/usr/include/trilinos/BelosOrthoManagerTest.hpp is in libtrilinos-belos-dev 12.4.2-2.
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// ************************************************************************
//
// Belos: Block Linear Solvers Package
// Copyright 2004 Sandia Corporation
//
// Under the terms of Contract DE-AC04-94AL85000 with Sandia Corporation,
// the U.S. Government retains certain rights in this software.
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// met:
//
// 1. Redistributions of source code must retain the above copyright
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// 2. Redistributions in binary form must reproduce the above copyright
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// documentation and/or other materials provided with the distribution.
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// contributors may be used to endorse or promote products derived from
// this software without specific prior written permission.
//
// THIS SOFTWARE IS PROVIDED BY SANDIA CORPORATION "AS IS" AND ANY
// EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
// IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
// PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL SANDIA CORPORATION OR THE
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// EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
// PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
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//@HEADER
/// \file BelosOrthoManagerTest.hpp
/// \brief Tests for Belos::OrthoManager and Belos::MatOrthoManager subclasses
///
#include <BelosConfigDefs.hpp>
#include <BelosMultiVecTraits.hpp>
#include <BelosOutputManager.hpp>
#include <BelosOrthoManagerFactory.hpp>
#include <Teuchos_StandardCatchMacros.hpp>
#include <Teuchos_TimeMonitor.hpp>
#include <iostream>
#include <stdexcept>
using std::endl;
namespace Belos {
namespace Test {
/// \class OrthoManagerBenchmarker
/// \brief OrthoManager benchmark
/// \author Mark Hoemmen
///
template<class Scalar, class MV>
class OrthoManagerBenchmarker {
private:
typedef Scalar scalar_type;
typedef typename Teuchos::ScalarTraits<Scalar>::magnitudeType magnitude_type;
typedef MultiVecTraits<Scalar, MV> MVT;
typedef Teuchos::SerialDenseMatrix<int, Scalar> mat_type;
public:
/// \brief Establish baseline run time for OrthoManager benchmark
///
/// Replacing a Belos OrthoManager or MatOrthoManager's
/// projection and normalization operations with the same number
/// of vector copies establishes a rough lower bound on run
/// time, because orthogonalization generally requires that much
/// data movement. This gives us a rough sense for how long the
/// orthogonalization should take, so we can calibrate the
/// number of trials needed for accurate timings.
static void
baseline (const Teuchos::RCP<const MV>& X,
const int numCols,
const int numBlocks,
const int numTrials)
{
using Teuchos::Array;
using Teuchos::RCP;
using Teuchos::rcp;
using Teuchos::Time;
using Teuchos::TimeMonitor;
// Make some blocks to "orthogonalize." Fill with random
// data. We only need X so that we can make clones (it knows
// its data distribution).
Array<RCP<MV> > V (numBlocks);
for (int k = 0; k < numBlocks; ++k) {
V[k] = MVT::Clone (*X, numCols);
MVT::MvRandom (*V[k]);
}
// Make timers with informative labels
RCP<Time> timer = TimeMonitor::getNewCounter ("Baseline for OrthoManager benchmark");
// Baseline benchmark just copies data. It's sort of a lower
// bound proxy for the volume of data movement done by a real
// OrthoManager.
{
TimeMonitor monitor (*timer);
for (int trial = 0; trial < numTrials; ++trial) {
for (int k = 0; k < numBlocks; ++k) {
for (int j = 0; j < k; ++j)
MVT::Assign (*V[j], *V[k]);
MVT::Assign (*X, *V[k]);
}
}
}
}
/// \brief Benchmark the given orthogonalization manager
///
/// \param orthoMan [in(/out)] The orthogonalization
/// manager to benchmark
/// \param orthoManName [in] Name of the orthogonalization
/// manager (e.g., "TSQR", "ICGS", "DGKS")
/// \param normalization [in] Normalization scheme used
/// by the orthogonalization manager (only applicable
/// to the "Simple" orthogonalization)
/// \param X [in] "Prototype" multivector; not modified
/// \param numCols [in] Number of columns per block
/// \param numBlocks [in] Number of blocks
/// \param numTrials [in] Number of trials in the timing run
/// \param outMan [out] Output manager
///
/// \param resultStream [out] Output stream for printing
/// benchmark results. If displayResultsCompactly is true, it
/// will be written by all MPI rank(s), so on ranks other than
/// 0, it should be set appropriately to a "black hole stream"
/// that doesn't write anything.
///
/// \param displayResultsCompactly [in] If false, rely on
/// TimeMonitor::summarize() to print results to resultStream
/// (and ensure only MPI Rank 0 does so). If true, print
/// results in a more compact format suitable for automatic
/// parsing, using a CSV (Comma-Delimited Values) parser. In
/// "compact" mode, two lines are printed, both of which are
/// comma-delimited ASCII text. The first line begins with a
/// "comment" character #; following that are column ("field")
/// labels. The second line contains the actual data, again
/// in ASCII comma-delimited format.
static void
benchmark (const Teuchos::RCP<OrthoManager<Scalar, MV> >& orthoMan,
const std::string& orthoManName,
const std::string& normalization,
const Teuchos::RCP<const MV>& X,
const int numCols,
const int numBlocks,
const int numTrials,
const Teuchos::RCP<OutputManager<Scalar> >& outMan,
std::ostream& resultStream,
const bool displayResultsCompactly=false)
{
using Teuchos::Array;
using Teuchos::ArrayView;
using Teuchos::RCP;
using Teuchos::rcp;
using Teuchos::Time;
using Teuchos::TimeMonitor;
using std::endl;
TEUCHOS_TEST_FOR_EXCEPTION(orthoMan.is_null(), std::invalid_argument,
"orthoMan is null");
TEUCHOS_TEST_FOR_EXCEPTION(X.is_null(), std::invalid_argument,
"X is null");
TEUCHOS_TEST_FOR_EXCEPTION(numCols < 1, std::invalid_argument,
"numCols = " << numCols << " < 1");
TEUCHOS_TEST_FOR_EXCEPTION(numBlocks < 1, std::invalid_argument,
"numBlocks = " << numBlocks << " < 1");
TEUCHOS_TEST_FOR_EXCEPTION(numTrials < 1, std::invalid_argument,
"numTrials = " << numTrials << " < 1");
// Debug output stream
std::ostream& debugOut = outMan->stream(Debug);
// If you like, you can add the "baseline" as an approximate
// lower bound for orthogonalization performance. It may be
// useful as a sanity check to make sure that your
// orthogonalizations are really computing something, though
// testing accuracy can help with that too.
//
//baseline (X, numCols, numBlocks, numTrials);
// Make space to put the projection and normalization
// coefficients.
Array<RCP<mat_type> > C (numBlocks);
for (int k = 0; k < numBlocks; ++k) {
C[k] = rcp (new mat_type (numCols, numCols));
}
RCP<mat_type> B (new mat_type (numCols, numCols));
// Make some blocks to orthogonalize. Fill with random data.
// We won't be orthogonalizing X, or even modifying X. We
// only need X so that we can make clones (since X knows its
// data distribution).
Array<RCP<MV> > V (numBlocks);
for (int k = 0; k < numBlocks; ++k) {
V[k] = MVT::Clone (*X, numCols);
MVT::MvRandom (*V[k]);
}
// Make timers with informative labels. We time an additional
// first run to measure the startup costs, if any, of the
// OrthoManager instance.
RCP<Time> firstRunTimer;
{
std::ostringstream os;
os << "OrthoManager: " << orthoManName << " first run";
firstRunTimer = TimeMonitor::getNewCounter (os.str());
}
RCP<Time> timer;
{
std::ostringstream os;
os << "OrthoManager: " << orthoManName << " total over "
<< numTrials << " trials (excluding first run above)";
timer = TimeMonitor::getNewCounter (os.str());
}
// The first run lets us measure the startup costs, if any, of
// the OrthoManager instance, without these costs influencing
// the following timing runs.
{
TimeMonitor monitor (*firstRunTimer);
{
(void) orthoMan->normalize (*V[0], B);
for (int k = 1; k < numBlocks; ++k) {
// k is the number of elements in the ArrayView. We
// have to assign first to an ArrayView-of-RCP-of-MV,
// rather than to an ArrayView-of-RCP-of-const-MV, since
// the latter requires a reinterpret cast. Don't you
// love C++ type inference?
ArrayView<RCP<MV> > V_0k_nonconst = V.view (0, k);
ArrayView<RCP<const MV> > V_0k =
Teuchos::av_reinterpret_cast<RCP<const MV> > (V_0k_nonconst);
(void) orthoMan->projectAndNormalize (*V[k], C, B, V_0k);
}
}
// "Test" that the trial run actually orthogonalized
// correctly. Results are printed to the OutputManager's
// Belos::Debug output stream, so depending on the
// OutputManager's chosen verbosity level, you may or may
// not see the results of the test.
//
// NOTE (mfh 22 Jan 2011) For now, these results have to be
// inspected visually. We should add a simple automatic
// test.
debugOut << "Orthogonality of V[0:" << (numBlocks-1)
<< "]:" << endl;
for (int k = 0; k < numBlocks; ++k) {
// Orthogonality of each block
debugOut << "For block V[" << k << "]:" << endl;
debugOut << " ||<V[" << k << "], V[" << k << "]> - I|| = "
<< orthoMan->orthonormError(*V[k]) << endl;
// Relative orthogonality with the previous blocks
for (int j = 0; j < k; ++j) {
debugOut << " ||< V[" << j << "], V[" << k << "] >|| = "
<< orthoMan->orthogError(*V[j], *V[k]) << endl;
}
}
}
// Run the benchmark for numTrials trials. Time all trials as
// a single run.
{
TimeMonitor monitor (*timer);
for (int trial = 0; trial < numTrials; ++trial) {
(void) orthoMan->normalize (*V[0], B);
for (int k = 1; k < numBlocks; ++k) {
ArrayView<RCP<MV> > V_0k_nonconst = V.view (0, k);
ArrayView<RCP<const MV> > V_0k =
Teuchos::av_reinterpret_cast<RCP<const MV> > (V_0k_nonconst);
(void) orthoMan->projectAndNormalize (*V[k], C, B, V_0k);
}
}
}
// Report timing results.
if (displayResultsCompactly)
{
// The "compact" format is suitable for automatic parsing,
// using a CSV (Comma-Delimited Values) parser. The first
// "comment" line may be parsed to extract column
// ("field") labels; the second line contains the actual
// data, in ASCII comma-delimited format.
using std::endl;
resultStream << "#orthoManName"
<< ",normalization"
<< ",numRows"
<< ",numCols"
<< ",numBlocks"
<< ",firstRunTimeInSeconds"
<< ",timeInSeconds"
<< ",numTrials"
<< endl;
resultStream << orthoManName
<< "," << (orthoManName=="Simple" ? normalization : "N/A")
<< "," << MVT::GetGlobalLength(*X)
<< "," << numCols
<< "," << numBlocks
<< "," << firstRunTimer->totalElapsedTime()
<< "," << timer->totalElapsedTime()
<< "," << numTrials
<< endl;
}
else {
TimeMonitor::summarize (resultStream);
}
}
};
/// \class OrthoManagerTester
/// \brief Wrapper around OrthoManager test functionality
///
template< class Scalar, class MV >
class OrthoManagerTester {
private:
typedef typename Teuchos::Array<Teuchos::RCP<MV> >::size_type size_type;
public:
typedef Scalar scalar_type;
typedef Teuchos::ScalarTraits<scalar_type> SCT;
typedef typename SCT::magnitudeType magnitude_type;
typedef Teuchos::ScalarTraits<magnitude_type> SMT;
typedef MultiVecTraits<scalar_type, MV> MVT;
typedef Teuchos::SerialDenseMatrix<int, scalar_type> mat_type;
/// \brief Run all the tests
///
/// \param OM [in/out] OrthoManager subclass instance to test
/// \param isRankRevealing [in] Whether that OrthoManager
/// subclass instance has a true rank-revealing capability.
/// If not, we do not test it on rank-deficient vectors.
/// \param S [in/out] Multivector instance
/// \param sizeX1 [in] Number of columns in X1 (a multivector
/// instance created internally for tests)
/// \param sizeX2 [in] Number of columns in X2 (a multivector
/// instance created internally for tests)
/// \param MyOM [out] Output manager for handling local output.
/// In Anasazi, this class is called BasicOutputManager. In
/// Belos, this class is called OutputManager.
///
/// \return Number of tests that failed (zero means success)
static int
runTests (const Teuchos::RCP<OrthoManager<Scalar, MV> >& OM,
const bool isRankRevealing,
const Teuchos::RCP<MV>& S,
const int sizeX1,
const int sizeX2,
const Teuchos::RCP<OutputManager<Scalar> >& MyOM)
{
using Teuchos::Array;
using Teuchos::null;
using Teuchos::RCP;
using Teuchos::rcp;
using Teuchos::rcp_dynamic_cast;
using Teuchos::tuple;
// Number of tests that have failed thus far.
int numFailed = 0;
// Relative tolerance against which all tests are performed.
const magnitude_type TOL = 1.0e-12;
// Absolute tolerance constant
//const magnitude_type ATOL = 10;
const scalar_type ZERO = SCT::zero();
const scalar_type ONE = SCT::one();
// Debug output stream
std::ostream& debugOut = MyOM->stream(Debug);
// Number of columns in the input "prototype" multivector S.
const int sizeS = MVT::GetNumberVecs (*S);
// Create multivectors X1 and X2, using the same map as multivector
// S. Then, test orthogonalizing X2 against X1. After doing so, X1
// and X2 should each be M-orthonormal, and should be mutually
// M-orthogonal.
debugOut << "Generating X1,X2 for testing... ";
RCP< MV > X1 = MVT::Clone (*S, sizeX1);
RCP< MV > X2 = MVT::Clone (*S, sizeX2);
debugOut << "done." << endl;
{
magnitude_type err;
//
// Fill X1 with random values, and test the normalization error.
//
debugOut << "Filling X1 with random values... ";
MVT::MvRandom(*X1);
debugOut << "done." << endl
<< "Calling normalize() on X1... ";
// The Anasazi and Belos OrthoManager interfaces differ.
// For example, Anasazi's normalize() method accepts either
// one or two arguments, whereas Belos' normalize() requires
// two arguments.
const int initialX1Rank = OM->normalize(*X1, Teuchos::null);
TEUCHOS_TEST_FOR_EXCEPTION(initialX1Rank != sizeX1,
std::runtime_error,
"normalize(X1) returned rank "
<< initialX1Rank << " from " << sizeX1
<< " vectors. Cannot continue.");
debugOut << "done." << endl
<< "Calling orthonormError() on X1... ";
err = OM->orthonormError(*X1);
TEUCHOS_TEST_FOR_EXCEPTION(err > TOL, std::runtime_error,
"After normalize(X1), orthonormError(X1) = "
<< err << " > TOL = " << TOL);
debugOut << "done: ||<X1,X1> - I|| = " << err << endl;
//
// Fill X2 with random values, project against X1 and normalize,
// and test the orthogonalization error.
//
debugOut << "Filling X2 with random values... ";
MVT::MvRandom(*X2);
debugOut << "done." << endl
<< "Calling projectAndNormalize(X2, C, B, tuple(X1))... "
<< std::flush;
// The projectAndNormalize() interface also differs between
// Anasazi and Belos. Anasazi's projectAndNormalize() puts
// the multivector and the array of multivectors first, and
// the (array of) SerialDenseMatrix arguments (which are
// optional) afterwards. Belos puts the (array of)
// SerialDenseMatrix arguments in the middle, and they are
// not optional.
int initialX2Rank;
{
Array<RCP<mat_type> > C (1);
RCP<mat_type> B = Teuchos::null;
initialX2Rank =
OM->projectAndNormalize (*X2, C, B, tuple<RCP<const MV> >(X1));
}
TEUCHOS_TEST_FOR_EXCEPTION(initialX2Rank != sizeX2,
std::runtime_error,
"projectAndNormalize(X2,X1) returned rank "
<< initialX2Rank << " from " << sizeX2
<< " vectors. Cannot continue.");
debugOut << "done." << endl
<< "Calling orthonormError() on X2... ";
err = OM->orthonormError (*X2);
TEUCHOS_TEST_FOR_EXCEPTION(err > TOL,
std::runtime_error,
"projectAndNormalize(X2,X1) did not meet tolerance: "
"orthonormError(X2) = " << err << " > TOL = " << TOL);
debugOut << "done: || <X2,X2> - I || = " << err << endl
<< "Calling orthogError(X2, X1)... ";
err = OM->orthogError (*X2, *X1);
TEUCHOS_TEST_FOR_EXCEPTION(err > TOL,
std::runtime_error,
"projectAndNormalize(X2,X1) did not meet tolerance: "
"orthogError(X2,X1) = " << err << " > TOL = " << TOL);
debugOut << "done: || <X2,X1> || = " << err << endl;
}
//
// If OM is an OutOfPlaceNormalizerMixin, exercise the
// out-of-place normalization routines.
//
typedef Belos::OutOfPlaceNormalizerMixin<Scalar, MV> mixin_type;
RCP<mixin_type> tsqr = rcp_dynamic_cast<mixin_type>(OM);
if (! tsqr.is_null())
{
magnitude_type err;
debugOut << endl
<< "=== OutOfPlaceNormalizerMixin tests ==="
<< endl << endl;
//
// Fill X1_in with random values, and test the normalization
// error with normalizeOutOfPlace().
//
// Don't overwrite X1, else you'll mess up the tests that
// follow!
//
RCP<MV> X1_in = MVT::CloneCopy (*X1);
debugOut << "Filling X1_in with random values... ";
MVT::MvRandom(*X1_in);
debugOut << "done." << endl;
debugOut << "Filling X1_out with different random values...";
RCP<MV> X1_out = MVT::Clone(*X1_in, MVT::GetNumberVecs(*X1_in));
MVT::MvRandom(*X1_out);
debugOut << "done." << endl
<< "Calling normalizeOutOfPlace(*X1_in, *X1_out, null)... ";
const int initialX1Rank =
tsqr->normalizeOutOfPlace(*X1_in, *X1_out, Teuchos::null);
TEUCHOS_TEST_FOR_EXCEPTION(initialX1Rank != sizeX1, std::runtime_error,
"normalizeOutOfPlace(*X1_in, *X1_out, null) "
"returned rank " << initialX1Rank << " from "
<< sizeX1 << " vectors. Cannot continue.");
debugOut << "done." << endl
<< "Calling orthonormError() on X1_out... ";
err = OM->orthonormError(*X1_out);
TEUCHOS_TEST_FOR_EXCEPTION(err > TOL, std::runtime_error,
"After calling normalizeOutOfPlace(*X1_in, "
"*X1_out, null), orthonormError(X1) = "
<< err << " > TOL = " << TOL);
debugOut << "done: ||<X1_out,X1_out> - I|| = " << err << endl;
//
// Fill X2_in with random values, project against X1_out
// and normalize via projectAndNormalizeOutOfPlace(), and
// test the orthogonalization error.
//
// Don't overwrite X2, else you'll mess up the tests that
// follow!
//
RCP<MV> X2_in = MVT::CloneCopy (*X2);
debugOut << "Filling X2_in with random values... ";
MVT::MvRandom(*X2_in);
debugOut << "done." << endl
<< "Filling X2_out with different random values...";
RCP<MV> X2_out = MVT::Clone(*X2_in, MVT::GetNumberVecs(*X2_in));
MVT::MvRandom(*X2_out);
debugOut << "done." << endl
<< "Calling projectAndNormalizeOutOfPlace(X2_in, X2_out, "
<< "C, B, X1_out)...";
int initialX2Rank;
{
Array<RCP<mat_type> > C (1);
RCP<mat_type> B = Teuchos::null;
initialX2Rank =
tsqr->projectAndNormalizeOutOfPlace (*X2_in, *X2_out, C, B,
tuple<RCP<const MV> >(X1_out));
}
TEUCHOS_TEST_FOR_EXCEPTION(initialX2Rank != sizeX2,
std::runtime_error,
"projectAndNormalizeOutOfPlace(*X2_in, "
"*X2_out, C, B, tuple(X1_out)) returned rank "
<< initialX2Rank << " from " << sizeX2
<< " vectors. Cannot continue.");
debugOut << "done." << endl
<< "Calling orthonormError() on X2_out... ";
err = OM->orthonormError (*X2_out);
TEUCHOS_TEST_FOR_EXCEPTION(err > TOL, std::runtime_error,
"projectAndNormalizeOutOfPlace(*X2_in, *X2_out, "
"C, B, tuple(X1_out)) did not meet tolerance: "
"orthonormError(X2_out) = "
<< err << " > TOL = " << TOL);
debugOut << "done: || <X2_out,X2_out> - I || = " << err << endl
<< "Calling orthogError(X2_out, X1_out)... ";
err = OM->orthogError (*X2_out, *X1_out);
TEUCHOS_TEST_FOR_EXCEPTION(err > TOL, std::runtime_error,
"projectAndNormalizeOutOfPlace(*X2_in, *X2_out, "
"C, B, tuple(X1_out)) did not meet tolerance: "
"orthogError(X2_out, X1_out) = "
<< err << " > TOL = " << TOL);
debugOut << "done: || <X2_out,X1_out> || = " << err << endl;
debugOut << endl
<< "=== Done with OutOfPlaceNormalizerMixin tests ==="
<< endl << endl;
}
{
//
// Test project() on a random multivector S, by projecting S
// against various combinations of X1 and X2.
//
MVT::MvRandom(*S);
debugOut << "Testing project() by projecting a random multivector S "
"against various combinations of X1 and X2 " << endl;
const int thisNumFailed = testProject(OM,S,X1,X2,MyOM);
numFailed += thisNumFailed;
if (thisNumFailed > 0)
debugOut << " *** " << thisNumFailed
<< (thisNumFailed > 1 ? " tests" : " test")
<< " failed." << endl;
}
if (isRankRevealing)
{
// run a X1,Y2 range multivector against P_{X1,X1} P_{Y2,Y2}
// note, this is allowed under the restrictions on project(),
// because <X1,Y2> = 0
// also, <Y2,Y2> = I, but <X1,X1> != I, so biOrtho must be set to false
// it should require randomization, as
// P_{X1,X1} P_{Y2,Y2} (X1*C1 + Y2*C2) = P_{X1,X1} X1*C1 = 0
mat_type C1(sizeX1,sizeS), C2(sizeX2,sizeS);
C1.random();
C2.random();
// S := X1*C1
MVT::MvTimesMatAddMv(ONE,*X1,C1,ZERO,*S);
// S := S + X2*C2
MVT::MvTimesMatAddMv(ONE,*X2,C2,ONE,*S);
debugOut << "Testing project() by projecting [X1 X2]-range multivector "
"against P_X1 P_X2 " << endl;
const int thisNumFailed = testProject(OM,S,X1,X2,MyOM);
numFailed += thisNumFailed;
if (thisNumFailed > 0)
debugOut << " *** " << thisNumFailed
<< (thisNumFailed > 1 ? " tests" : " test")
<< " failed." << endl;
}
// This test is only distinct from the rank-1 multivector test
// (below) if S has at least 3 columns.
if (isRankRevealing && sizeS > 2)
{
MVT::MvRandom(*S);
RCP<MV> mid = MVT::Clone(*S,1);
mat_type c(sizeS,1);
MVT::MvTimesMatAddMv(ONE,*S,c,ZERO,*mid);
std::vector<int> ind(1);
ind[0] = sizeS-1;
MVT::SetBlock(*mid,ind,*S);
debugOut << "Testing normalize() on a rank-deficient multivector " << endl;
const int thisNumFailed = testNormalize(OM,S,MyOM);
numFailed += thisNumFailed;
if (thisNumFailed > 0)
debugOut << " *** " << thisNumFailed
<< (thisNumFailed > 1 ? " tests" : " test")
<< " failed." << endl;
}
// This test will only exercise rank deficiency if S has at least 2
// columns.
if (isRankRevealing && sizeS > 1)
{
// rank-1
RCP<MV> one = MVT::Clone(*S,1);
MVT::MvRandom(*one);
// put multiple of column 0 in columns 0:sizeS-1
for (int i=0; i<sizeS; i++)
{
std::vector<int> ind(1);
ind[0] = i;
RCP<MV> Si = MVT::CloneViewNonConst(*S,ind);
MVT::MvAddMv(SCT::random(),*one,ZERO,*one,*Si);
}
debugOut << "Testing normalize() on a rank-1 multivector " << endl;
const int thisNumFailed = testNormalize(OM,S,MyOM);
numFailed += thisNumFailed;
if (thisNumFailed > 0)
debugOut << " *** " << thisNumFailed
<< (thisNumFailed > 1 ? " tests" : " test")
<< " failed." << endl;
}
{
std::vector<int> ind(1);
MVT::MvRandom(*S);
debugOut << "Testing projectAndNormalize() on a random multivector " << endl;
const int thisNumFailed = testProjectAndNormalize(OM,S,X1,X2,MyOM);
numFailed += thisNumFailed;
if (thisNumFailed > 0)
debugOut << " *** " << thisNumFailed
<< (thisNumFailed > 1 ? " tests" : " test")
<< " failed." << endl;
}
if (isRankRevealing)
{
// run a X1,X2 range multivector against P_X1 P_X2
// this is allowed as <X1,X2> == 0
// it should require randomization, as
// P_X1 P_X2 (X1*C1 + X2*C2) = P_X1 X1*C1 = 0
// and
// P_X2 P_X1 (X2*C2 + X1*C1) = P_X2 X2*C2 = 0
mat_type C1(sizeX1,sizeS), C2(sizeX2,sizeS);
C1.random();
C2.random();
MVT::MvTimesMatAddMv(ONE,*X1,C1,ZERO,*S);
MVT::MvTimesMatAddMv(ONE,*X2,C2,ONE,*S);
debugOut << "Testing projectAndNormalize() by projecting [X1 X2]-range "
"multivector against P_X1 P_X2 " << endl;
const int thisNumFailed = testProjectAndNormalize(OM,S,X1,X2,MyOM);
numFailed += thisNumFailed;
if (thisNumFailed > 0)
debugOut << " *** " << thisNumFailed
<< (thisNumFailed > 1 ? " tests" : " test")
<< " failed." << endl;
}
// This test is only distinct from the rank-1 multivector test
// (below) if S has at least 3 columns.
if (isRankRevealing && sizeS > 2)
{
MVT::MvRandom(*S);
RCP<MV> mid = MVT::Clone(*S,1);
mat_type c(sizeS,1);
MVT::MvTimesMatAddMv(ONE,*S,c,ZERO,*mid);
std::vector<int> ind(1);
ind[0] = sizeS-1;
MVT::SetBlock(*mid,ind,*S);
debugOut << "Testing projectAndNormalize() on a rank-deficient "
"multivector " << endl;
const int thisNumFailed = testProjectAndNormalize(OM,S,X1,X2,MyOM);
numFailed += thisNumFailed;
if (thisNumFailed > 0)
debugOut << " *** " << thisNumFailed
<< (thisNumFailed > 1 ? " tests" : " test")
<< " failed." << endl;
}
// This test will only exercise rank deficiency if S has at least 2
// columns.
if (isRankRevealing && sizeS > 1)
{
// rank-1
RCP<MV> one = MVT::Clone(*S,1);
MVT::MvRandom(*one);
// Put a multiple of column 0 in columns 0:sizeS-1.
for (int i=0; i<sizeS; i++)
{
std::vector<int> ind(1);
ind[0] = i;
RCP<MV> Si = MVT::CloneViewNonConst(*S,ind);
MVT::MvAddMv(SCT::random(),*one,ZERO,*one,*Si);
}
debugOut << "Testing projectAndNormalize() on a rank-1 multivector " << endl;
bool constantStride = true;
if (! MVT::HasConstantStride(*S)) {
debugOut << "-- S does not have constant stride" << endl;
constantStride = false;
}
if (! MVT::HasConstantStride(*X1)) {
debugOut << "-- X1 does not have constant stride" << endl;
constantStride = false;
}
if (! MVT::HasConstantStride(*X2)) {
debugOut << "-- X2 does not have constant stride" << endl;
constantStride = false;
}
if (! constantStride) {
debugOut << "-- Skipping this test, since TSQR does not work on "
"multivectors with nonconstant stride" << endl;
}
else {
const int thisNumFailed = testProjectAndNormalize(OM,S,X1,X2,MyOM);
numFailed += thisNumFailed;
if (thisNumFailed > 0) {
debugOut << " *** " << thisNumFailed
<< (thisNumFailed > 1 ? " tests" : " test")
<< " failed." << endl;
}
}
}
if (numFailed != 0) {
MyOM->stream(Errors) << numFailed << " total test failures." << endl;
}
return numFailed;
}
private:
/// \fn MVDiff
///
/// Compute and return $\|X - Y\|_F$, the Frobenius (sum of
/// squares) norm of the difference between X and Y.
static magnitude_type
MVDiff (const MV& X, const MV& Y)
{
using Teuchos::RCP;
const scalar_type ONE = SCT::one();
const int numCols = MVT::GetNumberVecs(X);
TEUCHOS_TEST_FOR_EXCEPTION( (MVT::GetNumberVecs(Y) != numCols),
std::logic_error,
"MVDiff: X and Y should have the same number of columns."
" X has " << numCols << " column(s) and Y has "
<< MVT::GetNumberVecs(Y) << " columns." );
// Resid := X
RCP< MV > Resid = MVT::CloneCopy(X);
// Resid := Resid - Y
MVT::MvAddMv (-ONE, Y, ONE, *Resid, *Resid);
return frobeniusNorm (*Resid);
}
/// \fn frobeniusNorm
///
/// Compute and return the Frobenius norm of X.
static magnitude_type
frobeniusNorm (const MV& X)
{
const scalar_type ONE = SCT::one();
const int numCols = MVT::GetNumberVecs(X);
mat_type C (numCols, numCols);
// $C := X^* X$
MVT::MvTransMv (ONE, X, X, C);
magnitude_type err (0);
for (int i = 0; i < numCols; ++i)
err += SCT::magnitude (C(i,i));
return SCT::magnitude (SCT::squareroot (err));
}
static int
testProjectAndNormalize (const Teuchos::RCP< Belos::OrthoManager< Scalar, MV > > OM,
const Teuchos::RCP< const MV >& S,
const Teuchos::RCP< const MV >& X1,
const Teuchos::RCP< const MV >& X2,
const Teuchos::RCP< Belos::OutputManager< Scalar > >& MyOM)
{
return testProjectAndNormalizeNew (OM, S, X1, X2, MyOM);
}
/// Test OrthoManager::projectAndNormalize() for the specific
/// OrthoManager instance.
///
/// \return Count of errors (should be zero)
static int
testProjectAndNormalizeOld (const Teuchos::RCP< Belos::OrthoManager< Scalar, MV > >& OM,
const Teuchos::RCP< const MV >& S,
const Teuchos::RCP< const MV >& X1,
const Teuchos::RCP< const MV >& X2,
const Teuchos::RCP< Belos::OutputManager< Scalar > >& MyOM)
{
using Teuchos::Array;
using Teuchos::null;
using Teuchos::RCP;
using Teuchos::rcp;
using Teuchos::tuple;
const scalar_type ONE = SCT::one();
const magnitude_type ZERO = SCT::magnitude(SCT::zero());
// Relative tolerance against which all tests are performed.
const magnitude_type TOL = 1.0e-12;
// Absolute tolerance constant
const magnitude_type ATOL = 10;
const int sizeS = MVT::GetNumberVecs(*S);
const int sizeX1 = MVT::GetNumberVecs(*X1);
const int sizeX2 = MVT::GetNumberVecs(*X2);
int numerr = 0;
std::ostringstream sout;
//
// output tests:
// <S_out,S_out> = I
// <S_out,X1> = 0
// <S_out,X2> = 0
// S_in = S_out B + X1 C1 + X2 C2
//
// we will loop over an integer specifying the test combinations
// the bit pattern for the different tests is listed in parenthesis
//
// for the projectors, test the following combinations:
// none (00)
// P_X1 (01)
// P_X2 (10)
// P_X1 P_X2 (11)
// P_X2 P_X1 (11)
// the latter two should be tested to give the same answer
//
// for each of these, we should test with C1, C2 and B
//
// if hasM:
// with and without MX1 (1--)
// with and without MX2 (1---)
// with and without MS (1----)
//
// as hasM controls the upper level bits, we need only run test cases 0-3 if hasM==false
// otherwise, we run test cases 0-31
//
int numtests = 4;
// test ortho error before orthonormalizing
if (X1 != null) {
magnitude_type err = OM->orthogError(*S,*X1);
sout << " || <S,X1> || before : " << err << endl;
}
if (X2 != null) {
magnitude_type err = OM->orthogError(*S,*X2);
sout << " || <S,X2> || before : " << err << endl;
}
for (int t=0; t<numtests; t++) {
Array< RCP< const MV > > theX;
RCP<mat_type > B = rcp( new mat_type(sizeS,sizeS) );
Array<RCP<mat_type > > C;
if ( (t % 3) == 0 ) {
// neither <X1,Y1> nor <X2,Y2>
// C, theX and theY are already empty
}
else if ( (t % 3) == 1 ) {
// X1
theX = tuple(X1);
C = tuple( rcp(new mat_type(sizeX1,sizeS)) );
}
else if ( (t % 3) == 2 ) {
// X2
theX = tuple(X2);
C = tuple( rcp(new mat_type(sizeX2,sizeS)) );
}
else {
// X1 and X2, and the reverse.
theX = tuple(X1,X2);
C = tuple( rcp(new mat_type(sizeX1,sizeS)),
rcp(new mat_type(sizeX2,sizeS)) );
}
// We wrap up all the OrthoManager calls in a try-catch
// block, in order to check whether any of the methods throw
// an exception. For the tests we perform, every thrown
// exception is a failure.
try {
// call routine
// if (t && 3) == 3, {
// call with reversed input: X2 X1
// }
// test all outputs for correctness
// test all outputs for equivalence
// here is where the outputs go
Array<RCP<MV> > S_outs;
Array<Array<RCP<mat_type > > > C_outs;
Array<RCP<mat_type > > B_outs;
RCP<MV> Scopy;
Array<int> ret_out;
// copies of S,MS
Scopy = MVT::CloneCopy(*S);
// randomize this data, it should be overwritten
B->random();
for (size_type i=0; i<C.size(); i++) {
C[i]->random();
}
// Run test. Since S was specified by the caller and
// Scopy is a copy of S, we don't know what rank to expect
// here -- though we do require that S have rank at least
// one.
//
// Note that Anasazi and Belos differ, among other places,
// in the order of arguments to projectAndNormalize().
int ret = OM->projectAndNormalize(*Scopy,C,B,theX);
sout << "projectAndNormalize() returned rank " << ret << endl;
if (ret == 0) {
sout << " *** Error: returned rank is zero, cannot continue tests" << endl;
numerr++;
break;
}
ret_out.push_back(ret);
// projectAndNormalize() is only required to return a
// basis of rank "ret"
// this is what we will test:
// the first "ret" columns in Scopy
// the first "ret" rows in B
// save just the parts that we want
// we allocate S and MS for each test, so we can save these as views
// however, save copies of the C and B
if (ret < sizeS) {
std::vector<int> ind(ret);
for (int i=0; i<ret; i++) {
ind[i] = i;
}
S_outs.push_back( MVT::CloneViewNonConst(*Scopy,ind) );
B_outs.push_back( rcp( new mat_type(Teuchos::Copy,*B,ret,sizeS) ) );
}
else {
S_outs.push_back( Scopy );
B_outs.push_back( rcp( new mat_type(*B) ) );
}
C_outs.push_back( Array<RCP<mat_type > >(0) );
if (C.size() > 0) {
C_outs.back().push_back( rcp( new mat_type(*C[0]) ) );
}
if (C.size() > 1) {
C_outs.back().push_back( rcp( new mat_type(*C[1]) ) );
}
// do we run the reversed input?
if ( (t % 3) == 3 ) {
// copies of S,MS
Scopy = MVT::CloneCopy(*S);
// Fill the B and C[i] matrices with random data. The
// data will be overwritten by projectAndNormalize().
// Filling these matrices here is only to catch some
// bugs in projectAndNormalize().
B->random();
for (size_type i=0; i<C.size(); i++) {
C[i]->random();
}
// flip the inputs
theX = tuple( theX[1], theX[0] );
// Run test.
// Note that Anasazi and Belos differ, among other places,
// in the order of arguments to projectAndNormalize().
ret = OM->projectAndNormalize(*Scopy,C,B,theX);
sout << "projectAndNormalize() returned rank " << ret << endl;
if (ret == 0) {
sout << " *** Error: returned rank is zero, cannot continue tests" << endl;
numerr++;
break;
}
ret_out.push_back(ret);
// projectAndNormalize() is only required to return a
// basis of rank "ret"
// this is what we will test:
// the first "ret" columns in Scopy
// the first "ret" rows in B
// save just the parts that we want
// we allocate S and MS for each test, so we can save these as views
// however, save copies of the C and B
if (ret < sizeS) {
std::vector<int> ind(ret);
for (int i=0; i<ret; i++) {
ind[i] = i;
}
S_outs.push_back( MVT::CloneViewNonConst(*Scopy,ind) );
B_outs.push_back( rcp( new mat_type(Teuchos::Copy,*B,ret,sizeS) ) );
}
else {
S_outs.push_back( Scopy );
B_outs.push_back( rcp( new mat_type(*B) ) );
}
C_outs.push_back( Array<RCP<mat_type > >() );
// reverse the Cs to compensate for the reverse projectors
C_outs.back().push_back( rcp( new mat_type(*C[1]) ) );
C_outs.back().push_back( rcp( new mat_type(*C[0]) ) );
// flip the inputs back
theX = tuple( theX[1], theX[0] );
}
// test all outputs for correctness
for (size_type o=0; o<S_outs.size(); o++) {
// S^T M S == I
{
magnitude_type err = OM->orthonormError(*S_outs[o]);
if (err > TOL) {
sout << endl
<< " *** Test (number " << (t+1) << " of " << numtests
<< " total tests) failed: Tolerance exceeded! Error = "
<< err << " > TOL = " << TOL << "."
<< endl << endl;
numerr++;
}
sout << " || <S,S> - I || after : " << err << endl;
}
// S_in = X1*C1 + C2*C2 + S_out*B
{
RCP<MV> tmp = MVT::Clone(*S,sizeS);
MVT::MvTimesMatAddMv(ONE,*S_outs[o],*B_outs[o],ZERO,*tmp);
if (C_outs[o].size() > 0) {
MVT::MvTimesMatAddMv(ONE,*X1,*C_outs[o][0],ONE,*tmp);
if (C_outs[o].size() > 1) {
MVT::MvTimesMatAddMv(ONE,*X2,*C_outs[o][1],ONE,*tmp);
}
}
magnitude_type err = MVDiff(*tmp,*S);
if (err > ATOL*TOL) {
sout << endl
<< " *** Test (number " << (t+1) << " of " << numtests
<< " total tests) failed: Tolerance exceeded! Error = "
<< err << " > ATOL*TOL = " << (ATOL*TOL) << "."
<< endl << endl;
numerr++;
}
sout << " " << t << "|| S_in - X1*C1 - X2*C2 - S_out*B || : " << err << endl;
}
// <X1,S> == 0
if (theX.size() > 0 && theX[0] != null) {
magnitude_type err = OM->orthogError(*theX[0],*S_outs[o]);
if (err > TOL) {
sout << endl
<< " *** Test (number " << (t+1) << " of " << numtests
<< " total tests) failed: Tolerance exceeded! Error = "
<< err << " > TOL = " << TOL << "."
<< endl << endl;
numerr++;
}
sout << " " << t << "|| <X[0],S> || after : " << err << endl;
}
// <X2,S> == 0
if (theX.size() > 1 && theX[1] != null) {
magnitude_type err = OM->orthogError(*theX[1],*S_outs[o]);
if (err > TOL) {
sout << endl
<< " *** Test (number " << (t+1) << " of " << numtests
<< " total tests) failed: Tolerance exceeded! Error = "
<< err << " > TOL = " << TOL << "."
<< endl << endl;
numerr++;
}
sout << " " << t << "|| <X[1],S> || after : " << err << endl;
}
}
}
catch (Belos::OrthoError& e) {
sout << " *** Error: OrthoManager threw exception: " << e.what() << endl;
numerr++;
}
} // test for
// NOTE (mfh 05 Nov 2010) Since Belos::MsgType is an enum,
// doing bitwise logical computations on Belos::MsgType values
// (such as "Debug | Errors") and passing the result into
// MyOM->stream() confuses the compiler. As a result, we have
// to do some type casts to make it work.
const int msgType = (numerr > 0) ?
(static_cast<int>(Debug) | static_cast<int>(Errors)) :
static_cast<int>(Debug);
// We report debug-level messages always. We also report
// errors if at least one test failed.
MyOM->stream(static_cast< MsgType >(msgType)) << sout.str() << endl;
return numerr;
}
/// Test OrthoManager::normalize() for the specific OrthoManager
/// instance.
///
/// \return Count of errors (should be zero)
static int
testNormalize (const Teuchos::RCP< Belos::OrthoManager< Scalar, MV > >& OM,
const Teuchos::RCP< const MV >& S,
const Teuchos::RCP< Belos::OutputManager< Scalar > >& MyOM)
{
using Teuchos::Array;
using Teuchos::RCP;
using Teuchos::rcp;
using Teuchos::tuple;
const scalar_type ONE = SCT::one();
std::ostringstream sout;
// Total number of failed tests in this call of this routine.
int numerr = 0;
// Relative tolerance against which all tests are performed.
// We are measuring things in the Frobenius norm $\| \cdot \|_F$.
// The following bounds hold for all $m \times n$ matrices $A$:
// \[
// \|A\|_2 \leq \|A\|_F \leq \sqrt{r} \|A\|_2,
// \]
// where $r$ is the (column) rank of $A$. We bound this above
// by the number of columns in $A$.
//
// An accurate normalization in the Euclidean norm of a matrix
// $A$ with at least as many rows m as columns n, should
// produce orthogonality $\|Q^* Q - I\|_2$ less than a factor
// of machine precision times a low-order polynomial in m and
// n, and residual $\|A - Q B\|_2$ (where $A = Q B$ is the
// computed normalization) less than that bound times the norm
// of $A$.
//
// Since we are measuring both of these quantitites in the
// Frobenius norm instead, we should scale this bound by
// $\sqrt{n}$.
const int numRows = MVT::GetGlobalLength(*S);
const int numCols = MVT::GetNumberVecs(*S);
const int sizeS = MVT::GetNumberVecs(*S);
// A good heuristic is to scale the bound by the square root
// of the number of floating-point operations. One could
// perhaps support this theoretically, since we are using
// uniform random test problems.
const magnitude_type fudgeFactor =
SMT::squareroot(magnitude_type(numRows) *
magnitude_type(numCols) *
magnitude_type(numCols));
const magnitude_type TOL = SMT::eps() * fudgeFactor *
SMT::squareroot(magnitude_type(numCols));
// Absolute tolerance scaling: the Frobenius norm of the test
// matrix S. TOL*ATOL is the absolute tolerance for the
// residual $\|A - Q*B\|_F$.
const magnitude_type ATOL = frobeniusNorm (*S);
sout << "The test matrix S has Frobenius norm " << ATOL
<< ", and the relative error tolerance is TOL = "
<< TOL << "." << endl;
const int numtests = 1;
for (int t = 0; t < numtests; ++t) {
try {
// call routine
// test all outputs for correctness
// S_copy gets a copy of S; we normalize in place, so we
// need a copy to check whether the normalization
// succeeded.
RCP< MV > S_copy = MVT::CloneCopy (*S);
// Matrix of coefficients from the normalization.
RCP< mat_type > B (new mat_type (sizeS, sizeS));
// The contents of B will be overwritten, but fill with
// random data just to make sure that the normalization
// operated on all the elements of B on which it should
// operate.
B->random();
const int reportedRank = OM->normalize (*S_copy, B);
sout << "normalize() returned rank " << reportedRank << endl;
if (reportedRank == 0) {
sout << " *** Error: Cannot continue, since normalize() "
"reports that S has rank 0" << endl;
numerr++;
break;
}
//
// We don't know in this routine whether the input
// multivector S has full rank; it is only required to
// have nonzero rank. Thus, we extract the first
// reportedRank columns of S_copy and the first
// reportedRank rows of B, and perform tests on them.
//
// Construct S_view, a view of the first reportedRank
// columns of S_copy.
std::vector<int> indices (reportedRank);
for (int j = 0; j < reportedRank; ++j)
indices[j] = j;
RCP< MV > S_view = MVT::CloneViewNonConst (*S_copy, indices);
// Construct B_top, a copy of the first reportedRank rows
// of B.
//
// NOTE: We create this as a copy and not a view, because
// otherwise it would not be safe with respect to RCPs.
// This is because mat_type uses raw pointers
// inside, so that a view would become invalid when B
// would fall out of scope.
RCP< mat_type > B_top (new mat_type (Teuchos::Copy, *B, reportedRank, sizeS));
// Check ||<S_view,S_view> - I||
{
const magnitude_type err = OM->orthonormError(*S_view);
if (err > TOL) {
sout << " *** Error: Tolerance exceeded: err = "
<< err << " > TOL = " << TOL << endl;
numerr++;
}
sout << " || <S,S> - I || after : " << err << endl;
}
// Check the residual ||Residual|| = ||S_view * B_top -
// S_orig||, where S_orig is a view of the first
// reportedRank columns of S.
{
// Residual is allocated with reportedRank columns. It
// will contain the result of testing the residual error
// of the normalization (i.e., $\|S - S_in*B\|$). It
// should have the dimensions of S. Its initial value
// is a copy of the first reportedRank columns of S.
RCP< MV > Residual = MVT::CloneCopy (*S);
// Residual := Residual - S_view * B_view
MVT::MvTimesMatAddMv (-ONE, *S_view, *B_top, ONE, *Residual);
// Compute ||Residual||
const magnitude_type err = frobeniusNorm (*Residual);
if (err > ATOL*TOL) {
sout << " *** Error: Tolerance exceeded: err = "
<< err << " > ATOL*TOL = " << (ATOL*TOL) << endl;
numerr++;
}
sout << " " << t << "|| S - Q*B || : " << err << endl;
}
}
catch (Belos::OrthoError& e) {
sout << " *** Error: the OrthoManager's normalize() method "
"threw an exception: " << e.what() << endl;
numerr++;
}
} // test for
const MsgType type = (numerr == 0) ? Debug : static_cast<MsgType> (static_cast<int>(Errors) | static_cast<int>(Debug));
MyOM->stream(type) << sout.str();
MyOM->stream(type) << endl;
return numerr;
}
/// Test OrthoManager::projectAndNormalize() for the specific
/// OrthoManager instance.
///
/// \return Count of errors (should be zero)
static int
testProjectAndNormalizeNew (const Teuchos::RCP< Belos::OrthoManager< Scalar, MV > > OM,
const Teuchos::RCP< const MV >& S,
const Teuchos::RCP< const MV >& X1,
const Teuchos::RCP< const MV >& X2,
const Teuchos::RCP< Belos::OutputManager< Scalar > >& MyOM)
{
using Teuchos::Array;
using Teuchos::null;
using Teuchos::RCP;
using Teuchos::rcp;
using Teuchos::tuple;
// We collect all the output in this string wrapper, and print
// it at the end.
std::ostringstream sout;
// Total number of failed tests in this call of this routine.
int numerr = 0;
const int numRows = MVT::GetGlobalLength(*S);
const int numCols = MVT::GetNumberVecs(*S);
const int sizeS = MVT::GetNumberVecs(*S);
// Relative tolerance against which all tests are performed.
// We are measuring things in the Frobenius norm $\| \cdot \|_F$.
// The following bounds hold for all $m \times n$ matrices $A$:
// \[
// \|A\|_2 \leq \|A\|_F \leq \sqrt{r} \|A\|_2,
// \]
// where $r$ is the (column) rank of $A$. We bound this above
// by the number of columns in $A$.
//
// Since we are measuring both of these quantitites in the
// Frobenius norm instead, we scale all error tests by
// $\sqrt{n}$.
//
// A good heuristic is to scale the bound by the square root
// of the number of floating-point operations. One could
// perhaps support this theoretically, since we are using
// uniform random test problems.
const magnitude_type fudgeFactor =
SMT::squareroot(magnitude_type(numRows) *
magnitude_type(numCols) *
magnitude_type(numCols));
const magnitude_type TOL = SMT::eps() * fudgeFactor *
SMT::squareroot(magnitude_type(numCols));
// Absolute tolerance scaling: the Frobenius norm of the test
// matrix S. TOL*ATOL is the absolute tolerance for the
// residual $\|A - Q*B\|_F$.
const magnitude_type ATOL = frobeniusNorm (*S);
sout << "-- The test matrix S has Frobenius norm " << ATOL
<< ", and the relative error tolerance is TOL = "
<< TOL << "." << endl;
// Q will contain the result of projectAndNormalize() on S.
RCP< MV > Q = MVT::CloneCopy(*S);
// We use this for collecting the residual error components
RCP< MV > Residual = MVT::CloneCopy(*S);
// Number of elements in the X array of blocks against which
// to project S.
const int num_X = 2;
Array< RCP< const MV > > X (num_X);
X[0] = MVT::CloneCopy(*X1);
X[1] = MVT::CloneCopy(*X2);
// Coefficients for the normalization
RCP< mat_type > B (new mat_type (sizeS, sizeS));
// Array of coefficients matrices from the projection.
// For our first test, we allocate each of these matrices
// with the proper dimensions.
Array< RCP< mat_type > > C (num_X);
for (int k = 0; k < num_X; ++k)
{
C[k] = rcp (new mat_type (MVT::GetNumberVecs(*X[k]), sizeS));
C[k]->random(); // will be overwritten
}
try {
// Q*B := (I - X X^*) S
const int reportedRank = OM->projectAndNormalize (*Q, C, B, X);
// Pick out the first reportedRank columns of Q.
std::vector<int> indices (reportedRank);
for (int j = 0; j < reportedRank; ++j)
indices[j] = j;
RCP< const MV > Q_left = MVT::CloneView (*Q, indices);
// Test whether the first reportedRank columns of Q are
// orthogonal.
{
const magnitude_type orthoError = OM->orthonormError (*Q_left);
sout << "-- ||Q(1:" << reportedRank << ")^* Q(1:" << reportedRank
<< ") - I||_F = " << orthoError << endl;
if (orthoError > TOL)
{
sout << " *** Error: ||Q(1:" << reportedRank << ")^* Q(1:"
<< reportedRank << ") - I||_F = " << orthoError
<< " > TOL = " << TOL << "." << endl;
numerr++;
}
}
// Compute the residual: if successful, S = Q*B +
// X (X^* S =: C) in exact arithmetic. So, the residual is
// S - Q*B - X1 C1 - X2 C2.
//
// Residual := S
MVT::MvAddMv (SCT::one(), *S, SCT::zero(), *Residual, *Residual);
{
// Pick out the first reportedRank rows of B. Make a deep
// copy, since mat_type is not safe with respect
// to RCP-based memory management (it uses raw pointers
// inside).
RCP< const mat_type > B_top (new mat_type (Teuchos::Copy, *B, reportedRank, B->numCols()));
// Residual := Residual - Q(:, 1:reportedRank) * B(1:reportedRank, :)
MVT::MvTimesMatAddMv (-SCT::one(), *Q_left, *B_top, SCT::one(), *Residual);
}
// Residual := Residual - X[k]*C[k]
for (int k = 0; k < num_X; ++k)
MVT::MvTimesMatAddMv (-SCT::one(), *X[k], *C[k], SCT::one(), *Residual);
const magnitude_type residErr = frobeniusNorm (*Residual);
sout << "-- ||S - Q(:, 1:" << reportedRank << ")*B(1:"
<< reportedRank << ", :) - X1*C1 - X2*C2||_F = "
<< residErr << endl;
if (residErr > ATOL * TOL)
{
sout << " *** Error: ||S - Q(:, 1:" << reportedRank
<< ")*B(1:" << reportedRank << ", :) "
<< "- X1*C1 - X2*C2||_F = " << residErr
<< " > ATOL*TOL = " << (ATOL*TOL) << "." << endl;
numerr++;
}
// Verify that Q(1:reportedRank) is orthogonal to X[k], for
// all k. This test only makes sense if reportedRank > 0.
if (reportedRank == 0)
{
sout << "-- Reported rank of Q is zero: skipping Q, X[k] "
"orthogonality test." << endl;
}
else
{
for (int k = 0; k < num_X; ++k)
{
// Q should be orthogonal to X[k], for all k.
const magnitude_type projErr = OM->orthogError(*X[k], *Q_left);
sout << "-- ||<Q(1:" << reportedRank << "), X[" << k
<< "]>||_F = " << projErr << endl;
if (projErr > ATOL*TOL)
{
sout << " *** Error: ||<Q(1:" << reportedRank << "), X["
<< k << "]>||_F = " << projErr << " > ATOL*TOL = "
<< (ATOL*TOL) << "." << endl;
numerr++;
}
}
}
} catch (Belos::OrthoError& e) {
sout << " *** Error: The OrthoManager subclass instance threw "
"an exception: " << e.what() << endl;
numerr++;
}
// Print out the collected diagnostic messages, which possibly
// include error messages.
const MsgType type = (numerr == 0) ? Debug : static_cast<MsgType> (static_cast<int>(Errors) | static_cast<int>(Debug));
MyOM->stream(type) << sout.str();
MyOM->stream(type) << endl;
return numerr;
}
/// Test OrthoManager::project() for the specific OrthoManager instance.
///
/// \return Count of errors (should be zero)
static int
testProjectNew (const Teuchos::RCP< Belos::OrthoManager< Scalar, MV > > OM,
const Teuchos::RCP< const MV >& S,
const Teuchos::RCP< const MV >& X1,
const Teuchos::RCP< const MV >& X2,
const Teuchos::RCP< Belos::OutputManager< Scalar > >& MyOM)
{
using Teuchos::Array;
using Teuchos::null;
using Teuchos::RCP;
using Teuchos::rcp;
using Teuchos::tuple;
// We collect all the output in this string wrapper, and print
// it at the end.
std::ostringstream sout;
// Total number of failed tests in this call of this routine.
int numerr = 0;
const int numRows = MVT::GetGlobalLength(*S);
const int numCols = MVT::GetNumberVecs(*S);
const int sizeS = MVT::GetNumberVecs(*S);
// Relative tolerance against which all tests are performed.
// We are measuring things in the Frobenius norm $\| \cdot \|_F$.
// The following bounds hold for all $m \times n$ matrices $A$:
// \[
// \|A\|_2 \leq \|A\|_F \leq \sqrt{r} \|A\|_2,
// \]
// where $r$ is the (column) rank of $A$. We bound this above
// by the number of columns in $A$.
//
// Since we are measuring both of these quantitites in the
// Frobenius norm instead, we scale all error tests by
// $\sqrt{n}$.
//
// A good heuristic is to scale the bound by the square root
// of the number of floating-point operations. One could
// perhaps support this theoretically, since we are using
// uniform random test problems.
const magnitude_type fudgeFactor =
SMT::squareroot(magnitude_type(numRows) *
magnitude_type(numCols) *
magnitude_type(numCols));
const magnitude_type TOL = SMT::eps() * fudgeFactor *
SMT::squareroot(magnitude_type(numCols));
// Absolute tolerance scaling: the Frobenius norm of the test
// matrix S. TOL*ATOL is the absolute tolerance for the
// residual $\|A - Q*B\|_F$.
const magnitude_type ATOL = frobeniusNorm (*S);
sout << "The test matrix S has Frobenius norm " << ATOL
<< ", and the relative error tolerance is TOL = "
<< TOL << "." << endl;
// Make some copies of S, X1, and X2. The OrthoManager's
// project() method shouldn't modify X1 or X2, but this is a a
// test and we don't know that it doesn't!
RCP< MV > S_copy = MVT::CloneCopy(*S);
RCP< MV > Residual = MVT::CloneCopy(*S);
const int num_X = 2;
Array< RCP< const MV > > X (num_X);
X[0] = MVT::CloneCopy(*X1);
X[1] = MVT::CloneCopy(*X2);
// Array of coefficients matrices from the projection.
// For our first test, we allocate each of these matrices
// with the proper dimensions.
Array< RCP< mat_type > > C (num_X);
for (int k = 0; k < num_X; ++k)
{
C[k] = rcp (new mat_type (MVT::GetNumberVecs(*X[k]), sizeS));
C[k]->random(); // will be overwritten
}
try {
// Compute the projection: S_copy := (I - X X^*) S
OM->project(*S_copy, C, X);
// Compute the residual: if successful, S = S_copy + X (X^*
// S =: C) in exact arithmetic. So, the residual is
// S - S_copy - X1 C1 - X2 C2.
//
// Residual := S - S_copy
MVT::MvAddMv (SCT::one(), *S, -SCT::one(), *S_copy, *Residual);
// Residual := Residual - X[k]*C[k]
for (int k = 0; k < num_X; ++k)
MVT::MvTimesMatAddMv (-SCT::one(), *X[k], *C[k], SCT::one(), *Residual);
magnitude_type residErr = frobeniusNorm (*Residual);
sout << " ||S - S_copy - X1*C1 - X2*C2||_F = " << residErr;
if (residErr > ATOL * TOL)
{
sout << " *** Error: ||S - S_copy - X1*C1 - X2*C2||_F = " << residErr
<< " > ATOL*TOL = " << (ATOL*TOL) << ".";
numerr++;
}
for (int k = 0; k < num_X; ++k)
{
// S_copy should be orthogonal to X[k] now.
const magnitude_type projErr = OM->orthogError(*X[k], *S_copy);
if (projErr > TOL)
{
sout << " *** Error: S is not orthogonal to X[" << k
<< "] by a factor of " << projErr << " > TOL = "
<< TOL << ".";
numerr++;
}
}
} catch (Belos::OrthoError& e) {
sout << " *** Error: The OrthoManager subclass instance threw "
"an exception: " << e.what() << endl;
numerr++;
}
// Print out the collected diagnostic messages, which possibly
// include error messages.
const MsgType type = (numerr == 0) ? Debug : static_cast<MsgType> (static_cast<int>(Errors) | static_cast<int>(Debug));
MyOM->stream(type) << sout.str();
MyOM->stream(type) << endl;
return numerr;
}
static int
testProject (const Teuchos::RCP< Belos::OrthoManager< Scalar, MV > > OM,
const Teuchos::RCP< const MV >& S,
const Teuchos::RCP< const MV >& X1,
const Teuchos::RCP< const MV >& X2,
const Teuchos::RCP< Belos::OutputManager< Scalar > >& MyOM)
{
return testProjectNew (OM, S, X1, X2, MyOM);
}
/// Test OrthoManager::project() for the specific OrthoManager instance.
///
/// \return Count of errors (should be zero)
static int
testProjectOld (const Teuchos::RCP< Belos::OrthoManager< Scalar, MV > > OM,
const Teuchos::RCP< const MV >& S,
const Teuchos::RCP< const MV >& X1,
const Teuchos::RCP< const MV >& X2,
const Teuchos::RCP< Belos::OutputManager< Scalar > >& MyOM)
{
using Teuchos::Array;
using Teuchos::null;
using Teuchos::RCP;
using Teuchos::rcp;
using Teuchos::tuple;
const scalar_type ONE = SCT::one();
// We collect all the output in this string wrapper, and print
// it at the end.
std::ostringstream sout;
// Total number of failed tests in this call of this routine.
int numerr = 0;
const int numRows = MVT::GetGlobalLength(*S);
const int numCols = MVT::GetNumberVecs(*S);
const int sizeS = MVT::GetNumberVecs(*S);
const int sizeX1 = MVT::GetNumberVecs(*X1);
const int sizeX2 = MVT::GetNumberVecs(*X2);
// Relative tolerance against which all tests are performed.
// We are measuring things in the Frobenius norm $\| \cdot \|_F$.
// The following bounds hold for all $m \times n$ matrices $A$:
// \[
// \|A\|_2 \leq \|A\|_F \leq \sqrt{r} \|A\|_2,
// \]
// where $r$ is the (column) rank of $A$. We bound this above
// by the number of columns in $A$.
//
// Since we are measuring both of these quantitites in the
// Frobenius norm instead, we scale all error tests by
// $\sqrt{n}$.
//
// A good heuristic is to scale the bound by the square root
// of the number of floating-point operations. One could
// perhaps support this theoretically, since we are using
// uniform random test problems.
const magnitude_type fudgeFactor =
SMT::squareroot(magnitude_type(numRows) *
magnitude_type(numCols) *
magnitude_type(numCols));
const magnitude_type TOL = SMT::eps() * fudgeFactor *
SMT::squareroot(magnitude_type(numCols));
// Absolute tolerance scaling: the Frobenius norm of the test
// matrix S. TOL*ATOL is the absolute tolerance for the
// residual $\|A - Q*B\|_F$.
const magnitude_type ATOL = frobeniusNorm (*S);
sout << "The test matrix S has Frobenius norm " << ATOL
<< ", and the relative error tolerance is TOL = "
<< TOL << "." << endl;
//
// Output tests:
// <S_out,X1> = 0
// <S_out,X2> = 0
// S_in = S_out + X1 C1 + X2 C2
//
// We will loop over an integer specifying the test combinations.
// The bit pattern for the different tests is listed in parentheses.
//
// For the projectors, test the following combinations:
// none (00)
// P_X1 (01)
// P_X2 (10)
// P_X1 P_X2 (11)
// P_X2 P_X1 (11)
// The latter two should be tested to give the same result.
//
// For each of these, we should test with C1 and C2:
//
// if hasM:
// with and without MX1 (1--)
// with and without MX2 (1---)
// with and without MS (1----)
//
// As hasM controls the upper level bits, we need only run test
// cases 0-3 if hasM==false. Otherwise, we run test cases 0-31.
//
int numtests = 8;
// test ortho error before orthonormalizing
if (X1 != null) {
magnitude_type err = OM->orthogError(*S,*X1);
sout << " || <S,X1> || before : " << err << endl;
}
if (X2 != null) {
magnitude_type err = OM->orthogError(*S,*X2);
sout << " || <S,X2> || before : " << err << endl;
}
for (int t = 0; t < numtests; ++t)
{
Array< RCP< const MV > > theX;
Array< RCP< mat_type > > C;
if ( (t % 3) == 0 ) {
// neither X1 nor X2
// C and theX are already empty
}
else if ( (t % 3) == 1 ) {
// X1
theX = tuple(X1);
C = tuple( rcp(new mat_type(sizeX1,sizeS)) );
}
else if ( (t % 3) == 2 ) {
// X2
theX = tuple(X2);
C = tuple( rcp(new mat_type(sizeX2,sizeS)) );
}
else {
// X1 and X2, and the reverse.
theX = tuple(X1,X2);
C = tuple( rcp(new mat_type(sizeX1,sizeS)),
rcp(new mat_type(sizeX2,sizeS)) );
}
try {
// call routine
// if (t && 3) == 3, {
// call with reversed input: X2 X1
// }
// test all outputs for correctness
// test all outputs for equivalence
// here is where the outputs go
Array< RCP< MV > > S_outs;
Array< Array< RCP< mat_type > > > C_outs;
RCP< MV > Scopy;
// copies of S,MS
Scopy = MVT::CloneCopy(*S);
// randomize this data, it should be overwritten
for (size_type i = 0; i < C.size(); ++i) {
C[i]->random();
}
// Run test.
// Note that Anasazi and Belos differ, among other places,
// in the order of arguments to project().
OM->project(*Scopy,C,theX);
// we allocate S and MS for each test, so we can save these as views
// however, save copies of the C
S_outs.push_back( Scopy );
C_outs.push_back( Array< RCP< mat_type > >(0) );
if (C.size() > 0) {
C_outs.back().push_back( rcp( new mat_type(*C[0]) ) );
}
if (C.size() > 1) {
C_outs.back().push_back( rcp( new mat_type(*C[1]) ) );
}
// do we run the reversed input?
if ( (t % 3) == 3 ) {
// copies of S,MS
Scopy = MVT::CloneCopy(*S);
// randomize this data, it should be overwritten
for (size_type i = 0; i < C.size(); ++i) {
C[i]->random();
}
// flip the inputs
theX = tuple( theX[1], theX[0] );
// Run test.
// Note that Anasazi and Belos differ, among other places,
// in the order of arguments to project().
OM->project(*Scopy,C,theX);
// we allocate S and MS for each test, so we can save these as views
// however, save copies of the C
S_outs.push_back( Scopy );
// we are in a special case: P_X1 and P_X2, so we know we applied
// two projectors, and therefore have two C[i]
C_outs.push_back( Array<RCP<mat_type > >() );
// reverse the Cs to compensate for the reverse projectors
C_outs.back().push_back( rcp( new mat_type(*C[1]) ) );
C_outs.back().push_back( rcp( new mat_type(*C[0]) ) );
// flip the inputs back
theX = tuple( theX[1], theX[0] );
}
// test all outputs for correctness
for (size_type o = 0; o < S_outs.size(); ++o) {
// S_in = X1*C1 + C2*C2 + S_out
{
RCP<MV> tmp = MVT::CloneCopy(*S_outs[o]);
if (C_outs[o].size() > 0) {
MVT::MvTimesMatAddMv(ONE,*X1,*C_outs[o][0],ONE,*tmp);
if (C_outs[o].size() > 1) {
MVT::MvTimesMatAddMv(ONE,*X2,*C_outs[o][1],ONE,*tmp);
}
}
magnitude_type err = MVDiff(*tmp,*S);
if (err > ATOL*TOL) {
sout << " vvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvv tolerance exceeded! test failed!" << endl;
numerr++;
}
sout << " " << t << "|| S_in - X1*C1 - X2*C2 - S_out || : " << err << endl;
}
// <X1,S> == 0
if (theX.size() > 0 && theX[0] != null) {
magnitude_type err = OM->orthogError(*theX[0],*S_outs[o]);
if (err > TOL) {
sout << " vvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvv tolerance exceeded! test failed!" << endl;
numerr++;
}
sout << " " << t << "|| <X[0],S> || after : " << err << endl;
}
// <X2,S> == 0
if (theX.size() > 1 && theX[1] != null) {
magnitude_type err = OM->orthogError(*theX[1],*S_outs[o]);
if (err > TOL) {
sout << " vvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvv tolerance exceeded! test failed!" << endl;
numerr++;
}
sout << " " << t << "|| <X[1],S> || after : " << err << endl;
}
}
// test all outputs for equivalence
// check all combinations:
// output 0 == output 1
// output 0 == output 2
// output 1 == output 2
for (size_type o1=0; o1<S_outs.size(); o1++) {
for (size_type o2=o1+1; o2<S_outs.size(); o2++) {
// don't need to check MS_outs because we check
// S_outs and MS_outs = M*S_outs
// don't need to check C_outs either
//
// check that S_outs[o1] == S_outs[o2]
magnitude_type err = MVDiff(*S_outs[o1],*S_outs[o2]);
if (err > TOL) {
sout << " vvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvv tolerance exceeded! test failed!" << endl;
numerr++;
}
}
}
}
catch (Belos::OrthoError& e) {
sout << " ------------------------------------------- project() threw exception" << endl;
sout << " Error: " << e.what() << endl;
numerr++;
}
} // test for
MsgType type = Debug;
if (numerr>0) type = Errors;
MyOM->stream(type) << sout.str();
MyOM->stream(type) << endl;
return numerr;
}
};
} // namespace Test
} // namespace Belos
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