/*
 * Copyright (c) 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.decomposition.qr;

import org.ejml.data.DMatrixRMaj;
import org.ejml.dense.row.CommonOps_DDRM;
import org.jetbrains.annotations.Nullable;

/**
 * <p>
 * The effects of adding and removing rows from the A matrix in a QR decomposition can
 * be computed much faster than simply recomputing the whole decomposition.  There are many real
 * world situations where this is useful.  For example, when computing a rolling solution to
 * the most recent N measurements.
 * </p>
 *
 * <p>
 * Definitions: A &isin; &real; <sup>m &times; n</sup>, m &ge; n, rank(A) = n and that A = QR, where
 * Q &isin; &real; <sup>m &times; m</sup> is orthogonal, and R &isin; &real; <sup>m &times; n</sup> is
 * upper triangular.
 * </p>
 *
 * <p>
 * ** IMPORTANT USAGE NOTE ** If auto grow is set to true then the internal data structures will grow automatically
 * to accommodate the matrices passed in.  When adding elements to the decomposition the matrices must have enough
 * data elements to grow before hand.
 * </p>
 *
 * <p>
 * For more information see David S. Watkins, "Fundamentals of Matrix Computations" 2nd edition, pages 249-259.
 * It is also possible to add and remove columns efficiently, but this is less common and is not supported at
 * this time.
 * </p>
 *
 * @author Peter Abeles
 */
@SuppressWarnings("NullAway")
public class QrUpdate_DDRM {

    // the decomposition that is being adjusted
    private @Nullable DMatrixRMaj Q, R;
    // product of planar multiplications
    private DMatrixRMaj U_tran; // using transpose of U reduces cache misses
    private DMatrixRMaj Qm;

    // used to temporarially store data
    private double[] r_row;

    // it can process matrices up to this size
    private int maxCols;
    private int maxRows;

    // number of rows and columns in the original A matrix that was decomposed
    private int m, n;
    // number of rows in the adjusted matrices
    private int m_m;

    // should it declare new internal data when what currently exists is too small or throw
    // and exception.
    private boolean autoGrow;

    /**
     * Creates an update which can decompose matrices up to the specified size.  Autogrow
     * is set to false.
     */
    public QrUpdate_DDRM( int maxRows, int maxCols ) {
        autoGrow = false;
        declareInternalData(maxRows, maxCols);
    }

    /**
     * Creates an update which can decompose matrices up to the specified size.  Autogrow
     * is configurable.
     */
    public QrUpdate_DDRM( int maxRows, int maxCols, boolean autoGrow ) {
        this.autoGrow = autoGrow;
        declareInternalData(maxRows, maxCols);
    }

    /**
     * Does not predeclare data and it will autogrow.
     */
    public QrUpdate_DDRM() {
        autoGrow = true;
    }

    /**
     * Declares the internal data structures so that it can process matrices up to the specified size.
     */
    public void declareInternalData( int maxRows, int maxCols ) {
        this.maxRows = maxRows;
        this.maxCols = maxCols;

        U_tran = new DMatrixRMaj(maxRows, maxRows);
        Qm = new DMatrixRMaj(maxRows, maxRows);

        r_row = new double[maxCols];
    }

    /**
     * <p>
     * Adjusts the values of the Q and R matrices to take in account the effects of inserting
     * a row to the 'A' matrix at the specified location.  This operation requires about 6mn + O(n) flops.
     * </p>
     *
     * <p>
     * If Q and/or R does not have enough data elements to grow then an exception is thrown.
     * </p>
     *
     * <p>
     * The adjustment done is by computing a series of planar Givens rotations that make the adjusted R
     * matrix upper triangular again.  This is then used to modify the Q matrix.
     * </p>
     *
     * @param Q The Q matrix which is to be modified, must be big enough to grow.  Must be n by n..  Is modified.
     * @param R The R matrix which is to be modified, must be big enough to grow.  Must be m by n.  Is modified.
     * @param row The row being inserted.  Not modified.
     * @param rowIndex Which row index it is to be inserted at.
     * @param resizeR Should the number of rows in R be changed?  The additional rows are all zero.
     */
    public void addRow( DMatrixRMaj Q, DMatrixRMaj R, double[] row, int rowIndex, boolean resizeR ) {
        // memory management and check precoditions
        setQR(Q, R, 1);
        m_m = m + 1;

        if (Q.data.length < m_m*m_m)
            throw new IllegalArgumentException("Q matrix does not have enough data to grow");

        if (resizeR && R.data.length < m_m*n)
            throw new IllegalArgumentException("R matrix does not have enough data to grow");

        if (resizeR)
            R.reshape(m_m, n, false);

        U_tran.reshape(m_m, m_m, false);

        // apply givens rotation to the first two rows of the augmented R matrix
        applyFirstGivens(row);
        applyLaterGivens();
        // compute new Q matrix
        updateInsertQ(rowIndex);

        // discard the reference since it is no longer needed
        this.Q = this.R = null;
    }

    /**
     * <p>
     * Adjusts the values of the Q and R matrices to take in account the effects of removing
     * a row from the 'A' matrix at the specified location.  This operation requires about 6mn + O(n) flops.
     * </p>
     *
     * <p>
     * The adjustment is done by computing a series of planar Givens rotations that make the removed row in Q
     * equal to [1 0 ... 0].
     * </p>
     *
     * @param Q The Q matrix.  Is modified.
     * @param R The R matrix.  Is modified.
     * @param rowIndex Which index of the row that is being removed.
     * @param resizeR should the shape of R be adjusted?
     */
    public void deleteRow( DMatrixRMaj Q, DMatrixRMaj R, int rowIndex, boolean resizeR ) {
        setQR(Q, R, 0);
        if (m - 1 < n) {
            throw new IllegalArgumentException("Removing any row would make the system under determined.");
        }

        m_m = m - 1;
        U_tran.reshape(m, m, false);

        if (resizeR)
            R.reshape(m_m, n, false);

        computeRemoveGivens(rowIndex);
        updateRemoveQ(rowIndex);

        updateRemoveR();

        // discard the reference since it is no longer needed
        this.Q = this.R = null;
    }

    /**
     * Provides the results of a QR decomposition.  These will be modified by adding or removing
     * rows from the original 'A' matrix.
     *
     * @param Q The Q matrix which is to be modified.  Is modified later and reference saved.
     * @param R The R matrix which is to be modified.  Is modified later and reference saved.
     */
    private void setQR( DMatrixRMaj Q, DMatrixRMaj R, int growRows ) {
        if (Q.numRows != Q.numCols) {
            throw new IllegalArgumentException("Q should be square.");
        }

        this.Q = Q;
        this.R = R;

        m = Q.numRows;
        n = R.numCols;

        if (m + growRows > maxRows || n > maxCols) {
            if (autoGrow) {
                declareInternalData(m + growRows, n);
            } else {
                throw new IllegalArgumentException("Autogrow has been set to false and the maximum number of rows" +
                        " or columns has been exceeded.");
            }
        }
    }

    /**
     * Updates the Q matrix to take in account the inserted matrix.
     *
     * @param rowIndex where the matrix has been inserted.
     */
    private void updateInsertQ( int rowIndex ) {
        Qm.setTo(Q);
        Q.reshape(m_m, m_m, false);

        for (int i = 0; i < rowIndex; i++) {
            for (int j = 0; j < m_m; j++) {
                double sum = 0;
                for (int k = 0; k < m; k++) {
                    sum += Qm.data[i*m + k]*U_tran.data[j*m_m + k + 1];
                }
                Q.data[i*m_m + j] = sum;
            }
        }

        for (int j = 0; j < m_m; j++) {
            Q.data[rowIndex*m_m + j] = U_tran.data[j*m_m];
        }

        for (int i = rowIndex + 1; i < m_m; i++) {
            for (int j = 0; j < m_m; j++) {
                double sum = 0;
                for (int k = 0; k < m; k++) {
                    sum += Qm.data[(i - 1)*m + k]*U_tran.data[j*m_m + k + 1];
                }
                Q.data[i*m_m + j] = sum;
            }
        }
    }

    /**
     * Updates the Q matrix to take in account the row that was removed by only multiplying elements that need to be.
     * There is still some room for improvement here...
     */
    private void updateRemoveQ( int rowIndex ) {
        Qm.setTo(Q);
        Q.reshape(m_m, m_m, false);

        for (int i = 0; i < rowIndex; i++) {
            for (int j = 1; j < m; j++) {
                double sum = 0;
                for (int k = 0; k < m; k++) {
                    sum += Qm.data[i*m + k]*U_tran.data[j*m + k];
                }
                Q.data[i*m_m + j - 1] = sum;
            }
        }

        for (int i = rowIndex + 1; i < m; i++) {
            for (int j = 1; j < m; j++) {
                double sum = 0;
                for (int k = 0; k < m; k++) {
                    sum += Qm.data[i*m + k]*U_tran.data[j*m + k];
                }
                Q.data[(i - 1)*m_m + j - 1] = sum;
            }
        }
    }

    /**
     * Updates the R matrix to take in account the removed row.
     */
    private void updateRemoveR() {
        for (int i = 1; i < n + 1; i++) {
            for (int j = 0; j < n; j++) {
                double sum = 0;
                for (int k = i - 1; k <= j; k++) {
                    sum += U_tran.data[i*m + k]*R.data[k*n + j];
                }
                R.data[(i - 1)*n + j] = sum;
            }
        }
    }

    private void applyFirstGivens( double[] row ) {
        double c, s;
        double xi = row[0];
        double xj = R.data[0];

        double r = xi*xi + xj*xj;
        if (r != 0) {
            r = Math.sqrt(r);
            c = xi/r;
            s = xj/r;
        } else {
            c = 1;
            s = 0;
        }

        R.data[0] = r;
        for (int col = 1; col < n; col++) {
            double vali = row[col];
            double valj = R.data[col];

            R.data[col] = c*vali + s*valj;
            r_row[col] = c*valj - s*vali;
        }

        // set U to its initial values
        CommonOps_DDRM.setIdentity(U_tran);
        U_tran.data[0] = c;
        U_tran.data[1] = s;
        U_tran.data[m_m] = -s;
        U_tran.data[m_m + 1] = c;
    }

    private void applyLaterGivens() {
        for (int row = 1; row < n; row++) {
            // first compute the rotation
            double c, s;
            double xi = r_row[row];
            double xj = R.data[n*row + row];

            double r = xi*xi + xj*xj;
            if (r != 0) {
                r = Math.sqrt(r);
                c = xi/r;
                s = xj/r;
            } else {
                c = 1;
                s = 0;
            }

            // update R matrix
            R.data[n*row + row] = r;
            for (int col = row + 1; col < n; col++) {
                double vali = r_row[col];
                double valj = R.data[n*row + col];

                R.data[n*row + col] = c*vali + s*valj;
                r_row[col] = c*valj - s*vali;
            }

            // compute U^T = U^T_(x+1) * U^T_x
            for (int col = 0; col <= row + 1; col++) {
                double q1 = U_tran.data[row*m_m + col];
                double q2 = U_tran.data[(row + 1)*m_m + col];

                U_tran.data[row*m_m + col] = c*q1 + s*q2;
                U_tran.data[(row + 1)*m_m + col] = c*q2 - s*q1;
            }
        }
    }

    private void computeRemoveGivens( int selectedRow ) {
        CommonOps_DDRM.setIdentity(U_tran);

        double xj = Q.data[selectedRow*m + m - 1];

        for (int j = m - 2; j >= 0; j--) {
            // first compute the rotation
            double c, s;
            double xi = Q.data[selectedRow*m + j];

            double r = xi*xi + xj*xj;
            if (r != 0) {
                r = Math.sqrt(r);
                c = xi/r;
                s = xj/r;
            } else {
                c = 1;
                s = 0;
            }

            // in the next iteration xj is r
            xj = r;

            // compute U^T = U^T_(x+1) * U^T_x
            for (int col = j; col < m; col++) {
                double q1 = U_tran.data[j*m + col];
                double q2 = U_tran.data[(j + 1)*m + col];

                U_tran.data[j*m + col] = c*q1 + s*q2;
                U_tran.data[(j + 1)*m + col] = c*q2 - s*q1;
            }
        }
    }

    public DMatrixRMaj getU_tran() {
        return U_tran;
    }
}
