When combining multiple datasets in Python in code repository, I want to put the dataset name in the first column. But I couldn't figure it out by accessing its path
#transform_df(
Output("/folder/folder1/datasets/mydatset"),
df1 = Input("A"),
df2 = Input("B"),
)
def compute(df1, df2, df3):
print(list(filter(os.path.isfile, os.listdir())))
How can I get my dataset name from within a transform?
This is not possible using the #transform_df decorator. However it is possible using the more powerful #transform decorator.
API Documentation for #transform
Using #transform will cause your function arguments to become of type TransformInput rather than dataframes directly, which have a property path. Note that you will also need to reference and write to the output dataset manually when using #transform.
For example:
#transform(
out=Output("/path/to/my/output"),
inp1=Input("/path/to/my/input1"),
inp2=Input("/path/to/my/input2"),
)
def compute(out, inp1, inp2):
# Add columns containing dataset paths.
df1 = inp1.dataframe().withColumn("dataset_path", F.lit(inp1.path))
df2 = inp2.dataframe().withColumn("dataset_path", F.lit(inp2.path))
# For example.
result = union_many(df1, df2, how="strict")
# Write output manually
out.write_dataframe(result)
However note that a dataset's path is an unstable identifier. If someone were to move or rename these inputs, it could cause unintended behaviour in your pipeline.
For this reason, for a production pipeline I would generally recommend using a more stable identifier. Either a manually chosen hard-coded one (in this case you can use #transform_df again):
#transform_df(
df1=Input("/path/to/my/input1"),
df2=Input("/path/to/my/input2"),
)
def compute(df1, df2):
df1 = df1.withColumn("input_dataset", F.lit("input_1"))
df2 = df2.withColumn("input_dataset", F.lit("input_2"))
# ...etc
or the dataset's RID, using inp1.rid instead of inp1.path.
Note that if you have a large number of inputs, all of these methods can be made neater using python's varargs syntax and comprehensions:
# Using path or rid
#transform(
out=Output("/path/to/my/output"),
inp1=Input("/path/to/my/input1"),
inp2=Input("/path/to/my/input2"),
# and many more...
)
def compute(out, **inps):
# Add columns containing dataset rids (or paths).
dfs = [
inp.dataframe().withColumn("dataset_rid", F.lit(inp.rid))
for key, inp in inps.items()
]
# For example
result = union_many(*dfs, how="strict")
out.write_dataframe(result)
# Using manual keys, we can reuse the argument names as keys.
#transform_df(
Output("/path/to/my/output"),
df1=Input("/path/to/my/input1"),
df2=Input("/path/to/my/input2"),
# and many more...
)
def compute(**dfs):
# Add columns containing dataset keys.
dfs = [
df.withColumn("dataset_key", F.lit(key))
for key, df in dfs.items()
]
# For example
return union_many(*dfs, how="strict")
i have an S3 was over 130k Json Files which i need to calculate numbers based on data in the json files (for example calculate the number of gender of Speakers). i am currently using s3 Paginator and JSON.load to read each file and extract information form. but it take a very long time to process such a large number of file (2-3 files per second). how can i speed up the process? please provide working code examples if possible. Thank you
here is some of my code:
client = boto3.client('s3')
paginator = client.get_paginator('list_objects_v2')
result = paginator.paginate(Bucket='bucket-name',StartAfter='')
for page in result:
if "Contents" in page:
for key in page[ "Contents" ]:
keyString = key[ "Key" ]
s3 = boto3.resource('s3')
content_object = s3.Bucket('bucket-name').Object(str(keyString))
file_content = content_object.get()['Body'].read().decode('utf-8')
json_content = json.loads(file_content)
x = (json_content['dict-name'])
In order to use the code below, I'm assuming you understand pandas (if not, you may want to get to know it). Also, it's not clear if your 2-3 seconds is on the read or includes part of the number crunching, nonetheless multiprocessing will speed this up dramatically. The gist is to read all the files in (as dataframes), concatenate them, then do your analysis.
To be useful for me, I run this on spot instances that have lots of vCPUs and memory. I've found the instances that are network optimized (like c5n - look for the n) and the inf1 (for machine learning) are much faster at reading/writing than T or M instance types, as examples.
My use case is reading 2000 'directories' with roughly 1200 files in each and analyzing them. The multithreading is orders of magnitude faster than single threading.
File 1: your main script
# create script.py file
import os
from multiprocessing import Pool
from itertools import repeat
import pandas as pd
import json
from utils_file_handling import *
ufh = file_utilities() #instantiate the class functions - see below (second file)
bucket = 'your-bucket'
prefix = 'your-prefix/here/' # if you don't have a prefix pass '' (empty string or function will fail)
#define multiprocessing function - get to know this to use multiple processors to read files simultaneously
def get_dflist_multiprocess(keys_list, num_proc=4):
with Pool(num_proc) as pool:
df_list = pool.starmap(ufh.reader_json, zip(repeat(bucket), keys_list), 15)
pool.close()
pool.join()
return df_list
#create your master keys list upfront; you can loop through all or slice the list to test
keys_list = ufh.get_keys_from_prefix(bucket, prefix)
# keys_list = keys_list[0:2000] # as an exampmle
num_proc = os.cpu_count() #tells you how many processors your machine has; function above defaults to 4 unelss given
df_list = get_dflist_multiprocess(keys_list, num_proc=num_proc) #collect dataframes for each file
df_new = pd.concat(df_list, sort=False)
df_new = df_new.reset_index(drop=True)
# do your analysis on the dataframe
File 2: class functions
#utils_file_handling.py
# create this in a separate file; name as you wish but change the import in the script.py file
import boto3
import json
import pandas as pd
#define client and resource
s3sr = boto3.resource('s3')
s3sc = boto3.client('s3')
class file_utilities:
"""file handling function"""
def get_keys_from_prefix(self, bucket, prefix):
'''gets list of keys and dates for given bucket and prefix'''
keys_list = []
paginator = s3sr.meta.client.get_paginator('list_objects_v2')
# use Delimiter to limit search to that level of hierarchy
for page in paginator.paginate(Bucket=bucket, Prefix=prefix, Delimiter='/'):
keys = [content['Key'] for content in page.get('Contents')]
print('keys in page: ', len(keys))
keys_list.extend(keys)
return keys_list
def read_json_file_from_s3(self, bucket, key):
"""read json file"""
bucket_obj = boto3.resource('s3').Bucket(bucket)
obj = boto3.client('s3').get_object(Bucket=bucket, Key=key)
data = obj['Body'].read().decode('utf-8')
return data
# you may need to tweak this for your ['dict-name'] example; I think I have it correct
def reader_json(self, bucket, key):
'''returns dataframe'''
return pd.DataFrame(json.loads(self.read_json_file_from_s3(bucket, key))['dict-name'])
I would like to estimate the parameters of a mixture model of normal distributions in OpenTURNS (that is, the distribution of a weighted sum of Gaussian random variables). OpenTURNS can create such a mixture, but it cannot estimate its parameters. Moreover, I need to create the mixture as an OpenTURNS distribution in order to propagate uncertainty through a function.
For example, I know how to create a mixture of two normal distributions:
import openturns as ot
mu1 = 1.0
sigma1 = 0.5
mu2 = 3.0
sigma2 = 2.0
weights = [0.3, 0.7]
n1 = ot.Normal(mu1, sigma1)
n2 = ot.Normal(mu2, sigma2)
m = ot.Mixture([n1, n2], weights)
In this example, I would like to estimate mu1, sigma1, mu2, sigma2 on a given sample. In order to create a working example, it is easy to generate a sample by simulation.
s = m.getSample(100)
You can rely on scikit-learn's GaussianMixture to estimate the parameters and then use them to define a Mixture model in OpenTURNS.
The script hereafter contains a Python class MixtureFactory that estimates the parameters of a scikitlearn GaussianMixture and outputs an OpenTURNS Mixture distribution:
from sklearn.mixture import GaussianMixture
from sklearn.utils.validation import check_is_fitted
import openturns as ot
import numpy as np
class MixtureFactory(GaussianMixture):
"""
Representation of a Gaussian mixture model probability distribution.
This class allows to estimate the parameters of a Gaussian mixture
distribution using scikit algorithms & provides openturns Mixture object.
Read more in scikit learn user guide & openturns theory.
Parameters:
-----------
n_components : int, defaults to 1.
The number of mixture components.
covariance_type : {'full' (default), 'tied', 'diag', 'spherical'}
String describing the type of covariance parameters to use.
Must be one of:
'full'
each component has its own general covariance matrix
'tied'
all components share the same general covariance matrix
'diag'
each component has its own diagonal covariance matrix
'spherical'
each component has its own single variance
tol : float, defaults to 1e-3.
The convergence threshold. EM iterations will stop when the
lower bound average gain is below this threshold.
reg_covar : float, defaults to 1e-6.
Non-negative regularization added to the diagonal of covariance.
Allows to assure that the covariance matrices are all positive.
max_iter : int, defaults to 100.
The number of EM iterations to perform.
n_init : int, defaults to 1.
The number of initializations to perform. The best results are kept.
init_params : {'kmeans', 'random'}, defaults to 'kmeans'.
The method used to initialize the weights, the means and the
precisions.
Must be one of::
'kmeans' : responsibilities are initialized using kmeans.
'random' : responsibilities are initialized randomly.
weights_init : array-like, shape (n_components, ), optional
The user-provided initial weights, defaults to None.
If it None, weights are initialized using the `init_params` method.
means_init : array-like, shape (n_components, n_features), optional
The user-provided initial means, defaults to None,
If it None, means are initialized using the `init_params` method.
precisions_init : array-like, optional.
The user-provided initial precisions (inverse of the covariance
matrices), defaults to None.
If it None, precisions are initialized using the 'init_params' method.
The shape depends on 'covariance_type'::
(n_components,) if 'spherical',
(n_features, n_features) if 'tied',
(n_components, n_features) if 'diag',
(n_components, n_features, n_features) if 'full'
random_state : int, RandomState instance or None, optional (default=None)
If int, random_state is the seed used by the random number generator;
If RandomState instance, random_state is the random number generator;
If None, the random number generator is the RandomState instance used
by `np.random`.
warm_start : bool, default to False.
If 'warm_start' is True, the solution of the last fitting is used as
initialization for the next call of fit(). This can speed up
convergence when fit is called several times on similar problems.
In that case, 'n_init' is ignored and only a single initialization
occurs upon the first call.
See :term:`the Glossary <warm_start>`.
verbose : int, default to 0.
Enable verbose output. If 1 then it prints the current
initialization and each iteration step. If greater than 1 then
it prints also the log probability and the time needed
for each step.
verbose_interval : int, default to 10.
Number of iteration done before the next print.
"""
def __init__(self, n_components=2, covariance_type='full', tol=1e-6,
reg_covar=1e-6, max_iter=1000, n_init=1, init_params='kmeans',
weights_init=None, means_init=None, precisions_init=None,
random_state=41, warm_start=False,
verbose=0, verbose_interval=10):
super().__init__(n_components, covariance_type, tol, reg_covar,
max_iter, n_init, init_params, weights_init, means_init,
precisions_init, random_state, warm_start, verbose, verbose_interval)
def fit(self, X):
"""
Fit the mixture model parameters.
EM algorithm is applied here to estimate the model parameters and build a
Mixture distribution (see openturns mixture).
The method fits the model ``n_init`` times and sets the parameters with
which the model has the largest likelihood or lower bound. Within each
trial, the method iterates between E-step and M-step for ``max_iter``
times until the change of likelihood or lower bound is less than
``tol``, otherwise, a ``ConvergenceWarning`` is raised.
If ``warm_start`` is ``True``, then ``n_init`` is ignored and a single
initialization is performed upon the first call. Upon consecutive
calls, training starts where it left off.
Parameters
----------
X : array-like, shape (n_samples, n_features)
List of n_features-dimensional data points. Each row
corresponds to a single data point.
Returns
-------
"""
data = np.array(X)
# Evaluate the model parameters.
super().fit(data)
# openturns mixture
# n_components ==> weight of size n_components
weights = self.weights_
n_components = len(weights)
# Create ot distribution
collection = n_components * [0]
# Covariance matrices
cov = self.covariances_
mu = self.means_
# means : n_components x n_features
n_components, n_features = mu.shape
# Following the type of covariance, we define the collection of gaussians
# Spherical : C_k = Identity * sigma_k
if self.covariance_type is 'spherical':
c = ot.CorrelationMatrix(n_features)
for l in range(n_components):
sigma = np.sqrt(cov[l])
collection[l] = ot.Normal(list(mu[l]), [ sigma ] * n_features , c)
elif self.covariance_type is 'diag' :
for l in range(n_components):
c = ot.CovarianceMatrix(n_features)
for i in range(n_features):
c[i,i] = cov[l, i]
collection[l] = ot.Normal(list(mu[l]), c)
elif self.covariance_type == 'tied':
# Same covariance for all clusters
c = ot.CovarianceMatrix(n_features)
for i in range(n_features):
for j in range(0, i+1):
c[i,j] = cov[i,j]
# Define the collection with the same covariance
for l in range(n_components):
collection[l] = ot.Normal(list(mu[l]), c)
else:
n_features = cov.shape[1]
for l in range(n_components):
c = ot.CovarianceMatrix(n_features)
for i in range(n_features):
for j in range(0, i+1):
c[i,j] = cov[l][i,j]
collection[l] = ot.Normal(list(mu[l]), c)
self._mixture = ot.Mixture(collection, weights)
return self
def get_mixture(self):
"""
Returns the Mixture object
"""
check_is_fitted(self)
return self._mixture
if __name__ == "__main__":
mu1 = 1.0
sigma1 = 0.5
mu2 = 3.0
sigma2 = 2.0
weights = [0.3, 0.7]
n1 = ot.Normal(mu1, sigma1)
n2 = ot.Normal(mu2, sigma2)
m = ot.Mixture([n1, n2], weights)
x = m.getSample(1000)
est_dist = MixtureFactory(random_state=1)
est_dist.fit(x)
print(est_dist.get_mixture())
I have actually tried this method and it works perfectly. On top of that the fit of the model through the SciKit GMM and the ulterior adjustment thanks to OpenTurns are very fast. I recommend future users to test several numbers of components and covariance matrix structures, as it will not take a lot of time and can substantially improve the goodness of fit to the data.
Thanks for the answer.
Here is a pure OpenTURNS solution. It is probably slower than the scikit-learn-based method, but it is more generic: you could use it to estimate the parameters of any mixture model, not necessarily a mixture of normal distributions.
The idea is to retrieve the log-likelihood function from the Mixture object and minimize it.
In the following, let us assume that s is the sample we want to fit the mixture on.
First, we need to build the mixture we want to estimate the parameters of. We can specify any valid set of parameters, it does not matter. In your example, you want a mixture of 2 normal distributions.
mixture = ot.Mixture([ot.Normal()]*2, [0.5]*2)
There is a small hurdle. All weights sum to 1, thus one of them is determined by the others: the solver must not be allowed to freely set it. The order of the parameters of an OpenTURNS Mixture is as follows:
weight of the first distribution;
parameters of the first distribution;
weight of the second distribution;
parameters of the second distribution:
...
You can view all parameters with mixture.getParameter() and their names with mixture.getParameterDescription(). The following is a helper function that:
takes as input the list containing of all mixture parameters except the weight of its first distribution;
outputs a Point containing all parameters including the weight of the first distribution.
def full(params):
"""
Point of all mixture parameters from a list that omits the first weight.
"""
params = ot.Point(params)
aux_mixture = ot.Mixture(mixture)
dist_number = aux_mixture.getDistributionCollection().getSize()
index = aux_mixture.getDistributionCollection()[0].getParameter().getSize()
list_weights = []
for num in range(1, dist_number):
list_weights.append(params[index])
index += 1 + aux_mixture.getDistributionCollection()[num].getParameter().getSize()
complementary_weight = ot.Point([abs(1.0 - sum(list_weights))])
complementary_weight.add(params)
return complementary_weight
The next function computes the opposite of the log-likelihood of a given list of parameters (except the first weight).
For the sake of numerical stability, it divides this value by the number of observations.
We will minimize this function in order to find the Maximum Likelihood Estimate.
def minus_log_pdf(params):
"""
- log-likelihood of a list of parameters excepting the first weight
divided by the number of observations
"""
aux_mixture = ot.Mixture(mixture)
full_params = full(params)
try:
aux_mixture.setParameter(full_params)
except TypeError:
# case where the proposed parameters are invalid:
# return a huge value
return [ot.SpecFunc.LogMaxScalar]
res = - aux_mixture.computeLogPDF(s).computeMean()
return res
To use OpenTURNS optimization facilities, we need to turn this function into a PythonFunction object.
OT_minus_log_pdf = ot.PythonFunction(mixture.getParameter().getSize()-1, 1, minus_log_pdf)
Cobyla is usually good at likelihood optimization.
problem = ot.OptimizationProblem(OT_minus_log_pdf)
algo = ot.Cobyla(problem)
In order to decrease chances of Cobyla being stuck on a local minimum, we are going to use MultiStart. We pick a starting set of parameters and randomly change the weights. The following helper function makes it easy:
def random_weights(params, nb):
"""
List of nb Points representing mixture parameters with randomly varying weights.
"""
aux_mixture = ot.Mixture(mixture)
full_params = full(params)
aux_mixture.setParameter(full_params)
list_params = []
for num in range(nb):
dirichlet = ot.Dirichlet([1.0] * aux_mixture.getDistributionCollection().getSize()).getRealization()
dirichlet.add(1.0 - sum(dirichlet))
aux_mixture.setWeights(dirichlet)
list_params.append(aux_mixture.getParameter()[1:])
return list_params
We pick 10 starting points and increase the number of maximum evaluations of the log-likelihood from 100 (by default) to 10000.
init = mixture.getParameter()[1:]
starting_points = random_weights(init, 10)
algo_multistart = ot.MultiStart(algo, starting_points)
algo_multistart.setMaximumEvaluationNumber(10000)
Let's run the solver and retrieve the result.
algo_multistart.run()
result = algo_multistart.getResult()
All that remains is to set the mixture's parameters to the optimal value.
We must not forget to add the first weight back!
optimal_parameters = result.getOptimalPoint()
mixture.setParameter(full(optimal_parameters))
Below is an alternative.
The first step creates a new GaussianMixture class, derived from PythonDistribution. The key point is to implement the computeLogPDF method and the set/getParameters methods. Notice that this parametrization of a mixture only has one single weight w.
class GaussianMixture(ot.PythonDistribution):
def __init__(self, mu1 = -5.0, sigma1 = 1.0, \
mu2 = 5.0, sigma2 = 1.0, \
w = 0.5):
super(GaussianMixture, self).__init__(1)
if w < 0.0 or w > 1.0:
raise ValueError('The weight is not in [0, 1]. w=%s.' % (w))
self.mu1 = mu2
self.sigma1 = sigma1
self.mu2 = mu2
self.sigma2 = sigma2
self.w = w
collDist = [ot.Normal(mu1, sigma1), ot.Normal(mu2, sigma2)]
weight = [w, 1.0 - w]
self.distribution = ot.Mixture(collDist, weight)
def computeCDF(self, x):
p = self.distribution.computeCDF(x)
return p
def computePDF(self, x):
p = self.distribution.computePDF(x)
return p
def computeQuantile(self, prob, tail = False):
quantile = self.distribution.computeQuantile(prob, tail)
return quantile
def getSample(self, size):
X = self.distribution.getSample(size)
return X
def getParameter(self):
parameter = ot.Point([self.mu1, self.sigma1, \
self.mu2, self.sigma2, \
self.w])
return parameter
def setParameter(self, parameter):
[mu1, sigma1, mu2, sigma2, w] = parameter
self.__init__(mu1, sigma1, mu2, sigma2, w)
return parameter
def computeLogPDF(self, sample):
logpdf = self.distribution.computeLogPDF(sample)
return logpdf
In order to create the distribution, we use the Distribution class:
gm = ot.Distribution(GaussianMixture())
Estimating the parameters of this distribution is straightforward with MaximumLikelihoodFactory. However, we must set the bounds, because sigma cannot be negative and that w is in (0, 1).
factory = ot.MaximumLikelihoodFactory(gm)
lowerBound = [0.0, 1.e-6, 0.0, 1.e-6, 0.01]
upperBound = [0.0, 0.0, 0.0, 0.0, 0.99]
finiteLowerBound = [False, True, False, True, True]
finiteUpperBound = [False, False, False, False, True]
bounds = ot.Interval(lowerBound, upperBound, finiteLowerBound, finiteUpperBound)
factory.setOptimizationBounds(bounds)
Then we configure the optimization solver.
solver = factory.getOptimizationAlgorithm()
startingPoint = [-4.0, 1.0, 7.0, 1.5, 0.3]
solver.setStartingPoint(startingPoint)
factory.setOptimizationAlgorithm(solver)
Estimating the parameters is based on the build method.
distribution = factory.build(sample)
There are two limitations with this implementation.
First, it is not as fast as it should be, because of a limitation of the PythonDistribution (see https://github.com/openturns/openturns/issues/1391).
Estimating the parameters may be difficult, because the problem may have local optimas that cannot be retrieved with the default algorithm in MaximumLikelihoodFactory. This kind of task is generally done with the EM algorithm.
In PyTorch, we can define architectures in multiple ways. Here, I'd like to create a simple LSTM network using the Sequential module.
In Lua's torch I would usually go with:
model = nn.Sequential()
model:add(nn.SplitTable(1,2))
model:add(nn.Sequencer(nn.LSTM(inputSize, hiddenSize)))
model:add(nn.SelectTable(-1)) -- last step of output sequence
model:add(nn.Linear(hiddenSize, classes_n))
However, in PyTorch, I don't find the equivalent of SelectTable to get the last output.
nn.Sequential(
nn.LSTM(inputSize, hiddenSize, 1, batch_first=True),
# what to put here to retrieve last output of LSTM ?,
nn.Linear(hiddenSize, classe_n))
Define a class to extract the last cell output:
# LSTM() returns tuple of (tensor, (recurrent state))
class extract_tensor(nn.Module):
def forward(self,x):
# Output shape (batch, features, hidden)
tensor, _ = x
# Reshape shape (batch, hidden)
return tensor[:, -1, :]
nn.Sequential(
nn.LSTM(inputSize, hiddenSize, 1, batch_first=True),
extract_tensor(),
nn.Linear(hiddenSize, classe_n)
)
According to the LSTM cell documentation the outputs parameter has a shape of (seq_len, batch, hidden_size * num_directions) so you can easily take the last element of the sequence in this way:
rnn = nn.LSTM(10, 20, 2)
input = Variable(torch.randn(5, 3, 10))
h0 = Variable(torch.randn(2, 3, 20))
c0 = Variable(torch.randn(2, 3, 20))
output, hn = rnn(input, (h0, c0))
print(output[-1]) # last element
Tensor manipulation and Neural networks design in PyTorch is incredibly easier than in Torch so you rarely have to use containers. In fact, as stated in the tutorial PyTorch for former Torch users PyTorch is built around Autograd so you don't need anymore to worry about containers. However, if you want to use your old Lua Torch code you can have a look to the Legacy package.
As far as I'm concerned there's nothing like a SplitTable or a SelectTable in PyTorch. That said, you are allowed to concatenate an arbitrary number of modules or blocks within a single architecture, and you can use this property to retrieve the output of a certain layer. Let's make it more clear with a simple example.
Suppose I want to build a simple two-layer MLP and retrieve the output of each layer. I can build a custom class inheriting from nn.Module:
class MyMLP(nn.Module):
def __init__(self, in_channels, out_channels_1, out_channels_2):
# first of all, calling base class constructor
super().__init__()
# now I can build my modular network
self.block1 = nn.Linear(in_channels, out_channels_1)
self.block2 = nn.Linear(out_channels_1, out_channels_2)
# you MUST implement a forward(input) method whenever inheriting from nn.Module
def forward(x):
# first_out will now be your output of the first block
first_out = self.block1(x)
x = self.block2(first_out)
# by returning both x and first_out, you can now access the first layer's output
return x, first_out
In your main file you can now declare the custom architecture and use it:
from myFile import MyMLP
import numpy as np
in_ch = out_ch_1 = out_ch_2 = 64
# some fake input instance
x = np.random.rand(in_ch)
my_mlp = MyMLP(in_ch, out_ch_1, out_ch_2)
# get your outputs
final_out, first_layer_out = my_mlp(x)
Moreover, you could concatenate two MyMLP in a more complex model definition and retrieve the output of each one in a similar way.
I hope this is enough to clarify, but in case you have more questions, please feel free to ask, since I may have omitted something.
I am trying to understand how FiPy works by working an example, in particular I would like to solve the following simple convection equation with periodic boundary:
$$\partial_t u + \partial_x u = 0$$
If initial data is given by $u(x, 0) = F(x)$, then the analytical solution is $u(x, t) = F(x - t)$. I do get a solution, but it is not correct.
What am I missing? Is there a better resource for understanding FiPy than the documentation? It is very sparse...
Here is my attempt
from fipy import *
import numpy as np
# Generate mesh
nx = 20
dx = 2*np.pi/nx
mesh = PeriodicGrid1D(nx=nx, dx=dx)
# Generate solution object with initial discontinuity
phi = CellVariable(name="solution variable", mesh=mesh)
phiAnalytical = CellVariable(name="analytical value", mesh=mesh)
phi.setValue(1.)
phi.setValue(0., where=x > 1.)
# Define the pde
D = [[-1.]]
eq = TransientTerm() == ConvectionTerm(coeff=D)
# Set discretization so analytical solution is exactly one cell translation
dt = 0.01*dx
steps = 2*int(dx/dt)
# Set the analytical value at the end of simulation
phiAnalytical.setValue(np.roll(phi.value, 1))
for step in range(steps):
eq.solve(var=phi, dt=dt)
print(phi.allclose(phiAnalytical, atol=1e-1))
As addressed on the FiPy mailing list, FiPy is not great at handling convection only PDEs (absent diffusion, pure hyperbolic) as it's missing higher order convection schemes. It is better to use CLAWPACK for this class of problem.
FiPy does have one second order scheme that might help with this problem, the VanLeerConvectionTerm, see an example.
If the VanLeerConvectionTerm is used in the above problem, it does do a better job of preserving the shock.
import numpy as np
import fipy
# Generate mesh
nx = 20
dx = 2*np.pi/nx
mesh = fipy.PeriodicGrid1D(nx=nx, dx=dx)
# Generate solution object with initial discontinuity
phi = fipy.CellVariable(name="solution variable", mesh=mesh)
phiAnalytical = fipy.CellVariable(name="analytical value", mesh=mesh)
phi.setValue(1.)
phi.setValue(0., where=mesh.x > 1.)
# Define the pde
D = [[-1.]]
eq = fipy.TransientTerm() == fipy.VanLeerConvectionTerm(coeff=D)
# Set discretization so analytical solution is exactly one cell translation
dt = 0.01*dx
steps = 2*int(dx/dt)
# Set the analytical value at the end of simulation
phiAnalytical.setValue(np.roll(phi.value, 1))
viewer = fipy.Viewer(phi)
for step in range(steps):
eq.solve(var=phi, dt=dt)
viewer.plot()
raw_input('stopped')
print(phi.allclose(phiAnalytical, atol=1e-1))