Python Programming for Biology: Bioinformatics and Beyond

Example: mean angle

Below  we  give  a  more  involved  example  that  uses  the  math  module  inside  a  function

definition. This function will be used later on in this book, where it is used to calculate the

average angle value from a list of input angles. Later, in context, it will be used to look at

the angles of chemical bonds that come from alternative molecular shapes (conformations)

to give the average bond angle. Because angles are a circular measure (i.e. 360° equals 0°)

we  cannot  take  the  simple  mean  value  of  the  numbers.  Instead  we  find  the  average  sine

and cosine of the angles, which oscillate between plus and minus one and so don’t have a

problem when angles go past a full turn or become negative. Both the sine and cosine are

required because each function on its own is not unique to a single angle, e.g. the sine of

45° equals the sine of 135°. Accordingly, we use the averages of both sine and cosine to

generate  the  average  angle  via  a  special  inverse  tangent  function,  and  naturally  the

mathematical operations come from the math module:

from math import sin, cos, degrees, radians, atan2

def meanAngle(angles, inDegrees=True):

sumCos = 0.0

---

sumSin = 0.0

for angle in angles:

if inDegrees:

angle = radians(angle)

sumCos += cos(angle)

sumSin += sin(angle)

N = len(angles)

meanAngle = atan2(sumSin/N, sumCos/N)

if inDegrees:

meanAngle = degrees(meanAngle)

return meanAngle

The inverse tangent function used is specifically atan2; while a normal inverse tangent

(atan)  operates  on  a  single  number  and  gives  an  angle  between  −90°  and  +90°,  this

function uses both sine and cosine values to calculate the inverse tangent and also which

quadrant  of  the  circle  it  lies  in.  Thus  the  result  is  an  angle  between  −180°  and  +180°.

Finally,  note  how  all  calculations  are  done  in  radians,  so  we  must  explicitly  convert  the

input and output when working with values specified in units of degrees, signalled by the

input argument inDegrees being True.