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  1. POLevenbergMarquardtOptimizer unable to perform Q.R decomposition on the 107x2 jacobian matrix
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    <p>I really need some help to get the LevenbergMarquardtOptimizer up and running. Please see the following compileable code (needs apache common math 3). No matter how I try to return the gradients an Exception will raise ... hmmm get stuck ... </p> <pre><code>package tryout; import java.sql.Date; import java.util.Calendar; import java.util.Arrays; import org.apache.commons.math3.linear.Array2DRowRealMatrix; import org.apache.commons.math3.linear.ArrayRealVector; import org.apache.commons.math3.linear.DecompositionSolver; import org.apache.commons.math3.linear.LUDecomposition; import org.apache.commons.math3.linear.RealMatrix; import org.apache.commons.math3.linear.RealVector; import org.apache.commons.math.util.FastMath; import org.apache.commons.math3.analysis.ParametricUnivariateFunction; import org.apache.commons.math3.analysis.differentiation.DerivativeStructure; import org.apache.commons.math3.fitting.CurveFitter; import org.apache.commons.math3.optim.nonlinear.vector.jacobian.LevenbergMarquardtOptimizer; import static org.apache.commons.math.util.FastMath.pow; import static org.apache.commons.math.util.FastMath.cos; import static org.apache.commons.math.util.FastMath.sin; public class Sornette2NoLogPriceLevenberg { static String[] T = new String[]{"2010-04-01","2010-04-05","2010-04-06","2010-04-07","2010-04-08","2010-04-09","2010-04-12","2010-04-13","2010-04-14","2010-04-15","2010-04-16","2010-04-19","2010-04-20","2010-04-21","2010-04-22","2010-04-23","2010-04-26","2010-04-27","2010-04-28","2010-04-29","2010-04-30","2010-05-03","2010-05-04","2010-05-05","2010-05-06","2010-05-07","2010-05-10","2010-05-11","2010-05-12","2010-05-13","2010-05-14","2010-05-18","2010-05-19","2010-05-20","2010-05-21","2010-05-24","2010-05-25","2010-05-26","2010-05-27","2010-05-28","2010-06-01","2010-06-02","2010-06-03","2010-06-04","2010-06-07","2010-06-08","2010-06-09","2010-06-10","2010-06-11","2010-06-14","2010-06-15","2010-06-16","2010-06-17","2010-06-18","2010-06-21","2010-06-22","2010-06-23","2010-06-24","2010-06-25","2010-06-28","2010-06-29","2010-06-30","2010-07-01","2010-07-02","2010-07-06","2010-07-07","2010-07-08","2010-07-09","2010-07-12","2010-07-13","2010-07-14","2010-07-15","2010-07-16","2010-07-19","2010-07-20","2010-07-21","2010-07-22","2010-07-23","2010-07-26","2010-07-27","2010-07-28","2010-07-29","2010-07-30","2010-08-02","2010-08-03","2010-08-04","2010-08-05","2010-08-06","2010-08-09","2010-08-10","2010-08-11","2010-08-12","2010-08-13","2010-08-16","2010-08-17","2010-08-18","2010-08-19","2010-08-20","2010-08-23","2010-08-24","2010-08-25","2010-08-26","2010-08-27","2010-08-30","2010-08-31","2010-09-01","2010-09-02","2010-09-03","2010-09-07","2010-09-08","2010-09-09","2010-09-10","2010-09-13","2010-09-14","2010-09-15","2010-09-16","2010-09-17","2010-09-20","2010-09-21","2010-09-22","2010-09-23","2010-09-24","2010-09-27","2010-09-28","2010-09-29","2010-09-30","2010-10-01","2010-10-04","2010-10-05","2010-10-06","2010-10-07","2010-10-08","2010-10-11","2010-10-12","2010-10-13","2010-10-14","2010-10-15","2010-10-18","2010-10-19","2010-10-20","2010-10-21","2010-10-22","2010-10-25","2010-10-26","2010-10-27","2010-10-28","2010-10-29","2010-11-01","2010-11-02","2010-11-03","2010-11-04","2010-11-05","2010-11-08","2010-11-09","2010-11-10","2010-11-11","2010-11-12","2010-11-15","2010-11-16","2010-11-17","2010-11-18","2010-11-19","2010-11-22","2010-11-23","2010-11-24","2010-11-26","2010-11-29","2010-11-30","2010-12-01","2010-12-02","2010-12-03","2010-12-06","2010-12-07","2010-12-08","2010-12-09","2010-12-10","2010-12-13","2010-12-14","2010-12-15","2010-12-16","2010-12-17","2010-12-20","2010-12-21","2010-12-22","2010-12-23","2010-12-27","2010-12-28","2010-12-29","2010-12-30","2010-12-31","2011-01-03","2011-01-04","2011-01-05","2011-01-06","2011-01-07","2011-01-10","2011-01-11","2011-01-12","2011-01-13","2011-01-14","2011-01-18","2011-01-19","2011-01-20","2011-01-21","2011-01-24","2011-01-25","2011-01-26","2011-01-27","2011-01-28","2011-01-31","2011-02-01","2011-02-02","2011-02-03","2011-02-04","2011-02-07","2011-02-08","2011-02-09","2011-02-10","2011-02-11","2011-02-14","2011-02-15","2011-02-16","2011-02-17","2011-02-18","2011-02-22","2011-02-23","2011-02-24","2011-02-25","2011-02-28","2011-03-01","2011-03-02","2011-03-03","2011-03-04","2011-03-07","2011-03-08","2011-03-09","2011-03-10","2011-03-11","2011-03-14","2011-03-15","2011-03-16","2011-03-17","2011-03-18","2011-03-21","2011-03-22","2011-03-23","2011-03-24","2011-03-25","2011-03-28","2011-03-29","2011-03-30","2011-03-31","2011-04-01","2011-04-04","2011-04-05","2011-04-06","2011-04-07","2011-04-08","2011-04-11","2011-04-12","2011-04-13","2011-04-14","2011-04-15","2011-04-18","2011-04-19","2011-04-20","2011-04-21","2011-04-25","2011-04-26","2011-04-27","2011-04-28","2011-04-29","2011-05-02","2011-05-03","2011-05-04","2011-05-05","2011-05-06","2011-05-09","2011-05-10","2011-05-11","2011-05-12","2011-05-13","2011-05-16","2011-05-17","2011-05-18","2011-05-19","2011-05-20","2011-05-23","2011-05-24","2011-05-25","2011-05-26","2011-05-27","2011-05-31","2011-06-01","2011-06-02","2011-06-03","2011-06-06","2011-06-07","2011-06-08","2011-06-09","2011-06-10","2011-06-13","2011-06-14","2011-06-15","2011-06-16","2011-06-17","2011-06-20","2011-06-21","2011-06-22","2011-06-23","2011-06-24","2011-06-27","2011-06-28","2011-06-29","2011-06-30","2011-07-01","2011-07-05","2011-07-06","2011-07-07","2011-07-08","2011-07-11","2011-07-12","2011-07-13","2011-07-14","2011-07-15","2011-07-18","2011-07-19","2011-07-20","2011-07-21","2011-07-22","2011-07-25","2011-07-26","2011-07-27","2011-07-28","2011-07-29","2011-08-01","2011-08-02","2011-08-03","2011-08-04","2011-08-05","2011-08-08","2011-08-09","2011-08-10","2011-08-11","2011-08-12","2011-08-15","2011-08-16","2011-08-17","2011-08-18","2011-08-19","2011-08-22","2011-08-23","2011-08-24","2011-08-25","2011-08-26","2011-08-29","2011-08-30","2011-08-31","2011-09-01","2011-09-02","2011-09-06","2011-09-07","2011-09-08","2011-09-09","2011-09-12","2011-09-13","2011-09-14","2011-09-15","2011-09-16","2011-09-19","2011-09-20","2011-09-21","2011-09-22","2011-09-23","2011-09-26","2011-09-27","2011-09-28","2011-09-29","2011-09-30","2011-10-03","2011-10-04","2011-10-05","2011-10-06","2011-10-07","2011-10-10","2011-10-11","2011-10-12","2011-10-13","2011-10-14","2011-10-17","2011-10-18","2011-10-19","2011-10-20","2011-10-21","2011-10-24","2011-10-25","2011-10-26","2011-10-27","2011-10-28","2011-10-31","2011-11-01","2011-11-02","2011-11-03","2011-11-04","2011-11-07","2011-11-08","2011-11-09","2011-11-10","2011-11-11","2011-11-14","2011-11-15","2011-11-16","2011-11-17","2011-11-18","2011-11-21","2011-11-22","2011-11-23","2011-11-25","2011-11-28","2011-11-29","2011-11-30","2011-12-01","2011-12-02","2011-12-05","2011-12-06","2011-12-07","2011-12-08","2011-12-09","2011-12-12","2011-12-13","2011-12-14","2011-12-15","2011-12-16","2011-12-19","2011-12-20","2011-12-21","2011-12-22","2011-12-23","2011-12-27","2011-12-28","2011-12-29","2011-12-30","2012-01-03","2012-01-04","2012-01-05","2012-01-06","2012-01-09","2012-01-10","2012-01-11","2012-01-12","2012-01-13","2012-01-17","2012-01-18","2012-01-19","2012-01-20","2012-01-23","2012-01-24","2012-01-25","2012-01-26","2012-01-27","2012-01-30","2012-01-31","2012-02-01","2012-02-02","2012-02-03","2012-02-06","2012-02-07","2012-02-08","2012-02-09","2012-02-10","2012-02-13","2012-02-14","2012-02-15","2012-02-16","2012-02-17","2012-02-21","2012-02-22","2012-02-23","2012-02-24","2012-02-27","2012-02-28","2012-02-29","2012-03-01","2012-03-02","2012-03-05","2012-03-06","2012-03-07","2012-03-08","2012-03-09","2012-03-12","2012-03-13","2012-03-14","2012-03-15","2012-03-16","2012-03-19","2012-03-20","2012-03-21","2012-03-22","2012-03-23","2012-03-26","2012-03-27","2012-03-28","2012-03-29","2012-03-30","2012-04-02","2012-04-03","2012-04-04","2012-04-05","2012-04-09","2012-04-10","2012-04-11","2012-04-12","2012-04-13","2012-04-16","2012-04-17","2012-04-18","2012-04-19","2012-04-20","2012-04-23","2012-04-24","2012-04-25","2012-04-26","2012-04-27","2012-04-30","2012-05-01","2012-05-02","2012-05-03","2012-05-04","2012-05-07","2012-05-08","2012-05-09","2012-05-10","2012-05-11","2012-05-14","2012-05-15","2012-05-16","2012-05-17","2012-05-18","2012-05-21","2012-05-22","2012-05-23","2012-05-24","2012-05-25","2012-05-29","2012-05-30","2012-05-31","2012-06-01","2012-06-04","2012-06-05","2012-06-06","2012-06-07","2012-06-08","2012-06-11","2012-06-12","2012-06-13","2012-06-14","2012-06-15","2012-06-18","2012-06-19","2012-06-20","2012-06-21","2012-06-22","2012-06-25","2012-06-26","2012-06-27","2012-06-28","2012-06-29","2012-07-02","2012-07-03","2012-07-05","2012-07-06","2012-07-09","2012-07-10","2012-07-11","2012-07-12","2012-07-13","2012-07-16","2012-07-17","2012-07-18","2012-07-19","2012-07-20","2012-07-23","2012-07-24","2012-07-25","2012-07-26","2012-07-27"}; static double[] p = new double[]{229.49,231.94,232.97,234,233.36,235.15,235.64,235.78,238.95,242.09,240.61,240.29,237.88,252.11,259.16,263.4,262.1,254.85,254.42,261.27,253.92,259.04,251.58,248.96,239.49,229.39,247.02,249.48,254.9,251.27,246.85,245.43,241.52,231.23,235.67,239.99,238.49,237.41,246.4,249.83,253.67,256.71,255.9,248.93,244.05,242.49,236.52,243.63,246.55,247.3,252.56,259.91,264.41,266.55,262.75,266.33,263.53,261.62,259.38,260.94,249.14,244.63,241.66,240.16,241.81,251.57,251.01,252.49,250.23,244.89,245.79,244.55,243.04,238.84,244.98,247.26,251.91,252.81,252.16,256.83,253.8,251.03,250.19,254.66,254.74,255.76,254.52,252.95,254.57,252.29,243.32,244.88,242.26,240.84,245.05,246.12,243.02,242.79,239.05,233.34,236.22,233.69,234.99,235.84,236.43,243.46,245.25,251.67,250.73,255.7,255.85,256.18,259.71,260.7,262.8,268.98,267.81,275.46,275.98,279.85,280.99,284.3,283.17,278.99,279.48,275.96,274.77,270.99,281.01,281.25,281.28,286,287.25,290.35,291.9,294.01,306.1,309.27,301,302.01,301.02,299.03,300.36,299.59,299.38,296.86,292.72,295.83,300.87,304.21,309.53,308.43,309.87,307.4,309.3,307.96,299.58,298.61,293.31,292.25,299.96,298.31,304.76,300.26,306.16,306.35,308.17,302.61,307.72,309.42,308.73,311.36,309.48,312.2,310.98,311.76,312.84,311.5,311.57,312.43,311.81,313.37,315.3,316.24,314.72,315.77,316.54,316.36,314.78,313.71,320.52,322.2,324.83,324.57,326.89,333.05,332.26,334.97,336.19,338.92,331.3,329.54,323.55,317.75,328.19,332.03,334.41,333.79,326.88,330.01,335.56,334.87,334.01,336.99,342.22,345.45,348.33,344.81,347.06,349.32,350.02,353.16,348.47,340.94,329.32,333.22,333.47,338.6,343.52,339.72,342.46,349.69,350.12,345.61,346,342.8,337.15,342.33,343.86,335.95,320.95,325.46,321.59,329.99,331.84,329.88,335.5,341.89,340.82,341.33,339.06,338.94,335.1,331.83,329.59,328.76,328.8,325.86,321.72,323.28,326.9,323.3,318.47,322.74,328.59,333.01,341.07,343.32,340.8,340.54,337.23,340.52,336.78,338.64,339.98,337.23,337.15,338.06,339.86,337.7,337.06,331.15,324.15,326.91,330.54,331.18,326.02,325.22,323.07,327.54,325.81,328.15,338.28,336.03,336.6,334.01,328.76,322.93,323.12,322.39,316.96,317.64,323.32,317.78,316.24,311.47,306.67,316.37,313.76,322.14,317.39,322.93,326.06,324.87,326.46,333.84,339.84,342.11,347.4,349.84,344.28,344.04,348.19,347.95,354.9,363.54,366.51,376.28,376.66,382.51,387.56,392.34,381.81,381.07,379.76,385.86,378.24,381.8,367.01,363.37,343.52,363.74,353.71,363.44,366.64,372.89,370.04,370,356,346.26,346.66,363.35,365.85,363.46,373.05,379.27,379.29,374.27,370.57,363.78,369.32,373.39,373.6,367.12,369.51,374.06,378.61,382.17,389.51,400.33,402.1,400.83,390.79,393.2,392.1,388.3,386.11,379.85,370.85,364.32,362.28,367.87,367.01,359.65,378.14,389.3,391.15,397.22,410.42,408.46,410.65,387.68,384.46,382.09,394.63,386.85,389.6,393.58,393.84,393.67,385.63,386.5,392.01,389.25,388.76,395.08,384.43,374.65,374.06,368.85,378.16,374.21,367.05,364.65,358.88,366.18,356.92,353.59,365.8,362.96,371.71,377.28,379,382.22,380.22,378.41,379.94,382.82,381.09,378.14,369.75,368.54,370.56,371.72,385.08,385.57,387.61,392.26,395.37,391.59,394,393.88,399.94,402.09,406.56,410.81,410.15,411.62,410.95,409.82,408.29,413.04,417.33,416.01,408.76,415.68,408.87,434.4,432.43,435,440.58,443.95,443.67,442.63,447.06,451.24,455.96,463.6,479.63,479.88,488.81,495.48,484.01,488.43,488.34,500.72,498.96,502.22,508.07,511.33,520.71,527.55,529.53,530.22,518.53,515.71,516.12,527.11,530.21,536.85,552.51,573.4,569.49,569.5,584.6,589.33,585.96,582.89,579.69,590.32,597.61,600.67,593.12,583.09,601.65,612.05,607.17,616.29,618.77,611.19,609.01,605.68,588.62,564.21,592.97,591.64,571.32,557.25,556.01,544.9,593.26,591.02,586.45,567.95,566.15,569.9,565.85,549.74,553.85,552.59,553.56,554.86,551.16,542.9,537.99,531.09,515.57,515.82,545.87,541.68,554.9,549.8,546.86,556.56,563.27,561.87,545.59,548.8,547.38,555.78,556.03,564.39,555.49,560.35,556.46,555.84,558.37,569.7,571.29,569.66,561.81,566.12,555.1,556.33,558.73,553.43,567.97,576.26,582.96,593.2,589.25,597.04,591.52,587.84,582.46,588.37,590.25,590.28,589.62,597.46,587.71,587.26,584.43,559.19,559.1,569.1}; static int N = 507; // T.length; // 507 is just right before all time high static int start = 400; public static void main(String[] args) throws Exception { System.out.println(T.length == p.length); if (args.length&gt;0) start = Integer.parseInt(args[0]); if (args.length&gt;1) N = Integer.parseInt(args[1]); double tc = decimalYear(T[N+2]); System.out.println("tc: " + tc); double m = 0.5; double w = 1d; // Fitting System.out.println("Curve fitting ... "); LogPeriodic lppl = new LogPeriodic(tc); final CurveFitter fitter = new CurveFitter(new LevenbergMarquardtOptimizer()); for (int i=start;i&lt;N;i++) fitter.addObservedPoint(decimalYear(T[i]), p[i]); double[] initialguess = new double[]{ 0.5, // m 9d // w }; double[] fitted = fitter.fit(lppl, initialguess); System.out.println("fitted m,w: " + Arrays.toString(fitted)); // print result as csv StringBuilder sb = new StringBuilder(); for (int i=start;i&lt;T.length;i++) { sb.append(T[i]).append(";"); sb.append(log(p[i])).append(";"); sb.append(p[i]).append(";"); sb.append(lppl.value(decimalYear(T[i]), fitted)).append(";"); sb.append(i&gt;=N?1:0).append(";"); // is predicted price sb.append("\n"); } System.out.println(sb.toString()); } public static double decimalYear(String date) { Calendar cal = Calendar.getInstance(); cal.setTime(Date.valueOf(date)); int doy = cal.get(Calendar.DAY_OF_YEAR); int year = cal.get(Calendar.YEAR); return doy/365.2425 + year; // return doy/(((year &amp; 3) == 0 &amp;&amp; ((year % 25) != 0 || (year &amp; 15) == 0)) ? 366 : 365) + year; } // helper to switch between log and log10 public static double log(double d) { return FastMath.log(d); } // Math.log10 // http://commons.apache.org/proper/commons-math/userguide/linear.html public static double[] getABCC(double tc, double m, double w) { double sum_fi=0,sum_gi=0,sum_fi2=0,sum_fi_gi=0,sum_gi2=0,sum_yi=0,sum_yi_fi=0,sum_yi_gi=0,sum_hi=0,sum_fi_hi=0,sum_gi_hi=0,sum_hi2=0,sum_yi_hi=0; for (int i=start;i&lt;N;i++) { double t = decimalYear(T[i]); double fi = pow((tc - t),m); double gi = fi * cos(w * log(tc - t)); double hi = fi * sin(w * log(tc - t)); // double yi = log(p[i]); double yi = p[i]; sum_fi += fi; sum_gi += gi; sum_fi2 += fi * fi; sum_fi_gi += fi * gi; sum_gi2 += gi * gi; sum_yi += yi; sum_yi_fi += yi * fi; sum_yi_gi += yi * gi; sum_hi += hi; sum_fi_hi += fi * hi; sum_gi_hi += gi * hi; sum_hi2 += hi * hi; sum_yi_hi += yi * hi; } RealMatrix coefficients = new Array2DRowRealMatrix(new double[][] { { N-start+0, sum_fi, sum_gi, sum_hi }, // interessanterweise passt der chart nicht so gut bei N+1 übereinander, der zeitpunkt war aber präzierser, ist das bei allen so? { sum_fi, sum_fi2, sum_fi_gi, sum_fi_hi }, { sum_gi, sum_fi_gi, sum_gi2, sum_gi_hi }, { sum_hi, sum_fi_hi, sum_gi_hi, sum_hi2 }}, false ); DecompositionSolver solver = new LUDecomposition(coefficients).getSolver(); //Next create a RealVector array to represent the constant vector B and use solve(RealVector) to solve the system RealVector constants = new ArrayRealVector(new double[] { sum_yi, sum_yi_fi, sum_yi_gi, sum_yi_hi }, false); // das hinter dem = in der matrix gleichung RealVector solution = solver.solve(constants); return new double[] {solution.getEntry(0),solution.getEntry(1),solution.getEntry(2),solution.getEntry(3)}; } // 12.6: http://commons.apache.org/proper/commons-math/userguide/optimization.html public static class LogPeriodic implements ParametricUnivariateFunction { public final double tc; public double A,B,C1,C2,w,m,o; public double[] best = new double[3]; public double[] info; public LogPeriodic(double tc) { this.tc = tc; } @Override public double value(double t, double... parameters) { m = parameters[0]; w = parameters[1]; // solve the linear parameters double[] ABCC = getABCC(tc, m, w); A = ABCC[0]; B = ABCC[1]; C1 = ABCC[2]; C2 = ABCC[3]; double a=pow((tc - t),m); return A + B * a + C1 * a * cos(w * log(tc - t)) + C2 * a * sin(w * log(tc - t)); } @Override public double[] gradient(double t, double... parameters) { int params = 2; int order = 2; DerivativeStructure m = new DerivativeStructure(params,order,0, parameters[0]); DerivativeStructure w = new DerivativeStructure(params,order,1, parameters[1]); double[] ABCC = getABCC(tc, parameters[0], parameters[1]); A = ABCC[0]; B = ABCC[1]; C1 = ABCC[2]; C2 = ABCC[3]; // return A + B * pow((tc - t),m) + C1 * pow((tc - t),m) * cos(w * log(tc - t)) + C2 * pow((tc - t),m) * sin(w * log(tc - t)); /* == A * + B * pow((tc - t),m) * + C1 * pow((tc - t),m) * cos(w * log(tc - t)) * + C2 * pow((tc - t),m) * sin(w * log(tc - t)); */ DerivativeStructure f = new DerivativeStructure(params, order, A); f = f.add(B).multiply(tc-t).pow(m); f = f.add(C1).multiply(tc-t).pow(m).multiply(w.multiply(log(tc-t)).cos()); f = f.add(C2).multiply(tc-t).pow(m).multiply(w.multiply(log(tc-t)).sin()); // throws java.lang.ArrayIndexOutOfBoundsException: 2 at org.apache.commons.math3.optim.nonlinear.vector.jacobian.LevenbergMarquardtOptimizer.qrDecomposition(LevenbergMarquardtOptimizer.java:862) // return f.getAllDerivatives(); // throws unable to perform Q.R decomposition on the 107x2 jacobian matrix return new double[] { f.getPartialDerivative(1,0), f.getPartialDerivative(1,1), }; } } } </code></pre> <p>EDIT - Stack:</p> <pre><code>Exception in thread "main" org.apache.commons.math3.exception.ConvergenceException: illegal state: unable to perform Q.R decomposition on the 107x2 jacobian matrix at org.apache.commons.math3.optim.nonlinear.vector.jacobian.LevenbergMarquardtOptimizer.qrDecomposition(LevenbergMarquardtOptimizer.java:884) at org.apache.commons.math3.optim.nonlinear.vector.jacobian.LevenbergMarquardtOptimizer.doOptimize(LevenbergMarquardtOptimizer.java:331) at org.apache.commons.math3.optim.nonlinear.vector.jacobian.LevenbergMarquardtOptimizer.doOptimize(LevenbergMarquardtOptimizer.java:113) at org.apache.commons.math3.optim.BaseOptimizer.optimize(BaseOptimizer.java:143) at org.apache.commons.math3.optim.BaseMultivariateOptimizer.optimize(BaseMultivariateOptimizer.java:66) at org.apache.commons.math3.optim.nonlinear.vector.MultivariateVectorOptimizer.optimize(MultivariateVectorOptimizer.java:87) at org.apache.commons.math3.optim.nonlinear.vector.JacobianMultivariateVectorOptimizer.optimize(JacobianMultivariateVectorOptimizer.java:83) at org.apache.commons.math3.optim.nonlinear.vector.jacobian.AbstractLeastSquaresOptimizer.optimize(AbstractLeastSquaresOptimizer.java:197) at org.apache.commons.math3.fitting.CurveFitter.fit(CurveFitter.java:172) at org.apache.commons.math3.fitting.CurveFitter.fit(CurveFitter.java:136) at tryout.Sornette2NoLogPriceLevenberg.main(Sornette2NoLogPriceLevenberg.java:62) Java Result: 1 </code></pre>
    singulars
    1. This table or related slice is empty.
    plurals
    1. This table or related slice is empty.
    1. This table or related slice is empty.
    1. This table or related slice is empty.
 

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