MatrixFeatures
org.ejml.ops

Class MatrixFeatures



  • public class MatrixFeaturesextends Object

    Used to compute features that describe the structure of a matrix.

    Unless explicitly stated otherwise it is assumed that the elements of input matrices contain only real numbers. If an element is NaN or infinite then the behavior is undefined. See IEEE 754 for more information on this issue.

    • Constructor Detail

      • MatrixFeatures

        public MatrixFeatures()
    • Method Detail

      • hasNaN

        public static boolean hasNaN(D1Matrix64F m)
        Checks to see if any element in the matrix is NaN.
        Parameters:
        m - A matrix. Not modified.
        Returns:
        True if any element in the matrix is NaN.
      • hasUncountable

        public static boolean hasUncountable(D1Matrix64F m)
        Checks to see if any element in the matrix is NaN of Infinite.
        Parameters:
        m - A matrix. Not modified.
        Returns:
        True if any element in the matrix is NaN of Infinite.
      • isVector

        public static boolean isVector(D1Matrix64F mat)
        Checks to see if the matrix is a vector or not.
        Parameters:
        mat - A matrix. Not modified.
        Returns:
        True if it is a vector and false if it is not.
      • isPositiveDefinite

        public static boolean isPositiveDefinite(DenseMatrix64F A)

        Checks to see if the matrix is positive definite.

        xT A x > 0
        for all x where x is a non-zero vector and A is a symmetric matrix.

        Parameters:
        A - square symmetric matrix. Not modified.
        Returns:
        True if it is positive definite and false if it is not.
      • isPositiveSemidefinite

        public static boolean isPositiveSemidefinite(DenseMatrix64F A)

        Checks to see if the matrix is positive semidefinite:

        xT A x >= 0
        for all x where x is a non-zero vector and A is a symmetric matrix.

        Parameters:
        A - square symmetric matrix. Not modified.
        Returns:
        True if it is positive semidefinite and false if it is not.
      • isSquare

        public static boolean isSquare(D1Matrix64F mat)
        Checks to see if it is a square matrix. A square matrix has the same number of rows and columns.
        Parameters:
        mat - A matrix. Not modified.
        Returns:
        True if it is a square matrix and false if it is not.
      • isSymmetric

        public static boolean isSymmetric(DenseMatrix64F m,                  double tol)

        Returns true if the matrix is symmetric within the tolerance. Only square matrices can be symmetric.

        A matrix is symmetric if:
        |aij - aji| ≤ tol

        Parameters:
        m - A matrix. Not modified.
        tol - Tolerance for how similar two elements need to be.
        Returns:
        true if it is symmetric and false if it is not.
      • isSymmetric

        public static boolean isSymmetric(DenseMatrix64F m)

        Returns true if the matrix is perfectly symmetric. Only square matrices can be symmetric.

        A matrix is symmetric if:
        aij == aji

        Parameters:
        m - A matrix. Not modified.
        Returns:
        true if it is symmetric and false if it is not.
      • isSkewSymmetric

        public static boolean isSkewSymmetric(DenseMatrix64F A,                      double tol)

        Checks to see if a matrix is skew symmetric with in tolerance:

        -A = AT
        or
        |aij + aji| ≤ tol

        Parameters:
        A - The matrix being tested.
        tol - Tolerance for being skew symmetric.
        Returns:
        True if it is skew symmetric and false if it is not.
      • isInverse

        public static boolean isInverse(DenseMatrix64F a,                DenseMatrix64F b,                double tol)
        Checks to see if the two matrices are inverses of each other.
        Parameters:
        a - A matrix. Not modified.
        b - A matrix. Not modified.
      • isEquals

        public static boolean isEquals(D1Matrix64F a,               D1Matrix64F b,               double tol)

        Checks to see if each element in the two matrices are within tolerance of each other: tol ≥ |aij - bij|.

        NOTE: If any of the elements are not countable then false is returned.
        NOTE: If a tolerance of zero is passed in this is equivalent to calling isEquals(org.ejml.data.D1Matrix64F, org.ejml.data.D1Matrix64F)

        Parameters:
        a - A matrix. Not modified.
        b - A matrix. Not modified.
        tol - How close to being identical each element needs to be.
        Returns:
        true if equals and false otherwise.
      • isEqualsTriangle

        public static boolean isEqualsTriangle(Matrix64F a,                       Matrix64F b,                       boolean upper,                       double tol)

        Checks to see if each element in the upper or lower triangular portion of the two matrices are within tolerance of each other: tol ≥ |aij - bij|.

        NOTE: If any of the elements are not countable then false is returned.
        NOTE: If a tolerance of zero is passed in this is equivalent to calling isEquals(org.ejml.data.D1Matrix64F, org.ejml.data.D1Matrix64F)

        Parameters:
        a - A matrix. Not modified.
        b - A matrix. Not modified.
        upper - true of upper triangular and false for lower.
        tol - How close to being identical each element needs to be.
        Returns:
        true if equals and false otherwise.
      • isEquals

        public static boolean isEquals(D1Matrix64F a,               D1Matrix64F b)

        Checks to see if each element in the two matrices are equal: aij == bij

        NOTE: If any of the elements are NaN then false is returned. If two corresponding elements are both positive or negative infinity then they are equal.

        Parameters:
        a - A matrix. Not modified.
        b - A matrix. Not modified.
        Returns:
        true if identical and false otherwise.
      • isIdentical

        public static boolean isIdentical(D1Matrix64F a,                  D1Matrix64F b,                  double tol)

        Checks to see if each corresponding element in the two matrices are within tolerance of each other or have the some symbolic meaning. This can handle NaN and Infinite numbers.

        If both elements are countable then the following equality test is used:
        |aij - bij| ≤ tol.
        Otherwise both numbers must both be Double.NaN, Double.POSITIVE_INFINITY, or Double.NEGATIVE_INFINITY to be identical.

        Parameters:
        a - A matrix. Not modified.
        b - A matrix. Not modified.
        tol - Tolerance for equality.
        Returns:
        true if identical and false otherwise.
      • isOrthogonal

        public static boolean isOrthogonal(DenseMatrix64F Q,                   double tol)

        Checks to see if a matrix is orthogonal or isometric.

        Parameters:
        Q - The matrix being tested. Not modified.
        tol - Tolerance.
        Returns:
        True if it passes the test.
      • isRowsLinearIndependent

        public static boolean isRowsLinearIndependent(DenseMatrix64F A)
        Checks to see if the rows of the provided matrix are linearly independent.
        Parameters:
        A - Matrix whose rows are being tested for linear independence.
        Returns:
        true if linearly independent and false otherwise.
      • isIdentity

        public static boolean isIdentity(DenseMatrix64F mat,                 double tol)
        Checks to see if the provided matrix is within tolerance to an identity matrix.
        Parameters:
        mat - Matrix being examined. Not modified.
        tol - Tolerance.
        Returns:
        True if it is within tolerance to an identify matrix.
      • isConstantVal

        public static boolean isConstantVal(DenseMatrix64F mat,                    double val,                    double tol)
        Checks to see if every value in the matrix is the specified value.
        Parameters:
        mat - The matrix being tested. Not modified.
        val - Checks to see if every element in the matrix has this value.
        tol - True if all the elements are within this tolerance.
        Returns:
        true if the test passes.
      • isDiagonalPositive

        public static boolean isDiagonalPositive(DenseMatrix64F a)
        Checks to see if all the diagonal elements in the matrix are positive.
        Parameters:
        a - A matrix. Not modified.
        Returns:
        true if all the diagonal elements are positive, false otherwise.
      • isNegative

        public static boolean isNegative(D1Matrix64F a,                 D1Matrix64F b,                 double tol)

        Checks to see if the two matrices are the negative of each other:

        aij = -bij

        Parameters:
        a - First matrix. Not modified.
        b - Second matrix. Not modified.
        tol - Numerical tolerance.
        Returns:
        True if they are the negative of each other within tolerance.
      • isUpperTriangle

        public static boolean isUpperTriangle(DenseMatrix64F A,                      int hessenberg,                      double tol)

        Checks to see if a matrix is upper triangular or Hessenberg. A Hessenberg matrix of degree N has the following property:

        aij ≤ 0 for all i < j+N

        A triangular matrix is a Hessenberg matrix of degree 0.

        Parameters:
        A - Matrix being tested. Not modified.
        hessenberg - The degree of being hessenberg.
        tol - How close to zero the lower left elements need to be.
        Returns:
        If it is an upper triangular/hessenberg matrix or not.
      • rank

        public static int rank(DenseMatrix64F A)
        Computes the rank of a matrix using a default tolerance.
        Parameters:
        A - Matrix whose rank is to be calculated. Not modified.
        Returns:
        The matrix's rank.
      • rank

        public static int rank(DenseMatrix64F A,       double threshold)
        Computes the rank of a matrix using the specified tolerance.
        Parameters:
        A - Matrix whose rank is to be calculated. Not modified.
        threshold - The numerical threshold used to determine a singular value.
        Returns:
        The matrix's rank.
      • nullity

        public static int nullity(DenseMatrix64F A)
        Computes the nullity of a matrix using the default tolerance.
        Parameters:
        A - Matrix whose rank is to be calculated. Not modified.
        Returns:
        The matrix's nullity.
      • nullity

        public static int nullity(DenseMatrix64F A,          double threshold)
        Computes the nullity of a matrix using the specified tolerance.
        Parameters:
        A - Matrix whose rank is to be calculated. Not modified.
        threshold - The numerical threshold used to determine a singular value.
        Returns:
        The matrix's nullity.

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