## Interface LinearSolver<T extends Matrix64F>

- All Known Subinterfaces:
- AdjustableLinearSolver

- All Known Implementing Classes:
- AdjLinearSolverQr, BaseLinearSolverQrp, BlockCholeskyOuterSolver, BlockQrHouseHolderSolver, LinearSolverAbstract, LinearSolverChol, LinearSolverCholBlock64, LinearSolverCholLDL, LinearSolverLu, LinearSolverLuBase, LinearSolverLuKJI, LinearSolverQr, LinearSolverQrBlock64, LinearSolverQrHouse, LinearSolverQrHouseCol, LinearSolverQrHouseTran, LinearSolverQrpHouseCol, LinearSolverSafe, LinearSolverUnrolled, SolvePseudoInverseQrp, SolvePseudoInverseSvd, WrapLinearSolverBlock64

`public interface LinearSolver<T extends Matrix64F>`

An implementation of LinearSolver solves a linear system or inverts a matrix. It masks more complex implementation details, while giving the programmer control over memory management and performance. To quickly detect nearly singular matrices without computing the SVD the

`quality()`

function is provided.A linear system is defined as: A*X = B.

where A ∈ ℜ^{m × n}, X ∈ ℜ^{n × p}, B ∈ ℜ^{m × p}. Different implementations can solve different types and shapes in input matrices and have different memory and runtime performance.To solve a system:

To invert a matrix:

A matrix can also be inverted by passing in an identity matrix to solve, but this will be slower and more memory intensive than the specialized invert() function.

**IMPORTANT:**Depending upon the implementation, input matrices might be overwritten by the solver. This reduces memory and computational requirements and give more control to the programmer. If the input matrices need to be not modified then`LinearSolverSafe`

can be used. The functions`modifiesA()`

and`modifiesB()`

specify which input matrices are being modified.

### Method Summary

Methods Modifier and Type Method and Description `void`

**invert**(T A_inv)Computes the inverse of of the 'A' matrix passed into`setA(org.ejml.data.Matrix64F)`

and writes the results to the provided matrix.`boolean`

**modifiesA**()Returns true if the passed in matrix to`setA(org.ejml.data.Matrix64F)`

is modified.`boolean`

**modifiesB**()Returns true if the passed in 'B' matrix to`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**(T A)Specifies the A matrix in the linear equation.`void`

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

### Method Detail

#### setA

boolean setA(T A)

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

`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.

- Parameters:
`A`

- The 'A' matrix in the linear equation. Might be modified or save the reference.- Returns:
- true if it can be processed.

#### quality

double quality()

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.

- Returns:
- The quality of the linear system.

#### solve

void solve(T B, T X)

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

`modifiesB()`

to determine if 'B' is modified.- Parameters:
`B`

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

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

#### invert

void invert(T A_inv)

Computes the inverse of of the 'A' matrix passed into`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.- Parameters:
`A_inv`

- Where the inverted matrix saved. Modified.

#### modifiesA

boolean modifiesA()

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

is modified.- Returns:
- true if A is modified in setA().

#### modifiesB

boolean modifiesB()

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

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

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