Пример #1
0
def lower_bound(gamma_1, gamma_2, alphas, Lambda, eta, r, votes, K, n_sens):

    gamma = np.array((gamma_1, gamma_2))
    res = lgamma(np.sum(gamma)) - np.sum(lgamma(gamma))
    res += lgamma(np.sum(alphas)) - np.sum(lgamma(alphas))
    lambda_sum = np.sum(Lambda)
    for k in range(K):
        dig_lambda = digamma(Lambda[k]) - digamma(lambda_sum)
        res += (alphas[k] - 1) * dig_lambda
        res -= (Lambda[k] - 1) * dig_lambda
        for j in range(K):
            eta_sum = np.sum(eta[:, j, k])
            for z in range(2):
                dig_eta = digamma(eta[z, j, k]) - digamma(eta_sum)
                res += (gamma[z] - 1) * dig_eta
                res -= (eta[z, j, k] - 1) * dig_eta
    for i in range(n_sens):
        for k in range(K):
            res += r[i, k] * (digamma(Lambda[k]) - digamma(lambda_sum))
            r_smooth = (r[i, k] + 1e-10) / np.sum(r[i, k] + 1e-10)
            res -= r_smooth * np.log(r_smooth)  #For numerical stability
            eta_sum = eta[0, :, k] + eta[1, :, k]
            res += r[i, k] * np.nansum(
                votes.iloc[i, :] * (digamma(eta[0, :, k]) - digamma(eta_sum)) +
                (1.0 - votes.iloc[i, :]) *
                (digamma(eta[1, :, k]) - digamma(eta_sum)))

    return (res)
Пример #2
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 def expected_utility(self, rewards, i, qs = np.linspace(0,1,1000)):
     log_p_marginal = (lgamma(self.a+i)
                      -lgamma(self.a)
                      +lgamma(self.a+self.m)
                      -lgamma(self.a+self.m+i))
     #integral = np.sum(self.q_pdf(qs)*qs**i)
     #for q in qs:
     #    integral+= self.q_pdf(q)*q**i
     exp_u = np.exp(log_p_marginal)*self.utility(rewards[i])
     return(exp_u)
Пример #3
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def dmvt(X,center,sigma,df,output,workarray,return_log=False):
  if df==None or df<=0:#no DF so we return a mvn density
    return dmvnorm(X,center,sigma,output,workarray,return_log=False)
  residuals = workarray[:,:2]
  residuals[:] = X[:]
  residuals -= center
  m = sigma.shape[0]
  icov = la.inv(sigma)
  logdet =np.log(la.det(sigma))
  distval = (np.dot(residuals,icov)*residuals).sum(1)
  output[:] = lgamma((m + df)/2.) - (lgamma(df/2.) + 0.5 * (logdet + m*np.log(pi * df))) - 0.5 * (df + m) * np.log(1 + distval/df)
  if not return_log: output[:] = np.exp(output)
Пример #4
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def objective_z(z, *args):

    x = args[1]
    mu_b = args[2]
    prec = args[3]
    alpha = np.exp(z)
    A = z - mu_b
    A = np.matrix(A)
    re = -np.sum(lgamma(alpha + x) - lgamma(alpha)) + (
        lgamma(np.sum(alpha + x)) - lgamma(np.sum(alpha))) + np.matmul(
            np.matmul(A, prec), A.T)
    return (float(re))
Пример #5
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def LLH_poisson(x, mu, deltamu=1e-1, vectorCalc=True):
    from scipy.special import loggamma as lgamma
    llh = 0
    if vectorCalc:
        mask_mu = mu != 0
        llh += np.sum(x[mask_mu]*np.log(mu[mask_mu]) - mu[mask_mu] - lgamma(x[mask_mu] + 1))
        llh += np.sum(x[~mask_mu] * np.log(deltamu) - mu[~mask_mu] - lgamma(x[~mask_mu] + 1))
    else:
        for i in range(len(x)):
            if mu[i] > 0:
                llh += x[i] * np.log(mu[i]) - mu[i] - lgamma(x[i] + 1)
            else:
                llh += x[i] * np.log(deltamu) - mu[i] - lgamma(x[i] + 1)
    return -llh
Пример #6
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def _log_kernel_norm(h, d, kernel):
    """Given a KernelType enumeration, compute the kernel normalization.

    h is the bandwidth, d is the dimension.
    """
#     cdef DTYPE_t tmp, factor = 0
#     cdef ITYPE_t k
    tmp = 0
    factor = 0
    k = 0
    if kernel == GAUSSIAN_KERNEL:
        factor = 0.5 * d * LOG_2PI
    elif kernel == TOPHAT_KERNEL:
        factor = logVn(d)
    elif kernel == EPANECHNIKOV_KERNEL:
        factor = logVn(d) + log(2. / (d + 2.))
    elif kernel == EXPONENTIAL_KERNEL:
        factor = logSn(d - 1) + lgamma(d)
    elif kernel == LINEAR_KERNEL:
        factor = logVn(d) - log(d + 1.)
    elif kernel == COSINE_KERNEL:
        # this is derived from a chain rule integration
        factor = 0
        tmp = 2. / PI
        for k in range(1, d + 1, 2):
            factor += tmp
            tmp *= -(d - k) * (d - k - 1) * (2. / PI) ** 2
        factor = log(factor) + logSn(d - 1)
    else:
        raise ValueError("Kernel code not recognized")
    return -factor - d * log(h)
Пример #7
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def LLH_dima(x, mu, os, deltamu=1e-1, nohit_penalty=False, vectorCalc=True) :
    from scipy.special import loggamma as lgamma
    x = x.copy()
    mu = mu.copy()
    '''
    Calculate dima LLH
    '''
    llh = 0
    if vectorCalc:
        mu_dima = (os*mu+x)/(os+1)
        mask_mu = mu != 0
        mask_x = x != 0
        llh += np.sum(os*mu[mask_mu]*np.log(mu_dima[mask_mu]/mu[mask_mu]))
        llh += np.sum(x[mask_x]*np.log(mu_dima[mask_x]/x[mask_x]))
        if nohit_penalty:
            # print "lel: ", np.sum(x[~mask_mu] * np.log(deltamu) - mu[~mask_mu] - lgamma(x[~mask_mu] + 1))
            llh += np.sum(x[~mask_mu] * np.log(deltamu) - mu[~mask_mu] - lgamma(x[~mask_mu] + 1))
    else:
        for i in range(len(x)):
            mu_dima = (os*mu[i]+x[i])/(os+1)
            if mu[i] != 0:
                llh += os*mu[i]*np.log(mu_dima/mu[i])

            if x[i] != 0:
                llh += x[i]*np.log(mu_dima/x[i])

    return -llh
Пример #8
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    def _ll_br(self, y, X, Z, params):
        nz = self.Z.shape[1]

        Xparams = params[:-nz]
        Zparams = params[-nz:]

        mu = self.link.inverse(np.dot(X, Xparams))
        phi = self.link_phi.inverse(np.dot(Z, Zparams))
        # TODO: derive a and b and constrain to > 0?

        if np.any(phi <= np.finfo(float).eps): return np.array(-np.inf)

        ll = lgamma(phi) - lgamma(mu * phi) - lgamma((1 - mu) * phi) \
                + (mu * phi - 1) * np.log(y) + (((1 - mu) * phi) - 1) \
                * np.log(1 - y)

        return ll
Пример #9
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    def _ll_br(self, y, X, Z, params):
        nz = self.Z.shape[1]

        Xparams = params[:-nz]
        Zparams = params[-nz:]

        mu = self.link.inverse(np.dot(X, Xparams))
        phi = self.link_phi.inverse(np.dot(Z, Zparams))
        # TODO: derive a and b and constrain to > 0?

        if np.any(phi <= np.finfo(float).eps): return np.array(-np.inf)

        ll = lgamma(phi) - lgamma(mu * phi) - lgamma((1 - mu) * phi) \
             + (mu * phi - 1) * np.log(y) + (((1 - mu) * phi) - 1) \
             * np.log(1 - y)

        return ll
Пример #10
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    def lhood1(self, seg, LOG=True):
        """
        Calculate the likelihood (defaults to log-lhood) for a single observation,
        which is either numeric or an ndarray.

        For likelihood of a group of observations, use .lhood().
        """
        nu = self._nu_n()
        mu = self._mu_n()
        s_nu = self._s_n()
        #print nu, mu, s_nu
        #print n, nu, mu, s_nu, lgamma, pi, log
        L = lgamma((nu+1)/2) - lgamma(nu/2) - 0.5*log(pi*s_nu) - 0.5*log((nu+1)/nu)
        L -= (nu+1)*0.5 * log(1 + (seg-mu)**2 * nu/(1+nu) / s_nu)
        if not LOG:
            return exp(L)
        else:
            return L
Пример #11
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 def lhood(self, seg, LOG=True):
     """
     Calcunlate the likelihood (defaults to log) of a given segment, which should
     be a RunningVar instance.
     """
     if not isinstance(seg, RunningVar):
         raise TypeError('seg must be a RunningVar instance (not %s)' % seg.__class__)
     n = seg.n
     nu = self._nu_n()
     mu = self._mu_n()
     s_nu = self._s_n()
     #print n, nu, mu, s_nu
     #print n, nu, mu, s_nu, lgamma, pi, log
     L = lgamma((nu+n)/2) - lgamma(nu/2) - n*0.5*log(pi*s_nu) - 0.5*log((nu+n)/nu)
     L -= (nu+n)*0.5 * log(1 + (seg.n*seg.s + (seg.m-mu)**2 * (n*nu)/(n+nu)) / s_nu)
     if not LOG:
         return exp(L)
     else:
         return L
Пример #12
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    def _llobs(self, endog, exog, exog_precision, params):
        """
        Loglikelihood for observations with data arguments.

        Parameters
        ----------
        endog : ndarray
            1d array of endogenous variable.
        exog : ndarray
            2d array of explanatory variables.
        exog_precision : ndarray
            2d array of explanatory variables for precision.
        params : ndarray
            The parameters of the model, coefficients for linear predictors
            of the mean and of the precision function.

        Returns
        -------
        loglike : ndarray
            The log likelihood for each observation of the model evaluated
            at `params`.
        """
        y, X, Z = endog, exog, exog_precision
        nz = Z.shape[1]

        params_mean = params[:-nz]
        params_prec = params[-nz:]
        linpred = np.dot(X, params_mean)
        linpred_prec = np.dot(Z, params_prec)

        mu = self.link.inverse(linpred)
        phi = self.link_precision.inverse(linpred_prec)

        eps_lb = 1e-200
        alpha = np.clip(mu * phi, eps_lb, np.inf)
        beta = np.clip((1 - mu) * phi, eps_lb, np.inf)

        ll = (lgamma(phi) - lgamma(alpha) - lgamma(beta) +
              (mu * phi - 1) * np.log(y) +
              (((1 - mu) * phi) - 1) * np.log(1 - y))

        return ll
Пример #13
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    def calc(self, dist1, dist2):
        """Calculate the test statistic between two input distributions

        Parameters
        ----------
        dist1 : array_like
            Input distribution.
        dist2 : array_like
            Input distribution.

        Returns
        -------
        stat : float
            Test statistic
        """
        dist1, dist2 = self.get_array_range(dist1, dist2)
        self.check_lengths(dist1, dist2)
        lnB = 0
        n1 = np.sum(dist1)
        n2 = np.sum(dist2)
        nFactor = lgamma(n1 + n2 + 2) - lgamma(n1 + 1) - lgamma(n2 + 1)

        lnB += nFactor
        for i in range(0, len(dist1)):
            lnB += lgamma(dist1[i] + 1) + lgamma(dist2[i] +
                                                 1) - lgamma(dist1[i] +
                                                             dist2[i] + 2)

        self.SetStat(lnB)
        self.stat = lnB

        return lnB
Пример #14
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    def __init__(self, *, data, maxid):

        self.maxid = maxid

        n = data.n
        N = data.N
        data = data.data
        mu0 = np.zeros(n)

        # Scoring parameters.
        am = 1
        aw = n + am + 1
        T0scale = am * (aw - n - 1) / (am + 1)
        T0 = T0scale * np.eye(n)
        TN = T0 + (N - 1) * np.cov(data.T) + ((am * N) / (am + N)) * np.outer(
            (mu0 - np.mean(data, axis=0)), (mu0 - np.mean(data, axis=0)))
        awpN = aw + N
        constscorefact = -(N / 2) * np.log(np.pi) + 0.5 * np.log(am / (am + N))
        scoreconstvec = np.zeros(n)
        for i in range(n):
            awp = aw - n + i + 1
            scoreconstvec[i] = constscorefact - lgamma(awp / 2) + lgamma(
                (awp + N) / 2) + (awp + i) / 2 * np.log(T0scale)

        # Just to keep the above calculations cleaner
        self.data = data
        self.n = n
        self.N = N
        self.mu0 = mu0
        self.am = am
        self.aw = aw
        self.T0scale = T0scale
        self.T0 = T0
        self.TN = TN
        self.awpN = awpN
        self.constscorefact = constscorefact
        self.scoreconstvec = scoreconstvec

        self._cache = {frozenset(): 0}
Пример #15
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    def TSCalc(self, N1, N2):
        N1, N2 = self.GetArrayRange(N1, N2)
        self.TestLengths(N1, N2)
        lnB = 0
        n1 = np.sum(N1)
        n2 = np.sum(N2)
        try:
            from scipy.special import gammaln as lgamma
        except e:
            print e
            raise ImportError

        nFactor = lgamma(n1 + n2 + 2) - lgamma(n1 + 1) - lgamma(n2 + 1)

        lnB += nFactor
        for i in xrange(0, len(N1)):
            lnB += lgamma(N1[i] + 1) + lgamma(N2[i] + 1) - lgamma(N1[i] +
                                                                  N2[i] + 2)

        self.SetStat(lnB)
Пример #16
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def lbetabinom(x, m, k, n, a, b):

    logpost = lgamma(m+1) + lgamma(a+b+n) + lgamma(a+k+x) + lgamma(b+n-k+m-x) - \
     lgamma(x+1) - lgamma(m-x+1) - lgamma(a+k) - lgamma(b+n-k) - lgamma(a+b+n+m)

    return logpost
Пример #17
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from pylab import *
from scipy.special import loggamma as lgamma

figure('poissoniana', figsize=[ 4.51,  2.7 ]).set_tight_layout(True)
clf()

poisson = lambda k, mu: exp(k * log(mu) - lgamma(k + 1) - mu)

n = 10

ks = arange(n + 1)

bar(ks, poisson(ks, 2), label="$\\mu=2$", width=.8, color='gray')
bar(ks, poisson(ks, 5), label="$\\mu=5$", width=.5, color='lightgray')
	
xlabel('$k$')
ylabel('$P(k;\mu)$')

legend(loc=0)

savefig('poisson.pdf')
Пример #18
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def logVn(n):
    """V_n = pi^(n/2) / gamma(n/2 - 1)"""
    return 0.5 * n * LOG_PI - lgamma(0.5 * n + 1)
Пример #19
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from pylab import *
from scipy.special import loggamma as lgamma

figure('binomiale', figsize=[4.51, 2.7]).set_tight_layout(True)
clf()

binom = lambda k, n, p: exp(lgamma(1 + n) - lgamma(1 + k) - lgamma(1 + n - k)
                            ) * p**k * (1 - p)**(n - k)

n = 5

ks = arange(n + 1)

bar(ks, binom(ks, n, 0.5), label="$p=%.1f$" % 0.5, width=.8, color='gray')
bar(ks, binom(ks, n, 0.8), label="$p=%.1f$" % 0.8, width=.5, color='lightgray')

xlabel('$k$')
ylabel('$P(k;n,p)$')

legend(loc=0)

savefig('binomiale.pdf')
Пример #20
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 def fact(x): return lgamma(x+1)
 
 n = n11+n12+n22
Пример #21
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def dt(x,mu,sd,df,log=False):
  c1 = lgamma((df+1)/2) - lgamma(df/2) + 0.5*np.log(1/(np.pi*df*sd))
  logret = c1 - (df+1)*0.5*np.log(1+np.power(x-mu,2)/(sd*df))
  if log: return logret
  else: return np.exp(logret)
Пример #22
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def ddirichlet (x,p,return_log=False):
    ans = lgamma(p.sum())-lgamma(p).sum() + ((p-1)*np.log(x)).sum()
    if not return_log: return np.exp(ans)
    else: return ans
Пример #23
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def diwishart (X,v,S,return_log=False):
    is_square(X)
    k = X.ndim
    if not return_log: 
        return np.exp(-0.5*(S*la.inv(X)).trace()) * pow(la.det(X),(-(v+k+1)/2.0)) * pow(la.det(S),(v/2.0)) / ( pow(2,(v*k/2.0)) * pow(pi,(k*(k-1)/4.0))* gamma((v+1-np.array(range(1,k)))/2.0).prod())
    else:
        return -0.5*(S*la.inv(X)).trace() + np.log(la.det(X))*(-(v+k+1)/2.) +np.log(la.det(S))*(v/2.0) - np.log(2)*(v*k/2.0) -np.log(pi)*(k*(k-1)/4.0) - lgamma((v+1-np.array(range(1,k)))/2.0).sum()
Пример #24
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def fisher_exact(table,
                 alternative="two-sided",
                 hybrid=False,
                 midP=False,
                 simulate_pval=False,
                 replicate=2000,
                 workspace=300,
                 attempt=2,
                 seed=None):
    """Performs a Fisher exact test on a 2x2 contingency table.
    Parameters
    ----------
    table : array_like of ints
        A 2x2 contingency table.  Elements should be non-negative integers.
    alternative : {'two-sided', 'less', 'greater'}, optional
        Which alternative hypothesis to the null hypothesis the test uses.
        Default is 'two-sided'.  Only used in the 2 x 2 case (with the scipy
        function). In every other case, the two-sided pval is returned.
    mult : int
        Specify the size of the workspace used in the network algorithm.
        Only used for non-simulated p-values larger than 2 x 2 table.
        You might want to increase this if the p-value failed!
    hybrid : bool
        Only used for larger than 2 x 2 tables, in which cases it indicates 
        whether the exact probabilities (default) or a hybrid approximation 
        thereof should be computed.
    midP : bool
        Use this to enable mid-P correction. Could lead to slow computation.
        This is not applicable for simulation p-values. `alternative` cannot 
        be used if you enable midpoint correction.
    simulate_pval : bool 
        Indicate whether to compute p-values by Monte Carlo simulation,
         in larger than 2 x 2 tables.
    replicate : int
        An integer specifying the number of replicates used in the MonteCarlo
        test.
    workspace : int
        An integer specifying the workspace size. Default value is 300. 
    attempt : int
        Number of attempts to try, if the workspace size is not enough. 
        On each attempt, the workspace size is doubled. 
    seed : int
        Random number to use as seed. If a seed isn't provided. 4 bytes will be
        read from os.urandom. If this fail, getrandbits of the random module 
        (with 32 random bits) will be used. In the particular case where both
        failed, the current time will be used

    Returns
    -------
    p_value : float
        The probability of a more extreme table, where 'extreme' is in a 
        probabilistic sense.

    Notes
    -----
    The calculated odds ratio is different from the one R uses. This scipy
    implementation returns the (more common) "unconditional Maximum
    Likelihood Estimate", while R uses the "conditional Maximum Likelihood
    Estimate".
    For tables with large numbers, the (inexact) chi-square test implemented
    in the function `chi2_contingency` can also be used.
    Examples
    --------
    Say we spend a few days counting whales and sharks in the Atlantic and
    Indian oceans. In the Atlantic ocean we find 8 whales and 1 shark, in the
    Indian ocean 2 whales, 5 sharks and in the Pacific 12 whales and 2 sharks.
    Then our contingency table is::
                Atlantic  Indian    Pacific
        whales     8        2       12
        sharks     1        5       2
    We use this table to find the p-value:
    >>> from Fisher import fisher_exact
    >>> pvalue = fisher_exact([[8, 2, 12], [1, 5, 2]])
    >>> pvalue
    0.01183...
    """

    workspace = 2 * int(workspace / 2)
    # int32 is not enough for the algorithm
    c = np.asarray(table, dtype=np.int64)

    if len(c.shape) > 2:
        raise ValueError(
            "The input `table` should not have more than 2 dimension.")

    if np.any(np.asarray(c.shape) < 2):
        raise ValueError("The input `table` must be at least of shape (2, 2).")

    # We expect all values to be non-negative
    if np.any(c < 0):
        raise ValueError("All values in `table` must be nonnegative.")

    nr, nc = c.shape

    if (nr == 2 and nc == 2):
        # I'm not sure what the fisher_exact module of ss do.
        # So use my own function if midp is asked
        if not midP:
            # in this case, just use the default scipy
            # could remove this in the future
            return ss.fisher_exact(c, alternative)[1]
        else:
            return _midp(c)

    else:
        pval = None
        if simulate_pval:
            sr = c.sum(axis=1)
            sc = c.sum(axis=0)
            # The zero colums and rows are droped here, see R function
            c = c[sr > 0, :][:, sc > 0]
            nr, nc = c.shape
            if nr < 2 or nc < 2:
                raise ValueError(
                    'Less than 2 non-zero column or row marginal,\n %s' % c)

            statistic = -np.sum(lgamma(c + 1))
            tmp_res = _fisher_sim(c, replicate, seed)
            almost = 1 + 64 * np.finfo(np.double).eps
            pval = (1 + np.sum(tmp_res <= statistic / almost)) / \
                (replicate + 1.)
        elif hybrid:
            expect, percnt, emin = 5, 80, 1  # this is the cochran condition
            pval = _execute_fexact(nr, nc, c, nr, expect, percnt, emin,
                                   workspace, attempt, midP)
        else:
            expect, percnt, emin = -1, 100, 0
            pval = _execute_fexact(nr, nc, c, nr, expect, percnt, emin,
                                   workspace, attempt, midP)

        return pval
Пример #25
0
def fisher_exact(table, alternative="two-sided", hybrid=False, midP=False,
                 simulate_pval=False, replicate=2000, workspace=300,
                 attempt=2, seed=None):
    """Performs a Fisher exact test on a 2x2 contingency table.
    Parameters
    ----------
    table : array_like of ints
        A 2x2 contingency table.  Elements should be non-negative integers.
    alternative : {'two-sided', 'less', 'greater'}, optional
        Which alternative hypothesis to the null hypothesis the test uses.
        Default is 'two-sided'.  Only used in the 2 x 2 case (with the scipy
        function). In every other case, the two-sided pval is returned.
    mult : int
        Specify the size of the workspace used in the network algorithm.
        Only used for non-simulated p-values larger than 2 x 2 table.
        You might want to increase this if the p-value failed!
    hybrid : bool
        Only used for larger than 2 x 2 tables, in which cases it indicates
        whether the exact probabilities (default) or a hybrid approximation
        thereof should be computed.
    midP : bool
        Use this to enable mid-P correction. Could lead to slow computation.
        This is not applicable for simulation p-values. `alternative` cannot
        be used if you enable midpoint correction.
    simulate_pval : bool
        Indicate whether to compute p-values by Monte Carlo simulation,
         in larger than 2 x 2 tables.
    replicate : int
        An integer specifying the number of replicates used in the MonteCarlo
        test.
    workspace : int
        An integer specifying the workspace size. Default value is 300.
    attempt : int
        Number of attempts to try, if the workspace size is not enough.
        On each attempt, the workspace size is doubled.
    seed : int
        Random number to use as seed. If a seed isn't provided. 4 bytes will be
        read from os.urandom. If this fail, getrandbits of the random module
        (with 32 random bits) will be used. In the particular case where both
        failed, the current time will be used

    Returns
    -------
    p_value : float
        The probability of a more extreme table, where 'extreme' is in a
        probabilistic sense.

    Notes
    -----
    The calculated odds ratio is different from the one R uses. This scipy
    implementation returns the (more common) "unconditional Maximum
    Likelihood Estimate", while R uses the "conditional Maximum Likelihood
    Estimate".
    For tables with large numbers, the (inexact) chi-square test implemented
    in the function `chi2_contingency` can also be used.
    Examples
    --------
    Say we spend a few days counting whales and sharks in the Atlantic and
    Indian oceans. In the Atlantic ocean we find 8 whales and 1 shark, in the
    Indian ocean 2 whales, 5 sharks and in the Pacific 12 whales and 2 sharks.
    Then our contingency table is::
                Atlantic  Indian    Pacific
        whales     8        2       12
        sharks     1        5       2
    We use this table to find the p-value:
    >>> from Fisher import fisher_exact
    >>> pvalue = fisher_exact([[8, 2, 12], [1, 5, 2]])
    >>> pvalue
    0.01183...
    """

    workspace = 2 * int(workspace / 2)
    # int32 is not enough for the algorithm
    c = np.asarray(table, dtype=np.int64)

    if len(c.shape) > 2:
        raise ValueError(
            "The input `table` should not have more than 2 dimension.")

    if np.any(np.asarray(c.shape) < 2):
        raise ValueError("The input `table` must be at least of shape (2, 2).")

    # We expect all values to be non-negative
    if np.any(c < 0):
        raise ValueError("All values in `table` must be nonnegative.")

    nr, nc = c.shape

    if (nr == 2 and nc == 2):
        # I'm not sure what the fisher_exact module of ss do.
        # So use my own function if midp is asked
        if not midP:
            # in this case, just use the default scipy
            # could remove this in the future
            return ss.fisher_exact(c, alternative)[1]
        else:
            return _midp(c)

    else:
        pval = None
        if simulate_pval:
            sr = c.sum(axis=1)
            sc = c.sum(axis=0)
            # The zero colums and rows are droped here, see R function
            c = c[sr > 0, :][:, sc > 0]
            nr, nc = c.shape
            if nr < 2 or nc < 2:
                raise ValueError(
                    'Less than 2 non-zero column or row marginal,\n %s' % c)

            statistic = -np.sum(lgamma(c + 1))
            tmp_res = _fisher_sim(c, replicate, seed)
            almost = 1 + 64 * np.finfo(np.double).eps
            pval = (1 + np.sum(tmp_res <= statistic / almost)) / \
                (replicate + 1.)
        elif hybrid:
            expect, percnt, emin = 5, 80, 1  # this is the cochran condition
            pval = _execute_fexact(nr, nc, c, nr, expect,
                                   percnt, emin, workspace, attempt, midP)
        else:
            expect, percnt, emin = -1, 100, 0
            pval = _execute_fexact(nr, nc, c, nr, expect,
                                   percnt, emin, workspace, attempt, midP)

        return pval