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Gillee

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Why is the frequency the highest for sub...

Gillee 242 Maple 2020
August 05 2020
1 1

ApproxBayesComp_for_loop.mw

The observed data were 6 out 16 people signed up. Priors were defined by a uniform distribution. A Generative Model utilized a binomial distribution. A distribution of subscribers were generated, see plot below. By filtering the subscribers distribution for the value is equal 6, the posterior distribution was obtained. Why is the frequency the highest for subscribers = 16? Where did I go wrong in coding this problem?

How to get a compiled procedure to work?...

Gillee 242 Maple 2019
compile
January 31 2020
1 1

Hello,

I have a procedure, SoS that returns the value for sos. After compiling the procedure, I get float(undefined) for the return value. How can this be fixed?

 

Thanks so much for your time.

 


 

restart; kernelopts(version); interface(version)

`Standard Worksheet Interface, Maple 2019.2, Windows 10, November 26 2019 Build ID 1435526`

 (1)

NULL``

Erealm := Array([1235.773, 1383.61, 1457.262, 1500.264, 1550.184, 1612.161, 512.7612, 656.6554, 743.6461, 793.375, 855.7937, 939.1199, 79.9523, 128.1375, 167.1459, 193.592, 230.5401, 287.8348, 22.389, 29.41424, 35.91883, 40.86366, 48.79128, 63.4475, 15.34275, 17.10101, 18.63288, 19.77424, 21.5671, 24.84739, 13.8321, 14.52843, 15.07626, 15.47014, 16.07713, 17.16574, 13.13383, 13.63704, 13.95888, 14.16849, 14.46123, 14.93971, 12.76736, 13.2203, 13.50072, 13.673, 13.89852, 14.23242], datatype = float[8]); LFm := Array([.156795, .1248161, .1108722, .1032334, 0.9474591e-1, 0.8496174e-1, .361361, .3020133, .2706018, .2546556, .2356126, .2121333, .6883826, .6532309, .6155578, .5906291, .5578895, .5123917, .394458, .5326358, .6095816, .6489291, .6894866, .7232845, .1456468, .2226473, .2826954, .3228541, .3789496, .4632182, 0.6758032e-1, 0.9437384e-1, .1198126, .1387971, .1680719, .2181531, 0.5173809e-1, 0.586771e-1, 0.6591736e-1, 0.7206892e-1, 0.8243504e-1, .1024519, 0.457877e-1, 0.493836e-1, 0.5191291e-1, 0.539114e-1, 0.5708074e-1, 0.6330242e-1], datatype = float[8]); maxx := ArrayNumElems(LFm); E0 := 13.; E00 := 4200.; alpha := .5; beta := 0.7e-1
NULL

``

SoS := proc (E0::float, E00::float, alpha::float, beta::float, maxx::integer, Erealm::(Array(datatype = float[8])), LFm::(Array(datatype = float[8])))::float; local k, omegatau, Ecomplex, Erealc, Eimagc, LFc, sos; sos := 0.; for k to maxx do Ecomplex := Complex(Erealm[k], Erealm[k]*LFm[k]); omegatau := abs(-I*(((E0-E00)/(Ecomplex-E00))^(1/beta)-1)^(1/alpha)); Erealc := Re(E00+(E0-E00)/(1+(I*omegatau)^alpha)^beta); Eimagc := Im(E00+(E0-E00)/(1+(I*omegatau)^alpha)^beta); LFc := Eimagc/Erealc; sos := sos+(log10(Erealm[k])-log10(Erealc))^2+(LFm[k]-LFc)^2 end do; return sos end proc

``

``

SoS(E0, E00, alpha, beta, maxx, Erealm, LFm)

HFloat(0.015392438292813794)

 (2)

cSoS := Compiler:-Compile(SoS); cSoS(E0, E00, alpha, beta, maxx, Erealm, LFm)

Float(undefined)

 (3)

``

``


 

Download Compile_proc.mw

 

How to calculate Vector[row] y2 using sp...

Gillee 242 Maple 2018
spline curvefitting cubic
April 01 2019
2 2

Hi, 

I was able to determine a cubic spline fit, F(v), to x1 and y1. Now I have vector x2 which I would like to use F(v) to calculate y2 as another Vector[row]. I am having trouble accomplishing this task. Any help is greatly appreciated. Thanks.
 

restart

 x1 := Vector[row]([0.8e-1, .28, .48, .68, .88, 1, 1.2, 1.4, 1.6, 1.8, 2, 2.2, 2.4, 2.6, 2.8, 3, 3.2, 3.4, 3.6, 3.8, 4, 4.2]);

 y1 := Vector[row]([-10.081, -10.054, -10.018, -9.982, -9.939, -9.911, -9.861, -9.8, -9.734, -9.659, -9.601, -9.509, -9.4, -9.293, -9.183, -9.057, -8.931, -8.806, -8.676, -8.542, -8.405, -8.265]);

 

m := ArrayTools[Dimensions](x1);

maxx := rhs(m[1]);

 

F := proc (v) options operator, arrow; CurveFitting:-Spline(x1, y1, v, degree = 3) end proc;

 

x2 := Vector[row]([seq(log10(2*10^x1[k]), k = 1 .. maxx)])

 

y2:=?

 

Pts1 := plot(x1, y1, style = point, symbol = diamond, gridlines = true, color = red);

plt_sp := plot(F(v), v = x1[1] .. x1[maxx], color = blue);

plots:-display(Pts1, plt_sp)``

"# How to calculate Vector y2 using spline fit F with x2"? " x1:=Vector[row]([0.08,0.28,0.48,0.68,0.88,1,1.2,1.4,1.6,1.8,2,2.2,2.4,2.6,2.8,3,3.2,3.4,3.6,3.8,4,4.2]): y1:=Vector[row]([-10.081,-10.054,-10.018,-9.982,-9.939,-9.911,-9.861,-9.8,-9.734,-9.659,-9.601,-9.509,-9.4,-9.293,-9.183,-9.057,-8.931,-8.806,-8.676,-8.542,-8.405,-8.265]): m:=ArrayTools[Dimensions](x1): maxx:=rhs(m[1]): F:=v->CurveFitting:-Spline(x1,y1, v,degree=3): x2:=Vector[row]([seq(log10(2*10^(x1[k])),k=1..maxx)]): #` PLOT RESULTS` Pts1:=plot(x1,y1,style=point,symbol = diamond, gridlines=true, color = red): plt_sp:=plot(F(v),v=x1[1]..x1[maxx],color = blue): plots:-display(Pts1,plt_sp); "

  

``

``


 

Download splfit.mw

How can decrease the evaluation time of ...

Gillee 242 Maple
nlpsolve
February 15 2019
1 1

Hi,

I am trying to curve fit data using NLPSolve. I noticed that the evaluation time for NLPSolve seems really long. Did I mess up in using NLPSolve? 

 

Thanks you for any suggests or comments.
 

restart; kernelopts(version); interface(version); multithread_capability := kernelopts(multithreaded); Number_of_CPUs := kernelopts(numcpus)
NULL

8

 (1)

``

``

"#` How` can I decrease the evaluation time of NLPSolve or are there better methods"?"" ""

``

SoS:=proc(E0::float,E00::float,alpha::float,beta:: float)::float;

NULL

NULL

Experimental Data

 

Erealm := Vector[row]([1235.773, 1383.61, 1457.262, 1500.264, 1550.184, 1612.161, 512.7612, 656.6554, 743.6461, 793.375, 855.7937, 939.1199, 79.9523, 128.1375, 167.1459, 193.592, 230.5401, 287.8348, 22.389, 29.41424, 35.91883, 40.86366, 48.79128, 63.4475, 15.34275, 17.10101, 18.63288, 19.77424, 21.5671, 24.84739, 13.8321, 14.52843, 15.07626, 15.47014, 16.07713, 17.16574, 13.13383, 13.63704, 13.95888, 14.16849, 14.46123, 14.93971, 12.76736, 13.2203, 13.50072, 13.673, 13.89852, 14.23242]); LFm := Vector[row]([.156795, .1248161, .1108722, .1032334, 0.9474591e-1, 0.8496174e-1, .361361, .3020133, .2706018, .2546556, .2356126, .2121333, .6883826, .6532309, .6155578, .5906291, .5578895, .5123917, .394458, .5326358, .6095816, .6489291, .6894866, .7232845, .1456468, .2226473, .2826954, .3228541, .3789496, .4632182, 0.6758032e-1, 0.9437384e-1, .1198126, .1387971, .1680719, .2181531, 0.5173809e-1, 0.586771e-1, 0.6591736e-1, 0.7206892e-1, 0.8243504e-1, .1024519, 0.457877e-1, 0.493836e-1, 0.5191291e-1, 0.539114e-1, 0.5708074e-1, 0.6330242e-1])

NULL``

Enter Initial Guesses for HN equation

 

ind0 := min[index](Erealm); ind00 := max[index](Erealm); indLF := max[index](LFm); E0_g := Erealm(ind0); E00_g := 3*Erealm(ind00); `α_g` := 2.0*LFm(indLF)/Pi; `β_g` := `α_g`/(10.0); m := ArrayTools[Dimensions](LFm); maxx := rhs(m[1]); Ecomplex := Vector[row]([seq(Complex(Erealm[k], Erealm[k]*LFm[k]), k = 1 .. maxx)]); `ωτ` := Vector[row]([seq(abs((((E0_g-E00_g)/(Ecomplex[k]-E00_g))^(1/`β_g`)-1)^(1/`α_g`)/(I)), k = 1 .. maxx)]); Erealc := Vector[row]([seq(Re(E00_g+(E0_g-E00_g)/(1+(I*`ωτ`[k])^`α_g`)^`β_g`), k = 1 .. maxx)]); Eimagc := Vector[row]([seq(Im(E00_g+(E0_g-E00_g)/(1+(I*`ωτ`[k])^`α_g`)^`β_g`), k = 1 .. maxx)]); LFc := Vector[row]([seq(Eimagc[k]/Erealc[k], k = 1 .. maxx)]); pltm := plots:-loglogplot(Erealm, LFm, style = point, symbol = solidcircle, gridlines = true, color = red); pltc := plots:-loglogplot(Erealc, LFc, style = point, symbol = diamond, gridlines = true, color = blue); plots:-display(pltm, pltc, title = "Wicket Plot from Guesses measured - red calculated - blue"); Sum_of_Squares := SoS(E0_g, E00_g, `α_g`, `β_g`)

.2049941769

(2.1)

``

NULL

NULL

NULL

Run Optimizer

 

lol := .7; hil := 1.3; le0 := lol*E0_g; he0 := hil*E0_g; le00 := lol*E00_g; he00 := hil*E00_g; al := lol*`α_g`; ah := hil*`α_g`; bl := lol*`β_g`; bh := hil*`β_g`; parameterRange := le0 .. he0, le00 .. he00, al .. ah, bl .. bh; soln := Optimization:-NLPSolve(SoS, parameterRange); HN := soln[2]; E0_s := HN[1]; E00_s := HN[2]; `α_s` := HN[3]; `β_s` := HN[4]; `ωτ_s` := Vector[row]([seq(abs((((E0_s-E00_s)/(Ecomplex[k]-E00_s))^(1/`β_s`)-1)^(1/`α_s`)/(I)), k = 1 .. maxx)]); Erealc_s := Vector[row]([seq(Re(E00_s+(E0_s-E00_s)/(1+(I*`ωτ_s`[k])^`α_s`)^`β_s`), k = 1 .. maxx)]); Eimagc_s := Vector[row]([seq(Im(E00_s+(E0_s-E00_s)/(1+(I*`ωτ_s`[k])^`α_s`)^`β_s`), k = 1 .. maxx)]); LFc_s := Vector[row]([seq(Eimagc_s[k]/Erealc_s[k], k = 1 .. maxx)])

[0.648163470800135894e-2, Vector[column](%id = 18446747242105787086)]

(3.1)

NULL

NULL

NULL

Plot Wicket Plot with Optimized HN Parameters

 

pltm_s := plots:-loglogplot(Erealm, LFm, style = point, symbol = solidcircle, gridlines = true, color = red); pltc_s := plots:-loglogplot(Erealc_s, LFc_s, style = point, symbol = diamond, gridlines = true, color = blue); plots:-display(pltm_s, pltc_s, title = "Wicket Plot after Optimization (measured - red calculated - blue)"); E0_soln := E0_s; E00_soln := E00_s; `α_soln` := `α_s`; `β_soln` := `β_s`; Sum_of_Squares := soln[1]

0.648163470800135894e-2

(4.1)

NULL


 

Download HN_fit_of_DMA_data_ss_proc_v5a.mw

How do I know that using Threads will ma...

Gillee 242 Maple 2017
August 20 2017
2 3

I am learning how to use Threads. I looked for an example code in Start / Programming / Example: Task Model and Multithreaded Programming. I found a MandelBrot code, which I was able to change a value in the If -then statement to run in Threads or no Threads mode. I added a time() function to get a sense of the execution time. The results are about 140s with Threads and 91s with no Threads. I would have thought that the execution time would be smaller in the Threads mode than in the no Threads mode. Did I assume incorrectly that I was creating a Threads and no Threads situations by modifying the if-then statement? Or is this not good example? Here is the code:

Threads_Ex3a.mw

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