Package org.openscience.cdk.graph.invariant

Class GIMatrix

  • public class GIMatrix
extends Object
    This class is intended to provide the user an efficient way of implementing matrix of double number and using normal operations (linear operations, addition, subtraction, multiplication, inversion, concatenation) on them. The internal representation of a matrix is an array of array of double objects. For the moment, double class is the best way I have developed to perform exact operation on numbers; however, for irdoubles, normal operations on float and doubles have to be performed, with the well-known risks of error this implies. This class also provides a way of representing matrix as arrays of String for output use.

    Please note that although in most books matrix elements' indexes take values between [1..n] I chose not to disturb Java language way of calling indexes; so the indexes used here take values between [0..n-1] instead.

    Version:
    1.0
    Author:
    Jean-Sebastien Senecal
    Source code:
    main
    Created on:
    1999-05-20

    • Constructor Summary

      Constructors 
      Constructor Description
      GIMatrix​(double[][] array)
      Class constructor.
      GIMatrix​(int[][] array)
      Class constructor.
      GIMatrix​(int line, int col)
      Class constructor.
      GIMatrix​(GIMatrix matrix)
      Class constructor.
      GIMatrix​(GIMatrix[][] table)
      Class constructor.

    • Method Summary

      All Methods Static Methods Instance Methods Concrete Methods 
      Modifier and Type Method Description
      GIMatrix add​(GIMatrix b)
      Addition from two matrices.
      GIMatrix addLine​(int i, int j, double c)
      Returns the resulting matrix of an elementary linear operation that consists of adding one line, multiplied by some constant factor, to another line.
      double determinant()
      Returns the determinant of this matrix.
      GIMatrix diagonal()
      Returns a matrix containing all of the diagonal elements of this matrix and zero (0) everywhere else.
      boolean equals​(Object obj)
      Verifies if two given matrix are equal or not.
      GIMatrix GaussJordan()
      Gauss-Jordan algorithm.
      double[][] getArrayValue()
      Returns the internal representation of the matrix, that is an array of double objects.
      GIMatrix getColumn​(int j)
      Returns the column-matrix at the given line index.
      GIMatrix getLine​(int i)
      Returns the line-matrix at the given line index.
      double getValueAt​(int i, int j)
      Returns the value of the given element.
      int hashCode()  
      int height()
      Returns the number of lines of the matrix.
      static GIMatrix identity​(int n)
      Returns the identity matrix.
      GIMatrix inverse()
      Returns the transpose of this matrix.
      GIMatrix invertLine​(int i, int j)
      Returns the resulting matrix of an elementary linear operation that consists of inverting two lines.
      boolean isAntisymmetric()
      Verifies if the matrix is antisymmetric, that is if the matrix is equal to the opposite of it's transpose.
      boolean isDiagonal()
      Verifies whether or not the matrix is diagonal.
      boolean isInvertible()
      Verifies if the matrix is invertible or not by asking for its determinant.
      boolean isSquare()
      Verifies if the matrix is square, that is if it has an equal number of lines and columns.
      boolean isSymmetric()
      Verifies if the matrix is symmetric, that is if the matrix is equal to it's transpose.
      boolean isTriangularInferior()
      Verifies if the matrix is triangular inferior or not.
      boolean isTriangularSuperior()
      Verifies if the matrix is triangular superior or not.
      GIMatrix multiply​(double c)
      Returns the result of the scalar multiplication of the matrix, that is the multiplication of every of its elements by a given number.
      GIMatrix multiply​(GIMatrix matrix)
      Returns the result of the matrix multiplication of this matrix by another one.
      GIMatrix multiplyLine​(int i, double c)
      Returns the resulting matrix of an elementary linear operation that consists of multiplying a single line of the matrix by a constant.
      void setArrayValue​(double[][] array)
      Resets the value of the matrix to the given array of double numbers.
      void setColumn​(int j, GIMatrix column)
      Sets the column of the matrix at the specified index to a new value.
      void setLine​(int i, GIMatrix line)
      Sets the line of the matrix at the specified index to a new value.
      void setValueAt​(int i, int j, double element)
      Sets the value of the element at the given index.
      double trace()
      Returns the trace of this matrix, that is the sum of the elements of its diagonal.
      GIMatrix transpose()
      Returns the transpose of this matrix.
      int width()
      Returns the number of columns of the matrix.
      static GIMatrix zero​(int m, int n)
      Returns a null matrix (with zeros everywhere) of given dimensions.

    • Constructor Detail

      • GIMatrix

        public GIMatrix​(int[][] array)
        Class constructor. Uses an array of integers to create a new Matrix object. Note that integers will be converted to double objects so mathematical operations may be properly performed and provide exact solutions. The given array should be properly instantiated as a matrix i.e. it must contain a fixed number of lines and columns, otherwise an exception will be thrown. Array must be at leat 1x1.
        Parameters:
        array - an array of integer (first index is the line, second is the column)

      • GIMatrix

        public GIMatrix​(double[][] array)
         throws BadMatrixFormatException
        Class constructor. Uses an array of doubles to create a new Matrix object. The given array should be properly instantiated as a matrix i.e. it must contain a fixed number of lines and columns, otherwise an exception will be thrown. Array must be at leat 1x1.
        Parameters:
        array - an array of double objects (first index is the line, second is the column)
        Throws:
        BadMatrixFormatException - in case the given array is unproper to construct a matrix

      • GIMatrix

        public GIMatrix​(int line,
                int col)
        Class constructor. Creates a new Matrix object with fixed dimensions. The matrix is initialised to the "zero" matrix.
        Parameters:
        line - number of lines
        col - number of columns

      • GIMatrix

        public GIMatrix​(GIMatrix matrix)
        Class constructor. Copies an already existing Matrix object in a new Matrix object.
        Parameters:
        matrix - a Matrix object

      • GIMatrix

        public GIMatrix​(GIMatrix[][] table)
         throws BadMatrixFormatException
        Class constructor. Creates a new Matrix object using a table of matrices (an array of Matrix objects). The given array should be properly instantiated i.e. it must contain a fixed number of lines and columns, otherwise an exception will be thrown.
        Parameters:
        table - an array of matrices
        Throws:
        BadMatrixFormatException - if the table is not properly instantiated

    • Method Detail

      • height

        public int height()
        Returns the number of lines of the matrix.
        Returns:
        the height of the matrix

      • width

        public int width()
        Returns the number of columns of the matrix.
        Returns:
        the width of the matrix

      • getArrayValue

        public double[][] getArrayValue()
        Returns the internal representation of the matrix, that is an array of double objects.
        Returns:
        an array of double equivalent to the matrix

      • setArrayValue

        public void setArrayValue​(double[][] array)
                   throws BadMatrixFormatException
        Resets the value of the matrix to the given array of double numbers.
        Parameters:
        array - an array of double objects (first index is the line, second is the column)
        Throws:
        BadMatrixFormatException - in case the given array is unproper to construct a matrix

      • getValueAt

        public double getValueAt​(int i,
                         int j)
                  throws IndexOutOfBoundsException
        Returns the value of the given element.
        Parameters:
        i - the line number
        j - the column number
        Returns:
        the double at the given index in the Matrix
        Throws:
        IndexOutOfBoundsException - if the given index is out of the matrix's range

      • setValueAt

        public void setValueAt​(int i,
                       int j,
                       double element)
                throws IndexOutOfBoundsException
        Sets the value of the element at the given index.
        Parameters:
        i - the line number
        j - the column number
        element - the double to place at the given index in the Matrix
        Throws:
        IndexOutOfBoundsException - if the given index is out of the matrix's range

      • getLine

        public GIMatrix getLine​(int i)
                 throws IndexOutOfBoundsException
        Returns the line-matrix at the given line index.
        Parameters:
        i - the line number
        Returns:
        the specified line as a Matrix object
        Throws:
        IndexOutOfBoundsException - if the given index is out of the matrix's range

      • getColumn

        public GIMatrix getColumn​(int j)
                   throws IndexOutOfBoundsException
        Returns the column-matrix at the given line index.
        Parameters:
        j - the column number
        Returns:
        the specified column as a Matrix object
        Throws:
        IndexOutOfBoundsException - if the given index is out of the matrix's range

      • identity

        public static GIMatrix identity​(int n)
        Returns the identity matrix.
        Parameters:
        n - the matrix's dimension (identity matrix is a square matrix)
        Returns:
        the identity matrix of format nxn

      • zero

        public static GIMatrix zero​(int m,
                            int n)
        Returns a null matrix (with zeros everywhere) of given dimensions.
        Parameters:
        m - number of lines
        n - number of columns
        Returns:
        the zero (null) matrix of format mxn

      • equals

        public boolean equals​(Object obj)
        Verifies if two given matrix are equal or not. The matrix must be of the same size and dimensions, otherwise an exception will be thrown.
        Overrides:
        equals in class Object
        Parameters:
        obj - the Matrix object to be compared to
        Returns:
        true if both matrix are equal element to element

      • hashCode

        public int hashCode()
        Overrides:
        hashCode in class Object

      • isSquare

        public boolean isSquare()
        Verifies if the matrix is square, that is if it has an equal number of lines and columns.
        Returns:
        true if this matrix is square

      • isSymmetric

        public boolean isSymmetric()
                    throws BadMatrixFormatException
        Verifies if the matrix is symmetric, that is if the matrix is equal to it's transpose.
        Returns:
        true if the matrix is symmetric
        Throws:
        BadMatrixFormatException - if the matrix is not square

      • isAntisymmetric

        public boolean isAntisymmetric()
                        throws BadMatrixFormatException
        Verifies if the matrix is antisymmetric, that is if the matrix is equal to the opposite of it's transpose.
        Returns:
        true if the matrix is antisymmetric
        Throws:
        BadMatrixFormatException - if the matrix is not square

      • isTriangularSuperior

        public boolean isTriangularSuperior()
                             throws BadMatrixFormatException
        Verifies if the matrix is triangular superior or not. A triangular superior matrix has zero (0) values everywhere under it's diagonal.
        Returns:
        true if the matrix is triangular superior
        Throws:
        BadMatrixFormatException - if the matrix is not square

      • isTriangularInferior

        public boolean isTriangularInferior()
                             throws BadMatrixFormatException
        Verifies if the matrix is triangular inferior or not. A triangular inferior matrix has zero (0) values everywhere upper it's diagonal.
        Returns:
        true if the matrix is triangular inferior
        Throws:
        BadMatrixFormatException - if the matrix is not square

      • isDiagonal

        public boolean isDiagonal()
                   throws BadMatrixFormatException
        Verifies whether or not the matrix is diagonal. A diagonal matrix only has elements on its diagonal and zeros (0) at every other index. The matrix must be square.
        Returns:
        true if the matrix is diagonal
        Throws:
        BadMatrixFormatException - if the matrix is not square

      • isInvertible

        public boolean isInvertible()
                     throws BadMatrixFormatException
        Verifies if the matrix is invertible or not by asking for its determinant.
        Returns:
        true if the matrix is invertible
        Throws:
        BadMatrixFormatException - if the matrix is not square

      • inverse

        public GIMatrix inverse()
                 throws MatrixNotInvertibleException
        Returns the transpose of this matrix. The transpose of a matrix A = {a(i,j)} is the matrix B = {b(i,j)} such that b(i,j) = a(j,i) for every i,j i.e. it is the symmetrical reflection of the matrix along its diagonal. The matrix must be square to use this method, otherwise an exception will be thrown.
        Returns:
        the matrix's transpose as a Matrix object
        Throws:
        MatrixNotInvertibleException - if the matrix is not square

      • GaussJordan

        public GIMatrix GaussJordan()
        Gauss-Jordan algorithm. Returns the reduced-echeloned matrix of this matrix. The algorithm has not yet been optimised but since it is quite simple, it should not be a serious problem.
        Returns:
        the reduced matrix

      • transpose

        public GIMatrix transpose()
                   throws BadMatrixFormatException
        Returns the transpose of this matrix. The transpose of a matrix A = {a(i,j)} is the matrix B = {b(i,j)} such that b(i,j) = a(j,i) for every i,j i.e. it is the symmetrical reflection of the matrix along its diagonal. The matrix must be square to use this method, otherwise an exception will be thrown.
        Returns:
        the matrix's transpose as a Matrix object
        Throws:
        BadMatrixFormatException - if the matrix is not square

      • diagonal

        public GIMatrix diagonal()
                  throws BadMatrixFormatException
        Returns a matrix containing all of the diagonal elements of this matrix and zero (0) everywhere else. This matrix is called the diagonal of the matrix.
        Returns:
        the diagonal of the matrix
        Throws:
        BadMatrixFormatException - if the matrix is not square

      • multiplyLine

        public GIMatrix multiplyLine​(int i,
                             double c)
                      throws IndexOutOfBoundsException
        Returns the resulting matrix of an elementary linear operation that consists of multiplying a single line of the matrix by a constant.
        Parameters:
        i - the line number
        c - the double constant that multiplies the line
        Returns:
        the resulting Matrix object of the linear operation
        Throws:
        IndexOutOfBoundsException - if the given index is out of the matrix's range

      • invertLine

        public GIMatrix invertLine​(int i,
                           int j)
                    throws IndexOutOfBoundsException
        Returns the resulting matrix of an elementary linear operation that consists of inverting two lines.
        Parameters:
        i - the first line number
        j - the second line number
        Returns:
        the resulting Matrix object of the linear operation
        Throws:
        IndexOutOfBoundsException - if the given index is out of the matrix's range

      • addLine

        public GIMatrix addLine​(int i,
                        int j,
                        double c)
                 throws IndexOutOfBoundsException
        Returns the resulting matrix of an elementary linear operation that consists of adding one line, multiplied by some constant factor, to another line.
        Parameters:
        i - the first line number
        j - the second line number (to be added to the first)
        c - the double constant that multiplies the first line
        Returns:
        the resulting Matrix object of the linear operation
        Throws:
        IndexOutOfBoundsException - if the given index is out of the matrix's range

      • multiply

        public GIMatrix multiply​(double c)
        Returns the result of the scalar multiplication of the matrix, that is the multiplication of every of its elements by a given number.
        Parameters:
        c - the constant by which the matrix is multiplied
        Returns:
        the resulting matrix of the scalar multiplication

      • multiply

        public GIMatrix multiply​(GIMatrix matrix)
                  throws BadMatrixFormatException
        Returns the result of the matrix multiplication of this matrix by another one. The matrix passed as parameter follows this matrix in the multiplication, so for an example if the dimension of the actual matrix is mxn, the dimension of the second one should be nxp in order for the multiplication to be performed (otherwise an exception will be thrown) and the resulting matrix will have dimension mxp.
        Parameters:
        matrix - the matrix following this one in the matrix multiplication
        Returns:
        the resulting matrix of the matrix multiplication
        Throws:
        BadMatrixFormatException - if the matrix passed in arguments has wrong dimensions

      • determinant

        public double determinant()
                   throws BadMatrixFormatException
        Returns the determinant of this matrix. The matrix must be square in order to use this method, otherwise an exception will be thrown. Warning: this algorithm is very inefficient and takes too much time to compute with large matrices.
        Returns:
        the determinant of the matrix
        Throws:
        BadMatrixFormatException - if the matrix is not square

      • trace

        public double trace()
             throws BadMatrixFormatException
        Returns the trace of this matrix, that is the sum of the elements of its diagonal. The matrix must be square in order to use this method, otherwise an exception will be thrown.
        Returns:
        the trace of the matrix
        Throws:
        BadMatrixFormatException - if the matrix is not square