matrix.java

一个关于java 的常用工具包

   @*/
  public void multiply(double factor) {
    for (int i=1; i <=getNbRows(); i++) {
      for (int j=1; j <=getNbColumns(); j++) {
        _array[j-1][i-1] = _array[j-1][i-1]*factor;
      }
    }
  }  

  /**
   * Divide this matrix by a given factor.
   *
   * @param factor
   *        The factor to divide this matrix by.
   */
 /*@
   @ public behavior
   @
   @ post (\forall int i; i>=1 && i<= getNbRows();
   @        (\forall int j; j>=1 && j<= getNbColumns();
   @          elementAt(i,j) == \old(elementAt(i,j)) / factor));
   @*/
  public void divide(double factor) {
    for (int i=1; i <=getNbRows(); i++) {
      for (int j=1; j <=getNbColumns(); j++) {
        _array[j-1][i-1] = _array[j-1][i-1]/factor;
      }
    }
  }  
	
	  
  /**
   * Transpose this matrix.
   */
 /*@
   @ public behavior
   @
   @ post getNbColumns() == \old(getNbRows());
   @ post getNbRows() == \old(getNbColumns());
   @ post (\forall int i; i>=1 && i<=getNbRows();
   @        (\forall int j; j>=1 && j<getNbColumns();
   @          elementAt(i,j) == \old(elementAt(j,i))));
   @*/
  public void transpose() {
    // inefficient : see returnTranspose()
    double[][] newArray = new double[getNbRows()][getNbColumns()];
    int rows=getNbRows();
    int columns=getNbColumns();
    for (int i= 0; i<rows; i++) {
      for(int j = 0; j<columns; j++) {
        newArray[i][j] = _array[j][i];
      }
    }
    _array=newArray;
  }

	/**
	 * <p>Perform a givens rotation on this matrix from the left side with the givens matrix defined by
	 * c, s, i and k as follows (m = getNbRows()).</p>
	 * <pre>
	 *     1       i       k       m
	 * 
	 * 1   1 . . . 0 . . . 0 . . . 0
	 *     . .     . .     . .     .
	 *     .   .   .   .   .   .   .
	 *     .     . .     . .     . .
	 * i   0 . . . c . . . s . . . 0
	 *     . .     . .     . .     .
	 *     .   .   .   .   .   .   .
	 *     .     . .     . .     . .
	 * k   0 . . .-s . . . c . . . 0
	 *     . .     . .     . .     .
	 *     .   .   .   .   .   .   .
	 *     .     . .     . .     . .
	 * m   0 . . . 0 . . . 0 . . . 1
	 * </pre>
	 * <p> This matrix (<code>A</code>) will be transformed into <code>G*A</code>.</p>
	 * @param c
	 *        The value of c
	 * @param c
	 *        The value of s
	 * @param i
	 *        The value of i
	 * @param k
	 *        The value of k
	 */
 /*@
	 @ public behavior
	 @
	 @ pre (1 <= i) && (i < k) && (k <= getNbRows());
	 @
	 @ post getColumn(i).equals(\old(getColumn(i).times(c).minus(getColumn(k).times(s))));
	 @ post getColumn(k).equals(\old(getColumn(i).times(s).plus(getColumn(k).times(c))));
	 @*/
	public void leftGivens(double c, double s, int i, int k) {
		//rows 1...i-1, i+1 ... k-1, k+1 ... n remain untouched.
		Row row_i = getRow(i);
		Row row_k = getRow(k);
		setRow(i,row_i.times(c).minus(row_k.times(s)).getRow(1));
		setRow(k,row_i.times(s).plus(row_k.times(c)).getRow(1));
  }
	
	/**
	 * <p>Perform a givens rotation on this matrix from the right side with the givens matrix defined by
	 * c, s, i and k as follows (n = getNbColumns()).</p>
	 * <pre>
	 *     1       i       k       n
	 * 
	 * 1   1 . . . 0 . . . 0 . . . 0
	 *     . .     . .     . .     .
	 *     .   .   .   .   .   .   .
	 *     .     . .     . .     . .
	 * i   0 . . . c . . . s . . . 0
	 *     . .     . .     . .     .
	 *     .   .   .   .   .   .   .
	 *     .     . .     . .     . .
	 * k   0 . . .-s . . . c . . . 0
	 *     . .     . .     . .     .
	 *     .   .   .   .   .   .   .
	 *     .     . .     . .     . .
	 * n   0 . . . 0 . . . 0 . . . 1
	 * </pre>
	 * <p> This matrix (<code>A</code>) will be transformed into <code>A*G</code>.</p>
	 * @param c
	 *        The value of c
	 * @param c
	 *        The value of s
	 * @param i
	 *        The value of i
	 * @param k
	 *        The value of k
	 */
 /*@
	 @ public behavior
	 @
	 @ pre (1 <= i) && (i < k) && (k <= getNbColumns());
	 @
	 @ post getColumn(i).equals(\old(getColumn(i).times(c).minus(getColumn(k).times(s))));
	 @ post getColumn(k).equals(\old(getColumn(i).times(s).plus(getColumn(k).times(c))));
	 @*/
	public void rightGivens(double c, double s, int i, int k) {
		//columns 1...i-1, i+1 ... k-1, k+1 ... n remain untouched.
		Column column_i = getColumn(i);
		Column column_k = getColumn(k);
		setColumn(i,column_i.times(c).minus(column_k.times(s)).getColumn(1));
		setColumn(k,column_i.times(s).plus(column_k.times(c)).getColumn(1));
  }
	  
  /**
   * Return the transpose of this matrix.
   */
 /*@
   @ public behavior
   @
   @ post \result.sameDimensions(this);
   @ post (\forall int i; i>0 && i<= getNbRows();
   @        (\forall int j; j>0 && j <getNbColumns();
   @          elementAt(i,j) == \result.elementAt(j,i)));
   @*/
  public Matrix returnTranspose() {
    // MvDMvDMvD : very inefficient. It would be better to have a
    //             boolean flag indicating whether the internal
    //             indices are [column][row] or [row][column].
    //             This however makes other operations slightly less
    //             efficient since a test has to be done.
    Matrix newMatrix = new Matrix(getNbColumns(), getNbRows());
    for (int i=1; i<=getNbRows(); i++) {
      for(int j=1; j<=getNbColumns(); j++) {
        newMatrix.setElementAt(j,i,elementAt(i,j));
      }
    }
    return newMatrix;
  }

  /**
   * Check wether the given matrix has the same dimensions as this one.
   *
   * @param other
   *        The other matrix
   */
 /*@
   @ public behavior
   @
   @ pre other != null;
   @
   @ post getNbColumns() == other.getNbColumns();
   @ post getNbRows() == other.getNbRows();
   @*/
  public boolean sameDimensions(Matrix other) {
    return ((getNbColumns() == other.getNbColumns()) && 
            (getNbRows() == other.getNbRows()));
  }

//   /**
// 	 * Return a reduced QR factorization of this matrix using 
// 	 * Gram-Schmidt orthogonalization.
// 	 */
//  /*@
//    @ public behavior
// 	 @
// 	 @ pre getNbRows() >= getNbColumns()
// 	 @*/
// 	public void GramQR() {
// 		Matrix Q = (Matrix) clone();
// 		int columns = getNbColumns();
// 		int rows = getNbRows();
// 		Matrix R = new Matrix(columns, columns);
// 		for (int i=1; i<= columns; i++) {
// 			double norm = Q.getColumn(i).norm(2);
// 			// rii = ||vi||
// 			R.setElementAt(i,i, norm);
// 			// qi = vi/rii
// 			for (int k=1; k<=rows; k++) {
// 				Q.setElementAt(k,i,Q.elementAt(k,i)/norm);
// 			}
// 			for (int j=i+1; j<=columns; j++) {
// 				// qi = vi
// 				// MvDMvDMvD
// 				// very inefficient. getColumn() clones and returnTranspose() clones again.
// 				double r = (Q.getColumn(i).returnTranspose().times(Q.getColumn(j))).elementAt(1,1);
// 				R.setElementAt(i,j,r);
// 				// vj = vj - rij*qi
// 				for (int k=1; k<= rows; k++) {
// 					Q.setElementAt(k,j,(Q.elementAt(k,j) - r*Q.elementAt(k,i)));
// 				}
// 			}
// 		}
// 		System.out.println(Q);
// 		System.out.println(R);
// 	}

	/**
	 * Return the submatrix starting from (x1,y1) to (x2,y2).
	 *
	 * @param x1
	 *        The row from which to start.
	 * @param y1
	 *        The column from which to start.
	 * @param x2
	 *        The end row.
	 * @param y2
	 *        The end column.
	 */
 /*@
   @ public behavior
	 @
	 @ pre validIndex(x1, y1);
	 @ pre validIndex(x2, y2);
	 @ pre x2 >= x1;
	 @ pre y2 >= y1;
	 @
	 @ post \fresh(\result);
	 @ post \result.getNbRows() == x2 - x1 + 1;
	 @ post \result.getNbColumns() == y2 - y1 + 1;
	 @ post (\forall int i; i>=x1 && i <=x2;
	 @        (\forall int j; j>=y1 && j <=y2;
	 @          \result.elementAt(i - x1 + 1, j - y1 + 1) == elementAt(i, j)));
	 @*/
	public Matrix subMatrix(int x1, int y1, int x2, int y2) {
		Matrix result = new Matrix(x2 - x1 + 1, y2 - y1 + 1);
		for (int i = x1; i <= x2; i++) {
			for (int j = y1; j <= y2; j++) {
				result.setElementAt(i - x1 + 1, j - y1 + 1, elementAt(i, j));
			}
		}
		return result;
	}

  /**
	 * Replace a submatrix of this matrix with the given matrix 
	 * at the given coordinates.
	 *
	 * @param row
	 *        The row of the top-left element of the submatrix that will be replaced.
	 * @param column
	 *        The column of the top-left element of the submatrix that will be replaced.
	 * @param matrix
	 *        The matrix to put into this matrix
	 */
 /*@
   @ public behavior
	 @
	 @ pre matrix != null;
	 @ pre validIndex(row, column);
	 @ pre validIndex(row + matrix.getNbRows() - 1, column + matrix.getNbColumns() - 1);
	 @
	 @ post subMatrix(row, column, row + matrix.getNbRows() - 1, column + matrix.getNbColumns() - 1).equals(matrix);
	 @*/
	public void setSubMatrix(int row, int column, Matrix matrix) {
		int rows = matrix.getNbRows();
		int columns = matrix.getNbColumns();
		for (int i = 1; i <= rows; i++) {
			for (int j = 1; j <= columns; j++) {
				setElementAt(i + row - 1, j + column - 1, matrix.elementAt(i, j));
			}
		}
	}


	/**
	 * Check whether or not this matrix is upper triangular
	 */
 /*@
   @ public behavior
	 @
	 @ post \result == (\forall int i; i>=1 && i<=getNbRows();
	 @	                 (\forall int j; j>=1 && j<=getNbColumns();
	 @                     (i < j) ==> elementAt(i,j) == 0));
	 @*/
	public boolean isUpperTriangular() {
		int rows=getNbRows();
		int columns=getNbColumns();
		for (int i=1; i<= rows; i++) {
			for (int j=1; j<= columns && j < i; j++) {
				if (elementAt(i,j) != 0) {
					return false;
				}
			}
		}
		return true;
	}

	/**
	 * Check whether or not this matrix is lower triangular
	 */
 /*@
   @ public behavior
	 @
	 @ post \result == (\forall int i; i>=1 && i<=getNbRows();
	 @	                 (\forall int j; j>=1 && j<=getNbColumns();
	 @                     (i > j) ==> elementAt(i,j) == 0));
	 @*/
	public boolean isLowerTriangular() {
		int rows=getNbRows();
		int columns=getNbColumns();
		for (int i=1; i<= rows; i++) {
			for (int j=i+1; j<= columns; j++) {
				if (elementAt(i,j) != 0) {
					return false;
				}
			}
		}
		return true;
	}

	/**
	 * Check whether or not this matrix is a diagonal matrix.
	 */
 /*@
   @ public behavior
	 @
	 @ post \result == (\forall int i; i>=1 && i<=getNbRows();
	 @	                 (\forall int j; j>=1 && j<=getNbColumns();
	 @                     (j != i) ==> elementAt(i,j) == 0));
	 @*/
	public boolean isDiagonal() {
		int rows=getNbRows();
		int columns=getNbColumns();
		for (int i=1; i<= rows; i++) {
			for (int j=1; j<= columns; j++) {
				if ((i != j) && (elementAt(i,j) != 0)) {
					return false;
				}
			}
		}
		return true;
	}
	
	/**
	 * see superclass
	 */
	public String toString() {
	  String result = "";
		int columns=getNbColumns();
		int rows=getNbRows();
		for (int i=1; i<=rows; i++) {
			for (int j=1; j<=columns - 1; j++) {
			  result += elementAt(i,j)+", ";
			}
			result += elementAt(i,columns) +"\n";
		}
		return result;
	}

  /**
   * Return a clone
   */
 /*@
   @ also public behavior
   @
   @ post equals(\result);
	 @ post \result instanceof Matrix;
   @*/
  public Object clone() {
    // MvDMvDMvD
    // should be made more efficient using a private constructor
    // which takes double[][] as an argument.
    Matrix newMatrix = new Matrix(getNbRows(), getNbColumns());
    for (int i=1; i<=getNbRows(); i++) {
      for(int j=1; j<=getNbColumns(); j++) {
        newMatrix.setElementAt(i,j,elementAt(i,j));
      }
    }
    return newMatrix;
  }  
  
  /**
   * Check whether the given object is equal to this matrix.
   */
 /*@
   @ also public behavior
   @
   @ post !(other instanceof Matrix) ==> false;
   @ post !(sameDimensions((Matrix)other)) ==> false;
   @ post (other instanceof Matrix) && (sameDimensions((Matrix)other)) ==>
   @       \result == (\forall int i; i>=1 && i<=getNbRows();
   @                     (\forall int j; j>=1 && j<=getNbColumns();
   @                       ((Matrix)other).elementAt(i,j) ==
   @                       elementAt(i,j)));
   @*/
  public boolean equals(Object other) {
    if (!(other instanceof Matrix)) {
      return false;
    }
    if (!(sameDimensions((Matrix)other))) {
      return false;
    }
    for (int i=1; i<=getNbRows(); i++) {
      for(int j=1; j<=getNbColumns(); j++) {
        if(_array[j-1][i-1] != ((Matrix)other).elementAt(i,j)) {
          return false;
        }
      }
    }
    return true;
  }

	/**
	 * Check whether or not this matrix is square.
	 */
 /*@
	 @ public behavior
	 @
	 @ post getNbColumns() == getNbRows();
	 @*/
	public boolean isSquare() {
		return getNbColumns() == getNbRows();
  }
	
	/**
	 * Check whether or not this matrix is symmetric.
	 */
 /*@
	 @ public behavior
	 @
	 @ post \result == isSquare() &&
	 @                 (\forall int i; i>=1 && i<=getNbRows();
	 @                   (\forall int j; j>=1 && j<=getNbColumns();
	 @                     elementAt(i,j) == elementAt(j,i)));
	 @*/
	public boolean isSymmetric() {
		if(! isSquare()) {
			return false;
    }
		boolean result = true;
		int rows = getNbRows();
		int columns = getNbColumns();
		// the last row need not be checked, so i<rows
		for(int i=1; result && i<rows; i++) {
			for(int j=i+1; result && j<=columns; j++) {
				result = (elementAt(i,j) == elementAt(j,i));
      }
    }
		return result;
  }

	/**
	 * Check whether or not this matrix is a permutation matrix.
	 */
 /*@
	 @ post \result == isSquare() &&
	 @                 // 1 non-zero element in each row
	 @                 (\forall int i; i>=1 && i<=getNbRows();
	 @                   (\num_of int j; j>=1 && j<=getNbColumns(); elementAt(i,j) != 0) == 1) &&
	 @                 // 1 non-zero element in each column
	 @                 (\forall int i; i>=1 && i<=getNbColumns();
	 @                   (\num_of int j; j>=1 && j<=getNbRows(); elementAt(j,i) != 0) == 1) &&
	 @                 // each element is 0 or 1
	 @                 (\forall int i; i>=1 && i<=getNbRows();
	 @                   (\forall int j; j>=1 && j<=getNbColumns();
	 @                     elementAt(i,j) == 0 || elementAt(i,j) == 1));
	 @*/
	public boolean isPermutationMatrix() {
		if(! isSquare()) {
			return false;
    }
		int n = getNbRows();
		boolean[] column_found = new boolean[n];
		for(int i=1; i<=n; i++) {
			boolean found = false;
			for(int j=1; j <= n; j++) {
				if((elementAt(i,j) != 0) && (elementAt(i,j) != 0)) {
					return false;
        }
				if(elementAt(i,j) == 1) {
					if(found == true) {
						// we had already found a 1 on this row.
						return false;
          }
					if(column_found[j-1]) {
						// we had already found in column j
						return false;
          }
					column_found[j-1] = true;
					found=true;
        }
    	}
    }
		return true;
  }
		  
  /**
   * The values are put in the array according to the following scheme
   * [column][row]
   * This makes it easier to extract a column from the matrix, which is used
   * more frequently than a column.
   */
 /*@
   @ private invariant _array != null;
   @ private invariant _array.length > 0;
   @ // All columns have the same length.
   @ private invariant (\forall int i; i>0 && i<_array.length;
   @                     _array[i].length == _array[i-1].length);
   @ private invariant _array[0].length > 0;
   @*/
  private double[][] _array;
}

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