function module¶

Utility functions¶

Functions complex_to_seq() and seq_to_complex() are useful to convert between the matrix representation of complex numbers and Python complex.

The function mean() evaluates the mean of a sequence.

Module contents¶

complex_to_seq(z)¶

Transform a complex number into a 4-element sequence

Parameters:	z – a number

If z = x + yj, then an array of the form [[x,-y],[y,x]] can be used to represent z in matrix computations.

Examples::

>>> import numpy
>>> z = 1 + 2j
>>> function.complex_to_seq(z)
(1.0, -2.0, 2.0, 1.0)

>>> m = numpy.array( function.complex_to_seq(z) )
>>> m.shape = (2,2)
>>> print( m )
[[ 1. -2.]
 [ 2.  1.]]

seq_to_complex(seq)¶

Transform a 4-element sequence into a complex number

Parameters:	seq – a 4-element sequence
Raises:	RuntimeError – if `seq` is ill-conditioned

If z = x + yj, then an array of the form [[x,-y],[y,x]] can be used to represent z in matrix computations.

Examples:

>>> import numpy
>>> seq = (1,-2,2,1)
>>> z = function.seq_to_complex( seq )
>>> z
(1+2j)
>>> a = numpy.array((1,-2,2,1))
>>> a.shape = 2,2
>>> a
array([[ 1, -2],
       [ 2,  1]])
>>> z = function.seq_to_complex(a)
>>> z
(1+2j)

mean(seq, *args, **kwargs)¶

Return the arithmetic mean of the elements in seq

Parameters:	seq – a sequence, `ndarray`, or iterable, of numbers or uncertain numbers args – optional arguments when `seq` is an `ndarray` kwargs – optional keyword arguments when `seq` is an `ndarray`

If the elements of seq are uncertain numbers, an uncertain number is returned.

Example

>>> seq = [ ureal(1,1), ureal(2,1), ureal(3,1) ]
>>> function.mean(seq)
ureal(2.0,0.5773502691896257,inf)