poi/src/main/java/org/apache/poi/ss/formula/functions/Irr.java

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   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
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       http://www.apache.org/licenses/LICENSE-2.0

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   distributed under the License is distributed on an "AS IS" BASIS,
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package org.apache.poi.ss.formula.functions;

import org.apache.poi.ss.formula.eval.ErrorEval;
import org.apache.poi.ss.formula.eval.EvaluationException;
import org.apache.poi.ss.formula.eval.NumberEval;
import org.apache.poi.ss.formula.eval.ValueEval;

/**
 * Calculates the internal rate of return.
 *
 * Syntax is IRR(values) or IRR(values,guess)
 *
 * @see <a href="http://en.wikipedia.org/wiki/Internal_rate_of_return#Numerical_solution">Wikipedia on IRR</a>
 * @see <a href="http://office.microsoft.com/en-us/excel-help/irr-HP005209146.aspx">Excel IRR</a>
 */
public final class Irr implements Function {
    private static final int MAX_ITERATION_COUNT = 20;
    private static final double ABSOLUTE_ACCURACY = 1E-7;


    public ValueEval evaluate(final ValueEval[] args, final int srcRowIndex, final int srcColumnIndex) {
        if(args.length == 0 || args.length > 2) {
            // Wrong number of arguments
            return ErrorEval.VALUE_INVALID;
        }

        try {
            double[] values = AggregateFunction.ValueCollector.collectValues(args[0]);
            double guess;
            if(args.length == 2) {
                guess = NumericFunction.singleOperandEvaluate(args[1], srcRowIndex, srcColumnIndex);
            } else {
                guess = 0.1d;
            }
            double result = irr(values, guess);
            NumericFunction.checkValue(result);
            return new NumberEval(result);
        } catch (EvaluationException e){
            return e.getErrorEval();
        }
    }

    /**
     * Computes the internal rate of return using an estimated irr of 10 percent.
     *
     * @param income the income values.
     * @return the irr.
     */
    public static double irr(double[] income) {
        return irr(income, 0.1d);
    }


    /**
     * Calculates IRR using the Newton-Raphson Method.
     * <p>
     * Starting with the guess, the method cycles through the calculation until the result
     * is accurate within 0.00001 percent. If IRR can't find a result that works
     * after 20 tries, the {@code Double.NaN} is returned.
     * </p>
     * <p>
     *   The implementation is inspired by the NewtonSolver from the Apache Commons-Math library,
     *   @see <a href="http://commons.apache.org">http://commons.apache.org</a>
     * </p>
     *
     * @param values        the income values.
     * @param guess         the initial guess of irr.
     * @return the irr value. The method returns {@code Double.NaN}
     *  if the maximum iteration count is exceeded
     *
     * @see <a href="http://en.wikipedia.org/wiki/Internal_rate_of_return#Numerical_solution">
     *     http://en.wikipedia.org/wiki/Internal_rate_of_return#Numerical_solution</a>
     * @see <a href="http://en.wikipedia.org/wiki/Newton%27s_method">
     *     http://en.wikipedia.org/wiki/Newton%27s_method</a>
     */
    public static double irr(double[] values, double guess) {

        double x0 = guess;

        for (int i = 0; i < MAX_ITERATION_COUNT; i++) {

            // the value of the function (NPV) and its derivate can be calculated in the same loop
            final double factor = 1.0 + x0;
            double denominator = factor;
            if (denominator == 0) {
                return Double.NaN;
            }

            double fValue = values[0];
            double fDerivative = 0;
            for (int k = 1; k < values.length; k++) {
                final double value = values[k];
                fValue += value / denominator;
                denominator *= factor;
                fDerivative -= k * value / denominator;
            }

            // the essence of the Newton-Raphson Method
            if (fDerivative == 0) {
                return Double.NaN;
            }
            double x1 =  x0 - fValue/fDerivative;

            if (Math.abs(x1 - x0) <= ABSOLUTE_ACCURACY) {
                return x1;
            }

            x0 = x1;
        }
        // maximum number of iterations is exceeded
        return Double.NaN;
    }
}