java.lang.Object
- org.arakhne.afc.math.matrix.Matrix3d

All Implemented Interfaces:

Serializable, Cloneable

Direct Known Subclasses:

Transform2D
```
public class Matrix3d
extends Object
implements Serializable, Cloneable
```
Is represented internally as a 3x3 floating point matrix. The mathematical representation is row major, as in traditional matrix mathematics.

Version:

17.0 2020-01-04 14:41:43

Author:

Stéphane GALLAND

See Also:

Serialized Form

Maven Group Id:

org.arakhne.afc.core

Maven Artifact Id:

mathgeom

Field Summary

Fields
Modifier and Type	Field	Description
`protected Boolean`	`isIdentity`	Indicates if the matrix is identity.
`protected double`	`m00`	The first matrix element in the first row.
`protected double`	`m01`	The second matrix element in the first row.
`protected double`	`m02`	The third matrix element in the first row.
`protected double`	`m10`	The first matrix element in the second row.
`protected double`	`m11`	The second matrix element in the second row.
`protected double`	`m12`	The third matrix element in the second row.
`protected double`	`m20`	The first matrix element in the third row.
`protected double`	`m21`	The second matrix element in the third row.
`protected double`	`m22`	The third matrix element in the third row.

Constructor Summary

Constructors
Constructor	Description
`Matrix3d()`	Constructs and initializes a Matrix3f to all zeros.
`Matrix3d(double[] values)`	Constructs and initializes a Matrix3f from the specified nine- element array.
`Matrix3d(double m00, double m01, double m02, double m10, double m11, double m12, double m20, double m21, double m22)`	Constructs and initializes a Matrix3f from the specified nine values.
`Matrix3d(Matrix3d matrix)`	Constructs a new matrix with the same values as the Matrix3f parameter.

Method Summary

All Methods Static Methods Instance Methods Concrete Methods
Modifier and Type	Method	Description
`Matrix3d`	`$bang()`	Replies the transposition of this matrix: `!this`.
`Matrix3d`	`$div(double scalar)`	Replies the division of this matrix by the given scalar: `this / scalar`.
`Matrix3d`	`$minus()`	Replies the negation of this matrix: `-this`.
`Matrix3d`	`$minus(double scalar)`	Replies the substraction of the given scalar to this matrix: `this - scalar`.
`Matrix3d`	`$minus(Matrix3d matrix)`	Replies the substraction of the given matrix to this matrix: `this - matrix`.
`Matrix3d`	`$plus(double scalar)`	Replies the addition of the given scalar to this matrix: `this + scalar`.
`Matrix3d`	`$plus(Matrix3d matrix)`	Replies the addition of the given matrix to this matrix: `this + matrix`.
`Matrix3d`	`$times(double scalar)`	Replies the multiplication of the given scalar and this matrix: `this * scalar`.
`Matrix3d`	`$times(Matrix3d matrix)`	Replies the multiplication of the given matrix and this matrix: `this * matrix`.
`void`	`add(double scalar)`	Adds a scalar to each component of this matrix.
`void`	`add(double scalar, Matrix3d matrix)`	Adds a scalar to each component of the matrix m1 and places the result into this.
`void`	`add(Matrix3d matrix)`	Sets the value of this matrix to the sum of itself and matrix m1.
`void`	`add(Matrix3d matrix1, Matrix3d matrix2)`	Sets the value of this matrix to the matrix sum of matrices m1 and m2.
`Matrix3d`	`clone()`	Creates a new object of the same class as this object.
`protected static void`	`computeSVD(double[] matrix, double[] outScale, double[] outRot)`	Compute the SVD of a matrix m.
`boolean`	`cov(Vector3D<?,?> result, Iterable<? extends Tuple3D<?>> tuples)`	Set this matrix with the covariance matrix's elements for the given set of tuples.
`boolean`	`cov(Vector3D<?,?> result, Point3D<?,?>... tuples)`	Set this matrix with the covariance matrix's elements for the given set of tuples.
`boolean`	`cov(Vector3D<?,?> result, Vector3D<?,?>... tuples)`	Set this matrix with the covariance matrix's elements for the given set of tuples.
`double`	`determinant()`	Computes the determinant of this matrix.
`double[]`	`eigenVectorsOfSymmetricMatrix(Matrix3d eigenVectors)`	Compute the eigenvectors of the given symmetric matrix according to the Jacobi Cyclic Method.
`boolean`	`epsilonEquals(Matrix3d matrix, double epsilon)`	Returns true if the L-infinite distance between this matrix and matrix m1 is less than or equal to the epsilon parameter, otherwise returns false.
`boolean`	`equals(Object object)`	Returns true if the Object t1 is of type Matrix3f and all of the data members of t1 are equal to the corresponding data members in this Matrix3f.
`boolean`	`equals(Matrix3d matrix)`	Returns true if all of the data members of Matrix3f m1 are equal to the corresponding data members in this Matrix3f.
`void`	`getColumn(int column, double[] vector)`	Copies the matrix values in the specified column into the array parameter.
`void`	`getColumn(int column, Vector3D<?,?> vector)`	Copies the matrix values in the specified column into the vector parameter.
`double`	`getElement(int row, int column)`	Retrieves the value at the specified row and column of the specified matrix.
`double`	`getM00()`	Get the first matrix element in the first row.
`double`	`getM01()`	Get the second matrix element in the first row.
`double`	`getM02()`	Get the third matrix element in the first row.
`double`	`getM10()`	Get first matrix element in the second row.
`double`	`getM11()`	Get second matrix element in the second row.
`double`	`getM12()`	Get the third matrix element in the second row.
`double`	`getM20()`	Get the first matrix element in the third row.
`double`	`getM21()`	Get the second matrix element in the third row.
`double`	`getM22()`	Get the third matrix element in the third row .
`void`	`getRow(int row, double[] vector)`	Copies the matrix values in the specified row into the array parameter.
`void`	`getRow(int row, Vector3D<?,?> vector)`	Copies the matrix values in the specified row into the vector parameter.
`int`	`hashCode()`	Returns a hash code value based on the data values in this object.
`void`	`invert()`	Inverts this matrix in place.
`void`	`invert(Matrix3d matrix)`	Sets the value of this matrix to the matrix inverse of the passed matrix m1.
`boolean`	`isIdentity()`	Replies if the matrix is identity.
`boolean`	`isSymmetric()`	Replies if the matrix is symmetric.
`void`	`mul(double scalar)`	Multiplies each element of this matrix by a scalar.
`void`	`mul(double scalar, Matrix3d matrix)`	Multiplies each element of matrix m1 by a scalar and places the result into this.
`void`	`mul(Vector3D<?,?> vector, Vector3D<?,?> result)`	Multiply this matrix by the given vector v and set the result..
`void`	`mul(Matrix3d matrix)`	Sets the value of this matrix to the result of multiplying itself with matrix m1.
`void`	`mul(Matrix3d matrix1, Matrix3d matrix2)`	Sets the value of this matrix to the result of multiplying the two argument matrices together.
`void`	`mulNormalize(Matrix3d matrix)`	Multiplies this matrix by matrix m1, does an SVD normalization of the result, and places the result back into this matrix this = SVDnorm(this*m1).
`void`	`mulNormalize(Matrix3d matrix1, Matrix3d matrix2)`	Multiplies matrix m1 by matrix m2, does an SVD normalization of the result, and places the result into this matrix this = SVDnorm(m1*m2).
`void`	`mulTransposeBoth(Matrix3d matrix1, Matrix3d matrix2)`	Multiplies the transpose of matrix m1 times the transpose of matrix m2, and places the result into this.
`void`	`mulTransposeLeft(Vector3D<?,?> vector, Vector3D<?,?> result)`	Multiply the transposing of this matrix by the given vector.
`void`	`mulTransposeLeft(Matrix3d matrix1, Matrix3d matrix2)`	Multiplies the transpose of matrix m1 times matrix m2, and places the result into this.
`void`	`mulTransposeRight(Matrix3d matrix1, Matrix3d matrix2)`	Multiplies matrix m1 times the transpose of matrix m2, and places the result into this.
`void`	`negate()`	Negates the value of this matrix: this = -this.
`void`	`negate(Matrix3d matrix)`	Sets the value of this matrix equal to the negation of of the Matrix3f parameter.
`void`	`normalize()`	Performs singular value decomposition normalization of this matrix.
`void`	`normalize(Matrix3d matrix)`	Perform singular value decomposition normalization of matrix m1 and place the normalized values into this.
`void`	`normalizeCP()`	Perform cross product normalization of this matrix.
`void`	`normalizeCP(Matrix3d matrix)`	Perform cross product normalization of matrix m1 and place the normalized values into this.
`void`	`operator_add(double scalar)`	Add the given scalar to this matrix: `this += scalar`.
`void`	`operator_add(Matrix3d matrix)`	Add the given matrix to this matrix: `this += matrix`.
`Matrix3d`	`operator_divide(double scalar)`	Replies the division of this matrix by the given scalar: `this / scalar`.
`Matrix3d`	`operator_minus()`	Replies the negation of this matrix: `-this`.
`Matrix3d`	`operator_minus(double scalar)`	Replies the substraction of the given scalar to this matrix: `this - scalar`.
`Matrix3d`	`operator_minus(Matrix3d matrix)`	Replies the substraction of the given matrix to this matrix: `this - matrix`.
`void`	`operator_moinsMoins()`	Increment this matrix: `this--`.
`Matrix3d`	`operator_multiply(double scalar)`	Replies the multiplication of the given scalar and this matrix: `this * scalar`.
`Matrix3d`	`operator_multiply(Matrix3d matrix)`	Replies the multiplication of the given matrix and this matrix: `this * matrix`.
`Matrix3d`	`operator_not()`	Replies the transposition of this matrix: `!this`.
`Matrix3d`	`operator_plus(double scalar)`	Replies the addition of the given scalar to this matrix: `this + scalar`.
`Matrix3d`	`operator_plus(Matrix3d matrix)`	Replies the addition of the given matrix to this matrix: `this + matrix`.
`void`	`operator_plusPlus()`	Increment this matrix: `this++`.
`void`	`operator_remove(double scalar)`	Substract the given scalar to this matrix: `this -= scalar`.
`void`	`operator_remove(Matrix3d matrix)`	Substract the given matrix to this matrix: `this -= matrix`.
`void`	`set(double[] matrix)`	Sets the values in this Matrix3f equal to the row-major array parameter (ie, the first three elements of the array will be copied into the first row of this matrix, etc.).
`void`	`set(double m00, double m01, double m02, double m10, double m11, double m12, double m20, double m21, double m22)`	Set the components of the matrix.
`void`	`set(Matrix3d matrix)`	Sets the value of this matrix to the double value of the Matrix3f argument.
`void`	`setColumn(int column, double[] vector)`	Sets the specified column of this Matrix3f to the three values provided.
`void`	`setColumn(int column, double x, double y, double z)`	Sets the specified column of this Matrix3f to the three values provided.
`void`	`setColumn(int column, Vector3D<?,?> vector)`	Sets the specified column of this Matrix3f to the vector provided.
`void`	`setDiagonal(double m00, double m11, double m22)`	Sets this matrix as diagonal.
`void`	`setElement(int row, int column, double value)`	Sets the specified element of this matrix3f to the value provided.
`void`	`setIdentity()`	Sets this Matrix3f to identity.
`void`	`setM00(double m00)`	Set the first matrix element in the first row.
`void`	`setM01(double m01)`	Set the second matrix element in the first row.
`void`	`setM02(double m02)`	Set the third matrix element in the first row.
`void`	`setM10(double m10)`	Set first matrix element in the second row.
`void`	`setM11(double m11)`	Set the second matrix element in the second row.
`void`	`setM12(double m11)`	Set the third matrix element in the second row.
`void`	`setM20(double m20)`	Set the first matrix element in the third row.
`void`	`setM21(double m21)`	Set the second matrix element in the third row.
`void`	`setM22(double m22)`	Set the third matrix element in the third row.
`void`	`setRow(int row, double[] vector)`	Sets the specified row of this Matrix3f to the three values provided.
`void`	`setRow(int row, double x, double y, double z)`	Sets the specified row of this Matrix3f to the 3 values provided.
`void`	`setRow(int row, Vector3D<?,?> vector)`	Sets the specified row of this Matrix3f to the Vector provided.
`void`	`setZero()`	Sets this matrix to all zeros.
`void`	`sub(Matrix3d matrix)`	Sets the value of this matrix to the matrix difference of itself and matrix m1 (this = this - m1).
`void`	`sub(Matrix3d matrix1, Matrix3d matrix2)`	Sets the value of this matrix to the matrix difference of matrices m1 and m2.
`String`	`toString()`	Returns a string that contains the values of this Matrix3f.
`void`	`transpose()`	Sets the value of this matrix to its transpose.
`void`	`transpose(Matrix3d matrix)`	Sets the value of this matrix to the transpose of the argument matrix.

Methods inherited from class java.lang.Object
finalize, getClass, notify, notifyAll, wait, wait, wait

- Field Detail
  - m00
```
protected double m00
```
    The first matrix element in the first row.
  - m01
```
protected double m01
```
    The second matrix element in the first row.
  - m02
```
protected double m02
```
    The third matrix element in the first row.
  - m10
```
protected double m10
```
    The first matrix element in the second row.
  - m11
```
protected double m11
```
    The second matrix element in the second row.
  - m12
```
protected double m12
```
    The third matrix element in the second row.
  - m20
```
protected double m20
```
    The first matrix element in the third row.
  - m21
```
protected double m21
```
    The second matrix element in the third row.
  - m22
```
protected double m22
```
    The third matrix element in the third row.
  - isIdentity
```
protected Boolean isIdentity
```
    Indicates if the matrix is identity. If null the identity flag must be determined.
- Constructor Detail
  - Matrix3d
```
public Matrix3d(double m00,
                double m01,
                double m02,
                double m10,
                double m11,
                double m12,
                double m20,
                double m21,
                double m22)
```
    Constructs and initializes a Matrix3f from the specified nine values.
    
    Parameters:
    
    m00 - the [0][0] element
    
    m01 - the [0][1] element
    
    m02 - the [0][2] element
    
    m10 - the [1][0] element
    
    m11 - the [1][1] element
    
    m12 - the [1][2] element
    
    m20 - the [2][0] element
    
    m21 - the [2][1] element
    
    m22 - the [2][2] element
  - Matrix3d
```
public Matrix3d(double[] values)
```
    Constructs and initializes a Matrix3f from the specified nine- element array.
    
    Parameters:
    
    values - the array of length 9 containing in order
  - Matrix3d
```
public Matrix3d(Matrix3d matrix)
```
    Constructs a new matrix with the same values as the Matrix3f parameter.
    
    Parameters:
    
    matrix - the source matrix
  - Matrix3d
```
public Matrix3d()
```
    Constructs and initializes a Matrix3f to all zeros.
- Method Detail
  - toString
```
@Pure
public String toString()
```
    Returns a string that contains the values of this Matrix3f.
    
    Overrides:
    
    toString in class Object
    
    Returns:
    
    the String representation
  - setIdentity
```
public void setIdentity()
```
    Sets this Matrix3f to identity.
  - setElement
```
public void setElement(int row,
                       int column,
                       double value)
```
    Sets the specified element of this matrix3f to the value provided.
    
    Parameters:
    
    row - the row number to be modified (zero indexed)
    
    column - the column number to be modified (zero indexed)
    
    value - the new value
  - getElement
```
@Pure
public double getElement(int row,
                         int column)
```
    Retrieves the value at the specified row and column of the specified matrix.
    
    Parameters:
    
    row - the row number to be retrieved (zero indexed)
    
    column - the column number to be retrieved (zero indexed)
    
    Returns:
    
    the value at the indexed element.
  - getRow
```
public void getRow(int row,
                   Vector3D<?,?> vector)
```
    Copies the matrix values in the specified row into the vector parameter.
    
    Parameters:
    
    row - the matrix row
    
    vector - the vector into which the matrix row values will be copied
  - getRow
```
public void getRow(int row,
                   double[] vector)
```
    Copies the matrix values in the specified row into the array parameter.
    
    Parameters:
    
    row - the matrix row
    
    vector - the array into which the matrix row values will be copied
  - getColumn
```
public void getColumn(int column,
                      Vector3D<?,?> vector)
```
    Copies the matrix values in the specified column into the vector parameter.
    
    Parameters:
    
    column - the matrix column
    
    vector - the vector into which the matrix row values will be copied
  - getColumn
```
public void getColumn(int column,
                      double[] vector)
```
    Copies the matrix values in the specified column into the array parameter.
    
    Parameters:
    
    column - the matrix column
    
    vector - the array into which the matrix row values will be copied
  - setRow
```
public void setRow(int row,
                   double x,
                   double y,
                   double z)
```
    Sets the specified row of this Matrix3f to the 3 values provided.
    
    Parameters:
    
    row - the row number to be modified (zero indexed)
    
    x - the first column element
    
    y - the second column element
    
    z - the third column element
  - setRow
```
public void setRow(int row,
                   Vector3D<?,?> vector)
```
    Sets the specified row of this Matrix3f to the Vector provided.
    
    Parameters:
    
    row - the row number to be modified (zero indexed)
    
    vector - the replacement row
  - setRow
```
public void setRow(int row,
                   double[] vector)
```
    Sets the specified row of this Matrix3f to the three values provided.
    
    Parameters:
    
    row - the row number to be modified (zero indexed)
    
    vector - the replacement row
  - setColumn
```
public void setColumn(int column,
                      double x,
                      double y,
                      double z)
```
    Sets the specified column of this Matrix3f to the three values provided.
    
    Parameters:
    
    column - the column number to be modified (zero indexed)
    
    x - the first row element
    
    y - the second row element
    
    z - the third row element
  - setColumn
```
public void setColumn(int column,
                      Vector3D<?,?> vector)
```
    Sets the specified column of this Matrix3f to the vector provided.
    
    Parameters:
    
    column - the column number to be modified (zero indexed)
    
    vector - the replacement column
  - setColumn
```
public void setColumn(int column,
                      double[] vector)
```
    Sets the specified column of this Matrix3f to the three values provided.
    
    Parameters:
    
    column - the column number to be modified (zero indexed)
    
    vector - the replacement column
  - add
```
public void add(double scalar)
```
    Adds a scalar to each component of this matrix.
    
    Parameters:
    
    scalar - the scalar adder
  - add
```
public void add(double scalar,
                Matrix3d matrix)
```
    Adds a scalar to each component of the matrix m1 and places the result into this. Matrix m1 is not modified.
    
    Parameters:
    
    scalar - the scalar adder
    
    matrix - the original matrix values
  - add
```
public void add(Matrix3d matrix1,
                Matrix3d matrix2)
```
    Sets the value of this matrix to the matrix sum of matrices m1 and m2.
    
    Parameters:
    
    matrix1 - the first matrix
    
    matrix2 - the second matrix
  - add
```
public void add(Matrix3d matrix)
```
    Sets the value of this matrix to the sum of itself and matrix m1.
    
    Parameters:
    
    matrix - the other matrix
  - sub
```
public void sub(Matrix3d matrix1,
                Matrix3d matrix2)
```
    Sets the value of this matrix to the matrix difference of matrices m1 and m2.
    
    Parameters:
    
    matrix1 - the first matrix
    
    matrix2 - the second matrix
  - sub
```
public void sub(Matrix3d matrix)
```
    Sets the value of this matrix to the matrix difference of itself and matrix m1 (this = this - m1).
    
    Parameters:
    
    matrix - the other matrix
  - transpose
```
public void transpose()
```
    Sets the value of this matrix to its transpose.
  - transpose
```
public void transpose(Matrix3d matrix)
```
    Sets the value of this matrix to the transpose of the argument matrix.
    
    Parameters:
    
    matrix - the matrix to be transposed
  - set
```
public void set(Matrix3d matrix)
```
    Sets the value of this matrix to the double value of the Matrix3f argument.
    
    Parameters:
    
    matrix - the Matrix3f to be converted to double
  - set
```
public void set(double[] matrix)
```
    Sets the values in this Matrix3f equal to the row-major array parameter (ie, the first three elements of the array will be copied into the first row of this matrix, etc.).
    
    Parameters:
    
    matrix - the double precision array of length 9
  - set
```
public void set(double m00,
                double m01,
                double m02,
                double m10,
                double m11,
                double m12,
                double m20,
                double m21,
                double m22)
```
    Set the components of the matrix.
    
    Parameters:
    
    m00 - the [0][0] element
    
    m01 - the [0][1] element
    
    m02 - the [0][2] element
    
    m10 - the [1][0] element
    
    m11 - the [1][1] element
    
    m12 - the [1][2] element
    
    m20 - the [2][0] element
    
    m21 - the [2][1] element
    
    m22 - the [2][2] element
  - invert
```
public void invert(Matrix3d matrix)
```
    Sets the value of this matrix to the matrix inverse of the passed matrix m1.
    
    Parameters:
    
    matrix - the matrix to be inverted
  - invert
```
public void invert()
```
    Inverts this matrix in place.
  - determinant
```
@Pure
public double determinant()
```
    Computes the determinant of this matrix.
    
    Returns:
    
    the determinant of the matrix
  - mul
```
public void mul(double scalar)
```
    Multiplies each element of this matrix by a scalar.
    
    Parameters:
    
    scalar - The scalar multiplier.
  - mul
```
public void mul(double scalar,
                Matrix3d matrix)
```
    Multiplies each element of matrix m1 by a scalar and places the result into this. Matrix m1 is not modified.
    
    Parameters:
    
    scalar - the scalar multiplier
    
    matrix - the original matrix
  - mul
```
public void mul(Matrix3d matrix)
```
    Sets the value of this matrix to the result of multiplying itself with matrix m1.
    
    Parameters:
    
    matrix - the other matrix
  - mul
```
public void mul(Matrix3d matrix1,
                Matrix3d matrix2)
```
    Sets the value of this matrix to the result of multiplying the two argument matrices together.
    
    Parameters:
    
    matrix1 - the first matrix
    
    matrix2 - the second matrix
  - mul
```
@Pure
public void mul(Vector3D<?,?> vector,
                Vector3D<?,?> result)
```
    Multiply this matrix by the given vector v and set the result..
    
    Parameters:
    
    vector - the vector.
    
    result - the vector resulting of this * v.
  - mulTransposeLeft
```
@Pure
public void mulTransposeLeft(Vector3D<?,?> vector,
                             Vector3D<?,?> result)
```
    Multiply the transposing of this matrix by the given vector.
    
    Parameters:
    
    vector - the vector.
    
    result - the vector resulting of transpose(this) * v.
  - mulTransposeLeft
```
public void mulTransposeLeft(Matrix3d matrix1,
                             Matrix3d matrix2)
```
    Multiplies the transpose of matrix m1 times matrix m2, and places the result into this.
    
    Parameters:
    
    matrix1 - the matrix on the left hand side of the multiplication
    
    matrix2 - the matrix on the right hand side of the multiplication
  - mulNormalize
```
public void mulNormalize(Matrix3d matrix)
```
    Multiplies this matrix by matrix m1, does an SVD normalization of the result, and places the result back into this matrix this = SVDnorm(this*m1).
    
    Parameters:
    
    matrix - the matrix on the right hand side of the multiplication
  - mulNormalize
```
public void mulNormalize(Matrix3d matrix1,
                         Matrix3d matrix2)
```
    Multiplies matrix m1 by matrix m2, does an SVD normalization of the result, and places the result into this matrix this = SVDnorm(m1*m2).
    
    Parameters:
    
    matrix1 - the matrix on the left hand side of the multiplication
    
    matrix2 - the matrix on the right hand side of the multiplication
  - mulTransposeBoth
```
public void mulTransposeBoth(Matrix3d matrix1,
                             Matrix3d matrix2)
```
    Multiplies the transpose of matrix m1 times the transpose of matrix m2, and places the result into this.
    
    Parameters:
    
    matrix1 - the matrix on the left hand side of the multiplication
    
    matrix2 - the matrix on the right hand side of the multiplication
  - mulTransposeRight
```
public void mulTransposeRight(Matrix3d matrix1,
                              Matrix3d matrix2)
```
    Multiplies matrix m1 times the transpose of matrix m2, and places the result into this.
    
    Parameters:
    
    matrix1 - the matrix on the left hand side of the multiplication
    
    matrix2 - the matrix on the right hand side of the multiplication
  - normalize
```
public void normalize(Matrix3d matrix)
```
    Perform singular value decomposition normalization of matrix m1 and place the normalized values into this.
    
    Parameters:
    
    matrix - Provides the matrix values to be normalized
  - normalize
```
public void normalize()
```
    Performs singular value decomposition normalization of this matrix.
  - normalizeCP
```
public void normalizeCP()
```
    Perform cross product normalization of this matrix.
  - normalizeCP
```
public void normalizeCP(Matrix3d matrix)
```
    Perform cross product normalization of matrix m1 and place the normalized values into this.
    
    Parameters:
    
    matrix - Provides the matrix values to be normalized
  - equals
```
@Pure
public boolean equals(Matrix3d matrix)
```
    Returns true if all of the data members of Matrix3f m1 are equal to the corresponding data members in this Matrix3f.
    
    Parameters:
    
    matrix - the matrix with which the comparison is made
    
    Returns:
    
    true or false
  - equals
```
@Pure
public boolean equals(Object object)
```
    Returns true if the Object t1 is of type Matrix3f and all of the data members of t1 are equal to the corresponding data members in this Matrix3f.
    
    Overrides:
    
    equals in class Object
    
    Parameters:
    
    object - the matrix with which the comparison is made
    
    Returns:
    
    true or false
  - epsilonEquals
```
@Pure
public boolean epsilonEquals(Matrix3d matrix,
                             double epsilon)
```
    Returns true if the L-infinite distance between this matrix and matrix m1 is less than or equal to the epsilon parameter, otherwise returns false. The L-infinite distance is equal to MAX[i=0, 1, 2 ; j=0, 1, 2 ; abs(this.m(i, j) - m1.m(i, j)]
    
    Parameters:
    
    matrix - the matrix to be compared to this matrix
    
    epsilon - the threshold value
    
    Returns:
    
    true if this matrix is equals to the specified matrix at epsilon.
  - hashCode
```
@Pure
public int hashCode()
```
    Returns a hash code value based on the data values in this object. Two different Matrix3f objects with identical data values (i.e., Matrix3f.equals returns true) will return the same hash code value. Two objects with different data members may return the same hash value, although this is not likely.
    
    Overrides:
    
    hashCode in class Object
    
    Returns:
    
    the integer hash code value
  - setZero
```
public void setZero()
```
    Sets this matrix to all zeros.
  - setDiagonal
```
public void setDiagonal(double m00,
                        double m11,
                        double m22)
```
    Sets this matrix as diagonal.
    
    Parameters:
    
    m00 - the first element of the diagonal
    
    m11 - the second element of the diagonal
    
    m22 - the third element of the diagonal
  - negate
```
public void negate()
```
    Negates the value of this matrix: this = -this.
  - negate
```
public void negate(Matrix3d matrix)
```
    Sets the value of this matrix equal to the negation of of the Matrix3f parameter.
    
    Parameters:
    
    matrix - the source matrix
  - computeSVD
```
protected static void computeSVD(double[] matrix,
                                 double[] outScale,
                                 double[] outRot)
```
    Compute the SVD of a matrix m.
    
    Parameters:
    
    matrix - the matrix.
    
    outScale - is set with the scaling factors.
    
    outRot - is set with the rotation factors.
  - clone
```
@Pure
public Matrix3d clone()
```
    Creates a new object of the same class as this object.
    
    Overrides:
    
    clone in class Object
    
    Returns:
    
    a clone of this instance.
    
    Throws:
    
    OutOfMemoryError - if there is not enough memory.
    
    See Also:
    
    Cloneable
  - getM00
```
@Pure
public double getM00()
```
    Get the first matrix element in the first row.
    
    Returns:
    
    Returns the m00.
  - setM00
```
public void setM00(double m00)
```
    Set the first matrix element in the first row.
    
    Parameters:
    
    m00 - The m00 to set.
  - getM01
```
@Pure
public double getM01()
```
    Get the second matrix element in the first row.
    
    Returns:
    
    Returns the m01.
  - setM01
```
public void setM01(double m01)
```
    Set the second matrix element in the first row.
    
    Parameters:
    
    m01 - The m01 to set.
  - getM02
```
@Pure
public double getM02()
```
    Get the third matrix element in the first row.
    
    Returns:
    
    Returns the m02.
  - setM02
```
public void setM02(double m02)
```
    Set the third matrix element in the first row.
    
    Parameters:
    
    m02 - The m02 to set.
  - getM10
```
@Pure
public double getM10()
```
    Get first matrix element in the second row.
    
    Returns:
    
    Returns the m10.
  - setM10
```
public void setM10(double m10)
```
    Set first matrix element in the second row.
    
    Parameters:
    
    m10 - The m10 to set.
  - getM11
```
@Pure
public double getM11()
```
    Get second matrix element in the second row.
    
    Returns:
    
    Returns the m11.
  - setM11
```
public void setM11(double m11)
```
    Set the second matrix element in the second row.
    
    Parameters:
    
    m11 - The m11 to set.
  - getM12
```
@Pure
public double getM12()
```
    Get the third matrix element in the second row.
    
    Returns:
    
    Returns the m12.
  - setM12
```
public void setM12(double m11)
```
    Set the third matrix element in the second row.
    
    Parameters:
    
    m11 - The m12 to set.
  - getM20
```
@Pure
public double getM20()
```
    Get the first matrix element in the third row.
    
    Returns:
    
    Returns the m20
  - setM20
```
public void setM20(double m20)
```
    Set the first matrix element in the third row.
    
    Parameters:
    
    m20 - The m20 to set.
  - getM21
```
@Pure
public double getM21()
```
    Get the second matrix element in the third row.
    
    Returns:
    
    Returns the m21.
  - setM21
```
public void setM21(double m21)
```
    Set the second matrix element in the third row.
    
    Parameters:
    
    m21 - The m21 to set.
  - getM22
```
@Pure
public double getM22()
```
    Get the third matrix element in the third row .
    
    Returns:
    
    Returns the m22.
  - setM22
```
public void setM22(double m22)
```
    Set the third matrix element in the third row.
    
    Parameters:
    
    m22 - The m22 to set.
  - cov
```
public boolean cov(Vector3D<?,?> result,
                   Vector3D<?,?>... tuples)
```
    Set this matrix with the covariance matrix's elements for the given set of tuples.
    
    Parameters:
    
    result - the mean of the tuples.
    
    tuples - the input tuples.
    
    Returns:
    
    true if the cov matrix is computed.
  - cov
```
public boolean cov(Vector3D<?,?> result,
                   Point3D<?,?>... tuples)
```
    Set this matrix with the covariance matrix's elements for the given set of tuples.
    
    Parameters:
    
    result - the mean of the tuples.
    
    tuples - the input tuples.
    
    Returns:
    
    true if the cov matrix is computed.
  - cov
```
public boolean cov(Vector3D<?,?> result,
                   Iterable<? extends Tuple3D<?>> tuples)
```
    Set this matrix with the covariance matrix's elements for the given set of tuples.
    
    Parameters:
    
    result - the mean of the tuples.
    
    tuples - the input tuples.
    
    Returns:
    
    true if the cov matrix is computed.
  - isSymmetric
```
@Pure
public boolean isSymmetric()
```
    Replies if the matrix is symmetric.
    
    Returns:
    
    true if the matrix is symmetric, otherwise false
  - eigenVectorsOfSymmetricMatrix
```
public double[] eigenVectorsOfSymmetricMatrix(Matrix3d eigenVectors)
```
    Compute the eigenvectors of the given symmetric matrix according to the Jacobi Cyclic Method.
    Given the n x n real symmetric matrix A, the routine Jacobi_Cyclic_Method calculates the eigenvalues and eigenvectors of A by successively sweeping through the matrix A annihilating off-diagonal non-zero elements by a rotation of the row and column in which the non-zero element occurs.
    The Jacobi procedure for finding the eigenvalues and eigenvectors of a symmetric matrix A is based on finding a similarity transformation which diagonalizes A. The similarity transformation is given by a product of a sequence of orthogonal (rotation) matrices each of which annihilates an off-diagonal element and its transpose. The rotation effects only the rows and columns containing the off-diagonal element and its transpose, i.e. if a[i][j] is an off-diagonal element, then the orthogonal transformation rotates rows a[i][] and a[j][], and equivalently it rotates columns a[][i] and a[][j], so that a[i][j] = 0 and a[j][i] = 0. The cyclic Jacobi method considers the off-diagonal elements in the following order: (0, 1),(0, 2),...,(0, n-1),(1, 2),...,(n-2, n-1). If the the magnitude of the off-diagonal element is greater than a treshold, then a rotation is performed to annihilate that off-diagnonal element. The process described above is called a sweep. After a sweep has been completed, the threshold is lowered and another sweep is performed with the new threshold. This process is completed until the final sweep is performed with the final threshold. The orthogonal transformation which annihilates the matrix element a[k][m], k != m, is Q = q[i][j], where q[i][j] = 0 if i != j, i, j != k i, j != m and q[i][j] = 1 if i = j, i, j != k, i, j != m, q[k][k] = q[m][m] = cos(phi), q[k][m] = -sin(phi), and q[m][k] = sin(phi), where the angle phi is determined by requiring a[k][m] -> 0. This condition on the angle phi is equivalent to
    cot(2 phi) = 0.5 * (a[k][k] - a[m][m]) / a[k][m]
    Since tan(2 phi) = 2 tan(phi) / (1.0 - tan(phi)^2),
    tan(phi)^2 + 2cot(2 phi) * tan(phi) - 1 = 0.
    Solving for tan(phi), choosing the solution with smallest magnitude, tan(phi) = - cot(2 phi) + sgn(cot(2 phi)) sqrt(cot(2phi)^2 + 1). Then cos(phi)^2 = 1 / (1 + tan(phi)^2) and sin(phi)^2 = 1 - cos(phi)^2. Finally by taking the sqrts and assigning the sign to the sin the same as that of the tan, the orthogonal transformation Q is determined. Let A" be the matrix obtained from the matrix A by applying the similarity transformation Q, since Q is orthogonal, A" = Q'AQ, where Q' is the transpose of Q (which is the same as the inverse of Q). Then a"[i][j] = Q'[i][p] a[p][q] Q[q][j] = Q[p][i] a[p][q] Q[q][j], where repeated indices are summed over. If i is not equal to either k or m, then Q[i][j] is the Kronecker delta. So if both i and j are not equal to either k or m, a"[i][j] = a[i][j]. If i = k, j = k,
    a"[k][k] = a[k][k]*cos(phi)^2 + a[k][m]*sin(2 phi) + a[m][m]*sin(phi)^2
    If i = k, j = m,
    a"[k][m] = a"[m][k] = 0 = a[k][m]*cos(2 phi) + 0.5 * (a[m][m] - a[k][k])*sin(2 phi)
    If i = k, j != k or m,
    a"[k][j] = a"[j][k] = a[k][j] * cos(phi) + a[m][j] * sin(phi)
    If i = m, j = k, a"[m][k] = 0
    If i = m, j = m,
    a"[m][m] = a[m][m]*cos(phi)^2 - a[k][m]*sin(2 phi) + a[k][k]*sin(phi)^2
    If i= m, j != k or m,
    a"[m][j] = a"[j][m] = a[m][j] * cos(phi) - a[k][j] * sin(phi)
    If X is the matrix of normalized eigenvectors stored so that the ith column corresponds to the ith eigenvalue, then AX = X Lamda, where Lambda is the diagonal matrix with the ith eigenvalue stored at Lambda[i][i], i.e. X'AX = Lambda and X is orthogonal, the eigenvectors are normalized and orthogonal. So, X = Q1 Q2 ... Qs, where Qi is the ith orthogonal matrix, i.e. X can be recursively approximated by the recursion relation X" = X Q, where Q is the orthogonal matrix and the initial estimate for X is the identity matrix.
    If j = k, then x"[i][k] = x[i][k] * cos(phi) + x[i][m] * sin(phi),
    if j = m, then x"[i][m] = x[i][m] * cos(phi) - x[i][k] * sin(phi), and
    if j != k and j != m, then x"[i][j] = x[i][j].
    
    Parameters:
    
    eigenVectors - are the matrix of vectors to fill. Eigen vectors are the columns of the matrix.
    
    Returns:
    
    the eigenvalues which are corresponding to the eigenVectors columns.
    
    See Also:
    
    "Mathematics for 3D Game Programming and Computer Graphics, 2nd edition; pp.437."
  - isIdentity
```
@Pure
public boolean isIdentity()
```
    Replies if the matrix is identity.
    This function uses the equal-to-zero test with the error Math.ulp(double).
    
    Returns:
    
    true if the matrix is identity; false otherwise.
    
    See Also:
    
    MathUtil.isEpsilonZero(double), MathUtil.isEpsilonEqual(double, double)
  - operator_add
```
public void operator_add(Matrix3d matrix)
```
    Add the given matrix to this matrix: this += matrix.
    This function is an implementation of the operator for the languages that defined or based on the Xtext framework.
    
    Parameters:
    
    matrix - the matrix.
    
    See Also:
    
    add(Matrix3d)
  - operator_add
```
public void operator_add(double scalar)
```
    Add the given scalar to this matrix: this += scalar.
    This function is an implementation of the operator for the languages that defined or based on the Xtext framework.
    
    Parameters:
    
    scalar - the scalar.
    
    See Also:
    
    add(double)
  - operator_remove
```
public void operator_remove(Matrix3d matrix)
```
    Substract the given matrix to this matrix: this -= matrix.
    This function is an implementation of the operator for the languages that defined or based on the Xtext framework.
    
    Parameters:
    
    matrix - the matrix.
    
    See Also:
    
    sub(Matrix3d)
  - operator_remove
```
public void operator_remove(double scalar)
```
    Substract the given scalar to this matrix: this -= scalar.
    This function is an implementation of the operator for the languages that defined or based on the Xtext framework.
    
    Parameters:
    
    scalar - the scalar.
    
    See Also:
    
    add(double)
  - operator_plus
```
@Pure
public Matrix3d operator_plus(Matrix3d matrix)
```
    Replies the addition of the given matrix to this matrix: this + matrix.
    This function is an implementation of the operator for the languages that defined or based on the Xtext framework.
    
    Parameters:
    
    matrix - the matrix.
    
    Returns:
    
    the sum of the matrices.
    
    See Also:
    
    add(Matrix3d)
  - operator_plus
```
@Pure
public Matrix3d operator_plus(double scalar)
```
    Replies the addition of the given scalar to this matrix: this + scalar.
    This function is an implementation of the operator for the languages that defined or based on the Xtext framework.
    The operation scalar + this is supported by MatrixExtensions.operator_plus(double, Matrix3d).
    
    Parameters:
    
    scalar - the scalar.
    
    Returns:
    
    the sum of the matrix and the scalar.
    
    See Also:
    
    add(double), MatrixExtensions.operator_plus(double, Matrix3d)
  - operator_minus
```
@Pure
public Matrix3d operator_minus(Matrix3d matrix)
```
    Replies the substraction of the given matrix to this matrix: this - matrix.
    This function is an implementation of the operator for the languages that defined or based on the Xtext framework.
    
    Parameters:
    
    matrix - the matrix.
    
    Returns:
    
    the result of the substraction.
    
    See Also:
    
    sub(Matrix3d)
  - operator_minus
```
@Pure
public Matrix3d operator_minus(double scalar)
```
    Replies the substraction of the given scalar to this matrix: this - scalar.
    This function is an implementation of the operator for the languages that defined or based on the Xtext framework.
    The operation scalar - this is supported by MatrixExtensions.operator_minus(double, Matrix3d).
    
    Parameters:
    
    scalar - the scalar.
    
    Returns:
    
    the result of the substraction.
    
    See Also:
    
    add(double), MatrixExtensions.operator_minus(double, Matrix3d)
  - operator_minus
```
@Pure
public Matrix3d operator_minus()
```
    Replies the negation of this matrix: -this.
    This function is an implementation of the operator for the languages that defined or based on the Xtext framework.
    
    Returns:
    
    the negation of this matrix.
    
    See Also:
    
    negate()
  - operator_multiply
```
@Pure
public Matrix3d operator_multiply(Matrix3d matrix)
```
    Replies the multiplication of the given matrix and this matrix: this * matrix.
    This function is an implementation of the operator for the languages that defined or based on the Xtext framework.
    
    Parameters:
    
    matrix - the matrix.
    
    Returns:
    
    the multiplication of the matrices.
    
    See Also:
    
    mul(Matrix3d)
  - operator_multiply
```
@Pure
public Matrix3d operator_multiply(double scalar)
```
    Replies the multiplication of the given scalar and this matrix: this * scalar.
    This function is an implementation of the operator for the languages that defined or based on the Xtext framework.
    The operation scalar * this is supported by MatrixExtensions.operator_multiply(double, Matrix2d).
    
    Parameters:
    
    scalar - the scalar.
    
    Returns:
    
    the multiplication of the scalar and the matrix.
    
    See Also:
    
    mul(Matrix3d), MatrixExtensions.operator_multiply(double, Matrix3d)
  - operator_divide
```
@Pure
public Matrix3d operator_divide(double scalar)
```
    Replies the division of this matrix by the given scalar: this / scalar.
    This function is an implementation of the operator for the languages that defined or based on the Xtext framework.
    The operation scalar / this is supported by MatrixExtensions.operator_divide(double, Matrix2d).
    
    Parameters:
    
    scalar - the scalar.
    
    Returns:
    
    the division of the matrix by the scalar.
    
    See Also:
    
    mul(double), MatrixExtensions.operator_divide(double, Matrix3d)
  - operator_plusPlus
```
public void operator_plusPlus()
```
    Increment this matrix: this++.
    This function is an implementation of the operator for the languages that defined or based on the Xtext framework.
    
    See Also:
    
    add(double)
  - operator_moinsMoins
```
public void operator_moinsMoins()
```
    Increment this matrix: this--.
    This function is an implementation of the operator for the languages that defined or based on the Xtext framework.
    
    See Also:
    
    add(double)
  - operator_not
```
public Matrix3d operator_not()
```
    Replies the transposition of this matrix: !this.
    This function is an implementation of the operator for the languages that defined or based on the Xtext framework.
    
    Returns:
    
    the transpose
    
    See Also:
    
    add(double)
  - $plus
```
@Pure
public Matrix3d $plus(Matrix3d matrix)
```
    Replies the addition of the given matrix to this matrix: this + matrix.
    This function is an implementation of the operator for the Scala Language.
    
    Parameters:
    
    matrix - the matrix.
    
    Returns:
    
    the sum of the matrices.
    
    See Also:
    
    add(Matrix3d)
  - $plus
```
@Pure
public Matrix3d $plus(double scalar)
```
    Replies the addition of the given scalar to this matrix: this + scalar.
    This function is an implementation of the operator for the Scala Language.
    The operation scalar + this is supported by MatrixExtensions.$plus(double, Matrix3d).
    
    Parameters:
    
    scalar - the scalar.
    
    Returns:
    
    the sum of the matrix and the scalar.
    
    See Also:
    
    add(double), MatrixExtensions.$plus(double, Matrix3d)
  - $minus
```
@Pure
public Matrix3d $minus(Matrix3d matrix)
```
    Replies the substraction of the given matrix to this matrix: this - matrix.
    This function is an implementation of the operator for the Scala Language.
    
    Parameters:
    
    matrix - the matrix.
    
    Returns:
    
    the result of the substraction.
    
    See Also:
    
    sub(Matrix3d)
  - $minus
```
@Pure
public Matrix3d $minus(double scalar)
```
    Replies the substraction of the given scalar to this matrix: this - scalar.
    This function is an implementation of the operator for the Scala Language.
    The operation scalar - this is supported by MatrixExtensions.$minus(double, Matrix3d).
    
    Parameters:
    
    scalar - the scalar.
    
    Returns:
    
    the result of the substraction.
    
    See Also:
    
    add(double), MatrixExtensions.$minus(double, Matrix3d)
  - $minus
```
@Pure
public Matrix3d $minus()
```
    Replies the negation of this matrix: -this.
    This function is an implementation of the operator for the Scala Language.
    
    Returns:
    
    the negation of this matrix.
    
    See Also:
    
    negate()
  - $times
```
@Pure
public Matrix3d $times(Matrix3d matrix)
```
    Replies the multiplication of the given matrix and this matrix: this * matrix.
    This function is an implementation of the operator for the Scala Language.
    
    Parameters:
    
    matrix - the matrix.
    
    Returns:
    
    the multiplication of the matrices.
    
    See Also:
    
    mul(Matrix3d)
  - $times
```
@Pure
public Matrix3d $times(double scalar)
```
    Replies the multiplication of the given scalar and this matrix: this * scalar.
    This function is an implementation of the operator for the Scala Language.
    The operation scalar * this is supported by MatrixExtensions.$times(double, Matrix2d).
    
    Parameters:
    
    scalar - the scalar.
    
    Returns:
    
    the multiplication of the scalar and the matrix.
    
    See Also:
    
    mul(Matrix3d), MatrixExtensions.$times(double, Matrix3d)
  - $div
```
@Pure
public Matrix3d $div(double scalar)
```
    Replies the division of this matrix by the given scalar: this / scalar.
    This function is an implementation of the operator for the Scala Language.
    The operation scalar / this is supported by MatrixExtensions.$div(double, Matrix2d).
    
    Parameters:
    
    scalar - the scalar.
    
    Returns:
    
    the division of the matrix by the scalar.
    
    See Also:
    
    mul(double), MatrixExtensions.$div(double, Matrix3d)
  - $bang
```
public Matrix3d $bang()
```
    Replies the transposition of this matrix: !this.
    This function is an implementation of the operator for the Scala Language.
    
    Returns:
    
    the transpose
    
    See Also:
    
    add(double)

Class Matrix3d

Field Summary

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Field Detail

m00

m01

m02

m10

m11

m12

m20

m21

m22

isIdentity

Constructor Detail

Matrix3d

Matrix3d

Matrix3d

Matrix3d

Method Detail

toString

setIdentity

setElement

getElement

getRow

getRow

getColumn

getColumn

setRow

setRow

setRow

setColumn

setColumn

setColumn

add

add

add

add

sub

sub

transpose

transpose

set

set

set

invert

invert

determinant

mul

mul

mul

mul

mul

mulTransposeLeft

mulTransposeLeft

mulNormalize

mulNormalize

mulTransposeBoth

mulTransposeRight

normalize

normalize

normalizeCP

normalizeCP

equals

equals

epsilonEquals

hashCode

setZero

setDiagonal

negate

negate

computeSVD

clone

getM00

setM00

getM01

setM01

getM02