org.apache.commons.math.linear

Interface FieldDecompositionSolver<T extends FieldElement<T>>

Type Parameters:

T - the type of the field elements

public interface FieldDecompositionSolver<T extends FieldElement<T>>

Interface handling decomposition algorithms that can solve A × X = B.

Decomposition algorithms decompose an A matrix has a product of several specific matrices from which they can solve A × X = B in least squares sense: they find X such that ||A × X - B|| is minimal.

Some solvers like LUDecomposition can only find the solution for square matrices and when the solution is an exact linear solution, i.e. when ||A × X - B|| is exactly 0. Other solvers can also find solutions with non-square matrix A and with non-null minimal norm. If an exact linear solution exists it is also the minimal norm solution.

Since:

2.0

Method Summary

Modifier and Type	Method and Description
FieldMatrix<T>	getInverse() Get the inverse (or pseudo-inverse) of the decomposed matrix.
boolean	isNonSingular() Check if the decomposed matrix is non-singular.
FieldMatrix<T>	solve(FieldMatrix<T> b) Solve the linear equation A × X = B for matrices A.
FieldVector<T>	solve(FieldVector<T> b) Solve the linear equation A × X = B for matrices A.
T[]	solve(T[] b) Solve the linear equation A × X = B for matrices A.

Method Detail

solve

T[] solve(T[] b)
   throws java.lang.IllegalArgumentException,
          InvalidMatrixException

Solve the linear equation A × X = B for matrices A.

The A matrix is implicit, it is provided by the underlying decomposition algorithm.

Parameters:

b - right-hand side of the equation A × X = B

Returns:

a vector X that minimizes the two norm of A × X - B

Throws:

java.lang.IllegalArgumentException - if matrices dimensions don't match

InvalidMatrixException - if decomposed matrix is singular

solve

FieldVector<T> solve(FieldVector<T> b)
              throws java.lang.IllegalArgumentException,
                     InvalidMatrixException

Solve the linear equation A × X = B for matrices A.

The A matrix is implicit, it is provided by the underlying decomposition algorithm.

Parameters:

b - right-hand side of the equation A × X = B

Returns:

a vector X that minimizes the two norm of A × X - B

Throws:

java.lang.IllegalArgumentException - if matrices dimensions don't match

InvalidMatrixException - if decomposed matrix is singular

solve

FieldMatrix<T> solve(FieldMatrix<T> b)
              throws java.lang.IllegalArgumentException,
                     InvalidMatrixException

Solve the linear equation A × X = B for matrices A.

The A matrix is implicit, it is provided by the underlying decomposition algorithm.

Parameters:

b - right-hand side of the equation A × X = B

Returns:

a matrix X that minimizes the two norm of A × X - B

Throws:

java.lang.IllegalArgumentException - if matrices dimensions don't match

InvalidMatrixException - if decomposed matrix is singular

isNonSingular

boolean isNonSingular()

Check if the decomposed matrix is non-singular.

Returns:

true if the decomposed matrix is non-singular

getInverse

FieldMatrix<T> getInverse()
                   throws InvalidMatrixException

Get the inverse (or pseudo-inverse) of the decomposed matrix.

Returns:

inverse matrix

Throws:

InvalidMatrixException - if decomposed matrix is singular