python类gamma()的实例源码

def setUp(self):
        '''
        Saves the current random state for later recovery, sets the random seed
        to get reproducible results and manually constructs a mixed vine.
        '''
        # Save random state for later recovery
        self.random_state = np.random.get_state()
        # Set fixed random seed
        np.random.seed(0)
        # Manually construct mixed vine
        self.dim = 3  # Dimension
        self.vine = MixedVine(self.dim)
        # Specify marginals
        self.vine.set_marginal(0, norm(0, 1))
        self.vine.set_marginal(1, poisson(5))
        self.vine.set_marginal(2, gamma(2, 0, 4))
        # Specify pair copulas
        self.vine.set_copula(1, 0, GaussianCopula(0.5))
        self.vine.set_copula(1, 1, FrankCopula(4))
        self.vine.set_copula(2, 0, ClaytonCopula(5))

def __init__(self, kernel='rbf', degree=3, gamma='auto', coef0=0.0,
                 tol=1e-3, C=1.0, epsilon=0.1, shrinking=True,
                 cache_size=200, verbose=False, max_iter=-1,
                 target_transform='identity', ml_score=False):
        super(TransformedSVR, self).__init__(
            kernel=kernel,
            degree=degree,
            gamma=gamma,
            coef0=coef0,
            tol=tol,
            C=C,
            epsilon=epsilon,
            verbose=verbose,
            shrinking=shrinking,
            cache_size=cache_size,
            max_iter=max_iter)

        # used in training
        if isinstance(target_transform, str):
            target_transform = transforms.transforms[target_transform]()

        self.target_transform = target_transform
        self.ml_score = ml_score

def poisson_dist(bin_values, K):
    """
    Poisson Distribution
    Parameters
    ---------
    K : int
        average counts of photons
    bin_values : array
        scattering bin values
    Returns
    -------
    poisson_dist : array
       Poisson Distribution
    Notes
    -----
    These implementations are based on the references under
    nbinom_distribution() function Notes
    :math ::
        P(K) = \frac{<K>^K}{K!}\exp(-<K>)
    """
    #poisson_dist = stats.poisson.pmf(K, bin_values)
    K = float(K)
    poisson_dist = np.exp(-K) * np.power(K, bin_values)/gamma(bin_values + 1)
    return poisson_dist

def poisson_dist(bin_values, K):
    """
    Poisson Distribution
    Parameters
    ---------
    K : int
        average counts of photons
    bin_values : array
        scattering bin values
    Returns
    -------
    poisson_dist : array
       Poisson Distribution
    Notes
    -----
    These implementations are based on the references under
    nbinom_distribution() function Notes
    :math ::
        P(K) = \frac{<K>^K}{K!}\exp(-<K>)
    """
    #poisson_dist = stats.poisson.pmf(K, bin_values)
    K = float(K)
    poisson_dist = np.exp(-K) * np.power(K, bin_values)/gamma(bin_values + 1)
    return poisson_dist

def gen(self, N, trials, normal_p_range, anomaly_p_range, anomaly_scale = 1.0):
    self.N = N
    self.trials = trials

    self.gens = [
      ?ompound_distribution(
        stats.uniform(loc=normal_p_range[0], scale=normal_p_range[1] - normal_p_range[0]),
        lambda a: stats.gamma(a = a, scale = 1.0)
      ),

      ?ompound_distribution(
        stats.uniform(loc=anomaly_p_range[0], scale=anomaly_p_range[1] - anomaly_p_range[0]),
        lambda a: stats.gamma(a = a, scale = anomaly_scale)
      )
    ]

    self.priors = np.array([0.9, 0.1])

    self.cats, self.params, self.X = compound_rvs(self.gens, self.priors, self.N, self.trials)

def testGammaLogPDF(self):
    with self.test_session():
      batch_size = 6
      alpha = constant_op.constant([2.0] * batch_size)
      beta = constant_op.constant([3.0] * batch_size)
      alpha_v = 2.0
      beta_v = 3.0
      x = np.array([2.5, 2.5, 4.0, 0.1, 1.0, 2.0], dtype=np.float32)
      gamma = gamma_lib.Gamma(alpha=alpha, beta=beta)
      expected_log_pdf = stats.gamma.logpdf(x, alpha_v, scale=1 / beta_v)
      log_pdf = gamma.log_prob(x)
      self.assertEqual(log_pdf.get_shape(), (6,))
      self.assertAllClose(log_pdf.eval(), expected_log_pdf)

      pdf = gamma.prob(x)
      self.assertEqual(pdf.get_shape(), (6,))
      self.assertAllClose(pdf.eval(), np.exp(expected_log_pdf))

def testGammaLogPDFMultidimensional(self):
    with self.test_session():
      batch_size = 6
      alpha = constant_op.constant([[2.0, 4.0]] * batch_size)
      beta = constant_op.constant([[3.0, 4.0]] * batch_size)
      alpha_v = np.array([2.0, 4.0])
      beta_v = np.array([3.0, 4.0])
      x = np.array([[2.5, 2.5, 4.0, 0.1, 1.0, 2.0]], dtype=np.float32).T
      gamma = gamma_lib.Gamma(alpha=alpha, beta=beta)
      expected_log_pdf = stats.gamma.logpdf(x, alpha_v, scale=1 / beta_v)
      log_pdf = gamma.log_prob(x)
      log_pdf_values = log_pdf.eval()
      self.assertEqual(log_pdf.get_shape(), (6, 2))
      self.assertAllClose(log_pdf_values, expected_log_pdf)

      pdf = gamma.prob(x)
      pdf_values = pdf.eval()
      self.assertEqual(pdf.get_shape(), (6, 2))
      self.assertAllClose(pdf_values, np.exp(expected_log_pdf))

def testGammaLogPDFMultidimensionalBroadcasting(self):
    with self.test_session():
      batch_size = 6
      alpha = constant_op.constant([[2.0, 4.0]] * batch_size)
      beta = constant_op.constant(3.0)
      alpha_v = np.array([2.0, 4.0])
      beta_v = 3.0
      x = np.array([[2.5, 2.5, 4.0, 0.1, 1.0, 2.0]], dtype=np.float32).T
      gamma = gamma_lib.Gamma(alpha=alpha, beta=beta)
      expected_log_pdf = stats.gamma.logpdf(x, alpha_v, scale=1 / beta_v)
      log_pdf = gamma.log_prob(x)
      log_pdf_values = log_pdf.eval()
      self.assertEqual(log_pdf.get_shape(), (6, 2))
      self.assertAllClose(log_pdf_values, expected_log_pdf)

      pdf = gamma.prob(x)
      pdf_values = pdf.eval()
      self.assertEqual(pdf.get_shape(), (6, 2))
      self.assertAllClose(pdf_values, np.exp(expected_log_pdf))

def testGammaSampleSmallAlpha(self):
    with session.Session():
      alpha_v = 0.05
      beta_v = 1.0
      alpha = constant_op.constant(alpha_v)
      beta = constant_op.constant(beta_v)
      n = 100000
      gamma = gamma_lib.Gamma(alpha=alpha, beta=beta)
      samples = gamma.sample(n, seed=137)
      sample_values = samples.eval()
      self.assertEqual(samples.get_shape(), (n,))
      self.assertEqual(sample_values.shape, (n,))
      self.assertAllClose(
          sample_values.mean(),
          stats.gamma.mean(
              alpha_v, scale=1 / beta_v),
          atol=.01)
      self.assertAllClose(
          sample_values.var(),
          stats.gamma.var(alpha_v, scale=1 / beta_v),
          atol=.15)
      self.assertTrue(self._kstest(alpha_v, beta_v, sample_values))

def testGammaSample(self):
    with session.Session():
      alpha_v = 4.0
      beta_v = 3.0
      alpha = constant_op.constant(alpha_v)
      beta = constant_op.constant(beta_v)
      n = 100000
      gamma = gamma_lib.Gamma(alpha=alpha, beta=beta)
      samples = gamma.sample(n, seed=137)
      sample_values = samples.eval()
      self.assertEqual(samples.get_shape(), (n,))
      self.assertEqual(sample_values.shape, (n,))
      self.assertAllClose(
          sample_values.mean(),
          stats.gamma.mean(
              alpha_v, scale=1 / beta_v),
          atol=.01)
      self.assertAllClose(
          sample_values.var(),
          stats.gamma.var(alpha_v, scale=1 / beta_v),
          atol=.15)
      self.assertTrue(self._kstest(alpha_v, beta_v, sample_values))

def testGammaPdfOfSampleMultiDims(self):
    with session.Session() as sess:
      gamma = gamma_lib.Gamma(alpha=[7., 11.], beta=[[5.], [6.]])
      num = 50000
      samples = gamma.sample(num, seed=137)
      pdfs = gamma.prob(samples)
      sample_vals, pdf_vals = sess.run([samples, pdfs])
      self.assertEqual(samples.get_shape(), (num, 2, 2))
      self.assertEqual(pdfs.get_shape(), (num, 2, 2))
      self.assertAllClose(
          stats.gamma.mean(
              [[7., 11.], [7., 11.]], scale=1 / np.array([[5., 5.], [6., 6.]])),
          sample_vals.mean(axis=0),
          atol=.1)
      self.assertAllClose(
          stats.gamma.var([[7., 11.], [7., 11.]],
                          scale=1 / np.array([[5., 5.], [6., 6.]])),
          sample_vals.var(axis=0),
          atol=.1)
      self._assertIntegral(sample_vals[:, 0, 0], pdf_vals[:, 0, 0], err=0.02)
      self._assertIntegral(sample_vals[:, 0, 1], pdf_vals[:, 0, 1], err=0.02)
      self._assertIntegral(sample_vals[:, 1, 0], pdf_vals[:, 1, 0], err=0.02)
      self._assertIntegral(sample_vals[:, 1, 1], pdf_vals[:, 1, 1], err=0.02)

def define_parameters(self):
        params=Parameters()

        params.append(Parameter("trend", multivariate_normal, (self.size,1)))
        params.append(Parameter("sigma2", invgamma, (1,1)))
        params.append(Parameter("lambda2", gamma, (1,1)))
        params.append(Parameter("omega", invgauss, (self.size-self.total_variation_order,1)))

        self.parameters = params

def get_var(var):
        if isinstance(var, float):
            var = gamma(a=var, scale=1)  # Initial target noise
            var = Parameter(var, Positive())
        return var

def get_regularizer(regularizer):
        if isinstance(regularizer, float):
            reg = gamma(a=regularizer, scale=1)  # Initial weight prior
            regularizer = Parameter(reg, Positive())
        return regularizer

def __init__(self, target_transform='identity', ml_score=False,
                 max_depth=3, learning_rate=0.1, n_estimators=100,
                 silent=True, objective="reg:linear",
                 nthread=1, gamma=0, min_child_weight=1,
                 max_delta_step=0,
                 subsample=1, colsample_bytree=1, colsample_bylevel=1,
                 reg_alpha=0, reg_lambda=1, scale_pos_weight=1,
                 base_score=0.5, seed=1, missing=None):

        if isinstance(target_transform, str):
            target_transform = transforms.transforms[target_transform]()
        self.target_transform = target_transform
        self.ml_score = ml_score

        super(XGBoost, self).__init__(max_depth=max_depth,
                                      learning_rate=learning_rate,
                                      n_estimators=n_estimators,
                                      silent=silent,
                                      objective=objective,
                                      nthread=nthread,
                                      gamma=gamma,
                                      min_child_weight=min_child_weight,
                                      max_delta_step=max_delta_step,
                                      subsample=subsample,
                                      colsample_bytree=colsample_bytree,
                                      colsample_bylevel=colsample_bylevel,
                                      reg_alpha=reg_alpha,
                                      reg_lambda=reg_lambda,
                                      scale_pos_weight=scale_pos_weight,
                                      base_score=base_score,
                                      seed=seed,
                                      missing=missing)

def gammaDist(x,params):
    '''Gamma distribution function
    M,K = params, where K is  average photon counts <x>,
    M is the number of coherent modes,
    In case of high intensity, the beam behavors like wave and
    the probability density of photon, P(x), satify this gamma function.
    '''

    K,M = params
    K = float(K)
    M = float(M)
    coeff = np.exp(M*np.log(M) + (M-1)*np.log(x) - gammaln(M) - M*np.log(K))
    Gd = coeff*np.exp(-M*x/K)
    return Gd

def gamma_dist(bin_values, K, M):
    """
    Gamma distribution function
    Parameters
    ----------
    bin_values : array
        scattering intensities
    K : int
        average number of photons
    M : int
        number of coherent modes
    Returns
    -------
    gamma_dist : array
        Gamma distribution
    Notes
    -----
    These implementations are based on the references under
    nbinom_distribution() function Notes

    : math ::
        P(K) =(\frac{M}{<K>})^M \frac{K^(M-1)}{\Gamma(M)}\exp(-M\frac{K}{<K>})
    """

    #gamma_dist = (stats.gamma(M, 0., K/M)).pdf(bin_values)
    x= bin_values
    coeff = np.exp(M*np.log(M) + (M-1)*np.log(x) - gammaln(M) - M*np.log(K))
    gamma_dist = coeff*np.exp(-M*x/K)
    return gamma_dist

def poisson(x,K):    
    '''Poisson distribution function.
    K is  average photon counts    
    In case of low intensity, the beam behavors like particle and
    the probability density of photon, P(x), satify this poisson function.
    '''
    K = float(K)    
    Pk = np.exp(-K)*power(K,x)/gamma(x+1)
    return Pk

def gammaDist(x,params):
    '''Gamma distribution function
    M,K = params, where K is  average photon counts <x>,
    M is the number of coherent modes,
    In case of high intensity, the beam behavors like wave and
    the probability density of photon, P(x), satify this gamma function.
    '''

    K,M = params
    K = float(K)
    M = float(M)
    coeff = np.exp(M*np.log(M) + (M-1)*np.log(x) - gammaln(M) - M*np.log(K))
    Gd = coeff*np.exp(-M*x/K)
    return Gd

def poisson(x,K):    
    '''Poisson distribution function.
    K is  average photon counts    
    In case of low intensity, the beam behavors like particle and
    the probability density of photon, P(x), satify this poisson function.
    '''
    K = float(K)    
    Pk = np.exp(-K)*power(K,x)/gamma(x+1)
    return Pk

def __init__(self, a, b, K):
        from operator import mul
        self._a = a
        self._b = b
        self._K = K
        theta = 1. / b
        self.gamma_dist = gamma_dist(a, 0, theta)
        # self._alpha = np.array(alpha)
        # self._coef = gamma(np.sum(self._alpha)) / \
        #              reduce(mul, [gamma(a) for a in self._alpha])

def gdir_pdf_integ(self, alpha1, alpha2, alpha3):
        from math import gamma
        from operator import mul
        alpha = np.array([alpha1, alpha2, alpha3])
        coef1 = gamma(np.sum(alpha)) / reduce(mul, [gamma(a) for a in alpha])
        coef2 = reduce(mul, [xx ** (aa - 1)
                             for (xx, aa) in zip(self.x, alpha)])

        coef3 = reduce(mul, [self.gamma_dist.pdf(local) for local in alpha])
        return coef1 * coef2 * coef3

def value(self,samples=1):
        """
        Samples number of values given from the specific distribution.
        ------------------------------------------------------------------------
        - samples: number of values that will be returned.
        """
        value=0
        try:
            for item in self.__params:
                if item==0: break
            if item==0: value=[0]*samples
            else:
                if self.__name=="b": value=self.binom(samples)
                if self.__name=="e": value=self.exponential(samples)
                if self.__name=="f": value=self.fixed(samples)
                if self.__name=="g": value=self.gamma(samples)
                if self.__name=="g1": value=self.gamma1(samples)
                if self.__name=="ln": value=self.lognormal(samples)
                if self.__name=="n": value=self.normal(samples)
                if self.__name=="nb": value=self.nbinom(samples)
                if self.__name=="p": value=self.poisson(samples)
                if self.__name=="u": value=self.uniform(samples)
        except Exception as ex:
            exc_type, exc_obj, exc_tb = sys.exc_info()
            fname = os.path.split(exc_tb.tb_frame.f_code.co_filename)[1]
            message="\n\tUnexpected: {0} | {1} - File: {2} - Line:{3}".format(\
                ex,exc_type, fname, exc_tb.tb_lineno)
            status=False
            raise Exception(message)
            # self.appLogger.error(message)
            # sys.exit()

        return value

def gamma1(self,samples):
        """
        Sampling from a Gamma distribution with mean 1
        ------------------------------------------------------------------------
        - samples: number of values that will be returned.
        - gamma parameterized with shape and scale
        """
        # E|x| = k.theta (alpha*theta)
        # If i want  mean=1, theta=E|x|/alpha=1/alpha
        shape=float(self.__params[0]*1.0)
        theta=float(1/(shape*1.0))
        distro=gamma(a=shape,scale=theta)
        f=distro.rvs(size=samples)
        return f

def gamma(self,samples):
        """
        Sampling from a Gamma distribution with mean 1

        The parameterization with alpha and beta is more common in Bayesian statistics,
        where the gamma distribution is used as a conjugate prior distribution
        for various types of inverse scale (aka rate) parameters, such as the
        lambda of an exponential distribution or a Poisson distribution[4]  or for
        t hat matter, the beta of the gamma distribution itself.
        (The closely related inverse gamma distribution is used as a conjugate
        prior for scale parameters, such as the variance of a normal distribution.)
        shape, scale = 2., 2. # mean=4, std=2*sqrt(2)

        (Wikipedia: https://en.wikipedia.org/wiki/Gamma_distribution)

        s = np.random.gamma(shape, scale, 1000)
        E|x| = k.theta (alpha*theta)
        If i want a specific mean, theta=E|x|/alpha
        ------------------------------------------------------------------------

        - samples: number of values that will be returned.
        """
        shape=float(self.__params[0]*1.0)
        theta=float(self.__params[1]*1.0)
        distro=gamma(a=shape,scale=theta)
        f=distro.rvs(size=samples)
        return f

def __init__(self, parameter_distribution = stats.gamma,
               signal_family = stats.poisson):
    self.parameter_distribution = parameter_distribution
    self.signal_family = signal_family

def testGammaShape(self):
    with self.test_session():
      alpha = constant_op.constant([3.0] * 5)
      beta = constant_op.constant(11.0)
      gamma = gamma_lib.Gamma(alpha=alpha, beta=beta)

      self.assertEqual(gamma.batch_shape().eval(), (5,))
      self.assertEqual(gamma.get_batch_shape(), tensor_shape.TensorShape([5]))
      self.assertAllEqual(gamma.event_shape().eval(), [])
      self.assertEqual(gamma.get_event_shape(), tensor_shape.TensorShape([]))

def testGammaCDF(self):
    with self.test_session():
      batch_size = 6
      alpha = constant_op.constant([2.0] * batch_size)
      beta = constant_op.constant([3.0] * batch_size)
      alpha_v = 2.0
      beta_v = 3.0
      x = np.array([2.5, 2.5, 4.0, 0.1, 1.0, 2.0], dtype=np.float32)

      gamma = gamma_lib.Gamma(alpha=alpha, beta=beta)
      expected_cdf = stats.gamma.cdf(x, alpha_v, scale=1 / beta_v)

      cdf = gamma.cdf(x)
      self.assertEqual(cdf.get_shape(), (6,))
      self.assertAllClose(cdf.eval(), expected_cdf)

def testGammaModeAllowNanStatsIsFalseWorksWhenAllBatchMembersAreDefined(self):
    with self.test_session():
      alpha_v = np.array([5.5, 3.0, 2.5])
      beta_v = np.array([1.0, 4.0, 5.0])
      gamma = gamma_lib.Gamma(alpha=alpha_v, beta=beta_v)
      expected_modes = (alpha_v - 1) / beta_v
      self.assertEqual(gamma.mode().get_shape(), (3,))
      self.assertAllClose(gamma.mode().eval(), expected_modes)

def testGammaModeAllowNanStatsFalseRaisesForUndefinedBatchMembers(self):
    with self.test_session():
      # Mode will not be defined for the first entry.
      alpha_v = np.array([0.5, 3.0, 2.5])
      beta_v = np.array([1.0, 4.0, 5.0])
      gamma = gamma_lib.Gamma(alpha=alpha_v, beta=beta_v, allow_nan_stats=False)
      with self.assertRaisesOpError("x < y"):
        gamma.mode().eval()