Python Programming for Biology: Bioinformatics and Beyond

Figure 9.1.  Example graphs and charts generated using Matplotlib. The examples

relate to the named line graph, scatter plot, histogram and pie chart functions that are

available in the ‘pyplot’ module, e.g. via pyplot.hist(data).

Linear algebra

In  this  section  we  give  a  short  introduction  to  linear  algebra  for  non-mathematicians.  A

familiarity with some of the concepts involved will be assumed when discussing various

parts  of  subsequent  chapters.  In  particular  for  this  book,  linear  algebra  is  helpful  in  the

understanding  and  manipulation  of  three-dimensional  coordinates.  Here,  rather  than

discussing  how  separate  positions  on  each  spatial  axis  (x,  y  and  z)  are  used,  we  can

describe a 3D point in its entirety as a single vector that groups the axis positions. Also,

changes of position (transformations) may be described with matrices, which specify how

vector  locations  are  relocated.  An  example  of  an  easily  visualised  transformation  is

rotation; a shape, defined by a collection of coordinate positions, is moved to a new set of

coordinates to change the orientation of the shape.

The way that data is represented in linear algebra is in terms of vectors, which represent

positions  in  space.  Although  the  ‘space’  we  mention  in  this  book  is  usually  the  three-

dimensional  in-out,  up-down  and  left-right  kind  we  all  recognise  it  can  also  be  used  for

more  abstract  spaces  where  the  ‘axes’  are  merely  independent  qualities.  An  example  of

this might be colour space where you can define a colour (or rather a colour vector) by its

red, green and blue components. In the language of Python a vector is represented by an

ordered collection of numbers, an array, where each number specifies the location of the

point  along  each  axis  (dimension).  You  can  think  of  these  just  as  a  list  of  floating  point

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numbers;  this  will  have  a  known  length  and  will  not  contain  any  other  kind  of  Python

object. To take a biological example, an atom in a molecule has a location (relative to the

other  atoms),  which  consists  of  three  coordinates  (x,  y  and  z)  and  it  is  normal  to  place

these values in an array; the three coordinates correspond to what is normally described as

a point in space. If you were studying the dynamics of a molecule then in addition there

would be a fourth coordinate, time, and you would be dealing with space-time, although

normally you would only consider one time value after the other, rather than all in one go.