Having problem with fixing the issue
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Hi guys.
Here are some weird functions which I'm trying to plot. I am a novice and did a few more graphs smoothly, however, this one is a bit more tricky. Seems like I'm having some problem with sytax or so. Looking for possible help.
Thanks
Waqar
x = linspace(0,5);
y1=(-15.17006719-10.19830710*I)*((-.3397894164*2^(2/3)-2.584061447*2^(1/3)+15.96541878)*hypergeom([4.811602425], [6.811602422], -6.723676050*exp(-(-.3666666667+.6297451706*2^(2/3)+.1067451175*2^(1/3))*x))+(-11.74363984+.3386696355*2^(2/3)+.9999999998*2^(1/3))*exp(-(-.3666666667+.6297451706*2^(2/3)+.1067451175*2^(1/3))*x)*hypergeom([5.811602424], [7.811602422], -6.723676050*exp(-(-.3666666667+.6297451706*2^(2/3)+.1067451175*2^(1/3))*x)))*(-exp(-(-.3666666667+.6297451706*2^(2/3)+.1067451175*2^(1/3))*x))^4.811602421;
plot(x,y1,'-.','Color','[0 0 0]','DisplayName','\fontname {Helvetica} \fontsize{20} \kappa;=0.1, s=-0.1','LineWidth', 2.0)
xlabel('\fontname{Times New Roman} Values of x', 'FontSize', 22)
ylabel('\fontname{Times New Roman} Velocity Profile','FontSize',22')
hold on
y2=(-41.76167543-277.1087639*I)*(-exp(-.6942370405*x))^4.547612589*((0.6153550094e-1*2^(2/3)-2.648960805*2^(1/3)+5.574199339)*hypergeom([4.547612586], [6.547612585], -8.572516010*exp(-.6942370405*x))+(-4.013958993+.1566293604*2^(2/3)+1.000000000*2^(1/3))*exp(-.6942370405*x)*hypergeom([5.547612584], [7.547612587], -8.572516010*exp(-.6942370405*x)));
plot(x,y2, ':','Color','[0 0 0]','DisplayName','\fontname {Helvetica} \fontsize{20} \kappa;=0.1, s=-0.3','LineWidth', 2.0)
y3=(8.054902998+2.463354463*I)*(-exp(-.8175736472*x))^3.90552941*((-2.482855195*2^(1/3)+14.73597244-.2149702398*2^(2/3))*hypergeom([3.905529413], [5.905529410], -5.761721393*exp(-.8175736472*x))+(-10.71834160+.4453954039*2^(2/3)+1.000000000*2^(1/3))*exp(-.8175736472*x)*hypergeom([4.905529411], [6.905529412], -5.761721393*exp(-.8175736472*x)));
plot(x,y3,'--','Color','[0 0 0]','DisplayName','\fontname {Helvetica} \fontsize{20} \kappa;=0.2, s=-0.1','LineWidth', 2.0)
y4=(-12.45342459+98.65993194*I)*((5.141075166+.1059158437*2^(2/3)-2.574899769*2^(1/3))*hypergeom([3.460032462], [5.460032468], -7.288618279*exp(-.7424204657*x))+(-3.715037183+.1994232887*2^(2/3)+1.000000000*2^(1/3))*exp(-.7424204657*x)*hypergeom([4.460032463], [6.460032464], -7.288618279*exp(-.7424204657*x)))*(-exp(-.7424204657*x))^3.460032466;
plot(x,y4,'Color','[0 0 0]','DisplayName','\fontname {Helvetica} \fontsize{20} \kappa;=0.2, s=-0.3','LineWidth', 2.0)
ax = gca;
ax.FontSize = 19;
set(gca,'XLim',[0 5]);
set(gca,'YLim',[0 1]);
set(gca,'XTick',[0 1 2 3 4 5])
box off
hold off
lgd = legend;
lgd.FontSize = 20;
lgd.Title.String = 'Values of \lambda';
legend;
legend('boxoff')
5 Comments
Walter Roberson
on 10 May 2020
Maple would generate a complex number in that situation as well.
eta := 2;
eta := 2
(-exp(-0.6942370405*eta))^4.547612589;
-0.0002697804212 + 0.001790122601 I
Answers (2)
Walter Roberson
on 10 May 2020
lambda = zeta.^(2/3)
However if you need negative values to have positive results, then
lambda = zeta.^2.^(1/3)
4 Comments
Walter Roberson
on 11 May 2020
In the below, the character vectors for y1_, y2_, y3_, y4_ are exactly the formulas you had in your code. The below code automatically vectorizes the formulas so there will not be any mistakes.
I = 1i;
y1_ = '(-15.17006719-10.19830710*I)*((-.3397894164*2^(2/3)-2.584061447*2^(1/3)+15.96541878)*hypergeom([4.811602425], [6.811602422], -6.723676050*exp(-(-.3666666667+.6297451706*2^(2/3)+.1067451175*2^(1/3))*x))+(-11.74363984+.3386696355*2^(2/3)+.9999999998*2^(1/3))*exp(-(-.3666666667+.6297451706*2^(2/3)+.1067451175*2^(1/3))*x)*hypergeom([5.811602424], [7.811602422], -6.723676050*exp(-(-.3666666667+.6297451706*2^(2/3)+.1067451175*2^(1/3))*x)))*(-exp(-(-.3666666667+.6297451706*2^(2/3)+.1067451175*2^(1/3))*x))^4.811602421';
y2_ = '(-41.76167543-277.1087639*I)*(-exp(-.6942370405*x))^4.547612589*((0.6153550094e-1*2^(2/3)-2.648960805*2^(1/3)+5.574199339)*hypergeom([4.547612586], [6.547612585], -8.572516010*exp(-.6942370405*x))+(-4.013958993+.1566293604*2^(2/3)+1.000000000*2^(1/3))*exp(-.6942370405*x)*hypergeom([5.547612584], [7.547612587], -8.572516010*exp(-.6942370405*x)))';
y3_ = '(8.054902998+2.463354463*I)*(-exp(-.8175736472*x))^3.90552941*((-2.482855195*2^(1/3)+14.73597244-.2149702398*2^(2/3))*hypergeom([3.905529413], [5.905529410], -5.761721393*exp(-.8175736472*x))+(-10.71834160+.4453954039*2^(2/3)+1.000000000*2^(1/3))*exp(-.8175736472*x)*hypergeom([4.905529411], [6.905529412], -5.761721393*exp(-.8175736472*x)))';
y4_ = '(-12.45342459+98.65993194*I)*((5.141075166+.1059158437*2^(2/3)-2.574899769*2^(1/3))*hypergeom([3.460032462], [5.460032468], -7.288618279*exp(-.7424204657*x))+(-3.715037183+.1994232887*2^(2/3)+1.000000000*2^(1/3))*exp(-.7424204657*x)*hypergeom([4.460032463], [6.460032464], -7.288618279*exp(-.7424204657*x)))*(-exp(-.7424204657*x))^3.460032466';
y1 = str2fun(['@(x,I)', vectorize(y1_)]);
y2 = str2fun(['@(x,I)', vectorize(y2_)]);
y3 = str2fun(['@(x,I)', vectorize(y3_)]);
y4 = str2fun(['@(x,I)', vectorize(y4_)]);
x = linspace(0,5);
plot(x,y1(x,I),'-.','Color','[0 0 0]','DisplayName','\fontname {Helvetica} \fontsize{20} \kappa;=0.1, s=-0.1','LineWidth', 2.0)
xlabel('\fontname{Times New Roman} Values of x', 'FontSize', 22)
ylabel('\fontname{Times New Roman} Velocity Profile','FontSize',22')
hold on
plot(x,y2(x,I), ':','Color','[0 0 0]','DisplayName','\fontname {Helvetica} \fontsize{20} \kappa;=0.1, s=-0.3','LineWidth', 2.0)
plot(x,y3(x,I),'--','Color','[0 0 0]','DisplayName','\fontname {Helvetica} \fontsize{20} \kappa;=0.2, s=-0.1','LineWidth', 2.0)
plot(x,y4(x,I),'Color','[0 0 0]','DisplayName','\fontname {Helvetica} \fontsize{20} \kappa;=0.2, s=-0.3','LineWidth', 2.0)
ax = gca;
ax.FontSize = 19;
set(gca,'XLim',[0 5]);
set(gca,'YLim',[0 1]);
set(gca,'XTick',[0 1 2 3 4 5])
box off
hold off
lgd = legend;
lgd.FontSize = 20;
lgd.Title.String = 'Values of \lambda';
legend;
legend('boxoff')
Ke Le
on 12 May 2020
4 Comments
Walter Roberson
on 21 May 2020
[number] asks MATLAB to build a vector that contains only the number. But in MATLAB every scalar is the exact same thing as a vector of length 1, so as far as MATLAB is concerned, [123] has an identical run-time representation as 123 without [] . The only difference is small run-time penalty.
The y1_ etc version automatically vectorizes so that you do not need to make the changes yourself (potentially missing some of them)
Ignoring the imaginary part is an important change though.
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