Peaklorentzian: Difference between revisions
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===Purpose=== | ===Purpose=== | ||
Outputs a Lorentzian function, Jacobian, and Hessian for a given set of input parameters and axis. | Outputs a Lorentzian function, Jacobian, and Hessian for a given set of input parameters and axis. | ||
===Synopsis=== | ===Synopsis=== | ||
: [y,y1,y2] = peaklorentzian(x,ax) | : [y,y1,y2] = peaklorentzian(x,ax) | ||
===Description=== | ===Description=== | ||
Given a 3-element vector of parameters (x) and a vector of independent variables e.g. a wavelength or frequency axis (ax), PEAKLORENTZIAN outputs a Lorentzian peak (y). If more than one output is requested, it also outputs the Jacobian (y1) and Hessian (y2). Derivatives are with respect to the parameters and are evaluated at (x). This function is called by PEAKFUNCTION. | Given a 3-element vector of parameters (x) and a vector of independent variables e.g. a wavelength or frequency axis (ax), PEAKLORENTZIAN outputs a Lorentzian peak (y). If more than one output is requested, it also outputs the Jacobian (y1) and Hessian (y2). Derivatives are with respect to the parameters and are evaluated at (x). This function is called by PEAKFUNCTION. | ||
====INPUTS==== | ====INPUTS==== | ||
* '''x''' = 3 element vector with parameters | * '''x''' = 3 element vector with parameters | ||
* '''x(1)''' = coefficient , | * '''x(1)''' = coefficient , | ||
* '''x(2)''' = mean , and | * '''x(2)''' = mean , and | ||
* '''x(3)''' = spread . | * '''x(3)''' = spread . | ||
* '''ax''' = vector of independent variables e.g. a wavelength or frequency axis with elements , . | * '''ax''' = vector of independent variables e.g. a wavelength or frequency axis with elements , . | ||
====OUTPUTS==== | ====OUTPUTS==== | ||
* '''y''' = vector with the Lorentzian function, . | * '''y''' = vector with the Lorentzian function, . | ||
* '''y1''' = matrix of the Jacobian of evaluated at (x). | * '''y1''' = matrix of the Jacobian of evaluated at (x). | ||
* '''y2''' = matrix of the Hessian of evaluated at (x). | * '''y2''' = matrix of the Hessian of evaluated at (x). | ||
===Algorithm=== | ===Algorithm=== | ||
The function is | The function is | ||
===Examples=== | ===Examples=== | ||
:%Make a single known peak | :%Make a single known peak | ||
: ax = 0:0.1:100; | : ax = 0:0.1:100; | ||
: y = peaklorentzian([2 51 8],ax); | : y = peaklorentzian([2 51 8],ax); | ||
: plot(ax,y) | : plot(ax,y) | ||
===See Also=== | ===See Also=== | ||
[[peakfunction]], [[peakgaussian]], [[peakpvoigt1]], [[peakpvoigt2]], [[peakstruct]] | [[peakfunction]], [[peakgaussian]], [[peakpvoigt1]], [[peakpvoigt2]], [[peakstruct]] | ||
Revision as of 14:26, 3 September 2008
Purpose
Outputs a Lorentzian function, Jacobian, and Hessian for a given set of input parameters and axis.
Synopsis
- [y,y1,y2] = peaklorentzian(x,ax)
Description
Given a 3-element vector of parameters (x) and a vector of independent variables e.g. a wavelength or frequency axis (ax), PEAKLORENTZIAN outputs a Lorentzian peak (y). If more than one output is requested, it also outputs the Jacobian (y1) and Hessian (y2). Derivatives are with respect to the parameters and are evaluated at (x). This function is called by PEAKFUNCTION.
INPUTS
- x = 3 element vector with parameters
- x(1) = coefficient ,
- x(2) = mean , and
- x(3) = spread .
- ax = vector of independent variables e.g. a wavelength or frequency axis with elements , .
OUTPUTS
- y = vector with the Lorentzian function, .
- y1 = matrix of the Jacobian of evaluated at (x).
- y2 = matrix of the Hessian of evaluated at (x).
Algorithm
The function is
Examples
- %Make a single known peak
- ax = 0:0.1:100;
- y = peaklorentzian([2 51 8],ax);
- plot(ax,y)
See Also
peakfunction, peakgaussian, peakpvoigt1, peakpvoigt2, peakstruct