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/*
 * Copyright (c) 2016 Jacob Rachiele
 *
 */

package optim;

/**
 * A class for performing cubic polynomial interpolation of a function.
 *
 * @author Jacob Rachiele
 *
 */
final class CubicInterpolation {

  private final double x1;
  private final double x2;
  private final double dydx1;
  private final double dydx2;
  private final double z;
  private final double w;

  public CubicInterpolation(final double x1, final double x2, final double y1, final double y2, final double dydx1,
      final double dydx2) {
    validate(x1, x2);
    double y21;
    double y11;
    if (x1 > x2) {
      this.x1 = x2;
      y11 = y2;
      this.dydx1 = dydx2;
      this.x2 = x1;
      y21 = y1;
      this.dydx2 = dydx1;
    } else {
      this.x1 = x1;
      this.x2 = x2;
      y11 = y1;
      y21 = y2;
      this.dydx1 = dydx1;
      this.dydx2 = dydx2;
    }
    double s = 3 * ((y21 - y11) / (this.x2 - this.x1));
    this.z = s - this.dydx1 - this.dydx2;
    this.w = Math.sqrt(z * z - this.dydx1 * this.dydx2);
  }

  final double minimum() {
    return x1 + (x2 - x1) * ((w - dydx1 - z) / (dydx2 - dydx1 + 2 * w));
  }

  private static void validate(final double x1, final double x2) {
    if (x1 == x2) {
      throw new RuntimeException("The two x values cannot be the same. x1 and x2 were both equal to: " + x1);
    }
  }
  
  static double minimum(final double x1, final double x2, final double y1, final double y2, final double dydx1,
                        final double dydx2) {
    validate(x1, x2);
    final double d1 = dydx2 + dydx1 - 3 * ((y2 - y1) / (x2 - x1));
    final double d2 = Math.signum(x1 - x2) * Math.sqrt(d1 * d1 - dydx2 * dydx1);
    return x1 - (x1 - x2) * ((dydx1 + d2 - d1) / (dydx1 - dydx2 + 2*d2));
  }
}