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;
}
static bool testSingularPreconditionedSolve (const Field &F,
VectorStream<SparseVector> &stream1,
VectorStream<Vector> &stream2,
const char *text,
Method::Wiedemann::Preconditioner preconditioner)
{
ostringstream str;
str << "Testing singular preconditioned solve (" << text << ")";
commentator().start (str.str ().c_str (), "testSingularPreconditionedSolve", stream1.m ());
VectorDomain<Field> VD (F);
typename WiedemannSolver<Field>::ReturnStatus status;
bool ret = true;
SparseVector d1;
typename Field::Element uTb;
typename LinBox::Vector<Field>::Dense d;
Vector b, x, y, u;
VectorWrapper::ensureDim (d, stream2.dim ());
VectorWrapper::ensureDim (b, stream2.dim ());
VectorWrapper::ensureDim (x, stream2.dim ());
VectorWrapper::ensureDim (y, stream2.dim ());
Method::Wiedemann traits;
traits.preconditioner (preconditioner);
while (stream1 && stream2) {
commentator().startIteration ((unsigned)stream1.j ());
stream1.next (d1);
stream2.next (b);
VD.copy (d, d1);
ostream &report = commentator().report (Commentator::LEVEL_UNIMPORTANT, 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);
Diagonal<Field> A (dd);
//Diagonal<Field> A (F, d);
status = solve (A, x, b, u, F, traits);
if (status == WiedemannSolver<Field>::INCONSISTENT) {
A.applyTranspose (y, u);
report << "Certificate of inconsistency found." << endl;
report << "Certificate is: ";
VD.write (report, u) << endl;
report << "u^T A = ";
VD.write (report, y) << endl;
VD.dot (uTb, u, b);
report << "u^T b = ";
F.write (report, uTb) << endl;
if (!VD.isZero (y)) {
commentator().report (Commentator::LEVEL_IMPORTANT, INTERNAL_ERROR)
<< "ERROR: u is not in the right nullspace of D" << endl;
ret = false;
}
if (F.isZero (uTb)) {
commentator().report (Commentator::LEVEL_IMPORTANT, INTERNAL_ERROR)
<< "ERROR: u^T b = 0" << endl;
ret = false;
}
}
else if (status == WiedemannSolver<Field>::FAILED) {
commentator().report (Commentator::LEVEL_IMPORTANT, INTERNAL_ERROR)
<< "ERROR: Solver refused to certify inconsistency" << endl;
ret = false;
}
else {
commentator().report (Commentator::LEVEL_IMPORTANT, INTERNAL_ERROR)
<< "ERROR: Solver gave solution even though system is inconsistent" << endl;
ret = false;
}
commentator().stop ("done");
commentator().progress ();
}
stream1.reset ();
stream2.reset ();
commentator().stop (MSG_STATUS (ret), (const char *) 0, "testSingularPreconditionedSolve");
return ret;
}
static bool testZeroApply (Field1 &F1, Field2 &F2, VectorStream<Vector> &stream1, VectorStream<Vector> &stream2)
{
commentator().start ("Testing zero apply", "testZeroApply", stream1.m ());
bool ret = true;
bool iter_passed = true;
Vector d1, d2, v, w, zero;
VectorDomain<Field1> VD (F1);
typename Field1::Element neg_one;
VectorWrapper::ensureDim (zero, stream1.dim ());
VectorWrapper::ensureDim (d1, stream1.dim ());
VectorWrapper::ensureDim (d2, stream1.dim ());
VectorWrapper::ensureDim (v, stream1.dim ());
VectorWrapper::ensureDim (w, stream2.dim ());
// F.init (neg_one, 1);
// F.negin (neg_one);
F1.init (neg_one, -1);
while (stream1) {
commentator().startIteration ((unsigned)stream1.j ());
iter_passed = true;
stream1.next (d1);
VD.mul (d2, d1, neg_one);
Diagonal <Field1> D1 (F1, d1), D2 (F1, d2);
Sum <Diagonal<Field1>,Diagonal <Field1> > A (&D1, &D2);
ostream &report = commentator().report (Commentator::LEVEL_IMPORTANT, INTERNAL_DESCRIPTION);
report << "Diagonal matrix: ";
VD.write (report, d1);
report << endl;
report << "Negative diagonal matrix: ";
VD.write (report, d2);
report << endl;
stream2.reset ();
while (stream2) {
stream2.next (w);
report << "Input vector: ";
VD.write (report, w);
report << endl;
A.apply (v, w);
report << "Output vector: ";
VD.write (report, v);
report << endl;
if (!VD.isZero (v))
ret = iter_passed = false;
}
if (!iter_passed)
commentator().report (Commentator::LEVEL_IMPORTANT, INTERNAL_ERROR)
<< "ERROR: Vector is not zero" << endl;
commentator().stop ("done");
commentator().progress ();
ret = ret && testBBrebind(F2, A);
}
commentator().stop (MSG_STATUS (ret), (const char *) 0, "testZeroApply");
return ret;
}