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/*
 * Copyright (c) 2016 Jacob Rachiele
 *
 * Permission is hereby granted, free of charge, to any person obtaining a copy of this software
 * and associated documentation files (the "Software"), to deal in the Software without restriction
 * including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense
 * and/or sell copies of the Software, and to permit persons to whom the Software is furnished to
 * do so, subject to the following conditions:
 *
 * The above copyright notice and this permission notice shall be included in all copies or
 * substantial portions of the Software.
 *
 * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED
 * INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR
 * PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE
 * LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT,
 * TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE
 * USE OR OTHER DEALINGS IN THE SOFTWARE.
 *
 * Contributors:
 *
 * Jacob Rachiele
 */
package math.function;

import math.Complex;
import math.Real;

/**
 * A univariate polynomial function of degree 2.
 *
 * @author Jacob Rachiele
 */
public class QuadraticFunction extends AbstractFunction {

    private final Real a;
    private final Real b;
    private final Real c;

    /**
     * Create a new quadratic function using the given coefficients.
     *
     * @param a the coefficient of the leading term of the polynomial.
     * @param b the coefficient of the first degree term of the polynomial.
     * @param c the constant term of the polynomial.
     */
    public QuadraticFunction(final Real a, final Real b, final Real c) {
        if (a.asDouble() == 0) {
            throw new IllegalArgumentException("The first coefficient, a, cannot be zero.");
        }
        this.a = a;
        this.b = b;
        this.c = c;
    }

    /**
     * Create a new quadratic function using the given coefficients.
     *
     * @param a the coefficient of the leading term of the polynomial.
     * @param b the coefficient of the first degree term of the polynomial.
     * @param c the constant term of the polynomial.
     */
    public QuadraticFunction(final double a, final double b, final double c) {
        if (a == 0) {
            throw new IllegalArgumentException("The first coefficient, a, cannot be zero.");
        }
        this.a = Real.from(a);
        this.b = Real.from(b);
        this.c = Real.from(c);
    }

    /**
     * Compute and return the zeros, or roots, of this function.
     *
     * @return the zeros, or roots, of this function.
     */
    public Complex[] zeros() {
        final Real fourAC = a.times(c).times(4.0);
        final Real bSquared = b.times(b);
        final Complex root1 = b.additiveInverse()
                               .plus(bSquared.minus(fourAC).complexSqrt())
                               .dividedBy(a.times(2).asDouble());
        final Complex root2 = b.additiveInverse()
                               .minus(bSquared.minus(fourAC).complexSqrt())
                               .dividedBy(a.times(2).asDouble());
        return new Complex[]{root1, root2};
    }

    /**
     * retrieve the coefficient of the leading term of the polynomial.
     *
     * @return the coefficient of the leading term of the polynomial.
     */
    public Real a() {
        return this.a;
    }

    /**
     * retrieve the coefficient of the first degree term of the polynomial.
     *
     * @return the coefficient of the first degree term of the polynomial.
     */
    public Real b() {
        return this.b;
    }

    /**
     * retrieve the constant term of the polynomial.
     *
     * @return the constant term of the polynomial.
     */
    public Real c() {
        return this.c;
    }

    public Real at(final Real point) {
        return Real.from(this.at(point.asDouble()));
    }

    @Override
    public double at(final double x) {
        return x * x * a.asDouble() + x * b.asDouble() + c.asDouble();
    }

    @Override
    public double slopeAt(final double x) {
        return 2 * x * a.asDouble() + b.asDouble();
    }

    /**
     * retrieve the coefficients of the polynomial.
     *
     * @return the coefficients of the polynomial.
     */
    public Real[] coefficients() {
        return new Real[]{this.a, this.b, this.c};
    }

    /**
     * retrieve the coefficients of the polynomial as primitives.
     *
     * @return the coefficients of the polynomial as primitives.
     */
    public double[] coefficientsDbl() {
        return new double[]{a.asDouble(), b.asDouble(), c.asDouble()};
    }

    /**
     * retrieve the point at which the localExtrema of this function occurs as a primitive.
     *
     * @return the point at which the localExtrema of this function occurs as a primitive.
     */
    public double extremePointDbl() {
        return -b.asDouble() / (2 * a.asDouble());
    }

    /**
     * retrieve the point at which the localExtrema of this function occurs.
     *
     * @return the point at which the localExtrema of this function occurs.
     */
    public Real extremePoint() {
        return Real.from(-b.asDouble() / (2 * a.asDouble()));
    }

    /**
     * retrieve the localExtrema of this function as a primitive.
     *
     * @return the localExtrema of this function as a primitive.
     */
    public double extremumDbl() {
        double x = extremePointDbl();
        return a.asDouble() * x * x + b.asDouble() * x + c.asDouble();
    }

    /**
     * retrieve the localExtrema of this function.
     *
     * @return the localExtrema of this function.
     */
    public Real extremum() {
        double x = extremePoint().asDouble();
        return Real.from(a.asDouble() * x * x + b.asDouble() * x + c.asDouble());
    }

    /**
     * Indicates if this function has a minimum or not.
     *
     * @return true if this function has a minimum, false otherwise.
     */
    public boolean hasMinimum() {
        return a.asDouble() > 0.0;
    }

    /**
     * Indicates if this function has a maximum or not.
     *
     * @return true if this function has a maximum, false otherwise.
     */
    public boolean hasMaximum() {
        return a.asDouble() < 0.0;
    }

    @Override
    public boolean equals(Object o) {
        if (this == o) return true;
        if (o == null || getClass() != o.getClass()) return false;

        QuadraticFunction that = (QuadraticFunction) o;

        if (!a.equals(that.a)) return false;
        if (!b.equals(that.b)) return false;
        return c.equals(that.c);
    }

    @Override
    public int hashCode() {
        int result = a.hashCode();
        result = 31 * result + b.hashCode();
        result = 31 * result + c.hashCode();
        return result;
    }

    @Override
    public String toString() {
        return "f(x) = " + a.asDouble() + "x^2 + " + b.asDouble() + "x + " + c.asDouble();
    }
}