SymmetricMatrix3d (Artisynth API documentation)

java.lang.Object
- maspack.matrix.MatrixBase
- - maspack.matrix.DenseMatrixBase
  - - maspack.matrix.Matrix3dBase
    - - maspack.matrix.SymmetricMatrix3d

All Implemented Interfaces:

java.io.Serializable, java.lang.Cloneable, DenseMatrix, LinearTransformNd, Matrix, Clonable
```
public class SymmetricMatrix3d
extends Matrix3dBase
```
A symmetric 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 SymmetricMatrix3d IDENTITY
Global identity matrix.

static SymmetricMatrix3d 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

Fields
Modifier and Type	Field and Description
`static SymmetricMatrix3d`	`IDENTITY` Global identity matrix.
`static SymmetricMatrix3d`	`ZERO` Global zero matrix.

Constructor Summary

Constructors
Constructor and Description
`SymmetricMatrix3d()` Creates a symmetric matrix and initializes it to zero.
`SymmetricMatrix3d(double[] vals)` Creates a symmetric matrix and initializes its elements from an array of doubles.
`SymmetricMatrix3d(double m00, double m11, double m22, double m01, double m02, double m12)` Creates a symmetric matrix and initializes its elements from the specified diagonal and uppper off-diagonal values.
`SymmetricMatrix3d(Matrix3dBase M)` Creates a symmetric matrix and initializes its elements from the diagonal and upper off-diagonal elements of M.

Method Summary

All Methods Instance Methods Concrete Methods
Modifier and Type	Method and Description
`void`	`add(SymmetricMatrix3d M1)` Adds this matrix to M1 and places the result in this matrix.
`void`	`add(SymmetricMatrix3d M1, SymmetricMatrix3d M2)` Adds matrix M1 to M2 and places the result in this matrix.
`void`	`addDyad(Vector3d a)` Adds the dyad
`void`	`addScaledDyad(double s, Vector3d a)` Adds the scaled dyad
`void`	`addScaledSymmetricDyad(double s, Vector3d a, Vector3d b)` Adds the scaled symmetric dyad
`void`	`addSymmetricDyad(Vector3d a, Vector3d b)` Adds the symmetric dyad
`void`	`deviator()` Sets this matrix to its deviator.
`void`	`deviator(SymmetricMatrix3d M)` Sets this matrix to the deviator of a given symmetric matrix, where the deviator is defined by
`void`	`dyad(Vector3d a)` Sets this matrix to the dyad
`double`	`fastInvert(Matrix3dBase M)` Quickly inverts the matrix M using the determinant formula and returns the computed determinant.
`void`	`getCholesky(Matrix3d L)` Computes the Cholesky decomposition of this matrix, which is assumed to be positive definite.
`void`	`getEigenValues_old(Vector3d eig, Matrix3dBase V)` Quickly computes the eigenvalues of this symmetric matrix.
`void`	`getEigenValues(double[] eig)`
`void`	`getEigenValues(Vector3d eig)` Quickly computes the eigenvalues of this symmetric matrix, as described for `getEigenValues`.
`void`	`getEigenValues(Vector3d eig, Matrix3dBase U)`
`void`	`getSVD(Matrix3dBase U, Vector3d sig, Matrix3dBase V)` Quickly computes the singular value decomposition U S V' of this symmetric 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.
`void`	`mulDiagTransposeRight(Matrix3dBase M, Vector3d diag)` Computes M D M', where D is a diagonal matrix given be a vector, and places the result in this matrix.
`void`	`mulLeftAndTransposeRight(Matrix3dBase M)` Computes M T M', where T is this matrix, and M' is the transpose of M, and places the result in this matrix.
`void`	`mulSymmetric(Matrix3dBase A, Matrix3dBase B)` Computes the symmetric product (AB + B'A')/2 and places the result in this matrix
`void`	`mulTransposeLeft(Matrix3dBase M)` Computes M' M, where M is a supplied matrix and M' is its transpose, and places the (symmetric) result in this matrix.
`void`	`mulTransposeLeftAndRight(Matrix3dBase M)` Computes M' T M, where T is this matrix, and M' is the transpose of M, and places the result in this matrix.
`void`	`mulTransposeLeftSymmetric(Matrix3dBase A, Matrix3dBase B)` Computes the symmetric product (A'B + B'A)/2 and places the result in this matrix
`void`	`mulTransposeRight(Matrix3dBase M)` Computes M M', where M is a supplied matrix and M' is its transpose, and places the (symmetric) result in this matrix.
`void`	`mulTransposeRightSymmetric(Matrix3dBase A, Matrix3dBase B)` Computes the symmetric product (AB' + BA')/2 and places the result in this matrix
`void`	`negate(SymmetricMatrix3d 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, SymmetricMatrix3d M1)` Scales the elements of matrix M1 by `s` and places the results in this matrix.
`void`	`scaledAdd(double s, SymmetricMatrix3d M1)` Computes s M1 and adds the result to this matrix.
`void`	`scaledAdd(double s, SymmetricMatrix3d M1, SymmetricMatrix3d M2)` Computes s M1 + M2 and places the result in this matrix.
`void`	`set(double[] vals)` Sets the elements of this matrix from an array of doubles.
`void`	`set(double m00, double m11, double m22, double m01, double m02, double m12)` Sets the values of this matrix from the specified diagonal and uppper off-diagonal values.
`void`	`set(Matrix3dBase M)` Sets the elements of this matrix from the the diagonal and upper off-diagonal elements of M.
`void`	`setDiagonal(double[] vals)` Sets this matrix to a diagonal matrix whose values are specified by the array vals.
`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`	`setSymmetric(Matrix3dBase M)` Sets this matrix to the symmetric part of M, defined by
`void`	`setZero()` Sets the elements of this matrix to zero.
`void`	`sub(SymmetricMatrix3d M1)` Subtracts this matrix from M1 and places the result in this matrix.
`void`	`sub(SymmetricMatrix3d M1, SymmetricMatrix3d M2)` Subtracts matrix M1 from M2 and places the result in this matrix.
`void`	`symmetricDyad(Vector3d a, Vector3d b)` Sets this matrix to the symmetric dyad

Methods inherited from class maspack.matrix.Matrix3dBase
clone, colSize, determinant, epsilonEquals, equals, factorQR, frobeniusNorm, get, get, getColumn, getColumn, getColumn, getRow, getRow, getRow, infinityNorm, inverseTransform, isIdentity, isSymmetric, main, mul, mul, mul, mul, mulAdd, mulAdd, mulInverse, mulInverse, mulInverseTranspose, mulInverseTranspose, mulTranspose, mulTranspose, mulTransposeAdd, negate, negateColumn, negateRow, oneNorm, orthogonalDeterminant, rowSize, scaleColumn, scaleRow, 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 SymmetricMatrix3d IDENTITY
```
    Global identity matrix. Should not be modified.
  - ZERO
```
public static final SymmetricMatrix3d ZERO
```
    Global zero matrix. Should not be modified.
- Constructor Detail
  - SymmetricMatrix3d
```
public SymmetricMatrix3d()
```
    Creates a symmetric matrix and initializes it to zero.
  - SymmetricMatrix3d
```
public SymmetricMatrix3d(double[] vals)
```
    Creates a symmetric matrix and initializes its elements from an array of doubles. Values in the array should be stored using row-major order, so that element (i,j) is stored at location i*colSize()+j. Only the diagonal and upper off-diagonal values are used; the lower off-diagonal elements are copied from the upper off-diagonal elements.
    
    Parameters:
    
    vals - array from which values are copied
  - SymmetricMatrix3d
```
public SymmetricMatrix3d(Matrix3dBase M)
```
    Creates a symmetric matrix and initializes its elements from the diagonal and upper off-diagonal elements of M.
    
    Parameters:
    
    M - matrix whose values are to be copied.
  - SymmetricMatrix3d
```
public SymmetricMatrix3d(double m00,
                         double m11,
                         double m22,
                         double m01,
                         double m02,
                         double m12)
```
    Creates a symmetric matrix and initializes its elements from the specified diagonal and uppper off-diagonal values.
    
    Parameters:
    
    m00 - element (0,0)
    
    m11 - element (1,1)
    
    m22 - element (2,2)
    
    m01 - element (0,1)
    
    m02 - element (0,2)
    
    m12 - element (1,2)
- Method Detail
  - set
```
public void set(Matrix3dBase M)
```
    Sets the elements of this matrix from the the diagonal and upper off-diagonal elements of M.
    
    Overrides:
    
    set in class Matrix3dBase
    
    Parameters:
    
    M - matrix whose values are to be copied.
  - 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. Only the diagonal and upper off-diaginal values are used; the lower off-diagonal elements are copied from the upper off-diagonal elements.
    
    Specified by:
    
    set in interface DenseMatrix
    
    Overrides:
    
    set in class Matrix3dBase
    
    Parameters:
    
    vals - array from which values are copied
  - set
```
public void set(double m00,
                double m11,
                double m22,
                double m01,
                double m02,
                double m12)
```
    Sets the values of this matrix from the specified diagonal and uppper off-diagonal values.
    
    Parameters:
    
    m00 - element (0,0)
    
    m11 - element (1,1)
    
    m22 - element (2,2)
    
    m01 - element (0,1)
    
    m02 - element (0,2)
    
    m12 - element (1,2)
  - 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
  - setSymmetric
```
public void setSymmetric(Matrix3dBase M)
```
    Sets this matrix to the symmetric part of M, defined by
```
 1/2 (M + M')
 
```
    Parameters:
    
    M - matrix to take symmetric part of
  - mulLeftAndTransposeRight
```
public void mulLeftAndTransposeRight(Matrix3dBase M)
```
    Computes M T M', where T is this matrix, and M' is the transpose of M, and places the result in this matrix.
    
    Parameters:
    
    M - matrix to multiply by
  - mulTransposeLeftAndRight
```
public void mulTransposeLeftAndRight(Matrix3dBase M)
```
    Computes M' T M, where T is this matrix, and M' is the transpose of M, and places the result in this matrix.
    
    Parameters:
    
    M - matrix to multiply by
  - mulDiagTransposeRight
```
public void mulDiagTransposeRight(Matrix3dBase M,
                                  Vector3d diag)
```
    Computes M D M', where D is a diagonal matrix given be a vector, and places the result in this matrix.
    
    Parameters:
    
    M - left (and right) matrix to multiply diagonal by
    
    diag - diagonal matrix values for D
  - mulTransposeLeft
```
public void mulTransposeLeft(Matrix3dBase M)
```
    Computes M' M, where M is a supplied matrix and M' is its transpose, and places the (symmetric) result in this matrix.
    
    Parameters:
    
    M - matrix to form product from
  - mulTransposeRight
```
public void mulTransposeRight(Matrix3dBase M)
```
    Computes M M', where M is a supplied matrix and M' is its transpose, and places the (symmetric) result in this matrix.
    
    Parameters:
    
    M - matrix to form product from
  - mulSymmetric
```
public void mulSymmetric(Matrix3dBase A,
                         Matrix3dBase B)
```
    Computes the symmetric product (AB + B'A')/2 and places the result in this matrix
    
    Parameters:
    
    A - left matrix
    
    B - right matrix
  - mulTransposeLeftSymmetric
```
public void mulTransposeLeftSymmetric(Matrix3dBase A,
                                      Matrix3dBase B)
```
    Computes the symmetric product (A'B + B'A)/2 and places the result in this matrix
    
    Parameters:
    
    A - left matrix
    
    B - right matrix
  - mulTransposeRightSymmetric
```
public void mulTransposeRightSymmetric(Matrix3dBase A,
                                       Matrix3dBase B)
```
    Computes the symmetric product (AB' + BA')/2 and places the result in this matrix
    
    Parameters:
    
    A - left matrix
    
    B - right matrix
  - add
```
public void add(SymmetricMatrix3d M1,
                SymmetricMatrix3d 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(SymmetricMatrix3d M1)
```
    Adds this matrix to M1 and places the result in this matrix.
    
    Parameters:
    
    M1 - right-hand matrix
  - sub
```
public void sub(SymmetricMatrix3d M1,
                SymmetricMatrix3d 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(SymmetricMatrix3d 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,
                  SymmetricMatrix3d 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,
                      SymmetricMatrix3d M1,
                      SymmetricMatrix3d 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,
                      SymmetricMatrix3d M1)
```
    Computes s M1 and adds the result to this matrix.
    
    Parameters:
    
    s - scaling factor
    
    M1 - matrix to be scaled and added
  - dyad
```
public void dyad(Vector3d a)
```
    Sets this matrix to the dyad
```
 a a^T.
 
```
    Parameters:
    
    a - dyad vector
  - addDyad
```
public void addDyad(Vector3d a)
```
    Adds the dyad
```
 a a^T
 
```
    to this matrix.
    Parameters:
    
    a - dyad vector
  - addScaledDyad
```
public void addScaledDyad(double s,
                          Vector3d a)
```
    Adds the scaled dyad
```
 s a a^T
 
```
    to this matrix.
    Parameters:
    
    s - scaling factor
    
    a - dyad vector
  - symmetricDyad
```
public void symmetricDyad(Vector3d a,
                          Vector3d b)
```
    Sets this matrix to the symmetric dyad
```
 a b^T + b^T a.
 
```
    Parameters:
    
    a - first dyad vector
    
    b - second dyad vector
  - addSymmetricDyad
```
public void addSymmetricDyad(Vector3d a,
                             Vector3d b)
```
    Adds the symmetric dyad
```
 a b^T + b^T a
 
```
    to this matrix.
    Parameters:
    
    a - first dyad vector
    
    b - second dyad vector
  - addScaledSymmetricDyad
```
public void addScaledSymmetricDyad(double s,
                                   Vector3d a,
                                   Vector3d b)
```
    Adds the scaled symmetric dyad
```
 s (a b^T + b^T a)
 
```
    to this matrix.
    Parameters:
    
    s - scaling factor
    
    a - first dyad vector
    
    b - second dyad vector
  - negate
```
public void negate(SymmetricMatrix3d M1)
```
    Sets this matrix to the negative of M1.
    
    Parameters:
    
    M1 - matrix to negate
  - deviator
```
public void deviator(SymmetricMatrix3d M)
```
    Sets this matrix to the deviator of a given symmetric matrix, where the deviator is defined by
```
    M - trace(M)/3 I
 
```
    Parameters:
    
    M - matrix to compute the deviator for
  - deviator
```
public void deviator()
```
    Sets this matrix to its deviator.
    
    See Also:
    
    deviator(SymmetricMatrix3d)
  - 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). Matrix symmetry is preserved.
  - setRandom
```
public void setRandom(double lower,
                      double upper)
```
    Sets the elements of this matrix to uniformly distributed random values in a specified range. Matrix symmetry is preserved.
    
    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. Matrix symmetry is preserved.
    
    Parameters:
    
    lower - lower random value (inclusive)
    
    upper - upper random value (exclusive)
    
    generator - random number generator
  - 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
  - getEigenValues
```
public void getEigenValues(double[] eig)
```
  - getEigenValues
```
public void getEigenValues(Vector3d eig)
```
    Quickly computes the eigenvalues of this symmetric matrix, as described for getEigenValues.
    
    Parameters:
    
    eig - resulting eigenvalues
  - getEigenValues_old
```
public void getEigenValues_old(Vector3d eig,
                               Matrix3dBase V)
```
    Quickly computes the eigenvalues of this symmetric matrix. These are computed from the cube roots of the characteristic polynomial, which is fast at the expense of some accuracy.
    
    Parameters:
    
    eig - resulting eigenvalues
    
    V - corresponding eigenvectors (optional)
  - getSVD
```
public void getSVD(Matrix3dBase U,
                   Vector3d sig,
                   Matrix3dBase V)
```
    Quickly computes the singular value decomposition U S V' of this symmetric matrix. This routine works by solving a cubic equation to obtain the eigenvalues, and so is around 5 times faster than the corresponding routine in javax.vecmath, though possibly at the expense of some precision.
    
    Parameters:
    
    U - if non-null, used to store the first orthogonal matrix in the decomposition.
    
    sig - required parameter, used to store the 3 singular values of the matrix, sorted from largest to smallest.
    
    V - if non-null, used to store the second orthogonal matrix in the decomposition (note that the returned value is V and not V').
  - getEigenValues
```
public void getEigenValues(Vector3d eig,
                           Matrix3dBase U)
```
  - getCholesky
```
public void getCholesky(Matrix3d L)
```
    Computes the Cholesky decomposition of this matrix, which is assumed to be positive definite. This decomposition takes the form
    M = L L'
    where M is the original matrix, L is a lower-triangular matrix and L' denotes its transpose. symmetric matrix.
    
    Parameters:
    
    L - returns the lower triangular part of the decomposition
    
    Throws:
    
    java.lang.IllegalArgumentException - if the matrix is not positive definite.

Class SymmetricMatrix3d

Nested Class Summary

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

Field Summary

Fields inherited from class maspack.matrix.Matrix3dBase

Fields inherited from interface maspack.matrix.Matrix

Constructor Summary

Method Summary

Methods inherited from class maspack.matrix.Matrix3dBase

Methods inherited from class maspack.matrix.DenseMatrixBase

Methods inherited from class maspack.matrix.MatrixBase

Methods inherited from class java.lang.Object

Methods inherited from interface maspack.matrix.Matrix

Field Detail

IDENTITY

ZERO

Constructor Detail

SymmetricMatrix3d

SymmetricMatrix3d

SymmetricMatrix3d

SymmetricMatrix3d

Method Detail

set

set

set

invert

fastInvert

invert

setSymmetric

mulLeftAndTransposeRight

mulTransposeLeftAndRight

mulDiagTransposeRight

mulTransposeLeft

mulTransposeRight

mulSymmetric

mulTransposeLeftSymmetric

mulTransposeRightSymmetric

add

add

sub

sub

scale

scale

scaledAdd

scaledAdd

dyad

addDyad

addScaledDyad

symmetricDyad

addSymmetricDyad

addScaledSymmetricDyad

negate

deviator

deviator

setZero

setRandom

setRandom

setRandom

setDiagonal

setDiagonal

getEigenValues

getEigenValues

getEigenValues_old

getSVD

getEigenValues

getCholesky