org.ejml.interfaces.linsol.LinearSolver Maven / Gradle / Ivy
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/*
* Copyright (c) 2009-2014, Peter Abeles. All Rights Reserved.
*
* This file is part of Efficient Java Matrix Library (EJML).
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
package org.ejml.interfaces.linsol;
import org.ejml.data.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 {@link #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:
*
* - Call {@link #setA(org.ejml.data.Matrix64F)}
*
- Call {@link #solve(org.ejml.data.Matrix64F, org.ejml.data.Matrix64F)}.
*
*
*
*
* To invert a matrix:
*
* - Call {@link #setA(org.ejml.data.Matrix64F)}
*
- Call {@link #invert(org.ejml.data.Matrix64F)}.
*
* 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 {@link org.ejml.alg.dense.linsol.LinearSolverSafe} can be used. The
* functions {@link #modifiesA()} and {@link #modifiesB()} specify which input matrices are being
* modified.
*
*
* @author Peter Abeles
*/
public interface LinearSolver< T extends Matrix64F> {
/**
*
* 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 {@link #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.
*
*
* @param A The 'A' matrix in the linear equation. Might be modified or save the reference.
* @return true if it can be processed.
*/
public boolean setA( T A );
/**
*
* 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.
*
*
* @return The quality of the linear system.
*/
public double quality();
/**
*
* 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
* {@link #modifiesB()} to determine if 'B' is modified.
*
*
* @param B A matrix ℜ m × p. Might be modified.
* @param X A matrix ℜ n × p, where the solution is written to. Modified.
*/
public void solve( T B , T X );
/**
* Computes the inverse of of the 'A' matrix passed into {@link #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.
*
* @param A_inv Where the inverted matrix saved. Modified.
*/
public void invert( T A_inv );
/**
* Returns true if the passed in matrix to {@link #setA(org.ejml.data.Matrix64F)}
* is modified.
*
* @return true if A is modified in setA().
*/
public boolean modifiesA();
/**
* Returns true if the passed in 'B' matrix to {@link #solve(org.ejml.data.Matrix64F, org.ejml.data.Matrix64F)}
* is modified.
*
* @return true if B is modified in solve(B,X).
*/
public boolean modifiesB();
}