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Introduction to Python for Science, Release 0.9.23
SciPy
provides a wide spectrum of mathematical functions and numerical
routines for Python. SciPy makes extensive use of NumPy arrays so
when you import SciPy, you should always import NumPy too. In
addition to providing basic mathematical functions, SciPy provides
Python “wrappers” for numerical software written in other languages,
like Fortran, C, or C++. A “wrapper” provides a transparent easy-to-
use Python interface to standard numerical software, such as routines
for doing curve fitting and numerically solving differential equations.
SciPy greatly extends the power of Python and saves you the trouble
of writing software in Python that someone else has already written
and optimized in some other language. You can find more information
about SciPy at
http://docs.scipy.org/doc/scipy/reference/
MatPlotLib
is the standard Python package for making two and three
dimensional plots.
MatPlotLib makes extensive use of NumPy
arrays.
You will make all of your plots in Python using this
package.
You can find more information about MatPlotLib at
http://MatPlotLib.sourceforge.net/
We will use these three modules extensively and therefore will provide introductions to
their capabilities as we develop Python in this manual. The links above provide much
more extensive information and you will certainly want to refer to them from time to
time.
These modules, NumPy, MatPlotLib, and SciPy, are built into the IPython shell so we
can use them freely in that environment. Later, when we introduce Python programs (or
scripts), we will see that in those cases you must explicitly load these modules using the
import
command to have access to them.
Finally, we note that you can write your own Python modules. They are a convenient way
of packaging and storing Python code so that you can reuse it. We defer learning about
how to write modules until after we have learned about Python.
2.6 Python functions: a first look
A function in Python is similar to a mathematical function. In consists of a name and and
one or more arguments contained inside parentheses, and it produces some output. For
example, the NumPy function
sin(x)
calculates the sine of the number
x
(where
x
is
expressed in radians). Let’s try it out in the IPython shell:
In [1]:
sin(
0.5
)
Out[1]:
0.47942553860420301
2.6. Python functions: a first look
15
Introduction to Python for Science, Release 0.9.23
The argument of the function can be a number or any kind of expression whose output
produces a number. For example, the function
log(x)
calculates the nature logarithm.
All of the following expressions are legal and produce the expected output:
In [2]:
log(sin(
0.5
))
Out[2]:
-
0.73516668638531424
In [3]:
log(sin(
0.5
)
+
1.0
)
Out[3]:
0.39165386283471759
In [4]:
log(
5.5
/
1.2
)
Out[4]:
1.5224265354444708
2.6.1 Some NumPy functions
NumPy includes an extensive library of mathematical functions. In the table below,
we list some of the most useful ones.
A much more complete list is available at
http://docs.scipy.org/doc/numpy/reference/ufuncs.html#math-operations
Function
Description
sqrt(x)
Square root of
x
exp(x)
Exponential of x,
i.e.
e
x
log(x)
Natural log of x,
i.e.
ln
x
log10(x)
Base 10 log of
x
degrees(x)
Converts
x
from radians to degrees
radians(x)
Converts
x
from degrees to radians
sin(x)
Sine of
x
(
x
in radians)
cos(x)
Cosine
x
(
x
in radians)
tan(x)
Tangent
x
(
x
in radians)
arcsin(x)
Arc sine (in radians) of
x
arccos(x)
Arc cosine (in radians) of
x
arctan(x)
Arc tangent (in radians) of
x
fabs(x)
Absolute value of
x
round(x)
Rounds a float to nearest integer
floor(x)
Rounds a float
down
to nearest integer
ceil(x)
Rounds a float
up
to nearest integer
sign(x)
-1 if
x <
0
, +1 if
x >
0
, 0 if
x
= 0
The functions discussed here all have one input and one output. Python functions can,
in general, have multiple inputs and multiple outputs. We will discuss these and other
features of functions later when we take up functions in the context of user-defined func-
tions.
16
Chapter 2. Launching Python
Introduction to Python for Science, Release 0.9.23
2.6.2 Keyword arguments
In addition to regular arguments, Python functions can have keyword arguments
(
kwargs
). Keyword arguments are
optional
arguments that need not be specified when
a function is called. See
for examples of the use of keyword arguments.
For the moment, we don’t need them so we defer a full discussion of keyword arguments
until we introduce
user defined functions
.
2.7 Variables
2.7.1 Names and the assignment operator
A variable is a name that is used to store data. It can be used to store different kinds of
data, but here we consider the simplest case where the data is a single numerical value.
Here are a few examples:
In [1]:
a
=
23
In [2]:
p, q
=
83.4
, sqrt(
2
)
The equal sign “
=
” is the assignment operator. In the first statement, it assigns the value
of 23 to the variable
a
. In the second statement it assigns a value of 83.4 to
p
and a value
of 1.4142135623730951 to
q
. To be more precise, the name of a variable, such as
a
, is
associated with a
memory location
in your computer; the assignment variable tells the
computer to put a particular piece of data, in this case a numerical value, in that memory
location. Note that Python stores the
numerical value
, not the expression used to generate
it. Thus,
q
is assigned the 17-digit number 1.4142135623730951 generated by evaluating
the expression
sqrt(2)
,
not
with
√
2
. (Actually the value of
q
is stored as a binary,
base 2, number using scientific notation with a mantissa and an exponent.)
Suppose we write
In [3]:
b
=
a
In this case Python associates a new memory location with the name
b
, distinct from the
one associated with
a
, and sets the value stored at that memory location to 23, the value
of
a
. The following sequence of statements demonstrate that fact. Can you see how?
Notice that simply typing a variable name and pressing
Return
prints out the value of
the variable.
In [4]:
a
=
23
2.7. Variables
17
Introduction to Python for Science, Release 0.9.23
In [5]:
b
=
a
In [6]:
a
Out[6]:
23
In [7]:
b
Out[7]:
23
In [8]:
a
=
12
In [9]:
a
Out[9]:
12
In [10]:
b
Out[10]:
23
The assignment variable works from right to left; that is, it assigns the value of the number
on the right to the variable name on the left. Therefore, the statement “
5=a
” makes no
sense in Python. The assignment operator “
=
” in Python is not equivalent to the equals
sign “
=
” we are accustomed to in algebra.
The assignment operator can be used to increment or change the value of a variable
In [11]:
b
=
b
+
1
In [12]:
b
Out[12]:
24
The statement,
b = b+1
makes no sense in algebra, but in Python (and most computer
languages), it makes perfect sense: it means “add 1 to the current value of
b
and assign
the result to
b
.” This construction appears so often in computer programming that there
is a special set of operators to perform such changes to a variable:
+=
,
-=
,
*=
, and
/=
.
Here are some examples of how they work:
In [13]:
c , d
=
4
,
7.92
In [14]:
c
+=
2
In [15]:
c
Out[15]:
6
In [16]:
c
*=
3
In [16]:
c
Out[16]:
18
18
Chapter 2. Launching Python
Introduction to Python for Science, Release 0.9.23
In [17]:
d
/= -
2
In [17]:
d
Out[17]:
-
3.96
In [18]:
d
-=
4
In [19]:
d
Out[19]:
-
7.96
Verify that you understand how the above operations work.
2.7.2 Legal and recommended variable names
Variable names in Python must start with a letter, and can be followed by as many al-
phanumeric characters as you like. Spaces are not allowed in variable names. However,
the underscore character “
_
” is allowed, but no other character that is not a letter or a
number is permitted.
Recall that Python is
case sensitive
, so the variable
a
is distinct from the variable
A
.
We recommend giving your variables descriptive names as in the following calculation:
In [20]:
distance
=
34.
In [21]:
time_traveled
=
0.59
In [22]:
velocity
=
distance
/
time_traveled
In [23]:
velocity
Out[23]:
57.6271186440678
The variable names
distance
,
time_traveled
, and
velocity
immediately re-
mind you of what is being calculated here. This is good practice. But so is keeping
variable names reasonably short, so don’t go nuts!
2.7.3 Reserved words in Python
There are also some names or words that are reserved by Python for special purposes or
functions. You must avoid using these names, which are provided here for your reference:
2.7. Variables
19