maspack.matrix

Class Matrix3d

java.lang.Object

maspack.matrix.MatrixBase

maspack.matrix.DenseMatrixBase

maspack.matrix.Matrix3dBase

maspack.matrix.Matrix3d

All Implemented Interfaces:

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

Direct Known Subclasses:

Matrix3x3Block

public class Matrix3d
extends Matrix3dBase

A general 3 x 3 matrix with the elements stored as explicit fields.

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
static Matrix3d	IDENTITY Global identity matrix.
static Matrix3d	ZERO Global zero matrix.

Fields inherited from class maspack.matrix.Matrix3dBase

m00, m01, m02, m10, m11, m12, m20, m21, m22

Fields inherited from interface maspack.matrix.Matrix

INDEFINITE, POSITIVE_DEFINITE, SPD, SYMMETRIC

Constructor Summary

Constructors

Constructor and Description
Matrix3d() Creates a matrix and initializes it to zero.
Matrix3d(double[] vals) Creates a matrix and initializes its elements from an array of values.
Matrix3d(double m00, double m01, double m02, double m10, double m11, double m12, double m20, double m21, double m22) Creates a matrix and initializes its elements from the specified values.
Matrix3d(Matrix M) Creates a matrix and initializes its elements to those of the matrix M.
Matrix3d(Matrix3dBase M) Creates a matrix and initializes its elements to those of the matrix M.

Method Summary

Modifier and Type	Method and Description
void	add(Matrix3dBase M1) Adds this matrix to M1 and places the result in this matrix.
void	add(Matrix3dBase M1, Matrix3dBase M2) Adds matrix M1 to M2 and places the result in this matrix.
void	addOuterProduct(double x0, double y0, double z0, double x1, double y1, double z1) Adds an outer product to this matrix.
void	addOuterProduct(Vector3d v0, Vector3d v1) Adds an outer product to this matrix.
void	addScaledOuterProduct(double s, Vector3d v) Adds a scaled outer product to this matrix.
void	addScaledOuterProduct(double s, Vector3d v0, Vector3d v1) Adds a scaled outer product to this matrix.
Matrix3d	clone()
void	crossProduct(Matrix3dBase M, Vector3d v) Computes the cross product of each row of M with v and places the result in this matrix.
void	crossProduct(Vector3d v, Matrix3dBase M) Computes the cross product of v with each column of M and places the result in this matrix.
void	factorQR(Matrix3d Q, Matrix3d R) Computes the QR decompostion for this matrix, for which
double	fastInvert(Matrix3dBase M) Quickly inverts the matrix M using the determinant formula and returns the computed determinant.
void	inverseTransform(RotationMatrix3d R) Applies an inverse rotational transformation R to this matrix, in place.
void	inverseTransform(RotationMatrix3d R, Matrix3dBase M) Applies an inverse rotational transformation R to a matrix M, 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	invert(Matrix3dBase M) Inverts the matrix M and places the result in this matrix, return false if M is detected to be singular.
static void	main(java.lang.String[] args)
void	mul(Matrix3dBase M1) Multiplies this matrix by M1 and places the result in this matrix.
void	mul(Matrix3dBase M1, Matrix3dBase M2) Multiplies matrix M1 by M2 and places the result in this matrix.
void	mulCols(double d00, double d11, double d22) Multiples the columns of this matrix by the values specified by d00, d11, and d22 and places the result in this matrix.
void	mulCols(Vector3d diag) Multiples the columns of this matrix by the values specified by diag and places the result in this matrix.
boolean	mulInverse(Matrix3dBase M1) Multiplies this matrix by the inverse of M1 and places the result in this matrix.
boolean	mulInverseBoth(Matrix3dBase M1, Matrix3dBase M2) Multiplies the inverse of matrix M1 by the inverse of M2 and places the result in this matrix.
boolean	mulInverseLeft(Matrix3dBase M1, Matrix3dBase M2) Multiplies the inverse of matrix M1 by M2 and places the result in this matrix.
boolean	mulInverseRight(Matrix3dBase M1, Matrix3dBase M2) Multiplies matrix M1 by the inverse of M2 and places the result in this matrix.
void	mulRows(double d00, double d11, double d22) Multiples the rows of this matrix by the values specified by d00, d11, and d22 and places the result in this matrix.
void	mulRows(Vector3d diag) Multiples the rows of this matrix by the values specified by diag and places the result in this matrix.
void	mulTranspose(Matrix3dBase M1) Multiplies this matrix by the transpose of M1 and places the result in this matrix.
void	mulTransposeBoth(Matrix3dBase M1, Matrix3dBase M2) Multiplies the transpose of matrix M1 by the transpose of M2 and places the result in this matrix.
void	mulTransposeLeft(Matrix3dBase M1, Matrix3dBase M2) Multiplies the transpose of matrix M1 by M2 and places the result in this matrix.
void	mulTransposeRight(Matrix3dBase M1, Matrix3dBase M2) Multiplies matrix M1 by the transpose of M2 and places the result in this matrix.
void	negate(Matrix3dBase M1) Sets this matrix to the negative of M1.
void	outerProduct(Vector3d v1, Vector3d v2) Sets this matrix to the outer product of the two vectors v1 and v2.
void	permuteColumns(int[] permutation) Rearrange the columns of this matrix according to the specified permutation, such that each column j is replaced by column permutation[j].
void	permuteColumns(int col0, int col1, int col2) Rearrange the columns of this matrix according to the specified permutation.
void	permuteRows(int[] permutation) Rearrange the rows of this matrix according to the specified permutation, such that each row i is replaced by row permutation[i].
void	permuteRows(int row0, int row1, int row2) Rearrange the rows of this matrix according to the specified permutation.
void	scale(double s) Scales the elements of this matrix by s.
void	scale(double s, Matrix3dBase M1) Scales the elements of matrix M1 by s and places the results in this matrix.
void	scaledAdd(double s, Matrix3dBase M1) Computes s M1 and adds the result to this matrix.
void	scaledAdd(double s, Matrix3dBase M1, Matrix3dBase M2) Computes s M1 + M2 and places the result in this matrix.
void	set(double m00, double m01, double m02, double m10, double m11, double m12, double m20, double m21, double m22) Sets the values of this matrix.
void	setColumns(Vector3d v0, Vector3d v1, Vector3d v2) Sets the columns of this matrix to the vectors v0, v1, and v2.
void	setDiagonal(double[] vals) Sets this matrix to a diagonal matrix whose values are specified by the array vals.
void	setDiagonal(double m00, double m11, double m22) Sets this matrix to a diagonal matrix whose values are specified.
void	setDiagonal(Vector3d diag) Sets this matrix to a diagonal matrix whose values are specified by diag.
void	setRandom() Sets the elements of this matrix to uniformly distributed random values in the range -0.5 (inclusive) to 0.5 (exclusive).
void	setRandom(double lower, double upper) Sets the elements of this matrix to uniformly distributed random values in a specified range.
void	setRandom(double lower, double upper, java.util.Random generator) Sets the elements of this matrix to uniformly distributed random values in a specified range, using a supplied random number generator.
void	setRows(Vector3d v0, Vector3d v1, Vector3d v2) Sets the rows of this matrix to the vectors v0, v1, and v2.
void	setSkewSymmetric(Vector3d v) Sets this matrix to the skew-symmetric matrix of vector v
void	setSymmetric(Matrix3dBase M1) Sets this matrix to the symmetric component of matrix M1
void	setZero() Sets the elements of this matrix to zero.
void	sub(Matrix3dBase M1) Subtracts this matrix from M1 and places the result in this matrix.
void	sub(Matrix3dBase M1, Matrix3dBase M2) Subtracts matrix M1 from M2 and places the result in this matrix.
void	transform(RotationMatrix3d R) Applies a rotational transformation R to this matrix, in place.
void	transform(RotationMatrix3d R, Matrix3dBase M) Applies a rotational transformation R to a matrix M, and place the result in this matrix.
void	transpose(Matrix3dBase M1) Sets this matrix to the transpose of M

Methods inherited from class maspack.matrix.Matrix3dBase

colSize, determinant, epsilonEquals, equals, factorQR, frobeniusNorm, get, get, getColumn, getColumn, getColumn, getRow, getRow, getRow, infinityNorm, isIdentity, isSymmetric, mul, mul, mul, mulAdd, mulAdd, mulInverse, mulInverse, mulInverseTranspose, mulInverseTranspose, mulTranspose, mulTranspose, mulTransposeAdd, negate, negateColumn, negateRow, oneNorm, orthogonalDeterminant, rowSize, scaleColumn, scaleRow, set, set, set, set, setColumn, setColumn, setIdentity, setRow, setRow, solve, solveTranspose, trace, transpose

Methods inherited from class maspack.matrix.DenseMatrixBase

add, checkConsistency, set, set, set, setCCSValues, setColumn, setCRSValues, 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, maxNorm, mul, mul, mulAdd, mulAdd, mulAdd, mulTranspose, mulTranspose, mulTranspose, mulTransposeAdd, mulTransposeAdd, mulTransposeAdd, numNonZeroVals, numNonZeroVals, scan, setCRSValues, setDefaultFormat, setSize, toString, toString, toString, 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

IDENTITY

public static final Matrix3d IDENTITY

Global identity matrix. Should not be modified.

ZERO

public static final Matrix3d ZERO

Global zero matrix. Should not be modified.

Constructor Detail

Matrix3d

public Matrix3d()

Creates a matrix and initializes it to zero.

Matrix3d

public Matrix3d(Matrix M)

Creates a matrix and initializes its elements to those of the matrix M.

Parameters:

M - matrix object to be copied.

Matrix3d

public Matrix3d(double[] vals)

Creates a matrix and initializes its elements from an array of values.

Parameters:

vals - element values for the matrix, with element (i,j) stored at location i*3+j

Matrix3d

public Matrix3d(double m00,
                double m01,
                double m02,
                double m10,
                double m11,
                double m12,
                double m20,
                double m21,
                double m22)

Creates a matrix and initializes its elements from the specified values.

Parameters:

m00 - element (0,0)

m01 - element (0,1)

m02 - element (0,2)

m10 - element (1,0)

m11 - element (1,1)

m12 - element (1,2)

m20 - element (2,0)

m21 - element (2,1)

m22 - element (2,2)

Matrix3d

public Matrix3d(Matrix3dBase M)

Creates a matrix and initializes its elements to those of the matrix M.

Parameters:

M - matrix object to be copied.

Method Detail

setColumns

public void setColumns(Vector3d v0,
                       Vector3d v1,
                       Vector3d v2)

Sets the columns of this matrix to the vectors v0, v1, and v2.

Parameters:

v0 - values for the first column

v1 - values for the second column

v2 - values for the third column

set

public void set(double m00,
                double m01,
                double m02,
                double m10,
                double m11,
                double m12,
                double m20,
                double m21,
                double m22)

Sets the values of this matrix.

Parameters:

m00 - element (0,0)

m01 - element (0,1)

m02 - element (0,2)

m10 - element (1,0)

m11 - element (1,1)

m12 - element (1,2)

m20 - element (2,0)

m21 - element (2,1)

m22 - element (2,2)

setRows

public void setRows(Vector3d v0,
                    Vector3d v1,
                    Vector3d v2)

Sets the rows of this matrix to the vectors v0, v1, and v2.

Parameters:

v0 - values for the first row

v1 - values for the second row

v2 - values for the third row

mul

public void mul(Matrix3dBase M1)

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

Parameters:

M1 - right-hand matrix

mul

public void mul(Matrix3dBase M1,
                Matrix3dBase M2)

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

Overrides:

mul in class Matrix3dBase

Parameters:

M1 - left-hand matrix

M2 - right-hand matrix

mulTranspose

public void mulTranspose(Matrix3dBase M1)

Multiplies this matrix by the transpose of M1 and places the result in this matrix.

Parameters:

M1 - right-hand matrix

mulTransposeLeft

public void mulTransposeLeft(Matrix3dBase M1,
                             Matrix3dBase M2)

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

Parameters:

M1 - left-hand matrix

M2 - right-hand matrix

mulTransposeRight

public void mulTransposeRight(Matrix3dBase M1,
                              Matrix3dBase M2)

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

Parameters:

M1 - left-hand matrix

M2 - right-hand matrix

mulTransposeBoth

public void mulTransposeBoth(Matrix3dBase M1,
                             Matrix3dBase M2)

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

Parameters:

M1 - left-hand matrix

M2 - right-hand matrix

mulInverse

public boolean mulInverse(Matrix3dBase M1)

Multiplies this matrix by the inverse of M1 and places the result in this matrix.

Parameters:

M1 - right-hand matrix

Returns:

false if M1 is singular

mulInverseRight

public boolean mulInverseRight(Matrix3dBase M1,
                               Matrix3dBase M2)

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

Parameters:

M1 - left-hand matrix

M2 - right-hand matrix

Returns:

false if M2 is singular

mulInverseLeft

public boolean mulInverseLeft(Matrix3dBase M1,
                              Matrix3dBase M2)

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

Parameters:

M1 - left-hand matrix

M2 - right-hand matrix

Returns:

false if M1 is singular

mulInverseBoth

public boolean mulInverseBoth(Matrix3dBase M1,
                              Matrix3dBase M2)

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

Parameters:

M1 - left-hand matrix

M2 - right-hand matrix

Returns:

false if M1 or M2 is singular

mulRows

public void mulRows(Vector3d diag)

Multiples the rows of this matrix by the values specified by diag and places the result in this matrix. This is equivalent to pre-multiplying this matrix by a diagonal matrix whose (diagonal) elements are specified by diag.

Parameters:

diag - specifies the row multipliers

mulRows

public void mulRows(double d00,
                    double d11,
                    double d22)

Multiples the rows of this matrix by the values specified by d00, d11, and d22 and places the result in this matrix. This is equivalent to pre-multiplying this matrix by a diagonal matrix with the specified diagonal elements.

Parameters:

d00 - multiplier for the first row

d11 - multiplier for the second row

d22 - multiplier for the third row

mulCols

public void mulCols(Vector3d diag)

Multiples the columns of this matrix by the values specified by diag and places the result in this matrix. This is equivalent to post-multiplying this matrix by a diagonal matrix whose (diagonal) elements are specified by diag.

Parameters:

diag - specifies the column multipliers

mulCols

public void mulCols(double d00,
                    double d11,
                    double d22)

Multiples the columns of this matrix by the values specified by d00, d11, and d22 and places the result in this matrix. This is equivalent to post-multiplying this matrix by a diagonal matrix with the specified diagonal elements.

Parameters:

d00 - multiplier for the first column

d11 - multiplier for the second column

d22 - multiplier for the third column

add

public void add(Matrix3dBase M1,
                Matrix3dBase M2)

Adds matrix M1 to M2 and places the result in this matrix.

Parameters:

M1 - left-hand matrix

M2 - right-hand matrix

add

public void add(Matrix3dBase M1)

Adds this matrix to M1 and places the result in this matrix.

Parameters:

M1 - right-hand matrix

sub

public void sub(Matrix3dBase M1,
                Matrix3dBase M2)

Subtracts matrix M1 from M2 and places the result in this matrix.

Parameters:

M1 - left-hand matrix

M2 - right-hand matrix

sub

public void sub(Matrix3dBase M1)

Subtracts this matrix from M1 and places the result in this matrix.

Parameters:

M1 - right-hand matrix

scale

public void scale(double s)

Scales the elements of this matrix by s.

Parameters:

s - scaling factor

scale

public void scale(double s,
                  Matrix3dBase M1)

Scales the elements of matrix M1 by s and places the results in this matrix.

Parameters:

s - scaling factor

M1 - matrix to be scaled

scaledAdd

public void scaledAdd(double s,
                      Matrix3dBase M1,
                      Matrix3dBase M2)

Computes s M1 + M2 and places the result in this matrix.

Parameters:

s - scaling factor

M1 - matrix to be scaled

M2 - matrix to be added

scaledAdd

public void scaledAdd(double s,
                      Matrix3dBase M1)

Computes s M1 and adds the result to this matrix.

Parameters:

s - scaling factor

M1 - matrix to be scaled and added

negate

public void negate(Matrix3dBase M1)

Sets this matrix to the negative of M1.

Parameters:

M1 - matrix to negate

transpose

public void transpose(Matrix3dBase M1)

Sets this matrix to the transpose of M

Parameters:

M1 - matrix to take the transpose of

setZero

public void setZero()

Sets the elements of this matrix to zero.

setRandom

public void setRandom()

Sets the elements of this matrix to uniformly distributed random values in the range -0.5 (inclusive) to 0.5 (exclusive).

setRandom

public void setRandom(double lower,
                      double upper)

Sets the elements of this matrix to uniformly distributed random values in a specified range.

Parameters:

lower - lower random value (inclusive)

upper - upper random value (exclusive)

setRandom

public void setRandom(double lower,
                      double upper,
                      java.util.Random generator)

Sets the elements of this matrix to uniformly distributed random values in a specified range, using a supplied random number generator.

Parameters:

lower - lower random value (inclusive)

upper - upper random value (exclusive)

generator - random number generator

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.

Overrides:

invert in class Matrix3dBase

fastInvert

public double fastInvert(Matrix3dBase M)

Quickly inverts the matrix M using the determinant formula and returns the computed determinant. If the determinant is 0, no inversion is performed.

Parameters:

M - matrix to invert

Returns:

determinant of M

invert

public boolean invert(Matrix3dBase M)

Inverts the matrix M and places the result in this matrix, return false if M is detected to be singular. The inverse is computed using an unrolled LU decomposition with partial pivoting.

Parameters:

M - matrix to invert

Returns:

false if M is singular

setDiagonal

public void setDiagonal(Vector3d diag)

Sets this matrix to a diagonal matrix whose values are specified by diag.

Parameters:

diag - diagonal values

setDiagonal

public void setDiagonal(double[] vals)

Sets this matrix to a diagonal matrix whose values are specified by the array vals.

Parameters:

vals - diagonal values

setDiagonal

public void setDiagonal(double m00,
                        double m11,
                        double m22)

Sets this matrix to a diagonal matrix whose values are specified.

Parameters:

m00 - first diagonal value

m11 - second diagonal value

m22 - third diagonal value

setSymmetric

public void setSymmetric(Matrix3dBase M1)

Sets this matrix to the symmetric component of matrix M1

setSkewSymmetric

public void setSkewSymmetric(Vector3d v)

Sets this matrix to the skew-symmetric matrix of vector v

outerProduct

public void outerProduct(Vector3d v1,
                         Vector3d v2)

Sets this matrix to the outer product of the two vectors v1 and v2.

Parameters:

v1 - first vector

v2 - second vector

addOuterProduct

public void addOuterProduct(double x0,
                            double y0,
                            double z0,
                            double x1,
                            double y1,
                            double z1)

Adds an outer product to this matrix. The outer product is formed from two vectors whose coordinates are given as arguments.

Parameters:

x0 - first vector x coordinate

y0 - first vector y coordinate

z0 - first vector z coordinate

x1 - second vector x coordinate

y1 - second vector y coordinate

z1 - second vector z coordinate

addOuterProduct

public void addOuterProduct(Vector3d v0,
                            Vector3d v1)

Adds an outer product to this matrix. The outer product is formed from two vectors are given as arguments.

Parameters:

v0 - first vector

v1 - second vector

addScaledOuterProduct

public void addScaledOuterProduct(double s,
                                  Vector3d v0,
                                  Vector3d v1)

Adds a scaled outer product to this matrix. The outer product is formed from two vectors are given as arguments, and takes the form

        T
 s v1 v2
 

Parameters:

s - scaling factor

v0 - first vector

v1 - second vector

addScaledOuterProduct

public void addScaledOuterProduct(double s,
                                  Vector3d v)

Adds a scaled outer product to this matrix. The outer product is formed from the single vector v and takes the form

      T
 s v v
 

The product is hence symmetric.

Parameters:

s - scaling factor

v - vector used to form outer product

crossProduct

public void crossProduct(Vector3d v,
                         Matrix3dBase M)

Computes the cross product of v with each column of M and places the result in this matrix. This is equivalent to computing

 this = [v] M
 

Parameters:

v - first cross product argument

M - matrix whose columns supply the second cross product argument

crossProduct

public void crossProduct(Matrix3dBase M,
                         Vector3d v)

Computes the cross product of each row of M with v and places the result in this matrix. This is equivalent to computing

 this = M [v]
 

Parameters:

M - matrix whose rows supply the first cross product argument

v - second cross product argument

permuteColumns

public void permuteColumns(int col0,
                           int col1,
                           int col2)

Rearrange the columns of this matrix according to the specified permutation. In particular, column 0 is set to the original value of column col0, column 1 is set to the original value of column col1, etc. If any index value is out of range, the associated column is left unchanged.

Parameters:

col0 - index of the original column which is to replace column 0

col1 - index of the original column which is to replace column 1

col2 - index of the original column which is to replace column 2

permuteColumns

public void permuteColumns(int[] permutation)

Rearrange the columns of this matrix according to the specified permutation, such that each column j is replaced by column permutation[j]. If any index value is out of range, the associated column is left unchanged.

Parameters:

permutation - describes the column exchanges

Throws:

ImproperSizeException - if the length of permutation is less than 3

permuteRows

public void permuteRows(int row0,
                        int row1,
                        int row2)

Rearrange the rows of this matrix according to the specified permutation. In particular, row 0 is set to the original value of row row0, row 1 is set to the original value of row row1, etc. If any index value is out of range, the associated row is left unchanged.

Parameters:

row0 - index of the original row which is to replace row 0

row1 - index of the original row which is to replace row 1

row2 - index of the original row which is to replace row 2

permuteRows

public void permuteRows(int[] permutation)

Rearrange the rows of this matrix according to the specified permutation, such that each row i is replaced by row permutation[i]. If any index value is out of range, the associated row is left unchanged.

Parameters:

permutation - describes the row exchanges

Throws:

ImproperSizeException - if the length of permutation is less than 3.

transform

public void transform(RotationMatrix3d R)

Applies a rotational transformation R to this matrix, in place. This is equivalent to forming the product

    R M R^T
 

where M is this matrix.

Parameters:

R - rotational transformation matrix

transform

public void transform(RotationMatrix3d R,
                      Matrix3dBase M)

Applies a rotational transformation R to a matrix M, and place the result in this matrix. This is equivalent to forming the product

    R M R^T
 

Parameters:

R - rotational transformation matrix

M - matrix to transform

inverseTransform

public void inverseTransform(RotationMatrix3d R)

Applies an inverse rotational transformation R to this matrix, in place. This is equivalent to forming the product

    R^T M R
 

where M is this matrix.

Parameters:

R - rotational transformation matrix

inverseTransform

public void inverseTransform(RotationMatrix3d R,
                             Matrix3dBase M)

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

    R^T M R
 

Overrides:

inverseTransform in class Matrix3dBase

Parameters:

R - rotational transformation matrix

M - matrix to transform

main

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

factorQR

public void factorQR(Matrix3d Q,
                     Matrix3d 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 Matrix3d clone()

Specified by:

clone in interface Clonable

Overrides:

clone in class Matrix3dBase