LongProperty
cern.colt.matrix.tlong.algo

Class LongProperty

  • All Implemented Interfaces:
    Serializable, Cloneable


    public class LongPropertyextends 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 LongProperty DEFAULT
        The default Property object;.
    • Constructor Detail

      • LongProperty

        public LongProperty()
        Constructs an instance with a tolerance of Math.abs(newTolerance).
    • Method Detail

      • density

        public int density(LongMatrix2D A)
        Returns the matrix's fraction of non-zero cells; A.cardinality() / A.size().
      • equals

        public boolean equals(LongMatrix1D A,             long 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(LongMatrix1D A,             LongMatrix1D 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(LongMatrix2D A,             long 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(LongMatrix2D A,             LongMatrix2D 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(LongMatrix3D A,             long 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(LongMatrix3D A,             LongMatrix3D 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(LongMatrix2D 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:
        IllegalArgumentException - if !isSquare(A).
      • isDiagonal

        public boolean isDiagonal(LongMatrix2D 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(LongMatrix2D 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(LongMatrix2D 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(LongMatrix2D 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(LongMatrix2D 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(LongMatrix2D 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(LongMatrix2D A)
        A matrix A is non-negative if A[i,j] >= 0 holds for all cells.

        Note: Ignores tolerance.

      • isPositive

        public boolean isPositive(LongMatrix2D A)
        A matrix A is positive if A[i,j] > 0 holds for all cells.

        Note: Ignores tolerance.

      • isSkewSymmetric

        public boolean isSkewSymmetric(LongMatrix2D A)
        A square matrix A is skew-symmetric if A = -transpose(A), that is A[i,j] == -A[j,i].
        Throws:
        IllegalArgumentException - if !isSquare(A).
      • isSquare

        public boolean isSquare(LongMatrix2D A)
        A matrix A is square if it has the same number of rows and columns.
      • isStrictlyLowerTriangular

        public boolean isStrictlyLowerTriangular(LongMatrix2D 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(LongMatrix2D 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(LongMatrix2D A)
        A matrix A is strictly upper triangular if A[i,j]==0 whenever i >= j. Matrix may but need not be square.
      • isTriangular

        public boolean isTriangular(LongMatrix2D 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(LongMatrix2D 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(LongMatrix2D 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(LongMatrix2D 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(LongMatrix2D 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(LongMatrix2D A)
        A matrix A is zero if all its cells are zero.
      • lowerBandwidth

        public int lowerBandwidth(LongMatrix2D 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:
        IllegalArgumentException - if !isSquare(A).
        See Also:
        semiBandwidth(LongMatrix2D), upperBandwidth(LongMatrix2D)
      • semiBandwidth

        public int semiBandwidth(LongMatrix2D 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:
        IllegalArgumentException - if !isSquare(A).
        See Also:
        lowerBandwidth(LongMatrix2D), upperBandwidth(LongMatrix2D)
      • toString

        public String toString(LongMatrix2D 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(LongMatrix2D 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:
        IllegalArgumentException - if !isSquare(A).
        See Also:
        semiBandwidth(LongMatrix2D), lowerBandwidth(LongMatrix2D)

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