pyyeti.ytools.max_complex_vector_sum

pyyeti.ytools.max_complex_vector_sum(x, y)

Compute maximum complex vector from x and y components

Parameters:

x, y (complex scalar or 1d array_like) – The x and y complex components to sum. If 1d arrays, each element is independently analyzed.

Returns:

• hypot (complex scalar or 1d ndarray) – The maximum vector sum of the complex vectors x and y

• theta (real scalar or 1d ndarray) – The maximizing angle(s)

• c (real scalar or 1d ndarray) – The cosine of the maximizing angle(s)

• s (real scalar or 1d ndarray) – The sine of the maximizing angle(s)

Notes

The return value hypot is the vector sum:

hypot = cos(theta) * x + sin(theta) * y

where, for each element in x and y, the angle theta maximizes the magnitude of hypot:

abs(hypot)

Examples

>>> import numpy as np
>>> from pyyeti import ytools
>>> x = 1.0 + 2.0j
>>> y = 3.0 + 4.0j
>>> h, th, c, s = ytools.max_complex_vector_sum(x, y)
>>> h
(3.148096...+4.467164...j)
>>> th
1.154305...
>>> c
0.404553...
>>> s
0.914514...
>>> with ytools.np_printoptions(precision=6):
...     x = [3.0, 1.0 + 2.0j]
...     y = [4.0, 3.0 + 4.0j]
...     h, th, c, s = ytools.max_complex_vector_sum(x, y)
...     print(h)
...     print(th)
...     print(c)
...     print(s)
[ 5.000000+0.j        3.148096+4.467164j]
[ 0.927295  1.154306]
[ 0.6       0.404554]
[ 0.8       0.914514]