false;
A.write( report, Tag::FileFormat::Maple ) << endl;
report << "ERROR v: matrix(" << v.size() << ",1,[";
for(auto itu=v.begin(); itu!=v.end();++itu)
report << *itu << ',';
report << "]);\n[";
report << "ERROR y: matrix(" << y.size() << ",1,[";
for(auto itu=y.begin(); itu!=y.end();++itu)
report << *itu << ',';
report << "]);\n[";
for(auto itv=x.begin(); itv!=x.end();++itv)
report << *itv << ' ';
report << "] != [";
for(auto itw=y.begin(); itw!=y.end();++itw)
report << *itw << ' ';
report << "]" << std::endl;
}
commentator().stop ("done");
commentator().progress ();
}
commentator().stop (MSG_STATUS (res), (const char *) 0, "testQLUPsolve");
return res;
}
bool testRandomApply2 (Field &F, const char *text, unsigned int iterations, VectorStream<Row> &A_stream)
{
typedef SparseMatrix <Field, Row> Blackbox;
ostringstream str;
str << "Testing sparse random apply (2, " << text << ")" << ends;
commentator().start (str.str ().c_str (), "testRandomApply2", iterations);
bool ret = true;
bool iter_passed;
size_t i, j, k;
VectorDomain<Field> VD (F);
typename Field::RandIter r (F);
typename Field::Element sum;
integer c;
// long width;
F.characteristic (c);
// width = logp (c, 10) + 1;
Vector v, w;
VectorWrapper::ensureDim (v, A_stream.n ());
VectorWrapper::ensureDim (w, A_stream.m ());
for (k = 0; k < A_stream.n (); k++)
F.init (VectorWrapper::ref<Field> (v, k), 1);
for (i = 0; i < iterations; i++) {
commentator().startIteration ((unsigned)i);
iter_passed = true;
Blackbox A (F, A_stream);
A_stream.reset ();
ostream &report = commentator().report (Commentator::LEVEL_UNIMPORTANT, INTERNAL_DESCRIPTION);
report << "Matrix:" << endl;
A.write (report, FORMAT_PRETTY);
A.apply (w, v);
for (j = 0; j < A_stream.m (); j++) {
F.init (sum, 0);
for (k = 0; k < A_stream.n (); k++)
F.addin (sum, A.getEntry (j, k));
if (!F.areEqual (sum, VectorWrapper::constRef<Field> (w, j)))
ret = iter_passed = false;
}
report << "Output vector: ";
VD.write (report, w) << endl;
if (!iter_passed)
commentator().report (Commentator::LEVEL_IMPORTANT, INTERNAL_ERROR)
<< "ERROR: Output vector was incorrect" << endl;
commentator().stop ("done");
commentator().progress ();
}
commentator().stop (MSG_STATUS (ret), (const char *) 0, "testRandomApply2");
return ret;
}
static bool testNilpotentApply (Field &F, const char *text, VectorStream<Vector> &stream)
{
typedef SparseMatrix <Field, Row> Blackbox;
ostringstream str;
str << "Testing nilpotent apply (" << text << ")" << ends;
commentator().start (str.str ().c_str (), "testNilpotentApply", stream.m ());
bool ret = true;
bool even, iter_passed;
StandardBasisStream<Field, Row> f1 (F, stream.n ());
Row tmp;
f1.next (tmp); // Small trick: pull the first vector out to shift elements up one row
Blackbox A (F, f1);
ostream &report = commentator().report (Commentator::LEVEL_UNIMPORTANT, INTERNAL_DESCRIPTION);
report << "Matrix:" << endl;
A.write (report, FORMAT_PRETTY);
size_t j;
NonzeroRandIter<Field> r (F, typename Field::RandIter (F));
VectorDomain<Field> VD (F);
Vector v, w;
VectorWrapper::ensureDim (v, stream.n ());
VectorWrapper::ensureDim (w, stream.n ());
while (stream) {
commentator().startIteration ((unsigned)stream.j ());
iter_passed = true;
even = false;
stream.next (v);
// Make sure last element is nonzero
r.random (VectorWrapper::ref<Field> (v, stream.n () - 1));
ostream &Report = commentator().report (Commentator::LEVEL_UNIMPORTANT, INTERNAL_DESCRIPTION);
Report << "Input vector: ";
VD.write (Report, v);
Report << endl;
commentator().start ("Applying vectors");
for (j = 0; j < stream.n () - 1; j++, even = !even)
if (even)
A.apply (v, w);
else
A.apply (w, v);
commentator().stop ("Done");
Report << "A^(n-1) v: ";
VD.write (Report, even ? w : v);
Report << endl;
if (VD.isZero (even ? w : v)) {
ret = false;
commentator().report (Commentator::LEVEL_IMPORTANT, INTERNAL_ERROR)
<< "ERROR: A^(n-1) v is prematurely zero" << endl;
}
if (even)
A.apply (v, w);
else
A.apply (w, v);
Report << "A^n v: ";
VD.write (Report, even ? v : w);
Report << endl;
if (!VD.isZero (even ? v : w))
ret = iter_passed = false;
if (!iter_passed)
commentator().report (Commentator::LEVEL_IMPORTANT, INTERNAL_ERROR)
<< "ERROR: A^n v is non-zero" << endl;
commentator().stop ("done");
commentator().progress ();
}
stream.reset ();
commentator().stop (MSG_STATUS (ret), (const char *) 0, "testNilpotentApply");
return ret;
}