invertiblematrix.java

一个一元曲线多项式数值演示例子

package numbercruncher.matrix;

/**
 * A matrix that can be inverted.  Also, compute its determinant,
 * norm, and condition number.
 */
public class InvertibleMatrix
    extends LinearSystem {
  /**
   * Constructor.
   * @param n the number of rows = the number of columns
   */
  public InvertibleMatrix(int n) {
    super(n);
  }

  /**
   * Constructor.
   * @param values the array of values
   */
  public InvertibleMatrix(float values[][]) {
    super(values);
  }

  /**
   * Compute the inverse of this matrix.
   * @return the inverse matrix
   * @throws matrix.MatrixException if an error occurred
   */
  public InvertibleMatrix inverse() throws MatrixException {
    InvertibleMatrix inverse = new InvertibleMatrix(nRows);
    IdentityMatrix identity = new IdentityMatrix(nRows);

    // Compute each column of the inverse matrix
    // using columns of the identity matrix.
    for (int c = 0; c < nCols; ++c) {
      ColumnVector col = solve(identity.getColumn(c), true);
      inverse.setColumn(col, c);
    }

    return inverse;
  }

  /**
   * Compute the determinant.
   * @return the determinant
   * @throws matrix.MatrixException if an error occurred
   */
  public float determinant() throws MatrixException {
    decompose();

    // Each row exchange during forward elimination flips the sign
    // of the determinant, so check for an odd number of exchanges.
    float determinant = ( (exchangeCount & 1) == 0) ? 1 : -1;

    // Form the product of the diagonal elements of matrix U.
    for (int i = 0; i < nRows; ++i) {
      int pi = permutation[i]; // permuted index
      determinant *= LU.at(pi, i);
    }

    return determinant;
  }

  /**
   * Compute the Euclidean norm of this matrix.
   * @return the norm
   */
  public float norm() {
    float sum = 0;

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

    return (float) Math.sqrt(sum);
  }

  /**
   * Compute the condition number based on the Euclidean norm.
   * @return the condition number
   */
  public float condition() throws MatrixException {
    return norm() * inverse().norm();
  }
}