resurrected the estimation package but with all interfaces and classes deprecated

this will help users switch smoothly to the new optimization.general package

git-svn-id: https://svn.apache.org/repos/asf/commons/proper/math/trunk@754732 13f79535-47bb-0310-9956-ffa450edef68

src/java/org/apache/commons/math/estimation/AbstractEstimator.java

@@ -0,0 +1,314 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements.  See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License.  You may obtain a copy of the License at
+ *
+ *      http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+package org.apache.commons.math.estimation;
+
+import java.util.Arrays;
+
+import org.apache.commons.math.linear.InvalidMatrixException;
+import org.apache.commons.math.linear.MatrixUtils;
+import org.apache.commons.math.linear.RealMatrix;
+import org.apache.commons.math.linear.decomposition.LUDecompositionImpl;
+
+/**
+ * Base class for implementing estimators.
+ * <p>This base class handles the boilerplates methods associated to thresholds
+ * settings, jacobian and error estimation.</p>
+ * @version $Revision$ $Date$
+ * @since 1.2
+ * @deprecated as of 2.0, everything in package org.apache.commons.math.estimation has
+ * been deprecated and replaced by package org.apache.commons.math.optimization.general
+ *
+ */
+@Deprecated
+public abstract class AbstractEstimator implements Estimator {
+
+    /** Default maximal number of cost evaluations allowed. */
+    public static final int DEFAULT_MAX_COST_EVALUATIONS = 100;
+
+    /**
+     * Build an abstract estimator for least squares problems.
+     * <p>The maximal number of cost evaluations allowed is set
+     * to its default value {@link #DEFAULT_MAX_COST_EVALUATIONS}.</p>
+     */
+    protected AbstractEstimator() {
+        setMaxCostEval(DEFAULT_MAX_COST_EVALUATIONS);
+    }
+
+    /**
+     * Set the maximal number of cost evaluations allowed.
+     * 
+     * @param maxCostEval maximal number of cost evaluations allowed
+     * @see #estimate
+     */
+    public final void setMaxCostEval(int maxCostEval) {
+        this.maxCostEval = maxCostEval;
+    }
+
+    /**
+     * Get the number of cost evaluations.
+     * 
+     * @return number of cost evaluations
+     * */
+    public final int getCostEvaluations() {
+        return costEvaluations;
+    }
+
+    /** 
+     * Get the number of jacobian evaluations.
+     * 
+     * @return number of jacobian evaluations
+     * */
+    public final int getJacobianEvaluations() {
+        return jacobianEvaluations;
+    }
+
+    /** 
+     * Update the jacobian matrix.
+     */
+    protected void updateJacobian() {
+        incrementJacobianEvaluationsCounter();
+        Arrays.fill(jacobian, 0);
+        for (int i = 0, index = 0; i < rows; i++) {
+            WeightedMeasurement wm = measurements[i];
+            double factor = -Math.sqrt(wm.getWeight());
+            for (int j = 0; j < cols; ++j) {
+                jacobian[index++] = factor * wm.getPartial(parameters[j]);
+            }
+        }
+    }
+
+    /**
+     * Increment the jacobian evaluations counter.
+     */
+    protected final void incrementJacobianEvaluationsCounter() {
+      ++jacobianEvaluations;
+    }
+
+    /** 
+     * Update the residuals array and cost function value.
+     * @exception EstimationException if the number of cost evaluations
+     * exceeds the maximum allowed
+     */
+    protected void updateResidualsAndCost()
+    throws EstimationException {
+
+        if (++costEvaluations > maxCostEval) {
+            throw new EstimationException("maximal number of evaluations exceeded ({0})",
+                                          maxCostEval);
+        }
+
+        cost = 0;
+        for (int i = 0, index = 0; i < rows; i++, index += cols) {
+            WeightedMeasurement wm = measurements[i];
+            double residual = wm.getResidual();
+            residuals[i] = Math.sqrt(wm.getWeight()) * residual;
+            cost += wm.getWeight() * residual * residual;
+        }
+        cost = Math.sqrt(cost);
+
+    }
+
+    /** 
+     * Get the Root Mean Square value.
+     * Get the Root Mean Square value, i.e. the root of the arithmetic
+     * mean of the square of all weighted residuals. This is related to the
+     * criterion that is minimized by the estimator as follows: if
+     * <em>c</em> if the criterion, and <em>n</em> is the number of
+     * measurements, then the RMS is <em>sqrt (c/n)</em>.
+     * 
+     * @param problem estimation problem
+     * @return RMS value
+     */
+    public double getRMS(EstimationProblem problem) {
+        WeightedMeasurement[] wm = problem.getMeasurements();
+        double criterion = 0;
+        for (int i = 0; i < wm.length; ++i) {
+            double residual = wm[i].getResidual();
+            criterion += wm[i].getWeight() * residual * residual;
+        }
+        return Math.sqrt(criterion / wm.length);
+    }
+
+    /**
+     * Get the Chi-Square value.
+     * @param problem estimation problem
+     * @return chi-square value
+     */
+    public double getChiSquare(EstimationProblem problem) {
+        WeightedMeasurement[] wm = problem.getMeasurements();
+        double chiSquare = 0;
+        for (int i = 0; i < wm.length; ++i) {
+            double residual = wm[i].getResidual();
+            chiSquare += residual * residual / wm[i].getWeight();
+        }
+        return chiSquare;
+    }
+
+    /**
+     * Get the covariance matrix of unbound estimated parameters.
+     * @param problem estimation problem
+     * @return covariance matrix
+     * @exception EstimationException if the covariance matrix
+     * cannot be computed (singular problem)
+     */
+    public double[][] getCovariances(EstimationProblem problem)
+      throws EstimationException {
+ 
+        // set up the jacobian
+        updateJacobian();
+
+        // compute transpose(J).J, avoiding building big intermediate matrices
+        final int rows = problem.getMeasurements().length;
+        final int cols = problem.getUnboundParameters().length;
+        final int max  = cols * rows;
+        double[][] jTj = new double[cols][cols];
+        for (int i = 0; i < cols; ++i) {
+            for (int j = i; j < cols; ++j) {
+                double sum = 0;
+                for (int k = 0; k < max; k += cols) {
+                    sum += jacobian[k + i] * jacobian[k + j];
+                }
+                jTj[i][j] = sum;
+                jTj[j][i] = sum;
+            }
+        }
+
+        try {
+            // compute the covariances matrix
+            RealMatrix inverse =
+                new LUDecompositionImpl(MatrixUtils.createRealMatrix(jTj)).getSolver().getInverse();
+            return inverse.getData();
+        } catch (InvalidMatrixException ime) {
+            throw new EstimationException("unable to compute covariances: singular problem");
+        }
+
+    }
+
+    /**
+     * Guess the errors in unbound estimated parameters.
+     * <p>Guessing is covariance-based, it only gives rough order of magnitude.</p>
+     * @param problem estimation problem
+     * @return errors in estimated parameters
+     * @exception EstimationException if the covariances matrix cannot be computed
+     * or the number of degrees of freedom is not positive (number of measurements
+     * lesser or equal to number of parameters)
+     */
+    public double[] guessParametersErrors(EstimationProblem problem)
+      throws EstimationException {
+        int m = problem.getMeasurements().length;
+        int p = problem.getUnboundParameters().length;
+        if (m <= p) {
+            throw new EstimationException(
+                    "no degrees of freedom ({0} measurements, {1} parameters)",
+                    m, p);
+        }
+        double[] errors = new double[problem.getUnboundParameters().length];
+        final double c = Math.sqrt(getChiSquare(problem) / (m - p));
+        double[][] covar = getCovariances(problem);
+        for (int i = 0; i < errors.length; ++i) {
+            errors[i] = Math.sqrt(covar[i][i]) * c;
+        }
+        return errors;
+    }
+
+    /**
+     * Initialization of the common parts of the estimation.
+     * <p>This method <em>must</em> be called at the start
+     * of the {@link #estimate(EstimationProblem) estimate}
+     * method.</p>
+     * @param problem estimation problem to solve
+     */
+    protected void initializeEstimate(EstimationProblem problem) {
+
+        // reset counters
+        costEvaluations     = 0;
+        jacobianEvaluations = 0;
+
+        // retrieve the equations and the parameters
+        measurements = problem.getMeasurements();
+        parameters   = problem.getUnboundParameters();
+
+        // arrays shared with the other private methods
+        rows      = measurements.length;
+        cols      = parameters.length;
+        jacobian  = new double[rows * cols];
+        residuals = new double[rows];
+
+        cost = Double.POSITIVE_INFINITY;
+
+    }
+
+    /** 
+     * Solve an estimation problem.
+     *
+     * <p>The method should set the parameters of the problem to several
+     * trial values until it reaches convergence. If this method returns
+     * normally (i.e. without throwing an exception), then the best
+     * estimate of the parameters can be retrieved from the problem
+     * itself, through the {@link EstimationProblem#getAllParameters
+     * EstimationProblem.getAllParameters} method.</p>
+     *
+     * @param problem estimation problem to solve
+     * @exception EstimationException if the problem cannot be solved
+     *
+     */
+    public abstract void estimate(EstimationProblem problem)
+    throws EstimationException;
+
+    /** Array of measurements. */
+    protected WeightedMeasurement[] measurements;
+
+    /** Array of parameters. */
+    protected EstimatedParameter[] parameters;
+
+    /** 
+     * Jacobian matrix.
+     * <p>This matrix is in canonical form just after the calls to
+     * {@link #updateJacobian()}, but may be modified by the solver
+     * in the derived class (the {@link LevenbergMarquardtEstimator
+     * Levenberg-Marquardt estimator} does this).</p>
+     */
+    protected double[] jacobian;
+
+    /** Number of columns of the jacobian matrix. */
+    protected int cols;
+
+    /** Number of rows of the jacobian matrix. */
+    protected int rows;
+
+    /** Residuals array.
+     * <p>This array is in canonical form just after the calls to
+     * {@link #updateJacobian()}, but may be modified by the solver
+     * in the derived class (the {@link LevenbergMarquardtEstimator
+     * Levenberg-Marquardt estimator} does this).</p>
+     */
+    protected double[] residuals;
+
+    /** Cost value (square root of the sum of the residuals). */
+    protected double cost;
+
+    /** Maximal allowed number of cost evaluations. */
+    private int maxCostEval;
+
+    /** Number of cost evaluations. */
+    private int costEvaluations;
+
+    /** Number of jacobian evaluations. */
+    private int jacobianEvaluations;
+
+}

src/java/org/apache/commons/math/estimation/EstimatedParameter.java

@@ -0,0 +1,126 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements.  See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License.  You may obtain a copy of the License at
+ *
+ *      http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+package org.apache.commons.math.estimation;
+
+import java.io.Serializable;
+
+/** This class represents the estimated parameters of an estimation problem.
+ *
+ * <p>The parameters of an estimation problem have a name, a value and
+ * a bound flag. The value of bound parameters is considered trusted
+ * and the solvers should not adjust them. On the other hand, the
+ * solvers should adjust the value of unbounds parameters until they
+ * satisfy convergence criterions specific to each solver.</p>
+ *
+ * @version $Revision$ $Date$
+ * @since 1.2
+ * @deprecated as of 2.0, everything in package org.apache.commons.math.estimation has
+ * been deprecated and replaced by package org.apache.commons.math.optimization.general
+ *
+ */
+@Deprecated
+public class EstimatedParameter
+  implements Serializable {
+
+  /** Simple constructor.
+   * Build an instance from a first estimate of the parameter,
+   * initially considered unbound.
+   * @param name name of the parameter
+   * @param firstEstimate first estimate of the parameter
+   */
+  public EstimatedParameter(String name, double firstEstimate) {
+    this.name = name;
+    estimate  = firstEstimate;
+    bound     = false;
+  }
+
+  /** Simple constructor.
+   * Build an instance from a first estimate of the parameter and a
+   * bound flag
+   * @param name name of the parameter
+   * @param firstEstimate first estimate of the parameter
+   * @param bound flag, should be true if the parameter is bound
+   */
+  public EstimatedParameter(String name,
+                            double firstEstimate,
+                            boolean bound) {
+    this.name  = name;
+    estimate   = firstEstimate;
+    this.bound = bound;
+  }
+
+  /** Copy constructor.
+   * Build a copy of a parameter
+   * @param parameter instance to copy
+   */
+  public EstimatedParameter(EstimatedParameter parameter) {
+    name     = parameter.name;
+    estimate = parameter.estimate;
+    bound    = parameter.bound;
+  }
+
+  /** Set a new estimated value for the parameter.
+   * @param estimate new estimate for the parameter
+   */
+  public void setEstimate(double estimate) {
+    this.estimate = estimate;
+  }
+
+  /** Get the current estimate of the parameter
+   * @return current estimate
+   */
+  public double getEstimate() {
+    return estimate;
+  }
+
+  /** get the name of the parameter
+   * @return parameter name
+   */
+  public String getName() {
+    return name;
+  }
+
+  /** Set the bound flag of the parameter
+   * @param bound this flag should be set to true if the parameter is
+   * bound (i.e. if it should not be adjusted by the solver).
+   */
+  public void setBound(boolean bound) {
+    this.bound = bound;
+  }
+
+  /** Check if the parameter is bound
+   * @return true if the parameter is bound */
+  public boolean isBound() {
+    return bound;
+  }
+
+  /** Name of the parameter */
+  private   String  name;
+
+  /** Current value of the parameter */
+  protected double  estimate;
+
+  /** Indicator for bound parameters
+   * (ie parameters that should not be estimated)
+   */
+  private   boolean bound;
+
+  /** Serializable version identifier */
+  private static final long serialVersionUID = -555440800213416949L;
+
+}

src/java/org/apache/commons/math/estimation/EstimationException.java

@@ -0,0 +1,48 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements.  See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License.  You may obtain a copy of the License at
+ *
+ *      http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+package org.apache.commons.math.estimation;
+
+import org.apache.commons.math.MathException;
+
+/** 
+ * This class represents exceptions thrown by the estimation solvers.
+ *
+ * @version $Revision$ $Date$
+ * @since 1.2
+ * @deprecated as of 2.0, everything in package org.apache.commons.math.estimation has
+ * been deprecated and replaced by package org.apache.commons.math.optimization.general
+ *
+ */
+@Deprecated
+public class EstimationException
+extends MathException {
+
+    /** Serializable version identifier. */
+    private static final long serialVersionUID = -573038581493881337L;
+
+    /** 
+     * Simple constructor.
+     * Build an exception by translating and formating a message
+     * @param specifier format specifier (to be translated)
+     * @param parts to insert in the format (no translation)
+     */
+    public EstimationException(String specifier, Object ... parts) {
+        super(specifier, parts);
+    }
+
+}

src/java/org/apache/commons/math/estimation/EstimationProblem.java

@@ -0,0 +1,67 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements.  See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License.  You may obtain a copy of the License at
+ *
+ *      http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+package org.apache.commons.math.estimation;
+
+/** 
+ * This interface represents an estimation problem.
+ *
+ * <p>This interface should be implemented by all real estimation
+ * problems before they can be handled by the estimators through the
+ * {@link Estimator#estimate Estimator.estimate} method.</p>
+ *
+ * <p>An estimation problem, as seen by a solver is a set of
+ * parameters and a set of measurements. The parameters are adjusted
+ * during the estimation through the {@link #getUnboundParameters
+ * getUnboundParameters} and {@link EstimatedParameter#setEstimate
+ * EstimatedParameter.setEstimate} methods. The measurements both have
+ * a measured value which is generally fixed at construction and a
+ * theoretical value which depends on the model and hence varies as
+ * the parameters are adjusted. The purpose of the solver is to reduce
+ * the residual between these values, it can retrieve the measurements
+ * through the {@link #getMeasurements getMeasurements} method.</p>
+ *
+ * @see Estimator
+ * @see WeightedMeasurement
+ *
+ * @version $Revision$ $Date$
+ * @since 1.2
+ * @deprecated as of 2.0, everything in package org.apache.commons.math.estimation has
+ * been deprecated and replaced by package org.apache.commons.math.optimization.general
+ *
+ */
+@Deprecated
+public interface EstimationProblem {
+  /** 
+   * Get the measurements of an estimation problem.
+   * @return measurements
+   */
+  public WeightedMeasurement[] getMeasurements();
+
+  /** 
+   * Get the unbound parameters of the problem.
+   * @return unbound parameters
+   */
+  public EstimatedParameter[] getUnboundParameters();
+
+  /** 
+   * Get all the parameters of the problem.
+   * @return parameters
+   */
+  public EstimatedParameter[] getAllParameters();
+
+}

src/java/org/apache/commons/math/estimation/Estimator.java

@@ -0,0 +1,93 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements.  See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License.  You may obtain a copy of the License at
+ *
+ *      http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+package org.apache.commons.math.estimation;
+
+/**
+ * This interface represents solvers for estimation problems.
+ *
+ * <p>The classes which are devoted to solve estimation problems
+ * should implement this interface. The problems which can be handled
+ * should implement the {@link EstimationProblem} interface which
+ * gather all the information needed by the solver.</p>
+ *
+ * <p>The interface is composed only of the {@link #estimate estimate}
+ * method.</p>
+ *
+ * @see EstimationProblem
+ *
+ * @version $Revision$ $Date$
+ * @since 1.2
+ * @deprecated as of 2.0, everything in package org.apache.commons.math.estimation has
+ * been deprecated and replaced by package org.apache.commons.math.optimization.general
+ *
+ */
+@Deprecated
+public interface Estimator {
+
+  /** 
+   * Solve an estimation problem.
+   *
+   * <p>The method should set the parameters of the problem to several
+   * trial values until it reaches convergence. If this method returns
+   * normally (i.e. without throwing an exception), then the best
+   * estimate of the parameters can be retrieved from the problem
+   * itself, through the {@link EstimationProblem#getAllParameters
+   * EstimationProblem.getAllParameters} method.</p>
+   *
+   * @param problem estimation problem to solve
+   * @exception EstimationException if the problem cannot be solved
+   *
+   */
+  public void estimate(EstimationProblem problem)
+    throws EstimationException;
+
+  /** 
+   * Get the Root Mean Square value.
+   * Get the Root Mean Square value, i.e. the root of the arithmetic
+   * mean of the square of all weighted residuals. This is related to the
+   * criterion that is minimized by the estimator as follows: if
+   * <em>c</em> is the criterion, and <em>n</em> is the number of
+   * measurements, then the RMS is <em>sqrt (c/n)</em>.
+   * @see #guessParametersErrors(EstimationProblem)
+   * 
+   * @param problem estimation problem
+   * @return RMS value
+   */
+  public double getRMS(EstimationProblem problem);
+
+  /**
+   * Get the covariance matrix of estimated parameters.
+   * @param problem estimation problem
+   * @return covariance matrix
+   * @exception EstimationException if the covariance matrix
+   * cannot be computed (singular problem)
+   */
+  public double[][] getCovariances(EstimationProblem problem)
+    throws EstimationException;
+
+  /**
+   * Guess the errors in estimated parameters.
+   * @see #getRMS(EstimationProblem)
+   * @param problem estimation problem
+   * @return errors in estimated parameters
+     * @exception EstimationException if the error cannot be guessed
+   */
+  public double[] guessParametersErrors(EstimationProblem problem)
+    throws EstimationException;
+
+}

src/java/org/apache/commons/math/estimation/GaussNewtonEstimator.java

@@ -0,0 +1,228 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements.  See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License.  You may obtain a copy of the License at
+ *
+ *      http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+package org.apache.commons.math.estimation;
+
+import java.io.Serializable;
+
+import org.apache.commons.math.linear.InvalidMatrixException;
+import org.apache.commons.math.linear.MatrixUtils;
+import org.apache.commons.math.linear.RealMatrix;
+import org.apache.commons.math.linear.RealVector;
+import org.apache.commons.math.linear.RealVectorImpl;
+import org.apache.commons.math.linear.decomposition.LUDecompositionImpl;
+
+/** 
+ * This class implements a solver for estimation problems.
+ *
+ * <p>This class solves estimation problems using a weighted least
+ * squares criterion on the measurement residuals. It uses a
+ * Gauss-Newton algorithm.</p>
+ *
+ * @version $Revision$ $Date$
+ * @since 1.2
+ * @deprecated as of 2.0, everything in package org.apache.commons.math.estimation has
+ * been deprecated and replaced by package org.apache.commons.math.optimization.general
+ *
+ */
+@Deprecated
+public class GaussNewtonEstimator extends AbstractEstimator implements Serializable {
+
+    /** Serializable version identifier */
+    private static final long serialVersionUID = 5485001826076289109L;
+
+    /** Default threshold for cost steady state detection. */
+    private static final double DEFAULT_STEADY_STATE_THRESHOLD = 1.0e-6;
+
+    /** Default threshold for cost convergence. */
+    private static final double DEFAULT_CONVERGENCE = 1.0e-6;
+
+    /** Threshold for cost steady state detection. */
+    private double steadyStateThreshold;
+
+    /** Threshold for cost convergence. */
+    private double convergence;
+
+    /** Simple constructor with default settings.
+     * <p>
+     * The estimator is built with default values for all settings.
+     * </p>
+     * @see #DEFAULT_STEADY_STATE_THRESHOLD
+     * @see #DEFAULT_CONVERGENCE
+     * @see AbstractEstimator#DEFAULT_MAX_COST_EVALUATIONS
+     */
+    public GaussNewtonEstimator() {
+        this.steadyStateThreshold = DEFAULT_STEADY_STATE_THRESHOLD;
+        this.convergence          = DEFAULT_CONVERGENCE;        
+    }
+
+    /** 
+     * Simple constructor.
+     *
+     * <p>This constructor builds an estimator and stores its convergence
+     * characteristics.</p>
+     *
+     * <p>An estimator is considered to have converged whenever either
+     * the criterion goes below a physical threshold under which
+     * improvements are considered useless or when the algorithm is
+     * unable to improve it (even if it is still high). The first
+     * condition that is met stops the iterations.</p>
+     *
+     * <p>The fact an estimator has converged does not mean that the
+     * model accurately fits the measurements. It only means no better
+     * solution can be found, it does not mean this one is good. Such an
+     * analysis is left to the caller.</p>
+     *
+     * <p>If neither conditions are fulfilled before a given number of
+     * iterations, the algorithm is considered to have failed and an
+     * {@link EstimationException} is thrown.</p>
+     *
+     * @param maxCostEval maximal number of cost evaluations allowed
+     * @param convergence criterion threshold below which we do not need
+     * to improve the criterion anymore
+     * @param steadyStateThreshold steady state detection threshold, the
+     * problem has converged has reached a steady state if
+     * <code>Math.abs(J<sub>n</sub> - J<sub>n-1</sub>) &lt;
+     * J<sub>n</sub> &times convergence</code>, where <code>J<sub>n</sub></code>
+     * and <code>J<sub>n-1</sub></code> are the current and preceding criterion
+     * values (square sum of the weighted residuals of considered measurements).
+     */
+    public GaussNewtonEstimator(final int maxCostEval, final double convergence,
+                                final double steadyStateThreshold) {
+        setMaxCostEval(maxCostEval);
+        this.steadyStateThreshold = steadyStateThreshold;
+        this.convergence          = convergence;
+    }
+
+    /**
+     * Set the convergence criterion threshold.
+     * @param convergence criterion threshold below which we do not need
+     * to improve the criterion anymore
+     */
+    public void setConvergence(final double convergence) {
+        this.convergence = convergence;
+    }
+
+    /**
+     * Set the steady state detection threshold.
+     * <p>
+     * The problem has converged has reached a steady state if
+     * <code>Math.abs(J<sub>n</sub> - J<sub>n-1</sub>) &lt;
+     * J<sub>n</sub> &times convergence</code>, where <code>J<sub>n</sub></code>
+     * and <code>J<sub>n-1</sub></code> are the current and preceding criterion
+     * values (square sum of the weighted residuals of considered measurements).
+     * </p>
+     * @param steadyStateThreshold steady state detection threshold
+     */
+    public void setSteadyStateThreshold(final double steadyStateThreshold) {
+        this.steadyStateThreshold = steadyStateThreshold;
+    }
+
+    /** 
+     * Solve an estimation problem using a least squares criterion.
+     *
+     * <p>This method set the unbound parameters of the given problem
+     * starting from their current values through several iterations. At
+     * each step, the unbound parameters are changed in order to
+     * minimize a weighted least square criterion based on the
+     * measurements of the problem.</p>
+     *
+     * <p>The iterations are stopped either when the criterion goes
+     * below a physical threshold under which improvement are considered
+     * useless or when the algorithm is unable to improve it (even if it
+     * is still high). The first condition that is met stops the
+     * iterations. If the convergence it not reached before the maximum
+     * number of iterations, an {@link EstimationException} is
+     * thrown.</p>
+     *
+     * @param problem estimation problem to solve
+     * @exception EstimationException if the problem cannot be solved
+     *
+     * @see EstimationProblem
+     *
+     */
+    public void estimate(EstimationProblem problem)
+    throws EstimationException {
+
+        initializeEstimate(problem);
+
+        // work matrices
+        double[] grad             = new double[parameters.length];
+        RealVectorImpl bDecrement = new RealVectorImpl(parameters.length);
+        double[] bDecrementData   = bDecrement.getDataRef();
+        RealMatrix wGradGradT     = MatrixUtils.createRealMatrix(parameters.length, parameters.length);
+
+        // iterate until convergence is reached
+        double previous = Double.POSITIVE_INFINITY;
+        do {
+
+            // build the linear problem
+            incrementJacobianEvaluationsCounter();
+            RealVector b = new RealVectorImpl(parameters.length);
+            RealMatrix a = MatrixUtils.createRealMatrix(parameters.length, parameters.length);
+            for (int i = 0; i < measurements.length; ++i) {
+                if (! measurements [i].isIgnored()) {
+
+                    double weight   = measurements[i].getWeight();
+                    double residual = measurements[i].getResidual();
+
+                    // compute the normal equation
+                    for (int j = 0; j < parameters.length; ++j) {
+                        grad[j] = measurements[i].getPartial(parameters[j]);
+                        bDecrementData[j] = weight * residual * grad[j];
+                    }
+
+                    // build the contribution matrix for measurement i
+                    for (int k = 0; k < parameters.length; ++k) {
+                        double gk = grad[k];
+                        for (int l = 0; l < parameters.length; ++l) {
+                            wGradGradT.setEntry(k, l, weight * gk * grad[l]);
+                        }
+                    }
+
+                    // update the matrices
+                    a = a.add(wGradGradT);
+                    b = b.add(bDecrement);
+
+                }
+            }
+
+            try {
+
+                // solve the linearized least squares problem
+                RealVector dX = new LUDecompositionImpl(a).getSolver().solve(b);
+
+                // update the estimated parameters
+                for (int i = 0; i < parameters.length; ++i) {
+                    parameters[i].setEstimate(parameters[i].getEstimate() + dX.getEntry(i));
+                }
+
+            } catch(InvalidMatrixException e) {
+                throw new EstimationException("unable to solve: singular problem");
+            }
+
+
+            previous = cost;
+            updateResidualsAndCost();
+
+        } while ((getCostEvaluations() < 2) ||
+                 (Math.abs(previous - cost) > (cost * steadyStateThreshold) &&
+                  (Math.abs(cost) > convergence)));
+
+    }
+
+}

src/java/org/apache/commons/math/estimation/LevenbergMarquardtEstimator.java

@@ -0,0 +1,874 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements.  See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License.  You may obtain a copy of the License at
+ *
+ *      http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+package org.apache.commons.math.estimation;
+
+import java.io.Serializable;
+import java.util.Arrays;
+
+
+/** 
+ * This class solves a least squares problem.
+ *
+ * <p>This implementation <em>should</em> work even for over-determined systems
+ * (i.e. systems having more variables than equations). Over-determined systems
+ * are solved by ignoring the variables which have the smallest impact according
+ * to their jacobian column norm. Only the rank of the matrix and some loop bounds
+ * are changed to implement this.</p>
+ *
+ * <p>The resolution engine is a simple translation of the MINPACK <a
+ * href="http://www.netlib.org/minpack/lmder.f">lmder</a> routine with minor
+ * changes. The changes include the over-determined resolution and the Q.R.
+ * decomposition which has been rewritten following the algorithm described in the
+ * P. Lascaux and R. Theodor book <i>Analyse num&eacute;rique matricielle
+ * appliqu&eacute;e &agrave; l'art de l'ing&eacute;nieur</i>, Masson 1986. The
+ * redistribution policy for MINPACK is available <a
+ * href="http://www.netlib.org/minpack/disclaimer">here</a>, for convenience, it
+ * is reproduced below.</p>
+ *
+ * <table border="0" width="80%" cellpadding="10" align="center" bgcolor="#E0E0E0">
+ * <tr><td>
+ *    Minpack Copyright Notice (1999) University of Chicago.
+ *    All rights reserved
+ * </td></tr>
+ * <tr><td>
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ * <ol>
+ *  <li>Redistributions of source code must retain the above copyright
+ *      notice, this list of conditions and the following disclaimer.</li>
+ * <li>Redistributions in binary form must reproduce the above
+ *     copyright notice, this list of conditions and the following
+ *     disclaimer in the documentation and/or other materials provided
+ *     with the distribution.</li>
+ * <li>The end-user documentation included with the redistribution, if any,
+ *     must include the following acknowledgment:
+ *     <code>This product includes software developed by the University of
+ *           Chicago, as Operator of Argonne National Laboratory.</code>
+ *     Alternately, this acknowledgment may appear in the software itself,
+ *     if and wherever such third-party acknowledgments normally appear.</li>
+ * <li><strong>WARRANTY DISCLAIMER. THE SOFTWARE IS SUPPLIED "AS IS"
+ *     WITHOUT WARRANTY OF ANY KIND. THE COPYRIGHT HOLDER, THE
+ *     UNITED STATES, THE UNITED STATES DEPARTMENT OF ENERGY, AND
+ *     THEIR EMPLOYEES: (1) DISCLAIM ANY WARRANTIES, EXPRESS OR
+ *     IMPLIED, INCLUDING BUT NOT LIMITED TO ANY IMPLIED WARRANTIES
+ *     OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE, TITLE
+ *     OR NON-INFRINGEMENT, (2) DO NOT ASSUME ANY LEGAL LIABILITY
+ *     OR RESPONSIBILITY FOR THE ACCURACY, COMPLETENESS, OR
+ *     USEFULNESS OF THE SOFTWARE, (3) DO NOT REPRESENT THAT USE OF
+ *     THE SOFTWARE WOULD NOT INFRINGE PRIVATELY OWNED RIGHTS, (4)
+ *     DO NOT WARRANT THAT THE SOFTWARE WILL FUNCTION
+ *     UNINTERRUPTED, THAT IT IS ERROR-FREE OR THAT ANY ERRORS WILL
+ *     BE CORRECTED.</strong></li>
+ * <li><strong>LIMITATION OF LIABILITY. IN NO EVENT WILL THE COPYRIGHT
+ *     HOLDER, THE UNITED STATES, THE UNITED STATES DEPARTMENT OF
+ *     ENERGY, OR THEIR EMPLOYEES: BE LIABLE FOR ANY INDIRECT,
+ *     INCIDENTAL, CONSEQUENTIAL, SPECIAL OR PUNITIVE DAMAGES OF
+ *     ANY KIND OR NATURE, INCLUDING BUT NOT LIMITED TO LOSS OF
+ *     PROFITS OR LOSS OF DATA, FOR ANY REASON WHATSOEVER, WHETHER
+ *     SUCH LIABILITY IS ASSERTED ON THE BASIS OF CONTRACT, TORT
+ *     (INCLUDING NEGLIGENCE OR STRICT LIABILITY), OR OTHERWISE,
+ *     EVEN IF ANY OF SAID PARTIES HAS BEEN WARNED OF THE
+ *     POSSIBILITY OF SUCH LOSS OR DAMAGES.</strong></li>
+ * <ol></td></tr>
+ * </table>
+
+ * @author Argonne National Laboratory. MINPACK project. March 1980 (original fortran)
+ * @author Burton S. Garbow (original fortran)
+ * @author Kenneth E. Hillstrom (original fortran)
+ * @author Jorge J. More (original fortran)
+
+ * @version $Revision$ $Date$
+ * @since 1.2
+ * @deprecated as of 2.0, everything in package org.apache.commons.math.estimation has
+ * been deprecated and replaced by package org.apache.commons.math.optimization.general
+ *
+ */
+@Deprecated
+public class LevenbergMarquardtEstimator extends AbstractEstimator implements Serializable {
+
+  /** 
+   * Build an estimator for least squares problems.
+   * <p>The default values for the algorithm settings are:
+   *   <ul>
+   *    <li>{@link #setInitialStepBoundFactor initial step bound factor}: 100.0</li>
+   *    <li>{@link #setMaxCostEval maximal cost evaluations}: 1000</li>
+   *    <li>{@link #setCostRelativeTolerance cost relative tolerance}: 1.0e-10</li>
+   *    <li>{@link #setParRelativeTolerance parameters relative tolerance}: 1.0e-10</li>
+   *    <li>{@link #setOrthoTolerance orthogonality tolerance}: 1.0e-10</li>
+   *   </ul>
+   * </p>
+   */
+  public LevenbergMarquardtEstimator() {
+
+    // set up the superclass with a default  max cost evaluations setting
+    setMaxCostEval(1000);
+
+    // default values for the tuning parameters
+    setInitialStepBoundFactor(100.0);
+    setCostRelativeTolerance(1.0e-10);
+    setParRelativeTolerance(1.0e-10);
+    setOrthoTolerance(1.0e-10);
+
+  }
+
+  /** 
+   * Set the positive input variable used in determining the initial step bound.
+   * This bound is set to the product of initialStepBoundFactor and the euclidean norm of diag*x if nonzero,
+   * or else to initialStepBoundFactor itself. In most cases factor should lie
+   * in the interval (0.1, 100.0). 100.0 is a generally recommended value
+   * 
+   * @param initialStepBoundFactor initial step bound factor
+   * @see #estimate
+   */
+  public void setInitialStepBoundFactor(double initialStepBoundFactor) {
+    this.initialStepBoundFactor = initialStepBoundFactor;
+  }
+
+  /** 
+   * Set the desired relative error in the sum of squares.
+   * 
+   * @param costRelativeTolerance desired relative error in the sum of squares
+   * @see #estimate
+   */
+  public void setCostRelativeTolerance(double costRelativeTolerance) {
+    this.costRelativeTolerance = costRelativeTolerance;
+  }
+
+  /** 
+   * Set the desired relative error in the approximate solution parameters.
+   * 
+   * @param parRelativeTolerance desired relative error
+   * in the approximate solution parameters
+   * @see #estimate
+   */
+  public void setParRelativeTolerance(double parRelativeTolerance) {
+    this.parRelativeTolerance = parRelativeTolerance;
+  }
+
+  /** 
+   * Set the desired max cosine on the orthogonality.
+   * 
+   * @param orthoTolerance desired max cosine on the orthogonality
+   * between the function vector and the columns of the jacobian
+   * @see #estimate
+   */
+  public void setOrthoTolerance(double orthoTolerance) {
+    this.orthoTolerance = orthoTolerance;
+  }
+
+  /** 
+   * Solve an estimation problem using the Levenberg-Marquardt algorithm.
+   * <p>The algorithm used is a modified Levenberg-Marquardt one, based
+   * on the MINPACK <a href="http://www.netlib.org/minpack/lmder.f">lmder</a>
+   * routine. The algorithm settings must have been set up before this method
+   * is called with the {@link #setInitialStepBoundFactor},
+   * {@link #setMaxCostEval}, {@link #setCostRelativeTolerance},
+   * {@link #setParRelativeTolerance} and {@link #setOrthoTolerance} methods.
+   * If these methods have not been called, the default values set up by the
+   * {@link #LevenbergMarquardtEstimator() constructor} will be used.</p>
+   * <p>The authors of the original fortran function are:</p>
+   * <ul>
+   *   <li>Argonne National Laboratory. MINPACK project. March 1980</li>
+   *   <li>Burton  S. Garbow</li>
+   *   <li>Kenneth E. Hillstrom</li>
+   *   <li>Jorge   J. More</li>
+   *   </ul>
+   * <p>Luc Maisonobe did the Java translation.</p>
+   * 
+   * @param problem estimation problem to solve
+   * @exception EstimationException if convergence cannot be
+   * reached with the specified algorithm settings or if there are more variables
+   * than equations
+   * @see #setInitialStepBoundFactor
+   * @see #setCostRelativeTolerance
+   * @see #setParRelativeTolerance
+   * @see #setOrthoTolerance
+   */
+  public void estimate(EstimationProblem problem)
+    throws EstimationException {
+
+    initializeEstimate(problem);
+
+    // arrays shared with the other private methods
+    solvedCols  = Math.min(rows, cols);
+    diagR       = new double[cols];
+    jacNorm     = new double[cols];
+    beta        = new double[cols];
+    permutation = new int[cols];
+    lmDir       = new double[cols];
+
+    // local variables
+    double   delta   = 0, xNorm = 0;
+    double[] diag    = new double[cols];
+    double[] oldX    = new double[cols];
+    double[] oldRes  = new double[rows];
+    double[] work1   = new double[cols];
+    double[] work2   = new double[cols];
+    double[] work3   = new double[cols];
+
+    // evaluate the function at the starting point and calculate its norm
+    updateResidualsAndCost();
+    
+    // outer loop
+    lmPar = 0;
+    boolean firstIteration = true;
+    while (true) {
+
+      // compute the Q.R. decomposition of the jacobian matrix
+      updateJacobian();
+      qrDecomposition();
+
+      // compute Qt.res
+      qTy(residuals);
+
+      // now we don't need Q anymore,
+      // so let jacobian contain the R matrix with its diagonal elements
+      for (int k = 0; k < solvedCols; ++k) {
+        int pk = permutation[k];
+        jacobian[k * cols + pk] = diagR[pk];
+      }
+
+      if (firstIteration) {
+
+        // scale the variables according to the norms of the columns
+        // of the initial jacobian
+        xNorm = 0;
+        for (int k = 0; k < cols; ++k) {
+          double dk = jacNorm[k];
+          if (dk == 0) {
+            dk = 1.0;
+          }
+          double xk = dk * parameters[k].getEstimate();
+          xNorm  += xk * xk;
+          diag[k] = dk;
+        }
+        xNorm = Math.sqrt(xNorm);
+        
+        // initialize the step bound delta
+        delta = (xNorm == 0) ? initialStepBoundFactor : (initialStepBoundFactor * xNorm);
+ 
+      }
+
+      // check orthogonality between function vector and jacobian columns
+      double maxCosine = 0;
+      if (cost != 0) {
+        for (int j = 0; j < solvedCols; ++j) {
+          int    pj = permutation[j];
+          double s  = jacNorm[pj];
+          if (s != 0) {
+            double sum = 0;
+            for (int i = 0, index = pj; i <= j; ++i, index += cols) {
+              sum += jacobian[index] * residuals[i];
+            }
+            maxCosine = Math.max(maxCosine, Math.abs(sum) / (s * cost));
+          }
+        }
+      }
+      if (maxCosine <= orthoTolerance) {
+        return;
+      }
+
+      // rescale if necessary
+      for (int j = 0; j < cols; ++j) {
+        diag[j] = Math.max(diag[j], jacNorm[j]);
+      }
+
+      // inner loop
+      for (double ratio = 0; ratio < 1.0e-4;) {
+
+        // save the state
+        for (int j = 0; j < solvedCols; ++j) {
+          int pj = permutation[j];
+          oldX[pj] = parameters[pj].getEstimate();
+        }
+        double previousCost = cost;
+        double[] tmpVec = residuals;
+        residuals = oldRes;
+        oldRes    = tmpVec;
+        
+        // determine the Levenberg-Marquardt parameter
+        determineLMParameter(oldRes, delta, diag, work1, work2, work3);
+
+        // compute the new point and the norm of the evolution direction
+        double lmNorm = 0;
+        for (int j = 0; j < solvedCols; ++j) {
+          int pj = permutation[j];
+          lmDir[pj] = -lmDir[pj];
+          parameters[pj].setEstimate(oldX[pj] + lmDir[pj]);
+          double s = diag[pj] * lmDir[pj];
+          lmNorm  += s * s;
+        }
+        lmNorm = Math.sqrt(lmNorm);
+
+        // on the first iteration, adjust the initial step bound.
+        if (firstIteration) {
+          delta = Math.min(delta, lmNorm);
+        }
+
+        // evaluate the function at x + p and calculate its norm
+        updateResidualsAndCost();
+
+        // compute the scaled actual reduction
+        double actRed = -1.0;
+        if (0.1 * cost < previousCost) {
+          double r = cost / previousCost;
+          actRed = 1.0 - r * r;
+        }
+
+        // compute the scaled predicted reduction
+        // and the scaled directional derivative
+        for (int j = 0; j < solvedCols; ++j) {
+          int pj = permutation[j];
+          double dirJ = lmDir[pj];
+          work1[j] = 0;
+          for (int i = 0, index = pj; i <= j; ++i, index += cols) {
+            work1[i] += jacobian[index] * dirJ;
+          }
+        }
+        double coeff1 = 0;
+        for (int j = 0; j < solvedCols; ++j) {
+         coeff1 += work1[j] * work1[j];
+        }
+        double pc2 = previousCost * previousCost;
+        coeff1 = coeff1 / pc2;
+        double coeff2 = lmPar * lmNorm * lmNorm / pc2;
+        double preRed = coeff1 + 2 * coeff2;
+        double dirDer = -(coeff1 + coeff2);
+
+        // ratio of the actual to the predicted reduction
+        ratio = (preRed == 0) ? 0 : (actRed / preRed);
+
+        // update the step bound
+        if (ratio <= 0.25) {
+          double tmp =
+            (actRed < 0) ? (0.5 * dirDer / (dirDer + 0.5 * actRed)) : 0.5;
+          if ((0.1 * cost >= previousCost) || (tmp < 0.1)) {
+            tmp = 0.1;
+          }
+          delta = tmp * Math.min(delta, 10.0 * lmNorm);
+          lmPar /= tmp;
+        } else if ((lmPar == 0) || (ratio >= 0.75)) {
+          delta = 2 * lmNorm;
+          lmPar *= 0.5;
+        }
+
+        // test for successful iteration.
+        if (ratio >= 1.0e-4) {
+          // successful iteration, update the norm
+          firstIteration = false;
+          xNorm = 0;
+          for (int k = 0; k < cols; ++k) {
+            double xK = diag[k] * parameters[k].getEstimate();
+            xNorm    += xK * xK;
+          }
+          xNorm = Math.sqrt(xNorm);
+        } else {
+          // failed iteration, reset the previous values
+          cost = previousCost;
+          for (int j = 0; j < solvedCols; ++j) {
+            int pj = permutation[j];
+            parameters[pj].setEstimate(oldX[pj]);
+          }
+          tmpVec    = residuals;
+          residuals = oldRes;
+          oldRes    = tmpVec;
+        }
+   
+        // tests for convergence.
+        if (((Math.abs(actRed) <= costRelativeTolerance) &&
+             (preRed <= costRelativeTolerance) &&
+             (ratio <= 2.0)) ||
+             (delta <= parRelativeTolerance * xNorm)) {
+          return;
+        }
+
+        // tests for termination and stringent tolerances
+        // (2.2204e-16 is the machine epsilon for IEEE754)
+        if ((Math.abs(actRed) <= 2.2204e-16) && (preRed <= 2.2204e-16) && (ratio <= 2.0)) {
+          throw new EstimationException("cost relative tolerance is too small ({0})," +
+                                        " no further reduction in the" +
+                                        " sum of squares is possible",
+                                        costRelativeTolerance);
+        } else if (delta <= 2.2204e-16 * xNorm) {
+          throw new EstimationException("parameters relative tolerance is too small" +
+                                        " ({0}), no further improvement in" +
+                                        " the approximate solution is possible",
+                                        parRelativeTolerance);
+        } else if (maxCosine <= 2.2204e-16)  {
+          throw new EstimationException("orthogonality tolerance is too small ({0})," +
+                                        " solution is orthogonal to the jacobian",
+                                        orthoTolerance);
+        }
+
+      }
+
+    }
+
+  }
+
+  /** 
+   * Determine the Levenberg-Marquardt parameter.
+   * <p>This implementation is a translation in Java of the MINPACK
+   * <a href="http://www.netlib.org/minpack/lmpar.f">lmpar</a>
+   * routine.</p>
+   * <p>This method sets the lmPar and lmDir attributes.</p>
+   * <p>The authors of the original fortran function are:</p>
+   * <ul>
+   *   <li>Argonne National Laboratory. MINPACK project. March 1980</li>
+   *   <li>Burton  S. Garbow</li>
+   *   <li>Kenneth E. Hillstrom</li>
+   *   <li>Jorge   J. More</li>
+   * </ul>
+   * <p>Luc Maisonobe did the Java translation.</p>
+   * 
+   * @param qy array containing qTy
+   * @param delta upper bound on the euclidean norm of diagR * lmDir
+   * @param diag diagonal matrix
+   * @param work1 work array
+   * @param work2 work array
+   * @param work3 work array
+   */
+  private void determineLMParameter(double[] qy, double delta, double[] diag,
+                                    double[] work1, double[] work2, double[] work3) {
+
+    // compute and store in x the gauss-newton direction, if the
+    // jacobian is rank-deficient, obtain a least squares solution
+    for (int j = 0; j < rank; ++j) {
+      lmDir[permutation[j]] = qy[j];
+    }
+    for (int j = rank; j < cols; ++j) {
+      lmDir[permutation[j]] = 0;
+    }
+    for (int k = rank - 1; k >= 0; --k) {
+      int pk = permutation[k];
+      double ypk = lmDir[pk] / diagR[pk];
+      for (int i = 0, index = pk; i < k; ++i, index += cols) {
+        lmDir[permutation[i]] -= ypk * jacobian[index];
+      }
+      lmDir[pk] = ypk;
+    }
+
+    // evaluate the function at the origin, and test
+    // for acceptance of the Gauss-Newton direction
+    double dxNorm = 0;
+    for (int j = 0; j < solvedCols; ++j) {
+      int pj = permutation[j];
+      double s = diag[pj] * lmDir[pj];
+      work1[pj] = s;
+      dxNorm += s * s;
+    }
+    dxNorm = Math.sqrt(dxNorm);
+    double fp = dxNorm - delta;
+    if (fp <= 0.1 * delta) {
+      lmPar = 0;
+      return;
+    }
+
+    // if the jacobian is not rank deficient, the Newton step provides
+    // a lower bound, parl, for the zero of the function,
+    // otherwise set this bound to zero
+    double sum2, parl = 0;
+    if (rank == solvedCols) {
+      for (int j = 0; j < solvedCols; ++j) {
+        int pj = permutation[j];
+        work1[pj] *= diag[pj] / dxNorm; 
+      }
+      sum2 = 0;
+      for (int j = 0; j < solvedCols; ++j) {
+        int pj = permutation[j];
+        double sum = 0;
+        for (int i = 0, index = pj; i < j; ++i, index += cols) {
+          sum += jacobian[index] * work1[permutation[i]];
+        }
+        double s = (work1[pj] - sum) / diagR[pj];
+        work1[pj] = s;
+        sum2 += s * s;
+      }
+      parl = fp / (delta * sum2);
+    }
+
+    // calculate an upper bound, paru, for the zero of the function
+    sum2 = 0;
+    for (int j = 0; j < solvedCols; ++j) {
+      int pj = permutation[j];
+      double sum = 0;
+      for (int i = 0, index = pj; i <= j; ++i, index += cols) {
+        sum += jacobian[index] * qy[i];
+      }
+      sum /= diag[pj];
+      sum2 += sum * sum;
+    }
+    double gNorm = Math.sqrt(sum2);
+    double paru = gNorm / delta;
+    if (paru == 0) {
+      // 2.2251e-308 is the smallest positive real for IEE754
+      paru = 2.2251e-308 / Math.min(delta, 0.1);
+    }
+
+    // if the input par lies outside of the interval (parl,paru),
+    // set par to the closer endpoint
+    lmPar = Math.min(paru, Math.max(lmPar, parl));
+    if (lmPar == 0) {
+      lmPar = gNorm / dxNorm;
+    }
+
+    for (int countdown = 10; countdown >= 0; --countdown) {
+
+      // evaluate the function at the current value of lmPar
+      if (lmPar == 0) {
+        lmPar = Math.max(2.2251e-308, 0.001 * paru);
+      }
+      double sPar = Math.sqrt(lmPar);
+      for (int j = 0; j < solvedCols; ++j) {
+        int pj = permutation[j];
+        work1[pj] = sPar * diag[pj];
+      }
+      determineLMDirection(qy, work1, work2, work3);
+
+      dxNorm = 0;
+      for (int j = 0; j < solvedCols; ++j) {
+        int pj = permutation[j];
+        double s = diag[pj] * lmDir[pj];
+        work3[pj] = s;
+        dxNorm += s * s;
+      }
+      dxNorm = Math.sqrt(dxNorm);
+      double previousFP = fp;
+      fp = dxNorm - delta;
+
+      // if the function is small enough, accept the current value
+      // of lmPar, also test for the exceptional cases where parl is zero
+      if ((Math.abs(fp) <= 0.1 * delta) ||
+          ((parl == 0) && (fp <= previousFP) && (previousFP < 0))) {
+        return;
+      }
+ 
+      // compute the Newton correction
+      for (int j = 0; j < solvedCols; ++j) {
+       int pj = permutation[j];
+        work1[pj] = work3[pj] * diag[pj] / dxNorm; 
+      }
+      for (int j = 0; j < solvedCols; ++j) {
+        int pj = permutation[j];
+        work1[pj] /= work2[j];
+        double tmp = work1[pj];
+        for (int i = j + 1; i < solvedCols; ++i) {
+          work1[permutation[i]] -= jacobian[i * cols + pj] * tmp;
+        }
+      }
+      sum2 = 0;
+      for (int j = 0; j < solvedCols; ++j) {
+        double s = work1[permutation[j]];
+        sum2 += s * s;
+      }
+      double correction = fp / (delta * sum2);
+
+      // depending on the sign of the function, update parl or paru.
+      if (fp > 0) {
+        parl = Math.max(parl, lmPar);
+      } else if (fp < 0) {
+        paru = Math.min(paru, lmPar);
+      }
+
+      // compute an improved estimate for lmPar
+      lmPar = Math.max(parl, lmPar + correction);
+
+    }
+  }
+
+  /** 
+   * Solve a*x = b and d*x = 0 in the least squares sense.
+   * <p>This implementation is a translation in Java of the MINPACK
+   * <a href="http://www.netlib.org/minpack/qrsolv.f">qrsolv</a>
+   * routine.</p>
+   * <p>This method sets the lmDir and lmDiag attributes.</p>
+   * <p>The authors of the original fortran function are:</p>
+   * <ul>
+   *   <li>Argonne National Laboratory. MINPACK project. March 1980</li>
+   *   <li>Burton  S. Garbow</li>
+   *   <li>Kenneth E. Hillstrom</li>
+   *   <li>Jorge   J. More</li>
+   * </ul>
+   * <p>Luc Maisonobe did the Java translation.</p>
+   * 
+   * @param qy array containing qTy
+   * @param diag diagonal matrix
+   * @param lmDiag diagonal elements associated with lmDir
+   * @param work work array
+   */
+  private void determineLMDirection(double[] qy, double[] diag,
+                                    double[] lmDiag, double[] work) {
+
+    // copy R and Qty to preserve input and initialize s
+    //  in particular, save the diagonal elements of R in lmDir
+    for (int j = 0; j < solvedCols; ++j) {
+      int pj = permutation[j];
+      for (int i = j + 1; i < solvedCols; ++i) {
+        jacobian[i * cols + pj] = jacobian[j * cols + permutation[i]];
+      }
+      lmDir[j] = diagR[pj];
+      work[j]  = qy[j];
+    }
+
+    // eliminate the diagonal matrix d using a Givens rotation
+    for (int j = 0; j < solvedCols; ++j) {
+
+      // prepare the row of d to be eliminated, locating the
+      // diagonal element using p from the Q.R. factorization
+      int pj = permutation[j];
+      double dpj = diag[pj];
+      if (dpj != 0) {
+        Arrays.fill(lmDiag, j + 1, lmDiag.length, 0);
+      }
+      lmDiag[j] = dpj;
+
+      //  the transformations to eliminate the row of d
+      // modify only a single element of Qty
+      // beyond the first n, which is initially zero.
+      double qtbpj = 0;
+      for (int k = j; k < solvedCols; ++k) {
+        int pk = permutation[k];
+
+        // determine a Givens rotation which eliminates the
+        // appropriate element in the current row of d
+        if (lmDiag[k] != 0) {
+
+          double sin, cos;
+          double rkk = jacobian[k * cols + pk];
+          if (Math.abs(rkk) < Math.abs(lmDiag[k])) {
+            double cotan = rkk / lmDiag[k];
+            sin   = 1.0 / Math.sqrt(1.0 + cotan * cotan);
+            cos   = sin * cotan;
+          } else {
+            double tan = lmDiag[k] / rkk;
+            cos = 1.0 / Math.sqrt(1.0 + tan * tan);
+            sin = cos * tan;
+          }
+
+          // compute the modified diagonal element of R and
+          // the modified element of (Qty,0)
+          jacobian[k * cols + pk] = cos * rkk + sin * lmDiag[k];
+          double temp = cos * work[k] + sin * qtbpj;
+          qtbpj = -sin * work[k] + cos * qtbpj;
+          work[k] = temp;
+
+          // accumulate the tranformation in the row of s
+          for (int i = k + 1; i < solvedCols; ++i) {
+            double rik = jacobian[i * cols + pk];
+            temp = cos * rik + sin * lmDiag[i];
+            lmDiag[i] = -sin * rik + cos * lmDiag[i];
+            jacobian[i * cols + pk] = temp;
+          }
+
+        }
+      }
+
+      // store the diagonal element of s and restore
+      // the corresponding diagonal element of R
+      int index = j * cols + permutation[j];
+      lmDiag[j]       = jacobian[index];
+      jacobian[index] = lmDir[j];
+
+    }
+
+    // solve the triangular system for z, if the system is
+    // singular, then obtain a least squares solution
+    int nSing = solvedCols;
+    for (int j = 0; j < solvedCols; ++j) {
+      if ((lmDiag[j] == 0) && (nSing == solvedCols)) {
+        nSing = j;
+      }
+      if (nSing < solvedCols) {
+        work[j] = 0;
+      }
+    }
+    if (nSing > 0) {
+      for (int j = nSing - 1; j >= 0; --j) {
+        int pj = permutation[j];
+        double sum = 0;
+        for (int i = j + 1; i < nSing; ++i) {
+          sum += jacobian[i * cols + pj] * work[i];
+        }
+        work[j] = (work[j] - sum) / lmDiag[j];
+      }
+    }
+
+    // permute the components of z back to components of lmDir
+    for (int j = 0; j < lmDir.length; ++j) {
+      lmDir[permutation[j]] = work[j];
+    }
+
+  }
+
+  /** 
+   * Decompose a matrix A as A.P = Q.R using Householder transforms.
+   * <p>As suggested in the P. Lascaux and R. Theodor book
+   * <i>Analyse num&eacute;rique matricielle appliqu&eacute;e &agrave;
+   * l'art de l'ing&eacute;nieur</i> (Masson, 1986), instead of representing
+   * the Householder transforms with u<sub>k</sub> unit vectors such that:
+   * <pre>
+   * H<sub>k</sub> = I - 2u<sub>k</sub>.u<sub>k</sub><sup>t</sup>
+   * </pre>
+   * we use <sub>k</sub> non-unit vectors such that:
+   * <pre>
+   * H<sub>k</sub> = I - beta<sub>k</sub>v<sub>k</sub>.v<sub>k</sub><sup>t</sup>
+   * </pre>
+   * where v<sub>k</sub> = a<sub>k</sub> - alpha<sub>k</sub> e<sub>k</sub>.
+   * The beta<sub>k</sub> coefficients are provided upon exit as recomputing
+   * them from the v<sub>k</sub> vectors would be costly.</p>
+   * <p>This decomposition handles rank deficient cases since the tranformations
+   * are performed in non-increasing columns norms order thanks to columns
+   * pivoting. The diagonal elements of the R matrix are therefore also in
+   * non-increasing absolute values order.</p>
+   * @exception EstimationException if the decomposition cannot be performed
+   */
+  private void qrDecomposition() throws EstimationException {
+
+    // initializations
+    for (int k = 0; k < cols; ++k) {
+      permutation[k] = k;
+      double norm2 = 0;
+      for (int index = k; index < jacobian.length; index += cols) {
+        double akk = jacobian[index];
+        norm2 += akk * akk;
+      }
+      jacNorm[k] = Math.sqrt(norm2);
+    }
+
+    // transform the matrix column after column
+    for (int k = 0; k < cols; ++k) {
+
+      // select the column with the greatest norm on active components
+      int nextColumn = -1;
+      double ak2 = Double.NEGATIVE_INFINITY;
+      for (int i = k; i < cols; ++i) {
+        double norm2 = 0;
+        int iDiag = k * cols + permutation[i];
+        for (int index = iDiag; index < jacobian.length; index += cols) {
+          double aki = jacobian[index];
+          norm2 += aki * aki;
+        }
+        if (Double.isInfinite(norm2) || Double.isNaN(norm2)) {
+            throw new EstimationException(
+                    "unable to perform Q.R decomposition on the {0}x{1} jacobian matrix",
+                    rows, cols);
+        }
+        if (norm2 > ak2) {
+          nextColumn = i;
+          ak2        = norm2;
+        }
+      }
+      if (ak2 == 0) {
+        rank = k;
+        return;
+      }
+      int pk                  = permutation[nextColumn];
+      permutation[nextColumn] = permutation[k];
+      permutation[k]          = pk;
+
+      // choose alpha such that Hk.u = alpha ek
+      int    kDiag = k * cols + pk;
+      double akk   = jacobian[kDiag];
+      double alpha = (akk > 0) ? -Math.sqrt(ak2) : Math.sqrt(ak2);
+      double betak = 1.0 / (ak2 - akk * alpha);
+      beta[pk]     = betak;
+
+      // transform the current column
+      diagR[pk]        = alpha;
+      jacobian[kDiag] -= alpha;
+
+      // transform the remaining columns
+      for (int dk = cols - 1 - k; dk > 0; --dk) {
+        int dkp = permutation[k + dk] - pk;
+        double gamma = 0;
+        for (int index = kDiag; index < jacobian.length; index += cols) {
+          gamma += jacobian[index] * jacobian[index + dkp];
+        }
+        gamma *= betak;
+        for (int index = kDiag; index < jacobian.length; index += cols) {
+          jacobian[index + dkp] -= gamma * jacobian[index];
+        }
+      }
+
+    }
+
+    rank = solvedCols;
+
+  }
+
+  /** 
+   * Compute the product Qt.y for some Q.R. decomposition.
+   * 
+   * @param y vector to multiply (will be overwritten with the result)
+   */
+  private void qTy(double[] y) {
+    for (int k = 0; k < cols; ++k) {
+      int pk = permutation[k];
+      int kDiag = k * cols + pk;
+      double gamma = 0;
+      for (int i = k, index = kDiag; i < rows; ++i, index += cols) {
+        gamma += jacobian[index] * y[i];
+      }
+      gamma *= beta[pk];
+      for (int i = k, index = kDiag; i < rows; ++i, index += cols) {
+        y[i] -= gamma * jacobian[index];
+      }
+    }
+  }
+
+  /** Number of solved variables. */
+  private int solvedCols;
+
+  /** Diagonal elements of the R matrix in the Q.R. decomposition. */
+  private double[] diagR;
+
+  /** Norms of the columns of the jacobian matrix. */
+  private double[] jacNorm;
+
+  /** Coefficients of the Householder transforms vectors. */
+  private double[] beta;
+
+  /** Columns permutation array. */
+  private int[] permutation;
+
+  /** Rank of the jacobian matrix. */
+  private int rank;
+
+  /** Levenberg-Marquardt parameter. */
+  private double lmPar;
+
+  /** Parameters evolution direction associated with lmPar. */
+  private double[] lmDir;
+
+  /** Positive input variable used in determining the initial step bound. */
+  private double initialStepBoundFactor;
+
+  /** Desired relative error in the sum of squares. */
+  private double costRelativeTolerance;
+
+  /**  Desired relative error in the approximate solution parameters. */
+  private double parRelativeTolerance;
+
+  /** Desired max cosine on the orthogonality between the function vector
+   * and the columns of the jacobian. */
+  private double orthoTolerance;
+
+  /** Serializable version identifier */
+  private static final long serialVersionUID = -5705952631533171019L;
+
+}

src/java/org/apache/commons/math/estimation/SimpleEstimationProblem.java

@@ -0,0 +1,111 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements.  See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License.  You may obtain a copy of the License at
+ *
+ *      http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+package org.apache.commons.math.estimation;
+
+import java.util.ArrayList;
+import java.util.List;
+
+/**
+ * Simple implementation of the {@link EstimationProblem
+ * EstimationProblem} interface for boilerplate data handling.
+ * <p>This class <em>only</em> handles parameters and measurements
+ * storage and unbound parameters filtering. It does not compute
+ * anything by itself. It should either be used with measurements
+ * implementation that are smart enough to know about the
+ * various parameters in order to compute the partial derivatives
+ * appropriately. Since the problem-specific logic is mainly related to
+ * the various measurements models, the simplest way to use this class
+ * is by extending it and using one internal class extending
+ * {@link WeightedMeasurement WeightedMeasurement} for each measurement
+ * type. The instances of the internal classes would have access to the
+ * various parameters and their current estimate.</p>
+
+ * @version $Revision$ $Date$
+ * @since 1.2
+ * @deprecated as of 2.0, everything in package org.apache.commons.math.estimation has
+ * been deprecated and replaced by package org.apache.commons.math.optimization.general
+
+ */
+@Deprecated
+public class SimpleEstimationProblem implements EstimationProblem {
+
+    /**
+     * Build an empty instance without parameters nor measurements.
+     */
+    public SimpleEstimationProblem() {
+        parameters   = new ArrayList<EstimatedParameter>();
+        measurements = new ArrayList<WeightedMeasurement>();
+    }
+
+    /** 
+     * Get all the parameters of the problem.
+     * @return parameters
+     */
+    public EstimatedParameter[] getAllParameters() {
+        return (EstimatedParameter[]) parameters.toArray(new EstimatedParameter[parameters.size()]);
+    }
+
+    /** 
+     * Get the unbound parameters of the problem.
+     * @return unbound parameters
+     */
+    public EstimatedParameter[] getUnboundParameters() {
+
+        // filter the unbound parameters
+        List<EstimatedParameter> unbound = new ArrayList<EstimatedParameter>(parameters.size());
+        for (EstimatedParameter p : parameters) {
+            if (! p.isBound()) {
+                unbound.add(p);
+            }
+        }
+
+        // convert to an array
+        return (EstimatedParameter[]) unbound.toArray(new EstimatedParameter[unbound.size()]);
+        
+    }
+
+    /** 
+     * Get the measurements of an estimation problem.
+     * @return measurements
+     */
+    public WeightedMeasurement[] getMeasurements() {
+        return (WeightedMeasurement[]) measurements.toArray(new WeightedMeasurement[measurements.size()]);
+    }
+
+    /** Add a parameter to the problem.
+     * @param p parameter to add
+     */
+    protected void addParameter(EstimatedParameter p) {
+        parameters.add(p);
+    }
+
+    /**
+     * Add a new measurement to the set.
+     * @param m measurement to add
+     */
+    protected void addMeasurement(WeightedMeasurement m) {
+        measurements.add(m);
+    }
+
+    /** Estimated parameters. */
+    private final List<EstimatedParameter> parameters;
+
+    /** Measurements. */
+    private final List<WeightedMeasurement> measurements;
+
+}

src/java/org/apache/commons/math/estimation/WeightedMeasurement.java

@@ -0,0 +1,172 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements.  See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License.  You may obtain a copy of the License at
+ *
+ *      http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+package org.apache.commons.math.estimation;
+
+import java.io.Serializable;
+
+/** 
+ * This class represents measurements in estimation problems.
+ *
+ * <p>This abstract class implements all the methods needed to handle
+ * measurements in a general way. It defines neither the {@link
+ * #getTheoreticalValue getTheoreticalValue} nor the {@link
+ * #getPartial getPartial} methods, which should be defined by
+ * sub-classes according to the specific problem.</p>
+ *
+ * <p>The {@link #getTheoreticalValue getTheoreticalValue} and {@link
+ * #getPartial getPartial} methods must always use the current
+ * estimate of the parameters set by the solver in the problem. These
+ * parameters can be retrieved through the {@link
+ * EstimationProblem#getAllParameters
+ * EstimationProblem.getAllParameters} method if the measurements are
+ * independent of the problem, or directly if they are implemented as
+ * inner classes of the problem.</p>
+ *
+ * <p>The instances for which the <code>ignored</code> flag is set
+ * through the {@link #setIgnored setIgnored} method are ignored by the
+ * solvers. This can be used to reject wrong measurements at some
+ * steps of the estimation.</p>
+ *
+ * @see EstimationProblem
+ *
+ * @version $Revision$ $Date$
+ * @since 1.2
+ * @deprecated as of 2.0, everything in package org.apache.commons.math.estimation has
+ * been deprecated and replaced by package org.apache.commons.math.optimization.general
+ */
+
+@Deprecated
+public abstract class WeightedMeasurement implements Serializable {
+
+    /** Serializable version identifier. */
+    private static final long serialVersionUID = 4360046376796901941L;
+
+    /** 
+   * Simple constructor.
+   * Build a measurement with the given parameters, and set its ignore
+   * flag to false.
+   * @param weight weight of the measurement in the least squares problem
+   * (two common choices are either to use 1.0 for all measurements, or to
+   * use a value proportional to the inverse of the variance of the measurement
+   * type)
+   * 
+   * @param measuredValue measured value
+   */
+  public WeightedMeasurement(double weight, double measuredValue) {
+    this.weight        = weight;
+    this.measuredValue = measuredValue;
+    ignored            = false;
+  }
+
+  /** Simple constructor.
+   * 
+   * Build a measurement with the given parameters
+   * 
+   * @param weight weight of the measurement in the least squares problem
+   * @param measuredValue measured value
+   * @param ignored true if the measurement should be ignored
+   */
+  public WeightedMeasurement(double weight, double measuredValue,
+                             boolean ignored) {
+    this.weight        = weight;
+    this.measuredValue = measuredValue;
+    this.ignored       = ignored;
+  }
+
+  /** 
+   * Get the weight of the measurement in the least squares problem
+   * 
+   * @return weight
+   */
+  public double getWeight() {
+    return weight;
+  }
+
+  /** 
+   * Get the measured value
+   * 
+   * @return measured value
+   */
+  public double getMeasuredValue() {
+    return measuredValue;
+  }
+
+  /** 
+   * Get the residual for this measurement
+   * The residual is the measured value minus the theoretical value.
+   * 
+   * @return residual
+   */
+  public double getResidual() {
+    return measuredValue - getTheoreticalValue();
+  }
+
+  /** 
+   * Get the theoretical value expected for this measurement
+   * <p>The theoretical value is the value expected for this measurement
+   * if the model and its parameter were all perfectly known.</p>
+   * <p>The value must be computed using the current estimate of the parameters
+   * set by the solver in the problem.</p>
+   * 
+   * @return theoretical value
+   */
+  public abstract double getTheoreticalValue();
+
+  /** 
+   * Get the partial derivative of the {@link #getTheoreticalValue
+   * theoretical value} according to the parameter.
+   * <p>The value must be computed using the current estimate of the parameters
+   * set by the solver in the problem.</p>
+   * 
+   * @param parameter parameter against which the partial derivative
+   * should be computed
+   * @return partial derivative of the {@link #getTheoreticalValue
+   * theoretical value}
+   */
+  public abstract double getPartial(EstimatedParameter parameter);
+
+  /** 
+   * Set the ignore flag to the specified value
+   * Setting the ignore flag to true allow to reject wrong
+   * measurements, which sometimes can be detected only rather late.
+   * 
+   * @param ignored value for the ignore flag
+   */
+  public void setIgnored(boolean ignored) {
+    this.ignored = ignored;
+  }
+
+  /** 
+   * Check if this measurement should be ignored
+   * 
+   * @return true if the measurement should be ignored
+   */
+  public boolean isIgnored() {
+    return ignored;
+  }
+
+  /** Measurement weight. */
+  private final double  weight;
+
+  /** Value of the measurements. */
+  private final double  measuredValue;
+
+  /** Ignore measurement indicator. */
+  private       boolean ignored;
+
+}

src/java/org/apache/commons/math/estimation/package.html

@@ -0,0 +1,25 @@
+<html>
+<!--
+   Licensed to the Apache Software Foundation (ASF) under one or more
+  contributor license agreements.  See the NOTICE file distributed with
+  this work for additional information regarding copyright ownership.
+  The ASF licenses this file to You under the Apache License, Version 2.0
+  (the "License"); you may not use this file except in compliance with
+  the License.  You may obtain a copy of the License at
+
+       http://www.apache.org/licenses/LICENSE-2.0
+
+   Unless required by applicable law or agreed to in writing, software
+   distributed under the License is distributed on an "AS IS" BASIS,
+   WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+   See the License for the specific language governing permissions and
+   limitations under the License.
+  -->
+    <!-- $Revision$ -->
+<body>
+This package provided classes to solve estimation problems, it is deprecated since 2.0.
+
+<p>This package has been deprecated as of 2.0. It is replaced by the optimization.general package.</p>
+
+</body>
+</html>

src/test/org/apache/commons/math/estimation/EstimatedParameterTest.java

@@ -0,0 +1,77 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements.  See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License.  You may obtain a copy of the License at
+ *
+ *      http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+package org.apache.commons.math.estimation;
+
+import org.apache.commons.math.estimation.EstimatedParameter;
+
+import junit.framework.*;
+
+@Deprecated
+public class EstimatedParameterTest
+  extends TestCase {
+
+  public EstimatedParameterTest(String name) {
+    super(name);
+  }
+
+  public void testConstruction() {
+
+    EstimatedParameter p1 = new EstimatedParameter("p1", 1.0);
+    assertTrue(p1.getName().equals("p1"));
+    checkValue(p1.getEstimate(), 1.0);
+    assertTrue(! p1.isBound());
+
+    EstimatedParameter p2 = new EstimatedParameter("p2", 2.0, true);
+    assertTrue(p2.getName().equals("p2"));
+    checkValue(p2.getEstimate(), 2.0);
+    assertTrue(p2.isBound());
+
+  }
+
+  public void testBound() {
+
+    EstimatedParameter p = new EstimatedParameter("p", 0.0);
+    assertTrue(! p.isBound());
+    p.setBound(true);
+    assertTrue(p.isBound());
+    p.setBound(false);
+    assertTrue(! p.isBound());
+
+  }
+
+  public void testEstimate() {
+
+    EstimatedParameter p = new EstimatedParameter("p", 0.0);
+    checkValue(p.getEstimate(), 0.0);
+
+    for (double e = 0.0; e < 10.0; e += 0.5) {
+      p.setEstimate(e);
+      checkValue(p.getEstimate(), e);
+    }
+
+  }
+
+  public static Test suite() {
+    return new TestSuite(EstimatedParameterTest.class);
+  }
+
+  private void checkValue(double value, double expected) {
+    assertTrue(Math.abs(value - expected) < 1.0e-10);
+  }
+
+}

src/test/org/apache/commons/math/estimation/GaussNewtonEstimatorTest.java

@@ -0,0 +1,732 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements.  See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License.  You may obtain a copy of the License at
+ *
+ *      http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+package org.apache.commons.math.estimation;
+
+import java.util.ArrayList;
+import java.util.HashSet;
+
+import junit.framework.Test;
+import junit.framework.TestCase;
+import junit.framework.TestSuite;
+
+/**
+ * <p>Some of the unit tests are re-implementations of the MINPACK <a
+ * href="http://www.netlib.org/minpack/ex/file17">file17</a> and <a
+ * href="http://www.netlib.org/minpack/ex/file22">file22</a> test files. 
+ * The redistribution policy for MINPACK is available <a
+ * href="http://www.netlib.org/minpack/disclaimer">here</a>, for
+ * convenience, it is reproduced below.</p>
+
+ * <table border="0" width="80%" cellpadding="10" align="center" bgcolor="#E0E0E0">
+ * <tr><td>
+ *    Minpack Copyright Notice (1999) University of Chicago.
+ *    All rights reserved
+ * </td></tr>
+ * <tr><td>
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ * <ol>
+ *  <li>Redistributions of source code must retain the above copyright
+ *      notice, this list of conditions and the following disclaimer.</li>
+ * <li>Redistributions in binary form must reproduce the above
+ *     copyright notice, this list of conditions and the following
+ *     disclaimer in the documentation and/or other materials provided
+ *     with the distribution.</li>
+ * <li>The end-user documentation included with the redistribution, if any,
+ *     must include the following acknowledgment:
+ *     <code>This product includes software developed by the University of
+ *           Chicago, as Operator of Argonne National Laboratory.</code>
+ *     Alternately, this acknowledgment may appear in the software itself,
+ *     if and wherever such third-party acknowledgments normally appear.</li>
+ * <li><strong>WARRANTY DISCLAIMER. THE SOFTWARE IS SUPPLIED "AS IS"
+ *     WITHOUT WARRANTY OF ANY KIND. THE COPYRIGHT HOLDER, THE
+ *     UNITED STATES, THE UNITED STATES DEPARTMENT OF ENERGY, AND
+ *     THEIR EMPLOYEES: (1) DISCLAIM ANY WARRANTIES, EXPRESS OR
+ *     IMPLIED, INCLUDING BUT NOT LIMITED TO ANY IMPLIED WARRANTIES
+ *     OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE, TITLE
+ *     OR NON-INFRINGEMENT, (2) DO NOT ASSUME ANY LEGAL LIABILITY
+ *     OR RESPONSIBILITY FOR THE ACCURACY, COMPLETENESS, OR
+ *     USEFULNESS OF THE SOFTWARE, (3) DO NOT REPRESENT THAT USE OF
+ *     THE SOFTWARE WOULD NOT INFRINGE PRIVATELY OWNED RIGHTS, (4)
+ *     DO NOT WARRANT THAT THE SOFTWARE WILL FUNCTION
+ *     UNINTERRUPTED, THAT IT IS ERROR-FREE OR THAT ANY ERRORS WILL
+ *     BE CORRECTED.</strong></li>
+ * <li><strong>LIMITATION OF LIABILITY. IN NO EVENT WILL THE COPYRIGHT
+ *     HOLDER, THE UNITED STATES, THE UNITED STATES DEPARTMENT OF
+ *     ENERGY, OR THEIR EMPLOYEES: BE LIABLE FOR ANY INDIRECT,
+ *     INCIDENTAL, CONSEQUENTIAL, SPECIAL OR PUNITIVE DAMAGES OF
+ *     ANY KIND OR NATURE, INCLUDING BUT NOT LIMITED TO LOSS OF
+ *     PROFITS OR LOSS OF DATA, FOR ANY REASON WHATSOEVER, WHETHER
+ *     SUCH LIABILITY IS ASSERTED ON THE BASIS OF CONTRACT, TORT
+ *     (INCLUDING NEGLIGENCE OR STRICT LIABILITY), OR OTHERWISE,
+ *     EVEN IF ANY OF SAID PARTIES HAS BEEN WARNED OF THE
+ *     POSSIBILITY OF SUCH LOSS OR DAMAGES.</strong></li>
+ * <ol></td></tr>
+ * </table>
+
+ * @author Argonne National Laboratory. MINPACK project. March 1980 (original fortran minpack tests)
+ * @author Burton S. Garbow (original fortran minpack tests)
+ * @author Kenneth E. Hillstrom (original fortran minpack tests)
+ * @author Jorge J. More (original fortran minpack tests)
+ * @author Luc Maisonobe (non-minpack tests and minpack tests Java translation)
+ */
+@Deprecated
+public class GaussNewtonEstimatorTest
+  extends TestCase {
+
+  public GaussNewtonEstimatorTest(String name) {
+    super(name);
+  }
+
+  public void testTrivial() throws EstimationException {
+    LinearProblem problem =
+      new LinearProblem(new LinearMeasurement[] {
+        new LinearMeasurement(new double[] {2},
+                              new EstimatedParameter[] {
+                                 new EstimatedParameter("p0", 0)
+                              }, 3.0)
+      });
+    GaussNewtonEstimator estimator = new GaussNewtonEstimator(100, 1.0e-6, 1.0e-6);
+    estimator.estimate(problem);
+    assertEquals(0, estimator.getRMS(problem), 1.0e-10);
+    assertEquals(1.5,
+                 problem.getUnboundParameters()[0].getEstimate(),
+                 1.0e-10);
+   }
+
+  public void testQRColumnsPermutation() throws EstimationException {
+
+    EstimatedParameter[] x = {
+       new EstimatedParameter("p0", 0), new EstimatedParameter("p1", 0)
+    };
+    LinearProblem problem = new LinearProblem(new LinearMeasurement[] {
+      new LinearMeasurement(new double[] { 1.0, -1.0 },
+                            new EstimatedParameter[] { x[0], x[1] },
+                            4.0),
+      new LinearMeasurement(new double[] { 2.0 },
+                            new EstimatedParameter[] { x[1] },
+                            6.0),
+      new LinearMeasurement(new double[] { 1.0, -2.0 },
+                            new EstimatedParameter[] { x[0], x[1] },
+                            1.0)
+    });
+
+    GaussNewtonEstimator estimator = new GaussNewtonEstimator(100, 1.0e-6, 1.0e-6);
+    estimator.estimate(problem);
+    assertEquals(0, estimator.getRMS(problem), 1.0e-10);
+    assertEquals(7.0, x[0].getEstimate(), 1.0e-10);
+    assertEquals(3.0, x[1].getEstimate(), 1.0e-10);
+
+  }
+
+  public void testNoDependency() throws EstimationException {
+    EstimatedParameter[] p = new EstimatedParameter[] {
+      new EstimatedParameter("p0", 0),
+      new EstimatedParameter("p1", 0),
+      new EstimatedParameter("p2", 0),
+      new EstimatedParameter("p3", 0),
+      new EstimatedParameter("p4", 0),
+      new EstimatedParameter("p5", 0)
+    };
+    LinearProblem problem = new LinearProblem(new LinearMeasurement[] {
+      new LinearMeasurement(new double[] {2}, new EstimatedParameter[] { p[0] }, 0.0),
+      new LinearMeasurement(new double[] {2}, new EstimatedParameter[] { p[1] }, 1.1),
+      new LinearMeasurement(new double[] {2}, new EstimatedParameter[] { p[2] }, 2.2),
+      new LinearMeasurement(new double[] {2}, new EstimatedParameter[] { p[3] }, 3.3),
+      new LinearMeasurement(new double[] {2}, new EstimatedParameter[] { p[4] }, 4.4),
+      new LinearMeasurement(new double[] {2}, new EstimatedParameter[] { p[5] }, 5.5)
+    });
+  GaussNewtonEstimator estimator = new GaussNewtonEstimator(100, 1.0e-6, 1.0e-6);
+  estimator.estimate(problem);
+  assertEquals(0, estimator.getRMS(problem), 1.0e-10);
+  for (int i = 0; i < p.length; ++i) {
+    assertEquals(0.55 * i, p[i].getEstimate(), 1.0e-10);
+  }
+}
+
+  public void testOneSet() throws EstimationException {
+
+    EstimatedParameter[] p = {
+       new EstimatedParameter("p0", 0),
+       new EstimatedParameter("p1", 0),
+       new EstimatedParameter("p2", 0)
+    };
+    LinearProblem problem = new LinearProblem(new LinearMeasurement[] {
+      new LinearMeasurement(new double[] { 1.0 },
+                            new EstimatedParameter[] { p[0] },
+                            1.0),
+      new LinearMeasurement(new double[] { -1.0, 1.0 },
+                            new EstimatedParameter[] { p[0], p[1] },
+                            1.0),
+      new LinearMeasurement(new double[] { -1.0, 1.0 },
+                            new EstimatedParameter[] { p[1], p[2] },
+                            1.0)
+    });
+
+    GaussNewtonEstimator estimator = new GaussNewtonEstimator(100, 1.0e-6, 1.0e-6);
+    estimator.estimate(problem);
+    assertEquals(0, estimator.getRMS(problem), 1.0e-10);
+    assertEquals(1.0, p[0].getEstimate(), 1.0e-10);
+    assertEquals(2.0, p[1].getEstimate(), 1.0e-10);
+    assertEquals(3.0, p[2].getEstimate(), 1.0e-10);
+
+  }
+
+  public void testTwoSets() throws EstimationException {
+    EstimatedParameter[] p = {
+      new EstimatedParameter("p0", 0),
+      new EstimatedParameter("p1", 1),
+      new EstimatedParameter("p2", 2),
+      new EstimatedParameter("p3", 3),
+      new EstimatedParameter("p4", 4),
+      new EstimatedParameter("p5", 5)
+    };
+
+    double epsilon = 1.0e-7;
+    LinearProblem problem = new LinearProblem(new LinearMeasurement[] {
+
+      // 4 elements sub-problem
+      new LinearMeasurement(new double[] {  2.0,  1.0,  4.0 },
+                            new EstimatedParameter[] { p[0], p[1], p[3] },
+                            2.0),
+      new LinearMeasurement(new double[] { -4.0, -2.0,   3.0, -7.0 },
+                           new EstimatedParameter[] { p[0], p[1], p[2], p[3] },
+                           -9.0),
+      new LinearMeasurement(new double[] {  4.0,  1.0,  -2.0,  8.0 },
+                            new EstimatedParameter[] { p[0], p[1], p[2], p[3] },
+                            2.0),
+      new LinearMeasurement(new double[] { -3.0, -12.0, -1.0 },
+                           new EstimatedParameter[] { p[1], p[2], p[3] },
+                           2.0),
+
+      // 2 elements sub-problem
+      new LinearMeasurement(new double[] { epsilon, 1.0 },
+                            new EstimatedParameter[] { p[4], p[5] },
+                            1.0 + epsilon * epsilon),
+      new LinearMeasurement(new double[] {  1.0, 1.0 },
+                            new EstimatedParameter[] { p[4], p[5] },
+                            2.0)
+
+    });
+
+    GaussNewtonEstimator estimator = new GaussNewtonEstimator(100, 1.0e-6, 1.0e-6);
+    estimator.estimate(problem);
+    assertEquals(0, estimator.getRMS(problem), 1.0e-10);
+    assertEquals( 3.0, p[0].getEstimate(), 1.0e-10);
+    assertEquals( 4.0, p[1].getEstimate(), 1.0e-10);
+    assertEquals(-1.0, p[2].getEstimate(), 1.0e-10);
+    assertEquals(-2.0, p[3].getEstimate(), 1.0e-10);
+    assertEquals( 1.0 + epsilon, p[4].getEstimate(), 1.0e-10);
+    assertEquals( 1.0 - epsilon, p[5].getEstimate(), 1.0e-10);
+
+  }
+
+  public void testNonInversible() throws EstimationException {
+
+    EstimatedParameter[] p = {
+       new EstimatedParameter("p0", 0),
+       new EstimatedParameter("p1", 0),
+       new EstimatedParameter("p2", 0)
+    };
+    LinearMeasurement[] m = new LinearMeasurement[] {
+      new LinearMeasurement(new double[] {  1.0, 2.0, -3.0 },
+                            new EstimatedParameter[] { p[0], p[1], p[2] },
+                            1.0),
+      new LinearMeasurement(new double[] {  2.0, 1.0,  3.0 },
+                            new EstimatedParameter[] { p[0], p[1], p[2] },
+                            1.0),
+      new LinearMeasurement(new double[] { -3.0, -9.0 },
+                            new EstimatedParameter[] { p[0], p[2] },
+                            1.0)
+    };
+    LinearProblem problem = new LinearProblem(m);
+
+    GaussNewtonEstimator estimator = new GaussNewtonEstimator(100, 1.0e-6, 1.0e-6);
+    try {
+      estimator.estimate(problem);
+      fail("an exception should have been caught");
+    } catch (EstimationException ee) {
+      // expected behavior
+    } catch (Exception e) {
+      fail("wrong exception type caught");
+    }
+  }
+
+  public void testIllConditioned() throws EstimationException {
+    EstimatedParameter[] p = {
+      new EstimatedParameter("p0", 0),
+      new EstimatedParameter("p1", 1),
+      new EstimatedParameter("p2", 2),
+      new EstimatedParameter("p3", 3)
+    };
+
+    LinearProblem problem1 = new LinearProblem(new LinearMeasurement[] {
+      new LinearMeasurement(new double[] { 10.0, 7.0,  8.0,  7.0 },
+                            new EstimatedParameter[] { p[0], p[1], p[2], p[3] },
+                            32.0),
+      new LinearMeasurement(new double[] {  7.0, 5.0,  6.0,  5.0 },
+                            new EstimatedParameter[] { p[0], p[1], p[2], p[3] },
+                            23.0),
+      new LinearMeasurement(new double[] {  8.0, 6.0, 10.0,  9.0 },
+                            new EstimatedParameter[] { p[0], p[1], p[2], p[3] },
+                            33.0),
+      new LinearMeasurement(new double[] {  7.0, 5.0,  9.0, 10.0 },
+                            new EstimatedParameter[] { p[0], p[1], p[2], p[3] },
+                            31.0)
+    });
+    GaussNewtonEstimator estimator1 = new GaussNewtonEstimator(100, 1.0e-6, 1.0e-6);
+    estimator1.estimate(problem1);
+    assertEquals(0, estimator1.getRMS(problem1), 1.0e-10);
+    assertEquals(1.0, p[0].getEstimate(), 1.0e-10);
+    assertEquals(1.0, p[1].getEstimate(), 1.0e-10);
+    assertEquals(1.0, p[2].getEstimate(), 1.0e-10);
+    assertEquals(1.0, p[3].getEstimate(), 1.0e-10);
+
+    LinearProblem problem2 = new LinearProblem(new LinearMeasurement[] {
+      new LinearMeasurement(new double[] { 10.0, 7.0,  8.1,  7.2 },
+                            new EstimatedParameter[] { p[0], p[1], p[2], p[3] },
+                            32.0),
+      new LinearMeasurement(new double[] {  7.08, 5.04,  6.0,  5.0 },
+                            new EstimatedParameter[] { p[0], p[1], p[2], p[3] },
+                            23.0),
+      new LinearMeasurement(new double[] {  8.0, 5.98, 9.89,  9.0 },
+                             new EstimatedParameter[] { p[0], p[1], p[2], p[3] },
+                            33.0),
+      new LinearMeasurement(new double[] {  6.99, 4.99,  9.0, 9.98 },
+                             new EstimatedParameter[] { p[0], p[1], p[2], p[3] },
+                            31.0)
+    });
+    GaussNewtonEstimator estimator2 = new GaussNewtonEstimator(100, 1.0e-6, 1.0e-6);
+    estimator2.estimate(problem2);
+    assertEquals(0, estimator2.getRMS(problem2), 1.0e-10);
+    assertEquals(-81.0, p[0].getEstimate(), 1.0e-8);
+    assertEquals(137.0, p[1].getEstimate(), 1.0e-8);
+    assertEquals(-34.0, p[2].getEstimate(), 1.0e-8);
+    assertEquals( 22.0, p[3].getEstimate(), 1.0e-8);
+
+  }
+
+  public void testMoreEstimatedParametersSimple() throws EstimationException {
+
+    EstimatedParameter[] p = {
+       new EstimatedParameter("p0", 7),
+       new EstimatedParameter("p1", 6),
+       new EstimatedParameter("p2", 5),
+       new EstimatedParameter("p3", 4)
+     };
+    LinearProblem problem = new LinearProblem(new LinearMeasurement[] {
+      new LinearMeasurement(new double[] { 3.0, 2.0 },
+                             new EstimatedParameter[] { p[0], p[1] },
+                             7.0),
+      new LinearMeasurement(new double[] { 1.0, -1.0, 1.0 },
+                             new EstimatedParameter[] { p[1], p[2], p[3] },
+                             3.0),
+      new LinearMeasurement(new double[] { 2.0, 1.0 },
+                             new EstimatedParameter[] { p[0], p[2] },
+                             5.0)
+    });
+
+    GaussNewtonEstimator estimator = new GaussNewtonEstimator(100, 1.0e-6, 1.0e-6);
+    try {
+        estimator.estimate(problem);
+        fail("an exception should have been caught");
+    } catch (EstimationException ee) {
+        // expected behavior
+    } catch (Exception e) {
+        fail("wrong exception type caught");
+    }
+
+  }
+
+  public void testMoreEstimatedParametersUnsorted() throws EstimationException {
+    EstimatedParameter[] p = {
+      new EstimatedParameter("p0", 2),
+      new EstimatedParameter("p1", 2),
+      new EstimatedParameter("p2", 2),
+      new EstimatedParameter("p3", 2),
+      new EstimatedParameter("p4", 2),
+      new EstimatedParameter("p5", 2)
+    };
+    LinearProblem problem = new LinearProblem(new LinearMeasurement[] {
+      new LinearMeasurement(new double[] { 1.0, 1.0 },
+                           new EstimatedParameter[] { p[0], p[1] },
+                           3.0),
+      new LinearMeasurement(new double[] { 1.0, 1.0, 1.0 },
+                           new EstimatedParameter[] { p[2], p[3], p[4] },
+                           12.0),
+      new LinearMeasurement(new double[] { 1.0, -1.0 },
+                           new EstimatedParameter[] { p[4], p[5] },
+                           -1.0),
+      new LinearMeasurement(new double[] { 1.0, -1.0, 1.0 },
+                           new EstimatedParameter[] { p[3], p[2], p[5] },
+                           7.0),
+      new LinearMeasurement(new double[] { 1.0, -1.0 },
+                           new EstimatedParameter[] { p[4], p[3] },
+                           1.0)
+    });
+
+    GaussNewtonEstimator estimator = new GaussNewtonEstimator(100, 1.0e-6, 1.0e-6);
+    try {
+        estimator.estimate(problem);
+        fail("an exception should have been caught");
+    } catch (EstimationException ee) {
+        // expected behavior
+    } catch (Exception e) {
+        fail("wrong exception type caught");
+    }
+
+  }
+
+  public void testRedundantEquations() throws EstimationException {
+    EstimatedParameter[] p = {
+      new EstimatedParameter("p0", 1),
+      new EstimatedParameter("p1", 1)
+    };
+    LinearProblem problem = new LinearProblem(new LinearMeasurement[] {
+      new LinearMeasurement(new double[] { 1.0, 1.0 },
+                             new EstimatedParameter[] { p[0], p[1] },
+                             3.0),
+      new LinearMeasurement(new double[] { 1.0, -1.0 },
+                             new EstimatedParameter[] { p[0], p[1] },
+                             1.0),
+      new LinearMeasurement(new double[] { 1.0, 3.0 },
+                             new EstimatedParameter[] { p[0], p[1] },
+                             5.0)
+    });
+
+    GaussNewtonEstimator estimator = new GaussNewtonEstimator(100, 1.0e-6, 1.0e-6);
+    estimator.estimate(problem);
+    assertEquals(0, estimator.getRMS(problem), 1.0e-10);
+    EstimatedParameter[] all = problem.getAllParameters();
+    for (int i = 0; i < all.length; ++i) {
+        assertEquals(all[i].getName().equals("p0") ? 2.0 : 1.0,
+                     all[i].getEstimate(), 1.0e-10);
+    }
+
+  }
+
+  public void testInconsistentEquations() throws EstimationException {
+    EstimatedParameter[] p = {
+      new EstimatedParameter("p0", 1),
+      new EstimatedParameter("p1", 1)
+    };
+    LinearProblem problem = new LinearProblem(new LinearMeasurement[] {
+      new LinearMeasurement(new double[] { 1.0, 1.0 },
+                            new EstimatedParameter[] { p[0], p[1] },
+                            3.0),
+      new LinearMeasurement(new double[] { 1.0, -1.0 },
+                            new EstimatedParameter[] { p[0], p[1] },
+                            1.0),
+      new LinearMeasurement(new double[] { 1.0, 3.0 },
+                            new EstimatedParameter[] { p[0], p[1] },
+                            4.0)
+    });
+
+    GaussNewtonEstimator estimator = new GaussNewtonEstimator(100, 1.0e-6, 1.0e-6);
+    estimator.estimate(problem);
+    assertTrue(estimator.getRMS(problem) > 0.1);
+
+  }
+
+  public void testBoundParameters() throws EstimationException {
+      EstimatedParameter[] p = {
+        new EstimatedParameter("unbound0", 2, false),
+        new EstimatedParameter("unbound1", 2, false),
+        new EstimatedParameter("bound",    2, true)
+      };
+      LinearProblem problem = new LinearProblem(new LinearMeasurement[] {
+        new LinearMeasurement(new double[] { 1.0, 1.0, 1.0 },
+                              new EstimatedParameter[] { p[0], p[1], p[2] },
+                              3.0),
+        new LinearMeasurement(new double[] { 1.0, -1.0, 1.0 },
+                              new EstimatedParameter[] { p[0], p[1], p[2] },
+                              1.0),
+        new LinearMeasurement(new double[] { 1.0, 3.0, 2.0 },
+                              new EstimatedParameter[] { p[0], p[1], p[2] },
+                              7.0)
+      });
+
+      GaussNewtonEstimator estimator = new GaussNewtonEstimator(100, 1.0e-6, 1.0e-6);
+      estimator.estimate(problem);
+      assertTrue(estimator.getRMS(problem) < 1.0e-10);
+      double[][] covariances = estimator.getCovariances(problem);
+      int i0 = 0, i1 = 1;
+      if (problem.getUnboundParameters()[0].getName().endsWith("1")) {
+          i0 = 1;
+          i1 = 0;
+      }
+      assertEquals(11.0 / 24, covariances[i0][i0], 1.0e-10);
+      assertEquals(-3.0 / 24, covariances[i0][i1], 1.0e-10);
+      assertEquals(-3.0 / 24, covariances[i1][i0], 1.0e-10);
+      assertEquals( 3.0 / 24, covariances[i1][i1], 1.0e-10);
+
+      double[] errors = estimator.guessParametersErrors(problem);
+      assertEquals(0, errors[i0], 1.0e-10);
+      assertEquals(0, errors[i1], 1.0e-10);
+
+  }
+
+  public void testMaxIterations() {
+      Circle circle = new Circle(98.680, 47.345);
+      circle.addPoint( 30.0,  68.0);
+      circle.addPoint( 50.0,  -6.0);
+      circle.addPoint(110.0, -20.0);
+      circle.addPoint( 35.0,  15.0);
+      circle.addPoint( 45.0,  97.0);
+      try {
+        GaussNewtonEstimator estimator = new GaussNewtonEstimator(4, 1.0e-14, 1.0e-14);
+        estimator.estimate(circle);
+        fail("an exception should have been caught");
+      } catch (EstimationException ee) {
+        // expected behavior
+      } catch (Exception e) {
+        fail("wrong exception type caught");
+      }
+    }
+
+  public void testCircleFitting() throws EstimationException {
+      Circle circle = new Circle(98.680, 47.345);
+      circle.addPoint( 30.0,  68.0);
+      circle.addPoint( 50.0,  -6.0);
+      circle.addPoint(110.0, -20.0);
+      circle.addPoint( 35.0,  15.0);
+      circle.addPoint( 45.0,  97.0);
+      GaussNewtonEstimator estimator = new GaussNewtonEstimator(100, 1.0e-10, 1.0e-10);
+      estimator.estimate(circle);
+      double rms = estimator.getRMS(circle);
+      assertEquals(1.768262623567235,  Math.sqrt(circle.getM()) * rms,  1.0e-10);
+      assertEquals(69.96016176931406, circle.getRadius(), 1.0e-10);
+      assertEquals(96.07590211815305, circle.getX(),      1.0e-10);
+      assertEquals(48.13516790438953, circle.getY(),      1.0e-10);
+    }
+
+  public void testCircleFittingBadInit() throws EstimationException {
+    Circle circle = new Circle(-12, -12);
+    double[][] points = new double[][] {
+      {-0.312967,  0.072366}, {-0.339248,  0.132965}, {-0.379780,  0.202724},
+      {-0.390426,  0.260487}, {-0.361212,  0.328325}, {-0.346039,  0.392619},
+      {-0.280579,  0.444306}, {-0.216035,  0.470009}, {-0.149127,  0.493832},
+      {-0.075133,  0.483271}, {-0.007759,  0.452680}, { 0.060071,  0.410235},
+      { 0.103037,  0.341076}, { 0.118438,  0.273884}, { 0.131293,  0.192201},
+      { 0.115869,  0.129797}, { 0.072223,  0.058396}, { 0.022884,  0.000718},
+      {-0.053355, -0.020405}, {-0.123584, -0.032451}, {-0.216248, -0.032862},
+      {-0.278592, -0.005008}, {-0.337655,  0.056658}, {-0.385899,  0.112526},
+      {-0.405517,  0.186957}, {-0.415374,  0.262071}, {-0.387482,  0.343398},
+      {-0.347322,  0.397943}, {-0.287623,  0.458425}, {-0.223502,  0.475513},
+      {-0.135352,  0.478186}, {-0.061221,  0.483371}, { 0.003711,  0.422737},
+      { 0.065054,  0.375830}, { 0.108108,  0.297099}, { 0.123882,  0.222850},
+      { 0.117729,  0.134382}, { 0.085195,  0.056820}, { 0.029800, -0.019138},
+      {-0.027520, -0.072374}, {-0.102268, -0.091555}, {-0.200299, -0.106578},
+      {-0.292731, -0.091473}, {-0.356288, -0.051108}, {-0.420561,  0.014926},
+      {-0.471036,  0.074716}, {-0.488638,  0.182508}, {-0.485990,  0.254068},
+      {-0.463943,  0.338438}, {-0.406453,  0.404704}, {-0.334287,  0.466119},
+      {-0.254244,  0.503188}, {-0.161548,  0.495769}, {-0.075733,  0.495560},
+      { 0.001375,  0.434937}, { 0.082787,  0.385806}, { 0.115490,  0.323807},
+      { 0.141089,  0.223450}, { 0.138693,  0.131703}, { 0.126415,  0.049174},
+      { 0.066518, -0.010217}, {-0.005184, -0.070647}, {-0.080985, -0.103635},
+      {-0.177377, -0.116887}, {-0.260628, -0.100258}, {-0.335756, -0.056251},
+      {-0.405195, -0.000895}, {-0.444937,  0.085456}, {-0.484357,  0.175597},
+      {-0.472453,  0.248681}, {-0.438580,  0.347463}, {-0.402304,  0.422428},
+      {-0.326777,  0.479438}, {-0.247797,  0.505581}, {-0.152676,  0.519380},
+      {-0.071754,  0.516264}, { 0.015942,  0.472802}, { 0.076608,  0.419077},
+      { 0.127673,  0.330264}, { 0.159951,  0.262150}, { 0.153530,  0.172681},
+      { 0.140653,  0.089229}, { 0.078666,  0.024981}, { 0.023807, -0.037022},
+      {-0.048837, -0.077056}, {-0.127729, -0.075338}, {-0.221271, -0.067526}
+    };
+    for (int i = 0; i < points.length; ++i) {
+      circle.addPoint(points[i][0], points[i][1]);
+    }
+    GaussNewtonEstimator estimator = new GaussNewtonEstimator(100, 1.0e-6, 1.0e-6);
+    try {
+        estimator.estimate(circle);
+        fail("an exception should have been caught");
+    } catch (EstimationException ee) {
+        // expected behavior
+    } catch (Exception e) {
+        fail("wrong exception type caught");
+    }
+}
+
+  private static class LinearProblem extends SimpleEstimationProblem {
+
+    public LinearProblem(LinearMeasurement[] measurements) {
+      HashSet<EstimatedParameter> set = new HashSet<EstimatedParameter>();
+      for (int i = 0; i < measurements.length; ++i) {
+        addMeasurement(measurements[i]);
+        EstimatedParameter[] parameters = measurements[i].getParameters();
+        for (int j = 0; j < parameters.length; ++j) {
+          set.add(parameters[j]);
+        }
+      }
+      for (EstimatedParameter p : set) {
+        addParameter(p);
+      }
+    }
+
+  }
+
+  private static class LinearMeasurement extends WeightedMeasurement {
+
+    public LinearMeasurement(double[] factors, EstimatedParameter[] parameters,
+                             double setPoint) {
+      super(1.0, setPoint, true);
+      this.factors = factors;
+      this.parameters = parameters;
+      setIgnored(false);
+    }
+
+    public double getTheoreticalValue() {
+      double v = 0;
+      for (int i = 0; i < factors.length; ++i) {
+        v += factors[i] * parameters[i].getEstimate();
+      }
+      return v;
+    }
+
+    public double getPartial(EstimatedParameter parameter) {
+      for (int i = 0; i < parameters.length; ++i) {
+        if (parameters[i] == parameter) {
+          return factors[i];
+        }
+      }
+      return 0;
+    }
+
+    public EstimatedParameter[] getParameters() {
+      return parameters;
+    }
+
+    private double[] factors;
+    private EstimatedParameter[] parameters;
+    private static final long serialVersionUID = -3922448707008868580L;
+
+  }
+
+  private static class Circle implements EstimationProblem {
+
+    public Circle(double cx, double cy) {
+      this.cx = new EstimatedParameter("cx", cx);
+      this.cy = new EstimatedParameter(new EstimatedParameter("cy", cy));
+      points  = new ArrayList<PointModel>();
+    }
+
+    public void addPoint(double px, double py) {
+      points.add(new PointModel(px, py));
+    }
+
+    public int getM() {
+      return points.size();
+    }
+
+    public WeightedMeasurement[] getMeasurements() {
+      return (WeightedMeasurement[]) points.toArray(new PointModel[points.size()]);
+    }
+
+    public EstimatedParameter[] getAllParameters() {
+      return new EstimatedParameter[] { cx, cy };
+    }
+
+    public EstimatedParameter[] getUnboundParameters() {
+      return new EstimatedParameter[] { cx, cy };
+    }
+
+    public double getPartialRadiusX() {
+      double dRdX = 0;
+      for (PointModel point : points) {
+        dRdX += point.getPartialDiX();
+      }
+      return dRdX / points.size();
+    }
+
+    public double getPartialRadiusY() {
+      double dRdY = 0;
+      for (PointModel point : points) {
+        dRdY += point.getPartialDiY();
+      }
+      return dRdY / points.size();
+    }
+
+   public double getRadius() {
+      double r = 0;
+      for (PointModel point : points) {
+        r += point.getCenterDistance();
+      }
+      return r / points.size();
+    }
+
+    public double getX() {
+      return cx.getEstimate();
+    }
+
+    public double getY() {
+      return cy.getEstimate();
+    }
+
+    private class PointModel extends WeightedMeasurement {
+
+      public PointModel(double px, double py) {
+        super(1.0, 0.0);
+        this.px = px;
+        this.py = py;
+      }
+
+      public double getPartial(EstimatedParameter parameter) {
+        if (parameter == cx) {
+          return getPartialDiX() - getPartialRadiusX();
+        } else if (parameter == cy) {
+          return getPartialDiY() - getPartialRadiusY();
+        }
+        return 0;
+      }
+
+      public double getCenterDistance() {
+        double dx = px - cx.getEstimate();
+        double dy = py - cy.getEstimate();
+        return Math.sqrt(dx * dx + dy * dy);
+      }
+
+      public double getPartialDiX() {
+        return (cx.getEstimate() - px) / getCenterDistance();
+      }
+
+      public double getPartialDiY() {
+        return (cy.getEstimate() - py) / getCenterDistance();
+      }
+
+      public double getTheoreticalValue() {
+        return getCenterDistance() - getRadius();
+      }
+
+      private double px;
+      private double py;
+      private static final long serialVersionUID = 1L;
+
+    }
+
+    private EstimatedParameter cx;
+    private EstimatedParameter cy;
+    private ArrayList<PointModel> points;
+
+  }
+
+  public static Test suite() {
+    return new TestSuite(GaussNewtonEstimatorTest.class);
+  }
+
+}

src/test/org/apache/commons/math/estimation/LevenbergMarquardtEstimatorTest.java

@@ -0,0 +1,844 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements.  See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License.  You may obtain a copy of the License at
+ *
+ *      http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+package org.apache.commons.math.estimation;
+
+import java.util.ArrayList;
+import java.util.HashSet;
+
+import junit.framework.Test;
+import junit.framework.TestCase;
+import junit.framework.TestSuite;
+
+/**
+ * <p>Some of the unit tests are re-implementations of the MINPACK <a
+ * href="http://www.netlib.org/minpack/ex/file17">file17</a> and <a
+ * href="http://www.netlib.org/minpack/ex/file22">file22</a> test files. 
+ * The redistribution policy for MINPACK is available <a
+ * href="http://www.netlib.org/minpack/disclaimer">here</a>, for
+ * convenience, it is reproduced below.</p>
+
+ * <table border="0" width="80%" cellpadding="10" align="center" bgcolor="#E0E0E0">
+ * <tr><td>
+ *    Minpack Copyright Notice (1999) University of Chicago.
+ *    All rights reserved
+ * </td></tr>
+ * <tr><td>
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ * <ol>
+ *  <li>Redistributions of source code must retain the above copyright
+ *      notice, this list of conditions and the following disclaimer.</li>
+ * <li>Redistributions in binary form must reproduce the above
+ *     copyright notice, this list of conditions and the following
+ *     disclaimer in the documentation and/or other materials provided
+ *     with the distribution.</li>
+ * <li>The end-user documentation included with the redistribution, if any,
+ *     must include the following acknowledgment:
+ *     <code>This product includes software developed by the University of
+ *           Chicago, as Operator of Argonne National Laboratory.</code>
+ *     Alternately, this acknowledgment may appear in the software itself,
+ *     if and wherever such third-party acknowledgments normally appear.</li>
+ * <li><strong>WARRANTY DISCLAIMER. THE SOFTWARE IS SUPPLIED "AS IS"
+ *     WITHOUT WARRANTY OF ANY KIND. THE COPYRIGHT HOLDER, THE
+ *     UNITED STATES, THE UNITED STATES DEPARTMENT OF ENERGY, AND
+ *     THEIR EMPLOYEES: (1) DISCLAIM ANY WARRANTIES, EXPRESS OR
+ *     IMPLIED, INCLUDING BUT NOT LIMITED TO ANY IMPLIED WARRANTIES
+ *     OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE, TITLE
+ *     OR NON-INFRINGEMENT, (2) DO NOT ASSUME ANY LEGAL LIABILITY
+ *     OR RESPONSIBILITY FOR THE ACCURACY, COMPLETENESS, OR
+ *     USEFULNESS OF THE SOFTWARE, (3) DO NOT REPRESENT THAT USE OF
+ *     THE SOFTWARE WOULD NOT INFRINGE PRIVATELY OWNED RIGHTS, (4)
+ *     DO NOT WARRANT THAT THE SOFTWARE WILL FUNCTION
+ *     UNINTERRUPTED, THAT IT IS ERROR-FREE OR THAT ANY ERRORS WILL
+ *     BE CORRECTED.</strong></li>
+ * <li><strong>LIMITATION OF LIABILITY. IN NO EVENT WILL THE COPYRIGHT
+ *     HOLDER, THE UNITED STATES, THE UNITED STATES DEPARTMENT OF
+ *     ENERGY, OR THEIR EMPLOYEES: BE LIABLE FOR ANY INDIRECT,
+ *     INCIDENTAL, CONSEQUENTIAL, SPECIAL OR PUNITIVE DAMAGES OF
+ *     ANY KIND OR NATURE, INCLUDING BUT NOT LIMITED TO LOSS OF
+ *     PROFITS OR LOSS OF DATA, FOR ANY REASON WHATSOEVER, WHETHER
+ *     SUCH LIABILITY IS ASSERTED ON THE BASIS OF CONTRACT, TORT
+ *     (INCLUDING NEGLIGENCE OR STRICT LIABILITY), OR OTHERWISE,
+ *     EVEN IF ANY OF SAID PARTIES HAS BEEN WARNED OF THE
+ *     POSSIBILITY OF SUCH LOSS OR DAMAGES.</strong></li>
+ * <ol></td></tr>
+ * </table>
+
+ * @author Argonne National Laboratory. MINPACK project. March 1980 (original fortran minpack tests)
+ * @author Burton S. Garbow (original fortran minpack tests)
+ * @author Kenneth E. Hillstrom (original fortran minpack tests)
+ * @author Jorge J. More (original fortran minpack tests)
+ * @author Luc Maisonobe (non-minpack tests and minpack tests Java translation)
+ */
+@Deprecated
+public class LevenbergMarquardtEstimatorTest
+  extends TestCase {
+
+  public LevenbergMarquardtEstimatorTest(String name) {
+    super(name);
+  }
+
+  public void testTrivial() throws EstimationException {
+    LinearProblem problem =
+      new LinearProblem(new LinearMeasurement[] {
+        new LinearMeasurement(new double[] {2},
+                              new EstimatedParameter[] {
+                                 new EstimatedParameter("p0", 0)
+                              }, 3.0)
+      });
+    LevenbergMarquardtEstimator estimator = new LevenbergMarquardtEstimator();
+    estimator.estimate(problem);
+    assertEquals(0, estimator.getRMS(problem), 1.0e-10);
+    try {
+        estimator.guessParametersErrors(problem);
+        fail("an exception should have been thrown");
+    } catch (EstimationException ee) {
+        // expected behavior
+    } catch (Exception e) {
+        fail("wrong exception caught");
+    }
+    assertEquals(1.5,
+                 problem.getUnboundParameters()[0].getEstimate(),
+                 1.0e-10);
+   }
+
+  public void testQRColumnsPermutation() throws EstimationException {
+
+    EstimatedParameter[] x = {
+       new EstimatedParameter("p0", 0), new EstimatedParameter("p1", 0)
+    };
+    LinearProblem problem = new LinearProblem(new LinearMeasurement[] {
+      new LinearMeasurement(new double[] { 1.0, -1.0 },
+                            new EstimatedParameter[] { x[0], x[1] },
+                            4.0),
+      new LinearMeasurement(new double[] { 2.0 },
+                            new EstimatedParameter[] { x[1] },
+                            6.0),
+      new LinearMeasurement(new double[] { 1.0, -2.0 },
+                            new EstimatedParameter[] { x[0], x[1] },
+                            1.0)
+    });
+
+    LevenbergMarquardtEstimator estimator = new LevenbergMarquardtEstimator();
+    estimator.estimate(problem);
+    assertEquals(0, estimator.getRMS(problem), 1.0e-10);
+    assertEquals(7.0, x[0].getEstimate(), 1.0e-10);
+    assertEquals(3.0, x[1].getEstimate(), 1.0e-10);
+
+  }
+
+  public void testNoDependency() throws EstimationException {
+    EstimatedParameter[] p = new EstimatedParameter[] {
+      new EstimatedParameter("p0", 0),
+      new EstimatedParameter("p1", 0),
+      new EstimatedParameter("p2", 0),
+      new EstimatedParameter("p3", 0),
+      new EstimatedParameter("p4", 0),
+      new EstimatedParameter("p5", 0)
+    };
+    LinearProblem problem = new LinearProblem(new LinearMeasurement[] {
+      new LinearMeasurement(new double[] {2}, new EstimatedParameter[] { p[0] }, 0.0),
+      new LinearMeasurement(new double[] {2}, new EstimatedParameter[] { p[1] }, 1.1),
+      new LinearMeasurement(new double[] {2}, new EstimatedParameter[] { p[2] }, 2.2),
+      new LinearMeasurement(new double[] {2}, new EstimatedParameter[] { p[3] }, 3.3),
+      new LinearMeasurement(new double[] {2}, new EstimatedParameter[] { p[4] }, 4.4),
+      new LinearMeasurement(new double[] {2}, new EstimatedParameter[] { p[5] }, 5.5)
+    });
+  LevenbergMarquardtEstimator estimator = new LevenbergMarquardtEstimator();
+  estimator.estimate(problem);
+  assertEquals(0, estimator.getRMS(problem), 1.0e-10);
+  for (int i = 0; i < p.length; ++i) {
+    assertEquals(0.55 * i, p[i].getEstimate(), 1.0e-10);
+  }
+}
+
+  public void testOneSet() throws EstimationException {
+
+    EstimatedParameter[] p = {
+       new EstimatedParameter("p0", 0),
+       new EstimatedParameter("p1", 0),
+       new EstimatedParameter("p2", 0)
+    };
+    LinearProblem problem = new LinearProblem(new LinearMeasurement[] {
+      new LinearMeasurement(new double[] { 1.0 },
+                            new EstimatedParameter[] { p[0] },
+                            1.0),
+      new LinearMeasurement(new double[] { -1.0, 1.0 },
+                            new EstimatedParameter[] { p[0], p[1] },
+                            1.0),
+      new LinearMeasurement(new double[] { -1.0, 1.0 },
+                            new EstimatedParameter[] { p[1], p[2] },
+                            1.0)
+    });
+
+    LevenbergMarquardtEstimator estimator = new LevenbergMarquardtEstimator();
+    estimator.estimate(problem);
+    assertEquals(0, estimator.getRMS(problem), 1.0e-10);
+    assertEquals(1.0, p[0].getEstimate(), 1.0e-10);
+    assertEquals(2.0, p[1].getEstimate(), 1.0e-10);
+    assertEquals(3.0, p[2].getEstimate(), 1.0e-10);
+
+  }
+
+  public void testTwoSets() throws EstimationException {
+    EstimatedParameter[] p = {
+      new EstimatedParameter("p0", 0),
+      new EstimatedParameter("p1", 1),
+      new EstimatedParameter("p2", 2),
+      new EstimatedParameter("p3", 3),
+      new EstimatedParameter("p4", 4),
+      new EstimatedParameter("p5", 5)
+    };
+
+    double epsilon = 1.0e-7;
+    LinearProblem problem = new LinearProblem(new LinearMeasurement[] {
+
+      // 4 elements sub-problem
+      new LinearMeasurement(new double[] {  2.0,  1.0,  4.0 },
+                            new EstimatedParameter[] { p[0], p[1], p[3] },
+                            2.0),
+      new LinearMeasurement(new double[] { -4.0, -2.0,   3.0, -7.0 },
+                           new EstimatedParameter[] { p[0], p[1], p[2], p[3] },
+                           -9.0),
+      new LinearMeasurement(new double[] {  4.0,  1.0,  -2.0,  8.0 },
+                            new EstimatedParameter[] { p[0], p[1], p[2], p[3] },
+                            2.0),
+      new LinearMeasurement(new double[] { -3.0, -12.0, -1.0 },
+                           new EstimatedParameter[] { p[1], p[2], p[3] },
+                           2.0),
+
+      // 2 elements sub-problem
+      new LinearMeasurement(new double[] { epsilon, 1.0 },
+                            new EstimatedParameter[] { p[4], p[5] },
+                            1.0 + epsilon * epsilon),
+      new LinearMeasurement(new double[] {  1.0, 1.0 },
+                            new EstimatedParameter[] { p[4], p[5] },
+                            2.0)
+
+    });
+
+    LevenbergMarquardtEstimator estimator = new LevenbergMarquardtEstimator();
+    estimator.estimate(problem);
+    assertEquals(0, estimator.getRMS(problem), 1.0e-10);
+    assertEquals( 3.0, p[0].getEstimate(), 1.0e-10);
+    assertEquals( 4.0, p[1].getEstimate(), 1.0e-10);
+    assertEquals(-1.0, p[2].getEstimate(), 1.0e-10);
+    assertEquals(-2.0, p[3].getEstimate(), 1.0e-10);
+    assertEquals( 1.0 + epsilon, p[4].getEstimate(), 1.0e-10);
+    assertEquals( 1.0 - epsilon, p[5].getEstimate(), 1.0e-10);
+
+  }
+
+  public void testNonInversible() throws EstimationException {
+
+    EstimatedParameter[] p = {
+       new EstimatedParameter("p0", 0),
+       new EstimatedParameter("p1", 0),
+       new EstimatedParameter("p2", 0)
+    };
+    LinearMeasurement[] m = new LinearMeasurement[] {
+      new LinearMeasurement(new double[] {  1.0, 2.0, -3.0 },
+                            new EstimatedParameter[] { p[0], p[1], p[2] },
+                            1.0),
+      new LinearMeasurement(new double[] {  2.0, 1.0,  3.0 },
+                            new EstimatedParameter[] { p[0], p[1], p[2] },
+                            1.0),
+      new LinearMeasurement(new double[] { -3.0, -9.0 },
+                            new EstimatedParameter[] { p[0], p[2] },
+                            1.0)
+    };
+    LinearProblem problem = new LinearProblem(m);
+
+    LevenbergMarquardtEstimator estimator = new LevenbergMarquardtEstimator();
+    double initialCost = estimator.getRMS(problem);
+    estimator.estimate(problem);
+    assertTrue(estimator.getRMS(problem) < initialCost);
+    assertTrue(Math.sqrt(m.length) * estimator.getRMS(problem) > 0.6);
+    try {
+        estimator.getCovariances(problem);
+        fail("an exception should have been thrown");
+    } catch (EstimationException ee) {
+        // expected behavior
+    } catch (Exception e) {
+        fail("wrong exception caught");
+    }
+   double dJ0 = 2 * (m[0].getResidual() * m[0].getPartial(p[0])
+                    + m[1].getResidual() * m[1].getPartial(p[0])
+                    + m[2].getResidual() * m[2].getPartial(p[0]));
+    double dJ1 = 2 * (m[0].getResidual() * m[0].getPartial(p[1])
+                    + m[1].getResidual() * m[1].getPartial(p[1]));
+    double dJ2 = 2 * (m[0].getResidual() * m[0].getPartial(p[2])
+                    + m[1].getResidual() * m[1].getPartial(p[2])
+                    + m[2].getResidual() * m[2].getPartial(p[2]));
+    assertEquals(0, dJ0, 1.0e-10);
+    assertEquals(0, dJ1, 1.0e-10);
+    assertEquals(0, dJ2, 1.0e-10);
+
+  }
+
+  public void testIllConditioned() throws EstimationException {
+    EstimatedParameter[] p = {
+      new EstimatedParameter("p0", 0),
+      new EstimatedParameter("p1", 1),
+      new EstimatedParameter("p2", 2),
+      new EstimatedParameter("p3", 3)
+    };
+
+    LinearProblem problem1 = new LinearProblem(new LinearMeasurement[] {
+      new LinearMeasurement(new double[] { 10.0, 7.0,  8.0,  7.0 },
+                            new EstimatedParameter[] { p[0], p[1], p[2], p[3] },
+                            32.0),
+      new LinearMeasurement(new double[] {  7.0, 5.0,  6.0,  5.0 },
+                            new EstimatedParameter[] { p[0], p[1], p[2], p[3] },
+                            23.0),
+      new LinearMeasurement(new double[] {  8.0, 6.0, 10.0,  9.0 },
+                            new EstimatedParameter[] { p[0], p[1], p[2], p[3] },
+                            33.0),
+      new LinearMeasurement(new double[] {  7.0, 5.0,  9.0, 10.0 },
+                            new EstimatedParameter[] { p[0], p[1], p[2], p[3] },
+                            31.0)
+    });
+    LevenbergMarquardtEstimator estimator1 = new LevenbergMarquardtEstimator();
+    estimator1.estimate(problem1);
+    assertEquals(0, estimator1.getRMS(problem1), 1.0e-10);
+    assertEquals(1.0, p[0].getEstimate(), 1.0e-10);
+    assertEquals(1.0, p[1].getEstimate(), 1.0e-10);
+    assertEquals(1.0, p[2].getEstimate(), 1.0e-10);
+    assertEquals(1.0, p[3].getEstimate(), 1.0e-10);
+
+    LinearProblem problem2 = new LinearProblem(new LinearMeasurement[] {
+      new LinearMeasurement(new double[] { 10.0, 7.0,  8.1,  7.2 },
+                            new EstimatedParameter[] { p[0], p[1], p[2], p[3] },
+                            32.0),
+      new LinearMeasurement(new double[] {  7.08, 5.04,  6.0,  5.0 },
+                            new EstimatedParameter[] { p[0], p[1], p[2], p[3] },
+                            23.0),
+      new LinearMeasurement(new double[] {  8.0, 5.98, 9.89,  9.0 },
+                             new EstimatedParameter[] { p[0], p[1], p[2], p[3] },
+                            33.0),
+      new LinearMeasurement(new double[] {  6.99, 4.99,  9.0, 9.98 },
+                             new EstimatedParameter[] { p[0], p[1], p[2], p[3] },
+                            31.0)
+    });
+    LevenbergMarquardtEstimator estimator2 = new LevenbergMarquardtEstimator();
+    estimator2.estimate(problem2);
+    assertEquals(0, estimator2.getRMS(problem2), 1.0e-10);
+    assertEquals(-81.0, p[0].getEstimate(), 1.0e-8);
+    assertEquals(137.0, p[1].getEstimate(), 1.0e-8);
+    assertEquals(-34.0, p[2].getEstimate(), 1.0e-8);
+    assertEquals( 22.0, p[3].getEstimate(), 1.0e-8);
+
+  }
+
+  public void testMoreEstimatedParametersSimple() throws EstimationException {
+
+    EstimatedParameter[] p = {
+       new EstimatedParameter("p0", 7),
+       new EstimatedParameter("p1", 6),
+       new EstimatedParameter("p2", 5),
+       new EstimatedParameter("p3", 4)
+     };
+    LinearProblem problem = new LinearProblem(new LinearMeasurement[] {
+      new LinearMeasurement(new double[] { 3.0, 2.0 },
+                             new EstimatedParameter[] { p[0], p[1] },
+                             7.0),
+      new LinearMeasurement(new double[] { 1.0, -1.0, 1.0 },
+                             new EstimatedParameter[] { p[1], p[2], p[3] },
+                             3.0),
+      new LinearMeasurement(new double[] { 2.0, 1.0 },
+                             new EstimatedParameter[] { p[0], p[2] },
+                             5.0)
+    });
+
+    LevenbergMarquardtEstimator estimator = new LevenbergMarquardtEstimator();
+    estimator.estimate(problem);
+    assertEquals(0, estimator.getRMS(problem), 1.0e-10);
+
+  }
+
+  public void testMoreEstimatedParametersUnsorted() throws EstimationException {
+    EstimatedParameter[] p = {
+      new EstimatedParameter("p0", 2),
+      new EstimatedParameter("p1", 2),
+      new EstimatedParameter("p2", 2),
+      new EstimatedParameter("p3", 2),
+      new EstimatedParameter("p4", 2),
+      new EstimatedParameter("p5", 2)
+    };
+    LinearProblem problem = new LinearProblem(new LinearMeasurement[] {
+      new LinearMeasurement(new double[] { 1.0, 1.0 },
+                           new EstimatedParameter[] { p[0], p[1] },
+                           3.0),
+      new LinearMeasurement(new double[] { 1.0, 1.0, 1.0 },
+                           new EstimatedParameter[] { p[2], p[3], p[4] },
+                           12.0),
+      new LinearMeasurement(new double[] { 1.0, -1.0 },
+                           new EstimatedParameter[] { p[4], p[5] },
+                           -1.0),
+      new LinearMeasurement(new double[] { 1.0, -1.0, 1.0 },
+                           new EstimatedParameter[] { p[3], p[2], p[5] },
+                           7.0),
+      new LinearMeasurement(new double[] { 1.0, -1.0 },
+                           new EstimatedParameter[] { p[4], p[3] },
+                           1.0)
+    });
+
+    LevenbergMarquardtEstimator estimator = new LevenbergMarquardtEstimator();
+    estimator.estimate(problem);
+    assertEquals(0, estimator.getRMS(problem), 1.0e-10);
+    assertEquals(3.0, p[2].getEstimate(), 1.0e-10);
+    assertEquals(4.0, p[3].getEstimate(), 1.0e-10);
+    assertEquals(5.0, p[4].getEstimate(), 1.0e-10);
+    assertEquals(6.0, p[5].getEstimate(), 1.0e-10);
+
+  }
+
+  public void testRedundantEquations() throws EstimationException {
+    EstimatedParameter[] p = {
+      new EstimatedParameter("p0", 1),
+      new EstimatedParameter("p1", 1)
+    };
+    LinearProblem problem = new LinearProblem(new LinearMeasurement[] {
+      new LinearMeasurement(new double[] { 1.0, 1.0 },
+                             new EstimatedParameter[] { p[0], p[1] },
+                             3.0),
+      new LinearMeasurement(new double[] { 1.0, -1.0 },
+                             new EstimatedParameter[] { p[0], p[1] },
+                             1.0),
+      new LinearMeasurement(new double[] { 1.0, 3.0 },
+                             new EstimatedParameter[] { p[0], p[1] },
+                             5.0)
+    });
+
+    LevenbergMarquardtEstimator estimator = new LevenbergMarquardtEstimator();
+    estimator.estimate(problem);
+    assertEquals(0, estimator.getRMS(problem), 1.0e-10);
+    assertEquals(2.0, p[0].getEstimate(), 1.0e-10);
+    assertEquals(1.0, p[1].getEstimate(), 1.0e-10);
+
+  }
+
+  public void testInconsistentEquations() throws EstimationException {
+    EstimatedParameter[] p = {
+      new EstimatedParameter("p0", 1),
+      new EstimatedParameter("p1", 1)
+    };
+    LinearProblem problem = new LinearProblem(new LinearMeasurement[] {
+      new LinearMeasurement(new double[] { 1.0, 1.0 },
+                            new EstimatedParameter[] { p[0], p[1] },
+                            3.0),
+      new LinearMeasurement(new double[] { 1.0, -1.0 },
+                            new EstimatedParameter[] { p[0], p[1] },
+                            1.0),
+      new LinearMeasurement(new double[] { 1.0, 3.0 },
+                            new EstimatedParameter[] { p[0], p[1] },
+                            4.0)
+    });
+
+    LevenbergMarquardtEstimator estimator = new LevenbergMarquardtEstimator();
+    estimator.estimate(problem);
+    assertTrue(estimator.getRMS(problem) > 0.1);
+
+  }
+
+  public void testControlParameters() throws EstimationException {
+      Circle circle = new Circle(98.680, 47.345);
+      circle.addPoint( 30.0,  68.0);
+      circle.addPoint( 50.0,  -6.0);
+      circle.addPoint(110.0, -20.0);
+      circle.addPoint( 35.0,  15.0);
+      circle.addPoint( 45.0,  97.0);
+      checkEstimate(circle, 0.1, 10, 1.0e-14, 1.0e-16, 1.0e-10, false);
+      checkEstimate(circle, 0.1, 10, 1.0e-15, 1.0e-17, 1.0e-10, true);
+      checkEstimate(circle, 0.1,  5, 1.0e-15, 1.0e-16, 1.0e-10, true);
+      circle.addPoint(300, -300);
+      checkEstimate(circle, 0.1, 20, 1.0e-18, 1.0e-16, 1.0e-10, true);
+  }
+
+  private void checkEstimate(EstimationProblem problem,
+                             double initialStepBoundFactor, int maxCostEval,
+                             double costRelativeTolerance, double parRelativeTolerance,
+                             double orthoTolerance, boolean shouldFail) {
+      try {
+        LevenbergMarquardtEstimator estimator = new LevenbergMarquardtEstimator();
+        estimator.setInitialStepBoundFactor(initialStepBoundFactor);
+        estimator.setMaxCostEval(maxCostEval);
+        estimator.setCostRelativeTolerance(costRelativeTolerance);
+        estimator.setParRelativeTolerance(parRelativeTolerance);
+        estimator.setOrthoTolerance(orthoTolerance);
+        estimator.estimate(problem);
+        assertTrue(! shouldFail);
+      } catch (EstimationException ee) {
+        assertTrue(shouldFail);
+      } catch (Exception e) {
+        fail("wrong exception type caught");
+      }
+    }
+
+  public void testCircleFitting() throws EstimationException {
+      Circle circle = new Circle(98.680, 47.345);
+      circle.addPoint( 30.0,  68.0);
+      circle.addPoint( 50.0,  -6.0);
+      circle.addPoint(110.0, -20.0);
+      circle.addPoint( 35.0,  15.0);
+      circle.addPoint( 45.0,  97.0);
+      LevenbergMarquardtEstimator estimator = new LevenbergMarquardtEstimator();
+      estimator.estimate(circle);
+      assertTrue(estimator.getCostEvaluations() < 10);
+      assertTrue(estimator.getJacobianEvaluations() < 10);
+      double rms = estimator.getRMS(circle);
+      assertEquals(1.768262623567235,  Math.sqrt(circle.getM()) * rms,  1.0e-10);
+      assertEquals(69.96016176931406, circle.getRadius(), 1.0e-10);
+      assertEquals(96.07590211815305, circle.getX(),      1.0e-10);
+      assertEquals(48.13516790438953, circle.getY(),      1.0e-10);
+      double[][] cov = estimator.getCovariances(circle);
+      assertEquals(1.839, cov[0][0], 0.001);
+      assertEquals(0.731, cov[0][1], 0.001);
+      assertEquals(cov[0][1], cov[1][0], 1.0e-14);
+      assertEquals(0.786, cov[1][1], 0.001);
+      double[] errors = estimator.guessParametersErrors(circle);
+      assertEquals(1.384, errors[0], 0.001);
+      assertEquals(0.905, errors[1], 0.001);
+  
+      // add perfect measurements and check errors are reduced
+      double cx = circle.getX();
+      double cy = circle.getY();
+      double  r = circle.getRadius();
+      for (double d= 0; d < 2 * Math.PI; d += 0.01) {
+          circle.addPoint(cx + r * Math.cos(d), cy + r * Math.sin(d));
+      }
+      estimator = new LevenbergMarquardtEstimator();
+      estimator.estimate(circle);
+      cov = estimator.getCovariances(circle);
+      assertEquals(0.004, cov[0][0], 0.001);
+      assertEquals(6.40e-7, cov[0][1], 1.0e-9);
+      assertEquals(cov[0][1], cov[1][0], 1.0e-14);
+      assertEquals(0.003, cov[1][1], 0.001);
+      errors = estimator.guessParametersErrors(circle);
+      assertEquals(0.004, errors[0], 0.001);
+      assertEquals(0.004, errors[1], 0.001);
+
+  }
+
+  public void testCircleFittingBadInit() throws EstimationException {
+    Circle circle = new Circle(-12, -12);
+    double[][] points = new double[][] {
+      {-0.312967,  0.072366}, {-0.339248,  0.132965}, {-0.379780,  0.202724},
+      {-0.390426,  0.260487}, {-0.361212,  0.328325}, {-0.346039,  0.392619},
+      {-0.280579,  0.444306}, {-0.216035,  0.470009}, {-0.149127,  0.493832},
+      {-0.075133,  0.483271}, {-0.007759,  0.452680}, { 0.060071,  0.410235},
+      { 0.103037,  0.341076}, { 0.118438,  0.273884}, { 0.131293,  0.192201},
+      { 0.115869,  0.129797}, { 0.072223,  0.058396}, { 0.022884,  0.000718},
+      {-0.053355, -0.020405}, {-0.123584, -0.032451}, {-0.216248, -0.032862},
+      {-0.278592, -0.005008}, {-0.337655,  0.056658}, {-0.385899,  0.112526},
+      {-0.405517,  0.186957}, {-0.415374,  0.262071}, {-0.387482,  0.343398},
+      {-0.347322,  0.397943}, {-0.287623,  0.458425}, {-0.223502,  0.475513},
+      {-0.135352,  0.478186}, {-0.061221,  0.483371}, { 0.003711,  0.422737},
+      { 0.065054,  0.375830}, { 0.108108,  0.297099}, { 0.123882,  0.222850},
+      { 0.117729,  0.134382}, { 0.085195,  0.056820}, { 0.029800, -0.019138},
+      {-0.027520, -0.072374}, {-0.102268, -0.091555}, {-0.200299, -0.106578},
+      {-0.292731, -0.091473}, {-0.356288, -0.051108}, {-0.420561,  0.014926},
+      {-0.471036,  0.074716}, {-0.488638,  0.182508}, {-0.485990,  0.254068},
+      {-0.463943,  0.338438}, {-0.406453,  0.404704}, {-0.334287,  0.466119},
+      {-0.254244,  0.503188}, {-0.161548,  0.495769}, {-0.075733,  0.495560},
+      { 0.001375,  0.434937}, { 0.082787,  0.385806}, { 0.115490,  0.323807},
+      { 0.141089,  0.223450}, { 0.138693,  0.131703}, { 0.126415,  0.049174},
+      { 0.066518, -0.010217}, {-0.005184, -0.070647}, {-0.080985, -0.103635},
+      {-0.177377, -0.116887}, {-0.260628, -0.100258}, {-0.335756, -0.056251},
+      {-0.405195, -0.000895}, {-0.444937,  0.085456}, {-0.484357,  0.175597},
+      {-0.472453,  0.248681}, {-0.438580,  0.347463}, {-0.402304,  0.422428},
+      {-0.326777,  0.479438}, {-0.247797,  0.505581}, {-0.152676,  0.519380},
+      {-0.071754,  0.516264}, { 0.015942,  0.472802}, { 0.076608,  0.419077},
+      { 0.127673,  0.330264}, { 0.159951,  0.262150}, { 0.153530,  0.172681},
+      { 0.140653,  0.089229}, { 0.078666,  0.024981}, { 0.023807, -0.037022},
+      {-0.048837, -0.077056}, {-0.127729, -0.075338}, {-0.221271, -0.067526}
+    };
+    for (int i = 0; i < points.length; ++i) {
+      circle.addPoint(points[i][0], points[i][1]);
+    }
+    LevenbergMarquardtEstimator estimator = new LevenbergMarquardtEstimator();
+    estimator.estimate(circle);
+    assertTrue(estimator.getCostEvaluations() < 15);
+    assertTrue(estimator.getJacobianEvaluations() < 10);
+    assertEquals( 0.030184491196225207, estimator.getRMS(circle), 1.0e-9);
+    assertEquals( 0.2922350065939634,   circle.getRadius(), 1.0e-9);
+    assertEquals(-0.15173845023862165,  circle.getX(),      1.0e-8);
+    assertEquals( 0.20750021499570379,  circle.getY(),      1.0e-8);
+  }
+
+  public void testMath199() {
+      try {
+          QuadraticProblem problem = new QuadraticProblem();
+          problem.addPoint (0, -3.182591015485607, 0.0);
+          problem.addPoint (1, -2.5581184967730577, 4.4E-323);
+          problem.addPoint (2, -2.1488478161387325, 1.0);
+          problem.addPoint (3, -1.9122489313410047, 4.4E-323);
+          problem.addPoint (4, 1.7785661310051026, 0.0);
+          new LevenbergMarquardtEstimator().estimate(problem);
+          fail("an exception should have been thrown");
+      } catch (EstimationException ee) {
+          // expected behavior
+      }
+
+  }
+
+  private static class LinearProblem implements EstimationProblem {
+
+    public LinearProblem(LinearMeasurement[] measurements) {
+      this.measurements = measurements;
+    }
+
+    public WeightedMeasurement[] getMeasurements() {
+      return measurements;
+    }
+
+    public EstimatedParameter[] getUnboundParameters() {
+      return getAllParameters();
+    }
+
+    public EstimatedParameter[] getAllParameters() {
+      HashSet<EstimatedParameter> set = new HashSet<EstimatedParameter>();
+      for (int i = 0; i < measurements.length; ++i) {
+        EstimatedParameter[] parameters = measurements[i].getParameters();
+        for (int j = 0; j < parameters.length; ++j) {
+          set.add(parameters[j]);
+        }
+      }
+      return (EstimatedParameter[]) set.toArray(new EstimatedParameter[set.size()]);
+    }
+  
+    private LinearMeasurement[] measurements;
+
+  }
+
+  private static class LinearMeasurement extends WeightedMeasurement {
+
+    public LinearMeasurement(double[] factors, EstimatedParameter[] parameters,
+                             double setPoint) {
+      super(1.0, setPoint);
+      this.factors = factors;
+      this.parameters = parameters;
+    }
+
+    public double getTheoreticalValue() {
+      double v = 0;
+      for (int i = 0; i < factors.length; ++i) {
+        v += factors[i] * parameters[i].getEstimate();
+      }
+      return v;
+    }
+
+    public double getPartial(EstimatedParameter parameter) {
+      for (int i = 0; i < parameters.length; ++i) {
+        if (parameters[i] == parameter) {
+          return factors[i];
+        }
+      }
+      return 0;
+    }
+
+    public EstimatedParameter[] getParameters() {
+      return parameters;
+    }
+
+    private double[] factors;
+    private EstimatedParameter[] parameters;
+    private static final long serialVersionUID = -3922448707008868580L;
+
+  }
+
+  private static class Circle implements EstimationProblem {
+
+    public Circle(double cx, double cy) {
+      this.cx = new EstimatedParameter("cx", cx);
+      this.cy = new EstimatedParameter("cy", cy);
+      points  = new ArrayList<PointModel>();
+    }
+
+    public void addPoint(double px, double py) {
+      points.add(new PointModel(px, py));
+    }
+
+    public int getM() {
+      return points.size();
+    }
+
+    public WeightedMeasurement[] getMeasurements() {
+      return (WeightedMeasurement[]) points.toArray(new PointModel[points.size()]);
+    }
+
+    public EstimatedParameter[] getAllParameters() {
+      return new EstimatedParameter[] { cx, cy };
+    }
+
+    public EstimatedParameter[] getUnboundParameters() {
+      return new EstimatedParameter[] { cx, cy };
+    }
+
+    public double getPartialRadiusX() {
+      double dRdX = 0;
+      for (PointModel point : points) {
+        dRdX += point.getPartialDiX();
+      }
+      return dRdX / points.size();
+    }
+
+    public double getPartialRadiusY() {
+      double dRdY = 0;
+      for (PointModel point : points) {
+        dRdY += point.getPartialDiY();
+      }
+      return dRdY / points.size();
+    }
+
+   public double getRadius() {
+      double r = 0;
+      for (PointModel point : points) {
+        r += point.getCenterDistance();
+      }
+      return r / points.size();
+    }
+
+    public double getX() {
+      return cx.getEstimate();
+    }
+
+    public double getY() {
+      return cy.getEstimate();
+    }
+
+    private class PointModel extends WeightedMeasurement {
+
+      public PointModel(double px, double py) {
+        super(1.0, 0.0);
+        this.px = px;
+        this.py = py;
+      }
+
+      public double getPartial(EstimatedParameter parameter) {
+        if (parameter == cx) {
+          return getPartialDiX() - getPartialRadiusX();
+        } else if (parameter == cy) {
+          return getPartialDiY() - getPartialRadiusY();
+        }
+        return 0;
+      }
+
+      public double getCenterDistance() {
+        double dx = px - cx.getEstimate();
+        double dy = py - cy.getEstimate();
+        return Math.sqrt(dx * dx + dy * dy);
+      }
+
+      public double getPartialDiX() {
+        return (cx.getEstimate() - px) / getCenterDistance();
+      }
+
+      public double getPartialDiY() {
+        return (cy.getEstimate() - py) / getCenterDistance();
+      }
+
+      public double getTheoreticalValue() {
+        return getCenterDistance() - getRadius();
+      }
+
+      private double px;
+      private double py;
+      private static final long serialVersionUID = 1L;
+
+    }
+
+    private EstimatedParameter cx;
+    private EstimatedParameter cy;
+    private ArrayList<PointModel> points;
+
+  }
+
+  private static class QuadraticProblem extends SimpleEstimationProblem {
+
+      private EstimatedParameter a;
+      private EstimatedParameter b;
+      private EstimatedParameter c;
+
+      public QuadraticProblem() {
+          a = new EstimatedParameter("a", 0.0);
+          b = new EstimatedParameter("b", 0.0);
+          c = new EstimatedParameter("c", 0.0);
+          addParameter(a);
+          addParameter(b);
+          addParameter(c);
+      }
+
+      public void addPoint(double x, double y, double w) {
+          addMeasurement(new LocalMeasurement(x, y, w));
+      }
+
+      public double getA() {
+          return a.getEstimate();
+      }
+
+      public double getB() {
+          return b.getEstimate();
+      }
+
+      public double getC() {
+          return c.getEstimate();
+      }
+
+      public double theoreticalValue(double x) {
+          return ( (a.getEstimate() * x + b.getEstimate() ) * x + c.getEstimate());
+      }
+
+      private double partial(double x, EstimatedParameter parameter) {
+          if (parameter == a) {
+              return x * x;
+          } else if (parameter == b) {
+              return x;
+          } else {
+              return 1.0;
+          }
+      }
+
+      private class LocalMeasurement extends WeightedMeasurement {
+
+        private static final long serialVersionUID = 1555043155023729130L;
+        private final double x;
+
+          // constructor
+          public LocalMeasurement(double x, double y, double w) {
+              super(w, y);
+              this.x = x;
+          }
+
+          public double getTheoreticalValue() {
+              return theoreticalValue(x);
+          }
+
+          public double getPartial(EstimatedParameter parameter) {
+              return partial(x, parameter);
+          }
+
+      }
+  }
+
+  public static Test suite() {
+    return new TestSuite(LevenbergMarquardtEstimatorTest.class);
+  }
+
+}

src/test/org/apache/commons/math/estimation/WeightedMeasurementTest.java

@@ -0,0 +1,127 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements.  See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License.  You may obtain a copy of the License at
+ *
+ *      http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+package org.apache.commons.math.estimation;
+
+import org.apache.commons.math.estimation.EstimatedParameter;
+import org.apache.commons.math.estimation.WeightedMeasurement;
+
+import junit.framework.*;
+
+@Deprecated
+public class WeightedMeasurementTest
+  extends TestCase {
+
+  public WeightedMeasurementTest(String name) {
+    super(name);
+    p1 = null;
+    p2 = null;
+  }
+
+  public void testConstruction() {
+    WeightedMeasurement m = new MyMeasurement(3.0, theoretical() + 0.1, this);
+    checkValue(m.getWeight(), 3.0);
+    checkValue(m.getMeasuredValue(), theoretical() + 0.1);
+  }
+
+  public void testIgnored() {
+    WeightedMeasurement m = new MyMeasurement(3.0, theoretical() + 0.1, this);
+    assertTrue(!m.isIgnored());
+    m.setIgnored(true);
+    assertTrue(m.isIgnored());
+    m.setIgnored(false);
+    assertTrue(!m.isIgnored());
+  }
+
+  public void testTheory() {
+    WeightedMeasurement m = new MyMeasurement(3.0, theoretical() + 0.1, this);
+    checkValue(m.getTheoreticalValue(), theoretical());
+    checkValue(m.getResidual(), 0.1);
+
+    double oldP1 = p1.getEstimate();
+    p1.setEstimate(oldP1 + m.getResidual() / m.getPartial(p1));
+    checkValue(m.getResidual(), 0.0);
+    p1.setEstimate(oldP1);
+    checkValue(m.getResidual(), 0.1);
+
+    double oldP2 = p2.getEstimate();
+    p2.setEstimate(oldP2 + m.getResidual() / m.getPartial(p2));
+    checkValue(m.getResidual(), 0.0);
+    p2.setEstimate(oldP2);
+    checkValue(m.getResidual(), 0.1);
+
+  }
+
+  public static Test suite() {
+    return new TestSuite(WeightedMeasurementTest.class);
+  }
+
+  public void setUp() {
+    p1 = new EstimatedParameter("p1", 1.0);
+    p2 = new EstimatedParameter("p2", 2.0);
+  }
+
+  public void tearDown() {
+    p1 = null;
+    p2 = null;
+  }
+
+  private void checkValue(double value, double expected) {
+   assertTrue(Math.abs(value - expected) < 1.0e-10);
+  }
+
+  private double theoretical() {
+   return 3 * p1.getEstimate() - p2.getEstimate();
+  }
+
+  private double partial(EstimatedParameter p) {
+    if (p == p1) {
+      return 3.0;
+    } else if (p == p2) {
+      return -1.0;
+    } else {
+      return 0.0;
+    }
+  }
+
+  private static class MyMeasurement
+    extends WeightedMeasurement {
+
+    public MyMeasurement(double weight, double measuredValue,
+                         WeightedMeasurementTest testInstance) {
+      super(weight, measuredValue);
+      this.testInstance = testInstance;
+    }
+
+    public double getTheoreticalValue() {
+      return testInstance.theoretical();
+    }
+
+    public double getPartial(EstimatedParameter p) {
+      return testInstance.partial(p);
+    }
+
+    private transient WeightedMeasurementTest testInstance;
+
+    private static final long serialVersionUID = -246712922500792332L;
+
+  }
+
+  private EstimatedParameter p1;
+  private EstimatedParameter p2;
+
+}