matrix.java

一个一元曲线多项式数值演示例子

package numbercruncher.matrix;

import numbercruncher.mathutils.*;

/**
 * The matrix class.
 */
public class Matrix {
  /** number of rows */
  protected int nRows;
  /** number of columns */
  protected int nCols;
  /** 2-d array of  values */
  protected float values[][];

  //--------------//
  // Constructors //
  //--------------//

  /**
   * Default constructor.
   */
  protected Matrix() {}

  /**
   * Constructor.
   * @param rowCount the number of rows
   * @param colCount the number of columns
   */
  public Matrix(int rowCount, int colCount) {
    nRows = (rowCount > 0) ? rowCount : 1;
    nCols = (colCount > 0) ? colCount : 1;
    values = new float[nRows][nCols];
  }

  /**
   * Constructor.
   * @param values the 2-d array of values
   */
  public Matrix(float values[][]) {
    set(values);
  }

  //---------//
  // Getters //
  //---------//

  /**
   * Get the row count.
   * @return the row count
   */
  public int rowCount() {
    return nRows;
  }

  /**
   * Get the column count.
   * @return the column count
   */
  public int columnCount() {
    return nCols;
  }

  /**
   * Get the value of element [r,c] in the matrix.
   * @param r the row index
   * @param c the column index
   * @return the value
   * @throws numbercruncher.MatrixException for an invalid index
   */
  public float at(int r, int c) throws MatrixException {
    if ( (r < 0) || (r >= nRows) || (c < 0) || (c >= nCols)) {
      throw new MatrixException(MatrixException.INVALID_INDEX);
    }

    return values[r][c];
  }

  /**
   * Get a row of this matrix.
   * @param r the row index
   * @return the row as a row vector
   * @throws numbercruncher.MatrixException for an invalid index
   */
  public RowVector getRow(int r) throws MatrixException {
    if ( (r < 0) || (r >= nRows)) {
      throw new MatrixException(MatrixException.INVALID_INDEX);
    }

    RowVector rv = new RowVector(nCols);
    for (int c = 0; c < nCols; ++c) {
      rv.values[0][c] = this.values[r][c];
    }

    return rv;
  }

  /**
   * Get a column of this matrix.
   * @param c the column index
   * @return the column as a column vector
   * @throws numbercruncher.MatrixException for an invalid index
   */
  public ColumnVector getColumn(int c) throws MatrixException {
    if ( (c < 0) || (c >= nCols)) {
      throw new MatrixException(MatrixException.INVALID_INDEX);
    }

    ColumnVector cv = new ColumnVector(nRows);
    for (int r = 0; r < nRows; ++r) {
      cv.values[r][0] = this.values[r][c];
    }

    return cv;
  }

  /**
   * Copy the values of this matrix.
   * @return the values
   */
  public float[][] values() {
    return values;
  }

  /**
   * Copy the values of this matrix.
   * @return the copied values
   */
  public float[][] copyValues2D() {
    float v[][] = new float[nRows][nCols];

    for (int r = 0; r < nRows; ++r) {
      for (int c = 0; c < nCols; ++c) {
        v[r][c] = values[r][c];
      }
    }

    return v;
  }

  //---------//
  // Setters //
  //---------//

  /**
   * Set the value of element [r,c].
   * @param r the row index
   * @param c the column index
   * @param value the value
   * @throws numbercruncher.MatrixException for an invalid index
   */
  public void set(int r, int c, float value) throws MatrixException {
    if ( (r < 0) || (r >= nRows) || (c < 0) || (c >= nCols)) {
      throw new MatrixException(MatrixException.INVALID_INDEX);
    }

    values[r][c] = value;
  }

  /**
   * Set this matrix from a 2-d array of values.
   * If the rows do not have the same length, then the matrix
   * column count is the length of the shortest row.
   * @param values the 2-d array of values
   */
  protected void set(float values[][]) {
    this.nRows = values.length;
    this.nCols = values[0].length;
    this.values = values;

    for (int r = 1; r < nRows; ++r) {
      nCols = Math.min(nCols, values[r].length);
    }
  }

  /**
   * Set a row of this matrix from a row vector.
   * @param rv the row vector
   * @param r the row index
   * @throws numbercruncher.MatrixException for an invalid index or
   *                                        an invalid vector size
   */
  public void setRow(RowVector rv, int r) throws MatrixException {
    if ( (r < 0) || (r >= nRows)) {
      throw new MatrixException(MatrixException.INVALID_INDEX);
    }
    if (nCols != rv.nCols) {
      throw new MatrixException(
          MatrixException.INVALID_DIMENSIONS);
    }

    for (int c = 0; c < nCols; ++c) {
      this.values[r][c] = rv.values[0][c];
    }
  }

  /**
   * Set a column of this matrix from a column vector.
   * @param cv the column vector
   * @param c the column index
   * @throws numbercruncher.MatrixException for an invalid index or
   *                                        an invalid vector size
   */
  public void setColumn(ColumnVector cv, int c) throws MatrixException {
    if ( (c < 0) || (c >= nCols)) {
      throw new MatrixException(MatrixException.INVALID_INDEX);
    }
    if (nRows != cv.nRows) {
      throw new MatrixException(
          MatrixException.INVALID_DIMENSIONS);
    }

    for (int r = 0; r < nRows; ++r) {
      this.values[r][c] = cv.values[r][0];
    }
  }

  //-------------------//
  // Matrix operations //
  //-------------------//

  /**
   * Return the transpose of this matrix.
   * @return the transposed matrix
   */
  public Matrix transpose() {
    float tv[][] = new float[nCols][nRows]; // transposed values

    // Set the values of the transpose.
    for (int r = 0; r < nRows; ++r) {
      for (int c = 0; c < nCols; ++c) {
        tv[c][r] = values[r][c];
      }
    }

    return new Matrix(tv);
  }

  /**
   * Add another matrix to this matrix.
   * @param m the matrix addend
   * @return the sum matrix
   * @throws numbercruncher.MatrixException for invalid size
   */
  public Matrix add(Matrix m) throws MatrixException {
    // Validate m's size.
    if ( (nRows != m.nRows) && (nCols != m.nCols)) {
      throw new MatrixException(
          MatrixException.INVALID_DIMENSIONS);
    }

    float sv[][] = new float[nRows][nCols]; // sum values

    // Compute values of the sum.
    for (int r = 0; r < nRows; ++r) {
      for (int c = 0; c < nCols; ++c) {
        sv[r][c] = values[r][c] + m.values[r][c];
      }
    }

    return new Matrix(sv);
  }

  /**
   * Subtract another matrix from this matrix.
   * @param m the matrix subrrahend
   * @return the difference matrix
   * @throws numbercruncher.MatrixException for invalid size
   */
  public Matrix subtract(Matrix m) throws MatrixException {
    // Validate m's size.
    if ( (nRows != m.nRows) && (nCols != m.nCols)) {
      throw new MatrixException(
          MatrixException.INVALID_DIMENSIONS);
    }

    float dv[][] = new float[nRows][nCols]; // difference values

    // Compute values of the difference.
    for (int r = 0; r < nRows; ++r) {
      for (int c = 0; c < nCols; ++c) {
        dv[r][c] = values[r][c] - m.values[r][c];
      }
    }

    return new Matrix(dv);
  }

  /**
   * Multiply this matrix by a constant.
   * @param k the constant
   * @return the product matrix
   */
  public Matrix multiply(float k) {
    float pv[][] = new float[nRows][nCols]; // product values

    // Compute values of the product.
    for (int r = 0; r < nRows; ++r) {
      for (int c = 0; c < nCols; ++c) {
        pv[r][c] = k * values[r][c];
      }
    }

    return new Matrix(pv);
  }

  /**
   * Multiply this matrix by another matrix.
   * @param m the matrix multiplier
   * @return the product matrix
   * @throws numbercruncher.MatrixException for invalid size
   */
  public Matrix multiply(Matrix m) throws MatrixException {
    // Validate m's dimensions.
    if (nCols != m.nRows) {
      throw new MatrixException(
          MatrixException.INVALID_DIMENSIONS);
    }

    float pv[][] = new float[nRows][m.nCols]; // product values

    // Compute values of the product.
    for (int r = 0; r < nRows; ++r) {
      for (int c = 0; c < m.nCols; ++c) {
        float dot = 0;
        for (int k = 0; k < nCols; ++k) {
          dot += values[r][k] * m.values[k][c];
        }
        pv[r][c] = dot;
      }
    }

    return new Matrix(pv);
  }

  /**
   * Multiply this matrix by a column vector: this*cv
   * @param cv the column vector
   * @return the product column vector
   * @throws numbercruncher.MatrixException for invalid size
   */
  public ColumnVector multiply(ColumnVector cv) throws MatrixException {
    // Validate cv's size.
    if (nRows != cv.nRows) {
      throw new MatrixException(
          MatrixException.INVALID_DIMENSIONS);
    }

    float pv[] = new float[nRows]; // product values

    // Compute the values of the product.
    for (int r = 0; r < nRows; ++r) {
      float dot = 0;
      for (int c = 0; c < nCols; ++c) {
        dot += values[r][c] * cv.values[c][0];
      }
      pv[r] = dot;
    }

    return new ColumnVector(pv);
  }

  /**
   * Multiply a row vector by this matrix: rv*this
   * @param rv the row vector
   * @return the product row vector
   * @throws numbercruncher.MatrixException for invalid size
   */
  public RowVector multiply(RowVector rv) throws MatrixException {
    // Validate rv's size.
    if (nCols != rv.nCols) {
      throw new MatrixException(
          MatrixException.INVALID_DIMENSIONS);
    }

    float pv[] = new float[nRows]; // product values

    // Compute the values of the product.
    for (int c = 0; c < nCols; ++c) {
      float dot = 0;
      for (int r = 0; r < nRows; ++r) {
        dot += rv.values[0][r] * values[r][c];
      }
      pv[c] = dot;
    }

    return new RowVector(pv);
  }

  /**
   * Print the matrix values.
   * @param width the column width
   */
  public void print(int width) {
    AlignRight ar = new AlignRight();

    for (int r = 0; r < nRows; ++r) {
      ar.print("Row ", 0);
      ar.print(r + 1, 2);
      ar.print(":", 0);

      for (int c = 0; c < nCols; ++c) {
        ar.print(values[r][c], width);
      }
      ar.println();
    }
  }
}