removed some issues

Author: mengaldo

README.md

@@ -25,23 +25,23 @@
   </a>
 </p>
 
-
 **PySPOD**: Python Spectral Proper Orthogonal Decomposition
 
 ## Table of contents
-* [Description](#description)
-* [Installation and dependencies](#installation-and-dependencies)
-	* [Installing via PIP](#installing-via-pip)
-	* [Installing from source](#installing-from-source)
-* [Documentation](#documentation)
-* [Testing](#testing)
-* [Tutorials](#tutorials)
-* [References](#references)
-* [Recent works with PySPOD](#recent-works-with-pyspod)
-* [Authors and contributors](#authors-and-contributors)
-* [License](#license)
 
+  * [Description](#description)
+
+  * [Installation and dependencies](#installation-and-dependencies)
+	 * [Installing via PIP](#installing-via-pip)
+	 * [Installing from source](#installing-from-source)
 
+  * [Documentation](#documentation)
+  * [Testing](#testing)
+  * [Tutorials](#tutorials)
+  * [References](#references)
+  * [Recent works with PySPOD](#recent-works-with-pyspod)
+  * [Authors and contributors](#authors-and-contributors)
+  * [License](#license)
 
 ## Description
 **PySPOD** is a Python package that implements the so-called **Spectral Proper Orthgonal Decomposition** whose name was first conied by (picard-&-delville-2000), and goes back to the original work by [(Lumley 1970)](#lumley-1970). The implementation proposed here follows the original contributions by [(Towne et al. 2018)](#towne-et-al-2018), [(Schmidt and Towne 2019)](#schmidt-and-towne-2019).
@@ -53,14 +53,12 @@ The SPOD approach targets statistically stationary problems and involves the dec
 This can help identifying relations to multiple variables or understanding the reduced order behavior of a given phenomenon of interest and represent a powerful tool for the data-driven analysis of nonlinear dynamical systems. The SPOD approach shares some relationships with the dynamic mode decomposition (DMD), and the resolvent analysis,  [(Towne et al. 2018)](#Towne-et-al-2018), that are also widely used approaches for the data-driven analysis of nonlinear systems. SPOD can be used for both experimental and simulation data, and a general description of its key parameters can be found in [(Schmidt and Colonius 2020)](#schmidt-and-colonius-2020).  
 
 In this package we implement three version of SPOD 
-- SPOD_low_storage: that is intended for large RAM machines or small datasets
-- SPOD_low_ram: that is intended for small RAM machines or large datasets, and 
-- SPOD_streaming: that is the algorithm presented in [(Schmidt and Towne 2019)](schmidt-and-towne-2019), and it is intended for large datasets.
+  - SPOD_low_storage: that is intended for large RAM machines or small datasets
+  - SPOD_low_ram: that is intended for small RAM machines or large datasets, and 
+  - SPOD_streaming: that is the algorithm presented in [(Schmidt and Towne 2019)](schmidt-and-towne-2019), and it is intended for large datasets.
 
 To see how to use the **PySPOD** package and its user-friendly interface, you can look at the [**Tutorials**](tutorials/README.md). 
 
-
-
 ## Installation and dependencies
 **PySPOD** requires `numpy`, `scipy`, `matplotlib`, `pyfftw`, `future`, `sphinx` (for the documentation). The code is developed and tested for Python 3 only. 
 It can be installed using `pip` or directly from the source code.
@@ -94,7 +92,6 @@ To uninstall the package you have to rerun the installation and record the insta
 > cat installed_files.txt | xargs rm -rf
 ```
 
-
 ## Get started with a simple analysis
 **PySPOD** comes with an extensive suite of [**Tutorials**](tutorials/README.md). 
 You can browse the [**Tutorials**](tutorials/README.md) to explore the capabilities 
@@ -173,8 +170,6 @@ spod_ls.plot_2D_modes_at_frequency(
 You can change `SPOD_low_storage` to `SPOD_low_ram` and `SPOD_streaming`, 
 to run the other two SPOD algorithms available.
 
-
-
 ## Documentation
 **PySPOD** uses [Sphinx](http://www.sphinx-doc.org/en/stable/) for code documentation. 
 You can view the documentation online [here](http://mengaldo.github.io/PySPOD/). 
@@ -189,8 +184,6 @@ by:
 This will generate a `docs/build/html` folder, where you can find an `index.html` file. 
 Open it with your browser and explore the documentation locally.
 
-
-
 ## Testing
 Regression tests are deployed using Travis CI, that is a continuous intergration framework. 
 You can check out the current status of **PySPOD** [here](https://travis-ci.org/mengaldo/PySPOD).
@@ -202,64 +195,71 @@ IF you want to run tests locally, you can do so by:
 > pytest -v
 ```
 
-
 ## References
+
 #### (Lumley 1970) 
 *Stochastic Tools in Turbulence.*
+
 [[DOI](https://www.elsevier.com/books/stochastic-tools-in-turbulence/lumey/978-0-12-395772-6?aaref=https%3A%2F%2Fwww.google.com)]
 
 #### (Picard and Delville 2000) 
+
 *Pressure velocity coupling in a subsonic round jet.*
 [[DOI](https://www.sciencedirect.com/science/article/abs/pii/S0142727X00000217)]
 
 #### (Tutkun and George 2017)
+
 *Lumley decomposition of turbulent boundary layer at high Reynolds numbers.*
 [[DOI](https://aip.scitation.org/doi/10.1063/1.4974746)]
 
 #### (Schmidt et al 2017) 
+
 *Wavepackets and trapped acoustic modes in a turbulent jet: coherent structure eduction and global stability.*
 [[DOI](https://doi.org/10.1017/jfm.2017.407)]
 
 #### (Araya et al 2017)
+
 *Transition to bluff-body dynamics in the wake of vertical-axis wind turbines.*
 [[DOI]( https://doi.org/10.1017/jfm.2016.862)]
 
 #### (Taira et al 2017) 
+
 *Modal analysis of fluid flows: An overview.*
 [[DOI](https://doi.org/10.2514/1.J056060)]
 
 #### (Towne et al 2018)
+
 *Spectral proper orthogonal decomposition and its relationship to dynamic mode decomposition and resolvent analysis.*
 [[DOI]( https://doi.org/10.1017/jfm.2018.283)]
 
 #### (Schmidt and Towne 2019)
+
 *An efficient streaming algorithm for spectral proper orthogonal decomposition.*
 [[DOI](https://doi.org/10.1016/j.cpc.2018.11.009)]
 
 #### (Schmidt et al 2019)
+
 *Spectral empirical orthogonal function analysis of weather and climate data.*
 [[DOI](https://doi.org/10.1175/MWR-D-18-0337.1)]
 
 #### (Schmidt and Colonius 2020)
+
 *Guide to spectral proper orthogonal decomposition.*
 [[DOI](https://doi.org/10.2514/1.J058809)]
 
-
-
 ## Recent works with **PySPOD**
-Please, [contact me](mailto:[email protected]) if you used PySPOD for a publication and you want it to be advertised here.
-
 
+Please, [contact me](mailto:[email protected]) if you used PySPOD for a publication and you want it to be advertised here.
 
 ## Authors and contributors
+
 **PySPOD** is currently developed and mantained by
 
-* [Gianmarco Mengaldo](mailto:[email protected]).
+  * [Gianmarco Mengaldo](mailto:[email protected]).
 
 Contact me by email for further information or questions about **PySPOD**, or suggest pull requests. 
 Contributions improving code and documentation, as well as suggestions about new features are more than welcome!
 
-
-
 ## License
+
 See the [LICENSE](LICENSE.rst) file for license rights and limitations (MIT).

pyspod/postprocessing.py

@@ -4,14 +4,12 @@
 
 # import standard python packages
 import os
-import sys
 import numpy as np
 from scipy.io import loadmat
 import matplotlib as mpl
 import matplotlib.pyplot as plt
 from matplotlib import animation
 import matplotlib.gridspec as gridspec
-from matplotlib import colors as mcolors
 from mpl_toolkits.axes_grid1 import make_axes_locatable
 mpl.rc('figure', max_open_warning = 0)
 from os.path import splitext
@@ -214,7 +212,6 @@ def plot_eigs_vs_frequency(eigs, freq, title='', xticks=None, yticks=None,
 		raise TypeError('`freq` must be ndarray type.')
 
 	# plot figure
-	dpi = 200
 	plt.figure(figsize=figsize, frameon=True, constrained_layout=False)
 	ax = plt.gca()
 	ratio = 1. / eigs.shape[1]
@@ -1044,7 +1041,7 @@ def plot_mode_tracers(modes, freq_required, freq, coords_list, x=None, vars_idx=
 					mode = np.fft.fftshift(mode, axes=1)
 				mode_point_phase = mode[idx_coords] * phase.conj()
 				ax = fig.add_subplot(spec[cnt,0])
-				ax_obj = ax.plot(t, np.real(mode_point_phase), 'k-')
+				_ = ax.plot(t, np.real(mode_point_phase), 'k-')
 				ax.set_ylabel('mode {}'.format(mode_id),
 								rotation=0,
 								labelpad=30,
@@ -1297,10 +1294,6 @@ def generate_2D_data_video(X, time_limits=[0,10], vars_idx=None, sampling=1,
 			'Data dimension Z = (N,M); x1 and x2 '
 			'must have dimension N and M, respectively.')
 
-	# get figure size
-	wsize = figsize[0]
-	hsize = figsize[1]
-
 	# overlay coastlines if required
 	cst = False
 	if coastlines.lower() == 'regular':

pyspod/spod_low_ram.py

@@ -6,15 +6,13 @@
 import os
 import sys
 import time
-import scipy.io
 import numpy as np
 from tqdm import tqdm
 from numpy import linalg as la
 import scipy.special as sc
 from scipy.fft import fft
 import warnings
 import shutil
-import psutil
 
 # Import PySPOD base class for SPOD_low_ram
 from pyspod.spod_base import SPOD_base

pyspod/spod_low_storage.py

@@ -6,7 +6,6 @@
 import os
 import sys
 import time
-import scipy.io
 import numpy as np
 from tqdm import tqdm
 from numpy import linalg as la
@@ -85,7 +84,6 @@ def fit(self):
 			# loop over number of blocks and generate Fourier realizations
 			for iBlk in range(0,self._n_blocks):
 
-				start0 = time.time()
 				# get time index for present block
 				offset = min(iBlk * (self._n_DFT - self._n_overlap) + self._n_DFT, self._nt) - self._n_DFT
 

pyspod/spod_streaming.py

@@ -4,16 +4,10 @@
 
 # import standard python packages
 import os
-import sys
 import time
-import scipy.io
 import numpy as np
-from tqdm import tqdm
 from numpy import linalg as la
 import scipy.special as sc
-import warnings
-import shutil
-import psutil
 
 # import PySPOD base class for SSPOD
 from pyspod.spod_base import SPOD_base

pyspod/weights.py

@@ -3,8 +3,6 @@
 """
 
 # import standard python packages
-import os
-import sys
 import numpy as np
 
 

tests/test_basic.py

@@ -3,8 +3,7 @@
 import shutil
 import pytest
 import subprocess
-import xarray as xr
-import numpy  as np
+import numpy as np
 
 # Import library specific modules
 sys.path.append("../")
@@ -71,7 +70,7 @@ def test_basic_spod_low_storage():
 
 	try:
 		bashCmd = ["ffmpeg", " --version"]
-		sbp = subprocess.Popen(bashCmd, stdin=subprocess.PIPE)
+		_ = subprocess.Popen(bashCmd, stdin=subprocess.PIPE)
 		spod_ls.generate_2D_data_video(
 			sampling=10,
 			time_limits=[0,t.shape[0]],

tests/test_earthquakes.py

@@ -357,7 +357,7 @@ def test_postprocessing():
 							filename='data_tracers.png')
 	try:
 		bashCmd = ["ffmpeg", " --version"]
-		sbp = subprocess.Popen(bashCmd, stdin=subprocess.PIPE)
+		_ = subprocess.Popen(bashCmd, stdin=subprocess.PIPE)
 		spod.generate_2D_data_video(
 			sampling=5,
 			time_limits=[0,t.shape[0]],

tests/test_fluidmechanics.py

@@ -289,9 +289,6 @@ def test_spod_low_storage_savefft():
 
 
 def test_spod_low_ram_savefft():
-	'''
-	spod tests on jet data for methodologies.
-	'''
 	'''
 	spod tests on jet data for methodologies.
 	'''

tutorials/README.md

@@ -7,7 +7,6 @@ These are organized in the form of `jupyter-notebooks`, along with their plain
 In particular, we divided the tutorials in such a way that they cover different 
 functionalities of the library and practical application areas.
 
-
 ### Basic
 
 #### [Tutorial: Basic 1](Basic/methods_comparison/methods_comparison.ipynb)
@@ -26,8 +25,6 @@ in this tutorial we highlight how one can define a function to read
 data and pass it to the constructor of the SPOD class, thereby allowing 
 for a reduced use of RAM (for large datasets).
 
-
-
 ### Climate 
 
 #### [Tutorial: 2D Multivariate ENSO Index](climate/ERA20C_MEI_2D/ERA20C_MEI_2D.ipynb)
@@ -40,7 +37,6 @@ pressure (MSL), zonal component of the surface wind (U10), meridional component
 of the surface wind (V10), sea surface temperature (SST), 2-meter temperature 
 (T2M), and, total cloud cover (TCC), on a 2D longitude-latitude grid.  
 
-
 #### [Tutorial: 3D Quasi-Bienniel Oscillation](climate/ERA20C_QBO_3D/ERA20C_QBO_3D.ipynb)
 
 This tutorial shows how to download data from an ECMWF reanalysis dataset (ERA20C), 
@@ -49,32 +45,23 @@ and use **PySPOD** to identify spatio-temporal coherent structured in univariate
 The data is composed by the monthly-averages of the zonal-mean zonal winds 
 on a 3D longitude, latitude, pressure-levels grid.
 
-
 #### [Tutorial: 2D ERA5 Mean-Sea Level Pressure](climate/ERA5_MSLP_2D/ERA5_MSLP_2D.ipynb)
 
 This tutorial shows how to download data from an ECMWF reanalysis dataset (ERA5), 
 and use **PySPOD** to identify spatio-temporal coherent structured in univariate 
 2D data. In particular, we seek to identify spatio-temporal coherent structure in 
 high-resolution mean-sea level pressure data from the ERA5 dataset.
 
-
-
 ### Fluidmechanics 
 
 #### [Tutorial: 2D Jet](fluidmechanics/jet_2D/jet_2D.ipynb)
 
 This tutorial shows a simple 2D application to a turbulent jet, where the variable 
 studied is pressure.
 
-
-
 ### Earthquakes 
 
 #### [Tutorial: 2D Slip Potency](earthquakes/slip_potency_2D/slip_potency_2D.ipynb)
 
 This tutorial shows a simple 2D application seismic data, where the variable studied 
-is the slip potency.
-
-
-
-
+is the slip potency.