maspack.matrix

Class Matrix3dBase

java.lang.Object

maspack.matrix.MatrixBase

maspack.matrix.DenseMatrixBase

maspack.matrix.Matrix3dBase

All Implemented Interfaces:

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

Direct Known Subclasses:

Matrix3d, RotationMatrix3d, SymmetricMatrix3d

public abstract class Matrix3dBase
extends DenseMatrixBase
implements java.io.Serializable, Clonable

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

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	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)

Fields inherited from interface maspack.matrix.Matrix

INDEFINITE, POSITIVE_DEFINITE, SPD, SYMMETRIC

Constructor Summary

Constructors

Constructor and Description
Matrix3dBase()

Method Summary

Modifier and Type	Method and Description
Matrix3dBase	clone()
int	colSize() Returns the number of columns in this matrix (which is always 3).
double	determinant() Returns the determinant of this matrix
boolean	epsilonEquals(Matrix3dBase M1, double eps) Returns true if the elements of this matrix equal those of matrix M1within a prescribed tolerance epsilon.
boolean	equals(Matrix3dBase M1) Returns true if the elements of this matrix exactly equal those of matrix M1.
void	factorQR(Matrix3dBase Q, Matrix3dBase R) Computes the QR decompostion for this matrix, for which
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, 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, double[] values, int off) Copies a row of this matrix into an array of doubles, starting at a specified offset.
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.
void	inverseTransform(RotationMatrix3d R, Matrix3dBase M1) Applies an inverse rotational transformation R to a matrix M1 and place the result in this matrix.
boolean	invert() Inverts this matrix in place, returning false if the matrix is detected to be singular.
boolean	isIdentity() Returns true if this matrix equals the identity.
boolean	isSymmetric(double tol) Returns true if this matrix is symmetric within a given absolute tolerance.
static void	main(java.lang.String[] args)
void	mul(Matrix3dBase M1, Matrix3dBase M2) Multiplies matrix M1 by M2 and places the result in this matrix.
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.
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(Vector3d vr, Vector3d v1, Vector3d v2) Multiplies this matrix by the column vector v1, adds the vector v2, 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	mulTransposeAdd(Vector3d vr, Vector3d v1, Vector3d v2) Multiplies the transpose of this matrix by the vector v1, adds the vector v2, 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.
void	negateColumn(int colIdx) Negates a column of this matrix.
void	negateRow(int rowIdx) Negates a row of this matrix.
double	oneNorm() Returns the 1 norm of this matrix.
double	orthogonalDeterminant() Returns the determinant of this matrix, assuming that it is orthogonal.
int	rowSize() Returns the number of rows in this matrix (which is always 3).
void	scaleColumn(int j, double s) Scale a column
void	scaleRow(int i, double s) Scale a row by a particular value
void	set(double[] vals) Sets the elements of this matrix from an array of doubles.
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(Matrix3dBase 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.
boolean	solve(Vector3d x, Vector3d b) Solves this matrix for x given a right hand side b, returning false if the matrix is detected to be singular.
boolean	solveTranspose(Vector3d x, Vector3d b) Solves the transpose of this matrix for x given a right hand side b, returning false if the matrix is detected to be singular.
double	trace() Returns the trace of this matrix.
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, isWritable, maxNorm, mul, mul, mulAdd, mulAdd, mulAdd, mulTranspose, mulTranspose, mulTranspose, mulTransposeAdd, mulTransposeAdd, mulTransposeAdd, numNonZeroVals, numNonZeroVals, scan, scan, setCRSValues, setDefaultFormat, setSize, toString, toString, toString, 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, maxNorm, mul, mul, mulAdd, mulAdd, mulAdd, mulTranspose, mulTranspose, mulTranspose, mulTransposeAdd, mulTransposeAdd, mulTransposeAdd, numNonZeroVals, numNonZeroVals, scan, setSize, toString, toString, write, write, write

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

Matrix3dBase

public Matrix3dBase()

Method Detail

rowSize

public final int rowSize()

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

Specified by:

rowSize in interface LinearTransformNd

Specified by:

rowSize in interface Matrix

Specified by:

rowSize in class MatrixBase

Returns:

3

colSize

public final int colSize()

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

Specified by:

colSize in interface LinearTransformNd

Specified by:

colSize in interface Matrix

Specified by:

colSize in class MatrixBase

Returns:

3

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,
                      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

scaleColumn

public void scaleColumn(int j,
                        double s)

Scale a column

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

scaleRow

public void scaleRow(int i,
                     double s)

Scale a row by a particular value

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 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

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,
                      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.

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,
                   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(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(Matrix3dBase 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(Matrix3dBase M1,
                Matrix3dBase M2)

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

Parameters:

M1 - left-hand matrix

M2 - right-hand matrix

inverseTransform

public void inverseTransform(RotationMatrix3d R,
                             Matrix3dBase M1)

Applies an inverse rotational transformation R to a matrix M1 and place the result in this matrix. This is equivalent to forming the product

    R^T M1 R
 

Parameters:

R - rotational transformation matrix

M1 - matrix to transform

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

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(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(Vector3d vr,
                   Vector3d v1,
                   Vector3d 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(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

mulTransposeAdd

public void mulTransposeAdd(Vector3d vr,
                            Vector3d v1,
                            Vector3d v2)

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

  vr = v1 M + v2
 

Parameters:

vr - result vector

v1 - vector to multiply by

v2 - vector to add

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. This is equivalent to solve(vr,v1).

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. This is equivalent to solveTranspose(vr,v1).

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(Matrix3dBase M1,
                             double eps)

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

Parameters:

M1 - matrix to compare with

eps - comparison tolerance

Returns:

false if the matrices are not equal within the specified tolerance

equals

public boolean equals(Matrix3dBase 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. The inverse is computed using an unrolled LU decomposition with partial pivoting.

solve

public boolean solve(Vector3d x,
                     Vector3d b)

Solves this matrix for x given a right hand side b, returning false if the matrix is detected to be singular. The solution is computed using partial pivoting.

Parameters:

x - result

b - right hand side

Returns:

false if this matrix is singular

solveTranspose

public boolean solveTranspose(Vector3d x,
                              Vector3d b)

Solves the transpose of this matrix for x given a right hand side b, returning false if the matrix is detected to be singular. The solution is computed using partial pivoting.

Parameters:

x - result

b - right hand side

Returns:

false if this matrix is 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

isIdentity

public boolean isIdentity()

Returns true if this matrix equals the identity.

Returns:

true if this matrix equals the identity

orthogonalDeterminant

public double orthogonalDeterminant()

Returns the determinant of this matrix, assuming that it is orthogonal. This is done by computing the cross product of the first two columns and then computing its dot product with the third column.

Returns:

orthogonal matrix determinant

factorQR

public void factorQR(Matrix3dBase Q,
                     Matrix3dBase R)

Computes the QR decompostion for this matrix, for which

    M = Q R
 

where Q is orthogonal and R is upper triangular.

Parameters:

Q - if non-null, returns Q

R - if non-null, returns R The computation is the same as that performed by the QRDecomposition class, except significantly faster.

clone

public Matrix3dBase clone()

Specified by:

clone in interface Clonable

Overrides:

clone in class java.lang.Object

trace

public double trace()

Returns the trace of this matrix.

Specified by:

trace in interface Matrix

Overrides:

trace in class MatrixBase

Returns:

matrix trace

isSymmetric

public boolean isSymmetric(double tol)

Returns true if this matrix is symmetric within a given absolute tolerance. Specifically, each off-diagonal element must equal it's transposed counterpart within the given tolerance.

Specified by:

isSymmetric in interface Matrix

Overrides:

isSymmetric in class MatrixBase

Parameters:

tol - absolute tolerance for checking equality of off-diagonal elements

negateColumn

public void negateColumn(int colIdx)

Negates a column of this matrix.

Parameters:

colIdx - index of the column to negate

negateRow

public void negateRow(int rowIdx)

Negates a row of this matrix.

Parameters:

rowIdx - index of the row to negate

main

public static void main(java.lang.String[] args)