/**
* Obtiene los primeros k autovectores y autovalores dominantes de la matriz.
*
* @param A matriz a investigar
* @param k cantidad de autovectores/autovalores a obtener
* @ret lista ordenada por dominancia decreciente del autopar
*/
std::list<EigenPair> decompose(Matrix deflated, int k, const Norm &norm, unsigned int iterations) {
if (k >= deflated.columns()) {
std::stringstream fmt;
fmt << "Cantidad de autovalores esperado es demasiado grande, " << k << " en una matriz de " << deflated.columns();
throw new std::out_of_range(fmt.str());
}
Timer timer("Decompose Timer");
std::list<EigenPair> output;
// Vector inicial para esta iteracion
std::vector<double> x0((unsigned long) deflated.columns(), 0.0);
for (int i = 0; i < k; ++i) {
for (int l = 0; l < deflated.columns(); ++l) {
x0[l] = random() % 1337 + 1;
}
// Obtenemos el i-esimo eigenpair dominante
EigenPair dominant = powerIteration(deflated, x0, norm, iterations);
if (dominant.first != dominant.first) {
std::cerr << "Error sacando el autovalor " << i << ". Vector: " << std::endl;
for (int i = 0; i < deflated.columns(); ++i) {
std::cerr << x0[i] << " ";
}
std::cerr << std::endl;
--i;
} else {
// Hacemos deflacion, para el proximo paso
deflation(deflated, dominant);
// Lo guardamos al final de la lista
output.push_back(dominant);
}
}
return output;
}
void iterativeSolvers_unitTest() {
// small matrix test
{
Vector4f test = makeVector4f(1.0f, 3.14f, 2.0f, 2.71f);
Matrix4f mat = makeRotX4f(0.32f) * makeRotY4f(-0.39f) * makeRotZ4f(0.76f);
mat += mat.transpose();
mat += IDENTITY4F*5;
Vector4f rhs = mat * test;
Matrix4f invMat = invertMatrix(mat);
Vector4f directFloat = invMat * rhs;
DVectorD testD(4); for (card32 i=0; i<4; i++) testD[i] = test[i];
DVectorD rhsD(4); for (card32 i=0; i<4; i++) rhsD[i] = rhs[i];
SparseMatrixD matS(4);
for (card32 r=0; r<4; r++) {
for (card32 c=0; c<4; c++) {
double v = mat[c][r];
if (v != 0) {
matS[r].setEntry(c, v);
}
}
}
output << "Matrix:\n" << mat.toString() << "\n";
output << "true solution: " << test.toString() << "\n";
output << "right hand side: " << rhs.toString() << "\n";
output << "direct float prec. solution: " << directFloat.toString() << "\n\n";
output << "Matrix:\n" << matS.toString() << "\n";
output << "true solution: " << testD.toString() << "\n";
output << "right hand side: " << rhsD.toString() << "\n\n";
DVectorD x = nullDVector<double>(4);
card32 numIterations = 1000;
gaussSeidelSolve(matS, x, rhsD, numIterations, 1E-20, 1E-5, false);
output << "Gauss-Seidel solution: " << x.toString() << "\n\n";
numIterations = 1000;
x = nullDVector<double>(4);
steepestDescentSolve(matS, x, rhsD, numIterations, 1E-5, false);
output << "Steepest-Descent solution: " << x.toString() << "\n\n";
numIterations = 1000;
x = nullDVector<double>(4);
conjugateGradientsSolve(matS, x, rhsD, numIterations, 1E-5, true);
output << "CG solution: " << x.toString() << "\n\n";
}
// large matrix test
{
SparseMatrixD mat(MDIM*MDIM);
for (int y=0; y<MDIM; y++) {
for (int x=0; x<MDIM; x++) {
addEntry(mat, x,y, x,y, -4, MDIM);
addEntry(mat, x,y, x+1,y, 1, MDIM);
addEntry(mat, x,y, x-1,y, 1, MDIM);
addEntry(mat, x,y, x,y+1, 1, MDIM);
addEntry(mat, x,y, x,y-1, 1, MDIM);
}
}
Timer T; card32 vt;
DVectorD x = nullDVector<double>(MDIM*MDIM);
DVectorD b = scalarDVector<double>(MDIM*MDIM, 1);
DVectorD gs, sd, cg;
x = nullDVector<double>(MDIM*MDIM);
T.getDeltaValue();
card32 numIterations = 100000;
conjugateGradientsSolve(mat, x, b, numIterations, 1E-7, false);
vt = T.getDeltaValue();
output << "CG time: " << vt << "\n\n";
output << "Large sytem CG solution (LAPL(f) == 1):\n";
for (int y=0; y<MDIM; y++) {
for (int xp=0; xp<MDIM; xp++) {
output << x[xp +y*MDIM] << "\t";
}
output.cr();
}
output.cr();
cg = x;
x = nullDVector<double>(MDIM*MDIM);
T.getDeltaValue();
numIterations = 100000;
gaussSeidelSolve(mat, x, b, numIterations, 1E-20, 1E-7, false);
vt = T.getDeltaValue();
output << "GS time: " << vt << "\n\n";
output << "Large sytem Gauss-Seidel solution (LAPL(f) == 1):\n";
for (int y=0; y<MDIM; y++) {
for (int xp=0; xp<MDIM; xp++) {
output << x[xp +y*MDIM] << "\t";
}
output.cr();
}
output.cr();
gs = x;
x = nullDVector<double>(MDIM*MDIM);
T.getDeltaValue();
numIterations = 100000;
steepestDescentSolve(mat, x, b, numIterations, 1E-7, false);
vt = T.getDeltaValue();
output << "SD time: " << vt << "\n\n";
output << "Large sytem steepest descent solution (LAPL(f) == 1):\n";
for (int y=0; y<MDIM; y++) {
for (int xp=0; xp<MDIM; xp++) {
output << (long double)x[xp +y*MDIM] << "\t";
}
output.cr();
}
output.cr();
sd = x;
x = nullDVector<double>(MDIM*MDIM);
output << "|gs-sd|_2 " << (long double)norm(gs-sd) << "\n";
output << "|gs-cg|_2 " << (long double)norm(gs-cg) << "\n";
vector< DVectorD > eigenVects;
vector< double > eigenvalues;
DVectorD eigenvector;
double eigenvalue;
for (int i=0; i<10; i++) {
powerIteration(mat, eigenVects, eigenvector, eigenvalue, 1.0001, 1000, false);
eigenVects.push_back(eigenvector);
eigenvalues.push_back(eigenvalue);
}
for (int i=0; i<10; i++) {
output << i << " largest of large sytem eigenvector (LAPL(f) == 1):\n";
for (int y=0; y<MDIM; y++) {
for (int xp=0; xp<MDIM; xp++) {
output << eigenVects[i][xp +y*MDIM] << "\t";
}
output.cr();
}
output.cr();
}
output << "eigenvalue:\n";
for (int i=0; i<10; i++) {
output << eigenvalues[i] << "\n";
}
T.getDeltaValue();
eigenVects.clear();
for (int i=0; i<10; i++) {
GaussSeidelSolver<double> linSolve;
inversePowerIteration(mat, eigenVects, eigenvector, eigenvalue, &linSolve, 1.0001, 1000, false);
eigenvalues.push_back(eigenvalue);
eigenVects.push_back(eigenvector);
}
output << "GS-PowerIt time: " << T.getDeltaValue() << "\n\n";
eigenVects.clear();
for (int i=0; i<10; i++) {
CGSolver<double> linSolve;
inversePowerIteration(mat, eigenVects, eigenvector, eigenvalue, &linSolve, 1.0001, 1000, false);
eigenvalues.push_back(eigenvalue);
eigenVects.push_back(eigenvector);
}
output << "CG-PowerIt time: " << T.getDeltaValue() << "\n\n";
eigenVects.clear();
for (int i=0; i<10; i++) {
SteepestDescentSolver<double> linSolve;
inversePowerIteration(mat, eigenVects, eigenvector, eigenvalue, &linSolve, 1.0001, 1000, false);
eigenvalues.push_back(eigenvalue);
eigenVects.push_back(eigenvector);
}
output << "Steepest descent-PowerIt time: " << T.getDeltaValue() << "\n\n";
for (int i=0; i<10; i++) {
output << i << " smallest of large sytem eigenvector (LAPL(f) == 1):\n";
for (int y=0; y<MDIM; y++) {
for (int xp=0; xp<MDIM; xp++) {
output << eigenVects[i][xp +y*MDIM] << "\t";
}
output.cr();
}
output.cr();
}
output << "eigenvalues:\n";
for (int i=0; i<10; i++) {
output << eigenvalues[i] << "\n";
}
}
{
Timer T;
output << "cg scaling test\n";
for (unsigned i=1; i<21; i++) {
const int size = i * 10;
SparseMatrixD mat(size*size);
for (int y=0; y<size; y++) {
for (int x=0; x<size; x++) {
addEntry(mat, x,y, x,y, -4, size);
addEntry(mat, x,y, x+1,y, 1, size);
addEntry(mat, x,y, x-1,y, 1, size);
addEntry(mat, x,y, x,y+1, 1, size);
addEntry(mat, x,y, x,y-1, 1, size);
}
}
Timer T; card32 vt;
DVectorD x = nullDVector<double>(size*size);
DVectorD b = scalarDVector<double>(size*size, 1);
T.getDeltaValue();
card32 numIterations = 100000;
conjugateGradientsSolve(mat, x, b, numIterations, 1E-7, false);
vt = T.getDeltaValue();
output << i << "\t" << vt << "\n";
}
}
{
Timer T;
output << "gs scaling test\n";
for (unsigned i=1; i<21; i++) {
const int size = i * 10;
SparseMatrixD mat(size*size);
for (int y=0; y<size; y++) {
for (int x=0; x<size; x++) {
addEntry(mat, x,y, x,y, -4, size);
addEntry(mat, x,y, x+1,y, 1, size);
addEntry(mat, x,y, x-1,y, 1, size);
addEntry(mat, x,y, x,y+1, 1, size);
addEntry(mat, x,y, x,y-1, 1, size);
}
}
Timer T; card32 vt;
DVectorD x = nullDVector<double>(size*size);
DVectorD b = scalarDVector<double>(size*size, 1);
T.getDeltaValue();
card32 numIterations = 100000;
gaussSeidelSolve(mat, x, b, numIterations, 1E-20, 1E-7, false);
vt = T.getDeltaValue();
output << i << "\t" << vt << "\n";
}
}
{
Timer T;
output << "sd scaling test\n";
for (unsigned i=1; i<21; i++) {
const int size = i * 10;
SparseMatrixD mat(size*size);
for (int y=0; y<size; y++) {
for (int x=0; x<size; x++) {
addEntry(mat, x,y, x,y, -4, size);
addEntry(mat, x,y, x+1,y, 1, size);
addEntry(mat, x,y, x-1,y, 1, size);
addEntry(mat, x,y, x,y+1, 1, size);
addEntry(mat, x,y, x,y-1, 1, size);
}
}
Timer T; card32 vt;
DVectorD x = nullDVector<double>(size*size);
DVectorD b = scalarDVector<double>(size*size, 1);
T.getDeltaValue();
card32 numIterations = 100000;
steepestDescentSolve(mat, x, b, numIterations, 1E-7, false);
vt = T.getDeltaValue();
output << i << "\t" << vt << "\n";
}
}
}
int main()
{
FILE* fin = NULL;
char c, fileName[20];
int i;
do
{
printf ("\n <<<<<<<<<<<<<<<<<<<<<< MENU >>>>>>>>>>>>>>>>>>>>>>\n\n");
printf ("\n 1. Generate a new test file AND display it;");
printf ("\n 2. Generate a new test file WITHOUT displaying it;\n");
printf ("\n 3. Load an existing test file AND display it;");
printf ("\n 4. Load an existing test file WITHOUT displaying it;\n");
printf ("\n 5. Exit the program.\n");
printf ("\n Choose an option ('c' to clear screen): ");
scanf (" %c", &c);
if (c == 'c')
{
for (i = 0; i < 100; i++)
{
printf ("\n");
}
}
else if (c == '1')
{
printf ("\nGenerate a new test file and display it. Input its name:\n");
scanf ("%s", fileName);
graphGenerator (fileName);
displayGraph (fin, fileName);
}
else if (c == '2')
{
printf ("\nGenerate a new test file. Input its name:\n");
scanf ("%s", fileName);
graphGenerator (fileName);
}
else if (c == '3')
{
printf ("\nLoad an existing test file and display it. Input its name:\n");
scanf ("%s", fileName);
displayGraph (fin, fileName);
}
else if (c == '4')
{
printf ("\nLoad an existing test file. Input its name:\n");
scanf ("%s", fileName);
}
else if (c == '5')
{
exit(1);
}
else
{
printf ("\nThe key you pressed is not a valid option. Please press 1, 2, 3, 4 or 5.\n\n");
}
if (c == '1' || c == '2' || c == '3' || c == '4')
{
fin = fopen (fileName, "r");
if (fin == NULL)
{
perror ("\n\tError opening file\n");
}
else
{
int nodes;
double beta;
printf ("\nDefine the damping factor (best between 0.8 and 0.9): ");
scanf ("%lf", &beta);
double **M = loadGraph (fin, nodes);
M = createMatrix_M (M, nodes, beta);
double **B = createMatrix_B (nodes, beta);
M = matrixSum (M, B, nodes);
deallocMatrix <double> (B, nodes);
//
printf("\n Matrix A = M + B \n");
displayMatrix (M, nodes, nodes);
//
powerIteration (M, nodes, beta);
fclose (fin);
}
}
} while (true);
return 0;
}
