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# Source for file LevenbergMarquardt.php Documentation is available at LevenbergMarquardt.php <?php // Levenberg-Marquardt in PHP // http://www.idiom.com/~zilla/Computer/Javanumeric/LM.java class LevenbergMarquardt { /** * Calculate the current sum-squared-error * * Chi-squared is the distribution of squared Gaussian errors, * thus the name. * * @param double[][] $x * @param double[] $a * @param double[] $y, * @param double[] $s, * @param object $f */ function chiSquared($x, $a, $y, $s, $f) { $npts = count($y); $sum = 0.0; for ($i = 0; $i < $npts; ++$i) { $d = $y[$i] - $f->val($x[$i], $a); $d = $d / $s[$i]; $sum = $sum + ($d*$d); } return $sum; } // function chiSquared() /** * Minimize E = sum {(y[k] - f(x[k],a)) / s[k]}^2 * The individual errors are optionally scaled by s[k]. * Note that LMfunc implements the value and gradient of f(x,a), * NOT the value and gradient of E with respect to a! * * @param x array of domain points, each may be multidimensional * @param y corresponding array of values * @param a the parameters/state of the model * @param vary false to indicate the corresponding a[k] is to be held fixed * @param s2 sigma^2 for point i * @param lambda blend between steepest descent (lambda high) and * jump to bottom of quadratic (lambda zero). * Start with 0.001. * @param termepsilon termination accuracy (0.01) * @param maxiter stop and return after this many iterations if not done * @param verbose set to zero (no prints), 1, 2 * * @return the new lambda for future iterations. * Can use this and maxiter to interleave the LM descent with some other * task, setting maxiter to something small. */ function solve($x, $a, $y, $s, $vary, $f, $lambda, $termepsilon, $maxiter, $verbose) { $npts = count($y); $nparm = count($a); if ($verbose > 0) { print("solve x[".count($x)."][".count($x[0])."]"); print(" a[".count($a)."]"); println(" y[".count(length)."]"); } $e0 = $this->chiSquared($x, $a, $y, $s, $f); //double lambda = 0.001; $done = false; // g = gradient, H = hessian, d = step to minimum // H d = -g, solve for d $H = array(); $g = array(); //double[] d = new double[nparm]; $oos2 = array(); for($i = 0; $i < $npts; ++$i) { $oos2[$i] = 1./($s[$i]*$s[$i]); } $iter = 0; $term = 0; // termination count test do { ++$iter; // hessian approximation for( $r = 0; $r < $nparm; ++$r) { for( $c = 0; $c < $nparm; ++$c) { for( $i = 0; $i < $npts; ++$i) { if ($i == 0) $H[$r][$c] = 0.; $xi = $x[$i]; $H[$r][$c] += ($oos2[$i] * $f->grad($xi, $a, $r) * $f->grad($xi, $a, $c)); } //npts } //c } //r // boost diagonal towards gradient descent for( $r = 0; $r < $nparm; ++$r) $H[$r][$r] *= (1. + $lambda); // gradient for( $r = 0; $r < $nparm; ++$r) { for( $i = 0; $i < $npts; ++$i) { if ($i == 0) $g[$r] = 0.; $xi = $x[$i]; $g[$r] += ($oos2[$i] * ($y[$i]-$f->val($xi,$a)) * $f->grad($xi, $a, $r)); } } //npts // scale (for consistency with NR, not necessary) if ($false) { for( $r = 0; $r < $nparm; ++$r) { $g[$r] = -0.5 * $g[$r]; for( $c = 0; $c < $nparm; ++$c) { $H[$r][$c] *= 0.5; } } } // solve H d = -g, evaluate error at new location //double[] d = DoubleMatrix.solve(H, g); // double[] d = (new Matrix(H)).lu().solve(new Matrix(g, nparm)).getRowPackedCopy(); //double[] na = DoubleVector.add(a, d); // double[] na = (new Matrix(a, nparm)).plus(new Matrix(d, nparm)).getRowPackedCopy(); // double e1 = chiSquared(x, na, y, s, f); // if (verbose > 0) { // System.out.println("\n\niteration "+iter+" lambda = "+lambda); // System.out.print("a = "); // (new Matrix(a, nparm)).print(10, 2); // if (verbose > 1) { // System.out.print("H = "); // (new Matrix(H)).print(10, 2); // System.out.print("g = "); // (new Matrix(g, nparm)).print(10, 2); // System.out.print("d = "); // (new Matrix(d, nparm)).print(10, 2); // } // System.out.print("e0 = " + e0 + ": "); // System.out.print("moved from "); // (new Matrix(a, nparm)).print(10, 2); // System.out.print("e1 = " + e1 + ": "); // if (e1 < e0) { // System.out.print("to "); // (new Matrix(na, nparm)).print(10, 2); // } else { // System.out.println("move rejected"); // } // } // termination test (slightly different than NR) // if (Math.abs(e1-e0) > termepsilon) { // term = 0; // } else { // term++; // if (term == 4) { // System.out.println("terminating after " + iter + " iterations"); // done = true; // } // } // if (iter >= maxiter) done = true; // in the C++ version, found that changing this to e1 >= e0 // was not a good idea. See comment there. // // if (e1 > e0 || Double.isNaN(e1)) { // new location worse than before // lambda *= 10.; // } else { // new location better, accept new parameters // lambda *= 0.1; // e0 = e1; // // simply assigning a = na will not get results copied back to caller // for( int i = 0; i < nparm; i++ ) { // if (vary[i]) a[i] = na[i]; // } // } } while(!$done); return $lambda; } // function solve() } // class LevenbergMarquardt Documentation generated on Sun, 27 Feb 2011 16:32:28 -0800 by phpDocumentor 1.4.3