| CI & Test Status | 
|
| Code Quality | 
 |
| Code Style | 
|
| Dependencies |  |
| Usage |  |
| Get It |  
 |
This library uses concepts typically taught in an introductory Calculus class to describe properties of continuous, differentiable, single-variable functions.
The func_analysis module defines the class AnalyzedFunc. An instance of
this class has several attributes describing the behavior of this function.
Required data include:
- A range
- The function to be analyzed
Special points include zeros, critical numbers, extrema, and points of inflection. It’s possible to calculate these when given the number of points wanted.
Optional data can be provided to improve precision and performance. Such data include:
- Any derivatives of the function
- Any known zeros, critical numbers, extrema, points of inflection
- Intervals of concavity, convexity, increase, decrease
- Any vertical axis of symmetry
Any of the above data can be calculated by an instance of AnalyzedFunc.
This paste from an interactive Python session showcases all the functionality
of AnalyzedFunc:
>>> from func_analysis import AnalyzedFunc
>>> import mpmath as mp; import numpy as np
>>> def example_func(x):
... return mp.cos(x ** 2) - mp.sin(x) + (x / 68)
...
>>> analyzed_example = AnalyzedFunc(
... func=example_func,
... x_range=(-47.05, -46.3499),
... zeros_wanted=21,
... crits_wanted=21,
... pois_wanted=21,
... zeros=[-47.038289673236127, -46.406755885040056],
... )
>>> analyzed_example.zeros
array([mpf('-47.038289673236127'), mpf('-47.018473233395284'),
mpf('-46.972318087653945'), mpf('-46.950739626397913'),
mpf('-46.906204518117636'), mpf('-46.882958270910017'),
mpf('-46.839955720658347'), mpf('-46.815121707485004'),
mpf('-46.77357601136889'), mpf('-46.747224922729004'),
mpf('-46.707068062964038'), mpf('-46.679264553080846'),
mpf('-46.640433373296687'), mpf('-46.611238416225623'),
mpf('-46.57367255467036'), mpf('-46.543145221101676'),
mpf('-46.506785519620839'), mpf('-46.474984380574834'),
mpf('-46.439771604599501'), mpf('-46.406755885040056'),
mpf('-46.372629655875102')], dtype=object)
>>> analyzed_example.crits
array([mpf('-47.028400867252276'), mpf('-46.995216177440788'),
mpf('-46.961552135996999'), mpf('-46.928318300227147'),
mpf('-46.894608617023608'), mpf('-46.861324416365338'),
mpf('-46.827569901478539'), mpf('-46.794234116960419'),
mpf('-46.760435575283916'), mpf('-46.72704699248236'),
mpf('-46.693205219083057'), mpf('-46.659762632756908'),
mpf('-46.625878408195688'), mpf('-46.592380626945829'),
mpf('-46.558454712583136'), mpf('-46.524900563516225'),
mpf('-46.490933696823733'), mpf('-46.457322030198712'),
mpf('-46.42331492009863'), mpf('-46.389644613934263'),
mpf('-46.355597936188148')], dtype=object)
>>> analyzed_example.pois
array([mpf('-47.04521505151731'), mpf('-47.011813891641338'),
mpf('-46.978389522478297'), mpf('-46.944940655832212'),
mpf('-46.911468800195282'), mpf('-46.877972023301726'),
mpf('-46.844452476333207'), mpf('-46.81090758498618'),
mpf('-46.777340139630388'), mpf('-46.743746928888186'),
mpf('-46.710131375870707'), mpf('-46.676489640045468'),
mpf('-46.64282576785548'), mpf('-46.60913530049924'),
mpf('-46.575422895374974'), mpf('-46.541683489262155'),
mpf('-46.507922335179564'), mpf('-46.474133782285819'),
mpf('-46.440323660950513'), mpf('-46.406485752427894'),
mpf('-46.372626443270374')], dtype=object)
>>> analyzed_example.increasing
[Interval(start=-47.05, stop=mpf('-47.028400867252276')),
Interval(start=mpf('-46.995216177440788'), stop=mpf('-46.961552135996999')),
Interval(start=mpf('-46.928318300227147'), stop=mpf('-46.894608617023608')),
Interval(start=mpf('-46.861324416365338'), stop=mpf('-46.827569901478539')),
Interval(start=mpf('-46.794234116960419'), stop=mpf('-46.760435575283916')),
Interval(start=mpf('-46.72704699248236'), stop=mpf('-46.693205219083057')),
Interval(start=mpf('-46.659762632756908'), stop=mpf('-46.625878408195688')),
Interval(start=mpf('-46.592380626945829'), stop=mpf('-46.558454712583136')),
Interval(start=mpf('-46.524900563516225'), stop=mpf('-46.490933696823733')),
Interval(start=mpf('-46.457322030198712'), stop=mpf('-46.42331492009863')),
Interval(start=mpf('-46.389644613934263'), stop=mpf('-46.355597936188148'))]
>>> analyzed_example.decreasing
[Interval(start=mpf('-47.028400867252276'), stop=mpf('-46.995216177440788')),
Interval(start=mpf('-46.961552135996999'), stop=mpf('-46.928318300227147')),
Interval(start=mpf('-46.894608617023608'), stop=mpf('-46.861324416365338')),
Interval(start=mpf('-46.827569901478539'), stop=mpf('-46.794234116960419')),
Interval(start=mpf('-46.760435575283916'), stop=mpf('-46.72704699248236')),
Interval(start=mpf('-46.693205219083057'), stop=mpf('-46.659762632756908')),
Interval(start=mpf('-46.625878408195688'), stop=mpf('-46.592380626945829')),
Interval(start=mpf('-46.558454712583136'), stop=mpf('-46.524900563516225')),
Interval(start=mpf('-46.490933696823733'), stop=mpf('-46.457322030198712')),
Interval(start=mpf('-46.42331492009863'), stop=mpf('-46.389644613934263')),
Interval(start=mpf('-46.355597936188148'), stop=-46.3499)]
>>> analyzed_example.concave
[Interval(start=-47.05, stop=mpf('-47.04521505151731')),
Interval(start=mpf('-47.011813891641338'), stop=mpf('-46.978389522478297')),
Interval(start=mpf('-46.944940655832212'), stop=mpf('-46.911468800195282')),
Interval(start=mpf('-46.877972023301726'), stop=mpf('-46.844452476333207')),
Interval(start=mpf('-46.81090758498618'), stop=mpf('-46.777340139630388')),
Interval(start=mpf('-46.743746928888186'), stop=mpf('-46.710131375870707')),
Interval(start=mpf('-46.676489640045468'), stop=mpf('-46.64282576785548')),
Interval(start=mpf('-46.60913530049924'), stop=mpf('-46.575422895374974')),
Interval(start=mpf('-46.541683489262155'), stop=mpf('-46.507922335179564')),
Interval(start=mpf('-46.474133782285819'), stop=mpf('-46.440323660950513')),
Interval(start=mpf('-46.406485752427894'), stop=mpf('-46.372626443270374'))]
>>> analyzed_example.convex
[Interval(start=mpf('-47.04521505151731'), stop=mpf('-47.011813891641338')),
Interval(start=mpf('-46.978389522478297'), stop=mpf('-46.944940655832212')),
Interval(start=mpf('-46.911468800195282'), stop=mpf('-46.877972023301726')),
Interval(start=mpf('-46.844452476333207'), stop=mpf('-46.81090758498618')),
Interval(start=mpf('-46.777340139630388'), stop=mpf('-46.743746928888186')),
Interval(start=mpf('-46.710131375870707'), stop=mpf('-46.676489640045468')),
Interval(start=mpf('-46.64282576785548'), stop=mpf('-46.60913530049924')),
Interval(start=mpf('-46.575422895374974'), stop=mpf('-46.541683489262155')),
Interval(start=mpf('-46.507922335179564'), stop=mpf('-46.474133782285819')),
Interval(start=mpf('-46.440323660950513'), stop=mpf('-46.406485752427894')),
Interval(start=mpf('-46.372626443270374'), stop=-46.3499)]
>>> analyzed_example.relative_maxima
array([mpf('-47.028400867252276'), mpf('-46.961552135996999'),
mpf('-46.894608617023608'), mpf('-46.827569901478539'),
mpf('-46.760435575283916'), mpf('-46.693205219083057'),
mpf('-46.625878408195688'), mpf('-46.558454712583136'),
mpf('-46.490933696823733'), mpf('-46.42331492009863'),
mpf('-46.355597936188148')], dtype=object)
>>> analyzed_example.relative_minima
array([mpf('-46.995216177440788'), mpf('-46.928318300227147'),
mpf('-46.861324416365338'), mpf('-46.794234116960419'),
mpf('-46.72704699248236'), mpf('-46.659762632756908'),
mpf('-46.592380626945829'), mpf('-46.524900563516225'),
mpf('-46.457322030198712'), mpf('-46.389644613934263')],
dtype=object)
>>> analyzed_example.absolute_maximum
Coordinate(x_val=mpf('-46.355597936188148'), y_val=mpf('1.0131766438615282'))
>>> analyzed_example.absolute_minimum
Coordinate(x_val=mpf('-46.995216177440788'), y_val=mpf('-1.5627299417380764'))
>>> analyzed_example.signed_area
mpf('-0.1835790011406907')
>>> analyzed_example.unsigned_area
mpf('0.46577475660746492')We can see that the inflection points of a function, the critical points of its first derivative, and the zeros of its second derivative are identical.
>>> np.array_equal(
... analyzed_example.pois, analyzed_example.rooted_first_derivative.crits
... )
True
>>> np.array_equal(
... analyzed_example.pois, analyzed_example.rooted_second_derivative.zeros
... )
TrueOther examples to demonstrate the relationship between derivatives:
>>> np.array_equal(analyzed_example.concave, analyzed_example.rooted_first_derivative.increasing)
True
>>> np.array_equal(analyzed_example.first_derivative.convex, analyzed_example.rooted_second_derivative.decreasing)
TrueA work-in-progress feature is listing x-values of vertical axes of symmetry. Here's an example of a function that's symmetric about the y-axis:
>>> def symmetric_func(x):
return mp.power(x, 2) - 4
>>> analyzed_symmetric_example = AnalyzedFunc(
... func=lambda x: mp.power(x, 2) - 4,
... x_range=(-8,8),
... zeros_wanted=2
... )
>>> analyzed_symmetric_example.vertical_axis_of_symmetry
[0.0]This program is licensed under the GNU Affero General Public License v3 or later.