improved precision and calculation methods, and modified readme

Author: hlouzada

README.md

@@ -1,10 +1,63 @@
 # labfis.py
-Small library (currently only one class) for uncertainty calculations. Made by and for Physics Laboratory students in IFSC, who can't use uncertainties.py because mean absolute deviation.
+
+## Description
+
+Small library (currently only one class) for uncertainty calculations and error propagation.
+
+The uncertainty calculations are in accordance with gaussian’s propagation, as calculated by an analytical method:
+
+$$\Delta_f = \sqrt{\left(\frac{\partial f}{\partial x}\right)^2{\Delta_x}^2 + \left(\frac{\partial f}{\partial y}\right)^2{\Delta_y}^2 + \left(\frac{\partial f}{\partial z}\right)^2{\Delta_z}^2 + ...}$$
+
+Made by and for Physics Laboratory students in IFSC, who can't use uncertainties.py because of mean’s absolute deviation used in its calculation.
 
 To get this library on google colaboratory:
-    
+
 ```
 !curl --remote-name \
-     -H 'Accept: application/vnd.github.v3.raw' \
-     --location https://raw.githubusercontent.com/phisgroup/labfis.py/development/labfis/main.py
+
+-H 'Accept: application/vnd.github.v3.raw' \
+
+--location https://raw.githubusercontent.com/phisgroup/labfis.py/development/labfis/main.py
+```
+
+## Usage
+
+Just import with `from labfis import labfloat` and create an *labfloat* object as:
+
 ```
+>>> from labfis import labfloat
+>>> a = labfloat(1,3)
+>>> b = labfloat(2,4)
+>>> a*b
+(2 ± 7)
+```
+
+## Instalation
+
+Intstall master releases with:
+
+```
+pip install labfis
+```
+
+Install development releases with:
+
+```
+pip install git+https://github.com/phisgroup/labfis.py/tree/development
+```
+
+## References
+
+ 1. Kirchner, James. ["Data Analysis Toolkit #5: Uncertainty Analysis and Error Propagation"](http://seismo.berkeley.edu/~kirchner/eps_120/Toolkits/Toolkit_05.pdf)  (PDF). _Berkeley Seismology Laboratory_. University of California. Retrieved  22 April  2016.
+ 2. [Goodman, Leo](https://en.wikipedia.org/wiki/Leo_Goodman "Leo Goodman") (1960). "On the Exact Variance of Products". _Journal of the American Statistical Association_. **55** (292): 708–713. [doi](https://en.wikipedia.org/wiki/Doi_(identifier) "Doi (identifier)"):[10.2307/2281592](https://doi.org/10.2307%2F2281592). [JSTOR](https://en.wikipedia.org/wiki/JSTOR_(identifier) "JSTOR (identifier)")  [2281592](https://www.jstor.org/stable/2281592).
+ 3. Ochoa1,Benjamin; Belongie, Serge ["Covariance Propagation for Guided Matching"](http://vision.ucsd.edu/sites/default/files/ochoa06.pdf)
+ 4. Ku, H. H. (October 1966). ["Notes on the use of propagation of error formulas"](http://nistdigitalarchives.contentdm.oclc.org/cdm/compoundobject/collection/p16009coll6/id/99848/rec/1). _Journal of Research of the National Bureau of Standards_. **70C** (4): 262. [doi](https://en.wikipedia.org/wiki/Doi_(identifier) "Doi (identifier)"):[10.6028/jres.070c.025](https://doi.org/10.6028%2Fjres.070c.025). [ISSN](https://en.wikipedia.org/wiki/ISSN_(identifier) "ISSN (identifier)")  [0022-4316](https://www.worldcat.org/issn/0022-4316). Retrieved  3 October  2012.
+ 5. Clifford, A. A. (1973). _Multivariate error analysis: a handbook of error propagation and calculation in many-parameter systems_. John Wiley & Sons. [ISBN](https://en.wikipedia.org/wiki/ISBN_(identifier) "ISBN (identifier)")  [978-0470160558](https://en.wikipedia.org/wiki/Special:BookSources/978-0470160558 "Special:BookSources/978-0470160558").
+ 6. Lee, S. H.; Chen, W. (2009). "A comparative study of uncertainty propagation methods for black-box-type problems". _Structural and Multidisciplinary Optimization_. **37** (3): 239–253. [doi](https://en.wikipedia.org/wiki/Doi_(identifier) "Doi (identifier)"):[10.1007/s00158-008-0234-7](https://doi.org/10.1007%2Fs00158-008-0234-7).
+ 7. Johnson, Norman L.; Kotz, Samuel; Balakrishnan, Narayanaswamy (1994). _Continuous Univariate Distributions, Volume 1_. Wiley. p. 171. [ISBN](https://en.wikipedia.org/wiki/ISBN_(identifier) "ISBN (identifier)")  [0-471-58495-9](https://en.wikipedia.org/wiki/Special:BookSources/0-471-58495-9 "Special:BookSources/0-471-58495-9").
+ 8. Lecomte, Christophe (May 2013). "Exact statistics of systems with uncertainties: an analytical theory of rank-one stochastic dynamic systems". _Journal of Sound and Vibrations_. **332** (11): 2750–2776. [doi](https://en.wikipedia.org/wiki/Doi_(identifier) "Doi (identifier)"):[10.1016/j.jsv.2012.12.009](https://doi.org/10.1016%2Fj.jsv.2012.12.009).
+ 9. ["A Summary of Error Propagation"](http://ipl.physics.harvard.edu/wp-uploads/2013/03/PS3_Error_Propagation_sp13.pdf)  (PDF). p. 2. Retrieved  2016-04-04.
+ 10. ["Propagation of Uncertainty through Mathematical Operations"](http://web.mit.edu/fluids-modules/www/exper_techniques/2.Propagation_of_Uncertaint.pdf)  (PDF). p. 5. Retrieved  2016-04-04. 
+ 11. ["Strategies for Variance Estimation"](http://www.sagepub.com/upm-data/6427_Chapter_4__Lee_%28Analyzing%29_I_PDF_6.pdf)  (PDF). p. 37. Retrieved  2013-01-18.
+ 12. Harris, Daniel C. (2003), [_Quantitative chemical analysis_](https://books.google.com/books?id=csTsQr-v0d0C&pg=PA56)(6th ed.), Macmillan, p. 56, [ISBN](https://en.wikipedia.org/wiki/ISBN_(identifier) "ISBN (identifier)")  [978-0-7167-4464-1](https://en.wikipedia.org/wiki/Special:BookSources/978-0-7167-4464-1 "Special:BookSources/978-0-7167-4464-1")
+ 13. ["Error Propagation tutorial"](http://www.foothill.edu/psme/daley/tutorials_files/10.%20Error%20Propagation.pdf)  (PDF).  _Foothill College_. October 9, 2009. Retrieved  2012-03-01.

labfis/main.py

@@ -1,4 +1,4 @@
-from math import floor, ceil, trunc, log, log10
+from math import floor, ceil, trunc, log, log10, sqrt
 from numbers import Number
 
 class LabFloatError(Exception):
@@ -193,7 +193,7 @@ def __ge__(self,other):
 
     def __add__(self, other):
         if isinstance(other, labfloat):
-            return labfloat(self.mean + other.mean, self.uncertainty + other.uncertainty)
+            return labfloat(self.mean + other.mean, sqrt(self.uncertainty ** 2 + other.uncertainty ** 2))
         if isinstance(other, Number):
             return labfloat(self.mean + other, self.uncertainty)
 
@@ -205,13 +205,13 @@ def __iadd__(self, other):
 
     def __sub__(self, other):
         if isinstance(other, labfloat):
-            return labfloat(self.mean - other.mean, self.uncertainty + other.uncertainty)
+            return labfloat(self.mean - other.mean, sqrt(self.uncertainty ** 2 + other.uncertainty ** 2))
         if isinstance(other, Number):
             return labfloat(self.mean - other, self.uncertainty)
 
     def __rsub__(self, other):
         if isinstance(other, labfloat):
-            pass
+            return labfloat(other.mean - self.mean, sqrt(other.uncertainty ** 2 + self.uncertainty ** 2))
         if isinstance(other, Number):
             return labfloat(other - self.mean, self.uncertainty)
 
@@ -220,9 +220,9 @@ def __isub__(self, other):
 
     def __mul__(self, other):
         if isinstance(other, labfloat):
-            return labfloat(self.mean * other.mean, self.mean * other.uncertainty + other.mean * self.uncertainty)
+            return labfloat(self.mean * other.mean, sqrt((other.mean * self.uncertainty) ** 2 + (self.mean * other.uncertainty) ** 2))
         if isinstance(other, Number):
-            return labfloat(self.mean * other, other * self.uncertainty)
+            return labfloat(self.mean * other, abs(other * self.uncertainty))
 
     def __rmul__(self, other):
         return self.__mul__(other)
@@ -232,9 +232,9 @@ def __imul__(self, other):
 
     def __div__(self, other):
         if isinstance(other, labfloat):
-            return labfloat(self.mean / other.mean, (self.mean * other.uncertainty + other.mean * self.uncertainty)/other.mean**2)
+            return labfloat(self.mean / other.mean, sqrt((self.uncertainty / other.mean) ** 2 + (self.mean * other.uncertainty / (other.mean ** 2)) ** 2 ))
         if isinstance(other, Number):
-            return labfloat(self.mean / other, self.uncertainty / other)
+            return labfloat(self.mean / other, abs(self.uncertainty / other))
 
     def __truediv__(self, other):
         return self.__div__(other)
@@ -247,24 +247,24 @@ def __itruediv__(self, other):
 
     def __rdiv__(self, other):
         if isinstance(other, labfloat):
-            return labfloat(other.mean / self.mean, (other.mean * self.uncertainty + self.mean * other.uncertainty)/self.mean**2)
+            return labfloat(other.mean / self.mean, sqrt((other.uncertainty / self.mean) ** 2 + (other.mean * self.uncertainty / (self.mean ** 2)) ** 2 ))
         if isinstance(other, Number):
-            return labfloat(other / self.mean, other * self.uncertainty / self.mean ** 2)
+            return labfloat(other / self.mean, abs(other * self.uncertainty / self.mean ** 2))
 
     def __rtruediv__(self, other):
         return self.__rdiv__(other)
 
     def __pow__(self, other):
         if isinstance(other, labfloat):
-            raise LabFloatError(0)
+            return labfloat(self.mean ** other.mean, sqrt((other.mean * self.mean ** (other.mean - 1) * self.uncertainty) ** 2 + (self.mean ** other.mean * log(abs(self.mean)) * other.uncertainty) ** 2))
         if isinstance(other, Number):
-            return labfloat(self.mean ** other, other * self.mean ** (other-1) * self.uncertainty)
+            return labfloat(self.mean ** other, abs(other * self.mean ** (other - 1) * self.uncertainty))
 
     def __rpow__(self, other):
         if isinstance(other, labfloat):
-            raise LabFloatError(0)
-        if isinstance(other, (float, int, hex, oct, complex)):
-            return labfloat(other ** self.mean, other ** self.mean * log(other) * self.uncertainty)
+            raise labfloat(other.mean ** self.mean, sqrt((self.mean * other.mean ** (self.mean - 1) * other.uncertainty) ** 2 + (other.mean ** self.mean * log(abs(other.mean)) * self.uncertainty) ** 2))
+        if isinstance(other, Number):
+            return labfloat(other ** self.mean, abs(other ** self.mean * log(abs(other)) * self.uncertainty))
 
     def __ipow__(self, other):
         return self.__pow__(other)