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ArrayInterpolation in contourplot...

Dkunb 65 Maple 2021
duplicate-question arrayinterpolation incomplete-question
September 12 2022
2 4

I wonder if there is any way to use ArrayInterpolation with contourplot or similar effect?

N_data.xlsx 

Thank you in advance,

> 

restart;
> 

with(CurveFitting)

[ArrayInterpolation, BSpline, BSplineCurve, Interactive, LeastSquares, Lowess, PolynomialInterpolation, RationalInterpolation, Spline, ThieleInterpolation]

 (1)
> 

with(plots);

[animate, animate3d, animatecurve, arrow, changecoords, complexplot, complexplot3d, conformal, conformal3d, contourplot, contourplot3d, coordplot, coordplot3d, densityplot, display, dualaxisplot, fieldplot, fieldplot3d, gradplot, gradplot3d, implicitplot, implicitplot3d, inequal, interactive, interactiveparams, intersectplot, listcontplot, listcontplot3d, listdensityplot, listplot, listplot3d, loglogplot, logplot, matrixplot, multiple, odeplot, pareto, plotcompare, pointplot, pointplot3d, polarplot, polygonplot, polygonplot3d, polyhedra_supported, polyhedraplot, rootlocus, semilogplot, setcolors, setoptions, setoptions3d, shadebetween, spacecurve, sparsematrixplot, surfdata, textplot, textplot3d, tubeplot]

 (2)
> 

alpha := <seq(0..10,evalf(10/50))>:
beta := <seq(0..10,evalf(10/50))>:
> 

excelfile:= FileTools:-JoinPath(["C:","Users","aimer","OneDrive","Desktop","Msc Thesis","Maple ref","N_data.xlsx"]);

"C:\Users\aimer\OneDrive\Desktop\Msc Thesis\Maple ref\N_data.xlsx"

 (3)
> 

NN:=ImportMatrix(excelfile,source=Excel):

_rtable[36893489576445216036]

 (4)
> 

#?ImportMatrix;
> 

#NN:=ImportMatrix(matlabData, source=MATLAB);
> 

#currentdir();

"C:\Users\aimer\OneDrive\Desktop\Msc Thesis\Maple ref"

 (5)
> 

 

> 

contourplot(ArrayInterpolation([beta,alpha],NN,[x,y]),x=0..10,y=0..10,contours=[0]);

Error, (in CurveFitting:-ArrayInterpolation) invalid input: xvalues are not specified correctly

  
> 

#?listcontplot
> 

 

Download test1.mw

ImportMatrix problem...

Dkunb 65 Maple 2021
importmatrix
September 12 2022
1 1

I do not know what is the problem with Using ImportMatrix. N_data.xlsx is in the same directory.

Any comment would be appreciated.

> 

restart;
> 

with(CurveFitting)

[ArrayInterpolation, BSpline, BSplineCurve, Interactive, LeastSquares, Lowess, PolynomialInterpolation, RationalInterpolation, Spline, ThieleInterpolation]

 (1)
> 

with(plots);

[animate, animate3d, animatecurve, arrow, changecoords, complexplot, complexplot3d, conformal, conformal3d, contourplot, contourplot3d, coordplot, coordplot3d, densityplot, display, dualaxisplot, fieldplot, fieldplot3d, gradplot, gradplot3d, implicitplot, implicitplot3d, inequal, interactive, interactiveparams, intersectplot, listcontplot, listcontplot3d, listdensityplot, listplot, listplot3d, loglogplot, logplot, matrixplot, multiple, odeplot, pareto, plotcompare, pointplot, pointplot3d, polarplot, polygonplot, polygonplot3d, polyhedra_supported, polyhedraplot, rootlocus, semilogplot, setcolors, setoptions, setoptions3d, shadebetween, spacecurve, sparsematrixplot, surfdata, textplot, textplot3d, tubeplot]

 (2)
> 

alpha := <seq(0..10,evalf(10/50))>:
beta := <seq(0..10,evalf(10/50))>:
> 

excelfile:= FileTools:-JoinPath(["C: ","Users","aimer","OneDrive","Desktop","Msc Thesis","Maple ref","N_data.xlsx"]);

"C: \Users\aimer\OneDrive\Desktop\Msc Thesis\Maple ref\N_data.xlsx"

 (3)
> 

NN:=ImportMatrix(excelfile,source=Excel);

Error, (in ImportMatrix) file or directory does not exist: C: \Users\aimer\OneDrive\Desktop\Msc Thesis\Maple ref\N_data.xlsx

  
> 

?ImportMatrix;
> 

#NN:=ImportMatrix(matlabData, source=MATLAB);
> 

currentdir();

"C:\Users\aimer\OneDrive\Desktop\Msc Thesis\Maple ref"

 (4)
> 

?Joinpath
> 

 

Download test1.mw

how to reduce evaluating time...

Dkunb 65 Maple 2021
performance integration numeric
August 31 2022
2 19

What should I do to reduce evaluating time?

> 

restart;
> 

with(plots):
> 

 

> 

F:=kappa->kappa;

proc (kappa) options operator, arrow; kappa end proc

 (1)
> 

f:=(alpha,delta)->exp(-abs(F(kappa))^2*(1+delta^2)/2-abs(F(kappa))*alpha)/abs(F(kappa));

proc (alpha, delta) options operator, arrow; exp(-(1/2)*abs(F(kappa))^2*(1+delta^2)-abs(F(kappa))*alpha)/abs(F(kappa)) end proc

 (2)
> 

L:=(alpha,delta,Lambda)->(lambda^2*exp(-alpha^2/2)/4)*(Int(f(alpha,delta),kappa= -infinity..-Lambda)+Int(f(alpha,delta),kappa= Lambda..infinity));

proc (alpha, delta, Lambda) options operator, arrow; (1/4)*lambda^2*exp(-(1/2)*alpha^2)*(Int(f(alpha, delta), kappa = -infinity .. -Lambda)+Int(f(alpha, delta), kappa = Lambda .. infinity)) end proc

 (3)
> 

evalf(L(4,1,0.001));

0.8209373770e-3*lambda^2

 (4)
> 

g:=(beta,delta)->exp(-I*kappa*beta-abs(F(kappa))^2*(1+delta^2)/2)/abs(F(kappa));

proc (beta, delta) options operator, arrow; exp(-I*kappa*beta-(1/2)*abs(F(kappa))^2*(1+delta^2))/abs(F(kappa)) end proc

 (5)
> 

E:=(omega,gamma)->exp(I*omega*gamma)*(1-erf((gamma+I*omega)/sqrt(2)));

proc (omega, gamma) options operator, arrow; exp(I*omega*gamma)*(1-erf((gamma+I*omega)/sqrt(2))) end proc

 (6)
> 

J:=(alpha,delta,Lambda,beta,gamma)->(lambda^2*exp(-alpha^2/2)/8)*abs(Int(g(beta,delta)*(E(abs(F(kappa)),gamma)+E(abs(F(kappa)),-gamma)),kappa=-infinity..-Lambda)+Int(g(beta,delta)*(E(abs(F(kappa)),gamma)+E(abs(F(kappa)),-gamma)),kappa=Lambda..infinity));

proc (alpha, delta, Lambda, beta, gamma) options operator, arrow; (1/8)*lambda^2*exp(-(1/2)*alpha^2)*abs(Int(g(beta, delta)*(E(abs(F(kappa)), gamma)+E(abs(F(kappa)), -gamma)), kappa = -infinity .. -Lambda)+Int(g(beta, delta)*(E(abs(F(kappa)), gamma)+E(abs(F(kappa)), -gamma)), kappa = Lambda .. infinity)) end proc

 (7)
> 

#evalf(J(4,1,0.001,8,3));
> 

N := (beta,alpha)-> (J(alpha,1,0.001,beta,3)-L(alpha,1,0.001))/\lambda^2;

proc (beta, alpha) options operator, arrow; (J(alpha, 1, 0.1e-2, beta, 3)-L(alpha, 1, 0.1e-2))/lambda^2 end proc

 (8)
> 

 

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> 

contourplot(evalf(N(beta,alpha)), beta=0..10,alpha=0..10,grid=[25,25]);

 
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Download Negativity_v1.mw

How do I solve this Integral (6) ?...

Dkunb 65 Maple
integration syntax
August 12 2022
1 1


 

> 

restart;
> 

assume(alpha>0)
> 

assume(delta:: real)
> 

assume(C>0)
> 

 

> 

f:= g->e^(-1/2*(C*g*(1-g^2))^2*(1+delta^2)-C*g*(1-g^2)*alpha)/(g*(1-g^2));

proc (g) options operator, arrow; e^(-(1/2)*C^2*g^2*(1-g^2)^2*(delta^2+1)-C*g*(1-g^2)*alpha)/(g*(1-g^2)) end proc

 (1)
> 

convert(1/(g*(1-g^2)),parfrac,g);

-(1/2)/(g+1)+1/g-(1/2)/(g-1)

 (2)
> 

f1:= g->-e^(-1/2*(C*g*(1-g^2))^2*(1+delta^2)-C*g*(1-g^2)*alpha)/(2*(g+1));

proc (g) options operator, arrow; -e^(-(1/2)*C^2*g^2*(1-g^2)^2*(delta^2+1)-C*g*(1-g^2)*alpha)/(2*g+2) end proc

 (3)
> 

f2 := g->e^(-1/2*(C*g*(1-g^2))^2*(1+delta^2)-C*g*(1-g^2)*alpha)/g;

proc (g) options operator, arrow; e^(-(1/2)*C^2*g^2*(1-g^2)^2*(delta^2+1)-C*g*(1-g^2)*alpha)/g end proc

 (4)
> 

f3:= g->-e^(-1/2*(C*g*(1-g^2))^2*(1+delta^2)-C*g*(1-g^2)*alpha)/(2*(g-1));

proc (g) options operator, arrow; -e^(-(1/2)*C^2*g^2*(1-g^2)^2*(delta^2+1)-C*g*(1-g^2)*alpha)/(2*g-2) end proc

 (5)
> 

int(f1(g),g=0..infinity);

int(-e^(-(1/2)*C^2*g^2*(-g^2+1)^2*(delta^2+1)-C*g*(-g^2+1)*alpha)/(2*g+2), g = 0 .. infinity)

 (6)
> 

 


 

Download 2022_integralIandJ.mw

I do not know why eq(6) does not evaluate. Could you help me?

DEplot warnings...

Dkunb 65 Maple 2021
differential-equations deplot plotting
January 05 2022
1 5

I have the following warnings. Could you help me fix the problem?

> 

restart;
> 

deS:=diff(x(t),t)=-0.5*x(t)*y(t)

diff(x(t), t) = -.5*x(t)*y(t)

 (1)
> 

deI:=diff(y(t),t)=0.5*x(t)*y(t)-0.15*y(t)

diff(y(t), t) = .5*x(t)*y(t)-.15*y(t)

 (2)
> 

with(DEtools):
> 

DEplot([deS,deI],[x(t),y(t)],t=0..40,x=0..1,y=0..0.6,[[x(0)=0.99,y(0)=0]])

Warning, plot may be incomplete, the following errors(s) were issued:
   incorrect number of arguments, got 51, expected 50

  

 
> 

 

> 

 

Download DEtools_example.mw

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