/*
 * Jalview - A Sequence Alignment Editor and Viewer (Version 2.9.0b1)
 * Copyright (C) 2015 The Jalview Authors
 * 
 * This file is part of Jalview.
 * 
 * Jalview is free software: you can redistribute it and/or
 * modify it under the terms of the GNU General Public License 
 * as published by the Free Software Foundation, either version 3
 * of the License, or (at your option) any later version.
 *  
 * Jalview is distributed in the hope that it will be useful, but 
 * WITHOUT ANY WARRANTY; without even the implied warranty 
 * of MERCHANTABILITY or FITNESS FOR A PARTICULAR 
 * PURPOSE.  See the GNU General Public License for more details.
 * 
 * You should have received a copy of the GNU General Public License
 * along with Jalview.  If not, see <http://www.gnu.org/licenses/>.
 * The Jalview Authors are detailed in the 'AUTHORS' file.
 */
package jalview.math;

import jalview.util.Format;
import jalview.util.MessageManager;

import java.io.PrintStream;

/**
 * DOCUMENT ME!
 * 
 * @author $author$
 * @version $Revision$
 */
public class Matrix
{
  /**
   * SMJSPUBLIC
   */
  public double[][] value;

  /** DOCUMENT ME!! */
  public int rows;

  /** DOCUMENT ME!! */
  public int cols;

  /** DOCUMENT ME!! */
  public double[] d; // Diagonal

  /** DOCUMENT ME!! */
  public double[] e; // off diagonal

  /**
   * maximum number of iterations for tqli
   * 
   */
  int maxIter = 45; // fudge - add 15 iterations, just in case

  /**
   * Creates a new Matrix object.
   * 
   * @param value
   *          DOCUMENT ME!
   * @param rows
   *          DOCUMENT ME!
   * @param cols
   *          DOCUMENT ME!
   */
  public Matrix(double[][] value, int rows, int cols)
  {
    this.rows = rows;
    this.cols = cols;
    this.value = value;
  }

  /**
   * DOCUMENT ME!
   * 
   * @return DOCUMENT ME!
   */
  public Matrix transpose()
  {
    double[][] out = new double[cols][rows];

    for (int i = 0; i < cols; i++)
    {
      for (int j = 0; j < rows; j++)
      {
        out[i][j] = value[j][i];
      }
    }

    return new Matrix(out, cols, rows);
  }

  /**
   * DOCUMENT ME!
   * 
   * @param ps
   *          DOCUMENT ME!
   */
  public void print(PrintStream ps)
  {
    for (int i = 0; i < rows; i++)
    {
      for (int j = 0; j < cols; j++)
      {
        Format.print(ps, "%8.2f", value[i][j]);
      }

      ps.println();
    }
  }

  /**
   * DOCUMENT ME!
   * 
   * @param in
   *          DOCUMENT ME!
   * 
   * @return DOCUMENT ME!
   */
  public Matrix preMultiply(Matrix in)
  {
    double[][] tmp = new double[in.rows][this.cols];

    for (int i = 0; i < in.rows; i++)
    {
      for (int j = 0; j < this.cols; j++)
      {
        tmp[i][j] = 0.0;

        for (int k = 0; k < in.cols; k++)
        {
          tmp[i][j] += (in.value[i][k] * this.value[k][j]);
        }
      }
    }

    return new Matrix(tmp, in.rows, this.cols);
  }

  /**
   * DOCUMENT ME!
   * 
   * @param in
   *          DOCUMENT ME!
   * 
   * @return DOCUMENT ME!
   */
  public double[] vectorPostMultiply(double[] in)
  {
    double[] out = new double[in.length];

    for (int i = 0; i < in.length; i++)
    {
      out[i] = 0.0;

      for (int k = 0; k < in.length; k++)
      {
        out[i] += (value[i][k] * in[k]);
      }
    }

    return out;
  }

  /**
   * DOCUMENT ME!
   * 
   * @param in
   *          DOCUMENT ME!
   * 
   * @return DOCUMENT ME!
   */
  public Matrix postMultiply(Matrix in)
  {
    double[][] out = new double[this.rows][in.cols];

    for (int i = 0; i < this.rows; i++)
    {
      for (int j = 0; j < in.cols; j++)
      {
        out[i][j] = 0.0;

        for (int k = 0; k < rows; k++)
        {
          out[i][j] = out[i][j] + (value[i][k] * in.value[k][j]);
        }
      }
    }

    return new Matrix(out, this.cols, in.rows);
  }

  /**
   * DOCUMENT ME!
   * 
   * @return DOCUMENT ME!
   */
  public Matrix copy()
  {
    double[][] newmat = new double[rows][cols];

    for (int i = 0; i < rows; i++)
    {
      for (int j = 0; j < cols; j++)
      {
        newmat[i][j] = value[i][j];
      }
    }

    return new Matrix(newmat, rows, cols);
  }

  /**
   * DOCUMENT ME!
   */
  public void tred()
  {
    int n = rows;
    int l;
    int k;
    int j;
    int i;

    double scale;
    double hh;
    double h;
    double g;
    double f;

    this.d = new double[rows];
    this.e = new double[rows];

    for (i = n; i >= 2; i--)
    {
      l = i - 1;
      h = 0.0;
      scale = 0.0;

      if (l > 1)
      {
        for (k = 1; k <= l; k++)
        {
          scale += Math.abs(value[i - 1][k - 1]);
        }

        if (scale == 0.0)
        {
          e[i - 1] = value[i - 1][l - 1];
        }
        else
        {
          for (k = 1; k <= l; k++)
          {
            value[i - 1][k - 1] /= scale;
            h += (value[i - 1][k - 1] * value[i - 1][k - 1]);
          }

          f = value[i - 1][l - 1];

          if (f > 0)
          {
            g = -1.0 * Math.sqrt(h);
          }
          else
          {
            g = Math.sqrt(h);
          }

          e[i - 1] = scale * g;
          h -= (f * g);
          value[i - 1][l - 1] = f - g;
          f = 0.0;

          for (j = 1; j <= l; j++)
          {
            value[j - 1][i - 1] = value[i - 1][j - 1] / h;
            g = 0.0;

            for (k = 1; k <= j; k++)
            {
              g += (value[j - 1][k - 1] * value[i - 1][k - 1]);
            }

            for (k = j + 1; k <= l; k++)
            {
              g += (value[k - 1][j - 1] * value[i - 1][k - 1]);
            }

            e[j - 1] = g / h;
            f += (e[j - 1] * value[i - 1][j - 1]);
          }

          hh = f / (h + h);

          for (j = 1; j <= l; j++)
          {
            f = value[i - 1][j - 1];
            g = e[j - 1] - (hh * f);
            e[j - 1] = g;

            for (k = 1; k <= j; k++)
            {
              value[j - 1][k - 1] -= ((f * e[k - 1]) + (g * value[i - 1][k - 1]));
            }
          }
        }
      }
      else
      {
        e[i - 1] = value[i - 1][l - 1];
      }

      d[i - 1] = h;
    }

    d[0] = 0.0;
    e[0] = 0.0;

    for (i = 1; i <= n; i++)
    {
      l = i - 1;

      if (d[i - 1] != 0.0)
      {
        for (j = 1; j <= l; j++)
        {
          g = 0.0;

          for (k = 1; k <= l; k++)
          {
            g += (value[i - 1][k - 1] * value[k - 1][j - 1]);
          }

          for (k = 1; k <= l; k++)
          {
            value[k - 1][j - 1] -= (g * value[k - 1][i - 1]);
          }
        }
      }

      d[i - 1] = value[i - 1][i - 1];
      value[i - 1][i - 1] = 1.0;

      for (j = 1; j <= l; j++)
      {
        value[j - 1][i - 1] = 0.0;
        value[i - 1][j - 1] = 0.0;
      }
    }
  }

  /**
   * DOCUMENT ME!
   */
  public void tqli() throws Exception
  {
    int n = rows;

    int m;
    int l;
    int iter;
    int i;
    int k;
    double s;
    double r;
    double p;
    ;

    double g;
    double f;
    double dd;
    double c;
    double b;

    for (i = 2; i <= n; i++)
    {
      e[i - 2] = e[i - 1];
    }

    e[n - 1] = 0.0;

    for (l = 1; l <= n; l++)
    {
      iter = 0;

      do
      {
        for (m = l; m <= (n - 1); m++)
        {
          dd = Math.abs(d[m - 1]) + Math.abs(d[m]);

          if ((Math.abs(e[m - 1]) + dd) == dd)
          {
            break;
          }
        }

        if (m != l)
        {
          iter++;

          if (iter == maxIter)
          {
            throw new Exception(MessageManager.formatMessage(
                    "exception.matrix_too_many_iteration", new String[] {
                        "tqli", Integer.valueOf(maxIter).toString() }));
          }
          else
          {
            // System.out.println("Iteration " + iter);
          }

          g = (d[l] - d[l - 1]) / (2.0 * e[l - 1]);
          r = Math.sqrt((g * g) + 1.0);
          g = d[m - 1] - d[l - 1] + (e[l - 1] / (g + sign(r, g)));
          c = 1.0;
          s = c;
          p = 0.0;

          for (i = m - 1; i >= l; i--)
          {
            f = s * e[i - 1];
            b = c * e[i - 1];

            if (Math.abs(f) >= Math.abs(g))
            {
              c = g / f;
              r = Math.sqrt((c * c) + 1.0);
              e[i] = f * r;
              s = 1.0 / r;
              c *= s;
            }
            else
            {
              s = f / g;
              r = Math.sqrt((s * s) + 1.0);
              e[i] = g * r;
              c = 1.0 / r;
              s *= c;
            }

            g = d[i] - p;
            r = ((d[i - 1] - g) * s) + (2.0 * c * b);
            p = s * r;
            d[i] = g + p;
            g = (c * r) - b;

            for (k = 1; k <= n; k++)
            {
              f = value[k - 1][i];
              value[k - 1][i] = (s * value[k - 1][i - 1]) + (c * f);
              value[k - 1][i - 1] = (c * value[k - 1][i - 1]) - (s * f);
            }
          }

          d[l - 1] = d[l - 1] - p;
          e[l - 1] = g;
          e[m - 1] = 0.0;
        }
      } while (m != l);
    }
  }

  /**
   * DOCUMENT ME!
   */
  public void tred2()
  {
    int n = rows;
    int l;
    int k;
    int j;
    int i;

    double scale;
    double hh;
    double h;
    double g;
    double f;

    this.d = new double[rows];
    this.e = new double[rows];

    for (i = n - 1; i >= 1; i--)
    {
      l = i - 1;
      h = 0.0;
      scale = 0.0;

      if (l > 0)
      {
        for (k = 0; k < l; k++)
        {
          scale += Math.abs(value[i][k]);
        }

        if (scale == 0.0)
        {
          e[i] = value[i][l];
        }
        else
        {
          for (k = 0; k < l; k++)
          {
            value[i][k] /= scale;
            h += (value[i][k] * value[i][k]);
          }

          f = value[i][l];

          if (f > 0)
          {
            g = -1.0 * Math.sqrt(h);
          }
          else
          {
            g = Math.sqrt(h);
          }

          e[i] = scale * g;
          h -= (f * g);
          value[i][l] = f - g;
          f = 0.0;

          for (j = 0; j < l; j++)
          {
            value[j][i] = value[i][j] / h;
            g = 0.0;

            for (k = 0; k < j; k++)
            {
              g += (value[j][k] * value[i][k]);
            }

            for (k = j; k < l; k++)
            {
              g += (value[k][j] * value[i][k]);
            }

            e[j] = g / h;
            f += (e[j] * value[i][j]);
          }

          hh = f / (h + h);

          for (j = 0; j < l; j++)
          {
            f = value[i][j];
            g = e[j] - (hh * f);
            e[j] = g;

            for (k = 0; k < j; k++)
            {
              value[j][k] -= ((f * e[k]) + (g * value[i][k]));
            }
          }
        }
      }
      else
      {
        e[i] = value[i][l];
      }

      d[i] = h;
    }

    d[0] = 0.0;
    e[0] = 0.0;

    for (i = 0; i < n; i++)
    {
      l = i - 1;

      if (d[i] != 0.0)
      {
        for (j = 0; j < l; j++)
        {
          g = 0.0;

          for (k = 0; k < l; k++)
          {
            g += (value[i][k] * value[k][j]);
          }

          for (k = 0; k < l; k++)
          {
            value[k][j] -= (g * value[k][i]);
          }
        }
      }

      d[i] = value[i][i];
      value[i][i] = 1.0;

      for (j = 0; j < l; j++)
      {
        value[j][i] = 0.0;
        value[i][j] = 0.0;
      }
    }
  }

  /**
   * DOCUMENT ME!
   */
  public void tqli2() throws Exception
  {
    int n = rows;

    int m;
    int l;
    int iter;
    int i;
    int k;
    double s;
    double r;
    double p;
    ;

    double g;
    double f;
    double dd;
    double c;
    double b;

    for (i = 2; i <= n; i++)
    {
      e[i - 2] = e[i - 1];
    }

    e[n - 1] = 0.0;

    for (l = 1; l <= n; l++)
    {
      iter = 0;

      do
      {
        for (m = l; m <= (n - 1); m++)
        {
          dd = Math.abs(d[m - 1]) + Math.abs(d[m]);

          if ((Math.abs(e[m - 1]) + dd) == dd)
          {
            break;
          }
        }

        if (m != l)
        {
          iter++;

          if (iter == maxIter)
          {
            throw new Exception(MessageManager.formatMessage(
                    "exception.matrix_too_many_iteration", new String[] {
                        "tqli2", Integer.valueOf(maxIter).toString() }));
          }
          else
          {
            // System.out.println("Iteration " + iter);
          }

          g = (d[l] - d[l - 1]) / (2.0 * e[l - 1]);
          r = Math.sqrt((g * g) + 1.0);
          g = d[m - 1] - d[l - 1] + (e[l - 1] / (g + sign(r, g)));
          c = 1.0;
          s = c;
          p = 0.0;

          for (i = m - 1; i >= l; i--)
          {
            f = s * e[i - 1];
            b = c * e[i - 1];

            if (Math.abs(f) >= Math.abs(g))
            {
              c = g / f;
              r = Math.sqrt((c * c) + 1.0);
              e[i] = f * r;
              s = 1.0 / r;
              c *= s;
            }
            else
            {
              s = f / g;
              r = Math.sqrt((s * s) + 1.0);
              e[i] = g * r;
              c = 1.0 / r;
              s *= c;
            }

            g = d[i] - p;
            r = ((d[i - 1] - g) * s) + (2.0 * c * b);
            p = s * r;
            d[i] = g + p;
            g = (c * r) - b;

            for (k = 1; k <= n; k++)
            {
              f = value[k - 1][i];
              value[k - 1][i] = (s * value[k - 1][i - 1]) + (c * f);
              value[k - 1][i - 1] = (c * value[k - 1][i - 1]) - (s * f);
            }
          }

          d[l - 1] = d[l - 1] - p;
          e[l - 1] = g;
          e[m - 1] = 0.0;
        }
      } while (m != l);
    }
  }

  /**
   * DOCUMENT ME!
   * 
   * @param a
   *          DOCUMENT ME!
   * @param b
   *          DOCUMENT ME!
   * 
   * @return DOCUMENT ME!
   */
  public double sign(double a, double b)
  {
    if (b < 0)
    {
      return -Math.abs(a);
    }
    else
    {
      return Math.abs(a);
    }
  }

  /**
   * DOCUMENT ME!
   * 
   * @param n
   *          DOCUMENT ME!
   * 
   * @return DOCUMENT ME!
   */
  public double[] getColumn(int n)
  {
    double[] out = new double[rows];

    for (int i = 0; i < rows; i++)
    {
      out[i] = value[i][n];
    }

    return out;
  }

  /**
   * DOCUMENT ME!
   * 
   * @param ps
   *          DOCUMENT ME!
   */
  public void printD(PrintStream ps)
  {
    for (int j = 0; j < rows; j++)
    {
      Format.print(ps, "%15.4e", d[j]);
    }
  }

  /**
   * DOCUMENT ME!
   * 
   * @param ps
   *          DOCUMENT ME!
   */
  public void printE(PrintStream ps)
  {
    for (int j = 0; j < rows; j++)
    {
      Format.print(ps, "%15.4e", e[j]);
    }
  }

  /**
   * DOCUMENT ME!
   * 
   * @param args
   *          DOCUMENT ME!
   */
  public static void main(String[] args) throws Exception
  {
    int n = Integer.parseInt(args[0]);
    double[][] in = new double[n][n];

    for (int i = 0; i < n; i++)
    {
      for (int j = 0; j < n; j++)
      {
        in[i][j] = (double) Math.random();
      }
    }

    Matrix origmat = new Matrix(in, n, n);

    // System.out.println(" --- Original matrix ---- ");
    // / origmat.print(System.out);
    // System.out.println();
    // System.out.println(" --- transpose matrix ---- ");
    Matrix trans = origmat.transpose();

    // trans.print(System.out);
    // System.out.println();
    // System.out.println(" --- OrigT * Orig ---- ");
    Matrix symm = trans.postMultiply(origmat);

    // symm.print(System.out);
    // System.out.println();
    // Copy the symmetric matrix for later
    // Matrix origsymm = symm.copy();

    // This produces the tridiagonal transformation matrix
    // long tstart = System.currentTimeMillis();
    symm.tred();

    // long tend = System.currentTimeMillis();

    // System.out.println("Time take for tred = " + (tend-tstart) + "ms");
    // System.out.println(" ---Tridiag transform matrix ---");
    // symm.print(System.out);
    // System.out.println();
    // System.out.println(" --- D vector ---");
    // symm.printD(System.out);
    // System.out.println();
    // System.out.println(" --- E vector ---");
    // symm.printE(System.out);
    // System.out.println();
    // Now produce the diagonalization matrix
    // tstart = System.currentTimeMillis();
    symm.tqli();
    // tend = System.currentTimeMillis();

    // System.out.println("Time take for tqli = " + (tend-tstart) + " ms");
    // System.out.println(" --- New diagonalization matrix ---");
    // symm.print(System.out);
    // System.out.println();
    // System.out.println(" --- D vector ---");
    // symm.printD(System.out);
    // System.out.println();
    // System.out.println(" --- E vector ---");
    // symm.printE(System.out);
    // System.out.println();
    // System.out.println(" --- First eigenvector --- ");
    // double[] eigenv = symm.getColumn(0);
    // for (int i=0; i < eigenv.length;i++) {
    // Format.print(System.out,"%15.4f",eigenv[i]);
    // }
    // System.out.println();
    // double[] neigenv = origsymm.vectorPostMultiply(eigenv);
    // for (int i=0; i < neigenv.length;i++) {
    // Format.print(System.out,"%15.4f",neigenv[i]/symm.d[0]);
    // }
    // System.out.println();
  }
}