267 lines
7.1 KiB
C++
Executable File
267 lines
7.1 KiB
C++
Executable File
/*==============================================================================
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Copyright 2018 by Roland Rabien, 2010 by 2010 by Alex Etchells
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For more information visit www.rabiensoftware.com
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==============================================================================*/
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void LeastSquaresRegression::addPoint (double x, double y)
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{
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pointArray.add ({x, y});
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}
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void LeastSquaresRegression::addPoint (juce::Point<double> point)
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{
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pointArray.add (point);
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}
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void LeastSquaresRegression::addPoints (Array<juce::Point<double>> points)
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{
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pointArray.addArray (points);
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}
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void LeastSquaresRegression::clear()
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{
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pointArray.clear();
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}
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bool LeastSquaresRegression::enoughPoints()
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{
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return pointArray.size() >= 3;
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}
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Array<double> LeastSquaresRegression::getTerms()
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{
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//notation sjk to mean the sum of x_i^j*y_i^k.
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double s40 = getSx4(); //sum of x^4
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double s30 = getSx3(); //sum of x^3
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double s20 = getSx2(); //sum of x^2
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double s10 = getSx(); //sum of x
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double s00 = pointArray.size();
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//sum of x^0 * y^0 ie 1 * number of entries
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double s21 = getSx2y(); //sum of x^2*y
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double s11 = getSxy(); //sum of x*y
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double s01 = getSy(); //sum of y
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double a = (s21*(s20 * s00 - s10 * s10) -
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s11*(s30 * s00 - s10 * s20) +
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s01*(s30 * s10 - s20 * s20))
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/
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(s40*(s20 * s00 - s10 * s10) -
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s30*(s30 * s00 - s10 * s20) +
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s20*(s30 * s10 - s20 * s20));
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double b = (s40*(s11 * s00 - s01 * s10) -
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s30*(s21 * s00 - s01 * s20) +
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s20*(s21 * s10 - s11 * s20))
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/
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(s40 * (s20 * s00 - s10 * s10) -
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s30 * (s30 * s00 - s10 * s20) +
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s20 * (s30 * s10 - s20 * s20));
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double c = (s40*(s20 * s01 - s10 * s11) -
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s30*(s30 * s01 - s10 * s21) +
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s20*(s30 * s11 - s20 * s21))
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/
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(s40 * (s20 * s00 - s10 * s10) -
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s30 * (s30 * s00 - s10 * s20) +
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s20 * (s30 * s10 - s20 * s20));
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Array<double> terms;
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terms.add (a);
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terms.add (b);
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terms.add (c);
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return terms;
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}
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double LeastSquaresRegression::aTerm()
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{
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//notation sjk to mean the sum of x_i^j*y_i^k.
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double s40 = getSx4(); //sum of x^4
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double s30 = getSx3(); //sum of x^3
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double s20 = getSx2(); //sum of x^2
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double s10 = getSx(); //sum of x
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double s00 = pointArray.size();
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//sum of x^0 * y^0 ie 1 * number of entries
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double s21 = getSx2y(); //sum of x^2*y
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double s11 = getSxy(); //sum of x*y
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double s01 = getSy(); //sum of y
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//a = Da/D
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return (s21*(s20 * s00 - s10 * s10) -
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s11*(s30 * s00 - s10 * s20) +
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s01*(s30 * s10 - s20 * s20))
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/
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(s40*(s20 * s00 - s10 * s10) -
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s30*(s30 * s00 - s10 * s20) +
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s20*(s30 * s10 - s20 * s20));
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}
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double LeastSquaresRegression::bTerm()
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{
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//notation sjk to mean the sum of x_i^j*y_i^k.
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double s40 = getSx4(); //sum of x^4
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double s30 = getSx3(); //sum of x^3
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double s20 = getSx2(); //sum of x^2
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double s10 = getSx(); //sum of x
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double s00 = pointArray.size();
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//sum of x^0 * y^0 ie 1 * number of entries
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double s21 = getSx2y(); //sum of x^2*y
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double s11 = getSxy(); //sum of x*y
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double s01 = getSy(); //sum of y
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//b = Db/D
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return (s40*(s11 * s00 - s01 * s10) -
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s30*(s21 * s00 - s01 * s20) +
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s20*(s21 * s10 - s11 * s20))
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/
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(s40 * (s20 * s00 - s10 * s10) -
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s30 * (s30 * s00 - s10 * s20) +
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s20 * (s30 * s10 - s20 * s20));
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}
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double LeastSquaresRegression::cTerm()
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{
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//notation sjk to mean the sum of x_i^j*y_i^k.
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double s40 = getSx4(); //sum of x^4
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double s30 = getSx3(); //sum of x^3
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double s20 = getSx2(); //sum of x^2
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double s10 = getSx(); //sum of x
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double s00 = pointArray.size();
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//sum of x^0 * y^0 ie 1 * number of entries
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double s21 = getSx2y(); //sum of x^2*y
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double s11 = getSxy(); //sum of x*y
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double s01 = getSy(); //sum of y
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//c = Dc/D
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return (s40*(s20 * s01 - s10 * s11) -
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s30*(s30 * s01 - s10 * s21) +
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s20*(s30 * s11 - s20 * s21))
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/
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(s40 * (s20 * s00 - s10 * s10) -
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s30 * (s30 * s00 - s10 * s20) +
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s20 * (s30 * s10 - s20 * s20));
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}
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double LeastSquaresRegression::rSquare() // get r-squared
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{
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// 1 - (residual sum of squares / total sum of squares)
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return 1 - getSSerr() / getSStot();
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}
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/*helper methods*/
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double LeastSquaresRegression::getSx() // get sum of x
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{
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double Sx = 0;
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for (auto it : pointArray)
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{
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Sx += it.getX();
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}
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return Sx;
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}
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double LeastSquaresRegression::getSy() // get sum of y
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{
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double Sy = 0;
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for (auto it : pointArray)
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{
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Sy += it.getY();
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}
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return Sy;
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}
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double LeastSquaresRegression::getSx2() // get sum of x^2
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{
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double Sx2 = 0;
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for (auto it : pointArray)
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{
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Sx2 += std::pow (it.getX(), 2); // sum of x^2
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}
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return Sx2;
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}
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double LeastSquaresRegression::getSx3() // get sum of x^3
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{
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double Sx3 = 0;
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for (auto it : pointArray)
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{
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Sx3 += std::pow (it.getX(), 3); // sum of x^3
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}
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return Sx3;
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}
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double LeastSquaresRegression::getSx4() // get sum of x^4
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{
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double Sx4 = 0;
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for (auto it : pointArray)
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{
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Sx4 += std::pow (it.getX(), 4); // sum of x^4
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}
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return Sx4;
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}
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double LeastSquaresRegression::getSxy() // get sum of x*y
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{
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double Sxy = 0;
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for (auto it : pointArray)
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{
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Sxy += it.getX() * it.getY(); // sum of x*y
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}
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return Sxy;
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}
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double LeastSquaresRegression::getSx2y() // get sum of x^2*y
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{
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double Sx2y = 0;
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for (auto it : pointArray)
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{
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Sx2y += pow(it.getX(), 2) * it.getY(); // sum of x^2*y
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}
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return Sx2y;
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}
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double LeastSquaresRegression::getYMean() // mean value of y
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{
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double y_tot = 0;
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for (auto it : pointArray)
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{
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y_tot += it.getY();
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}
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return y_tot / pointArray.size();
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}
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double LeastSquaresRegression::getSStot() // total sum of squares
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{
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//the sum of the squares of the differences between
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//the measured y values and the mean y value
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double ss_tot = 0;
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for (auto it : pointArray)
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{
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ss_tot += std::pow (it.getY() - getYMean(), 2);
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}
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return ss_tot;
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}
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double LeastSquaresRegression::getSSerr() // residual sum of squares
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{
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//the sum of the squares of te difference between
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//the measured y values and the values of y predicted by the equation
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double ss_err = 0;
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for (auto it : pointArray)
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{
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ss_err += std::pow (it.getY() - getPredictedY (it.getX()), 2);
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}
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return ss_err;
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}
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double LeastSquaresRegression::getPredictedY (double x)
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{
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//returns value of y predicted by the equation for a given value of x
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return aTerm() * std::pow(x, 2) + bTerm() * x + cTerm();
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}
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