MATLAB: Matrix dimension problem with integrals

matrix problem integram

Matrix dimensions must agree. Can't figure out what's the prob. Tried a lot,but nothing helped.

Best Answer

The easiest way to solve that is to use the linspace function to define ‘x’ and ‘y’. It allows you to specify the length of the vector, varying the increment to accomodate that. (The colon operator fixes the increment and lets the length vary.)

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Use .* instead of *

Also use ./ instead of /

MATLAB: Integral Error in Dimension

You need to use element-wise operations in several places in ‘integrand’ and ‘grsp_fun’. With those corrected, your code is:

% input value
v=1520;  % Phase speed
n=1;     % Mode number
f=30;
% Pekeris waveguide parameters
H=100;    % Source & Receiver Depth (m)
cb=1800;  % Half-space speed (m/s)
cw=1500;  % Water Column isospeed (m/s)
m=2.2;    % Density ratio
v1=1560;v2=1570;
integrand=@(v)  (dept_fun(v,n,f,2.2,1800,1500).*grsp_fun(v,n,dept_fun(v,n,f,2.2,1800,1500),2.2,1800,1500))./( v-grsp_fun(v,n,dept_fun(v,n,f,2.2,1800,1500),2.2,1800,1500).*sqrt(v2.^2-v.^2));
ycs1=2*cot(0.05)*integral(@(v)integrand(v),v1,v2)
function dept=dept_fun(v,n,f,m,cb,cw)
    dum1=sqrt(cw.^(-2)-v.^(-2));
    dum2=sqrt((cw.^(-2)-v.^(-2))/(v.^(-2)-cb.^(-2)));
    dept=1./(2*pi*f*dum1)*(pi*n-atan(m*dum2));
end
function grsp=grsp_fun(v,n,H,m,cb,cw)
    dum2_1=sqrt((cw.^(-2)-v.^(-2))/(v.^(-2)-cb.^(-2)));
    dum1=1./(v.^(2)*cw.^(-2)-1);
    dum_2_up=m.*(cw.^(-2)-cb.^(-2)).*(v.^2.*cw.^(-2)-1).^(-.5).*(-(v.^2).*cb.^-2+1).^(-.5);
    dum_2_low=(pi*n-atan(m*dum2_1))*(m.^2*cw.^-2-cb.^-2-(m.^2-1)*v.^-2);
    dum_all=dum1+dum_2_up./dum_2_low;
    grsp=v.*(1+(dum_all).^-1).^-1;
end

However it throws this Warning:

Warning: Minimum step size reached near x = 1570. There may be a singularity, or the tolerances may be
too tight for this problem.

eventually returning:

ycs1 =
    -2.920669390162302e+02

See the documentation on Array vs. Matrix Operations (link) for details.

Best Answer

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MATLAB: Integral Error in Dimension

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