{
    "info": {
        "author": "Rohan Kumar",
        "author_email": "seirdy@pm.ch",
        "bugtrack_url": null,
        "classifiers": [
            "Development Status :: 2 - Pre-Alpha",
            "Intended Audience :: Developers",
            "Intended Audience :: Education",
            "License :: OSI Approved :: GNU Affero General Public License v3 or later (AGPLv3+)",
            "Natural Language :: English",
            "Operating System :: OS Independent",
            "Programming Language :: Python",
            "Programming Language :: Python :: 3.7",
            "Programming Language :: Python :: 3 :: Only",
            "Programming Language :: Python :: Implementation :: CPython",
            "Topic :: Scientific/Engineering :: Mathematics"
        ],
        "description": "=================\nFunction Analysis\n=================\n\n+------------------+-------------------------------------------------------+\n| CI & Test Status | |Gitlab Pipeline Status| |Coverage Report|            |\n+------------------+-------------------------------------------------------+\n| Code Quality     | |Code Climate| |Codacy| |codebeat| |CodeFactor|       |\n|                  | |LGTM|                                                |\n+------------------+-------------------------------------------------------+\n| Code Style       | |code style: black|                                   |\n+------------------+-------------------------------------------------------+\n| Dependencies     | |Requirements Status|                                 |\n+------------------+-------------------------------------------------------+\n| Usage            | |license|                                             |\n+------------------+-------------------------------------------------------+\n| PyPI             | |python version| |latest release|                     |\n+------------------+-------------------------------------------------------+\n\nThis library uses concepts typically taught in an introductory Calculus class\nto describe properties of continuous, differentiable, single-variable\nfunctions.\n\nUsing this library\n==================\n\nThe ``func_analysis`` module defines the class ``AnalyzedFunc``. An instance of\nthis class has several attributes describing the behavior of this function.\n\nRequired data include:\n\n-  A range\n-  The function to be analyzed\n\nSpecial points include zeros, critical numbers, extrema, and points of\ninflection. It\u2019s possible to calculate these when given the number of points\nwanted.\n\nOptional data can be provided to improve precision and performance. Such data\ninclude:\n\n-  Any derivatives of the function\n-  Any known zeros, critical numbers, extrema, points of inflection\n-  Intervals of concavity, convexity, increase, decrease\n-  Any vertical axis of symmetry\n\nAny of the above data can be calculated by an instance of ``AnalyzedFunc``.\n\nExample Usage\n-------------\n\nThis paste from an interactive Python session showcases all the functionality\nof ``AnalyzedFunc``:\n\n.. code:: python\n\n   >>> from func_analysis import AnalyzedFunc\n\n   >>> import mpmath as mp; import numpy as np\n\n   >>> mp.pretty = True\n\n   >>> def example_func(x):\n   ...     return mp.cos(x ** 2) - mp.sin(x) + (x / 68)\n   ...\n\n   >>> analyzed_example = AnalyzedFunc(\n   ...     func=example_func,\n   ...     x_range=(-47.05, -46.3499),\n   ...     zeros_wanted=21,\n   ...     crits_wanted=21,\n   ...     pois_wanted=21,\n   ...     zeros=[-47.038289673236127, -46.406755885040056],\n   ... )\n\n   >>> analyzed_example.zeros\n   array([mpf('-47.038289673236127'), mpf('-47.018473233395284'),\n          mpf('-46.972318087653945'), mpf('-46.950739626397913'),\n          mpf('-46.906204518117636'), mpf('-46.882958270910017'),\n          mpf('-46.839955720658347'), mpf('-46.815121707485004'),\n          mpf('-46.77357601136889'), mpf('-46.747224922729004'),\n          mpf('-46.707068062964038'), mpf('-46.679264553080846'),\n          mpf('-46.640433373296687'), mpf('-46.611238416225623'),\n          mpf('-46.57367255467036'), mpf('-46.543145221101676'),\n          mpf('-46.506785519620839'), mpf('-46.474984380574834'),\n          mpf('-46.439771604599501'), mpf('-46.406755885040056'),\n          mpf('-46.372629655875102')], dtype=object)\n\n   >>> analyzed_example.crits\n   array([mpf('-47.028400867252276'), mpf('-46.995216177440788'),\n          mpf('-46.961552135996999'), mpf('-46.928318300227147'),\n          mpf('-46.894608617023608'), mpf('-46.861324416365338'),\n          mpf('-46.827569901478539'), mpf('-46.794234116960419'),\n          mpf('-46.760435575283916'), mpf('-46.72704699248236'),\n          mpf('-46.693205219083057'), mpf('-46.659762632756908'),\n          mpf('-46.625878408195688'), mpf('-46.592380626945829'),\n          mpf('-46.558454712583136'), mpf('-46.524900563516225'),\n          mpf('-46.490933696823733'), mpf('-46.457322030198712'),\n          mpf('-46.42331492009863'), mpf('-46.389644613934263'),\n          mpf('-46.355597936188148')], dtype=object)\n\n   >>> analyzed_example.pois\n   array([mpf('-47.04521505151731'), mpf('-47.011813891641338'),\n          mpf('-46.978389522478297'), mpf('-46.944940655832212'),\n          mpf('-46.911468800195282'), mpf('-46.877972023301726'),\n          mpf('-46.844452476333207'), mpf('-46.81090758498618'),\n          mpf('-46.777340139630388'), mpf('-46.743746928888186'),\n          mpf('-46.710131375870707'), mpf('-46.676489640045468'),\n          mpf('-46.64282576785548'), mpf('-46.60913530049924'),\n          mpf('-46.575422895374974'), mpf('-46.541683489262155'),\n          mpf('-46.507922335179564'), mpf('-46.474133782285819'),\n          mpf('-46.440323660950513'), mpf('-46.406485752427894'),\n          mpf('-46.372626443270374')], dtype=object)\n\n   >>> analyzed_example.increasing\n   [Interval(start=-47.05, stop=mpf('-47.028400867252276')),\n    Interval(start=mpf('-46.995216177440788'), stop=mpf('-46.961552135996999')),\n    Interval(start=mpf('-46.928318300227147'), stop=mpf('-46.894608617023608')),\n    Interval(start=mpf('-46.861324416365338'), stop=mpf('-46.827569901478539')),\n    Interval(start=mpf('-46.794234116960419'), stop=mpf('-46.760435575283916')),\n    Interval(start=mpf('-46.72704699248236'), stop=mpf('-46.693205219083057')),\n    Interval(start=mpf('-46.659762632756908'), stop=mpf('-46.625878408195688')),\n    Interval(start=mpf('-46.592380626945829'), stop=mpf('-46.558454712583136')),\n    Interval(start=mpf('-46.524900563516225'), stop=mpf('-46.490933696823733')),\n    Interval(start=mpf('-46.457322030198712'), stop=mpf('-46.42331492009863')),\n    Interval(start=mpf('-46.389644613934263'), stop=mpf('-46.355597936188148'))]\n\n   >>> analyzed_example.decreasing\n   [Interval(start=mpf('-47.028400867252276'), stop=mpf('-46.995216177440788')),\n    Interval(start=mpf('-46.961552135996999'), stop=mpf('-46.928318300227147')),\n    Interval(start=mpf('-46.894608617023608'), stop=mpf('-46.861324416365338')),\n    Interval(start=mpf('-46.827569901478539'), stop=mpf('-46.794234116960419')),\n    Interval(start=mpf('-46.760435575283916'), stop=mpf('-46.72704699248236')),\n    Interval(start=mpf('-46.693205219083057'), stop=mpf('-46.659762632756908')),\n    Interval(start=mpf('-46.625878408195688'), stop=mpf('-46.592380626945829')),\n    Interval(start=mpf('-46.558454712583136'), stop=mpf('-46.524900563516225')),\n    Interval(start=mpf('-46.490933696823733'), stop=mpf('-46.457322030198712')),\n    Interval(start=mpf('-46.42331492009863'), stop=mpf('-46.389644613934263')),\n    Interval(start=mpf('-46.355597936188148'), stop=-46.3499)]\n\n   >>> analyzed_example.concave\n   [Interval(start=-47.05, stop=mpf('-47.04521505151731')),\n    Interval(start=mpf('-47.011813891641338'), stop=mpf('-46.978389522478297')),\n    Interval(start=mpf('-46.944940655832212'), stop=mpf('-46.911468800195282')),\n    Interval(start=mpf('-46.877972023301726'), stop=mpf('-46.844452476333207')),\n    Interval(start=mpf('-46.81090758498618'), stop=mpf('-46.777340139630388')),\n    Interval(start=mpf('-46.743746928888186'), stop=mpf('-46.710131375870707')),\n    Interval(start=mpf('-46.676489640045468'), stop=mpf('-46.64282576785548')),\n    Interval(start=mpf('-46.60913530049924'), stop=mpf('-46.575422895374974')),\n    Interval(start=mpf('-46.541683489262155'), stop=mpf('-46.507922335179564')),\n    Interval(start=mpf('-46.474133782285819'), stop=mpf('-46.440323660950513')),\n    Interval(start=mpf('-46.406485752427894'), stop=mpf('-46.372626443270374'))]\n\n   >>> analyzed_example.convex\n   [Interval(start=mpf('-47.04521505151731'), stop=mpf('-47.011813891641338')),\n    Interval(start=mpf('-46.978389522478297'), stop=mpf('-46.944940655832212')),\n    Interval(start=mpf('-46.911468800195282'), stop=mpf('-46.877972023301726')),\n    Interval(start=mpf('-46.844452476333207'), stop=mpf('-46.81090758498618')),\n    Interval(start=mpf('-46.777340139630388'), stop=mpf('-46.743746928888186')),\n    Interval(start=mpf('-46.710131375870707'), stop=mpf('-46.676489640045468')),\n    Interval(start=mpf('-46.64282576785548'), stop=mpf('-46.60913530049924')),\n    Interval(start=mpf('-46.575422895374974'), stop=mpf('-46.541683489262155')),\n    Interval(start=mpf('-46.507922335179564'), stop=mpf('-46.474133782285819')),\n    Interval(start=mpf('-46.440323660950513'), stop=mpf('-46.406485752427894')),\n    Interval(start=mpf('-46.372626443270374'), stop=-46.3499)]\n\n   >>> analyzed_example.relative_maxima\n   array([mpf('-47.028400867252276'), mpf('-46.961552135996999'),\n          mpf('-46.894608617023608'), mpf('-46.827569901478539'),\n          mpf('-46.760435575283916'), mpf('-46.693205219083057'),\n          mpf('-46.625878408195688'), mpf('-46.558454712583136'),\n          mpf('-46.490933696823733'), mpf('-46.42331492009863'),\n          mpf('-46.355597936188148')], dtype=object)\n\n   >>> analyzed_example.relative_minima\n   array([mpf('-46.995216177440788'), mpf('-46.928318300227147'),\n          mpf('-46.861324416365338'), mpf('-46.794234116960419'),\n          mpf('-46.72704699248236'), mpf('-46.659762632756908'),\n          mpf('-46.592380626945829'), mpf('-46.524900563516225'),\n          mpf('-46.457322030198712'), mpf('-46.389644613934263')],\n         dtype=object)\n\n   >>> analyzed_example.absolute_maximum\n   Coordinate(x_val=mpf('-46.355597936188148'), y_val=mpf('1.0131766438615282'))\n\n   >>> analyzed_example.absolute_minimum\n   Coordinate(x_val=mpf('-46.995216177440788'), y_val=mpf('-1.5627299417380764'))\n\n   >>> analyzed_example.signed_area\n   mpf('-0.1835790011406907')\n\n   >>> analyzed_example.unsigned_area\n   mpf('0.46577475660746492')\n\nWe can see that the inflection points of a function, the critical points of its\nfirst derivative, and the zeros of its second derivative are identical.\n\n.. code:: python\n\n   >>> np.array_equal(\n   ...     analyzed_example.pois, analyzed_example.rooted_first_derivative.crits\n   ... )\n   True\n\n   >>> np.array_equal(\n   ...     analyzed_example.pois, analyzed_example.rooted_second_derivative.zeros\n   ... )\n   True\n\nOther examples to demonstrate the relationship between derivatives:\n\n.. code:: python\n\n   >>> np.array_equal(analyzed_example.concave, analyzed_example.rooted_first_derivative.increasing)\n   True\n\n   >>> np.array_equal(analyzed_example.first_derivative.convex, analyzed_example.rooted_second_derivative.decreasing)\n   True\n\nA 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