JMatrixNS.cc

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#include <string>
#include <iostream>
#include <iomanip>
#include <chrono>

#include "TRandom3.h"
#include "TMatrixTSym.h"

#include "JLang/JException.hh"
#include "JMath/JVectorND.hh"
#include "JMath/JMatrixNS.hh"
#include "JMath/JMathTestkit.hh"

#include "Jeep/JParser.hh"
#include "Jeep/JMessage.hh"


/**
 * \file
 *
 * Example program to test inversion of symmetric matrix.
 * \author mdejong
 */
int main(int argc, char**argv)
{
  using namespace std;
  using namespace JPP;

  int       N;
  double    precision;
  size_t    numberOfInversions;
  UInt_t    seed;
  int       debug;

  try {

    JParser<> zap("Example program to test inversion of symmetric matrix.");

    zap['N'] = make_field(N);
    zap['e'] = make_field(precision)          = 1.0e-6;
    zap['n'] = make_field(numberOfInversions) = 1;
    zap['S'] = make_field(seed)               = 0;
    zap['d'] = make_field(debug)              = 3;

    zap(argc, argv);
  }
  catch(const exception &error) {
    FATAL(error.what() << endl);
  }

  
  gRandom->SetSeed(seed);

  numberOfInversions += (numberOfInversions%2 == 0 ? 1 : 0);

  const Double_t xmin = -1.0;
  const Double_t xmax = +1.0;
 
  JMatrixNS A(N);

  for (int i = 0; i != N; ++i) {

    A(i,i) = gRandom->Uniform(xmin,xmax); 

    for (int j = 0; j != i; ++j) {
      A(j,i) = A(i,j) = gRandom->Uniform(xmin,xmax); 
    }
  }

  DEBUG("Matrix A" << endl);
  DEBUG(A << endl);

  try {
 
    JMatrixNS B(A);

    const chrono::steady_clock::time_point t0 = chrono::steady_clock::now();

    for (size_t i = numberOfInversions; i != 0; --i) {
      B.invert();
    }

    const chrono::steady_clock::time_point t1 = chrono::steady_clock::now();

    NOTICE("Elapsed time (Jpp)  [us] " << setw(8) << chrono::duration_cast<chrono::microseconds>(t1 - t0).count() << endl);
    DEBUG("Matrix A^-1" << endl);
    DEBUG(B << endl);

    JMatrixNS C(A);

    C.mul(B);
    
    DEBUG("Matrix A x A^-1" << endl);
    DEBUG(C << endl);
    
    NOTICE("A x A^-1 = I ? "                     << C.isIdentity(precision)                 << endl);
    
    if (!C.isIdentity(precision)) {
      ERROR("Matrix A x A^-1 /= I" << endl);
    }

    ASSERT(C.isIdentity(precision));
  }
  catch (const JException& error) {
    FATAL(error << endl);
  }

  try {

    TMatrixTSym<double> B(A.size());

    for (size_t row = 0; row != A.size(); ++row) {
      for (size_t col = 0; col != A.size(); ++col) {
        B(row, col) = A(row, col);
      }
    }

    const chrono::steady_clock::time_point t0 = chrono::steady_clock::now();

    for (size_t i = numberOfInversions; i != 0; --i) {
      B.InvertFast();
    }

    const chrono::steady_clock::time_point t1 = chrono::steady_clock::now();

    NOTICE("Elapsed time (ROOT) [us] " << setw(8) << chrono::duration_cast<chrono::microseconds>(t1 - t0).count() << endl);
  }
  catch (const JException& error) {
    FATAL(error << endl);
  }

  try {

    JMatrixNS B(A);

    B.invert();

    JVectorND X(N);

    for (int i = 0; i != N; ++i) {
      X[i] = gRandom->Uniform(xmin,xmax); 
    }

    JVectorND Y(N);

    for (int i = 0; i != N; ++i) {
      for (int j = 0; j != N; ++j) {
        Y[i] += B(i,j) * X[j];
      }
    }

    JMatrixNS C(A);

    C.solve(X);
    
    for (int i = 0; i != N; ++i) {

      DEBUG(setw(4) << i << ' ' << FIXED(9,5) << X[i] << ' ' << FIXED(9,5) << Y[i] << endl);

      ASSERT(fabs(X[i] - Y[i]) <= precision);
    }
  }
  catch (const JException& error) {
    FATAL(error << endl);
  }

  try {

    JMatrixNS B(A);

    B.invert();

    const double big = 1.0e5;

    for (int i = 0; i != N; ++i) {

      A(i,i) += big;
 
      const chrono::steady_clock::time_point t0 = chrono::steady_clock::now();

      B.update(i, big);

      const chrono::steady_clock::time_point t1 = chrono::steady_clock::now();

      NOTICE("Elapsed time [us] " << setw(8) << chrono::duration_cast<chrono::microseconds>(t1 - t0).count() << endl);
      NOTICE("Pivot " << setw(2) << i << '+' << big << ' ' << (JMatrixNS(A).mul(B).isIdentity(precision) ? "okay" : "error") << endl);

      ASSERT(JMatrixNS(A).mul(B).isIdentity(precision));

      A(i,i) -= big;

      B.update(i, -big);
    }
  }
  catch (const JException& error) {
    FATAL(error << endl);
  }

  {
    A.reset();

    for (int i = 0; i != N; ++i) {
      for (int j = 0; j != N; ++j) {
        ASSERT(A(i,j) == 0, "Test reset (" << i << "," << j << ")");
      }
    }
  }

  return 0;
}