org.ejml.alg.dense.linsol.svd

Class SolvePseudoInverseSvd

java.lang.Object

org.ejml.alg.dense.linsol.svd.SolvePseudoInverseSvd

All Implemented Interfaces:

LinearSolver<DenseMatrix64F>

public class SolvePseudoInverseSvd
extends Object
implements LinearSolver<DenseMatrix64F>

The pseudo-inverse is typically used to solve over determined system for which there is no unique solution.
x=inv(A^TA)A^Tb
where A ∈ ℜ ^{m × n} and m ≥ n.

This class implements the Moore-Penrose pseudo-inverse using SVD and should never fail. Alternative implementations can use Cholesky decomposition, but those will fail if the A^TA matrix is singular. However the Cholesky implementation is much faster.

Author:

Peter Abeles

Constructor Summary

Constructors

Constructor and Description
SolvePseudoInverseSvd() Creates a solver targeted at matrices around 100x100
SolvePseudoInverseSvd(int maxRows, int maxCols) Creates a new solver targeted at the specified matrix size.

Method Summary

Methods

Modifier and Type	Method and Description
void	invert(DenseMatrix64F A_inv) Computes the inverse of of the 'A' matrix passed into LinearSolver.setA(org.ejml.data.Matrix64F) and writes the results to the provided matrix.
boolean	modifiesA() Returns true if the passed in matrix to LinearSolver.setA(org.ejml.data.Matrix64F) is modified.
boolean	modifiesB() Returns true if the passed in 'B' matrix to LinearSolver.solve(org.ejml.data.Matrix64F, org.ejml.data.Matrix64F) is modified.
double	quality() Returns a very quick to compute measure of how singular the system is.
boolean	setA(DenseMatrix64F A) Specifies the A matrix in the linear equation.
void	setThreshold(double threshold) Specify the relative threshold used to select singular values.
void	solve(DenseMatrix64F b, DenseMatrix64F x) Solves for X in the linear system, A*X=B.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

SolvePseudoInverseSvd

public SolvePseudoInverseSvd(int maxRows,
                     int maxCols)

Creates a new solver targeted at the specified matrix size.

Parameters:

maxRows - The expected largest matrix it might have to process. Can be larger.

maxCols - The expected largest matrix it might have to process. Can be larger.

SolvePseudoInverseSvd

public SolvePseudoInverseSvd()

Creates a solver targeted at matrices around 100x100

Method Detail

setA

public boolean setA(DenseMatrix64F A)

Description copied from interface: LinearSolver

Specifies the A matrix in the linear equation. A reference might be saved and it might also be modified depending on the implementation. If it is modified then LinearSolver.modifiesA() will return true.

If this value returns true that does not guarantee a valid solution was generated. This is because some decompositions don't detect singular matrices.

Specified by:

setA in interface LinearSolver<DenseMatrix64F>

Parameters:

A - The 'A' matrix in the linear equation. Might be modified or save the reference.

Returns:

true if it can be processed.

quality

public double quality()

Description copied from interface: LinearSolver

Returns a very quick to compute measure of how singular the system is. This measure will be invariant to the scale of the matrix and always be positive, with larger values indicating it is less singular. If not supported by the solver then the runtime exception IllegalArgumentException is thrown. This is NOT the matrix's condition.

How this function is implemented is not specified. One possible implementation is the following: In many decompositions a triangular matrix is extracted. The determinant of a triangular matrix is easily computed and once normalized to be scale invariant and its absolute value taken it will provide functionality described above.

Specified by:

quality in interface LinearSolver<DenseMatrix64F>

Returns:

The quality of the linear system.

solve

public void solve(DenseMatrix64F b,
         DenseMatrix64F x)

Description copied from interface: LinearSolver

Solves for X in the linear system, A*X=B.

In some implementations 'B' and 'X' can be the same instance of a variable. Call LinearSolver.modifiesB() to determine if 'B' is modified.

Specified by:

solve in interface LinearSolver<DenseMatrix64F>

Parameters:

b - A matrix ℜ ^{m × p}. Might be modified.

x - A matrix ℜ ^{n × p}, where the solution is written to. Modified.

invert

public void invert(DenseMatrix64F A_inv)

Description copied from interface: LinearSolver

Computes the inverse of of the 'A' matrix passed into LinearSolver.setA(org.ejml.data.Matrix64F) and writes the results to the provided matrix. If 'A_inv' needs to be different from 'A' is implementation dependent.

Specified by:

invert in interface LinearSolver<DenseMatrix64F>

Parameters:

A_inv - Where the inverted matrix saved. Modified.

modifiesA

public boolean modifiesA()

Description copied from interface: LinearSolver

Returns true if the passed in matrix to LinearSolver.setA(org.ejml.data.Matrix64F) is modified.

Specified by:

modifiesA in interface LinearSolver<DenseMatrix64F>

Returns:

true if A is modified in setA().

modifiesB

public boolean modifiesB()

Description copied from interface: LinearSolver

Returns true if the passed in 'B' matrix to LinearSolver.solve(org.ejml.data.Matrix64F, org.ejml.data.Matrix64F) is modified.

Specified by:

modifiesB in interface LinearSolver<DenseMatrix64F>

Returns:

true if B is modified in solve(B,X).

setThreshold

public void setThreshold(double threshold)

Specify the relative threshold used to select singular values. By default it's UtilEjml.EPS.

Parameters:

threshold - The singular value threshold