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lsLibla.cpp
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/**
* LibStruct, original author: Frank Bergmann.
* Fixes and improvments: Totte Karsson
*/
#pragma hdrstop
#include <iostream>
#include <fstream>
#include <string>
#include <math.h>
#include <stdlib.h>
#include <cmath>
#include <sstream>
#include <string.h>
#include "lsLibla.h"
#include "lsMatrix.h"
#include "lsUtils.h"
extern "C"
{
#include "f2c.h"
#include "clapack.h"
}
//---------------------------------------------------------------------------
namespace ls {
using namespace std;
using namespace ls;
double gLapackTolerance = 1.0E-12;
double getTolerance() {
return gLapackTolerance;
}
void setTolerance(double dTolerance) {
gLapackTolerance = dTolerance;
}
vector<Complex> getEigenValues(DoubleMatrix &oMatrix) {
//Log(lDebug5) << "======================================================" << endl;
//Log(lDebug5) << "=== getEigenValues " << endl;
//Log(lDebug5) << "======================================================" << endl << endl;
vector<Complex> oResult;
integer numRows = oMatrix.numRows();
integer numCols = oMatrix.numCols();
integer lwork = 2 * numRows;
integer info;
if (numRows != numCols) {
throw ApplicationException("Input Matrix must be square", "Expecting a Square Matrix");
}
if (numRows == 0) return oResult;
doublecomplex *A = new doublecomplex[numRows * numRows];
memset(A, 0, sizeof(doublecomplex) * numRows * numRows);
doublecomplex *eigVals = new doublecomplex[numRows];
memset(eigVals, 0, sizeof(doublecomplex) * numRows);
doublecomplex *work = new doublecomplex[lwork];
memset(work, 0, sizeof(doublecomplex) * lwork);
doublereal *rwork = new doublereal[lwork];
memset(rwork, 0, sizeof(doublereal) * lwork);
int index;
for (int i = 0; i < numRows; i++) {
for (int j = 0; j < numCols; j++) {
index = (j + numRows * i);
A[index].r = oMatrix(i, j);
}
}
char job = 'N'; // do not compute eigenvectors
zgeev_(&job, &job, &numRows, A, &numRows, eigVals, NULL, &numRows, NULL, &numRows, work, &lwork, rwork, &info);
for (int i = 0; i < numRows; i++) {
Complex complex(ls::RoundToTolerance(eigVals[i].r, gLapackTolerance),
ls::RoundToTolerance(eigVals[i].i, gLapackTolerance));
oResult.push_back(complex);
}
delete[] eigVals;
delete[] A;
delete[] work;
delete[] rwork;
return oResult;
}
vector<ls::Complex> ZgetEigenValues(ComplexMatrix &oMatrix) {
//Log(lDebug5) << "======================================================" << endl;
//Log(lDebug5) << "=== ZgetEigenValues " << endl;
//Log(lDebug5) << "======================================================" << endl << endl;
vector<Complex> oResult;
integer numRows = oMatrix.numRows();
integer numCols = oMatrix.numCols();
integer lwork = 2 * numRows;
integer info;
if (numRows != numCols)
throw ApplicationException("Input Matrix must be square", "Expecting a Square Matrix");
doublecomplex *A = new doublecomplex[numRows * numRows];
memset(A, 0, sizeof(doublecomplex) * numRows * numRows);
doublecomplex *eigVals = new doublecomplex[numRows];
memset(eigVals, 0, sizeof(doublecomplex) * numRows);
doublecomplex *work = new doublecomplex[lwork];
memset(work, 0, sizeof(doublecomplex) * lwork);
doublereal *rwork = new doublereal[lwork];
memset(rwork, 0, sizeof(doublereal) * lwork);
int index;
for (int i = 0; i < numRows; i++) {
for (int j = 0; j < numCols; j++) {
index = (j + numRows * i);
A[index].r = real(oMatrix(j, i));
A[index].i = imag(oMatrix(j, i));
}
}
char job = 'N'; // do not compute eigenvectors
zgeev_(&job, &job, &numRows, A, &numRows, eigVals, NULL, &numRows, NULL, &numRows, work, &lwork, rwork, &info);
for (int i = 0; i < numRows; i++) {
Complex complex(ls::RoundToTolerance(eigVals[i].r, gLapackTolerance),
ls::RoundToTolerance(eigVals[i].i, gLapackTolerance));
oResult.push_back(complex);
}
delete[] eigVals;
delete[] A;
delete[] work;
delete[] rwork;
return oResult;
}
vector<DoubleMatrix *> getQRWithPivot(DoubleMatrix &oMatrix) {
//Log(lDebug5) << "======================================================" << endl;
//Log(lDebug5) << "=== getQRWithPivot " << endl;
//Log(lDebug5) << "======================================================" << endl << endl;
vector<DoubleMatrix *> oResult;
integer row = oMatrix.numRows();
integer col = oMatrix.numCols();
if (row * col == 0) {
DoubleMatrix *oMatrixQ = new DoubleMatrix(row, row);
DoubleMatrix *oMatrixR = new DoubleMatrix(row, col);
DoubleMatrix *oMatrixP = new DoubleMatrix(col, col);
oResult.push_back(oMatrixQ);
oResult.push_back(oMatrixR);
oResult.push_back(oMatrixP);
return oResult;
}
integer minRowCol = min(row, col);
//lwork has different optimum sizes for the two functions where we use it:
integer lwork_for_dgeqp3 = 2 * col + 16 * (col + 1);
integer lwork_for_dorgqr = 16 * row;
integer lwork = max(lwork_for_dgeqp3, lwork_for_dorgqr);
doublereal *A = oMatrix.getCopy(true);
doublereal *Q = NULL;
if (row * row) {
Q = new doublereal[row * row];
memset(Q, 0, sizeof(doublereal) * row * row);
}
doublereal *R = NULL;
if (row * col) {
R = new doublereal[row * col];
memset(R, 0, sizeof(doublereal) * row * col);
}
doublereal *P = NULL;
if (col * col) {
P = new doublereal[col * col];
memset(P, 0, sizeof(doublereal) * col * col);
}
//Log(lDebug5) << "before dorgqr A:\n" << ls::print(row, col, A);
//Log(lDebug5) << endl << endl << "Q: \n" << ls::print(row, row, Q);
//Log(lDebug5) << endl << endl << "R: \n" << ls::print(row, col, R);
//Log(lDebug5) << endl << endl << "P: \n" << ls::print(col, col, P);
doublereal *tau = NULL;
if (minRowCol) {
tau = new doublereal[minRowCol];
memset(tau, 0, sizeof(doublereal) * minRowCol);
}
integer *jpvt = NULL;
if (col) {
jpvt = new integer[col];
memset(jpvt, 0, sizeof(integer) * col);
}
doublereal *work = NULL;
if (lwork) {
work = new doublereal[lwork];
memset(work, 0, lwork);
}
integer info;
int out;
//Log(lDebug5) << "Input:\n"<<ls::print(row, col, A);
// call lapack routine dgepq3_ to generate householder reflections
out = dgeqp3_(&row, &col, A, &row, jpvt, tau, work, &lwork, &info);
//Log(lDebug5) << "before permutation" << endl;
// Building permutation matrix P and
for (int i = 0; i < col; i++) {
size_t pos = i * col + (jpvt[i] - 1);
if (pos < col * col)
P[pos] = 1;
}
//Log(lDebug5) << "before memcpy" << endl;
// set R to A before calling dorgqr
memcpy(R, A, sizeof(doublereal) * row * col);
//Log(lDebug5) << "after memcpy" << endl;
// make R a trapezoidal matrix
// set Q to A before calling dorgqr
int index = 0;
for (int i = 0; i < row; i++) {
for (int j = 0; j < minRowCol; j++) {
index = i + row * j;
Q[index] = A[index];
}
if (i >= 1)
for (int j = 0; j < min(i, (int)col); j++) {
R[i + row * j] = 0.0;
}
}
//Log(lDebug5) << "before dorgqr:\n"<<ls::print(row, col, A);
//Log(lDebug5) << endl << endl << "Q: \n"<<ls::print(row, row, Q);
//Log(lDebug5) << endl << endl << "R: \n"<<ls::print(row, col, R);
//Log(lDebug5) << endl << endl << "P: \n"<<ls::print(col, col, P);
// call routine dorgqr_ to build orthogonal matrix Q
out = dorgqr_(&row, &row, &minRowCol, Q, &row, tau, work, &lwork, &info);
//Log(lDebug5) << endl << endl << "Q: \n"<<ls::print(row, row, Q);
//Log(lDebug5) << endl << endl << "R: \n"<<ls::print(row, col, R);
//Log(lDebug5) << endl << endl << "P: \n"<<ls::print(col, col, P);
DoubleMatrix *oMatrixQ = new DoubleMatrix(Q, row, row, true);
RoundMatrixToTolerance(*oMatrixQ, gLapackTolerance);
DoubleMatrix *oMatrixR = new DoubleMatrix(R, row, col, true);
RoundMatrixToTolerance(*oMatrixR, gLapackTolerance);
DoubleMatrix *oMatrixP = new DoubleMatrix(P, col, col, true);
RoundMatrixToTolerance(*oMatrixP, gLapackTolerance);
oResult.push_back(oMatrixQ);
oResult.push_back(oMatrixR);
oResult.push_back(oMatrixP);
// free
if (row * col) {
delete[] A;
}
if (row * row) {
delete[] Q;
}
if (row * col) {
delete[] R;
}
if (col * col) {
delete[] P;
}
if (tau) {
delete[] tau;
}
if (jpvt) {
delete[] jpvt;
}
if (work) {
delete[] work;
}
return oResult;
}
vector<DoubleMatrix *> getQR(DoubleMatrix &oMatrix) {
//Log(lDebug5) << "======================================================" << endl;
//Log(lDebug5) << "=== getQR " << endl;
//Log(lDebug5) << "======================================================" << endl << endl;
integer row = oMatrix.numRows();
integer col = oMatrix.numCols();
if (row * col == 0) {
vector<DoubleMatrix *> oResult;
DoubleMatrix *oMatrixQ = new DoubleMatrix(row, row);
DoubleMatrix *oMatrixR = new DoubleMatrix(row, col);
oResult.push_back(oMatrixQ);
oResult.push_back(oMatrixR);
return oResult;
}
integer lwork = 16 * col;
integer minRowCol = min(row, col);
doublereal *Q = new doublereal[row * row];
doublereal *R = new doublereal[row * col];
doublereal *tau = new doublereal[minRowCol];
doublereal *work = new doublereal[lwork];
doublereal *A = (doublereal *) oMatrix.getCopy(true);
//Log(lDebug5) << "Input:\n"<<ls::print(row, col, A);
integer info;
dgeqrf_(&row, &col, A, &row, tau, work, &lwork, &info);
//Log(lDebug5) << "A: after dgeqrt)\n"<<ls::print(row, col, A);
//Log(lDebug5) << "tau: after dgeqrt)\n"<<ls::print(1, minRowCol, tau);
// set R to A before calling dorgqr
memcpy(R, A, sizeof(double) * row * col);
int index;
for (int i = 0; i < row; i++) {
if (i > 0)
for (int j = 0; j < min(i, (int)col); j++) {
R[i + row * j] = 0.0;
}
for (int j = 0; j < minRowCol; j++) {
index = i + row * j;
Q[index] = A[index];
}
}
dorgqr_(&row, &row, &minRowCol, Q, &row, tau, work, &lwork, &info);
ls::checkTolerance(row * row, Q, getTolerance());
ls::checkTolerance(row * col, R, getTolerance());
//Log(lDebug5) << endl << endl << "Q: )\n"<<ls::print(row, row, Q);
//Log(lDebug5) << endl << endl << "R: )\n"<<ls::print(row, col, R);
vector<DoubleMatrix *> oResult;
DoubleMatrix *oMatrixQ = new DoubleMatrix(Q, row, row, true);
ls::RoundMatrixToTolerance(*oMatrixQ, gLapackTolerance);
DoubleMatrix *oMatrixR = new DoubleMatrix(R, row, col, true);
ls::RoundMatrixToTolerance(*oMatrixR, gLapackTolerance);
oResult.push_back(oMatrixQ);
oResult.push_back(oMatrixR);
delete[] A;
delete[] Q;
delete[] R;
delete[] tau;
delete[] work;
return oResult;
}
DoubleMatrix *getLeftNullSpace(DoubleMatrix &oMatrixIn) {
//Log(lDebug5) << "======================================================" << endl;
//Log(lDebug5) << "=== getLeftNullSpace " << endl;
//Log(lDebug5) << "======================================================" << endl << endl;
DoubleMatrix *oMatrix = oMatrixIn.getTranspose();
DoubleMatrix *oMatrixResult = getRightNullSpace(*oMatrix);
delete oMatrix;
//return oMatrixResult;
DoubleMatrix *oFinalMatrix = oMatrixResult->getTranspose();
delete oMatrixResult;
return oFinalMatrix;
}
DoubleMatrix *getScaledLeftNullSpace(DoubleMatrix &oMatrixIn) {
//Log(lDebug5) << "======================================================" << endl;
//Log(lDebug5) << "=== getScaledLeftNullSpace " << endl;
//Log(lDebug5) << "======================================================" << endl << endl;
DoubleMatrix *oMatrix = oMatrixIn.getTranspose();
DoubleMatrix *oMatrixResult = getScaledRightNullSpace(*oMatrix);
delete oMatrix;
//return oMatrixResult;
DoubleMatrix *oFinalMatrix = oMatrixResult->getTranspose();
delete oMatrixResult;
return oFinalMatrix;
}
DoubleMatrix *getScaledRightNullSpace(DoubleMatrix &oMatrix) {
//Log(lDebug5) << "======================================================" << endl;
//Log(lDebug5) << "=== getScaledRightNullSpace " << endl;
//Log(lDebug5) << "======================================================" << endl << endl;
DoubleMatrix *oTemp = getRightNullSpace(oMatrix);
DoubleMatrix *oTranspose = oTemp->getTranspose();
delete oTemp;
ls::GaussJordan(*oTranspose, gLapackTolerance);
DoubleMatrix *oResult = oTranspose->getTranspose();
delete oTranspose;
ls::RoundMatrixToTolerance(oMatrix, gLapackTolerance);
return oResult;
}
DoubleMatrix *getRightNullSpace(DoubleMatrix &oMatrix) {
//Log(lDebug5) << "======================================================" << endl;
//Log(lDebug5) << "=== getRightNullSpace " << endl;
//Log(lDebug5) << "======================================================" << endl << endl;
DoubleMatrix *oTranspose = oMatrix.getTranspose();
integer numRows = oTranspose->numRows();
integer numCols = oTranspose->numCols();
// determine sizes
integer min_MN = min(numRows, numCols);
integer max_MN = max(numRows, numCols);
integer lwork = 3 * min_MN * min_MN + max(max_MN, 4 * min_MN * min_MN + 4 * min_MN); // 'A'
// allocate arrays for lapack
doublereal *A = oTranspose->getCopy(true);
doublereal *S = new doublereal[min_MN];
memset(S, 0, sizeof(doublereal) * min_MN);
doublereal *work = new doublereal[lwork];
memset(work, 0, sizeof(doublereal) * lwork);
doublereal *U = new doublereal[numRows * numRows];
memset(U, 0, sizeof(doublereal) * numRows * numRows);
doublereal *VT = new doublereal[numCols * numCols];
memset(VT, 0, sizeof(doublereal) * numCols * numCols);
integer *iwork = new integer[8 * min_MN];
integer info;
char jobz = 'A';
dgesdd_(&jobz, &numRows, &numCols, A, &numRows, S, U, &numRows, VT, &numCols, work, &lwork, iwork, &info);
// now we have everything we could get, now extract the nullspace. In Matlab this would look like:
// [U,S,V] = svd(A');
// r = rank(A)
// Z = U(:,r+1:end)
int rank = getRank(oMatrix);
int nResultColumns = numRows - rank;
DoubleMatrix *oMatrixU = new DoubleMatrix(U, numRows, numRows, true);
//Log(lDebug5) << " SVD: U " << endl;
ls::print(*oMatrixU);
DoubleMatrix *oResultMatrix = new DoubleMatrix(numRows, nResultColumns);
for (int i = 0; i < nResultColumns; i++) {
for (int j = 0; j < numRows; j++) {
(*oResultMatrix)(j, i) = (*oMatrixU)(j, rank + i);
}
}
//Log(lDebug5) << " Nullspace: " << endl;
ls::print(*oResultMatrix);
delete[] S;
delete[]
work;
delete[] U;
delete[] VT;
delete[] iwork;
delete[] A;
delete oTranspose;
delete oMatrixU;
ls::RoundMatrixToTolerance(*oResultMatrix, gLapackTolerance);
return oResultMatrix;
}
int getRank(DoubleMatrix &oMatrix) {
//Log(lDebug5) << "======================================================" << endl;
//Log(lDebug5) << "=== getRank " << endl;
//Log(lDebug5) << "======================================================" << endl << endl;
int rank = 0;
vector<double> oSingularVals = getSingularValsBySVD(oMatrix);
for (unsigned int i = 0; i < oSingularVals.size(); i++) {
if (fabs(oSingularVals[i]) > gLapackTolerance) {
rank++;
}
}
return rank;
}
vector<double> getSingularValsBySVD(DoubleMatrix &oMatrix) {
//Log(lDebug5) << "======================================================" << endl;
//Log(lDebug5) << "=== getSingularValsBySVD " << endl;
//Log(lDebug5) << "======================================================" << endl << endl;
vector<double> oResult;
integer numRows = oMatrix.numRows();
integer numCols = oMatrix.numCols();
integer min_MN = min(numRows, numCols);
integer max_MN = max(numRows, numCols);
if (min_MN == 0) return oResult;
integer lwork = 3 * min_MN + max(max_MN, 7 * min_MN); // specified in dgesdd description
doublereal *A = oMatrix.getCopy(true);
doublereal *S = new doublereal[min_MN];
memset(S, 0, sizeof(doublereal) * min_MN);
doublereal *work = new doublereal[lwork];
memset(work, 0, sizeof(doublereal) * lwork);
integer *iwork = new integer[8 * min_MN];
integer info;
char jobz = 'N';
dgesdd_(&jobz, &numRows, &numCols, A, &numRows, S, NULL, &numRows, NULL, &numCols, work, &lwork, iwork, &info);
for (int i = 0; i < min_MN; i++) {
oResult.push_back(ls::RoundToTolerance(S[i], gLapackTolerance));
}
// free memory
delete[] A;
delete[] S;
delete[] work;
delete[] iwork;
return oResult;
}
ComplexMatrix *getEigenVectors(DoubleMatrix &oMatrix) {
//Log(lDebug5) << "======================================================" << endl;
//Log(lDebug5) << "=== getEigenVectors " << endl;
//Log(lDebug5) << "======================================================" << endl << endl;
integer numRows = oMatrix.numRows();
integer numCols = oMatrix.numCols();
integer lwork = 2 * numRows;
integer info;
if (numRows != numCols)
throw ApplicationException("Input Matrix must be square", "Expecting a Square Matrix");
if (numRows == 0) return new ComplexMatrix();
doublecomplex *A = new doublecomplex[numRows * numRows];
memset(A, 0, sizeof(doublecomplex) * numRows * numRows);
doublecomplex *eigVals = new doublecomplex[numRows];
memset(eigVals, 0, sizeof(doublecomplex) * numRows);
doublecomplex *vr = new doublecomplex[numRows * numRows];
memset(vr, 0, sizeof(doublecomplex) * numRows * numRows);
doublecomplex *work = new doublecomplex[lwork];
memset(work, 0, sizeof(doublecomplex) * lwork);
doublereal *rwork = new doublereal[lwork];
memset(rwork, 0, sizeof(doublereal) * lwork);
int index;
for (int i = 0; i < numRows; i++) {
for (int j = 0; j < numCols; j++) {
index = (j + numRows * i);
A[index].r = oMatrix(j, i);
}
}
char job = 'N';
char jobR = 'V'; // compute the right eigenvectors
zgeev_(&job, &jobR, &numRows, A, &numRows, eigVals, NULL, &numRows, vr, &numRows, work, &lwork, rwork, &info);
ComplexMatrix *oResult = new ComplexMatrix(numRows, numRows);
for (int i = 0; i < numRows; i++) {
for (int j = 0; j < numRows; j++) {
index = (j + numRows * i);
Complex complexNr(
ls::RoundToTolerance(vr[index].r, gLapackTolerance),
ls::RoundToTolerance(vr[index].i, gLapackTolerance));
(*oResult)(i, j) = complexNr;//(.set(complex.Real, complex.Imag);
}
}
delete[] eigVals;
delete[] A;
delete[] work;
delete[] rwork;
delete[] vr;
return oResult;
}
ComplexMatrix *ZgetEigenVectors(ComplexMatrix &oMatrix) {
//Log(lDebug5) << "======================================================" << endl;
//Log(lDebug5) << "=== getEigenVectors " << endl;
//Log(lDebug5) << "======================================================" << endl << endl;
integer numRows = oMatrix.numRows();
integer numCols = oMatrix.numCols();
integer lwork = 2 * numRows;
integer info;
if (numRows != numCols)
throw ApplicationException("Input Matrix must be square", "Expecting a Square Matrix");
if (numRows == 0) return new ComplexMatrix();
doublecomplex *A = new doublecomplex[numRows * numRows];
memset(A, 0, sizeof(doublecomplex) * numRows * numRows);
doublecomplex *eigVals = new doublecomplex[numRows];
memset(eigVals, 0, sizeof(doublecomplex) * numRows);
doublecomplex *vr = new doublecomplex[numRows * numRows];
memset(vr, 0, sizeof(doublecomplex) * numRows * numRows);
doublecomplex *work = new doublecomplex[lwork];
memset(work, 0, sizeof(doublecomplex) * lwork);
doublereal *rwork = new doublereal[lwork];
memset(rwork, 0, sizeof(doublereal) * lwork);
int index;
for (int i = 0; i < numRows; i++) {
for (int j = 0; j < numCols; j++) {
index = (j + numRows * i);
A[index].r = real(oMatrix(j, i));
A[index].i = imag(oMatrix(j, i));
}
}
char job = 'N';
char jobR = 'V'; // compute the right eigenvectors
zgeev_(&job, &jobR, &numRows, A, &numRows, eigVals, NULL, &numRows, vr, &numRows, work, &lwork, rwork, &info);
ComplexMatrix *oResult = new ComplexMatrix(numRows, numRows);
for (int i = 0; i < numRows; i++) {
for (int j = 0; j < numRows; j++) {
index = (j + numRows * i);
Complex complexNr(
ls::RoundToTolerance(vr[index].r, gLapackTolerance),
ls::RoundToTolerance(vr[index].i, gLapackTolerance));
(*oResult)(i, j) = complexNr;//.set(complex.Real, complex.Imag);
}
}
delete[] eigVals;
delete[] A;
delete[] work;
delete[] rwork;
delete[] vr;
return oResult;
}
void
getSVD(DoubleMatrix &inputMatrix, DoubleMatrix *&outU, std::vector<double> *&outSingularVals, DoubleMatrix *&outV) {
//Log(lDebug5) << "======================================================" << endl;
//Log(lDebug5) << "=== getSingularValsBySVD " << endl;
//Log(lDebug5) << "======================================================" << endl << endl;
integer numRows = inputMatrix.numRows();
integer numCols = inputMatrix.numCols();
integer min_MN = min(numRows, numCols);
integer max_MN = max(numRows, numCols);
if (min_MN == 0) return;
//integer lwork = 3*min_MN + max(max_MN, 7*min_MN); // specified in dgesdd description
integer lwork = 3 * min_MN * min_MN +
max(max_MN, 4 * min_MN * min_MN + 4 * min_MN); // specified in dgesdd description for job 'A'
doublereal *A = inputMatrix.getCopy(true);
doublereal *U = new doublereal[numRows * numRows];
memset(U, 0, sizeof(doublereal) * numRows * numRows);
doublereal *VT = new doublereal[numCols * numCols];
memset(VT, 0, sizeof(doublereal) * numCols * numCols);
doublereal *S = new doublereal[min_MN];
memset(S, 0, sizeof(doublereal) * min_MN);
doublereal *work = new doublereal[lwork];
memset(work, 0, sizeof(doublereal) * lwork);
integer *iwork = new integer[8 * min_MN];
integer info;
char jobz = 'A';
dgesdd_(&jobz, &numRows, &numCols, A, &numRows, S, U, &numRows, VT, &numCols, work, &lwork, iwork, &info);
outU = new DoubleMatrix(numRows, numRows);
int index;
for (int i = 0; i < numRows; i++) {
for (int j = 0; j < numRows; j++) {
index = (j + numRows * i);
(*outU)(j, i) = U[index];
}
}
ls::RoundMatrixToTolerance(*outU, gLapackTolerance);
outV = new DoubleMatrix(numCols, numCols);
for (int i = 0; i < numCols; i++) {
for (int j = 0; j < numCols; j++) {
index = (j + numCols * i);
(*outV)(i, j) = VT[index];
}
}
ls::RoundMatrixToTolerance(*outV, gLapackTolerance);
outSingularVals = new std::vector<double>();
for (int i = 0; i < min_MN; i++) {
outSingularVals->push_back(ls::RoundToTolerance(S[i], gLapackTolerance));
}
// free memory
delete[] A;
delete[] S;
delete[] work;
delete[] iwork;
delete[] U;
delete[] VT;
}
void ZgetSVD(ComplexMatrix &inputMatrix, ComplexMatrix *&outU, std::vector<double> *&outSingularVals,
ComplexMatrix *&outV) {
//Log(lDebug5) << "======================================================" << endl;
//Log(lDebug5) << "=== getSingularValsBySVD " << endl;
//Log(lDebug5) << "======================================================" << endl << endl;
integer numRows = inputMatrix.numRows();
integer numCols = inputMatrix.numCols();
integer min_MN = min(numRows, numCols);
integer max_MN = max(numRows, numCols);
if (min_MN == 0) return;
integer lwork = min_MN * min_MN + 2 * min_MN + max_MN; // specified in dgesdd description for job 'A'
integer lrwork = 5 * min_MN * min_MN + 7 * min_MN;
doublecomplex *A = new doublecomplex[numRows * numCols];
memset(A, 0, sizeof(doublecomplex) * numRows * numCols);
doublecomplex *U = new doublecomplex[numRows * numRows];
memset(U, 0, sizeof(doublecomplex) * numRows * numRows);
doublecomplex *VT = new doublecomplex[numCols * numCols];
memset(VT, 0, sizeof(doublecomplex) * numCols * numCols);
doublereal *S = new doublereal[min_MN];
memset(S, 0, sizeof(doublereal) * min_MN);
doublecomplex *work = new doublecomplex[lwork];
memset(work, 0, sizeof(doublecomplex) * lwork);
doublereal *rwork = new doublereal[lrwork];
memset(rwork, 0, sizeof(doublereal) * lrwork);
integer *iwork = new integer[8 * min_MN];
int index;
for (int i = 0; i < numRows; i++) {
for (int j = 0; j < numCols; j++) {
index = (j + numRows * i);
A[index].r = real(inputMatrix(j, i));
A[index].i = imag(inputMatrix(j, i));
}
}
integer info;
char jobz = 'A';
zgesdd_(&jobz, &numRows, &numCols, A, &numRows, S, U, &numRows, VT, &numCols, work, &lwork, rwork, iwork,
&info);
outU = new ComplexMatrix(numRows, numRows);
for (int i = 0; i < numRows; i++) {
for (int j = 0; j < numRows; j++) {
index = (j + numRows * i);
(*outU)(j, i) = Complex((ls::RoundToTolerance(U[index].r, gLapackTolerance),
ls::RoundToTolerance(U[index].i, gLapackTolerance)));
}
}
outV = new ComplexMatrix(numCols, numCols);
for (int i = 0; i < numCols; i++) {
for (int j = 0; j < numCols; j++) {
index = (j + numCols * i);
(*outV)(i, j) = Complex(ls::RoundToTolerance(VT[index].r, gLapackTolerance),
ls::RoundToTolerance(-VT[index].i, gLapackTolerance));
}
}
outSingularVals = new std::vector<double>();
for (int i = 0; i < min_MN; i++) {
outSingularVals->push_back(ls::RoundToTolerance(S[i], gLapackTolerance));
}
// free memory
delete[] A;
delete[] S;
delete[] work;
delete[] iwork;
delete[] U;
delete[] VT;
return;
}
double getRCond(DoubleMatrix &oMatrix) {
integer numRows = oMatrix.numRows();
integer numCols = oMatrix.numCols();
integer minRC = min(numRows, numCols);
if (minRC == 0) {
return 0.0;
}
doublereal *A = (doublereal *) oMatrix.getCopy(true);
integer *vecP = new integer[minRC];
memset(vecP, 0, (sizeof(integer) * minRC));
integer info;
char norm = '1';
integer order = numRows * numCols;
double *work = new doublereal[4 * order];
memset(work, 0, sizeof(double) * 4 * order);
double dnorm = dlange_(&norm, &numRows, &numCols, A, &numRows, work);
dgetrf_(&numRows, &numCols, A, &numRows, vecP, &info);
ls::checkTolerance(numRows * numCols, A, gLapackTolerance);
integer *iwork = new integer[numRows];
memset(iwork, 0, sizeof(integer) * numRows);
memset(work, 0, sizeof(double) * 4 * order);
double rcond = 0.0;
dgecon_(&norm, &numRows, A, &numRows, &dnorm, &rcond, work, iwork, &info);
delete[] vecP;
delete[] A;
delete[] work;
delete[] iwork;
return rcond;
}
LU_Result *getLU(DoubleMatrix &oMatrix) {
//Log(lDebug5) << "======================================================" << endl;
//Log(lDebug5) << "=== getLU " << endl;
//Log(lDebug5) << "======================================================" << endl << endl;
integer numRows = oMatrix.numRows();
integer numCols = oMatrix.numCols();
int minRC = min(numRows, numCols);
if (minRC == 0) {
LU_Result *oResult = new LU_Result();
DoubleMatrix *L = new DoubleMatrix(numRows, minRC);
DoubleMatrix *U = new DoubleMatrix(minRC, numCols);
IntMatrix *P = new IntMatrix(numRows, numRows);
oResult->L = L;
oResult->U = U;
oResult->P = P;
oResult->nInfo = -1;
return oResult;
}
doublereal *A = (doublereal *) oMatrix.getCopy(true);
integer *vecP = new integer[minRC];
memset(vecP, 0, (sizeof(integer) * minRC));
integer info;
dgetrf_(&numRows, &numCols, A, &numRows, vecP, &info);
ls::print(numRows, numCols, A);
DoubleMatrix *L = new DoubleMatrix(numRows, minRC);
DoubleMatrix *U = new DoubleMatrix(minRC, numCols);
// Assign values to Lmat and Umat
for (int i = 0; i < minRC; i++) {
(*L)(i, i) = 1.0;
(*U)(i, i) = A[i + numRows * i];
for (int j = 0; j < i; j++) {
(*L)(i, j) = A[i + numRows * j];
}
for (int j = i + 1; j < minRC; j++) {
(*U)(i, j) = A[i + numRows * j];
}
}
if (numRows > numCols) {
for (int i = numCols; i < numRows; i++) {
for (int j = 0; j < numCols; j++) {
(*L)(i, j) = A[i + numRows * j];
}
}
} else {
for (int i = 0; i < numRows; i++) {
for (int j = numRows; j < numCols; j++) {
(*U)(i, j) = A[i + numRows * j];
}
}
}
// build permutation matrix
IntMatrix *P = new IntMatrix(numRows, numRows);
for (int i = 0; i < numRows; i++)
(*P)(i, i) = 1;
for (int i = 0; i < minRC; i++) {
if (vecP[i] != 0 && vecP[i] - 1 != i)
P->swapRows(i, vecP[i] - 1);
}
LU_Result *oResult = new LU_Result();
ls::RoundMatrixToTolerance(*L, gLapackTolerance);
ls::RoundMatrixToTolerance(*U, gLapackTolerance);
oResult->L = L;
oResult->U = U;
oResult->P = P;
oResult->nInfo = info;
delete[] A;
delete[] vecP;
return oResult;
}
LU_Result *getLUwithFullPivoting(DoubleMatrix &oMatrix) {
//Log(lDebug5) << "======================================================" << endl;
//Log(lDebug5) << "=== getLUwithFullPivoting " << endl;
//Log(lDebug5) << "======================================================" << endl << endl;
integer numRows = oMatrix.numRows();
integer numCols = oMatrix.numCols();
if (numRows != numCols)
throw ApplicationException("Input Matrix must be square", "Expecting a Square Matrix");
doublereal *A = (doublereal *) oMatrix.getCopy(true);
integer *vecP = new integer[numRows];
memset(vecP, 0, (sizeof(integer) * numRows));
integer *vecQ = new integer[numRows];
memset(vecQ, 0, (sizeof(integer) * numRows));
integer info;
dgetc2_(&numRows, A, &numRows, vecP, vecQ, &info);
DoubleMatrix *L = new DoubleMatrix(numRows, numRows);
DoubleMatrix *U = new DoubleMatrix(numRows, numCols);
// Assign values to Lmat and Umat
for (int i = 0; i < numRows; i++) {
(*L)(i, i) = 1.0;
(*U)(i, i) = A[i + numRows * i];
for (int j = 0; j < i; j++) {
(*L)(i, j) = A[i + numRows * j];
}
for (int j = i + 1; j < numRows; j++) {
(*U)(i, j) = A[i + numRows * j];
}
}
if (numRows > numCols) {
for (int i = numCols; i < numRows; i++) {
for (int j = 0; j < numCols; j++) {
(*L)(i, j) = A[i + numRows * j];
}
}
} else {
for (int i = 0; i < numRows; i++) {
for (int j = numRows; j < numCols; j++) {
(*U)(i, j) = A[i + numRows * j];
}
}
}
// build permutation matrix
IntMatrix *P = new IntMatrix(numRows, numRows);
for (int i = 0; i < numRows; i++)
(*P)(i, i) = 1;
for (int i = 0; i < numRows; i++) {