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+/PyDTMC-8.2.0.tar.gz
diff --git a/python-pydtmc.spec b/python-pydtmc.spec
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+%global _empty_manifest_terminate_build 0
+Name:		python-PyDTMC
+Version:	8.2.0
+Release:	1
+Summary:	A full-featured and lightweight library for discrete-time Markov chains analysis.
+License:	MIT
+URL:		https://github.com/TommasoBelluzzo/PyDTMC
+Source0:	https://mirrors.nju.edu.cn/pypi/web/packages/64/b0/8f7ab69998f60976805efe15c2bf086259aed3d423196726e035faef2741/PyDTMC-8.2.0.tar.gz
+BuildArch:	noarch
+
+Requires:	python3-matplotlib
+Requires:	python3-networkx
+Requires:	python3-numpy
+Requires:	python3-scipy
+Requires:	python3-setuptools
+Requires:	python3-wheel
+Requires:	python3-twine
+Requires:	python3-docutils
+Requires:	python3-typing-extensions
+Requires:	python3-sphinx
+Requires:	python3-sphinx-autodoc-typehints
+Requires:	python3-sphinx-rtd-theme
+Requires:	python3-flake8
+Requires:	python3-pylint
+Requires:	python3-defusedxml
+Requires:	python3-numpydoc
+Requires:	python3-pandas
+Requires:	python3-pydot
+Requires:	python3-coverage
+Requires:	python3-pytest
+Requires:	python3-pytest-benchmark
+Requires:	python3-pytest-cov
+Requires:	python3-coveralls
+
+%description
+PyDTMC is a full-featured and lightweight library for discrete-time Markov chains analysis. It provides classes and functions for creating, manipulating, simulating and visualizing Markov processes.
+
+<table>
+  <tr>
+    <td align="right">Status:</td>
+    <td align="left">
+      <a href="https://github.com/TommasoBelluzzo/PyDTMC/actions/workflows/continuous_integration.yml"><img alt="Build" src="https://img.shields.io/github/workflow/status/TommasoBelluzzo/PyDTMC/Continuous%20Integration?style=flat&label=Build&color=1081C2"/></a>
+      <a href="https://pydtmc.readthedocs.io/"><img alt="Docs" src="https://img.shields.io/readthedocs/pydtmc?style=flat&label=Docs&color=1081C2"/></a>
+      <a href="https://coveralls.io/github/TommasoBelluzzo/PyDTMC?branch=master"><img alt="Coverage" src="https://img.shields.io/coveralls/github/TommasoBelluzzo/PyDTMC?style=flat&label=Coverage&color=1081C2"/></a>
+    </td>
+  </tr>
+  <tr>
+    <td align="right">Info:</td>
+    <td align="left">
+      <a href="#"><img alt="License" src="https://img.shields.io/github/license/TommasoBelluzzo/PyDTMC?style=flat&label=License&color=1081C2"/></a>
+      <a href="#"><img alt="Lines" src="https://img.shields.io/tokei/lines/github/TommasoBelluzzo/PyDTMC?style=flat&label=Lines&color=1081C2"/></a>
+      <a href="#"><img alt="Size" src="https://img.shields.io/github/repo-size/TommasoBelluzzo/PyDTMC?style=flat&label=Size&color=1081C2"/></a>
+    </td>
+  </tr>
+  <tr>
+    <td align="right">PyPI:</td>
+    <td align="left">
+      <a href="https://pypi.org/project/PyDTMC/"><img alt="Version" src="https://img.shields.io/pypi/v/PyDTMC?style=flat&label=Version&color=1081C2"/></a>
+      <a href="https://pypi.org/project/PyDTMC/"><img alt="Python" src="https://img.shields.io/pypi/pyversions/PyDTMC?style=flat&label=Python&color=1081C2"/></a>
+      <a href="https://pypi.org/project/PyDTMC/"><img alt="Wheel" src="https://img.shields.io/pypi/wheel/PyDTMC?style=flat&label=Wheel&color=1081C2"/></a>
+      <a href="https://pypi.org/project/PyDTMC/"><img alt="Downloads" src="https://img.shields.io/pypi/dm/PyDTMC?style=flat&label=Downloads&color=1081C2"/></a>
+    </td>
+  </tr>
+  <tr>
+    <td align="right">Conda:</td>
+    <td align="left">
+      <a href="https://anaconda.org/conda-forge/pydtmc/"><img alt="Version" src="https://img.shields.io/conda/vn/conda-forge/pydtmc?style=flat&label=Version"/></a>
+      <a href="https://anaconda.org/conda-forge/pydtmc/"><img alt="Python" src="https://img.shields.io/pypi/pyversions/PyDTMC?style=flat&label=Python&color=1081C2"/></a>
+      <a href="https://anaconda.org/conda-forge/pydtmc/"><img alt="Platforms" src="https://img.shields.io/conda/pn/conda-forge/pydtmc?style=flat&label=Platforms&color=1081C2"/></a>
+      <a href="https://anaconda.org/conda-forge/pydtmc/"><img alt="Downloads" src="https://img.shields.io/conda/dn/conda-forge/pydtmc?style=flat&label=Downloads&color=1081C2"/></a>
+    </td>
+  </tr>
+  <tr>
+    <td align="right">Donation:</td>
+    <td align="left">
+      <a href="https://www.paypal.com/cgi-bin/webscr?cmd=_s-xclick&hosted_button_id=D8LH6DNYN7EN8"><img alt="PayPal" src="https://www.paypalobjects.com/en_US/i/btn/btn_donate_LG.gif"/></a>
+    </td>
+  </tr>
+</table>
+
+## Requirements
+
+The `Python` environment must include the following packages:
+
+* [Matplotlib](https://matplotlib.org/)
+* [NetworkX](https://networkx.github.io/)
+* [NumPy](https://www.numpy.org/)
+* [SciPy](https://www.scipy.org/)
+
+*Notes:*
+
+* It's recommended to install [Graphviz](https://www.graphviz.org/) and [pydot](https://pypi.org/project/pydot/) before using the `plot_graph` function.
+* The packages [pytest](https://pytest.org/) and [pytest-benchmark](https://pypi.org/project/pytest-benchmark/) are required for performing unit tests.
+* The package [Sphinx](https://www.sphinx-doc.org/) is required for building the package documentation.
+
+## Installation & Upgrade
+
+[PyPI](https://pypi.org/):
+
+```sh
+$ pip install PyDTMC
+$ pip install --upgrade PyDTMC
+```
+
+[Git](https://git-scm.com/):
+
+```sh
+$ pip install https://github.com/TommasoBelluzzo/PyDTMC/tarball/master
+$ pip install --upgrade https://github.com/TommasoBelluzzo/PyDTMC/tarball/master
+
+$ pip install git+https://github.com/TommasoBelluzzo/PyDTMC.git#egg=PyDTMC
+$ pip install --upgrade git+https://github.com/TommasoBelluzzo/PyDTMC.git#egg=PyDTMC
+```
+
+[Conda](https://docs.conda.io/):
+
+```sh
+$ conda install -c conda-forge pydtmc
+$ conda update -c conda-forge pydtmc
+
+$ conda install -c tommasobelluzzo pydtmc
+$ conda update -c tommasobelluzzo pydtmc
+```
+
+## Usage: MarkovChain Class
+
+The `MarkovChain` class can be instantiated as follows:
+
+```console
+>>> p = [[0.2, 0.7, 0.0, 0.1], [0.0, 0.6, 0.3, 0.1], [0.0, 0.0, 1.0, 0.0], [0.5, 0.0, 0.5, 0.0]]
+>>> mc = MarkovChain(p, ['A', 'B', 'C', 'D'])
+>>> print(mc)
+
+DISCRETE-TIME MARKOV CHAIN
+ SIZE:           4
+ RANK:           4
+ CLASSES:        2
+  > RECURRENT:   1
+  > TRANSIENT:   1
+ ERGODIC:        NO
+  > APERIODIC:   YES
+  > IRREDUCIBLE: NO
+ ABSORBING:      YES
+ REGULAR:        NO
+ REVERSIBLE:     YES
+ SYMMETRIC:      NO
+```
+
+Below a few examples of `MarkovChain` properties:
+
+```console
+>>> print(mc.is_ergodic)
+False
+
+>>> print(mc.recurrent_states)
+['C']
+
+>>> print(mc.transient_states)
+['A', 'B', 'D']
+
+>>> print(mc.steady_states)
+[array([0.0, 0.0, 1.0, 0.0])]
+
+>>> print(mc.is_absorbing)
+True
+
+>>> print(mc.fundamental_matrix)
+[[1.50943396, 2.64150943, 0.41509434]
+ [0.18867925, 2.83018868, 0.30188679]
+ [0.75471698, 1.32075472, 1.20754717]]
+ 
+>>> print(mc.kemeny_constant)
+5.547169811320755
+
+>>> print(mc.entropy_rate)
+0.0
+```
+
+Below a few examples of `MarkovChain` methods:
+
+```console
+>>> print(mc.absorption_probabilities())
+[1.0 1.0 1.0]
+
+>>> print(mc.expected_rewards(10, [2, -3, 8, -7]))
+[44.96611926, 52.03057032, 88.00000000, 51.74779651]
+
+>>> print(mc.expected_transitions(2))
+[[0.0850, 0.2975, 0.0000, 0.0425]
+ [0.0000, 0.3450, 0.1725, 0.0575]
+ [0.0000, 0.0000, 0.7000, 0.0000]
+ [0.1500, 0.0000, 0.1500, 0.0000]]
+
+>>> print(mc.first_passage_probabilities(5, 3))
+[[0.5000, 0.0000, 0.5000, 0.0000]
+ [0.0000, 0.3500, 0.0000, 0.0500]
+ [0.0000, 0.0700, 0.1300, 0.0450]
+ [0.0000, 0.0315, 0.1065, 0.0300]
+ [0.0000, 0.0098, 0.0761, 0.0186]]
+ 
+>>> print(mc.hitting_probabilities([0, 1]))
+[1.0, 1.0, 0.0, 0.5]
+ 
+>>> print(mc.mean_absorption_times())
+[4.56603774, 3.32075472, 3.28301887]
+
+>>> print(mc.mean_number_visits())
+[[0.50943396, 2.64150943, INF, 0.41509434]
+ [0.18867925, 1.83018868, INF, 0.30188679]
+ [0.00000000, 0.00000000, INF, 0.00000000]
+ [0.75471698, 1.32075472, INF, 0.20754717]]
+ 
+>>> print(mc.simulate(10, seed=32))
+['D', 'A', 'B', 'B', 'C', 'C', 'C', 'C', 'C', 'C', 'C']
+```
+
+```console
+>>> sequence = ["A"]
+>>> for i in range(1, 11):
+...     current_state = sequence[-1]
+...     next_state = mc.next(current_state, seed=32)
+...     print((' ' if i < 10 else '') + f'{i}) {current_state} -> {next_state}')
+...     sequence.append(next_state)
+ 1) A -> B
+ 2) B -> C
+ 3) C -> C
+ 4) C -> C
+ 5) C -> C
+ 6) C -> C
+ 7) C -> C
+ 8) C -> C
+ 9) C -> C
+10) C -> C
+```
+
+Below a few examples of `MarkovChain` plotting functions; in order to display the output of plots immediately, the [interactive mode](https://matplotlib.org/stable/users/interactive.html#interactive-mode) of [Matplotlib](https://matplotlib.org/) must be turned on:
+
+```console
+>>> plot_eigenvalues(mc, dpi=300)
+>>> plot_graph(mc, dpi=300)
+>>> plot_sequence(mc, 10, plot_type='histogram', dpi=300)
+>>> plot_sequence(mc, 10, plot_type='heatmap', dpi=300)
+>>> plot_sequence(mc, 10, plot_type='matrix', dpi=300)
+>>> plot_redistributions(mc, 10, plot_type='heatmap', dpi=300)
+>>> plot_redistributions(mc, 10, plot_type='projection', dpi=300)
+```
+
+![Screenshots](https://i.imgur.com/bltMSi5.gif)
+
+## Usage: HiddenMarkovModel Class
+
+The `HiddenMarkovModel` class can be instantiated as follows:
+
+```console
+>>> p = [[0.4, 0.6], [0.8, 0.2]]
+>>> states = ['A', 'B']
+>>> e = [[0.5, 0.0, 0.0, 0.5], [0.2, 0.2, 0.2, 0.4]]
+>>> symbols = ['H1', 'H2', 'H3', 'H4']
+>>> hmm = HiddenMarkovModel(p, e, states, symbols)
+>>> print(hmm)
+    
+HIDDEN MARKOV MODEL
+ STATES:  2
+ SYMBOLS: 4
+ ERGODIC: NO
+ REGULAR: NO
+```
+
+Below a few examples of `HiddenMarkovModel` methods:
+
+```console
+>>> sim_states, sim_symbols = hmm.simulate(12, seed=1488)
+>>> print(sim_states)
+['B', 'A', 'A', 'A', 'B', 'A', 'A']
+>>> print(sim_symbols)
+['H2', 'H4', 'H4', 'H4', 'H3', 'H4', 'H4']
+
+>>> est_hmm = hmm.estimate(states, symbols, sim_states, sim_symbols)
+>>> print(est_hmm.p)
+[[0.75, 0.25]
+ [1.00, 0.00]]
+>>> print(est_hmm.e)
+[[0.0, 0.0, 0.0, 1.0]
+ [0.0, 0.5, 0.5, 0.0]]
+
+>>> dec_lp, dec_posterior, dec_backward, dec_forward, _ = hmm.decode(sim_symbols)
+>>> print(dec_lp)
+-8.77549587
+>>> print(dec_posterior)
+[[0.00000000, 0.84422968, 0.41785105, 0.84422968, 0.00000000, 0.82089552, 0.52238806]
+ [1.00000000, 0.15577032, 0.58214895, 0.15577032, 1.00000000, 0.17910448, 0.47761194]]
+>>> print(dec_backward)
+[[1.50000000, 0.88942581, 1.01307561, 0.79988630, 1.31154065, 0.94776119, 0.98507463, 1.00000000]
+ [0.50000000, 1.00000000, 0.93462194, 1.21887436, 0.43718022, 1.00000000, 1.07462687, 1.00000000]]
+>>> print(dec_forward)
+[[0.50000000, 0.00000000, 0.83333333, 0.52238806, 0.64369311, 0.00000000, 0.83333333 0.52238806]
+ [0.50000000, 1.00000000, 0.16666667, 0.47761194, 0.35630689, 1.00000000, 0.16666667 0.47761194]]
+
+>>> pre_lp, pre_states = hmm.predict('viterbi', sim_symbols)
+>>> print(pre_lp)
+-13.24482936
+>>> print(pre_states)
+['B', 'A', 'B', 'A', 'B', 'A', 'B']
+```
+
+Below a few examples of `HiddenMarkovModel` plotting functions; in order to display the output of plots immediately, the [interactive mode](https://matplotlib.org/stable/users/interactive.html#interactive-mode) of [Matplotlib](https://matplotlib.org/) must be turned on:
+
+```console
+>>> plot_graph(hmm, dpi=300)
+>>> plot_sequence(hmm, 10, plot_type='histogram', dpi=300)
+>>> plot_sequence(hmm, 10, plot_type='heatmap', dpi=300)
+>>> plot_sequence(hmm, 10, plot_type='matrix', dpi=300)
+>>> plot_trellis(hmm, 10, dpi=300)
+```
+
+![Screenshots](https://i.imgur.com/rSNUbdX.gif)
+
+
+%package -n python3-PyDTMC
+Summary:	A full-featured and lightweight library for discrete-time Markov chains analysis.
+Provides:	python-PyDTMC
+BuildRequires:	python3-devel
+BuildRequires:	python3-setuptools
+BuildRequires:	python3-pip
+%description -n python3-PyDTMC
+PyDTMC is a full-featured and lightweight library for discrete-time Markov chains analysis. It provides classes and functions for creating, manipulating, simulating and visualizing Markov processes.
+
+<table>
+  <tr>
+    <td align="right">Status:</td>
+    <td align="left">
+      <a href="https://github.com/TommasoBelluzzo/PyDTMC/actions/workflows/continuous_integration.yml"><img alt="Build" src="https://img.shields.io/github/workflow/status/TommasoBelluzzo/PyDTMC/Continuous%20Integration?style=flat&label=Build&color=1081C2"/></a>
+      <a href="https://pydtmc.readthedocs.io/"><img alt="Docs" src="https://img.shields.io/readthedocs/pydtmc?style=flat&label=Docs&color=1081C2"/></a>
+      <a href="https://coveralls.io/github/TommasoBelluzzo/PyDTMC?branch=master"><img alt="Coverage" src="https://img.shields.io/coveralls/github/TommasoBelluzzo/PyDTMC?style=flat&label=Coverage&color=1081C2"/></a>
+    </td>
+  </tr>
+  <tr>
+    <td align="right">Info:</td>
+    <td align="left">
+      <a href="#"><img alt="License" src="https://img.shields.io/github/license/TommasoBelluzzo/PyDTMC?style=flat&label=License&color=1081C2"/></a>
+      <a href="#"><img alt="Lines" src="https://img.shields.io/tokei/lines/github/TommasoBelluzzo/PyDTMC?style=flat&label=Lines&color=1081C2"/></a>
+      <a href="#"><img alt="Size" src="https://img.shields.io/github/repo-size/TommasoBelluzzo/PyDTMC?style=flat&label=Size&color=1081C2"/></a>
+    </td>
+  </tr>
+  <tr>
+    <td align="right">PyPI:</td>
+    <td align="left">
+      <a href="https://pypi.org/project/PyDTMC/"><img alt="Version" src="https://img.shields.io/pypi/v/PyDTMC?style=flat&label=Version&color=1081C2"/></a>
+      <a href="https://pypi.org/project/PyDTMC/"><img alt="Python" src="https://img.shields.io/pypi/pyversions/PyDTMC?style=flat&label=Python&color=1081C2"/></a>
+      <a href="https://pypi.org/project/PyDTMC/"><img alt="Wheel" src="https://img.shields.io/pypi/wheel/PyDTMC?style=flat&label=Wheel&color=1081C2"/></a>
+      <a href="https://pypi.org/project/PyDTMC/"><img alt="Downloads" src="https://img.shields.io/pypi/dm/PyDTMC?style=flat&label=Downloads&color=1081C2"/></a>
+    </td>
+  </tr>
+  <tr>
+    <td align="right">Conda:</td>
+    <td align="left">
+      <a href="https://anaconda.org/conda-forge/pydtmc/"><img alt="Version" src="https://img.shields.io/conda/vn/conda-forge/pydtmc?style=flat&label=Version"/></a>
+      <a href="https://anaconda.org/conda-forge/pydtmc/"><img alt="Python" src="https://img.shields.io/pypi/pyversions/PyDTMC?style=flat&label=Python&color=1081C2"/></a>
+      <a href="https://anaconda.org/conda-forge/pydtmc/"><img alt="Platforms" src="https://img.shields.io/conda/pn/conda-forge/pydtmc?style=flat&label=Platforms&color=1081C2"/></a>
+      <a href="https://anaconda.org/conda-forge/pydtmc/"><img alt="Downloads" src="https://img.shields.io/conda/dn/conda-forge/pydtmc?style=flat&label=Downloads&color=1081C2"/></a>
+    </td>
+  </tr>
+  <tr>
+    <td align="right">Donation:</td>
+    <td align="left">
+      <a href="https://www.paypal.com/cgi-bin/webscr?cmd=_s-xclick&hosted_button_id=D8LH6DNYN7EN8"><img alt="PayPal" src="https://www.paypalobjects.com/en_US/i/btn/btn_donate_LG.gif"/></a>
+    </td>
+  </tr>
+</table>
+
+## Requirements
+
+The `Python` environment must include the following packages:
+
+* [Matplotlib](https://matplotlib.org/)
+* [NetworkX](https://networkx.github.io/)
+* [NumPy](https://www.numpy.org/)
+* [SciPy](https://www.scipy.org/)
+
+*Notes:*
+
+* It's recommended to install [Graphviz](https://www.graphviz.org/) and [pydot](https://pypi.org/project/pydot/) before using the `plot_graph` function.
+* The packages [pytest](https://pytest.org/) and [pytest-benchmark](https://pypi.org/project/pytest-benchmark/) are required for performing unit tests.
+* The package [Sphinx](https://www.sphinx-doc.org/) is required for building the package documentation.
+
+## Installation & Upgrade
+
+[PyPI](https://pypi.org/):
+
+```sh
+$ pip install PyDTMC
+$ pip install --upgrade PyDTMC
+```
+
+[Git](https://git-scm.com/):
+
+```sh
+$ pip install https://github.com/TommasoBelluzzo/PyDTMC/tarball/master
+$ pip install --upgrade https://github.com/TommasoBelluzzo/PyDTMC/tarball/master
+
+$ pip install git+https://github.com/TommasoBelluzzo/PyDTMC.git#egg=PyDTMC
+$ pip install --upgrade git+https://github.com/TommasoBelluzzo/PyDTMC.git#egg=PyDTMC
+```
+
+[Conda](https://docs.conda.io/):
+
+```sh
+$ conda install -c conda-forge pydtmc
+$ conda update -c conda-forge pydtmc
+
+$ conda install -c tommasobelluzzo pydtmc
+$ conda update -c tommasobelluzzo pydtmc
+```
+
+## Usage: MarkovChain Class
+
+The `MarkovChain` class can be instantiated as follows:
+
+```console
+>>> p = [[0.2, 0.7, 0.0, 0.1], [0.0, 0.6, 0.3, 0.1], [0.0, 0.0, 1.0, 0.0], [0.5, 0.0, 0.5, 0.0]]
+>>> mc = MarkovChain(p, ['A', 'B', 'C', 'D'])
+>>> print(mc)
+
+DISCRETE-TIME MARKOV CHAIN
+ SIZE:           4
+ RANK:           4
+ CLASSES:        2
+  > RECURRENT:   1
+  > TRANSIENT:   1
+ ERGODIC:        NO
+  > APERIODIC:   YES
+  > IRREDUCIBLE: NO
+ ABSORBING:      YES
+ REGULAR:        NO
+ REVERSIBLE:     YES
+ SYMMETRIC:      NO
+```
+
+Below a few examples of `MarkovChain` properties:
+
+```console
+>>> print(mc.is_ergodic)
+False
+
+>>> print(mc.recurrent_states)
+['C']
+
+>>> print(mc.transient_states)
+['A', 'B', 'D']
+
+>>> print(mc.steady_states)
+[array([0.0, 0.0, 1.0, 0.0])]
+
+>>> print(mc.is_absorbing)
+True
+
+>>> print(mc.fundamental_matrix)
+[[1.50943396, 2.64150943, 0.41509434]
+ [0.18867925, 2.83018868, 0.30188679]
+ [0.75471698, 1.32075472, 1.20754717]]
+ 
+>>> print(mc.kemeny_constant)
+5.547169811320755
+
+>>> print(mc.entropy_rate)
+0.0
+```
+
+Below a few examples of `MarkovChain` methods:
+
+```console
+>>> print(mc.absorption_probabilities())
+[1.0 1.0 1.0]
+
+>>> print(mc.expected_rewards(10, [2, -3, 8, -7]))
+[44.96611926, 52.03057032, 88.00000000, 51.74779651]
+
+>>> print(mc.expected_transitions(2))
+[[0.0850, 0.2975, 0.0000, 0.0425]
+ [0.0000, 0.3450, 0.1725, 0.0575]
+ [0.0000, 0.0000, 0.7000, 0.0000]
+ [0.1500, 0.0000, 0.1500, 0.0000]]
+
+>>> print(mc.first_passage_probabilities(5, 3))
+[[0.5000, 0.0000, 0.5000, 0.0000]
+ [0.0000, 0.3500, 0.0000, 0.0500]
+ [0.0000, 0.0700, 0.1300, 0.0450]
+ [0.0000, 0.0315, 0.1065, 0.0300]
+ [0.0000, 0.0098, 0.0761, 0.0186]]
+ 
+>>> print(mc.hitting_probabilities([0, 1]))
+[1.0, 1.0, 0.0, 0.5]
+ 
+>>> print(mc.mean_absorption_times())
+[4.56603774, 3.32075472, 3.28301887]
+
+>>> print(mc.mean_number_visits())
+[[0.50943396, 2.64150943, INF, 0.41509434]
+ [0.18867925, 1.83018868, INF, 0.30188679]
+ [0.00000000, 0.00000000, INF, 0.00000000]
+ [0.75471698, 1.32075472, INF, 0.20754717]]
+ 
+>>> print(mc.simulate(10, seed=32))
+['D', 'A', 'B', 'B', 'C', 'C', 'C', 'C', 'C', 'C', 'C']
+```
+
+```console
+>>> sequence = ["A"]
+>>> for i in range(1, 11):
+...     current_state = sequence[-1]
+...     next_state = mc.next(current_state, seed=32)
+...     print((' ' if i < 10 else '') + f'{i}) {current_state} -> {next_state}')
+...     sequence.append(next_state)
+ 1) A -> B
+ 2) B -> C
+ 3) C -> C
+ 4) C -> C
+ 5) C -> C
+ 6) C -> C
+ 7) C -> C
+ 8) C -> C
+ 9) C -> C
+10) C -> C
+```
+
+Below a few examples of `MarkovChain` plotting functions; in order to display the output of plots immediately, the [interactive mode](https://matplotlib.org/stable/users/interactive.html#interactive-mode) of [Matplotlib](https://matplotlib.org/) must be turned on:
+
+```console
+>>> plot_eigenvalues(mc, dpi=300)
+>>> plot_graph(mc, dpi=300)
+>>> plot_sequence(mc, 10, plot_type='histogram', dpi=300)
+>>> plot_sequence(mc, 10, plot_type='heatmap', dpi=300)
+>>> plot_sequence(mc, 10, plot_type='matrix', dpi=300)
+>>> plot_redistributions(mc, 10, plot_type='heatmap', dpi=300)
+>>> plot_redistributions(mc, 10, plot_type='projection', dpi=300)
+```
+
+![Screenshots](https://i.imgur.com/bltMSi5.gif)
+
+## Usage: HiddenMarkovModel Class
+
+The `HiddenMarkovModel` class can be instantiated as follows:
+
+```console
+>>> p = [[0.4, 0.6], [0.8, 0.2]]
+>>> states = ['A', 'B']
+>>> e = [[0.5, 0.0, 0.0, 0.5], [0.2, 0.2, 0.2, 0.4]]
+>>> symbols = ['H1', 'H2', 'H3', 'H4']
+>>> hmm = HiddenMarkovModel(p, e, states, symbols)
+>>> print(hmm)
+    
+HIDDEN MARKOV MODEL
+ STATES:  2
+ SYMBOLS: 4
+ ERGODIC: NO
+ REGULAR: NO
+```
+
+Below a few examples of `HiddenMarkovModel` methods:
+
+```console
+>>> sim_states, sim_symbols = hmm.simulate(12, seed=1488)
+>>> print(sim_states)
+['B', 'A', 'A', 'A', 'B', 'A', 'A']
+>>> print(sim_symbols)
+['H2', 'H4', 'H4', 'H4', 'H3', 'H4', 'H4']
+
+>>> est_hmm = hmm.estimate(states, symbols, sim_states, sim_symbols)
+>>> print(est_hmm.p)
+[[0.75, 0.25]
+ [1.00, 0.00]]
+>>> print(est_hmm.e)
+[[0.0, 0.0, 0.0, 1.0]
+ [0.0, 0.5, 0.5, 0.0]]
+
+>>> dec_lp, dec_posterior, dec_backward, dec_forward, _ = hmm.decode(sim_symbols)
+>>> print(dec_lp)
+-8.77549587
+>>> print(dec_posterior)
+[[0.00000000, 0.84422968, 0.41785105, 0.84422968, 0.00000000, 0.82089552, 0.52238806]
+ [1.00000000, 0.15577032, 0.58214895, 0.15577032, 1.00000000, 0.17910448, 0.47761194]]
+>>> print(dec_backward)
+[[1.50000000, 0.88942581, 1.01307561, 0.79988630, 1.31154065, 0.94776119, 0.98507463, 1.00000000]
+ [0.50000000, 1.00000000, 0.93462194, 1.21887436, 0.43718022, 1.00000000, 1.07462687, 1.00000000]]
+>>> print(dec_forward)
+[[0.50000000, 0.00000000, 0.83333333, 0.52238806, 0.64369311, 0.00000000, 0.83333333 0.52238806]
+ [0.50000000, 1.00000000, 0.16666667, 0.47761194, 0.35630689, 1.00000000, 0.16666667 0.47761194]]
+
+>>> pre_lp, pre_states = hmm.predict('viterbi', sim_symbols)
+>>> print(pre_lp)
+-13.24482936
+>>> print(pre_states)
+['B', 'A', 'B', 'A', 'B', 'A', 'B']
+```
+
+Below a few examples of `HiddenMarkovModel` plotting functions; in order to display the output of plots immediately, the [interactive mode](https://matplotlib.org/stable/users/interactive.html#interactive-mode) of [Matplotlib](https://matplotlib.org/) must be turned on:
+
+```console
+>>> plot_graph(hmm, dpi=300)
+>>> plot_sequence(hmm, 10, plot_type='histogram', dpi=300)
+>>> plot_sequence(hmm, 10, plot_type='heatmap', dpi=300)
+>>> plot_sequence(hmm, 10, plot_type='matrix', dpi=300)
+>>> plot_trellis(hmm, 10, dpi=300)
+```
+
+![Screenshots](https://i.imgur.com/rSNUbdX.gif)
+
+
+%package help
+Summary:	Development documents and examples for PyDTMC
+Provides:	python3-PyDTMC-doc
+%description help
+PyDTMC is a full-featured and lightweight library for discrete-time Markov chains analysis. It provides classes and functions for creating, manipulating, simulating and visualizing Markov processes.
+
+<table>
+  <tr>
+    <td align="right">Status:</td>
+    <td align="left">
+      <a href="https://github.com/TommasoBelluzzo/PyDTMC/actions/workflows/continuous_integration.yml"><img alt="Build" src="https://img.shields.io/github/workflow/status/TommasoBelluzzo/PyDTMC/Continuous%20Integration?style=flat&label=Build&color=1081C2"/></a>
+      <a href="https://pydtmc.readthedocs.io/"><img alt="Docs" src="https://img.shields.io/readthedocs/pydtmc?style=flat&label=Docs&color=1081C2"/></a>
+      <a href="https://coveralls.io/github/TommasoBelluzzo/PyDTMC?branch=master"><img alt="Coverage" src="https://img.shields.io/coveralls/github/TommasoBelluzzo/PyDTMC?style=flat&label=Coverage&color=1081C2"/></a>
+    </td>
+  </tr>
+  <tr>
+    <td align="right">Info:</td>
+    <td align="left">
+      <a href="#"><img alt="License" src="https://img.shields.io/github/license/TommasoBelluzzo/PyDTMC?style=flat&label=License&color=1081C2"/></a>
+      <a href="#"><img alt="Lines" src="https://img.shields.io/tokei/lines/github/TommasoBelluzzo/PyDTMC?style=flat&label=Lines&color=1081C2"/></a>
+      <a href="#"><img alt="Size" src="https://img.shields.io/github/repo-size/TommasoBelluzzo/PyDTMC?style=flat&label=Size&color=1081C2"/></a>
+    </td>
+  </tr>
+  <tr>
+    <td align="right">PyPI:</td>
+    <td align="left">
+      <a href="https://pypi.org/project/PyDTMC/"><img alt="Version" src="https://img.shields.io/pypi/v/PyDTMC?style=flat&label=Version&color=1081C2"/></a>
+      <a href="https://pypi.org/project/PyDTMC/"><img alt="Python" src="https://img.shields.io/pypi/pyversions/PyDTMC?style=flat&label=Python&color=1081C2"/></a>
+      <a href="https://pypi.org/project/PyDTMC/"><img alt="Wheel" src="https://img.shields.io/pypi/wheel/PyDTMC?style=flat&label=Wheel&color=1081C2"/></a>
+      <a href="https://pypi.org/project/PyDTMC/"><img alt="Downloads" src="https://img.shields.io/pypi/dm/PyDTMC?style=flat&label=Downloads&color=1081C2"/></a>
+    </td>
+  </tr>
+  <tr>
+    <td align="right">Conda:</td>
+    <td align="left">
+      <a href="https://anaconda.org/conda-forge/pydtmc/"><img alt="Version" src="https://img.shields.io/conda/vn/conda-forge/pydtmc?style=flat&label=Version"/></a>
+      <a href="https://anaconda.org/conda-forge/pydtmc/"><img alt="Python" src="https://img.shields.io/pypi/pyversions/PyDTMC?style=flat&label=Python&color=1081C2"/></a>
+      <a href="https://anaconda.org/conda-forge/pydtmc/"><img alt="Platforms" src="https://img.shields.io/conda/pn/conda-forge/pydtmc?style=flat&label=Platforms&color=1081C2"/></a>
+      <a href="https://anaconda.org/conda-forge/pydtmc/"><img alt="Downloads" src="https://img.shields.io/conda/dn/conda-forge/pydtmc?style=flat&label=Downloads&color=1081C2"/></a>
+    </td>
+  </tr>
+  <tr>
+    <td align="right">Donation:</td>
+    <td align="left">
+      <a href="https://www.paypal.com/cgi-bin/webscr?cmd=_s-xclick&hosted_button_id=D8LH6DNYN7EN8"><img alt="PayPal" src="https://www.paypalobjects.com/en_US/i/btn/btn_donate_LG.gif"/></a>
+    </td>
+  </tr>
+</table>
+
+## Requirements
+
+The `Python` environment must include the following packages:
+
+* [Matplotlib](https://matplotlib.org/)
+* [NetworkX](https://networkx.github.io/)
+* [NumPy](https://www.numpy.org/)
+* [SciPy](https://www.scipy.org/)
+
+*Notes:*
+
+* It's recommended to install [Graphviz](https://www.graphviz.org/) and [pydot](https://pypi.org/project/pydot/) before using the `plot_graph` function.
+* The packages [pytest](https://pytest.org/) and [pytest-benchmark](https://pypi.org/project/pytest-benchmark/) are required for performing unit tests.
+* The package [Sphinx](https://www.sphinx-doc.org/) is required for building the package documentation.
+
+## Installation & Upgrade
+
+[PyPI](https://pypi.org/):
+
+```sh
+$ pip install PyDTMC
+$ pip install --upgrade PyDTMC
+```
+
+[Git](https://git-scm.com/):
+
+```sh
+$ pip install https://github.com/TommasoBelluzzo/PyDTMC/tarball/master
+$ pip install --upgrade https://github.com/TommasoBelluzzo/PyDTMC/tarball/master
+
+$ pip install git+https://github.com/TommasoBelluzzo/PyDTMC.git#egg=PyDTMC
+$ pip install --upgrade git+https://github.com/TommasoBelluzzo/PyDTMC.git#egg=PyDTMC
+```
+
+[Conda](https://docs.conda.io/):
+
+```sh
+$ conda install -c conda-forge pydtmc
+$ conda update -c conda-forge pydtmc
+
+$ conda install -c tommasobelluzzo pydtmc
+$ conda update -c tommasobelluzzo pydtmc
+```
+
+## Usage: MarkovChain Class
+
+The `MarkovChain` class can be instantiated as follows:
+
+```console
+>>> p = [[0.2, 0.7, 0.0, 0.1], [0.0, 0.6, 0.3, 0.1], [0.0, 0.0, 1.0, 0.0], [0.5, 0.0, 0.5, 0.0]]
+>>> mc = MarkovChain(p, ['A', 'B', 'C', 'D'])
+>>> print(mc)
+
+DISCRETE-TIME MARKOV CHAIN
+ SIZE:           4
+ RANK:           4
+ CLASSES:        2
+  > RECURRENT:   1
+  > TRANSIENT:   1
+ ERGODIC:        NO
+  > APERIODIC:   YES
+  > IRREDUCIBLE: NO
+ ABSORBING:      YES
+ REGULAR:        NO
+ REVERSIBLE:     YES
+ SYMMETRIC:      NO
+```
+
+Below a few examples of `MarkovChain` properties:
+
+```console
+>>> print(mc.is_ergodic)
+False
+
+>>> print(mc.recurrent_states)
+['C']
+
+>>> print(mc.transient_states)
+['A', 'B', 'D']
+
+>>> print(mc.steady_states)
+[array([0.0, 0.0, 1.0, 0.0])]
+
+>>> print(mc.is_absorbing)
+True
+
+>>> print(mc.fundamental_matrix)
+[[1.50943396, 2.64150943, 0.41509434]
+ [0.18867925, 2.83018868, 0.30188679]
+ [0.75471698, 1.32075472, 1.20754717]]
+ 
+>>> print(mc.kemeny_constant)
+5.547169811320755
+
+>>> print(mc.entropy_rate)
+0.0
+```
+
+Below a few examples of `MarkovChain` methods:
+
+```console
+>>> print(mc.absorption_probabilities())
+[1.0 1.0 1.0]
+
+>>> print(mc.expected_rewards(10, [2, -3, 8, -7]))
+[44.96611926, 52.03057032, 88.00000000, 51.74779651]
+
+>>> print(mc.expected_transitions(2))
+[[0.0850, 0.2975, 0.0000, 0.0425]
+ [0.0000, 0.3450, 0.1725, 0.0575]
+ [0.0000, 0.0000, 0.7000, 0.0000]
+ [0.1500, 0.0000, 0.1500, 0.0000]]
+
+>>> print(mc.first_passage_probabilities(5, 3))
+[[0.5000, 0.0000, 0.5000, 0.0000]
+ [0.0000, 0.3500, 0.0000, 0.0500]
+ [0.0000, 0.0700, 0.1300, 0.0450]
+ [0.0000, 0.0315, 0.1065, 0.0300]
+ [0.0000, 0.0098, 0.0761, 0.0186]]
+ 
+>>> print(mc.hitting_probabilities([0, 1]))
+[1.0, 1.0, 0.0, 0.5]
+ 
+>>> print(mc.mean_absorption_times())
+[4.56603774, 3.32075472, 3.28301887]
+
+>>> print(mc.mean_number_visits())
+[[0.50943396, 2.64150943, INF, 0.41509434]
+ [0.18867925, 1.83018868, INF, 0.30188679]
+ [0.00000000, 0.00000000, INF, 0.00000000]
+ [0.75471698, 1.32075472, INF, 0.20754717]]
+ 
+>>> print(mc.simulate(10, seed=32))
+['D', 'A', 'B', 'B', 'C', 'C', 'C', 'C', 'C', 'C', 'C']
+```
+
+```console
+>>> sequence = ["A"]
+>>> for i in range(1, 11):
+...     current_state = sequence[-1]
+...     next_state = mc.next(current_state, seed=32)
+...     print((' ' if i < 10 else '') + f'{i}) {current_state} -> {next_state}')
+...     sequence.append(next_state)
+ 1) A -> B
+ 2) B -> C
+ 3) C -> C
+ 4) C -> C
+ 5) C -> C
+ 6) C -> C
+ 7) C -> C
+ 8) C -> C
+ 9) C -> C
+10) C -> C
+```
+
+Below a few examples of `MarkovChain` plotting functions; in order to display the output of plots immediately, the [interactive mode](https://matplotlib.org/stable/users/interactive.html#interactive-mode) of [Matplotlib](https://matplotlib.org/) must be turned on:
+
+```console
+>>> plot_eigenvalues(mc, dpi=300)
+>>> plot_graph(mc, dpi=300)
+>>> plot_sequence(mc, 10, plot_type='histogram', dpi=300)
+>>> plot_sequence(mc, 10, plot_type='heatmap', dpi=300)
+>>> plot_sequence(mc, 10, plot_type='matrix', dpi=300)
+>>> plot_redistributions(mc, 10, plot_type='heatmap', dpi=300)
+>>> plot_redistributions(mc, 10, plot_type='projection', dpi=300)
+```
+
+![Screenshots](https://i.imgur.com/bltMSi5.gif)
+
+## Usage: HiddenMarkovModel Class
+
+The `HiddenMarkovModel` class can be instantiated as follows:
+
+```console
+>>> p = [[0.4, 0.6], [0.8, 0.2]]
+>>> states = ['A', 'B']
+>>> e = [[0.5, 0.0, 0.0, 0.5], [0.2, 0.2, 0.2, 0.4]]
+>>> symbols = ['H1', 'H2', 'H3', 'H4']
+>>> hmm = HiddenMarkovModel(p, e, states, symbols)
+>>> print(hmm)
+    
+HIDDEN MARKOV MODEL
+ STATES:  2
+ SYMBOLS: 4
+ ERGODIC: NO
+ REGULAR: NO
+```
+
+Below a few examples of `HiddenMarkovModel` methods:
+
+```console
+>>> sim_states, sim_symbols = hmm.simulate(12, seed=1488)
+>>> print(sim_states)
+['B', 'A', 'A', 'A', 'B', 'A', 'A']
+>>> print(sim_symbols)
+['H2', 'H4', 'H4', 'H4', 'H3', 'H4', 'H4']
+
+>>> est_hmm = hmm.estimate(states, symbols, sim_states, sim_symbols)
+>>> print(est_hmm.p)
+[[0.75, 0.25]
+ [1.00, 0.00]]
+>>> print(est_hmm.e)
+[[0.0, 0.0, 0.0, 1.0]
+ [0.0, 0.5, 0.5, 0.0]]
+
+>>> dec_lp, dec_posterior, dec_backward, dec_forward, _ = hmm.decode(sim_symbols)
+>>> print(dec_lp)
+-8.77549587
+>>> print(dec_posterior)
+[[0.00000000, 0.84422968, 0.41785105, 0.84422968, 0.00000000, 0.82089552, 0.52238806]
+ [1.00000000, 0.15577032, 0.58214895, 0.15577032, 1.00000000, 0.17910448, 0.47761194]]
+>>> print(dec_backward)
+[[1.50000000, 0.88942581, 1.01307561, 0.79988630, 1.31154065, 0.94776119, 0.98507463, 1.00000000]
+ [0.50000000, 1.00000000, 0.93462194, 1.21887436, 0.43718022, 1.00000000, 1.07462687, 1.00000000]]
+>>> print(dec_forward)
+[[0.50000000, 0.00000000, 0.83333333, 0.52238806, 0.64369311, 0.00000000, 0.83333333 0.52238806]
+ [0.50000000, 1.00000000, 0.16666667, 0.47761194, 0.35630689, 1.00000000, 0.16666667 0.47761194]]
+
+>>> pre_lp, pre_states = hmm.predict('viterbi', sim_symbols)
+>>> print(pre_lp)
+-13.24482936
+>>> print(pre_states)
+['B', 'A', 'B', 'A', 'B', 'A', 'B']
+```
+
+Below a few examples of `HiddenMarkovModel` plotting functions; in order to display the output of plots immediately, the [interactive mode](https://matplotlib.org/stable/users/interactive.html#interactive-mode) of [Matplotlib](https://matplotlib.org/) must be turned on:
+
+```console
+>>> plot_graph(hmm, dpi=300)
+>>> plot_sequence(hmm, 10, plot_type='histogram', dpi=300)
+>>> plot_sequence(hmm, 10, plot_type='heatmap', dpi=300)
+>>> plot_sequence(hmm, 10, plot_type='matrix', dpi=300)
+>>> plot_trellis(hmm, 10, dpi=300)
+```
+
+![Screenshots](https://i.imgur.com/rSNUbdX.gif)
+
+
+%prep
+%autosetup -n PyDTMC-8.2.0
+
+%build
+%py3_build
+
+%install
+%py3_install
+install -d -m755 %{buildroot}/%{_pkgdocdir}
+if [ -d doc ]; then cp -arf doc %{buildroot}/%{_pkgdocdir}; fi
+if [ -d docs ]; then cp -arf docs %{buildroot}/%{_pkgdocdir}; fi
+if [ -d example ]; then cp -arf example %{buildroot}/%{_pkgdocdir}; fi
+if [ -d examples ]; then cp -arf examples %{buildroot}/%{_pkgdocdir}; fi
+pushd %{buildroot}
+if [ -d usr/lib ]; then
+	find usr/lib -type f -printf "/%h/%f\n" >> filelist.lst
+fi
+if [ -d usr/lib64 ]; then
+	find usr/lib64 -type f -printf "/%h/%f\n" >> filelist.lst
+fi
+if [ -d usr/bin ]; then
+	find usr/bin -type f -printf "/%h/%f\n" >> filelist.lst
+fi
+if [ -d usr/sbin ]; then
+	find usr/sbin -type f -printf "/%h/%f\n" >> filelist.lst
+fi
+touch doclist.lst
+if [ -d usr/share/man ]; then
+	find usr/share/man -type f -printf "/%h/%f.gz\n" >> doclist.lst
+fi
+popd
+mv %{buildroot}/filelist.lst .
+mv %{buildroot}/doclist.lst .
+
+%files -n python3-PyDTMC -f filelist.lst
+%dir %{python3_sitelib}/*
+
+%files help -f doclist.lst
+%{_docdir}/*
+
+%changelog
+* Fri May 05 2023 Python_Bot <Python_Bot@openeuler.org> - 8.2.0-1
+- Package Spec generated
diff --git a/sources b/sources
new file mode 100644
index 0000000..f2caf25
--- /dev/null
+++ b/sources
@@ -0,0 +1 @@
+226f530ecbd02c2c063108b5ed2ae6f9  PyDTMC-8.2.0.tar.gz