org.ejml.ops
Class MatrixFeatures

java.lang.Object
  org.ejml.ops.MatrixFeatures

public class MatrixFeatures
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.

Author:

Peter Abeles

Constructor Summary

MatrixFeatures()

Method Summary

static boolean	hasNaN(D1Matrix64F m) Checks to see if any element in the matrix is NaN.
static boolean	hasUncountable(D1Matrix64F m) Checks to see if any element in the matrix is NaN of Infinite.
static boolean	isConstantVal(DenseMatrix64F mat, double val, double tol) Checks to see if every value in the matrix is the specified value.
static boolean	isDiagonalPositive(DenseMatrix64F a) Checks to see if all the diagonal elements in the matrix are positive.
static boolean	isEquals(D1Matrix64F a, D1Matrix64F b) Checks to see if each element in the two matrices are equal: aij == bij
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|.
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|.
static boolean	isFullRank(DenseMatrix64F a)
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.
static boolean	isIdentity(DenseMatrix64F mat, double tol) Checks to see if the provided matrix is within tolerance to an identity matrix.
static boolean	isInverse(DenseMatrix64F a, DenseMatrix64F b, double tol) Checks to see if the two matrices are inverses of each other.
static boolean	isNegative(D1Matrix64F a, D1Matrix64F b, double tol) Checks to see if the two matrices are the negative of each other: aij = -bij
static boolean	isOrthogonal(DenseMatrix64F Q, double tol) Checks to see if a matrix is orthogonal or isometric.
static boolean	isPositiveDefinite(DenseMatrix64F A) Checks to see if the matrix is positive definite.
static boolean	isPositiveSemidefinite(DenseMatrix64F A) Checks to see if the matrix is positive semidefinite:
static boolean	isRowsLinearIndependent(DenseMatrix64F A) Checks to see if the rows of the provided matrix are linearly independent.
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
static boolean	isSquare(D1Matrix64F mat) Checks to see if it is a square matrix.
static boolean	isSymmetric(DenseMatrix64F m) Returns true if the matrix is perfectly symmetric.
static boolean	isSymmetric(DenseMatrix64F m, double tol) Returns true if the matrix is symmetric within the tolerance.
static boolean	isUpperTriangle(DenseMatrix64F A, int hessenberg, double tol) Checks to see if a matrix is upper triangular or Hessenberg.
static boolean	isVector(D1Matrix64F mat) Checks to see if the matrix is a vector or not.
static int	nullity(DenseMatrix64F A) Computes the nullity of a matrix using the default tolerance.
static int	nullity(DenseMatrix64F A, double threshold) Computes the nullity of a matrix using the specified tolerance.
static int	rank(DenseMatrix64F A) Computes the rank of a matrix using a default tolerance.
static int	rank(DenseMatrix64F A, double threshold) Computes the rank of a matrix using the specified tolerance.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

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.

x^T 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:

x^T 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:
|a_ij - a_ji| ≤ 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:
a_ij == a_ji

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 = A^T
or
|a_ij + a_ji| ≤ 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 ≥ |a_ij - b_ij|.

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 ≥ |a_ij - b_ij|.

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: a_ij == b_ij

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:
|a_ij - b_ij| ≤ 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.

isFullRank

public static boolean isFullRank(DenseMatrix64F a)

isNegative

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

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

a_ij = -b_ij

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:

a_ij ≤ 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.