com.numericalmethod.suanshu.matrix.doubles.operation
Class Measure

java.lang.Object
  com.numericalmethod.suanshu.matrix.doubles.operation.Measure

public class Measure
extends java.lang.Object

A measure, μ, of a matrix, A, is a map from the DenseMatrix space to the real line. That is,

μ: A -> R

Constructor Summary

Measure()

Method Summary

static double	det(Matrix A) Compute the determinant of a matrix.
static double	Frobenius(Matrix A) Compute the Frobenius norm, i.e., the sqrt of the sum of squares of all elements of a matrix.
static double	max(Matrix A) Compute the maximal entry in a matrix.
static double	min(Matrix A) Compute the minimal entry in a matrix.
static int	nullity(Matrix A) Deprecated. Not supported yet.
static int	rank(Matrix A) Compute the numerical rank of a matrix.
static int	rank(Matrix A, double epsilon) Compute the numerical rank of a matrix.
static double	tr(Matrix A) Compute the sum of the diagonal elements, i.e., the trace of a matrix.

Methods inherited from class java.lang.Object

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

Constructor Detail

Measure

public Measure()

Method Detail

rank

public static int rank(Matrix A,
                       double epsilon)

Compute the numerical rank of a matrix.

Ignore all singular values less than a threshold.

Parameters:

A - a matrix

epsilon - a precision parameter: when a number |x| ≤ ε, it is considered 0

Returns:

the numerical rank of A

See Also:

Wikipedia: Rank (linear algebra)

rank

public static int rank(Matrix A)

Compute the numerical rank of a matrix.

Igore all singular values less than a threshold.

Parameters:

A - a matrix

Returns:

the numerical rank of A

nullity

@Deprecated
public static int nullity(Matrix A)

Deprecated. Not supported yet.

Compute the nullity of a matrix.

Parameters:

A - a matrix

Returns:

the nullity of A

See Also:

Wikipedia: Rank–nullity theorem

det

public static double det(Matrix A)

Compute the determinant of a matrix.

Parameters:

A - a matrix

Returns:

the determinant of A

See Also:

Wikipedia: Determinant

tr

public static double tr(Matrix A)

Compute the sum of the diagonal elements, i.e., the trace of a matrix.

Parameters:

A - a matrix

Returns:

the trace of A

See Also:

Wikipedia: Trace (linear algebra)

Frobenius

public static double Frobenius(Matrix A)

Compute the Frobenius norm, i.e., the sqrt of the sum of squares of all elements of a matrix.

Parameters:

A - a matrix

Returns:

sqrt of sum of squares of all elements in A

See Also:

Wikipedia: Frobenius norm

max

public static double max(Matrix A)

Compute the maximal entry in a matrix.

Parameters:

A - a matrix

Returns:

the maximal entry

min

public static double min(Matrix A)

Compute the minimal entry in a matrix.

Parameters:

A - a matrix

Returns:

the minimal entry