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A Java's Collaborative Filtering library to carry out experiments in research of Collaborative Filtering based Recommender Systems. The library has been designed from researchers to researchers.
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/*
 * 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.math3.fitting.leastsquares;

import org.apache.commons.math3.linear.RealMatrix;
import org.apache.commons.math3.linear.RealVector;
import org.apache.commons.math3.optim.OptimizationProblem;

/**
 * The data necessary to define a non-linear least squares problem.
 * 
 * Includes the observed values, computed model function, and
 * convergence/divergence criteria. Weights are implicit in {@link
 * Evaluation#getResiduals()} and {@link Evaluation#getJacobian()}.
 * 
 * 
 * Instances are typically either created progressively using a {@link
 * LeastSquaresBuilder builder} or created at once using a {@link LeastSquaresFactory
 * factory}.
 * 
 * @see LeastSquaresBuilder
 * @see LeastSquaresFactory
 * @see LeastSquaresAdapter
 *
 * @since 3.3
 */
public interface LeastSquaresProblem extends OptimizationProblem {

    /**
     * Gets the initial guess.
     *
     * @return the initial guess values.
     */
    RealVector getStart();

    /**
     * Get the number of observations (rows in the Jacobian) in this problem.
     *
     * @return the number of scalar observations
     */
    int getObservationSize();

    /**
     * Get the number of parameters (columns in the Jacobian) in this problem.
     *
     * @return the number of scalar parameters
     */
    int getParameterSize();

    /**
     * Evaluate the model at the specified point.
     *
     *
     * @param point the parameter values.
     * @return the model's value and derivative at the given point.
     * @throws org.apache.commons.math3.exception.TooManyEvaluationsException
     *          if the maximal number of evaluations (of the model vector function) is
     *          exceeded.
     */
    Evaluation evaluate(RealVector point);

    /**
     * An evaluation of a {@link LeastSquaresProblem} at a particular point. This class
     * also computes several quantities derived from the value and its Jacobian.
     */
    public interface Evaluation {

        /**
         * Get the covariance matrix of the optimized parameters. 
 Note that this
         * operation involves the inversion of the J^TJ matrix,
         * where {@code J} is the Jacobian matrix. The {@code threshold} parameter is a
         * way for the caller to specify that the result of this computation should be
         * considered meaningless, and thus trigger an exception.
         *
         *
         * @param threshold Singularity threshold.
         * @return the covariance matrix.
         * @throws org.apache.commons.math3.linear.SingularMatrixException
         *          if the covariance matrix cannot be computed (singular problem).
         */
        RealMatrix getCovariances(double threshold);

        /**
         * Get an estimate of the standard deviation of the parameters. The returned
         * values are the square root of the diagonal coefficients of the covariance
         * matrix, {@code sd(a[i]) ~= sqrt(C[i][i])}, where {@code a[i]} is the optimized
         * value of the {@code i}-th parameter, and {@code C} is the covariance matrix.
         *
         *
         * @param covarianceSingularityThreshold Singularity threshold (see {@link
         *                                       #getCovariances(double) computeCovariances}).
         * @return an estimate of the standard deviation of the optimized parameters
         * @throws org.apache.commons.math3.linear.SingularMatrixException
         *          if the covariance matrix cannot be computed.
         */
        RealVector getSigma(double covarianceSingularityThreshold);

        /**
         * Get the normalized cost. It is the square-root of the sum of squared of
         * the residuals, divided by the number of measurements.
         *
         * @return the cost.
         */
        double getRMS();

        /**
         * Get the weighted Jacobian matrix.
         *
         * @return the weighted Jacobian: W^1/2 J.
         * @throws org.apache.commons.math3.exception.DimensionMismatchException
         * if the Jacobian dimension does not match problem dimension.
         */
        RealMatrix getJacobian();

        /**
         * Get the cost.
         *
         * @return the cost.
         * @see #getResiduals()
         */
        double getCost();

        /**
         * Get the weighted residuals. The residual is the difference between the
         * observed (target) values and the model (objective function) value. There is one
         * residual for each element of the vector-valued function. The raw residuals are
         * then multiplied by the square root of the weight matrix.
         *
         * @return the weighted residuals: W^1/2 K.
         * @throws org.apache.commons.math3.exception.DimensionMismatchException
         * if the residuals have the wrong length.
         */
        RealVector getResiduals();

        /**
         * Get the abscissa (independent variables) of this evaluation.
         *
         * @return the point provided to {@link #evaluate(RealVector)}.
         */
        RealVector getPoint();
    }
}