/*
 * Copyright (c) 2009-2020, 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.dense.row.misc;

import org.ejml.data.DMatrix1Row;
import org.ejml.data.DMatrixRMaj;

/**
 * <p>
 * Computes the determinant of a matrix using Laplace expansion.  This is done
 * using minor matrices as is shown below:<br>
 * <br>
 * |A| = Sum{ i=1:k ; a<sub>ij</sub> C<sub>ij</sub> }<br>
 * <br>
 * C<sub>ij</sub> = (-1)<sup>i+j</sup> M<sub>ij</sub><br>
 * <br>
 * Where M_ij is the minor of matrix A formed by eliminating row i and column j from A.
 * </p>
 *
 * <p>
 * This is significantly more computationally expensive than using LU decomposition, but
 * its computation has the advantage being independent of the matrices value.
 * </p>
 *
 * @author Peter Abeles
 * @see org.ejml.dense.row.decomposition.lu.LUDecompositionAlt_DDRM
 */
public class DeterminantFromMinor_DDRM {

    // how wide the square matrix is
    private final int width;

    // used to decide at which point it uses a direct algorithm to compute the determinant
    private final int minWidth;

    // used to keep track of which submatrix it is computing the results for
    private final int[] levelIndexes;
    // the results at different levels of minor matrices
    private final double[] levelResults;
    // which columns where removed at what level
    private final int[] levelRemoved;

    // columns that are currently open
    private final int[] open;
    private int numOpen;
    // a minor matrix which is created at the lowest level
    private final DMatrixRMaj tempMat;

    private boolean dirty = false;

    /**
     * @param width The width of the matrices that it will be computing the determinant for
     */
    public DeterminantFromMinor_DDRM( int width ) {
        this(width, 5);
    }

    /**
     * @param width The width of the matrices that it will be computing the determinant for
     * @param minWidth At which point should it use a predefined function to compute the determinant.
     */
    public DeterminantFromMinor_DDRM( int width, int minWidth ) {
        if (minWidth > 5 || minWidth < 2) {
            throw new IllegalArgumentException("No direct function for that width");
        }

        if (width < minWidth)
            minWidth = width;

        this.minWidth = minWidth;
        this.width = width;

        int numLevels = width - (minWidth - 2);

        levelResults = new double[numLevels];
        levelRemoved = new int[numLevels];
        levelIndexes = new int[numLevels];

        open = new int[width];

        tempMat = new DMatrixRMaj(minWidth - 1, minWidth - 1);
    }

    /**
     * Computes the determinant for the specified matrix.  It must be square and have
     * the same width and height as what was specified in the constructor.
     *
     * @param mat The matrix whose determinant is to be computed.
     * @return The determinant.
     */
    public double compute( DMatrix1Row mat ) {
        if (width != mat.numCols || width != mat.numRows) {
            throw new RuntimeException("Unexpected matrix dimension");
        }

        // make sure everything is in the proper state before it starts
        initStructures();

//        System.arraycopy(mat.data,0,minorMatrix[0],0,mat.data.length);

        int level = 0;
        while (true) {
            int levelWidth = width - level;
            int levelIndex = levelIndexes[level];

            if (levelIndex == levelWidth) {
                if (level == 0) {
                    return levelResults[0];
                }
                int prevLevelIndex = levelIndexes[level - 1]++;

                double val = mat.get((level - 1)*width + levelRemoved[level - 1]);
                if (prevLevelIndex%2 == 0) {
                    levelResults[level - 1] += val*levelResults[level];
                } else {
                    levelResults[level - 1] -= val*levelResults[level];
                }

                putIntoOpen(level - 1);

                levelResults[level] = 0;
                levelIndexes[level] = 0;
                level--;
            } else {
                int excluded = openRemove(levelIndex);

                levelRemoved[level] = excluded;

                if (levelWidth == minWidth) {
                    createMinor(mat);
                    double subresult = mat.get(level*width + levelRemoved[level]);

                    subresult *= UnrolledDeterminantFromMinor_DDRM.det(tempMat);

                    if (levelIndex%2 == 0) {
                        levelResults[level] += subresult;
                    } else {
                        levelResults[level] -= subresult;
                    }

                    // put it back into the list
                    putIntoOpen(level);
                    levelIndexes[level]++;
                } else {
                    level++;
                }
            }
        }
    }

    private void initStructures() {
        for (int i = 0; i < width; i++) {
            open[i] = i;
        }
        numOpen = width;

        if (dirty) {
            for (int i = 0; i < levelIndexes.length; i++) {
                levelIndexes[i] = 0;
                levelResults[i] = 0;
                levelRemoved[i] = 0;
            }
        }
        dirty = true;
    }

    private int openRemove( int where ) {
        int val = open[where];

        System.arraycopy(open, where + 1, open, where, (numOpen - where - 1));
        numOpen--;

        return val;
    }

    private void openAdd( int where, int val ) {
        for (int i = numOpen; i > where; i--) {
            open[i] = open[i - 1];
        }
        numOpen++;
        open[where] = val;
    }

    private void openAdd( int val ) {
        open[numOpen++] = val;
    }

    private void putIntoOpen( int level ) {
        boolean added = false;
        for (int i = 0; i < numOpen; i++) {
            if (open[i] > levelRemoved[level]) {
                added = true;
                openAdd(i, levelRemoved[level]);
                break;
            }
        }
        if (!added) {
            openAdd(levelRemoved[level]);
        }
    }

    private void createMinor( DMatrix1Row mat ) {

        int w = minWidth - 1;
        int firstRow = (width - w)*width;

        for (int i = 0; i < numOpen; i++) {
            int col = open[i];
            int srcIndex = firstRow + col;
            int dstIndex = i;

            for (int j = 0; j < w; j++) {
                tempMat.set(dstIndex, mat.get(srcIndex));
                dstIndex += w;
                srcIndex += width;
            }
        }
    }
}
