agi.foundation.coordinates

(agi.foundation.core-2024r3.jar)

Class Matrix3By3Symmetric

java.lang.Object

agi.foundation.coordinates.Matrix3By3Symmetric

All Implemented Interfaces:

IEquatable<Matrix3By3Symmetric>, ImmutableValueType, ValueType, IEquatableEpsilon<Matrix3By3Symmetric>

public final class Matrix3By3Symmetric
extends Object
implements IEquatable<Matrix3By3Symmetric>, IEquatableEpsilon<Matrix3By3Symmetric>, ImmutableValueType

A 3-by-3 symmetric matrix. This type is often used to represent position covariance.

Constructor Summary

Constructors

Constructor and Description
Matrix3By3Symmetric() Initializes a new instance.
Matrix3By3Symmetric(Matrix3By3 matrix) Initializes this instance as a symmetrical matrix constructed from the given symmetrical or nearly symmetrical Matrix3By3.

Method Summary

Modifier and Type	Method and Description
Matrix3By3	add(Matrix3By3 matrix) Adds a matrix to this matrix.
Matrix3By3Symmetric	add(Matrix3By3Symmetric matrix) Adds a matrix to this matrix.
static Matrix3By3	add(Matrix3By3Symmetric left, Matrix3By3 right) Adds a matrix to this matrix.
static Matrix3By3Symmetric	add(Matrix3By3Symmetric left, Matrix3By3Symmetric right) Adds a matrix to this matrix.
double	determinant() Calculates the determinant of the matrix.
static Matrix3By3Symmetric	diagonalMatrix(Cartesian vector) Forms a diagonal matrix from the input vector.
static Matrix3By3Symmetric	diagonalMatrix(double m11, double m22, double m33) Forms a diagonal matrix from the input elements.
static Matrix3By3Symmetric	diagonalMatrix(UnitCartesian vector) Forms a diagonal matrix from the input unit vector.
EigenDecomposition	eigenDecomposition() Determines the eigenvectors and eigenvalues of the matrix.
boolean	equals(Matrix3By3 other) Indicates whether another instance of this type is exactly equal to this instance.
static boolean	equals(Matrix3By3Symmetric left, Matrix3By3Symmetric right) Returns true if the two instances are exactly equal.
boolean	equals(Object obj) Indicates whether another object is exactly equal to this instance.
boolean	equalsEpsilon(Matrix3By3Symmetric other, double epsilon) Returns true if all of the elements of this matrix are within epsilon of the same elements of the specified matrix.
boolean	equalsType(Matrix3By3Symmetric other) Indicates whether another instance of this type is exactly equal to this instance.
double	frobeniusNorm() Computes the Frobenius norm of the matrix.
double	frobeniusNormSquared() Computes the square of the Frobenius norm of the matrix.
static Matrix3By3Symmetric	fromLowerTriangular(double m11, double m21, double m22, double m31, double m32, double m33) Forms a symmetric matrix from the lower triangular elements.
static Matrix3By3Symmetric	fromLowerTriangular(Matrix3By3 matrix) Forms a symmetric matrix from the lower triangular elements of the provided matrix.
static Matrix3By3Symmetric	fromUpperTriangular(double m11, double m12, double m13, double m22, double m23, double m33) Forms a symmetric matrix from the upper triangular elements.
static Matrix3By3Symmetric	fromUpperTriangular(Matrix3By3 matrix) Forms a symmetric matrix from the upper triangular elements of the provided matrix.
double	get(int row, int column) Accesses the matrix elements using zero-based indexing.
static Matrix3By3Symmetric	getIdentity() Gets a Matrix3By3Symmetric representing an identity transformation.
boolean	getIsUndefined() Gets a value indicating whether any of the matrix values are Double.NaN.
double	getM11() Gets the element in the first row, first column.
double	getM12() Gets the element in the first row, second column.
double	getM13() Gets the element in the first row, third column.
double	getM21() Gets the element in the second row, first column.
double	getM22() Gets the element in the second row, second column.
double	getM23() Gets the element in the second row, third column.
double	getM31() Gets the element in the third row, first column.
double	getM32() Gets the element in the third row, second column.
double	getM33() Gets the element in the third row, third column.
static Matrix3By3Symmetric	getUndefined() Gets a Matrix3By3Symmetric with elements of Double.NaN.
static Matrix3By3Symmetric	getZero() Gets a Matrix3By3Symmetric representing the zero matrix.
int	hashCode() Returns a hash code for this instance, which is suitable for use in hashing algorithms and data structures like a hash table.
Matrix3By3Symmetric	invert() Inverts the matrix.
Cartesian	multiply(Cartesian vector) Forms a new Cartesian vector as the product of this 3-by-3 matrix and the provided Cartesian vector.
Matrix3By3Symmetric	multiply(double scalar) Multiplies this matrix by a scalar.
static Matrix3By3Symmetric	multiply(double scalar, Matrix3By3Symmetric matrix) Multiplies a scalar by a matrix.
Matrix3By3	multiply(Matrix3By3 matrix) Multiplies this matrix by a matrix.
Matrix3By3Symmetric	multiply(Matrix3By3Symmetric matrix) Multiplies this matrix by a matrix.
static Cartesian	multiply(Matrix3By3Symmetric matrix, Cartesian vector) Multiplies the 3-by-3 matrix by the Cartesian vector.
static Matrix3By3Symmetric	multiply(Matrix3By3Symmetric matrix, double scalar) Multiplies a matrix by a scalar.
static Matrix3By3	multiply(Matrix3By3Symmetric left, Matrix3By3 right) Multiplies the left matrix by the right matrix.
static Matrix3By3Symmetric	multiply(Matrix3By3Symmetric left, Matrix3By3Symmetric right) Multiplies the left matrix by the right matrix.
static boolean	notEquals(Matrix3By3Symmetric left, Matrix3By3Symmetric right) Returns true if the two instances are not exactly equal.
Matrix3By3	subtract(Matrix3By3 matrix) Subtracts a matrix from this matrix.
Matrix3By3Symmetric	subtract(Matrix3By3Symmetric matrix) Subtracts a matrix from this matrix.
static Matrix3By3	subtract(Matrix3By3Symmetric left, Matrix3By3 right) Subtracts the second matrix from the first.
static Matrix3By3Symmetric	subtract(Matrix3By3Symmetric left, Matrix3By3Symmetric right) Subtracts the second matrix from the first.
Matrix3By3Symmetric	transpose() Transposes the matrix.

Methods inherited from class java.lang.Object

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

Constructor Detail

Matrix3By3Symmetric

public Matrix3By3Symmetric()

Initializes a new instance.

Matrix3By3Symmetric

public Matrix3By3Symmetric(@Nonnull
                           Matrix3By3 matrix)

Initializes this instance as a symmetrical matrix constructed from the given symmetrical or nearly symmetrical Matrix3By3. Mxy and Myx of this matrix will be equal to the average Mxy and Myx of the given matrix.

Parameters:

matrix - The symmetrical or nearly symmetrical Matrix3By3.

Method Detail

getIdentity

@Nonnull
public static Matrix3By3Symmetric getIdentity()

Gets a Matrix3By3Symmetric representing an identity transformation.

Returns:

The 3-by-3 identity matrix.

getUndefined

@Nonnull
public static Matrix3By3Symmetric getUndefined()

Gets a Matrix3By3Symmetric with elements of Double.NaN.

Use IsUndefined (get) to test whether a Matrix3By3Symmetric instance is undefined since it will return true if any of the element values are Double.NaN.

getZero

@Nonnull
public static Matrix3By3Symmetric getZero()

Gets a Matrix3By3Symmetric representing the zero matrix.

Returns:

The 3-by-3 zero matrix.

diagonalMatrix

@Nonnull
public static Matrix3By3Symmetric diagonalMatrix(double m11,
                                                           double m22,
                                                           double m33)

Forms a diagonal matrix from the input elements.

Parameters:

m11 - 1,1

m22 - 2,2

m33 - 3,3

Returns:

The diagonal matrix.

diagonalMatrix

@Nonnull
public static Matrix3By3Symmetric diagonalMatrix(@Nonnull
                                                           Cartesian vector)

Forms a diagonal matrix from the input vector.

Parameters:

vector - The vector.

Returns:

The diagonal matrix

diagonalMatrix

@Nonnull
public static Matrix3By3Symmetric diagonalMatrix(@Nonnull
                                                           UnitCartesian vector)

Forms a diagonal matrix from the input unit vector.

Parameters:

vector - The vector.

Returns:

The diagonal matrix.

fromLowerTriangular

@Nonnull
public static Matrix3By3Symmetric fromLowerTriangular(double m11,
                                                                double m21,
                                                                double m22,
                                                                double m31,
                                                                double m32,
                                                                double m33)

Forms a symmetric matrix from the lower triangular elements.

Parameters:

m11 - 1,1

m21 - 2,1

m22 - 2,2

m31 - 3,1

m32 - 3,2

m33 - 3,3

Returns:

The symmetric matrix.

fromLowerTriangular

@Nonnull
public static Matrix3By3Symmetric fromLowerTriangular(@Nonnull
                                                                Matrix3By3 matrix)

Forms a symmetric matrix from the lower triangular elements of the provided matrix.

Parameters:

matrix - The original matrix.

Returns:

The symmetric matrix.

fromUpperTriangular

@Nonnull
public static Matrix3By3Symmetric fromUpperTriangular(double m11,
                                                                double m12,
                                                                double m13,
                                                                double m22,
                                                                double m23,
                                                                double m33)

Forms a symmetric matrix from the upper triangular elements.

Parameters:

m11 - 1,1

m12 - 1,2

m13 - 1,3

m22 - 2,2

m23 - 2,3

m33 - 3,3

Returns:

The symmetric matrix.

fromUpperTriangular

@Nonnull
public static Matrix3By3Symmetric fromUpperTriangular(@Nonnull
                                                                Matrix3By3 matrix)

Forms a symmetric matrix from the upper triangular elements of the provided matrix.

Parameters:

matrix - The original matrix.

Returns:

The symmetric matrix.

get

public final double get(int row,
                        int column)

Accesses the matrix elements using zero-based indexing.

Parameters:

row - The row index.

column - The column index.

Returns:

The value corresponding to the indicated element of the matrix.

Throws:

ArgumentOutOfRangeException - Thrown when either row or column is less than 0 or greater than 2.

getM11

public final double getM11()

Gets the element in the first row, first column.

getM12

public final double getM12()

Gets the element in the first row, second column.

getM13

public final double getM13()

Gets the element in the first row, third column.

getM21

public final double getM21()

Gets the element in the second row, first column.

getM22

public final double getM22()

Gets the element in the second row, second column.

getM23

public final double getM23()

Gets the element in the second row, third column.

getM31

public final double getM31()

Gets the element in the third row, first column.

getM32

public final double getM32()

Gets the element in the third row, second column.

getM33

public final double getM33()

Gets the element in the third row, third column.

transpose

@Nonnull
public final Matrix3By3Symmetric transpose()

Transposes the matrix.

Returns:

The transposed matrix.

determinant

public final double determinant()

Calculates the determinant of the matrix.

Returns:

The determinant of the matrix.

invert

@Nonnull
public final Matrix3By3Symmetric invert()

Inverts the matrix.

Returns:

The inverted matrix.

Throws:

ArithmeticException - Thrown when the absolute value of the Matrix3By3Symmetric.determinant() is less than Constants.Epsilon15.

getIsUndefined

public final boolean getIsUndefined()

Gets a value indicating whether any of the matrix values are Double.NaN.

frobeniusNormSquared

public final double frobeniusNormSquared()

Computes the square of the Frobenius norm of the matrix.

Returns:

The square of the Frobenius norm.

frobeniusNorm

public final double frobeniusNorm()

Computes the Frobenius norm of the matrix.

Returns:

The Frobenius norm.

eigenDecomposition

public final EigenDecomposition eigenDecomposition()

Determines the eigenvectors and eigenvalues of the matrix. The eigenvalues appear in ascending order (smallest to largest) down the diagonal of the Values (get) matrix.

Returns:

The eigenvectors and eigenvalues.

add

@Nonnull
public final Matrix3By3Symmetric add(@Nonnull
                                               Matrix3By3Symmetric matrix)

Adds a matrix to this matrix.

Parameters:

matrix - The matrix.

Returns:

The sum of the matrices.

add

@Nonnull
public final Matrix3By3 add(@Nonnull
                                      Matrix3By3 matrix)

Adds a matrix to this matrix.

Parameters:

matrix - The matrix.

Returns:

The sum of the matrices.

subtract

@Nonnull
public final Matrix3By3Symmetric subtract(@Nonnull
                                                    Matrix3By3Symmetric matrix)

Subtracts a matrix from this matrix.

Parameters:

matrix - The matrix to subtract.

Returns:

The result of the subtraction.

subtract

@Nonnull
public final Matrix3By3 subtract(@Nonnull
                                           Matrix3By3 matrix)

Subtracts a matrix from this matrix.

Parameters:

matrix - The matrix to subtract.

Returns:

The result of the subtraction.

multiply

@Nonnull
public final Matrix3By3Symmetric multiply(double scalar)

Multiplies this matrix by a scalar.

Parameters:

scalar - The scalar to multiply by.

Returns:

The result of the multiplication.

multiply

@Nonnull
public final Matrix3By3Symmetric multiply(@Nonnull
                                                    Matrix3By3Symmetric matrix)

Multiplies this matrix by a matrix.

Parameters:

matrix - The matrix to multiply by.

Returns:

The result of the multiplication.

multiply

@Nonnull
public final Matrix3By3 multiply(@Nonnull
                                           Matrix3By3 matrix)

Multiplies this matrix by a matrix.

Parameters:

matrix - The matrix to multiply by.

Returns:

The result of the multiplication.

multiply

@Nonnull
public final Cartesian multiply(@Nonnull
                                          Cartesian vector)

Forms a new Cartesian vector as the product of this 3-by-3 matrix and the provided Cartesian vector.

Parameters:

vector - The vector.

Returns:

The resulting Cartesian vector.

multiply

@Nonnull
public static Matrix3By3Symmetric multiply(@Nonnull
                                                     Matrix3By3Symmetric matrix,
                                                     double scalar)

Multiplies a matrix by a scalar.

Parameters:

matrix - The matrix.

scalar - The scalar.

Returns:

The result of the multiplication.

multiply

@Nonnull
public static Matrix3By3Symmetric multiply(double scalar,
                                                     @Nonnull
                                                     Matrix3By3Symmetric matrix)

Multiplies a scalar by a matrix.

Parameters:

scalar - The scalar.

matrix - The matrix.

Returns:

The result of the multiplication.

multiply

@Nonnull
public static Matrix3By3Symmetric multiply(@Nonnull
                                                     Matrix3By3Symmetric left,
                                                     @Nonnull
                                                     Matrix3By3Symmetric right)

Multiplies the left matrix by the right matrix.

Parameters:

left - The matrix on the left.

right - The matrix on the right.

Returns:

The result of the multiplication.

multiply

@Nonnull
public static Matrix3By3 multiply(@Nonnull
                                            Matrix3By3Symmetric left,
                                            @Nonnull
                                            Matrix3By3 right)

Multiplies the left matrix by the right matrix.

Parameters:

left - The matrix on the left.

right - The matrix on the right.

Returns:

The result of the multiplication.

multiply

@Nonnull
public static Cartesian multiply(@Nonnull
                                           Matrix3By3Symmetric matrix,
                                           @Nonnull
                                           Cartesian vector)

Multiplies the 3-by-3 matrix by the Cartesian vector.

Parameters:

matrix - The matrix.

vector - The vector.

Returns:

The result of the multiplication.

add

@Nonnull
public static Matrix3By3Symmetric add(@Nonnull
                                                Matrix3By3Symmetric left,
                                                @Nonnull
                                                Matrix3By3Symmetric right)

Adds a matrix to this matrix.

Parameters:

left - The left matrix.

right - The right matrix.

Returns:

The sum of the matrices.

add

@Nonnull
public static Matrix3By3 add(@Nonnull
                                       Matrix3By3Symmetric left,
                                       @Nonnull
                                       Matrix3By3 right)

Adds a matrix to this matrix.

Parameters:

left - The left matrix.

right - The right matrix.

Returns:

The sum of the matrices.

subtract

@Nonnull
public static Matrix3By3Symmetric subtract(@Nonnull
                                                     Matrix3By3Symmetric left,
                                                     @Nonnull
                                                     Matrix3By3Symmetric right)

Subtracts the second matrix from the first.

Parameters:

left - The left matrix.

right - The right matrix.

Returns:

The result of subtracting the second matrix from the first.

subtract

@Nonnull
public static Matrix3By3 subtract(@Nonnull
                                            Matrix3By3Symmetric left,
                                            @Nonnull
                                            Matrix3By3 right)

Subtracts the second matrix from the first.

Parameters:

left - The left matrix.

right - The right matrix.

Returns:

The result of subtracting the second matrix from the first.

equals

public boolean equals(Object obj)

Indicates whether another object is exactly equal to this instance.

Overrides:

equals in class Object

Parameters:

obj - The object to compare to this instance.

Returns:

true if obj is an instance of this type and represents the same value as this instance; otherwise false.

See Also:

Object.hashCode(), HashMap

equalsType

public final boolean equalsType(@Nonnull
                                Matrix3By3Symmetric other)

Indicates whether another instance of this type is exactly equal to this instance.

Specified by:

equalsType in interface IEquatable<Matrix3By3Symmetric>

Parameters:

other - The instance to compare to this instance.

Returns:

true if other represents the same value as this instance; otherwise false.

equals

public final boolean equals(@Nonnull
                            Matrix3By3 other)

Indicates whether another instance of this type is exactly equal to this instance.

Parameters:

other - The instance to compare to this instance.

Returns:

true if other represents the same value as this instance; otherwise false.

equalsEpsilon

public final boolean equalsEpsilon(@Nonnull
                                   Matrix3By3Symmetric other,
                                   double epsilon)

Returns true if all of the elements of this matrix are within epsilon of the same elements of the specified matrix. That is, in order for the matrices to be considered equal (and for this function to return true), the absolute value of the difference between each of their elements must be less than or equal to epsilon.

Specified by:

equalsEpsilon in interface IEquatableEpsilon<Matrix3By3Symmetric>

Parameters:

other - The Matrix3By3Symmetric to compare to this matrix.

epsilon - The largest difference between the elements of the matrices for which they will be considered equal.

Returns:

true if the matrices are equal as defined by the epsilon value.

hashCode

public int hashCode()

Returns a hash code for this instance, which is suitable for use in hashing algorithms and data structures like a hash table.

Overrides:

hashCode in class Object

Returns:

A hash code for the current object.

See Also:

Object.equals(java.lang.Object), System.identityHashCode(java.lang.Object)

equals

public static boolean equals(@Nonnull
                             Matrix3By3Symmetric left,
                             @Nonnull
                             Matrix3By3Symmetric right)

Returns true if the two instances are exactly equal.

Parameters:

left - The instance to compare to right.

right - The instance to compare to left.

Returns:

true if left represents the same value as right; otherwise false.

notEquals

public static boolean notEquals(@Nonnull
                                Matrix3By3Symmetric left,
                                @Nonnull
                                Matrix3By3Symmetric right)

Returns true if the two instances are not exactly equal.

Parameters:

left - The instance to compare to right.

right - The instance to compare to left.

Returns:

true if left does not represent the same value as right; otherwise false.