maspack.matrix
Class Matrix3dObject

java.lang.Object
  maspack.matrix.MatrixObject
      maspack.matrix.Matrix3dObject

All Implemented Interfaces:

java.io.Serializable

Direct Known Subclasses:

Matrix3d, RotationMatrix3d, SymmetricMatrix3d

public abstract class Matrix3dObject

extends MatrixObject

implements java.io.Serializable

Base class for 3 x 3 matrices in which the elements are stored as explicit fields. A primary motivation for such objects is computational speed.

See Also:

Serialized Form

Field Summary

double	m00 Matrix element (0,0)
double	m01 Matrix element (0,1)
double	m02 Matrix element (0,2)
double	m10 Matrix element (1,0)
double	m11 Matrix element (1,1)
double	m12 Matrix element (1,2)
double	m20 Matrix element (2,0)
double	m21 Matrix element (2,1)
double	m22 Matrix element (2,2)

Constructor Summary

Matrix3dObject()

Method Summary

int	colSize() Returns the number of columns in this matrix (which is always 3).
double	determinant() Returns the determinant of this matrix
boolean	epsilonEquals(Matrix3dObject M1, double epsilon) Returns true if the elements of this matrix equal those of matrix M1within a prescribed tolerance epsilon.
boolean	equals(Matrix3dObject M1) Returns true if the elements of this matrix exactly equal those of matrix M1.
double	frobeniusNorm() Returns the Frobenius norm of this matrix.
void	get(double[] values) Copies the elements of this matrix into an array of doubles. The elements are stored using row-major order, so that element (i,j) is stored at location i*colSize()+j.
double	get(int i, int j) Gets a single element of this matrix.
void	getColumn(int j, double[] values) Copies a column of this matrix into an array of doubles.
void	getColumn(int j, Vector3d col) Copies a column of this matrix into a 3-vector.
void	getRow(int i, double[] values) Copies a row of this matrix into an array of doubles.
void	getRow(int i, Vector3d row) Copies a row of this matrix into a 3-vector.
double	infinityNorm() Returns the infinity norm of this matrix.
boolean	invert() Inverts this matrix in place, returning false if the matrix is detected to be singular.
void	mul(Vector3d vr) Multiplies this matrix by the column vector vr and places the result back into vr.
void	mul(Vector3d vr, Vector3d v1) Multiplies this matrix by the column vector v1 and places the result in the vector vr.
boolean	mulInverse(Vector3d vr) Multiplies the column vector vr by the inverse of this matrix and places the result back in vr.
boolean	mulInverse(Vector3d vr, Vector3d v1) Multiplies the column vector v1 by the inverse of this matrix and places the result in vr.
boolean	mulInverseTranspose(Vector3d vr) Multiplies the column vector vr by the inverse transpose of this matrix and places the result back in vr.
boolean	mulInverseTranspose(Vector3d vr, Vector3d v1) Multiplies the column vector v1 by the inverse transpose of this matrix and places the result in vr.
void	mulTranspose(Vector3d vr) Multiplies the transpose of this matrix by the vector vr and places the result back in vr.
void	mulTranspose(Vector3d vr, Vector3d v1) Multiplies the transpose of this matrix by the vector v1 and places the result in vr.
void	negate() Negates this matrix in place.
double	oneNorm() Returns the 1 norm of this matrix.
int	rowSize() Returns the number of rows in this matrix (which is always 3).
void	set(double[] vals) Sets the elements of this matrix from an array of doubles. The elements in the array should be stored using row-major order, so that element (i,j) is stored at location i*colSize()+j.
void	set(int i, int j, double value) Sets a single element of this matrix.
void	set(Matrix3dObject M) Sets the values of this matrix to those of matrix M.
void	setColumn(int j, double[] values) Sets a column of this matrix from an array of doubles.
void	setColumn(int j, Vector3d col) Sets a column of this matrix to the specified 3-vector.
void	setIdentity() Sets this matrix to the identity.
void	setRow(int i, double[] values) Set a row of this matrix from an array of doubles.
void	setRow(int i, Vector3d row) Sets a row of this matrix to the specified 3-vector.
void	transpose() Transposes this matrix in place.

Methods inherited from class maspack.matrix.MatrixObject

epsilonEquals, equals, equals, get, getColumn, getRow, isFixedSize, scan, set, set, setColumn, setRow, setSize, toString, toString, toString

Methods inherited from class java.lang.Object

getClass, hashCode, notify, notifyAll, wait, wait, wait

Field Detail

m00

public double m00

Matrix element (0,0)

m01

public double m01

Matrix element (0,1)

m02

public double m02

Matrix element (0,2)

m10

public double m10

Matrix element (1,0)

m11

public double m11

Matrix element (1,1)

m12

public double m12

Matrix element (1,2)

m20

public double m20

Matrix element (2,0)

m21

public double m21

Matrix element (2,1)

m22

public double m22

Matrix element (2,2)

Constructor Detail

Matrix3dObject

public Matrix3dObject()

Method Detail

rowSize

public final int rowSize()

Returns the number of rows in this matrix (which is always 3).

Specified by:

rowSize in class MatrixObject

Returns:

3

colSize

public final int colSize()

Returns the number of columns in this matrix (which is always 3).

Specified by:

colSize in class MatrixObject

Returns:

3

get

public double get(int i,
                  int j)

Gets a single element of this matrix.

Specified by:

get in class MatrixObject

Parameters:

i - element row index

j - element column index

Returns:

element value

get

public void get(double[] values)

Copies the elements of this matrix into an array of doubles. The elements are stored using row-major order, so that element (i,j) is stored at location i*colSize()+j.

Overrides:

get in class MatrixObject

Parameters:

values - array into which values are copied

getColumn

public void getColumn(int j,
                      double[] values)

Copies a column of this matrix into an array of doubles.

Overrides:

getColumn in class MatrixObject

Parameters:

j - column index

values - array into which the column is copied

getColumn

public void getColumn(int j,
                      Vector3d col)

Copies a column of this matrix into a 3-vector.

Parameters:

j - column index

col - 3-vector into which the column is copied

getRow

public void getRow(int i,
                   double[] values)

Copies a row of this matrix into an array of doubles.

Overrides:

getRow in class MatrixObject

Parameters:

i - row index

values - array into which the row is copied

getRow

public void getRow(int i,
                   Vector3d row)

Copies a row of this matrix into a 3-vector.

Parameters:

i - row index

row - 3-vector into which the row is copied

set

public final void set(int i,
                      int j,
                      double value)

Sets a single element of this matrix.

Specified by:

set in class MatrixObject

Parameters:

i - element row index

j - element column index

value - element value

set

public void set(double[] vals)

Sets the elements of this matrix from an array of doubles. The elements in the array should be stored using row-major order, so that element (i,j) is stored at location i*colSize()+j.

Overrides:

set in class MatrixObject

Parameters:

vals - array from which values are copied

setColumn

public void setColumn(int j,
                      double[] values)

Sets a column of this matrix from an array of doubles.

Overrides:

setColumn in class MatrixObject

Parameters:

j - column index

values - array from which column values are copied

setColumn

public void setColumn(int j,
                      Vector3d col)

Sets a column of this matrix to the specified 3-vector.

Parameters:

j - column index

col - 3-vector from which the column is copied

setRow

public void setRow(int i,
                   double[] values)

Set a row of this matrix from an array of doubles.

Overrides:

setRow in class MatrixObject

Parameters:

i - row index

values - array from which the row is copied

setRow

public void setRow(int i,
                   Vector3d row)

Sets a row of this matrix to the specified 3-vector.

Parameters:

i - row index

row - 3-vector from which the row is copied

set

public void set(Matrix3dObject M)

Sets the values of this matrix to those of matrix M.

Parameters:

M - matrix whose values are to be copied

mul

public void mul(Vector3d vr,
                Vector3d v1)

Multiplies this matrix by the column vector v1 and places the result in the vector vr. If M represents this matrix, this is equivalent to computing

  vr = M v1
 

Parameters:

vr - result vector

v1 - vector to multiply by

mul

public void mul(Vector3d vr)

Multiplies this matrix by the column vector vr and places the result back into vr. If M represents this matrix, this is equivalent to computing

  vr = M vr
 

Parameters:

vr - vector to multiply (in place)

mulTranspose

public void mulTranspose(Vector3d vr,
                         Vector3d v1)

Multiplies the transpose of this matrix by the vector v1 and places the result in vr. If M represents this matrix, this is equivalent to computing

  vr = v1 M
 

Parameters:

vr - result vector

v1 - vector to multiply by

mulTranspose

public void mulTranspose(Vector3d vr)

Multiplies the transpose of this matrix by the vector vr and places the result back in vr. If M represents this matrix, this is equivalent to computing

  vr = vr M
 

Parameters:

vr - vector to multiply by (in place)

mulInverse

public boolean mulInverse(Vector3d vr,
                          Vector3d v1)

Multiplies the column vector v1 by the inverse of this matrix and places the result in vr.

Parameters:

vr - result vector

v1 - vector to multiply by

Returns:

false if this matrix is singular

mulInverse

public boolean mulInverse(Vector3d vr)

Multiplies the column vector vr by the inverse of this matrix and places the result back in vr.

Parameters:

vr - vector to multiply by (in place)

Returns:

false if this matrix is singular

mulInverseTranspose

public boolean mulInverseTranspose(Vector3d vr,
                                   Vector3d v1)

Multiplies the column vector v1 by the inverse transpose of this matrix and places the result in vr.

Parameters:

vr - result vector

v1 - vector to multiply by

Returns:

false if this matrix is singular

mulInverseTranspose

public boolean mulInverseTranspose(Vector3d vr)

Multiplies the column vector vr by the inverse transpose of this matrix and places the result back in vr.

Parameters:

vr - vector to multiply by (in place)

Returns:

false if this matrix is singular

negate

public void negate()

Negates this matrix in place.

transpose

public void transpose()

Transposes this matrix in place.

setIdentity

public void setIdentity()

Sets this matrix to the identity.

epsilonEquals

public boolean epsilonEquals(Matrix3dObject M1,
                             double epsilon)

Returns true if the elements of this matrix equal those of matrix M1within a prescribed tolerance epsilon.

Parameters:

M1 - matrix to compare with

epsilon - comparison tolerance

Returns:

false if the matrices are not equal within the specified tolerance

equals

public boolean equals(Matrix3dObject M1)

Returns true if the elements of this matrix exactly equal those of matrix M1.

Parameters:

M1 - matrix to compare with

Returns:

false if the matrices are not equal

infinityNorm

public double infinityNorm()

Returns the infinity norm of this matrix. This is equal to the maximum of the vector 1-norm of each row.

Overrides:

infinityNorm in class MatrixObject

Returns:

infinity norm of this matrix

oneNorm

public double oneNorm()

Returns the 1 norm of this matrix. This is equal to the maximum of the vector 1-norm of each column.

Overrides:

oneNorm in class MatrixObject

Returns:

1 norm of this matrix

frobeniusNorm

public double frobeniusNorm()

Returns the Frobenius norm of this matrix. This is equal to the square root of the sum of the squares of each element.

Overrides:

frobeniusNorm in class MatrixObject

Returns:

Frobenius norm of this matrix

invert

public boolean invert()

Inverts this matrix in place, returning false if the matrix is detected to be singular. The inverse is computed using an unrolled LU decomposition with partial pivoting.

determinant

public double determinant()
                   throws ImproperSizeException

Returns the determinant of this matrix

Overrides:

determinant in class MatrixObject

Returns:

matrix determinant

Throws:

ImproperSizeException - if the matrix is not square