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  /* ====================================================================
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     Licensed to the Apache Software Foundation (ASF) under one or more
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     contributor license agreements.  See the NOTICE file distributed with
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     this work for additional information regarding copyright ownership.
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     The ASF licenses this file to You under the Apache License, Version 2.0
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     (the "License"); you may not use this file except in compliance with
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     the License.  You may obtain a copy of the License at
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         http://www.apache.org/licenses/LICENSE-2.0
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    Unless required by applicable law or agreed to in writing, software
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    distributed under the License is distributed on an "AS IS" BASIS,
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    WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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    See the License for the specific language governing permissions and
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    limitations under the License.
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 ==================================================================== */
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 package org.apache.poi.ss.formula.functions;
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Calculates the internal rate of return. Syntax is IRR(values) or IRR(values,guess)

Author(s):
Marcel May
Yegor Kozlov
See also:
Wikipedia on IRR
Excel IRR
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 public final class Irr implements Function {
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     public ValueEval evaluate(final ValueEval[] args, final int srcRowIndex, final int srcColumnIndex) {
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         if(args.length == 0 || args.length > 2) {
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             // Wrong number of arguments
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             return .;
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         }
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         try {
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             double[] values = AggregateFunction.ValueCollector.collectValues(args[0]);
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             double guess;
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             if(args.length == 2) {
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                 guess = NumericFunction.singleOperandEvaluate(args[1], srcRowIndex, srcColumnIndex);
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             } else {
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                 guess = 0.1d;
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             }
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             double result = irr(values, guess);
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             NumericFunction.checkValue(result);
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             return new NumberEval(result);
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         } catch (EvaluationException e){
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             return e.getErrorEval();
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         }
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     }

    
Computes the internal rate of return using an estimated irr of 10 percent.

Parameters:
income the income values.
Returns:
the irr.
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     public static double irr(double[] income) {
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         return irr(income, 0.1d);
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     }


    
Calculates IRR using the Newton-Raphson Method.

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 Double.NaN<> is returned.

The implementation is inspired by the NewtonSolver from the Apache Commons-Math library,

Parameters:
values the income values.
guess the initial guess of irr.
Returns:
the irr value. The method returns Double.NaN if the maximum iteration count is exceeded
See also:
{http://commons.apache.org/}
{http://en.wikipedia.org/wiki/Internal_rate_of_return.Numerical_solution}
{http://en.wikipedia.org/wiki/Newton%27s_method}
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     public static double irr(double[] values, double guess) {
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         int maxIterationCount = 20;
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         double absoluteAccuracy = 1E-7;
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         double x0 = guess;
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         double x1;
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         int i = 0;
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         while (i < maxIterationCount) {
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             // the value of the function (NPV) and its derivate can be calculated in the same loop
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            double fValue = 0;
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            double fDerivative = 0;
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            for (int k = 0; k < values.length; k++) {
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                fValue += values[k] / Math.pow(1.0 + x0, k);
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                fDerivative += -k * values[k] / Math.pow(1.0 + x0, k + 1);
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            }
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            // the essense of the Newton-Raphson Method
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            x1 = x0 - fValue/fDerivative;
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            if (Math.abs(x1 - x0) <= absoluteAccuracy) {
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                return x1;
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            }
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            x0 = x1;
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            ++i;
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        }
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        // maximum number of iterations is exceeded
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        return .;
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    }
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