org.ejml.alg.dense.linsol
Class SolvePseudoInverse

java.lang.Object
  org.ejml.alg.dense.linsol.SolvePseudoInverse

All Implemented Interfaces:

LinearSolver<DenseMatrix64F>

public class SolvePseudoInverse
extends Object
implements LinearSolver<DenseMatrix64F>

The pseudo-inverse is used to solve an over determined system:
x=inv(A^TA)A^Tb
where A ∈ ℜ ^{m × n} and m ≥ n.

Thus allowing a linear solver to be used that can only invert square matrices. The downside of this approach is that the final solution is less precise in some situations. QRDecomposition will produce a more accurate solution in these situations.

This pseudo-inverse is also known as the Moore-Penrose pseudo-inverse and can be easily derived through matrix algebra.

Author:

Peter Abeles

Constructor Summary

SolvePseudoInverse()
Creates a new solver using a cholesky decomposition as its default solver.

SolvePseudoInverse(int maxCols)
Creates a new solver using a cholesky decomposition as its default solver.

SolvePseudoInverse(LinearSolver<DenseMatrix64F> inverter)
Creates a new solver from an arbitrary linear solver.

Method Summary

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	setMaxSize(int maxRows, int maxCols)
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

SolvePseudoInverse

public SolvePseudoInverse(LinearSolver<DenseMatrix64F> inverter)

Creates a new solver from an arbitrary linear solver.

Parameters:

inverter - Used to compute an inverse of a matrix.

SolvePseudoInverse

public SolvePseudoInverse(int maxCols)

Creates a new solver using a cholesky decomposition as its default solver.

Parameters:

maxCols - An estimate of how large of a matrix it might be inverting. Better to overestimate than underestimate.

SolvePseudoInverse

public SolvePseudoInverse()

Creates a new solver using a cholesky decomposition as its default solver.

Method Detail

setMaxSize

public void setMaxSize(int maxRows,
                       int maxCols)

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 have 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).