Below we show how to execute the MatLab function fminsearch with a user defined

Below we show how to execute the matlab function

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by []). Below we show how to execute the MatLab function fminsearch with a user defined function sumsq vonBert , including an initial guess and the data sets. 1 [ p1 , J , f l a g ] = fminsearch ( @sumsq vonBert , [ 1 0 0 , 0 . 1 ] , [ ] , tdfish , l d f i s h ) MatLab returns the best fitting parameter values in the vector p 1 (which could be used in another iteration if one is uncertain of convergence), the least sum of square errors, J , and a variable flag , which is 1 if MatLab thinks fminsearch has converged and 0 if it failed to converge. For our
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particular problem, MatLab returns the results p 1 = [92 . 401 , 0 . 14553], J = 1 , 107 . 3, and flag = 1, so the best fitting parameters are L * = 92 . 401 and b = 0 . 14553 and our best model for the length of Lake Trout as it ages is L ( t ) = 92 . 401 1 - e - 0 . 14553 t . A MatLab script file is developed to graph this best fitting model and the data. This best fitting model is shown with the data in the graph below. The script, vonBert plot.m , is available from the Lecture notes (including initial clear and final text and output controls, which are omitted here for clarity). 1 2 c l e a r % Clear previous d e f i n i t i o n s 3 f i g u r e (1) % Assign f i g u r e number 4 c l f % Clear previous f i g u r e s 5 hold o f f % Start with f r e s h graph 6 7 mytitle = ’ Length of Lake Trout ’ ; % T i t l e 8 xlab = ’Age ( Years ) ’ ; % X - l a b e l 9 ylab = ’ Length (cm) ’ ; % Y - l a b e l 10 11 load ( ’ f i s h d a t ’ ) ; % Provide vectors of Lake Trout data 12 13 tt = l i n s p a c e (0 ,20 ,500) ; % t domain of function 14 Lt = 92.404 * (1 - exp ( - 0.14553 * tt ) ) ; % Function f o r von Bertalanffy 15 16 plot ( tt , Lt , ’b - , ’ LineWidth ’ , 1 . 5 ) ; % Plot model 17 hold on % Plots Multiple graphs 18 plot ( tdfish , l d f i s h , ’ bo ’ , ’ LineWidth ’ , 1 . 5 ) ; % Plot data with c i r c l e s 19 20 grid % Adds Gridlines 21 22 xlim ( [ 0 2 0 ] ) ; % Defines l i m i t s of graph 23 ylim ( [ 0 100]) ; 24 25 f o n t l a b s = ’ Times New Roman ’ ; % Font type used in l a b e l s 26 x l a b e l ( xlab , ’ FontSize ’ ,14 , ’FontName ’ , fontlabs , ’ i n t e r p r e t e r ’ , ’ latex ’ ) ; 27 % x - Label s i z e and font 28 y l a b e l ( ylab , ’ FontSize ’ ,14 , ’FontName ’ , fontlabs , ’ i n t e r p r e t e r ’ , ’ latex ’ ) ; 29 % y - Label s i z e and font 30 t i t l e ( mytitle , ’ FontSize ’ ,16 , ’FontName ’ , ’ Times New Roman ’ , ’ i n t e r p r e t e r ’ , ’ latex ’ ) ; 31 % T i t l e s i z e / font 32 set ( gca , ’ FontSize ’ ,12) ; % Axis t i c k font s i z e 33 34 print - depsc vonBert . eps % Create f i g u r e as EPS f i l e 35 %print - djpeg vonBert . jpg % Create f i g u r e as JPEG f i l e The graph of the von Bertalanffy model with the relevant data is below.
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0 2 4 6 8 10 12 14 16 18 20 0 10 20 30 40 50 60 70 80 90 100 Age (Years) Length (cm) Length of Lake Trout Relation Between Weight and Length The next step in the modeling for this problem is to find a functional relationship between the weight and the length of the Lake Trout. This is known as Allometric modeling or a Power Law relationship. Specifically, we examine a relationship of the form W = kL a .
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