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;
}
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
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;
}
static bool testSingularConsistentSolve (const Field &F,
unsigned int n,
VectorStream<Vector> &stream1,
VectorStream<Vector> &stream2,
const char *text,
MethodTraits method)
{
typedef Diagonal <Field, Vector> Blackbox;
ostringstream str;
str << "Testing singular consistent solve (" << text << ")";
commentator().start (str.str ().c_str (), "testSingularConsistentSolve", stream1.m ());
VectorDomain<Field> VD (F);
bool ret = true;
Vector d1, b1, d, b, x, y;
VectorWrapper::ensureDim (d, n);
VectorWrapper::ensureDim (b, n);
VectorWrapper::ensureDim (x, n);
VectorWrapper::ensureDim (y, n);
VectorWrapper::ensureDim (d1, n);
VectorWrapper::ensureDim (b1, n);
MethodTraits traits (method);
traits.preconditioner (MethodTraits::NO_PRECONDITIONER);
while (stream1 && stream2) {
commentator().startIteration ((unsigned)stream1.j ());
ActivityState state = commentator().saveActivityState ();
stream1.next (d1);
stream2.next (b1);
VD.copy (d, d1);
VD.copy (b, b1);
ostream &report = commentator().report (Commentator::LEVEL_IMPORTANT, INTERNAL_DESCRIPTION);
report << "Diagonal entries: ";
VD.write (report, d);
report << endl;
report << "Right-hand side: ";
VD.write (report, b);
report << endl;
BlasVector<Field> dd(F,d);
Blackbox D (dd);
//Blackbox D (d);
try {
bool iter_passed = true;
solve (D, x, b, F, traits);
report << "System solution: ";
VD.write (report, x);
report << endl;
D.apply (y, x);
report << "Output: ";
VD.write (report, y);
report << endl;
if (!VD.areEqual (y, b))
ret = iter_passed = false;
if (!iter_passed)
commentator().report (Commentator::LEVEL_IMPORTANT, INTERNAL_ERROR)
<< "ERROR: Computed solution is incorrect" << endl;
}
catch (SolveFailed) {
commentator().restoreActivityState (state);
commentator().report (Commentator::LEVEL_IMPORTANT, INTERNAL_ERROR)
<< "ERROR: System solution failed" << endl;
ret = false;
}
catch (InconsistentSystem<Vector> e) {
commentator().restoreActivityState (state);
ostream &Report = commentator().report (Commentator::LEVEL_IMPORTANT, INTERNAL_ERROR);
Report << "ERROR: Inconsistent system exception" << endl;
Report << "Certificate is: ";
VD.write (Report, e.u ()) << endl;
ret = false;
commentator().restoreActivityState (state);
}
commentator().stop ("done");
commentator().progress ();
}
stream1.reset ();
stream2.reset ();
commentator().stop (MSG_STATUS (ret), (const char *) 0, "testSingularConsistentSolve");
return ret;
}
static bool testNonsingularSolve (const Field &F,
VectorStream<Vector> &stream1,
VectorStream<Vector> &stream2,
const char *text,
MethodTraits method)
{
typedef Diagonal <Field> Blackbox;
ostringstream str;
str << "Testing nonsingular solve (" << text << ")";
commentator().start (str.str ().c_str (), "testNonsingularSolve", stream1.m ());
VectorDomain<Field> VD (F);
bool ret = true;
size_t n= stream1.n ();
Vector d(F,n), b(F,n), x(F,n), y(F,n);
// VectorWrapper::ensureDim (d, stream1.n ());
// VectorWrapper::ensureDim (b, stream1.n ());
// VectorWrapper::ensureDim (x, stream1.n ());
// VectorWrapper::ensureDim (y, stream1.n ());
MethodTraits traits (method);
while (stream1 && stream2) {
commentator().startIteration ((unsigned)stream1.j ());
ActivityState state = commentator().saveActivityState ();
bool iter_passed = true;
stream1.next (d);
stream2.next (b);
ostream &report = commentator().report (Commentator::LEVEL_IMPORTANT, INTERNAL_DESCRIPTION);
report << "Diagonal entries: ";
VD.write (report, d);
report << endl;
report << "Right-hand side: ";
VD.write (report, b);
report << endl;
BlasVector<Field> dd(F,d);
Blackbox D (dd);
try {
solve (x, D, b, method);
}
catch (SolveFailed) {
commentator().restoreActivityState (state);
commentator().report (Commentator::LEVEL_IMPORTANT, INTERNAL_ERROR)
<< "ERROR: System solution failed" << endl;
ret = iter_passed = false;
}
catch (InconsistentSystem<Vector> e) {
commentator().restoreActivityState (state);
commentator().report (Commentator::LEVEL_IMPORTANT, INTERNAL_ERROR)
<< "ERROR: solve reported inconsistent system" << endl;
ret = iter_passed = false;
}
if (iter_passed) {
report << "System solution: ";
VD.write (report, x);
report << endl;
D.apply (y, x);
report << "Output: ";
VD.write (report, y);
report << endl;
if (!VD.areEqual (y, b))
ret = iter_passed = false;
if (!iter_passed)
commentator().report (Commentator::LEVEL_IMPORTANT, INTERNAL_ERROR)
<< "ERROR: Computed solution is incorrect" << endl;
}
commentator().stop ("done");
commentator().progress ();
}
stream1.reset ();
stream2.reset ();
commentator().stop (MSG_STATUS (ret), (const char *) 0, "testNonsingularSolve");
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;
}