683 lines
17 KiB
C++
683 lines
17 KiB
C++
/* $Header: /var/lib/cvs/dynare_cpp/sylv/cc/QuasiTriangular.cpp,v 1.1.1.1 2004/06/04 13:00:31 kamenik Exp $ */
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/* Tag $Name: $ */
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#include "QuasiTriangular.h"
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#include "SylvException.h"
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#include "SchurDecomp.h"
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#include <dynblas.h>
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#include <cstdio>
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#include <cmath>
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using namespace std;
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double DiagonalBlock::getDeterminant() const
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{
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return (*alpha)*(*alpha) + getSBeta();
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}
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double DiagonalBlock::getSBeta() const
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{
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return -(*beta1)*(*beta2);
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}
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double DiagonalBlock::getSize() const
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{
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if (real)
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return abs(*alpha);
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else
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return sqrt(getDeterminant());
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}
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// this function makes Diagonal inconsistent, it should only be used
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// on temorary matrices, which will not be used any more, e.g. in
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// QuasiTriangular::solve (we need fast performance)
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void DiagonalBlock::setReal()
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{
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*beta1 = 0;
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*beta2 = 0;
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real = true;
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}
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void DiagonalBlock::checkBlock(const double* d, int d_size)
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{
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const double* a1 = d + jbar*d_size+jbar;
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const double* b1 = a1 + d_size;
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const double* b2 = a1 + 1;
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const double* a2 = b1 + 1;
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if (a1 != alpha.a1)
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throw SYLV_MES_EXCEPTION("Bad alpha1.");
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if (!real && b1 != beta1)
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throw SYLV_MES_EXCEPTION("Bad beta1.");
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if (!real && b2 != beta2)
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throw SYLV_MES_EXCEPTION("Bad beta2.");
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if (!real && a2 != alpha.a2)
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throw SYLV_MES_EXCEPTION("Bad alpha2.");
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}
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Diagonal::Diagonal(double* data, int d_size)
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{
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int nc = getNumComplex(data, d_size); // return nc <= d_size/2
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num_all = d_size - nc;
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num_real = d_size - 2*nc;
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int jbar = 0;
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int j = 0;
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while (j < num_all) {
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int id = jbar*d_size + jbar; // index of diagonal block in data
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int ill = id + 1; // index of element below the diagonal
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int iur = id + d_size; // index of element right to diagonal
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int idd = id + d_size + 1; // index of element next on diagonal
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if ((jbar < d_size-1) && !isZero(data[ill])) {
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// it is not last column and we have nonzero below diagonal
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DiagonalBlock b(jbar, false, &data[id], &data[idd],
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&data[iur], &data[ill]);
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blocks.push_back(b);
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jbar++;
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} else {
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// it is last column or we have zero below diagonal
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DiagonalBlock b(jbar, true, &data[id], &data[id], NULL, NULL);
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blocks.push_back(b);
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}
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jbar++;
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j++;
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}
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}
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Diagonal::Diagonal(double* data, const Diagonal& d)
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{
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num_all = d.num_all;
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num_real = d.num_real;
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int d_size = d.getSize();
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for (const_diag_iter it = d.begin(); it != d.end(); ++it) {
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const DiagonalBlock& dit = *it;
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double* beta1 = NULL;
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double* beta2 = NULL;
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int id = dit.getIndex()*(d_size+1);
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int idd = id;
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if (! dit.isReal()) {
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beta1 = &data[id+d_size];
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beta2 = &data[id+1];
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idd = id + d_size + 1;
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}
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DiagonalBlock b(dit.getIndex(), dit.isReal(),
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&data[id], &data[idd], beta1, beta2);
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blocks.push_back(b);
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}
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}
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void Diagonal::copy(const Diagonal& d)
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{
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num_all = d.num_all;
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num_real = d.num_real;
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blocks = d.blocks;
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}
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int Diagonal::getNumComplex(const double* data, int d_size)
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{
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int num_complex = 0;
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int in = 1;
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for (int i = 0; i < d_size-1; i++, in = in + d_size + 1) {
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if (! isZero(data[in])) {
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num_complex++;
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if (in < d_size - 2 && ! isZero(data[in + d_size +1])) {
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throw SYLV_MES_EXCEPTION("Matrix is not quasi-triangular");
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}
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}
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}
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return num_complex;
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}
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void Diagonal::changeBase(double* p)
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{
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int d_size = getSize();
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for (diag_iter it = begin(); it != end(); ++it) {
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const DiagonalBlock& b = *it;
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int jbar = b.getIndex();
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int base = d_size*jbar + jbar;
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if (b.isReal()) {
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DiagonalBlock bnew(jbar, true, &p[base], &p[base],
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NULL, NULL);
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*it = bnew;
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} else {
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DiagonalBlock bnew(jbar, false, &p[base], &p[base+d_size+1],
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&p[base+d_size], &p[base+1]);
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*it = bnew;
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}
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}
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}
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void Diagonal::getEigenValues(Vector& eig) const
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{
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int d_size = getSize();
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if (eig.length() != 2*d_size) {
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char mes[500];
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sprintf(mes, "Wrong length of vector for eigenvalues len=%d, should be=%d.\n",
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eig.length(), 2*d_size);
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throw SYLV_MES_EXCEPTION(mes);
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}
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for (const_diag_iter it = begin(); it != end(); ++it) {
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const DiagonalBlock& b = *it;
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int ind = b.getIndex();
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eig[2*ind] = *(b.getAlpha());
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if (b.isReal()) {
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eig[2*ind+1] = 0.0;
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} else {
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double beta = sqrt(b.getSBeta());
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eig[2*ind+1] = beta;
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eig[2*ind+2] = eig[2*ind];
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eig[2*ind+3] = -beta;
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}
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}
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}
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/* swaps logically blocks 'it', and '++it'. remember to move also
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* addresses, alpha, beta1, beta2. This is a dirty (but most
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* effective) way how to do it. */
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void Diagonal::swapLogically(diag_iter it)
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{
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diag_iter itp = it;
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++itp;
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if ((*it).isReal() && !(*itp).isReal()) {
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// first is real, second is complex
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double* d1 = (*it).alpha.a1;
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double* d2 = (*itp).alpha.a1;
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double* d3 = (*itp).alpha.a2;
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// swap
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DiagonalBlock new_it((*it).jbar, d1, d2);
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*it = new_it;
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DiagonalBlock new_itp((*itp).jbar+1, d3);
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*itp = new_itp;
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} else if (!(*it).isReal() && (*itp).isReal()) {
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// first is complex, second is real
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double* d1 = (*it).alpha.a1;
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double* d2 = (*it).alpha.a2;
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double* d3 = (*itp).alpha.a1;
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// swap
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DiagonalBlock new_it((*it).jbar, d1);
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*it = new_it;
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DiagonalBlock new_itp((*itp).jbar-1, d2, d3);
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*itp = new_itp;
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}
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}
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void Diagonal::checkConsistency(diag_iter it)
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{
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if (!(*it).isReal() && isZero((*it).getBeta2())) {
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(*it).getBeta2() = 0.0; // put exact zero
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int jbar = (*it).getIndex();
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double* d2 = (*it).alpha.a2;
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(*it).alpha.a2 = (*it).alpha.a1;
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(*it).real = true;
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(*it).beta1 = 0;
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(*it).beta2 = 0;
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DiagonalBlock b(jbar+1, d2);
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blocks.insert((++it).iter(), b);
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num_real += 2;
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num_all++;
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}
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}
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double Diagonal::getAverageSize(diag_iter start, diag_iter end)
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{
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double res = 0;
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int num = 0;
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for (diag_iter run = start; run != end; ++run) {
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num++;
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res += (*run).getSize();
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}
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if (num > 0)
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res = res/num;
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return res;
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}
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Diagonal::diag_iter Diagonal::findClosestBlock(diag_iter start, diag_iter end, double a)
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{
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diag_iter closest = start;
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double minim = 1.0e100;
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for (diag_iter run = start; run != end; ++run) {
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double dist = abs(a - (*run).getSize());
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if (dist < minim) {
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minim = dist;
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closest = run;
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}
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}
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return closest;
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}
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Diagonal::diag_iter Diagonal::findNextLargerBlock(diag_iter start, diag_iter end, double a)
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{
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diag_iter closest = start;
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double minim = 1.0e100;
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for (diag_iter run = start; run != end; ++run) {
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double dist = (*run).getSize() - a;
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if ((0 <= dist) && (dist < minim)) {
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minim = dist;
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closest = run;
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}
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}
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return closest;
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}
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void Diagonal::print() const
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{
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printf("Num real: %d, num complex: %d\n",getNumReal(), getNumComplex());
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for (const_diag_iter it = begin(); it != end(); ++it) {
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if ((*it).isReal()) {
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printf("real: jbar=%d, alpha=%f\n", (*it).getIndex(), *((*it).getAlpha()));
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}
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else {
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printf("complex: jbar=%d, alpha=%f, beta1=%f, beta2=%f\n",
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(*it).getIndex(), *((*it).getAlpha()), (*it).getBeta1(), (*it).getBeta2());
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}
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}
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}
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double Diagonal::EPS = 1.0e-300;
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bool Diagonal::isZero(double p)
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{
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return (abs(p)<EPS);
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}
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QuasiTriangular::const_col_iter
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QuasiTriangular::col_begin(const DiagonalBlock& b) const
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{
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int jbar = b.getIndex();
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int d_size = diagonal.getSize();
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return const_col_iter(&getData()[jbar*d_size], d_size, b.isReal(), 0);
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}
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QuasiTriangular::col_iter
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QuasiTriangular::col_begin(const DiagonalBlock& b)
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{
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int jbar = b.getIndex();
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int d_size = diagonal.getSize();
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return col_iter(&getData()[jbar*d_size], d_size, b.isReal(), 0);
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}
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QuasiTriangular::const_row_iter
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QuasiTriangular::row_begin(const DiagonalBlock& b) const
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{
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int jbar = b.getIndex();
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int d_size = diagonal.getSize();
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int off = jbar*d_size+jbar+d_size;
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int col = jbar+1;
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if (!b.isReal()) {
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off = off + d_size;
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col++;
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}
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return const_row_iter(&getData()[off], d_size, b.isReal(), col);
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}
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QuasiTriangular::row_iter
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QuasiTriangular::row_begin(const DiagonalBlock& b)
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{
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int jbar = b.getIndex();
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int d_size = diagonal.getSize();
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int off = jbar*d_size+jbar+d_size;
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int col = jbar+1;
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if (!b.isReal()) {
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off = off + d_size;
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col++;
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}
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return row_iter(&getData()[off], d_size, b.isReal(), col);
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}
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QuasiTriangular::const_col_iter
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QuasiTriangular::col_end(const DiagonalBlock& b) const
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{
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int jbar = b.getIndex();
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int d_size = diagonal.getSize();
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return const_col_iter(getData().base()+jbar*d_size+jbar, d_size, b.isReal(),
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jbar);
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}
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QuasiTriangular::col_iter
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QuasiTriangular::col_end(const DiagonalBlock& b)
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{
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int jbar = b.getIndex();
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int d_size = diagonal.getSize();
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return col_iter(&getData()[jbar*d_size+jbar], d_size, b.isReal(), jbar);
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}
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QuasiTriangular::const_row_iter
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QuasiTriangular::row_end(const DiagonalBlock& b) const
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{
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int jbar = b.getIndex();
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int d_size = diagonal.getSize();
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return const_row_iter(&getData()[d_size*d_size+jbar], d_size, b.isReal(),
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d_size);
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}
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QuasiTriangular::row_iter
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QuasiTriangular::row_end(const DiagonalBlock& b)
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{
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int jbar = b.getIndex();
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int d_size = diagonal.getSize();
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return row_iter(&getData()[d_size*d_size+jbar], d_size, b.isReal(), d_size);
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}
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QuasiTriangular::QuasiTriangular(double r, const QuasiTriangular& t)
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: SqSylvMatrix(t.numRows()), diagonal(getData().base(), t.diagonal)
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{
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setMatrix(r, t);
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}
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QuasiTriangular::QuasiTriangular(double r, const QuasiTriangular& t,
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double rr, const QuasiTriangular& tt)
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: SqSylvMatrix(t.numRows()), diagonal(getData().base(), t.diagonal)
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{
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setMatrix(r, t);
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addMatrix(rr, tt);
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}
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QuasiTriangular::QuasiTriangular(const QuasiTriangular& t)
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: SqSylvMatrix(t), diagonal(getData().base(), t.diagonal)
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{
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}
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QuasiTriangular::QuasiTriangular(const double* d, int d_size)
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: SqSylvMatrix(d, d_size), diagonal(getData().base(), d_size)
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{}
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QuasiTriangular::~QuasiTriangular()
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{
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}
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QuasiTriangular::QuasiTriangular(int p, const QuasiTriangular& t)
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: SqSylvMatrix(t.numRows()), diagonal(getData().base(), t.diagonal)
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{
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Vector aux(t.getData());
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blas_int d_size = diagonal.getSize();
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double alpha = 1.0;
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double beta = 0.0;
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dgemm("N", "N", &d_size, &d_size, &d_size, &alpha, aux.base(),
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&d_size, t.getData().base(), &d_size, &beta, getData().base(), &d_size);
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}
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QuasiTriangular::QuasiTriangular(const SchurDecomp& decomp)
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: SqSylvMatrix(decomp.getT()),
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diagonal(getData().base(), decomp.getDim())
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{
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}
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/* this pads matrix with intial columns with zeros */
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QuasiTriangular::QuasiTriangular(const SchurDecompZero& decomp)
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: SqSylvMatrix(decomp.getDim())
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{
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// nullify first decomp.getZeroCols() columns
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int zeros = decomp.getZeroCols()*decomp.getDim();
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Vector zv(getData(), 0, zeros);
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zv.zeros();
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// fill right upper part with decomp.getRU()
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for (int i = 0; i < decomp.getRU().numRows(); i++) {
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for (int j = 0; j < decomp.getRU().numCols(); j++) {
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getData()[(j+decomp.getZeroCols())*decomp.getDim()+i] = decomp.getRU().get(i,j);
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}
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}
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// fill right lower part with decomp.getT()
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for (int i = 0; i < decomp.getT().numRows(); i++) {
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for (int j = 0; j < decomp.getT().numCols(); j++) {
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getData()[(j+decomp.getZeroCols())*decomp.getDim()+decomp.getZeroCols()+i] =
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decomp.getT().get(i,j);
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}
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}
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// construct diagonal
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Diagonal* const d = new Diagonal(getData().base(), decomp.getDim());
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diagonal = *d;
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delete d;
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}
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void QuasiTriangular::setMatrix(double r, const QuasiTriangular& t)
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{
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getData().zeros();
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getData().add(r, t.getData());
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}
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void QuasiTriangular::setMatrixViaIter(double r, const QuasiTriangular& t)
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{
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register double rr = r;
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diag_iter dil = diag_begin();
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const_diag_iter dir = t.diag_begin();
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for ( ; dil != diag_end(); ++dil, ++dir) {
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(*dil).getAlpha() = rr*(*(*dir).getAlpha());
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if (! (*dil).isReal()) {
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(*dil).getBeta1() = rr*(*dir).getBeta1();
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(*dil).getBeta2() = rr*(*dir).getBeta2();
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}
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col_iter cil = col_begin(*dil);
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const_col_iter cir = t.col_begin(*dir);
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for ( ; cil != col_end(*dil); ++cil, ++cir) {
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if ((*dil).isReal()) {
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*cil = rr*(*cir);
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} else {
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cil.a() = rr*cir.a();
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cil.b() = rr*cir.b();
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}
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}
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}
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}
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void QuasiTriangular::addMatrix(double r, const QuasiTriangular& t)
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{
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getData().add(r, t.getData());
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}
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void QuasiTriangular::addMatrixViaIter(double r, const QuasiTriangular& t)
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{
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register double rr = r;
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diag_iter dil = diag_begin();
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const_diag_iter dir = t.diag_begin();
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for ( ; dil != diag_end(); ++dil, ++dir) {
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(*dil).getAlpha() = (*(*dil).getAlpha()) + rr*(*(*dir).getAlpha());
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if (! (*dil).isReal()) {
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(*dil).getBeta1() += rr*(*dir).getBeta1();
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(*dil).getBeta2() += rr*(*dir).getBeta2();
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}
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col_iter cil = col_begin(*dil);
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const_col_iter cir = t.col_begin(*dir);
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for ( ; cil != col_end(*dil); ++cil, ++cir) {
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if ((*dil).isReal()) {
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*cil += rr*(*cir);
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} else {
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cil.a() += rr*cir.a();
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cil.b() += rr*cir.b();
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}
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}
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}
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}
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|
|
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void QuasiTriangular::addUnit()
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|
{
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for (diag_iter di = diag_begin(); di != diag_end(); ++di) {
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(*di).getAlpha() = *((*di).getAlpha()) + 1.0;
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}
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|
}
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|
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void QuasiTriangular::solve(Vector& x, const ConstVector& b, double& eig_min)
|
|
{
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|
x = b;
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|
solvePre(x, eig_min);
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|
}
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|
|
|
void QuasiTriangular::solveTrans(Vector& x, const ConstVector& b, double& eig_min)
|
|
{
|
|
x = b;
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|
solvePreTrans(x, eig_min);
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|
}
|
|
|
|
void QuasiTriangular::solvePre(Vector& x, double& eig_min)
|
|
{
|
|
addUnit();
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|
for (diag_iter di = diag_begin(); di != diag_end(); ++di) {
|
|
double eig_size;
|
|
if (!(*di).isReal()) {
|
|
eig_size = (*di).getDeterminant();
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|
eliminateLeft((*di).getIndex()+1, (*di).getIndex(), x);
|
|
} else {
|
|
eig_size = *(*di).getAlpha()*(*(*di).getAlpha());
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|
}
|
|
if (eig_size < eig_min)
|
|
eig_min = eig_size;
|
|
}
|
|
|
|
blas_int nn = diagonal.getSize();
|
|
blas_int lda = diagonal.getSize();
|
|
blas_int incx = x.skip();
|
|
dtrsv("U", "N", "N", &nn, getData().base(), &lda, x.base(), &incx);
|
|
}
|
|
|
|
void QuasiTriangular::solvePreTrans(Vector& x, double& eig_min)
|
|
{
|
|
addUnit();
|
|
for (diag_iter di = diag_begin(); di != diag_end(); ++di) {
|
|
double eig_size;
|
|
if (!(*di).isReal()) {
|
|
eig_size = (*di).getDeterminant();
|
|
eliminateRight((*di).getIndex()+1, (*di).getIndex(), x);
|
|
} else {
|
|
eig_size = *(*di).getAlpha()*(*(*di).getAlpha());
|
|
}
|
|
if (eig_size < eig_min)
|
|
eig_min = eig_size;
|
|
}
|
|
|
|
blas_int nn = diagonal.getSize();
|
|
blas_int lda = diagonal.getSize();
|
|
blas_int incx = x.skip();
|
|
dtrsv("U", "T", "N", &nn, getData().base(), &lda, x.base(), &incx);
|
|
}
|
|
|
|
|
|
/* calculates x = Tb */
|
|
void QuasiTriangular::multVec(Vector& x, const ConstVector& b) const
|
|
{
|
|
x = b;
|
|
blas_int nn = diagonal.getSize();
|
|
blas_int lda = diagonal.getSize();
|
|
blas_int incx = x.skip();
|
|
dtrmv("U", "N", "N", &nn, getData().base(), &lda, x.base(), &incx);
|
|
for (const_diag_iter di = diag_begin(); di != diag_end(); ++di) {
|
|
if (!(*di).isReal()) {
|
|
int jbar = (*di).getIndex();
|
|
x[jbar+1] += (*di).getBeta2()*(b[jbar]);
|
|
}
|
|
}
|
|
}
|
|
|
|
|
|
void QuasiTriangular::multVecTrans(Vector& x, const ConstVector& b) const
|
|
{
|
|
x = b;
|
|
blas_int nn = diagonal.getSize();
|
|
blas_int lda = diagonal.getSize();
|
|
blas_int incx = x.skip();
|
|
dtrmv("U", "T", "N", &nn, getData().base(), &lda, x.base(), &incx);
|
|
for (const_diag_iter di = diag_begin(); di != diag_end(); ++di) {
|
|
if (!(*di).isReal()) {
|
|
int jbar = (*di).getIndex();
|
|
x[jbar] += (*di).getBeta2()*b[jbar+1];
|
|
}
|
|
}
|
|
}
|
|
|
|
void QuasiTriangular::multaVec(Vector& x, const ConstVector& b) const
|
|
{
|
|
Vector tmp((const Vector&) x); // new copy
|
|
multVec(x, b);
|
|
x.add(1.0, tmp);
|
|
}
|
|
|
|
void QuasiTriangular::multaVecTrans(Vector& x, const ConstVector& b) const
|
|
{
|
|
Vector tmp((const Vector&) x); // new copy
|
|
multVecTrans(x, b);
|
|
x.add(1.0, tmp);
|
|
}
|
|
|
|
/* calculates x=x+(T\otimes I)b, where size of I is given by b (KronVector) */
|
|
void QuasiTriangular::multaKron(KronVector& x, const ConstKronVector& b) const
|
|
{
|
|
int id = b.getN()*power(b.getM(), b.getDepth()-1);
|
|
ConstGeneralMatrix b_resh(b.base(), id, b.getM());
|
|
GeneralMatrix x_resh(x.base(), id, b.getM());
|
|
x_resh.multAndAdd(b_resh, ConstGeneralMatrix(*this), "trans");
|
|
}
|
|
|
|
|
|
/* calculates x=x+(T'\otimes I)b, where size of I is given by b (KronVector) */
|
|
void
|
|
QuasiTriangular::multaKronTrans(KronVector& x, const ConstKronVector& b) const
|
|
{
|
|
int id = b.getN()*power(b.getM(), b.getDepth()-1);
|
|
ConstGeneralMatrix b_resh(b.base(), id, b.getM());
|
|
GeneralMatrix x_resh(x.base(), id, b.getM());
|
|
x_resh.multAndAdd(b_resh, ConstGeneralMatrix(*this));
|
|
}
|
|
|
|
|
|
void QuasiTriangular::multKron(KronVector& x) const
|
|
{
|
|
KronVector b((const KronVector&)x); // make copy
|
|
x.zeros();
|
|
multaKron(x, b);
|
|
}
|
|
|
|
void
|
|
QuasiTriangular::multKronTrans(KronVector& x) const
|
|
{
|
|
KronVector b((const KronVector&)x); // make copy
|
|
x.zeros();
|
|
multaKronTrans(x, b);
|
|
}
|
|
|
|
void QuasiTriangular::multLeftOther(GeneralMatrix& a) const
|
|
{
|
|
a.multLeft(*this);
|
|
}
|
|
|
|
void QuasiTriangular::multLeftOtherTrans(GeneralMatrix& a) const
|
|
{
|
|
a.multLeftTrans(*this);
|
|
}
|
|
|
|
void QuasiTriangular::swapDiagLogically(diag_iter it)
|
|
{
|
|
diagonal.swapLogically(it);
|
|
}
|
|
|
|
void QuasiTriangular::checkDiagConsistency(diag_iter it)
|
|
{
|
|
diagonal.checkConsistency(it);
|
|
}
|
|
|
|
double QuasiTriangular::getAverageDiagSize(diag_iter start, diag_iter end)
|
|
{
|
|
return diagonal.getAverageSize(start, end);
|
|
}
|
|
|
|
QuasiTriangular::diag_iter
|
|
QuasiTriangular::findClosestDiagBlock(diag_iter start, diag_iter end, double a)
|
|
{
|
|
return diagonal.findClosestBlock(start, end, a);
|
|
}
|
|
|
|
QuasiTriangular::diag_iter
|
|
QuasiTriangular::findNextLargerBlock(diag_iter start, diag_iter end, double a)
|
|
{
|
|
return diagonal.findNextLargerBlock(start, end, a);
|
|
}
|
|
|
|
int QuasiTriangular::getNumOffdiagonal() const
|
|
{
|
|
return diagonal.getSize()*(diagonal.getSize()-1)/2 - diagonal.getNumComplex();
|
|
}
|