How can I wide the space between curves in the figure and between the numbers on the curves?

Unrecognized function or variable 'xsphere'.

[Shreen El-Sapa]

Thanks you are right.

Answer 1

[dpb]

The only thing that can separate the lines more would be to have fewer of them; the data are what they are as far as the magnitude and location of a given surface outline. Experiment with setting the contour function optional levels input to some set of specifcally chosen levels or a fewer number. You can control the spacing between the labels, but they're either 'on' or 'off' and it puts them where it wants; you can't move them around. You could make the fontsize smaller -- well, maybe you can't, either; it doesn't seem to be a visible property.

The above code is missing the other half of the data, it seems, but that probably doesn't really matter to the question.

The normal way would be to use 'LevelStep' with a larger value, but the range of data in you have is so limited, there's not much to be done.

lambda=2.5;
eta=1;
%beta1=10.^10;beta2=10.^10;
beta1=10;beta2=10;
alpha=20;
eta1=1;w=1;k=(1/eta.^2).^(0.5);  a=1;   % w=w2/w1
alpha1=((k.^2+(k.^4-4.*alpha.^2).^(0.5))./2).^(0.5);
alpha2=((k.^2-(k.^4-4.*alpha.^2).^(0.5))./2).^(0.5);
a11=(-(alpha1 .^ 2 .* eta - 2 .* eta - 2 .* eta1 - 1) .* alpha1 ./ beta1 .* besselk(0.1e1 ./ 0.2e1, alpha1) - ((alpha1 .^ 2 .* eta) - beta1 - (6 .* eta) - (6 .* eta1) - 0.3e1) .* besselk(0.3e1 ./ 0.2e1, alpha1) ./ beta1) ; ...
    a12=(-alpha2 .* (alpha2 .^ 2 .* eta - 2 .* eta - 2 .* eta1 - 1) ./ beta1 .* besselk(0.1e1 ./ 0.2e1, alpha2) - ((alpha2 .^ 2 .* eta) - beta1 - (6 .* eta) - (6 .* eta1) - 0.3e1) .* besselk(0.3e1 ./ 0.2e1, alpha2) ./ beta1) ;
a13= ((alpha1 .^ 2 .* eta - 2 .* eta - 2 .* eta1 - 1) .* alpha1 ./ beta1 .* besseli(0.1e1 ./ 0.2e1, alpha1) - ((alpha1 .^ 2 .* eta) - beta1 - (6 .* eta) - (6 .* eta1) - 0.3e1) .* besseli(0.3e1 ./ 0.2e1, alpha1) ./ beta1) ;
a14=(alpha2 .* (alpha2 .^ 2 .* eta - 2 .* eta - 2 .* eta1 - 1) ./ beta1 .* besseli(0.1e1 ./ 0.2e1, alpha2) - ((alpha2 .^ 2 .* eta) - beta1 - (6 .* eta) - (6 .* eta1) - 0.3e1) .* besseli(0.3e1 ./ 0.2e1, alpha2) ./ beta1) ;
a21=(-0.2e1 .* (eta + eta1) .* alpha1 .* besselk(0.1e1 ./ 0.2e1, alpha1) + (-0.2e1 .* alpha1 .^ 2 .* eta - 0.6e1 .* eta - 0.6e1 .* eta1) .* besselk(0.3e1 ./ 0.2e1, alpha1)) ;
a22=(-0.2e1 .* (eta + eta1) .* alpha2 .* besselk(0.1e1 ./ 0.2e1, alpha2) + (-0.2e1 .* alpha2 .^ 2 .* eta - 0.6e1 .* eta - 0.6e1 .* eta1) .* besselk(0.3e1 ./ 0.2e1, alpha2)) ;
a23=(0.2e1 .* (eta + eta1) .* alpha1 .* besseli(0.1e1 ./ 0.2e1, alpha1) + (-0.2e1 .* alpha1 .^ 2 .* eta - 0.6e1 .* eta - 0.6e1 .* eta1) .* besseli(0.3e1 ./ 0.2e1, alpha1));
a24=(0.2e1 .* (eta + eta1) .* besseli(0.1e1 ./ 0.2e1, alpha2) .* alpha2 + (-0.2e1 .* alpha2 .^ 2 .* eta - 0.6e1 .* eta - 0.6e1 .* eta1) .* besseli(0.3e1 ./ 0.2e1, alpha2));
a31=((alpha1 .^ 2 .* eta .* lambda .^ 2 - lambda .^ 2 - 2 .* eta - 2 .* eta1) .* alpha1 .* (lambda .^ (-0.5e1 ./ 0.2e1)) ./ beta2 .* besselk(0.1e1 ./ 0.2e1, (lambda .* alpha1)) + ((alpha1 .^ 2 .* eta .* lambda .^ 2) + beta2 .* (lambda .^ 3) - (3 .* lambda .^ 2) - (6 .* eta) - (6 .* eta1)) .* (lambda .^ (-0.7e1 ./ 0.2e1)) ./ beta2 .* besselk(0.3e1 ./ 0.2e1, (lambda .* alpha1))) ;
a32= (alpha2 .* (alpha2 .^ 2 .* eta .* lambda .^ 2 - lambda .^ 2 - 2 .* eta - 2 .* eta1) .* (lambda .^ (-0.5e1 ./ 0.2e1)) ./ beta2 .* besselk(0.1e1 ./ 0.2e1, (lambda .* alpha2)) + ((alpha2 .^ 2 .* eta .* lambda .^ 2) + beta2 .* (lambda .^ 3) - (3 .* lambda .^ 2) - (6 .* eta) - (6 .* eta1)) .* (lambda .^ (-0.7e1 ./ 0.2e1)) ./ beta2 .* besselk(0.3e1 ./ 0.2e1, (lambda .* alpha2))) ;
a33= (-(alpha1 .^ 2 .* eta .* lambda .^ 2 - lambda .^ 2 - 2 .* eta - 2 .* eta1) .* alpha1 .* (lambda .^ (-0.5e1 ./ 0.2e1)) ./ beta2 .* besseli(0.1e1 ./ 0.2e1, (lambda .* alpha1)) + ((alpha1 .^ 2 .* eta .* lambda .^ 2) + beta2 .* (lambda .^ 3) - (3 .* lambda .^ 2) - (6 .* eta) - (6 .* eta1)) .* (lambda .^ (-0.7e1 ./ 0.2e1)) ./ beta2 .* besseli(0.3e1 ./ 0.2e1, (lambda .* alpha1))) ;
a34= (-alpha2 .* (alpha2 .^ 2 .* eta .* lambda .^ 2 - lambda .^ 2 - 2 .* eta - 2 .* eta1) .* (lambda .^ (-0.5e1 ./ 0.2e1)) ./ beta2 .* besseli(0.1e1 ./ 0.2e1, (lambda .* alpha2)) + ((alpha2 .^ 2 .* eta .* lambda .^ 2) + beta2 .* (lambda .^ 3) - (3 .* lambda .^ 2) - (6 .* eta) - (6 .* eta1)) .* (lambda .^ (-0.7e1 ./ 0.2e1)) ./ beta2 .* besseli(0.3e1 ./ 0.2e1, (lambda .* alpha2)));
a41=(-0.2e1 .* lambda .^ (-0.3e1 ./ 0.2e1) .* (eta + eta1) .* alpha1 .* besselk(0.1e1 ./ 0.2e1, lambda .* alpha1) - 0.2e1 .* (alpha1 .^ 2 .* eta .* lambda .^ 2 + 0.3e1 .* eta + 0.3e1 .* eta1) .* lambda .^ (-0.5e1 ./ 0.2e1) .* besselk(0.3e1 ./ 0.2e1, lambda .* alpha1)) ;
a42=(-0.2e1 .* lambda .^ (-0.3e1 ./ 0.2e1) .* (eta + eta1) .* alpha2 .* besselk(0.1e1 ./ 0.2e1, lambda .* alpha2) - 0.2e1 .* (alpha2 .^ 2 .* eta .* lambda .^ 2 + 0.3e1 .* eta + 0.3e1 .* eta1) .* lambda .^ (-0.5e1 ./ 0.2e1) .* besselk(0.3e1 ./ 0.2e1, lambda .* alpha2)) ;
a43= (0.2e1 .* lambda .^ (-0.3e1 ./ 0.2e1) .* (eta + eta1) .* alpha1 .* besseli(0.1e1 ./ 0.2e1, lambda .* alpha1) - 0.2e1 .* (alpha1 .^ 2 .* eta .* lambda .^ 2 + 0.3e1 .* eta + 0.3e1 .* eta1) .* lambda .^ (-0.5e1 ./ 0.2e1) .* besseli(0.3e1 ./ 0.2e1, lambda .* alpha1)) ;
a44= (0.2e1 .* lambda .^ (-0.3e1 ./ 0.2e1) .* (eta + eta1) .* alpha2 .* besseli(0.1e1 ./ 0.2e1, lambda .* alpha2) - 0.2e1 .* (alpha2 .^ 2 .* eta .* lambda .^ 2 + 0.3e1 .* eta + 0.3e1 .* eta1) .* lambda .^ (-0.5e1 ./ 0.2e1) .* besseli(0.3e1 ./ 0.2e1, lambda .* alpha2)) ;
A1 = (((a14 .* lambda .* w - a34) .* a43 - a44 .* (a13 .* lambda .* w - a33)) .* a22 + ((-a14 .* lambda .* w + a34) .* a42 + a44 .* (a12 .* lambda .* w - a32)) .* a23 + ((a13 .* lambda .* w - a33) .* a42 - a43 .* (a12 .* lambda .* w - a32)) .* a24) ./ (((-a11 .* a34 + a14 .* a31) .* a43 + (a11 .* a33 - a13 .* a31) .* a44 - a41 .* (-a13 .* a34 + a14 .* a33)) .* a22 + ((a11 .* a34 - a14 .* a31) .* a42 + (-a11 .* a32 + a12 .* a31) .* a44 + a41 .* (-a12 .* a34 + a14 .* a32)) .* a23 + ((-a11 .* a33 + a13 .* a31) .* a42 + (a11 .* a32 - a12 .* a31) .* a43 - a41 .* (-a12 .* a33 + a13 .* a32)) .* a24 - ((a13 .* a34 - a14 .* a33) .* a42 + (-a12 .* a34 + a14 .* a32) .* a43 - a44 .* (-a12 .* a33 + a13 .* a32)) .* a21) ;
B1 = (((-a14 .* lambda .* w + a34) .* a43 + a44 .* (a13 .* lambda .* w - a33)) .* a21 + ((a14 .* lambda .* w - a34) .* a41 - a44 .* (a11 .* lambda .* w - a31)) .* a23 - ((a13 .* lambda .* w - a33) .* a41 - a43 .* (a11 .* lambda .* w - a31)) .* a24) ./ (((a12 .* a34 - a14 .* a32) .* a43 + a44 .* (-a12 .* a33 + a13 .* a32) + a42 .* (-a13 .* a34 + a14 .* a33)) .* a21 + (a41 .* (-a12 .* a34 + a14 .* a32) + (-a11 .* a32 + a12 .* a31) .* a44 - a42 .* (-a11 .* a34 + a14 .* a31)) .* a23 + ((a12 .* a33 - a13 .* a32) .* a41 + (a11 .* a32 - a12 .* a31) .* a43 + (-a11 .* a33 + a13 .* a31) .* a42) .* a24 + a22 .* ((a13 .* a34 - a14 .* a33) .* a41 + (-a11 .* a34 + a14 .* a31) .* a43 - a44 .* (-a11 .* a33 + a13 .* a31))) ;
C1 = (((a14 .* lambda .* w - a34) .* a42 - a44 .* (a12 .* lambda .* w - a32)) .* a21 + ((-a14 .* lambda .* w + a34) .* a41 + a44 .* (a11 .* lambda .* w - a31)) .* a22 + ((a12 .* lambda .* w - a32) .* a41 - a42 .* (a11 .* lambda .* w - a31)) .* a24) ./ ((a42 .* (-a13 .* a34 + a14 .* a33) + a44 .* (-a12 .* a33 + a13 .* a32) - (-a12 .* a34 + a14 .* a32) .* a43) .* a21 + ((a13 .* a34 - a14 .* a33) .* a41 + (a11 .* a33 - a13 .* a31) .* a44 + (-a11 .* a34 + a14 .* a31) .* a43) .* a22 + ((a12 .* a33 - a13 .* a32) .* a41 + (-a11 .* a33 + a13 .* a31) .* a42 - a43 .* (-a11 .* a32 + a12 .* a31)) .* a24 - ((a12 .* a34 - a14 .* a32) .* a41 + a42 .* (-a11 .* a34 + a14 .* a31) - (-a11 .* a32 + a12 .* a31) .* a44) .* a23) ;
D1 = (((-a13 .* lambda .* w + a33) .* a42 + a43 .* (a12 .* lambda .* w - a32)) .* a21 + ((a13 .* lambda .* w - a33) .* a41 - a43 .* (a11 .* lambda .* w - a31)) .* a22 - ((a12 .* lambda .* w - a32) .* a41 - a42 .* (a11 .* lambda .* w - a31)) .* a23) ./ (((a12 .* a34 - a14 .* a32) .* a43 + a44 .* (-a12 .* a33 + a13 .* a32) + a42 .* (-a13 .* a34 + a14 .* a33)) .* a21 + a22 .* ((a13 .* a34 - a14 .* a33) .* a41 + (-a11 .* a34 + a14 .* a31) .* a43 - a44 .* (-a11 .* a33 + a13 .* a31)) + ((a11 .* a34 - a14 .* a31) .* a42 + (-a11 .* a32 + a12 .* a31) .* a44 + a41 .* (-a12 .* a34 + a14 .* a32)) .* a23 + ((a12 .* a33 - a13 .* a32) .* a41 + (-a11 .* a33 + a13 .* a31) .* a42 - a43 .* (-a11 .* a32 + a12 .* a31)) .* a24);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
Rmin = 1;
Rmax = 2.5;
range = -Rmax:0.05:Rmax;
[x,y] = meshgrid(range);
r = sqrt(x.^2+y.^2);
%v1=real((A1 .* besselk(0.3e1 ./ 0.2e1, r .* alpha1) + B1 .* besselk(0.3e1 ./ 0.2e1, r .* alpha2) + C1 .* besseli(0.3e1 ./ 0.2e1, r .* alpha1) + D1 .* besseli(0.3e1 ./ 0.2e1, r .* alpha2)) .* r .^ (-0.1e1 ./ 0.2e1)) ;
v1=(A1 .* besselk(0.3e1 ./ 0.2e1, r .* alpha1) + B1 .* besselk(0.3e1 ./ 0.2e1, r .* alpha2) + C1 .* besseli(0.3e1 ./ 0.2e1, r .* alpha1) + D1 .* besseli(0.3e1 ./ 0.2e1, r .* alpha2)) .* r .^ (-0.1e1 ./ 0.2e1) ;
v1(r<Rmin)=NaN;
v1(r>Rmax)=NaN;
v1(y<0) = NaN;
hC=contour(x,y,v1,'ShowText','on','LabelFormat','%0.2f','LabelSpacing',300,'LevelStep',0.15);
%p1=contour(x,y,v1,'--k','LineWidth',1);
%p2=contour(x,y,v1,[0.02 0.02],'--b','LineWidth',1);
%p3=contour(x,y,v1,[0.3 0.3],'--r','LineWidth',1.,'ShowText','on');
%p4=contour(x,y,v1,[.4 .4],'--g','LineWidth',1.,'ShowText','on');
hold on
theta = linspace(0,pi,100);
xfill = Rmin*cos(theta);
yfill = Rmin*sin(theta);
fill([-Rmin,Rmin,xfill],[0,0,yfill],[0.7 0.7 0.7])
%plot(xsphere,ysphere,'Color',"k")
%plot(xsphere,ysphere,'Color','k','LineWidth',1.1)
%hold off
colorbar
axis equal
ylim([0 Rmax])
title('$(10)~\hat{\beta_1}=\hat{\beta_2}=10,\;\alpha=10,\;\lambda=2.5\;\hat{\eta}=\hat{\eta}=1.0;\hat{\Omega}=1.0$','Interpreter','latex','FontSize',10,'FontName','Times New Roman','FontWeight','Normal')

The above is with

hC=contour(x,y,v1,'ShowText','on','LabelFormat','%0.2f','LabelSpacing',300,'LevelStep',0.15);

"Salt to suit!" from there -- that you can't set the font size and that it doesn't have enough smarts to not put the labels all on roughly the radial makes for difficulty in getting the labels to not overwrite each other. All the spacing control there is is a multiplier about how far apart they are (in some unspecified measure), but not a way to rotate a given contour's labels relative to others--here, being able to rotate the 0.15 level say beteen 10 and 30 degrees counterclockwise would make a big difference in appearance.

You'll just have to play with what controls there are and see what you can come up with that suits.

[dpb]

"...that you can't set the font size"

It does boggle the mind that the font size, etc., for the contour labels is total opaque -- even <Yair's UNDOCUMENTED tool> can't find handles to those text/annotation objects.