Document Text Contents
Page 1
OVER
2 HOURSOF VIDEO TUTORIALS
Over 20
incredible
projects
The ultimate guide to coding with Python
Learn to use Python
Python
The
NEW
Page 2
Page 90
90 T
he Python BookWork with Python
SciPy is built on top of NumPy
and is more advanced
09 Plotting with Matplotlib
The fi
rst move you should make is to
install Matplotlib. As you can see, Matplotlib has
many dependencies that you should also install.
The fi
rst thing you will learn is how to
plot a polynomial function. The necessary
commands for plotting the 3x^2-x+1
polynomial are the following:
import numpy as np
import matplotlib.pyplot as plt
myPoly = np.poly1d(np.array([3, -1, 1]).
astype(float))
x = np.linspace(-5, 5, 100)
y = myPoly(x)
plt.xlabel('x values')
plt.ylabel('f(x) values')
xticks = np.arange(-5, 5, 10)
yticks = np.arange(0, 100, 10)
plt.xticks(xticks)
plt.yticks(yticks)
plt.grid(True)
plt.plot(x,y)
The variable that holds the polynomial
is myPoly. The range of values that will
be plotted for x is defi
ned using “x =
np.linspace(-5, 5, 100)”. The other important
variable is y, which calculates and holds the
values of f(x) for each x value.
It is important that you start ipython using
the “ipython --pylab=qt” parameters in order
to see the output on your screen. If you are
interested in plotting polynomial functions,
you should experiment more, as NumPy can
also calculate the derivatives of a function and
plot multiple functions in the same output.
10 About SciPy
SciPy is built on top of NumPy and
is more advanced than NumPy. It supports
numerical integration, optimisations, signal
processing, image and audio processing,
and statistics. The example in
Fig. 01
(to the left)
uses a small part of the scipy.stats package that
is about statistics.
The example uses two statistics distributions
and may be diffi
cult to understand even if you
know mathematics, but it is presented in order
to give you a better taste of SciPy commands.
11 Using SciPy for image processing
Now we will show you how to process
and transform a PNG image using SciPy.
The most important part of the code is the
following line:
In [36]: from scipy.stats import poisson, lognorm
In [37]: mySh = 10;
In [38]: myMu = 10;
In [39]: ln = lognorm(mySh)
In [40]: p = poisson(myMu)
In [41]: ln.rvs((10,))
Out[41]:
array([ 9.29393114e-02, 1.15957068e+01, 9.78411983e+01,
8.26370734e-07, 5.64451441e-03, 4.61744055e-09,
4.98471222e-06, 1.45947948e+02, 9.25502852e-06,
5.87353720e-02])
In [42]: p.rvs((10,))
Out[42]: array([12, 11, 9, 9, 9, 10, 9, 4, 13, 8])
In [43]: ln.pdf(3)
Out[43]: 0.013218067177522842Fig 01
09Plotting with
Matplotlib
Page 91
The Python Book 91Work with Python
Process and transform a PNG
image using SciPy
12 Other useful functions
It is very useful to be able to fi
nd out
the data type of the elements in an array; it
can be done using the dtype() function.
Similarly, the ndim() function returns the
number of dimensions of an array.
When reading data from external fi
les, you
can save their data columns into separate
variables using the following way:
In [10]: aa1,aa2 = np.loadtxt("timeN.txt",
usecols=(0,1), unpack=True)
The aforementioned command saves column
1 into variable aa1 and column 2 into variable
aa2. The “unpack=True” allows the data to be
assigned to two different variables. Please
note that the numbering of columns starts
with 0.
14 Array broadcasting in NumPy
To close, we will talk more about
array broadcasting because it is a very
useful characteristic. First, you should know
that array broadcasting has a rule: in order
for two arrays to be considered for array
broadcasting, “the size of the trailing axes for
both arrays in an operation must either be the
same size or one of them must be one.”
Put simply, array broadcasting allows
NumPy to “change” the dimensions of an array
by fi
lling it with data in order to be able to do
calculations with another array. Nevertheless,
you cannot stretch both dimensions of an
array to do your job.
13 Fitting to polynomials
The NumPy polyfi
t() function tries to fi
t a set of data points to a polynomial. The data
was found from the timeN.txt fi
le, created
earlier in this article.
The Python script uses a fi
fth degree
polynomial, but if you want to use a different
degree instead then you only have to change
the following line:
coefficients = np.polyfit(aa1, aa2, 5)
image = np.array(Image.open('SA.png').
convert('L
'))
This line allows you to read a usual PNG
fi le and convert it into a NumPy array for
additional processing. The program will
also separate the output into four parts and
displays a different image for each of these
four parts.
11 Using SciPy for
image processing
13 Fitting to
Polynomials
Page 179
Page 180
The ultimate guide to coding with Python
Put Python to work
Supercharge your system and make life
easier with handy coding tutorials
Use Python with Raspberry Pi
Work on any Raspberry Pi model using its
officially recognised language
Get to grips with the basics
Learn Python the right way and complete
basic projects with our simple guides
OVER
2 HOURSOF VIDEO TUTORIALS
Python
The
250essential tips
inside
OVER
2 HOURSOF VIDEO TUTORIALS
Over 20
incredible
projects
The ultimate guide to coding with Python
Learn to use Python
Python
The
NEW
Page 2
Page 90
90 T
he Python BookWork with Python
SciPy is built on top of NumPy
and is more advanced
09 Plotting with Matplotlib
The fi
rst move you should make is to
install Matplotlib. As you can see, Matplotlib has
many dependencies that you should also install.
The fi
rst thing you will learn is how to
plot a polynomial function. The necessary
commands for plotting the 3x^2-x+1
polynomial are the following:
import numpy as np
import matplotlib.pyplot as plt
myPoly = np.poly1d(np.array([3, -1, 1]).
astype(float))
x = np.linspace(-5, 5, 100)
y = myPoly(x)
plt.xlabel('x values')
plt.ylabel('f(x) values')
xticks = np.arange(-5, 5, 10)
yticks = np.arange(0, 100, 10)
plt.xticks(xticks)
plt.yticks(yticks)
plt.grid(True)
plt.plot(x,y)
The variable that holds the polynomial
is myPoly. The range of values that will
be plotted for x is defi
ned using “x =
np.linspace(-5, 5, 100)”. The other important
variable is y, which calculates and holds the
values of f(x) for each x value.
It is important that you start ipython using
the “ipython --pylab=qt” parameters in order
to see the output on your screen. If you are
interested in plotting polynomial functions,
you should experiment more, as NumPy can
also calculate the derivatives of a function and
plot multiple functions in the same output.
10 About SciPy
SciPy is built on top of NumPy and
is more advanced than NumPy. It supports
numerical integration, optimisations, signal
processing, image and audio processing,
and statistics. The example in
Fig. 01
(to the left)
uses a small part of the scipy.stats package that
is about statistics.
The example uses two statistics distributions
and may be diffi
cult to understand even if you
know mathematics, but it is presented in order
to give you a better taste of SciPy commands.
11 Using SciPy for image processing
Now we will show you how to process
and transform a PNG image using SciPy.
The most important part of the code is the
following line:
In [36]: from scipy.stats import poisson, lognorm
In [37]: mySh = 10;
In [38]: myMu = 10;
In [39]: ln = lognorm(mySh)
In [40]: p = poisson(myMu)
In [41]: ln.rvs((10,))
Out[41]:
array([ 9.29393114e-02, 1.15957068e+01, 9.78411983e+01,
8.26370734e-07, 5.64451441e-03, 4.61744055e-09,
4.98471222e-06, 1.45947948e+02, 9.25502852e-06,
5.87353720e-02])
In [42]: p.rvs((10,))
Out[42]: array([12, 11, 9, 9, 9, 10, 9, 4, 13, 8])
In [43]: ln.pdf(3)
Out[43]: 0.013218067177522842Fig 01
09Plotting with
Matplotlib
Page 91
The Python Book 91Work with Python
Process and transform a PNG
image using SciPy
12 Other useful functions
It is very useful to be able to fi
nd out
the data type of the elements in an array; it
can be done using the dtype() function.
Similarly, the ndim() function returns the
number of dimensions of an array.
When reading data from external fi
les, you
can save their data columns into separate
variables using the following way:
In [10]: aa1,aa2 = np.loadtxt("timeN.txt",
usecols=(0,1), unpack=True)
The aforementioned command saves column
1 into variable aa1 and column 2 into variable
aa2. The “unpack=True” allows the data to be
assigned to two different variables. Please
note that the numbering of columns starts
with 0.
14 Array broadcasting in NumPy
To close, we will talk more about
array broadcasting because it is a very
useful characteristic. First, you should know
that array broadcasting has a rule: in order
for two arrays to be considered for array
broadcasting, “the size of the trailing axes for
both arrays in an operation must either be the
same size or one of them must be one.”
Put simply, array broadcasting allows
NumPy to “change” the dimensions of an array
by fi
lling it with data in order to be able to do
calculations with another array. Nevertheless,
you cannot stretch both dimensions of an
array to do your job.
13 Fitting to polynomials
The NumPy polyfi
t() function tries to fi
t a set of data points to a polynomial. The data
was found from the timeN.txt fi
le, created
earlier in this article.
The Python script uses a fi
fth degree
polynomial, but if you want to use a different
degree instead then you only have to change
the following line:
coefficients = np.polyfit(aa1, aa2, 5)
image = np.array(Image.open('SA.png').
convert('L
'))
This line allows you to read a usual PNG
fi le and convert it into a NumPy array for
additional processing. The program will
also separate the output into four parts and
displays a different image for each of these
four parts.
11 Using SciPy for
image processing
13 Fitting to
Polynomials
Page 179
Page 180
The ultimate guide to coding with Python
Put Python to work
Supercharge your system and make life
easier with handy coding tutorials
Use Python with Raspberry Pi
Work on any Raspberry Pi model using its
officially recognised language
Get to grips with the basics
Learn Python the right way and complete
basic projects with our simple guides
OVER
2 HOURSOF VIDEO TUTORIALS
Python
The
250essential tips
inside
