Instalaciones cedidas por¶
Who are we?¶
Siro Moreno¶
* **Aerospace Engineer**
* Working at:
Álex Sáez¶
- Aerospace Engineer
- Flight Test Methods Engineer at AIRBUS Defence & Space on behalf of ALTRAN
- Co-creator of AeroPython --> PyFME
- Member of Python EspaƱa (come and join us!)
0. Introduction¶
Python in the Scientific environment¶
Principal Python Packages for scientific purposes¶
Anaconda & conda¶
http://conda.pydata.org/docs/intro.html
Conda is a package manager application that quickly installs, runs, and updates packages and their dependencies. The conda command is the primary interface for managing installations of various packages. It can query and search the package index and current installation, create new environments, and install and update packages into existing conda environments.
from IPython.display import HTML
HTML('<iframe src="http://conda.pydata.org/docs/_downloads/conda-cheatsheet.pdf" width="700" height="400"></iframe>')
Main objectives of this workshop¶
- Provide you with a first insight into the principal Python tools & libraries used in Science:
- conda.
- Jupyter Notebook and preview of JupyterLab
- NumPy, matplotlib, SciPy
- SymPy
Other common libraries that will not be covered here are:¶
- Pandas
- scikit-learn
- Numba & Cython
1. Jupyter Notebook¶
The Jupyter Notebook is a web application that allows you to create and share documents that contain live code, equations, visualizations and explanatory text. Uses include: data cleaning and transformation, numerical simulation, statistical modeling, machine learning and much more.
It has been widely recognised as a great way to distribute scientific papers, because of the capability to have an integrated format with text and executable code, highly reproducible. Top level investigators around the world are already using it, like the team behind the Gravitational Waves discovery (LIGO), whose analysis was translated to an interactive dowloadable Jupyter notebook. You can see it here: https://github.com/minrk/ligo-binder/blob/master/GW150914_tutorial.ipynb
2. Using arrays: NumPy¶
ndarray object¶
| index | 0 | 1 | 2 | 3 | ... | n-1 | n |
|---|---|---|---|---|---|---|---|
| value | 2.1 | 3.6 | 7.8 | 1.5 | ... | 5.4 | 6.3 |
- N-dimensional data structure.
- Homogeneously typed.
- Efficient!
A universal function (or ufunc for short) is a function that operates on ndarrays. It is a āvectorized function".
Let's have a look at the efficiency of a ndarray against the efficiency of a list:
# List
my_list = list(range(0,100000))
# Array
my_array =
1000 loops, best of 3: 1.41 ms per loop
10000 loops, best of 3: 95 Āµs per loop
Another example:
10 loops, best of 3: 52.7 ms per loop
1000 loops, best of 3: 856 Āµs per loop
Array creation¶
# [1, 2, 3, 4]
one_dim_array =
array([1, 2, 3, 4])
# [1, 2, 3],
# [4, 5, 6],
# [7, 8, 9]
two_dim_array =
array([[1, 2, 3],
[4, 5, 6],
[7, 8, 9]])
# size
9
# shape
(3, 3)
# dtype
dtype('int64')
array([[ 1., 2., 3.],
[ 4., 5., 6.],
[ 7., 8., 9.]])
# Other interesting functions for array creation
zeros_arr =
ones_arr =
eye_arr =
# range
range_arr =
array([ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14])
# reshape
array([[ 0, 1, 2, 3, 4],
[ 5, 6, 7, 8, 9],
[10, 11, 12, 13, 14]])
# linspace
array([ 0. , 0.5, 1. , 1.5, 2. , 2.5, 3. , 3.5, 4. ,
4.5, 5. , 5.5, 6. , 6.5, 7. , 7.5, 8. , 8.5,
9. , 9.5, 10. ])
Basic slicing¶
# 1d
1
# 2d
9
[start:stop:step]
array([ 0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32,
34, 36, 38, 40, 42, 44, 46, 48, 50, 52, 54, 56, 58, 60, 62, 64, 66,
68, 70, 72, 74, 76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 96, 98])
chess_board =
array([[0, 1, 0, 1, 0, 1, 0, 1],
[1, 0, 1, 0, 1, 0, 1, 0],
[0, 1, 0, 1, 0, 1, 0, 1],
[1, 0, 1, 0, 1, 0, 1, 0],
[0, 1, 0, 1, 0, 1, 0, 1],
[1, 0, 1, 0, 1, 0, 1, 0],
[0, 1, 0, 1, 0, 1, 0, 1],
[1, 0, 1, 0, 1, 0, 1, 0]])
2. Drawing: Matplotlib¶
<matplotlib.image.AxesImage at 0x7fe1491d95c0>
Operations & linalg¶
# numpy functions: sin
# let's plot it
[<matplotlib.lines.Line2D at 0x7fe14b7644a8>]
# another function
[<matplotlib.lines.Line2D at 0x7fe148bf99e8>]
Some linear algebra¶
two_dim_array =
# Transponse
array([[10, 40, 77],
[25, 25, 68],
[33, 16, 91]])
# matrix multiplication
array([[ 3641, 3119, 3733],
[ 2632, 2713, 3176],
[10497, 9813, 11910]])
one_dim_array =
# matrix-vector multiplication
array([ 240.4, 250.8, 783.1])
# inv
array([[-0.05372256, 0.00140303, 0.01923512],
[ 0.10898393, 0.07381761, -0.05250057],
[-0.03598099, -0.05634759, 0.03394433]])
# eigenvectors & eigenvalues
(array([ 133.6946629, -17.266221 , 9.5715581]),
array([[-0.29580975, -0.74274264, 0.0661375 ],
[-0.24477775, 0.65983255, -0.79576005],
[-0.92335283, 0.1138173 , 0.60198985]]))
Air quality data¶
from IPython.display import HTML
HTML('<iframe src="http://www.mambiente.munimadrid.es/sica/scripts/index.php" \
width="700" height="400"></iframe>')
Loading the data¶
# Linux command
!head ./data/barrio_del_pilar-20160322.csv
# Windows
# !gc log.txt | select -first 10 # head
EstaciĆ³n: Barrio del Pilar;;;; Fecha;Hora;CO;NO2;O3 ;;mg/mĀ³;Āµg/mĀ³;Āµg/mĀ³ 22/03/2016;01:00;0.2;14;73 22/03/2016;02:00;0.2;10;77 22/03/2016;03:00;0.2;9;75 22/03/2016;04:00;0.2;3;81 22/03/2016;05:00;0.2;3;81 22/03/2016;06:00;0.2;6;79 22/03/2016;07:00;0.2;24;59
# loading the data
# ./data/barrio_del_pilar-20160322.csv
data1 =
array([[ 0.2, 14. , 73. ],
[ 0.2, 10. , 77. ],
[ 0.2, 9. , 75. ],
[ 0.2, 3. , 81. ],
[ 0.2, 3. , 81. ],
[ 0.2, 6. , 79. ],
[ 0.2, 24. , 59. ],
[ 0.3, 48. , 37. ],
[ 0.3, 40. , 43. ],
[ 0.3, 41. , 44. ],
[ 0.3, 20. , 68. ],
[ 0.3, 17. , 74. ],
[ 0.2, 14. , 84. ],
[ 0.3, 16. , 88. ],
[ 0.3, 15. , 94. ],
[ 0.4, 29. , 81. ],
[ 0.3, 23. , 82. ],
[ 0.3, 26. , 81. ],
[ 0.3, 30. , 75. ],
[ 0.4, 57. , 39. ],
[ 0.4, 73. , 17. ],
[ 0.4, 51. , 42. ],
[ 0.4, 72. , 16. ],
[ 0.4, 61. , 28. ],
[ 0.3, 25. , 62. ],
[ 0.3, 21. , 64. ],
[ 0.3, 40. , 39. ],
[ 0.4, 52. , 19. ],
[ 0.4, 47. , 8. ],
[ 0.4, 42. , 8. ],
[ 0.5, 68. , 8. ],
[ 0.6, 71. , 9. ],
[ 0.9, 76. , 10. ],
[ 0.7, 63. , 29. ],
[ 0.3, 27. , 66. ],
[ 0.3, 13. , 88. ],
[ 0.2, 10. , 92. ],
[ 0.3, 10. , 98. ],
[ 0.3, 11. , 99. ],
[ 0.3, 12. , 99. ],
[ 0.2, 11. , 98. ],
[ 0.2, 8. , 101. ],
[ 0.2, 13. , 92. ],
[ 0.2, 23. , 79. ],
[ 0.5, 40. , 56. ],
[ 0.6, 49. , 43. ],
[ 0.5, 66. , 25. ],
[ 0.4, 47. , 44. ],
[ 0.3, 18. , 76. ],
[ 0.3, 25. , 64. ],
[ 0.3, 16. , 77. ],
[ 0.3, 16. , 59. ],
[ 0.3, 34. , 31. ],
[ 0.3, 27. , 33. ],
[ 0.3, 44. , 17. ],
[ 0.4, 45. , 9. ],
[ 0.5, 52. , 22. ],
[ 0.4, 37. , 53. ],
[ 0.3, 21. , 73. ],
[ 0.3, 20. , 76. ],
[ 0.3, 24. , 76. ],
[ 0.4, 38. , 71. ],
[ 0.3, 32. , 78. ],
[ 0.3, 21. , 89. ],
[ 0.2, 10. , 105. ],
[ 0.3, 15. , 102. ],
[ 0.3, 21. , 93. ],
[ 0.3, 45. , 63. ],
[ 0.4, 59. , 47. ],
[ 0.4, 59. , 44. ],
[ 0.7, 99. , 9. ],
[ 0.6, 88. , 9. ],
[ 0.8, 93. , 9. ],
[ 0.9, 89. , 9. ],
[ 0.8, 84. , 8. ],
[ 0.5, 64. , 10. ],
[ 0.4, 58. , 11. ],
[ 0.5, 53. , 9. ],
[ 0.4, 41. , 8. ],
[ 0.5, 43. , 9. ],
[ 0.5, 45. , 13. ],
[ 0.6, 51. , 25. ],
[ 0.5, 44. , 40. ],
[ 0.4, 36. , 59. ],
[ 0.4, 36. , 68. ],
[ 0.3, 26. , 84. ],
[ 0.3, 16. , 98. ],
[ 0.3, 17. , 97. ],
[ 0.3, 24. , 89. ],
[ 0.3, 17. , 99. ],
[ 0.3, 12. , 100. ],
[ 0.3, 42. , 61. ],
[ 0.4, 52. , 44. ],
[ 0.5, 54. , 39. ],
[ 0.5, 60. , 28. ],
[ 0.6, 73. , 13. ],
[ 0.5, 58. , 23. ],
[ 0.4, 58. , 16. ],
[ 0.5, 61. , 10. ],
[ 0.5, 59. , 9. ],
[ 0.4, 50. , 9. ],
[ 0.3, 31. , 10. ],
[ 0.4, 36. , 9. ],
[ 0.6, 45. , 9. ],
[ 0.5, 43. , 18. ],
[ 0.5, 37. , 24. ],
[ 0.5, 40. , 38. ],
[ 0.4, 26. , 59. ],
[ 0.3, 14. , 67. ],
[ 0.3, 12. , 64. ],
[ 0.3, 13. , 62. ],
[ 0.2, 10. , 63. ],
[ 0.2, 7. , 58. ],
[ 0.2, 8. , 53. ],
[ 0.2, 11. , 51. ],
[ 0.3, 16. , 47. ],
[ 0.2, 19. , 42. ],
[ 0.3, 22. , 38. ],
[ 0.3, 23. , 36. ],
[ 0.3, 16. , 43. ],
[ 0.2, 9. , 49. ],
[ 0.2, 6. , 48. ],
[ nan, nan, nan],
[ 0.2, 4. , 64. ],
[ 0.2, 3. , 89. ],
[ 0.2, 4. , 90. ],
[ 0.2, 3. , 92. ],
[ 0.2, 6. , 89. ],
[ 0.3, 11. , 83. ],
[ 0.3, 9. , 87. ],
[ 0.3, 8. , 84. ],
[ 0.3, 10. , 82. ],
[ 0.3, 10. , 80. ],
[ 0.3, 12. , 80. ],
[ 0.3, 12. , 81. ],
[ 0.3, 8. , 84. ],
[ 0.3, 10. , 85. ],
[ 0.2, 10. , 85. ],
[ 0.2, 14. , 82. ],
[ 0.3, 18. , 72. ],
[ 0.3, 28. , 60. ],
[ 0.3, 30. , 55. ],
[ 0.3, 21. , 61. ],
[ 0.3, 16. , 63. ],
[ 0.3, 12. , 65. ],
[ 0.2, 9. , 67. ],
[ 0.2, 5. , 70. ],
[ 0.2, 5. , 69. ],
[ 0.2, 6. , 65. ],
[ 0.2, 7. , 63. ],
[ 0.3, 16. , 55. ],
[ 0.3, 30. , 45. ],
[ 0.3, 38. , 39. ],
[ 0.3, 37. , 41. ],
[ 0.3, 29. , 53. ],
[ 0.3, 27. , 53. ],
[ 0.3, 27. , 49. ],
[ 0.3, 23. , 54. ],
[ 0.3, 22. , 57. ],
[ 0.3, 19. , 61. ],
[ 0.3, 17. , 63. ],
[ 0.3, 22. , 59. ],
[ 0.3, 27. , 53. ],
[ 0.3, 29. , 50. ],
[ 0.3, 34. , 44. ],
[ 0.3, 33. , 45. ],
[ 0.3, 26. , 50. ],
[ 0.3, 19. , 56. ],
[ 0.2, 11. , 63. ],
[ 0.2, 8. , 63. ],
[ 0.2, 9. , 58. ],
[ 0.2, 6. , 63. ],
[ 0.2, 5. , 66. ],
[ 0.2, 7. , 62. ],
[ 0.3, 18. , 53. ],
[ 0.4, 38. , 37. ],
[ 0.4, 49. , 28. ],
[ 0.4, 45. , 35. ],
[ 0.3, 34. , 47. ],
[ 0.3, 24. , 62. ],
[ 0.3, 24. , 68. ],
[ 0.3, 28. , 68. ],
[ 0.3, 23. , 78. ],
[ 0.3, 21. , 82. ],
[ 0.3, 17. , 87. ],
[ 0.3, 23. , 80. ],
[ 0.3, 28. , 75. ],
[ 0.3, 29. , 71. ],
[ 0.3, 46. , 50. ],
[ 0.4, 66. , 27. ],
[ 0.3, 51. , 38. ],
[ 0.3, 42. , 46. ]])
Dealing with missing values¶
# mean
array([ nan, nan, nan])
array([ 0.33717277, 29.79581152, 55.47643979])
# masking invalid data
masked_array(data = [0.3371727748691094 29.79581151832461 55.47643979057592],
mask = [False False False],
fill_value = 1e+20)
# data2:
# './data/barrio_del_pilar-20151222.csv'
data2 =
# masking
Plotting the data¶
** Maximum values ** from: http://www.mambiente.munimadrid.es/opencms/export/sites/default/calaire/Anexos/valores_limite_1.pdf
- NO2
- Media anual: 40 Āµg/m3
- Media horaria: 200 Āµg/m3
(0, 220)
from IPython.display import HTML
HTML('<iframe src="http://ccaa.elpais.com/ccaa/2015/12/24/madrid/1450960217_181674.html" width="700" height="400"></iframe>')
- CO
- MĆ”xima diaria de las medias mĆ³viles octohorarias: 10 mg/mĀ³
# http://docs.scipy.org/doc/numpy-1.10.0/reference/generated/numpy.convolve.html
def moving_average(x, N=8):
return np.convolve(x, np.ones(N)/N, mode='same')
<matplotlib.legend.Legend at 0x7fe148249080>
- O3
- MĆ”xima diaria de las medias mĆ³viles octohorarias: 120 Āµg/m3
- Umbral de informaciĆ³n. 180 Āµg/m3
- Media horaria. Umbral de alerta. 240 Āµg/m3
<matplotlib.legend.Legend at 0x7fe148234c88>
4. Scientific functions: SciPy¶
scipy.linalg: ATLAS LAPACK and BLAS libraries
scipy.stats: distributions, statistical functions...
scipy.integrate: integration of functions and ODEs
scipy.optimization: local and global optimization, fitting, root finding...
scipy.interpolate: interpolation, splines...
scipy.fftpack: Fourier trasnforms
scipy.signal, scipy.special, scipy.io
Temperature data¶
Now, we will use some temperature data from the Spanish Ministry of Agriculture.
HTML('<iframe src="http://eportal.magrama.gob.es/websiar/Ficha.aspx?IdProvincia=28&IdEstacion=1" width="700" height="400"></iframe>')
The file contains data from 2004 to 2015 (included). Each row corresponds to a day of the year, so evey 365 lines contain data from a whole year*
Note1: 29th February has been removed for leap-years. Note2: Missing values have been replaced with the immediately prior valid data.
These kind of events are better handled with Pandas!
!head data/M01_Center_Finca_temperature_data_2004_2015.csv
# mean; max; min 3.49;10.87;-2.75 5.10;10.88;-2.36 8.77;11.86;3.80 6.07;14.77;-1.36 2.48;12.06;-3.68 1.69;11.47;-3.81 2.57;9.29;-3.81 6.28;11.08;0.49 11.66;16.24;8.76
# Loading the data;
# 'data/M01_Center_Finca_temperature_data_2004_2015.csv'
temp_data =
# Importing SciPy stats
import scipy.stats as st
# Applying some functions: describe, mode, mean...
DescribeResult(nobs=4380, minmax=(array([ -4.21, -0.04, -11.88]), array([ 30.59, 42. , 21.77])), mean=array([ 14.03399543, 21.22098858, 6.86335388]), variance=array([ 59.25648501, 76.46548678, 44.03205308]), skewness=array([ 0.07277802, 0.10781561, -0.0989195 ]), kurtosis=array([-1.09612434, -1.11634177, -0.94371617]))
ModeResult(mode=array([[ 9, 12, 0]]), count=array([[199, 228, 393]]))
array([ 14.03399543, 21.22098858, 6.86335388])
array([ 13.52, 20.62, 7.09])
We can also get information about percentiles!
array([ 7.65 , 13.665, 1.32 ])
1.1415525114155249
0.022831050228310501
19.315068493150687
Rearranging the data¶
temp_data2 = np.zeros([365, 3, 12])
for year in range(12):
temp_data2[:, :, year] =
# Calculating mean of mean temp
mean_mean =
# max of max
max_max =
# min of min
min_min =
Let's visualize data!¶
Using matplotlib styles http://matplotlib.org/users/whats_new.html#styles
%matplotlib inline
plt.style.available
['seaborn-dark-palette', 'bmh', 'fivethirtyeight', 'grayscale', 'seaborn-white', 'seaborn-ticks', 'seaborn-bright', 'seaborn-deep', 'classic', 'seaborn-notebook', 'seaborn-dark', 'seaborn-talk', 'dark_background', 'seaborn-darkgrid', 'seaborn-poster', 'ggplot', 'seaborn-muted', 'seaborn-paper', 'seaborn-whitegrid', 'seaborn-colorblind', 'seaborn-pastel']
days = np.arange(1, 366)
(1, 365)
Let's see if 2015 was a normal year...
(1, 365)
(1, 365)
Matplotlib AGAIN, Now with 2D COLOURSSS!!1!1!11¶
For example, lets represent a function over a 2D domain!
For this we will use the contour function, which requires some special inputs...
#we will use numpy functions in order to work with numpy arrays
def funcion(x,y):
'''This is the help of the function funcion.
This function receives two parameters and returns another.
Such sicence. Wow.'''
return ????
# 0D: works?
funcion(,)
# 1D: works?
x = np.???(0,5, 100)
z = funcion(,)
z
plt.plot(x, z)
In oder to plot the 2D function, we will need a grid.
For 1D domain, we just needed one 1D array containning the X position and another 1D array containing the value.
Now, we will create a grid, a distribution of points covering a surface. For the 2D domain, we will need:
- One 2D array containing the X coordinate of the points.
- One 2D array containing the Y coordinate of the points.
- One 2D array containing the function value at the points.
The three matrices must have the exact same dimensions, because each cell of them represents a particular point.
#We can create the X and Y matrices by hand, or use a function designed to make ir easy:
#we create two 1D arrays of the desired lengths:
x_1d = np.linspace(0, 5, 5)
y_1d = np.linspace(-2, 4, 7)
x_1d
y_1d
#And we use the meshgrid function to create the X and Y matrices!
X, Y = np.????(x_1d, y_1d)
X
Y
Note that with the meshgrid function we can only create rectangular grids
#Using Numpy arrays, calculating the function value at the points is easy!
Z =
#Let's plot it!
plt.????(X, Y, Z)
plt.colorbar()
We can try a little more resolution...
n = 7
x_1d = np.linspace(0, 5, n)
y_1d = np.linspace(-2, 4, n)
X, Y = np.???(x_1d, y_1d)
Z = funcion(X,Y)
plt.contour(X, Y, Z) #How about adding a new parameter? np.linspace(-2, 2, 6)
plt.colorbar()
The countourf function is simmilar, but it colours also between the lines. In both functions, we can manually adjust the number of lines/zones we want to differentiate on the plot.
n = 7
plt.contourf(X, Y, Z, np.linspace(-2, 2, n),cmap=plt.cm.Spectral) #With cmap, a color map is specified
plt.colorbar()
#We can even combine them!
n = 100
plt.contourf(X, Y, Z, np.linspace(-2, 2, n),cmap=plt.cm.Spectral)
plt.colorbar()
cs = plt.contour(X, Y, Z, np.linspace(-2, 2, 9), colors='k') #Colors = 'k'?? Why would you do that??
plt.clabel(cs) #Vaya, quƩ harƔ esto??
These functions can be enormously useful when you want to visualize something.
And remember!
Always visualize data!¶
Let's try it with Real data!
time_vector = np.loadtxt('data/ligo_tiempos.txt')
frequency_vector = np.loadtxt('data/ligo_frecuencias.txt')
intensity_matrix = np.loadtxt('data/ligo_datos.txt')
The time and frequency vectors contain the values at which the instrument was reading, and the intensity matrix, the postprocessed strength measured for each frequency at each time.
We need again to create the 2D arrays of coordinates.
time_vector
frequency_vector
time_2D, freq_2D = np.????(time_vector, frequency_vector)
plt.figure(figsize=(10,6)) #We can manually adjust the sice of the picture
plt.???Pintarrelleno???(time_2D, freq_2D,intensity_matrix,np.linspace(0, 0.02313, 200),cmap='bone')
plt.xlabel('time (s)')
plt.ylabel('Frequency (Hz)')
plt.colorbar()
Wow! What is that? Let's zoom into it!
plt.figure(figsize=(10,6))
plt.???Pintarrelleno???(time_2D, freq_2D,intensity_matrix,np.linspace(0, 0.02313, 200),cmap = plt.cm.Spectral)
plt.colorbar()
plt.???Pintarallasdenivel???(time_2D, freq_2D,intensity_matrix,np.linspace(0, 0.02313, 9), colors='k')
plt.xlabel('time (s)')
plt.ylabel('Frequency (Hz)')
plt.axis([9.9, 10.05, 0, 300])#HERE HAPPENS THE ZOOM MAGIC
IPython Widgets¶
The IPython Widgets are interactive tools to use in the notebook. They are fun and very useful to quickly understand how different parameters affect a certain function.
This is based on a section of the PyConEs 14 talk by Kiko Correoso "Hacking the notebook": http://nbviewer.jupyter.org/github/kikocorreoso/PyConES14_talk-Hacking_the_Notebook/blob/master/notebooks/Using%20Interact.ipynb
from ipywidgets import interact
#Lets define a extremely simple function:
def ejemplo(x):
print(x*3)
???(???, x =10) #Try changing the value of x to True, 'Hello' or ['hello', 'world']
#We can control the slider values with more precission:
???(???, x = (9, 10, 0.1))
If you want a dropdown menu that passes non-string values to the Python function, you can pass a dictionary. The keys in the dictionary are used for the names in the dropdown menu UI and the values are the arguments that are passed to the underlying Python function.
???(???, x={'Puerta A': , 'Puerta B': , 'Puerta C':})
Let's have some fun! We talked before about frequencys and waves. Have you ever learn about AM and FM modulation? It's the process used to send radio communications!
x = np.linspace(-1, 7, 1000)
fig = plt.figure()
plt.subplot(211)#This allows us to display multiple sub-plots, and where to put them
plt.plot(x, np.sin(x))
plt.grid(False)
plt.title("Audio signal: modulator")
plt.subplot(212)
plt.plot(x, np.sin(50 * x))
plt.grid(False)
plt.title("Radio signal: carrier")
<matplotlib.text.Text at 0x7fe13b5b6400>
#Am modulation simply works like this:
am_wave = np.sin(50 * x) * (0.5 + 0.5 * np.sin(x))
plt.plot(x, am_wave)
[<matplotlib.lines.Line2D at 0x7fe13b4c5e10>]
In order to interact with it, we will need to transform it into a function
def am_mod (f_carr=50, f_mod=1, depth=0.5): #The default values will be the starting points of the sliders
x = np.???(-1, 7, 1000)
am_wave = np.sin(f_carr * x) * (1- depth/2 + depth/2 * np.sin(f_mod * x))
plt.???(x, am_wave)
???(???,
f_carr = (1,100,2),
f_mod = (0.2, 2, 0.1),
depth = (0, 1, 0.1))
Other options...¶
5. Other packages¶
Symbolic calculations with SymPy¶
SymPy is a Python package for symbolic math. We will not cover it in depth, but let's take a picure of the basics!
# ImportaciĆ³n
from sympy import init_session
init_session(use_latex='matplotlib') #We must start calling this function
The basic unit of this package is the symbol. A simbol object has name and graphic representation, which can be different:
coef_traccion = symbols('c_T')
coef_traccion
w = symbols('omega')
W = symbols('Omega')
w, W
By default, SymPy takes symbols as complex numbers. That can lead to unexpected results in front of certain operations, like logarithms. We can explicitly signal that a symbol is real when we create it. We can also create several symbols at a time.
x, y, z, t = symbols('x y z t', real=True)
x.assumptions0
Expressions can be created from symbols:
expr = cos(x)**2 + sin(x)**2
expr
simplify(expr)
expr
#We can substitute pieces of the expression:
expr.subs(x, y**2)
#We can particularize on a certain value:
(sin(x) + 3 * x).subs(x, pi)
#We can evaluate the numerical value with a certain precission:
(sin(x) + 3 * x).subs(x, pi).???()
We can manipulate the expression in several ways. For example:
expr1 = (x ** 3 + 3 * y + 2) ** 2
expr1
expr1.expand()
We can derivate and integrate:
expr = cos(2*x)
expr.diff(x, x, x)
expr_xy = y ** 3 * sin(x) ** 2 + x ** 2 * cos(y)
expr_xy
diff(expr_xy, x, 2, y, 2)
int2 = 1 / sin(x)
integrate(int2)
x, a = symbols('x a', real=True)
int3 = 1 / (x**2 + a**2)**2
integrate(int3, x)
We also have ecuations and differential ecuations:
a, x, t, C = symbols('a, x, t, C', real=True)
ecuacion = Eq(a * exp(x/t), C)
ecuacion
???(ecuacion ,x)
x = symbols('x')
f = Function('y')
ecuacion_dif = Eq(f(x).diff(x,2) + f(x).diff(x) + f(x), cos(x))
ecuacion_dif
???(ecuacion_dif, f(x))
Data Analysis with pandas¶
Pandas is a package that focus on data structures and data analysis tools. We won't focus a lot on it, but you can check this awesome workshop from Kiko! https://github.com/PyDataMadrid2016/Conference-Info/tree/master/workshops_materials/20160408_1100_Pandas_for_beginners
Machine Learning with scikit-learn¶
Scikit-learn is a very complete Python package focusing on machin learning, and data mining and analysis. We will not cover it in depth because it deserves its own workshop.
A world of possibilities...¶
¡Gracias por vuetra atención!¶
¿Alguna pregunta?¶
# Notebook style
from IPython.core.display import HTML
css_file = './static/style.css'
HTML(open(css_file, "r").read())