/*
 * Licensed to the Apache Software Foundation (ASF) under one or more
 * contributor license agreements.  See the NOTICE file distributed with
 * this work for additional information regarding copyright ownership.
 * The ASF licenses this file to You 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.apache.commons.math3.linear;

import org.apache.commons.math3.exception.DimensionMismatchException;
import org.apache.commons.math3.exception.MaxCountExceededException;
import org.apache.commons.math3.exception.NullArgumentException;
import org.apache.commons.math3.util.IterationManager;
import org.apache.commons.math3.util.MathUtils;

/**
 * This abstract class defines preconditioned iterative solvers. When A is ill-conditioned, instead
 * of solving system A &middot; x = b directly, it is preferable to solve either <center> (M
 * &middot; A) &middot; x = M &middot; b </center> (left preconditioning), or <center> (A &middot;
 * M) &middot; y = b, &nbsp;&nbsp;&nbsp;&nbsp;followed by M &middot; y = x </center> (right
 * preconditioning), where M approximates in some way A<sup>-1</sup>, while matrix-vector products
 * of the type M &middot; y remain comparatively easy to compute. In this library, M (not
 * M<sup>-1</sup>!) is called the <em>preconditionner</em>.
 *
 * <p>Concrete implementations of this abstract class must be provided with the preconditioner M, as
 * a {@link RealLinearOperator}.
 *
 * @since 3.0
 */
public abstract class PreconditionedIterativeLinearSolver extends IterativeLinearSolver {

    /**
     * Creates a new instance of this class, with default iteration manager.
     *
     * @param maxIterations the maximum number of iterations
     */
    public PreconditionedIterativeLinearSolver(final int maxIterations) {
        super(maxIterations);
    }

    /**
     * Creates a new instance of this class, with custom iteration manager.
     *
     * @param manager the custom iteration manager
     * @throws NullArgumentException if {@code manager} is {@code null}
     */
    public PreconditionedIterativeLinearSolver(final IterationManager manager)
            throws NullArgumentException {
        super(manager);
    }

    /**
     * Returns an estimate of the solution to the linear system A &middot; x = b.
     *
     * @param a the linear operator A of the system
     * @param m the preconditioner, M (can be {@code null})
     * @param b the right-hand side vector
     * @param x0 the initial guess of the solution
     * @return a new vector containing the solution
     * @throws NullArgumentException if one of the parameters is {@code null}
     * @throws NonSquareOperatorException if {@code a} or {@code m} is not square
     * @throws DimensionMismatchException if {@code m}, {@code b} or {@code x0} have dimensions
     *     inconsistent with {@code a}
     * @throws MaxCountExceededException at exhaustion of the iteration count, unless a custom
     *     {@link org.apache.commons.math3.util.Incrementor.MaxCountExceededCallback callback} has
     *     been set at construction of the {@link IterationManager}
     */
    public RealVector solve(
            final RealLinearOperator a,
            final RealLinearOperator m,
            final RealVector b,
            final RealVector x0)
            throws NullArgumentException,
                    NonSquareOperatorException,
                    DimensionMismatchException,
                    MaxCountExceededException {
        MathUtils.checkNotNull(x0);
        return solveInPlace(a, m, b, x0.copy());
    }

    /** {@inheritDoc} */
    @Override
    public RealVector solve(final RealLinearOperator a, final RealVector b)
            throws NullArgumentException,
                    NonSquareOperatorException,
                    DimensionMismatchException,
                    MaxCountExceededException {
        MathUtils.checkNotNull(a);
        final RealVector x = new ArrayRealVector(a.getColumnDimension());
        x.set(0.);
        return solveInPlace(a, null, b, x);
    }

    /** {@inheritDoc} */
    @Override
    public RealVector solve(final RealLinearOperator a, final RealVector b, final RealVector x0)
            throws NullArgumentException,
                    NonSquareOperatorException,
                    DimensionMismatchException,
                    MaxCountExceededException {
        MathUtils.checkNotNull(x0);
        return solveInPlace(a, null, b, x0.copy());
    }

    /**
     * Performs all dimension checks on the parameters of {@link #solve(RealLinearOperator,
     * RealLinearOperator, RealVector, RealVector) solve} and {@link
     * #solveInPlace(RealLinearOperator, RealLinearOperator, RealVector, RealVector) solveInPlace},
     * and throws an exception if one of the checks fails.
     *
     * @param a the linear operator A of the system
     * @param m the preconditioner, M (can be {@code null})
     * @param b the right-hand side vector
     * @param x0 the initial guess of the solution
     * @throws NullArgumentException if one of the parameters is {@code null}
     * @throws NonSquareOperatorException if {@code a} or {@code m} is not square
     * @throws DimensionMismatchException if {@code m}, {@code b} or {@code x0} have dimensions
     *     inconsistent with {@code a}
     */
    protected static void checkParameters(
            final RealLinearOperator a,
            final RealLinearOperator m,
            final RealVector b,
            final RealVector x0)
            throws NullArgumentException, NonSquareOperatorException, DimensionMismatchException {
        checkParameters(a, b, x0);
        if (m != null) {
            if (m.getColumnDimension() != m.getRowDimension()) {
                throw new NonSquareOperatorException(m.getColumnDimension(), m.getRowDimension());
            }
            if (m.getRowDimension() != a.getRowDimension()) {
                throw new DimensionMismatchException(m.getRowDimension(), a.getRowDimension());
            }
        }
    }

    /**
     * Returns an estimate of the solution to the linear system A &middot; x = b.
     *
     * @param a the linear operator A of the system
     * @param m the preconditioner, M (can be {@code null})
     * @param b the right-hand side vector
     * @return a new vector containing the solution
     * @throws NullArgumentException if one of the parameters is {@code null}
     * @throws NonSquareOperatorException if {@code a} or {@code m} is not square
     * @throws DimensionMismatchException if {@code m} or {@code b} have dimensions inconsistent
     *     with {@code a}
     * @throws MaxCountExceededException at exhaustion of the iteration count, unless a custom
     *     {@link org.apache.commons.math3.util.Incrementor.MaxCountExceededCallback callback} has
     *     been set at construction of the {@link IterationManager}
     */
    public RealVector solve(RealLinearOperator a, RealLinearOperator m, RealVector b)
            throws NullArgumentException,
                    NonSquareOperatorException,
                    DimensionMismatchException,
                    MaxCountExceededException {
        MathUtils.checkNotNull(a);
        final RealVector x = new ArrayRealVector(a.getColumnDimension());
        return solveInPlace(a, m, b, x);
    }

    /**
     * Returns an estimate of the solution to the linear system A &middot; x = b. The solution is
     * computed in-place (initial guess is modified).
     *
     * @param a the linear operator A of the system
     * @param m the preconditioner, M (can be {@code null})
     * @param b the right-hand side vector
     * @param x0 the initial guess of the solution
     * @return a reference to {@code x0} (shallow copy) updated with the solution
     * @throws NullArgumentException if one of the parameters is {@code null}
     * @throws NonSquareOperatorException if {@code a} or {@code m} is not square
     * @throws DimensionMismatchException if {@code m}, {@code b} or {@code x0} have dimensions
     *     inconsistent with {@code a}
     * @throws MaxCountExceededException at exhaustion of the iteration count, unless a custom
     *     {@link org.apache.commons.math3.util.Incrementor.MaxCountExceededCallback callback} has
     *     been set at construction of the {@link IterationManager}
     */
    public abstract RealVector solveInPlace(
            RealLinearOperator a, RealLinearOperator m, RealVector b, RealVector x0)
            throws NullArgumentException,
                    NonSquareOperatorException,
                    DimensionMismatchException,
                    MaxCountExceededException;

    /** {@inheritDoc} */
    @Override
    public RealVector solveInPlace(
            final RealLinearOperator a, final RealVector b, final RealVector x0)
            throws NullArgumentException,
                    NonSquareOperatorException,
                    DimensionMismatchException,
                    MaxCountExceededException {
        return solveInPlace(a, null, b, x0);
    }
}