Integral Error in Dimension

I have the following code like this:

When I try to do integral at

ycs1=2*cot(0.05)*integral(@(v)integrand(v),v1,v2);

It returns error and it says that dimension in the grsp_fun, may I ask how to fix it? Thank you!

clear;clc;close all
% 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

Answer 1

[Star Strider]

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.

[Tsuwei Tan]

Thank you so much for the quick and correct answer, I will be more careful on this elementary operation!

[Star Strider]

As always, my pleasure!