# MIT License
#
# Copyright (C) IBM Corporation 2019
#
# Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated
# documentation files (the "Software"), to deal in the Software without restriction, including without limitation the
# rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit
# persons to whom the Software is furnished to do so, subject to the following conditions:
#
# The above copyright notice and this permission notice shall be included in all copies or substantial portions of the
# Software.
#
# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE
# WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
# AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT,
# TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
# SOFTWARE.
#
#
# Copyright (c) 2005-2019, NumPy Developers.
# 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 name of the NumPy Developers nor the names of any 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 AND CONTRIBUTORS "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 OWNER OR CONTRIBUTORS 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.
"""
Differentially private histogram-related functions
Builds upon the histogram functionality of Numpy
"""
import warnings
from sys import maxsize

import numpy as np

from diffprivlib.accountant import BudgetAccountant
from diffprivlib.mechanisms import GeometricTruncated
from diffprivlib.utils import PrivacyLeakWarning, warn_unused_args


# noinspection PyShadowingBuiltins
def histogram(sample, epsilon=1.0, bins=10, range=None, weights=None, density=None, accountant=None, **unused_args):
    r"""
    Compute the differentially private histogram of a set of data.

    The histogram is computed using :obj:`numpy.histogram`, and noise added using :class:`.GeometricTruncated` to
    satisfy differential privacy.  If the `range` parameter is not specified correctly, a :class:`.PrivacyLeakWarning`
    is thrown.  Users are referred to :obj:`numpy.histogram` for more usage notes.

    Parameters
    ----------
    sample : array_like
        Input data.  The histogram is computed over the flattened array.

    epsilon : float, default: 1.0
        Privacy parameter :math:`\epsilon` to be applied.

    bins : int or sequence of scalars or str, default: 10
        If `bins` is an int, it defines the number of equal-width bins in the given range (10, by default).  If `bins`
        is a sequence, it defines a monotonically increasing array of bin edges, including the rightmost edge, allowing
        for non-uniform bin widths.

        If `bins` is a string, it defines the method used to calculate the optimal bin width, as defined by
        `histogram_bin_edges`.

    range : (float, float), optional
        The lower and upper range of the bins.  If not provided, range is simply ``(a.min(), a.max())``.  Values outside
        the range are ignored.  The first element of the range must be less than or equal to the second. `range` affects
        the automatic bin computation as well.  While bin width is computed to be optimal based on the actual data
        within `range`, the bin count will fill the entire range including portions containing no data.

    weights : array_like, optional
        An array of weights, of the same shape as `a`.  Each value in `a` only contributes its associated weight
        towards the bin count (instead of 1).  If `density` is True, the weights are normalized, so that the integral
        of the density over the range remains 1.

    density : bool, optional
        If ``False``, the result will contain the number of samples in each bin.  If ``True``, the result is the value
        of the probability *density* function at the bin, normalized such that the *integral* over the range is 1.
        Note that the sum of the histogram values will not be equal to 1 unless bins of unity width are chosen; it is
        not a probability *mass* function.

    accountant : BudgetAccountant, optional
        Accountant to keep track of privacy budget.

    Returns
    -------
    hist : array
        The values of the histogram.  See `density` and `weights` for a
        description of the possible semantics.
    bin_edges : array of dtype float
        Return the bin edges ``(length(hist)+1)``.


    See Also
    --------
    histogramdd, histogram2d

    Notes
    -----
    All but the last (righthand-most) bin is half-open.  In other words, if `bins` is::

      [1, 2, 3, 4]

    then the first bin is ``[1, 2)`` (including 1, but excluding 2) and the second ``[2, 3)``.  The last bin, however,
    is ``[3, 4]``, which *includes* 4.

    """
    warn_unused_args(unused_args)

    accountant = BudgetAccountant.load_default(accountant)
    accountant.check(epsilon, 0)

    if range is None:
        warnings.warn("Range parameter has not been specified. Falling back to taking range from the data.\n"
                      "To ensure differential privacy, and no additional privacy leakage, the range must be "
                      "specified independently of the data (i.e., using domain knowledge).", PrivacyLeakWarning)

    hist, bin_edges = np.histogram(sample, bins=bins, range=range, weights=weights, density=None)

    dp_mech = GeometricTruncated().set_epsilon(epsilon).set_sensitivity(1).set_bounds(0, maxsize)

    dp_hist = np.zeros_like(hist)

    for i in np.arange(dp_hist.shape[0]):
        dp_hist[i] = dp_mech.randomise(int(hist[i]))

    # dp_hist = dp_hist.astype(float, casting='safe')

    accountant.spend(epsilon, 0)

    if density:
        bin_sizes = np.array(np.diff(bin_edges), float)
        return dp_hist / bin_sizes / dp_hist.sum(), bin_edges

    return dp_hist, bin_edges


# noinspection PyShadowingBuiltins
def histogramdd(sample, epsilon=1.0, bins=10, range=None, weights=None, density=None, accountant=None, **unused_args):
    r"""
    Compute the differentially private multidimensional histogram of some data.

    The histogram is computed using :obj:`numpy.histogramdd`, and noise added using :class:`.GeometricTruncated` to
    satisfy differential privacy.  If the `range` parameter is not specified correctly, a :class:`.PrivacyLeakWarning`
    is thrown.  Users are referred to :obj:`numpy.histogramdd` for more usage notes.

    Parameters
    ----------
    sample : (N, D) array, or (D, N) array_like
        The data to be histogrammed.

        Note the unusual interpretation of sample when an array_like:

        * When an array, each row is a coordinate in a D-dimensional space - such as
          ``histogramgramdd(np.array([p1, p2, p3]))``.
        * When an array_like, each element is the list of values for single coordinate - such as
          ``histogramgramdd((X, Y, Z))``.

        The first form should be preferred.

    epsilon : float, default: 1.0
        Privacy parameter :math:`\epsilon` to be applied.

    bins : sequence or int, default: 10
        The bin specification:

        * A sequence of arrays describing the monotonically increasing bin edges along each dimension.
        * The number of bins for each dimension (nx, ny, ... =bins)
        * The number of bins for all dimensions (nx=ny=...=bins).

    range : sequence, optional
        A sequence of length D, each an optional (lower, upper) tuple giving the outer bin edges to be used if the edges
        are not given explicitly in `bins`.
        An entry of None in the sequence results in the minimum and maximum values being used for the corresponding
        dimension.
        The default, None, is equivalent to passing a tuple of D None values.

    density : bool, optional
        If False, the default, returns the number of samples in each bin.  If True, returns the probability *density*
        function at the bin, ``bin_count / sample_count / bin_volume``.

    weights : (N,) array_like, optional
        An array of values `w_i` weighing each sample `(x_i, y_i, z_i, ...)`.  Weights are normalized to 1 if normed is
        True.  If normed is False, the values of the returned histogram are equal to the sum of the weights belonging to
        the samples falling into each bin.

    accountant : BudgetAccountant, optional
        Accountant to keep track of privacy budget.

    Returns
    -------
    H : ndarray
        The multidimensional histogram of sample x.  See normed and weights for the different possible semantics.
    edges : list
        A list of D arrays describing the bin edges for each dimension.

    See Also
    --------
    histogram: 1-D differentially private histogram
    histogram2d: 2-D differentially private histogram

    """
    warn_unused_args(unused_args)

    accountant = BudgetAccountant.load_default(accountant)
    accountant.check(epsilon, 0)

    if range is None or (isinstance(range, list) and None in range):
        warnings.warn("Range parameter has not been specified (or has missing elements). Falling back to taking range "
                      "from the data.\n "
                      "To ensure differential privacy, and no additional privacy leakage, the range must be "
                      "specified for each dimension independently of the data (i.e., using domain knowledge).",
                      PrivacyLeakWarning)

    hist, bin_edges = np.histogramdd(sample, bins=bins, range=range, normed=None, weights=weights, density=None)

    dp_mech = GeometricTruncated().set_epsilon(epsilon).set_sensitivity(1).set_bounds(0, maxsize)

    dp_hist = np.zeros_like(hist)
    iterator = np.nditer(hist, flags=['multi_index'])

    while not iterator.finished:
        dp_hist[iterator.multi_index] = dp_mech.randomise(int(iterator[0]))
        iterator.iternext()

    dp_hist = dp_hist.astype(float, casting='safe')

    if density:
        # calculate the probability density function
        dims = len(dp_hist.shape)
        dp_hist_sum = dp_hist.sum()
        for i in np.arange(dims):
            shape = np.ones(dims, int)
            shape[i] = dp_hist.shape[i]
            # noinspection PyUnresolvedReferences
            dp_hist = dp_hist / np.diff(bin_edges[i]).reshape(shape)
        dp_hist /= dp_hist_sum

    accountant.spend(epsilon, 0)

    return dp_hist, bin_edges


# noinspection PyShadowingBuiltins
def histogram2d(array_x, array_y, epsilon=1.0, bins=10, range=None, weights=None, density=None, accountant=None,
                **unused_args):
    r"""
    Compute the differentially private bi-dimensional histogram of two data samples.

    Parameters
    ----------
    array_x : array_like, shape (N,)
        An array containing the x coordinates of the points to be histogrammed.

    array_y : array_like, shape (N,)
        An array containing the y coordinates of the points to be histogrammed.

    epsilon : float, default: 1.0
        Privacy parameter :math:`\epsilon` to be applied.

    bins : int or array_like or [int, int] or [array, array], default: 10
        The bin specification:

          * If int, the number of bins for the two dimensions (nx=ny=bins).
          * If array_like, the bin edges for the two dimensions (x_edges=y_edges=bins).
          * If [int, int], the number of bins in each dimension (nx, ny = bins).
          * If [array, array], the bin edges in each dimension (x_edges, y_edges = bins).
          * A combination [int, array] or [array, int], where int is the number of bins and array is the bin edges.

    range : array_like, shape(2,2), optional
        The leftmost and rightmost edges of the bins along each dimension (if not specified explicitly in the `bins`
        parameters): ``[[xmin, xmax], [ymin, ymax]]``.  All values outside of this range will be considered outliers and
        not tallied in the histogram.

    density : bool, optional
        If False, the default, returns the number of samples in each bin.  If True, returns the probability *density*
        function at the bin, ``bin_count / sample_count / bin_area``.

    weights : array_like, shape(N,), optional
        An array of values ``w_i`` weighing each sample ``(x_i, y_i)``.  Weights are normalized to 1 if `normed` is
        True.  If `normed` is False, the values of the returned histogram are equal to the sum of the weights belonging
        to the samples falling into each bin.

    accountant : BudgetAccountant, optional
        Accountant to keep track of privacy budget.

    Returns
    -------
    H : ndarray, shape(nx, ny)
        The bi-dimensional histogram of samples `x` and `y`.  Values in `x` are histogrammed along the first dimension
        and values in `y` are histogrammed along the second dimension.

    xedges : ndarray, shape(nx+1,)
        The bin edges along the first dimension.

    yedges : ndarray, shape(ny+1,)
        The bin edges along the second dimension.

    See Also
    --------
    histogram : 1D differentially private histogram
    histogramdd : Differentially private Multidimensional histogram

    Notes
    -----
    When `normed` is True, then the returned histogram is the sample density, defined such that the sum over bins of the
    product ``bin_value * bin_area`` is 1.

    Please note that the histogram does not follow the Cartesian convention where `x` values are on the abscissa and `y`
    values on the ordinate axis.  Rather, `x` is histogrammed along the first dimension of the array (vertical), and `y`
    along the second dimension of the array (horizontal).  This ensures compatibility with `histogramdd`.

    """
    warn_unused_args(unused_args)

    try:
        num_bins = len(bins)
    except TypeError:
        num_bins = 1

    if num_bins not in (1, 2):
        xedges = yedges = np.asarray(bins)
        bins = [xedges, yedges]

    hist, edges = histogramdd([array_x, array_y], epsilon=epsilon, bins=bins, range=range, weights=weights,
                              density=density, accountant=accountant)
    return hist, edges[0], edges[1]

# MIT License
#
# Copyright (C) IBM Corporation 2019
#
# Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated
# documentation files (the "Software"), to deal in the Software without restriction, including without limitation the
# rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit
# persons to whom the Software is furnished to do so, subject to the following conditions:
#
# The above copyright notice and this permission notice shall be included in all copies or substantial portions of the
# Software.
#
# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE
# WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
# AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT,
# TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
# SOFTWARE.
#
#
# Copyright (c) 2005-2019, NumPy Developers.
# 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 name of the NumPy Developers nor the names of any 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 AND CONTRIBUTORS "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 OWNER OR CONTRIBUTORS 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.
"""
Differentially private histogram-related functions
Builds upon the histogram functionality of Numpy
"""
import warnings
from sys import maxsize

import numpy as np

from diffprivlib.accountant import BudgetAccountant
from diffprivlib.mechanisms import GeometricTruncated
from diffprivlib.utils import PrivacyLeakWarning, warn_unused_args


# noinspection PyShadowingBuiltins
def histogram(sample, epsilon=1.0, bins=10, range=None, weights=None, density=None, accountant=None, **unused_args):
    r"""
    Compute the differentially private histogram of a set of data.

    The histogram is computed using :obj:`numpy.histogram`, and noise added using :class:`.GeometricTruncated` to
    satisfy differential privacy.  If the `range` parameter is not specified correctly, a :class:`.PrivacyLeakWarning`
    is thrown.  Users are referred to :obj:`numpy.histogram` for more usage notes.

    Parameters
    ----------
    sample : array_like
        Input data.  The histogram is computed over the flattened array.

    epsilon : float, default: 1.0
        Privacy parameter :math:`\epsilon` to be applied.

    bins : int or sequence of scalars or str, default: 10
        If `bins` is an int, it defines the number of equal-width bins in the given range (10, by default).  If `bins`
        is a sequence, it defines a monotonically increasing array of bin edges, including the rightmost edge, allowing
        for non-uniform bin widths.

        If `bins` is a string, it defines the method used to calculate the optimal bin width, as defined by
        `histogram_bin_edges`.

    range : (float, float), optional
        The lower and upper range of the bins.  If not provided, range is simply ``(a.min(), a.max())``.  Values outside
        the range are ignored.  The first element of the range must be less than or equal to the second. `range` affects
        the automatic bin computation as well.  While bin width is computed to be optimal based on the actual data
        within `range`, the bin count will fill the entire range including portions containing no data.

    weights : array_like, optional
        An array of weights, of the same shape as `a`.  Each value in `a` only contributes its associated weight
        towards the bin count (instead of 1).  If `density` is True, the weights are normalized, so that the integral
        of the density over the range remains 1.

    density : bool, optional
        If ``False``, the result will contain the number of samples in each bin.  If ``True``, the result is the value
        of the probability *density* function at the bin, normalized such that the *integral* over the range is 1.
        Note that the sum of the histogram values will not be equal to 1 unless bins of unity width are chosen; it is
        not a probability *mass* function.

    accountant : BudgetAccountant, optional
        Accountant to keep track of privacy budget.

    Returns
    -------
    hist : array
        The values of the histogram.  See `density` and `weights` for a
        description of the possible semantics.
    bin_edges : array of dtype float
        Return the bin edges ``(length(hist)+1)``.


    See Also
    --------
    histogramdd, histogram2d

    Notes
    -----
    All but the last (righthand-most) bin is half-open.  In other words, if `bins` is::

      [1, 2, 3, 4]

    then the first bin is ``[1, 2)`` (including 1, but excluding 2) and the second ``[2, 3)``.  The last bin, however,
    is ``[3, 4]``, which *includes* 4.

    """
    warn_unused_args(unused_args)

    accountant = BudgetAccountant.load_default(accountant)
    accountant.check(epsilon, 0)

    if range is None:
        warnings.warn("Range parameter has not been specified. Falling back to taking range from the data.\n"
                      "To ensure differential privacy, and no additional privacy leakage, the range must be "
                      "specified independently of the data (i.e., using domain knowledge).", PrivacyLeakWarning)

    hist, bin_edges = np.histogram(sample, bins=bins, range=range, weights=weights, density=None)

    dp_mech = GeometricTruncated().set_epsilon(epsilon).set_sensitivity(1).set_bounds(0, maxsize)

    dp_hist = np.zeros_like(hist)

    for i in np.arange(dp_hist.shape[0]):
        dp_hist[i] = dp_mech.randomise(int(hist[i]))

    # dp_hist = dp_hist.astype(float, casting='safe')

    accountant.spend(epsilon, 0)

    if density:
        bin_sizes = np.array(np.diff(bin_edges), float)
        return dp_hist / bin_sizes / dp_hist.sum(), bin_edges

    return dp_hist, bin_edges


# noinspection PyShadowingBuiltins
def histogramdd(sample, epsilon=1.0, bins=10, range=None, weights=None, density=None, accountant=None, **unused_args):
    r"""
    Compute the differentially private multidimensional histogram of some data.

    The histogram is computed using :obj:`numpy.histogramdd`, and noise added using :class:`.GeometricTruncated` to
    satisfy differential privacy.  If the `range` parameter is not specified correctly, a :class:`.PrivacyLeakWarning`
    is thrown.  Users are referred to :obj:`numpy.histogramdd` for more usage notes.

    Parameters
    ----------
    sample : (N, D) array, or (D, N) array_like
        The data to be histogrammed.

        Note the unusual interpretation of sample when an array_like:

        * When an array, each row is a coordinate in a D-dimensional space - such as
          ``histogramgramdd(np.array([p1, p2, p3]))``.
        * When an array_like, each element is the list of values for single coordinate - such as
          ``histogramgramdd((X, Y, Z))``.

        The first form should be preferred.

    epsilon : float, default: 1.0
        Privacy parameter :math:`\epsilon` to be applied.

    bins : sequence or int, default: 10
        The bin specification:

        * A sequence of arrays describing the monotonically increasing bin edges along each dimension.
        * The number of bins for each dimension (nx, ny, ... =bins)
        * The number of bins for all dimensions (nx=ny=...=bins).

    range : sequence, optional
        A sequence of length D, each an optional (lower, upper) tuple giving the outer bin edges to be used if the edges
        are not given explicitly in `bins`.
        An entry of None in the sequence results in the minimum and maximum values being used for the corresponding
        dimension.
        The default, None, is equivalent to passing a tuple of D None values.

    density : bool, optional
        If False, the default, returns the number of samples in each bin.  If True, returns the probability *density*
        function at the bin, ``bin_count / sample_count / bin_volume``.

    weights : (N,) array_like, optional
        An array of values `w_i` weighing each sample `(x_i, y_i, z_i, ...)`.  Weights are normalized to 1 if normed is
        True.  If normed is False, the values of the returned histogram are equal to the sum of the weights belonging to
        the samples falling into each bin.

    accountant : BudgetAccountant, optional
        Accountant to keep track of privacy budget.

    Returns
    -------
    H : ndarray
        The multidimensional histogram of sample x.  See normed and weights for the different possible semantics.
    edges : list
        A list of D arrays describing the bin edges for each dimension.

    See Also
    --------
    histogram: 1-D differentially private histogram
    histogram2d: 2-D differentially private histogram

    """
    warn_unused_args(unused_args)

    accountant = BudgetAccountant.load_default(accountant)
    accountant.check(epsilon, 0)

    if range is None or (isinstance(range, list) and None in range):
        warnings.warn("Range parameter has not been specified (or has missing elements). Falling back to taking range "
                      "from the data.\n "
                      "To ensure differential privacy, and no additional privacy leakage, the range must be "
                      "specified for each dimension independently of the data (i.e., using domain knowledge).",
                      PrivacyLeakWarning)

    hist, bin_edges = np.histogramdd(sample, bins=bins, range=range, normed=None, weights=weights, density=None)

    dp_mech = GeometricTruncated().set_epsilon(epsilon).set_sensitivity(1).set_bounds(0, maxsize)

    dp_hist = np.zeros_like(hist)
    iterator = np.nditer(hist, flags=['multi_index'])

    while not iterator.finished:
        dp_hist[iterator.multi_index] = dp_mech.randomise(int(iterator[0]))
        iterator.iternext()

    dp_hist = dp_hist.astype(float, casting='safe')

    if density:
        # calculate the probability density function
        dims = len(dp_hist.shape)
        dp_hist_sum = dp_hist.sum()
        for i in np.arange(dims):
            shape = np.ones(dims, int)
            shape[i] = dp_hist.shape[i]
            # noinspection PyUnresolvedReferences
            dp_hist = dp_hist / np.diff(bin_edges[i]).reshape(shape)
        dp_hist /= dp_hist_sum

    accountant.spend(epsilon, 0)

    return dp_hist, bin_edges


# noinspection PyShadowingBuiltins
def histogram2d(array_x, array_y, epsilon=1.0, bins=10, range=None, weights=None, density=None, accountant=None,
                **unused_args):
    r"""
    Compute the differentially private bi-dimensional histogram of two data samples.

    Parameters
    ----------
    array_x : array_like, shape (N,)
        An array containing the x coordinates of the points to be histogrammed.

    array_y : array_like, shape (N,)
        An array containing the y coordinates of the points to be histogrammed.

    epsilon : float, default: 1.0
        Privacy parameter :math:`\epsilon` to be applied.

    bins : int or array_like or [int, int] or [array, array], default: 10
        The bin specification:

          * If int, the number of bins for the two dimensions (nx=ny=bins).
          * If array_like, the bin edges for the two dimensions (x_edges=y_edges=bins).
          * If [int, int], the number of bins in each dimension (nx, ny = bins).
          * If [array, array], the bin edges in each dimension (x_edges, y_edges = bins).
          * A combination [int, array] or [array, int], where int is the number of bins and array is the bin edges.

    range : array_like, shape(2,2), optional
        The leftmost and rightmost edges of the bins along each dimension (if not specified explicitly in the `bins`
        parameters): ``[[xmin, xmax], [ymin, ymax]]``.  All values outside of this range will be considered outliers and
        not tallied in the histogram.

    density : bool, optional
        If False, the default, returns the number of samples in each bin.  If True, returns the probability *density*
        function at the bin, ``bin_count / sample_count / bin_area``.

    weights : array_like, shape(N,), optional
        An array of values ``w_i`` weighing each sample ``(x_i, y_i)``.  Weights are normalized to 1 if `normed` is
        True.  If `normed` is False, the values of the returned histogram are equal to the sum of the weights belonging
        to the samples falling into each bin.

    accountant : BudgetAccountant, optional
        Accountant to keep track of privacy budget.

    Returns
    -------
    H : ndarray, shape(nx, ny)
        The bi-dimensional histogram of samples `x` and `y`.  Values in `x` are histogrammed along the first dimension
        and values in `y` are histogrammed along the second dimension.

    xedges : ndarray, shape(nx+1,)
        The bin edges along the first dimension.

    yedges : ndarray, shape(ny+1,)
        The bin edges along the second dimension.

    See Also
    --------
    histogram : 1D differentially private histogram
    histogramdd : Differentially private Multidimensional histogram

    Notes
    -----
    When `normed` is True, then the returned histogram is the sample density, defined such that the sum over bins of the
    product ``bin_value * bin_area`` is 1.

    Please note that the histogram does not follow the Cartesian convention where `x` values are on the abscissa and `y`
    values on the ordinate axis.  Rather, `x` is histogrammed along the first dimension of the array (vertical), and `y`
    along the second dimension of the array (horizontal).  This ensures compatibility with `histogramdd`.

    """
    warn_unused_args(unused_args)

    try:
        num_bins = len(bins)
    except TypeError:
        num_bins = 1

    if num_bins not in (1, 2):
        xedges = yedges = np.asarray(bins)
        bins = [xedges, yedges]

    hist, edges = histogramdd([array_x, array_y], epsilon=epsilon, bins=bins, range=range, weights=weights,
                              density=density, accountant=accountant)
    return hist, edges[0], edges[1]

# MIT License # # Copyright (C) IBM Corporation 2019 # # Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated # documentation files (the "Software"), to deal in the Software without restriction, including without limitation the # rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit # persons to whom the Software is furnished to do so, subject to the following conditions: # # The above copyright notice and this permission notice shall be included in all copies or substantial portions of the # Software. # # THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE # WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE # AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, # TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE # SOFTWARE. # # # Copyright (c) 2005-2019, NumPy Developers. # 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 name of the NumPy Developers nor the names of any 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 AND CONTRIBUTORS "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 OWNER OR CONTRIBUTORS 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. Differentially private histogram-related functions Builds upon the histogram functionality of Numpy # noinspection PyShadowingBuiltins Compute the differentially private histogram of a set of data.      The histogram is computed using :obj:`numpy.histogram`, and noise added using :class:`.GeometricTruncated` to     satisfy differential privacy.  If the `range` parameter is not specified correctly, a :class:`.PrivacyLeakWarning`     is thrown.  Users are referred to :obj:`numpy.histogram` for more usage notes.      Parameters     ----------     sample : array_like         Input data.  The histogram is computed over the flattened array.      epsilon : float, default: 1.0         Privacy parameter :math:`\epsilon` to be applied.      bins : int or sequence of scalars or str, default: 10         If `bins` is an int, it defines the number of equal-width bins in the given range (10, by default).  If `bins`         is a sequence, it defines a monotonically increasing array of bin edges, including the rightmost edge, allowing         for non-uniform bin widths.          If `bins` is a string, it defines the method used to calculate the optimal bin width, as defined by         `histogram_bin_edges`.      range : (float, float), optional         The lower and upper range of the bins.  If not provided, range is simply ``(a.min(), a.max())``.  Values outside         the range are ignored.  The first element of the range must be less than or equal to the second. `range` affects         the automatic bin computation as well.  While bin width is computed to be optimal based on the actual data         within `range`, the bin count will fill the entire range including portions containing no data.      weights : array_like, optional         An array of weights, of the same shape as `a`.  Each value in `a` only contributes its associated weight         towards the bin count (instead of 1).  If `density` is True, the weights are normalized, so that the integral         of the density over the range remains 1.      density : bool, optional         If ``False``, the result will contain the number of samples in each bin.  If ``True``, the result is the value         of the probability *density* function at the bin, normalized such that the *integral* over the range is 1.         Note that the sum of the histogram values will not be equal to 1 unless bins of unity width are chosen; it is         not a probability *mass* function.      accountant : BudgetAccountant, optional         Accountant to keep track of privacy budget.      Returns     -------     hist : array         The values of the histogram.  See `density` and `weights` for a         description of the possible semantics.     bin_edges : array of dtype float         Return the bin edges ``(length(hist)+1)``.       See Also     --------     histogramdd, histogram2d      Notes     -----     All but the last (righthand-most) bin is half-open.  In other words, if `bins` is::        [1, 2, 3, 4]      then the first bin is ``[1, 2)`` (including 1, but excluding 2) and the second ``[2, 3)``.  The last bin, however,     is ``[3, 4]``, which *includes* 4. # dp_hist = dp_hist.astype(float, casting='safe') # noinspection PyShadowingBuiltins Compute the differentially private multidimensional histogram of some data.      The histogram is computed using :obj:`numpy.histogramdd`, and noise added using :class:`.GeometricTruncated` to     satisfy differential privacy.  If the `range` parameter is not specified correctly, a :class:`.PrivacyLeakWarning`     is thrown.  Users are referred to :obj:`numpy.histogramdd` for more usage notes.      Parameters     ----------     sample : (N, D) array, or (D, N) array_like         The data to be histogrammed.          Note the unusual interpretation of sample when an array_like:          * When an array, each row is a coordinate in a D-dimensional space - such as           ``histogramgramdd(np.array([p1, p2, p3]))``.         * When an array_like, each element is the list of values for single coordinate - such as           ``histogramgramdd((X, Y, Z))``.          The first form should be preferred.      epsilon : float, default: 1.0         Privacy parameter :math:`\epsilon` to be applied.      bins : sequence or int, default: 10         The bin specification:          * A sequence of arrays describing the monotonically increasing bin edges along each dimension.         * The number of bins for each dimension (nx, ny, ... =bins)         * The number of bins for all dimensions (nx=ny=...=bins).      range : sequence, optional         A sequence of length D, each an optional (lower, upper) tuple giving the outer bin edges to be used if the edges         are not given explicitly in `bins`.         An entry of None in the sequence results in the minimum and maximum values being used for the corresponding         dimension.         The default, None, is equivalent to passing a tuple of D None values.      density : bool, optional         If False, the default, returns the number of samples in each bin.  If True, returns the probability *density*         function at the bin, ``bin_count / sample_count / bin_volume``.      weights : (N,) array_like, optional         An array of values `w_i` weighing each sample `(x_i, y_i, z_i, ...)`.  Weights are normalized to 1 if normed is         True.  If normed is False, the values of the returned histogram are equal to the sum of the weights belonging to         the samples falling into each bin.      accountant : BudgetAccountant, optional         Accountant to keep track of privacy budget.      Returns     -------     H : ndarray         The multidimensional histogram of sample x.  See normed and weights for the different possible semantics.     edges : list         A list of D arrays describing the bin edges for each dimension.      See Also     --------     histogram: 1-D differentially private histogram     histogram2d: 2-D differentially private histogram # calculate the probability density function # noinspection PyUnresolvedReferences # noinspection PyShadowingBuiltins Compute the differentially private bi-dimensional histogram of two data samples.      Parameters     ----------     array_x : array_like, shape (N,)         An array containing the x coordinates of the points to be histogrammed.      array_y : array_like, shape (N,)         An array containing the y coordinates of the points to be histogrammed.      epsilon : float, default: 1.0         Privacy parameter :math:`\epsilon` to be applied.      bins : int or array_like or [int, int] or [array, array], default: 10         The bin specification:            * If int, the number of bins for the two dimensions (nx=ny=bins).           * If array_like, the bin edges for the two dimensions (x_edges=y_edges=bins).           * If [int, int], the number of bins in each dimension (nx, ny = bins).           * If [array, array], the bin edges in each dimension (x_edges, y_edges = bins).           * A combination [int, array] or [array, int], where int is the number of bins and array is the bin edges.      range : array_like, shape(2,2), optional         The leftmost and rightmost edges of the bins along each dimension (if not specified explicitly in the `bins`         parameters): ``[[xmin, xmax], [ymin, ymax]]``.  All values outside of this range will be considered outliers and         not tallied in the histogram.      density : bool, optional         If False, the default, returns the number of samples in each bin.  If True, returns the probability *density*         function at the bin, ``bin_count / sample_count / bin_area``.      weights : array_like, shape(N,), optional         An array of values ``w_i`` weighing each sample ``(x_i, y_i)``.  Weights are normalized to 1 if `normed` is         True.  If `normed` is False, the values of the returned histogram are equal to the sum of the weights belonging         to the samples falling into each bin.      accountant : BudgetAccountant, optional         Accountant to keep track of privacy budget.      Returns     -------     H : ndarray, shape(nx, ny)         The bi-dimensional histogram of samples `x` and `y`.  Values in `x` are histogrammed along the first dimension         and values in `y` are histogrammed along the second dimension.      xedges : ndarray, shape(nx+1,)         The bin edges along the first dimension.      yedges : ndarray, shape(ny+1,)         The bin edges along the second dimension.      See Also     --------     histogram : 1D differentially private histogram     histogramdd : Differentially private Multidimensional histogram      Notes     -----     When `normed` is True, then the returned histogram is the sample density, defined such that the sum over bins of the     product ``bin_value * bin_area`` is 1.      Please note that the histogram does not follow the Cartesian convention where `x` values are on the abscissa and `y`     values on the ordinate axis.  Rather, `x` is histogrammed along the first dimension of the array (vertical), and `y`     along the second dimension of the array (horizontal).  This ensures compatibility with `histogramdd`.