Lambdify support

[cjayross]

Addresses #3

This is an important merge as it provides a convenient and efficient way to convert tensor expressions into numerical functions that can be used in algorithms like Runge-Kutta.

I defined a new class called NumericalArray which has two important attributes. The first is an attribute called _lambda which is the lambdified function for the entire array. The second is _generator which is an array where each individual component is a lambda function for that specific component. This is an important distinction since this allows for calculating single components without having to do calculations for every other component as well (which is what _lambda does).

These attributes are accessed very easily by defining the __call__ and __getitem__ attributes. Calling an instance of NumericalArray is equivalent to calling it's _lambda argument while accessing a component like an array returns a lambda for that component, which can be subsequently called just the same.

>>> t, r, th, ph = symbols('t r theta phi', real=True)
>>> schw = diag(1-1/r, -1/(1-1/r), -r**2, -r**2*sin(th)**2)
>>> g = Metric('g', (t, r, th, ph), schw)
>>> narr = lambdify_tensor((r, th), g(-mu,-nu))
>>> narr(2, 0)
array([[ 0.5,  0. ,  0. ,  0. ],
       [ 0. , -2. ,  0. ,  0. ],
       [ 0. ,  0. , -4. ,  0. ],
       [ 0. ,  0. ,  0. , -0. ]])
>>> narr[0,0]
<function _lambdifygenerated(r, theta)>
>>> narr[0,0](2, 0)
0.5

Note: The changes currently lack test cases unfortunately.

[pep8speaks]

Hello @cjayross! Thanks for updating this PR. We checked the lines you've touched for PEP 8 issues, and found:

• In the file src/riccipy/numerical.py:

Line 15:81: E501 line too long (84 > 80 characters)
Line 17:81: E501 line too long (86 > 80 characters)
Line 18:81: E501 line too long (86 > 80 characters)
Line 21:81: E501 line too long (85 > 80 characters)
Line 33:81: E501 line too long (86 > 80 characters)
Line 64:81: E501 line too long (86 > 80 characters)
Line 75:81: E501 line too long (84 > 80 characters)
Line 85:81: E501 line too long (82 > 80 characters)
Line 88:81: E501 line too long (81 > 80 characters)
Line 91:81: E501 line too long (84 > 80 characters)

• In the file src/riccipy/tests/test_numerical.py:

Line 9:1: E302 expected 2 blank lines, found 1
Line 17:1: E302 expected 2 blank lines, found 1
Line 21:29: E231 missing whitespace after ','
Line 23:29: E231 missing whitespace after ','
Line 24:18: E231 missing whitespace after ','
Line 24:23: E231 missing whitespace after ','
Line 26:1: E302 expected 2 blank lines, found 1
Line 28:42: E231 missing whitespace after ','

Comment last updated at 2019-07-09 07:07:47 UTC

[codecov-io]

Codecov Report

Merging #12 into master will decrease coverage by 6.22%.
The diff coverage is 0%.

@@            Coverage Diff            @@
##           master     #12      +/-   ##
=========================================
- Coverage   94.72%   88.5%   -6.23%     
=========================================
  Files           9      10       +1     
  Lines         512     548      +36     
=========================================
  Hits          485     485              
- Misses         27      63      +36

Impacted Files	Coverage Δ
src/riccipy/__init__.py	100% <ø> (ø)	⬆️
src/riccipy/numerical.py	0% <0%> (ø)

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