maspack.matrix

Class Matrix6d

java.lang.Object

maspack.matrix.MatrixBase

maspack.matrix.DenseMatrixBase

maspack.matrix.Matrix6dBase

maspack.matrix.Matrix6d

All Implemented Interfaces:

java.lang.Cloneable, DenseMatrix, LinearTransformNd, Matrix, VectorObject<Matrix6d>, Clonable, Scannable

Direct Known Subclasses:

Matrix6dBlock

public class Matrix6d
extends Matrix6dBase
implements VectorObject<Matrix6d>

A general 4 x 4 matrix with the elements stored as explicit fields.

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 Matrix6d	ZERO Global zero matrix.

Fields inherited from class maspack.matrix.Matrix6dBase

m00, m01, m02, m03, m04, m05, m10, m11, m12, m13, m14, m15, m20, m21, m22, m23, m24, m25, m30, m31, m32, m33, m34, m35, m40, m41, m42, m43, m44, m45, m50, m51, m52, m53, m54, m55

Fields inherited from interface maspack.matrix.Matrix

INDEFINITE, POSITIVE_DEFINITE, SPD, SYMMETRIC

Constructor Summary

Constructors

Constructor and Description
Matrix6d() Creates a matrix and initializes it to zero.
Matrix6d(double[] vals) Creates a matrix and initializes its elements from an array of values.
Matrix6d(Matrix M) Creates a matrix and initializes its elements to those of the matrix M.

Method Summary

Modifier and Type	Method and Description
void	add(Matrix6dBase M1) Adds this matrix to M1 and places the result in this matrix.
void	add(Matrix6dBase M1, Matrix6dBase M2) Adds matrix M1 to M2 and places the result in this matrix.
void	addObj(Matrix6d M1) Adds v1 to this vector.
void	addSubMatrix00(Matrix3dBase M) Adds to 3x3 sub-matrix of this matrix starting at (0, 0).
void	addSubMatrix03(Matrix3dBase M) Adds to the 3x3 sub-matrix of this matrix starting at (0, 3).
void	addSubMatrix30(Matrix3dBase M) Adds to the 3x3 sub-matrix of this matrix starting at (3, 0).
void	addSubMatrix33(Matrix3dBase M) Adds to the 3x3 sub-matrix of this matrix starting at (3, 3).
Matrix6d	clone()
void	crossProductTransform(Vector3d p, Matrix6d M1) Applies an cross product transformation to a matrix M1 and places the result in this matrix.
boolean	epsilonEquals(Matrix6d M1, double tol) Returns true if the components of this vector are equal to those of v1, within the tolerance tol.
void	getSubMatrix00(Matrix3dBase M) Gets the 3x3 sub-matrix of this matrix starting at (0, 0).
void	getSubMatrix03(Matrix3dBase M) Gets the 3x3 sub-matrix of this matrix starting at (0, 3).
void	getSubMatrix30(Matrix3dBase M) Gets the 3x3 sub-matrix of this matrix starting at (3, 0).
void	getSubMatrix33(Matrix3dBase M) Gets the 3x3 sub-matrix of this matrix starting at (3, 3).
void	inverseTransform(RotationMatrix3d R) Applies an inverse rotational transformation R to this matrix, in place.
void	inverseTransform(RotationMatrix3d R, Matrix6d M1) Applies an inverse rotational transformation R to a matrix M1 and place the result in this matrix.
boolean	invert(Matrix6dBase M) Inverts the matrix M and places the result in this matrix, return false if M is detected to be singular.
void	mul(Matrix6dBase M1) Multiplies this matrix by M1 and places the result in this matrix.
void	mul(Matrix6dBase M1, Matrix6dBase M2) Multiplies matrix M1 by M2 and places the result in this matrix.
void	mulAdd(Matrix M1, Matrix M2) Multiplies M1 by M2 and places the result in this matrix.
boolean	mulInverse(Matrix6dBase M1) Multiplies this matrix by the inverse of M1 and places the result in this matrix.
boolean	mulInverseBoth(Matrix6dBase M1, Matrix6dBase M2) Multiplies the inverse of matrix M1 by the inverse of M2 and places the result in this matrix.
boolean	mulInverseLeft(Matrix6dBase M1, Matrix6dBase M2) Multiplies the inverse of matrix M1 by M2 and places the result in this matrix.
boolean	mulInverseRight(Matrix6dBase M1, Matrix6dBase M2) Multiplies matrix M1 by the inverse of M2 and places the result in this matrix.
void	mulTranspose(Matrix6dBase M1) Multiplies this matrix by the transpose of M1 and places the result in this matrix.
void	mulTransposeBoth(Matrix6dBase M1, Matrix6dBase M2) Multiplies the transpose of matrix M1 by the transpose of M2 and places the result in this matrix.
void	mulTransposeLeft(Matrix6dBase M1, Matrix6dBase M2) Multiplies the transpose of matrix M1 by M2 and places the result in this matrix.
void	mulTransposeLeftAdd(Matrix M1, Matrix M2) Multiplies M1^T by M2 and places the result in this matrix.
void	mulTransposeRight(Matrix6dBase M1, Matrix6dBase M2) Multiplies matrix M1 by the transpose of 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(Matrix6dBase M1) Sets this matrix to the negative of M1.
void	scale(double s) Scales the elements of this matrix by s.
void	scale(double s, Matrix6dBase M1) Scales the elements of matrix M1 by s and places the results in this matrix.
void	scaledAddObj(double s, Matrix6d M1) Scales v1 by s and adds it to this vector.
void	scaleObj(double s) Scales this vector by s.
void	set(Matrix6d M1) Sets this vector to v1
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, double m33, double m44, double m55) Sets this matrix to a diagonal matrix whose values are specified.
void	setDiagonal(VectorNd diag)
void	setLowerToUpper() Makes this matrix symmetric by setting its lower triangular elements equal to the corresponding upper triangular elements.
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	setSubMatrix00(Matrix3dBase M) Sets the 3x3 sub-matrix of this matrix starting at (0, 0).
void	setSubMatrix03(Matrix3dBase M) Sets the 3x3 sub-matrix of this matrix starting at (0, 3).
void	setSubMatrix30(Matrix3dBase M) Sets the 3x3 sub-matrix of this matrix starting at (3, 0).
void	setSubMatrix33(Matrix3dBase M) Sets the 3x3 sub-matrix of this matrix starting at (3, 3).
void	setZero() Sets the elements of this matrix to zero.
void	sub(Matrix6dBase M1) Subtracts this matrix from M1 and places the result in this matrix.
void	sub(Matrix6dBase M1, Matrix6dBase 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, Matrix6d M1) Applies a rotational transformation R to M1 and place the result in this matrix.
void	transpose(Matrix6dBase M1) Sets this matrix to the transpose of M

Methods inherited from class maspack.matrix.Matrix6dBase

colSize, determinant, epsilonEquals, equals, frobeniusNorm, get, get, get, getColumn, getColumn, getRow, getRow, infinityNorm, invert, mul, mul, mulInverse, mulInverse, mulInverseTranspose, mulInverseTranspose, mulTranspose, mulTranspose, negate, oneNorm, rowSize, scaledAdd, set, set, set, set, setColumn, setIdentity, setRow, 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, isSymmetric, isWritable, maxNorm, mul, mul, mulAdd, mulAdd, mulAdd, 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.VectorObject

getThreeVectorValue

Methods inherited from interface maspack.util.Scannable

isWritable, scan, write

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, mulTransposeAdd, mulTransposeAdd, mulTransposeAdd, numNonZeroVals, numNonZeroVals, scan, setSize, toString, toString, trace, write, write, write

Field Detail

ZERO

public static final Matrix6d ZERO

Global zero matrix. Should not be modified.

Constructor Detail

Matrix6d

public Matrix6d()

Creates a matrix and initializes it to zero.

Matrix6d

public Matrix6d(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*6+j

Matrix6d

public Matrix6d(Matrix M)

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

Parameters:

M - matrix object to be copied.

Method Detail

getSubMatrix00

public void getSubMatrix00(Matrix3dBase M)

Gets the 3x3 sub-matrix of this matrix starting at (0, 0).

Parameters:

M - returns the sub matrix

getSubMatrix30

public void getSubMatrix30(Matrix3dBase M)

Gets the 3x3 sub-matrix of this matrix starting at (3, 0).

Parameters:

M - returns the sub matrix

getSubMatrix03

public void getSubMatrix03(Matrix3dBase M)

Gets the 3x3 sub-matrix of this matrix starting at (0, 3).

Parameters:

M - returns the sub matrix

getSubMatrix33

public void getSubMatrix33(Matrix3dBase M)

Gets the 3x3 sub-matrix of this matrix starting at (3, 3).

Parameters:

M - returns the sub matrix

setSubMatrix00

public void setSubMatrix00(Matrix3dBase M)

Sets the 3x3 sub-matrix of this matrix starting at (0, 0).

Parameters:

M - new sub matrix value

setSubMatrix30

public void setSubMatrix30(Matrix3dBase M)

Sets the 3x3 sub-matrix of this matrix starting at (3, 0).

Parameters:

M - new sub matrix value

setSubMatrix03

public void setSubMatrix03(Matrix3dBase M)

Sets the 3x3 sub-matrix of this matrix starting at (0, 3).

Parameters:

M - new sub matrix value

setSubMatrix33

public void setSubMatrix33(Matrix3dBase M)

Sets the 3x3 sub-matrix of this matrix starting at (3, 3).

Parameters:

M - new sub matrix value

addSubMatrix00

public void addSubMatrix00(Matrix3dBase M)

Adds to 3x3 sub-matrix of this matrix starting at (0, 0).

Parameters:

M - sub matrix to add

addSubMatrix30

public void addSubMatrix30(Matrix3dBase M)

Adds to the 3x3 sub-matrix of this matrix starting at (3, 0).

Parameters:

M - sub matrix to add

addSubMatrix03

public void addSubMatrix03(Matrix3dBase M)

Adds to the 3x3 sub-matrix of this matrix starting at (0, 3).

Parameters:

M - sub matrix to add

addSubMatrix33

public void addSubMatrix33(Matrix3dBase M)

Adds to the 3x3 sub-matrix of this matrix starting at (3, 3).

Parameters:

M - sub matrix to add

mul

public void mul(Matrix6dBase M1)

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

Parameters:

M1 - right-hand matrix

mul

public void mul(Matrix6dBase M1,
                Matrix6dBase M2)

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

Parameters:

M1 - left-hand matrix

M2 - right-hand matrix

mulTranspose

public void mulTranspose(Matrix6dBase 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(Matrix6dBase M1,
                             Matrix6dBase 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(Matrix6dBase M1,
                              Matrix6dBase 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(Matrix6dBase M1,
                             Matrix6dBase 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(Matrix6dBase 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(Matrix6dBase M1,
                               Matrix6dBase 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(Matrix6dBase M1,
                              Matrix6dBase 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(Matrix6dBase M1,
                              Matrix6dBase 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

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

add

public void add(Matrix6dBase M1,
                Matrix6dBase 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(Matrix6dBase M1)

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

Parameters:

M1 - right-hand matrix

sub

public void sub(Matrix6dBase M1,
                Matrix6dBase 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(Matrix6dBase 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,
                  Matrix6dBase 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

negate

public void negate(Matrix6dBase M1)

Sets this matrix to the negative of M1.

Parameters:

M1 - matrix to negate

transpose

public void transpose(Matrix6dBase 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.

Specified by:

setZero in interface VectorObject<Matrix6d>

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).

Overrides:

setRandom in class DenseMatrixBase

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(Matrix6dBase 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 LU decomposition with partial pivoting.

Parameters:

M - matrix to invert

Returns:

false if M is singular

setDiagonal

public void setDiagonal(VectorNd diag)

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,
                        double m33,
                        double m44,
                        double m55)

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

Parameters:

m00 - first diagonal value

m11 - second diagonal value

m22 - third diagonal value

m33 - fourth diagonal value

m44 - fifth diagonal value

m55 - sixth diagonal value

transform

public void transform(RotationMatrix3d R)

Applies a rotational transformation R to this matrix, in place. Equivalent to transform(R,M) with M equal to this matrix.

Parameters:

R - rotational transformation matrix

transform

public void transform(RotationMatrix3d R,
                      Matrix6d M1)

Applies a rotational transformation R to M1 and place the result in this matrix. This is equivalent to applying a rotational transform to each of the 4 3x3 submatrices:

    [ R  0 ]      [ R^T 0  ]
    [      ]  M1  [        ]
    [ 0  R ]      [ 0  R^T ]
 

Parameters:

R - rotational transformation matrix

M1 - matrix to transform

inverseTransform

public void inverseTransform(RotationMatrix3d R)

Applies an inverse rotational transformation R to this matrix, in place. Equivalent to inverseTransform(R,M) with M equal to this matrix.

Parameters:

R - rotational transformation matrix

inverseTransform

public void inverseTransform(RotationMatrix3d R,
                             Matrix6d M1)

Applies an inverse rotational transformation R to a matrix M1 and place the result in this matrix. This is equivalent to applying an inverse rotational transform to each of the 4 3x3 submatrices:

    [ R^T  0 ]      [ R  0 ]
    [        ]  M1  [      ]
    [ 0  R^T ]      [ 0  R ]
 

Parameters:

R - rotational transformation matrix

M1 - matrix to transform

crossProductTransform

public void crossProductTransform(Vector3d p,
                                  Matrix6d M1)

Applies an cross product transformation to a matrix M1 and places the result in this matrix. This transform is defined by

    [  I   0 ]      [ I -[p] ]
    [        ]  M1  [        ]
    [ [p]  I ]      [ 0   I  ]
 

where [p] is the 3 x 3 skew-symmetric matrix that implements the cross product for a vector p.

Parameters:

p - vector defining the cross product

M1 - matrix to transform

setLowerToUpper

public void setLowerToUpper()

Makes this matrix symmetric by setting its lower triangular elements equal to the corresponding upper triangular elements.

clone

public Matrix6d clone()

Specified by:

clone in interface Clonable

Overrides:

clone in class Matrix6dBase

scaleObj

public void scaleObj(double s)

Scales this vector by s.

Specified by:

scaleObj in interface VectorObject<Matrix6d>

addObj

public void addObj(Matrix6d M1)

Adds v1 to this vector.

Specified by:

addObj in interface VectorObject<Matrix6d>

scaledAddObj

public void scaledAddObj(double s,
                         Matrix6d M1)

Scales v1 by s and adds it to this vector.

Specified by:

scaledAddObj in interface VectorObject<Matrix6d>

set

public void set(Matrix6d M1)

Sets this vector to v1

Specified by:

set in interface VectorObject<Matrix6d>

epsilonEquals

public boolean epsilonEquals(Matrix6d M1,
                             double tol)

Returns true if the components of this vector are equal to those of v1, within the tolerance tol. If tol = 0, then exact equality is required.

Specified by:

epsilonEquals in interface VectorObject<Matrix6d>