int main(int argc, char *argv[])
{
int stat = 0;
try
{
GlobalMPISession session(&argc, &argv);
/* create a distributed vector space for the multivector's vectors */
VectorType<double> rowType = new EpetraVectorType();
int nLocalRows = 2;
VectorSpace<double> space
= rowType.createEvenlyPartitionedSpace(MPIComm::world(), nLocalRows);
/* create a replicated vector space for the small space of columns */
int nVecs = 3;
VectorType<double> colType = new SerialVectorType();
VectorSpace<double> replSpace
= colType.createEvenlyPartitionedSpace(MPIComm::world(), nVecs);
/* create some random vectors */
Teuchos::Array<Vector<double> > vecs(nVecs);
for (int i=0; i<nVecs; i++)
{
vecs[i] = space.createMember();
vecs[i].randomize();
}
/* Test multiplication by a multivector operator. We will compute
* y1 by directly summing columns, and y2 by applying the operator */
LinearOperator<double> A = multiVectorOperator<double>(vecs, replSpace);
Vector<double> y1 = space.createMember();
Vector<double> y2 = space.createMember();
y1.zero();
y2.zero();
/* Sum columns, putting the weights into x */
Vector<double> x = replSpace.createMember();
Out::os() << "A=" << A << std::endl;
for (int j=0; j<replSpace.numLocalElements(); j++)
{
x[j] = 2.0*(drand48()-0.5);
y1 = y1 + x[j] * vecs[j];
Out::os() << "x[" << j << "]=" << x[j] << std::endl;
Out::os() << "vecs[j]=" << vecs[j] << std::endl;
}
Out::os() << "y1=" << std::endl << y1 << std::endl;
/* Apply the operator to the vector of weights */
y2 = A * x;
Out::os() << "y2=A*x=" << std::endl << y2 << std::endl;
Vector<double> y12 = y1-y2;
Vector<double> y21 = y2-y1;
Out::os() << "y1-y2=" << std::endl << y12 << std::endl;
Out::os() << "y2-y1=" << std::endl << y21 << std::endl;
double errA = (y1-y2).norm2();
Out::root() << "error in A*x = " << errA << std::endl;
/* Now test z = A^T * y */
LinearOperator<double> At = A.transpose();
Vector<double> z1 = replSpace.createMember();
z1.zero();
Vector<double> z2 = replSpace.createMember();
z2.zero();
Vector<double> y = y1.copy();
/* compute by vectorwise multiplication */
for (int j=0; j<replSpace.numLocalElements(); j++)
{
z1[j] = vecs[j].dot(y);
}
/* compute with operator */
z2 = At * y;
double errAt = (z1-z2).normInf();
Out::root() << "error in At*y = " << errA << std::endl;
double tol = 1.0e-13;
bool pass = errA + errAt < tol;
pass = globalAnd(pass);
if (pass)
{
Out::root() << "multivector op test PASSED" << std::endl;
}
else
{
stat = -1;
Out::root() << "multivector op test FAILED" << std::endl;
}
}
catch(std::exception& e)
{
stat = -1;
std::cerr << "Caught exception: " << e.what() << std::endl;
}
return stat;
}
int main(int argc, char *argv[])
{
int stat = 0;
try
{
GlobalMPISession session(&argc, &argv);
VectorType<double> vecType = new SerialVectorType();
VectorSpace<double> domain
= vecType.createEvenlyPartitionedSpace(MPIComm::world(), 3);
VectorSpace<double> range
= vecType.createEvenlyPartitionedSpace(MPIComm::world(), 5);
RCP<MatrixFactory<double> > mf
= vecType.createMatrixFactory(domain, range);
LinearOperator<double> A = mf->createMatrix();
RCP<DenseSerialMatrix> APtr
= rcp_dynamic_cast<DenseSerialMatrix>(A.ptr());
APtr->setRow(0, tuple(1.0, 2.0, 3.0));
APtr->setRow(1, tuple(4.0, 5.0, 6.0));
APtr->setRow(2, tuple(7.0, 8.0, 9.0));
APtr->setRow(3, tuple(10.0, 11.0, 12.0));
APtr->setRow(4, tuple(13.0, 14.0, 15.0));
Out::os() << "A = " << std::endl;
A.setVerb(10);
Out::os() << A << std::endl;
LinearOperator<double> U;
LinearOperator<double> Vt;
Vector<double> sigma;
denseSVD(A, U, sigma, Vt);
Out::os() << "U = " << std::endl;
U.setVerb(10);
Out::os() << U << std::endl;
Out::os() << "sigma = " << std::endl;
Out::os() << sigma << std::endl;
Out::os() << "Vt = " << std::endl;
Vt.setVerb(10);
Out::os() << Vt << std::endl;
int nSamples = 10;
bool allOK = true;
double tol = 1.0e-13;
for (int i=0; i<nSamples; i++)
{
Out::os() << "Sample #" << i << " of " << nSamples << std::endl;
Vector<double> x = domain.createMember();
x.randomize();
U.setVerb(0);
Vt.setVerb(0);
A.setVerb(0);
LinearOperator<double> Sigma = diagonalOperator(sigma);
Vector<double> z = (U * Sigma * Vt)*x - A*x;
double ez = z.norm2();
Out::os() << "|| (U Sigma Vt - A)*x || = " << ez << std::endl;
Vector<double> y = (U.transpose() * U)*x - x;
double ey = y.norm2();
Out::os() << "|| (U^T U - I)*x || = " << ey << std::endl;
Vector<double> w = (Vt * Vt.transpose())*x - x;
double ew = w.norm2();
Out::os() << "|| (V^T*V - I)*x || = " << ew << std::endl;
if (ew > tol || ez > tol || ey > tol) allOK = false;
}
if (allOK)
{
Out::os() << "SVD test PASSED" << std::endl;
}
else
{
Out::os() << "SVD test FAILED" << std::endl;
stat = -1;
}
}
catch(std::exception& e)
{
stat = -1;
Out::os() << "Caught exception: " << e.what() << std::endl;
}
return stat;
}