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// Copyright (c) 2015, Mikhail Vorotilov
// All rights reserved.
//
// Redistribution and use in source and binary forms, with or without
// modification, are permitted provided that the following conditions are met:
//
// * Redistributions of source code must retain the above copyright notice, this
//   list of conditions and the following disclaimer.
//
// * Redistributions in binary form must reproduce the above copyright notice,
//   this list of conditions and the following disclaimer in the documentation
//   and/or other materials provided with the distribution.
//
// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
// AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
// IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
// DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE
// FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
// DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
// SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
// CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
// OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
// OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.

use super::super::FloatType;
use super::SearchError;
use super::Convergency;

/// Illinois modification to the classical method
#[derive(Debug,PartialEq)]
enum Edge {
  /// Value is close to X1, reduce the Y1 weight
  EdgeX1,
  /// Value is in the middle of the interval
  NoEdge,
  /// Value is close to X2, reduce the Y2 weight
  EdgeX2,
}

/// Find a root of the function f(x) = 0 using the Illinois modification of the regula falsi method.
///
/// Pro
///
/// + Simple
/// + Robust
/// + No need for derivative function
///
/// Contra
///
/// - Slow
/// - Needs initial bracketing
///
/// # Failures
/// ## NoBracketing
/// Initial values do not bracket the root.
/// ## NoConvergency
/// Algorithm cannot find a root within the given number of iterations.
/// # Examples
///
/// ```
/// use roots::SimpleConvergency;
/// use roots::find_root_regula_falsi;
///
/// let f = |x| { 1f64*x*x - 1f64 };
/// let convergency = SimpleConvergency { eps:1e-15f64, max_iter:30 };
///
/// let root1 = find_root_regula_falsi(10f64, 0f64, &f, &convergency);
/// // Returns approximately Ok(1);
///
/// let root2 = find_root_regula_falsi(-10f64, 0f64, &f, &convergency);
/// // Returns approximately Ok(-1);
/// ```
pub fn find_root_regula_falsi<F:FloatType>(a:F, b:F, f:&Fn(F)->F, convergency:&Convergency<F>) -> (Result<F,SearchError>) {
  let _2 = F::one() + F::one();
  let (mut x1, mut x2) = if a > b { (b, a) } else { (a, b) };
  let mut y1 = f(x1);
  if convergency.is_root_found(y1) { return Ok(x1); }
  let mut y2 = f(x2);
  if convergency.is_root_found(y2) { return Ok(x2); }
  if y1 * y2 > F::zero() { return Err(SearchError::NoBracketing); }
  let mut edge = Edge::NoEdge;
  let mut iter = 0;
  loop {
    let x = (x1*y2-x2*y1)/(y2-y1);
    if convergency.is_converged(x1,x2) { return Ok(x); }
    let y = f(x);
    if convergency.is_root_found(y) { return Ok(x); }

    if y * y1 > F::zero() {
      x1 = x;
      y1 = y;
      if edge == Edge::EdgeX1 {
        y2 = y2 / _2;
      }
      edge = Edge::EdgeX1;
    }
    else if y * y2 > F::zero() {
      x2 = x;
      y2 = y;
      if edge == Edge::EdgeX2 {
        y1 = y1 / _2;
      }
      edge = Edge::EdgeX2;
    }
    else {
      return Ok(x);
    }

    iter = iter + 1;
    if convergency.is_iteration_limit_reached(iter) { return Err(SearchError::NoConvergency); }
  }
}

#[test]
fn test_find_root_regula_falsi() {
  let f = |x| { 1f64*x*x - 1f64 };
  let conv = super::debug_convergency::DebugConvergency::new(1e-15f64, 30);

  conv.reset();
  assert_float_eq!(1e-15f64, find_root_regula_falsi(10f64, 0f64, &f, &conv).ok().unwrap(), 1f64);
  assert_eq!(11, conv.get_iter_count());

  conv.reset();
  assert_float_eq!(1e-15f64, find_root_regula_falsi(-10f64, 0f64, &f, &conv).ok().unwrap(), -1f64);
  assert_eq!(11, conv.get_iter_count());

  conv.reset();
  assert_eq!(find_root_regula_falsi(10f64, 20f64, &f, &conv), Err(SearchError::NoBracketing));
  assert_eq!(0, conv.get_iter_count());
}