com.numericalmethod.suanshu.matrix.doubles

Class IsMatrix

java.lang.Object

com.numericalmethod.suanshu.matrix.doubles.IsMatrix

public class IsMatrix
extends java.lang.Object

These are the boolean operators that take a matrix or a vector and check if it satisfies a certain property.

Method Summary

Modifier and Type	Method and Description
static boolean	diagonal(Matrix A, double epsilon) Check if a square matrix is a diagonal matrix, up to a precision.
static boolean	idempotent(Matrix A, double epsilon) Check if a matrix is idempotent.
static boolean	identity(Matrix A, double epsilon) Check if a matrix is an identity matrix, up to a precision.
static boolean	lowerBidiagonal(Matrix A, double epsilon) Check if a matrix is lower bidiagonal, up to a precision.
static boolean	lowerTriangular(Matrix A, double epsilon) Check if a matrix is lower triangular, up to a precision.
static boolean	magicSquare(Matrix A) Deprecated. Not supported yet.
static boolean	orthogonal(Matrix A, double epsilon) Check if a matrix is orthogonal, up to a precision.
static boolean	positiveDefinite(Matrix A) Check if a square matrix is positive definite; the matrix needs not be symmetric.
static boolean	positiveSemiDefinite(Matrix A, double epsilon) Check if a square matrix is positive definite, up to a precision.
static boolean	quasiTriangular(Matrix A, double epsilon) Check if a matrix is quasi (upper) triangular, up to a precision.
static boolean	reducedRowEchelonForm(Matrix A, double epsilon) Check if a matrix is in the reduced row echelon form, up to a precision.
static boolean	rowEchelonForm(Matrix A, double epsilon) Check if a matrix is in the row echelon form, up to a precision.
static boolean	scalar(Matrix A, double epsilon) Deprecated. Not supported yet.
static boolean	singular(Matrix A, double epsilon) Check if a square matrix is singular, i.e, having no inverse, up to a precision.
static boolean	skewSymmetric(Matrix A, double epsilon) Check if a matrix is skew symmetric.
static boolean	symmetric(Matrix A, double epsilon) Check if a matrix is symmetric.
static boolean	symmetricPositiveDefinite(Matrix A) Check if a square matrix is symmetric and positive definite.
static boolean	tridiagonal(Matrix A, double epsilon) Check if a matrix is tridiagonal, up to a precision.
static boolean	upperBidiagonal(Matrix A, double epsilon) Check if a matrix is upper bidiagonal, up to a precision.
static boolean	upperTriangular(Matrix A, double epsilon) Check if a matrix is upper triangular, up to a precision.
static boolean	zero(Vector v, double epsilon) Check if a vector is a zero vector, i.e., all its entries are 0, up to a precision.

Methods inherited from class java.lang.Object

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

Method Detail

symmetric

public static boolean symmetric(Matrix A,
                                double epsilon)

Check if a matrix is symmetric.

Parameters:

A - a matrix

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

Returns:

true if

A.t() == A

skewSymmetric

public static boolean skewSymmetric(Matrix A,
                                    double epsilon)

Check if a matrix is skew symmetric.

Parameters:

A - a matrix

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

Returns:

true if

A.t() == -A

idempotent

public static boolean idempotent(Matrix A,
                                 double epsilon)

Check if a matrix is idempotent.

Parameters:

A - a matrix

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

Returns:

true if

A = A*A or A = A2

orthogonal

public static boolean orthogonal(Matrix A,
                                 double epsilon)

Check if a matrix is orthogonal, up to a precision.

Parameters:

A - a matrix

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

Returns:

true if

AA' = 1

magicSquare

@Deprecated
public static boolean magicSquare(Matrix A)

Deprecated. Not supported yet.

Check if a matrix is a magic square. Not yet implemented.

Parameters:

A - a matrix

Returns:

true if A is a square matrix having distinct positive integers, arranged such that the sums of the numbers in any rows, columns, or diagonals are equal

singular

public static boolean singular(Matrix A,
                               double epsilon)

Check if a square matrix is singular, i.e, having no inverse, up to a precision.

Parameters:

A - a matrix

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

Returns:

true if A^-1 does not exist

diagonal

public static boolean diagonal(Matrix A,
                               double epsilon)

Check if a square matrix is a diagonal matrix, up to a precision.

Parameters:

A - a matrix

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

Returns:

true if A is square and A_ij=0, for all i != j.

identity

public static boolean identity(Matrix A,
                               double epsilon)

Check if a matrix is an identity matrix, up to a precision.

Parameters:

A - a matrix

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

Returns:

true if A is square, and A_ij=0 for all i != j, and A_ij=1, for all i == j.

upperTriangular

public static boolean upperTriangular(Matrix A,
                                      double epsilon)

Check if a matrix is upper triangular, up to a precision.

Parameters:

A - a matrix

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

Returns:

true if the matrix is upper triangular

lowerTriangular

public static boolean lowerTriangular(Matrix A,
                                      double epsilon)

Check if a matrix is lower triangular, up to a precision.

Parameters:

A - a matrix

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

Returns:

true if the matrix is lower triangular

quasiTriangular

public static boolean quasiTriangular(Matrix A,
                                      double epsilon)

Check if a matrix is quasi (upper) triangular, up to a precision.

Parameters:

A - a matrix

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

Returns:

true if the matrix is quasi (upper) triangular

upperBidiagonal

public static boolean upperBidiagonal(Matrix A,
                                      double epsilon)

Check if a matrix is upper bidiagonal, up to a precision.

Parameters:

A - a matrix

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

Returns:

true if the matrix is upper bidiagonal

lowerBidiagonal

public static boolean lowerBidiagonal(Matrix A,
                                      double epsilon)

Check if a matrix is lower bidiagonal, up to a precision.

Parameters:

A - a matrix

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

Returns:

true if the matrix is lower bidiagonal

tridiagonal

public static boolean tridiagonal(Matrix A,
                                  double epsilon)

Check if a matrix is tridiagonal, up to a precision.

Parameters:

A - a matrix

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

Returns:

true if the matrix is tridiagonal

rowEchelonForm

public static boolean rowEchelonForm(Matrix A,
                                     double epsilon)

Check if a matrix is in the row echelon form, up to a precision.

Parameters:

A - a matrix

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

Returns:

true if the matrix is in row echelon form

See Also:

Wikipedia: Row echelon form

reducedRowEchelonForm

public static boolean reducedRowEchelonForm(Matrix A,
                                            double epsilon)

Check if a matrix is in the reduced row echelon form, up to a precision.

Parameters:

A - a matrix

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

Returns:

true if the matrix is in reduced row echelon form

See Also:

Wikipedia: Row echelon form

scalar

@Deprecated
public static boolean scalar(Matrix A,
                                         double epsilon)

Deprecated. Not supported yet.

Check if a square matrix is a scalar matrix, up to a precision.

Parameters:

A - a matrix

Returns:

true if A is diagonal and, a_ij=c, for all i == j, c is a constant.

symmetricPositiveDefinite

public static boolean symmetricPositiveDefinite(Matrix A)

Check if a square matrix is symmetric and positive definite.

Parameters:

A - a matrix

Returns:

true if A is symmetric, and z'Mz > 0, for all non-zero real vectors z.

See Also:

Wikipedia: Positive-definite matrix

positiveDefinite

public static boolean positiveDefinite(Matrix A)

Check if a square matrix is positive definite; the matrix needs not be symmetric. A real matrix A is positive definite if the symmetric part A_symmetric = 1/2 * (A + A') is symmetric positive definite.

Parameters:

A - a matrix

Returns:

true if A satisfies z'Mz > 0, for all non-zero real vectors z.

See Also:

Wikipedia: Positive-definite matrix

positiveSemiDefinite

public static boolean positiveSemiDefinite(Matrix A,
                                           double epsilon)

Check if a square matrix is positive definite, up to a precision.

Parameters:

A - a matrix

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

Returns:

true if A satisfies z'Mz > 0, for all non-zero real vectors z.

See Also:

Wikipedia: Negative-definite, semidefinite and indefinite matrices

zero

public static boolean zero(Vector v,
                           double epsilon)

Check if a vector is a zero vector, i.e., all its entries are 0, up to a precision.

Parameters:

v - a vector

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

Returns:

true if v is a zero vector