SVDecomposition3d (Artisynth API documentation)

java.lang.Object
- maspack.matrix.SVDecomposition3d

```
public class SVDecomposition3d
extends java.lang.Object
```
Constructs the singular value decomposition (SVD) of a 3x3 matrix. This takes the form
M = U S V'
where M is the original matrix, U and V are orthogonal matrices, V' indicates the transpose of V, and S is a diagonal matrix. Once an SVD has been constructed, it can be used to perform various computations related to M, such as solving equations, computing the determinant, or estimating the condition number.
Providing a separate class for the SVD allows an application to perform such decompositions repeatedly without having to reallocate temporary storage space.

Field Summary

Fields
Modifier and Type Field and Description

static int DEFAULT_ITERATION_LIMIT
The iteration limit for computing the SVD.

Fields
Modifier and Type	Field and Description
`static int`	`DEFAULT_ITERATION_LIMIT` The iteration limit for computing the SVD.

Constructor Summary

Constructors
Constructor and Description
`SVDecomposition3d()` Creates an uninitialized SVDecomposition with U and V internally allocated.
`SVDecomposition3d(Matrix3dBase M)` Creates an SVDecomposition with U and V internally allocated and initializes it to the SVD for the matrix M.
`SVDecomposition3d(Matrix3d U, Matrix3d V)` Creates an SVDecomposition with the matrices U and V.
`SVDecomposition3d(Matrix3d U, Matrix3d V, Matrix3dBase M)` Creates an SVDecomposition with the matrices U and V, and initializes it to the SVD for the matrix M.

Method Summary

All Methods Instance Methods Concrete Methods
Modifier and Type	Method and Description
`double`	`condition()` Computes the condition number of the original matrix M associated with this SVD.
`double`	`determinant()` Computes the determinant of the original matrix M associated with this SVD.
`void`	`factor(Matrix3dBase M)` Peforms an SVD on the Matrix3dBase M.
`boolean`	`factorSafe(Matrix3dBase M)` Peforms an SVD on the Matrix3dBase M, without throwing an exception max iterations being surpassed
`int`	`getIterationLimit()` Gets the iteration limit for SVD computations.
`Vector3d[]`	`getNullSpace()`
`Vector3d[]`	`getNullSpace(double eps)`
`Vector3d[]`	`getRangeSpace()`
`Vector3d[]`	`getRangeSpace(double eps)`
`void`	`getS(Vector3d svec)` Gets the singular values associated with this SVD.
`Matrix3d`	`getU()` Returns the U matrix associated with this SVD, or null if no such matrix has been set.
`Matrix3d`	`getV()` Returns the V matrix associated with this SVD, or null if no such matrix has been set.
`boolean`	`inverse(Matrix3d R)` Computes the inverse of the original matrix M associated this SVD, and places the result in R.
`boolean`	`isCanonical()`
`void`	`leftPolarDecomposition(Matrix3d P, Matrix3dBase R, Matrix3dBase F)` Factors a 3 x 3 matrix F into a left polar decomposition
`double`	`norm()` Computes the 2-norm of the original matrix M associated with this SVD.
`void`	`polarDecomposition(Matrix3dBase R, Matrix3d P, Matrix3dBase F)` Factors a 3 x 3 matrix F into a right polar decomposition
`void`	`polarDecomposition(Matrix3dBase R, SymmetricMatrix3d P, Matrix3dBase F)` Factors a 3 x 3 matrix F into a right polar decomposition
`boolean`	`pseudoInverse(Matrix3d R)` Computes the pseudo inverse of the original matrix M associated this SVD, and places the result in R.
`void`	`setCanonical(boolean enable)` Ensure that singular values are positive and sorted from largest to smallest.
`void`	`setIterationLimit(int lim)` Sets the iteration limit for SVD computations.
`void`	`setU(Matrix3d U)` Sets the U matrix associated with this SVD.
`void`	`setV(Matrix3d V)` Sets the V matrix associated with this SVD.
`boolean`	`solve(Vector3d x, Vector3d b)` Solves the linear equation M x = b where M is the original matrix associated with this SVD, and x and b are vectors.

Methods inherited from class java.lang.Object
equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

- Field Detail
  - DEFAULT_ITERATION_LIMIT
```
public static final int DEFAULT_ITERATION_LIMIT
```
    The iteration limit for computing the SVD.
    
    See Also:
    
    Constant Field Values
- Constructor Detail
  - SVDecomposition3d
```
public SVDecomposition3d(Matrix3d U,
                         Matrix3d V,
                         Matrix3dBase M)
```
    Creates an SVDecomposition with the matrices U and V, and initializes it to the SVD for the matrix M. Either U and V or V may be omitted if the user does not desire these values.
    
    Parameters:
    
    U - optional U matrix for this SVD
    
    V - optional V matrix for this SVD
    
    M - matrix to perform the SVD on
  - SVDecomposition3d
```
public SVDecomposition3d(Matrix3d U,
                         Matrix3d V)
```
    Creates an SVDecomposition with the matrices U and V. Either U and V or V may be omitted if the user does not desire these values.
    
    Parameters:
    
    U - optional U matrix for this SVD
    
    V - optional V matrix for this SVD
  - SVDecomposition3d
```
public SVDecomposition3d(Matrix3dBase M)
```
    Creates an SVDecomposition with U and V internally allocated and initializes it to the SVD for the matrix M.
    
    Parameters:
    
    M - matrix to perform the SVD on
  - SVDecomposition3d
```
public SVDecomposition3d()
```
    Creates an uninitialized SVDecomposition with U and V internally allocated.
- Method Detail
  - setCanonical
```
public void setCanonical(boolean enable)
```
    Ensure that singular values are positive and sorted from largest to smallest. The default value for this is true. If false, then no effort will be made to ensure that the values are positive or sorted.
  - isCanonical
```
public boolean isCanonical()
```
  - getIterationLimit
```
public int getIterationLimit()
```
    Gets the iteration limit for SVD computations. The actual number of iterations allowed is this limit value times the minimum dimension of the matrix.
    
    Returns:
    
    iteration limit
    
    See Also:
    
    setIterationLimit(int)
  - setIterationLimit
```
public void setIterationLimit(int lim)
```
    Sets the iteration limit for SVD computations. The actual number of iterations allowed is this limit value times the minimum dimension of the matrix.
    
    Parameters:
    
    lim - iteration limit
    
    See Also:
    
    getIterationLimit()
  - factor
```
public void factor(Matrix3dBase M)
```
    Peforms an SVD on the Matrix3dBase M.
    
    Parameters:
    
    M - matrix to perform the SVD on
  - factorSafe
```
public boolean factorSafe(Matrix3dBase M)
```
    Peforms an SVD on the Matrix3dBase M, without throwing an exception max iterations being surpassed
    
    Parameters:
    
    M - matrix to perform the SVD on
    
    Returns:
    
    true if successful, false otherwise
  - setU
```
public void setU(Matrix3d U)
```
    Sets the U matrix associated with this SVD. If a previous U matrix has been set, its contents will be copied into this new matrix. Setting the matrix to null will disable the calculation of U.
    
    Parameters:
    
    U - new U matrix for this SVD
  - getU
```
public Matrix3d getU()
```
    Returns the U matrix associated with this SVD, or null if no such matrix has been set.
    
    Returns:
    
    U matrix
  - setV
```
public void setV(Matrix3d V)
```
    Sets the V matrix associated with this SVD. If a previous V matrix has been set, its contents will be copied into this new matrix. Setting the matrix to null will disable the calculation of V.
    
    Parameters:
    
    V - new V matrix for this SVD
  - getV
```
public Matrix3d getV()
```
    Returns the V matrix associated with this SVD, or null if no such matrix has been set.
    
    Returns:
    
    V matrix
  - getS
```
public void getS(Vector3d svec)
```
    Gets the singular values associated with this SVD.
    
    Parameters:
    
    svec - vector giving the diagonal elements of S
  - condition
```
public double condition()
```
    Computes the condition number of the original matrix M associated with this SVD. This is simply the absolute value of the ratio of the maximum and minimum singular values.
    
    Returns:
    
    condition number
    
    Throws:
    
    ImproperStateException - if this SVDecomposition is uninitialized
  - norm
```
public double norm()
```
    Computes the 2-norm of the original matrix M associated with this SVD. This is simply the absolute value of the maximum singular value.
    
    Returns:
    
    2-norm
    
    Throws:
    
    ImproperStateException - if this SVDecomposition is uninitialized
  - determinant
```
public double determinant()
```
    Computes the determinant of the original matrix M associated with this SVD.
    
    Returns:
    
    determinant
    
    Throws:
    
    ImproperStateException - if this SVDecomposition is uninitialized
  - solve
```
public boolean solve(Vector3d x,
                     Vector3d b)
```
    Solves the linear equation
    M x = b
    where M is the original matrix associated with this SVD, and x and b are vectors.
    
    Parameters:
    
    x - unknown vector to solve for
    
    b - constant vector
    
    Returns:
    
    false if M is singular (within working precision)
    
    Throws:
    
    ImproperStateException - if this decomposition is uninitialized, or if U and V are not present
  - inverse
```
public boolean inverse(Matrix3d R)
```
    Computes the inverse of the original matrix M associated this SVD, and places the result in R.
    
    Parameters:
    
    R - matrix in which the inverse is stored
    
    Returns:
    
    false if M is singular (within working precision)
    
    Throws:
    
    ImproperStateException - if this decomposition is uninitialized, or if U and V are not present
  - pseudoInverse
```
public boolean pseudoInverse(Matrix3d R)
```
    Computes the pseudo inverse of the original matrix M associated this SVD, and places the result in R.
    
    Parameters:
    
    R - matrix in which the inverse is stored
    
    Returns:
    
    false if M is singular (within working precision)
    
    Throws:
    
    ImproperStateException - if this decomposition is uninitialized, or if U and V are not present
  - getNullSpace
```
public Vector3d[] getNullSpace(double eps)
```
  - getRangeSpace
```
public Vector3d[] getRangeSpace(double eps)
```
  - getNullSpace
```
public Vector3d[] getNullSpace()
```
  - getRangeSpace
```
public Vector3d[] getRangeSpace()
```
  - polarDecomposition
```
public void polarDecomposition(Matrix3dBase R,
                               Matrix3d P,
                               Matrix3dBase F)
```
    Factors a 3 x 3 matrix F into a right polar decomposition
```
 F = R P
 
```
    where R is a rotation matrix (with determinant 1) and P is a symmetric matrix.
  - polarDecomposition
```
public void polarDecomposition(Matrix3dBase R,
                               SymmetricMatrix3d P,
                               Matrix3dBase F)
```
    Factors a 3 x 3 matrix F into a right polar decomposition
```
 F = R P
 
```
    where R is a rotation matrix (with determinant 1) and P is a symmetric matrix.
  - leftPolarDecomposition
```
public void leftPolarDecomposition(Matrix3d P,
                                   Matrix3dBase R,
                                   Matrix3dBase F)
```
    Factors a 3 x 3 matrix F into a left polar decomposition
```
 F = P R
 
```
    where R is a rotation matrix (with determinant 1) and P is a symmetric matrix.

Class SVDecomposition3d

Field Summary

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Field Detail

DEFAULT_ITERATION_LIMIT

Constructor Detail

SVDecomposition3d

SVDecomposition3d

SVDecomposition3d

SVDecomposition3d

Method Detail

setCanonical

isCanonical

getIterationLimit

setIterationLimit

factor

factorSafe

setU

getU

setV

getV

getS

condition

norm

determinant

solve

inverse

pseudoInverse

getNullSpace

getRangeSpace

getNullSpace

getRangeSpace

polarDecomposition

polarDecomposition

leftPolarDecomposition