Polytransform and Peaksigmoid: Difference between pages

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===Purpose===
===Purpose===
Outputs a sigmoid function.


Add new variables to a dataset object or matrix formed as power transforms and cross terms of the original variables.


===Synopsis===
===Synopsis===


:[xout, model] = polytransform(x, options);
:[i0,iw] = peakfind(x,width,tolfac,w,options)
:[xout] = polytransform(x, model);
:[i0,iw] = peakfind(x,width,options)


===Description===


Add polynomial and cross terms to data matrix or dataset. Input dataset x has new transformed variables added. These can include existing variables raised to second, third, fourth power, or second order product of variables.
====Inputs====
The data can be preprocessed before transformed variables are calculated.
preprocessingtype option specifies the type of preprocessing to apply,  'none', 'mncn', 'auto', or 'custom'. If 'custom' is specified then the  'preprocessing' option must be a valid preprocessing structure.  If pca = 'on' the data are converted to PCA scores after preprocessing,  but before the transformed variables are calculated.


===Inputs===
* '''x''' =   3 element vector where x(1) = coefficient, x(2) = offset and x(3) is equal to the decay constant


* '''x''' =  Dataset or matrix to be augmented by the addition of transformed variables.


===Outputs===
====Outputs====


* '''xout''' =  The augmented dataset or matrix.
* '''model''' =  A standard model structure with ''modeltype = polytransform''. This model can be used to augment new data in the same way as the original data was augmented, using the same options, including preprocessing.


===Options===


'''''options''''' is a structure array with the following fields:
* '''squares''': [ 'on' | {'off'} ], governs level of display,
* '''cubes''': [ 'on' | {'off'} ], governs level of display,
* '''quadratics''': [ 'on' | {'off'} ], governs level of display,
* '''crossterms''': [ 'on' | {'off'} ], governs level of display,
* '''preprocessingtype''': ['none' | 'mncn' | {'auto'} | 'pcrtile' | 'custom'], governs data preprocessing behavior,
* '''preprocessing''': A preprocessing structure which is used if ''preprocessingtype = custom'',
* '''pca''': [ 'on' | {'off'} ], governs whether PCA is applied to the preprocessed data before transformed terms are calculated,
* '''maxpcs''': Integer indicating how many PCs to use if ''pca = on'',
* '''preprocessoriginalvars''': [ 0| {1} ], governs whether the original variables are returned preprocessed or raw.


===Examples===
<math>\sqrt{1-e^2}</math>


If x is a 100 by 5 matrix, options are default, except for the squares option:
<math>f\left( {{a}_{i}},\mathbf{x} \right)={{x}_{1}}\left[ {{x}_{4}}{{\operatorname{e}}^{\frac{-4\ln \left( 2 \right){{\left( {{a}_{i}}-{{x}_{2}} \right)}^{2}}}{x_{3}^{2}}}}+\left( 1-{{x}_{4}} \right)\left[ \frac{x_{3}^{2}}{{{\left( {{a}_{i}}-{{x}_{2}} \right)}^{2}}+x_{3}^{2}} \right] \right]</math>
<pre>
popts = polytransform('options');
popts.squares = 'on';
[xout, model] = polytrnasform(x,popts)
</pre>  
gives the 100 by 10 matrix where the columns 6 to 10 are the squares of the first five.


===See Also===
*'''<math>{\operatorname{d2}\!y\over\operatorname{d2}\!x}</math>'''
 
 
* '''<math>{\operatorname{d}\!y\over\operatorname{d}\!{x}_{i}}</math>'''

Revision as of 13:31, 1 August 2016

Purpose

Outputs a sigmoid function.


Synopsis

[i0,iw] = peakfind(x,width,tolfac,w,options)
[i0,iw] = peakfind(x,width,options)


Inputs

  • x = 3 element vector where x(1) = coefficient, x(2) = offset and x(3) is equal to the decay constant


Outputs