Package org.ejml.dense.row

Class MatrixFeatures_DDRM

java.lang.Object
org.ejml.dense.row.MatrixFeatures_DDRM
public class MatrixFeatures_DDRM extends 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.

  • Method Details

    • hasNaN

      public static boolean hasNaN(DMatrixD1 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(DMatrixD1 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.

    • isZeros

      public static boolean isZeros(DMatrixD1 m, double tol)
      Checks to see all the elements in the matrix are zeros
      Parameters:
      m - A matrix. Not modified.
      Returns:
      True if all elements are zeros or false if not

    • isVector

      public static boolean isVector(Matrix 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(DMatrixRMaj 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(DMatrixRMaj 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(DMatrixD1 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(DMatrixRMaj 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(DMatrixRMaj 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(DMatrixRMaj 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(DMatrixRMaj a, DMatrixRMaj 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(DMatrixD1 a, DMatrixD1 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(DMatrixD1, DMatrixD1)

      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(DMatrix a, DMatrix 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(DMatrixD1, DMatrixD1)

      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(DMatrixD1 a, DMatrixD1 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.

    • isEquals

      public static boolean isEquals(BMatrixRMaj a, BMatrixRMaj 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(DMatrixD1 a, DMatrixD1 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(DMatrixRMaj 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(DMatrixRMaj 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(DMatrixRMaj 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(DMatrixRMaj 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.

    • isDiagonalNotNegative

      public static boolean isDiagonalNotNegative(DMatrixRMaj a)
      Checks to see if diagonal element are all not negative, i.e. greater than or equal to 0.
      Parameters:
      a - A matrix. Not modified.
      Returns:
      True if diagonal element are all not negative. False otherwise.

    • isDiagonalPositive

      public static boolean isDiagonalPositive(DMatrixRMaj 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.

    • isFullRank

      public static boolean isFullRank(DMatrixRMaj a)

    • isNegative

      public static boolean isNegative(DMatrixD1 a, DMatrixD1 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(DMatrixRMaj 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.

    • isLowerTriangle

      public static boolean isLowerTriangle(DMatrixRMaj A, int hessenberg, double tol)

      Checks to see if a matrix is lower 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(DMatrixRMaj 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(DMatrixRMaj 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(DMatrixRMaj 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(DMatrixRMaj 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.

    • countNonZero

      public static int countNonZero(DMatrixRMaj A)
      Counts the number of elements in A which are not zero.
      Parameters:
      A - A matrix
      Returns:
      number of non-zero elements