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/*
 * Copyright (c) 1998-2018 University Corporation for Atmospheric Research/Unidata
 * See LICENSE for license information.
 */

package ucar.unidata.util;

import ucar.nc2.util.HashMapLRU;

import javax.annotation.concurrent.Immutable;

/**
 * Calculate Gaussian Latitudes by finding the roots of the ordinary Legendre polynomial of degree
 * NLAT using Newton's iteration method.
 * Moderately expensive to compute, so keep LRU cache.
 *
 * @author caron port to Java
 * @author Amy Solomon, 28 Jan 1991, via http://dss.ucar.edu/libraries/gridinterps/gaus-lats.f
 */
@Immutable
public class GaussianLatitudes {
  private static final double XLIM  = 1.0E-7;
  private static final HashMapLRU hash = new HashMapLRU<>(10, 20);

  public static GaussianLatitudes factory(int nlats) {
    GaussianLatitudes glats = hash.get(nlats);
    if (glats == null) {
      glats = new GaussianLatitudes(nlats);
      hash.put(nlats, glats);
    }
    return glats;
  }

  // all these have size nlat
  public final double[] cosc; // cos(colatitude) or sin(latitude)
  public final double[] colat; // the colatitudes in radians
  public final double[] gaussw; // the Gaussian weights
  public final double[] latd; // the latitudes in degrees
  public final double[] sinc; // sin(colatitude) or cos(latitude)
  public final double[] wos2; // Gaussian weight over sin**2(colatitude)

  /**
   * Constructor
   * @param nlat the total number of latitudes from pole to pole (degree of the polynomial)
   */
  private GaussianLatitudes(int nlat) {
    if (nlat == 0) throw new IllegalArgumentException("nlats may not be zero");

    // the number of latitudes between pole and equator
    int  nzero = nlat/2;
    cosc = new double[nlat];
    colat = new double[nlat];
    gaussw = new double[nlat];
    latd = new double[nlat];
    sinc = new double[nlat];
    wos2 = new double[nlat];

    /* set first guess for cos(colat)
      PI = 3.141592653589793
      DO 10 I=1,NZERO
         COSC(I) = SIN( (I-0.5)*PI/NLAT + PI*0.5 )
   10 CONTINUE */
    for (int i=0; i