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# Source code for SALib.sample.sobol_sequence

    import math
    import sys

    import numpy as np

    from .directions import directions

    if sys.version_info[0] > 2:
        long = int

    # ==============================================================================
    # The following code is based on the Sobol sequence generator by Frances
    # Y. Kuo and Stephen Joe. The license terms are provided below.
    #
    # Copyright (c) 2008, Frances Y. Kuo and Stephen Joe
    # All rights reserved.
    #
    # Redistribution and use in source and binary forms, with or without
    # modification, are permitted provided that the following conditions are
    # met:
    #
    # Redistributions of source code must retain the above copyright
    # notice, this list of conditions and the following disclaimer.
    #
    # Redistributions in binary form must reproduce the above copyright
    # notice, this list of conditions and the following disclaimer in the
    # documentation and/or other materials provided with the distribution.
    #
    # Neither the names of the copyright holders nor the names of the
    # University of New South Wales and the University of Waikato
    # and its contributors may be used to endorse or promote products derived
    # from this software without specific prior written permission.
    #
    # THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS ``AS IS'' AND ANY
    # EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
    # WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
    # DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDERS BE LIABLE FOR ANY
    # DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
    # DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
    # OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
    # HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
    # STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
    # ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
    # POSSIBILITY OF SUCH DAMAGE.
    # ==============================================================================

    def sample(N, D):
        """Generate (N x D) numpy array of Sobol sequence samples"""
        scale = 31
        result = np.zeros([N, D])

        if D > len(directions) + 1:
            raise ValueError("Error in Sobol sequence: not enough dimensions")

        L = int(math.ceil(math.log(N) / math.log(2)))

        if L > scale:
            raise ValueError("Error in Sobol sequence: not enough bits")

        for i in range(D):
            V = np.zeros(L + 1, dtype=long)

            if i == 0:
                for j in range(1, L + 1):
                    V[j] = 1 << (scale - j)  # all m's = 1
            else:
                m = np.array(directions[i - 1], dtype=int)
                a = m[0]
                s = len(m) - 1

                # The following code discards the first row of the ``m`` array
                # Because it has floating point errors, e.g. values of 2.24e-314
                if L <= s:
                    for j in range(1, L + 1):
                        V[j] = m[j] << (scale - j)
                else:
                    for j in range(1, s + 1):
                        V[j] = m[j] << (scale - j)
                    for j in range(s + 1, L + 1):
                        V[j] = V[j - s] ^ (V[j - s] >> s)
                        for k in range(1, s):
                            V[j] ^= ((a >> (s - 1 - k)) & 1) * V[j - k]

            X = long(0)
            for j in range(1, N):
                X ^= V[index_of_least_significant_zero_bit(j - 1)]
                result[j][i] = float(X / math.pow(2, scale))

        return result

    def index_of_least_significant_zero_bit(value):
        index = 1
        while (value & 1) != 0:
            value >>= 1
            index += 1

        return index