Solving 4 non-linear equations: error using syms/subsindex

Hello,

I am trying to solve a set of four complicated equations for four variables on MATLAB. I have attached my code below (I hope it is decodable .. it appears to have lost format in the copy/paste process). I have been given the error 'Error using sym/subsindex (line 766) Invalid indexing or function definition. When defining a function, ensure that the arguments are symbolic variables and the body of the function is a SYM expression. When indexing, the input must be numeric, logical, or ':'.' Where line 766 is the first equation (EQ_1). Could someone please help me rectify this error?

Thanks, Alex.

============================================================================================================ %Defining Parameters and Variables n=3; %number of iterations

a_inc=0.3; %amplitude of incoming wave [m] T=10; %period [s] kf=[3, 4, 5]; %wave number for non-reef sections kr=[3, 4, 5]; %wave number for reef section df=0.6; %depth of water [m] dr=df-0.43; %depth of reef [m] g=9.81; %graviational constant [m/s^2] B=0.507; %width of reef [m]

l=1;

%Solving the 4 equations

syms a_i b_i c_i d_i h

EQ_1=symsum((a_i*kf(h)*g*(exp(-1i*w*t))/(w*cosh(kf(h)*df)))*int(cosh(kf(h)*(z+df))*cosh(kf(l)*(z+df)), z, 0, -df),h, 1, n)+ (a_inc*kf(1)*g*exp(-1i*w*t)/(w*cosh(kf(1)*df)))*int(cosh(kf(1)*(z+df))*cosh(kf(l)*(z+df)), z, 0, -df)-(symsum((b_i*kr(h)*g*exp(-1i*w*t)/(w*cosh(kr(h)*dr)))*int(cosh(kr(h)*(z+dr))*cosh(kf(l)*(z+df)), z, 0, -dr),h, 1, n)+ symsum((c_i*kr(h)*g*exp(1i*kr(h)*-B)*exp(-1i*w*t)/(w*cosh(kr(h)*dr)))*int(cosh(kr(h)*(z+dr))*cosh(kf(l)*(z+df)), z, 0, -dr),h, 1, n)); EQ_2=symsum((a_i*-1i*g*exp(-1i*w*t)/(w*cosh(kf(h)*df)))*int(cosh(kf(h)*(z+df))*cosh(kr(l)*(z+dr)), z, 0, -dr), h, 1, n)+ (a_inc*-1i*g*exp(-1i*w*t)/(w*cosh(kf(1)*df)))*int(cosh(kf(1)*(z+df))*cosh(kr(l)*(z+dr)))-(symsum((b_i*-1i*g*exp(-1i*w*t)/(w*cosh(kr(h)*dr)))*int(cosh(kr(h)*(z+dr))*cosh(kr(l)*(z+dr)), z, 0, -dr), h, 1, n)+ symsum((c_i*-1i*g*exp(1i*kr(h)*-B)*exp(-1i*w*t)/(w*cosh(kr(h)*dr)))*int(cosh(kr(h)*(z+dr))*cosh(kr(l)*(z+dr)), z, 0, -dr), h, 1, n)); EQ_3=symsum((b_i*kr(h)*g*exp(1i*kr*B)*exp(-1i*w*t)/(w*cosh(kr(h)*dr)))*int(cosh(kr(h)*(z+dr))*cosh(kr(l)*(z+dr)), z, 0, -dr), h, 1, n)+ symsum((c_i*kr(h)*g*exp(-1i*w*t)/(w*cosh(kr(h)*dr)))*int(cosh(kr(h)*(z+dr))*cosh(kr(l)*(z+dr)), z, 0, -dr), h, 1, n)-(symsum((d_i*kr(h)*g*exp(-1i*w*t)/(w*cosh(kr(h)*dr)))*int(cosh(kf(h)*(z+df))*cosh(kf(l)*(z+df)), z, 0, -dr), h, 1, n)); EQ_4=symsum((b_i*-1i*g*exp(1i*kr*B)*exp(-1i*w*t)/(w*cosh(kr(h)*dr)))*int(cosh(kr(h)*(z+dr))*cosh(kr(l)*(z+dr)), z, 0, -dr), h, 1, n)+ symsum((c_i*-1i*g*exp(-1i*w*t)/(w*cosh(kr(h)*dr)))*int(cosh(kr(h)*(z+dr))*cosh(kr(l)*(z+dr)), z, 0, -dr), h, 1, n)-(symsum((d_i*-1i*g*exp*exp(-1i*w*t)/(w*cosh(kr(h)*dr)))*int(cosh(kf(h)*(z+df))*cosh(kr(l)*(z+dr)), z, 0, -dr), h, 1, n));

[a_i, b_i, c_i, d_i] = solve(EQ_1, EQ_2, EQ_3, EQ_4, 'a_i', 'b_i', 'c_i', 'd_i')

=============================================================================================================

Answer 1

[Walter Roberson]

You cannot use a symbolic variable such as h as an index. You need to construct a a vector of definite terms and sum() those. You might possibly be able to use h as a numeric vector to calculate the terms in vectorized form, but watch out for / vs ./ and * vs .*

[Alex Wylie]

As you can see, I am not simply summing a vector .. I won't be able to define definite terms as this program is meant to be functional. Is there a different type that I can define h to be to remove this problem ?

[Walter Roberson]

Your first equation a symsum from 1 to n where n is 3. If symbolic variables were permitted as indices then that would be the equivalent of evaluating the expression first with h = 1,then with 2,then with 3,and adding those. So do that. Vectorize the expression inside the symsum, use h = 1:n numeric, evaluate to get three array entries, sum() them.