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Bayesian data analysis with PyMC3


Thomas Wiecki


Quantopian Inc.



First navigate **down** and then **right** to view all slides.

About me

  • PhD candidate at Brown studying decision making using Bayesian modeling.
  • Quantitative Researcher at Quantopian Inc: Building the world's first algorithmic trading platform in the web browser.




In [1]:



    


from IPython.display import Image
Image('quantopian.png')



    


















    
Out[1]:

Why should you care about Bayesian Data Analysis?





In [2]:



    


from IPython.display import Image
import prettyplotlib as ppl
from prettyplotlib import plt
import numpy as np
from matplotlib import rc
rc('font',**{'family':'sans-serif','sans-serif':['Helvetica'], 'size': 22})
rc('xtick', labelsize=14) 
rc('ytick', labelsize=14)
## for Palatino and other serif fonts use:
#rc('font',**{'family':'serif','serif':['Palatino']})
rc('text', usetex=True)
%matplotlib inline



    











In [3]:



    


Image('backbox_ml.png')



    


















    
Out[3]:
  • Blackbox models not good at conveying what they have learned.




In [4]:



    


Image('openbox_pp.png')



    


















    
Out[4]:

Probabilistic Programming

  • Model unknown causes of a phenomenon as random variables.
  • Write a programmatic story of how unknown causes result in observable data.
  • Use Bayes formula to invert generative model to infer unknown causes.

Random Variables as Probability Distributions

  • Represents our beliefs about an unknown state.
  • Probability distribution assigns a probability to each possible state.
  • Not a single number (e.g. most likely state).

Coin-flipping experiment.

  • Given multiple flips, what is probability of getting heads?
  • Maximum Likelihood answer:
$$\frac{\# \text{heads}}{\text{total throws}}$$
  • However:
$$\frac{50}{100} = \frac{1}{2}$$
  • Clearly something is missing!
  • Quantification of uncertainty.

Moreover...

  • Consider a single flip which comes up heads:
$$ P(\text{heads}) = \frac{1}{1} = 1 $$
  • Again, this doesn't seem right.
  • Incorporate prior knowledge.




In [5]:



    


from scipy import stats
# set every possibility to be equally possible
x_coin = np.linspace(0, 1, 101)

$$ \text{Express probability of heads as random variable } \theta$$





In [6]:



    


import prettyplotlib as ppl
fig = plt.figure(figsize=(8, 6))
ax = fig.add_subplot(111, xlabel=r'Hypothesis for chance of heads', 
            ylabel=r'Probability of hypothesis', 
            title=r'Prior probability distribution after no coin tosses')
ppl.plot(ax, x_coin, stats.beta(2, 2).pdf(x_coin), linewidth=3.)
ax.set_xticklabels([r'0\%', r'20\%', r'40\%', r'60\%', r'80\%', r'100\%']);
fig.savefig('coin1.png')



    


















    
























In [7]:



    


Image('coin1.png')



    


















    
Out[7]:
$$ \theta \sim \text{Beta}(2, 2) $$$$ P(\theta) = \text{Beta}(2, 2) $$ 




In [8]:



    


fig = plt.figure(figsize=(8, 6))
ax = fig.add_subplot(111, xlabel='Hypothesis for chance of heads', 
            ylabel='Probability of hypothesis', 
            title='Posterior probability distribution after first heads')
ppl.plot(ax, x_coin, stats.beta(3, 2).pdf(x_coin), linewidth=3.)
ax.set_xticklabels([r'0\%', r'20\%', r'40\%', r'60\%', r'80\%', r'100\%']);
plt.savefig('coin2.png')



    


















    
























In [9]:



    


Image('coin2.png')



    


















    
Out[9]:
$$ P(\theta | h=1) = \text{Beta}(3, 2) $$ 




In [10]:



    


fig = plt.figure(figsize=(8, 6))
ax = fig.add_subplot(111, xlabel='Hypothesis for chance of heads', 
            ylabel='Probability of hypothesis', 
            title='Posterior probability distribution after 1 head, 1 tail')
ppl.plot(ax, x_coin, stats.beta(3, 3).pdf(x_coin), linewidth=3.)
ax.set_xticklabels(['0\%', '20\%', '40\%', '60\%', '80\%', '100\%']);
fig.savefig('coin3.png')



    


















    
























In [11]:



    


Image('coin3.png')



    


















    
Out[11]:
$$ P(\theta | [h=1, t=1]) = \text{Beta}(3, 3) $$ 




In [12]:



    


fig = plt.figure(figsize=(8, 6))
ax = fig.add_subplot(111, xlabel='Hypothesis for chance of heads', 
            ylabel='Probability of hypothesis', 
            title='Posterior probability distribution after 20 heads and 20 tails')
ppl.plot(ax, x_coin, stats.beta(22, 22).pdf(x_coin), linewidth=3.)
ax.set_xticklabels(['0\%', '20\%', '40\%', '60\%', '80\%', '100\%']);
fig.savefig('coin4.png')



    


















    
























In [13]:



    


Image('coin4.png')



    


















    
Out[13]:
$$ P(\theta | [h=20, t=20]) = \text{Beta}(22, 22) $$

Bayes Formula

$$P(\theta| \text{data}) \propto P(\theta) \ast P(\text{data} |\theta)$$$$\text{posterior} \propto \text{prior} \ast \text{likelihood}$$

$\theta$: Parameters of model (chance of getting heads)).

  • Except in simple cases, posterior impossible to compute analytically.
  • Blackbox approximation algorithm: Markov-Chain Monte Carlo (MCMC) instead draws samples from the posterior.




In [15]:



    


from scipy import stats
fig = ppl.plt.figure(figsize=(14, 6))
ax1 = fig.add_subplot(121, title='What we want', ylim=(0, .5), xlabel=r'$\theta$', ylabel=r'$P(\theta)$')
ppl.plot(ax1, np.linspace(-4, 4, 100), stats.norm.pdf(np.linspace(-3, 3, 100)), linewidth=4.)
ax2 = fig.add_subplot(122, title='What we get', xlim=(-4, 4), ylim=(0, 1800), xlabel=r'$\theta$', ylabel='\# of samples')
ppl.hist(ax2, np.random.randn(10000), bins=20);
fig.savefig('wantget.png')

Approximating the posterior with MCMC sampling





In [ ]:



    


Image('wantget.png')

PyMC3

  • Probabilistic Programming framework written in Python.
  • Allows for construction of probabilistic models using intuitive syntax.
  • Features advanced MCMC samplers.
  • Fast: Just-in-time compiled by Theano.
  • Extensible: easily incorporates custom MCMC algorithms and unusual probability distributions.

Linear Models

  • Assumes a linear relationship between two variables.
  • E.g. stock price between Gold and Gold Miners.




In [16]:



    


size = 200
true_intercept = 1
true_slope = 2

x = np.linspace(0, 1, size)
# y = a + b*x
true_regression_line = true_intercept + true_slope * x
# add noise
y = true_regression_line + np.random.normal(scale=.5, size=size)

data = dict(x=x, y=y)



    











In [19]:



    


fig = plt.figure(figsize=(7, 7))
ax = fig.add_subplot(111, xlabel='Value of gold', ylabel='Value of gold miners', title='Synthetic data and underlying model')
ppl.scatter(ax, x, y, label='sampled data')
ppl.plot(ax, x, true_regression_line, label='true regression line', linewidth=4.)
ax.legend(loc=2);
fig.savefig('synth_data.png')



    


















    
























In [20]:



    


Image('synth_data.png')



    


















    
Out[20]:

Linear Regression

$$ y_i = \alpha + \beta \ast x_i + \epsilon $$

with $$ \epsilon \sim \mathcal{N}(0, \sigma^2) $$

Probabilistic Reformulation

$$ y_i \sim \mathcal{N}(\alpha + \beta \ast x_i, \sigma^2) $$

Priors

$$ \alpha \sim \mathcal{N}(0, 20^2) $$$$ \beta \sim \mathcal{N}(0, 20^2) $$$$ \sigma \sim \mathcal{U}(0, 20) $$

Constructing model in PyMC3





In [23]:



    


!conda install pymc



    


















    






Conda package not available for pymc, attempting to install via pip
Downloading/unpacking pymc
  Downloading pymc-2.3.tar.gz (13.1MB): 13.1MB downloaded
  Running setup.py egg_info for package pymc
    build_src
    building extension "pymc.flib" sources
    f2py options: ['skip:ppnd7']
    f2py:> build/src.macosx-10.5-x86_64-2.7/pymc/flibmodule.c
    IOError: [Errno 2] No such file or directory: 'skip:ppnd7'. Skipping file "skip:ppnd7".
    updatevars:gradlike: attempt to change 'dimension(nx)' to 'dimension(na)'. Ignoring.
    updatevars:gradlike: attempt to change 'dimension(nx)' to 'dimension(nb)'. Ignoring.
    updatevars:gradlike: attempt to change 'dimension (nmu)' to 'dimension(nmu)'. Ignoring.
    updatevars:gradlike: attempt to change 'dimension (na)' to 'dimension(na)'. Ignoring.
    rmbadname1: Replacing "index" with "index_bn".
    updatevars: "character curterms(20)*24" is mapped to "character curterms(20,24)"
    updatevars: "character septerms(20)*24" is mapped to "character septerms(20,24)"
    updatevars: "character tokens(maxtok)*(*)" is mapped to "character tokens(maxtok,(*))"
    rmbadname1: Replacing "index" with "index_bn".
    rmbadname1: Replacing "len" with "len_bn".
    sortvarnames: failed to compute dependencies because of cyclic dependencies between x, nx
    sortvarnames: failed to compute dependencies because of cyclic dependencies between w, x, nx
    sortvarnames: failed to compute dependencies because of cyclic dependencies between n, nx, bin0, delta, x, d
    "object of type 'builtin_function_or_method' has no len()" in evaluating 'len(ord)' (available names: [])
    Reading fortran codes...
    	Reading file 'pymc/flib.f' (format:fix,strict)
    	Reading file 'pymc/histogram.f' (format:fix,strict)
    	Reading file 'pymc/flib_blas.f' (format:fix,strict)
    	Reading file 'pymc/blas_wrap.f' (format:fix,strict)
    	Reading file 'pymc/math.f' (format:fix,strict)
    	Reading file 'pymc/gibbsit.f' (format:fix,strict)
    Line #1125 in pymc/gibbsit.f:"      DOUBLE PRECISION INTENT(CACHE,HIDE), DIMENSION(2*ITERACNT) :: WORK"
    	updatevars: attempt to change the type of "work" ("integer") to "double precision". Ignoring.
    Post-processing...
    	Block: flib
    			Block: symmetrize
    			Block: logsum
    			Block: logsum_cpx
    			Block: combinationln
    {'attrspec': ['intent(hide)']}
    In: :flib:pymc/flib.f:expand_triangular
    vars2fortran: No typespec for argument "nf".
    {'attrspec': ['intent(hide)']}
    In: :flib:pymc/flib.f:expand_triangular
    vars2fortran: No typespec for argument "n".
    			Block: expand_triangular
    			Block: mod_to_circle
    			Block: standardize
    			Block: gammln
    			Block: mvgammln
    			Block: factrl
    			Block: factln
    			Block: normcdf
    			Block: sn_like
    			Block: rskewnorm
    			Block: uniform_like
    			Block: uniform_grad_x
    			Block: uniform_grad_l
    			Block: uniform_grad_u
    			Block: duniform_like
    			Block: exponweib
    			Block: exponweib_gx
    			Block: exponweib_gl
    			Block: exponweib_gk
    			Block: exponweib_ga
    			Block: exponweib_gs
    			Block: exponweib_ppf
    			Block: constrain
    			Block: poisson
    			Block: poisson_gmu
    			Block: trpoisson
    			Block: trpoisson_gmu
    			Block: t
    			Block: t_grad_x
    			Block: t_grad_nu
    			Block: chi2_grad_nu
    			Block: nct
    			Block: multinomial
    			Block: weibull
    			Block: weibull_gx
    			Block: weibull_ga
    			Block: weibull_gb
    			Block: logistic
    			Block: normal
    			Block: normal_grad_tau
    			Block: normal_grad_x
    			Block: normal_grad_mu
    			Block: hnormal
    			Block: hnormal_gradx
    			Block: hnormal_gradtau
    			Block: lognormal
    			Block: lognormal_gradx
    			Block: lognormal_gradmu
    			Block: lognormal_gradtau
    			Block: arlognormal
    			Block: gev
    			Block: gev_ppf
    			Block: gamma
    			Block: gamma_grad_x
    			Block: gamma_grad_alpha
    			Block: gamma_grad_beta
    			Block: igamma
    			Block: igamma_grad_x
    			Block: igamma_grad_alpha
    			Block: igamma_grad_beta
    			Block: hyperg
    			Block: geometric
    			Block: geometric_gp
    			Block: dirichlet
    			Block: cauchy
    			Block: cauchy_grad_x
    			Block: cauchy_grad_a
    			Block: cauchy_grad_b
    			Block: negbin
    			Block: negbin2
    			Block: negbin2_gmu
    			Block: negbin2_ga
    			Block: binomial
    			Block: binomial_gp
    			Block: bernoulli
    			Block: bern_grad_p
    			Block: beta_like
    			Block: beta_grad_x
    			Block: beta_grad_a
    			Block: beta_grad_b
    			Block: betabin_like
    			Block: betabin_ga
    			Block: betabin_gb
    			Block: mvhyperg
    			Block: dirmultinom
    			Block: wishart
    			Block: trace
    			Block: gamfun
    			Block: gammds
    			Block: psi
    			Block: gser
    			Block: gcf
    			Block: gammq
    			Block: trans
    			Block: matmult
    			Block: dtrm
    			Block: elgs
    			Block: bico
    			Block: chol
    			Block: hermpoly
    			Block: set_uniform
    			Block: categorical
    			Block: rcat
    			Block: logit
    			Block: invlogit
    			Block: stukel_logit
    			Block: stukel_invlogit
    			Block: vonmises
    			Block: pareto
    			Block: truncated_pareto
    			Block: fixed_binsize
    			Block: weighted_fixed_binsize
    			Block: fixed_binsize_nd
    {'attrspec': ['dimension(n)']}
    In: :flib:pymc/histogram.f:qsorti
    vars2fortran: No typespec for argument "ord".
    			Block: qsorti
    			Block: checksymm
    			Block: chol_mvnorm
    			Block: cov_mvnorm
    			Block: prec_mvnorm
    			Block: blas_wishart
    			Block: blas_wishart_cov
    {'attrspec': ['intent(hide)']}
    In: :flib:pymc/blas_wrap.f:dcopy_wrap
    vars2fortran: No typespec for argument "nx".
    			Block: dcopy_wrap
    			Block: dtrmm_wrap
    			Block: dtrsm_wrap
    			Block: dpotrf_wrap
    			Block: dchdc_wrap
    			Block: dpotrs_wrap
    			Block: ppnd16
    			Block: calerf
    			Block: derf
    			Block: derfc
    			Block: derfcx
    			Block: gibbsit
    			Block: matinput
    			Block: vecinput
    			Block: oneparse
    			Block: gibbmain
    			Block: empquant
    			Block: dichot
    			Block: thin
    			Block: mctest
    			Block: indtest
    			Block: mcest
    			Block: ppnd7
    			Block: ssort
    Post-processing (stage 2)...
    Building modules...
    	Building module "flib"...
    		Constructing wrapper function "symmetrize"...
    		  symmetrize(c,[cmin,cmax])
    		Constructing wrapper function "logsum"...
    		  s = logsum(x)
    		Constructing wrapper function "logsum_cpx"...
    		  s = logsum_cpx(x)
    		Creating wrapper for Fortran function "combinationln"("combinationln")...
    		Constructing wrapper function "combinationln"...
    		  combinationln = combinationln(n,k)
    		Constructing wrapper function "expand_triangular"...
    		  t = expand_triangular(d,f)
    		Constructing wrapper function "mod_to_circle"...
    		  mx = mod_to_circle(x,u,l)
    		Constructing wrapper function "standardize"...
    		  z = standardize(x,loc,scale)
    		Creating wrapper for Fortran function "gammln"("gammln")...
    		Constructing wrapper function "gammln"...
    		  gammln = gammln(xx)
    		Creating wrapper for Fortran function "mvgammln"("mvgammln")...
    		Constructing wrapper function "mvgammln"...
    		  mvgammln = mvgammln(x,k)
    		Creating wrapper for Fortran function "factrl"("factrl")...
    		Constructing wrapper function "factrl"...
    		  factrl = factrl(n)
    		Creating wrapper for Fortran function "factln"("factln")...
    		Constructing wrapper function "factln"...
    		  factln = factln(n)
    		Constructing wrapper function "normcdf"...
    		  normcdf(x)
    		Constructing wrapper function "sn_like"...
    		  like = sn_like(x,mu,tau,alph)
    		Constructing wrapper function "rskewnorm"...
    		  x = rskewnorm(nx,mu,tau,alph,rn)
    		Constructing wrapper function "uniform_like"...
    		  like = uniform_like(x,lower,upper)
    		Constructing wrapper function "uniform_grad_x"...
    		  gradxlike = uniform_grad_x(x,lower,upper)
    		Constructing wrapper function "uniform_grad_l"...
    		  gradllike = uniform_grad_l(x,lower,upper)
    		Constructing wrapper function "uniform_grad_u"...
    		  gradulike = uniform_grad_u(x,lower,upper)
    		Constructing wrapper function "duniform_like"...
    		  like = duniform_like(x,lower,upper)
    		Constructing wrapper function "exponweib"...
    		  like = exponweib(x,a,c,loc,scale)
    		Constructing wrapper function "exponweib_gx"...
    		  gradlike = exponweib_gx(x,alpha,k,loc,scale)
    		Constructing wrapper function "exponweib_gl"...
    		  gradlike = exponweib_gl(x,alpha,k,loc,scale)
    		Constructing wrapper function "exponweib_gk"...
    		  gradlike = exponweib_gk(x,alpha,k,loc,scale)
    		Constructing wrapper function "exponweib_ga"...
    		  gradlike = exponweib_ga(x,alpha,k,loc,scale,[nk])
    		Constructing wrapper function "exponweib_gs"...
    		  gradlike = exponweib_gs(x,alpha,k,loc,scale)
    		Constructing wrapper function "exponweib_ppf"...
    		  ppf = exponweib_ppf(q,a,c)
    		Constructing wrapper function "constrain"...
    		  pass = constrain(x,a,b,allow_equal)
    		Constructing wrapper function "poisson"...
    		  like = poisson(x,mu)
    		Constructing wrapper function "poisson_gmu"...
    		  gradlike = poisson_gmu(x,mu)
    		Constructing wrapper function "trpoisson"...
    		  like = trpoisson(x,mu,k)
    		Constructing wrapper function "trpoisson_gmu"...
    		  gradlike = trpoisson_gmu(x,mu,k)
    		Constructing wrapper function "t"...
    		  like = t(x,nu)
    		Constructing wrapper function "t_grad_x"...
    		  gradlikex = t_grad_x(x,nu)
    		Constructing wrapper function "t_grad_nu"...
    		  gradlikenu = t_grad_nu(x,nu)
    		Constructing wrapper function "chi2_grad_nu"...
    		  gradlikenu = chi2_grad_nu(x,nu)
    		Constructing wrapper function "nct"...
    		  like = nct(x,mu,lam,nu)
    		Constructing wrapper function "multinomial"...
    		  like = multinomial(x,n,p)
    		Constructing wrapper function "weibull"...
    		  like = weibull(x,alpha,beta)
    		Constructing wrapper function "weibull_gx"...
    		  gradlike = weibull_gx(x,alpha,beta)
    		Constructing wrapper function "weibull_ga"...
    		  gradlike = weibull_ga(x,alpha,beta)
    		Constructing wrapper function "weibull_gb"...
    		  gradlike = weibull_gb(x,alpha,beta)
    		Constructing wrapper function "logistic"...
    		  like = logistic(x,mu,tau)
    		Constructing wrapper function "normal"...
    		  like = normal(x,mu,tau)
    		Constructing wrapper function "normal_grad_tau"...
    		  grad_tau_like = normal_grad_tau(x,mu,tau)
    		Constructing wrapper function "normal_grad_x"...
    		  grad_x_like = normal_grad_x(x,mu,tau)
    		Constructing wrapper function "normal_grad_mu"...
    		  gradmulike = normal_grad_mu(x,mu,tau)
    		Constructing wrapper function "hnormal"...
    		  like = hnormal(x,tau)
    		Constructing wrapper function "hnormal_gradx"...
    		  gradlike = hnormal_gradx(x,tau)
    		Constructing wrapper function "hnormal_gradtau"...
    		  gradlike = hnormal_gradtau(x,tau)
    		Constructing wrapper function "lognormal"...
    		  like = lognormal(x,mu,tau)
    		Constructing wrapper function "lognormal_gradx"...
    		  gradlike = lognormal_gradx(x,mu,tau)
    		Constructing wrapper function "lognormal_gradmu"...
    		  gradlike = lognormal_gradmu(x,mu,tau)
    		Constructing wrapper function "lognormal_gradtau"...
    		  gradlike = lognormal_gradtau(x,mu,tau)
    		Constructing wrapper function "arlognormal"...
    		  like = arlognormal(x,mu,sigma,rho,beta)
    		Constructing wrapper function "gev"...
    		  like = gev(x,xi,mu,sigma)
    		Constructing wrapper function "gev_ppf"...
    		  ppf = gev_ppf(q,xi)
    		Constructing wrapper function "gamma"...
    		  like = gamma(x,alpha,beta)
    		Constructing wrapper function "gamma_grad_x"...
    		  gradxlike = gamma_grad_x(x,alpha,beta)
    		Constructing wrapper function "gamma_grad_alpha"...
    		  gradalphalike = gamma_grad_alpha(x,alpha,beta)
    		Constructing wrapper function "gamma_grad_beta"...
    		  gradbetalike = gamma_grad_beta(x,alpha,beta)
    		Constructing wrapper function "igamma"...
    		  like = igamma(x,alpha,beta)
    		Constructing wrapper function "igamma_grad_x"...
    		  gradxlike = igamma_grad_x(x,alpha,beta)
    		Constructing wrapper function "igamma_grad_alpha"...
    		  gradalphalike = igamma_grad_alpha(x,alpha,beta)
    		Constructing wrapper function "igamma_grad_beta"...
    		  gradbetalike = igamma_grad_beta(x,alpha,beta)
    		Constructing wrapper function "hyperg"...
    		  like = hyperg(x,draws,success,total)
    		Constructing wrapper function "geometric"...
    		  like = geometric(x,p)
    		Constructing wrapper function "geometric_gp"...
    		  gradlike = geometric_gp(x,p)
    		Constructing wrapper function "dirichlet"...
    		  like = dirichlet(x,theta)
    		Constructing wrapper function "cauchy"...
    		  like = cauchy(x,alpha,beta)
    		Constructing wrapper function "cauchy_grad_x"...
    		  gradlike = cauchy_grad_x(x,alpha,beta)
    		Constructing wrapper function "cauchy_grad_a"...
    		  gradlike = cauchy_grad_a(x,alpha,beta)
    		Constructing wrapper function "cauchy_grad_b"...
    		  gradlike = cauchy_grad_b(x,alpha,beta)
    		Constructing wrapper function "negbin"...
    		  like = negbin(x,r,p)
    		Constructing wrapper function "negbin2"...
    		  like = negbin2(x,mu,a)
    		Constructing wrapper function "negbin2_gmu"...
    		  gradlike = negbin2_gmu(x,mu,alpha)
    		Constructing wrapper function "negbin2_ga"...
    		  gradlike = negbin2_ga(x,mu,alpha)
    		Constructing wrapper function "binomial"...
    		  like = binomial(x,n,p)
    		Constructing wrapper function "binomial_gp"...
    		  gradlike = binomial_gp(x,n,p)
    		Constructing wrapper function "bernoulli"...
    		  like = bernoulli(x,p)
    		Constructing wrapper function "bern_grad_p"...
    		  grad_like = bern_grad_p(x,p)
    		Constructing wrapper function "beta_like"...
    		  like = beta_like(x,alpha,beta)
    		Constructing wrapper function "beta_grad_x"...
    		  gradlikex = beta_grad_x(x,alpha,beta)
    		Constructing wrapper function "beta_grad_a"...
    		  gradlikea = beta_grad_a(x,alpha,beta)
    		Constructing wrapper function "beta_grad_b"...
    		  gradlikeb = beta_grad_b(x,alpha,beta)
    		Constructing wrapper function "betabin_like"...
    		  like = betabin_like(x,alpha,beta,n)
    		Constructing wrapper function "betabin_ga"...
    		  gradlike = betabin_ga(x,alpha,beta,n)
    		Constructing wrapper function "betabin_gb"...
    		  gradlike = betabin_gb(x,alpha,beta,n)
    		Constructing wrapper function "mvhyperg"...
    		  like = mvhyperg(x,color)
    		Constructing wrapper function "dirmultinom"...
    		  like = dirmultinom(x,theta)
    		Constructing wrapper function "wishart"...
    		  like = wishart(x,n,sigma)
    		Constructing wrapper function "trace"...
    		  trace(mat,tr,[k])
    		Constructing wrapper function "gamfun"...
    		  gx = gamfun(xx)
    		Creating wrapper for Fortran function "gammds"("gammds")...
    		Constructing wrapper function "gammds"...
    		  gammds = gammds(y,p,ifault)
    		Creating wrapper for Fortran function "psi"("psi")...
    		Constructing wrapper function "psi"...
    		  psi = psi(x)
    		Constructing wrapper function "gser"...
    		  gser(gamser,a,x,gln)
    		Constructing wrapper function "gcf"...
    		  gcf(gammcf,a,x,gln)
    		Creating wrapper for Fortran function "gammq"("gammq")...
    		Constructing wrapper function "gammq"...
    		  gammq = gammq(a,x)
    		Constructing wrapper function "trans"...
    		  tmat = trans(mat)
    		Constructing wrapper function "matmult"...
    		  prod = matmult(mat1,mat2)
    		Constructing wrapper function "dtrm"...
    		  d = dtrm(a)
    		Constructing wrapper function "elgs"...
    		  elgs(a,indx,[n])
    		Creating wrapper for Fortran function "bico"("bico")...
    		Constructing wrapper function "bico"...
    		  bico = bico(n,k)
    		Constructing wrapper function "chol"...
    		  c = chol(a,[n])
    		Constructing wrapper function "hermpoly"...
    		  cx = hermpoly(n,x)
    		Constructing wrapper function "set_uniform"...
    		  set_uniform(seed1,seed2)
    		Constructing wrapper function "categorical"...
    		  like = categorical(x,p)
    		Constructing wrapper function "rcat"...
    		  s = rcat(p,rands)
    		Constructing wrapper function "logit"...
    		  ltheta = logit(theta)
    		Constructing wrapper function "invlogit"...
    		  theta = invlogit(ltheta)
    		Constructing wrapper function "stukel_logit"...
    		  ltheta = stukel_logit(theta,a1,a2,[overwrite_theta])
    		Constructing wrapper function "stukel_invlogit"...
    		  theta = stukel_invlogit(ltheta,a1,a2,[overwrite_ltheta])
    		Constructing wrapper function "vonmises"...
    		  like = vonmises(x,mu,kappa)
    		Constructing wrapper function "pareto"...
    		  like = pareto(x,alpha,m)
    		Constructing wrapper function "truncated_pareto"...
    		  like = truncated_pareto(x,alpha,m,b)
    		Constructing wrapper function "fixed_binsize"...
    		  h = fixed_binsize(x,bin0,delta,n)
    		Constructing wrapper function "weighted_fixed_binsize"...
    		  h = weighted_fixed_binsize(x,w,bin0,delta,n)
    		Constructing wrapper function "fixed_binsize_nd"...
    		  count = fixed_binsize_nd(x,bin0,delta,n,nc)
    		Constructing wrapper function "qsorti"...
    		  qsorti(ord,a,[n])
    		Constructing wrapper function "checksymm"...
    		  cs = checksymm(x)
    		Constructing wrapper function "chol_mvnorm"...
    		  like = chol_mvnorm(x,mu,sig,[overwrite_x,overwrite_mu])
    		Constructing wrapper function "cov_mvnorm"...
    		  like = cov_mvnorm(x,mu,c,[overwrite_x,overwrite_mu,overwrite_c])
    		Constructing wrapper function "prec_mvnorm"...
    		  like = prec_mvnorm(x,mu,tau,[overwrite_x,overwrite_mu,overwrite_tau])
    		Constructing wrapper function "blas_wishart"...
    		  like = blas_wishart(x,n,t,[overwrite_x,overwrite_t])
    		Constructing wrapper function "blas_wishart_cov"...
    		  like = blas_wishart_cov(x,n,v,[overwrite_x,overwrite_v])
    		Constructing wrapper function "dcopy_wrap"...
    		  dcopy_wrap(x,y)
    		Constructing wrapper function "dtrmm_wrap"...
    		  dtrmm_wrap(a,b,side,transa,uplo,alpha)
    		Constructing wrapper function "dtrsm_wrap"...
    		  dtrsm_wrap(a,b,side,transa,uplo,alpha)
    		Constructing wrapper function "dpotrf_wrap"...
    		  info = dpotrf_wrap(a)
    		Constructing wrapper function "dchdc_wrap"...
    		  piv,info = dchdc_wrap(a)
    		Constructing wrapper function "dpotrs_wrap"...
    		  info = dpotrs_wrap(chol_fac,b,[uplo])
    		Creating wrapper for Fortran function "ppnd16"("ppnd16")...
    		Constructing wrapper function "ppnd16"...
    		  ppnd16 = ppnd16(p,ifault)
    		Constructing wrapper function "calerf"...
    		  calerf(arg,result,jint)
    		Creating wrapper for Fortran function "derf"("derf")...
    		Constructing wrapper function "derf"...
    		  derf = derf(x)
    		Creating wrapper for Fortran function "derfc"("derfc")...
    		Constructing wrapper function "derfc"...
    		  derfc = derfc(x)
    		Creating wrapper for Fortran function "derfcx"("derfcx")...
    		Constructing wrapper function "derfcx"...
    		  derfcx = derfcx(x)
    		Constructing wrapper function "matinput"...
    		  matinput(uid,matout,rowused,colused,r15,[rowmax,colmax])
    		Constructing wrapper function "vecinput"...
    		  vecinput(uid,vecout,vecused,r15,[vecmax])
    		Constructing wrapper function "oneparse"...
    getarrdims:warning: assumed shape array, using 0 instead of '(*)'
    		  oneparse(instring,delimit,tokens,tokcnt,r15,[maxtok])
    		Constructing wrapper function "gibbmain"...
    		  nmin,kthin,nburn,nprec,kmind = gibbmain(original,q,r,s,epsilon)
    		Creating wrapper for Fortran function "empquant"("empquant")...
    		Constructing wrapper function "empquant"...
    getarrdims:warning: assumed shape array, using 0 instead of '*'
    		  empquant = empquant(data,q,work,[iteracnt])
    		Constructing wrapper function "dichot"...
    		  dichot(data,cutpt,zt,[iteracnt])
    		Constructing wrapper function "thin"...
    		  thin(series,kthin,result,thincnt,[iteracnt])
    		Constructing wrapper function "mctest"...
    		  mctest(data,g2,bic,[datacnt])
    		Constructing wrapper function "indtest"...
    		  indtest(data,g2,bic,[datacnt])
    		Constructing wrapper function "mcest"...
    		  mcest(data,alpha,beta,[datacnt])
    		Creating wrapper for Fortran function "ppnd7"("ppnd7")...
    		Constructing wrapper function "ppnd7"...
    		  ppnd7 = ppnd7(p,ifault)
    		Constructing wrapper function "ssort"...
    		  ssort(x,y,kflag,[n])
    		Constructing COMMON block support for "unif_seeds"...
    		  s1,s2
    	Wrote C/API module "flib" to file "build/src.macosx-10.5-x86_64-2.7/pymc/flibmodule.c"
    	Fortran 77 wrappers are saved to "build/src.macosx-10.5-x86_64-2.7/pymc/flib-f2pywrappers.f"
      adding 'build/src.macosx-10.5-x86_64-2.7/fortranobject.c' to sources.
      adding 'build/src.macosx-10.5-x86_64-2.7' to include_dirs.
      adding 'build/src.macosx-10.5-x86_64-2.7/pymc/flib-f2pywrappers.f' to sources.
    building extension "pymc.LazyFunction" sources
    building extension "pymc.Container_values" sources
    building extension "pymc.gp.linalg_utils" sources
    f2py options: []
    f2py:> build/src.macosx-10.5-x86_64-2.7/pymc/gp/linalg_utilsmodule.c
    Reading fortran codes...
    	Reading file 'pymc/gp/linalg_utils.f' (format:fix,strict)
    	Reading file 'pymc/blas_wrap.f' (format:fix,strict)
    Post-processing...
    	Block: linalg_utils
    			Block: remove_duplicates
    			Block: check_repeats
    			Block: diag_call
    					Block: cov_fun
    {'attrspec': ['intent(hide)']}
    In: :linalg_utils:pymc/gp/linalg_utils.f:basis_diag_call
    vars2fortran: No typespec for argument "nbas".
    			Block: basis_diag_call
    			Block: gp_array_logp
    			Block: asqs
    {'attrspec': ['intent(hide)']}
    In: :linalg_utils:pymc/blas_wrap.f:dcopy_wrap
    vars2fortran: No typespec for argument "nx".
    			Block: dcopy_wrap
    			Block: dtrmm_wrap
    			Block: dtrsm_wrap
    			Block: dpotrf_wrap
    			Block: dchdc_wrap
    			Block: dpotrs_wrap
    Post-processing (stage 2)...
    Building modules...
    	Constructing call-back function "cb_cov_fun_in_diag_call__user__routines"
    	  def cov_fun(xe): return q
    	Building module "linalg_utils"...
    		Constructing wrapper function "remove_duplicates"...
    		  nr,rf,rt,nu,xu,ui = remove_duplicates(x)
    		Constructing wrapper function "check_repeats"...
    		  f,new_indices,n_new_indices = check_repeats(x,x_sofar,f_sofar)
    		Constructing wrapper function "diag_call"...
    		  v = diag_call(x,cov_fun,[cov_fun_extra_args])
    		Constructing wrapper function "basis_diag_call"...
    		  v = basis_diag_call(basis_x)
    		Constructing wrapper function "gp_array_logp"...
    		  like = gp_array_logp(x,mu,sig,[overwrite_x,overwrite_mu])
    		Constructing wrapper function "asqs"...
    		  asqs(c,s,[cmin,cmax])
    		Constructing wrapper function "dcopy_wrap"...
    		  dcopy_wrap(x,y)
    		Constructing wrapper function "dtrmm_wrap"...
    		  dtrmm_wrap(a,b,side,transa,uplo,alpha)
    		Constructing wrapper function "dtrsm_wrap"...
    		  dtrsm_wrap(a,b,side,transa,uplo,alpha)
    		Constructing wrapper function "dpotrf_wrap"...
    		  info = dpotrf_wrap(a)
    		Constructing wrapper function "dchdc_wrap"...
    		  piv,info = dchdc_wrap(a)
    		Constructing wrapper function "dpotrs_wrap"...
    		  info = dpotrs_wrap(chol_fac,b,[uplo])
    	Wrote C/API module "linalg_utils" to file "build/src.macosx-10.5-x86_64-2.7/pymc/gp/linalg_utilsmodule.c"
      adding 'build/src.macosx-10.5-x86_64-2.7/fortranobject.c' to sources.
      adding 'build/src.macosx-10.5-x86_64-2.7' to include_dirs.
    building extension "pymc.gp.incomplete_chol" sources
    f2py options: []
    f2py:> build/src.macosx-10.5-x86_64-2.7/pymc/gp/incomplete_cholmodule.c
    Reading fortran codes...
    	Reading file 'pymc/gp/incomplete_chol.f' (format:fix,strict)
    Post-processing...
    	Block: incomplete_chol
    			Block: ichol_continue
    					Block: rowfun
    			Block: ichol
    					Block: rowfun
    {'attrspec': ['intent(hide)']}
    In: :incomplete_chol:pymc/gp/incomplete_chol.f:ichol_basis
    vars2fortran: No typespec for argument "n_nug".
    			Block: ichol_basis
    			Block: ichol_full
    Post-processing (stage 2)...
    Building modules...
    	Constructing call-back function "cb_rowfun_in_ichol_continue__user__routines"
    	  def rowfun(itot,x,rowvec): return
    	Constructing call-back function "cb_rowfun_in_ichol__user__routines"
    	  def rowfun(i,x,rowvec): return
    	Building module "incomplete_chol"...
    		Constructing wrapper function "ichol_continue"...
    		  m,piv = ichol_continue(sig,diag,piv,reltol,x,rowfun,mold,[overwrite_x,rowfun_extra_args])
    		Constructing wrapper function "ichol"...
    		  sig,m,piv = ichol(diag,reltol,x,rowfun,rl,[overwrite_x,rowfun_extra_args])
    		Constructing wrapper function "ichol_basis"...
    		  sig,p,m = ichol_basis(basis,nug,reltol)
    		Constructing wrapper function "ichol_full"...
    		  sig,m,p = ichol_full(c,reltol)
    	Wrote C/API module "incomplete_chol" to file "build/src.macosx-10.5-x86_64-2.7/pymc/gp/incomplete_cholmodule.c"
      adding 'build/src.macosx-10.5-x86_64-2.7/fortranobject.c' to sources.
      adding 'build/src.macosx-10.5-x86_64-2.7' to include_dirs.
    building extension "pymc.gp.cov_funs.isotropic_cov_funs" sources
    f2py options: []
    f2py:> build/src.macosx-10.5-x86_64-2.7/pymc/gp/cov_funs/isotropic_cov_funsmodule.c
    Reading fortran codes...
    	Reading file 'pymc/gp/cov_funs/isotropic_cov_funs.f' (format:fix,strict)
    	Reading file 'blas/BLAS/dscal.f' (format:fix,strict)
    Post-processing...
    	Block: isotropic_cov_funs
    			Block: imul
    			Block: symmetrize
    			Block: matern
    			Block: nsmatrn
    			Block: stein_spatiotemporal
    			Block: nsst
    			Block: gaussian
    			Block: exponential
    			Block: brownian
    			Block: frac_brownian
    			Block: pow_exp
    			Block: sphere
    			Block: quadratic
    			Block: dgamma
    			Block: rkbesl
    			Block: dscal
    Post-processing (stage 2)...
    Building modules...
    	Building module "isotropic_cov_funs"...
    		Constructing wrapper function "imul"...
    		  imul(c,a,[cmin,cmax,symm])
    		Constructing wrapper function "symmetrize"...
    		  symmetrize(c,[cmin,cmax])
    		Constructing wrapper function "matern"...
    		  matern(c,diff_degree,[cmin,cmax,symm])
    		Constructing wrapper function "nsmatrn"...
    		  nsmatrn(c,ddx,ddy,hx,hy,nmax,[cmin,cmax,symm])
    		Constructing wrapper function "stein_spatiotemporal"...
    		  stein_spatiotemporal(c,gt,origin_val,[cmin,cmax,symm])
    		Constructing wrapper function "nsst"...
    		  nsst(c,gt,origin_val,hx,hy,[cmin,cmax,symm])
    		Constructing wrapper function "gaussian"...
    		  gaussian(c,[cmin,cmax,symm])
    		Constructing wrapper function "exponential"...
    		  exponential(c,[cmin,cmax,symm])
    		Constructing wrapper function "brownian"...
    		  brownian(c,x,y,[cmin,cmax,symm])
    		Constructing wrapper function "frac_brownian"...
    		  frac_brownian(c,x,y,h,[cmin,cmax,symm])
    		Constructing wrapper function "pow_exp"...
    		  pow_exp(c,pow,[cmin,cmax,symm])
    		Constructing wrapper function "sphere"...
    		  sphere(c,[cmin,cmax,symm])
    		Constructing wrapper function "quadratic"...
    		  quadratic(c,phi,[cmin,cmax,symm])
    		Creating wrapper for Fortran function "dgamma"("dgamma")...
    		Constructing wrapper function "dgamma"...
    		  dgamma = dgamma(x)
    		Constructing wrapper function "rkbesl"...
    		  bk = rkbesl(x,alpha,nb,ize,ncalc)
    		Constructing wrapper function "dscal"...
    getarrdims:warning: assumed shape array, using 0 instead of '*'
    		  dscal(n,da,dx,incx)
    	Wrote C/API module "isotropic_cov_funs" to file "build/src.macosx-10.5-x86_64-2.7/pymc/gp/cov_funs/isotropic_cov_funsmodule.c"
    	Fortran 77 wrappers are saved to "build/src.macosx-10.5-x86_64-2.7/pymc/gp/cov_funs/isotropic_cov_funs-f2pywrappers.f"
      adding 'build/src.macosx-10.5-x86_64-2.7/fortranobject.c' to sources.
      adding 'build/src.macosx-10.5-x86_64-2.7' to include_dirs.
      adding 'build/src.macosx-10.5-x86_64-2.7/pymc/gp/cov_funs/isotropic_cov_funs-f2pywrappers.f' to sources.
    building extension "pymc.gp.cov_funs.distances" sources
    f2py options: []
    f2py:> build/src.macosx-10.5-x86_64-2.7/pymc/gp/cov_funs/distancesmodule.c
    Reading fortran codes...
    	Reading file 'pymc/gp/cov_funs/distances.f' (format:fix,strict)
    Post-processing...
    	Block: distances
    			Block: euclidean
    			Block: geographic
    			Block: paniso_geo_rad
    			Block: aniso_geo_rad
    Post-processing (stage 2)...
    Building modules...
    	Building module "distances"...
    		Constructing wrapper function "euclidean"...
    		  euclidean(d,x,y,[cmin,cmax,symm])
    		Constructing wrapper function "geographic"...
    		  geographic(d,x,y,[cmin,cmax,symm])
    		Constructing wrapper function "paniso_geo_rad"...
    		  paniso_geo_rad(d,x,y,ctrs,scals,[cmin,cmax,symm])
    		Constructing wrapper function "aniso_geo_rad"...
    		  aniso_geo_rad(d,x,y,inc,ecc,[cmin,cmax,symm])
    	Wrote C/API module "distances" to file "build/src.macosx-10.5-x86_64-2.7/pymc/gp/cov_funs/distancesmodule.c"
      adding 'build/src.macosx-10.5-x86_64-2.7/fortranobject.c' to sources.
      adding 'build/src.macosx-10.5-x86_64-2.7' to include_dirs.
    build_src: building npy-pkg config files
    
    warning: no files found matching 'README.txt'
    warning: no files found matching 'INSTALL.txt'
    warning: no files found matching 'docs/UserGuide.pdf'
Installing collected packages: pymc
  Running setup.py install for pymc
    unifing config_cc, config, build_clib, build_ext, build commands --compiler options
    unifing config_fc, config, build_clib, build_ext, build commands --fcompiler options
    build_src
    building extension "pymc.flib" sources
    f2py options: ['skip:ppnd7']
      adding 'build/src.macosx-10.5-x86_64-2.7/fortranobject.c' to sources.
      adding 'build/src.macosx-10.5-x86_64-2.7' to include_dirs.
      adding 'build/src.macosx-10.5-x86_64-2.7/pymc/flib-f2pywrappers.f' to sources.
    building extension "pymc.LazyFunction" sources
    building extension "pymc.Container_values" sources
    building extension "pymc.gp.linalg_utils" sources
    f2py options: []
      adding 'build/src.macosx-10.5-x86_64-2.7/fortranobject.c' to sources.
      adding 'build/src.macosx-10.5-x86_64-2.7' to include_dirs.
    building extension "pymc.gp.incomplete_chol" sources
    f2py options: []
      adding 'build/src.macosx-10.5-x86_64-2.7/fortranobject.c' to sources.
      adding 'build/src.macosx-10.5-x86_64-2.7' to include_dirs.
    building extension "pymc.gp.cov_funs.isotropic_cov_funs" sources
    f2py options: []
      adding 'build/src.macosx-10.5-x86_64-2.7/fortranobject.c' to sources.
      adding 'build/src.macosx-10.5-x86_64-2.7' to include_dirs.
      adding 'build/src.macosx-10.5-x86_64-2.7/pymc/gp/cov_funs/isotropic_cov_funs-f2pywrappers.f' to sources.
    building extension "pymc.gp.cov_funs.distances" sources
    f2py options: []
      adding 'build/src.macosx-10.5-x86_64-2.7/fortranobject.c' to sources.
      adding 'build/src.macosx-10.5-x86_64-2.7' to include_dirs.
    build_src: building npy-pkg config files
    customize UnixCCompiler
    customize UnixCCompiler using build_ext
    customize Gnu95FCompiler
    Found executable /usr/local/bin/gfortran
    customize Gnu95FCompiler
    customize Gnu95FCompiler using build_ext
    building 'pymc.flib' extension
    compiling C sources
    C compiler: gcc -fno-strict-aliasing -I//anaconda/include -arch x86_64 -DNDEBUG -g -fwrapv -O3 -Wall -Wstrict-prototypes -I/usr/local/opt/zlib/include
    
    compile options: '-DNO_ATLAS_INFO=3 -Ibuild/src.macosx-10.5-x86_64-2.7 -I//anaconda/lib/python2.7/site-packages/numpy/core/include -I//anaconda/include/python2.7 -c'
    extra options: '-msse3'
    gcc: cephes/i0.c
    gcc: cephes/c2f.c
    gcc: build/src.macosx-10.5-x86_64-2.7/fortranobject.c
    In file included from build/src.macosx-10.5-x86_64-2.7/fortranobject.c:2:
    In file included from build/src.macosx-10.5-x86_64-2.7/fortranobject.h:13:
    In file included from //anaconda/lib/python2.7/site-packages/numpy/core/include/numpy/arrayobject.h:15:
    In file included from //anaconda/lib/python2.7/site-packages/numpy/core/include/numpy/ndarrayobject.h:17:
    In file included from //anaconda/lib/python2.7/site-packages/numpy/core/include/numpy/ndarraytypes.h:1728:
    //anaconda/lib/python2.7/site-packages/numpy/core/include/numpy/npy_deprecated_api.h:11:2: warning: "Using deprecated NumPy API, disable it by #defining NPY_NO_DEPRECATED_API NPY_1_7_API_VERSION" [-W#warnings]
    #warning "Using deprecated NumPy API, disable it by #defining NPY_NO_DEPRECATED_API NPY_1_7_API_VERSION"
     ^
    build/src.macosx-10.5-x86_64-2.7/fortranobject.c:338:30: warning: equality comparison with extraneous parentheses [-Wparentheses-equality]
            if ((fp->defs[i].func==NULL)) {
                 ~~~~~~~~~~~~~~~~^~~~~~
    build/src.macosx-10.5-x86_64-2.7/fortranobject.c:338:30: note: remove extraneous parentheses around the comparison to silence this warning
            if ((fp->defs[i].func==NULL)) {
                ~                ^     ~
    build/src.macosx-10.5-x86_64-2.7/fortranobject.c:338:30: note: use '=' to turn this equality comparison into an assignment
            if ((fp->defs[i].func==NULL)) {
                                 ^~
                                 =
    2 warnings generated.
    gcc: build/src.macosx-10.5-x86_64-2.7/pymc/flibmodule.c
    In file included from build/src.macosx-10.5-x86_64-2.7/pymc/flibmodule.c:18:
    In file included from build/src.macosx-10.5-x86_64-2.7/fortranobject.h:13:
    In file included from //anaconda/lib/python2.7/site-packages/numpy/core/include/numpy/arrayobject.h:15:
    In file included from //anaconda/lib/python2.7/site-packages/numpy/core/include/numpy/ndarrayobject.h:17:
    In file included from //anaconda/lib/python2.7/site-packages/numpy/core/include/numpy/ndarraytypes.h:1728:
    //anaconda/lib/python2.7/site-packages/numpy/core/include/numpy/npy_deprecated_api.h:11:2: warning: "Using deprecated NumPy API, disable it by #defining NPY_NO_DEPRECATED_API NPY_1_7_API_VERSION" [-W#warnings]
    #warning "Using deprecated NumPy API, disable it by #defining NPY_NO_DEPRECATED_API NPY_1_7_API_VERSION"
     ^
    build/src.macosx-10.5-x86_64-2.7/pymc/flibmodule.c:16934:7: warning: array index 2 is past the end of the array (which contains 2 elements) [-Warray-bounds]
      d = shape(x,2);
          ^       ~
    build/src.macosx-10.5-x86_64-2.7/pymc/flibmodule.c:86:24: note: expanded from macro 'shape'
    #define shape(var,dim) var ## _Dims[dim]
                           ^
    <scratch space>:394:1: note: expanded from here
    x_Dims
    ^
    build/src.macosx-10.5-x86_64-2.7/pymc/flibmodule.c:16835:3: note: array 'x_Dims' declared here
      npy_intp x_Dims[2] = {-1, -1};
      ^
    build/src.macosx-10.5-x86_64-2.7/pymc/flibmodule.c:181:12: warning: unused function 'f2py_size' [-Wunused-function]
    static int f2py_size(PyArrayObject* var, ...)
               ^
    3 warnings generated.
    gcc: cephes/chbevl.c
    compiling Fortran sources
    Fortran f77 compiler: /usr/local/bin/gfortran -Wall -ffixed-form -fno-second-underscore -m64 -fPIC -O3 -funroll-loops
    Fortran f90 compiler: /usr/local/bin/gfortran -Wall -fno-second-underscore -m64 -fPIC -O3 -funroll-loops
    Fortran fix compiler: /usr/local/bin/gfortran -Wall -ffixed-form -fno-second-underscore -Wall -fno-second-underscore -m64 -fPIC -O3 -funroll-loops
    compile options: '-DNO_ATLAS_INFO=3 -Ibuild/src.macosx-10.5-x86_64-2.7 -I//anaconda/lib/python2.7/site-packages/numpy/core/include -I//anaconda/include/python2.7 -c'
    gfortran:f77: pymc/flib.f
    Warning: Nonconforming tab character in column 1 of line 509
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    pymc/flib.f:316.55:
    
          DOUBLE PRECISION mu_now, tau_now, alph_now, d_now, like
                                                           1
    Warning: Unused variable 'd_now' declared at (1)
    pymc/flib.f:314.42:
    
          INTEGER i, nx, nalph, nmu, ntau, tnx
                                              1
    Warning: Unused variable 'tnx' declared at (1)
    pymc/flib.f:442.71:
    
          subroutine uniform_grad_x(x,lower,upper,n,nlower,nupper,gradxlike)
                                                                           1
    Warning: Unused dummy argument 'gradxlike' at (1)
    pymc/flib.f:461.40:
    
            DOUBLE PRECISION like, low, high
                                            1
    Warning: Unused variable 'high' declared at (1)
    pymc/flib.f:458.36:
    
            INTEGER n, nlower, nupper, i
                                        1
    Warning: Unused variable 'i' declared at (1)
    pymc/flib.f:461.29:
    
            DOUBLE PRECISION like, low, high
                                 1
    Warning: Unused variable 'like' declared at (1)
    pymc/flib.f:461.34:
    
            DOUBLE PRECISION like, low, high
                                      1
    Warning: Unused variable 'low' declared at (1)
    pymc/flib.f:442.39:
    
          subroutine uniform_grad_x(x,lower,upper,n,nlower,nupper,gradxlike)
                                           1
    Warning: Unused dummy argument 'lower' at (1)
    pymc/flib.f:442.45:
    
          subroutine uniform_grad_x(x,lower,upper,n,nlower,nupper,gradxlike)
                                                 1
    Warning: Unused dummy argument 'upper' at (1)
    pymc/flib.f:442.33:
    
          subroutine uniform_grad_x(x,lower,upper,n,nlower,nupper,gradxlike)
                                     1
    Warning: Unused dummy argument 'x' at (1)
    pymc/flib.f:692.41:
    
          DOUBLE PRECISION aa, cc, sigma, pdf
                                             1
    Warning: Unused variable 'pdf' declared at (1)
    pymc/flib.f:760.41:
    
          DOUBLE PRECISION aa, cc, sigma, pdf
                                             1
    Warning: Unused variable 'pdf' declared at (1)
    pymc/flib.f:834.41:
    
          DOUBLE PRECISION aa, cc, sigma, pdf
                                             1
    Warning: Unused variable 'pdf' declared at (1)
    pymc/flib.f:906.41:
    
          DOUBLE PRECISION aa, cc, sigma, pdf
                                             1
    Warning: Unused variable 'pdf' declared at (1)
    pymc/flib.f:976.41:
    
          DOUBLE PRECISION aa, cc, sigma, pdf
                                             1
    Warning: Unused variable 'pdf' declared at (1)
    pymc/flib.f:1186.29:
    
          DOUBLE PRECISION factln
                                 1
    Warning: Unused variable 'factln' declared at (1)
    pymc/flib.f:1185.51:
    
          DOUBLE PRECISION sumx, mut, infinity, sumfact
                                                       1
    Warning: Unused variable 'sumfact' declared at (1)
    pymc/flib.f:1185.27:
    
          DOUBLE PRECISION sumx, mut, infinity, sumfact
                               1
    Warning: Unused variable 'sumx' declared at (1)
    pymc/flib.f:1300.55:
    
          DOUBLE PRECISION mu(nmu), gradlike(nmu),grad, cdf
                                                           1
    Warning: Unused variable 'cdf' declared at (1)
    pymc/flib.f:1302.29:
    
          DOUBLE PRECISION factln, gammq
                                 1
    Warning: Unused variable 'factln' declared at (1)
    pymc/flib.f:1302.36:
    
          DOUBLE PRECISION factln, gammq
                                        1
    Warning: Unused variable 'gammq' declared at (1)
    pymc/flib.f:1301.59:
    
          DOUBLE PRECISION sumx, mut, infinity, sumfact, sumcdf
                                                               1
    Warning: Unused variable 'sumcdf' declared at (1)
    pymc/flib.f:1301.51:
    
          DOUBLE PRECISION sumx, mut, infinity, sumfact, sumcdf
                                                       1
    Warning: Unused variable 'sumfact' declared at (1)
    pymc/flib.f:1301.27:
    
          DOUBLE PRECISION sumx, mut, infinity, sumfact, sumcdf
                               1
    Warning: Unused variable 'sumx' declared at (1)
    pymc/flib.f:1402.29:
    
          DOUBLE PRECISION gammln
                                 1
    Warning: Unused variable 'gammln' declared at (1)
    pymc/flib.f:2154.40:
    
          DOUBLE PRECISION gradlike(n), grad
                                            1
    Warning: Unused variable 'grad' declared at (1)
    pymc/flib.f:2665.29:
    
          DOUBLE PRECISION gammln
                                 1
    Warning: Unused variable 'gammln' declared at (1)
    pymc/flib.f:2728.29:
    
          DOUBLE PRECISION gammln, psi
                                 1
    Warning: Unused variable 'gammln' declared at (1)
    pymc/flib.f:2793.29:
    
          DOUBLE PRECISION gammln
                                 1
    Warning: Unused variable 'gammln' declared at (1)
    pymc/flib.f:2903.29:
    
          DOUBLE PRECISION gammln
                                 1
    Warning: Unused variable 'gammln' declared at (1)
    pymc/flib.f:2959.29:
    
          DOUBLE PRECISION gammln, psi
                                 1
    Warning: Unused variable 'gammln' declared at (1)
    pymc/flib.f:3021.29:
    
          DOUBLE PRECISION gammln
                                 1
    Warning: Unused variable 'gammln' declared at (1)
    pymc/flib.f:3396.58:
    
          DOUBLE PRECISION gradlike(nx), atmp, btmp, PI, glike
                                                              1
    Warning: Unused variable 'glike' declared at (1)
    pymc/flib.f:3646.37:
    
          DOUBLE PRECISION gammln, factln
                                         1
    Warning: Unused variable 'factln' declared at (1)
    pymc/flib.f:3646.29:
    
          DOUBLE PRECISION gammln, factln
                                 1
    Warning: Unused variable 'gammln' declared at (1)
    pymc/flib.f:3706.37:
    
          DOUBLE PRECISION gammln, factln, psi
                                         1
    Warning: Unused variable 'factln' declared at (1)
    pymc/flib.f:3706.29:
    
          DOUBLE PRECISION gammln, factln, psi
                                 1
    Warning: Unused variable 'gammln' declared at (1)
    pymc/flib.f:3836.29:
    
          DOUBLE PRECISION factln
                                 1
    Warning: Unused variable 'factln' declared at (1)
    pymc/flib.f:4039.26:
    
          DOUBLE PRECISION psi
                              1
    Warning: Unused variable 'psi' declared at (1)
    pymc/flib.f:4266.29:
    
          DOUBLE PRECISION gammln, psi
                                 1
    Warning: Unused variable 'gammln' declared at (1)
    pymc/flib.f:4332.29:
    
          DOUBLE PRECISION gammln, psi
                                 1
    Warning: Unused variable 'gammln' declared at (1)
    pymc/flib.f:5184.35:
    
          DOUBLE PRECISION like, factln, infinity, sump
                                       1
    Warning: Unused variable 'factln' declared at (1)
    pymc/flib.f:5186.23:
    
          INTEGER i,j,n_tmp
                           1
    Warning: Unused variable 'n_tmp' declared at (1)
    pymc/flib.f:5434.26:
    
          DOUBLE PRECISION tmp
                              1
    Warning: Unused variable 'tmp' declared at (1)
    pymc/flib.f:5488.25:
    
          DOUBLE PRECISION i0
                             1
    Warning: Unused variable 'i0' declared at (1)
    pymc/flib.f:5481.26:
    
          DOUBLE PRECISION tmp
                              1
    Warning: Unused variable 'tmp' declared at (1)
    pymc/flib.f:5535.25:
    
          DOUBLE PRECISION i0
                             1
    Warning: Unused variable 'i0' declared at (1)
    pymc/flib.f:5528.26:
    
          DOUBLE PRECISION tmp
                              1
    Warning: Unused variable 'tmp' declared at (1)
    pymc/flib.f: In function 'elgs':
    pymc/flib.f:4882:0: warning: 'k' may be used uninitialized in this function [-Wmaybe-uninitialized]
    pymc/flib.f: In function 'exponweib_gl':
    pymc/flib.f:778:0: warning: 'nc' may be used uninitialized in this function [-Wuninitialized]
    pymc/flib.f: In function 'exponweib_gs':
    pymc/flib.f:994:0: warning: 'nc' may be used uninitialized in this function [-Wuninitialized]
    gfortran:f77: pymc/histogram.f
    gfortran:f77: pymc/flib_blas.f
    pymc/flib_blas.f:202.25:
    
          DOUBLE PRECISION PI
                             1
    Warning: Unused variable 'pi' declared at (1)
    gfortran:f77: pymc/blas_wrap.f
    gfortran:f77: pymc/math.f
    pymc/math.f:396.6:
    
          DOUBLE PRECISION FUNCTION DERF(X)
          1
    Warning: 'derf' declared at (1) is also the name of an intrinsic.  It can only be called via an explicit interface or if declared EXTERNAL.
    pymc/math.f:417.6:
    
          DOUBLE PRECISION FUNCTION DERFC(X)
          1
    Warning: 'derfc' declared at (1) is also the name of an intrinsic.  It can only be called via an explicit interface or if declared EXTERNAL.
    gfortran:f77: pymc/gibbsit.f
    pymc/gibbsit.f:2160.5:
    
      215 IF (R .GT. .5898437) GO TO 220
         1
    Warning: Label 215 at (1) defined but not used
    pymc/gibbsit.f:2077.5:
    
      115 IF (R .GT. .5898437) GO TO 120
         1
    Warning: Label 115 at (1) defined but not used
    pymc/gibbsit.f:2064.5:
    
       15 IF (KFLAG.GE.1) GO TO 30
         1
    Warning: Label 15 at (1) defined but not used
    pymc/gibbsit.f:1204.48:
    
            cutpt = empquant(original,iteracnt,qhat,work)
                                                    1
    Warning: Type mismatch in argument 'work' at (1); passed INTEGER(4) to REAL(8)
    gfortran:f77: build/src.macosx-10.5-x86_64-2.7/pymc/flib-f2pywrappers.f
    /usr/local/bin/gfortran -Wall -L/usr/local/opt/zlib/lib build/temp.macosx-10.5-x86_64-2.7/cephes/i0.o build/temp.macosx-10.5-x86_64-2.7/cephes/c2f.o build/temp.macosx-10.5-x86_64-2.7/cephes/chbevl.o build/temp.macosx-10.5-x86_64-2.7/build/src.macosx-10.5-x86_64-2.7/pymc/flibmodule.o build/temp.macosx-10.5-x86_64-2.7/build/src.macosx-10.5-x86_64-2.7/fortranobject.o build/temp.macosx-10.5-x86_64-2.7/pymc/flib.o build/temp.macosx-10.5-x86_64-2.7/pymc/histogram.o build/temp.macosx-10.5-x86_64-2.7/pymc/flib_blas.o build/temp.macosx-10.5-x86_64-2.7/pymc/blas_wrap.o build/temp.macosx-10.5-x86_64-2.7/pymc/math.o build/temp.macosx-10.5-x86_64-2.7/pymc/gibbsit.o build/temp.macosx-10.5-x86_64-2.7/build/src.macosx-10.5-x86_64-2.7/pymc/flib-f2pywrappers.o -L/usr/local/Cellar/gfortran/4.7.2/gfortran/lib/gcc/x86_64-apple-darwin12.2.0/4.7.2 -lgfortran -o build/lib.macosx-10.5-x86_64-2.7/pymc/flib.so -Wl,-framework -Wl,Accelerate
    Undefined symbols for architecture x86_64:
      "_PyArg_ParseTupleAndKeywords", referenced from:
          _f2py_rout_flib_symmetrize in flibmodule.o
          _f2py_rout_flib_logsum in flibmodule.o
          _f2py_rout_flib_logsum_cpx in flibmodule.o
          _f2py_rout_flib_combinationln in flibmodule.o
          _f2py_rout_flib_expand_triangular in flibmodule.o
          _f2py_rout_flib_mod_to_circle in flibmodule.o
          _f2py_rout_flib_standardize in flibmodule.o
          ...
      "_PyCObject_AsVoidPtr", referenced from:
          _initflib in flibmodule.o
          _F2PyCapsule_AsVoidPtr in fortranobject.o
      "_PyCObject_FromVoidPtr", referenced from:
          _fortran_getattr in fortranobject.o
          _F2PyCapsule_FromVoidPtr in fortranobject.o
      "_PyCObject_Type", referenced from:
          _initflib in flibmodule.o
          _F2PyCapsule_Check in fortranobject.o
      "_PyComplex_FromDoubles", referenced from:
          _f2py_rout_flib_logsum_cpx in flibmodule.o
      "_PyComplex_Type", referenced from:
          _int_from_pyobj in flibmodule.o
          _double_from_pyobj in flibmodule.o
      "_PyDict_DelItemString", referenced from:
          _fortran_setattr in fortranobject.o
      "_PyDict_GetItemString", referenced from:
          _initflib in flibmodule.o
          _fortran_getattr in fortranobject.o
      "_PyDict_New", referenced from:
          _PyFortranObject_New in fortranobject.o
          _PyFortranObject_NewAsAttr in fortranobject.o
          _fortran_setattr in fortranobject.o
      "_PyDict_SetItemString", referenced from:
          _initflib in flibmodule.o
          _F2PyDict_SetItemString in fortranobject.o
          _PyFortranObject_New in fortranobject.o
          _fortran_getattr in fortranobject.o
          _fortran_setattr in fortranobject.o
      "_PyErr_Clear", referenced from:
          _int_from_pyobj in flibmodule.o
          _double_from_pyobj in flibmodule.o
          _F2PyDict_SetItemString in fortranobject.o
          _fortran_repr in fortranobject.o
      "_PyErr_Format", referenced from:
          _initflib in flibmodule.o
          _fortran_call in fortranobject.o
      "_PyErr_NewException", referenced from:
          _initflib in flibmodule.o
      "_PyErr_Occurred", referenced from:
          _initflib in flibmodule.o
          _f2py_rout_flib_symmetrize in flibmodule.o
          _f2py_rout_flib_logsum in flibmodule.o
          _f2py_rout_flib_logsum_cpx in flibmodule.o
          _f2py_rout_flib_combinationln in flibmodule.o
          _f2py_rout_flib_expand_triangular in flibmodule.o
          _f2py_rout_flib_mod_to_circle in flibmodule.o
          ...
      "_PyErr_Print", referenced from:
          _initflib in flibmodule.o
          _F2PyDict_SetItemString in fortranobject.o
      "_PyErr_SetString", referenced from:
          _initflib in flibmodule.o
          _f2py_rout_flib_symmetrize in flibmodule.o
          _f2py_rout_flib_logsum in flibmodule.o
          _f2py_rout_flib_logsum_cpx in flibmodule.o
          _f2py_rout_flib_expand_triangular in flibmodule.o
          _f2py_rout_flib_mod_to_circle in flibmodule.o
          _f2py_rout_flib_standardize in flibmodule.o
          ...
      "_PyEval_RestoreThread", referenced from:
          _f2py_rout_flib_symmetrize in flibmodule.o
          _f2py_rout_flib_logsum in flibmodule.o
          _f2py_rout_flib_logsum_cpx in flibmodule.o
          _f2py_rout_flib_expand_triangular in flibmodule.o
          _f2py_rout_flib_standardize in flibmodule.o
          _f2py_rout_flib_sn_like in flibmodule.o
          _f2py_rout_flib_rskewnorm in flibmodule.o
          ...
      "_PyEval_SaveThread", referenced from:
          _f2py_rout_flib_symmetrize in flibmodule.o
          _f2py_rout_flib_logsum in flibmodule.o
          _f2py_rout_flib_logsum_cpx in flibmodule.o
          _f2py_rout_flib_expand_triangular in flibmodule.o
          _f2py_rout_flib_standardize in flibmodule.o
          _f2py_rout_flib_sn_like in flibmodule.o
          _f2py_rout_flib_rskewnorm in flibmodule.o
          ...
      "_PyExc_AttributeError", referenced from:
          _initflib in flibmodule.o
          _fortran_setattr in fortranobject.o
      "_PyExc_ImportError", referenced from:
          _initflib in flibmodule.o
      "_PyExc_MemoryError", referenced from:
          _string_from_pyobj in flibmodule.o
      "_PyExc_RuntimeError", referenced from:
          _initflib in flibmodule.o
          _fortran_call in fortranobject.o
      "_PyExc_TypeError", referenced from:
          _fortran_call in fortranobject.o
          _array_from_pyobj in fortranobject.o
      "_PyExc_ValueError", referenced from:
          _string_from_pyobj in flibmodule.o
          _array_from_pyobj in fortranobject.o
      "_PyFloat_Type", referenced from:
          _double_from_pyobj in flibmodule.o
      "_PyImport_ImportModule", referenced from:
          _initflib in flibmodule.o
      "_PyMem_Free", referenced from:
          _fortran_dealloc in fortranobject.o
      "_PyModule_GetDict", referenced from:
          _initflib in flibmodule.o
      "_PyNumber_Float", referenced from:
          _double_from_pyobj in flibmodule.o
      "_PyNumber_Int", referenced from:
          _int_from_pyobj in flibmodule.o
      "_PyObject_GetAttrString", referenced from:
          _initflib in flibmodule.o
          _int_from_pyobj in flibmodule.o
          _double_from_pyobj in flibmodule.o
          _fortran_repr in fortranobject.o
      "_PyObject_IsTrue", referenced from:
          _f2py_rout_flib_constrain in flibmodule.o
      "_PyObject_SetAttrString", referenced from:
          _initflib in flibmodule.o
      "_PyObject_Str", referenced from:
          _string_from_pyobj in flibmodule.o
          _array_from_pyobj in fortranobject.o
      "_PyObject_Type", referenced from:
          _array_from_pyobj in fortranobject.o
      "_PySequence_Check", referenced from:
          _int_from_pyobj in flibmodule.o
          _double_from_pyobj in flibmodule.o
      "_PySequence_GetItem", referenced from:
          _int_from_pyobj in flibmodule.o
          _double_from_pyobj in flibmodule.o
      "_PyString_AsString", referenced from:
          _fortran_repr in fortranobject.o
          _array_from_pyobj in fortranobject.o
      "_PyString_ConcatAndDel", referenced from:
          _fortran_getattr in fortranobject.o
      "_PyString_FromFormat", referenced from:
          _fortran_repr in fortranobject.o
      "_PyString_FromString", referenced from:
          _initflib in flibmodule.o
          _fortran_getattr in fortranobject.o
          _fortran_repr in fortranobject.o
      "_PyType_IsSubtype", referenced from:
          _int_from_pyobj in flibmodule.o
          _double_from_pyobj in flibmodule.o
          _string_from_pyobj in flibmodule.o
          _array_from_pyobj in fortranobject.o
      "_PyType_Type", referenced from:
          _initflib in flibmodule.o
      "_Py_BuildValue", referenced from:
          _f2py_rout_flib_symmetrize in flibmodule.o
          _f2py_rout_flib_logsum in flibmodule.o
          _f2py_rout_flib_logsum_cpx in flibmodule.o
          _f2py_rout_flib_combinationln in flibmodule.o
          _f2py_rout_flib_expand_triangular in flibmodule.o
          _f2py_rout_flib_mod_to_circle in flibmodule.o
          _f2py_rout_flib_standardize in flibmodule.o
          ...
      "_Py_FindMethod", referenced from:
          _fortran_getattr in fortranobject.o
      "_Py_InitModule4_64", referenced from:
          _initflib in flibmodule.o
      "__PyObject_New", referenced from:
          _PyFortranObject_New in fortranobject.o
          _PyFortranObject_NewAsAttr in fortranobject.o
      "__Py_NoneStruct", referenced from:
          _f2py_rout_flib_symmetrize in flibmodule.o
          _f2py_rout_flib_logsum in flibmodule.o
          _f2py_rout_flib_logsum_cpx in flibmodule.o
          _f2py_rout_flib_combinationln in flibmodule.o
          _f2py_rout_flib_expand_triangular in flibmodule.o
          _f2py_rout_flib_mod_to_circle in flibmodule.o
          _f2py_rout_flib_standardize in flibmodule.o
          ...
    ld: symbol(s) not found for architecture x86_64
    collect2: error: ld returned 1 exit status
    Undefined symbols for architecture x86_64:
      "_PyArg_ParseTupleAndKeywords", referenced from:
          _f2py_rout_flib_symmetrize in flibmodule.o
          _f2py_rout_flib_logsum in flibmodule.o
          _f2py_rout_flib_logsum_cpx in flibmodule.o
          _f2py_rout_flib_combinationln in flibmodule.o
          _f2py_rout_flib_expand_triangular in flibmodule.o
          _f2py_rout_flib_mod_to_circle in flibmodule.o
          _f2py_rout_flib_standardize in flibmodule.o
          ...
      "_PyCObject_AsVoidPtr", referenced from:
          _initflib in flibmodule.o
          _F2PyCapsule_AsVoidPtr in fortranobject.o
      "_PyCObject_FromVoidPtr", referenced from:
          _fortran_getattr in fortranobject.o
          _F2PyCapsule_FromVoidPtr in fortranobject.o
      "_PyCObject_Type", referenced from:
          _initflib in flibmodule.o
          _F2PyCapsule_Check in fortranobject.o
      "_PyComplex_FromDoubles", referenced from:
          _f2py_rout_flib_logsum_cpx in flibmodule.o
      "_PyComplex_Type", referenced from:
          _int_from_pyobj in flibmodule.o
          _double_from_pyobj in flibmodule.o
      "_PyDict_DelItemString", referenced from:
          _fortran_setattr in fortranobject.o
      "_PyDict_GetItemString", referenced from:
          _initflib in flibmodule.o
          _fortran_getattr in fortranobject.o
      "_PyDict_New", referenced from:
          _PyFortranObject_New in fortranobject.o
          _PyFortranObject_NewAsAttr in fortranobject.o
          _fortran_setattr in fortranobject.o
      "_PyDict_SetItemString", referenced from:
          _initflib in flibmodule.o
          _F2PyDict_SetItemString in fortranobject.o
          _PyFortranObject_New in fortranobject.o
          _fortran_getattr in fortranobject.o
          _fortran_setattr in fortranobject.o
      "_PyErr_Clear", referenced from:
          _int_from_pyobj in flibmodule.o
          _double_from_pyobj in flibmodule.o
          _F2PyDict_SetItemString in fortranobject.o
          _fortran_repr in fortranobject.o
      "_PyErr_Format", referenced from:
          _initflib in flibmodule.o
          _fortran_call in fortranobject.o
      "_PyErr_NewException", referenced from:
          _initflib in flibmodule.o
      "_PyErr_Occurred", referenced from:
          _initflib in flibmodule.o
          _f2py_rout_flib_symmetrize in flibmodule.o
          _f2py_rout_flib_logsum in flibmodule.o
          _f2py_rout_flib_logsum_cpx in flibmodule.o
          _f2py_rout_flib_combinationln in flibmodule.o
          _f2py_rout_flib_expand_triangular in flibmodule.o
          _f2py_rout_flib_mod_to_circle in flibmodule.o
          ...
      "_PyErr_Print", referenced from:
          _initflib in flibmodule.o
          _F2PyDict_SetItemString in fortranobject.o
      "_PyErr_SetString", referenced from:
          _initflib in flibmodule.o
          _f2py_rout_flib_symmetrize in flibmodule.o
          _f2py_rout_flib_logsum in flibmodule.o
          _f2py_rout_flib_logsum_cpx in flibmodule.o
          _f2py_rout_flib_expand_triangular in flibmodule.o
          _f2py_rout_flib_mod_to_circle in flibmodule.o
          _f2py_rout_flib_standardize in flibmodule.o
          ...
      "_PyEval_RestoreThread", referenced from:
          _f2py_rout_flib_symmetrize in flibmodule.o
          _f2py_rout_flib_logsum in flibmodule.o
          _f2py_rout_flib_logsum_cpx in flibmodule.o
          _f2py_rout_flib_expand_triangular in flibmodule.o
          _f2py_rout_flib_standardize in flibmodule.o
          _f2py_rout_flib_sn_like in flibmodule.o
          _f2py_rout_flib_rskewnorm in flibmodule.o
          ...
      "_PyEval_SaveThread", referenced from:
          _f2py_rout_flib_symmetrize in flibmodule.o
          _f2py_rout_flib_logsum in flibmodule.o
          _f2py_rout_flib_logsum_cpx in flibmodule.o
          _f2py_rout_flib_expand_triangular in flibmodule.o
          _f2py_rout_flib_standardize in flibmodule.o
          _f2py_rout_flib_sn_like in flibmodule.o
          _f2py_rout_flib_rskewnorm in flibmodule.o
          ...
      "_PyExc_AttributeError", referenced from:
          _initflib in flibmodule.o
          _fortran_setattr in fortranobject.o
      "_PyExc_ImportError", referenced from:
          _initflib in flibmodule.o
      "_PyExc_MemoryError", referenced from:
          _string_from_pyobj in flibmodule.o
      "_PyExc_RuntimeError", referenced from:
          _initflib in flibmodule.o
          _fortran_call in fortranobject.o
      "_PyExc_TypeError", referenced from:
          _fortran_call in fortranobject.o
          _array_from_pyobj in fortranobject.o
      "_PyExc_ValueError", referenced from:
          _string_from_pyobj in flibmodule.o
          _array_from_pyobj in fortranobject.o
      "_PyFloat_Type", referenced from:
          _double_from_pyobj in flibmodule.o
      "_PyImport_ImportModule", referenced from:
          _initflib in flibmodule.o
      "_PyMem_Free", referenced from:
          _fortran_dealloc in fortranobject.o
      "_PyModule_GetDict", referenced from:
          _initflib in flibmodule.o
      "_PyNumber_Float", referenced from:
          _double_from_pyobj in flibmodule.o
      "_PyNumber_Int", referenced from:
          _int_from_pyobj in flibmodule.o
      "_PyObject_GetAttrString", referenced from:
          _initflib in flibmodule.o
          _int_from_pyobj in flibmodule.o
          _double_from_pyobj in flibmodule.o
          _fortran_repr in fortranobject.o
      "_PyObject_IsTrue", referenced from:
          _f2py_rout_flib_constrain in flibmodule.o
      "_PyObject_SetAttrString", referenced from:
          _initflib in flibmodule.o
      "_PyObject_Str", referenced from:
          _string_from_pyobj in flibmodule.o
          _array_from_pyobj in fortranobject.o
      "_PyObject_Type", referenced from:
          _array_from_pyobj in fortranobject.o
      "_PySequence_Check", referenced from:
          _int_from_pyobj in flibmodule.o
          _double_from_pyobj in flibmodule.o
      "_PySequence_GetItem", referenced from:
          _int_from_pyobj in flibmodule.o
          _double_from_pyobj in flibmodule.o
      "_PyString_AsString", referenced from:
          _fortran_repr in fortranobject.o
          _array_from_pyobj in fortranobject.o
      "_PyString_ConcatAndDel", referenced from:
          _fortran_getattr in fortranobject.o
      "_PyString_FromFormat", referenced from:
          _fortran_repr in fortranobject.o
      "_PyString_FromString", referenced from:
          _initflib in flibmodule.o
          _fortran_getattr in fortranobject.o
          _fortran_repr in fortranobject.o
      "_PyType_IsSubtype", referenced from:
          _int_from_pyobj in flibmodule.o
          _double_from_pyobj in flibmodule.o
          _string_from_pyobj in flibmodule.o
          _array_from_pyobj in fortranobject.o
      "_PyType_Type", referenced from:
          _initflib in flibmodule.o
      "_Py_BuildValue", referenced from:
          _f2py_rout_flib_symmetrize in flibmodule.o
          _f2py_rout_flib_logsum in flibmodule.o
          _f2py_rout_flib_logsum_cpx in flibmodule.o
          _f2py_rout_flib_combinationln in flibmodule.o
          _f2py_rout_flib_expand_triangular in flibmodule.o
          _f2py_rout_flib_mod_to_circle in flibmodule.o
          _f2py_rout_flib_standardize in flibmodule.o
          ...
      "_Py_FindMethod", referenced from:
          _fortran_getattr in fortranobject.o
      "_Py_InitModule4_64", referenced from:
          _initflib in flibmodule.o
      "__PyObject_New", referenced from:
          _PyFortranObject_New in fortranobject.o
          _PyFortranObject_NewAsAttr in fortranobject.o
      "__Py_NoneStruct", referenced from:
          _f2py_rout_flib_symmetrize in flibmodule.o
          _f2py_rout_flib_logsum in flibmodule.o
          _f2py_rout_flib_logsum_cpx in flibmodule.o
          _f2py_rout_flib_combinationln in flibmodule.o
          _f2py_rout_flib_expand_triangular in flibmodule.o
          _f2py_rout_flib_mod_to_circle in flibmodule.o
          _f2py_rout_flib_standardize in flibmodule.o
          ...
    ld: symbol(s) not found for architecture x86_64
    collect2: error: ld returned 1 exit status
    error: Command "/usr/local/bin/gfortran -Wall -L/usr/local/opt/zlib/lib build/temp.macosx-10.5-x86_64-2.7/cephes/i0.o build/temp.macosx-10.5-x86_64-2.7/cephes/c2f.o build/temp.macosx-10.5-x86_64-2.7/cephes/chbevl.o build/temp.macosx-10.5-x86_64-2.7/build/src.macosx-10.5-x86_64-2.7/pymc/flibmodule.o build/temp.macosx-10.5-x86_64-2.7/build/src.macosx-10.5-x86_64-2.7/fortranobject.o build/temp.macosx-10.5-x86_64-2.7/pymc/flib.o build/temp.macosx-10.5-x86_64-2.7/pymc/histogram.o build/temp.macosx-10.5-x86_64-2.7/pymc/flib_blas.o build/temp.macosx-10.5-x86_64-2.7/pymc/blas_wrap.o build/temp.macosx-10.5-x86_64-2.7/pymc/math.o build/temp.macosx-10.5-x86_64-2.7/pymc/gibbsit.o build/temp.macosx-10.5-x86_64-2.7/build/src.macosx-10.5-x86_64-2.7/pymc/flib-f2pywrappers.o -L/usr/local/Cellar/gfortran/4.7.2/gfortran/lib/gcc/x86_64-apple-darwin12.2.0/4.7.2 -lgfortran -o build/lib.macosx-10.5-x86_64-2.7/pymc/flib.so -Wl,-framework -Wl,Accelerate" failed with exit status 1
    Complete output from command //anaconda/bin/python -c "import setuptools;__file__='/private/var/folders/6l/83vj6nxn6g1b6l2c9ycym4hc0000gn/T/pip_build_olga/pymc/setup.py';exec(compile(open(__file__).read().replace('\r\n', '\n'), __file__, 'exec'))" install --record /var/folders/6l/83vj6nxn6g1b6l2c9ycym4hc0000gn/T/pip-PlF1xm-record/install-record.txt --single-version-externally-managed:
    running install

running build

running config_cc

unifing config_cc, config, build_clib, build_ext, build commands --compiler options

running config_fc

unifing config_fc, config, build_clib, build_ext, build commands --fcompiler options

running build_src

build_src

building extension "pymc.flib" sources

f2py options: ['skip:ppnd7']

  adding 'build/src.macosx-10.5-x86_64-2.7/fortranobject.c' to sources.

  adding 'build/src.macosx-10.5-x86_64-2.7' to include_dirs.

  adding 'build/src.macosx-10.5-x86_64-2.7/pymc/flib-f2pywrappers.f' to sources.

building extension "pymc.LazyFunction" sources

building extension "pymc.Container_values" sources

building extension "pymc.gp.linalg_utils" sources

f2py options: []

  adding 'build/src.macosx-10.5-x86_64-2.7/fortranobject.c' to sources.

  adding 'build/src.macosx-10.5-x86_64-2.7' to include_dirs.

building extension "pymc.gp.incomplete_chol" sources

f2py options: []

  adding 'build/src.macosx-10.5-x86_64-2.7/fortranobject.c' to sources.

  adding 'build/src.macosx-10.5-x86_64-2.7' to include_dirs.

building extension "pymc.gp.cov_funs.isotropic_cov_funs" sources

f2py options: []

  adding 'build/src.macosx-10.5-x86_64-2.7/fortranobject.c' to sources.

  adding 'build/src.macosx-10.5-x86_64-2.7' to include_dirs.

  adding 'build/src.macosx-10.5-x86_64-2.7/pymc/gp/cov_funs/isotropic_cov_funs-f2pywrappers.f' to sources.

building extension "pymc.gp.cov_funs.distances" sources

f2py options: []

  adding 'build/src.macosx-10.5-x86_64-2.7/fortranobject.c' to sources.

  adding 'build/src.macosx-10.5-x86_64-2.7' to include_dirs.

build_src: building npy-pkg config files

running build_py

creating build/lib.macosx-10.5-x86_64-2.7

creating build/lib.macosx-10.5-x86_64-2.7/pymc

copying pymc/__init__.py -> build/lib.macosx-10.5-x86_64-2.7/pymc

copying pymc/calc_utils.py -> build/lib.macosx-10.5-x86_64-2.7/pymc

copying pymc/CircularStochastic.py -> build/lib.macosx-10.5-x86_64-2.7/pymc

copying pymc/CommonDeterministics.py -> build/lib.macosx-10.5-x86_64-2.7/pymc

copying pymc/Container.py -> build/lib.macosx-10.5-x86_64-2.7/pymc

copying pymc/datatypes.py -> build/lib.macosx-10.5-x86_64-2.7/pymc

copying pymc/decorators.py -> build/lib.macosx-10.5-x86_64-2.7/pymc

copying pymc/diagnostics.py -> build/lib.macosx-10.5-x86_64-2.7/pymc

copying pymc/distributions.py -> build/lib.macosx-10.5-x86_64-2.7/pymc

copying pymc/graph.py -> build/lib.macosx-10.5-x86_64-2.7/pymc

copying pymc/InstantiationDecorators.py -> build/lib.macosx-10.5-x86_64-2.7/pymc

copying pymc/Matplot.py -> build/lib.macosx-10.5-x86_64-2.7/pymc

copying pymc/MCMC.py -> build/lib.macosx-10.5-x86_64-2.7/pymc

copying pymc/Model.py -> build/lib.macosx-10.5-x86_64-2.7/pymc

copying pymc/Node.py -> build/lib.macosx-10.5-x86_64-2.7/pymc

copying pymc/NormalApproximation.py -> build/lib.macosx-10.5-x86_64-2.7/pymc

copying pymc/NumpyDeterministics.py -> build/lib.macosx-10.5-x86_64-2.7/pymc

copying pymc/progressbar.py -> build/lib.macosx-10.5-x86_64-2.7/pymc

copying pymc/PyMCObjects.py -> build/lib.macosx-10.5-x86_64-2.7/pymc

copying pymc/ScipyDistributions.py -> build/lib.macosx-10.5-x86_64-2.7/pymc

copying pymc/six.py -> build/lib.macosx-10.5-x86_64-2.7/pymc

copying pymc/StepMethods.py -> build/lib.macosx-10.5-x86_64-2.7/pymc

copying pymc/threadpool.py -> build/lib.macosx-10.5-x86_64-2.7/pymc

copying pymc/utils.py -> build/lib.macosx-10.5-x86_64-2.7/pymc

creating build/lib.macosx-10.5-x86_64-2.7/pymc/database

copying pymc/database/__init__.py -> build/lib.macosx-10.5-x86_64-2.7/pymc/database

copying pymc/database/base.py -> build/lib.macosx-10.5-x86_64-2.7/pymc/database

copying pymc/database/hdf5.py -> build/lib.macosx-10.5-x86_64-2.7/pymc/database

copying pymc/database/hdf5ea.py -> build/lib.macosx-10.5-x86_64-2.7/pymc/database

copying pymc/database/no_trace.py -> build/lib.macosx-10.5-x86_64-2.7/pymc/database

copying pymc/database/pickle.py -> build/lib.macosx-10.5-x86_64-2.7/pymc/database

copying pymc/database/ram.py -> build/lib.macosx-10.5-x86_64-2.7/pymc/database

copying pymc/database/sqlite.py -> build/lib.macosx-10.5-x86_64-2.7/pymc/database

copying pymc/database/txt.py -> build/lib.macosx-10.5-x86_64-2.7/pymc/database

creating build/lib.macosx-10.5-x86_64-2.7/pymc/examples

copying pymc/examples/__init__.py -> build/lib.macosx-10.5-x86_64-2.7/pymc/examples

copying pymc/examples/custom_step.py -> build/lib.macosx-10.5-x86_64-2.7/pymc/examples

copying pymc/examples/disaster_model.py -> build/lib.macosx-10.5-x86_64-2.7/pymc/examples

copying pymc/examples/disaster_model_gof.py -> build/lib.macosx-10.5-x86_64-2.7/pymc/examples

copying pymc/examples/disaster_model_linear.py -> build/lib.macosx-10.5-x86_64-2.7/pymc/examples

copying pymc/examples/disaster_model_missing.py -> build/lib.macosx-10.5-x86_64-2.7/pymc/examples

copying pymc/examples/disaster_model_null.py -> build/lib.macosx-10.5-x86_64-2.7/pymc/examples

copying pymc/examples/gelman_bioassay.py -> build/lib.macosx-10.5-x86_64-2.7/pymc/examples

copying pymc/examples/melanoma.py -> build/lib.macosx-10.5-x86_64-2.7/pymc/examples

copying pymc/examples/melanoma_data.py -> build/lib.macosx-10.5-x86_64-2.7/pymc/examples

copying pymc/examples/weibull_fit.py -> build/lib.macosx-10.5-x86_64-2.7/pymc/examples

copying pymc/examples/zip.py -> build/lib.macosx-10.5-x86_64-2.7/pymc/examples

creating build/lib.macosx-10.5-x86_64-2.7/pymc/examples/gp

copying pymc/examples/gp/__init__.py -> build/lib.macosx-10.5-x86_64-2.7/pymc/examples/gp

copying pymc/examples/gp/basiscov.py -> build/lib.macosx-10.5-x86_64-2.7/pymc/examples/gp

copying pymc/examples/gp/cov.py -> build/lib.macosx-10.5-x86_64-2.7/pymc/examples/gp

copying pymc/examples/gp/covparams.py -> build/lib.macosx-10.5-x86_64-2.7/pymc/examples/gp

copying pymc/examples/gp/MCMC.py -> build/lib.macosx-10.5-x86_64-2.7/pymc/examples/gp

copying pymc/examples/gp/mean.py -> build/lib.macosx-10.5-x86_64-2.7/pymc/examples/gp

copying pymc/examples/gp/mesh_choice.py -> build/lib.macosx-10.5-x86_64-2.7/pymc/examples/gp

copying pymc/examples/gp/observation.py -> build/lib.macosx-10.5-x86_64-2.7/pymc/examples/gp

copying pymc/examples/gp/PyMCmodel.py -> build/lib.macosx-10.5-x86_64-2.7/pymc/examples/gp

copying pymc/examples/gp/realizations.py -> build/lib.macosx-10.5-x86_64-2.7/pymc/examples/gp

creating build/lib.macosx-10.5-x86_64-2.7/pymc/tests

copying pymc/tests/__init__.py -> build/lib.macosx-10.5-x86_64-2.7/pymc/tests

copying pymc/tests/objectmodel.py -> build/lib.macosx-10.5-x86_64-2.7/pymc/tests

copying pymc/tests/test_adaptive.py -> build/lib.macosx-10.5-x86_64-2.7/pymc/tests

copying pymc/tests/test_AM.py -> build/lib.macosx-10.5-x86_64-2.7/pymc/tests

copying pymc/tests/test_basiscov.py -> build/lib.macosx-10.5-x86_64-2.7/pymc/tests

copying pymc/tests/test_binary_step.py -> build/lib.macosx-10.5-x86_64-2.7/pymc/tests

copying pymc/tests/test_container.py -> build/lib.macosx-10.5-x86_64-2.7/pymc/tests

copying pymc/tests/test_convergence.py -> build/lib.macosx-10.5-x86_64-2.7/pymc/tests

copying pymc/tests/test_cov.py -> build/lib.macosx-10.5-x86_64-2.7/pymc/tests

copying pymc/tests/test_database.py -> build/lib.macosx-10.5-x86_64-2.7/pymc/tests

copying pymc/tests/test_distributions.py -> build/lib.macosx-10.5-x86_64-2.7/pymc/tests

copying pymc/tests/test_GP_MCMC.py -> build/lib.macosx-10.5-x86_64-2.7/pymc/tests

copying pymc/tests/test_gradients.py -> build/lib.macosx-10.5-x86_64-2.7/pymc/tests

copying pymc/tests/test_graph.py -> build/lib.macosx-10.5-x86_64-2.7/pymc/tests

copying pymc/tests/test_instantiation.py -> build/lib.macosx-10.5-x86_64-2.7/pymc/tests

copying pymc/tests/test_interactive.py -> build/lib.macosx-10.5-x86_64-2.7/pymc/tests

copying pymc/tests/test_MCMCSampler.py -> build/lib.macosx-10.5-x86_64-2.7/pymc/tests

copying pymc/tests/test_mean.py -> build/lib.macosx-10.5-x86_64-2.7/pymc/tests

copying pymc/tests/test_missing.py -> build/lib.macosx-10.5-x86_64-2.7/pymc/tests

copying pymc/tests/test_norm_approx.py -> build/lib.macosx-10.5-x86_64-2.7/pymc/tests

copying pymc/tests/test_observation.py -> build/lib.macosx-10.5-x86_64-2.7/pymc/tests

copying pymc/tests/test_realization.py -> build/lib.macosx-10.5-x86_64-2.7/pymc/tests

copying pymc/tests/test_special_methods.py -> build/lib.macosx-10.5-x86_64-2.7/pymc/tests

copying pymc/tests/test_utils.py -> build/lib.macosx-10.5-x86_64-2.7/pymc/tests

creating build/lib.macosx-10.5-x86_64-2.7/pymc/gp

copying pymc/gp/__init__.py -> build/lib.macosx-10.5-x86_64-2.7/pymc/gp

copying pymc/gp/BasisCovariance.py -> build/lib.macosx-10.5-x86_64-2.7/pymc/gp

copying pymc/gp/Covariance.py -> build/lib.macosx-10.5-x86_64-2.7/pymc/gp

copying pymc/gp/FullRankCovariance.py -> build/lib.macosx-10.5-x86_64-2.7/pymc/gp

copying pymc/gp/gp_submodel.py -> build/lib.macosx-10.5-x86_64-2.7/pymc/gp

copying pymc/gp/gpplots.py -> build/lib.macosx-10.5-x86_64-2.7/pymc/gp

copying pymc/gp/GPutils.py -> build/lib.macosx-10.5-x86_64-2.7/pymc/gp

copying pymc/gp/Mean.py -> build/lib.macosx-10.5-x86_64-2.7/pymc/gp

copying pymc/gp/NearlyFullRankCovariance.py -> build/lib.macosx-10.5-x86_64-2.7/pymc/gp

copying pymc/gp/Realization.py -> build/lib.macosx-10.5-x86_64-2.7/pymc/gp

copying pymc/gp/step_methods.py -> build/lib.macosx-10.5-x86_64-2.7/pymc/gp

creating build/lib.macosx-10.5-x86_64-2.7/pymc/gp/cov_funs

copying pymc/gp/cov_funs/__init__.py -> build/lib.macosx-10.5-x86_64-2.7/pymc/gp/cov_funs

copying pymc/gp/cov_funs/bases.py -> build/lib.macosx-10.5-x86_64-2.7/pymc/gp/cov_funs

copying pymc/gp/cov_funs/brownian.py -> build/lib.macosx-10.5-x86_64-2.7/pymc/gp/cov_funs

copying pymc/gp/cov_funs/cov_utils.py -> build/lib.macosx-10.5-x86_64-2.7/pymc/gp/cov_funs

copying pymc/gp/cov_funs/nsmatern.py -> build/lib.macosx-10.5-x86_64-2.7/pymc/gp/cov_funs

copying pymc/gp/cov_funs/wrapped_distances.py -> build/lib.macosx-10.5-x86_64-2.7/pymc/gp/cov_funs

running build_ext

customize UnixCCompiler

customize UnixCCompiler using build_ext

customize Gnu95FCompiler

Found executable /usr/local/bin/gfortran

customize Gnu95FCompiler

customize Gnu95FCompiler using build_ext

building 'pymc.flib' extension

compiling C sources

C compiler: gcc -fno-strict-aliasing -I//anaconda/include -arch x86_64 -DNDEBUG -g -fwrapv -O3 -Wall -Wstrict-prototypes -I/usr/local/opt/zlib/include



creating build/temp.macosx-10.5-x86_64-2.7

creating build/temp.macosx-10.5-x86_64-2.7/cephes

creating build/temp.macosx-10.5-x86_64-2.7/build

creating build/temp.macosx-10.5-x86_64-2.7/build/src.macosx-10.5-x86_64-2.7

creating build/temp.macosx-10.5-x86_64-2.7/build/src.macosx-10.5-x86_64-2.7/pymc

compile options: '-DNO_ATLAS_INFO=3 -Ibuild/src.macosx-10.5-x86_64-2.7 -I//anaconda/lib/python2.7/site-packages/numpy/core/include -I//anaconda/include/python2.7 -c'

extra options: '-msse3'

gcc: cephes/i0.c

gcc: cephes/c2f.c

gcc: build/src.macosx-10.5-x86_64-2.7/fortranobject.c

In file included from build/src.macosx-10.5-x86_64-2.7/fortranobject.c:2:

In file included from build/src.macosx-10.5-x86_64-2.7/fortranobject.h:13:

In file included from //anaconda/lib/python2.7/site-packages/numpy/core/include/numpy/arrayobject.h:15:

In file included from //anaconda/lib/python2.7/site-packages/numpy/core/include/numpy/ndarrayobject.h:17:

In file included from //anaconda/lib/python2.7/site-packages/numpy/core/include/numpy/ndarraytypes.h:1728:

//anaconda/lib/python2.7/site-packages/numpy/core/include/numpy/npy_deprecated_api.h:11:2: warning: "Using deprecated NumPy API, disable it by #defining NPY_NO_DEPRECATED_API NPY_1_7_API_VERSION" [-W#warnings]

#warning "Using deprecated NumPy API, disable it by #defining NPY_NO_DEPRECATED_API NPY_1_7_API_VERSION"

 ^

build/src.macosx-10.5-x86_64-2.7/fortranobject.c:338:30: warning: equality comparison with extraneous parentheses [-Wparentheses-equality]

        if ((fp->defs[i].func==NULL)) {

             ~~~~~~~~~~~~~~~~^~~~~~

build/src.macosx-10.5-x86_64-2.7/fortranobject.c:338:30: note: remove extraneous parentheses around the comparison to silence this warning

        if ((fp->defs[i].func==NULL)) {

            ~                ^     ~

build/src.macosx-10.5-x86_64-2.7/fortranobject.c:338:30: note: use '=' to turn this equality comparison into an assignment

        if ((fp->defs[i].func==NULL)) {

                             ^~

                             =

2 warnings generated.

gcc: build/src.macosx-10.5-x86_64-2.7/pymc/flibmodule.c

In file included from build/src.macosx-10.5-x86_64-2.7/pymc/flibmodule.c:18:

In file included from build/src.macosx-10.5-x86_64-2.7/fortranobject.h:13:

In file included from //anaconda/lib/python2.7/site-packages/numpy/core/include/numpy/arrayobject.h:15:

In file included from //anaconda/lib/python2.7/site-packages/numpy/core/include/numpy/ndarrayobject.h:17:

In file included from //anaconda/lib/python2.7/site-packages/numpy/core/include/numpy/ndarraytypes.h:1728:

//anaconda/lib/python2.7/site-packages/numpy/core/include/numpy/npy_deprecated_api.h:11:2: warning: "Using deprecated NumPy API, disable it by #defining NPY_NO_DEPRECATED_API NPY_1_7_API_VERSION" [-W#warnings]

#warning "Using deprecated NumPy API, disable it by #defining NPY_NO_DEPRECATED_API NPY_1_7_API_VERSION"

 ^

build/src.macosx-10.5-x86_64-2.7/pymc/flibmodule.c:16934:7: warning: array index 2 is past the end of the array (which contains 2 elements) [-Warray-bounds]

  d = shape(x,2);

      ^       ~

build/src.macosx-10.5-x86_64-2.7/pymc/flibmodule.c:86:24: note: expanded from macro 'shape'

#define shape(var,dim) var ## _Dims[dim]

                       ^

<scratch space>:394:1: note: expanded from here

x_Dims

^

build/src.macosx-10.5-x86_64-2.7/pymc/flibmodule.c:16835:3: note: array 'x_Dims' declared here

  npy_intp x_Dims[2] = {-1, -1};

  ^

build/src.macosx-10.5-x86_64-2.7/pymc/flibmodule.c:181:12: warning: unused function 'f2py_size' [-Wunused-function]

static int f2py_size(PyArrayObject* var, ...)

           ^

3 warnings generated.

gcc: cephes/chbevl.c

compiling Fortran sources

Fortran f77 compiler: /usr/local/bin/gfortran -Wall -ffixed-form -fno-second-underscore -m64 -fPIC -O3 -funroll-loops

Fortran f90 compiler: /usr/local/bin/gfortran -Wall -fno-second-underscore -m64 -fPIC -O3 -funroll-loops

Fortran fix compiler: /usr/local/bin/gfortran -Wall -ffixed-form -fno-second-underscore -Wall -fno-second-underscore -m64 -fPIC -O3 -funroll-loops

creating build/temp.macosx-10.5-x86_64-2.7/pymc

compile options: '-DNO_ATLAS_INFO=3 -Ibuild/src.macosx-10.5-x86_64-2.7 -I//anaconda/lib/python2.7/site-packages/numpy/core/include -I//anaconda/include/python2.7 -c'

gfortran:f77: pymc/flib.f

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pymc/flib.f:316.55:





                                                       1

Warning: Unused variable 'd_now' declared at (1)

pymc/flib.f:314.42:



      INTEGER i, nx, nalph, nmu, ntau, tnx

                                          1

Warning: Unused variable 'tnx' declared at (1)

pymc/flib.f:442.71:



      subroutine uniform_grad_x(x,lower,upper,n,nlower,nupper,gradxlike)

                                                                       1

Warning: Unused dummy argument 'gradxlike' at (1)

pymc/flib.f:461.40:



        DOUBLE PRECISION like, low, high

                                        1

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pymc/flib.f:458.36:



        INTEGER n, nlower, nupper, i

                                    1

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pymc/flib.f:461.29:



        DOUBLE PRECISION like, low, high

                             1

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pymc/flib.f:461.34:



        DOUBLE PRECISION like, low, high

                                  1

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pymc/flib.f:442.39:



      subroutine uniform_grad_x(x,lower,upper,n,nlower,nupper,gradxlike)

                                       1

Warning: Unused dummy argument 'lower' at (1)

pymc/flib.f:442.45:



      subroutine uniform_grad_x(x,lower,upper,n,nlower,nupper,gradxlike)

                                             1

Warning: Unused dummy argument 'upper' at (1)

pymc/flib.f:442.33:



      subroutine uniform_grad_x(x,lower,upper,n,nlower,nupper,gradxlike)

                                 1

Warning: Unused dummy argument 'x' at (1)

pymc/flib.f:692.41:



      DOUBLE PRECISION aa, cc, sigma, pdf

                                         1

Warning: Unused variable 'pdf' declared at (1)

pymc/flib.f:760.41:



      DOUBLE PRECISION aa, cc, sigma, pdf

                                         1

Warning: Unused variable 'pdf' declared at (1)

pymc/flib.f:834.41:



      DOUBLE PRECISION aa, cc, sigma, pdf

                                         1

Warning: Unused variable 'pdf' declared at (1)

pymc/flib.f:906.41:



      DOUBLE PRECISION aa, cc, sigma, pdf

                                         1

Warning: Unused variable 'pdf' declared at (1)

pymc/flib.f:976.41:



      DOUBLE PRECISION aa, cc, sigma, pdf

                                         1

Warning: Unused variable 'pdf' declared at (1)

pymc/flib.f:1186.29:



      DOUBLE PRECISION factln

                             1

Warning: Unused variable 'factln' declared at (1)

pymc/flib.f:1185.51:



      DOUBLE PRECISION sumx, mut, infinity, sumfact

                                                   1

Warning: Unused variable 'sumfact' declared at (1)

pymc/flib.f:1185.27:



      DOUBLE PRECISION sumx, mut, infinity, sumfact

                           1

Warning: Unused variable 'sumx' declared at (1)

pymc/flib.f:1300.55:



      DOUBLE PRECISION mu(nmu), gradlike(nmu),grad, cdf

                                                       1

Warning: Unused variable 'cdf' declared at (1)

pymc/flib.f:1302.29:



      DOUBLE PRECISION factln, gammq

                             1

Warning: Unused variable 'factln' declared at (1)

pymc/flib.f:1302.36:



      DOUBLE PRECISION factln, gammq

                                    1

Warning: Unused variable 'gammq' declared at (1)

pymc/flib.f:1301.59:



      DOUBLE PRECISION sumx, mut, infinity, sumfact, sumcdf

                                                           1

Warning: Unused variable 'sumcdf' declared at (1)

pymc/flib.f:1301.51:



      DOUBLE PRECISION sumx, mut, infinity, sumfact, sumcdf

                                                   1

Warning: Unused variable 'sumfact' declared at (1)

pymc/flib.f:1301.27:



      DOUBLE PRECISION sumx, mut, infinity, sumfact, sumcdf

                           1

Warning: Unused variable 'sumx' declared at (1)

pymc/flib.f:1402.29:



      DOUBLE PRECISION gammln

                             1

Warning: Unused variable 'gammln' declared at (1)

pymc/flib.f:2154.40:



      DOUBLE PRECISION gradlike(n), grad

                                        1

Warning: Unused variable 'grad' declared at (1)

pymc/flib.f:2665.29:



      DOUBLE PRECISION gammln

                             1

Warning: Unused variable 'gammln' declared at (1)

pymc/flib.f:2728.29:



      DOUBLE PRECISION gammln, psi

                             1

Warning: Unused variable 'gammln' declared at (1)

pymc/flib.f:2793.29:



      DOUBLE PRECISION gammln

                             1

Warning: Unused variable 'gammln' declared at (1)

pymc/flib.f:2903.29:



      DOUBLE PRECISION gammln

                             1

Warning: Unused variable 'gammln' declared at (1)

pymc/flib.f:2959.29:



      DOUBLE PRECISION gammln, psi

                             1

Warning: Unused variable 'gammln' declared at (1)

pymc/flib.f:3021.29:



      DOUBLE PRECISION gammln

                             1

Warning: Unused variable 'gammln' declared at (1)

pymc/flib.f:3396.58:



      DOUBLE PRECISION gradlike(nx), atmp, btmp, PI, glike

                                                          1

Warning: Unused variable 'glike' declared at (1)

pymc/flib.f:3646.37:



      DOUBLE PRECISION gammln, factln

                                     1

Warning: Unused variable 'factln' declared at (1)

pymc/flib.f:3646.29:



      DOUBLE PRECISION gammln, factln

                             1

Warning: Unused variable 'gammln' declared at (1)

pymc/flib.f:3706.37:



      DOUBLE PRECISION gammln, factln, psi

                                     1

Warning: Unused variable 'factln' declared at (1)

pymc/flib.f:3706.29:



      DOUBLE PRECISION gammln, factln, psi

                             1

Warning: Unused variable 'gammln' declared at (1)

pymc/flib.f:3836.29:



      DOUBLE PRECISION factln

                             1

Warning: Unused variable 'factln' declared at (1)

pymc/flib.f:4039.26:



      DOUBLE PRECISION psi

                          1

Warning: Unused variable 'psi' declared at (1)

pymc/flib.f:4266.29:



      DOUBLE PRECISION gammln, psi

                             1

Warning: Unused variable 'gammln' declared at (1)

pymc/flib.f:4332.29:



      DOUBLE PRECISION gammln, psi

                             1

Warning: Unused variable 'gammln' declared at (1)

pymc/flib.f:5184.35:



      DOUBLE PRECISION like, factln, infinity, sump

                                   1

Warning: Unused variable 'factln' declared at (1)

pymc/flib.f:5186.23:



      INTEGER i,j,n_tmp

                       1

Warning: Unused variable 'n_tmp' declared at (1)

pymc/flib.f:5434.26:



      DOUBLE PRECISION tmp

                          1

Warning: Unused variable 'tmp' declared at (1)

pymc/flib.f:5488.25:



      DOUBLE PRECISION i0

                         1

Warning: Unused variable 'i0' declared at (1)

pymc/flib.f:5481.26:



      DOUBLE PRECISION tmp

                          1

Warning: Unused variable 'tmp' declared at (1)

pymc/flib.f:5535.25:



      DOUBLE PRECISION i0

                         1

Warning: Unused variable 'i0' declared at (1)

pymc/flib.f:5528.26:



      DOUBLE PRECISION tmp

                          1

Warning: Unused variable 'tmp' declared at (1)

pymc/flib.f: In function 'elgs':

pymc/flib.f:4882:0: warning: 'k' may be used uninitialized in this function [-Wmaybe-uninitialized]

pymc/flib.f: In function 'exponweib_gl':

pymc/flib.f:778:0: warning: 'nc' may be used uninitialized in this function [-Wuninitialized]

pymc/flib.f: In function 'exponweib_gs':

pymc/flib.f:994:0: warning: 'nc' may be used uninitialized in this function [-Wuninitialized]

gfortran:f77: pymc/histogram.f

gfortran:f77: pymc/flib_blas.f

pymc/flib_blas.f:202.25:



      DOUBLE PRECISION PI

                         1

Warning: Unused variable 'pi' declared at (1)

gfortran:f77: pymc/blas_wrap.f

gfortran:f77: pymc/math.f

pymc/math.f:396.6:



      DOUBLE PRECISION FUNCTION DERF(X)

      1

Warning: 'derf' declared at (1) is also the name of an intrinsic.  It can only be called via an explicit interface or if declared EXTERNAL.

pymc/math.f:417.6:



      DOUBLE PRECISION FUNCTION DERFC(X)

      1

Warning: 'derfc' declared at (1) is also the name of an intrinsic.  It can only be called via an explicit interface or if declared EXTERNAL.

gfortran:f77: pymc/gibbsit.f

pymc/gibbsit.f:2160.5:



  215 IF (R .GT. .5898437) GO TO 220

     1

Warning: Label 215 at (1) defined but not used

pymc/gibbsit.f:2077.5:





     1

Warning: Label 115 at (1) defined but not used

pymc/gibbsit.f:2064.5:



   15 IF (KFLAG.GE.1) GO TO 30

     1

Warning: Label 15 at (1) defined but not used

pymc/gibbsit.f:1204.48:



        cutpt = empquant(original,iteracnt,qhat,work)

                                                1

Warning: Type mismatch in argument 'work' at (1); passed INTEGER(4) to REAL(8)

gfortran:f77: build/src.macosx-10.5-x86_64-2.7/pymc/flib-f2pywrappers.f

/usr/local/bin/gfortran -Wall -L/usr/local/opt/zlib/lib build/temp.macosx-10.5-x86_64-2.7/cephes/i0.o build/temp.macosx-10.5-x86_64-2.7/cephes/c2f.o build/temp.macosx-10.5-x86_64-2.7/cephes/chbevl.o build/temp.macosx-10.5-x86_64-2.7/build/src.macosx-10.5-x86_64-2.7/pymc/flibmodule.o build/temp.macosx-10.5-x86_64-2.7/build/src.macosx-10.5-x86_64-2.7/fortranobject.o build/temp.macosx-10.5-x86_64-2.7/pymc/flib.o build/temp.macosx-10.5-x86_64-2.7/pymc/histogram.o build/temp.macosx-10.5-x86_64-2.7/pymc/flib_blas.o build/temp.macosx-10.5-x86_64-2.7/pymc/blas_wrap.o build/temp.macosx-10.5-x86_64-2.7/pymc/math.o build/temp.macosx-10.5-x86_64-2.7/pymc/gibbsit.o build/temp.macosx-10.5-x86_64-2.7/build/src.macosx-10.5-x86_64-2.7/pymc/flib-f2pywrappers.o -L/usr/local/Cellar/gfortran/4.7.2/gfortran/lib/gcc/x86_64-apple-darwin12.2.0/4.7.2 -lgfortran -o build/lib.macosx-10.5-x86_64-2.7/pymc/flib.so -Wl,-framework -Wl,Accelerate

Undefined symbols for architecture x86_64:

  "_PyArg_ParseTupleAndKeywords", referenced from:

      _f2py_rout_flib_symmetrize in flibmodule.o

      _f2py_rout_flib_logsum in flibmodule.o

      _f2py_rout_flib_logsum_cpx in flibmodule.o

      _f2py_rout_flib_combinationln in flibmodule.o

      _f2py_rout_flib_expand_triangular in flibmodule.o

      _f2py_rout_flib_mod_to_circle in flibmodule.o

      _f2py_rout_flib_standardize in flibmodule.o

      ...

  "_PyCObject_AsVoidPtr", referenced from:

      _initflib in flibmodule.o

      _F2PyCapsule_AsVoidPtr in fortranobject.o

  "_PyCObject_FromVoidPtr", referenced from:

      _fortran_getattr in fortranobject.o

      _F2PyCapsule_FromVoidPtr in fortranobject.o

  "_PyCObject_Type", referenced from:

      _initflib in flibmodule.o

      _F2PyCapsule_Check in fortranobject.o

  "_PyComplex_FromDoubles", referenced from:

      _f2py_rout_flib_logsum_cpx in flibmodule.o

  "_PyComplex_Type", referenced from:

      _int_from_pyobj in flibmodule.o

      _double_from_pyobj in flibmodule.o

  "_PyDict_DelItemString", referenced from:

      _fortran_setattr in fortranobject.o

  "_PyDict_GetItemString", referenced from:

      _initflib in flibmodule.o

      _fortran_getattr in fortranobject.o

  "_PyDict_New", referenced from:

      _PyFortranObject_New in fortranobject.o

      _PyFortranObject_NewAsAttr in fortranobject.o

      _fortran_setattr in fortranobject.o

  "_PyDict_SetItemString", referenced from:

      _initflib in flibmodule.o

      _F2PyDict_SetItemString in fortranobject.o

      _PyFortranObject_New in fortranobject.o

      _fortran_getattr in fortranobject.o

      _fortran_setattr in fortranobject.o

  "_PyErr_Clear", referenced from:

      _int_from_pyobj in flibmodule.o

      _double_from_pyobj in flibmodule.o

      _F2PyDict_SetItemString in fortranobject.o

      _fortran_repr in fortranobject.o

  "_PyErr_Format", referenced from:

      _initflib in flibmodule.o

      _fortran_call in fortranobject.o

  "_PyErr_NewException", referenced from:

      _initflib in flibmodule.o

  "_PyErr_Occurred", referenced from:

      _initflib in flibmodule.o

      _f2py_rout_flib_symmetrize in flibmodule.o

      _f2py_rout_flib_logsum in flibmodule.o

      _f2py_rout_flib_logsum_cpx in flibmodule.o

      _f2py_rout_flib_combinationln in flibmodule.o

      _f2py_rout_flib_expand_triangular in flibmodule.o

      _f2py_rout_flib_mod_to_circle in flibmodule.o

      ...

  "_PyErr_Print", referenced from:

      _initflib in flibmodule.o

      _F2PyDict_SetItemString in fortranobject.o

  "_PyErr_SetString", referenced from:

      _initflib in flibmodule.o

      _f2py_rout_flib_symmetrize in flibmodule.o

      _f2py_rout_flib_logsum in flibmodule.o

      _f2py_rout_flib_logsum_cpx in flibmodule.o

      _f2py_rout_flib_expand_triangular in flibmodule.o

      _f2py_rout_flib_mod_to_circle in flibmodule.o

      _f2py_rout_flib_standardize in flibmodule.o

      ...

  "_PyEval_RestoreThread", referenced from:

      _f2py_rout_flib_symmetrize in flibmodule.o

      _f2py_rout_flib_logsum in flibmodule.o

      _f2py_rout_flib_logsum_cpx in flibmodule.o

      _f2py_rout_flib_expand_triangular in flibmodule.o

      _f2py_rout_flib_standardize in flibmodule.o

      _f2py_rout_flib_sn_like in flibmodule.o

      _f2py_rout_flib_rskewnorm in flibmodule.o

      ...

  "_PyEval_SaveThread", referenced from:

      _f2py_rout_flib_symmetrize in flibmodule.o

      _f2py_rout_flib_logsum in flibmodule.o

      _f2py_rout_flib_logsum_cpx in flibmodule.o

      _f2py_rout_flib_expand_triangular in flibmodule.o

      _f2py_rout_flib_standardize in flibmodule.o

      _f2py_rout_flib_sn_like in flibmodule.o

      _f2py_rout_flib_rskewnorm in flibmodule.o

      ...

  "_PyExc_AttributeError", referenced from:

      _initflib in flibmodule.o

      _fortran_setattr in fortranobject.o

  "_PyExc_ImportError", referenced from:

      _initflib in flibmodule.o

  "_PyExc_MemoryError", referenced from:

      _string_from_pyobj in flibmodule.o

  "_PyExc_RuntimeError", referenced from:

      _initflib in flibmodule.o

      _fortran_call in fortranobject.o

  "_PyExc_TypeError", referenced from:

      _fortran_call in fortranobject.o

      _array_from_pyobj in fortranobject.o

  "_PyExc_ValueError", referenced from:

      _string_from_pyobj in flibmodule.o

      _array_from_pyobj in fortranobject.o

  "_PyFloat_Type", referenced from:

      _double_from_pyobj in flibmodule.o

  "_PyImport_ImportModule", referenced from:

      _initflib in flibmodule.o

  "_PyMem_Free", referenced from:

      _fortran_dealloc in fortranobject.o

  "_PyModule_GetDict", referenced from:

      _initflib in flibmodule.o

  "_PyNumber_Float", referenced from:

      _double_from_pyobj in flibmodule.o

  "_PyNumber_Int", referenced from:

      _int_from_pyobj in flibmodule.o

  "_PyObject_GetAttrString", referenced from:

      _initflib in flibmodule.o

      _int_from_pyobj in flibmodule.o

      _double_from_pyobj in flibmodule.o

      _fortran_repr in fortranobject.o

  "_PyObject_IsTrue", referenced from:

      _f2py_rout_flib_constrain in flibmodule.o

  "_PyObject_SetAttrString", referenced from:

      _initflib in flibmodule.o

  "_PyObject_Str", referenced from:

      _string_from_pyobj in flibmodule.o

      _array_from_pyobj in fortranobject.o

  "_PyObject_Type", referenced from:

      _array_from_pyobj in fortranobject.o

  "_PySequence_Check", referenced from:

      _int_from_pyobj in flibmodule.o

      _double_from_pyobj in flibmodule.o

  "_PySequence_GetItem", referenced from:

      _int_from_pyobj in flibmodule.o

      _double_from_pyobj in flibmodule.o

  "_PyString_AsString", referenced from:

      _fortran_repr in fortranobject.o

      _array_from_pyobj in fortranobject.o

  "_PyString_ConcatAndDel", referenced from:

      _fortran_getattr in fortranobject.o

  "_PyString_FromFormat", referenced from:

      _fortran_repr in fortranobject.o

  "_PyString_FromString", referenced from:

      _initflib in flibmodule.o

      _fortran_getattr in fortranobject.o

      _fortran_repr in fortranobject.o

  "_PyType_IsSubtype", referenced from:

      _int_from_pyobj in flibmodule.o

      _double_from_pyobj in flibmodule.o

      _string_from_pyobj in flibmodule.o

      _array_from_pyobj in fortranobject.o

  "_PyType_Type", referenced from:

      _initflib in flibmodule.o

  "_Py_BuildValue", referenced from:

      _f2py_rout_flib_symmetrize in flibmodule.o

      _f2py_rout_flib_logsum in flibmodule.o

      _f2py_rout_flib_logsum_cpx in flibmodule.o

      _f2py_rout_flib_combinationln in flibmodule.o

      _f2py_rout_flib_expand_triangular in flibmodule.o

      _f2py_rout_flib_mod_to_circle in flibmodule.o

      _f2py_rout_flib_standardize in flibmodule.o

      ...

  "_Py_FindMethod", referenced from:

      _fortran_getattr in fortranobject.o

  "_Py_InitModule4_64", referenced from:

      _initflib in flibmodule.o

  "__PyObject_New", referenced from:

      _PyFortranObject_New in fortranobject.o

      _PyFortranObject_NewAsAttr in fortranobject.o

  "__Py_NoneStruct", referenced from:

      _f2py_rout_flib_symmetrize in flibmodule.o

      _f2py_rout_flib_logsum in flibmodule.o

      _f2py_rout_flib_logsum_cpx in flibmodule.o

      _f2py_rout_flib_combinationln in flibmodule.o

      _f2py_rout_flib_expand_triangular in flibmodule.o

      _f2py_rout_flib_mod_to_circle in flibmodule.o

      _f2py_rout_flib_standardize in flibmodule.o

      ...

ld: symbol(s) not found for architecture x86_64

collect2: error: ld returned 1 exit status

Undefined symbols for architecture x86_64:

  "_PyArg_ParseTupleAndKeywords", referenced from:

      _f2py_rout_flib_symmetrize in flibmodule.o

      _f2py_rout_flib_logsum in flibmodule.o

      _f2py_rout_flib_logsum_cpx in flibmodule.o

      _f2py_rout_flib_combinationln in flibmodule.o

      _f2py_rout_flib_expand_triangular in flibmodule.o

      _f2py_rout_flib_mod_to_circle in flibmodule.o

      _f2py_rout_flib_standardize in flibmodule.o

      ...

  "_PyCObject_AsVoidPtr", referenced from:

      _initflib in flibmodule.o

      _F2PyCapsule_AsVoidPtr in fortranobject.o

  "_PyCObject_FromVoidPtr", referenced from:

      _fortran_getattr in fortranobject.o

      _F2PyCapsule_FromVoidPtr in fortranobject.o

  "_PyCObject_Type", referenced from:

      _initflib in flibmodule.o

      _F2PyCapsule_Check in fortranobject.o

  "_PyComplex_FromDoubles", referenced from:

      _f2py_rout_flib_logsum_cpx in flibmodule.o

  "_PyComplex_Type", referenced from:

      _int_from_pyobj in flibmodule.o

      _double_from_pyobj in flibmodule.o

  "_PyDict_DelItemString", referenced from:

      _fortran_setattr in fortranobject.o

  "_PyDict_GetItemString", referenced from:

      _initflib in flibmodule.o

      _fortran_getattr in fortranobject.o

  "_PyDict_New", referenced from:

      _PyFortranObject_New in fortranobject.o

      _PyFortranObject_NewAsAttr in fortranobject.o

      _fortran_setattr in fortranobject.o

  "_PyDict_SetItemString", referenced from:

      _initflib in flibmodule.o

      _F2PyDict_SetItemString in fortranobject.o

      _PyFortranObject_New in fortranobject.o

      _fortran_getattr in fortranobject.o

      _fortran_setattr in fortranobject.o

  "_PyErr_Clear", referenced from:

      _int_from_pyobj in flibmodule.o

      _double_from_pyobj in flibmodule.o

      _F2PyDict_SetItemString in fortranobject.o

      _fortran_repr in fortranobject.o

  "_PyErr_Format", referenced from:

      _initflib in flibmodule.o

      _fortran_call in fortranobject.o

  "_PyErr_NewException", referenced from:

      _initflib in flibmodule.o

  "_PyErr_Occurred", referenced from:

      _initflib in flibmodule.o

      _f2py_rout_flib_symmetrize in flibmodule.o

      _f2py_rout_flib_logsum in flibmodule.o

      _f2py_rout_flib_logsum_cpx in flibmodule.o

      _f2py_rout_flib_combinationln in flibmodule.o

      _f2py_rout_flib_expand_triangular in flibmodule.o

      _f2py_rout_flib_mod_to_circle in flibmodule.o

      ...

  "_PyErr_Print", referenced from:

      _initflib in flibmodule.o

      _F2PyDict_SetItemString in fortranobject.o

  "_PyErr_SetString", referenced from:

      _initflib in flibmodule.o

      _f2py_rout_flib_symmetrize in flibmodule.o

      _f2py_rout_flib_logsum in flibmodule.o

      _f2py_rout_flib_logsum_cpx in flibmodule.o

      _f2py_rout_flib_expand_triangular in flibmodule.o

      _f2py_rout_flib_mod_to_circle in flibmodule.o

      _f2py_rout_flib_standardize in flibmodule.o

      ...

  "_PyEval_RestoreThread", referenced from:

      _f2py_rout_flib_symmetrize in flibmodule.o

      _f2py_rout_flib_logsum in flibmodule.o

      _f2py_rout_flib_logsum_cpx in flibmodule.o

      _f2py_rout_flib_expand_triangular in flibmodule.o

      _f2py_rout_flib_standardize in flibmodule.o

      _f2py_rout_flib_sn_like in flibmodule.o

      _f2py_rout_flib_rskewnorm in flibmodule.o

      ...

  "_PyEval_SaveThread", referenced from:

      _f2py_rout_flib_symmetrize in flibmodule.o

      _f2py_rout_flib_logsum in flibmodule.o

      _f2py_rout_flib_logsum_cpx in flibmodule.o

      _f2py_rout_flib_expand_triangular in flibmodule.o

      _f2py_rout_flib_standardize in flibmodule.o

      _f2py_rout_flib_sn_like in flibmodule.o

      _f2py_rout_flib_rskewnorm in flibmodule.o

      ...

  "_PyExc_AttributeError", referenced from:

      _initflib in flibmodule.o

      _fortran_setattr in fortranobject.o

  "_PyExc_ImportError", referenced from:

      _initflib in flibmodule.o

  "_PyExc_MemoryError", referenced from:

      _string_from_pyobj in flibmodule.o

  "_PyExc_RuntimeError", referenced from:

      _initflib in flibmodule.o

      _fortran_call in fortranobject.o

  "_PyExc_TypeError", referenced from:

      _fortran_call in fortranobject.o

      _array_from_pyobj in fortranobject.o

  "_PyExc_ValueError", referenced from:

      _string_from_pyobj in flibmodule.o

      _array_from_pyobj in fortranobject.o

  "_PyFloat_Type", referenced from:

      _double_from_pyobj in flibmodule.o

  "_PyImport_ImportModule", referenced from:

      _initflib in flibmodule.o

  "_PyMem_Free", referenced from:

      _fortran_dealloc in fortranobject.o

  "_PyModule_GetDict", referenced from:

      _initflib in flibmodule.o

  "_PyNumber_Float", referenced from:

      _double_from_pyobj in flibmodule.o

  "_PyNumber_Int", referenced from:

      _int_from_pyobj in flibmodule.o

  "_PyObject_GetAttrString", referenced from:

      _initflib in flibmodule.o

      _int_from_pyobj in flibmodule.o

      _double_from_pyobj in flibmodule.o

      _fortran_repr in fortranobject.o

  "_PyObject_IsTrue", referenced from:

      _f2py_rout_flib_constrain in flibmodule.o

  "_PyObject_SetAttrString", referenced from:

      _initflib in flibmodule.o

  "_PyObject_Str", referenced from:

      _string_from_pyobj in flibmodule.o

      _array_from_pyobj in fortranobject.o

  "_PyObject_Type", referenced from:

      _array_from_pyobj in fortranobject.o

  "_PySequence_Check", referenced from:

      _int_from_pyobj in flibmodule.o

      _double_from_pyobj in flibmodule.o

  "_PySequence_GetItem", referenced from:

      _int_from_pyobj in flibmodule.o

      _double_from_pyobj in flibmodule.o

  "_PyString_AsString", referenced from:

      _fortran_repr in fortranobject.o

      _array_from_pyobj in fortranobject.o

  "_PyString_ConcatAndDel", referenced from:

      _fortran_getattr in fortranobject.o

  "_PyString_FromFormat", referenced from:

      _fortran_repr in fortranobject.o

  "_PyString_FromString", referenced from:

      _initflib in flibmodule.o

      _fortran_getattr in fortranobject.o

      _fortran_repr in fortranobject.o

  "_PyType_IsSubtype", referenced from:

      _int_from_pyobj in flibmodule.o

      _double_from_pyobj in flibmodule.o

      _string_from_pyobj in flibmodule.o

      _array_from_pyobj in fortranobject.o

  "_PyType_Type", referenced from:

      _initflib in flibmodule.o

  "_Py_BuildValue", referenced from:

      _f2py_rout_flib_symmetrize in flibmodule.o

      _f2py_rout_flib_logsum in flibmodule.o

      _f2py_rout_flib_logsum_cpx in flibmodule.o

      _f2py_rout_flib_combinationln in flibmodule.o

      _f2py_rout_flib_expand_triangular in flibmodule.o

      _f2py_rout_flib_mod_to_circle in flibmodule.o

      _f2py_rout_flib_standardize in flibmodule.o

      ...

  "_Py_FindMethod", referenced from:

      _fortran_getattr in fortranobject.o

  "_Py_InitModule4_64", referenced from:

      _initflib in flibmodule.o

  "__PyObject_New", referenced from:

      _PyFortranObject_New in fortranobject.o

      _PyFortranObject_NewAsAttr in fortranobject.o

  "__Py_NoneStruct", referenced from:

      _f2py_rout_flib_symmetrize in flibmodule.o

      _f2py_rout_flib_logsum in flibmodule.o

      _f2py_rout_flib_logsum_cpx in flibmodule.o

      _f2py_rout_flib_combinationln in flibmodule.o

      _f2py_rout_flib_expand_triangular in flibmodule.o

      _f2py_rout_flib_mod_to_circle in flibmodule.o

      _f2py_rout_flib_standardize in flibmodule.o

      ...

ld: symbol(s) not found for architecture x86_64

collect2: error: ld returned 1 exit status

error: Command "/usr/local/bin/gfortran -Wall -L/usr/local/opt/zlib/lib build/temp.macosx-10.5-x86_64-2.7/cephes/i0.o build/temp.macosx-10.5-x86_64-2.7/cephes/c2f.o build/temp.macosx-10.5-x86_64-2.7/cephes/chbevl.o build/temp.macosx-10.5-x86_64-2.7/build/src.macosx-10.5-x86_64-2.7/pymc/flibmodule.o build/temp.macosx-10.5-x86_64-2.7/build/src.macosx-10.5-x86_64-2.7/fortranobject.o build/temp.macosx-10.5-x86_64-2.7/pymc/flib.o build/temp.macosx-10.5-x86_64-2.7/pymc/histogram.o build/temp.macosx-10.5-x86_64-2.7/pymc/flib_blas.o build/temp.macosx-10.5-x86_64-2.7/pymc/blas_wrap.o build/temp.macosx-10.5-x86_64-2.7/pymc/math.o build/temp.macosx-10.5-x86_64-2.7/pymc/gibbsit.o build/temp.macosx-10.5-x86_64-2.7/build/src.macosx-10.5-x86_64-2.7/pymc/flib-f2pywrappers.o -L/usr/local/Cellar/gfortran/4.7.2/gfortran/lib/gcc/x86_64-apple-darwin12.2.0/4.7.2 -lgfortran -o build/lib.macosx-10.5-x86_64-2.7/pymc/flib.so -Wl,-framework -Wl,Accelerate" failed with exit status 1

----------------------------------------
Cleaning up...
Command //anaconda/bin/python -c "import setuptools;__file__='/private/var/folders/6l/83vj6nxn6g1b6l2c9ycym4hc0000gn/T/pip_build_olga/pymc/setup.py';exec(compile(open(__file__).read().replace('\r\n', '\n'), __file__, 'exec'))" install --record /var/folders/6l/83vj6nxn6g1b6l2c9ycym4hc0000gn/T/pip-PlF1xm-record/install-record.txt --single-version-externally-managed failed with error code 1 in /private/var/folders/6l/83vj6nxn6g1b6l2c9ycym4hc0000gn/T/pip_build_olga/pymc
Storing complete log in /Users/olga/.pip/pip.log
Could not install 'pymc' using pip

















In [24]:



    


import pymc as pm

with pm.Model() as model: # model specifications in PyMC3 are wrapped in a with-statement
    # Define priors
    alpha = pm.Normal('alpha', mu=0, sd=20)
    beta = pm.Normal('beta', mu=0, sd=20)
    sigma = pm.Uniform('sigma', lower=0, upper=20)
    
    # Define linear regression
    y_est = alpha + beta * x
    
    # Define likelihood
    likelihood = pm.Normal('y', mu=y_est, sd=sigma, observed=y)
    
    # Inference!
    start = pm.find_MAP() # Find starting value by optimization
    step = pm.NUTS(state=start) # Instantiate MCMC sampling algorithm
    trace = pm.sample(2000, step, start=start, progressbar=False) # draw 2000 posterior samples using NUTS sampling



    


















    






---------------------------------------------------------------------------
ImportError                               Traceback (most recent call last)
<ipython-input-24-262be0b52243> in <module>()
----> 1 import pymc as pm
      2 
      3 with pm.Model() as model: # model specifications in PyMC3 are wrapped in a with-statement
      4     # Define priors
      5     alpha = pm.Normal('alpha', mu=0, sd=20)

ImportError: No module named pymc

Covenience function glm()





In [ ]:



    


with pm.Model() as model:
    # specify glm and pass in data. The resulting linear model, its likelihood and 
    # and all its parameters are automatically added to our model.
    pm.glm.glm('y ~ x', data)
    step = pm.NUTS() # Instantiate MCMC sampling algorithm
    trace = pm.sample(2000, step, progressbar=False) # draw 2000 posterior samples using NUTS sampling

Posterior





In [ ]:



    


fig = pm.traceplot(trace, lines={'alpha': 1, 'beta': 2, 'sigma': .5});



    











In [ ]:



    


fig = plt.figure(figsize=(10, 10))
ax = fig.add_subplot(111, xlabel='Value of gold', ylabel='Value of gold miners', title='Posterior predictive regression lines')
ppl.scatter(ax, x, y, label='data')
glm.plot_posterior_predictive(trace, samples=100, 
                              label='posterior predictive regression lines')
ppl.plot(ax, x, true_regression_line, label='true regression line', linewidth=5.)
ax.legend(loc=0);
fig.savefig('ppc1.png')



    











In [ ]:



    


Image('ppc1.png')

Robust Regression





In [ ]:



    


# Add outliers
x_out = np.append(x, [.1, .15, .2, .25, .25])
y_out = np.append(y, [8, 6, 9, 7, 9])

data_out = dict(x=x_out, y=y_out)
fig = plt.figure(figsize=(7, 7))
ax = fig.add_subplot(111,  xlabel='Value of gold', ylabel='Value of gold miners', title='Posterior predictive regression lines')
ppl.scatter(ax, x_out, y_out, label='data')



    











In [ ]:



    


with Model() as model:
    glm.glm('y ~ x', data_out)
    trace = sample(2000, NUTS(), progressbar=False)



    











In [ ]:



    


fig = plt.figure(figsize=(10, 10))
ax = fig.add_subplot(111,  xlabel='Value of gold', ylabel='Value of gold miners', title='Posterior predictive regression lines')
ppl.scatter(ax, x_out, y_out, label='data')
glm.plot_posterior_predictive(trace, samples=100, 
                              label='posterior predictive regression lines')
ppl.plot(ax, x, true_regression_line, 
         label='true regression line', linewidth=5.)

plt.legend(loc=0);
fig.savefig('ppc2.png')



    











In [ ]:



    


Image('ppc2.png')



    











In [ ]:



    


fig = plt.figure(figsize=(8, 6))
ax = fig.add_subplot(111)
normal_dist = Normal.dist(mu=0, sd=1)
t_dist = T.dist(mu=0, lam=1, nu=1)
x_eval = np.linspace(-8, 8, 300)
ppl.plot(ax, x_eval, theano.tensor.exp(normal_dist.logp(x_eval)).eval(), label='Normal', linewidth=2.)
ppl.plot(ax, x_eval, theano.tensor.exp(t_dist.logp(x_eval)).eval(), label='Student T', linewidth=2.)
plt.xlabel('x')
plt.ylabel('Probability density')
plt.legend();
fig.savefig('t-dist.png')

Fit strongly biased by outliers

  • Normal distribution has very light tails.
  • -> sensitive to outliers.
  • Instead, use Student T distribution with heavier tails.




In [ ]:



    


Image('t-dist.png')



    











In [ ]:



    


with pm.Model() as model_robust:
    family = pm.glm.families.T()
    pm.glm.glm('y ~ x', data_out, family=family)
    
    trace_robust = pm.sample(2000, pm.NUTS(), progressbar=False)



    











In [ ]:



    


fig = plt.figure(figsize=(10, 10))
ax = fig.add_subplot(111, xlabel='Value of gold', ylabel='Value of gold miners', title='Posterior predictive regression lines')
ppl.scatter(ax, x_out, y_out)
glm.plot_posterior_predictive(trace_robust, samples=100,
                              label='posterior predictive regression lines')
ppl.plot(ax, x, true_regression_line, 
         label='true regression line', linewidth=5.)
plt.legend();
fig.savefig('ppc3.png')



    











In [ ]:



    


Image('ppc3.png')

Real-world example: Algorithmic Trading

  • Pairtrading is a famous technique that plays two stocks against each other.
  • For this to work, stocks must be correlated (cointegrated).
  • One common example is the price of gold (GLD) and the price of gold mining operations (GDX).




In [ ]:



    


import zipline
import pytz
from datetime import datetime
fig = plt.figure(figsize=(8, 4))

prices = zipline.data.load_from_yahoo(stocks=['GLD', 'GDX'], 
                                 end=datetime(2013, 8, 1, 0, 0, 0, 0, pytz.utc)).dropna()[:1000]
prices.plot();



    











In [ ]:



    


fig = plt.figure(figsize=(9, 6))
ax = fig.add_subplot(111, xlabel='Price GDX in \$', ylabel='Price GLD in \$')
colors = np.linspace(0.1, 1, len(prices))
mymap = plt.get_cmap("winter")
sc = ax.scatter(prices.GDX, prices.GLD, c=colors, cmap=mymap, lw=0)
cb = plt.colorbar(sc)
cb.ax.set_yticklabels([str(p.date()) for p in prices[::len(prices)//10].index]);
fig.savefig('price_corr.png')



    











In [ ]:



    


Image('price_corr.png')

Naive model assumes constant linear regression.





In [ ]:



    


with pm.Model() as model_reg:
    family = pm.glm.families.Normal()
    pm.glm.glm('GLD ~ GDX', prices, family=family)
    trace_reg = pm.sample(2000, pm.NUTS(), progressbar=False)

Hm... kinda unsatisfying...





In [ ]:



    


fig = plt.figure(figsize=(9, 6))
ax = fig.add_subplot(111, xlabel='Price GDX in $', ylabel='Price GLD in $', 
            title='Posterior predictive regression lines')
sc = ax.scatter(prices.GDX, prices.GLD, c=colors, cmap=mymap, lw=0)
glm.plot_posterior_predictive(trace_reg, samples=100, 
                              label='posterior predictive regression lines',
                              lm=lambda x, sample: sample['Intercept'] + sample['GDX'] * x,
                              eval=np.linspace(prices.GDX.min(), prices.GDX.max(), 100))
cb = plt.colorbar(sc)
cb.ax.set_yticklabels([str(p.date()) for p in prices[::len(prices)//10].index]);
ax.legend(loc=0);
fig.savefig('ppc4.png')



    











In [ ]:



    


Image('ppc4.png')
  • Clearly the regression between GDX and GLD changes over time.
  • But it does so gradually.
  • Can we build a model that allows for gradual changes in the coefficients?
  • YES!

Improved model

  • Assumes that intercept and slope follow a random walk.
  • At each time-point, the coefficients can move a step from their previous values.
  • This allows the coefficients to track the regression as it changes over time.
$$ \alpha_t \sim \mathcal{N}(\alpha_{t-1}, \sigma_\alpha^2) $$$$ \beta_t \sim \mathcal{N}(\beta_{t-1}, \sigma_\beta^2) $$ 




In [ ]:



    


from pymc.distributions.timeseries import *
from theano.tensor import repeat

$$\text{Priors for }\sigma_{\alpha}\text{ and }\sigma_{\beta}$$





In [ ]:



    


model_randomwalk = pm.Model()
with model_randomwalk:
    # std of random walk, best sampled in log space.
    sigma_alpha, log_sigma_alpha = model_randomwalk.TransformedVar(
                            'sigma_alpha', 
                            pm.Exponential.dist(1./.02, testval = .1), 
                            pm.logtransform
    )
    sigma_beta, log_sigma_beta = model_randomwalk.TransformedVar(
                            'sigma_beta', 
                            pm.Exponential.dist(1./.02, testval = .1),
                            pm.logtransform
    )

Define regression coefficients to follow a random walk.





In [ ]:



    


# To make the model simpler, we will apply the same coefficient for 50 data points at a time
subsample_alpha = 50
subsample_beta = 50

with model_randomwalk:
    alpha = pm.GaussianRandomWalk('alpha', sigma_alpha**-2, 
                               shape=len(prices) / subsample_alpha)
    beta = pm.GaussianRandomWalk('beta', sigma_beta**-2, 
                              shape=len(prices) / subsample_beta)
    
    # Make coefficients have the same length as prices
    alpha_r = repeat(alpha, subsample_alpha)
    beta_r = repeat(beta, subsample_beta)

Define regression and likelihood





In [ ]:



    


with model_randomwalk:
    # Define regression
    regression = alpha_r + beta_r * prices.GDX.values
    
    # Assume prices are Normally distributed, the mean comes from the regression.
    sd = pm.Uniform('sd', 0, 20)
    likelihood = pm.Normal('y', 
                           mu=regression, 
                           sd=sd, 
                           observed=prices.GLD.values)

Inference!





In [ ]:



    


from scipy import optimize
with model_randomwalk:
    # First optimize random walk
    start = pm.find_MAP(vars=[alpha, beta], fmin=optimize.fmin_l_bfgs_b)
    
    # Sample
    step = pm.NUTS(scaling=start)
    trace_rw = pm.sample(2000, step, start=start, progressbar=False)

intercept changes over time.





In [ ]:



    


fig = plt.figure(figsize=(8, 6))
ax = plt.subplot(111, xlabel='time', ylabel='alpha', title='Change of alpha over time.')
ppl.plot(ax, trace_rw[-1000:][alpha].T, 'r', alpha=.05);
ax.set_xticklabels([str(p.date()) for p in prices[::len(prices)//5].index]);
fig.savefig('rwalk_alpha.png')



    











In [ ]:



    


Image('rwalk_alpha.png')

Slope changes over time.





In [ ]:



    


fig = plt.figure(figsize=(8, 6))
ax = fig.add_subplot(111, xlabel='time', ylabel='beta', title='Change of beta over time')
ppl.plot(ax, trace_rw[-1000:][beta].T, 'b', alpha=.05);
ax.set_xticklabels([str(p.date()) for p in prices[::len(prices)//5].index]);
fig.savefig('rwalk_beta.png')



    











In [ ]:



    


Image('rwalk_beta.png')

Regression slowly adapts to best fit current data





In [ ]:



    


fig = plt.figure(figsize=(8, 6))
ax = fig.add_subplot(111, xlabel='Price GDX in \$', ylabel='Price GLD in \$', 
            title='Posterior predictive regression lines')

colors = np.linspace(0.1, 1, len(prices))
colors_sc = np.linspace(0.1, 1, len(trace_rw[-500::10]['alpha'].T))
mymap = plt.get_cmap('winter')
mymap_sc = plt.get_cmap('winter')

xi = np.linspace(prices.GDX.min(), prices.GDX.max(), 50)
for i, (alpha, beta) in enumerate(zip(trace_rw[-500::10]['alpha'].T, trace_rw[-500::10]['beta'].T)):
    for a, b in zip(alpha, beta):
        ax.plot(xi, a + b*xi, alpha=.05, lw=1, c=mymap_sc(colors_sc[i]))
        
sc = ax.scatter(prices.GDX, prices.GLD, label='data', cmap=mymap, c=colors)
cb = plt.colorbar(sc)
cb.ax.set_yticklabels([str(p.date()) for p in prices[::len(prices)//10].index]);
fig.savefig('ppc5.png')



    











In [ ]:



    


Image('ppc5.png')

Conclusions

  • Probabilistic Programming allows you to tell a genarative story.
  • Blackbox inference algorithms allow estimation of complex models.
  • PyMC3 puts advanced samplers at your fingertips.

Outstanding Issues

Scalability

  • Variational Inference
  • see also Max Welling's work for scaling MCMC

Usability

  • still too difficult to use
  • wanted: library on top of PyMC3 with common models

Further reading

Content source: olgabot/prettyplotlib

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