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typedef double (*__pyx_t_6mtrand_rk_cont0)(rk_state *);

typedef double (*__pyx_t_6mtrand_rk_cont1)(rk_state *, double);

typedef double (*__pyx_t_6mtrand_rk_cont2)(rk_state *, double, double);

typedef double (*__pyx_t_6mtrand_rk_cont3)(rk_state *, double, double, double);

typedef long (*__pyx_t_6mtrand_rk_disc0)(rk_state *);

typedef long (*__pyx_t_6mtrand_rk_discnp)(rk_state *, long, double);

typedef long (*__pyx_t_6mtrand_rk_discdd)(rk_state *, double, double);

typedef long (*__pyx_t_6mtrand_rk_discnmN)(rk_state *, long, long, long);

typedef long (*__pyx_t_6mtrand_rk_discd)(rk_state *, double);

/* "mtrand.pyx":522
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 * cdef class RandomState:             # <<<<<<<<<<<<<<
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 *     RandomState(seed=None)
 */

struct __pyx_obj_6mtrand_RandomState {
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static PyObject *__Pyx_Import(PyObject *name, PyObject *from_list); /*proto*/

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static PyTypeObject *__Pyx_ImportType(const char *module_name, const char *class_name, long size, int strict);  /*proto*/

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static PyTypeObject *__pyx_ptype_6mtrand_ndarray = 0;
static PyTypeObject *__pyx_ptype_6mtrand_flatiter = 0;
static PyTypeObject *__pyx_ptype_6mtrand_broadcast = 0;
static PyTypeObject *__pyx_ptype_6mtrand_RandomState = 0;
static PyObject *__pyx_f_6mtrand_cont0_array(rk_state *, __pyx_t_6mtrand_rk_cont0, PyObject *); /*proto*/
static PyObject *__pyx_f_6mtrand_cont1_array_sc(rk_state *, __pyx_t_6mtrand_rk_cont1, PyObject *, double); /*proto*/
static PyObject *__pyx_f_6mtrand_cont1_array(rk_state *, __pyx_t_6mtrand_rk_cont1, PyObject *, PyArrayObject *); /*proto*/
static PyObject *__pyx_f_6mtrand_cont2_array_sc(rk_state *, __pyx_t_6mtrand_rk_cont2, PyObject *, double, double); /*proto*/
static PyObject *__pyx_f_6mtrand_cont2_array(rk_state *, __pyx_t_6mtrand_rk_cont2, PyObject *, PyArrayObject *, PyArrayObject *); /*proto*/
static PyObject *__pyx_f_6mtrand_cont3_array_sc(rk_state *, __pyx_t_6mtrand_rk_cont3, PyObject *, double, double, double); /*proto*/
static PyObject *__pyx_f_6mtrand_cont3_array(rk_state *, __pyx_t_6mtrand_rk_cont3, PyObject *, PyArrayObject *, PyArrayObject *, PyArrayObject *); /*proto*/
static PyObject *__pyx_f_6mtrand_disc0_array(rk_state *, __pyx_t_6mtrand_rk_disc0, PyObject *); /*proto*/
static PyObject *__pyx_f_6mtrand_discnp_array_sc(rk_state *, __pyx_t_6mtrand_rk_discnp, PyObject *, long, double); /*proto*/
static PyObject *__pyx_f_6mtrand_discnp_array(rk_state *, __pyx_t_6mtrand_rk_discnp, PyObject *, PyArrayObject *, PyArrayObject *); /*proto*/
static PyObject *__pyx_f_6mtrand_discdd_array_sc(rk_state *, __pyx_t_6mtrand_rk_discdd, PyObject *, double, double); /*proto*/
static PyObject *__pyx_f_6mtrand_discdd_array(rk_state *, __pyx_t_6mtrand_rk_discdd, PyObject *, PyArrayObject *, PyArrayObject *); /*proto*/
static PyObject *__pyx_f_6mtrand_discnmN_array_sc(rk_state *, __pyx_t_6mtrand_rk_discnmN, PyObject *, long, long, long); /*proto*/
static PyObject *__pyx_f_6mtrand_discnmN_array(rk_state *, __pyx_t_6mtrand_rk_discnmN, PyObject *, PyArrayObject *, PyArrayObject *, PyArrayObject *); /*proto*/
static PyObject *__pyx_f_6mtrand_discd_array_sc(rk_state *, __pyx_t_6mtrand_rk_discd, PyObject *, double); /*proto*/
static PyObject *__pyx_f_6mtrand_discd_array(rk_state *, __pyx_t_6mtrand_rk_discd, PyObject *, PyArrayObject *); /*proto*/
static double __pyx_f_6mtrand_kahan_sum(double *, long); /*proto*/
#define __Pyx_MODULE_NAME "mtrand"
static int __pyx_module_is_main_mtrand = 0;

/* Implementation of mtrand */
static PyObject *__pyx_builtin_ValueError;
static PyObject *__pyx_builtin_TypeError;
static char __pyx_k_1[] = "size is not compatible with inputs";
static char __pyx_k_9[] = "algorithm must be 'MT19937'";
static char __pyx_k_11[] = "state must be 624 longs";
static char __pyx_k_13[] = "low >= high";
static char __pyx_k_19[] = "scale <= 0";
static char __pyx_k_22[] = "a <= 0";
static char __pyx_k_24[] = "b <= 0";
static char __pyx_k_31[] = "shape <= 0";
static char __pyx_k_41[] = "dfnum <= 0";
static char __pyx_k_43[] = "dfden <= 0";
static char __pyx_k_45[] = "dfnum <= 1";
static char __pyx_k_48[] = "nonc < 0";
static char __pyx_k_53[] = "df <= 0";
static char __pyx_k_57[] = "nonc <= 0";
static char __pyx_k_59[] = "df <= 1";
static char __pyx_k_64[] = "kappa < 0";
static char __pyx_k_87[] = "sigma <= 0";
static char __pyx_k_89[] = "sigma <= 0.0";
static char __pyx_k_93[] = "scale <= 0.0";
static char __pyx_k_95[] = "mean <= 0";
static char __pyx_k_98[] = "mean <= 0.0";
static char __pyx_k__a[] = "a";
static char __pyx_k__b[] = "b";
static char __pyx_k__f[] = "f";
static char __pyx_k__l[] = "l";
static char __pyx_k__n[] = "n";
static char __pyx_k__p[] = "p";
static char __pyx_k_101[] = "left > mode";
static char __pyx_k_103[] = "mode > right";
static char __pyx_k_105[] = "left == right";
static char __pyx_k_110[] = "n <= 0";
static char __pyx_k_112[] = "p < 0";
static char __pyx_k_114[] = "p > 1";
static char __pyx_k_126[] = "lam < 0";
static char __pyx_k_128[] = "lam value too large";
static char __pyx_k_131[] = "lam value too large.";
static char __pyx_k_133[] = "a <= 1.0";
static char __pyx_k_136[] = "p < 0.0";
static char __pyx_k_138[] = "p > 1.0";
static char __pyx_k_142[] = "ngood < 1";
static char __pyx_k_144[] = "nbad < 1";
static char __pyx_k_146[] = "nsample < 1";
static char __pyx_k_148[] = "ngood + nbad < nsample";
static char __pyx_k_154[] = "p <= 0.0";
static char __pyx_k_156[] = "p >= 1.0";
static char __pyx_k_160[] = "mean must be 1 dimensional";
static char __pyx_k_162[] = "cov must be 2 dimensional and square";
static char __pyx_k_164[] = "mean and cov must have same length";
static char __pyx_k_166[] = "numpy.dual";
static char __pyx_k_167[] = "sum(pvals[:-1]) > 1.0";
static char __pyx_k_171[] = "standard_exponential";
static char __pyx_k_172[] = "noncentral_chisquare";
static char __pyx_k_173[] = "RandomState.random_sample (line 719)";
static char __pyx_k_174[] = "\n        random_sample(size=None)\n\n        Return random floats in the half-open interval [0.0, 1.0).\n\n        Results are from the \"continuous uniform\" distribution over the\n        stated interval.  To sample :math:`Unif[a, b), b > a` multiply\n        the output of `random_sample` by `(b-a)` and add `a`::\n\n          (b - a) * random_sample() + a\n\n        Parameters\n        ----------\n        size : int or tuple of ints, optional\n            Defines the shape of the returned array of random floats. If None\n            (the default), returns a single float.\n\n        Returns\n        -------\n        out : float or ndarray of floats\n            Array of random floats of shape `size` (unless ``size=None``, in which\n            case a single float is returned).\n\n        Examples\n        --------\n        >>> np.random.random_sample()\n        0.47108547995356098\n        >>> type(np.random.random_sample())\n        <type 'float'>\n        >>> np.random.random_sample((5,))\n        array([ 0.30220482,  0.86820401,  0.1654503 ,  0.11659149,  0.54323428])\n\n        Three-by-two array of random numbers from [-5, 0):\n\n        >>> 5 * np.random.random_sample((3, 2)) - 5\n        array([[-3.99149989, -0.52338984],\n               [-2.99091858, -0.79479508],\n               [-1.23204345, -1.75224494]])\n\n        ";
static char __pyx_k_175[] = "RandomState.tomaxint (line 762)";
static char __pyx_k_176[] = "\n        tomaxint(size=None)\n\n        Random integers between 0 and ``sys.maxint``, inclusive.\n\n        Return a sample of uniformly distributed random integers in the interval\n        [0, ``sys.maxint``].\n\n        Parameters\n        ----------\n        size : tuple of ints, int, optional\n            Shape of output.  If this is, for example, (m,n,k), m*n*k samples\n            are generated.  If no shape is specified, a single sample is\n            returned.\n\n        Returns\n        -------\n        out : ndarray\n            Drawn samples, with shape `size`.\n\n        See Also\n        --------\n        randint : Uniform sampling over a given half-open interval of integers.\n        random_integers : Uniform sampling over a given closed interval of\n            integers.\n\n        Examples\n        --------\n        >>> RS = np.random.mtrand.RandomState() # need a RandomState object\n        >>> RS.tomaxint((2,2,2))\n        array([[[1170048599, 1600360186],\n                [ 739731006, 1947757578]],\n               [[1871712945,  752307660],\n                [1601631370, 1479324245]]])\n        >>> import sys\n        >>> sys.maxint\n        2147483647\n        >>> RS.tomaxint((2,2,2)) < sys.maxint\n        array([[[ True,  True],\n                [ True,  True]],\n               [[ True,  True],\n                [ True,  True]]], dtype=bool)\n\n        ";
static char __pyx_k_177[] = "RandomState.randint (line 809)";
static char __pyx_k_178[] = "\n        randint(low, high=None, size=None)\n\n        Return random integers from `low` (inclusive) to `high` (exclusive).\n\n        Return random integers from the \"discrete uniform\" distribution in the\n        \"half-open\" interval [`low`, `high`). If `high` is None (the default),\n        then results are from [0, `low`).\n\n        Parameters\n        ----------\n        low : int\n            Lowest (signed) integer to be drawn from the distribution (unless\n            ``high=None``, in which case this parameter is the *highest* such\n            integer).\n        high : int, optional\n            If provided, one above the largest (signed) integer to be drawn\n            from the distribution (see above for behavior if ``high=None``).\n        size : int or tuple of ints, optional\n            Output shape. Default is None, in which case a single int is\n            returned.\n\n        Returns\n        -------\n        out : int or ndarray of ints\n            `size`-shaped array of random integers from the appropriate\n            distribution, or a single such random int if `size` not provided.\n\n        See Also\n        --------\n        random.random_integers : similar to `randint`, only for the closed\n            interval [`low`, `high`], and 1 is the lowest value if `high` is\n            omitted. In particular, this other one is the one to use to generate\n            uniformly distributed discrete non-integers.\n\n        Examples\n        --------\n        >>> np.random.randint(2, size=10)\n        array([1, 0, 0, 0, 1, 1, 0, 0, 1, 0])\n        >>> np.random.randint(1, size=10)\n        array([0, 0, 0, 0, 0, 0, 0, 0, 0, 0])\n\n        Generate a 2 x 4 array of ints between 0 and 4, inclusive:\n\n        >>> np.random.randint(5, size=(2, 4))\n        array([[4, 0, 2, 1],\n               [3, 2, 2, 0]])\n\n        ";
static char __pyx_k_179[] = "RandomState.bytes (line 889)";
static char __pyx_k_180[] = "\n        bytes(length)\n\n        Return random bytes.\n\n        Parameters\n        ----------\n        length : int\n            Number of random bytes.\n\n        Returns\n        -------\n        out : str\n            String of length `length`.\n\n        Examples\n        --------\n        >>> np.random.bytes(10)\n        ' eh\\x85\\x022SZ\\xbf\\xa4' #random\n\n        ";
static char __pyx_k_181[] = "RandomState.uniform (line 916)";
static char __pyx_k_182[] = "\n        uniform(low=0.0, high=1.0, size=1)\n\n        Draw samples from a uniform distribution.\n\n        Samples are uniformly distributed over the half-open interval\n        ``[low, high)`` (includes low, but excludes high).  In other words,\n        any value within the given interval is equally likely to be drawn\n        by `uniform`.\n\n        Parameters\n        ----------\n        low : float, optional\n            Lower boundary of the output interval.  All values generated will be\n            greater than or equal to low.  The default value is 0.\n        high : float\n            Upper boundary of the output interval.  All values generated will be\n            less than high.  The default value is 1.0.\n        size : int or tuple of ints, optional\n            Shape of output.  If the given size is, for example, (m,n,k),\n            m*n*k samples are generated.  If no shape is specified, a single sample\n            is returned.\n\n        Returns\n        -------\n        out : ndarray\n            Drawn samples, with shape `size`.\n\n        See Also\n        --------\n        randint : Discrete uniform distribution, yielding integers.\n        random_integers : Discrete uniform distribution over the closed\n                          interval ``[low, high]``.\n        random_sample : Floats uniformly distributed over ``[0, 1)``.\n        random : Alias for `random_sample`.\n        rand : Convenience function that accepts dimensions as input, e.g.,\n               ``rand(2,2)`` would generate a 2-by-2 array of floats,\n               uniformly distributed over ``[0, 1)``.\n\n        Notes\n        -----\n        The probability density function of the uniform distribution is\n\n        .. math:: p(x) = \\frac{1}{b - a}\n\n        anywhere within the interval ``[a, b)``, and zero elsewhere.\n\n        Examples\n        --------\n        Draw samples from the distribution:\n\n        >>> s = np.random.uniform(-1,0,1000)\n\n        All values are w""ithin the given interval:\n\n        >>> np.all(s >= -1)\n        True\n        >>> np.all(s < 0)\n        True\n\n        Display the histogram of the samples, along with the\n        probability density function:\n\n        >>> import matplotlib.pyplot as plt\n        >>> count, bins, ignored = plt.hist(s, 15, normed=True)\n        >>> plt.plot(bins, np.ones_like(bins), linewidth=2, color='r')\n        >>> plt.show()\n\n        ";
static char __pyx_k_183[] = "RandomState.rand (line 1003)";
static char __pyx_k_184[] = "\n        rand(d0, d1, ..., dn)\n\n        Random values in a given shape.\n\n        Create an array of the given shape and propagate it with\n        random samples from a uniform distribution\n        over ``[0, 1)``.\n\n        Parameters\n        ----------\n        d0, d1, ..., dn : int\n            Shape of the output.\n\n        Returns\n        -------\n        out : ndarray, shape ``(d0, d1, ..., dn)``\n            Random values.\n\n        See Also\n        --------\n        random\n\n        Notes\n        -----\n        This is a convenience function. If you want an interface that\n        takes a shape-tuple as the first argument, refer to\n        `random`.\n\n        Examples\n        --------\n        >>> np.random.rand(3,2)\n        array([[ 0.14022471,  0.96360618],  #random\n               [ 0.37601032,  0.25528411],  #random\n               [ 0.49313049,  0.94909878]]) #random\n\n        ";
static char __pyx_k_185[] = "RandomState.randn (line 1046)";
static char __pyx_k_186[] = "\n        randn([d1, ..., dn])\n\n        Return a sample (or samples) from the \"standard normal\" distribution.\n\n        If positive, int_like or int-convertible arguments are provided,\n        `randn` generates an array of shape ``(d1, ..., dn)``, filled\n        with random floats sampled from a univariate \"normal\" (Gaussian)\n        distribution of mean 0 and variance 1 (if any of the :math:`d_i` are\n        floats, they are first converted to integers by truncation). A single\n        float randomly sampled from the distribution is returned if no\n        argument is provided.\n\n        This is a convenience function.  If you want an interface that takes a\n        tuple as the first argument, use `numpy.random.standard_normal` instead.\n\n        Parameters\n        ----------\n        d1, ..., dn : `n` ints, optional\n            The dimensions of the returned array, should be all positive.\n\n        Returns\n        -------\n        Z : ndarray or float\n            A ``(d1, ..., dn)``-shaped array of floating-point samples from\n            the standard normal distribution, or a single such float if\n            no parameters were supplied.\n\n        See Also\n        --------\n        random.standard_normal : Similar, but takes a tuple as its argument.\n\n        Notes\n        -----\n        For random samples from :math:`N(\\mu, \\sigma^2)`, use:\n\n        ``sigma * np.random.randn(...) + mu``\n\n        Examples\n        --------\n        >>> np.random.randn()\n        2.1923875335537315 #random\n\n        Two-by-four array of samples from N(3, 6.25):\n\n        >>> 2.5 * np.random.randn(2, 4) + 3\n        array([[-4.49401501,  4.00950034, -1.81814867,  7.29718677],  #random\n               [ 0.39924804,  4.68456316,  4.99394529,  4.84057254]]) #random\n\n        ";
static char __pyx_k_187[] = "RandomState.random_integers (line 1102)";
static char __pyx_k_188[] = "\n        random_integers(low, high=None, size=None)\n\n        Return random integers between `low` and `high`, inclusive.\n\n        Return random integers from the \"discrete uniform\" distribution in the\n        closed interval [`low`, `high`].  If `high` is None (the default),\n        then results are from [1, `low`].\n\n        Parameters\n        ----------\n        low : int\n            Lowest (signed) integer to be drawn from the distribution (unless\n            ``high=None``, in which case this parameter is the *highest* such\n            integer).\n        high : int, optional\n            If provided, the largest (signed) integer to be drawn from the\n            distribution (see above for behavior if ``high=None``).\n        size : int or tuple of ints, optional\n            Output shape. Default is None, in which case a single int is returned.\n\n        Returns\n        -------\n        out : int or ndarray of ints\n            `size`-shaped array of random integers from the appropriate\n            distribution, or a single such random int if `size` not provided.\n\n        See Also\n        --------\n        random.randint : Similar to `random_integers`, only for the half-open\n            interval [`low`, `high`), and 0 is the lowest value if `high` is\n            omitted.\n\n        Notes\n        -----\n        To sample from N evenly spaced floating-point numbers between a and b,\n        use::\n\n          a + (b - a) * (np.random.random_integers(N) - 1) / (N - 1.)\n\n        Examples\n        --------\n        >>> np.random.random_integers(5)\n        4\n        >>> type(np.random.random_integers(5))\n        <type 'int'>\n        >>> np.random.random_integers(5, size=(3.,2.))\n        array([[5, 4],\n               [3, 3],\n               [4, 5]])\n\n        Choose five random numbers from the set of five evenly-spaced\n        numbers between 0 and 2.5, inclusive (*i.e.*, from the set\n        :math:`{0, 5/8, 10/8, 15/8, 20/8}`):\n""\n        >>> 2.5 * (np.random.random_integers(5, size=(5,)) - 1) / 4.\n        array([ 0.625,  1.25 ,  0.625,  0.625,  2.5  ])\n\n        Roll two six sided dice 1000 times and sum the results:\n\n        >>> d1 = np.random.random_integers(1, 6, 1000)\n        >>> d2 = np.random.random_integers(1, 6, 1000)\n        >>> dsums = d1 + d2\n\n        Display results as a histogram:\n\n        >>> import matplotlib.pyplot as plt\n        >>> count, bins, ignored = plt.hist(dsums, 11, normed=True)\n        >>> plt.show()\n\n        ";
static char __pyx_k_189[] = "RandomState.standard_normal (line 1180)";
static char __pyx_k_190[] = "\n        standard_normal(size=None)\n\n        Returns samples from a Standard Normal distribution (mean=0, stdev=1).\n\n        Parameters\n        ----------\n        size : int or tuple of ints, optional\n            Output shape. Default is None, in which case a single value is\n            returned.\n\n        Returns\n        -------\n        out : float or ndarray\n            Drawn samples.\n\n        Examples\n        --------\n        >>> s = np.random.standard_normal(8000)\n        >>> s\n        array([ 0.6888893 ,  0.78096262, -0.89086505, ...,  0.49876311, #random\n               -0.38672696, -0.4685006 ])                               #random\n        >>> s.shape\n        (8000,)\n        >>> s = np.random.standard_normal(size=(3, 4, 2))\n        >>> s.shape\n        (3, 4, 2)\n\n        ";
static char __pyx_k_191[] = "RandomState.normal (line 1212)";
static char __pyx_k_192[] = "\n        normal(loc=0.0, scale=1.0, size=None)\n\n        Draw random samples from a normal (Gaussian) distribution.\n\n        The probability density function of the normal distribution, first\n        derived by De Moivre and 200 years later by both Gauss and Laplace\n        independently [2]_, is often called the bell curve because of\n        its characteristic shape (see the example below).\n\n        The normal distributions occurs often in nature.  For example, it\n        describes the commonly occurring distribution of samples influenced\n        by a large number of tiny, random disturbances, each with its own\n        unique distribution [2]_.\n\n        Parameters\n        ----------\n        loc : float\n            Mean (\"centre\") of the distribution.\n        scale : float\n            Standard deviation (spread or \"width\") of the distribution.\n        size : tuple of ints\n            Output shape.  If the given shape is, e.g., ``(m, n, k)``, then\n            ``m * n * k`` samples are drawn.\n\n        See Also\n        --------\n        scipy.stats.distributions.norm : probability density function,\n            distribution or cumulative density function, etc.\n\n        Notes\n        -----\n        The probability density for the Gaussian distribution is\n\n        .. math:: p(x) = \\frac{1}{\\sqrt{ 2 \\pi \\sigma^2 }}\n                         e^{ - \\frac{ (x - \\mu)^2 } {2 \\sigma^2} },\n\n        where :math:`\\mu` is the mean and :math:`\\sigma` the standard deviation.\n        The square of the standard deviation, :math:`\\sigma^2`, is called the\n        variance.\n\n        The function has its peak at the mean, and its \"spread\" increases with\n        the standard deviation (the function reaches 0.607 times its maximum at\n        :math:`x + \\sigma` and :math:`x - \\sigma` [2]_).  This implies that\n        `numpy.random.normal` is more likely to return samples lying close to the\n        mean, rather than those far away.\n""\n        References\n        ----------\n        .. [1] Wikipedia, \"Normal distribution\",\n               http://en.wikipedia.org/wiki/Normal_distribution\n        .. [2] P. R. Peebles Jr., \"Central Limit Theorem\" in \"Probability, Random\n               Variables and Random Signal Principles\", 4th ed., 2001,\n               pp. 51, 51, 125.\n\n        Examples\n        --------\n        Draw samples from the distribution:\n\n        >>> mu, sigma = 0, 0.1 # mean and standard deviation\n        >>> s = np.random.normal(mu, sigma, 1000)\n\n        Verify the mean and the variance:\n\n        >>> abs(mu - np.mean(s)) < 0.01\n        True\n\n        >>> abs(sigma - np.std(s, ddof=1)) < 0.01\n        True\n\n        Display the histogram of the samples, along with\n        the probability density function:\n\n        >>> import matplotlib.pyplot as plt\n        >>> count, bins, ignored = plt.hist(s, 30, normed=True)\n        >>> plt.plot(bins, 1/(sigma * np.sqrt(2 * np.pi)) *\n        ...                np.exp( - (bins - mu)**2 / (2 * sigma**2) ),\n        ...          linewidth=2, color='r')\n        >>> plt.show()\n\n        ";
static char __pyx_k_193[] = "RandomState.standard_exponential (line 1425)";
static char __pyx_k_194[] = "\n        standard_exponential(size=None)\n\n        Draw samples from the standard exponential distribution.\n\n        `standard_exponential` is identical to the exponential distribution\n        with a scale parameter of 1.\n\n        Parameters\n        ----------\n        size : int or tuple of ints\n            Shape of the output.\n\n        Returns\n        -------\n        out : float or ndarray\n            Drawn samples.\n\n        Examples\n        --------\n        Output a 3x8000 array:\n\n        >>> n = np.random.standard_exponential((3, 8000))\n\n        ";
static char __pyx_k_195[] = "RandomState.standard_gamma (line 1453)";
static char __pyx_k_196[] = "\n        standard_gamma(shape, size=None)\n\n        Draw samples from a Standard Gamma distribution.\n\n        Samples are drawn from a Gamma distribution with specified parameters,\n        shape (sometimes designated \"k\") and scale=1.\n\n        Parameters\n        ----------\n        shape : float\n            Parameter, should be > 0.\n        size : int or tuple of ints\n            Output shape.  If the given shape is, e.g., ``(m, n, k)``, then\n            ``m * n * k`` samples are drawn.\n\n        Returns\n        -------\n        samples : ndarray or scalar\n            The drawn samples.\n\n        See Also\n        --------\n        scipy.stats.distributions.gamma : probability density function,\n            distribution or cumulative density function, etc.\n\n        Notes\n        -----\n        The probability density for the Gamma distribution is\n\n        .. math:: p(x) = x^{k-1}\\frac{e^{-x/\\theta}}{\\theta^k\\Gamma(k)},\n\n        where :math:`k` is the shape and :math:`\\theta` the scale,\n        and :math:`\\Gamma` is the Gamma function.\n\n        The Gamma distribution is often used to model the times to failure of\n        electronic components, and arises naturally in processes for which the\n        waiting times between Poisson distributed events are relevant.\n\n        References\n        ----------\n        .. [1] Weisstein, Eric W. \"Gamma Distribution.\" From MathWorld--A\n               Wolfram Web Resource.\n               http://mathworld.wolfram.com/GammaDistribution.html\n        .. [2] Wikipedia, \"Gamma-distribution\",\n               http://en.wikipedia.org/wiki/Gamma-distribution\n\n        Examples\n        --------\n        Draw samples from the distribution:\n\n        >>> shape, scale = 2., 1. # mean and width\n        >>> s = np.random.standard_gamma(shape, 1000000)\n\n        Display the histogram of the samples, along with\n        the probability density function:\n\n        >>> import matplotlib.pyplot as plt""\n        >>> import scipy.special as sps\n        >>> count, bins, ignored = plt.hist(s, 50, normed=True)\n        >>> y = bins**(shape-1) * ((np.exp(-bins/scale))/ \\\n        ...                       (sps.gamma(shape) * scale**shape))\n        >>> plt.plot(bins, y, linewidth=2, color='r')\n        >>> plt.show()\n\n        ";
static char __pyx_k_197[] = "RandomState.gamma (line 1535)";
static char __pyx_k_198[] = "\n        gamma(shape, scale=1.0, size=None)\n\n        Draw samples from a Gamma distribution.\n\n        Samples are drawn from a Gamma distribution with specified parameters,\n        `shape` (sometimes designated \"k\") and `scale` (sometimes designated\n        \"theta\"), where both parameters are > 0.\n\n        Parameters\n        ----------\n        shape : scalar > 0\n            The shape of the gamma distribution.\n        scale : scalar > 0, optional\n            The scale of the gamma distribution.  Default is equal to 1.\n        size : shape_tuple, optional\n            Output shape.  If the given shape is, e.g., ``(m, n, k)``, then\n            ``m * n * k`` samples are drawn.\n\n        Returns\n        -------\n        out : ndarray, float\n            Returns one sample unless `size` parameter is specified.\n\n        See Also\n        --------\n        scipy.stats.distributions.gamma : probability density function,\n            distribution or cumulative density function, etc.\n\n        Notes\n        -----\n        The probability density for the Gamma distribution is\n\n        .. math:: p(x) = x^{k-1}\\frac{e^{-x/\\theta}}{\\theta^k\\Gamma(k)},\n\n        where :math:`k` is the shape and :math:`\\theta` the scale,\n        and :math:`\\Gamma` is the Gamma function.\n\n        The Gamma distribution is often used to model the times to failure of\n        electronic components, and arises naturally in processes for which the\n        waiting times between Poisson distributed events are relevant.\n\n        References\n        ----------\n        .. [1] Weisstein, Eric W. \"Gamma Distribution.\" From MathWorld--A\n               Wolfram Web Resource.\n               http://mathworld.wolfram.com/GammaDistribution.html\n        .. [2] Wikipedia, \"Gamma-distribution\",\n               http://en.wikipedia.org/wiki/Gamma-distribution\n\n        Examples\n        --------\n        Draw samples from the distribution:\n\n        >>> shape, scale = 2.,"" 2. # mean and dispersion\n        >>> s = np.random.gamma(shape, scale, 1000)\n\n        Display the histogram of the samples, along with\n        the probability density function:\n\n        >>> import matplotlib.pyplot as plt\n        >>> import scipy.special as sps\n        >>> count, bins, ignored = plt.hist(s, 50, normed=True)\n        >>> y = bins**(shape-1)*(np.exp(-bins/scale) /\n        ...                      (sps.gamma(shape)*scale**shape))\n        >>> plt.plot(bins, y, linewidth=2, color='r')\n        >>> plt.show()\n\n        ";
static char __pyx_k_199[] = "RandomState.f (line 1626)";
static char __pyx_k_200[] = "\n        f(dfnum, dfden, size=None)\n\n        Draw samples from a F distribution.\n\n        Samples are drawn from an F distribution with specified parameters,\n        `dfnum` (degrees of freedom in numerator) and `dfden` (degrees of freedom\n        in denominator), where both parameters should be greater than zero.\n\n        The random variate of the F distribution (also known as the\n        Fisher distribution) is a continuous probability distribution\n        that arises in ANOVA tests, and is the ratio of two chi-square\n        variates.\n\n        Parameters\n        ----------\n        dfnum : float\n            Degrees of freedom in numerator. Should be greater than zero.\n        dfden : float\n            Degrees of freedom in denominator. Should be greater than zero.\n        size : {tuple, int}, optional\n            Output shape.  If the given shape is, e.g., ``(m, n, k)``,\n            then ``m * n * k`` samples are drawn. By default only one sample\n            is returned.\n\n        Returns\n        -------\n        samples : {ndarray, scalar}\n            Samples from the Fisher distribution.\n\n        See Also\n        --------\n        scipy.stats.distributions.f : probability density function,\n            distribution or cumulative density function, etc.\n\n        Notes\n        -----\n\n        The F statistic is used to compare in-group variances to between-group\n        variances. Calculating the distribution depends on the sampling, and\n        so it is a function of the respective degrees of freedom in the\n        problem.  The variable `dfnum` is the number of samples minus one, the\n        between-groups degrees of freedom, while `dfden` is the within-groups\n        degrees of freedom, the sum of the number of samples in each group\n        minus the number of groups.\n\n        References\n        ----------\n        .. [1] Glantz, Stanton A. \"Primer of Biostatistics.\", McGraw-Hill,\n               Fifth Edition, 2002.""\n        .. [2] Wikipedia, \"F-distribution\",\n               http://en.wikipedia.org/wiki/F-distribution\n\n        Examples\n        --------\n        An example from Glantz[1], pp 47-40.\n        Two groups, children of diabetics (25 people) and children from people\n        without diabetes (25 controls). Fasting blood glucose was measured,\n        case group had a mean value of 86.1, controls had a mean value of\n        82.2. Standard deviations were 2.09 and 2.49 respectively. Are these\n        data consistent with the null hypothesis that the parents diabetic\n        status does not affect their children's blood glucose levels?\n        Calculating the F statistic from the data gives a value of 36.01.\n\n        Draw samples from the distribution:\n\n        >>> dfnum = 1. # between group degrees of freedom\n        >>> dfden = 48. # within groups degrees of freedom\n        >>> s = np.random.f(dfnum, dfden, 1000)\n\n        The lower bound for the top 1% of the samples is :\n\n        >>> sort(s)[-10]\n        7.61988120985\n\n        So there is about a 1% chance that the F statistic will exceed 7.62,\n        the measured value is 36, so the null hypothesis is rejected at the 1%\n        level.\n\n        ";
static char __pyx_k_201[] = "RandomState.noncentral_f (line 1729)";
static char __pyx_k_202[] = "\n        noncentral_f(dfnum, dfden, nonc, size=None)\n\n        Draw samples from the noncentral F distribution.\n\n        Samples are drawn from an F distribution with specified parameters,\n        `dfnum` (degrees of freedom in numerator) and `dfden` (degrees of\n        freedom in denominator), where both parameters > 1.\n        `nonc` is the non-centrality parameter.\n\n        Parameters\n        ----------\n        dfnum : int\n            Parameter, should be > 1.\n        dfden : int\n            Parameter, should be > 1.\n        nonc : float\n            Parameter, should be >= 0.\n        size : int or tuple of ints\n            Output shape. If the given shape is, e.g., ``(m, n, k)``, then\n            ``m * n * k`` samples are drawn.\n\n        Returns\n        -------\n        samples : scalar or ndarray\n            Drawn samples.\n\n        Notes\n        -----\n        When calculating the power of an experiment (power = probability of\n        rejecting the null hypothesis when a specific alternative is true) the\n        non-central F statistic becomes important.  When the null hypothesis is\n        true, the F statistic follows a central F distribution. When the null\n        hypothesis is not true, then it follows a non-central F statistic.\n\n        References\n        ----------\n        Weisstein, Eric W. \"Noncentral F-Distribution.\" From MathWorld--A Wolfram\n        Web Resource.  http://mathworld.wolfram.com/NoncentralF-Distribution.html\n\n        Wikipedia, \"Noncentral F distribution\",\n        http://en.wikipedia.org/wiki/Noncentral_F-distribution\n\n        Examples\n        --------\n        In a study, testing for a specific alternative to the null hypothesis\n        requires use of the Noncentral F distribution. We need to calculate the\n        area in the tail of the distribution that exceeds the value of the F\n        distribution for the null hypothesis.  We'll plot the two probability\n        distributions for comp""arison.\n\n        >>> dfnum = 3 # between group deg of freedom\n        >>> dfden = 20 # within groups degrees of freedom\n        >>> nonc = 3.0\n        >>> nc_vals = np.random.noncentral_f(dfnum, dfden, nonc, 1000000)\n        >>> NF = np.histogram(nc_vals, bins=50, normed=True)\n        >>> c_vals = np.random.f(dfnum, dfden, 1000000)\n        >>> F = np.histogram(c_vals, bins=50, normed=True)\n        >>> plt.plot(F[1][1:], F[0])\n        >>> plt.plot(NF[1][1:], NF[0])\n        >>> plt.show()\n\n        ";
static char __pyx_k_203[] = "RandomState.chisquare (line 1824)";
static char __pyx_k_204[] = "\n        chisquare(df, size=None)\n\n        Draw samples from a chi-square distribution.\n\n        When `df` independent random variables, each with standard normal\n        distributions (mean 0, variance 1), are squared and summed, the\n        resulting distribution is chi-square (see Notes).  This distribution\n        is often used in hypothesis testing.\n\n        Parameters\n        ----------\n        df : int\n             Number of degrees of freedom.\n        size : tuple of ints, int, optional\n             Size of the returned array.  By default, a scalar is\n             returned.\n\n        Returns\n        -------\n        output : ndarray\n            Samples drawn from the distribution, packed in a `size`-shaped\n            array.\n\n        Raises\n        ------\n        ValueError\n            When `df` <= 0 or when an inappropriate `size` (e.g. ``size=-1``)\n            is given.\n\n        Notes\n        -----\n        The variable obtained by summing the squares of `df` independent,\n        standard normally distributed random variables:\n\n        .. math:: Q = \\sum_{i=0}^{\\mathtt{df}} X^2_i\n\n        is chi-square distributed, denoted\n\n        .. math:: Q \\sim \\chi^2_k.\n\n        The probability density function of the chi-squared distribution is\n\n        .. math:: p(x) = \\frac{(1/2)^{k/2}}{\\Gamma(k/2)}\n                         x^{k/2 - 1} e^{-x/2},\n\n        where :math:`\\Gamma` is the gamma function,\n\n        .. math:: \\Gamma(x) = \\int_0^{-\\infty} t^{x - 1} e^{-t} dt.\n\n        References\n        ----------\n        `NIST/SEMATECH e-Handbook of Statistical Methods\n        <http://www.itl.nist.gov/div898/handbook/eda/section3/eda3666.htm>`_\n\n        Examples\n        --------\n        >>> np.random.chisquare(2,4)\n        array([ 1.89920014,  9.00867716,  3.13710533,  5.62318272])\n\n        ";
static char __pyx_k_205[] = "RandomState.noncentral_chisquare (line 1902)";
static char __pyx_k_206[] = "\n        noncentral_chisquare(df, nonc, size=None)\n\n        Draw samples from a noncentral chi-square distribution.\n\n        The noncentral :math:`\\chi^2` distribution is a generalisation of\n        the :math:`\\chi^2` distribution.\n\n        Parameters\n        ----------\n        df : int\n            Degrees of freedom, should be >= 1.\n        nonc : float\n            Non-centrality, should be > 0.\n        size : int or tuple of ints\n            Shape of the output.\n\n        Notes\n        -----\n        The probability density function for the noncentral Chi-square distribution\n        is\n\n        .. math:: P(x;df,nonc) = \\sum^{\\infty}_{i=0}\n                               \\frac{e^{-nonc/2}(nonc/2)^{i}}{i!}P_{Y_{df+2i}}(x),\n\n        where :math:`Y_{q}` is the Chi-square with q degrees of freedom.\n\n        In Delhi (2007), it is noted that the noncentral chi-square is useful in\n        bombing and coverage problems, the probability of killing the point target\n        given by the noncentral chi-squared distribution.\n\n        References\n        ----------\n        .. [1] Delhi, M.S. Holla, \"On a noncentral chi-square distribution in the\n               analysis of weapon systems effectiveness\", Metrika, Volume 15,\n               Number 1 / December, 1970.\n        .. [2] Wikipedia, \"Noncentral chi-square distribution\"\n               http://en.wikipedia.org/wiki/Noncentral_chi-square_distribution\n\n        Examples\n        --------\n        Draw values from the distribution and plot the histogram\n\n        >>> import matplotlib.pyplot as plt\n        >>> values = plt.hist(np.random.noncentral_chisquare(3, 20, 100000),\n        ...                   bins=200, normed=True)\n        >>> plt.show()\n\n        Draw values from a noncentral chisquare with very small noncentrality,\n        and compare to a chisquare.\n\n        >>> plt.figure()\n        >>> values = plt.hist(np.random.noncentral_chisquare(3, .0000001, 100000),\n     ""   ...                   bins=np.arange(0., 25, .1), normed=True)\n        >>> values2 = plt.hist(np.random.chisquare(3, 100000),\n        ...                    bins=np.arange(0., 25, .1), normed=True)\n        >>> plt.plot(values[1][0:-1], values[0]-values2[0], 'ob')\n        >>> plt.show()\n\n        Demonstrate how large values of non-centrality lead to a more symmetric\n        distribution.\n\n        >>> plt.figure()\n        >>> values = plt.hist(np.random.noncentral_chisquare(3, 20, 100000),\n        ...                   bins=200, normed=True)\n        >>> plt.show()\n\n        ";
static char __pyx_k_207[] = "RandomState.standard_cauchy (line 1994)";
static char __pyx_k_208[] = "\n        standard_cauchy(size=None)\n\n        Standard Cauchy distribution with mode = 0.\n\n        Also known as the Lorentz distribution.\n\n        Parameters\n        ----------\n        size : int or tuple of ints\n            Shape of the output.\n\n        Returns\n        -------\n        samples : ndarray or scalar\n            The drawn samples.\n\n        Notes\n        -----\n        The probability density function for the full Cauchy distribution is\n\n        .. math:: P(x; x_0, \\gamma) = \\frac{1}{\\pi \\gamma \\bigl[ 1+\n                  (\\frac{x-x_0}{\\gamma})^2 \\bigr] }\n\n        and the Standard Cauchy distribution just sets :math:`x_0=0` and\n        :math:`\\gamma=1`\n\n        The Cauchy distribution arises in the solution to the driven harmonic\n        oscillator problem, and also describes spectral line broadening. It\n        also describes the distribution of values at which a line tilted at\n        a random angle will cut the x axis.\n\n        When studying hypothesis tests that assume normality, seeing how the\n        tests perform on data from a Cauchy distribution is a good indicator of\n        their sensitivity to a heavy-tailed distribution, since the Cauchy looks\n        very much like a Gaussian distribution, but with heavier tails.\n\n        References\n        ----------\n        ..[1] NIST/SEMATECH e-Handbook of Statistical Methods, \"Cauchy\n              Distribution\",\n              http://www.itl.nist.gov/div898/handbook/eda/section3/eda3663.htm\n        ..[2] Weisstein, Eric W. \"Cauchy Distribution.\" From MathWorld--A\n              Wolfram Web Resource.\n              http://mathworld.wolfram.com/CauchyDistribution.html\n        ..[3] Wikipedia, \"Cauchy distribution\"\n              http://en.wikipedia.org/wiki/Cauchy_distribution\n\n        Examples\n        --------\n        Draw samples and plot the distribution:\n\n        >>> s = np.random.standard_cauchy(1000000)\n        >>> s = s[(s>-25) & (s<25)""]  # truncate distribution so it plots well\n        >>> plt.hist(s, bins=100)\n        >>> plt.show()\n\n        ";
static char __pyx_k_209[] = "RandomState.standard_t (line 2055)";
static char __pyx_k_210[] = "\n        standard_t(df, size=None)\n\n        Standard Student's t distribution with df degrees of freedom.\n\n        A special case of the hyperbolic distribution.\n        As `df` gets large, the result resembles that of the standard normal\n        distribution (`standard_normal`).\n\n        Parameters\n        ----------\n        df : int\n            Degrees of freedom, should be > 0.\n        size : int or tuple of ints, optional\n            Output shape. Default is None, in which case a single value is\n            returned.\n\n        Returns\n        -------\n        samples : ndarray or scalar\n            Drawn samples.\n\n        Notes\n        -----\n        The probability density function for the t distribution is\n\n        .. math:: P(x, df) = \\frac{\\Gamma(\\frac{df+1}{2})}{\\sqrt{\\pi df}\n                  \\Gamma(\\frac{df}{2})}\\Bigl( 1+\\frac{x^2}{df} \\Bigr)^{-(df+1)/2}\n\n        The t test is based on an assumption that the data come from a Normal\n        distribution. The t test provides a way to test whether the sample mean\n        (that is the mean calculated from the data) is a good estimate of the true\n        mean.\n\n        The derivation of the t-distribution was forst published in 1908 by William\n        Gisset while working for the Guinness Brewery in Dublin. Due to proprietary\n        issues, he had to publish under a pseudonym, and so he used the name\n        Student.\n\n        References\n        ----------\n        .. [1] Dalgaard, Peter, \"Introductory Statistics With R\",\n               Springer, 2002.\n        .. [2] Wikipedia, \"Student's t-distribution\"\n               http://en.wikipedia.org/wiki/Student's_t-distribution\n\n        Examples\n        --------\n        From Dalgaard page 83 [1]_, suppose the daily energy intake for 11\n        women in Kj is:\n\n        >>> intake = np.array([5260., 5470, 5640, 6180, 6390, 6515, 6805, 7515, \\\n        ...                    7515, 8230, 8770])\n\n        Doe""s their energy intake deviate systematically from the recommended\n        value of 7725 kJ?\n\n        We have 10 degrees of freedom, so is the sample mean within 95% of the\n        recommended value?\n\n        >>> s = np.random.standard_t(10, size=100000)\n        >>> np.mean(intake)\n        6753.636363636364\n        >>> intake.std(ddof=1)\n        1142.1232221373727\n\n        Calculate the t statistic, setting the ddof parameter to the unbiased\n        value so the divisor in the standard deviation will be degrees of\n        freedom, N-1.\n\n        >>> t = (np.mean(intake)-7725)/(intake.std(ddof=1)/np.sqrt(len(intake)))\n        >>> import matplotlib.pyplot as plt\n        >>> h = plt.hist(s, bins=100, normed=True)\n\n        For a one-sided t-test, how far out in the distribution does the t\n        statistic appear?\n\n        >>> >>> np.sum(s<t) / float(len(s))\n        0.0090699999999999999  #random\n\n        So the p-value is about 0.009, which says the null hypothesis has a\n        probability of about 99% of being true.\n\n        ";
static char __pyx_k_211[] = "RandomState.vonmises (line 2156)";
static char __pyx_k_212[] = "\n        vonmises(mu, kappa, size=None)\n\n        Draw samples from a von Mises distribution.\n\n        Samples are drawn from a von Mises distribution with specified mode\n        (mu) and dispersion (kappa), on the interval [-pi, pi].\n\n        The von Mises distribution (also known as the circular normal\n        distribution) is a continuous probability distribution on the unit\n        circle.  It may be thought of as the circular analogue of the normal\n        distribution.\n\n        Parameters\n        ----------\n        mu : float\n            Mode (\"center\") of the distribution.\n        kappa : float\n            Dispersion of the distribution, has to be >=0.\n        size : int or tuple of int\n            Output shape.  If the given shape is, e.g., ``(m, n, k)``, then\n            ``m * n * k`` samples are drawn.\n\n        Returns\n        -------\n        samples : scalar or ndarray\n            The returned samples, which are in the interval [-pi, pi].\n\n        See Also\n        --------\n        scipy.stats.distributions.vonmises : probability density function,\n            distribution, or cumulative density function, etc.\n\n        Notes\n        -----\n        The probability density for the von Mises distribution is\n\n        .. math:: p(x) = \\frac{e^{\\kappa cos(x-\\mu)}}{2\\pi I_0(\\kappa)},\n\n        where :math:`\\mu` is the mode and :math:`\\kappa` the dispersion,\n        and :math:`I_0(\\kappa)` is the modified Bessel function of order 0.\n\n        The von Mises is named for Richard Edler von Mises, who was born in\n        Austria-Hungary, in what is now the Ukraine.  He fled to the United\n        States in 1939 and became a professor at Harvard.  He worked in\n        probability theory, aerodynamics, fluid mechanics, and philosophy of\n        science.\n\n        References\n        ----------\n        Abramowitz, M. and Stegun, I. A. (ed.), *Handbook of Mathematical\n        Functions*, New York: Dover, 1965.\n\n      ""  von Mises, R., *Mathematical Theory of Probability and Statistics*,\n        New York: Academic Press, 1964.\n\n        Examples\n        --------\n        Draw samples from the distribution:\n\n        >>> mu, kappa = 0.0, 4.0 # mean and dispersion\n        >>> s = np.random.vonmises(mu, kappa, 1000)\n\n        Display the histogram of the samples, along with\n        the probability density function:\n\n        >>> import matplotlib.pyplot as plt\n        >>> import scipy.special as sps\n        >>> count, bins, ignored = plt.hist(s, 50, normed=True)\n        >>> x = np.arange(-np.pi, np.pi, 2*np.pi/50.)\n        >>> y = -np.exp(kappa*np.cos(x-mu))/(2*np.pi*sps.jn(0,kappa))\n        >>> plt.plot(x, y/max(y), linewidth=2, color='r')\n        >>> plt.show()\n\n        ";
static char __pyx_k_213[] = "RandomState.pareto (line 2250)";
static char __pyx_k_214[] = "\n        pareto(a, size=None)\n\n        Draw samples from a Pareto II or Lomax distribution with specified shape.\n\n        The Lomax or Pareto II distribution is a shifted Pareto distribution. The\n        classical Pareto distribution can be obtained from the Lomax distribution\n        by adding the location parameter m, see below. The smallest value of the\n        Lomax distribution is zero while for the classical Pareto distribution it\n        is m, where the standard Pareto distribution has location m=1.\n        Lomax can also be considered as a simplified version of the Generalized\n        Pareto distribution (available in SciPy), with the scale set to one and\n        the location set to zero.\n\n        The Pareto distribution must be greater than zero, and is unbounded above.\n        It is also known as the \"80-20 rule\".  In this distribution, 80 percent of\n        the weights are in the lowest 20 percent of the range, while the other 20\n        percent fill the remaining 80 percent of the range.\n\n        Parameters\n        ----------\n        shape : float, > 0.\n            Shape of the distribution.\n        size : tuple of ints\n            Output shape.  If the given shape is, e.g., ``(m, n, k)``, then\n            ``m * n * k`` samples are drawn.\n\n        See Also\n        --------\n        scipy.stats.distributions.lomax.pdf : probability density function,\n            distribution or cumulative density function, etc.\n        scipy.stats.distributions.genpareto.pdf : probability density function,\n            distribution or cumulative density function, etc.\n\n        Notes\n        -----\n        The probability density for the Pareto distribution is\n\n        .. math:: p(x) = \\frac{am^a}{x^{a+1}}\n\n        where :math:`a` is the shape and :math:`m` the location\n\n        The Pareto distribution, named after the Italian economist Vilfredo Pareto,\n        is a power law probability distribution useful in many real world probl""ems.\n        Outside the field of economics it is generally referred to as the Bradford\n        distribution. Pareto developed the distribution to describe the\n        distribution of wealth in an economy.  It has also found use in insurance,\n        web page access statistics, oil field sizes, and many other problems,\n        including the download frequency for projects in Sourceforge [1].  It is\n        one of the so-called \"fat-tailed\" distributions.\n\n\n        References\n        ----------\n        .. [1] Francis Hunt and Paul Johnson, On the Pareto Distribution of\n               Sourceforge projects.\n        .. [2] Pareto, V. (1896). Course of Political Economy. Lausanne.\n        .. [3] Reiss, R.D., Thomas, M.(2001), Statistical Analysis of Extreme\n               Values, Birkhauser Verlag, Basel, pp 23-30.\n        .. [4] Wikipedia, \"Pareto distribution\",\n               http://en.wikipedia.org/wiki/Pareto_distribution\n\n        Examples\n        --------\n        Draw samples from the distribution:\n\n        >>> a, m = 3., 1. # shape and mode\n        >>> s = np.random.pareto(a, 1000) + m\n\n        Display the histogram of the samples, along with\n        the probability density function:\n\n        >>> import matplotlib.pyplot as plt\n        >>> count, bins, ignored = plt.hist(s, 100, normed=True, align='center')\n        >>> fit = a*m**a/bins**(a+1)\n        >>> plt.plot(bins, max(count)*fit/max(fit),linewidth=2, color='r')\n        >>> plt.show()\n\n        ";
static char __pyx_k_215[] = "RandomState.weibull (line 2346)";
static char __pyx_k_216[] = "\n        weibull(a, size=None)\n\n        Weibull distribution.\n\n        Draw samples from a 1-parameter Weibull distribution with the given\n        shape parameter `a`.\n\n        .. math:: X = (-ln(U))^{1/a}\n\n        Here, U is drawn from the uniform distribution over (0,1].\n\n        The more common 2-parameter Weibull, including a scale parameter\n        :math:`\\lambda` is just :math:`X = \\lambda(-ln(U))^{1/a}`.\n\n        Parameters\n        ----------\n        a : float\n            Shape of the distribution.\n        size : tuple of ints\n            Output shape.  If the given shape is, e.g., ``(m, n, k)``, then\n            ``m * n * k`` samples are drawn.\n\n        See Also\n        --------\n        scipy.stats.distributions.weibull : probability density function,\n            distribution or cumulative density function, etc.\n\n        gumbel, scipy.stats.distributions.genextreme\n\n        Notes\n        -----\n        The Weibull (or Type III asymptotic extreme value distribution for smallest\n        values, SEV Type III, or Rosin-Rammler distribution) is one of a class of\n        Generalized Extreme Value (GEV) distributions used in modeling extreme\n        value problems.  This class includes the Gumbel and Frechet distributions.\n\n        The probability density for the Weibull distribution is\n\n        .. math:: p(x) = \\frac{a}\n                         {\\lambda}(\\frac{x}{\\lambda})^{a-1}e^{-(x/\\lambda)^a},\n\n        where :math:`a` is the shape and :math:`\\lambda` the scale.\n\n        The function has its peak (the mode) at\n        :math:`\\lambda(\\frac{a-1}{a})^{1/a}`.\n\n        When ``a = 1``, the Weibull distribution reduces to the exponential\n        distribution.\n\n        References\n        ----------\n        .. [1] Waloddi Weibull, Professor, Royal Technical University, Stockholm,\n               1939 \"A Statistical Theory Of The Strength Of Materials\",\n               Ingeniorsvetenskapsakademiens Handlingar"" Nr 151, 1939,\n               Generalstabens Litografiska Anstalts Forlag, Stockholm.\n        .. [2] Waloddi Weibull, 1951 \"A Statistical Distribution Function of Wide\n               Applicability\",  Journal Of Applied Mechanics ASME Paper.\n        .. [3] Wikipedia, \"Weibull distribution\",\n               http://en.wikipedia.org/wiki/Weibull_distribution\n\n        Examples\n        --------\n        Draw samples from the distribution:\n\n        >>> a = 5. # shape\n        >>> s = np.random.weibull(a, 1000)\n\n        Display the histogram of the samples, along with\n        the probability density function:\n\n        >>> import matplotlib.pyplot as plt\n        >>> x = np.arange(1,100.)/50.\n        >>> def weib(x,n,a):\n        ...     return (a / n) * (x / n)**(a - 1) * np.exp(-(x / n)**a)\n\n        >>> count, bins, ignored = plt.hist(np.random.weibull(5.,1000))\n        >>> x = np.arange(1,100.)/50.\n        >>> scale = count.max()/weib(x, 1., 5.).max()\n        >>> plt.plot(x, weib(x, 1., 5.)*scale)\n        >>> plt.show()\n\n        ";
static char __pyx_k_217[] = "RandomState.power (line 2446)";
static char __pyx_k_218[] = "\n        power(a, size=None)\n\n        Draws samples in [0, 1] from a power distribution with positive\n        exponent a - 1.\n\n        Also known as the power function distribution.\n\n        Parameters\n        ----------\n        a : float\n            parameter, > 0\n        size : tuple of ints\n            Output shape.  If the given shape is, e.g., ``(m, n, k)``, then\n                    ``m * n * k`` samples are drawn.\n\n        Returns\n        -------\n        samples : {ndarray, scalar}\n            The returned samples lie in [0, 1].\n\n        Raises\n        ------\n        ValueError\n            If a<1.\n\n        Notes\n        -----\n        The probability density function is\n\n        .. math:: P(x; a) = ax^{a-1}, 0 \\le x \\le 1, a>0.\n\n        The power function distribution is just the inverse of the Pareto\n        distribution. It may also be seen as a special case of the Beta\n        distribution.\n\n        It is used, for example, in modeling the over-reporting of insurance\n        claims.\n\n        References\n        ----------\n        .. [1] Christian Kleiber, Samuel Kotz, \"Statistical size distributions\n               in economics and actuarial sciences\", Wiley, 2003.\n        .. [2] Heckert, N. A. and Filliben, James J. (2003). NIST Handbook 148:\n               Dataplot Reference Manual, Volume 2: Let Subcommands and Library\n               Functions\", National Institute of Standards and Technology Handbook\n               Series, June 2003.\n               http://www.itl.nist.gov/div898/software/dataplot/refman2/auxillar/powpdf.pdf\n\n        Examples\n        --------\n        Draw samples from the distribution:\n\n        >>> a = 5. # shape\n        >>> samples = 1000\n        >>> s = np.random.power(a, samples)\n\n        Display the histogram of the samples, along with\n        the probability density function:\n\n        >>> import matplotlib.pyplot as plt\n        >>> count, bins, ignored = plt.hist(s, bins=""30)\n        >>> x = np.linspace(0, 1, 100)\n        >>> y = a*x**(a-1.)\n        >>> normed_y = samples*np.diff(bins)[0]*y\n        >>> plt.plot(x, normed_y)\n        >>> plt.show()\n\n        Compare the power function distribution to the inverse of the Pareto.\n\n        >>> from scipy import stats\n        >>> rvs = np.random.power(5, 1000000)\n        >>> rvsp = np.random.pareto(5, 1000000)\n        >>> xx = np.linspace(0,1,100)\n        >>> powpdf = stats.powerlaw.pdf(xx,5)\n\n        >>> plt.figure()\n        >>> plt.hist(rvs, bins=50, normed=True)\n        >>> plt.plot(xx,powpdf,'r-')\n        >>> plt.title('np.random.power(5)')\n\n        >>> plt.figure()\n        >>> plt.hist(1./(1.+rvsp), bins=50, normed=True)\n        >>> plt.plot(xx,powpdf,'r-')\n        >>> plt.title('inverse of 1 + np.random.pareto(5)')\n\n        >>> plt.figure()\n        >>> plt.hist(1./(1.+rvsp), bins=50, normed=True)\n        >>> plt.plot(xx,powpdf,'r-')\n        >>> plt.title('inverse of stats.pareto(5)')\n\n        ";
static char __pyx_k_219[] = "RandomState.laplace (line 2555)";
static char __pyx_k_220[] = "\n        laplace(loc=0.0, scale=1.0, size=None)\n\n        Draw samples from the Laplace or double exponential distribution with\n        specified location (or mean) and scale (decay).\n\n        The Laplace distribution is similar to the Gaussian/normal distribution,\n        but is sharper at the peak and has fatter tails. It represents the\n        difference between two independent, identically distributed exponential\n        random variables.\n\n        Parameters\n        ----------\n        loc : float\n            The position, :math:`\\mu`, of the distribution peak.\n        scale : float\n            :math:`\\lambda`, the exponential decay.\n\n        Notes\n        -----\n        It has the probability density function\n\n        .. math:: f(x; \\mu, \\lambda) = \\frac{1}{2\\lambda}\n                                       \\exp\\left(-\\frac{|x - \\mu|}{\\lambda}\\right).\n\n        The first law of Laplace, from 1774, states that the frequency of an error\n        can be expressed as an exponential function of the absolute magnitude of\n        the error, which leads to the Laplace distribution. For many problems in\n        Economics and Health sciences, this distribution seems to model the data\n        better than the standard Gaussian distribution\n\n\n        References\n        ----------\n        .. [1] Abramowitz, M. and Stegun, I. A. (Eds.). Handbook of Mathematical\n               Functions with Formulas, Graphs, and Mathematical Tables, 9th\n               printing.  New York: Dover, 1972.\n\n        .. [2] The Laplace distribution and generalizations\n               By Samuel Kotz, Tomasz J. Kozubowski, Krzysztof Podgorski,\n               Birkhauser, 2001.\n\n        .. [3] Weisstein, Eric W. \"Laplace Distribution.\"\n               From MathWorld--A Wolfram Web Resource.\n               http://mathworld.wolfram.com/LaplaceDistribution.html\n\n        .. [4] Wikipedia, \"Laplace distribution\",\n               http://en.wikipedia.org/wik""i/Laplace_distribution\n\n        Examples\n        --------\n        Draw samples from the distribution\n\n        >>> loc, scale = 0., 1.\n        >>> s = np.random.laplace(loc, scale, 1000)\n\n        Display the histogram of the samples, along with\n        the probability density function:\n\n        >>> import matplotlib.pyplot as plt\n        >>> count, bins, ignored = plt.hist(s, 30, normed=True)\n        >>> x = np.arange(-8., 8., .01)\n        >>> pdf = np.exp(-abs(x-loc/scale))/(2.*scale)\n        >>> plt.plot(x, pdf)\n\n        Plot Gaussian for comparison:\n\n        >>> g = (1/(scale * np.sqrt(2 * np.pi)) * \n        ...      np.exp( - (x - loc)**2 / (2 * scale**2) ))\n        >>> plt.plot(x,g)\n\n        ";
static char __pyx_k_221[] = "RandomState.gumbel (line 2645)";
static char __pyx_k_222[] = "\n        gumbel(loc=0.0, scale=1.0, size=None)\n\n        Gumbel distribution.\n\n        Draw samples from a Gumbel distribution with specified location and scale.\n        For more information on the Gumbel distribution, see Notes and References\n        below.\n\n        Parameters\n        ----------\n        loc : float\n            The location of the mode of the distribution.\n        scale : float\n            The scale parameter of the distribution.\n        size : tuple of ints\n            Output shape.  If the given shape is, e.g., ``(m, n, k)``, then\n            ``m * n * k`` samples are drawn.\n\n        Returns\n        -------\n        out : ndarray\n            The samples\n\n        See Also\n        --------\n        scipy.stats.gumbel_l\n        scipy.stats.gumbel_r\n        scipy.stats.genextreme\n            probability density function, distribution, or cumulative density\n            function, etc. for each of the above\n        weibull\n\n        Notes\n        -----\n        The Gumbel (or Smallest Extreme Value (SEV) or the Smallest Extreme Value\n        Type I) distribution is one of a class of Generalized Extreme Value (GEV)\n        distributions used in modeling extreme value problems.  The Gumbel is a\n        special case of the Extreme Value Type I distribution for maximums from\n        distributions with \"exponential-like\" tails.\n\n        The probability density for the Gumbel distribution is\n\n        .. math:: p(x) = \\frac{e^{-(x - \\mu)/ \\beta}}{\\beta} e^{ -e^{-(x - \\mu)/\n                  \\beta}},\n\n        where :math:`\\mu` is the mode, a location parameter, and :math:`\\beta` is\n        the scale parameter.\n\n        The Gumbel (named for German mathematician Emil Julius Gumbel) was used\n        very early in the hydrology literature, for modeling the occurrence of\n        flood events. It is also used for modeling maximum wind speed and rainfall\n        rates.  It is a \"fat-tailed\" distribution - the ""probability of an event in\n        the tail of the distribution is larger than if one used a Gaussian, hence\n        the surprisingly frequent occurrence of 100-year floods. Floods were\n        initially modeled as a Gaussian process, which underestimated the frequency\n        of extreme events.\n\n\n        It is one of a class of extreme value distributions, the Generalized\n        Extreme Value (GEV) distributions, which also includes the Weibull and\n        Frechet.\n\n        The function has a mean of :math:`\\mu + 0.57721\\beta` and a variance of\n        :math:`\\frac{\\pi^2}{6}\\beta^2`.\n\n        References\n        ----------\n        Gumbel, E. J., *Statistics of Extremes*, New York: Columbia University\n        Press, 1958.\n\n        Reiss, R.-D. and Thomas, M., *Statistical Analysis of Extreme Values from\n        Insurance, Finance, Hydrology and Other Fields*, Basel: Birkhauser Verlag,\n        2001.\n\n        Examples\n        --------\n        Draw samples from the distribution:\n\n        >>> mu, beta = 0, 0.1 # location and scale\n        >>> s = np.random.gumbel(mu, beta, 1000)\n\n        Display the histogram of the samples, along with\n        the probability density function:\n\n        >>> import matplotlib.pyplot as plt\n        >>> count, bins, ignored = plt.hist(s, 30, normed=True)\n        >>> plt.plot(bins, (1/beta)*np.exp(-(bins - mu)/beta)\n        ...          * np.exp( -np.exp( -(bins - mu) /beta) ),\n        ...          linewidth=2, color='r')\n        >>> plt.show()\n\n        Show how an extreme value distribution can arise from a Gaussian process\n        and compare to a Gaussian:\n\n        >>> means = []\n        >>> maxima = []\n        >>> for i in range(0,1000) :\n        ...    a = np.random.normal(mu, beta, 1000)\n        ...    means.append(a.mean())\n        ...    maxima.append(a.max())\n        >>> count, bins, ignored = plt.hist(maxima, 30, normed=True)\n        >>> beta = np.std(maxima)*np.pi/np.sqrt(6)""\n        >>> mu = np.mean(maxima) - 0.57721*beta\n        >>> plt.plot(bins, (1/beta)*np.exp(-(bins - mu)/beta)\n        ...          * np.exp(-np.exp(-(bins - mu)/beta)),\n        ...          linewidth=2, color='r')\n        >>> plt.plot(bins, 1/(beta * np.sqrt(2 * np.pi))\n        ...          * np.exp(-(bins - mu)**2 / (2 * beta**2)),\n        ...          linewidth=2, color='g')\n        >>> plt.show()\n\n        ";
static char __pyx_k_223[] = "RandomState.logistic (line 2776)";
static char __pyx_k_224[] = "\n        logistic(loc=0.0, scale=1.0, size=None)\n\n        Draw samples from a Logistic distribution.\n\n        Samples are drawn from a Logistic distribution with specified\n        parameters, loc (location or mean, also median), and scale (>0).\n\n        Parameters\n        ----------\n        loc : float\n\n        scale : float > 0.\n\n        size : {tuple, int}\n            Output shape.  If the given shape is, e.g., ``(m, n, k)``, then\n            ``m * n * k`` samples are drawn.\n\n        Returns\n        -------\n        samples : {ndarray, scalar}\n                  where the values are all integers in  [0, n].\n\n        See Also\n        --------\n        scipy.stats.distributions.logistic : probability density function,\n            distribution or cumulative density function, etc.\n\n        Notes\n        -----\n        The probability density for the Logistic distribution is\n\n        .. math:: P(x) = P(x) = \\frac{e^{-(x-\\mu)/s}}{s(1+e^{-(x-\\mu)/s})^2},\n\n        where :math:`\\mu` = location and :math:`s` = scale.\n\n        The Logistic distribution is used in Extreme Value problems where it\n        can act as a mixture of Gumbel distributions, in Epidemiology, and by\n        the World Chess Federation (FIDE) where it is used in the Elo ranking\n        system, assuming the performance of each player is a logistically\n        distributed random variable.\n\n        References\n        ----------\n        .. [1] Reiss, R.-D. and Thomas M. (2001), Statistical Analysis of Extreme\n               Values, from Insurance, Finance, Hydrology and Other Fields,\n               Birkhauser Verlag, Basel, pp 132-133.\n        .. [2] Weisstein, Eric W. \"Logistic Distribution.\" From\n               MathWorld--A Wolfram Web Resource.\n               http://mathworld.wolfram.com/LogisticDistribution.html\n        .. [3] Wikipedia, \"Logistic-distribution\",\n               http://en.wikipedia.org/wiki/Logistic-distribution\n\n        Examples\n   ""     --------\n        Draw samples from the distribution:\n\n        >>> loc, scale = 10, 1\n        >>> s = np.random.logistic(loc, scale, 10000)\n        >>> count, bins, ignored = plt.hist(s, bins=50)\n\n        #   plot against distribution\n\n        >>> def logist(x, loc, scale):\n        ...     return exp((loc-x)/scale)/(scale*(1+exp((loc-x)/scale))**2)\n        >>> plt.plot(bins, logist(bins, loc, scale)*count.max()/\\\n        ... logist(bins, loc, scale).max())\n        >>> plt.show()\n\n        ";
static char __pyx_k_225[] = "RandomState.lognormal (line 2864)";
static char __pyx_k_226[] = "\n        lognormal(mean=0.0, sigma=1.0, size=None)\n\n        Return samples drawn from a log-normal distribution.\n\n        Draw samples from a log-normal distribution with specified mean, standard\n        deviation, and shape. Note that the mean and standard deviation are not the\n        values for the distribution itself, but of the underlying normal\n        distribution it is derived from.\n\n\n        Parameters\n        ----------\n        mean : float\n            Mean value of the underlying normal distribution\n        sigma : float, >0.\n            Standard deviation of the underlying normal distribution\n        size : tuple of ints\n            Output shape.  If the given shape is, e.g., ``(m, n, k)``, then\n            ``m * n * k`` samples are drawn.\n\n        See Also\n        --------\n        scipy.stats.lognorm : probability density function, distribution,\n            cumulative density function, etc.\n\n        Notes\n        -----\n        A variable `x` has a log-normal distribution if `log(x)` is normally\n        distributed.\n\n        The probability density function for the log-normal distribution is\n\n        .. math:: p(x) = \\frac{1}{\\sigma x \\sqrt{2\\pi}}\n                         e^{(-\\frac{(ln(x)-\\mu)^2}{2\\sigma^2})}\n\n        where :math:`\\mu` is the mean and :math:`\\sigma` is the standard deviation\n        of the normally distributed logarithm of the variable.\n\n        A log-normal distribution results if a random variable is the *product* of\n        a large number of independent, identically-distributed variables in the\n        same way that a normal distribution results if the variable is the *sum*\n        of a large number of independent, identically-distributed variables\n        (see the last example). It is one of the so-called \"fat-tailed\"\n        distributions.\n\n        The log-normal distribution is commonly used to model the lifespan of units\n        with fatigue-stress failure modes. Since thi""s includes\n        most mechanical systems, the log-normal distribution has widespread\n        application.\n\n        It is also commonly used to model oil field sizes, species abundance, and\n        latent periods of infectious diseases.\n\n        References\n        ----------\n        .. [1] Eckhard Limpert, Werner A. Stahel, and Markus Abbt, \"Log-normal\n               Distributions across the Sciences: Keys and Clues\", May 2001\n               Vol. 51 No. 5 BioScience\n               http://stat.ethz.ch/~stahel/lognormal/bioscience.pdf\n        .. [2] Reiss, R.D., Thomas, M.(2001), Statistical Analysis of Extreme\n               Values, Birkhauser Verlag, Basel, pp 31-32.\n        .. [3] Wikipedia, \"Lognormal distribution\",\n               http://en.wikipedia.org/wiki/Lognormal_distribution\n\n        Examples\n        --------\n        Draw samples from the distribution:\n\n        >>> mu, sigma = 3., 1. # mean and standard deviation\n        >>> s = np.random.lognormal(mu, sigma, 1000)\n\n        Display the histogram of the samples, along with\n        the probability density function:\n\n        >>> import matplotlib.pyplot as plt\n        >>> count, bins, ignored = plt.hist(s, 100, normed=True, align='mid')\n\n        >>> x = np.linspace(min(bins), max(bins), 10000)\n        >>> pdf = (np.exp(-(np.log(x) - mu)**2 / (2 * sigma**2))\n        ...        / (x * sigma * np.sqrt(2 * np.pi)))\n\n        >>> plt.plot(x, pdf, linewidth=2, color='r')\n        >>> plt.axis('tight')\n        >>> plt.show()\n\n        Demonstrate that taking the products of random samples from a uniform\n        distribution can be fit well by a log-normal probability density function.\n\n        >>> # Generate a thousand samples: each is the product of 100 random\n        >>> # values, drawn from a normal distribution.\n        >>> b = []\n        >>> for i in range(1000):\n        ...    a = 10. + np.random.random(100)\n        ...    b.append(np.product(a))\n\n        >>> b"" = np.array(b) / np.min(b) # scale values to be positive\n\n        >>> count, bins, ignored = plt.hist(b, 100, normed=True, align='center')\n\n        >>> sigma = np.std(np.log(b))\n        >>> mu = np.mean(np.log(b))\n\n        >>> x = np.linspace(min(bins), max(bins), 10000)\n        >>> pdf = (np.exp(-(np.log(x) - mu)**2 / (2 * sigma**2))\n        ...        / (x * sigma * np.sqrt(2 * np.pi)))\n\n        >>> plt.plot(x, pdf, color='r', linewidth=2)\n        >>> plt.show()\n\n        ";
static char __pyx_k_227[] = "RandomState.rayleigh (line 2995)";
static char __pyx_k_228[] = "\n        rayleigh(scale=1.0, size=None)\n\n        Draw samples from a Rayleigh distribution.\n\n        The :math:`\\chi` and Weibull distributions are generalizations of the\n        Rayleigh.\n\n        Parameters\n        ----------\n        scale : scalar\n            Scale, also equals the mode. Should be >= 0.\n        size : int or tuple of ints, optional\n            Shape of the output. Default is None, in which case a single\n            value is returned.\n\n        Notes\n        -----\n        The probability density function for the Rayleigh distribution is\n\n        .. math:: P(x;scale) = \\frac{x}{scale^2}e^{\\frac{-x^2}{2 \\cdotp scale^2}}\n\n        The Rayleigh distribution arises if the wind speed and wind direction are\n        both gaussian variables, then the vector wind velocity forms a Rayleigh\n        distribution. The Rayleigh distribution is used to model the expected\n        output from wind turbines.\n\n        References\n        ----------\n        ..[1] Brighton Webs Ltd., Rayleigh Distribution,\n              http://www.brighton-webs.co.uk/distributions/rayleigh.asp\n        ..[2] Wikipedia, \"Rayleigh distribution\"\n              http://en.wikipedia.org/wiki/Rayleigh_distribution\n\n        Examples\n        --------\n        Draw values from the distribution and plot the histogram\n\n        >>> values = hist(np.random.rayleigh(3, 100000), bins=200, normed=True)\n\n        Wave heights tend to follow a Rayleigh distribution. If the mean wave\n        height is 1 meter, what fraction of waves are likely to be larger than 3\n        meters?\n\n        >>> meanvalue = 1\n        >>> modevalue = np.sqrt(2 / np.pi) * meanvalue\n        >>> s = np.random.rayleigh(modevalue, 1000000)\n\n        The percentage of waves larger than 3 meters is:\n\n        >>> 100.*sum(s>3)/1000000.\n        0.087300000000000003\n\n        ";
static char __pyx_k_229[] = "RandomState.wald (line 3067)";
static char __pyx_k_230[] = "\n        wald(mean, scale, size=None)\n\n        Draw samples from a Wald, or Inverse Gaussian, distribution.\n\n        As the scale approaches infinity, the distribution becomes more like a\n        Gaussian.\n\n        Some references claim that the Wald is an Inverse Gaussian with mean=1, but\n        this is by no means universal.\n\n        The Inverse Gaussian distribution was first studied in relationship to\n        Brownian motion. In 1956 M.C.K. Tweedie used the name Inverse Gaussian\n        because there is an inverse relationship between the time to cover a unit\n        distance and distance covered in unit time.\n\n        Parameters\n        ----------\n        mean : scalar\n            Distribution mean, should be > 0.\n        scale : scalar\n            Scale parameter, should be >= 0.\n        size : int or tuple of ints, optional\n            Output shape. Default is None, in which case a single value is\n            returned.\n\n        Returns\n        -------\n        samples : ndarray or scalar\n            Drawn sample, all greater than zero.\n\n        Notes\n        -----\n        The probability density function for the Wald distribution is\n\n        .. math:: P(x;mean,scale) = \\sqrt{\\frac{scale}{2\\pi x^3}}e^\n                                    \\frac{-scale(x-mean)^2}{2\\cdotp mean^2x}\n\n        As noted above the Inverse Gaussian distribution first arise from attempts\n        to model Brownian Motion. It is also a competitor to the Weibull for use in\n        reliability modeling and modeling stock returns and interest rate\n        processes.\n\n        References\n        ----------\n        ..[1] Brighton Webs Ltd., Wald Distribution,\n              http://www.brighton-webs.co.uk/distributions/wald.asp\n        ..[2] Chhikara, Raj S., and Folks, J. Leroy, \"The Inverse Gaussian\n              Distribution: Theory : Methodology, and Applications\", CRC Press,\n              1988.\n        ..[3] Wikipedia, \"Wald distributio""n\"\n              http://en.wikipedia.org/wiki/Wald_distribution\n\n        Examples\n        --------\n        Draw values from the distribution and plot the histogram:\n\n        >>> import matplotlib.pyplot as plt\n        >>> h = plt.hist(np.random.wald(3, 2, 100000), bins=200, normed=True)\n        >>> plt.show()\n\n        ";
static char __pyx_k_231[] = "RandomState.triangular (line 3153)";
static char __pyx_k_232[] = "\n        triangular(left, mode, right, size=None)\n\n        Draw samples from the triangular distribution.\n\n        The triangular distribution is a continuous probability distribution with\n        lower limit left, peak at mode, and upper limit right. Unlike the other\n        distributions, these parameters directly define the shape of the pdf.\n\n        Parameters\n        ----------\n        left : scalar\n            Lower limit.\n        mode : scalar\n            The value where the peak of the distribution occurs.\n            The value should fulfill the condition ``left <= mode <= right``.\n        right : scalar\n            Upper limit, should be larger than `left`.\n        size : int or tuple of ints, optional\n            Output shape. Default is None, in which case a single value is\n            returned.\n\n        Returns\n        -------\n        samples : ndarray or scalar\n            The returned samples all lie in the interval [left, right].\n\n        Notes\n        -----\n        The probability density function for the Triangular distribution is\n\n        .. math:: P(x;l, m, r) = \\begin{cases}\n                  \\frac{2(x-l)}{(r-l)(m-l)}& \\text{for $l \\leq x \\leq m$},\\\\\n                  \\frac{2(m-x)}{(r-l)(r-m)}& \\text{for $m \\leq x \\leq r$},\\\\\n                  0& \\text{otherwise}.\n                  \\end{cases}\n\n        The triangular distribution is often used in ill-defined problems where the\n        underlying distribution is not known, but some knowledge of the limits and\n        mode exists. Often it is used in simulations.\n\n        References\n        ----------\n        ..[1] Wikipedia, \"Triangular distribution\"\n              http://en.wikipedia.org/wiki/Triangular_distribution\n\n        Examples\n        --------\n        Draw values from the distribution and plot the histogram:\n\n        >>> import matplotlib.pyplot as plt\n        >>> h = plt.hist(np.random.triangular(-3, 0, 8, 100000), bins=2""00,\n        ...              normed=True)\n        >>> plt.show()\n\n        ";
static char __pyx_k_233[] = "RandomState.binomial (line 3241)";
static char __pyx_k_234[] = "\n        binomial(n, p, size=None)\n\n        Draw samples from a binomial distribution.\n\n        Samples are drawn from a Binomial distribution with specified\n        parameters, n trials and p probability of success where\n        n an integer > 0 and p is in the interval [0,1]. (n may be\n        input as a float, but it is truncated to an integer in use)\n\n        Parameters\n        ----------\n        n : float (but truncated to an integer)\n                parameter, > 0.\n        p : float\n                parameter, >= 0 and <=1.\n        size : {tuple, int}\n            Output shape.  If the given shape is, e.g., ``(m, n, k)``, then\n            ``m * n * k`` samples are drawn.\n\n        Returns\n        -------\n        samples : {ndarray, scalar}\n                  where the values are all integers in  [0, n].\n\n        See Also\n        --------\n        scipy.stats.distributions.binom : probability density function,\n            distribution or cumulative density function, etc.\n\n        Notes\n        -----\n        The probability density for the Binomial distribution is\n\n        .. math:: P(N) = \\binom{n}{N}p^N(1-p)^{n-N},\n\n        where :math:`n` is the number of trials, :math:`p` is the probability\n        of success, and :math:`N` is the number of successes.\n\n        When estimating the standard error of a proportion in a population by\n        using a random sample, the normal distribution works well unless the\n        product p*n <=5, where p = population proportion estimate, and n =\n        number of samples, in which case the binomial distribution is used\n        instead. For example, a sample of 15 people shows 4 who are left\n        handed, and 11 who are right handed. Then p = 4/15 = 27%. 0.27*15 = 4,\n        so the binomial distribution should be used in this case.\n\n        References\n        ----------\n        .. [1] Dalgaard, Peter, \"Introductory Statistics with R\",\n               Springer-Verlag, 2002.\n    ""    .. [2] Glantz, Stanton A. \"Primer of Biostatistics.\", McGraw-Hill,\n               Fifth Edition, 2002.\n        .. [3] Lentner, Marvin, \"Elementary Applied Statistics\", Bogden\n               and Quigley, 1972.\n        .. [4] Weisstein, Eric W. \"Binomial Distribution.\" From MathWorld--A\n               Wolfram Web Resource.\n               http://mathworld.wolfram.com/BinomialDistribution.html\n        .. [5] Wikipedia, \"Binomial-distribution\",\n               http://en.wikipedia.org/wiki/Binomial_distribution\n\n        Examples\n        --------\n        Draw samples from the distribution:\n\n        >>> n, p = 10, .5 # number of trials, probability of each trial\n        >>> s = np.random.binomial(n, p, 1000)\n        # result of flipping a coin 10 times, tested 1000 times.\n\n        A real world example. A company drills 9 wild-cat oil exploration\n        wells, each with an estimated probability of success of 0.1. All nine\n        wells fail. What is the probability of that happening?\n\n        Let's do 20,000 trials of the model, and count the number that\n        generate zero positive results.\n\n        >>> sum(np.random.binomial(9,0.1,20000)==0)/20000.\n        answer = 0.38885, or 38%.\n\n        ";
static char __pyx_k_235[] = "RandomState.negative_binomial (line 3349)";
static char __pyx_k_236[] = "\n        negative_binomial(n, p, size=None)\n\n        Draw samples from a negative_binomial distribution.\n\n        Samples are drawn from a negative_Binomial distribution with specified\n        parameters, `n` trials and `p` probability of success where `n` is an\n        integer > 0 and `p` is in the interval [0, 1].\n\n        Parameters\n        ----------\n        n : int\n            Parameter, > 0.\n        p : float\n            Parameter, >= 0 and <=1.\n        size : int or tuple of ints\n            Output shape. If the given shape is, e.g., ``(m, n, k)``, then\n            ``m * n * k`` samples are drawn.\n\n        Returns\n        -------\n        samples : int or ndarray of ints\n            Drawn samples.\n\n        Notes\n        -----\n        The probability density for the Negative Binomial distribution is\n\n        .. math:: P(N;n,p) = \\binom{N+n-1}{n-1}p^{n}(1-p)^{N},\n\n        where :math:`n-1` is the number of successes, :math:`p` is the probability\n        of success, and :math:`N+n-1` is the number of trials.\n\n        The negative binomial distribution gives the probability of n-1 successes\n        and N failures in N+n-1 trials, and success on the (N+n)th trial.\n\n        If one throws a die repeatedly until the third time a \"1\" appears, then the\n        probability distribution of the number of non-\"1\"s that appear before the\n        third \"1\" is a negative binomial distribution.\n\n        References\n        ----------\n        .. [1] Weisstein, Eric W. \"Negative Binomial Distribution.\" From\n               MathWorld--A Wolfram Web Resource.\n               http://mathworld.wolfram.com/NegativeBinomialDistribution.html\n        .. [2] Wikipedia, \"Negative binomial distribution\",\n               http://en.wikipedia.org/wiki/Negative_binomial_distribution\n\n        Examples\n        --------\n        Draw samples from the distribution:\n\n        A real world example. A company drills wild-cat oil exploration well""s, each\n        with an estimated probability of success of 0.1.  What is the probability\n        of having one success for each successive well, that is what is the\n        probability of a single success after drilling 5 wells, after 6 wells,\n        etc.?\n\n        >>> s = np.random.negative_binomial(1, 0.1, 100000)\n        >>> for i in range(1, 11):\n        ...    probability = sum(s<i) / 100000.\n        ...    print i, \"wells drilled, probability of one success =\", probability\n\n        ";
static char __pyx_k_237[] = "RandomState.poisson (line 3444)";
static char __pyx_k_238[] = "\n        poisson(lam=1.0, size=None)\n\n        Draw samples from a Poisson distribution.\n\n        The Poisson distribution is the limit of the Binomial\n        distribution for large N.\n\n        Parameters\n        ----------\n        lam : float\n            Expectation of interval, should be >= 0.\n        size : int or tuple of ints, optional\n            Output shape. If the given shape is, e.g., ``(m, n, k)``, then\n            ``m * n * k`` samples are drawn.\n\n        Notes\n        -----\n        The Poisson distribution\n\n        .. math:: f(k; \\lambda)=\\frac{\\lambda^k e^{-\\lambda}}{k!}\n\n        For events with an expected separation :math:`\\lambda` the Poisson\n        distribution :math:`f(k; \\lambda)` describes the probability of\n        :math:`k` events occurring within the observed interval :math:`\\lambda`.\n\n        Because the output is limited to the range of the C long type, a\n        ValueError is raised when `lam` is within 10 sigma of the maximum\n        representable value.\n\n        References\n        ----------\n        .. [1] Weisstein, Eric W. \"Poisson Distribution.\" From MathWorld--A Wolfram\n               Web Resource. http://mathworld.wolfram.com/PoissonDistribution.html\n        .. [2] Wikipedia, \"Poisson distribution\",\n           http://en.wikipedia.org/wiki/Poisson_distribution\n\n        Examples\n        --------\n        Draw samples from the distribution:\n\n        >>> import numpy as np\n        >>> s = np.random.poisson(5, 10000)\n\n        Display histogram of the sample:\n\n        >>> import matplotlib.pyplot as plt\n        >>> count, bins, ignored = plt.hist(s, 14, normed=True)\n        >>> plt.show()\n\n        ";
static char __pyx_k_239[] = "RandomState.zipf (line 3515)";
static char __pyx_k_240[] = "\n        zipf(a, size=None)\n\n        Draw samples from a Zipf distribution.\n\n        Samples are drawn from a Zipf distribution with specified parameter\n        `a` > 1.\n\n        The Zipf distribution (also known as the zeta distribution) is a\n        continuous probability distribution that satisfies Zipf's law: the\n        frequency of an item is inversely proportional to its rank in a\n        frequency table.\n\n        Parameters\n        ----------\n        a : float > 1\n            Distribution parameter.\n        size : int or tuple of int, optional\n            Output shape.  If the given shape is, e.g., ``(m, n, k)``, then\n            ``m * n * k`` samples are drawn; a single integer is equivalent in\n            its result to providing a mono-tuple, i.e., a 1-D array of length\n            *size* is returned.  The default is None, in which case a single\n            scalar is returned.\n\n        Returns\n        -------\n        samples : scalar or ndarray\n            The returned samples are greater than or equal to one.\n\n        See Also\n        --------\n        scipy.stats.distributions.zipf : probability density function,\n            distribution, or cumulative density function, etc.\n\n        Notes\n        -----\n        The probability density for the Zipf distribution is\n\n        .. math:: p(x) = \\frac{x^{-a}}{\\zeta(a)},\n\n        where :math:`\\zeta` is the Riemann Zeta function.\n\n        It is named for the American linguist George Kingsley Zipf, who noted\n        that the frequency of any word in a sample of a language is inversely\n        proportional to its rank in the frequency table.\n\n        References\n        ----------\n        Zipf, G. K., *Selected Studies of the Principle of Relative Frequency\n        in Language*, Cambridge, MA: Harvard Univ. Press, 1932.\n\n        Examples\n        --------\n        Draw samples from the distribution:\n\n        >>> a = 2. # parameter\n        >>> s = np.random.zipf""(a, 1000)\n\n        Display the histogram of the samples, along with\n        the probability density function:\n\n        >>> import matplotlib.pyplot as plt\n        >>> import scipy.special as sps\n        Truncate s values at 50 so plot is interesting\n        >>> count, bins, ignored = plt.hist(s[s<50], 50, normed=True)\n        >>> x = np.arange(1., 50.)\n        >>> y = x**(-a)/sps.zetac(a)\n        >>> plt.plot(x, y/max(y), linewidth=2, color='r')\n        >>> plt.show()\n\n        ";
static char __pyx_k_241[] = "RandomState.geometric (line 3603)";
static char __pyx_k_242[] = "\n        geometric(p, size=None)\n\n        Draw samples from the geometric distribution.\n\n        Bernoulli trials are experiments with one of two outcomes:\n        success or failure (an example of such an experiment is flipping\n        a coin).  The geometric distribution models the number of trials\n        that must be run in order to achieve success.  It is therefore\n        supported on the positive integers, ``k = 1, 2, ...``.\n\n        The probability mass function of the geometric distribution is\n\n        .. math:: f(k) = (1 - p)^{k - 1} p\n\n        where `p` is the probability of success of an individual trial.\n\n        Parameters\n        ----------\n        p : float\n            The probability of success of an individual trial.\n        size : tuple of ints\n            Number of values to draw from the distribution.  The output\n            is shaped according to `size`.\n\n        Returns\n        -------\n        out : ndarray\n            Samples from the geometric distribution, shaped according to\n            `size`.\n\n        Examples\n        --------\n        Draw ten thousand values from the geometric distribution,\n        with the probability of an individual success equal to 0.35:\n\n        >>> z = np.random.geometric(p=0.35, size=10000)\n\n        How many trials succeeded after a single run?\n\n        >>> (z == 1).sum() / 10000.\n        0.34889999999999999 #random\n\n        ";
static char __pyx_k_243[] = "RandomState.hypergeometric (line 3669)";
static char __pyx_k_244[] = "\n        hypergeometric(ngood, nbad, nsample, size=None)\n\n        Draw samples from a Hypergeometric distribution.\n\n        Samples are drawn from a Hypergeometric distribution with specified\n        parameters, ngood (ways to make a good selection), nbad (ways to make\n        a bad selection), and nsample = number of items sampled, which is less\n        than or equal to the sum ngood + nbad.\n\n        Parameters\n        ----------\n        ngood : float (but truncated to an integer)\n                parameter, > 0.\n        nbad  : float\n                parameter, >= 0.\n        nsample  : float\n                   parameter, > 0 and <= ngood+nbad\n        size : {tuple, int}\n            Output shape.  If the given shape is, e.g., ``(m, n, k)``, then\n            ``m * n * k`` samples are drawn.\n\n        Returns\n        -------\n        samples : {ndarray, scalar}\n                  where the values are all integers in  [0, n].\n\n        See Also\n        --------\n        scipy.stats.distributions.hypergeom : probability density function,\n            distribution or cumulative density function, etc.\n\n        Notes\n        -----\n        The probability density for the Hypergeometric distribution is\n\n        .. math:: P(x) = \\frac{\\binom{m}{n}\\binom{N-m}{n-x}}{\\binom{N}{n}},\n\n        where :math:`0 \\le x \\le m` and :math:`n+m-N \\le x \\le n`\n\n        for P(x) the probability of x successes, n = ngood, m = nbad, and\n        N = number of samples.\n\n        Consider an urn with black and white marbles in it, ngood of them\n        black and nbad are white. If you draw nsample balls without\n        replacement, then the Hypergeometric distribution describes the\n        distribution of black balls in the drawn sample.\n\n        Note that this distribution is very similar to the Binomial\n        distribution, except that in this case, samples are drawn without\n        replacement, whereas in the Binomial case samples are drawn wit""h\n        replacement (or the sample space is infinite). As the sample space\n        becomes large, this distribution approaches the Binomial.\n\n        References\n        ----------\n        .. [1] Lentner, Marvin, \"Elementary Applied Statistics\", Bogden\n               and Quigley, 1972.\n        .. [2] Weisstein, Eric W. \"Hypergeometric Distribution.\" From\n               MathWorld--A Wolfram Web Resource.\n               http://mathworld.wolfram.com/HypergeometricDistribution.html\n        .. [3] Wikipedia, \"Hypergeometric-distribution\",\n               http://en.wikipedia.org/wiki/Hypergeometric-distribution\n\n        Examples\n        --------\n        Draw samples from the distribution:\n\n        >>> ngood, nbad, nsamp = 100, 2, 10\n        # number of good, number of bad, and number of samples\n        >>> s = np.random.hypergeometric(ngood, nbad, nsamp, 1000)\n        >>> hist(s)\n        #   note that it is very unlikely to grab both bad items\n\n        Suppose you have an urn with 15 white and 15 black marbles.\n        If you pull 15 marbles at random, how likely is it that\n        12 or more of them are one color?\n\n        >>> s = np.random.hypergeometric(15, 15, 15, 100000)\n        >>> sum(s>=12)/100000. + sum(s<=3)/100000.\n        #   answer = 0.003 ... pretty unlikely!\n\n        ";
static char __pyx_k_245[] = "RandomState.logseries (line 3788)";
static char __pyx_k_246[] = "\n        logseries(p, size=None)\n\n        Draw samples from a Logarithmic Series distribution.\n\n        Samples are drawn from a Log Series distribution with specified\n        parameter, p (probability, 0 < p < 1).\n\n        Parameters\n        ----------\n        loc : float\n\n        scale : float > 0.\n\n        size : {tuple, int}\n            Output shape.  If the given shape is, e.g., ``(m, n, k)``, then\n            ``m * n * k`` samples are drawn.\n\n        Returns\n        -------\n        samples : {ndarray, scalar}\n                  where the values are all integers in  [0, n].\n\n        See Also\n        --------\n        scipy.stats.distributions.logser : probability density function,\n            distribution or cumulative density function, etc.\n\n        Notes\n        -----\n        The probability density for the Log Series distribution is\n\n        .. math:: P(k) = \\frac{-p^k}{k \\ln(1-p)},\n\n        where p = probability.\n\n        The Log Series distribution is frequently used to represent species\n        richness and occurrence, first proposed by Fisher, Corbet, and\n        Williams in 1943 [2].  It may also be used to model the numbers of\n        occupants seen in cars [3].\n\n        References\n        ----------\n        .. [1] Buzas, Martin A.; Culver, Stephen J.,  Understanding regional\n               species diversity through the log series distribution of\n               occurrences: BIODIVERSITY RESEARCH Diversity & Distributions,\n               Volume 5, Number 5, September 1999 , pp. 187-195(9).\n        .. [2] Fisher, R.A,, A.S. Corbet, and C.B. Williams. 1943. The\n               relation between the number of species and the number of\n               individuals in a random sample of an animal population.\n               Journal of Animal Ecology, 12:42-58.\n        .. [3] D. J. Hand, F. Daly, D. Lunn, E. Ostrowski, A Handbook of Small\n               Data Sets, CRC Press, 1994.\n        .. [4] Wikipedia, \"Log""arithmic-distribution\",\n               http://en.wikipedia.org/wiki/Logarithmic-distribution\n\n        Examples\n        --------\n        Draw samples from the distribution:\n\n        >>> a = .6\n        >>> s = np.random.logseries(a, 10000)\n        >>> count, bins, ignored = plt.hist(s)\n\n        #   plot against distribution\n\n        >>> def logseries(k, p):\n        ...     return -p**k/(k*log(1-p))\n        >>> plt.plot(bins, logseries(bins, a)*count.max()/\n                     logseries(bins, a).max(), 'r')\n        >>> plt.show()\n\n        ";
static char __pyx_k_247[] = "RandomState.multivariate_normal (line 3883)";
static char __pyx_k_248[] = "\n        multivariate_normal(mean, cov[, size])\n\n        Draw random samples from a multivariate normal distribution.\n\n        The multivariate normal, multinormal or Gaussian distribution is a\n        generalization of the one-dimensional normal distribution to higher\n        dimensions.  Such a distribution is specified by its mean and\n        covariance matrix.  These parameters are analogous to the mean\n        (average or \"center\") and variance (standard deviation, or \"width,\"\n        squared) of the one-dimensional normal distribution.\n\n        Parameters\n        ----------\n        mean : 1-D array_like, of length N\n            Mean of the N-dimensional distribution.\n        cov : 2-D array_like, of shape (N, N)\n            Covariance matrix of the distribution.  Must be symmetric and\n            positive semi-definite for \"physically meaningful\" results.\n        size : tuple of ints, optional\n            Given a shape of, for example, ``(m,n,k)``, ``m*n*k`` samples are\n            generated, and packed in an `m`-by-`n`-by-`k` arrangement.  Because\n            each sample is `N`-dimensional, the output shape is ``(m,n,k,N)``.\n            If no shape is specified, a single (`N`-D) sample is returned.\n\n        Returns\n        -------\n        out : ndarray\n            The drawn samples, of shape *size*, if that was provided.  If not,\n            the shape is ``(N,)``.\n\n            In other words, each entry ``out[i,j,...,:]`` is an N-dimensional\n            value drawn from the distribution.\n\n        Notes\n        -----\n        The mean is a coordinate in N-dimensional space, which represents the\n        location where samples are most likely to be generated.  This is\n        analogous to the peak of the bell curve for the one-dimensional or\n        univariate normal distribution.\n\n        Covariance indicates the level to which two variables vary together.\n        From the multivariate normal distribution, we draw ""N-dimensional\n        samples, :math:`X = [x_1, x_2, ... x_N]`.  The covariance matrix\n        element :math:`C_{ij}` is the covariance of :math:`x_i` and :math:`x_j`.\n        The element :math:`C_{ii}` is the variance of :math:`x_i` (i.e. its\n        \"spread\").\n\n        Instead of specifying the full covariance matrix, popular\n        approximations include:\n\n          - Spherical covariance (*cov* is a multiple of the identity matrix)\n          - Diagonal covariance (*cov* has non-negative elements, and only on\n            the diagonal)\n\n        This geometrical property can be seen in two dimensions by plotting\n        generated data-points:\n\n        >>> mean = [0,0]\n        >>> cov = [[1,0],[0,100]] # diagonal covariance, points lie on x or y-axis\n\n        >>> import matplotlib.pyplot as plt\n        >>> x,y = np.random.multivariate_normal(mean,cov,5000).T\n        >>> plt.plot(x,y,'x'); plt.axis('equal'); plt.show()\n\n        Note that the covariance matrix must be non-negative definite.\n\n        References\n        ----------\n        Papoulis, A., *Probability, Random Variables, and Stochastic Processes*,\n        3rd ed., New York: McGraw-Hill, 1991.\n\n        Duda, R. O., Hart, P. E., and Stork, D. G., *Pattern Classification*,\n        2nd ed., New York: Wiley, 2001.\n\n        Examples\n        --------\n        >>> mean = (1,2)\n        >>> cov = [[1,0],[1,0]]\n        >>> x = np.random.multivariate_normal(mean,cov,(3,3))\n        >>> x.shape\n        (3, 3, 2)\n\n        The following is probably true, given that 0.6 is roughly twice the\n        standard deviation:\n\n        >>> print list( (x[0,0,:] - mean) < 0.6 )\n        [True, True]\n\n        ";
static char __pyx_k_249[] = "RandomState.multinomial (line 4015)";
static char __pyx_k_250[] = "\n        multinomial(n, pvals, size=None)\n\n        Draw samples from a multinomial distribution.\n\n        The multinomial distribution is a multivariate generalisation of the\n        binomial distribution.  Take an experiment with one of ``p``\n        possible outcomes.  An example of such an experiment is throwing a dice,\n        where the outcome can be 1 through 6.  Each sample drawn from the\n        distribution represents `n` such experiments.  Its values,\n        ``X_i = [X_0, X_1, ..., X_p]``, represent the number of times the outcome\n        was ``i``.\n\n        Parameters\n        ----------\n        n : int\n            Number of experiments.\n        pvals : sequence of floats, length p\n            Probabilities of each of the ``p`` different outcomes.  These\n            should sum to 1 (however, the last element is always assumed to\n            account for the remaining probability, as long as\n            ``sum(pvals[:-1]) <= 1)``.\n        size : tuple of ints\n            Given a `size` of ``(M, N, K)``, then ``M*N*K`` samples are drawn,\n            and the output shape becomes ``(M, N, K, p)``, since each sample\n            has shape ``(p,)``.\n\n        Examples\n        --------\n        Throw a dice 20 times:\n\n        >>> np.random.multinomial(20, [1/6.]*6, size=1)\n        array([[4, 1, 7, 5, 2, 1]])\n\n        It landed 4 times on 1, once on 2, etc.\n\n        Now, throw the dice 20 times, and 20 times again:\n\n        >>> np.random.multinomial(20, [1/6.]*6, size=2)\n        array([[3, 4, 3, 3, 4, 3],\n               [2, 4, 3, 4, 0, 7]])\n\n        For the first run, we threw 3 times 1, 4 times 2, etc.  For the second,\n        we threw 2 times 1, 4 times 2, etc.\n\n        A loaded dice is more likely to land on number 6:\n\n        >>> np.random.multinomial(100, [1/7.]*5)\n        array([13, 16, 13, 16, 42])\n\n        ";
static char __pyx_k_251[] = "RandomState.dirichlet (line 4108)";
static char __pyx_k_252[] = "\n        dirichlet(alpha, size=None)\n\n        Draw samples from the Dirichlet distribution.\n\n        Draw `size` samples of dimension k from a Dirichlet distribution. A\n        Dirichlet-distributed random variable can be seen as a multivariate\n        generalization of a Beta distribution. Dirichlet pdf is the conjugate\n        prior of a multinomial in Bayesian inference.\n\n        Parameters\n        ----------\n        alpha : array\n            Parameter of the distribution (k dimension for sample of\n            dimension k).\n        size : array\n            Number of samples to draw.\n\n        Returns\n        -------\n        samples : ndarray,\n            The drawn samples, of shape (alpha.ndim, size).\n\n        Notes\n        -----\n        .. math:: X \\approx \\prod_{i=1}^{k}{x^{\\alpha_i-1}_i}\n\n        Uses the following property for computation: for each dimension,\n        draw a random sample y_i from a standard gamma generator of shape\n        `alpha_i`, then\n        :math:`X = \\frac{1}{\\sum_{i=1}^k{y_i}} (y_1, \\ldots, y_n)` is\n        Dirichlet distributed.\n\n        References\n        ----------\n        .. [1] David McKay, \"Information Theory, Inference and Learning\n               Algorithms,\" chapter 23,\n               http://www.inference.phy.cam.ac.uk/mackay/\n        .. [2] Wikipedia, \"Dirichlet distribution\",\n               http://en.wikipedia.org/wiki/Dirichlet_distribution\n\n        Examples\n        --------\n        Taking an example cited in Wikipedia, this distribution can be used if\n        one wanted to cut strings (each of initial length 1.0) into K pieces\n        with different lengths, where each piece had, on average, a designated\n        average length, but allowing some variation in the relative sizes of the\n        pieces.\n\n        >>> s = np.random.dirichlet((10, 5, 3), 20).transpose()\n\n        >>> plt.barh(range(20), s[0])\n        >>> plt.barh(range(20), s[1], left=s[0], color='g')""\n        >>> plt.barh(range(20), s[2], left=s[0]+s[1], color='r')\n        >>> plt.title(\"Lengths of Strings\")\n\n        ";
static char __pyx_k_253[] = "RandomState.shuffle (line 4224)";
static char __pyx_k_254[] = "\n        shuffle(x)\n\n        Modify a sequence in-place by shuffling its contents.\n\n        Parameters\n        ----------\n        x : array_like\n            The array or list to be shuffled.\n\n        Returns\n        -------\n        None\n\n        Examples\n        --------\n        >>> arr = np.arange(10)\n        >>> np.random.shuffle(arr)\n        >>> arr\n        [1 7 5 2 9 4 3 6 0 8]\n\n        This function only shuffles the array along the first index of a\n        multi-dimensional array:\n\n        >>> arr = np.arange(9).reshape((3, 3))\n        >>> np.random.shuffle(arr)\n        >>> arr\n        array([[3, 4, 5],\n               [6, 7, 8],\n               [0, 1, 2]])\n\n        ";
static char __pyx_k_255[] = "RandomState.permutation (line 4286)";
static char __pyx_k_256[] = "\n        permutation(x)\n\n        Randomly permute a sequence, or return a permuted range.\n\n        If `x` is a multi-dimensional array, it is only shuffled along its\n        first index.\n\n        Parameters\n        ----------\n        x : int or array_like\n            If `x` is an integer, randomly permute ``np.arange(x)``.\n            If `x` is an array, make a copy and shuffle the elements\n            randomly.\n\n        Returns\n        -------\n        out : ndarray\n            Permuted sequence or array range.\n\n        Examples\n        --------\n        >>> np.random.permutation(10)\n        array([1, 7, 4, 3, 0, 9, 2, 5, 8, 6])\n\n        >>> np.random.permutation([1, 4, 9, 12, 15])\n        array([15,  1,  9,  4, 12])\n\n        >>> arr = np.arange(9).reshape((3, 3))\n        >>> np.random.permutation(arr)\n        array([[6, 7, 8],\n               [0, 1, 2],\n               [3, 4, 5]])\n\n        ";
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static char __pyx_k__mu[] = "mu";
static char __pyx_k__nd[] = "nd";
static char __pyx_k__np[] = "np";
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static char __pyx_k__any[] = "any";
static char __pyx_k__cov[] = "cov";
static char __pyx_k__dot[] = "dot";
static char __pyx_k__key[] = "key";
static char __pyx_k__lam[] = "lam";
static char __pyx_k__loc[] = "loc";
static char __pyx_k__low[] = "low";
static char __pyx_k__max[] = "max";
static char __pyx_k__pos[] = "pos";
static char __pyx_k__svd[] = "svd";
static char __pyx_k__beta[] = "beta";
static char __pyx_k__copy[] = "copy";
static char __pyx_k__data[] = "data";
static char __pyx_k__high[] = "high";
static char __pyx_k__left[] = "left";
static char __pyx_k__less[] = "less";
static char __pyx_k__mean[] = "mean";
static char __pyx_k__mode[] = "mode";
static char __pyx_k__nbad[] = "nbad";
static char __pyx_k__nonc[] = "nonc";
static char __pyx_k__rand[] = "rand";
static char __pyx_k__seed[] = "seed";
static char __pyx_k__size[] = "size";
static char __pyx_k__sqrt[] = "sqrt";
static char __pyx_k__uint[] = "uint";
static char __pyx_k__wald[] = "wald";
static char __pyx_k__zipf[] = "zipf";
static char __pyx_k___rand[] = "_rand";
static char __pyx_k__alpha[] = "alpha";
static char __pyx_k__array[] = "array";
static char __pyx_k__bytes[] = "bytes";
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static char __pyx_k__dfnum[] = "dfnum";
static char __pyx_k__empty[] = "empty";
static char __pyx_k__equal[] = "equal";
static char __pyx_k__gamma[] = "gamma";
static char __pyx_k__gauss[] = "gauss";
static char __pyx_k__iinfo[] = "iinfo";
static char __pyx_k__kappa[] = "kappa";
static char __pyx_k__ngood[] = "ngood";
static char __pyx_k__numpy[] = "numpy";
static char __pyx_k__power[] = "power";
static char __pyx_k__pvals[] = "pvals";
static char __pyx_k__randn[] = "randn";
static char __pyx_k__right[] = "right";
static char __pyx_k__scale[] = "scale";
static char __pyx_k__shape[] = "shape";
static char __pyx_k__sigma[] = "sigma";
static char __pyx_k__zeros[] = "zeros";
static char __pyx_k__append[] = "append";
static char __pyx_k__arange[] = "arange";
static char __pyx_k__gumbel[] = "gumbel";
static char __pyx_k__normal[] = "normal";
static char __pyx_k__pareto[] = "pareto";
static char __pyx_k__random[] = "random";
static char __pyx_k__reduce[] = "reduce";
static char __pyx_k__uint32[] = "uint32";
static char __pyx_k__MT19937[] = "MT19937";
static char __pyx_k__asarray[] = "asarray";
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static char __pyx_k__float64[] = "float64";
static char __pyx_k__greater[] = "greater";
static char __pyx_k__integer[] = "integer";
static char __pyx_k__laplace[] = "laplace";
static char __pyx_k__nsample[] = "nsample";
static char __pyx_k__poisson[] = "poisson";
static char __pyx_k__randint[] = "randint";
static char __pyx_k__shuffle[] = "shuffle";
static char __pyx_k__uniform[] = "uniform";
static char __pyx_k__weibull[] = "weibull";
static char __pyx_k____main__[] = "__main__";
static char __pyx_k____test__[] = "__test__";
static char __pyx_k__binomial[] = "binomial";
static char __pyx_k__logistic[] = "logistic";
static char __pyx_k__multiply[] = "multiply";
static char __pyx_k__rayleigh[] = "rayleigh";
static char __pyx_k__subtract[] = "subtract";
static char __pyx_k__vonmises[] = "vonmises";
static char __pyx_k__TypeError[] = "TypeError";
static char __pyx_k__chisquare[] = "chisquare";
static char __pyx_k__dirichlet[] = "dirichlet";
static char __pyx_k__geometric[] = "geometric";
static char __pyx_k__get_state[] = "get_state";
static char __pyx_k__has_gauss[] = "has_gauss";
static char __pyx_k__lognormal[] = "lognormal";
static char __pyx_k__logseries[] = "logseries";
static char __pyx_k__set_state[] = "set_state";
static char __pyx_k__ValueError[] = "ValueError";
static char __pyx_k__dimensions[] = "dimensions";
static char __pyx_k__less_equal[] = "less_equal";
static char __pyx_k__standard_t[] = "standard_t";
static char __pyx_k__triangular[] = "triangular";
static char __pyx_k__exponential[] = "exponential";
static char __pyx_k__multinomial[] = "multinomial";
static char __pyx_k__permutation[] = "permutation";
static char __pyx_k__noncentral_f[] = "noncentral_f";
static char __pyx_k__greater_equal[] = "greater_equal";
static char __pyx_k__random_sample[] = "random_sample";
static char __pyx_k__hypergeometric[] = "hypergeometric";
static char __pyx_k__internal_state[] = "internal_state";
static char __pyx_k__standard_gamma[] = "standard_gamma";
static char __pyx_k__poisson_lam_max[] = "poisson_lam_max";
static char __pyx_k__random_integers[] = "random_integers";
static char __pyx_k__standard_cauchy[] = "standard_cauchy";
static char __pyx_k__standard_normal[] = "standard_normal";
static char __pyx_k__negative_binomial[] = "negative_binomial";
static char __pyx_k____RandomState_ctor[] = "__RandomState_ctor";
static char __pyx_k__multivariate_normal[] = "multivariate_normal";
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static char __pyx_doc_6mtrand_11RandomState_23f[] = "\n        f(dfnum, dfden, size=None)\n\n        Draw samples from a F distribution.\n\n        Samples are drawn from an F distribution with specified parameters,\n        `dfnum` (degrees of freedom in numerator) and `dfden` (degrees of freedom\n        in denominator), where both parameters should be greater than zero.\n\n        The random variate of the F distribution (also known as the\n        Fisher distribution) is a continuous probability distribution\n        that arises in ANOVA tests, and is the ratio of two chi-square\n        variates.\n\n        Parameters\n        ----------\n        dfnum : float\n            Degrees of freedom in numerator. Should be greater than zero.\n        dfden : float\n            Degrees of freedom in denominator. Should be greater than zero.\n        size : {tuple, int}, optional\n            Output shape.  If the given shape is, e.g., ``(m, n, k)``,\n            then ``m * n * k`` samples are drawn. By default only one sample\n            is returned.\n\n        Returns\n        -------\n        samples : {ndarray, scalar}\n            Samples from the Fisher distribution.\n\n        See Also\n        --------\n        scipy.stats.distributions.f : probability density function,\n            distribution or cumulative density function, etc.\n\n        Notes\n        -----\n\n        The F statistic is used to compare in-group variances to between-group\n        variances. Calculating the distribution depends on the sampling, and\n        so it is a function of the respective degrees of freedom in the\n        problem.  The variable `dfnum` is the number of samples minus one, the\n        between-groups degrees of freedom, while `dfden` is the within-groups\n        degrees of freedom, the sum of the number of samples in each group\n        minus the number of groups.\n\n        References\n        ----------\n        .. [1] Glantz, Stanton A. \"Primer of Biostatistics.\", McGraw-Hill,\n               Fifth Edition, 2002.""\n        .. [2] Wikipedia, \"F-distribution\",\n               http://en.wikipedia.org/wiki/F-distribution\n\n        Examples\n        --------\n        An example from Glantz[1], pp 47-40.\n        Two groups, children of diabetics (25 people) and children from people\n        without diabetes (25 controls). Fasting blood glucose was measured,\n        case group had a mean value of 86.1, controls had a mean value of\n        82.2. Standard deviations were 2.09 and 2.49 respectively. Are these\n        data consistent with the null hypothesis that the parents diabetic\n        status does not affect their children's blood glucose levels?\n        Calculating the F statistic from the data gives a value of 36.01.\n\n        Draw samples from the distribution:\n\n        >>> dfnum = 1. # between group degrees of freedom\n        >>> dfden = 48. # within groups degrees of freedom\n        >>> s = np.random.f(dfnum, dfden, 1000)\n\n        The lower bound for the top 1% of the samples is :\n\n        >>> sort(s)[-10]\n        7.61988120985\n\n        So there is about a 1% chance that the F statistic will exceed 7.62,\n        the measured value is 36, so the null hypothesis is rejected at the 1%\n        level.\n\n        ";
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/* "mtrand.pyx":1729
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static PyObject *__pyx_pf_6mtrand_11RandomState_24noncentral_f(PyObject *__pyx_v_self, PyObject *__pyx_args, PyObject *__pyx_kwds); /*proto*/
static char __pyx_doc_6mtrand_11RandomState_24noncentral_f[] = "\n        noncentral_f(dfnum, dfden, nonc, size=None)\n\n        Draw samples from the noncentral F distribution.\n\n        Samples are drawn from an F distribution with specified parameters,\n        `dfnum` (degrees of freedom in numerator) and `dfden` (degrees of\n        freedom in denominator), where both parameters > 1.\n        `nonc` is the non-centrality parameter.\n\n        Parameters\n        ----------\n        dfnum : int\n            Parameter, should be > 1.\n        dfden : int\n            Parameter, should be > 1.\n        nonc : float\n            Parameter, should be >= 0.\n        size : int or tuple of ints\n            Output shape. If the given shape is, e.g., ``(m, n, k)``, then\n            ``m * n * k`` samples are drawn.\n\n        Returns\n        -------\n        samples : scalar or ndarray\n            Drawn samples.\n\n        Notes\n        -----\n        When calculating the power of an experiment (power = probability of\n        rejecting the null hypothesis when a specific alternative is true) the\n        non-central F statistic becomes important.  When the null hypothesis is\n        true, the F statistic follows a central F distribution. When the null\n        hypothesis is not true, then it follows a non-central F statistic.\n\n        References\n        ----------\n        Weisstein, Eric W. \"Noncentral F-Distribution.\" From MathWorld--A Wolfram\n        Web Resource.  http://mathworld.wolfram.com/NoncentralF-Distribution.html\n\n        Wikipedia, \"Noncentral F distribution\",\n        http://en.wikipedia.org/wiki/Noncentral_F-distribution\n\n        Examples\n        --------\n        In a study, testing for a specific alternative to the null hypothesis\n        requires use of the Noncentral F distribution. We need to calculate the\n        area in the tail of the distribution that exceeds the value of the F\n        distribution for the null hypothesis.  We'll plot the two probability\n        distributions for comp""arison.\n\n        >>> dfnum = 3 # between group deg of freedom\n        >>> dfden = 20 # within groups degrees of freedom\n        >>> nonc = 3.0\n        >>> nc_vals = np.random.noncentral_f(dfnum, dfden, nonc, 1000000)\n        >>> NF = np.histogram(nc_vals, bins=50, normed=True)\n        >>> c_vals = np.random.f(dfnum, dfden, 1000000)\n        >>> F = np.histogram(c_vals, bins=50, normed=True)\n        >>> plt.plot(F[1][1:], F[0])\n        >>> plt.plot(NF[1][1:], NF[0])\n        >>> plt.show()\n\n        ";
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static char __pyx_doc_6mtrand_11RandomState_26noncentral_chisquare[] = "\n        noncentral_chisquare(df, nonc, size=None)\n\n        Draw samples from a noncentral chi-square distribution.\n\n        The noncentral :math:`\\chi^2` distribution is a generalisation of\n        the :math:`\\chi^2` distribution.\n\n        Parameters\n        ----------\n        df : int\n            Degrees of freedom, should be >= 1.\n        nonc : float\n            Non-centrality, should be > 0.\n        size : int or tuple of ints\n            Shape of the output.\n\n        Notes\n        -----\n        The probability density function for the noncentral Chi-square distribution\n        is\n\n        .. math:: P(x;df,nonc) = \\sum^{\\infty}_{i=0}\n                               \\frac{e^{-nonc/2}(nonc/2)^{i}}{i!}P_{Y_{df+2i}}(x),\n\n        where :math:`Y_{q}` is the Chi-square with q degrees of freedom.\n\n        In Delhi (2007), it is noted that the noncentral chi-square is useful in\n        bombing and coverage problems, the probability of killing the point target\n        given by the noncentral chi-squared distribution.\n\n        References\n        ----------\n        .. [1] Delhi, M.S. Holla, \"On a noncentral chi-square distribution in the\n               analysis of weapon systems effectiveness\", Metrika, Volume 15,\n               Number 1 / December, 1970.\n        .. [2] Wikipedia, \"Noncentral chi-square distribution\"\n               http://en.wikipedia.org/wiki/Noncentral_chi-square_distribution\n\n        Examples\n        --------\n        Draw values from the distribution and plot the histogram\n\n        >>> import matplotlib.pyplot as plt\n        >>> values = plt.hist(np.random.noncentral_chisquare(3, 20, 100000),\n        ...                   bins=200, normed=True)\n        >>> plt.show()\n\n        Draw values from a noncentral chisquare with very small noncentrality,\n        and compare to a chisquare.\n\n        >>> plt.figure()\n        >>> values = plt.hist(np.random.noncentral_chisquare(3, .0000001, 100000),\n     ""   ...                   bins=np.arange(0., 25, .1), normed=True)\n        >>> values2 = plt.hist(np.random.chisquare(3, 100000),\n        ...                    bins=np.arange(0., 25, .1), normed=True)\n        >>> plt.plot(values[1][0:-1], values[0]-values2[0], 'ob')\n        >>> plt.show()\n\n        Demonstrate how large values of non-centrality lead to a more symmetric\n        distribution.\n\n        >>> plt.figure()\n        >>> values = plt.hist(np.random.noncentral_chisquare(3, 20, 100000),\n        ...                   bins=200, normed=True)\n        >>> plt.show()\n\n        ";
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static char __pyx_doc_6mtrand_11RandomState_29vonmises[] = "\n        vonmises(mu, kappa, size=None)\n\n        Draw samples from a von Mises distribution.\n\n        Samples are drawn from a von Mises distribution with specified mode\n        (mu) and dispersion (kappa), on the interval [-pi, pi].\n\n        The von Mises distribution (also known as the circular normal\n        distribution) is a continuous probability distribution on the unit\n        circle.  It may be thought of as the circular analogue of the normal\n        distribution.\n\n        Parameters\n        ----------\n        mu : float\n            Mode (\"center\") of the distribution.\n        kappa : float\n            Dispersion of the distribution, has to be >=0.\n        size : int or tuple of int\n            Output shape.  If the given shape is, e.g., ``(m, n, k)``, then\n            ``m * n * k`` samples are drawn.\n\n        Returns\n        -------\n        samples : scalar or ndarray\n            The returned samples, which are in the interval [-pi, pi].\n\n        See Also\n        --------\n        scipy.stats.distributions.vonmises : probability density function,\n            distribution, or cumulative density function, etc.\n\n        Notes\n        -----\n        The probability density for the von Mises distribution is\n\n        .. math:: p(x) = \\frac{e^{\\kappa cos(x-\\mu)}}{2\\pi I_0(\\kappa)},\n\n        where :math:`\\mu` is the mode and :math:`\\kappa` the dispersion,\n        and :math:`I_0(\\kappa)` is the modified Bessel function of order 0.\n\n        The von Mises is named for Richard Edler von Mises, who was born in\n        Austria-Hungary, in what is now the Ukraine.  He fled to the United\n        States in 1939 and became a professor at Harvard.  He worked in\n        probability theory, aerodynamics, fluid mechanics, and philosophy of\n        science.\n\n        References\n        ----------\n        Abramowitz, M. and Stegun, I. A. (ed.), *Handbook of Mathematical\n        Functions*, New York: Dover, 1965.\n\n      ""  von Mises, R., *Mathematical Theory of Probability and Statistics*,\n        New York: Academic Press, 1964.\n\n        Examples\n        --------\n        Draw samples from the distribution:\n\n        >>> mu, kappa = 0.0, 4.0 # mean and dispersion\n        >>> s = np.random.vonmises(mu, kappa, 1000)\n\n        Display the histogram of the samples, along with\n        the probability density function:\n\n        >>> import matplotlib.pyplot as plt\n        >>> import scipy.special as sps\n        >>> count, bins, ignored = plt.hist(s, 50, normed=True)\n        >>> x = np.arange(-np.pi, np.pi, 2*np.pi/50.)\n        >>> y = -np.exp(kappa*np.cos(x-mu))/(2*np.pi*sps.jn(0,kappa))\n        >>> plt.plot(x, y/max(y), linewidth=2, color='r')\n        >>> plt.show()\n\n        ";
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static char __pyx_doc_6mtrand_11RandomState_30pareto[] = "\n        pareto(a, size=None)\n\n        Draw samples from a Pareto II or Lomax distribution with specified shape.\n\n        The Lomax or Pareto II distribution is a shifted Pareto distribution. The\n        classical Pareto distribution can be obtained from the Lomax distribution\n        by adding the location parameter m, see below. The smallest value of the\n        Lomax distribution is zero while for the classical Pareto distribution it\n        is m, where the standard Pareto distribution has location m=1.\n        Lomax can also be considered as a simplified version of the Generalized\n        Pareto distribution (available in SciPy), with the scale set to one and\n        the location set to zero.\n\n        The Pareto distribution must be greater than zero, and is unbounded above.\n        It is also known as the \"80-20 rule\".  In this distribution, 80 percent of\n        the weights are in the lowest 20 percent of the range, while the other 20\n        percent fill the remaining 80 percent of the range.\n\n        Parameters\n        ----------\n        shape : float, > 0.\n            Shape of the distribution.\n        size : tuple of ints\n            Output shape.  If the given shape is, e.g., ``(m, n, k)``, then\n            ``m * n * k`` samples are drawn.\n\n        See Also\n        --------\n        scipy.stats.distributions.lomax.pdf : probability density function,\n            distribution or cumulative density function, etc.\n        scipy.stats.distributions.genpareto.pdf : probability density function,\n            distribution or cumulative density function, etc.\n\n        Notes\n        -----\n        The probability density for the Pareto distribution is\n\n        .. math:: p(x) = \\frac{am^a}{x^{a+1}}\n\n        where :math:`a` is the shape and :math:`m` the location\n\n        The Pareto distribution, named after the Italian economist Vilfredo Pareto,\n        is a power law probability distribution useful in many real world probl""ems.\n        Outside the field of economics it is generally referred to as the Bradford\n        distribution. Pareto developed the distribution to describe the\n        distribution of wealth in an economy.  It has also found use in insurance,\n        web page access statistics, oil field sizes, and many other problems,\n        including the download frequency for projects in Sourceforge [1].  It is\n        one of the so-called \"fat-tailed\" distributions.\n\n\n        References\n        ----------\n        .. [1] Francis Hunt and Paul Johnson, On the Pareto Distribution of\n               Sourceforge projects.\n        .. [2] Pareto, V. (1896). Course of Political Economy. Lausanne.\n        .. [3] Reiss, R.D., Thomas, M.(2001), Statistical Analysis of Extreme\n               Values, Birkhauser Verlag, Basel, pp 23-30.\n        .. [4] Wikipedia, \"Pareto distribution\",\n               http://en.wikipedia.org/wiki/Pareto_distribution\n\n        Examples\n        --------\n        Draw samples from the distribution:\n\n        >>> a, m = 3., 1. # shape and mode\n        >>> s = np.random.pareto(a, 1000) + m\n\n        Display the histogram of the samples, along with\n        the probability density function:\n\n        >>> import matplotlib.pyplot as plt\n        >>> count, bins, ignored = plt.hist(s, 100, normed=True, align='center')\n        >>> fit = a*m**a/bins**(a+1)\n        >>> plt.plot(bins, max(count)*fit/max(fit),linewidth=2, color='r')\n        >>> plt.show()\n\n        ";
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static char __pyx_doc_6mtrand_11RandomState_33laplace[] = "\n        laplace(loc=0.0, scale=1.0, size=None)\n\n        Draw samples from the Laplace or double exponential distribution with\n        specified location (or mean) and scale (decay).\n\n        The Laplace distribution is similar to the Gaussian/normal distribution,\n        but is sharper at the peak and has fatter tails. It represents the\n        difference between two independent, identically distributed exponential\n        random variables.\n\n        Parameters\n        ----------\n        loc : float\n            The position, :math:`\\mu`, of the distribution peak.\n        scale : float\n            :math:`\\lambda`, the exponential decay.\n\n        Notes\n        -----\n        It has the probability density function\n\n        .. math:: f(x; \\mu, \\lambda) = \\frac{1}{2\\lambda}\n                                       \\exp\\left(-\\frac{|x - \\mu|}{\\lambda}\\right).\n\n        The first law of Laplace, from 1774, states that the frequency of an error\n        can be expressed as an exponential function of the absolute magnitude of\n        the error, which leads to the Laplace distribution. For many problems in\n        Economics and Health sciences, this distribution seems to model the data\n        better than the standard Gaussian distribution\n\n\n        References\n        ----------\n        .. [1] Abramowitz, M. and Stegun, I. A. (Eds.). Handbook of Mathematical\n               Functions with Formulas, Graphs, and Mathematical Tables, 9th\n               printing.  New York: Dover, 1972.\n\n        .. [2] The Laplace distribution and generalizations\n               By Samuel Kotz, Tomasz J. Kozubowski, Krzysztof Podgorski,\n               Birkhauser, 2001.\n\n        .. [3] Weisstein, Eric W. \"Laplace Distribution.\"\n               From MathWorld--A Wolfram Web Resource.\n               http://mathworld.wolfram.com/LaplaceDistribution.html\n\n        .. [4] Wikipedia, \"Laplace distribution\",\n               http://en.wikipedia.org/wik""i/Laplace_distribution\n\n        Examples\n        --------\n        Draw samples from the distribution\n\n        >>> loc, scale = 0., 1.\n        >>> s = np.random.laplace(loc, scale, 1000)\n\n        Display the histogram of the samples, along with\n        the probability density function:\n\n        >>> import matplotlib.pyplot as plt\n        >>> count, bins, ignored = plt.hist(s, 30, normed=True)\n        >>> x = np.arange(-8., 8., .01)\n        >>> pdf = np.exp(-abs(x-loc/scale))/(2.*scale)\n        >>> plt.plot(x, pdf)\n\n        Plot Gaussian for comparison:\n\n        >>> g = (1/(scale * np.sqrt(2 * np.pi)) * \n        ...      np.exp( - (x - loc)**2 / (2 * scale**2) ))\n        >>> plt.plot(x,g)\n\n        ";
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static char __pyx_doc_6mtrand_11RandomState_34gumbel[] = "\n        gumbel(loc=0.0, scale=1.0, size=None)\n\n        Gumbel distribution.\n\n        Draw samples from a Gumbel distribution with specified location and scale.\n        For more information on the Gumbel distribution, see Notes and References\n        below.\n\n        Parameters\n        ----------\n        loc : float\n            The location of the mode of the distribution.\n        scale : float\n            The scale parameter of the distribution.\n        size : tuple of ints\n            Output shape.  If the given shape is, e.g., ``(m, n, k)``, then\n            ``m * n * k`` samples are drawn.\n\n        Returns\n        -------\n        out : ndarray\n            The samples\n\n        See Also\n        --------\n        scipy.stats.gumbel_l\n        scipy.stats.gumbel_r\n        scipy.stats.genextreme\n            probability density function, distribution, or cumulative density\n            function, etc. for each of the above\n        weibull\n\n        Notes\n        -----\n        The Gumbel (or Smallest Extreme Value (SEV) or the Smallest Extreme Value\n        Type I) distribution is one of a class of Generalized Extreme Value (GEV)\n        distributions used in modeling extreme value problems.  The Gumbel is a\n        special case of the Extreme Value Type I distribution for maximums from\n        distributions with \"exponential-like\" tails.\n\n        The probability density for the Gumbel distribution is\n\n        .. math:: p(x) = \\frac{e^{-(x - \\mu)/ \\beta}}{\\beta} e^{ -e^{-(x - \\mu)/\n                  \\beta}},\n\n        where :math:`\\mu` is the mode, a location parameter, and :math:`\\beta` is\n        the scale parameter.\n\n        The Gumbel (named for German mathematician Emil Julius Gumbel) was used\n        very early in the hydrology literature, for modeling the occurrence of\n        flood events. It is also used for modeling maximum wind speed and rainfall\n        rates.  It is a \"fat-tailed\" distribution - the ""probability of an event in\n        the tail of the distribution is larger than if one used a Gaussian, hence\n        the surprisingly frequent occurrence of 100-year floods. Floods were\n        initially modeled as a Gaussian process, which underestimated the frequency\n        of extreme events.\n\n\n        It is one of a class of extreme value distributions, the Generalized\n        Extreme Value (GEV) distributions, which also includes the Weibull and\n        Frechet.\n\n        The function has a mean of :math:`\\mu + 0.57721\\beta` and a variance of\n        :math:`\\frac{\\pi^2}{6}\\beta^2`.\n\n        References\n        ----------\n        Gumbel, E. J., *Statistics of Extremes*, New York: Columbia University\n        Press, 1958.\n\n        Reiss, R.-D. and Thomas, M., *Statistical Analysis of Extreme Values from\n        Insurance, Finance, Hydrology and Other Fields*, Basel: Birkhauser Verlag,\n        2001.\n\n        Examples\n        --------\n        Draw samples from the distribution:\n\n        >>> mu, beta = 0, 0.1 # location and scale\n        >>> s = np.random.gumbel(mu, beta, 1000)\n\n        Display the histogram of the samples, along with\n        the probability density function:\n\n        >>> import matplotlib.pyplot as plt\n        >>> count, bins, ignored = plt.hist(s, 30, normed=True)\n        >>> plt.plot(bins, (1/beta)*np.exp(-(bins - mu)/beta)\n        ...          * np.exp( -np.exp( -(bins - mu) /beta) ),\n        ...          linewidth=2, color='r')\n        >>> plt.show()\n\n        Show how an extreme value distribution can arise from a Gaussian process\n        and compare to a Gaussian:\n\n        >>> means = []\n        >>> maxima = []\n        >>> for i in range(0,1000) :\n        ...    a = np.random.normal(mu, beta, 1000)\n        ...    means.append(a.mean())\n        ...    maxima.append(a.max())\n        >>> count, bins, ignored = plt.hist(maxima, 30, normed=True)\n        >>> beta = np.std(maxima)*np.pi/np.sqrt(6)""\n        >>> mu = np.mean(maxima) - 0.57721*beta\n        >>> plt.plot(bins, (1/beta)*np.exp(-(bins - mu)/beta)\n        ...          * np.exp(-np.exp(-(bins - mu)/beta)),\n        ...          linewidth=2, color='r')\n        >>> plt.plot(bins, 1/(beta * np.sqrt(2 * np.pi))\n        ...          * np.exp(-(bins - mu)**2 / (2 * beta**2)),\n        ...          linewidth=2, color='g')\n        >>> plt.show()\n\n        ";
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static char __pyx_doc_6mtrand_11RandomState_35logistic[] = "\n        logistic(loc=0.0, scale=1.0, size=None)\n\n        Draw samples from a Logistic distribution.\n\n        Samples are drawn from a Logistic distribution with specified\n        parameters, loc (location or mean, also median), and scale (>0).\n\n        Parameters\n        ----------\n        loc : float\n\n        scale : float > 0.\n\n        size : {tuple, int}\n            Output shape.  If the given shape is, e.g., ``(m, n, k)``, then\n            ``m * n * k`` samples are drawn.\n\n        Returns\n        -------\n        samples : {ndarray, scalar}\n                  where the values are all integers in  [0, n].\n\n        See Also\n        --------\n        scipy.stats.distributions.logistic : probability density function,\n            distribution or cumulative density function, etc.\n\n        Notes\n        -----\n        The probability density for the Logistic distribution is\n\n        .. math:: P(x) = P(x) = \\frac{e^{-(x-\\mu)/s}}{s(1+e^{-(x-\\mu)/s})^2},\n\n        where :math:`\\mu` = location and :math:`s` = scale.\n\n        The Logistic distribution is used in Extreme Value problems where it\n        can act as a mixture of Gumbel distributions, in Epidemiology, and by\n        the World Chess Federation (FIDE) where it is used in the Elo ranking\n        system, assuming the performance of each player is a logistically\n        distributed random variable.\n\n        References\n        ----------\n        .. [1] Reiss, R.-D. and Thomas M. (2001), Statistical Analysis of Extreme\n               Values, from Insurance, Finance, Hydrology and Other Fields,\n               Birkhauser Verlag, Basel, pp 132-133.\n        .. [2] Weisstein, Eric W. \"Logistic Distribution.\" From\n               MathWorld--A Wolfram Web Resource.\n               http://mathworld.wolfram.com/LogisticDistribution.html\n        .. [3] Wikipedia, \"Logistic-distribution\",\n               http://en.wikipedia.org/wiki/Logistic-distribution\n\n        Examples\n   ""     --------\n        Draw samples from the distribution:\n\n        >>> loc, scale = 10, 1\n        >>> s = np.random.logistic(loc, scale, 10000)\n        >>> count, bins, ignored = plt.hist(s, bins=50)\n\n        #   plot against distribution\n\n        >>> def logist(x, loc, scale):\n        ...     return exp((loc-x)/scale)/(scale*(1+exp((loc-x)/scale))**2)\n        >>> plt.plot(bins, logist(bins, loc, scale)*count.max()/\\\n        ... logist(bins, loc, scale).max())\n        >>> plt.show()\n\n        ";
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static char __pyx_doc_6mtrand_11RandomState_36lognormal[] = "\n        lognormal(mean=0.0, sigma=1.0, size=None)\n\n        Return samples drawn from a log-normal distribution.\n\n        Draw samples from a log-normal distribution with specified mean, standard\n        deviation, and shape. Note that the mean and standard deviation are not the\n        values for the distribution itself, but of the underlying normal\n        distribution it is derived from.\n\n\n        Parameters\n        ----------\n        mean : float\n            Mean value of the underlying normal distribution\n        sigma : float, >0.\n            Standard deviation of the underlying normal distribution\n        size : tuple of ints\n            Output shape.  If the given shape is, e.g., ``(m, n, k)``, then\n            ``m * n * k`` samples are drawn.\n\n        See Also\n        --------\n        scipy.stats.lognorm : probability density function, distribution,\n            cumulative density function, etc.\n\n        Notes\n        -----\n        A variable `x` has a log-normal distribution if `log(x)` is normally\n        distributed.\n\n        The probability density function for the log-normal distribution is\n\n        .. math:: p(x) = \\frac{1}{\\sigma x \\sqrt{2\\pi}}\n                         e^{(-\\frac{(ln(x)-\\mu)^2}{2\\sigma^2})}\n\n        where :math:`\\mu` is the mean and :math:`\\sigma` is the standard deviation\n        of the normally distributed logarithm of the variable.\n\n        A log-normal distribution results if a random variable is the *product* of\n        a large number of independent, identically-distributed variables in the\n        same way that a normal distribution results if the variable is the *sum*\n        of a large number of independent, identically-distributed variables\n        (see the last example). It is one of the so-called \"fat-tailed\"\n        distributions.\n\n        The log-normal distribution is commonly used to model the lifespan of units\n        with fatigue-stress failure modes. Since thi""s includes\n        most mechanical systems, the log-normal distribution has widespread\n        application.\n\n        It is also commonly used to model oil field sizes, species abundance, and\n        latent periods of infectious diseases.\n\n        References\n        ----------\n        .. [1] Eckhard Limpert, Werner A. Stahel, and Markus Abbt, \"Log-normal\n               Distributions across the Sciences: Keys and Clues\", May 2001\n               Vol. 51 No. 5 BioScience\n               http://stat.ethz.ch/~stahel/lognormal/bioscience.pdf\n        .. [2] Reiss, R.D., Thomas, M.(2001), Statistical Analysis of Extreme\n               Values, Birkhauser Verlag, Basel, pp 31-32.\n        .. [3] Wikipedia, \"Lognormal distribution\",\n               http://en.wikipedia.org/wiki/Lognormal_distribution\n\n        Examples\n        --------\n        Draw samples from the distribution:\n\n        >>> mu, sigma = 3., 1. # mean and standard deviation\n        >>> s = np.random.lognormal(mu, sigma, 1000)\n\n        Display the histogram of the samples, along with\n        the probability density function:\n\n        >>> import matplotlib.pyplot as plt\n        >>> count, bins, ignored = plt.hist(s, 100, normed=True, align='mid')\n\n        >>> x = np.linspace(min(bins), max(bins), 10000)\n        >>> pdf = (np.exp(-(np.log(x) - mu)**2 / (2 * sigma**2))\n        ...        / (x * sigma * np.sqrt(2 * np.pi)))\n\n        >>> plt.plot(x, pdf, linewidth=2, color='r')\n        >>> plt.axis('tight')\n        >>> plt.show()\n\n        Demonstrate that taking the products of random samples from a uniform\n        distribution can be fit well by a log-normal probability density function.\n\n        >>> # Generate a thousand samples: each is the product of 100 random\n        >>> # values, drawn from a normal distribution.\n        >>> b = []\n        >>> for i in range(1000):\n        ...    a = 10. + np.random.random(100)\n        ...    b.append(np.product(a))\n\n        >>> b"" = np.array(b) / np.min(b) # scale values to be positive\n\n        >>> count, bins, ignored = plt.hist(b, 100, normed=True, align='center')\n\n        >>> sigma = np.std(np.log(b))\n        >>> mu = np.mean(np.log(b))\n\n        >>> x = np.linspace(min(bins), max(bins), 10000)\n        >>> pdf = (np.exp(-(np.log(x) - mu)**2 / (2 * sigma**2))\n        ...        / (x * sigma * np.sqrt(2 * np.pi)))\n\n        >>> plt.plot(x, pdf, color='r', linewidth=2)\n        >>> plt.show()\n\n        ";
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static char __pyx_doc_6mtrand_11RandomState_38wald[] = "\n        wald(mean, scale, size=None)\n\n        Draw samples from a Wald, or Inverse Gaussian, distribution.\n\n        As the scale approaches infinity, the distribution becomes more like a\n        Gaussian.\n\n        Some references claim that the Wald is an Inverse Gaussian with mean=1, but\n        this is by no means universal.\n\n        The Inverse Gaussian distribution was first studied in relationship to\n        Brownian motion. In 1956 M.C.K. Tweedie used the name Inverse Gaussian\n        because there is an inverse relationship between the time to cover a unit\n        distance and distance covered in unit time.\n\n        Parameters\n        ----------\n        mean : scalar\n            Distribution mean, should be > 0.\n        scale : scalar\n            Scale parameter, should be >= 0.\n        size : int or tuple of ints, optional\n            Output shape. Default is None, in which case a single value is\n            returned.\n\n        Returns\n        -------\n        samples : ndarray or scalar\n            Drawn sample, all greater than zero.\n\n        Notes\n        -----\n        The probability density function for the Wald distribution is\n\n        .. math:: P(x;mean,scale) = \\sqrt{\\frac{scale}{2\\pi x^3}}e^\n                                    \\frac{-scale(x-mean)^2}{2\\cdotp mean^2x}\n\n        As noted above the Inverse Gaussian distribution first arise from attempts\n        to model Brownian Motion. It is also a competitor to the Weibull for use in\n        reliability modeling and modeling stock returns and interest rate\n        processes.\n\n        References\n        ----------\n        ..[1] Brighton Webs Ltd., Wald Distribution,\n              http://www.brighton-webs.co.uk/distributions/wald.asp\n        ..[2] Chhikara, Raj S., and Folks, J. Leroy, \"The Inverse Gaussian\n              Distribution: Theory : Methodology, and Applications\", CRC Press,\n              1988.\n        ..[3] Wikipedia, \"Wald distributio""n\"\n              http://en.wikipedia.org/wiki/Wald_distribution\n\n        Examples\n        --------\n        Draw values from the distribution and plot the histogram:\n\n        >>> import matplotlib.pyplot as plt\n        >>> h = plt.hist(np.random.wald(3, 2, 100000), bins=200, normed=True)\n        >>> plt.show()\n\n        ";
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static char __pyx_doc_6mtrand_11RandomState_40binomial[] = "\n        binomial(n, p, size=None)\n\n        Draw samples from a binomial distribution.\n\n        Samples are drawn from a Binomial distribution with specified\n        parameters, n trials and p probability of success where\n        n an integer > 0 and p is in the interval [0,1]. (n may be\n        input as a float, but it is truncated to an integer in use)\n\n        Parameters\n        ----------\n        n : float (but truncated to an integer)\n                parameter, > 0.\n        p : float\n                parameter, >= 0 and <=1.\n        size : {tuple, int}\n            Output shape.  If the given shape is, e.g., ``(m, n, k)``, then\n            ``m * n * k`` samples are drawn.\n\n        Returns\n        -------\n        samples : {ndarray, scalar}\n                  where the values are all integers in  [0, n].\n\n        See Also\n        --------\n        scipy.stats.distributions.binom : probability density function,\n            distribution or cumulative density function, etc.\n\n        Notes\n        -----\n        The probability density for the Binomial distribution is\n\n        .. math:: P(N) = \\binom{n}{N}p^N(1-p)^{n-N},\n\n        where :math:`n` is the number of trials, :math:`p` is the probability\n        of success, and :math:`N` is the number of successes.\n\n        When estimating the standard error of a proportion in a population by\n        using a random sample, the normal distribution works well unless the\n        product p*n <=5, where p = population proportion estimate, and n =\n        number of samples, in which case the binomial distribution is used\n        instead. For example, a sample of 15 people shows 4 who are left\n        handed, and 11 who are right handed. Then p = 4/15 = 27%. 0.27*15 = 4,\n        so the binomial distribution should be used in this case.\n\n        References\n        ----------\n        .. [1] Dalgaard, Peter, \"Introductory Statistics with R\",\n               Springer-Verlag, 2002.\n    ""    .. [2] Glantz, Stanton A. \"Primer of Biostatistics.\", McGraw-Hill,\n               Fifth Edition, 2002.\n        .. [3] Lentner, Marvin, \"Elementary Applied Statistics\", Bogden\n               and Quigley, 1972.\n        .. [4] Weisstein, Eric W. \"Binomial Distribution.\" From MathWorld--A\n               Wolfram Web Resource.\n               http://mathworld.wolfram.com/BinomialDistribution.html\n        .. [5] Wikipedia, \"Binomial-distribution\",\n               http://en.wikipedia.org/wiki/Binomial_distribution\n\n        Examples\n        --------\n        Draw samples from the distribution:\n\n        >>> n, p = 10, .5 # number of trials, probability of each trial\n        >>> s = np.random.binomial(n, p, 1000)\n        # result of flipping a coin 10 times, tested 1000 times.\n\n        A real world example. A company drills 9 wild-cat oil exploration\n        wells, each with an estimated probability of success of 0.1. All nine\n        wells fail. What is the probability of that happening?\n\n        Let's do 20,000 trials of the model, and count the number that\n        generate zero positive results.\n\n        >>> sum(np.random.binomial(9,0.1,20000)==0)/20000.\n        answer = 0.38885, or 38%.\n\n        ";
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static char __pyx_doc_6mtrand_11RandomState_41negative_binomial[] = "\n        negative_binomial(n, p, size=None)\n\n        Draw samples from a negative_binomial distribution.\n\n        Samples are drawn from a negative_Binomial distribution with specified\n        parameters, `n` trials and `p` probability of success where `n` is an\n        integer > 0 and `p` is in the interval [0, 1].\n\n        Parameters\n        ----------\n        n : int\n            Parameter, > 0.\n        p : float\n            Parameter, >= 0 and <=1.\n        size : int or tuple of ints\n            Output shape. If the given shape is, e.g., ``(m, n, k)``, then\n            ``m * n * k`` samples are drawn.\n\n        Returns\n        -------\n        samples : int or ndarray of ints\n            Drawn samples.\n\n        Notes\n        -----\n        The probability density for the Negative Binomial distribution is\n\n        .. math:: P(N;n,p) = \\binom{N+n-1}{n-1}p^{n}(1-p)^{N},\n\n        where :math:`n-1` is the number of successes, :math:`p` is the probability\n        of success, and :math:`N+n-1` is the number of trials.\n\n        The negative binomial distribution gives the probability of n-1 successes\n        and N failures in N+n-1 trials, and success on the (N+n)th trial.\n\n        If one throws a die repeatedly until the third time a \"1\" appears, then the\n        probability distribution of the number of non-\"1\"s that appear before the\n        third \"1\" is a negative binomial distribution.\n\n        References\n        ----------\n        .. [1] Weisstein, Eric W. \"Negative Binomial Distribution.\" From\n               MathWorld--A Wolfram Web Resource.\n               http://mathworld.wolfram.com/NegativeBinomialDistribution.html\n        .. [2] Wikipedia, \"Negative binomial distribution\",\n               http://en.wikipedia.org/wiki/Negative_binomial_distribution\n\n        Examples\n        --------\n        Draw samples from the distribution:\n\n        A real world example. A company drills wild-cat oil exploration well""s, each\n        with an estimated probability of success of 0.1.  What is the probability\n        of having one success for each successive well, that is what is the\n        probability of a single success after drilling 5 wells, after 6 wells,\n        etc.?\n\n        >>> s = np.random.negative_binomial(1, 0.1, 100000)\n        >>> for i in range(1, 11):\n        ...    probability = sum(s<i) / 100000.\n        ...    print i, \"wells drilled, probability of one success =\", probability\n\n        ";
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static char __pyx_doc_6mtrand_11RandomState_42poisson[] = "\n        poisson(lam=1.0, size=None)\n\n        Draw samples from a Poisson distribution.\n\n        The Poisson distribution is the limit of the Binomial\n        distribution for large N.\n\n        Parameters\n        ----------\n        lam : float\n            Expectation of interval, should be >= 0.\n        size : int or tuple of ints, optional\n            Output shape. If the given shape is, e.g., ``(m, n, k)``, then\n            ``m * n * k`` samples are drawn.\n\n        Notes\n        -----\n        The Poisson distribution\n\n        .. math:: f(k; \\lambda)=\\frac{\\lambda^k e^{-\\lambda}}{k!}\n\n        For events with an expected separation :math:`\\lambda` the Poisson\n        distribution :math:`f(k; \\lambda)` describes the probability of\n        :math:`k` events occurring within the observed interval :math:`\\lambda`.\n\n        Because the output is limited to the range of the C long type, a\n        ValueError is raised when `lam` is within 10 sigma of the maximum\n        representable value.\n\n        References\n        ----------\n        .. [1] Weisstein, Eric W. \"Poisson Distribution.\" From MathWorld--A Wolfram\n               Web Resource. http://mathworld.wolfram.com/PoissonDistribution.html\n        .. [2] Wikipedia, \"Poisson distribution\",\n           http://en.wikipedia.org/wiki/Poisson_distribution\n\n        Examples\n        --------\n        Draw samples from the distribution:\n\n        >>> import numpy as np\n        >>> s = np.random.poisson(5, 10000)\n\n        Display histogram of the sample:\n\n        >>> import matplotlib.pyplot as plt\n        >>> count, bins, ignored = plt.hist(s, 14, normed=True)\n        >>> plt.show()\n\n        ";
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static char __pyx_doc_6mtrand_11RandomState_45hypergeometric[] = "\n        hypergeometric(ngood, nbad, nsample, size=None)\n\n        Draw samples from a Hypergeometric distribution.\n\n        Samples are drawn from a Hypergeometric distribution with specified\n        parameters, ngood (ways to make a good selection), nbad (ways to make\n        a bad selection), and nsample = number of items sampled, which is less\n        than or equal to the sum ngood + nbad.\n\n        Parameters\n        ----------\n        ngood : float (but truncated to an integer)\n                parameter, > 0.\n        nbad  : float\n                parameter, >= 0.\n        nsample  : float\n                   parameter, > 0 and <= ngood+nbad\n        size : {tuple, int}\n            Output shape.  If the given shape is, e.g., ``(m, n, k)``, then\n            ``m * n * k`` samples are drawn.\n\n        Returns\n        -------\n        samples : {ndarray, scalar}\n                  where the values are all integers in  [0, n].\n\n        See Also\n        --------\n        scipy.stats.distributions.hypergeom : probability density function,\n            distribution or cumulative density function, etc.\n\n        Notes\n        -----\n        The probability density for the Hypergeometric distribution is\n\n        .. math:: P(x) = \\frac{\\binom{m}{n}\\binom{N-m}{n-x}}{\\binom{N}{n}},\n\n        where :math:`0 \\le x \\le m` and :math:`n+m-N \\le x \\le n`\n\n        for P(x) the probability of x successes, n = ngood, m = nbad, and\n        N = number of samples.\n\n        Consider an urn with black and white marbles in it, ngood of them\n        black and nbad are white. If you draw nsample balls without\n        replacement, then the Hypergeometric distribution describes the\n        distribution of black balls in the drawn sample.\n\n        Note that this distribution is very similar to the Binomial\n        distribution, except that in this case, samples are drawn without\n        replacement, whereas in the Binomial case samples are drawn wit""h\n        replacement (or the sample space is infinite). As the sample space\n        becomes large, this distribution approaches the Binomial.\n\n        References\n        ----------\n        .. [1] Lentner, Marvin, \"Elementary Applied Statistics\", Bogden\n               and Quigley, 1972.\n        .. [2] Weisstein, Eric W. \"Hypergeometric Distribution.\" From\n               MathWorld--A Wolfram Web Resource.\n               http://mathworld.wolfram.com/HypergeometricDistribution.html\n        .. [3] Wikipedia, \"Hypergeometric-distribution\",\n               http://en.wikipedia.org/wiki/Hypergeometric-distribution\n\n        Examples\n        --------\n        Draw samples from the distribution:\n\n        >>> ngood, nbad, nsamp = 100, 2, 10\n        # number of good, number of bad, and number of samples\n        >>> s = np.random.hypergeometric(ngood, nbad, nsamp, 1000)\n        >>> hist(s)\n        #   note that it is very unlikely to grab both bad items\n\n        Suppose you have an urn with 15 white and 15 black marbles.\n        If you pull 15 marbles at random, how likely is it that\n        12 or more of them are one color?\n\n        >>> s = np.random.hypergeometric(15, 15, 15, 100000)\n        >>> sum(s>=12)/100000. + sum(s<=3)/100000.\n        #   answer = 0.003 ... pretty unlikely!\n\n        ";
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static char __pyx_doc_6mtrand_11RandomState_47multivariate_normal[] = "\n        multivariate_normal(mean, cov[, size])\n\n        Draw random samples from a multivariate normal distribution.\n\n        The multivariate normal, multinormal or Gaussian distribution is a\n        generalization of the one-dimensional normal distribution to higher\n        dimensions.  Such a distribution is specified by its mean and\n        covariance matrix.  These parameters are analogous to the mean\n        (average or \"center\") and variance (standard deviation, or \"width,\"\n        squared) of the one-dimensional normal distribution.\n\n        Parameters\n        ----------\n        mean : 1-D array_like, of length N\n            Mean of the N-dimensional distribution.\n        cov : 2-D array_like, of shape (N, N)\n            Covariance matrix of the distribution.  Must be symmetric and\n            positive semi-definite for \"physically meaningful\" results.\n        size : tuple of ints, optional\n            Given a shape of, for example, ``(m,n,k)``, ``m*n*k`` samples are\n            generated, and packed in an `m`-by-`n`-by-`k` arrangement.  Because\n            each sample is `N`-dimensional, the output shape is ``(m,n,k,N)``.\n            If no shape is specified, a single (`N`-D) sample is returned.\n\n        Returns\n        -------\n        out : ndarray\n            The drawn samples, of shape *size*, if that was provided.  If not,\n            the shape is ``(N,)``.\n\n            In other words, each entry ``out[i,j,...,:]`` is an N-dimensional\n            value drawn from the distribution.\n\n        Notes\n        -----\n        The mean is a coordinate in N-dimensional space, which represents the\n        location where samples are most likely to be generated.  This is\n        analogous to the peak of the bell curve for the one-dimensional or\n        univariate normal distribution.\n\n        Covariance indicates the level to which two variables vary together.\n        From the multivariate normal distribution, we draw ""N-dimensional\n        samples, :math:`X = [x_1, x_2, ... x_N]`.  The covariance matrix\n        element :math:`C_{ij}` is the covariance of :math:`x_i` and :math:`x_j`.\n        The element :math:`C_{ii}` is the variance of :math:`x_i` (i.e. its\n        \"spread\").\n\n        Instead of specifying the full covariance matrix, popular\n        approximations include:\n\n          - Spherical covariance (*cov* is a multiple of the identity matrix)\n          - Diagonal covariance (*cov* has non-negative elements, and only on\n            the diagonal)\n\n        This geometrical property can be seen in two dimensions by plotting\n        generated data-points:\n\n        >>> mean = [0,0]\n        >>> cov = [[1,0],[0,100]] # diagonal covariance, points lie on x or y-axis\n\n        >>> import matplotlib.pyplot as plt\n        >>> x,y = np.random.multivariate_normal(mean,cov,5000).T\n        >>> plt.plot(x,y,'x'); plt.axis('equal'); plt.show()\n\n        Note that the covariance matrix must be non-negative definite.\n\n        References\n        ----------\n        Papoulis, A., *Probability, Random Variables, and Stochastic Processes*,\n        3rd ed., New York: McGraw-Hill, 1991.\n\n        Duda, R. O., Hart, P. E., and Stork, D. G., *Pattern Classification*,\n        2nd ed., New York: Wiley, 2001.\n\n        Examples\n        --------\n        >>> mean = (1,2)\n        >>> cov = [[1,0],[1,0]]\n        >>> x = np.random.multivariate_normal(mean,cov,(3,3))\n        >>> x.shape\n        (3, 3, 2)\n\n        The following is probably true, given that 0.6 is roughly twice the\n        standard deviation:\n\n        >>> print list( (x[0,0,:] - mean) < 0.6 )\n        [True, True]\n\n        ";
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static char __pyx_doc_6mtrand_11RandomState_49dirichlet[] = "\n        dirichlet(alpha, size=None)\n\n        Draw samples from the Dirichlet distribution.\n\n        Draw `size` samples of dimension k from a Dirichlet distribution. A\n        Dirichlet-distributed random variable can be seen as a multivariate\n        generalization of a Beta distribution. Dirichlet pdf is the conjugate\n        prior of a multinomial in Bayesian inference.\n\n        Parameters\n        ----------\n        alpha : array\n            Parameter of the distribution (k dimension for sample of\n            dimension k).\n        size : array\n            Number of samples to draw.\n\n        Returns\n        -------\n        samples : ndarray,\n            The drawn samples, of shape (alpha.ndim, size).\n\n        Notes\n        -----\n        .. math:: X \\approx \\prod_{i=1}^{k}{x^{\\alpha_i-1}_i}\n\n        Uses the following property for computation: for each dimension,\n        draw a random sample y_i from a standard gamma generator of shape\n        `alpha_i`, then\n        :math:`X = \\frac{1}{\\sum_{i=1}^k{y_i}} (y_1, \\ldots, y_n)` is\n        Dirichlet distributed.\n\n        References\n        ----------\n        .. [1] David McKay, \"Information Theory, Inference and Learning\n               Algorithms,\" chapter 23,\n               http://www.inference.phy.cam.ac.uk/mackay/\n        .. [2] Wikipedia, \"Dirichlet distribution\",\n               http://en.wikipedia.org/wiki/Dirichlet_distribution\n\n        Examples\n        --------\n        Taking an example cited in Wikipedia, this distribution can be used if\n        one wanted to cut strings (each of initial length 1.0) into K pieces\n        with different lengths, where each piece had, on average, a designated\n        average length, but allowing some variation in the relative sizes of the\n        pieces.\n\n        >>> s = np.random.dirichlet((10, 5, 3), 20).transpose()\n\n        >>> plt.barh(range(20), s[0])\n        >>> plt.barh(range(20), s[1], left=s[0], color='g')""\n        >>> plt.barh(range(20), s[2], left=s[0]+s[1], color='r')\n        >>> plt.title(\"Lengths of Strings\")\n\n        ";
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  if (PyDict_SetItem(__pyx_t_4, ((PyObject *)__pyx_kp_u_185), ((PyObject *)__pyx_kp_u_186)) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  if (PyDict_SetItem(__pyx_t_4, ((PyObject *)__pyx_kp_u_187), ((PyObject *)__pyx_kp_u_188)) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  if (PyDict_SetItem(__pyx_t_4, ((PyObject *)__pyx_kp_u_189), ((PyObject *)__pyx_kp_u_190)) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  if (PyDict_SetItem(__pyx_t_4, ((PyObject *)__pyx_kp_u_191), ((PyObject *)__pyx_kp_u_192)) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  if (PyDict_SetItem(__pyx_t_4, ((PyObject *)__pyx_kp_u_193), ((PyObject *)__pyx_kp_u_194)) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  if (PyDict_SetItem(__pyx_t_4, ((PyObject *)__pyx_kp_u_195), ((PyObject *)__pyx_kp_u_196)) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  if (PyDict_SetItem(__pyx_t_4, ((PyObject *)__pyx_kp_u_197), ((PyObject *)__pyx_kp_u_198)) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  if (PyDict_SetItem(__pyx_t_4, ((PyObject *)__pyx_kp_u_199), ((PyObject *)__pyx_kp_u_200)) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  if (PyDict_SetItem(__pyx_t_4, ((PyObject *)__pyx_kp_u_201), ((PyObject *)__pyx_kp_u_202)) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  if (PyDict_SetItem(__pyx_t_4, ((PyObject *)__pyx_kp_u_203), ((PyObject *)__pyx_kp_u_204)) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  if (PyDict_SetItem(__pyx_t_4, ((PyObject *)__pyx_kp_u_205), ((PyObject *)__pyx_kp_u_206)) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  if (PyDict_SetItem(__pyx_t_4, ((PyObject *)__pyx_kp_u_207), ((PyObject *)__pyx_kp_u_208)) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  if (PyDict_SetItem(__pyx_t_4, ((PyObject *)__pyx_kp_u_209), ((PyObject *)__pyx_kp_u_210)) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  if (PyDict_SetItem(__pyx_t_4, ((PyObject *)__pyx_kp_u_211), ((PyObject *)__pyx_kp_u_212)) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  if (PyDict_SetItem(__pyx_t_4, ((PyObject *)__pyx_kp_u_213), ((PyObject *)__pyx_kp_u_214)) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  if (PyDict_SetItem(__pyx_t_4, ((PyObject *)__pyx_kp_u_215), ((PyObject *)__pyx_kp_u_216)) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  if (PyDict_SetItem(__pyx_t_4, ((PyObject *)__pyx_kp_u_217), ((PyObject *)__pyx_kp_u_218)) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  if (PyDict_SetItem(__pyx_t_4, ((PyObject *)__pyx_kp_u_219), ((PyObject *)__pyx_kp_u_220)) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  if (PyDict_SetItem(__pyx_t_4, ((PyObject *)__pyx_kp_u_221), ((PyObject *)__pyx_kp_u_222)) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  if (PyDict_SetItem(__pyx_t_4, ((PyObject *)__pyx_kp_u_223), ((PyObject *)__pyx_kp_u_224)) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  if (PyDict_SetItem(__pyx_t_4, ((PyObject *)__pyx_kp_u_225), ((PyObject *)__pyx_kp_u_226)) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  if (PyDict_SetItem(__pyx_t_4, ((PyObject *)__pyx_kp_u_227), ((PyObject *)__pyx_kp_u_228)) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  if (PyDict_SetItem(__pyx_t_4, ((PyObject *)__pyx_kp_u_229), ((PyObject *)__pyx_kp_u_230)) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  if (PyDict_SetItem(__pyx_t_4, ((PyObject *)__pyx_kp_u_231), ((PyObject *)__pyx_kp_u_232)) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  if (PyDict_SetItem(__pyx_t_4, ((PyObject *)__pyx_kp_u_233), ((PyObject *)__pyx_kp_u_234)) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  if (PyDict_SetItem(__pyx_t_4, ((PyObject *)__pyx_kp_u_235), ((PyObject *)__pyx_kp_u_236)) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  if (PyDict_SetItem(__pyx_t_4, ((PyObject *)__pyx_kp_u_237), ((PyObject *)__pyx_kp_u_238)) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  if (PyDict_SetItem(__pyx_t_4, ((PyObject *)__pyx_kp_u_239), ((PyObject *)__pyx_kp_u_240)) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  if (PyDict_SetItem(__pyx_t_4, ((PyObject *)__pyx_kp_u_241), ((PyObject *)__pyx_kp_u_242)) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  if (PyDict_SetItem(__pyx_t_4, ((PyObject *)__pyx_kp_u_243), ((PyObject *)__pyx_kp_u_244)) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  if (PyDict_SetItem(__pyx_t_4, ((PyObject *)__pyx_kp_u_245), ((PyObject *)__pyx_kp_u_246)) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  if (PyDict_SetItem(__pyx_t_4, ((PyObject *)__pyx_kp_u_247), ((PyObject *)__pyx_kp_u_248)) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  if (PyDict_SetItem(__pyx_t_4, ((PyObject *)__pyx_kp_u_249), ((PyObject *)__pyx_kp_u_250)) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  if (PyDict_SetItem(__pyx_t_4, ((PyObject *)__pyx_kp_u_251), ((PyObject *)__pyx_kp_u_252)) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  if (PyDict_SetItem(__pyx_t_4, ((PyObject *)__pyx_kp_u_253), ((PyObject *)__pyx_kp_u_254)) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  if (PyDict_SetItem(__pyx_t_4, ((PyObject *)__pyx_kp_u_255), ((PyObject *)__pyx_kp_u_256)) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  if (PyObject_SetAttr(__pyx_m, __pyx_n_s____test__, ((PyObject *)__pyx_t_4)) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  __Pyx_DECREF(((PyObject *)__pyx_t_4)); __pyx_t_4 = 0;
  goto __pyx_L0;
  __pyx_L1_error:;
  __Pyx_XDECREF(__pyx_t_1);
  __Pyx_XDECREF(__pyx_t_2);
  __Pyx_XDECREF(__pyx_t_3);
  __Pyx_XDECREF(__pyx_t_4);
  if (__pyx_m) {
    __Pyx_AddTraceback("init mtrand");
    Py_DECREF(__pyx_m); __pyx_m = 0;
  } else if (!PyErr_Occurred()) {
    PyErr_SetString(PyExc_ImportError, "init mtrand");
  }
  __pyx_L0:;
  __Pyx_RefNannyFinishContext();
  #if PY_MAJOR_VERSION < 3
  return;
  #else
  return __pyx_m;
  #endif
}

/* Runtime support code */

static PyObject *__Pyx_GetName(PyObject *dict, PyObject *name) {
    PyObject *result;
    result = PyObject_GetAttr(dict, name);
    if (!result)
        PyErr_SetObject(PyExc_NameError, name);
    return result;
}

static CYTHON_INLINE void __Pyx_ErrRestore(PyObject *type, PyObject *value, PyObject *tb) {
    PyObject *tmp_type, *tmp_value, *tmp_tb;
    PyThreadState *tstate = PyThreadState_GET();

    tmp_type = tstate->curexc_type;
    tmp_value = tstate->curexc_value;
    tmp_tb = tstate->curexc_traceback;
    tstate->curexc_type = type;
    tstate->curexc_value = value;
    tstate->curexc_traceback = tb;
    Py_XDECREF(tmp_type);
    Py_XDECREF(tmp_value);
    Py_XDECREF(tmp_tb);
}

static CYTHON_INLINE void __Pyx_ErrFetch(PyObject **type, PyObject **value, PyObject **tb) {
    PyThreadState *tstate = PyThreadState_GET();
    *type = tstate->curexc_type;
    *value = tstate->curexc_value;
    *tb = tstate->curexc_traceback;

    tstate->curexc_type = 0;
    tstate->curexc_value = 0;
    tstate->curexc_traceback = 0;
}


#if PY_MAJOR_VERSION < 3
static void __Pyx_Raise(PyObject *type, PyObject *value, PyObject *tb) {
    Py_XINCREF(type);
    Py_XINCREF(value);
    Py_XINCREF(tb);
    /* First, check the traceback argument, replacing None with NULL. */
    if (tb == Py_None) {
        Py_DECREF(tb);
        tb = 0;
    }
    else if (tb != NULL && !PyTraceBack_Check(tb)) {
        PyErr_SetString(PyExc_TypeError,
            "raise: arg 3 must be a traceback or None");
        goto raise_error;
    }
    /* Next, replace a missing value with None */
    if (value == NULL) {
        value = Py_None;
        Py_INCREF(value);
    }
    #if PY_VERSION_HEX < 0x02050000
    if (!PyClass_Check(type))
    #else
    if (!PyType_Check(type))
    #endif
    {
        /* Raising an instance.  The value should be a dummy. */
        if (value != Py_None) {
            PyErr_SetString(PyExc_TypeError,
                "instance exception may not have a separate value");
            goto raise_error;
        }
        /* Normalize to raise <class>, <instance> */
        Py_DECREF(value);
        value = type;
        #if PY_VERSION_HEX < 0x02050000
            if (PyInstance_Check(type)) {
                type = (PyObject*) ((PyInstanceObject*)type)->in_class;
                Py_INCREF(type);
            }
            else {
                type = 0;
                PyErr_SetString(PyExc_TypeError,
                    "raise: exception must be an old-style class or instance");
                goto raise_error;
            }
        #else
            type = (PyObject*) Py_TYPE(type);
            Py_INCREF(type);
            if (!PyType_IsSubtype((PyTypeObject *)type, (PyTypeObject *)PyExc_BaseException)) {
                PyErr_SetString(PyExc_TypeError,
                    "raise: exception class must be a subclass of BaseException");
                goto raise_error;
            }
        #endif
    }

    __Pyx_ErrRestore(type, value, tb);
    return;
raise_error:
    Py_XDECREF(value);
    Py_XDECREF(type);
    Py_XDECREF(tb);
    return;
}

#else /* Python 3+ */

static void __Pyx_Raise(PyObject *type, PyObject *value, PyObject *tb) {
    if (tb == Py_None) {
        tb = 0;
    } else if (tb && !PyTraceBack_Check(tb)) {
        PyErr_SetString(PyExc_TypeError,
            "raise: arg 3 must be a traceback or None");
        goto bad;
    }
    if (value == Py_None)
        value = 0;

    if (PyExceptionInstance_Check(type)) {
        if (value) {
            PyErr_SetString(PyExc_TypeError,
                "instance exception may not have a separate value");
            goto bad;
        }
        value = type;
        type = (PyObject*) Py_TYPE(value);
    } else if (!PyExceptionClass_Check(type)) {
        PyErr_SetString(PyExc_TypeError,
            "raise: exception class must be a subclass of BaseException");
        goto bad;
    }

    PyErr_SetObject(type, value);

    if (tb) {
        PyThreadState *tstate = PyThreadState_GET();
        PyObject* tmp_tb = tstate->curexc_traceback;
        if (tb != tmp_tb) {
            Py_INCREF(tb);
            tstate->curexc_traceback = tb;
            Py_XDECREF(tmp_tb);
        }
    }

bad:
    return;
}
#endif

static void __Pyx_RaiseDoubleKeywordsError(
    const char* func_name,
    PyObject* kw_name)
{
    PyErr_Format(PyExc_TypeError,
        #if PY_MAJOR_VERSION >= 3
        "%s() got multiple values for keyword argument '%U'", func_name, kw_name);
        #else
        "%s() got multiple values for keyword argument '%s'", func_name,
        PyString_AS_STRING(kw_name));
        #endif
}

static int __Pyx_ParseOptionalKeywords(
    PyObject *kwds,
    PyObject **argnames[],
    PyObject *kwds2,
    PyObject *values[],
    Py_ssize_t num_pos_args,
    const char* function_name)
{
    PyObject *key = 0, *value = 0;
    Py_ssize_t pos = 0;
    PyObject*** name;
    PyObject*** first_kw_arg = argnames + num_pos_args;

    while (PyDict_Next(kwds, &pos, &key, &value)) {
        name = first_kw_arg;
        while (*name && (**name != key)) name++;
        if (*name) {
            values[name-argnames] = value;
        } else {
            #if PY_MAJOR_VERSION < 3
            if (unlikely(!PyString_CheckExact(key)) && unlikely(!PyString_Check(key))) {
            #else
            if (unlikely(!PyUnicode_CheckExact(key)) && unlikely(!PyUnicode_Check(key))) {
            #endif
                goto invalid_keyword_type;
            } else {
                for (name = first_kw_arg; *name; name++) {
                    #if PY_MAJOR_VERSION >= 3
                    if (PyUnicode_GET_SIZE(**name) == PyUnicode_GET_SIZE(key) &&
                        PyUnicode_Compare(**name, key) == 0) break;
                    #else
                    if (PyString_GET_SIZE(**name) == PyString_GET_SIZE(key) &&
                        _PyString_Eq(**name, key)) break;
                    #endif
                }
                if (*name) {
                    values[name-argnames] = value;
                } else {
                    /* unexpected keyword found */
                    for (name=argnames; name != first_kw_arg; name++) {
                        if (**name == key) goto arg_passed_twice;
                        #if PY_MAJOR_VERSION >= 3
                        if (PyUnicode_GET_SIZE(**name) == PyUnicode_GET_SIZE(key) &&
                            PyUnicode_Compare(**name, key) == 0) goto arg_passed_twice;
                        #else
                        if (PyString_GET_SIZE(**name) == PyString_GET_SIZE(key) &&
                            _PyString_Eq(**name, key)) goto arg_passed_twice;
                        #endif
                    }
                    if (kwds2) {
                        if (unlikely(PyDict_SetItem(kwds2, key, value))) goto bad;
                    } else {
                        goto invalid_keyword;
                    }
                }
            }
        }
    }
    return 0;
arg_passed_twice:
    __Pyx_RaiseDoubleKeywordsError(function_name, **name);
    goto bad;
invalid_keyword_type:
    PyErr_Format(PyExc_TypeError,
        "%s() keywords must be strings", function_name);
    goto bad;
invalid_keyword:
    PyErr_Format(PyExc_TypeError,
    #if PY_MAJOR_VERSION < 3
        "%s() got an unexpected keyword argument '%s'",
        function_name, PyString_AsString(key));
    #else
        "%s() got an unexpected keyword argument '%U'",
        function_name, key);
    #endif
bad:
    return -1;
}

static void __Pyx_RaiseArgtupleInvalid(
    const char* func_name,
    int exact,
    Py_ssize_t num_min,
    Py_ssize_t num_max,
    Py_ssize_t num_found)
{
    Py_ssize_t num_expected;
    const char *number, *more_or_less;

    if (num_found < num_min) {
        num_expected = num_min;
        more_or_less = "at least";
    } else {
        num_expected = num_max;
        more_or_less = "at most";
    }
    if (exact) {
        more_or_less = "exactly";
    }
    number = (num_expected == 1) ? "" : "s";
    PyErr_Format(PyExc_TypeError,
        #if PY_VERSION_HEX < 0x02050000
            "%s() takes %s %d positional argument%s (%d given)",
        #else
            "%s() takes %s %zd positional argument%s (%zd given)",
        #endif
        func_name, more_or_less, num_expected, number, num_found);
}


static CYTHON_INLINE void __Pyx_RaiseNeedMoreValuesError(Py_ssize_t index) {
    PyErr_Format(PyExc_ValueError,
        #if PY_VERSION_HEX < 0x02050000
                 "need more than %d value%s to unpack", (int)index,
        #else
                 "need more than %zd value%s to unpack", index,
        #endif
                 (index == 1) ? "" : "s");
}

static CYTHON_INLINE void __Pyx_RaiseTooManyValuesError(Py_ssize_t expected) {
    PyErr_Format(PyExc_ValueError,
        #if PY_VERSION_HEX < 0x02050000
            "too many values to unpack (expected %d)", (int)expected);
        #else
            "too many values to unpack (expected %zd)", expected);
        #endif
}

static PyObject *__Pyx_UnpackItem(PyObject *iter, Py_ssize_t index) {
    PyObject *item;
    if (!(item = PyIter_Next(iter))) {
        if (!PyErr_Occurred()) {
            __Pyx_RaiseNeedMoreValuesError(index);
        }
    }
    return item;
}

static int __Pyx_EndUnpack(PyObject *iter, Py_ssize_t expected) {
    PyObject *item;
    if ((item = PyIter_Next(iter))) {
        Py_DECREF(item);
        __Pyx_RaiseTooManyValuesError(expected);
        return -1;
    }
    else if (!PyErr_Occurred())
        return 0;
    else
        return -1;
}

static int __Pyx_GetException(PyObject **type, PyObject **value, PyObject **tb) {
    PyObject *local_type, *local_value, *local_tb;
    PyObject *tmp_type, *tmp_value, *tmp_tb;
    PyThreadState *tstate = PyThreadState_GET();
    local_type = tstate->curexc_type;
    local_value = tstate->curexc_value;
    local_tb = tstate->curexc_traceback;
    tstate->curexc_type = 0;
    tstate->curexc_value = 0;
    tstate->curexc_traceback = 0;
    PyErr_NormalizeException(&local_type, &local_value, &local_tb);
    if (unlikely(tstate->curexc_type))
        goto bad;
    #if PY_MAJOR_VERSION >= 3
    if (unlikely(PyException_SetTraceback(local_value, local_tb) < 0))
        goto bad;
    #endif
    *type = local_type;
    *value = local_value;
    *tb = local_tb;
    Py_INCREF(local_type);
    Py_INCREF(local_value);
    Py_INCREF(local_tb);
    tmp_type = tstate->exc_type;
    tmp_value = tstate->exc_value;
    tmp_tb = tstate->exc_traceback;
    tstate->exc_type = local_type;
    tstate->exc_value = local_value;
    tstate->exc_traceback = local_tb;
    /* Make sure tstate is in a consistent state when we XDECREF
       these objects (XDECREF may run arbitrary code). */
    Py_XDECREF(tmp_type);
    Py_XDECREF(tmp_value);
    Py_XDECREF(tmp_tb);
    return 0;
bad:
    *type = 0;
    *value = 0;
    *tb = 0;
    Py_XDECREF(local_type);
    Py_XDECREF(local_value);
    Py_XDECREF(local_tb);
    return -1;
}


static CYTHON_INLINE int __Pyx_CheckKeywordStrings(
    PyObject *kwdict,
    const char* function_name,
    int kw_allowed)
{
    PyObject* key = 0;
    Py_ssize_t pos = 0;
    while (PyDict_Next(kwdict, &pos, &key, 0)) {
        #if PY_MAJOR_VERSION < 3
        if (unlikely(!PyString_CheckExact(key)) && unlikely(!PyString_Check(key)))
        #else
        if (unlikely(!PyUnicode_CheckExact(key)) && unlikely(!PyUnicode_Check(key)))
        #endif
            goto invalid_keyword_type;
    }
    if ((!kw_allowed) && unlikely(key))
        goto invalid_keyword;
    return 1;
invalid_keyword_type:
    PyErr_Format(PyExc_TypeError,
        "%s() keywords must be strings", function_name);
    return 0;
invalid_keyword:
    PyErr_Format(PyExc_TypeError,
    #if PY_MAJOR_VERSION < 3
        "%s() got an unexpected keyword argument '%s'",
        function_name, PyString_AsString(key));
    #else
        "%s() got an unexpected keyword argument '%U'",
        function_name, key);
    #endif
    return 0;
}

static CYTHON_INLINE int __Pyx_TypeTest(PyObject *obj, PyTypeObject *type) {
    if (unlikely(!type)) {
        PyErr_Format(PyExc_SystemError, "Missing type object");
        return 0;
    }
    if (likely(PyObject_TypeCheck(obj, type)))
        return 1;
    PyErr_Format(PyExc_TypeError, "Cannot convert %.200s to %.200s",
                 Py_TYPE(obj)->tp_name, type->tp_name);
    return 0;
}


static CYTHON_INLINE void __Pyx_ExceptionSave(PyObject **type, PyObject **value, PyObject **tb) {
    PyThreadState *tstate = PyThreadState_GET();
    *type = tstate->exc_type;
    *value = tstate->exc_value;
    *tb = tstate->exc_traceback;
    Py_XINCREF(*type);
    Py_XINCREF(*value);
    Py_XINCREF(*tb);
}

static void __Pyx_ExceptionReset(PyObject *type, PyObject *value, PyObject *tb) {
    PyObject *tmp_type, *tmp_value, *tmp_tb;
    PyThreadState *tstate = PyThreadState_GET();
    tmp_type = tstate->exc_type;
    tmp_value = tstate->exc_value;
    tmp_tb = tstate->exc_traceback;
    tstate->exc_type = type;
    tstate->exc_value = value;
    tstate->exc_traceback = tb;
    Py_XDECREF(tmp_type);
    Py_XDECREF(tmp_value);
    Py_XDECREF(tmp_tb);
}

static PyObject *__Pyx_Import(PyObject *name, PyObject *from_list) {
    PyObject *py_import = 0;
    PyObject *empty_list = 0;
    PyObject *module = 0;
    PyObject *global_dict = 0;
    PyObject *empty_dict = 0;
    PyObject *list;
    py_import = __Pyx_GetAttrString(__pyx_b, "__import__");
    if (!py_import)
        goto bad;
    if (from_list)
        list = from_list;
    else {
        empty_list = PyList_New(0);
        if (!empty_list)
            goto bad;
        list = empty_list;
    }
    global_dict = PyModule_GetDict(__pyx_m);
    if (!global_dict)
        goto bad;
    empty_dict = PyDict_New();
    if (!empty_dict)
        goto bad;
    module = PyObject_CallFunctionObjArgs(py_import,
        name, global_dict, empty_dict, list, NULL);
bad:
    Py_XDECREF(empty_list);
    Py_XDECREF(py_import);
    Py_XDECREF(empty_dict);
    return module;
}

static CYTHON_INLINE unsigned char __Pyx_PyInt_AsUnsignedChar(PyObject* x) {
    const unsigned char neg_one = (unsigned char)-1, const_zero = 0;
    const int is_unsigned = neg_one > const_zero;
    if (sizeof(unsigned char) < sizeof(long)) {
        long val = __Pyx_PyInt_AsLong(x);
        if (unlikely(val != (long)(unsigned char)val)) {
            if (!unlikely(val == -1 && PyErr_Occurred())) {
                PyErr_SetString(PyExc_OverflowError,
                    (is_unsigned && unlikely(val < 0)) ?
                    "can't convert negative value to unsigned char" :
                    "value too large to convert to unsigned char");
            }
            return (unsigned char)-1;
        }
        return (unsigned char)val;
    }
    return (unsigned char)__Pyx_PyInt_AsUnsignedLong(x);
}

static CYTHON_INLINE unsigned short __Pyx_PyInt_AsUnsignedShort(PyObject* x) {
    const unsigned short neg_one = (unsigned short)-1, const_zero = 0;
    const int is_unsigned = neg_one > const_zero;
    if (sizeof(unsigned short) < sizeof(long)) {
        long val = __Pyx_PyInt_AsLong(x);
        if (unlikely(val != (long)(unsigned short)val)) {
            if (!unlikely(val == -1 && PyErr_Occurred())) {
                PyErr_SetString(PyExc_OverflowError,
                    (is_unsigned && unlikely(val < 0)) ?
                    "can't convert negative value to unsigned short" :
                    "value too large to convert to unsigned short");
            }
            return (unsigned short)-1;
        }
        return (unsigned short)val;
    }
    return (unsigned short)__Pyx_PyInt_AsUnsignedLong(x);
}

static CYTHON_INLINE unsigned int __Pyx_PyInt_AsUnsignedInt(PyObject* x) {
    const unsigned int neg_one = (unsigned int)-1, const_zero = 0;
    const int is_unsigned = neg_one > const_zero;
    if (sizeof(unsigned int) < sizeof(long)) {
        long val = __Pyx_PyInt_AsLong(x);
        if (unlikely(val != (long)(unsigned int)val)) {
            if (!unlikely(val == -1 && PyErr_Occurred())) {
                PyErr_SetString(PyExc_OverflowError,
                    (is_unsigned && unlikely(val < 0)) ?
                    "can't convert negative value to unsigned int" :
                    "value too large to convert to unsigned int");
            }
            return (unsigned int)-1;
        }
        return (unsigned int)val;
    }
    return (unsigned int)__Pyx_PyInt_AsUnsignedLong(x);
}

static CYTHON_INLINE char __Pyx_PyInt_AsChar(PyObject* x) {
    const char neg_one = (char)-1, const_zero = 0;
    const int is_unsigned = neg_one > const_zero;
    if (sizeof(char) < sizeof(long)) {
        long val = __Pyx_PyInt_AsLong(x);
        if (unlikely(val != (long)(char)val)) {
            if (!unlikely(val == -1 && PyErr_Occurred())) {
                PyErr_SetString(PyExc_OverflowError,
                    (is_unsigned && unlikely(val < 0)) ?
                    "can't convert negative value to char" :
                    "value too large to convert to char");
            }
            return (char)-1;
        }
        return (char)val;
    }
    return (char)__Pyx_PyInt_AsLong(x);
}

static CYTHON_INLINE short __Pyx_PyInt_AsShort(PyObject* x) {
    const short neg_one = (short)-1, const_zero = 0;
    const int is_unsigned = neg_one > const_zero;
    if (sizeof(short) < sizeof(long)) {
        long val = __Pyx_PyInt_AsLong(x);
        if (unlikely(val != (long)(short)val)) {
            if (!unlikely(val == -1 && PyErr_Occurred())) {
                PyErr_SetString(PyExc_OverflowError,
                    (is_unsigned && unlikely(val < 0)) ?
                    "can't convert negative value to short" :
                    "value too large to convert to short");
            }
            return (short)-1;
        }
        return (short)val;
    }
    return (short)__Pyx_PyInt_AsLong(x);
}

static CYTHON_INLINE int __Pyx_PyInt_AsInt(PyObject* x) {
    const int neg_one = (int)-1, const_zero = 0;
    const int is_unsigned = neg_one > const_zero;
    if (sizeof(int) < sizeof(long)) {
        long val = __Pyx_PyInt_AsLong(x);
        if (unlikely(val != (long)(int)val)) {
            if (!unlikely(val == -1 && PyErr_Occurred())) {
                PyErr_SetString(PyExc_OverflowError,
                    (is_unsigned && unlikely(val < 0)) ?
                    "can't convert negative value to int" :
                    "value too large to convert to int");
            }
            return (int)-1;
        }
        return (int)val;
    }
    return (int)__Pyx_PyInt_AsLong(x);
}

static CYTHON_INLINE signed char __Pyx_PyInt_AsSignedChar(PyObject* x) {
    const signed char neg_one = (signed char)-1, const_zero = 0;
    const int is_unsigned = neg_one > const_zero;
    if (sizeof(signed char) < sizeof(long)) {
        long val = __Pyx_PyInt_AsLong(x);
        if (unlikely(val != (long)(signed char)val)) {
            if (!unlikely(val == -1 && PyErr_Occurred())) {
                PyErr_SetString(PyExc_OverflowError,
                    (is_unsigned && unlikely(val < 0)) ?
                    "can't convert negative value to signed char" :
                    "value too large to convert to signed char");
            }
            return (signed char)-1;
        }
        return (signed char)val;
    }
    return (signed char)__Pyx_PyInt_AsSignedLong(x);
}

static CYTHON_INLINE signed short __Pyx_PyInt_AsSignedShort(PyObject* x) {
    const signed short neg_one = (signed short)-1, const_zero = 0;
    const int is_unsigned = neg_one > const_zero;
    if (sizeof(signed short) < sizeof(long)) {
        long val = __Pyx_PyInt_AsLong(x);
        if (unlikely(val != (long)(signed short)val)) {
            if (!unlikely(val == -1 && PyErr_Occurred())) {
                PyErr_SetString(PyExc_OverflowError,
                    (is_unsigned && unlikely(val < 0)) ?
                    "can't convert negative value to signed short" :
                    "value too large to convert to signed short");
            }
            return (signed short)-1;
        }
        return (signed short)val;
    }
    return (signed short)__Pyx_PyInt_AsSignedLong(x);
}

static CYTHON_INLINE signed int __Pyx_PyInt_AsSignedInt(PyObject* x) {
    const signed int neg_one = (signed int)-1, const_zero = 0;
    const int is_unsigned = neg_one > const_zero;
    if (sizeof(signed int) < sizeof(long)) {
        long val = __Pyx_PyInt_AsLong(x);
        if (unlikely(val != (long)(signed int)val)) {
            if (!unlikely(val == -1 && PyErr_Occurred())) {
                PyErr_SetString(PyExc_OverflowError,
                    (is_unsigned && unlikely(val < 0)) ?
                    "can't convert negative value to signed int" :
                    "value too large to convert to signed int");
            }
            return (signed int)-1;
        }
        return (signed int)val;
    }
    return (signed int)__Pyx_PyInt_AsSignedLong(x);
}

static CYTHON_INLINE int __Pyx_PyInt_AsLongDouble(PyObject* x) {
    const int neg_one = (int)-1, const_zero = 0;
    const int is_unsigned = neg_one > const_zero;
    if (sizeof(int) < sizeof(long)) {
        long val = __Pyx_PyInt_AsLong(x);
        if (unlikely(val != (long)(int)val)) {
            if (!unlikely(val == -1 && PyErr_Occurred())) {
                PyErr_SetString(PyExc_OverflowError,
                    (is_unsigned && unlikely(val < 0)) ?
                    "can't convert negative value to int" :
                    "value too large to convert to int");
            }
            return (int)-1;
        }
        return (int)val;
    }
    return (int)__Pyx_PyInt_AsLong(x);
}

static CYTHON_INLINE unsigned long __Pyx_PyInt_AsUnsignedLong(PyObject* x) {
    const unsigned long neg_one = (unsigned long)-1, const_zero = 0;
    const int is_unsigned = neg_one > const_zero;
#if PY_VERSION_HEX < 0x03000000
    if (likely(PyInt_Check(x))) {
        long val = PyInt_AS_LONG(x);
        if (is_unsigned && unlikely(val < 0)) {
            PyErr_SetString(PyExc_OverflowError,
                            "can't convert negative value to unsigned long");
            return (unsigned long)-1;
        }
        return (unsigned long)val;
    } else
#endif
    if (likely(PyLong_Check(x))) {
        if (is_unsigned) {
            if (unlikely(Py_SIZE(x) < 0)) {
                PyErr_SetString(PyExc_OverflowError,
                                "can't convert negative value to unsigned long");
                return (unsigned long)-1;
            }
            return PyLong_AsUnsignedLong(x);
        } else {
            return PyLong_AsLong(x);
        }
    } else {
        unsigned long val;
        PyObject *tmp = __Pyx_PyNumber_Int(x);
        if (!tmp) return (unsigned long)-1;
        val = __Pyx_PyInt_AsUnsignedLong(tmp);
        Py_DECREF(tmp);
        return val;
    }
}

static CYTHON_INLINE unsigned PY_LONG_LONG __Pyx_PyInt_AsUnsignedLongLong(PyObject* x) {
    const unsigned PY_LONG_LONG neg_one = (unsigned PY_LONG_LONG)-1, const_zero = 0;
    const int is_unsigned = neg_one > const_zero;
#if PY_VERSION_HEX < 0x03000000
    if (likely(PyInt_Check(x))) {
        long val = PyInt_AS_LONG(x);
        if (is_unsigned && unlikely(val < 0)) {
            PyErr_SetString(PyExc_OverflowError,
                            "can't convert negative value to unsigned PY_LONG_LONG");
            return (unsigned PY_LONG_LONG)-1;
        }
        return (unsigned PY_LONG_LONG)val;
    } else
#endif
    if (likely(PyLong_Check(x))) {
        if (is_unsigned) {
            if (unlikely(Py_SIZE(x) < 0)) {
                PyErr_SetString(PyExc_OverflowError,
                                "can't convert negative value to unsigned PY_LONG_LONG");
                return (unsigned PY_LONG_LONG)-1;
            }
            return PyLong_AsUnsignedLongLong(x);
        } else {
            return PyLong_AsLongLong(x);
        }
    } else {
        unsigned PY_LONG_LONG val;
        PyObject *tmp = __Pyx_PyNumber_Int(x);
        if (!tmp) return (unsigned PY_LONG_LONG)-1;
        val = __Pyx_PyInt_AsUnsignedLongLong(tmp);
        Py_DECREF(tmp);
        return val;
    }
}

static CYTHON_INLINE long __Pyx_PyInt_AsLong(PyObject* x) {
    const long neg_one = (long)-1, const_zero = 0;
    const int is_unsigned = neg_one > const_zero;
#if PY_VERSION_HEX < 0x03000000
    if (likely(PyInt_Check(x))) {
        long val = PyInt_AS_LONG(x);
        if (is_unsigned && unlikely(val < 0)) {
            PyErr_SetString(PyExc_OverflowError,
                            "can't convert negative value to long");
            return (long)-1;
        }
        return (long)val;
    } else
#endif
    if (likely(PyLong_Check(x))) {
        if (is_unsigned) {
            if (unlikely(Py_SIZE(x) < 0)) {
                PyErr_SetString(PyExc_OverflowError,
                                "can't convert negative value to long");
                return (long)-1;
            }
            return PyLong_AsUnsignedLong(x);
        } else {
            return PyLong_AsLong(x);
        }
    } else {
        long val;
        PyObject *tmp = __Pyx_PyNumber_Int(x);
        if (!tmp) return (long)-1;
        val = __Pyx_PyInt_AsLong(tmp);
        Py_DECREF(tmp);
        return val;
    }
}

static CYTHON_INLINE PY_LONG_LONG __Pyx_PyInt_AsLongLong(PyObject* x) {
    const PY_LONG_LONG neg_one = (PY_LONG_LONG)-1, const_zero = 0;
    const int is_unsigned = neg_one > const_zero;
#if PY_VERSION_HEX < 0x03000000
    if (likely(PyInt_Check(x))) {
        long val = PyInt_AS_LONG(x);
        if (is_unsigned && unlikely(val < 0)) {
            PyErr_SetString(PyExc_OverflowError,
                            "can't convert negative value to PY_LONG_LONG");
            return (PY_LONG_LONG)-1;
        }
        return (PY_LONG_LONG)val;
    } else
#endif
    if (likely(PyLong_Check(x))) {
        if (is_unsigned) {
            if (unlikely(Py_SIZE(x) < 0)) {
                PyErr_SetString(PyExc_OverflowError,
                                "can't convert negative value to PY_LONG_LONG");
                return (PY_LONG_LONG)-1;
            }
            return PyLong_AsUnsignedLongLong(x);
        } else {
            return PyLong_AsLongLong(x);
        }
    } else {
        PY_LONG_LONG val;
        PyObject *tmp = __Pyx_PyNumber_Int(x);
        if (!tmp) return (PY_LONG_LONG)-1;
        val = __Pyx_PyInt_AsLongLong(tmp);
        Py_DECREF(tmp);
        return val;
    }
}

static CYTHON_INLINE signed long __Pyx_PyInt_AsSignedLong(PyObject* x) {
    const signed long neg_one = (signed long)-1, const_zero = 0;
    const int is_unsigned = neg_one > const_zero;
#if PY_VERSION_HEX < 0x03000000
    if (likely(PyInt_Check(x))) {
        long val = PyInt_AS_LONG(x);
        if (is_unsigned && unlikely(val < 0)) {
            PyErr_SetString(PyExc_OverflowError,
                            "can't convert negative value to signed long");
            return (signed long)-1;
        }
        return (signed long)val;
    } else
#endif
    if (likely(PyLong_Check(x))) {
        if (is_unsigned) {
            if (unlikely(Py_SIZE(x) < 0)) {
                PyErr_SetString(PyExc_OverflowError,
                                "can't convert negative value to signed long");
                return (signed long)-1;
            }
            return PyLong_AsUnsignedLong(x);
        } else {
            return PyLong_AsLong(x);
        }
    } else {
        signed long val;
        PyObject *tmp = __Pyx_PyNumber_Int(x);
        if (!tmp) return (signed long)-1;
        val = __Pyx_PyInt_AsSignedLong(tmp);
        Py_DECREF(tmp);
        return val;
    }
}

static CYTHON_INLINE signed PY_LONG_LONG __Pyx_PyInt_AsSignedLongLong(PyObject* x) {
    const signed PY_LONG_LONG neg_one = (signed PY_LONG_LONG)-1, const_zero = 0;
    const int is_unsigned = neg_one > const_zero;
#if PY_VERSION_HEX < 0x03000000
    if (likely(PyInt_Check(x))) {
        long val = PyInt_AS_LONG(x);
        if (is_unsigned && unlikely(val < 0)) {
            PyErr_SetString(PyExc_OverflowError,
                            "can't convert negative value to signed PY_LONG_LONG");
            return (signed PY_LONG_LONG)-1;
        }
        return (signed PY_LONG_LONG)val;
    } else
#endif
    if (likely(PyLong_Check(x))) {
        if (is_unsigned) {
            if (unlikely(Py_SIZE(x) < 0)) {
                PyErr_SetString(PyExc_OverflowError,
                                "can't convert negative value to signed PY_LONG_LONG");
                return (signed PY_LONG_LONG)-1;
            }
            return PyLong_AsUnsignedLongLong(x);
        } else {
            return PyLong_AsLongLong(x);
        }
    } else {
        signed PY_LONG_LONG val;
        PyObject *tmp = __Pyx_PyNumber_Int(x);
        if (!tmp) return (signed PY_LONG_LONG)-1;
        val = __Pyx_PyInt_AsSignedLongLong(tmp);
        Py_DECREF(tmp);
        return val;
    }
}

#ifndef __PYX_HAVE_RT_ImportType
#define __PYX_HAVE_RT_ImportType
static PyTypeObject *__Pyx_ImportType(const char *module_name, const char *class_name,
    long size, int strict)
{
    PyObject *py_module = 0;
    PyObject *result = 0;
    PyObject *py_name = 0;
    char warning[200];

    py_module = __Pyx_ImportModule(module_name);
    if (!py_module)
        goto bad;
    #if PY_MAJOR_VERSION < 3
    py_name = PyString_FromString(class_name);
    #else
    py_name = PyUnicode_FromString(class_name);
    #endif
    if (!py_name)
        goto bad;
    result = PyObject_GetAttr(py_module, py_name);
    Py_DECREF(py_name);
    py_name = 0;
    Py_DECREF(py_module);
    py_module = 0;
    if (!result)
        goto bad;
    if (!PyType_Check(result)) {
        PyErr_Format(PyExc_TypeError,
            "%s.%s is not a type object",
            module_name, class_name);
        goto bad;
    }
    if (!strict && ((PyTypeObject *)result)->tp_basicsize > size) {
        PyOS_snprintf(warning, sizeof(warning),
            "%s.%s size changed, may indicate binary incompatibility",
            module_name, class_name);
        #if PY_VERSION_HEX < 0x02050000
        PyErr_Warn(NULL, warning);
        #else
        PyErr_WarnEx(NULL, warning, 0);
        #endif
    }
    else if (((PyTypeObject *)result)->tp_basicsize != size) {
        PyErr_Format(PyExc_ValueError,
            "%s.%s has the wrong size, try recompiling",
            module_name, class_name);
        goto bad;
    }
    return (PyTypeObject *)result;
bad:
    Py_XDECREF(py_module);
    Py_XDECREF(result);
    return 0;
}
#endif

#ifndef __PYX_HAVE_RT_ImportModule
#define __PYX_HAVE_RT_ImportModule
static PyObject *__Pyx_ImportModule(const char *name) {
    PyObject *py_name = 0;
    PyObject *py_module = 0;

    #if PY_MAJOR_VERSION < 3
    py_name = PyString_FromString(name);
    #else
    py_name = PyUnicode_FromString(name);
    #endif
    if (!py_name)
        goto bad;
    py_module = PyImport_Import(py_name);
    Py_DECREF(py_name);
    return py_module;
bad:
    Py_XDECREF(py_name);
    return 0;
}
#endif

#include "compile.h"
#include "frameobject.h"
#include "traceback.h"

static void __Pyx_AddTraceback(const char *funcname) {
    PyObject *py_srcfile = 0;
    PyObject *py_funcname = 0;
    PyObject *py_globals = 0;
    PyCodeObject *py_code = 0;
    PyFrameObject *py_frame = 0;

    #if PY_MAJOR_VERSION < 3
    py_srcfile = PyString_FromString(__pyx_filename);
    #else
    py_srcfile = PyUnicode_FromString(__pyx_filename);
    #endif
    if (!py_srcfile) goto bad;
    if (__pyx_clineno) {
        #if PY_MAJOR_VERSION < 3
        py_funcname = PyString_FromFormat( "%s (%s:%d)", funcname, __pyx_cfilenm, __pyx_clineno);
        #else
        py_funcname = PyUnicode_FromFormat( "%s (%s:%d)", funcname, __pyx_cfilenm, __pyx_clineno);
        #endif
    }
    else {
        #if PY_MAJOR_VERSION < 3
        py_funcname = PyString_FromString(funcname);
        #else
        py_funcname = PyUnicode_FromString(funcname);
        #endif
    }
    if (!py_funcname) goto bad;
    py_globals = PyModule_GetDict(__pyx_m);
    if (!py_globals) goto bad;
    py_code = PyCode_New(
        0,            /*int argcount,*/
        #if PY_MAJOR_VERSION >= 3
        0,            /*int kwonlyargcount,*/
        #endif
        0,            /*int nlocals,*/
        0,            /*int stacksize,*/
        0,            /*int flags,*/
        __pyx_empty_bytes, /*PyObject *code,*/
        __pyx_empty_tuple,  /*PyObject *consts,*/
        __pyx_empty_tuple,  /*PyObject *names,*/
        __pyx_empty_tuple,  /*PyObject *varnames,*/
        __pyx_empty_tuple,  /*PyObject *freevars,*/
        __pyx_empty_tuple,  /*PyObject *cellvars,*/
        py_srcfile,   /*PyObject *filename,*/
        py_funcname,  /*PyObject *name,*/
        __pyx_lineno,   /*int firstlineno,*/
        __pyx_empty_bytes  /*PyObject *lnotab*/
    );
    if (!py_code) goto bad;
    py_frame = PyFrame_New(
        PyThreadState_GET(), /*PyThreadState *tstate,*/
        py_code,             /*PyCodeObject *code,*/
        py_globals,          /*PyObject *globals,*/
        0                    /*PyObject *locals*/
    );
    if (!py_frame) goto bad;
    py_frame->f_lineno = __pyx_lineno;
    PyTraceBack_Here(py_frame);
bad:
    Py_XDECREF(py_srcfile);
    Py_XDECREF(py_funcname);
    Py_XDECREF(py_code);
    Py_XDECREF(py_frame);
}

static int __Pyx_InitStrings(__Pyx_StringTabEntry *t) {
    while (t->p) {
        #if PY_MAJOR_VERSION < 3
        if (t->is_unicode) {
            *t->p = PyUnicode_DecodeUTF8(t->s, t->n - 1, NULL);
        } else if (t->intern) {
            *t->p = PyString_InternFromString(t->s);
        } else {
            *t->p = PyString_FromStringAndSize(t->s, t->n - 1);
        }
        #else  /* Python 3+ has unicode identifiers */
        if (t->is_unicode | t->is_str) {
            if (t->intern) {
                *t->p = PyUnicode_InternFromString(t->s);
            } else if (t->encoding) {
                *t->p = PyUnicode_Decode(t->s, t->n - 1, t->encoding, NULL);
            } else {
                *t->p = PyUnicode_FromStringAndSize(t->s, t->n - 1);
            }
        } else {
            *t->p = PyBytes_FromStringAndSize(t->s, t->n - 1);
        }
        #endif
        if (!*t->p)
            return -1;
        ++t;
    }
    return 0;
}

/* Type Conversion Functions */

static CYTHON_INLINE int __Pyx_PyObject_IsTrue(PyObject* x) {
   int is_true = x == Py_True;
   if (is_true | (x == Py_False) | (x == Py_None)) return is_true;
   else return PyObject_IsTrue(x);
}

static CYTHON_INLINE PyObject* __Pyx_PyNumber_Int(PyObject* x) {
  PyNumberMethods *m;
  const char *name = NULL;
  PyObject *res = NULL;
#if PY_VERSION_HEX < 0x03000000
  if (PyInt_Check(x) || PyLong_Check(x))
#else
  if (PyLong_Check(x))
#endif
    return Py_INCREF(x), x;
  m = Py_TYPE(x)->tp_as_number;
#if PY_VERSION_HEX < 0x03000000
  if (m && m->nb_int) {
    name = "int";
    res = PyNumber_Int(x);
  }
  else if (m && m->nb_long) {
    name = "long";
    res = PyNumber_Long(x);
  }
#else
  if (m && m->nb_int) {
    name = "int";
    res = PyNumber_Long(x);
  }
#endif
  if (res) {
#if PY_VERSION_HEX < 0x03000000
    if (!PyInt_Check(res) && !PyLong_Check(res)) {
#else
    if (!PyLong_Check(res)) {
#endif
      PyErr_Format(PyExc_TypeError,
                   "__%s__ returned non-%s (type %.200s)",
                   name, name, Py_TYPE(res)->tp_name);
      Py_DECREF(res);
      return NULL;
    }
  }
  else if (!PyErr_Occurred()) {
    PyErr_SetString(PyExc_TypeError,
                    "an integer is required");
  }
  return res;
}

static CYTHON_INLINE Py_ssize_t __Pyx_PyIndex_AsSsize_t(PyObject* b) {
  Py_ssize_t ival;
  PyObject* x = PyNumber_Index(b);
  if (!x) return -1;
  ival = PyInt_AsSsize_t(x);
  Py_DECREF(x);
  return ival;
}

static CYTHON_INLINE PyObject * __Pyx_PyInt_FromSize_t(size_t ival) {
#if PY_VERSION_HEX < 0x02050000
   if (ival <= LONG_MAX)
       return PyInt_FromLong((long)ival);
   else {
       unsigned char *bytes = (unsigned char *) &ival;
       int one = 1; int little = (int)*(unsigned char*)&one;
       return _PyLong_FromByteArray(bytes, sizeof(size_t), little, 0);
   }
#else
   return PyInt_FromSize_t(ival);
#endif
}

static CYTHON_INLINE size_t __Pyx_PyInt_AsSize_t(PyObject* x) {
   unsigned PY_LONG_LONG val = __Pyx_PyInt_AsUnsignedLongLong(x);
   if (unlikely(val == (unsigned PY_LONG_LONG)-1 && PyErr_Occurred())) {
       return (size_t)-1;
   } else if (unlikely(val != (unsigned PY_LONG_LONG)(size_t)val)) {
       PyErr_SetString(PyExc_OverflowError,
                       "value too large to convert to size_t");
       return (size_t)-1;
   }
   return (size_t)val;
}


#endif /* Py_PYTHON_H */
