org.apache.commons.math.linear
Interface FieldDecompositionSolver<T extends FieldElement<T>>

Type Parameters:
T - the type of the field elements
All Known Implementing Classes:
FieldLUDecompositionImpl.Solver

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
Version:
$Revision: 781122 $ $Date: 2009-06-02 20:53:23 +0200 (mar. 02 juin 2009) $

Method Summary
 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


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