Need help; Fixing error and plotting functions

Hi everyone,

I am working with plotting the following set of expressions. It shows some error that I can't fix. Kindly look into it and help show the plots.

x = linspace(0, 5);
y1=(-(2.844015460*(1+(2.787032085*(1-4163863*x*(1/4166463)))./((1+1603*x*(1/997)).*(1-x).^2.5))).*hypergeom(((-2.787032085)*(1-4163863*x*(1/4166463)))./((1+1603*x*(1/997)).*(1-x).^2.5), 2-(2.787032085*(1-4163863*x*(1/4166463)))./((1+1603*x*(1/997)).*(1-x).^2.5), (2.844015460*(1-4163863*x*(1/4166463)))./((1+1603*x*(1/997)).*(1-x).^2.5)).*(1-4163863*x*(1/4166463))./((1+1603*x*(1/997)).*(1-x).^2.5)+2.787032085.*hypergeom(-1-(2.787032085*(1-4163863*x*(1/4166463)))./((1+1603*x*(1/997)).*(1-x).^2.5), 1-(2.787032085*(1-4163863*x*(1/4166463)))./((1+1603*x*(1/997)).*(1-x).^2.5), (2.844015460*(1-4163863*x*(1/4166463)))./((1+1603*x*(1/997)).*(1-x).^2.5)).*(1-4163863*x*(1/4166463)).*(-1+(2.787032085*(1-4163863*x*(1/4166463)))./((1+1603*x*(1/997)).*(1-x).^2.5))./((1+1603*x*(1/997)).*(1-x).^2.5))./(-(2.844015460*(1+(2.787032085*(1-4163863*x*(1/4166463)))./((1+1603*x*(1/997)).*(1-x).^2.5))).*hypergeom(((-2.787032085)*(1-4163863*x*(1/4166463)))./((1+1603*x*(1/997)).*(1-x).^2.5), 2-(2.787032085*(1-4163863*x*(1/4166463)))./((1+1603*x*(1/997)).*(1-x).^2.5), (2.844015460*(1-4163863*x*(1/4166463)))./((1+1603*x*(1/997)).*(1-x).^2.5)).*(1-4163863*x*(1/4166463))./((1+1603*x*(1/997)).*(1-x).^2.5)+hypergeom(-1-(2.787032085.*(1-4163863*x*(1/4166463)))./((1+1603*x*(1/997)).*(1-x).^2.5), 1-(2.787032085*(1-4163863*x*(1/4166463)))./((1+1603*x.*(1/997)).*(1-x).^2.5), (2.844015460*(1-4163863*x*(1/4166463)))./((1+1603*x*(1/997)).*(1-x).^2.5)).*(-1+(2.787032085*(1-4163863*x*(1/4166463)))./((1+1603*x*(1/997)).*(1-x).^2.5)).^2);
plot(x,y1,'-','Color','[0 0 0]','DisplayName','\fontname {Helvetica} \fontsize{18} s=-0.5','LineWidth', 2.0, 'HandleVisibility','off')
 
 
xlabel('\fontname{Times New Roman} Values of x','FontSize',22)
ylabel('\fontname{Times New Roman} Values of y', 'FontSize', 22)
hold on
 
 
y2=(((-1.260902791).*(1+(.1992256641).*(1-4163863.*x.*(1/4166463))./((1+1603.*x.*(1/997)).*(1-x).^2.5))).*hypergeom(((-.1992256641).*(1-4163863.*x.*(1/4166463)))./((1+1603.*x.*(1/997)).*(1-x).^2.5), 2+((-.1992256641).*(1-4163863.*x.*(1/4166463)))./((1+1603.*x.*(1/997)).*(1-x).^2.5), (1.260902791.*(1-4163863.*x.*(1/4166463)))./((1+1603.*x.*(1/997)).*(1-x).^2.5)).*(1-4163863.*x.*(1/4166463))./((1+1603.*x.*(1/997)).*(1-x).^2.5)+.1992256641.*hypergeom(-1+((-.1992256641).*(1-4163863.*x.*(1/4166463)))./((1+1603.*x.*(1/997)).*(1-x).^2.5), 1+((-.1992256641).*(1-4163863.*x.*(1/4166463)))./((1+1603.*x.*(1/997)).*(1-x).^2.5), (1.260902791.*(1-4163863.*x.*(1/4166463)))./((1+1603.*x.*(1/997)).*(1-x).^2.5)).*(1-4163863.*x.*(1/4166463)).*(-1+(.1992256641.*(1-4163863.*x.*(1/4166463)))./((1+1603.*x.*(1/997)).*(1-x).^2.5))./((1+1603.*x.*(1/997)).*(1-x).^2.5))./(-1.891354186.*hypergeom(((-.1992256641).*(1-4163863.*x.*(1/4166463)))./((1+1603.*x.*(1/997)).*(1-x).^2.5), 2+(-.1992256641).*(1-4163863.*x.*(1/4166463))./((1+1603.*x.*(1/997)).*(1-x).^2.5), (1.260902791.*(1-4163863.*x.*(1/4166463)))./((1+1603.*x.*(1/997)).*(1-x).^2.5)).*(1+(.1992256641.*(1-4163863.*x.*(1/4166463)))./((1+1603.*x.*(1/997)).*(1-x).^2.5)).*(1-4163863.*x.*(1/4166463))./((1+1603.*x.*(1/997)).*(1-x).^2.5)+hypergeom(-1+((-.1992256641).*(1-4163863.*x.*(1/4166463)))./((1+1603.*x.*(1/997)).*(1-x).^2.5), 1+((-.1992256641).*(1-4163863.*x.*(1/4166463)))./((1+1603.*x.*(1/997)).*(1-x).^2.5), (1.260902791.*(1-4163863.*x.*(1/4166463)))./((1+1603.*x.*(1/997)).*(1-x).^2.5)).*(-1+(.1992256641.*(1-4163863.*x.*(1/4166463)))./((1+1603.*x.*(1/997)).*(1-x).^2.5)).*(-1.+(.2988384962.*(1-4163863.*x.*(1/4166463)))./((1+1603.*x.*(1/997)).*(1-x).^2.5)));
 
 
plot(x,y2,'-','Color','[0 0 0]','DisplayName','\fontname {Helvetica} \fontsize{18} s=-0.5','LineWidth', 2.0, 'HandleVisibility','off')
 
y3=((.2205657803.*(1-(1.498354984.*(1-4163863.*x.*(1/4166463)))./((1+1603.*x.*(1/997)).*(1-x).^2.5))).*hypergeom((1.498354984.*(1-4163863.*x.*(1/4166463)))./((1+1603.*x.*(1/997)).*(1-x).^2.5), 2+(1.498354984.*(1-4163863.*x.*(1/4166463)))./((1+1603.*x.*(1/997)).*(1-x).^2.5), ((-.2205657803).*(1-4163863.*x.*(1/4166463)))./((1+1603.*x.*(1/997)).*(1-x).^2.5)).*(1-4163863.*x.*(1/4166463))./((1+1603.*x.*(1/997)).*(1-x).^2.5)-1.498354984.*hypergeom(-1+(1.498354984.*(1-4163863.*x.*(1/4166463)))./((1+1603.*x.*(1/997)).*(1-x).^2.5), 1+(1.498354984.*(1-4163863.*x.*(1/4166463)))./((1+1603.*x.*(1/997)).*(1-x).^2.5), ((-.2205657803).*(1-4163863.*x.*(1/4166463)))./((1+1603.*x.*(1/997)).*(1-x).^2.5)).*(1-4163863.*x.*(1/4166463)).*(-1-(1.498354984.*(1-4163863.*x.*(1/4166463)))./((1+1603.*x.*(1/997)).*(1-x).^2.5))./((1+1603.*x.*(1/997)).*(1-x).^2.5))./(.4411315605.*hypergeom((1.498354984.*(1-4163863.*x.*(1/4166463)))./((1+1603.*x.*(1/997)).*(1-x).^2.5), 2+(1.498354984.*(1-4163863.*x.*(1/4166463)))./((1+1603.*x.*(1/997)).*(1-x).^2.5), ((-.2205657803).*(1-4163863.*x.*(1/4166463)))./((1+1603.*x.*(1/997)).*(1-x).^2.5)).*(1-(1.498354984.*(1-4163863.*x.*(1/4166463)))./((1+1603.*x.*(1/997)).*(1-x).^2.5)).*(1-4163863.*x.*(1/4166463))./((1+1603.*x.*(1/997)).*(1-x).^2.5)+hypergeom(-1+(1.498354984.*(1-4163863.*x.*(1/4166463)))./((1+1603.*x.*(1/997)).*(1-x).^2.5), 1+(1.498354984.*(1-4163863.*x.*(1/4166463)))./((1+1603.*x.*(1/997)).*(1-x).^2.5), ((-.2205657803).*(1-4163863.*x.*(1/4166463)))./((1+1603.*x.*(1/997)).*(1-x).^2.5)).*(-1-(1.498354984.*(1-4163863.*x.*(1/4166463)))./((1+1603.*x.*(1/997)).*(1-x).^2.5)).*(-1-(2.996709968.*(1-4163863.*x.*(1/4166463)))./((1+1603.*x.*(1/997)).*(1-x).^2.5)));
plot(x,y2,'-','Color','[0 0 0]','DisplayName','\fontname {Helvetica} \fontsize{18} s=-0.5','LineWidth', 2.0, 'HandleVisibility','off')
 
 
y4=(-(2.878360445.*(1+(2.820688929.*(1-4164863.*x.*(1/4166463)))./((1+603.*x.*(1/997)).*(1-x).^2.5))).*hypergeom(((-2.820688929).*(1-4164863.*x.*(1/4166463)))./((1+603.*x.*(1/997)).*(1-x).^2.5), 2-(2.820688929.*(1-4164863.*x.*(1/4166463)))./((1+603.*x.*(1/997)).*(1-x).^2.5), (2.878360445.*(1-4164863.*x.*(1/4166463)))./((1+603.*x.*(1/997)).*(1-x).^2.5)).*(1-4164863.*x.*(1/4166463))./((1+603.*x.*(1/997)).*(1-x).^2.5)+2.820688929.*hypergeom(-1-(2.820688929.*(1-4164863.*x.*(1/4166463)))./((1+603.*x.*(1/997)).*(1-x).^2.5), 1-(2.820688929.*(1-4164863.*x.*(1/4166463)))./((1+603.*x.*(1/997)).*(1-x).^2.5), (2.878360445.*(1-4164863.*x.*(1/4166463)))./((1+603.*x.*(1/997)).*(1-x).^2.5)).*(1-4164863.*x.*(1/4166463)).*(-1+(2.820688929.*(1-4164863.*x.*(1/4166463)))./((1+603.*x.*(1/997)).*(1-x).^2.5))./((1+603.*x.*(1/997)).*(1-x).^2.5))./(-(2.878360445.*(1+(2.820688929.*(1-4164863.*x.*(1/4166463)))./((1+603.*x.*(1/997)).*(1-x).^2.5))).*hypergeom(((-2.820688929).*(1-4164863.*x.*(1/4166463)))./((1+603.*x.*(1/997)).*(1-x).^2.5), 2-(2.820688929.*(1-4164863.*x.*(1/4166463)))./((1+603.*x.*(1/997)).*(1-x).^2.5), (2.878360445.*(1-4164863.*x.*(1/4166463)))./((1+603.*x.*(1/997)).*(1-x).^2.5)).*(1-4164863.*x.*(1/4166463))./((1+603.*x.*(1/997)).*(1-x).^2.5)+hypergeom(-1-(2.820688929.*(1-4164863.*x.*(1/4166463)))./((1+603.*x.*(1/997)).*(1-x).^2.5), 1-(2.820688929.*(1-4164863.*x.*(1/4166463)))./((1+603.*x.*(1/997)).*(1-x).^2.5), (2.878360445.*(1-4164863.*x.*(1/4166463)))./((1+603.*x.*(1/997)).*(1-x).^2.5)).*(-1+(2.820688929.*(1-4164863.*x.*(1/4166463)))./((1+603.*x.*(1/997)).*(1-x).^2.5)).^2);
plot(x,y4,'-.','Color','[0 0 0]','DisplayName','\fontname {Helvetica} \fontsize{18} MWCNT','LineWidth', 2.0)
 
 
y5=(((-1.291684341).*(1+(.2040892228.*(1-4164863.*x.*(1/4166463)))./((1+603.*x.*(1/997)).*(1-x).^2.5))).*hypergeom(((-.2040892228).*(1-4164863.*x.*(1/4166463)))./((1+603.*x.*(1/997)).*(1-x).^2.5), 2+((-.2040892228).*(1-4164863.*x.*(1/4166463)))./((1+603.*x.*(1/997)).*(1-x).^2.5), (1.291684341.*(1-4164863.*x.*(1/4166463)))./((1+603.*x.*(1/997)).*(1-x).^2.5)).*(1-4164863.*x.*(1/4166463))./((1+603.*x.*(1/997)).*(1-x).^2.5)+.2040892228.*hypergeom(-1+((-.2040892228).*(1-4164863.*x.*(1/4166463)))./((1+603.*x.*(1/997)).*(1-x).^2.5), 1+((-.2040892228).*(1-4164863.*x.*(1/4166463)))./((1+603.*x.*(1/997)).*(1-x).^2.5), (1.291684341.*(1-4164863.*x.*(1/4166463)))./((1+603.*x.*(1/997)).*(1-x).^2.5)).*(1-4164863.*x.*(1/4166463)).*(-1+(.2040892228.*(1-4164863.*x.*(1/4166463)))./((1+603.*x.*(1/997)).*(1-x).^2.5))./((1+603.*x.*(1/997)).*(1-x).^2.5))./(-1.937526512.*hypergeom(((-.2040892228).*(1-4164863.*x.*(1/4166463)))./((1+603.*x.*(1/997)).*(1-x).^2.5), 2+((-.2040892228).*(1-4164863.*x.*(1/4166463)))./((1+603.*x.*(1/997)).*(1-x).^2.5), (1.291684341.*(1-4164863.*x.*(1/4166463)))./((1+603.*x.*(1/997)).*(1-x).^2.5)).*(1+(.2040892228.*(1-4164863.*x.*(1/4166463)))./((1+603.*x.*(1/997)).*(1-x).^2.5)).*(1-4164863.*x.*(1/4166463))./((1+603.*x.*(1/997)).*(1-x).^2.5)+hypergeom(-1+((-.2040892228).*(1-4164863.*x.*(1/4166463)))./((1+603.*x.*(1/997)).*(1-x).^2.5), 1+((-.2040892228).*(1-4164863.*x.*(1/4166463)))./((1+603.*x.*(1/997)).*(1-x).^2.5), (1.291684341.*(1-4164863.*x.*(1/4166463)))./((1+603.*x.*(1/997)).*(1-x).^2.5)).*(-1+(.2040892228.*(1-4164863.*x.*(1/4166463)))./((1+603.*x.*(1/997)).*(1-x).^2.5)).*(-1.+(.3061338342.*(1-4164863.*x.*(1/4166463)))./((1+603.*x.*(1/997)).*(1-x).^2.5)));
plot(x,y5,'-.','Color','[0 0 0]','DisplayName','\fontname {Helvetica} \fontsize{18} s=1.0','LineWidth', 2.0, 'HandleVisibility','off')
 
 
y6=((.2306233919.*(1-(1.566678694.*(1-4164863.*x.*(1/4166463)))./((1+603.*x.*(1/997)).*(1-x).^2.5))).*hypergeom((1.566678694.*(1-4164863.*x.*(1/4166463)))./((1+603.*x.*(1/997)).*(1-x).^2.5), 2+(1.566678694.*(1-4164863.*x.*(1/4166463)))./((1+603.*x.*(1/997)).*(1-x).^2.5), ((-.2306233919).*(1-4164863.*x.*(1/4166463)))./((1+603.*x.*(1/997)).*(1-x).^2.5)).*(1-4164863.*x.*(1/4166463))./((1+603.*x.*(1/997)).*(1-x).^2.5)-1.566678694.*hypergeom(-1+(1.566678694.*(1-4164863.*x.*(1/4166463)))./((1+603.*x.*(1/997)).*(1-x).^2.5), 1+(1.566678694.*(1-4164863.*x.*(1/4166463)))./((1+603.*x.*(1/997)).*(1-x).^2.5), ((-.2306233919).*(1-4164863.*x.*(1/4166463)))./((1+603.*x.*(1/997)).*(1-x).^2.5)).*(1-4164863.*x.*(1/4166463)).*(-1-(1.566678694.*(1-4164863.*x.*(1/4166463)))./((1+603.*x.*(1/997)).*(1-x).^2.5))./((1+603.*x.*(1/997)).*(1-x).^2.5))./(.4612467837.*hypergeom((1.566678694.*(1-4164863.*x.*(1/4166463)))./((1+603.*x.*(1/997)).*(1-x).^2.5), 2+(1.566678694.*(1-4164863.*x.*(1/4166463)))./((1+603.*x.*(1/997)).*(1-x).^2.5), ((-.2306233919).*(1-4164863.*x.*(1/4166463)))./((1+603.*x.*(1/997)).*(1-x).^2.5)).*(1-(1.566678694.*(1-4164863.*x.*(1/4166463)))./((1+603.*x.*(1/997)).*(1-x).^2.5)).*(1-4164863.*x.*(1/4166463))./((1+603.*x.*(1/997)).*(1-x).^2.5)+hypergeom(-1+(1.566678694.*(1-4164863.*x.*(1/4166463)))./((1+603.*x.*(1/997)).*(1-x).^2.5), 1+(1.566678694.*(1-4164863.*x.*(1/4166463)))./((1+603.*x.*(1/997)).*(1-x).^2.5), ((-.2306233919).*(1-4164863.*x.*(1/4166463)))./((1+603.*x.*(1/997)).*(1-x).^2.5)).*(-1-(1.566678694.*(1-4164863.*x.*(1/4166463)))./((1+603.*x.*(1/997)).*(1-x).^2.5)).*(-1-(3.133357388.*(1-4164863.*x.*(1/4166463)))./((1+603.*x.*(1/997)).*(1-x).^2.5)));
plot(x,y6,'-.','Color','[0 0 0]','DisplayName','\fontname {Helvetica} \fontsize{18} s=1.0','LineWidth', 2.0, 'HandleVisibility','off')
 
 
ax = gca; % current axes
ax.FontSize = 22;
set(gca,'XLim',[0 5]);
set(gca,'YLim',[-1 1]);
 
box off
hold off

Here is the error message:

Error using sym/hypergeom (line 43)

Unable to evaluate to Boolean.

Error in sym.useSymForNumeric (line 165)

res = cast(fn(args{:}),superiorfloat(varargin{:}));

Error in hypergeom (line 41)

h = sym.useSymForNumeric(@hypergeom,n,d,z);

Error in TemNuss (line 543)

y1=(-(2.844015460*(1+(2.787032085*(1-4163863*x*(1/4166463)))./((1+1603*x*(1/997)).*(1-x).^2.5))).*hypergeom(((-2.787032085)*(1-4163863*x*(1/4166463)))./((1+1603*x*(1/997)).*(1-x).^2.5),

2-(2.787032085*(1-4163863*x*(1/4166463)))./((1+1603*x*(1/997)).*(1-x).^2.5),

(2.844015460*(1-4163863*x*(1/4166463)))./((1+1603*x*(1/997)).*(1-x).^2.5)).*(1-4163863*x*(1/4166463))./((1+1603*x*(1/997)).*(1-x).^2.5)+2.787032085.*hypergeom(-1-(2.787032085*(1-4163863*x*(1/4166463)))./((1+1603*x*(1/997)).*(1-x).^2.5),

1-(2.787032085*(1-4163863*x*(1/4166463)))./((1+1603*x*(1/997)).*(1-x).^2.5),

(2.844015460*(1-4163863*x*(1/4166463)))./((1+1603*x*(1/997)).*(1-x).^2.5)).*(1-4163863*x*(1/4166463)).*(-1+(2.787032085*(1-4163863*x*(1/4166463)))./((1+1603*x*(1/997)).*(1-x).^2.5))./((1+1603*x*(1/997)).*(1-x).^2.5))./(-(2.844015460*(1+(2.787032085*(1-4163863*x*(1/4166463)))./((1+1603*x*(1/997)).*(1-x).^2.5))).*hypergeom(((-2.787032085)*(1-4163863*x*(1/4166463)))./((1+1603*x*(1/997)).*(1-x).^2.5),

2-(2.787032085*(1-4163863*x*(1/4166463)))./((1+1603*x*(1/997)).*(1-x).^2.5),

(2.844015460*(1-4163863*x*(1/4166463)))./((1+1603*x*(1/997)).*(1-x).^2.5)).*(1-4163863*x*(1/4166463))./((1+1603*x*(1/997)).*(1-x).^2.5)+hypergeom(-1-(2.787032085.*(1-4163863*x*(1/4166463)))./((1+1603*x*(1/997)).*(1-x).^2.5),

1-(2.787032085*(1-4163863*x*(1/4166463)))./((1+1603*x.*(1/997)).*(1-x).^2.5),

(2.844015460*(1-4163863*x*(1/4166463)))./((1+1603*x*(1/997)).*(1-x).^2.5)).*(-1+(2.787032085*(1-4163863*x*(1/4166463)))./((1+1603*x*(1/997)).*(1-x).^2.5)).^2);

[darova]

Can you make your code more clear?

[Ke Le]

One can take only a single expression and try plotting.

Answer 1

[Walter Roberson]

I do not encounter that error. However, the code was pretty slow, so I cleaned it up and told it to optimize the calculations.

Caution: every one of your results is complex valued because of the values that you are taking ^2.5 are mostly negative. In the below code, I plot abs() of the values.

The Q() you see are converting the numbers to symbolic rational numbers. This makes the calculations more consistent and gives greater optimization opportunities (floating point calculations are not commutative but rational calculations are.)

You were using the same floating point constants over 100 times in some cases. I gave names to them.

Next time that you are generating code like you did this time, put in variables in place of the constants and generate the code with the variables and then you can insert assignments of values to the variables. This will make the generated code easier to read and less error prone.

X = linspace(0, 5, 25);

syms x
Q = @(v) sym(v);

C603_ = Q(603);
C997_ = 1/Q(997);
C1603_ = Q(1603);
C4163_ = Q(4163863);
C4164_ = Q(4164863);
C4166_ = 1/Q(4166463);

C0199 = Q(.1992256641);
C0204 = Q(.2040892228);
C0220 = Q(.2205657803);
C0230 = Q(.2306233919);
C0298 = Q(.2988384962);
C0306 = Q(.3061338342);
C0441 = Q(.4411315605);
C0461 = Q(.4612467837);
C1260 = Q(1.260902791);
C1291 = Q(1.291684341);
C1487 = Q(1.498354984);
C1566 = Q(1.566678694);
C1891 = Q(1.891354186);
C1937 = Q(1.937526512);
C2500 = Q(2.5);
C2787 = Q(2.787032085);
C2820 = Q(2.820688929);
C2844 = Q(2.844015460);
C2878 = Q(2.878360445);
C2996 = Q(2.996709968);
C3133 = Q(3.133357388);


P43_46 = C4163_ .* C4166_;
P44_46 = C4164_ .* C4166_;
P1_9 = C1603_ .* C997_;
P6_9 = C603_ .* C997_;

f1 = (-(C2844*(1+(C2787*(1-P43_46.*x))./((1+P1_9.*x).*(1-x).^C2500))).*hypergeom(((-C2787)*(1-P43_46.*x))./((1+P1_9.*x).*(1-x).^C2500), 2-(C2787*(1-P43_46.*x))./((1+P1_9.*x).*(1-x).^C2500), (C2844*(1-P43_46.*x))./((1+P1_9.*x).*(1-x).^C2500)).*(1-P43_46.*x)./((1+P1_9.*x).*(1-x).^C2500)+C2787.*hypergeom(-1-(C2787*(1-P43_46.*x))./((1+P1_9.*x).*(1-x).^C2500), 1-(C2787*(1-P43_46.*x))./((1+P1_9.*x).*(1-x).^C2500), (C2844*(1-P43_46.*x))./((1+P1_9.*x).*(1-x).^C2500)).*(1-P43_46.*x).*(-1+(C2787*(1-P43_46.*x))./((1+P1_9.*x).*(1-x).^C2500))./((1+P1_9.*x).*(1-x).^C2500))./(-(C2844*(1+(C2787*(1-P43_46.*x))./((1+P1_9.*x).*(1-x).^C2500))).*hypergeom(((-C2787)*(1-P43_46.*x))./((1+P1_9.*x).*(1-x).^C2500), 2-(C2787*(1-P43_46.*x))./((1+P1_9.*x).*(1-x).^C2500), (C2844*(1-P43_46.*x))./((1+P1_9.*x).*(1-x).^C2500)).*(1-P43_46.*x)./((1+P1_9.*x).*(1-x).^C2500)+hypergeom(-1-(C2787.*(1-P43_46.*x))./((1+P1_9.*x).*(1-x).^C2500), 1-(C2787*(1-P43_46.*x))./((1+P1_9.*x).*(1-x).^C2500), (C2844*(1-P43_46.*x))./((1+P1_9.*x).*(1-x).^C2500)).*(-1+(C2787*(1-P43_46.*x))./((1+P1_9.*x).*(1-x).^C2500)).^2);
F1 = matlabFunction(f1, 'File', 'F1.m', 'optimize', true);
y1 = F1(X);

plot(X, abs(y1), '-','Color','[0 0 0]','DisplayName','\fontname {Helvetica} \fontsize{18} s=-0.5','LineWidth', 2.0, 'HandleVisibility','off') 
xlabel('\fontname{Times New Roman} Values of x','FontSize',22)
ylabel('\fontname{Times New Roman} Values of y', 'FontSize', 22)
hold on
 
 
f2 = (((-C1260).*(1+(C0199).*(1-P43_46.*x)./((1+P1_9.*x).*(1-x).^C2500))).*hypergeom(((-C0199).*(1-P43_46.*x))./((1+P1_9.*x).*(1-x).^C2500), 2+((-C0199).*(1-P43_46.*x))./((1+P1_9.*x).*(1-x).^C2500), (C1260.*(1-P43_46.*x))./((1+P1_9.*x).*(1-x).^C2500)).*(1-P43_46.*x)./((1+P1_9.*x).*(1-x).^C2500)+C0199.*hypergeom(-1+((-C0199).*(1-P43_46.*x))./((1+P1_9.*x).*(1-x).^C2500), 1+((-C0199).*(1-P43_46.*x))./((1+P1_9.*x).*(1-x).^C2500), (C1260.*(1-P43_46.*x))./((1+P1_9.*x).*(1-x).^C2500)).*(1-P43_46.*x).*(-1+(C0199.*(1-P43_46.*x))./((1+P1_9.*x).*(1-x).^C2500))./((1+P1_9.*x).*(1-x).^C2500))./(-C1891.*hypergeom(((-C0199).*(1-P43_46.*x))./((1+P1_9.*x).*(1-x).^C2500), 2+(-C0199).*(1-P43_46.*x)./((1+P1_9.*x).*(1-x).^C2500), (C1260.*(1-P43_46.*x))./((1+P1_9.*x).*(1-x).^C2500)).*(1+(C0199.*(1-P43_46.*x))./((1+P1_9.*x).*(1-x).^C2500)).*(1-P43_46.*x)./((1+P1_9.*x).*(1-x).^C2500)+hypergeom(-1+((-C0199).*(1-P43_46.*x))./((1+P1_9.*x).*(1-x).^C2500), 1+((-C0199).*(1-P43_46.*x))./((1+P1_9.*x).*(1-x).^C2500), (C1260.*(1-P43_46.*x))./((1+P1_9.*x).*(1-x).^C2500)).*(-1+(C0199.*(1-P43_46.*x))./((1+P1_9.*x).*(1-x).^C2500)).*(-1.+(C0298.*(1-P43_46.*x))./((1+P1_9.*x).*(1-x).^C2500)));
F2 = matlabFunction(f2, 'File', 'F2.m', 'optimize', true);
y2 = F2(X);
 
plot(X, abs(y2), '-','Color','[0 0 0]','DisplayName','\fontname {Helvetica} \fontsize{18} s=-0.5','LineWidth', 2.0, 'HandleVisibility','off')
 
f3 = ((C0220.*(1-(C1487.*(1-P43_46.*x))./((1+P1_9.*x).*(1-x).^C2500))).*hypergeom((C1487.*(1-P43_46.*x))./((1+P1_9.*x).*(1-x).^C2500), 2+(C1487.*(1-P43_46.*x))./((1+P1_9.*x).*(1-x).^C2500), ((-C0220).*(1-P43_46.*x))./((1+P1_9.*x).*(1-x).^C2500)).*(1-P43_46.*x)./((1+P1_9.*x).*(1-x).^C2500)-C1487.*hypergeom(-1+(C1487.*(1-P43_46.*x))./((1+P1_9.*x).*(1-x).^C2500), 1+(C1487.*(1-P43_46.*x))./((1+P1_9.*x).*(1-x).^C2500), ((-C0220).*(1-P43_46.*x))./((1+P1_9.*x).*(1-x).^C2500)).*(1-P43_46.*x).*(-1-(C1487.*(1-P43_46.*x))./((1+P1_9.*x).*(1-x).^C2500))./((1+P1_9.*x).*(1-x).^C2500))./(C0441.*hypergeom((C1487.*(1-P43_46.*x))./((1+P1_9.*x).*(1-x).^C2500), 2+(C1487.*(1-P43_46.*x))./((1+P1_9.*x).*(1-x).^C2500), ((-C0220).*(1-P43_46.*x))./((1+P1_9.*x).*(1-x).^C2500)).*(1-(C1487.*(1-P43_46.*x))./((1+P1_9.*x).*(1-x).^C2500)).*(1-P43_46.*x)./((1+P1_9.*x).*(1-x).^C2500)+hypergeom(-1+(C1487.*(1-P43_46.*x))./((1+P1_9.*x).*(1-x).^C2500), 1+(C1487.*(1-P43_46.*x))./((1+P1_9.*x).*(1-x).^C2500), ((-C0220).*(1-P43_46.*x))./((1+P1_9.*x).*(1-x).^C2500)).*(-1-(C1487.*(1-P43_46.*x))./((1+P1_9.*x).*(1-x).^C2500)).*(-1-(C2996.*(1-P43_46.*x))./((1+P1_9.*x).*(1-x).^C2500)));
F3 = matlabFunction(f3, 'File', 'F3.m', 'optimize', true);
y3 = F3(X);

plot(X, abs(y3), '-','Color','[0 0 0]','DisplayName','\fontname {Helvetica} \fontsize{18} s=-0.5','LineWidth', 2.0, 'HandleVisibility','off')
 
f4 = (-(C2878.*(1+(C2820.*(1-P44_46.*x))./((1+P6_9.*x).*(1-x).^C2500))).*hypergeom(((-C2820).*(1-P44_46.*x))./((1+P6_9.*x).*(1-x).^C2500), 2-(C2820.*(1-P44_46.*x))./((1+P6_9.*x).*(1-x).^C2500), (C2878.*(1-P44_46.*x))./((1+P6_9.*x).*(1-x).^C2500)).*(1-P44_46.*x)./((1+P6_9.*x).*(1-x).^C2500)+C2820.*hypergeom(-1-(C2820.*(1-P44_46.*x))./((1+P6_9.*x).*(1-x).^C2500), 1-(C2820.*(1-P44_46.*x))./((1+P6_9.*x).*(1-x).^C2500), (C2878.*(1-P44_46.*x))./((1+P6_9.*x).*(1-x).^C2500)).*(1-P44_46.*x).*(-1+(C2820.*(1-P44_46.*x))./((1+P6_9.*x).*(1-x).^C2500))./((1+P6_9.*x).*(1-x).^C2500))./(-(C2878.*(1+(C2820.*(1-P44_46.*x))./((1+P6_9.*x).*(1-x).^C2500))).*hypergeom(((-C2820).*(1-P44_46.*x))./((1+P6_9.*x).*(1-x).^C2500), 2-(C2820.*(1-P44_46.*x))./((1+P6_9.*x).*(1-x).^C2500), (C2878.*(1-P44_46.*x))./((1+P6_9.*x).*(1-x).^C2500)).*(1-P44_46.*x)./((1+P6_9.*x).*(1-x).^C2500)+hypergeom(-1-(C2820.*(1-P44_46.*x))./((1+P6_9.*x).*(1-x).^C2500), 1-(C2820.*(1-P44_46.*x))./((1+P6_9.*x).*(1-x).^C2500), (C2878.*(1-P44_46.*x))./((1+P6_9.*x).*(1-x).^C2500)).*(-1+(C2820.*(1-P44_46.*x))./((1+P6_9.*x).*(1-x).^C2500)).^2);
F4 = matlabFunction(f4, 'File', 'F4.m', 'optimize', true);
y4 = F4(X);
plot(X, abs(y4), '-.','Color','[0 0 0]','DisplayName','\fontname {Helvetica} \fontsize{18} MWCNT','LineWidth', 2.0)

f5 = (((-C1291).*(1+(C0204.*(1-P44_46.*x))./((1+P6_9.*x).*(1-x).^C2500))).*hypergeom(((-C0204).*(1-P44_46.*x))./((1+P6_9.*x).*(1-x).^C2500), 2+((-C0204).*(1-P44_46.*x))./((1+P6_9.*x).*(1-x).^C2500), (C1291.*(1-P44_46.*x))./((1+P6_9.*x).*(1-x).^C2500)).*(1-P44_46.*x)./((1+P6_9.*x).*(1-x).^C2500)+C0204.*hypergeom(-1+((-C0204).*(1-P44_46.*x))./((1+P6_9.*x).*(1-x).^C2500), 1+((-C0204).*(1-P44_46.*x))./((1+P6_9.*x).*(1-x).^C2500), (C1291.*(1-P44_46.*x))./((1+P6_9.*x).*(1-x).^C2500)).*(1-P44_46.*x).*(-1+(C0204.*(1-P44_46.*x))./((1+P6_9.*x).*(1-x).^C2500))./((1+P6_9.*x).*(1-x).^C2500))./(-C1937.*hypergeom(((-C0204).*(1-P44_46.*x))./((1+P6_9.*x).*(1-x).^C2500), 2+((-C0204).*(1-P44_46.*x))./((1+P6_9.*x).*(1-x).^C2500), (C1291.*(1-P44_46.*x))./((1+P6_9.*x).*(1-x).^C2500)).*(1+(C0204.*(1-P44_46.*x))./((1+P6_9.*x).*(1-x).^C2500)).*(1-P44_46.*x)./((1+P6_9.*x).*(1-x).^C2500)+hypergeom(-1+((-C0204).*(1-P44_46.*x))./((1+P6_9.*x).*(1-x).^C2500), 1+((-C0204).*(1-P44_46.*x))./((1+P6_9.*x).*(1-x).^C2500), (C1291.*(1-P44_46.*x))./((1+P6_9.*x).*(1-x).^C2500)).*(-1+(C0204.*(1-P44_46.*x))./((1+P6_9.*x).*(1-x).^C2500)).*(-1.+(C0306.*(1-P44_46.*x))./((1+P6_9.*x).*(1-x).^C2500)));
F5 = matlabFunction(f5, 'File', 'F5.m', 'optimize', true);
y5 = F5(X);
plot(X, abs(y5), '-.','Color','[0 0 0]','DisplayName','\fontname {Helvetica} \fontsize{18} s=1.0','LineWidth', 2.0, 'HandleVisibility','off')
 
 
f6 =((C0230.*(1-(C1566.*(1-P44_46.*x))./((1+P6_9.*x).*(1-x).^C2500))).*hypergeom((C1566.*(1-P44_46.*x))./((1+P6_9.*x).*(1-x).^C2500), 2+(C1566.*(1-P44_46.*x))./((1+P6_9.*x).*(1-x).^C2500), ((-C0230).*(1-P44_46.*x))./((1+P6_9.*x).*(1-x).^C2500)).*(1-P44_46.*x)./((1+P6_9.*x).*(1-x).^C2500)-C1566.*hypergeom(-1+(C1566.*(1-P44_46.*x))./((1+P6_9.*x).*(1-x).^C2500), 1+(C1566.*(1-P44_46.*x))./((1+P6_9.*x).*(1-x).^C2500), ((-C0230).*(1-P44_46.*x))./((1+P6_9.*x).*(1-x).^C2500)).*(1-P44_46.*x).*(-1-(C1566.*(1-P44_46.*x))./((1+P6_9.*x).*(1-x).^C2500))./((1+P6_9.*x).*(1-x).^C2500))./(C0461.*hypergeom((C1566.*(1-P44_46.*x))./((1+P6_9.*x).*(1-x).^C2500), 2+(C1566.*(1-P44_46.*x))./((1+P6_9.*x).*(1-x).^C2500), ((-C0230).*(1-P44_46.*x))./((1+P6_9.*x).*(1-x).^C2500)).*(1-(C1566.*(1-P44_46.*x))./((1+P6_9.*x).*(1-x).^C2500)).*(1-P44_46.*x)./((1+P6_9.*x).*(1-x).^C2500)+hypergeom(-1+(C1566.*(1-P44_46.*x))./((1+P6_9.*x).*(1-x).^C2500), 1+(C1566.*(1-P44_46.*x))./((1+P6_9.*x).*(1-x).^C2500), ((-C0230).*(1-P44_46.*x))./((1+P6_9.*x).*(1-x).^C2500)).*(-1-(C1566.*(1-P44_46.*x))./((1+P6_9.*x).*(1-x).^C2500)).*(-1-(C3133.*(1-P44_46.*x))./((1+P6_9.*x).*(1-x).^C2500)));
F6 = matlabFunction(f6, 'File', 'F6.m', 'optimize', true);
y6 = F6(X);
plot(X, abs(y6), '-.','Color','[0 0 0]','DisplayName','\fontname {Helvetica} \fontsize{18} s=1.0','LineWidth', 2.0, 'HandleVisibility','off')


ax = gca; % current axes
ax.FontSize = 22;
set(gca,'XLim',[0 5]);
set(gca,'YLim',[-1 12]);
 
box off
hold off

[Walter Roberson]

Unfortunately I forgot that there is currently a bug that can cause mis-optimization when you use matlabFunction with 'optimize', true . You should probably change the 'optimize' to false to be sure.

(Or you could test both ways, and see if they give the same result; the bug might not affect all expressions.)

[Ke Le]

It worked for me. I love the part when the code is running very fast. Thank you very much. I just wonder how the first time, you didn't encouter an issue? It would mean we're using different versions or what should I do not to encounter such issues in future?

[Walter Roberson]

I was working in R2020a; which release were you working in?

[Ke Le]

I am wokring with the same system. It is because I didn't install the full version, that is, I didn't opt some programs for my installation?

[Walter Roberson]

Gosh your original code is slow!

How long did you have to execute before you got the error about unable to convert to boolean?

[Ke Le]

The previous ones were good, but a new value for a paramter made it too slow. The last time I ran it took me half an hour or even more.