{ From user Lonnie, Model Convolution_example at Fri, Sep 29, 2006 2:00 PM~~
}
Softwareversion 3.1.1


{ System Variables with non-default values: }
Windows := 2
Usetable := 0
Typechecking := 1
Checking := 1
Graphwindows := 9
Saveoptions := 2
Savevalues := 0
Webhelper := -1
Allwarnings := 0


{ Non-default Time SysVar value: }
Time := [0,1,2]
Title Time: Time
Description Time: Dynamic simulation periods are specified in Time's ~~
definition. This is usually a list of numbers or labels, typically in~~
 some unit of time (days, weeks, months, etc.).  Use the ÒDynamic()Ó ~~
function in your variables to perform dynamic simulation.

Model Convolution_example
Title: Convolution example
Description: This example model contains a convolution function, that~~
 convolves two curves over time, along with some examples of its use.~~

Author: Lonnie Chrisman, Ph.D.~
Lumina Decision Systems
Date: Fri, Sep 29, 2006 12:07 PM
Saveauthor: Lonnie
Savedate: Fri, Sep 29, 2006 2:00 PM
Defaultsize: 48,24
Diagstate: 1,1,0,550,414,17
Fontstyle: Arial, 15
Fileinfo: 0,Model Convolution_example,2,2,0,0,W:\TestModels\Convoluti~~
on.ANA

Function Convolve(Y,Z : Numeric[I] ; T : Numeric ascending[I] ; I  :I~~
ndexType )
Title: Convolve (Y,Z, X, I )
Description: Computes the convolution of Y and Z.  T contains the X-a~~
xis values, which need not be spaced equally, but which do need to be~~
 increasing.  I is the dimension over which the convolution occurs.  ~~
Assumes both functions Y and Z are 0-valued outside the limits of I, ~~
and linearly interpolates between the values contained in Y and Z.
Definition: var t0 := min(T,I);~
var tn := max(T,I);~
var incU := (tn-t0) / (size(I)-1);~
~
var t_ [] := T do (~
  { range bounds for integration }~
  var u0 := max([t0,t_-tn]);~
  var uN := min([tn,t_-t0]);~
  { integration dimension }~
  index U := Sequence(u0,uN,incU);~
  { Do the integration }~
  area2( LinearInterp( T, Y, u, I ) * LinearInterp( T, Z, T_-u, I), U~~
, U )~
)
Nodelocation: 88,64,1
Nodesize: 48,24
Windstate: 2,175,96,650,531
Paramnames: Y,Z,T,I

Index T
Title: T
Definition: Sequence( -5, 5, 0.1 )
Nodelocation: 96,232,1
Nodesize: 48,24

Variable X1
Title: X1
Definition: if abs(t)>2 then 0 ~
else 1-abs(T/2)
Nodelocation: 232,224,1
Nodesize: 48,24
Valuestate: 2,24,5,416,303,1,MIDM

Variable X2
Title: X2
Definition: exp(-T^2)
Nodelocation: 344,224,1
Nodesize: 48,24
Valuestate: 2,450,13,416,303,1,MIDM

Variable X1____x2
Title: X1 ** X2
Definition: Convolve(X1,X2,T,T)
Nodelocation: 232,288,1
Nodesize: 48,24
Valuestate: 2,149,58,793,549,1,MIDM
Reformval: [, T ]

Variable X1____x1
Title: X1 ** X1
Definition: Convolve(X1,X1,T,T)
Nodelocation: 344,288,1
Nodesize: 48,24
Valuestate: 2,80,313,416,303,1,MIDM

Variable X3
Title: X3
Definition: T=-1 or T=1
Nodelocation: 456,224,1
Nodesize: 48,24
Valuestate: 2,40,50,416,303,1,MIDM

Variable X2____x3
Title: X2 ** X3
Definition: Convolve(X2,X3,T,T)
Nodelocation: 456,288,1
Nodesize: 48,24
Valuestate: 2,56,66,812,303,1,MIDM
Reformval: [, T ]

Function Area2(Y : Numeric[I] ; X : ascending numeric[I]; I : IndexTy~~
pe)
Title: Area2 (Y,X,I)
Description: Computes the area under a curve given by the points in (~~
X,Y), using the trapezoidal rule.  Like the built-in Area function, e~~
xcept the bulit-in one has a problem with local indexes, and also thi~~
s one allows X to be separate from I.  This does only indefinite inte~~
gration -- it doesn't have the bounds of a definite integral that the~~
 built-in Area function has.~
(Note: the built-in function can be used for both these purposes in A~~
nalytica 4.0 or later)
Definition: var pos := cumulate(1,I);~
var prevY := Slice(Y,I,if pos>1 then pos-1 else 1);~
var prevX := Slice(X,I,if pos>1 then pos-1 else 1);~
sum( (X-prevX) * (Y+prevY)/2, I )
Nodelocation: 200,64,1
Nodesize: 48,24
Windstate: 2,102,5,476,309
Paramnames: Y,X,I

Text Te1
Description: Some Examples:
Nodelocation: 128,176,-1
Nodesize: 72,16

Close Convolution_example