Documentation of 'cern.colt.matrix.tint.algo.IntProperty' Java class
IntProperty
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cern.colt.matrix.tint.algo

Class IntProperty

  • All Implemented Interfaces:
    java.io.Serializable, java.lang.Cloneable

    public class IntProperty
extends PersistentObject
    Tests matrices for linear algebraic properties (equality, tridiagonality, symmetry, singularity, etc).

    Note that this implementation is not synchronized.

    Here are some example properties

    matrix 4 x 4 
    0 0 0 0
    0 0 0 0
    0 0 0 0
    0 0 0 0     		4 x 4
    1 0 0 0
    0 0 0 0
    0 0 0 0
    0 0 0 1     		4 x 4
    1 1 0 0
    1 1 1 0
    0 1 1 1
    0 0 1 1     		4 x 4
    0 1 1 1
    0 1 1 1
    0 0 0 1
    0 0 0 1     		4 x 4
    0 0 0 0
    1 1 0 0
    1 1 0 0
    1 1 1 1     		4 x 4
    1 1 0 0
    0 1 1 0
    0 1 0 1
    1 0 1 1     		4 x 4
    1 1 1 0
    0 1 0 0
    1 1 0 1
    0 0 1 1
    upperBandwidth
    0
    0
    1
    		 3 0
    1
    2
    lowerBandwidth
    0
    0
    1
    		 0 3
    3
    2
    semiBandwidth
    1
    1
    2
    		 4 4
    4
    3
    description
    zero
    diagonal
    tridiagonal
    		 upper triangular lower triangular
    unstructured
    unstructured
    See Also:
    Serialized Form

    • Field Detail

      • DEFAULT

        public static final IntProperty DEFAULT
        The default Property object;.

    • Constructor Detail

      • IntProperty

        public IntProperty()
        Constructs an instance with a tolerance of Math.abs(newTolerance).

    • Method Detail

      • checkRectangular

        public void checkRectangular(IntMatrix2D A)
        Checks whether the given matrix A is rectangular.
        Throws:
        java.lang.IllegalArgumentException - if A.rows() < A.columns().

      • checkSquare

        public void checkSquare(IntMatrix2D A)
        Checks whether the given matrix A is square.
        Throws:
        java.lang.IllegalArgumentException - if A.rows() != A.columns().

      • density

        public int density(IntMatrix2D A)
        Returns the matrix's fraction of non-zero cells; A.cardinality() / A.size().

      • equals

        public boolean equals(IntMatrix1D A,
                      int value)
        Returns whether all cells of the given matrix A are equal to the given value. The result is true if and only if A != null and ! (Math.abs(value - A[i]) > tolerance()) holds for all coordinates.
        Parameters:
        A - the first matrix to compare.
        value - the value to compare against.
        Returns:
        true if the matrix is equal to the value; false otherwise.

      • equals

        public boolean equals(IntMatrix1D A,
                      IntMatrix1D B)
        Returns whether both given matrices A and B are equal. The result is true if A==B. Otherwise, the result is true if and only if both arguments are != null, have the same size and ! (Math.abs(A[i] - B[i]) > tolerance()) holds for all indexes.
        Parameters:
        A - the first matrix to compare.
        B - the second matrix to compare.
        Returns:
        true if both matrices are equal; false otherwise.

      • equals

        public boolean equals(IntMatrix2D A,
                      int value)
        Returns whether all cells of the given matrix A are equal to the given value. The result is true if and only if A != null and ! (Math.abs(value - A[row,col]) > tolerance()) holds for all coordinates.
        Parameters:
        A - the first matrix to compare.
        value - the value to compare against.
        Returns:
        true if the matrix is equal to the value; false otherwise.

      • equals

        public boolean equals(IntMatrix2D A,
                      IntMatrix2D B)
        Returns whether both given matrices A and B are equal. The result is true if A==B. Otherwise, the result is true if and only if both arguments are != null, have the same number of columns and rows and ! (Math.abs(A[row,col] - B[row,col]) > tolerance()) holds for all coordinates.
        Parameters:
        A - the first matrix to compare.
        B - the second matrix to compare.
        Returns:
        true if both matrices are equal; false otherwise.

      • equals

        public boolean equals(IntMatrix3D A,
                      int value)
        Returns whether all cells of the given matrix A are equal to the given value. The result is true if and only if A != null and ! (Math.abs(value - A[slice,row,col]) > tolerance()) holds for all coordinates.
        Parameters:
        A - the first matrix to compare.
        value - the value to compare against.
        Returns:
        true if the matrix is equal to the value; false otherwise.

      • equals

        public boolean equals(IntMatrix3D A,
                      IntMatrix3D B)
        Returns whether both given matrices A and B are equal. The result is true if A==B. Otherwise, the result is true if and only if both arguments are != null, have the same number of columns, rows and slices, and ! (Math.abs(A[slice,row,col] - B[slice,row,col]) > tolerance()) holds for all coordinates.
        Parameters:
        A - the first matrix to compare.
        B - the second matrix to compare.
        Returns:
        true if both matrices are equal; false otherwise.

      • generateNonSingular

        public void generateNonSingular(IntMatrix2D A)
        Modifies the given matrix square matrix A such that it is diagonally dominant by row and column, hence non-singular, hence invertible. For testing purposes only.
        Parameters:
        A - the square matrix to modify.
        Throws:
        java.lang.IllegalArgumentException - if !isSquare(A).

      • isDiagonal

        public boolean isDiagonal(IntMatrix2D A)
        A matrix A is diagonal if A[i,j] == 0 whenever i != j. Matrix may but need not be square.

      • isDiagonallyDominantByColumn

        public boolean isDiagonallyDominantByColumn(IntMatrix2D A)
        A matrix A is diagonally dominant by column if the absolute value of each diagonal element is larger than the sum of the absolute values of the off-diagonal elements in the corresponding column. returns true if for all i: abs(A[i,i]) > Sum(abs(A[j,i])); j != i. Matrix may but need not be square.

        Note: Ignores tolerance.

      • isDiagonallyDominantByRow

        public boolean isDiagonallyDominantByRow(IntMatrix2D A)
        A matrix A is diagonally dominant by row if the absolute value of each diagonal element is larger than the sum of the absolute values of the off-diagonal elements in the corresponding row. returns true if for all i: abs(A[i,i]) > Sum(abs(A[i,j])); j != i. Matrix may but need not be square.

        Note: Ignores tolerance.

      • isIdentity

        public boolean isIdentity(IntMatrix2D A)
        A matrix A is an identity matrix if A[i,i] == 1 and all other cells are zero. Matrix may but need not be square.

      • isLowerBidiagonal

        public boolean isLowerBidiagonal(IntMatrix2D A)
        A matrix A is lower bidiagonal if A[i,j]==0 unless i==j || i==j+1. Matrix may but need not be square.

      • isLowerTriangular

        public boolean isLowerTriangular(IntMatrix2D A)
        A matrix A is lower triangular if A[i,j]==0 whenever i < j. Matrix may but need not be square.

      • isNonNegative

        public boolean isNonNegative(IntMatrix2D A)
        A matrix A is non-negative if A[i,j] >= 0 holds for all cells.

        Note: Ignores tolerance.

      • isOrthogonal

        public boolean isOrthogonal(IntMatrix2D A)
        A square matrix A is orthogonal if A*transpose(A) = I.
        Throws:
        java.lang.IllegalArgumentException - if !isSquare(A).

      • isPositive

        public boolean isPositive(IntMatrix2D A)
        A matrix A is positive if A[i,j] > 0 holds for all cells.

        Note: Ignores tolerance.

      • isSkewSymmetric

        public boolean isSkewSymmetric(IntMatrix2D A)
        A square matrix A is skew-symmetric if A = -transpose(A), that is A[i,j] == -A[j,i].
        Throws:
        java.lang.IllegalArgumentException - if !isSquare(A).

      • isSquare

        public boolean isSquare(IntMatrix2D A)
        A matrix A is square if it has the same number of rows and columns.

      • isStrictlyLowerTriangular

        public boolean isStrictlyLowerTriangular(IntMatrix2D A)
        A matrix A is strictly lower triangular if A[i,j]==0 whenever i <= j. Matrix may but need not be square.

      • isStrictlyTriangular

        public boolean isStrictlyTriangular(IntMatrix2D A)
        A matrix A is strictly triangular if it is triangular and its diagonal elements all equal 0. Matrix may but need not be square.

      • isStrictlyUpperTriangular

        public boolean isStrictlyUpperTriangular(IntMatrix2D A)
        A matrix A is strictly upper triangular if A[i,j]==0 whenever i >= j. Matrix may but need not be square.

      • isSymmetric

        public boolean isSymmetric(IntMatrix2D A)
        A matrix A is symmetric if A = tranpose(A), that is A[i,j] == A[j,i].
        Throws:
        java.lang.IllegalArgumentException - if !isSquare(A).

      • isTriangular

        public boolean isTriangular(IntMatrix2D A)
        A matrix A is triangular iff it is either upper or lower triangular. Matrix may but need not be square.

      • isTridiagonal

        public boolean isTridiagonal(IntMatrix2D A)
        A matrix A is tridiagonal if A[i,j]==0 whenever Math.abs(i-j) > 1. Matrix may but need not be square.

      • isUnitTriangular

        public boolean isUnitTriangular(IntMatrix2D A)
        A matrix A is unit triangular if it is triangular and its diagonal elements all equal 1. Matrix may but need not be square.

      • isUpperBidiagonal

        public boolean isUpperBidiagonal(IntMatrix2D A)
        A matrix A is upper bidiagonal if A[i,j]==0 unless i==j || i==j-1. Matrix may but need not be square.

      • isUpperTriangular

        public boolean isUpperTriangular(IntMatrix2D A)
        A matrix A is upper triangular if A[i,j]==0 whenever i > j. Matrix may but need not be square.

      • isZero

        public boolean isZero(IntMatrix2D A)
        A matrix A is zero if all its cells are zero.

      • lowerBandwidth

        public int lowerBandwidth(IntMatrix2D A)
        The lower bandwidth of a square matrix A is the maximum i-j for which A[i,j] is nonzero and i > j. A banded matrix has a "band" about the diagonal. Diagonal, tridiagonal and triangular matrices are special cases.
        Parameters:
        A - the square matrix to analyze.
        Returns:
        the lower bandwith.
        Throws:
        java.lang.IllegalArgumentException - if !isSquare(A).
        See Also:
        semiBandwidth(IntMatrix2D), upperBandwidth(IntMatrix2D)

      • semiBandwidth

        public int semiBandwidth(IntMatrix2D A)
        Returns the semi-bandwidth of the given square matrix A. A banded matrix has a "band" about the diagonal. It is a matrix with all cells equal to zero, with the possible exception of the cells along the diagonal line, the k diagonal lines above the diagonal, and the k diagonal lines below the diagonal. The semi-bandwith l is the number k+1. The bandwidth p is the number 2*k + 1. For example, a tridiagonal matrix corresponds to k=1, l=2, p=3, a diagonal or zero matrix corresponds to k=0, l=1, p=1,

        The upper bandwidth is the maximum j-i for which A[i,j] is nonzero and j > i. The lower bandwidth is the maximum i-j for which A[i,j] is nonzero and i > j. Diagonal, tridiagonal and triangular matrices are special cases.

        Examples:

        matrix 4 x 4 
        0 0 0 0
        0 0 0 0
        0 0 0 0
        0 0 0 0         		4 x 4
        1 0 0 0
        0 0 0 0
        0 0 0 0
        0 0 0 1         		4 x 4
        1 1 0 0
        1 1 1 0
        0 1 1 1
        0 0 1 1         		4 x 4
        0 1 1 1
        0 1 1 1
        0 0 0 1
        0 0 0 1         		4 x 4
        0 0 0 0
        1 1 0 0
        1 1 0 0
        1 1 1 1         		4 x 4
        1 1 0 0
        0 1 1 0
        0 1 0 1
        1 0 1 1         		4 x 4
        1 1 1 0
        0 1 0 0
        1 1 0 1
        0 0 1 1
        upperBandwidth
        0
        0
        1
        		 3 0
        1
        2
        lowerBandwidth
        0
        0
        1
        		 0 3
        3
        2
        semiBandwidth
        1
        1
        2
        		 4 4
        4
        3
        description
        zero
        diagonal
        tridiagonal
        		 upper triangular lower triangular
        unstructured
        unstructured
        Parameters:
        A - the square matrix to analyze.
        Returns:
        the semi-bandwith l.
        Throws:
        java.lang.IllegalArgumentException - if !isSquare(A).
        See Also:
        lowerBandwidth(IntMatrix2D), upperBandwidth(IntMatrix2D)

      • toString

        public java.lang.String toString(IntMatrix2D A)
        Returns summary information about the given matrix A. That is a String with (propertyName, propertyValue) pairs. Useful for debugging or to quickly get the rough picture of a matrix. For example, 
           density                      : 0.9
   isDiagonal                   : false
   isDiagonallyDominantByRow    : false
   isDiagonallyDominantByColumn : false
   isIdentity                   : false
   isLowerBidiagonal            : false
   isLowerTriangular            : false
   isNonNegative                : true
   isOrthogonal                 : Illegal operation or error: Matrix must be square.
   isPositive                   : true
   isSingular                   : Illegal operation or error: Matrix must be square.
   isSkewSymmetric              : Illegal operation or error: Matrix must be square.
   isSquare                     : false
   isStrictlyLowerTriangular    : false
   isStrictlyTriangular         : false
   isStrictlyUpperTriangular    : false
   isSymmetric                  : Illegal operation or error: Matrix must be square.
   isTriangular                 : false
   isTridiagonal                : false
   isUnitTriangular             : false
   isUpperBidiagonal            : false
   isUpperTriangular            : false
   isZero                       : false
   lowerBandwidth               : Illegal operation or error: Matrix must be square.
   semiBandwidth                : Illegal operation or error: Matrix must be square.
   upperBandwidth               : Illegal operation or error: Matrix must be square.

      • upperBandwidth

        public int upperBandwidth(IntMatrix2D A)
        The upper bandwidth of a square matrix A is the maximum j-i for which A[i,j] is nonzero and j > i. A banded matrix has a "band" about the diagonal. Diagonal, tridiagonal and triangular matrices are special cases.
        Parameters:
        A - the square matrix to analyze.
        Returns:
        the upper bandwith.
        Throws:
        java.lang.IllegalArgumentException - if !isSquare(A).
        See Also:
        semiBandwidth(IntMatrix2D), lowerBandwidth(IntMatrix2D)
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