## Class SolvePseudoInverseSvd

- java.lang.Object
- org.ejml.alg.dense.linsol.svd.SolvePseudoInverseSvd

- All Implemented Interfaces:
- LinearSolver<DenseMatrix64F>

public class SolvePseudoInverseSvdextends Objectimplements LinearSolver<DenseMatrix64F>

The pseudo-inverse is typically used to solve over determined system for which there is no unique solution.

x=inv(A^{T}A)A^{T}b

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

^{T}A matrix is singular. However the Cholesky implementation is much faster.

### 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`

**solve**(DenseMatrix64F b, DenseMatrix64F x)Solves for X in the linear system, A*X=B.

### 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).

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