=========================================================================
numericalunits: Units and dimensional analysis compatible with everything
=========================================================================

`Package homepage at PyPI <http://pypi.python.org/pypi/numericalunits>`_ -- 
`Source code at github <http://github.com/sbyrnes321/numericalunits>`_ -- 
`Package author information <http://sjbyrnes.com>`_

This package implements units and dimensional analysis in an unconventional 
way that has the following unique advantages:

* **Compatible with everything:** Compatible with virtually any numerical 
  calculation routine, including numpy and scipy, and even including routines 
  not written in Python! That means, for example, if you have a decades-old 
  closed-source C routine for numerical integration, you can pass it a 
  quantity with units of velocity and an integration range with units of 
  time, and the final answer will magically have units of distance. This 
  extreme compatibility is possible because if the variable ``x`` represents 
  a quantity with dimensions (like "3.3 kg"), ``x`` is actually stored 
  internally as an ordinary floating-point number. The dimension is 
  encoded in the value as a multiplicative factor. When two numbers are 
  multiplied, their dimensions are automatically multiplied, and so on. 


* **Modular and non-intrusive:** When you input data, you say what units 
  they are in. When you display results, you say what units you want to 
  display them in. These steps are very little trouble, and in fact help you 
  create nice, self-documenting code. Other than that, you have to do nothing 
  at all to pass dimensionful quantities into and out of any already-written 
  programs or routines.

* **Powerful tool for debugging:** Not *all* calculation mistakes cause 
  violations of dimensional analysis, but *most* do--for example, if you 
  accidentally multiply two lengths instead of adding them, the result will 
  have the wrong dimension. If you use this package, it will alert you to 
  these sorts of mistakes.

* **Zero storage overhead**

* **Zero calculation overhead**

These great features come with the disadvantage that the interface is less  
*slick* than other unit packages. If you have a quantity with units, you 
cannot directly see what the units are. You are supposed to already know 
what the units are, and then the package will tell you whether you made a 
mistake. Even worse, you only get alerted to the mistake after running a 
calculation all the way through twice.

Therefore the package is *not* suggested for students who are just learning 
how units work and want spoon-fed answers. It *is* suggested for engineering 
and science professionals who want to their code to be more self-documenting 
and self-debugging.

Installation
============

You can install from PyPI: ::

    pip install numericalunits

Alternatively---since it's a single module that requires no setup or 
compilation---you can download ``numericalunits.py`` from `PyPI 
<http://pypi.python.org/pypi/numericalunits>`_ or `github 
<http://github.com/sbyrnes321/numericalunits>`_ and use it directly.

Usage and examples
==================

At the top of the code you're working on, write::

    import numericalunits as nu
    nu.reset_units()

Unit errors, like trying to add a length to a mass, will not *immediately*
announce themselves as unit errors. Instead, you need to run the whole
calculation (including the ``reset_units()`` part) twice. If you get the
same final answers both times, then congratulations, all your calculations
are almost guaranteed to pass dimensional analysis! If you get different
answers every time you run, then you made a unit error! It is up to you to
figure out where and what the error is.

To assign a unit to a quantity, **multiply** by the unit, e.g.
``my_length = 100 * mm``. (In normal text you would write "100 mm", but
unfortunately Python does not have "implied multiplication".)

To express a dimensionful quantity in a certain unit, **divide** by that unit,
e.g. when you see ``my_length / cm``, you pronounce it "my_length expressed
in cm".

**Example 1:** What is 5 mL expressed in cubic nanometers?::

    import numericalunits as nu
    nu.reset_units()
    x = 5 * nu.mL  # "Read: x is equal to 5 milliliters"
    x / nu.nm**3   # "Read: x expressed in cubic nanometers is..." --> 5e21

**Example 2:** An electron is in a 1e5 V/cm electric field. What is its
acceleration? (Express the answer in m/s^2.) ::

    import numericalunits as nu
    nu.reset_units()
    efield = 1e5 * (nu.V / nu.cm)
    force = nu.e * efield # (nu.e is the elementary charge)
    accel = force / nu.me # (nu.me is the electron mass)
    accel / (nu.m / nu.s**2) # Answer --> 1.7588e18

**Example 3:** You measured a voltage as a function of the position of dial: 
10 volts when the dial is at 1cm, 11 volts when the dial is at 2cm, etc. 
etc. Interpolate from this data to get the expected voltage when the dial is 
at 41mm, and express the answer in mV. ::

    import numericalunits as nu
    nu.reset_units()
    from numpy import array
    from scipy.interpolate import interp1d
    voltage_data = array([[1 * nu.cm, 10 * nu.V],
                          [2 * nu.cm, 11 * nu.V],
                          [3 * nu.cm, 13 * nu.V],
                          [4 * nu.cm, 16 * nu.V],
                          [5 * nu.cm, 18 * nu.V]])
    f = interp1d(voltage_data[:,0], voltage_data[:,1])
    f(41 * nu.mm) / nu.mV # Answer --> 16200
	

**Example 4:** A unit mistake ... what is 1 cm expressed in atmospheres? ::

    import numericalunits as nu
    nu.reset_units()
    (1 * nu.cm) / nu.atm # --> a randomly-varying number
    # The answer randomly varies every time you run this, indicating that you
    # are violating dimensional analysis.

How it works
============

A complete set of independent base units (meters, kilograms, seconds, 
coulombs, kelvins) are defined as randomly-chosen positive floating-point 
numbers. All other units and constants are defined in terms of those. In a 
dimensionally-correct calculation, the units all cancel out, so the final 
answer is deterministic, not random. In a dimensionally-incorrect 
calculations, there will be random factors causing a randomly-varying final 
answer.

Included units and constants
============================

Includes a variety of common units, both SI and non-SI, everything from 
frequency to magnetic flux. Also includes common physical constants like 
Planck's constant and the speed of light. Browse the source code to see a 
complete list. It is very easy to add in any extra units and constants that
were left out.

Notes
=====

Notes on implementation and use
-------------------------------

* The units should not be reset in the *middle* of a calculation. They 
  should be randomly chosen *once* at the beginning, then carried through 
  consistently. For example, if multiple python modules need access to the 
  unit definitions, use ``import numericalunits as nu`` in all of them, but 
  make sure that ``nu.reset_units()`` is run only once at the very beginning 
  of execution.

* While debugging a program, it may be annoying to have intermediate values 
  in the calculation that randomly vary every time you run the program. In 
  this case, you can use ``reset_units('SI')`` instead of the normal 
  ``reset_units()``. This puts all dimensionful variables in standard (MKS)
  SI units: All times are in seconds, all lengths are in meters, all forces
  are in newtons, etc. Alternatively, ``reset_units(123)`` uses ``123`` as
  the seed for the random-number generator. Obviously, in these modes, you
  will *not* get any indication of dimensional-analysis errors.

* ``from``-style imports are not supported!! (The fundamental problem is 
  that ``float``'s are immutable...so ``reset_units()`` will not work as 
  expected.) In other words,

  - **Do not use** ``from numericalunits import *``
  - **Do not use** ``from numericalunits import cm``
  - etc.

* There are very rare, strange cases where the final answer does not seem to 
  randomly vary even though there was a dimensional-analysis violation: For 
  example, the expression ``(1 + 1e-50 * cm / atm)`` fails dimensional 
  analysis, so if you calculate it the answer is randomly-varying. But, it is 
  only randomly varying around the 50th decimal point, so the variation is
  hidden from view. You would not notice it as an error.

* Since units are normal Python floating-point numbers, they follow the 
  normal casting rules. For example, ``2 * cm`` is a python ``float``, not an 
  ``int``. This is usually the sensible and desired behavior.

* You can give a dimension to complex numbers in the same way as real 
  numbers--for example ``(2.1e3 + 3.9e4j) * ohm``.

* I tested only in Python 2.7, but as far as I can tell it should be compatible with any Python version 2.x or 3.x. Please email me if you have checked.

Notes on unit definitions
-------------------------

* For electromagnetism, all units are intended for use in SI formulas. If 
  you plug them into cgs-gaussian electromagnetism formulas, or cgs-esu 
  electromagnetism formulas, etc., you will get nonsense results.

* The package does not keep track of "radians" as an independent unit 
  assigned a random number. The reason is that the "radians" factor does not 
  always neatly cancel out of formulas.

* The package does not keep track of "moles" as an independent unit assigned 
  a random number; instead "mol" is just a pure number (~6e23), like you
  would say "dozen"=12. One consequence, for example, is that the ideal gas
  constant is exactly the same as the Boltzmann constant. There are two
  reasons for this behavior: (1) If you mistakenly miss a factor of
  Avogadro's number in a calculation, you will not need any help to see that
  something is wrong, since the answer will be wrong by 24 orders of 
  magnitude! (2) It is nice to be able to convert between (for example) 
  kcal/mol and eV, without having to explicitly multiply or divide by
  Avogadro's number.

* The package cannot convert temperatures between Fahrenheit, Celsius, and 
  kelvin. The reason is that these scales have different zeros, so the units 
  cannot be treated as multiplicative factors. It is, however, possible to 
  convert temperature *intervals*, via the units ``degCinterval`` (which is a 
  synonym of kelvin, ``K``) and ``degFinterval``.