How to plot a Vector Field from symbolic Matrix?

This code will be used to help me study Maxwell's equations using vector fields presented in Cylindrical Coordinates. I am a lowly Electronics Technician reviewing physics, so that I may one day have a shot at completing Electrical Engineering Curriculum when I return back to Engineering School one day. I have consulted with 3 of the best engineers that use MatLab from my work place, and none of them have experience with the symbolic package. I have tinkered more around this code over the Easter weekend, but I haven't presented any of my modified variants.

INPUT: "cyl" - A vector in cylindrical coordinates.

"A Cylindrical-to-Cartesian transformation matrix is specified called "trans".

OUTPUT: "rec" - rectangular coordinate obtained by matrix multiplication.

So far, it LOOKS like the matrix obtained is correct, but something is happening. A 2D plot is made, but the following error message is given:

 error: set: invalid number of arguments error: called from _quiver_ at line 301 column 7 quiver3 at line 83 column 10

It seems to me like I am using the correct number of arguments, so I don't understand why there is a problem.

_____________MY CODE:_______________

clear

syms x y z phi(x,y) r(x,y,z) u v w trans cyl rec

phi = atan2(y,x);

r = sqrt(x.^2+y.^2);

trans = [cos(phi), -sin(phi), 0; sin(phi), cos(phi), 0; phi.*0, 0, 1];

cyl = [z ./ r;r; r.^2.*z];

rec = trans * cyl;

u = rec(1,1);

v = rec(2,1);

w = rec(3,1);

[x,y,z] = meshgrid([-1:.2:1]);

figure

quiver3(x,y,z,u,v,w)

[DJ Mac Farlane]

Here is another Example that WORKS:

clear

pkg load symbolic;

syms x y z phi(x,y) r(x,y,z) u v w trans cyl rec

[x,y] = meshgrid([-1:.2:1]);
u = sin(pi*y/2);
v = -sin(pi*x/2);

#rec = [sin(pi*y/2), -sin(pi*x/2)]
#u = rec(1,1);
#v = rec(1,2);

#w = rec(3,1);

figure

quiver(x,y,u,v);

VS. SAME EXAMPLE THAT DOES NOT WORK:

clear

pkg load symbolic;

syms x y z phi(x,y) r(x,y,z) u v w trans cyl rec

[x,y] = meshgrid([-1:.2:1]);
#u = sin(pi*y/2);
#v = -sin(pi*x/2);

rec = [sin(pi*y/2), -sin(pi*x/2)]
u = rec(1,1);
v = rec(1,2);

#w = rec(3,1);

figure

quiver(x,y,u,v);

[DJ Mac Farlane]

I have found the answer. It looks like the key to converting a symbolic function to a form that is usable by quiver3 is by using function_handle() or equivalently, matlabFunction(). My corrected code is below:

clear

syms x y z 

phi = atan2(y,x);

r = sqrt(x.^2+y.^2);

trans = [cos(phi), -sin(phi), 0; sin(phi), cos(phi), 0; phi.*0, 0, 1];

cyl = [z ./ r;r; r.^2.*z];

#cyl = [1 ./ r;0; 0];

rec = trans * cyl;

u = matlabFunction(rec(1,1));

v = matlabFunction(rec(2,1));

w = matlabFunction(rec(3,1));

[X,Y,Z] = meshgrid([-1:.5:1]);

figure

quiver3(X,Y,Z,u(X,Y,Z),v(X,Y,Z),w(X,Y,Z))

[Andrew Newell]

Nicely done! Just for curiosity, what's with the hash marks? Is that the comment symbol on your machine? Normally it's a percent sign.

Answer 1

[Walter Roberson]

"pkg load" and use of # for comments tells us that you are using Octave rather than MATLAB.

[Andrew Newell]

I guess there isn't an Octave Answers!

[DJ Mac Farlane]

I chose Octave as my weapon of choice for the high compatibility with MatLab, and having a better chance of finding documentation and help in the event that I get utterly stuck. If you guys like I can edit my code to reflect a MatLab compatible Script. I also have a Spherical Coordinate version, that takes in a spherical Vector Field, and then plots a Vector Field. I figure such an operation would be useful to allot of Physics and Engineering students. Would you guys like me to post this as well?