|
6 | 6 |
|
7 | 7 | Small library for uncertainty calculations and error propagation. |
8 | 8 |
|
9 | | -The uncertainty calculations are in accordance with gaussian’s propagation, as calculated by an analytical method: |
| 9 | +### Error propagation: |
| 10 | + |
| 11 | +The uncertainty is calculated analytically in accordance with the gaussian propagation: |
10 | 12 |
|
11 | 13 | <p align="center"> |
12 | 14 | <img src="https://latex.codecogs.com/svg.latex?%5Cdpi%7B120%7D%20%5CDelta_f%20%3D%20%5Csqrt%7B%5Cleft%28%5Cfrac%7B%5Cpartial%20f%7D%7B%5Cpartial%20x%7D%5Cright%29%5E2%7B%5CDelta_x%7D%5E2%20+%20%5Cleft%28%5Cfrac%7B%5Cpartial%20f%7D%7B%5Cpartial%20y%7D%5Cright%29%5E2%7B%5CDelta_y%7D%5E2%20+%20%5Cleft%28%5Cfrac%7B%5Cpartial%20f%7D%7B%5Cpartial%20z%7D%5Cright%29%5E2%7B%5CDelta_z%7D%5E2%20+%20...%7D"> |
13 | 15 | </p> |
14 | 16 |
|
| 17 | + |
| 18 | +### To compare two labfloats it is used the following methods: |
| 19 | + |
| 20 | +Assuming: |
| 21 | +<img src="https://latex.codecogs.com/svg.image?%5Cbg_white%20%5Cinline%20labfloat(x_i,%5Csigma_i)%5Cequiv%20x_i%20%5Cpm%20%5Csigma_i"> |
| 22 | + |
| 23 | +- If they are equal they must satisfy: |
| 24 | +<img src="https://latex.codecogs.com/svg.image?%5Cbg_white%20%5Cinline%20%5Cleft%7Cx_1%20-%20x_2%5Cright%7C%20%3C%202(%5Csigma_1%20+%20%5Csigma_2)"> |
| 25 | + |
| 26 | +- If they are different they must satisfy: |
| 27 | +<img src="https://latex.codecogs.com/svg.image?%5Cbg_white%20%5Cinline%20%5Cleft%7Cx_1%20-%20x_2%5Cright%7C%20%3E%203(%5Csigma_1%20+%20%5Csigma_2)"> |
| 28 | + |
| 29 | +> **_NOTE:_** Two labfloats can be not different and not equal at the same time by these methods. |
| 30 | +
|
15 | 31 | 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. |
16 | 32 |
|
17 | 33 | ## Usage |
@@ -57,3 +73,5 @@ pip install git+https://github.com/phisgroup/labfis.py@development |
57 | 73 | 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. |
58 | 74 | 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") |
59 | 75 | 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. |
| 76 | + 14. Helene, O.; Vanin, V.. Tratamento estatístico de dados em física experimental. São Paulo: Editora Edgard Blücher, 1981. |
| 77 | + 15. Vuolo, J. E.. Fundamentos da teoria de erros. 2. ed. São Paulo: Editora Edgard Blücher, 1993. |
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