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package org.apache.commons.math3.linear;

import org.apache.commons.math3.FieldElement;


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 FieldLUDecomposition 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.
Type parameters:
<T> – the type of the field elements
Since:
2.0/**
 * Interface handling decomposition algorithms that can solve A &times; X = B.
 * <p>Decomposition algorithms decompose an A matrix has a product of several specific
 * matrices from which they can solve A &times; X = B in least squares sense: they find X
 * such that ||A &times; X - B|| is minimal.</p>
 * <p>Some solvers like {@link FieldLUDecomposition} can only find the solution for
 * square matrices and when the solution is an exact linear solution, i.e. when
 * ||A &times; 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.</p>
 *
 * @param <T> the type of the field elements
 * @since 2.0
 */
public interface FieldDecompositionSolver<T extends FieldElement<T>> {

    
Solve the linear equation A × X = B for matrices A.
The A matrix is implicit, it is provided by the underlying
decomposition algorithm.
Params:
b – right-hand side of the equation A × X = B
Throws:
DimensionMismatchException – 
if the matrices dimensions do not match.
SingularMatrixException – 
if the decomposed matrix is singular.
Returns:
a vector X that minimizes the two norm of A × X - B/** Solve the linear equation A &times; X = B for matrices A.
     * <p>The A matrix is implicit, it is provided by the underlying
     * decomposition algorithm.</p>
     * @param b right-hand side of the equation A &times; X = B
     * @return a vector X that minimizes the two norm of A &times; X - B
     * @throws org.apache.commons.math3.exception.DimensionMismatchException
     * if the matrices dimensions do not match.
     * @throws SingularMatrixException
     * if the decomposed matrix is singular.
     */
    FieldVector<T> solve(final FieldVector<T> b);

    
Solve the linear equation A × X = B for matrices A.
The A matrix is implicit, it is provided by the underlying
decomposition algorithm.
Params:
b – right-hand side of the equation A × X = B
Throws:
DimensionMismatchException – 
if the matrices dimensions do not match.
SingularMatrixException – 
if the decomposed matrix is singular.
Returns:
a matrix X that minimizes the two norm of A × X - B/** Solve the linear equation A &times; X = B for matrices A.
     * <p>The A matrix is implicit, it is provided by the underlying
     * decomposition algorithm.</p>
     * @param b right-hand side of the equation A &times; X = B
     * @return a matrix X that minimizes the two norm of A &times; X - B
     * @throws org.apache.commons.math3.exception.DimensionMismatchException
     * if the matrices dimensions do not match.
     * @throws SingularMatrixException
     * if the decomposed matrix is singular.
     */
    FieldMatrix<T> solve(final FieldMatrix<T> b);

    
Check if the decomposed matrix is non-singular.
Returns:
true if the decomposed matrix is non-singular/**
     * Check if the decomposed matrix is non-singular.
     * @return true if the decomposed matrix is non-singular
     */
    boolean isNonSingular();

    
Get the inverse (or pseudo-inverse) of the decomposed matrix.
Throws:
SingularMatrixException – 
if the decomposed matrix is singular.
Returns:
inverse matrix/** Get the inverse (or pseudo-inverse) of the decomposed matrix.
     * @return inverse matrix
     * @throws SingularMatrixException
     * if the decomposed matrix is singular.
     */
    FieldMatrix<T> getInverse();
}