A mathematics module for the scripting

Last update:2/06/14

Description

The module mathematics.py provides useful functions and a class to do basic mathematics with Python/Jython lists and tuples.

Useful functions

• Convert FWHM to \(\sigma\):

  >>> sigma = fwhmToSigma(fwhm)
  

• Convert \(\sigma\) to FWHM:

  >>> fwhm = sigmatoFwhm(sigma)
  

• Create an evenly spaced numbers over a specified interval

The general syntax is:

>>> numbers = linspace(start, stop, num=num, endpoint=endpoint, retstep=retstep)

• Generate the values between 1 and 10 (the default number of values is 50):

  >>> print linspace(1, 10)
  [1.0, 1.183673469387755, 1.3673469387755102,..., 10]
  

• Generate the 10 values between 1 and 10:

  >>> print linspace(1, 10, num=10)
  [1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0, 10.0]
  

• Generate the 10 values between 1 and 10 but don’t include the end point:

  >>> print linspace(1, 10, num=10, endpoint=False)
  [1.0, 1.9, 2.8, 3.7, 4.6, 5.5, 6.4, 7.3, 8.2, 9.1]
  

• Generate the values between 1 and 10 and return the step:

  >>> print linspace(1, 10, retstep=True)
  ([1.0, 1.183673469387755, 1.3673469387755102,..., 10], 0.1836734693877551)
  

The Array class

As CASSIS uses Jython as a scripting language (Python implemented in Java), libraries like numpy are not available in Jython. The class Array in mathematics.py aims to provide some useful equivalent functionalities for 1-dimension arrays such as:

• operations on the array
• selection of indexes
• basic statistical functions
• plotting

The class Array roughly emulates numpy.array for 1-dimensional arrays:

>>> from mathematics import Array

Creation of an array

You can create an empty Array instance by specifying a number of values:

>>> emptyArray = Array(100)

or create it from an iterable:

>>> a = Array([1, 2, 3, 4])

Operations on the array

Operations on the array can be performed with scalars or other arrays.

Mathematical operators

Basic mathematical operators are available:

• addition
• subtraction
• multiplication
• division
• power
• modulo

Example:

>>> print a + 42
[43 44 45 56]

# Another array
>>> b = Array([-20, 17, 3, 67])

>>> print a+b
[-19 19 6 71]

>>> print a**2
[1 4 9 16]

>>> print a % 2
[1 0 1 0]

Logical operators

The available logical operators are:

• >
• >=
• <
• <=
• ==
• != (different)

Example:

>>> print a > 2
[0 0 1 1]

>>> print a > b
[1 0 0 0]

Accessing the values in the array

You can access any value in the array like you would do for a Python list.

• You can select a single index:

  >>> print a[0]
  1
  

• Or a range of indexes:

  >>> print a[0:2]
  [1 2]
  

• You can set a new index:

  >>> a[0] = 10
  >>> print a
  [10 2 3 4]
  

• Or a range of indexes::

  >>> a[0:2] = 10
  >>> print a
  [10 10 3 4]
  >>> a[0:2] = 100, 200
  >>> print a
  [100 200 3 4]
  

Array also allows a more advanced way of accessing the values by specifying a condition on the array.

• Select all the positive values in b:

  >>> print b[b > 0]
  [17 3 67]
  

• Select all the even values in a:

  >>> print a[b % 2 == 0]
  [2 4]
  

Note

Compound conditions are supported yet.

Basic statistical functions

The Array instance provides its own statistical functions:

• mean
• median
• std
• min
• max
• sum
• cumsum (the cumulative sum)

Examples:

>>> print a.sum()
10

>>> print a.mean()
2.5

>>> print a.cumsum()
[1 3 6 10]

Plotting

You can plot the values stored in the Array instance with the plot method:

>>> # y is an Array whose values are the intensity of a spectrum
>>> y.plot(title="CO line")

plots the following graph

(the indexes of the array are represented on the x axis.)

Note

You can use all the available optional keywords that you would use with the Plot class.