com.numericalmethod.suanshu.matrix.doubles
Class AreMatrices

java.lang.Object
  com.numericalmethod.suanshu.matrix.doubles.AreMatrices

public class AreMatrices
extends java.lang.Object

This class collects the boolean operators that take two or more matrices or vectors and compare their properties.

Method Summary

static boolean	equal(Matrix A1, Matrix A2, double epsilon) Check the equality of two matrices up to a precision.
static boolean	equal(Vector v1, Vector v2, double epsilon) Check if two vectors are equal up to a precision.
static boolean	orthogonal(Vector[] v, double epsilon) Check if a set of vectors are orthogonal.
static boolean	orthogonal(Vector v1, Vector v2, double epsilon) Check if two vectors are orthogonal.
static boolean	orthogonormal(Vector[] v, double epsilon) Check if a set of vectors are orthogonormal.
static boolean	orthogonormal(Vector v1, Vector v2, double epsilon) Check if two vectors are orthogonormal.

Methods inherited from class java.lang.Object

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

Method Detail

equal

public static boolean equal(Matrix A1,
                            Matrix A2,
                            double epsilon)

Check the equality of two matrices up to a precision.

Two matrices are equal iff

1. the dimensions are the same;
2. all entries are equal

Parameters:

A1 - a matrix

A2 - a matrix

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

Returns:

true iff all entries are equal, entry by entry

equal

public static boolean equal(Vector v1,
                            Vector v2,
                            double epsilon)

Check if two vectors are equal up to a precision.

Parameters:

v1 - a vector

v2 - a vector

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

Returns:

true iff v1 - v2 is a zero vector, up to a precision

orthogonal

public static boolean orthogonal(Vector v1,
                                 Vector v2,
                                 double epsilon)

Check if two vectors are orthogonal.

Parameters:

v1 - a vector

v2 - a vector

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

Returns:

true iff

v1 ∙ v2 == 0

orthogonal

public static boolean orthogonal(Vector[] v,
                                 double epsilon)

Check if a set of vectors are orthogonal.

Parameters:

v - a set of vectors

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

Returns:

true iff

v1 ∙ v2 == 0

for any v1, v2 in v

orthogonormal

public static boolean orthogonormal(Vector v1,
                                    Vector v2,
                                    double epsilon)

Check if two vectors are orthogonormal.

Parameters:

v1 - a vector

v2 - a vector

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

Returns:

true iff {v1, v2} are orthogonal and

||v1|| = ||v2|| = 1

orthogonormal

public static boolean orthogonormal(Vector[] v,
                                    double epsilon)

Check if a set of vectors are orthogonormal.

Parameters:

v - a set of vectors

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

Returns:

true iff {v1, v2} are orthogonormal, for any v1, v2 in v