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        "author": "Valentin Boettcher",
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        "description": "# Secondary Value\n[![Coverage Status](https://coveralls.io/repos/github/vale981/SecondaryValue/badge.svg)](https://coveralls.io/github/vale981/SecondaryValue)\n[![Build Status](https://travis-ci.org/vale981/SecondaryValue.svg?branch=master)](https://travis-ci.org/vale981/SecondaryValue)\n\nThis is a utility to simplify the calculation of values and their\nuncertaintues from symbolic formulas by using `sympy` and `numpy`.\n\n## Installation\nJust a quick `pip install SecondaryValue` will do.\n\n## Examples\n(A Documentation will follow soon. For now: look at the docstrings!)\n\n### Basic Usage\n```python\nfrom SecondaryValue import SecondaryValue\n\n# create a secondary value\n# the argument can be either a string or a sympy expression\nx = SecondaryValue(\"a*b/sqrt(c)\")\n\n# Calculate a result value by substi3tuting the keyword arguments\n# where a keyword agument may consist of (value, error_1, error_2, ...)\n# and (...) stands for any iterable.\nresult = x(a=(1, 20), b=(2,  30), c=2)\n\n# The calculation returns a numpy array with the length of the longest\n# keyword argument above: [value, error_1, error_2]\n# For each error_n the uncertainties error_n of the keyword args above are\n# used if present. This may be useful to calculate statistical and systemic\n# errors in one go.\nprint(result)\n# >> (1.41421356, 35.35533906)\n\n# As a goodie, you can print out the gaussian error distribution in\n# symbolic form. (Works best in Jupyter Notebooks)\nx.pretty_gauss_propagation('a', 'b', 'c')\n```\n\n### Default Values\nTo reduce boilerplate one can set default substitutions for symbols (with errors).\nThis especially useful for constants.\n\n```python\nfrom SecondaryValue import SecondaryValue\n\n# create a secondary value with default arguments\nx = SecondaryValue(\"a + b\", defaults=dict(b=1/2))\n\n# this works because `b` is substituted from the defaults\nresult = x(a=1/2)\nprint(result)\n# >> 1.0\n\n# As a goodie, you can print out the gaussian error distribution in\n# symbolic form. (Works best in Jupyter Notebooks)\nx.pretty_gauss_propagation('a', 'b', 'c')\n```\n\n### Vectorized Input\n`SecondaryValue` supports vectorized input. As a rule-of-thump: Put\nthe iterable (list, np.array) where you would put scalars.\n\nYou can mix scalars and vectors as long as all errors and values are\neither scalar or have the same length.\n\n```python\nfrom SecondaryValue import SecondaryValue\nx = SecondaryValue('a**2+b')\n\nx(a=[[1,2,3]], b=1)\n# >> array([ 2.,  5., 10.])\n\nx(a=([1,2,3], 1), b=1)\n# >> (array([ 2.,  5., 10.]), array([2., 4., 6.]))\n\nx(a=([1,2,3], [1,2,3]), b=1)\n# >> (array([ 2.,  5., 10.]), array([ 2.,  8., 18.]))\n\nx(a=([1,2,3], [1,2,3]), b=([1,2,3], 1))\n# >> (array([ 2.,  6., 12.]), array([ 2.23606798,  8.06225775, 18.02775638]))\n\n# THAT DOES NOT WORK:\nx(a=([1,2,3], [1,2,3]), b=([1,2], 1))\n```\n\nIf all the returned arrays in the tuple have the same shape, you can\neasily convert that tuple to a numpy array:\n`np.array(x(a=([1,2,3], [1,2,3]), b=([1,2,3], 1)))`\n\n### Dependencies\nTo make the calculation of complex values easier, one can define\ndependencies for a `SecondaryValue`:\n\n```python\nfrom SecondaryValue import SecondaryValue\n\ndep = SecondaryValue('u')\nx = SecondaryValue(\"a + b\", dependencies=dict(a=dep))\n\n# x will now accept u as an additional kwarg and calculate d==dep on the fly\n# and return a dictionary containing it as a second return value if you\n# specify `retdeps=True`.\nprint(x(b=1, u=(1, 2), retdeps=True))\n# >> ((2.0, 2.0), {'a': ((1.0, 2.0), {})})\n\n# To make the output predictable, the dependencies aren't returned by deafult.\nprint(x(b=1, u=(1, 2)))\n# >> (2.0, 2.0)\n\n# you can overwrite the dependency calculation\nprint(x(b=1/2, a=1/2))\n# >> 1.0\n```\n\nIf there are no dependency values, an empty dict will be returned when\n`retdeps=True` is specified.",
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