Error Using Gradient Function

I am attempting to write a program that will solve for the electric field and charge density (rho_v) at a point P given a function for voltage. This is a very straight forward problem on paper but I'm having some issues translating this to code. E is found with E = -(del)V and rho_v found with Gauss' Law. To start I shift the coordinates given for P from Cartesian to spherical since I find it makes Gauss' Law easier later. I believe I am using the gradient function correctly as it is described on the mathworks description page. But every time I run the program I get the following error:

Error in ==> gradient at 49
[msg,f,ndim,loc,rflag] = parse_inputs(f,varargin);

??? Output argument "varargout{2}" (and maybe others) not assigned during call to "C:\Program
Files\MATLAB\R2011a Student\toolbox\matlab\datafun\gradient.m>gradient".

Error in ==> Test at 19
[V_r,V_theta,V_phi] = gradient(V);

CODE

x = -3;

y = 1;

z = 2;

eta_0 = 8.85*10^-12;

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

theta = atan(sqrt(x^2 + y^2)/z);

phi = atan(y/x);

x = r*cos(theta); 

y = r*sin(theta)*cos(phi);

z = r*cos(theta);

V = 5*x.^3*y.^2*z;

[V_r,V_theta,V_phi] = gradient(V);

E = [V_r,V_theta,V_phi];

rho_i = @(r,theta,phi)r.^2*sin(theta);

rho_f = triplequad(rho_i,0,r,0,pi,0,2*pi);

rho_v = (eta_0*E)/rho_f;

Any assistance solving this error would be greatly appreciated.

Answer 1

[Jan]

You "believe" that you are running gradient correctly, but did you check this? If you use the debugger either by setting a breakpoint or by dbtop if error you can find out very fast, that V is scalar, to be exact with the value 720. And you cannot calculate a gradient with 3 dimensions from a scalar.

Do you want the partial derivatives of "5*x.^3*y.^2*z"? This can be computed manually.