From ae47f9f7835b5381dfa1dad7c75f6113842dcd7a Mon Sep 17 00:00:00 2001 From: Anders Markvardsen Date: Mon, 21 Jul 2014 10:56:30 +0100 Subject: [PATCH] Updated error propagation page. re #9690 --- .../source/algorithms/BinaryOperation.txt | 2 + .../source/concepts/Error_Propagation.rst | 38 +++++++++---------- 2 files changed, 20 insertions(+), 20 deletions(-) diff --git a/Code/Mantid/docs/source/algorithms/BinaryOperation.txt b/Code/Mantid/docs/source/algorithms/BinaryOperation.txt index ba9dd7a5e29f..50e6d5cc00fd 100644 --- a/Code/Mantid/docs/source/algorithms/BinaryOperation.txt +++ b/Code/Mantid/docs/source/algorithms/BinaryOperation.txt @@ -10,6 +10,8 @@ Workspaces are compatible if: * the units of the axes match * the distribution status/counts units match +For information about how errors are handled and propagated see :ref:`Error Propagation`. + Compatible Sizes ################ diff --git a/Code/Mantid/docs/source/concepts/Error_Propagation.rst b/Code/Mantid/docs/source/concepts/Error_Propagation.rst index 636e35c7212e..e1e561e94447 100644 --- a/Code/Mantid/docs/source/concepts/Error_Propagation.rst +++ b/Code/Mantid/docs/source/concepts/Error_Propagation.rst @@ -9,45 +9,43 @@ Propogation and how it is used in its algorithms. Theory ------ -In order to deal with error propagation, Mantid treats errors as a -guassian curve (also known as a bell curve or normal curve). Meaning -that if X = 100 +- 1 then it is still possible for a value of 102 to -occur, but far less likely than 101 or 99, then a value of 105 is far -less likely still than 102, and then 110 is simply unheard of. - -This allows Mantid to work with the errors quite simply. +In order to deal with error propagation, Mantid treats errors as guassian +probabilities (also known as a bell curve or normal probabilities) and each +observation as independent. Meaning that if X = 100 +- 1 then it is still +possible for a value of 102 to occur, but less likely than 101 or 99, and a +value of 105 is far less likely still than any of these values. Plus and Minus Algorithm ------------------------ -The plus algorithm adds a selection of datasets together, including -their margin of errors. Mantid has to therefore adapt the margin of -error so it continues to work with just one margin of error. The way it -does this is by simply adding together the certain values, for this -example we will use X\ :sub:`1` and X\ :sub:`2`. X\ :sub:`1` = 101 ± 2 -and X\ :sub:`2` = 99 ± 2, Just to make it easier. Mantid takes the -average of the two definite values, 101 and 99. +The plus algorithm adds a selection of datasets together, including their +margin of errors. Mantid has to therefore adapt the margin of error so it +continues to work with just one margin of error. The way it does this is by +simply adding together the certain values. Consider the example where: +X\ :sub:`1` = 101 ± 2 and X\ :sub:`2` = 99 ± 2. Then for the Plus algorithm X = 200 = (101 + 99). -The average of the error is calculated by taking the root of the sum of -the squares of the two error margins: +The propagated error is calculated by taking the root of the sum of the +squares of the two error margins: (√2:sup:`2` + 2\ :sup:`2`) = √8 +Hence the result of the Plus algorithm can be summarised as: + X = 200 ± √8 -Mantid deals with the minus algorithm similarly, doing the inverse -function of Plus. +Mantid deals with the Minus algorithm similarly. Multiply and Divide Algorithm ----------------------------- The Multiply and Divide Algorithm work slightly different from the Plus -and Minus Algorithms, in the sense that they have to be more complex. +and Minus Algorithms, in the sense that they have to be more complex, +see also `here `_. To calculate error propagation, of say X\ :sub:`1` and X\ :sub:`2`. -X\ :sub:`1` = 101 ± 2 and X\ :sub:`2` = 99 ± 2 again, Mantid would +X\ :sub:`1` = 101 ± 2 and X\ :sub:`2` = 99 ± 2 ,Mantid would undertake the following calculation for divide: Q = X\ :sub:`1`/X:sub:`2` = 101/99