Having problem with fixing the issue

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')

[Walter Roberson]

Is it or is it ?

[Ke Le]

Dear Walter, it is \lambda=\zeta^(2/3).

[Walter Roberson]

The only thing I see obviously wrong is that

xlabel('\fontname{Times New Roman} Values of \x', 'FontSize', 22)

should be using something other than \x

I can make a guess that I is probably sqrt(-1)

You are generating complex values regardless of whether I is sqrt(-1) or is real valued. Look at your

(-exp(-.6942370405*eta))^4.547612589

exp(something) is going to be positive for real-valued eta, and - of that is going to be negative, and when that negative is raised to a fraction such as 4.54whatever then you are going to get a complex value.

[Ke Le]

That is very true. So, it would mean I should go back to the other tools (Maple, Mathematica etc) beacsue I can't do it here in Matlab.

[Walter Roberson]

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

Answer 1

[Walter Roberson]

lambda = zeta.^(2/3)

However if you need negative values to have positive results, then

lambda = zeta.^2.^(1/3)

[Ke Le]

In fact, what I'm trying is to convert these longer function into Matlab language from Maple, where I see no issue. In Matlab it shows some sort of this issue:

Error using *

Incorrect dimensions for matrix multiplication. Check that the number of columns in the first matrix matches the number of rows in the

second matrix. To perform elementwise multiplication, use '.*'.

[Walter Roberson]

In MATLAB, * is the algebraic matrix multiplication operator, inner product. You are working with row vectors and asking to * those row vectors, which is a dimension error for inner product. You should convert all of your * to .* and all of your ^ to .^ (though you can use * or ^ if you are certain the parts are scalar.) For example,

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;

[Ke Le]

That's perfect for the first expression. Is there any further explanation for dimension error issue? I can't actually work out with rest of the three expressions.

[Walter Roberson]

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')

Answer 2

[Ke Le]

Great. Thank you very much

[Walter Roberson]

You accepted your own Answer, which implies that you came up with a different solution that works for you when the other Answers do not. It would be beneficial for you to post that alternative solution so that people could study it and see how your needs turned out to differ from what volunteers came up with.

[Ke Le]

Walter, there's till some running issue with your code. What I did:

1. Remove [ ] in Hypergeometric to () or even leave it without ()
2. Replace * and ^ with .* and .^ (you said it earlier and it helped)
3. Ignore the imaginary part in every expression

[Walter Roberson]

[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.

[Ke Le]

Very true. Thanks