maspack.matrix

Class Matrix2dBase

java.lang.Object

maspack.matrix.MatrixBase

maspack.matrix.DenseMatrixBase

maspack.matrix.Matrix2dBase

All Implemented Interfaces:

java.lang.Cloneable, DenseMatrix, LinearTransformNd, Matrix, Clonable

Direct Known Subclasses:

Matrix2d, RotationMatrix2d

public abstract class Matrix2dBase
extends DenseMatrixBase
implements Clonable

Base class for 2 x 2 matrices in which the elements are stored as explicit fields. A primary motivation for such objects is computational speed.

Nested Class Summary

Nested classes/interfaces inherited from interface maspack.matrix.Matrix

Matrix.Partition, Matrix.WriteFormat

Field Summary

Fields

Modifier and Type	Field and Description
double	m00 Matrix element (0,0)
double	m01 Matrix element (0,1)
double	m10 Matrix element (1,0)
double	m11 Matrix element (1,1)

Fields inherited from interface maspack.matrix.Matrix

INDEFINITE, POSITIVE_DEFINITE, SPD, SYMMETRIC

Constructor Summary

Constructors

Constructor and Description
Matrix2dBase()

Method Summary

Modifier and Type	Method and Description
Matrix2dBase	clone()
int	colSize() Returns the number of columns in this matrix (which is always 2).
double	determinant() Returns the determinant of this matrix
boolean	epsilonEquals(Matrix2dBase M1, double epsilon) Returns true if the elements of this matrix equal those of matrix M1within a prescribed tolerance epsilon.
boolean	equals(Matrix2dBase 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.
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, double[] values, int off) Copies a column of this matrix into an array of doubles, starting at a specified offset.
void	getColumn(int j, Vector2d col) Copies a column of this matrix into a 2-vector.
void	getRow(int i, double[] values) Copies a row of this matrix into an array of doubles.
void	getRow(int i, double[] values, int off) Copies a row of this matrix into an array of doubles, starting at a specified offset.
void	getRow(int i, Vector2d row) Copies a row of this matrix into a 2-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(Vector2d vr) Multiplies this matrix by the column vector vr and places the result back into vr.
void	mul(Vector2d vr, Vector2d v1) Multiplies this matrix by the column vector v1 and places the result in the vector vr.
void	mul(VectorNd vr, VectorNd v1) Multiplies this matrix by the column vector v1 and places the result in the vector vr.
void	mulAdd(Matrix M1, Matrix M2) Multiplies M1 by M2 and places the result in this matrix.
void	mulAdd(Vector2d vr, Vector2d v1, Vector2d v2) Multiplies this matrix by the column vector v1, adds the vector v2, and places the result in the vector vr.
boolean	mulInverse(Vector2d vr) Multiplies the column vector vr by the inverse of this matrix and places the result back in vr.
boolean	mulInverse(Vector2d vr, Vector2d v1) Multiplies the column vector v1 by the inverse of this matrix and places the result in vr.
boolean	mulInverseTranspose(Vector2d vr) Multiplies the column vector vr by the inverse transpose of this matrix and places the result back in vr.
boolean	mulInverseTranspose(Vector2d vr, Vector2d v1) Multiplies the column vector v1 by the inverse transpose of this matrix and places the result in vr.
void	mulTranspose(Vector2d vr) Multiplies the transpose of this matrix by the vector vr and places the result back in vr.
void	mulTranspose(Vector2d vr, Vector2d v1) Multiplies the transpose of this matrix by the vector v1 and places the result in vr.
void	mulTransposeLeftAdd(Matrix M1, Matrix M2) Multiplies M1^T by M2 and places the result in this matrix.
void	mulTransposeRightAdd(Matrix M1, Matrix M2) Multiplies M1 by M2^T and places the result in this matrix.
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 2).
void	set(double[] vals) Sets the elements of this matrix from an array of doubles.
void	set(double m00, double m01, double m10, double m11) Sets the matrix elements
void	set(int i, int j, double value) Sets a single element of this matrix.
void	set(Matrix M) Sets the values of this matrix to those of matrix M.
void	set(Matrix2dBase 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, Vector2d col) Sets a column of this matrix to the specified 2-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, Vector2d row) Sets a row of this matrix to the specified 2-vector.
void	transpose() Transposes this matrix in place.

Methods inherited from class maspack.matrix.DenseMatrixBase

add, checkConsistency, set, set, set, setCCSValues, setColumn, setCRSValues, setRandom, setRow, setSubMatrix

Methods inherited from class maspack.matrix.MatrixBase

containsNaN, epsilonEquals, equals, frobeniusNormSquared, get, getCCSIndices, getCCSIndices, getCCSIndices, getCCSValues, getCCSValues, getCCSValues, getColumn, getCRSIndices, getCRSIndices, getCRSIndices, getCRSValues, getCRSValues, getCRSValues, getDefaultFormat, getRow, getSize, getSubMatrix, hasNaN, idString, isFixedSize, isSymmetric, isWritable, maxNorm, mul, mul, mulAdd, mulAdd, mulAdd, mulTranspose, mulTranspose, mulTranspose, mulTransposeAdd, mulTransposeAdd, mulTransposeAdd, numNonZeroVals, numNonZeroVals, scan, scan, setCRSValues, setDefaultFormat, setSize, toString, toString, toString, trace, write, write, write, write, write, write, write, writeToFile

Methods inherited from class java.lang.Object

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

Methods inherited from interface maspack.matrix.Matrix

epsilonEquals, equals, frobeniusNormSquared, getCCSIndices, getCCSIndices, getCCSIndices, getCCSValues, getCCSValues, getCCSValues, getColumn, getCRSIndices, getCRSIndices, getCRSIndices, getCRSValues, getCRSValues, getCRSValues, getRow, getSize, getSubMatrix, isFixedSize, isSymmetric, maxNorm, mul, mul, mulAdd, mulAdd, mulAdd, mulTranspose, mulTranspose, mulTranspose, mulTransposeAdd, mulTransposeAdd, mulTransposeAdd, numNonZeroVals, numNonZeroVals, scan, setSize, toString, toString, trace, write, write, write

Field Detail

m00

public double m00

Matrix element (0,0)

m01

public double m01

Matrix element (0,1)

m10

public double m10

Matrix element (1,0)

m11

public double m11

Matrix element (1,1)

Constructor Detail

Matrix2dBase

public Matrix2dBase()

Method Detail

rowSize

public final int rowSize()

Returns the number of rows in this matrix (which is always 2).

Specified by:

rowSize in interface LinearTransformNd

Specified by:

rowSize in interface Matrix

Specified by:

rowSize in class MatrixBase

Returns:

2

colSize

public final int colSize()

Returns the number of columns in this matrix (which is always 2).

Specified by:

colSize in interface LinearTransformNd

Specified by:

colSize in interface Matrix

Specified by:

colSize in class MatrixBase

Returns:

2

get

public double get(int i,
                  int j)

Gets a single element of this matrix.

Specified by:

get in interface Matrix

Specified by:

get in class MatrixBase

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.

Specified by:

get in interface Matrix

Overrides:

get in class MatrixBase

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.

Specified by:

getColumn in interface Matrix

Overrides:

getColumn in class MatrixBase

Parameters:

j - column index

values - array into which the column is copied

getColumn

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

Copies a column of this matrix into an array of doubles, starting at a specified offset.

Specified by:

getColumn in interface Matrix

Overrides:

getColumn in class MatrixBase

Parameters:

j - column index

values - array into which the column is copied

off - offset in values where copying should begin

getColumn

public void getColumn(int j,
                      Vector2d col)

Copies a column of this matrix into a 2-vector.

Parameters:

j - column index

col - 2-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.

Specified by:

getRow in interface Matrix

Overrides:

getRow in class MatrixBase

Parameters:

i - row index

values - array into which the row is copied

getRow

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

Copies a row of this matrix into an array of doubles, starting at a specified offset.

Specified by:

getRow in interface Matrix

Overrides:

getRow in class MatrixBase

Parameters:

i - row index

values - array into which the row is copied

off - offset in values where copying should begin

getRow

public void getRow(int i,
                   Vector2d row)

Copies a row of this matrix into a 2-vector.

Parameters:

i - row index

row - 2-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 interface DenseMatrix

Specified by:

set in class DenseMatrixBase

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.

Specified by:

set in interface DenseMatrix

Overrides:

set in class DenseMatrixBase

Parameters:

vals - array from which values are copied

set

public void set(double m00,
                double m01,
                double m10,
                double m11)

Sets the matrix elements

Parameters:

m00 - top-left

m01 - top-right

m10 - bottom-left

m11 - bottom-right

setColumn

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

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

Specified by:

setColumn in interface DenseMatrix

Overrides:

setColumn in class DenseMatrixBase

Parameters:

j - column index

values - array from which column values are copied

setColumn

public void setColumn(int j,
                      Vector2d col)

Sets a column of this matrix to the specified 2-vector.

Parameters:

j - column index

col - 2-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.

Specified by:

setRow in interface DenseMatrix

Overrides:

setRow in class DenseMatrixBase

Parameters:

i - row index

values - array from which the row is copied

setRow

public void setRow(int i,
                   Vector2d row)

Sets a row of this matrix to the specified 2-vector.

Parameters:

i - row index

row - 2-vector from which the row is copied

set

public void set(Matrix M)

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

Specified by:

set in interface Matrix

Overrides:

set in class DenseMatrixBase

Parameters:

M - matrix whose values are to be copied

set

public void set(Matrix2dBase 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(Vector2d vr,
                Vector2d 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(VectorNd vr,
                VectorNd 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
 

Specified by:

mul in interface LinearTransformNd

Specified by:

mul in interface Matrix

Overrides:

mul in class MatrixBase

Parameters:

vr - result vector

v1 - vector to multiply by

mulAdd

public void mulAdd(Vector2d vr,
                   Vector2d v1,
                   Vector2d v2)

Multiplies this matrix by the column vector v1, adds the vector v2, and places the result in the vector vr. If M represents this matrix, this is equivalent to computing

  vr = M v1 + v2
 

Parameters:

vr - result vector

v1 - vector to multiply by

v2 - vector to add

mul

public void mul(Vector2d 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(Vector2d vr,
                         Vector2d 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(Vector2d 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(Vector2d vr,
                          Vector2d 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(Vector2d 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(Vector2d vr,
                                   Vector2d 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(Vector2d 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

mulAdd

public void mulAdd(Matrix M1,
                   Matrix M2)

Multiplies M1 by M2 and places the result in this matrix.

Parameters:

M1 - left matrix term

M2 - right matrix term

mulTransposeRightAdd

public void mulTransposeRightAdd(Matrix M1,
                                 Matrix M2)

Multiplies M1 by M2^T and places the result in this matrix.

Parameters:

M1 - left matrix term

M2 - right matrix term

mulTransposeLeftAdd

public void mulTransposeLeftAdd(Matrix M1,
                                Matrix M2)

Multiplies M1^T by M2 and places the result in this matrix.

Parameters:

M1 - left matrix term

M2 - right matrix term

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(Matrix2dBase 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(Matrix2dBase 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.

Specified by:

infinityNorm in interface Matrix

Overrides:

infinityNorm in class MatrixBase

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.

Specified by:

oneNorm in interface Matrix

Overrides:

oneNorm in class MatrixBase

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.

Specified by:

frobeniusNorm in interface Matrix

Overrides:

frobeniusNorm in class MatrixBase

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.

determinant

public double determinant()
                   throws ImproperSizeException

Returns the determinant of this matrix

Specified by:

determinant in interface Matrix

Overrides:

determinant in class MatrixBase

Returns:

matrix determinant

Throws:

ImproperSizeException - if the matrix is not square

clone

public Matrix2dBase clone()

Specified by:

clone in interface Clonable

Overrides:

clone in class java.lang.Object