How to solve equation with "Error using symengine A square matrix is expected",

Hello

My code below written to solve an equation works well with a single input parameter d (line 8). However, when I have a vector for the input "d" as shown in line 9, Matlab complain that I have "symengine". here is my code.Any help is appreciated.

clear all
clc
close all

% definition of constants

Y=9*10^(-13);       
%  d=20*10^-3;   
  d= linspace(1*10^-3,20*10^-3,10);             
q=1.6*10^(-19);            
kB=4.0434e-21;            
er=2.8320e-11;
mp=1*10^-9;                
mn=1*10^-9;                

c=3.2520e+23;

kr=q*(mp+mn)/(er);
no=Y/(q*(mp+mn));
kdo=kr*no*no/c;

Lb= (q^2)/(8*pi*er*kB);

syms Vs

b=(Lb*q*(Vs./d))./(kB );
num=besselj(1,sqrt(-8*b));
den=sqrt(-2*b);

Fb=num./den;
kd=kdo*Fb;
eqn = (((kd*kr*c)^0.5).*d.^2)./(mp+mn)==Vs;

solVs = solve(eqn,Vs);
vpa(solVs)

Answer 1

[Walter Roberson]

eqn = (((kd*kr*c).^0.5).*d.^2)./(mp+mn)==Vs;

Notice the .^ instead of ^

[friet]

Thanks However, how do I get my final answer as a function of the vector? When I enter d as a single number I get the final answer(Vs). However when i enter d as a vector like d= linspace(10*10^-3,20*10^-3,10); it gives me Empty sym: 0-by-1.

[Walter Roberson]

That answer is correct.

You have 10 equations in 1 variable (Vs).

When you ask to solve() multiple equations, you are asking what combination of variable values can satisfy all of the equations at the same time.

There is no single value Vs that can satisfy all 10 of your equations at the same time.

You could arrayfun() your solve() -- though I recommend vpasolve() instead of solve() . Also, if you do use arrayfun() you will need to use 'uniform', 0, as arrayfun() cannot handle symbolic results directly.

[friet]

Thanks for your comment. May be my previous comment was a little bit unclear and I would like to make it clear here. When I entre d=10*10^-3; I have Vs=1634.9 and for d=2*10^-3; I have Vs=6736.5. When I put just single d it works fine. however when I enter d=[10*10^-3; 2*10^-3] i was expecting to see vs=[1634.9;6736.5]. But it is giving me empty matrix. I have no idea how to create matrix. is it like to make a for loop for each variable d?

[Walter Roberson]

temp = arrayfun( @vpasolve, eqn, 'Uniform', 0);
solVs = horzcat( temp{:} );

[friet]

Thanks!