/* ***** BEGIN LICENSE BLOCK *****
 * Version: MPL 1.1/GPL 2.0/LGPL 2.1
 *
 * The contents of this file are subject to the Mozilla Public License Version
 * 1.1 (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.mozilla.org/MPL/
 *
 * Software distributed under the License is distributed on an "AS IS" basis,
 * WITHOUT WARRANTY OF ANY KIND, either express or implied. See the License
 * for the specific language governing rights and limitations under the
 * License.
 *
 * The Original Code is JTransforms.
 *
 * The Initial Developer of the Original Code is
 * Piotr Wendykier, Emory University.
 * Portions created by the Initial Developer are Copyright (C) 2007-2009
 * the Initial Developer. All Rights Reserved.
 *
 * Alternatively, the contents of this file may be used under the terms of
 * either the GNU General Public License Version 2 or later (the "GPL"), or
 * the GNU Lesser General Public License Version 2.1 or later (the "LGPL"),
 * in which case the provisions of the GPL or the LGPL are applicable instead
 * of those above. If you wish to allow use of your version of this file only
 * under the terms of either the GPL or the LGPL, and not to allow others to
 * use your version of this file under the terms of the MPL, indicate your
 * decision by deleting the provisions above and replace them with the notice
 * and other provisions required by the GPL or the LGPL. If you do not delete
 * the provisions above, a recipient may use your version of this file under
 * the terms of any one of the MPL, the GPL or the LGPL.
 *
 * ***** END LICENSE BLOCK ***** */

package edu.emory.mathcs.jtransforms.fft;

import java.util.concurrent.Future;

import edu.emory.mathcs.utils.ConcurrencyUtils;

/**
 * Computes 2D Discrete Fourier Transform (DFT) of complex and real, double
 * precision data. The sizes of both dimensions can be arbitrary numbers. This
 * is a parallel implementation of split-radix and mixed-radix algorithms
 * optimized for SMP systems. <br>
 * <br>
 * Part of the code is derived from General Purpose FFT Package written by Takuya Ooura
 * (http://www.kurims.kyoto-u.ac.jp/~ooura/fft.html)
 * 
 * @author Piotr Wendykier (piotr.wendykier@gmail.com)
 * 
 */
public class DoubleFFT_2D {

    private int rows;

    private int columns;

    private double[] t;

    private DoubleFFT_1D fftColumns, fftRows;

    private int oldNthreads;

    private int nt;

    private boolean isPowerOfTwo = false;

    private boolean useThreads = false;

    /**
     * Creates new instance of DoubleFFT_2D.
     * 
     * @param rows
     *            number of rows
     * @param columns
     *            number of columns
     */
    public DoubleFFT_2D(int rows, int columns) {
        if (rows <= 1 || columns <= 1) {
            throw new IllegalArgumentException("rows and columns must be greater than 1");
        }
        this.rows = rows;
        this.columns = columns;
        if (rows * columns >= ConcurrencyUtils.getThreadsBeginN_2D()) {
            this.useThreads = true;
        }
        if (ConcurrencyUtils.isPowerOf2(rows) && ConcurrencyUtils.isPowerOf2(columns)) {
            isPowerOfTwo = true;
            oldNthreads = ConcurrencyUtils.getNumberOfThreads();
            nt = 8 * oldNthreads * rows;
            if (2 * columns == 4 * oldNthreads) {
                nt >>= 1;
            } else if (2 * columns < 4 * oldNthreads) {
                nt >>= 2;
            }
            t = new double[nt];
        }
        fftRows = new DoubleFFT_1D(rows);
        if (rows == columns) {
            fftColumns = fftRows;
        } else {
            fftColumns = new DoubleFFT_1D(columns);
        }
    }

    /**
     * Computes 2D forward DFT of complex data leaving the result in
     * <code>a</code>. The data is stored in 1D array in row-major order.
     * Complex number is stored as two double values in sequence: the real and
     * imaginary part, i.e. the input array must be of size rows*2*columns. The
     * physical layout of the input data has to be as follows:<br>
     * 
     * <pre>
     * a[k1*2*columns+2*k2] = Re[k1][k2], 
     * a[k1*2*columns+2*k2+1] = Im[k1][k2], 0&lt;=k1&lt;rows, 0&lt;=k2&lt;columns,
     * </pre>
     * 
     * @param a
     *            data to transform
     */
    public void complexForward(final double[] a) {
        int nthreads = ConcurrencyUtils.getNumberOfThreads();
        if (isPowerOfTwo) {
            int oldn2 = columns;
            columns = 2 * columns;
            if (nthreads != oldNthreads) {
                nt = 8 * nthreads * rows;
                if (columns == 4 * nthreads) {
                    nt >>= 1;
                } else if (columns < 4 * nthreads) {
                    nt >>= 2;
                }
                t = new double[nt];
                oldNthreads = nthreads;
            }
            if ((nthreads > 1) && useThreads) {
                xdft2d0_subth1(0, -1, a, true);
                cdft2d_subth(-1, a, true);
            } else {
                for (int r = 0; r < rows; r++) {
                    fftColumns.complexForward(a, r * columns);
                }
                cdft2d_sub(-1, a, true);
            }
            columns = oldn2;
        } else {
            final int rowStride = 2 * columns;
            if ((nthreads > 1) && useThreads && (rows >= nthreads) && (columns >= nthreads)) {
                Future<?>[] futures = new Future[nthreads];
                int p = rows / nthreads;
                for (int l = 0; l < nthreads; l++) {
                    final int firstRow = l * p;
                    final int lastRow = (l == (nthreads - 1)) ? rows : firstRow + p;
                    futures[l] = ConcurrencyUtils.submit(new Runnable() {
                        @Override
                                                public void run() {
                            for (int r = firstRow; r < lastRow; r++) {
                                fftColumns.complexForward(a, r * rowStride);
                            }
                        }
                    });
                }
                ConcurrencyUtils.waitForCompletion(futures);
                p = columns / nthreads;
                for (int l = 0; l < nthreads; l++) {
                    final int firstColumn = l * p;
                    final int lastColumn = (l == (nthreads - 1)) ? columns : firstColumn + p;
                    futures[l] = ConcurrencyUtils.submit(new Runnable() {
                        @Override
                                                public void run() {
                            double[] temp = new double[2 * rows];
                            for (int c = firstColumn; c < lastColumn; c++) {
                                int idx0 = 2 * c;
                                for (int r = 0; r < rows; r++) {
                                    int idx1 = 2 * r;
                                    int idx2 = r * rowStride + idx0;
                                    temp[idx1] = a[idx2];
                                    temp[idx1 + 1] = a[idx2 + 1];
                                }
                                fftRows.complexForward(temp);
                                for (int r = 0; r < rows; r++) {
                                    int idx1 = 2 * r;
                                    int idx2 = r * rowStride + idx0;
                                    a[idx2] = temp[idx1];
                                    a[idx2 + 1] = temp[idx1 + 1];
                                }
                            }
                        }
                    });
                }
                ConcurrencyUtils.waitForCompletion(futures);
            } else {
                for (int r = 0; r < rows; r++) {
                    fftColumns.complexForward(a, r * rowStride);
                }
                double[] temp = new double[2 * rows];
                for (int c = 0; c < columns; c++) {
                    int idx0 = 2 * c;
                    for (int r = 0; r < rows; r++) {
                        int idx1 = 2 * r;
                        int idx2 = r * rowStride + idx0;
                        temp[idx1] = a[idx2];
                        temp[idx1 + 1] = a[idx2 + 1];
                    }
                    fftRows.complexForward(temp);
                    for (int r = 0; r < rows; r++) {
                        int idx1 = 2 * r;
                        int idx2 = r * rowStride + idx0;
                        a[idx2] = temp[idx1];
                        a[idx2 + 1] = temp[idx1 + 1];
                    }
                }
            }
        }
    }

    /**
     * Computes 2D forward DFT of complex data leaving the result in
     * <code>a</code>. The data is stored in 2D array. Complex data is
     * represented by 2 double values in sequence: the real and imaginary part,
     * i.e. the input array must be of size rows by 2*columns. The physical
     * layout of the input data has to be as follows:<br>
     * 
     * <pre>
     * a[k1][2*k2] = Re[k1][k2], 
     * a[k1][2*k2+1] = Im[k1][k2], 0&lt;=k1&lt;rows, 0&lt;=k2&lt;columns,
     * </pre>
     * 
     * @param a
     *            data to transform
     */
    public void complexForward(final double[][] a) {
        int nthreads = ConcurrencyUtils.getNumberOfThreads();
        if (isPowerOfTwo) {
            int oldn2 = columns;
            columns = 2 * columns;
            if (nthreads != oldNthreads) {
                nt = 8 * nthreads * rows;
                if (columns == 4 * nthreads) {
                    nt >>= 1;
                } else if (columns < 4 * nthreads) {
                    nt >>= 2;
                }
                t = new double[nt];
                oldNthreads = nthreads;
            }
            if ((nthreads > 1) && useThreads) {
                xdft2d0_subth1(0, -1, a, true);
                cdft2d_subth(-1, a, true);
            } else {
                for (int r = 0; r < rows; r++) {
                    fftColumns.complexForward(a[r]);
                }
                cdft2d_sub(-1, a, true);
            }
            columns = oldn2;
        } else {
            if ((nthreads > 1) && useThreads && (rows >= nthreads) && (columns >= nthreads)) {
                Future<?>[] futures = new Future[nthreads];
                int p = rows / nthreads;
                for (int l = 0; l < nthreads; l++) {
                    final int firstRow = l * p;
                    final int lastRow = (l == (nthreads - 1)) ? rows : firstRow + p;
                    futures[l] = ConcurrencyUtils.submit(new Runnable() {
                        @Override
                                                public void run() {
                            for (int r = firstRow; r < lastRow; r++) {
                                fftColumns.complexForward(a[r]);
                            }
                        }
                    });
                }
                ConcurrencyUtils.waitForCompletion(futures);
                p = columns / nthreads;
                for (int l = 0; l < nthreads; l++) {
                    final int firstColumn = l * p;
                    final int lastColumn = (l == (nthreads - 1)) ? columns : firstColumn + p;
                    futures[l] = ConcurrencyUtils.submit(new Runnable() {
                        @Override
                                                public void run() {
                            double[] temp = new double[2 * rows];
                            for (int c = firstColumn; c < lastColumn; c++) {
                                int idx1 = 2 * c;
                                for (int r = 0; r < rows; r++) {
                                    int idx2 = 2 * r;
                                    temp[idx2] = a[r][idx1];
                                    temp[idx2 + 1] = a[r][idx1 + 1];
                                }
                                fftRows.complexForward(temp);
                                for (int r = 0; r < rows; r++) {
                                    int idx2 = 2 * r;
                                    a[r][idx1] = temp[idx2];
                                    a[r][idx1 + 1] = temp[idx2 + 1];
                                }
                            }
                        }
                    });
                }
                ConcurrencyUtils.waitForCompletion(futures);
            } else {
                for (int r = 0; r < rows; r++) {
                    fftColumns.complexForward(a[r]);
                }
                double[] temp = new double[2 * rows];
                for (int c = 0; c < columns; c++) {
                    int idx1 = 2 * c;
                    for (int r = 0; r < rows; r++) {
                        int idx2 = 2 * r;
                        temp[idx2] = a[r][idx1];
                        temp[idx2 + 1] = a[r][idx1 + 1];
                    }
                    fftRows.complexForward(temp);
                    for (int r = 0; r < rows; r++) {
                        int idx2 = 2 * r;
                        a[r][idx1] = temp[idx2];
                        a[r][idx1 + 1] = temp[idx2 + 1];
                    }
                }
            }
        }
    }

    /**
     * Computes 2D inverse DFT of complex data leaving the result in
     * <code>a</code>. The data is stored in 1D array in row-major order.
     * Complex number is stored as two double values in sequence: the real and
     * imaginary part, i.e. the input array must be of size rows*2*columns. The
     * physical layout of the input data has to be as follows:<br>
     * 
     * <pre>
     * a[k1*2*columns+2*k2] = Re[k1][k2], 
     * a[k1*2*columns+2*k2+1] = Im[k1][k2], 0&lt;=k1&lt;rows, 0&lt;=k2&lt;columns,
     * </pre>
     * 
     * @param a
     *            data to transform
     * @param scale
     *            if true then scaling is performed
     * 
     */
    public void complexInverse(final double[] a, final boolean scale) {
        int nthreads = ConcurrencyUtils.getNumberOfThreads();
        if (isPowerOfTwo) {
            int oldn2 = columns;
            columns = 2 * columns;
            if (nthreads != oldNthreads) {
                nt = 8 * nthreads * rows;
                if (columns == 4 * nthreads) {
                    nt >>= 1;
                } else if (columns < 4 * nthreads) {
                    nt >>= 2;
                }
                t = new double[nt];
                oldNthreads = nthreads;
            }
            if ((nthreads > 1) && useThreads) {
                xdft2d0_subth1(0, 1, a, scale);
                cdft2d_subth(1, a, scale);
            } else {

                for (int r = 0; r < rows; r++) {
                    fftColumns.complexInverse(a, r * columns, scale);
                }
                cdft2d_sub(1, a, scale);
            }
            columns = oldn2;
        } else {
            final int rowspan = 2 * columns;
            if ((nthreads > 1) && useThreads && (rows >= nthreads) && (columns >= nthreads)) {
                Future<?>[] futures = new Future[nthreads];
                int p = rows / nthreads;
                for (int l = 0; l < nthreads; l++) {
                    final int firstRow = l * p;
                    final int lastRow = (l == (nthreads - 1)) ? rows : firstRow + p;
                    futures[l] = ConcurrencyUtils.submit(new Runnable() {
                        @Override
                                                public void run() {
                            for (int r = firstRow; r < lastRow; r++) {
                                fftColumns.complexInverse(a, r * rowspan, scale);
                            }
                        }
                    });
                }
                ConcurrencyUtils.waitForCompletion(futures);
                p = columns / nthreads;
                for (int l = 0; l < nthreads; l++) {
                    final int firstColumn = l * p;
                    final int lastColumn = (l == (nthreads - 1)) ? columns : firstColumn + p;
                    futures[l] = ConcurrencyUtils.submit(new Runnable() {
                        @Override
                                                public void run() {
                            double[] temp = new double[2 * rows];
                            for (int c = firstColumn; c < lastColumn; c++) {
                                int idx1 = 2 * c;
                                for (int r = 0; r < rows; r++) {
                                    int idx2 = 2 * r;
                                    int idx3 = r * rowspan + idx1;
                                    temp[idx2] = a[idx3];
                                    temp[idx2 + 1] = a[idx3 + 1];
                                }
                                fftRows.complexInverse(temp, scale);
                                for (int r = 0; r < rows; r++) {
                                    int idx2 = 2 * r;
                                    int idx3 = r * rowspan + idx1;
                                    a[idx3] = temp[idx2];
                                    a[idx3 + 1] = temp[idx2 + 1];
                                }
                            }
                        }
                    });
                }
                ConcurrencyUtils.waitForCompletion(futures);
            } else {
                for (int r = 0; r < rows; r++) {
                    fftColumns.complexInverse(a, r * rowspan, scale);
                }
                double[] temp = new double[2 * rows];
                for (int c = 0; c < columns; c++) {
                    int idx1 = 2 * c;
                    for (int r = 0; r < rows; r++) {
                        int idx2 = 2 * r;
                        int idx3 = r * rowspan + idx1;
                        temp[idx2] = a[idx3];
                        temp[idx2 + 1] = a[idx3 + 1];
                    }
                    fftRows.complexInverse(temp, scale);
                    for (int r = 0; r < rows; r++) {
                        int idx2 = 2 * r;
                        int idx3 = r * rowspan + idx1;
                        a[idx3] = temp[idx2];
                        a[idx3 + 1] = temp[idx2 + 1];
                    }
                }
            }
        }
    }

    /**
     * Computes 2D inverse DFT of complex data leaving the result in
     * <code>a</code>. The data is stored in 2D array. Complex data is
     * represented by 2 double values in sequence: the real and imaginary part,
     * i.e. the input array must be of size rows by 2*columns. The physical
     * layout of the input data has to be as follows:<br>
     * 
     * <pre>
     * a[k1][2*k2] = Re[k1][k2], 
     * a[k1][2*k2+1] = Im[k1][k2], 0&lt;=k1&lt;rows, 0&lt;=k2&lt;columns,
     * </pre>
     * 
     * @param a
     *            data to transform
     * @param scale
     *            if true then scaling is performed
     * 
     */
    public void complexInverse(final double[][] a, final boolean scale) {
        int nthreads = ConcurrencyUtils.getNumberOfThreads();
        if (isPowerOfTwo) {
            int oldn2 = columns;
            columns = 2 * columns;

            if (nthreads != oldNthreads) {
                nt = 8 * nthreads * rows;
                if (columns == 4 * nthreads) {
                    nt >>= 1;
                } else if (columns < 4 * nthreads) {
                    nt >>= 2;
                }
                t = new double[nt];
                oldNthreads = nthreads;
            }
            if ((nthreads > 1) && useThreads) {
                xdft2d0_subth1(0, 1, a, scale);
                cdft2d_subth(1, a, scale);
            } else {

                for (int r = 0; r < rows; r++) {
                    fftColumns.complexInverse(a[r], scale);
                }
                cdft2d_sub(1, a, scale);
            }
            columns = oldn2;
        } else {
            if ((nthreads > 1) && useThreads && (rows >= nthreads) && (columns >= nthreads)) {
                Future<?>[] futures = new Future[nthreads];
                int p = rows / nthreads;
                for (int l = 0; l < nthreads; l++) {
                    final int firstRow = l * p;
                    final int lastRow = (l == (nthreads - 1)) ? rows : firstRow + p;
                    futures[l] = ConcurrencyUtils.submit(new Runnable() {
                        @Override
                                                public void run() {
                            for (int r = firstRow; r < lastRow; r++) {
                                fftColumns.complexInverse(a[r], scale);
                            }
                        }
                    });
                }
                ConcurrencyUtils.waitForCompletion(futures);
                p = columns / nthreads;
                for (int l = 0; l < nthreads; l++) {
                    final int firstColumn = l * p;
                    final int lastColumn = (l == (nthreads - 1)) ? columns : firstColumn + p;
                    futures[l] = ConcurrencyUtils.submit(new Runnable() {
                        @Override
                                                public void run() {
                            double[] temp = new double[2 * rows];
                            for (int c = firstColumn; c < lastColumn; c++) {
                                int idx1 = 2 * c;
                                for (int r = 0; r < rows; r++) {
                                    int idx2 = 2 * r;
                                    temp[idx2] = a[r][idx1];
                                    temp[idx2 + 1] = a[r][idx1 + 1];
                                }
                                fftRows.complexInverse(temp, scale);
                                for (int r = 0; r < rows; r++) {
                                    int idx2 = 2 * r;
                                    a[r][idx1] = temp[idx2];
                                    a[r][idx1 + 1] = temp[idx2 + 1];
                                }
                            }
                        }
                    });
                }
                ConcurrencyUtils.waitForCompletion(futures);
            } else {
                for (int r = 0; r < rows; r++) {
                    fftColumns.complexInverse(a[r], scale);
                }
                double[] temp = new double[2 * rows];
                for (int c = 0; c < columns; c++) {
                    int idx1 = 2 * c;
                    for (int r = 0; r < rows; r++) {
                        int idx2 = 2 * r;
                        temp[idx2] = a[r][idx1];
                        temp[idx2 + 1] = a[r][idx1 + 1];
                    }
                    fftRows.complexInverse(temp, scale);
                    for (int r = 0; r < rows; r++) {
                        int idx2 = 2 * r;
                        a[r][idx1] = temp[idx2];
                        a[r][idx1 + 1] = temp[idx2 + 1];
                    }
                }
            }
        }
    }

    /**
     * Computes 2D forward DFT of real data leaving the result in <code>a</code>
     * . This method only works when the sizes of both dimensions are
     * power-of-two numbers. The physical layout of the output data is as
     * follows:
     * 
     * <pre>
     * a[k1*columns+2*k2] = Re[k1][k2] = Re[rows-k1][columns-k2], 
     * a[k1*columns+2*k2+1] = Im[k1][k2] = -Im[rows-k1][columns-k2], 
     *       0&lt;k1&lt;rows, 0&lt;k2&lt;columns/2, 
     * a[2*k2] = Re[0][k2] = Re[0][columns-k2], 
     * a[2*k2+1] = Im[0][k2] = -Im[0][columns-k2], 
     *       0&lt;k2&lt;columns/2, 
     * a[k1*columns] = Re[k1][0] = Re[rows-k1][0], 
     * a[k1*columns+1] = Im[k1][0] = -Im[rows-k1][0], 
     * a[(rows-k1)*columns+1] = Re[k1][columns/2] = Re[rows-k1][columns/2], 
     * a[(rows-k1)*columns] = -Im[k1][columns/2] = Im[rows-k1][columns/2], 
     *       0&lt;k1&lt;rows/2, 
     * a[0] = Re[0][0], 
     * a[1] = Re[0][columns/2], 
     * a[(rows/2)*columns] = Re[rows/2][0], 
     * a[(rows/2)*columns+1] = Re[rows/2][columns/2]
     * </pre>
     * 
     * This method computes only half of the elements of the real transform. The
     * other half satisfies the symmetry condition. If you want the full real
     * forward transform, use <code>realForwardFull</code>. To get back the
     * original data, use <code>realInverse</code> on the output of this method.
     * 
     * @param a
     *            data to transform
     */
    public void realForward(double[] a) {
        if (isPowerOfTwo == false) {
            throw new IllegalArgumentException("rows and columns must be power of two numbers");
        } else {
            int nthreads;

            nthreads = ConcurrencyUtils.getNumberOfThreads();
            if (nthreads != oldNthreads) {
                nt = 8 * nthreads * rows;
                if (columns == 4 * nthreads) {
                    nt >>= 1;
                } else if (columns < 4 * nthreads) {
                    nt >>= 2;
                }
                t = new double[nt];
                oldNthreads = nthreads;
            }
            if ((nthreads > 1) && useThreads) {
                xdft2d0_subth1(1, 1, a, true);
                cdft2d_subth(-1, a, true);
                rdft2d_sub(1, a);
            } else {
                for (int r = 0; r < rows; r++) {
                    fftColumns.realForward(a, r * columns);
                }
                cdft2d_sub(-1, a, true);
                rdft2d_sub(1, a);
            }
        }
    }

    /**
     * Computes 2D forward DFT of real data leaving the result in <code>a</code>
     * . This method only works when the sizes of both dimensions are
     * power-of-two numbers. The physical layout of the output data is as
     * follows:
     * 
     * <pre>
     * a[k1][2*k2] = Re[k1][k2] = Re[rows-k1][columns-k2], 
     * a[k1][2*k2+1] = Im[k1][k2] = -Im[rows-k1][columns-k2], 
     *       0&lt;k1&lt;rows, 0&lt;k2&lt;columns/2, 
     * a[0][2*k2] = Re[0][k2] = Re[0][columns-k2], 
     * a[0][2*k2+1] = Im[0][k2] = -Im[0][columns-k2], 
     *       0&lt;k2&lt;columns/2, 
     * a[k1][0] = Re[k1][0] = Re[rows-k1][0], 
     * a[k1][1] = Im[k1][0] = -Im[rows-k1][0], 
     * a[rows-k1][1] = Re[k1][columns/2] = Re[rows-k1][columns/2], 
     * a[rows-k1][0] = -Im[k1][columns/2] = Im[rows-k1][columns/2], 
     *       0&lt;k1&lt;rows/2, 
     * a[0][0] = Re[0][0], 
     * a[0][1] = Re[0][columns/2], 
     * a[rows/2][0] = Re[rows/2][0], 
     * a[rows/2][1] = Re[rows/2][columns/2]
     * </pre>
     * 
     * This method computes only half of the elements of the real transform. The
     * other half satisfies the symmetry condition. If you want the full real
     * forward transform, use <code>realForwardFull</code>. To get back the
     * original data, use <code>realInverse</code> on the output of this method.
     * 
     * @param a
     *            data to transform
     */
    public void realForward(double[][] a) {
        if (isPowerOfTwo == false) {
            throw new IllegalArgumentException("rows and columns must be power of two numbers");
        } else {
            int nthreads;

            nthreads = ConcurrencyUtils.getNumberOfThreads();
            if (nthreads != oldNthreads) {
                nt = 8 * nthreads * rows;
                if (columns == 4 * nthreads) {
                    nt >>= 1;
                } else if (columns < 4 * nthreads) {
                    nt >>= 2;
                }
                t = new double[nt];
                oldNthreads = nthreads;
            }
            if ((nthreads > 1) && useThreads) {
                xdft2d0_subth1(1, 1, a, true);
                cdft2d_subth(-1, a, true);
                rdft2d_sub(1, a);
            } else {
                for (int r = 0; r < rows; r++) {
                    fftColumns.realForward(a[r]);
                }
                cdft2d_sub(-1, a, true);
                rdft2d_sub(1, a);
            }
        }
    }

    /**
     * Computes 2D forward DFT of real data leaving the result in <code>a</code>
     * . This method computes full real forward transform, i.e. you will get the
     * same result as from <code>complexForward</code> called with all imaginary
     * part equal 0. Because the result is stored in <code>a</code>, the input
     * array must be of size rows*2*columns, with only the first rows*columns
     * elements filled with real data. To get back the original data, use
     * <code>complexInverse</code> on the output of this method.
     * 
     * @param a
     *            data to transform
     */
    public void realForwardFull(double[] a) {
        if (isPowerOfTwo) {
            int nthreads;

            nthreads = ConcurrencyUtils.getNumberOfThreads();
            if (nthreads != oldNthreads) {
                nt = 8 * nthreads * rows;
                if (columns == 4 * nthreads) {
                    nt >>= 1;
                } else if (columns < 4 * nthreads) {
                    nt >>= 2;
                }
                t = new double[nt];
                oldNthreads = nthreads;
            }
            if ((nthreads > 1) && useThreads) {
                xdft2d0_subth1(1, 1, a, true);
                cdft2d_subth(-1, a, true);
                rdft2d_sub(1, a);
            } else {
                for (int r = 0; r < rows; r++) {
                    fftColumns.realForward(a, r * columns);
                }
                cdft2d_sub(-1, a, true);
                rdft2d_sub(1, a);
            }
            fillSymmetric(a);
        } else {
            mixedRadixRealForwardFull(a);
        }
    }

    /**
     * Computes 2D forward DFT of real data leaving the result in <code>a</code>
     * . This method computes full real forward transform, i.e. you will get the
     * same result as from <code>complexForward</code> called with all imaginary
     * part equal 0. Because the result is stored in <code>a</code>, the input
     * array must be of size rows by 2*columns, with only the first rows by
     * columns elements filled with real data. To get back the original data,
     * use <code>complexInverse</code> on the output of this method.
     * 
     * @param a
     *            data to transform
     */
    public void realForwardFull(double[][] a) {
        if (isPowerOfTwo) {
            int nthreads;

            nthreads = ConcurrencyUtils.getNumberOfThreads();
            if (nthreads != oldNthreads) {
                nt = 8 * nthreads * rows;
                if (columns == 4 * nthreads) {
                    nt >>= 1;
                } else if (columns < 4 * nthreads) {
                    nt >>= 2;
                }
                t = new double[nt];
                oldNthreads = nthreads;
            }
            if ((nthreads > 1) && useThreads) {
                xdft2d0_subth1(1, 1, a, true);
                cdft2d_subth(-1, a, true);
                rdft2d_sub(1, a);
            } else {
                for (int r = 0; r < rows; r++) {
                    fftColumns.realForward(a[r]);
                }
                cdft2d_sub(-1, a, true);
                rdft2d_sub(1, a);
            }
            fillSymmetric(a);
        } else {
            mixedRadixRealForwardFull(a);
        }
    }

    /**
     * Computes 2D inverse DFT of real data leaving the result in <code>a</code>
     * . This method only works when the sizes of both dimensions are
     * power-of-two numbers. The physical layout of the input data has to be as
     * follows:
     * 
     * <pre>
     * a[k1*columns+2*k2] = Re[k1][k2] = Re[rows-k1][columns-k2], 
     * a[k1*columns+2*k2+1] = Im[k1][k2] = -Im[rows-k1][columns-k2], 
     *       0&lt;k1&lt;rows, 0&lt;k2&lt;columns/2, 
     * a[2*k2] = Re[0][k2] = Re[0][columns-k2], 
     * a[2*k2+1] = Im[0][k2] = -Im[0][columns-k2], 
     *       0&lt;k2&lt;columns/2, 
     * a[k1*columns] = Re[k1][0] = Re[rows-k1][0], 
     * a[k1*columns+1] = Im[k1][0] = -Im[rows-k1][0], 
     * a[(rows-k1)*columns+1] = Re[k1][columns/2] = Re[rows-k1][columns/2], 
     * a[(rows-k1)*columns] = -Im[k1][columns/2] = Im[rows-k1][columns/2], 
     *       0&lt;k1&lt;rows/2, 
     * a[0] = Re[0][0], 
     * a[1] = Re[0][columns/2], 
     * a[(rows/2)*columns] = Re[rows/2][0], 
     * a[(rows/2)*columns+1] = Re[rows/2][columns/2]
     * </pre>
     * 
     * This method computes only half of the elements of the real transform. The
     * other half satisfies the symmetry condition. If you want the full real
     * inverse transform, use <code>realInverseFull</code>.
     * 
     * @param a
     *            data to transform
     * 
     * @param scale
     *            if true then scaling is performed
     */
    public void realInverse(double[] a, boolean scale) {
        if (isPowerOfTwo == false) {
            throw new IllegalArgumentException("rows and columns must be power of two numbers");
        } else {
            int nthreads;
            nthreads = ConcurrencyUtils.getNumberOfThreads();
            if (nthreads != oldNthreads) {
                nt = 8 * nthreads * rows;
                if (columns == 4 * nthreads) {
                    nt >>= 1;
                } else if (columns < 4 * nthreads) {
                    nt >>= 2;
                }
                t = new double[nt];
                oldNthreads = nthreads;
            }
            if ((nthreads > 1) && useThreads) {
                rdft2d_sub(-1, a);
                cdft2d_subth(1, a, scale);
                xdft2d0_subth1(1, -1, a, scale);
            } else {
                rdft2d_sub(-1, a);
                cdft2d_sub(1, a, scale);
                for (int r = 0; r < rows; r++) {
                    fftColumns.realInverse(a, r * columns, scale);
                }
            }
        }
    }

    /**
     * Computes 2D inverse DFT of real data leaving the result in <code>a</code>
     * . This method only works when the sizes of both dimensions are
     * power-of-two numbers. The physical layout of the input data has to be as
     * follows:
     * 
     * <pre>
     * a[k1][2*k2] = Re[k1][k2] = Re[rows-k1][columns-k2], 
     * a[k1][2*k2+1] = Im[k1][k2] = -Im[rows-k1][columns-k2], 
     *       0&lt;k1&lt;rows, 0&lt;k2&lt;columns/2, 
     * a[0][2*k2] = Re[0][k2] = Re[0][columns-k2], 
     * a[0][2*k2+1] = Im[0][k2] = -Im[0][columns-k2], 
     *       0&lt;k2&lt;columns/2, 
     * a[k1][0] = Re[k1][0] = Re[rows-k1][0], 
     * a[k1][1] = Im[k1][0] = -Im[rows-k1][0], 
     * a[rows-k1][1] = Re[k1][columns/2] = Re[rows-k1][columns/2], 
     * a[rows-k1][0] = -Im[k1][columns/2] = Im[rows-k1][columns/2], 
     *       0&lt;k1&lt;rows/2, 
     * a[0][0] = Re[0][0], 
     * a[0][1] = Re[0][columns/2], 
     * a[rows/2][0] = Re[rows/2][0], 
     * a[rows/2][1] = Re[rows/2][columns/2]
     * </pre>
     * 
     * This method computes only half of the elements of the real transform. The
     * other half satisfies the symmetry condition. If you want the full real
     * inverse transform, use <code>realInverseFull</code>.
     * 
     * @param a
     *            data to transform
     * 
     * @param scale
     *            if true then scaling is performed
     */
    public void realInverse(double[][] a, boolean scale) {
        if (isPowerOfTwo == false) {
            throw new IllegalArgumentException("rows and columns must be power of two numbers");
        } else {
            int nthreads;

            nthreads = ConcurrencyUtils.getNumberOfThreads();
            if (nthreads != oldNthreads) {
                nt = 8 * nthreads * rows;
                if (columns == 4 * nthreads) {
                    nt >>= 1;
                } else if (columns < 4 * nthreads) {
                    nt >>= 2;
                }
                t = new double[nt];
                oldNthreads = nthreads;
            }
            if ((nthreads > 1) && useThreads) {
                rdft2d_sub(-1, a);
                cdft2d_subth(1, a, scale);
                xdft2d0_subth1(1, -1, a, scale);
            } else {
                rdft2d_sub(-1, a);
                cdft2d_sub(1, a, scale);
                for (int r = 0; r < rows; r++) {
                    fftColumns.realInverse(a[r], scale);
                }
            }
        }
    }

    /**
     * Computes 2D inverse DFT of real data leaving the result in <code>a</code>
     * . This method computes full real inverse transform, i.e. you will get the
     * same result as from <code>complexInverse</code> called with all imaginary
     * part equal 0. Because the result is stored in <code>a</code>, the input
     * array must be of size rows*2*columns, with only the first rows*columns
     * elements filled with real data.
     * 
     * @param a
     *            data to transform
     * 
     * @param scale
     *            if true then scaling is performed
     */
    public void realInverseFull(double[] a, boolean scale) {
        if (isPowerOfTwo) {
            int nthreads;

            nthreads = ConcurrencyUtils.getNumberOfThreads();
            if (nthreads != oldNthreads) {
                nt = 8 * nthreads * rows;
                if (columns == 4 * nthreads) {
                    nt >>= 1;
                } else if (columns < 4 * nthreads) {
                    nt >>= 2;
                }
                t = new double[nt];
                oldNthreads = nthreads;
            }
            if ((nthreads > 1) && useThreads) {
                xdft2d0_subth2(1, -1, a, scale);
                cdft2d_subth(1, a, scale);
                rdft2d_sub(1, a);
            } else {
                for (int r = 0; r < rows; r++) {
                    fftColumns.realInverse2(a, r * columns, scale);
                }
                cdft2d_sub(1, a, scale);
                rdft2d_sub(1, a);
            }
            fillSymmetric(a);
        } else {
            mixedRadixRealInverseFull(a, scale);
        }
    }

    /**
     * Computes 2D inverse DFT of real data leaving the result in <code>a</code>
     * . This method computes full real inverse transform, i.e. you will get the
     * same result as from <code>complexInverse</code> called with all imaginary
     * part equal 0. Because the result is stored in <code>a</code>, the input
     * array must be of size rows by 2*columns, with only the first rows by
     * columns elements filled with real data.
     * 
     * @param a
     *            data to transform
     * 
     * @param scale
     *            if true then scaling is performed
     */
    public void realInverseFull(double[][] a, boolean scale) {
        if (isPowerOfTwo) {
            int nthreads;

            nthreads = ConcurrencyUtils.getNumberOfThreads();
            if (nthreads != oldNthreads) {
                nt = 8 * nthreads * rows;
                if (columns == 4 * nthreads) {
                    nt >>= 1;
                } else if (columns < 4 * nthreads) {
                    nt >>= 2;
                }
                t = new double[nt];
                oldNthreads = nthreads;
            }
            if ((nthreads > 1) && useThreads) {
                xdft2d0_subth2(1, -1, a, scale);
                cdft2d_subth(1, a, scale);
                rdft2d_sub(1, a);
            } else {
                for (int r = 0; r < rows; r++) {
                    fftColumns.realInverse2(a[r], 0, scale);
                }
                cdft2d_sub(1, a, scale);
                rdft2d_sub(1, a);
            }
            fillSymmetric(a);
        } else {
            mixedRadixRealInverseFull(a, scale);
        }
    }

    private void mixedRadixRealForwardFull(final double[][] a) {
        final int n2d2 = columns / 2 + 1;
        final double[][] temp = new double[n2d2][2 * rows];

        int nthreads = ConcurrencyUtils.getNumberOfThreads();
        if ((nthreads > 1) && useThreads && (rows >= nthreads) && (n2d2 - 2 >= nthreads)) {
            Future<?>[] futures = new Future[nthreads];
            int p = rows / nthreads;
            for (int l = 0; l < nthreads; l++) {
                final int firstRow = l * p;
                final int lastRow = (l == (nthreads - 1)) ? rows : firstRow + p;
                futures[l] = ConcurrencyUtils.submit(new Runnable() {
                    @Override
                                        public void run() {
                        for (int i = firstRow; i < lastRow; i++) {
                            fftColumns.realForward(a[i]);
                        }
                    }
                });
            }
            ConcurrencyUtils.waitForCompletion(futures);

            for (int r = 0; r < rows; r++) {
                temp[0][r] = a[r][0]; //first column is always real
            }
            fftRows.realForwardFull(temp[0]);

            p = (n2d2 - 2) / nthreads;
            for (int l = 0; l < nthreads; l++) {
                final int firstColumn = 1 + l * p;
                final int lastColumn = (l == (nthreads - 1)) ? n2d2 - 1 : firstColumn + p;
                futures[l] = ConcurrencyUtils.submit(new Runnable() {
                    @Override
                                        public void run() {
                        for (int c = firstColumn; c < lastColumn; c++) {
                            int idx2 = 2 * c;
                            for (int r = 0; r < rows; r++) {
                                int idx1 = 2 * r;
                                temp[c][idx1] = a[r][idx2];
                                temp[c][idx1 + 1] = a[r][idx2 + 1];
                            }
                            fftRows.complexForward(temp[c]);
                        }
                    }
                });
            }
            ConcurrencyUtils.waitForCompletion(futures);

            if ((columns % 2) == 0) {
                for (int r = 0; r < rows; r++) {
                    temp[n2d2 - 1][r] = a[r][1];
                    //imaginary part = 0;
                }
                fftRows.realForwardFull(temp[n2d2 - 1]);

            } else {
                for (int r = 0; r < rows; r++) {
                    int idx1 = 2 * r;
                    int idx2 = n2d2 - 1;
                    temp[idx2][idx1] = a[r][2 * idx2];
                    temp[idx2][idx1 + 1] = a[r][1];
                }
                fftRows.complexForward(temp[n2d2 - 1]);

            }

            p = rows / nthreads;
            for (int l = 0; l < nthreads; l++) {
                final int firstRow = l * p;
                final int lastRow = (l == (nthreads - 1)) ? rows : firstRow + p;
                futures[l] = ConcurrencyUtils.submit(new Runnable() {
                    @Override
                                        public void run() {
                        for (int r = firstRow; r < lastRow; r++) {
                            int idx1 = 2 * r;
                            for (int c = 0; c < n2d2; c++) {
                                int idx2 = 2 * c;
                                a[r][idx2] = temp[c][idx1];
                                a[r][idx2 + 1] = temp[c][idx1 + 1];
                            }
                        }
                    }
                });
            }
            ConcurrencyUtils.waitForCompletion(futures);

            for (int l = 0; l < nthreads; l++) {
                final int firstRow = 1 + l * p;
                final int lastRow = (l == (nthreads - 1)) ? rows : firstRow + p;
                futures[l] = ConcurrencyUtils.submit(new Runnable() {
                    @Override
                                        public void run() {
                        for (int r = firstRow; r < lastRow; r++) {
                            int idx3 = rows - r;
                            for (int c = n2d2; c < columns; c++) {
                                int idx1 = 2 * c;
                                int idx2 = 2 * (columns - c);
                                a[0][idx1] = a[0][idx2];
                                a[0][idx1 + 1] = -a[0][idx2 + 1];
                                a[r][idx1] = a[idx3][idx2];
                                a[r][idx1 + 1] = -a[idx3][idx2 + 1];
                            }
                        }
                    }
                });
            }
            ConcurrencyUtils.waitForCompletion(futures);

        } else {
            for (int r = 0; r < rows; r++) {
                fftColumns.realForward(a[r]);
            }

            for (int r = 0; r < rows; r++) {
                temp[0][r] = a[r][0]; //first column is always real
            }
            fftRows.realForwardFull(temp[0]);

            for (int c = 1; c < n2d2 - 1; c++) {
                int idx2 = 2 * c;
                for (int r = 0; r < rows; r++) {
                    int idx1 = 2 * r;
                    temp[c][idx1] = a[r][idx2];
                    temp[c][idx1 + 1] = a[r][idx2 + 1];
                }
                fftRows.complexForward(temp[c]);
            }

            if ((columns % 2) == 0) {
                for (int r = 0; r < rows; r++) {
                    temp[n2d2 - 1][r] = a[r][1];
                    //imaginary part = 0;
                }
                fftRows.realForwardFull(temp[n2d2 - 1]);

            } else {
                for (int r = 0; r < rows; r++) {
                    int idx1 = 2 * r;
                    int idx2 = n2d2 - 1;
                    temp[idx2][idx1] = a[r][2 * idx2];
                    temp[idx2][idx1 + 1] = a[r][1];
                }
                fftRows.complexForward(temp[n2d2 - 1]);

            }

            for (int r = 0; r < rows; r++) {
                int idx1 = 2 * r;
                for (int c = 0; c < n2d2; c++) {
                    int idx2 = 2 * c;
                    a[r][idx2] = temp[c][idx1];
                    a[r][idx2 + 1] = temp[c][idx1 + 1];
                }
            }

            //fill symmetric
            for (int r = 1; r < rows; r++) {
                int idx3 = rows - r;
                for (int c = n2d2; c < columns; c++) {
                    int idx1 = 2 * c;
                    int idx2 = 2 * (columns - c);
                    a[0][idx1] = a[0][idx2];
                    a[0][idx1 + 1] = -a[0][idx2 + 1];
                    a[r][idx1] = a[idx3][idx2];
                    a[r][idx1 + 1] = -a[idx3][idx2 + 1];
                }
            }
        }
    }

    private void mixedRadixRealForwardFull(final double[] a) {
        final int rowStride = 2 * columns;
        final int n2d2 = columns / 2 + 1;
        final double[][] temp = new double[n2d2][2 * rows];

        int nthreads = ConcurrencyUtils.getNumberOfThreads();
        if ((nthreads > 1) && useThreads && (rows >= nthreads) && (n2d2 - 2 >= nthreads)) {
            Future<?>[] futures = new Future[nthreads];
            int p = rows / nthreads;
            for (int l = 0; l < nthreads; l++) {
                final int firstRow = l * p;
                final int lastRow = (l == (nthreads - 1)) ? rows : firstRow + p;
                futures[l] = ConcurrencyUtils.submit(new Runnable() {
                    @Override
                                        public void run() {
                        for (int i = firstRow; i < lastRow; i++) {
                            fftColumns.realForward(a, i * columns);
                        }
                    }
                });
            }
            ConcurrencyUtils.waitForCompletion(futures);

            for (int r = 0; r < rows; r++) {
                temp[0][r] = a[r * columns]; //first column is always real
            }
            fftRows.realForwardFull(temp[0]);

            p = (n2d2 - 2) / nthreads;
            for (int l = 0; l < nthreads; l++) {
                final int firstColumn = 1 + l * p;
                final int lastColumn = (l == (nthreads - 1)) ? n2d2 - 1 : firstColumn + p;
                futures[l] = ConcurrencyUtils.submit(new Runnable() {
                    @Override
                                        public void run() {
                        for (int c = firstColumn; c < lastColumn; c++) {
                            int idx0 = 2 * c;
                            for (int r = 0; r < rows; r++) {
                                int idx1 = 2 * r;
                                int idx2 = r * columns + idx0;
                                temp[c][idx1] = a[idx2];
                                temp[c][idx1 + 1] = a[idx2 + 1];
                            }
                            fftRows.complexForward(temp[c]);
                        }
                    }
                });
            }
            ConcurrencyUtils.waitForCompletion(futures);
            
            if ((columns % 2) == 0) {
                for (int r = 0; r < rows; r++) {
                    temp[n2d2 - 1][r] = a[r * columns + 1];
                    //imaginary part = 0;
                }
                fftRows.realForwardFull(temp[n2d2 - 1]);

            } else {
                for (int r = 0; r < rows; r++) {
                    int idx1 = 2 * r;
                    int idx2 = r * columns;
                    int idx3 = n2d2 - 1;
                    temp[idx3][idx1] = a[idx2 + 2 * idx3];
                    temp[idx3][idx1 + 1] = a[idx2 + 1];
                }
                fftRows.complexForward(temp[n2d2 - 1]);
            }

            p = rows / nthreads;
            for (int l = 0; l < nthreads; l++) {
                final int firstRow = l * p;
                final int lastRow = (l == (nthreads - 1)) ? rows : firstRow + p;
                futures[l] = ConcurrencyUtils.submit(new Runnable() {
                    @Override
                                        public void run() {
                        for (int r = firstRow; r < lastRow; r++) {
                            int idx1 = 2 * r;
                            for (int c = 0; c < n2d2; c++) {
                                int idx0 = 2 * c;
                                int idx2 = r * rowStride + idx0;
                                a[idx2] = temp[c][idx1];
                                a[idx2 + 1] = temp[c][idx1 + 1];
                            }
                        }
                    }
                });
            }
            ConcurrencyUtils.waitForCompletion(futures);
            
            for (int l = 0; l < nthreads; l++) {
                final int firstRow = 1 + l * p;
                final int lastRow = (l == (nthreads - 1)) ? rows : firstRow + p;
                futures[l] = ConcurrencyUtils.submit(new Runnable() {
                    @Override
                                        public void run() {
                        for (int r = firstRow; r < lastRow; r++) {
                            int idx5 = r * rowStride;
                            int idx6 = (rows - r + 1) * rowStride;
                            for (int c = n2d2; c < columns; c++) {
                                int idx1 = 2 * c;
                                int idx2 = 2 * (columns - c);
                                a[idx1] = a[idx2];
                                a[idx1 + 1] = -a[idx2 + 1];
                                int idx3 = idx5 + idx1;
                                int idx4 = idx6 - idx1;
                                a[idx3] = a[idx4];
                                a[idx3 + 1] = -a[idx4 + 1];
                            }
                        }
                    }
                });
            }
            ConcurrencyUtils.waitForCompletion(futures);
            
        } else {
            for (int r = 0; r < rows; r++) {
                fftColumns.realForward(a, r * columns);
            }
            for (int r = 0; r < rows; r++) {
                temp[0][r] = a[r * columns]; //first column is always real
            }
            fftRows.realForwardFull(temp[0]);

            for (int c = 1; c < n2d2 - 1; c++) {
                int idx0 = 2 * c;
                for (int r = 0; r < rows; r++) {
                    int idx1 = 2 * r;
                    int idx2 = r * columns + idx0;
                    temp[c][idx1] = a[idx2];
                    temp[c][idx1 + 1] = a[idx2 + 1];
                }
                fftRows.complexForward(temp[c]);
            }

            if ((columns % 2) == 0) {
                for (int r = 0; r < rows; r++) {
                    temp[n2d2 - 1][r] = a[r * columns + 1];
                    //imaginary part = 0;
                }
                fftRows.realForwardFull(temp[n2d2 - 1]);

            } else {
                for (int r = 0; r < rows; r++) {
                    int idx1 = 2 * r;
                    int idx2 = r * columns;
                    int idx3 = n2d2 - 1;
                    temp[idx3][idx1] = a[idx2 + 2 * idx3];
                    temp[idx3][idx1 + 1] = a[idx2 + 1];
                }
                fftRows.complexForward(temp[n2d2 - 1]);
            }

            for (int r = 0; r < rows; r++) {
                int idx1 = 2 * r;
                for (int c = 0; c < n2d2; c++) {
                    int idx0 = 2 * c;
                    int idx2 = r * rowStride + idx0;
                    a[idx2] = temp[c][idx1];
                    a[idx2 + 1] = temp[c][idx1 + 1];
                }
            }

            //fill symmetric
            for (int r = 1; r < rows; r++) {
                int idx5 = r * rowStride;
                int idx6 = (rows - r + 1) * rowStride;
                for (int c = n2d2; c < columns; c++) {
                    int idx1 = 2 * c;
                    int idx2 = 2 * (columns - c);
                    a[idx1] = a[idx2];
                    a[idx1 + 1] = -a[idx2 + 1];
                    int idx3 = idx5 + idx1;
                    int idx4 = idx6 - idx1;
                    a[idx3] = a[idx4];
                    a[idx3 + 1] = -a[idx4 + 1];
                }
            }
        }
    }

    private void mixedRadixRealInverseFull(final double[][] a, final boolean scale) {
        final int n2d2 = columns / 2 + 1;
        final double[][] temp = new double[n2d2][2 * rows];

        int nthreads = ConcurrencyUtils.getNumberOfThreads();
        if ((nthreads > 1) && useThreads && (rows >= nthreads) && (n2d2 - 2 >= nthreads)) {
            Future<?>[] futures = new Future[nthreads];
            int p = rows / nthreads;
            for (int l = 0; l < nthreads; l++) {
                final int firstRow = l * p;
                final int lastRow = (l == (nthreads - 1)) ? rows : firstRow + p;
                futures[l] = ConcurrencyUtils.submit(new Runnable() {
                    @Override
                                        public void run() {
                        for (int i = firstRow; i < lastRow; i++) {
                            fftColumns.realInverse2(a[i], 0, scale);
                        }
                    }
                });
            }
            ConcurrencyUtils.waitForCompletion(futures);

            for (int r = 0; r < rows; r++) {
                temp[0][r] = a[r][0]; //first column is always real
            }
            fftRows.realInverseFull(temp[0], scale);

            p = (n2d2 - 2) / nthreads;
            for (int l = 0; l < nthreads; l++) {
                final int firstColumn = 1 + l * p;
                final int lastColumn = (l == (nthreads - 1)) ? n2d2 - 1 : firstColumn + p;
                futures[l] = ConcurrencyUtils.submit(new Runnable() {
                    @Override
                                        public void run() {
                        for (int c = firstColumn; c < lastColumn; c++) {
                            int idx2 = 2 * c;
                            for (int r = 0; r < rows; r++) {
                                int idx1 = 2 * r;
                                temp[c][idx1] = a[r][idx2];
                                temp[c][idx1 + 1] = a[r][idx2 + 1];
                            }
                            fftRows.complexInverse(temp[c], scale);
                        }
                    }
                });
            }
            ConcurrencyUtils.waitForCompletion(futures);

            if ((columns % 2) == 0) {
                for (int r = 0; r < rows; r++) {
                    temp[n2d2 - 1][r] = a[r][1];
                    //imaginary part = 0;
                }
                fftRows.realInverseFull(temp[n2d2 - 1], scale);

            } else {
                for (int r = 0; r < rows; r++) {
                    int idx1 = 2 * r;
                    int idx2 = n2d2 - 1;
                    temp[idx2][idx1] = a[r][2 * idx2];
                    temp[idx2][idx1 + 1] = a[r][1];
                }
                fftRows.complexInverse(temp[n2d2 - 1], scale);

            }

            p = rows / nthreads;
            for (int l = 0; l < nthreads; l++) {
                final int firstRow = l * p;
                final int lastRow = (l == (nthreads - 1)) ? rows : firstRow + p;
                futures[l] = ConcurrencyUtils.submit(new Runnable() {
                    @Override
                                        public void run() {
                        for (int r = firstRow; r < lastRow; r++) {
                            int idx1 = 2 * r;
                            for (int c = 0; c < n2d2; c++) {
                                int idx2 = 2 * c;
                                a[r][idx2] = temp[c][idx1];
                                a[r][idx2 + 1] = temp[c][idx1 + 1];
                            }
                        }
                    }
                });
            }
            ConcurrencyUtils.waitForCompletion(futures);

            for (int l = 0; l < nthreads; l++) {
                final int firstRow = 1 + l * p;
                final int lastRow = (l == (nthreads - 1)) ? rows : firstRow + p;
                futures[l] = ConcurrencyUtils.submit(new Runnable() {
                    @Override
                                        public void run() {
                        for (int r = firstRow; r < lastRow; r++) {
                            int idx3 = rows - r;
                            for (int c = n2d2; c < columns; c++) {
                                int idx1 = 2 * c;
                                int idx2 = 2 * (columns - c);
                                a[0][idx1] = a[0][idx2];
                                a[0][idx1 + 1] = -a[0][idx2 + 1];
                                a[r][idx1] = a[idx3][idx2];
                                a[r][idx1 + 1] = -a[idx3][idx2 + 1];
                            }
                        }
                    }
                });
            }
            ConcurrencyUtils.waitForCompletion(futures);

        } else {
            for (int r = 0; r < rows; r++) {
                fftColumns.realInverse2(a[r], 0, scale);
            }

            for (int r = 0; r < rows; r++) {
                temp[0][r] = a[r][0]; //first column is always real
            }
            fftRows.realInverseFull(temp[0], scale);

            for (int c = 1; c < n2d2 - 1; c++) {
                int idx2 = 2 * c;
                for (int r = 0; r < rows; r++) {
                    int idx1 = 2 * r;
                    temp[c][idx1] = a[r][idx2];
                    temp[c][idx1 + 1] = a[r][idx2 + 1];
                }
                fftRows.complexInverse(temp[c], scale);
            }

            if ((columns % 2) == 0) {
                for (int r = 0; r < rows; r++) {
                    temp[n2d2 - 1][r] = a[r][1];
                    //imaginary part = 0;
                }
                fftRows.realInverseFull(temp[n2d2 - 1], scale);

            } else {
                for (int r = 0; r < rows; r++) {
                    int idx1 = 2 * r;
                    int idx2 = n2d2 - 1;
                    temp[idx2][idx1] = a[r][2 * idx2];
                    temp[idx2][idx1 + 1] = a[r][1];
                }
                fftRows.complexInverse(temp[n2d2 - 1], scale);

            }

            for (int r = 0; r < rows; r++) {
                int idx1 = 2 * r;
                for (int c = 0; c < n2d2; c++) {
                    int idx2 = 2 * c;
                    a[r][idx2] = temp[c][idx1];
                    a[r][idx2 + 1] = temp[c][idx1 + 1];
                }
            }

            //fill symmetric
            for (int r = 1; r < rows; r++) {
                int idx3 = rows - r;
                for (int c = n2d2; c < columns; c++) {
                    int idx1 = 2 * c;
                    int idx2 = 2 * (columns - c);
                    a[0][idx1] = a[0][idx2];
                    a[0][idx1 + 1] = -a[0][idx2 + 1];
                    a[r][idx1] = a[idx3][idx2];
                    a[r][idx1 + 1] = -a[idx3][idx2 + 1];
                }
            }
        }
    }

    private void mixedRadixRealInverseFull(final double[] a, final boolean scale) {
        final int rowStride = 2 * columns;
        final int n2d2 = columns / 2 + 1;
        final double[][] temp = new double[n2d2][2 * rows];

        int nthreads = ConcurrencyUtils.getNumberOfThreads();
        if ((nthreads > 1) && useThreads && (rows >= nthreads) && (n2d2 - 2 >= nthreads)) {
            Future<?>[] futures = new Future[nthreads];
            int p = rows / nthreads;
            for (int l = 0; l < nthreads; l++) {
                final int firstRow = l * p;
                final int lastRow = (l == (nthreads - 1)) ? rows : firstRow + p;
                futures[l] = ConcurrencyUtils.submit(new Runnable() {
                    @Override
                                        public void run() {
                        for (int i = firstRow; i < lastRow; i++) {
                            fftColumns.realInverse2(a, i * columns, scale);
                        }
                    }
                });
            }
            ConcurrencyUtils.waitForCompletion(futures);

            for (int r = 0; r < rows; r++) {
                temp[0][r] = a[r * columns]; //first column is always real
            }
            fftRows.realInverseFull(temp[0], scale);

            p = (n2d2 - 2) / nthreads;
            for (int l = 0; l < nthreads; l++) {
                final int firstColumn = 1 + l * p;
                final int lastColumn = (l == (nthreads - 1)) ? n2d2 - 1 : firstColumn + p;
                futures[l] = ConcurrencyUtils.submit(new Runnable() {
                    @Override
                                        public void run() {
                        for (int c = firstColumn; c < lastColumn; c++) {
                            int idx0 = 2 * c;
                            for (int r = 0; r < rows; r++) {
                                int idx1 = 2 * r;
                                int idx2 = r * columns + idx0;
                                temp[c][idx1] = a[idx2];
                                temp[c][idx1 + 1] = a[idx2 + 1];
                            }
                            fftRows.complexInverse(temp[c], scale);
                        }
                    }
                });
            }
            ConcurrencyUtils.waitForCompletion(futures);

            if ((columns % 2) == 0) {
                for (int r = 0; r < rows; r++) {
                    temp[n2d2 - 1][r] = a[r * columns + 1];
                    //imaginary part = 0;
                }
                fftRows.realInverseFull(temp[n2d2 - 1], scale);

            } else {
                for (int r = 0; r < rows; r++) {
                    int idx1 = 2 * r;
                    int idx2 = r * columns;
                    int idx3 = n2d2 - 1;
                    temp[idx3][idx1] = a[idx2 + 2 * idx3];
                    temp[idx3][idx1 + 1] = a[idx2 + 1];
                }
                fftRows.complexInverse(temp[n2d2 - 1], scale);
            }

            p = rows / nthreads;
            for (int l = 0; l < nthreads; l++) {
                final int firstRow = l * p;
                final int lastRow = (l == (nthreads - 1)) ? rows : firstRow + p;
                futures[l] = ConcurrencyUtils.submit(new Runnable() {
                    @Override
                                        public void run() {
                        for (int r = firstRow; r < lastRow; r++) {
                            int idx1 = 2 * r;
                            for (int c = 0; c < n2d2; c++) {
                                int idx0 = 2 * c;
                                int idx2 = r * rowStride + idx0;
                                a[idx2] = temp[c][idx1];
                                a[idx2 + 1] = temp[c][idx1 + 1];
                            }
                        }
                    }
                });
            }
            ConcurrencyUtils.waitForCompletion(futures);

            for (int l = 0; l < nthreads; l++) {
                final int firstRow = 1 + l * p;
                final int lastRow = (l == (nthreads - 1)) ? rows : firstRow + p;
                futures[l] = ConcurrencyUtils.submit(new Runnable() {
                    @Override
                                        public void run() {
                        for (int r = firstRow; r < lastRow; r++) {
                            int idx5 = r * rowStride;
                            int idx6 = (rows - r + 1) * rowStride;
                            for (int c = n2d2; c < columns; c++) {
                                int idx1 = 2 * c;
                                int idx2 = 2 * (columns - c);
                                a[idx1] = a[idx2];
                                a[idx1 + 1] = -a[idx2 + 1];
                                int idx3 = idx5 + idx1;
                                int idx4 = idx6 - idx1;
                                a[idx3] = a[idx4];
                                a[idx3 + 1] = -a[idx4 + 1];
                            }
                        }
                    }
                });
            }
            ConcurrencyUtils.waitForCompletion(futures);
        } else {
            for (int r = 0; r < rows; r++) {
                fftColumns.realInverse2(a, r * columns, scale);
            }
            for (int r = 0; r < rows; r++) {
                temp[0][r] = a[r * columns]; //first column is always real
            }
            fftRows.realInverseFull(temp[0], scale);

            for (int c = 1; c < n2d2 - 1; c++) {
                int idx0 = 2 * c;
                for (int r = 0; r < rows; r++) {
                    int idx1 = 2 * r;
                    int idx2 = r * columns + idx0;
                    temp[c][idx1] = a[idx2];
                    temp[c][idx1 + 1] = a[idx2 + 1];
                }
                fftRows.complexInverse(temp[c], scale);
            }

            if ((columns % 2) == 0) {
                for (int r = 0; r < rows; r++) {
                    temp[n2d2 - 1][r] = a[r * columns + 1];
                    //imaginary part = 0;
                }
                fftRows.realInverseFull(temp[n2d2 - 1], scale);

            } else {
                for (int r = 0; r < rows; r++) {
                    int idx1 = 2 * r;
                    int idx2 = r * columns;
                    int idx3 = n2d2 - 1;
                    temp[idx3][idx1] = a[idx2 + 2 * idx3];
                    temp[idx3][idx1 + 1] = a[idx2 + 1];
                }
                fftRows.complexInverse(temp[n2d2 - 1], scale);
            }

            for (int r = 0; r < rows; r++) {
                int idx1 = 2 * r;
                for (int c = 0; c < n2d2; c++) {
                    int idx0 = 2 * c;
                    int idx2 = r * rowStride + idx0;
                    a[idx2] = temp[c][idx1];
                    a[idx2 + 1] = temp[c][idx1 + 1];
                }
            }

            //fill symmetric
            for (int r = 1; r < rows; r++) {
                int idx5 = r * rowStride;
                int idx6 = (rows - r + 1) * rowStride;
                for (int c = n2d2; c < columns; c++) {
                    int idx1 = 2 * c;
                    int idx2 = 2 * (columns - c);
                    a[idx1] = a[idx2];
                    a[idx1 + 1] = -a[idx2 + 1];
                    int idx3 = idx5 + idx1;
                    int idx4 = idx6 - idx1;
                    a[idx3] = a[idx4];
                    a[idx3 + 1] = -a[idx4 + 1];
                }
            }
        }
    }

    private void rdft2d_sub(int isgn, double[] a) {
        int n1h, j;
        double xi;
        int idx1, idx2;

        n1h = rows >> 1;
        if (isgn < 0) {
            for (int i = 1; i < n1h; i++) {
                j = rows - i;
                idx1 = i * columns;
                idx2 = j * columns;
                xi = a[idx1] - a[idx2];
                a[idx1] += a[idx2];
                a[idx2] = xi;
                xi = a[idx2 + 1] - a[idx1 + 1];
                a[idx1 + 1] += a[idx2 + 1];
                a[idx2 + 1] = xi;
            }
        } else {
            for (int i = 1; i < n1h; i++) {
                j = rows - i;
                idx1 = i * columns;
                idx2 = j * columns;
                a[idx2] = 0.5f * (a[idx1] - a[idx2]);
                a[idx1] -= a[idx2];
                a[idx2 + 1] = 0.5f * (a[idx1 + 1] + a[idx2 + 1]);
                a[idx1 + 1] -= a[idx2 + 1];
            }
        }
    }

    private void rdft2d_sub(int isgn, double[][] a) {
        int n1h, j;
        double xi;

        n1h = rows >> 1;
        if (isgn < 0) {
            for (int i = 1; i < n1h; i++) {
                j = rows - i;
                xi = a[i][0] - a[j][0];
                a[i][0] += a[j][0];
                a[j][0] = xi;
                xi = a[j][1] - a[i][1];
                a[i][1] += a[j][1];
                a[j][1] = xi;
            }
        } else {
            for (int i = 1; i < n1h; i++) {
                j = rows - i;
                a[j][0] = 0.5f * (a[i][0] - a[j][0]);
                a[i][0] -= a[j][0];
                a[j][1] = 0.5f * (a[i][1] + a[j][1]);
                a[i][1] -= a[j][1];
            }
        }
    }

    private void cdft2d_sub(int isgn, double[] a, boolean scale) {
        int idx1, idx2, idx3, idx4, idx5;
        if (isgn == -1) {
            if (columns > 4) {
                for (int c = 0; c < columns; c += 8) {
                    for (int r = 0; r < rows; r++) {
                        idx1 = r * columns + c;
                        idx2 = 2 * r;
                        idx3 = 2 * rows + 2 * r;
                        idx4 = idx3 + 2 * rows;
                        idx5 = idx4 + 2 * rows;
                        t[idx2] = a[idx1];
                        t[idx2 + 1] = a[idx1 + 1];
                        t[idx3] = a[idx1 + 2];
                        t[idx3 + 1] = a[idx1 + 3];
                        t[idx4] = a[idx1 + 4];
                        t[idx4 + 1] = a[idx1 + 5];
                        t[idx5] = a[idx1 + 6];
                        t[idx5 + 1] = a[idx1 + 7];
                    }
                    fftRows.complexForward(t, 0);
                    fftRows.complexForward(t, 2 * rows);
                    fftRows.complexForward(t, 4 * rows);
                    fftRows.complexForward(t, 6 * rows);
                    for (int r = 0; r < rows; r++) {
                        idx1 = r * columns + c;
                        idx2 = 2 * r;
                        idx3 = 2 * rows + 2 * r;
                        idx4 = idx3 + 2 * rows;
                        idx5 = idx4 + 2 * rows;
                        a[idx1] = t[idx2];
                        a[idx1 + 1] = t[idx2 + 1];
                        a[idx1 + 2] = t[idx3];
                        a[idx1 + 3] = t[idx3 + 1];
                        a[idx1 + 4] = t[idx4];
                        a[idx1 + 5] = t[idx4 + 1];
                        a[idx1 + 6] = t[idx5];
                        a[idx1 + 7] = t[idx5 + 1];
                    }
                }
            } else if (columns == 4) {
                for (int r = 0; r < rows; r++) {
                    idx1 = r * columns;
                    idx2 = 2 * r;
                    idx3 = 2 * rows + 2 * r;
                    t[idx2] = a[idx1];
                    t[idx2 + 1] = a[idx1 + 1];
                    t[idx3] = a[idx1 + 2];
                    t[idx3 + 1] = a[idx1 + 3];
                }
                fftRows.complexForward(t, 0);
                fftRows.complexForward(t, 2 * rows);
                for (int r = 0; r < rows; r++) {
                    idx1 = r * columns;
                    idx2 = 2 * r;
                    idx3 = 2 * rows + 2 * r;
                    a[idx1] = t[idx2];
                    a[idx1 + 1] = t[idx2 + 1];
                    a[idx1 + 2] = t[idx3];
                    a[idx1 + 3] = t[idx3 + 1];
                }
            } else if (columns == 2) {
                for (int r = 0; r < rows; r++) {
                    idx1 = r * columns;
                    idx2 = 2 * r;
                    t[idx2] = a[idx1];
                    t[idx2 + 1] = a[idx1 + 1];
                }
                fftRows.complexForward(t, 0);
                for (int r = 0; r < rows; r++) {
                    idx1 = r * columns;
                    idx2 = 2 * r;
                    a[idx1] = t[idx2];
                    a[idx1 + 1] = t[idx2 + 1];
                }
            }
        } else {
            if (columns > 4) {
                for (int c = 0; c < columns; c += 8) {
                    for (int r = 0; r < rows; r++) {
                        idx1 = r * columns + c;
                        idx2 = 2 * r;
                        idx3 = 2 * rows + 2 * r;
                        idx4 = idx3 + 2 * rows;
                        idx5 = idx4 + 2 * rows;
                        t[idx2] = a[idx1];
                        t[idx2 + 1] = a[idx1 + 1];
                        t[idx3] = a[idx1 + 2];
                        t[idx3 + 1] = a[idx1 + 3];
                        t[idx4] = a[idx1 + 4];
                        t[idx4 + 1] = a[idx1 + 5];
                        t[idx5] = a[idx1 + 6];
                        t[idx5 + 1] = a[idx1 + 7];
                    }
                    fftRows.complexInverse(t, 0, scale);
                    fftRows.complexInverse(t, 2 * rows, scale);
                    fftRows.complexInverse(t, 4 * rows, scale);
                    fftRows.complexInverse(t, 6 * rows, scale);
                    for (int r = 0; r < rows; r++) {
                        idx1 = r * columns + c;
                        idx2 = 2 * r;
                        idx3 = 2 * rows + 2 * r;
                        idx4 = idx3 + 2 * rows;
                        idx5 = idx4 + 2 * rows;
                        a[idx1] = t[idx2];
                        a[idx1 + 1] = t[idx2 + 1];
                        a[idx1 + 2] = t[idx3];
                        a[idx1 + 3] = t[idx3 + 1];
                        a[idx1 + 4] = t[idx4];
                        a[idx1 + 5] = t[idx4 + 1];
                        a[idx1 + 6] = t[idx5];
                        a[idx1 + 7] = t[idx5 + 1];
                    }
                }
            } else if (columns == 4) {
                for (int r = 0; r < rows; r++) {
                    idx1 = r * columns;
                    idx2 = 2 * r;
                    idx3 = 2 * rows + 2 * r;
                    t[idx2] = a[idx1];
                    t[idx2 + 1] = a[idx1 + 1];
                    t[idx3] = a[idx1 + 2];
                    t[idx3 + 1] = a[idx1 + 3];
                }
                fftRows.complexInverse(t, 0, scale);
                fftRows.complexInverse(t, 2 * rows, scale);
                for (int r = 0; r < rows; r++) {
                    idx1 = r * columns;
                    idx2 = 2 * r;
                    idx3 = 2 * rows + 2 * r;
                    a[idx1] = t[idx2];
                    a[idx1 + 1] = t[idx2 + 1];
                    a[idx1 + 2] = t[idx3];
                    a[idx1 + 3] = t[idx3 + 1];
                }
            } else if (columns == 2) {
                for (int r = 0; r < rows; r++) {
                    idx1 = r * columns;
                    idx2 = 2 * r;
                    t[idx2] = a[idx1];
                    t[idx2 + 1] = a[idx1 + 1];
                }
                fftRows.complexInverse(t, 0, scale);
                for (int r = 0; r < rows; r++) {
                    idx1 = r * columns;
                    idx2 = 2 * r;
                    a[idx1] = t[idx2];
                    a[idx1 + 1] = t[idx2 + 1];
                }
            }
        }
    }

    private void cdft2d_sub(int isgn, double[][] a, boolean scale) {
        int idx2, idx3, idx4, idx5;
        if (isgn == -1) {
            if (columns > 4) {
                for (int c = 0; c < columns; c += 8) {
                    for (int r = 0; r < rows; r++) {
                        idx2 = 2 * r;
                        idx3 = 2 * rows + 2 * r;
                        idx4 = idx3 + 2 * rows;
                        idx5 = idx4 + 2 * rows;
                        t[idx2] = a[r][c];
                        t[idx2 + 1] = a[r][c + 1];
                        t[idx3] = a[r][c + 2];
                        t[idx3 + 1] = a[r][c + 3];
                        t[idx4] = a[r][c + 4];
                        t[idx4 + 1] = a[r][c + 5];
                        t[idx5] = a[r][c + 6];
                        t[idx5 + 1] = a[r][c + 7];
                    }
                    fftRows.complexForward(t, 0);
                    fftRows.complexForward(t, 2 * rows);
                    fftRows.complexForward(t, 4 * rows);
                    fftRows.complexForward(t, 6 * rows);
                    for (int r = 0; r < rows; r++) {
                        idx2 = 2 * r;
                        idx3 = 2 * rows + 2 * r;
                        idx4 = idx3 + 2 * rows;
                        idx5 = idx4 + 2 * rows;
                        a[r][c] = t[idx2];
                        a[r][c + 1] = t[idx2 + 1];
                        a[r][c + 2] = t[idx3];
                        a[r][c + 3] = t[idx3 + 1];
                        a[r][c + 4] = t[idx4];
                        a[r][c + 5] = t[idx4 + 1];
                        a[r][c + 6] = t[idx5];
                        a[r][c + 7] = t[idx5 + 1];
                    }
                }
            } else if (columns == 4) {
                for (int r = 0; r < rows; r++) {
                    idx2 = 2 * r;
                    idx3 = 2 * rows + 2 * r;
                    t[idx2] = a[r][0];
                    t[idx2 + 1] = a[r][1];
                    t[idx3] = a[r][2];
                    t[idx3 + 1] = a[r][3];
                }
                fftRows.complexForward(t, 0);
                fftRows.complexForward(t, 2 * rows);
                for (int r = 0; r < rows; r++) {
                    idx2 = 2 * r;
                    idx3 = 2 * rows + 2 * r;
                    a[r][0] = t[idx2];
                    a[r][1] = t[idx2 + 1];
                    a[r][2] = t[idx3];
                    a[r][3] = t[idx3 + 1];
                }
            } else if (columns == 2) {
                for (int r = 0; r < rows; r++) {
                    idx2 = 2 * r;
                    t[idx2] = a[r][0];
                    t[idx2 + 1] = a[r][1];
                }
                fftRows.complexForward(t, 0);
                for (int r = 0; r < rows; r++) {
                    idx2 = 2 * r;
                    a[r][0] = t[idx2];
                    a[r][1] = t[idx2 + 1];
                }
            }
        } else {
            if (columns > 4) {
                for (int c = 0; c < columns; c += 8) {
                    for (int r = 0; r < rows; r++) {
                        idx2 = 2 * r;
                        idx3 = 2 * rows + 2 * r;
                        idx4 = idx3 + 2 * rows;
                        idx5 = idx4 + 2 * rows;
                        t[idx2] = a[r][c];
                        t[idx2 + 1] = a[r][c + 1];
                        t[idx3] = a[r][c + 2];
                        t[idx3 + 1] = a[r][c + 3];
                        t[idx4] = a[r][c + 4];
                        t[idx4 + 1] = a[r][c + 5];
                        t[idx5] = a[r][c + 6];
                        t[idx5 + 1] = a[r][c + 7];
                    }
                    fftRows.complexInverse(t, 0, scale);
                    fftRows.complexInverse(t, 2 * rows, scale);
                    fftRows.complexInverse(t, 4 * rows, scale);
                    fftRows.complexInverse(t, 6 * rows, scale);
                    for (int r = 0; r < rows; r++) {
                        idx2 = 2 * r;
                        idx3 = 2 * rows + 2 * r;
                        idx4 = idx3 + 2 * rows;
                        idx5 = idx4 + 2 * rows;
                        a[r][c] = t[idx2];
                        a[r][c + 1] = t[idx2 + 1];
                        a[r][c + 2] = t[idx3];
                        a[r][c + 3] = t[idx3 + 1];
                        a[r][c + 4] = t[idx4];
                        a[r][c + 5] = t[idx4 + 1];
                        a[r][c + 6] = t[idx5];
                        a[r][c + 7] = t[idx5 + 1];
                    }
                }
            } else if (columns == 4) {
                for (int r = 0; r < rows; r++) {
                    idx2 = 2 * r;
                    idx3 = 2 * rows + 2 * r;
                    t[idx2] = a[r][0];
                    t[idx2 + 1] = a[r][1];
                    t[idx3] = a[r][2];
                    t[idx3 + 1] = a[r][3];
                }
                fftRows.complexInverse(t, 0, scale);
                fftRows.complexInverse(t, 2 * rows, scale);
                for (int r = 0; r < rows; r++) {
                    idx2 = 2 * r;
                    idx3 = 2 * rows + 2 * r;
                    a[r][0] = t[idx2];
                    a[r][1] = t[idx2 + 1];
                    a[r][2] = t[idx3];
                    a[r][3] = t[idx3 + 1];
                }
            } else if (columns == 2) {
                for (int r = 0; r < rows; r++) {
                    idx2 = 2 * r;
                    t[idx2] = a[r][0];
                    t[idx2 + 1] = a[r][1];
                }
                fftRows.complexInverse(t, 0, scale);
                for (int r = 0; r < rows; r++) {
                    idx2 = 2 * r;
                    a[r][0] = t[idx2];
                    a[r][1] = t[idx2 + 1];
                }
            }
        }
    }

    private void xdft2d0_subth1(final int icr, final int isgn, final double[] a, final boolean scale) {
        final int nthreads = ConcurrencyUtils.getNumberOfThreads() > rows ? rows : ConcurrencyUtils.getNumberOfThreads();

        Future<?>[] futures = new Future[nthreads];
        for (int i = 0; i < nthreads; i++) {
            final int n0 = i;
            futures[i] = ConcurrencyUtils.submit(new Runnable() {
                @Override
                                public void run() {
                    if (icr == 0) {
                        if (isgn == -1) {
                            for (int r = n0; r < rows; r += nthreads) {
                                fftColumns.complexForward(a, r * columns);
                            }
                        } else {
                            for (int r = n0; r < rows; r += nthreads) {
                                fftColumns.complexInverse(a, r * columns, scale);
                            }
                        }
                    } else {
                        if (isgn == 1) {
                            for (int r = n0; r < rows; r += nthreads) {
                                fftColumns.realForward(a, r * columns);
                            }
                        } else {
                            for (int r = n0; r < rows; r += nthreads) {
                                fftColumns.realInverse(a, r * columns, scale);
                            }
                        }
                    }
                }
            });
        }
        ConcurrencyUtils.waitForCompletion(futures);
    }

    private void xdft2d0_subth2(final int icr, final int isgn, final double[] a, final boolean scale) {
        final int nthreads = ConcurrencyUtils.getNumberOfThreads() > rows ? rows : ConcurrencyUtils.getNumberOfThreads();

        Future<?>[] futures = new Future[nthreads];
        for (int i = 0; i < nthreads; i++) {
            final int n0 = i;
            futures[i] = ConcurrencyUtils.submit(new Runnable() {
                @Override
                                public void run() {
                    if (icr == 0) {
                        if (isgn == -1) {
                            for (int r = n0; r < rows; r += nthreads) {
                                fftColumns.complexForward(a, r * columns);
                            }
                        } else {
                            for (int r = n0; r < rows; r += nthreads) {
                                fftColumns.complexInverse(a, r * columns, scale);
                            }
                        }
                    } else {
                        if (isgn == 1) {
                            for (int r = n0; r < rows; r += nthreads) {
                                fftColumns.realForward(a, r * columns);
                            }
                        } else {
                            for (int r = n0; r < rows; r += nthreads) {
                                fftColumns.realInverse2(a, r * columns, scale);
                            }
                        }
                    }
                }
            });
        }
        ConcurrencyUtils.waitForCompletion(futures);
    }

    private void xdft2d0_subth1(final int icr, final int isgn, final double[][] a, final boolean scale) {
        final int nthreads = ConcurrencyUtils.getNumberOfThreads() > rows ? rows : ConcurrencyUtils.getNumberOfThreads();

        Future<?>[] futures = new Future[nthreads];
        for (int i = 0; i < nthreads; i++) {
            final int n0 = i;
            futures[i] = ConcurrencyUtils.submit(new Runnable() {
                @Override
                                public void run() {
                    if (icr == 0) {
                        if (isgn == -1) {
                            for (int r = n0; r < rows; r += nthreads) {
                                fftColumns.complexForward(a[r]);
                            }
                        } else {
                            for (int r = n0; r < rows; r += nthreads) {
                                fftColumns.complexInverse(a[r], scale);
                            }
                        }
                    } else {
                        if (isgn == 1) {
                            for (int r = n0; r < rows; r += nthreads) {
                                fftColumns.realForward(a[r]);
                            }
                        } else {
                            for (int r = n0; r < rows; r += nthreads) {
                                fftColumns.realInverse(a[r], scale);
                            }
                        }
                    }
                }
            });
        }
        ConcurrencyUtils.waitForCompletion(futures);
    }

    private void xdft2d0_subth2(final int icr, final int isgn, final double[][] a, final boolean scale) {
        final int nthreads = ConcurrencyUtils.getNumberOfThreads() > rows ? rows : ConcurrencyUtils.getNumberOfThreads();

        Future<?>[] futures = new Future[nthreads];
        for (int i = 0; i < nthreads; i++) {
            final int n0 = i;
            futures[i] = ConcurrencyUtils.submit(new Runnable() {
                @Override
                                public void run() {
                    if (icr == 0) {
                        if (isgn == -1) {
                            for (int r = n0; r < rows; r += nthreads) {
                                fftColumns.complexForward(a[r]);
                            }
                        } else {
                            for (int r = n0; r < rows; r += nthreads) {
                                fftColumns.complexInverse(a[r], scale);
                            }
                        }
                    } else {
                        if (isgn == 1) {
                            for (int r = n0; r < rows; r += nthreads) {
                                fftColumns.realForward(a[r]);
                            }
                        } else {
                            for (int r = n0; r < rows; r += nthreads) {
                                fftColumns.realInverse2(a[r], 0, scale);
                            }
                        }
                    }
                }
            });
        }
        ConcurrencyUtils.waitForCompletion(futures);
    }

    private void cdft2d_subth(final int isgn, final double[] a, final boolean scale) {
        int nthread = ConcurrencyUtils.getNumberOfThreads();
        int nt = 8 * rows;
        if (columns == 4 * nthread) {
            nt >>= 1;
        } else if (columns < 4 * nthread) {
            nthread = columns >> 1;
            nt >>= 2;
        }
        Future<?>[] futures = new Future[nthread];
        final int nthreads = nthread;
        for (int i = 0; i < nthread; i++) {
            final int n0 = i;
            final int startt = nt * i;
            futures[i] = ConcurrencyUtils.submit(new Runnable() {
                @Override
                                public void run() {
                    int idx1, idx2, idx3, idx4, idx5;
                    if (isgn == -1) {
                        if (columns > 4 * nthreads) {
                            for (int c = 8 * n0; c < columns; c += 8 * nthreads) {
                                for (int r = 0; r < rows; r++) {
                                    idx1 = r * columns + c;
                                    idx2 = startt + 2 * r;
                                    idx3 = startt + 2 * rows + 2 * r;
                                    idx4 = idx3 + 2 * rows;
                                    idx5 = idx4 + 2 * rows;
                                    t[idx2] = a[idx1];
                                    t[idx2 + 1] = a[idx1 + 1];
                                    t[idx3] = a[idx1 + 2];
                                    t[idx3 + 1] = a[idx1 + 3];
                                    t[idx4] = a[idx1 + 4];
                                    t[idx4 + 1] = a[idx1 + 5];
                                    t[idx5] = a[idx1 + 6];
                                    t[idx5 + 1] = a[idx1 + 7];
                                }
                                fftRows.complexForward(t, startt);
                                fftRows.complexForward(t, startt + 2 * rows);
                                fftRows.complexForward(t, startt + 4 * rows);
                                fftRows.complexForward(t, startt + 6 * rows);
                                for (int r = 0; r < rows; r++) {
                                    idx1 = r * columns + c;
                                    idx2 = startt + 2 * r;
                                    idx3 = startt + 2 * rows + 2 * r;
                                    idx4 = idx3 + 2 * rows;
                                    idx5 = idx4 + 2 * rows;
                                    a[idx1] = t[idx2];
                                    a[idx1 + 1] = t[idx2 + 1];
                                    a[idx1 + 2] = t[idx3];
                                    a[idx1 + 3] = t[idx3 + 1];
                                    a[idx1 + 4] = t[idx4];
                                    a[idx1 + 5] = t[idx4 + 1];
                                    a[idx1 + 6] = t[idx5];
                                    a[idx1 + 7] = t[idx5 + 1];
                                }
                            }
                        } else if (columns == 4 * nthreads) {
                            for (int r = 0; r < rows; r++) {
                                idx1 = r * columns + 4 * n0;
                                idx2 = startt + 2 * r;
                                idx3 = startt + 2 * rows + 2 * r;
                                t[idx2] = a[idx1];
                                t[idx2 + 1] = a[idx1 + 1];
                                t[idx3] = a[idx1 + 2];
                                t[idx3 + 1] = a[idx1 + 3];
                            }
                            fftRows.complexForward(t, startt);
                            fftRows.complexForward(t, startt + 2 * rows);
                            for (int r = 0; r < rows; r++) {
                                idx1 = r * columns + 4 * n0;
                                idx2 = startt + 2 * r;
                                idx3 = startt + 2 * rows + 2 * r;
                                a[idx1] = t[idx2];
                                a[idx1 + 1] = t[idx2 + 1];
                                a[idx1 + 2] = t[idx3];
                                a[idx1 + 3] = t[idx3 + 1];
                            }
                        } else if (columns == 2 * nthreads) {
                            for (int r = 0; r < rows; r++) {
                                idx1 = r * columns + 2 * n0;
                                idx2 = startt + 2 * r;
                                t[idx2] = a[idx1];
                                t[idx2 + 1] = a[idx1 + 1];
                            }
                            fftRows.complexForward(t, startt);
                            for (int r = 0; r < rows; r++) {
                                idx1 = r * columns + 2 * n0;
                                idx2 = startt + 2 * r;
                                a[idx1] = t[idx2];
                                a[idx1 + 1] = t[idx2 + 1];
                            }
                        }
                    } else {
                        if (columns > 4 * nthreads) {
                            for (int c = 8 * n0; c < columns; c += 8 * nthreads) {
                                for (int r = 0; r < rows; r++) {
                                    idx1 = r * columns + c;
                                    idx2 = startt + 2 * r;
                                    idx3 = startt + 2 * rows + 2 * r;
                                    idx4 = idx3 + 2 * rows;
                                    idx5 = idx4 + 2 * rows;
                                    t[idx2] = a[idx1];
                                    t[idx2 + 1] = a[idx1 + 1];
                                    t[idx3] = a[idx1 + 2];
                                    t[idx3 + 1] = a[idx1 + 3];
                                    t[idx4] = a[idx1 + 4];
                                    t[idx4 + 1] = a[idx1 + 5];
                                    t[idx5] = a[idx1 + 6];
                                    t[idx5 + 1] = a[idx1 + 7];
                                }
                                fftRows.complexInverse(t, startt, scale);
                                fftRows.complexInverse(t, startt + 2 * rows, scale);
                                fftRows.complexInverse(t, startt + 4 * rows, scale);
                                fftRows.complexInverse(t, startt + 6 * rows, scale);
                                for (int r = 0; r < rows; r++) {
                                    idx1 = r * columns + c;
                                    idx2 = startt + 2 * r;
                                    idx3 = startt + 2 * rows + 2 * r;
                                    idx4 = idx3 + 2 * rows;
                                    idx5 = idx4 + 2 * rows;
                                    a[idx1] = t[idx2];
                                    a[idx1 + 1] = t[idx2 + 1];
                                    a[idx1 + 2] = t[idx3];
                                    a[idx1 + 3] = t[idx3 + 1];
                                    a[idx1 + 4] = t[idx4];
                                    a[idx1 + 5] = t[idx4 + 1];
                                    a[idx1 + 6] = t[idx5];
                                    a[idx1 + 7] = t[idx5 + 1];
                                }
                            }
                        } else if (columns == 4 * nthreads) {
                            for (int r = 0; r < rows; r++) {
                                idx1 = r * columns + 4 * n0;
                                idx2 = startt + 2 * r;
                                idx3 = startt + 2 * rows + 2 * r;
                                t[idx2] = a[idx1];
                                t[idx2 + 1] = a[idx1 + 1];
                                t[idx3] = a[idx1 + 2];
                                t[idx3 + 1] = a[idx1 + 3];
                            }
                            fftRows.complexInverse(t, startt, scale);
                            fftRows.complexInverse(t, startt + 2 * rows, scale);
                            for (int r = 0; r < rows; r++) {
                                idx1 = r * columns + 4 * n0;
                                idx2 = startt + 2 * r;
                                idx3 = startt + 2 * rows + 2 * r;
                                a[idx1] = t[idx2];
                                a[idx1 + 1] = t[idx2 + 1];
                                a[idx1 + 2] = t[idx3];
                                a[idx1 + 3] = t[idx3 + 1];
                            }
                        } else if (columns == 2 * nthreads) {
                            for (int r = 0; r < rows; r++) {
                                idx1 = r * columns + 2 * n0;
                                idx2 = startt + 2 * r;
                                t[idx2] = a[idx1];
                                t[idx2 + 1] = a[idx1 + 1];
                            }
                            fftRows.complexInverse(t, startt, scale);
                            for (int r = 0; r < rows; r++) {
                                idx1 = r * columns + 2 * n0;
                                idx2 = startt + 2 * r;
                                a[idx1] = t[idx2];
                                a[idx1 + 1] = t[idx2 + 1];
                            }
                        }
                    }
                }
            });
        }
        ConcurrencyUtils.waitForCompletion(futures);
    }

    private void cdft2d_subth(final int isgn, final double[][] a, final boolean scale) {
        int nthread = ConcurrencyUtils.getNumberOfThreads();
        int nt = 8 * rows;
        if (columns == 4 * nthread) {
            nt >>= 1;
        } else if (columns < 4 * nthread) {
            nthread = columns >> 1;
            nt >>= 2;
        }
        Future<?>[] futures = new Future[nthread];
        final int nthreads = nthread;
        for (int i = 0; i < nthreads; i++) {
            final int n0 = i;
            final int startt = nt * i;
            futures[i] = ConcurrencyUtils.submit(new Runnable() {
                @Override
                                public void run() {
                    int idx2, idx3, idx4, idx5;
                    if (isgn == -1) {
                        if (columns > 4 * nthreads) {
                            for (int c = 8 * n0; c < columns; c += 8 * nthreads) {
                                for (int r = 0; r < rows; r++) {
                                    idx2 = startt + 2 * r;
                                    idx3 = startt + 2 * rows + 2 * r;
                                    idx4 = idx3 + 2 * rows;
                                    idx5 = idx4 + 2 * rows;
                                    t[idx2] = a[r][c];
                                    t[idx2 + 1] = a[r][c + 1];
                                    t[idx3] = a[r][c + 2];
                                    t[idx3 + 1] = a[r][c + 3];
                                    t[idx4] = a[r][c + 4];
                                    t[idx4 + 1] = a[r][c + 5];
                                    t[idx5] = a[r][c + 6];
                                    t[idx5 + 1] = a[r][c + 7];
                                }
                                fftRows.complexForward(t, startt);
                                fftRows.complexForward(t, startt + 2 * rows);
                                fftRows.complexForward(t, startt + 4 * rows);
                                fftRows.complexForward(t, startt + 6 * rows);
                                for (int r = 0; r < rows; r++) {
                                    idx2 = startt + 2 * r;
                                    idx3 = startt + 2 * rows + 2 * r;
                                    idx4 = idx3 + 2 * rows;
                                    idx5 = idx4 + 2 * rows;
                                    a[r][c] = t[idx2];
                                    a[r][c + 1] = t[idx2 + 1];
                                    a[r][c + 2] = t[idx3];
                                    a[r][c + 3] = t[idx3 + 1];
                                    a[r][c + 4] = t[idx4];
                                    a[r][c + 5] = t[idx4 + 1];
                                    a[r][c + 6] = t[idx5];
                                    a[r][c + 7] = t[idx5 + 1];
                                }
                            }
                        } else if (columns == 4 * nthreads) {
                            for (int r = 0; r < rows; r++) {
                                idx2 = startt + 2 * r;
                                idx3 = startt + 2 * rows + 2 * r;
                                t[idx2] = a[r][4 * n0];
                                t[idx2 + 1] = a[r][4 * n0 + 1];
                                t[idx3] = a[r][4 * n0 + 2];
                                t[idx3 + 1] = a[r][4 * n0 + 3];
                            }
                            fftRows.complexForward(t, startt);
                            fftRows.complexForward(t, startt + 2 * rows);
                            for (int r = 0; r < rows; r++) {
                                idx2 = startt + 2 * r;
                                idx3 = startt + 2 * rows + 2 * r;
                                a[r][4 * n0] = t[idx2];
                                a[r][4 * n0 + 1] = t[idx2 + 1];
                                a[r][4 * n0 + 2] = t[idx3];
                                a[r][4 * n0 + 3] = t[idx3 + 1];
                            }
                        } else if (columns == 2 * nthreads) {
                            for (int r = 0; r < rows; r++) {
                                idx2 = startt + 2 * r;
                                t[idx2] = a[r][2 * n0];
                                t[idx2 + 1] = a[r][2 * n0 + 1];
                            }
                            fftRows.complexForward(t, startt);
                            for (int r = 0; r < rows; r++) {
                                idx2 = startt + 2 * r;
                                a[r][2 * n0] = t[idx2];
                                a[r][2 * n0 + 1] = t[idx2 + 1];
                            }
                        }
                    } else {
                        if (columns > 4 * nthreads) {
                            for (int c = 8 * n0; c < columns; c += 8 * nthreads) {
                                for (int r = 0; r < rows; r++) {
                                    idx2 = startt + 2 * r;
                                    idx3 = startt + 2 * rows + 2 * r;
                                    idx4 = idx3 + 2 * rows;
                                    idx5 = idx4 + 2 * rows;
                                    t[idx2] = a[r][c];
                                    t[idx2 + 1] = a[r][c + 1];
                                    t[idx3] = a[r][c + 2];
                                    t[idx3 + 1] = a[r][c + 3];
                                    t[idx4] = a[r][c + 4];
                                    t[idx4 + 1] = a[r][c + 5];
                                    t[idx5] = a[r][c + 6];
                                    t[idx5 + 1] = a[r][c + 7];
                                }
                                fftRows.complexInverse(t, startt, scale);
                                fftRows.complexInverse(t, startt + 2 * rows, scale);
                                fftRows.complexInverse(t, startt + 4 * rows, scale);
                                fftRows.complexInverse(t, startt + 6 * rows, scale);
                                for (int r = 0; r < rows; r++) {
                                    idx2 = startt + 2 * r;
                                    idx3 = startt + 2 * rows + 2 * r;
                                    idx4 = idx3 + 2 * rows;
                                    idx5 = idx4 + 2 * rows;
                                    a[r][c] = t[idx2];
                                    a[r][c + 1] = t[idx2 + 1];
                                    a[r][c + 2] = t[idx3];
                                    a[r][c + 3] = t[idx3 + 1];
                                    a[r][c + 4] = t[idx4];
                                    a[r][c + 5] = t[idx4 + 1];
                                    a[r][c + 6] = t[idx5];
                                    a[r][c + 7] = t[idx5 + 1];
                                }
                            }
                        } else if (columns == 4 * nthreads) {
                            for (int r = 0; r < rows; r++) {
                                idx2 = startt + 2 * r;
                                idx3 = startt + 2 * rows + 2 * r;
                                t[idx2] = a[r][4 * n0];
                                t[idx2 + 1] = a[r][4 * n0 + 1];
                                t[idx3] = a[r][4 * n0 + 2];
                                t[idx3 + 1] = a[r][4 * n0 + 3];
                            }
                            fftRows.complexInverse(t, startt, scale);
                            fftRows.complexInverse(t, startt + 2 * rows, scale);
                            for (int r = 0; r < rows; r++) {
                                idx2 = startt + 2 * r;
                                idx3 = startt + 2 * rows + 2 * r;
                                a[r][4 * n0] = t[idx2];
                                a[r][4 * n0 + 1] = t[idx2 + 1];
                                a[r][4 * n0 + 2] = t[idx3];
                                a[r][4 * n0 + 3] = t[idx3 + 1];
                            }
                        } else if (columns == 2 * nthreads) {
                            for (int r = 0; r < rows; r++) {
                                idx2 = startt + 2 * r;
                                t[idx2] = a[r][2 * n0];
                                t[idx2 + 1] = a[r][2 * n0 + 1];
                            }
                            fftRows.complexInverse(t, startt, scale);
                            for (int r = 0; r < rows; r++) {
                                idx2 = startt + 2 * r;
                                a[r][2 * n0] = t[idx2];
                                a[r][2 * n0 + 1] = t[idx2 + 1];
                            }
                        }
                    }
                }
            });
        }
        ConcurrencyUtils.waitForCompletion(futures);
    }

    private void fillSymmetric(final double[] a) {
        final int twon2 = 2 * columns;
        int idx1, idx2, idx3, idx4;
        int n1d2 = rows / 2;

        for (int r = (rows - 1); r >= 1; r--) {
            idx1 = r * columns;
            idx2 = 2 * idx1;
            for (int c = 0; c < columns; c += 2) {
                a[idx2 + c] = a[idx1 + c];
                a[idx1 + c] = 0;
                a[idx2 + c + 1] = a[idx1 + c + 1];
                a[idx1 + c + 1] = 0;
            }
        }
        int nthreads = ConcurrencyUtils.getNumberOfThreads();
        if ((nthreads > 1) && useThreads && (n1d2 >= nthreads)) {
            Future<?>[] futures = new Future[nthreads];
            int l1k = n1d2 / nthreads;
            final int newn2 = 2 * columns;
            for (int i = 0; i < nthreads; i++) {
                final int l1offa, l1stopa, l2offa, l2stopa;
                if (i == 0)
                    l1offa = i * l1k + 1;
                else {
                    l1offa = i * l1k;
                }
                l1stopa = i * l1k + l1k;
                l2offa = i * l1k;
                if (i == nthreads - 1) {
                    l2stopa = i * l1k + l1k + 1;
                } else {
                    l2stopa = i * l1k + l1k;
                }
                futures[i] = ConcurrencyUtils.submit(new Runnable() {
                    @Override
                                        public void run() {
                        int idx1, idx2, idx3, idx4;

                        for (int r = l1offa; r < l1stopa; r++) {
                            idx1 = r * newn2;
                            idx2 = (rows - r) * newn2;
                            idx3 = idx1 + columns;
                            a[idx3] = a[idx2 + 1];
                            a[idx3 + 1] = -a[idx2];
                        }
                        for (int r = l1offa; r < l1stopa; r++) {
                            idx1 = r * newn2;
                            idx3 = (rows - r + 1) * newn2;
                            for (int c = columns + 2; c < newn2; c += 2) {
                                idx2 = idx3 - c;
                                idx4 = idx1 + c;
                                a[idx4] = a[idx2];
                                a[idx4 + 1] = -a[idx2 + 1];

                            }
                        }
                        for (int r = l2offa; r < l2stopa; r++) {
                            idx3 = ((rows - r) % rows) * newn2;
                            idx4 = r * newn2;
                            for (int c = 0; c < newn2; c += 2) {
                                idx1 = idx3 + (newn2 - c) % newn2;
                                idx2 = idx4 + c;
                                a[idx1] = a[idx2];
                                a[idx1 + 1] = -a[idx2 + 1];
                            }
                        }
                    }
                });
            }
            ConcurrencyUtils.waitForCompletion(futures);

        } else {

            for (int r = 1; r < n1d2; r++) {
                idx2 = r * twon2;
                idx3 = (rows - r) * twon2;
                a[idx2 + columns] = a[idx3 + 1];
                a[idx2 + columns + 1] = -a[idx3];
            }

            for (int r = 1; r < n1d2; r++) {
                idx2 = r * twon2;
                idx3 = (rows - r + 1) * twon2;
                for (int c = columns + 2; c < twon2; c += 2) {
                    a[idx2 + c] = a[idx3 - c];
                    a[idx2 + c + 1] = -a[idx3 - c + 1];

                }
            }
            for (int r = 0; r <= rows / 2; r++) {
                idx1 = r * twon2;
                idx4 = ((rows - r) % rows) * twon2;
                for (int c = 0; c < twon2; c += 2) {
                    idx2 = idx1 + c;
                    idx3 = idx4 + (twon2 - c) % twon2;
                    a[idx3] = a[idx2];
                    a[idx3 + 1] = -a[idx2 + 1];
                }
            }
        }
        a[columns] = -a[1];
        a[1] = 0;
        idx1 = n1d2 * twon2;
        a[idx1 + columns] = -a[idx1 + 1];
        a[idx1 + 1] = 0;
        a[idx1 + columns + 1] = 0;
    }

    private void fillSymmetric(final double[][] a) {
        final int newn2 = 2 * columns;
        int n1d2 = rows / 2;

        int nthreads = ConcurrencyUtils.getNumberOfThreads();
        if ((nthreads > 1) && useThreads && (n1d2 >= nthreads)) {
            Future<?>[] futures = new Future[nthreads];
            int l1k = n1d2 / nthreads;
            for (int i = 0; i < nthreads; i++) {
                final int l1offa, l1stopa, l2offa, l2stopa;
                if (i == 0)
                    l1offa = i * l1k + 1;
                else {
                    l1offa = i * l1k;
                }
                l1stopa = i * l1k + l1k;
                l2offa = i * l1k;
                if (i == nthreads - 1) {
                    l2stopa = i * l1k + l1k + 1;
                } else {
                    l2stopa = i * l1k + l1k;
                }
                futures[i] = ConcurrencyUtils.submit(new Runnable() {
                    @Override
                                        public void run() {
                        int idx1, idx2;
                        for (int r = l1offa; r < l1stopa; r++) {
                            idx1 = rows - r;
                            a[r][columns] = a[idx1][1];
                            a[r][columns + 1] = -a[idx1][0];
                        }
                        for (int r = l1offa; r < l1stopa; r++) {
                            idx1 = rows - r;
                            for (int c = columns + 2; c < newn2; c += 2) {
                                idx2 = newn2 - c;
                                a[r][c] = a[idx1][idx2];
                                a[r][c + 1] = -a[idx1][idx2 + 1];

                            }
                        }
                        for (int r = l2offa; r < l2stopa; r++) {
                            idx1 = (rows - r) % rows;
                            for (int c = 0; c < newn2; c = c + 2) {
                                idx2 = (newn2 - c) % newn2;
                                a[idx1][idx2] = a[r][c];
                                a[idx1][idx2 + 1] = -a[r][c + 1];
                            }
                        }
                    }
                });
            }
            ConcurrencyUtils.waitForCompletion(futures);
        } else {

            for (int r = 1; r < n1d2; r++) {
                int idx1 = rows - r;
                a[r][columns] = a[idx1][1];
                a[r][columns + 1] = -a[idx1][0];
            }
            for (int r = 1; r < n1d2; r++) {
                int idx1 = rows - r;
                for (int c = columns + 2; c < newn2; c += 2) {
                    int idx2 = newn2 - c;
                    a[r][c] = a[idx1][idx2];
                    a[r][c + 1] = -a[idx1][idx2 + 1];
                }
            }
            for (int r = 0; r <= rows / 2; r++) {
                int idx1 = (rows - r) % rows;
                for (int c = 0; c < newn2; c += 2) {
                    int idx2 = (newn2 - c) % newn2;
                    a[idx1][idx2] = a[r][c];
                    a[idx1][idx2 + 1] = -a[r][c + 1];
                }
            }
        }
        a[0][columns] = -a[0][1];
        a[0][1] = 0;
        a[n1d2][columns] = -a[n1d2][1];
        a[n1d2][1] = 0;
        a[n1d2][columns + 1] = 0;
    }
}