int main(int argc, char* argv[])
{
#ifdef HAVE_MPI
MPI_Init(&argc,&argv);
#endif
// Creating a double-precision matrix can be done in several ways:
// Create an empty matrix with no dimension
Teuchos::SerialDenseMatrix<int,double> Empty_Matrix;
// Create an empty 3x4 matrix
Teuchos::SerialDenseMatrix<int,double> My_Matrix( 3, 4 );
// Basic copy of My_Matrix
Teuchos::SerialDenseMatrix<int,double> My_Copy1( My_Matrix ),
// (Deep) Copy of principle 3x3 submatrix of My_Matrix
My_Copy2( Teuchos::Copy, My_Matrix, 3, 3 ),
// (Shallow) Copy of 2x3 submatrix of My_Matrix
My_Copy3( Teuchos::View, My_Matrix, 2, 3, 1, 1 );
// The matrix dimensions and strided storage information can be obtained:
int rows, cols, stride;
rows = My_Copy3.numRows(); // number of rows
cols = My_Copy3.numCols(); // number of columns
stride = My_Copy3.stride(); // storage stride
// Matrices can change dimension:
Empty_Matrix.shape( 3, 3 ); // size non-dimensional matrices
My_Matrix.reshape( 3, 3 ); // resize matrices and save values
// Filling matrices with numbers can be done in several ways:
My_Matrix.random(); // random numbers
My_Copy1.putScalar( 1.0 ); // every entry is 1.0
My_Copy2(1,1) = 10.0; // individual element access
Empty_Matrix = My_Matrix; // copy My_Matrix to Empty_Matrix
// Basic matrix arithmetic can be performed:
Teuchos::SerialDenseMatrix<int,double> My_Prod( 3, 2 );
// Matrix multiplication ( My_Prod = 1.0*My_Matrix*My_Copy^T )
My_Prod.multiply( Teuchos::NO_TRANS, Teuchos::TRANS,
1.0, My_Matrix, My_Copy3, 0.0 );
My_Copy2 += My_Matrix; // Matrix addition
My_Copy2.scale( 0.5 ); // Matrix scaling
// The pointer to the array of matrix values can be obtained:
double *My_Array, *My_Column;
My_Array = My_Matrix.values(); // pointer to matrix values
My_Column = My_Matrix[2]; // pointer to third column values
// The norm of a matrix can be computed:
double norm_one, norm_inf, norm_fro;
norm_one = My_Matrix.normOne(); // one norm
norm_inf = My_Matrix.normInf(); // infinity norm
norm_fro = My_Matrix.normFrobenius(); // frobenius norm
// Matrices can be compared:
// Check if the matrices are equal in dimension and values
if (Empty_Matrix == My_Matrix) {
cout<< "The matrices are the same!" <<endl;
}
// Check if the matrices are different in dimension or values
if (My_Copy2 != My_Matrix) {
cout<< "The matrices are different!" <<endl;
}
// A matrix can be sent to the output stream:
cout<< My_Matrix << endl;
#ifdef HAVE_MPI
MPI_Finalize();
#endif
return 0;
}
int main(int argc, char* argv[])
{
std::cout << Teuchos::Teuchos_Version() << std::endl << std::endl;
// Creating a double-precision matrix can be done in several ways:
// Create an empty matrix with no dimension
Teuchos::SerialSymDenseMatrix<int,double> Empty_Matrix;
// Create an empty 4x4 matrix
Teuchos::SerialSymDenseMatrix<int,double> My_Matrix( 4 );
// Basic copy of My_Matrix
Teuchos::SerialSymDenseMatrix<int,double> My_Copy1( My_Matrix ),
// (Deep) Copy of principle 3x3 submatrix of My_Matrix
My_Copy2( Teuchos::Copy, My_Matrix, 3 ),
// (Shallow) Copy of 3x3 submatrix of My_Matrix
My_Copy3( Teuchos::View, My_Matrix, 3, 1 );
// The matrix dimensions and strided storage information can be obtained:
int rows, cols, stride;
rows = My_Copy3.numRows(); // number of rows
cols = My_Copy3.numCols(); // number of columns
stride = My_Copy3.stride(); // storage stride
TEUCHOS_ASSERT_EQUALITY(rows, 3);
TEUCHOS_ASSERT_EQUALITY(cols, 3);
TEUCHOS_ASSERT_EQUALITY(stride, 4);
// Matrices can change dimension:
Empty_Matrix.shape( 3 ); // size non-dimensional matrices
My_Matrix.reshape( 3 ); // resize matrices and save values
// Filling matrices with numbers can be done in several ways:
My_Matrix.random(); // random numbers
My_Copy1.putScalar( 1.0 ); // every entry is 1.0
My_Copy1 = 1.0; // every entry is 1.0 (still)
My_Copy2(1,1) = 10.0; // individual element access
Empty_Matrix = My_Matrix; // copy My_Matrix to Empty_Matrix
// Basic matrix arithmetic can be performed:
Teuchos::SerialDenseMatrix<int,double> My_Prod( 4, 3 ), My_GenMatrix( 4, 3 );
My_GenMatrix = 1.0;
// Matrix multiplication ( My_Prod = 1.0*My_GenMatrix*My_Matrix )
My_Prod.multiply( Teuchos::RIGHT_SIDE, 1.0, My_Matrix, My_GenMatrix, 0.0 );
My_Copy2 += My_Matrix; // Matrix addition
My_Copy2 *= 0.5; // Matrix scaling
// Matrices can be compared:
// Check if the matrices are equal in dimension and values
if (Empty_Matrix == My_Matrix) {
std::cout<< "The matrices are the same!" <<std::endl;
}
// Check if the matrices are different in dimension or values
if (My_Copy2 != My_Matrix) {
std::cout<< "The matrices are different!" <<std::endl;
}
// The norm of a matrix can be computed:
double norm_one, norm_inf, norm_fro;
norm_one = My_Matrix.normOne(); // one norm
norm_inf = My_Matrix.normInf(); // infinity norm
norm_fro = My_Matrix.normFrobenius(); // frobenius norm
std::cout << std::endl << "|| My_Matrix ||_1 = " << norm_one << std::endl;
std::cout << "|| My_Matrix ||_Inf = " << norm_inf << std::endl;
std::cout << "|| My_Matrix ||_F = " << norm_fro << std::endl << std::endl;
// A matrix can be factored and solved using Teuchos::SerialDenseSolver.
Teuchos::SerialSpdDenseSolver<int,double> My_Solver;
Teuchos::SerialSymDenseMatrix<int,double> My_Matrix2( 3 );
My_Matrix2.random();
Teuchos::SerialDenseMatrix<int,double> X(3,1), B(3,1);
X = 1.0;
B.multiply( Teuchos::LEFT_SIDE, 1.0, My_Matrix2, X, 0.0 );
X = 0.0; // Make sure the computed answer is correct.
int info = 0;
My_Solver.setMatrix( Teuchos::rcp( &My_Matrix2, false ) );
My_Solver.setVectors( Teuchos::rcp( &X, false ), Teuchos::rcp( &B, false ) );
info = My_Solver.factor();
if (info != 0)
std::cout << "Teuchos::SerialSpdDenseSolver::factor() returned : " << info << std::endl;
info = My_Solver.solve();
if (info != 0)
std::cout << "Teuchos::SerialSpdDenseSolver::solve() returned : " << info << std::endl;
// A matrix triple-product can be computed: C = alpha*W'*A*W
double alpha=0.5;
Teuchos::SerialDenseMatrix<int,double> W(3,2);
Teuchos::SerialSymDenseMatrix<int,double> A1(2), A2(3);
A1(0,0) = 1.0, A1(1,1) = 2.0;
A2(0,0) = 1.0, A2(1,1) = 2.0, A2(2,2) = 3.00;
W = 1.0;
Teuchos::SerialSymDenseMatrix<int,double> C1(3), C2(2);
Teuchos::symMatTripleProduct<int,double>( Teuchos::NO_TRANS, alpha, A1, W, C1);
Teuchos::symMatTripleProduct<int,double>( Teuchos::TRANS, alpha, A2, W, C2 );
// A matrix can be sent to the output stream:
std::cout<< My_Matrix << std::endl;
std::cout<< X << std::endl;
return 0;
}
int main(int argc, char* argv[])
{
int i;
bool verbose = 0;
if (argc>1) if (argv[1][0]=='-' && argv[1][1]=='v') verbose = true;
if (verbose)
std::cout << Teuchos::Teuchos_Version() << std::endl << std::endl;
int numberFailedTests = 0;
int returnCode = 0;
std::string testName = "";
if (verbose) std::cout<<std::endl<<"********** CHECKING TEUCHOS SERIAL SYMMETRIC DENSE MATRIX **********"<<std::endl<<std::endl;
// default constructor test
SDMatrix DefConTest;
if (verbose) std::cout <<"default constructor -- construct empty matrix ";
if ( DefConTest.values()!=NULL || DefConTest.numCols()!=0 || DefConTest.numRows()!=0 ||DefConTest.stride()!=0 ||DefConTest.empty()!=true ) {
if (verbose) std::cout << "unsuccessful."<<std::endl;
numberFailedTests++;
} else {
if (verbose) std::cout << "successful."<<std::endl;
}
// constructor 1 (matrix w/ dimension but empty)
SDMatrix Con1Test( 4 );
if (verbose) std::cout <<"constructor 1 -- empty matrix with given dimensions ";
if ( Con1Test.numRows()!=4 || Con1Test.numCols()!=4 || Con1Test( 1, 2 )!=0.0 ) {
if (verbose) std::cout << "unsuccessful."<<std::endl;
numberFailedTests++;
} else {
if (verbose) std::cout << "successful."<<std::endl;
}
// constructor 2 (from array) tests
STYPE a[9];
for(i = 0; i < 9; i++)
{
a[i] = i;
}
SDMatrix Con2Test1ExpRes;
Con2Test1ExpRes.shape(3);
Con2Test1ExpRes(0, 0) = 0;
Con2Test1ExpRes(1, 0) = 1; Con2Test1ExpRes(1, 1) = 4;
Con2Test1ExpRes(2, 0) = 2; Con2Test1ExpRes(2, 1) = 5; Con2Test1ExpRes(2, 2) = 8;
// Create another lower triangular matrix with a view of 'a'.
SDMatrix Con2Test1(Teuchos::View, false, a, 3, 3);
numberFailedTests += PrintTestResults("constructor 2 -- construct matrix from array subrange", Con2Test1, Con2Test1ExpRes, verbose);
// constructor 3 (copy constructor)
SDMatrix Con3TestCopy( Con2Test1ExpRes );
if(verbose) std::cout <<"constructor 3 -- copy constructor ";
if ( Con3TestCopy != Con2Test1ExpRes ) {
if (verbose) std::cout << "unsuccessful."<<std::endl;
numberFailedTests++;
} else {
if (verbose) std::cout << "successful."<<std::endl;
}
SDMatrix Con3TestCopyTrans( Con2Test1ExpRes );
Con3TestCopyTrans.setUpper();
if(verbose) std::cout <<"constructor 3 -- copy constructor (upper active storage) ";
if ( Con3TestCopyTrans(2, 0) != Con2Test1ExpRes(2, 0) ) {
if (verbose) std::cout << "unsuccessful."<<std::endl;
numberFailedTests++;
} else {
if (verbose) std::cout << "successful."<<std::endl;
}
// constructor 4 (submatrix)
SDMatrix Con4TestOrig(Teuchos::Copy, false, a, 3, 3);
SDMatrix Con4TestSubmatrix;
Con4TestSubmatrix.shape( 2 );
Con4TestSubmatrix(0, 0) = 4;
Con4TestSubmatrix(1, 0) = 5; Con4TestSubmatrix(1, 1) = 8;
SDMatrix Con4TestCopy1(Teuchos::Copy, Con4TestOrig, 2, 1);
numberFailedTests += PrintTestResults("constructor 4 -- submatrix copy", Con4TestCopy1, Con4TestSubmatrix, verbose);
SDMatrix Con4TestCopy2(Teuchos::Copy, Con4TestOrig, 3, 0);
numberFailedTests += PrintTestResults("constructor 4 -- full matrix copy", Con4TestCopy2, Con4TestOrig, verbose);
SDMatrix Con4TestView1(Teuchos::View, Con4TestOrig, 2, 1);
numberFailedTests += PrintTestResults("constructor 4 -- full matrix view", Con4TestView1, Con4TestSubmatrix, verbose);
SDMatrix Con4TestView2(Teuchos::View, Con4TestOrig, 3, 0);
numberFailedTests += PrintTestResults("constructor 4 -- submatrix view", Con4TestView2, Con4TestOrig, verbose);
// Norm Tests
SDMatrix AAA;
AAA.shape( 3 );
AAA(0, 0) = 8;
AAA(1, 0) = 1; AAA(1, 1) = 8;
AAA(2, 0) = 2; AAA(2, 1) = 3; AAA(2, 2) = 8;
SDMatrix BBB;
numberFailedTests += PrintTestResults("normOne of a 3x3", AAA.normOne(), 13.0, verbose);
numberFailedTests += PrintTestResults("normInf of a 3x3", AAA.normInf(), 13.0, verbose);
AAA = Teuchos::ScalarTraits<STYPE>::one();
numberFailedTests += PrintTestResults("normFrobenius of a 3x3", AAA.normFrobenius(), 3.0, verbose);
numberFailedTests += PrintTestResults("normOne of a 0x0", BBB.normOne(), 0.0, verbose);
numberFailedTests += PrintTestResults("normInf of a 0x0", BBB.normInf(), 0.0, verbose);
numberFailedTests += PrintTestResults("normFrobenius of a 0x0", BBB.normFrobenius(), 0.0, verbose);
// Multiplication Tests
// Reset values of AAA.
AAA(0, 0) = 8;
AAA(1, 0) = 1; AAA(1, 1) = 8;
AAA(2, 0) = 2; AAA(2, 1) = 3; AAA(2, 2) = 8;
DMatrix My_Prod( 4, 3 ), My_GenMatrix( 4, 3 );
My_GenMatrix = Teuchos::ScalarTraits<STYPE>::one();
// Matrix multiplication ( My_Prod = 1.0*My_GenMatrix*My_Matrix )
My_Prod.multiply( Teuchos::RIGHT_SIDE, 1.0, AAA, My_GenMatrix, 0.0 );
numberFailedTests += PrintTestResults("multiply() -- general times symmetric matrix (storage = lower tri)", My_Prod.normOne(), 52.0, verbose);
AAA.setUpper();
AAA(2, 1) = 1.0;
My_Prod.multiply( Teuchos::RIGHT_SIDE, 1.0, AAA, My_GenMatrix, 0.0 );
numberFailedTests += PrintTestResults("multiply() -- general times symmetric matrix (storage = upper tri)", My_Prod.normOne(), 44.0, verbose);
// Set Method Tests.
SDMatrix CCC( 5 );
// Randomize the entries in CCC.
testName = "random() -- enter random entries into matrix";
returnCode = CCC.random();
numberFailedTests += ReturnCodeCheck(testName, returnCode, 0, verbose);
// Set the entries of CCC to 1.0.
testName = "putScalar() -- set every entry of this matrix to 1.0";
returnCode = CCC.putScalar(Teuchos::ScalarTraits<STYPE>::one());
numberFailedTests += ReturnCodeCheck(testName, returnCode, 0, verbose);
// Check assignment operator.
SDMatrix CCC2( 5 );
CCC2.assign( CCC );
if (verbose) std::cout << "assign() -- copy the values of an input matrix ";
if ( CCC( 3, 4 ) == Teuchos::ScalarTraits<STYPE>::one() ) {
if (verbose) std::cout<< "successful" <<std::endl;
} else {
if (verbose) std::cout<< "unsuccessful" <<std::endl;
numberFailedTests++;
}
// Create a view into a submatrix of CCC
SDMatrix CCCview( Teuchos::View, CCC, 3 );
SDMatrix CCCtest1( 2 );
CCCtest1 = CCCview;
if (verbose) std::cout << "operator= -- small(empty) = large(view) ";
if (CCCtest1.numRows()==3 && CCCtest1.values()==CCC.values()) {
if (verbose) std::cout<< "successful" <<std::endl;
} else {
if (verbose) std::cout<< "unsuccessful" <<std::endl;
numberFailedTests++;
}
CCCtest1 = CCC;
if (verbose) std::cout << "operator= -- small(view) = large(copy) ";
if (CCCtest1.numRows()==5 && CCCtest1.values()!=CCC.values()) {
if (verbose) std::cout<< "successful"<<std::endl;
} else {
if (verbose) std::cout<< "unsuccessful"<<std::endl;
numberFailedTests++;
}
SDMatrix CCCtest2( 2 );
CCCtest2 = Teuchos::ScalarTraits<STYPE>::one();
CCCtest1 = CCCtest2;
if (verbose) std::cout << "operator= -- large(copy) = small(copy) ";
if (CCCtest1.numRows()==2 ) {
if (verbose) std::cout<< "successful"<<std::endl;
} else {
if (verbose) std::cout<< "unsuccessful"<<std::endl;
numberFailedTests++;
}
CCCtest1 = CCCview;
if (verbose) std::cout << "operator= -- large(copy) = small(view) ";
if (CCCtest1.numRows()==3 && CCCtest1.stride()==5) {
if(verbose) std::cout<<"successful" <<std::endl;
} else {
if (verbose) std::cout<<"unsuccessful"<<std::endl;
numberFailedTests++;
}
SDMatrix CCCtest3( CCCview );
CCCtest1 += CCCtest3;
if (verbose) std::cout << "operator+= -- add two matrices of the same size, but different leading dimension ";
if (CCCtest1(1,1)==2.0) {
if(verbose) std::cout<<"successful" <<std::endl;
} else {
if (verbose) std::cout<<"unsuccessful"<<std::endl;
numberFailedTests++;
}
if (verbose) std::cout << "operator+= -- add two matrices of different size (nothing should change) ";
CCCtest1 += CCC;
if (CCCtest1(1,1)==2.0) {
if(verbose) std::cout<<"successful" <<std::endl;
} else {
if (verbose) std::cout<<"unsuccessful"<<std::endl;
numberFailedTests++;
}
// Scale Tests.
SDMatrix ScalTest( 8 );
ScalTest = Teuchos::ScalarTraits<STYPE>::one();
// Scale the entries by 8, it should be 8.
// The matrix is lower triangular, by default, so check a lower triangular entry.
if (verbose) std::cout << "operator*= -- scale matrix by some number ";
ScalTest *= 8.0;
if (ScalTest(7, 1) == 8.0) {
if (verbose) std::cout<< "successful." <<std::endl;
} else {
if (verbose) std::cout<< "unsuccessful." <<std::endl;
numberFailedTests++;
}
// Matrix Triple-Product Test
STYPE alpha=0.5*Teuchos::ScalarTraits<STYPE>::one();
DMatrix W(3,2);
SDMatrix A1(2), A2(3);
A1(0,0) = 1.0, A1(1,1) = 2.0;
A2(0,0) = 1.0, A2(1,1) = 2.0, A2(2,2) = 3.00;
W = Teuchos::ScalarTraits<STYPE>::one();
SDMatrix C1upper(3), C1lower(3), C2upper(2), C2lower(2);
C1upper.setUpper(); C2upper.setUpper();
C1lower.setLower(); C2lower.setLower();
// Test all combinations of triple products.
// These should return a matrix with 1.5 in all entries
STYPE C1result = 1.5*Teuchos::ScalarTraits<STYPE>::one();
Teuchos::symMatTripleProduct<OTYPE,STYPE>( Teuchos::NO_TRANS, alpha, A1, W, C1upper );
Teuchos::symMatTripleProduct<OTYPE,STYPE>( Teuchos::NO_TRANS, alpha, A1, W, C1lower );
// These should return a matrix with 3 in all entries
STYPE C2result = 3.0*Teuchos::ScalarTraits<STYPE>::one();
Teuchos::symMatTripleProduct<OTYPE,STYPE>( Teuchos::TRANS, alpha, A2, W, C2upper );
Teuchos::symMatTripleProduct<OTYPE,STYPE>( Teuchos::TRANS, alpha, A2, W, C2lower );
if (verbose) std::cout << "triple product -- compute C = W'*A*W or C = W*A*W' ";
if (C1upper(2,1)==C1result && C1lower(1,2)==C1result && C2upper(1,0)==C2result && C2lower(0,1)==C2result) {
if (verbose) std::cout<< "successful." <<std::endl;
} else {
if (verbose) std::cout<< "unsuccessful." <<std::endl;
numberFailedTests++;
}
//
// If a test failed output the number of failed tests.
//
if(numberFailedTests > 0)
{
if (verbose) {
std::cout << "Number of failed tests: " << numberFailedTests << std::endl;
std::cout << "End Result: TEST FAILED" << std::endl;
return -1;
}
}
if(numberFailedTests == 0)
std::cout << "End Result: TEST PASSED" << std::endl;
return 0;
}
