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//   http://www.apache.org/licenses/LICENSE-2.0
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package org.spaceroots.mantissa.linalg;

import java.io.Serializable;

/** This class factor all services common to matrices.

 * <p>This class is the base class of all matrix implementations, it
 * is also the base class of the {@link SquareMatrix} class which adds
 * methods specific to square matrices.</p>

 * <p>This class both handles the storage of matrix elements and
 * implements the classical operations on matrices (addition,
 * substraction, multiplication, transposition). It relies on two
 * protected methods ({@link #getRangeForRow} and {@link
 * #getRangeForColumn}) to get tight loop bounds for matrices with
 * known structures full of zeros. These methods should be
 * implemented by derived classes to provide information about their
 * specific shape to the general algorithms implemented by this
 * abstract class.</p>

 * @version $Id$
 * @author L. Maisonobe

 */

public abstract class Matrix
  implements Serializable {
  /** Simple constructor.
   * Build a matrix with null elements.
   * @param rows number of rows of the matrix
   * @param columns number of columns of the matrix
   */
  protected Matrix(int rows, int columns) {
    // sanity check
    if (rows <= 0 || columns <= 0) {
      throw new IllegalArgumentException("cannot build a matrix"
                                         + " with negative or null dimension");
    }

    this.rows    = rows;
    this.columns = columns;
    data = new double[rows * columns];
    for (int i = 0; i < data.length; ++i) {
      data[i] = 0.0;
    }

  }

  /** Simple constructor.
   * Build a matrix with specified elements.
   * @param rows number of rows of the matrix
   * @param columns number of columns of the matrix
   * @param data table of the matrix elements (stored row after row)
   */
  public Matrix(int rows, int columns, double[] data) {
    // sanity check
    if (rows <= 0 || columns <= 0) {
      throw new IllegalArgumentException("cannot build a matrix"
                                         + " with negative or null dimension");
    }

    this.rows    = rows;
    this.columns = columns;
    this.data    = (data == null) ? null : (double[]) data.clone();

  }

  /** Copy constructor.
   * @param m matrix to copy
   */
  protected Matrix(Matrix m) {
    rows    = m.rows;
    columns = m.columns;
    data    = new double[rows * columns];
    System.arraycopy(m.data, 0, data, 0, m.data.length);
  }

  /** Polymorphic copy operator.
   * This method build a new object of the same type of the
   * instance. It is somewhat similar to the {@link Object#clone}
   * method, except that it has public access, it doesn't throw any
   * specific exception and it returns a Matrix.
   *@see Object#clone
   */
  public abstract Matrix duplicate();

  /** Get the number of rows of the matrix.
   * @return number of rows
   * @see #getColumns
   */
  public int getRows() {
    return rows;
  }

  /** Get the number of columns of the matrix.
   * @return number of columns
   * @see #getRows
   */
  public int getColumns() {
    return columns;
  }

  /** Get a matrix element.
   * @param i row index, from 0 to rows - 1
   * @param j column index, from 0 to cols - 1
   * @return value of the element
   * @exception ArrayIndexOutOfBoundsException if the indices are wrong
   * @see #setElement
   */
  public double getElement(int i, int j) {
    if (i < 0 || i >= rows || j < 0 || j >= columns) {
      throw new IllegalArgumentException("cannot get element ("
                                         + i + ", " + j + ") from a "
                                         + rows + 'x' + columns
                                         + " matrix");
    }
    return data[i * columns + j];
  }

  /** Set a matrix element.
   * @param i row index, from 0 to rows - 1
   * @param j column index, from 0 to cols - 1
   * @param value value of the element
   * @exception ArrayIndexOutOfBoundsException if the indices are wrong
   * @see #getElement
   */
  public void setElement(int i, int j, double value) {
    if (i < 0 || i >= rows || j < 0 || j >= columns) {
      throw new IllegalArgumentException("cannot set element ("
                                         + i + ", " + j + ") in a "
                                         + rows + 'x' + columns
                                         + " matrix");
    }
    data[i * columns + j] = value;
  }

  /** Add a matrix to the instance.
   * This method adds a matrix to the instance. It returns a new
   * matrix and does not modify the instance.
   * @param m matrix to add
   * @return a new matrix containing the result
   * @exception IllegalArgumentException if there is a dimension mismatch
   */
  public Matrix add(Matrix m) {

    // validity check
    if ((rows != m.rows) || (columns != m.columns)) {
      throw new IllegalArgumentException("cannot add a "
                                         + m.rows + 'x' + m.columns
                                         + " matrix to a "
                                         + rows + 'x' + columns
                                         + " matrix");
    }

    double[] resultData    = new double[rows * columns];
    int      resultIndex   = 0;
    int      lowerElements = 0;
    int      upperElements = 0;

    // external loop through the rows
    for (int i = 0; i < rows; ++i) {
      // compute the indices of the internal loop
      NonNullRange r = NonNullRange.reunion(getRangeForRow(i),
                                            m.getRangeForRow(i));

      // assign the zeros before the non null range
      int j = 0;
      while (j < r.begin) {
        resultData[resultIndex] = 0.0;
        ++resultIndex;
        ++j;
      }

      // compute the possibly non null elements
      while (j < r.end) {

        // compute the current element
        resultData[resultIndex] = data[resultIndex] + m.data[resultIndex];

        // count the affected upper and lower elements
        // (in order to deduce the shape of the resulting matrix)
        if (j < i) {
          ++lowerElements;
        } else if (i < j) {
          ++upperElements;
        }

        ++resultIndex;
        ++j;

      }

      // assign the zeros after the non null range
      while (j < columns) {
        resultData[resultIndex++] = 0.0;
        ++resultIndex;
        ++j;
      }
    }

    return MatrixFactory.buildMatrix(rows, columns, resultData,
                                     lowerElements, upperElements);

  }

  /** Substract a matrix from the instance.
   * This method substracts a matrix from the instance. It returns a new
   * matrix and does not modify the instance.
   * @param m matrix to substract
   * @return a new matrix containing the result
   * @exception IllegalArgumentException if there is a dimension mismatch
   */
  public Matrix sub(Matrix m) {

    // validity check
    if ((rows != m.rows) || (columns != m.columns)) {
      throw new IllegalArgumentException("cannot substract a "
                                         + m.rows + 'x' + m.columns
                                         + " matrix from a "
                                         + rows + 'x' + columns
                                         + " matrix");
    }

    double[] resultData    = new double[rows * columns];
    int      resultIndex   = 0;
    int      lowerElements = 0;
    int      upperElements = 0;

    // external loop through the rows
    for (int i = 0; i < rows; ++i) {
      // compute the indices of the internal loop
      NonNullRange r = NonNullRange.reunion(getRangeForRow(i),
                                            m.getRangeForRow(i));

      // assign the zeros before the non null range
      int j = 0;
      while (j < r.begin) {
        resultData[resultIndex] = 0.0;
        ++resultIndex;
        ++j;
      }

      // compute the possibly non null elements
      while (j < r.end) {

        // compute the current element
        resultData[resultIndex] = data[resultIndex] - m.data[resultIndex];

        // count the affected upper and lower elements
        // (in order to deduce the shape of the resulting matrix)
        if (j < i) {
          ++lowerElements;
        } else if (i < j) {
          ++upperElements;
        }

        ++resultIndex;
        ++j;

      }

      // assign the zeros after the non null range
      while (j < columns) {
        resultData[resultIndex++] = 0.0;
        ++resultIndex;
        ++j;
      }
    }

    return MatrixFactory.buildMatrix(rows, columns, resultData,
                                     lowerElements, upperElements);

  }

  /** Multiply the instance by a matrix.
   * This method multiplies the instance by a matrix. It returns a new
   * matrix and does not modify the instance.
   * @param m matrix by which to multiply
   * @return a new matrix containing the result
   * @exception IllegalArgumentException if there is a dimension mismatch
   */
  public Matrix mul(Matrix m) {

    // validity check
    if (columns != m.rows) {
      throw new IllegalArgumentException("cannot multiply a "
                                         + rows + 'x' + columns
                                         + " matrix by a "
                                         + m.rows + 'x' + m.columns
                                         + " matrix");
    }

    double[] resultData = new double[rows * m.columns];
    int resultIndex     = 0;
    int lowerElements   = 0;
    int upperElements   = 0;

    for (int i = 0; i < rows; ++i) {
      for (int j = 0; j < m.columns; ++j) {
        double value = 0.0;

        // compute the tighter possible indices of the internal loop
        NonNullRange r = NonNullRange.intersection(getRangeForRow(i),
                                                   m.getRangeForColumn(j));

        if (r.begin < r.end) {
          int k    = r.begin;
          int idx  = i * columns + k;
          int midx = k * m.columns + j;
          while (k++ < r.end) {
            value += data[idx++] * m.data[midx];
            midx  += m.columns;
          }

          // count the affected upper and lower elements
          // (in order to deduce the shape of the resulting matrix)
          if (j < i) {
            ++lowerElements;
          } else if (i < j) {
            ++upperElements;
          }

        }

        // store the element value
        resultData[resultIndex++] = value;

      }
    }

    return MatrixFactory.buildMatrix(rows, m.columns, resultData,
                                     lowerElements, upperElements);

  }

  /** Multiply the instance by a scalar.
   * This method multiplies the instance by a scalar. It returns a new
   * matrix and does not modify the instance.
   * @param a scalar by which to multiply
   * @return a new matrix containing the result
   * @see #selfMul(double)
   */
  public Matrix mul(double a) {
    Matrix copy = duplicate();
    copy.selfMul(a);
    return copy;
  }

  /** Multiply the instance by a scalar.
   * This method multiplies the instance by a scalar.
   * It does modify the instance.
   * @param a scalar by which to multiply
   * @see #mul(double)
   */
  public void selfMul(double a) {
    for (int i = 0; i < rows; ++i) {
      NonNullRange r = getRangeForRow(i);
      for (int j = r.begin, index = i * columns + r.begin; j < r.end; ++j) {
        data[index++] *= a;
      }
    }

  }

  /** Compute the transpose of the instance.
   * This method transposes the instance. It returns a new
   * matrix and does not modify the instance.
   * @return a new matrix containing the result
   */
  public Matrix getTranspose() {

    double[] resultData    = new double[columns * rows];
    int      resultIndex   = 0;
    int      upperElements = 0;
    int      lowerElements = 0;

    for (int i = 0; i < columns; ++i) {
      // compute the indices of the internal loop
      NonNullRange range = getRangeForColumn(i);

      int j     = 0;
      int index = i;

      // assign the zeros before the non null range
      while (j < range.begin) {
        resultData[resultIndex++] = 0.0;
        index += columns;
        ++j;
      }

      // compute the possibly non null elements
      while (j < range.end) {
        resultData[resultIndex] = data[index];

        // count the affected upper and lower elements
        // (in order to deduce the shape of the resulting matrix)
        if (j < i) {
          ++lowerElements;
        } else if (i < j) {
          ++upperElements;
        }

        index += columns;
        ++resultIndex;
        ++j;

      }

      // assign the zeros after the non null range
      while (j < rows) {
        resultData[resultIndex] = 0.0;
        ++resultIndex;
        ++j;
      }

    }

    return MatrixFactory.buildMatrix(columns, rows, resultData,
                                     lowerElements, upperElements);

  }

  /** Set a range to the non null part covered by a row.
   * @param i index of the row
   * @return range of non nul elements in the specified row
   * @see #getRangeForColumn
   */
  protected abstract NonNullRange getRangeForRow(int i);

  /** Set a range to the non null part covered by a column.
   * @param j index of the column
   * @return range of non nul elements in the specified column
   * @see #getRangeForRow
   */
  protected abstract NonNullRange getRangeForColumn(int j);

  public String toString() {
    String separator = System.getProperty("line.separator");

    StringBuffer buf = new StringBuffer();
    for (int index = 0; index < rows * columns; ++index) {
      if (index > 0) {
        if (index % columns == 0) {
          buf.append(separator);
        } else {
          buf.append(' ');
        }
      }
      buf.append(Double.toString(data[index]));
    }

    return buf.toString();

  }

  /** number of rows of the matrix. */
  protected final int rows;

  /** number of columns of the matrix. */
  protected final int columns;

  /** array of the matrix elements.
   * the elements are stored in a one dimensional array, row after row
   */
  protected final double[] data;

}