Unrecognized function or variable 'quad8'

Greetings,

Currenlty working on a project for a radar class I am taking and I keep getting an error for Unrecognized function or variable 'quad8'. As far as I know quad is supposed to numerciallly evaluate an integral. I tried using quall and intgeral instead but keep getting an error. I am basically troubleshooting this entire code which is lengthy and I can certainly use some advice. The end result is a Power Spectral Density plot and a isodop footprint plot which is describing a radar travelling horizontally with a narrow beam antenna squinted at 45 degrees.I attached pics of what plots should look like. I am including the code here.Thank you in advance for any help you may offer!

clear all;
close;
format long;
global r;
%
%Setup of the parameters
%
u=7.5e+3;              %speed of the plane
alpha0=2.5*pi/180;     %beam depth in radians
alpha_lim=1.5*alpha0;  %limit angle for integration
phi=45*pi/180;         %squinted angkle in radiians
theta=30*pi/180;       %vertial plotting anglein radians

%Finding the limit in the integration
%path in terms of relative Doppler frequency
%

c = cos(alpha_lim);
s = sin(alpha_lim);

fu = (8*c*c-7)/(-2*sqrt(14)*s+2*sqrt(2)*c)
fl = (8*c*c-7)/(2*sqrt(14)*s+2*sqrt(2)*c)
%
% Computing the power spectral density(psd)
%
fd = linspace(fu,fl,502);    % rrelative Doppler frequency
fr = 1./fd;                  % fr parameter
Num = length(fr);
psd = zeros(1,Num-2);        % We exclude the boundary points
% in the psd
footprint_u = zeros(1,Num-2);
footprint_l = zeros(1,Num-2);
footprint_f = zeros(1,Num-2);

for n = 2:Num-1,
    r = fr(n);
    
    t1 = sqrt(r*r-1);
    t2 = sqrt(7*(r*r-1)-(1-2*sqrt(2)*c*r)^2);
    t3 = 1+t1-2*sqrt(2)*c*r;
    
    su = (-sqrt(6)*t1-t2)/t3;
    sl = (-sqrt(6)*t1+t2)/t3;
    
    uu = log(su);
    ul = log(sl);
    footprint_u(n-1) = uu;
    footprint_l(n-1) = ul;
    footprint_f(n-1) = r;
    psd(n-1) = quad8('f_int',ul,uu)/(sqrt(1-1/r/r))^3;
end
psd= psd/max(psd);
fd_plot = fd(2:Num-1);

plot(fd_plot,psd);
%semilogy(fd_plot,psd);
hold on
x_fl=[fd(1) fd(1)];
y_fl=[0 1];
plot(x_fl,y_fl,'k')
%semilogy(x_fl,y_fl,'k')
x_fu=[fd(Num) fd(Num)];
y_fu=[0 1];
plot(x_fu,y_fu,'k')
%semilogy(x_fu,y_fu,'k')
title('Fading Spectrum')
xlabel('f_{D}/f_{D_{0}}')
ylabel('PSD/PSD_{0}')
text(0.281,.5,'lowest f_{d}/f_{d_{0}}=0.292');
text(0.385,.5,'highest f_{d}/f_{d_{0}}=0.414');
%
% generating the Limit Isodops and
% The footprint
%
figure(2)

u_hyp=linspace(0,1,100);
x_hyp_low=cosh(u_hyp)./(sqrt((1/fu)^2-1));
y_hyp_low_sinh(u_hyp);
plot(x_hyp_low,y_hyp_low,'k--')

hold on;

x_hyp_up=cosh(u_hyp)./(sqrt((1/fl)^2-1));
y_hyp_up=sinh(u_hyp);
plot(x_hyp_up,y_hyp_up,'k--')

% The footprint
% Those point belong to thte isodops
% and for those points u=uu or ul
% 
u_footprint = zeros(1,2*Num-4);
f_footprint = zeros(1,2*Num-4);
for n = 1:Num-2,
    u_footprint1(n)=footprint_u(n);
    u_footprint2(n)=footprint_1(n);
    f_footprint1(n)=footprint_f(n);
    f_footprint2(n)=footprint_f(n);
end

x_footprint1=cosh(u_footprint1)./(sqrt((f_footprint1).^2-1));
y_footprint1=sinh(u_footprint1);
plot(x_footprint1,y_footprint1);
x_footprint2=cosh(u_footprint2)./(sqrt((f_footprint2).^2-1));
y_footprint2=sinh(u_footprint2);
plot(x_footprint2,y_footprint2);
axis equal;
set(gca, 'xlim', [0 0.8], 'ylim', [0 0.8])
title('Footprint')
xlabel('X=x/h')
ylabel('Y=y/h')
grid on
text(0.25, 0.1, 'f_{d}/f_{d}_{0}=0.292')
text(0.5, 0.7, 'f_{d}/f_{d}_{0}=0.414')

%
% This is the integrand for the psd
%
function y = f_int(x)
global r
s = exp(x);

rterm = sqrt(r*r-1);
alpha0 = 2.5*pi/180;
alpha = acos(((1+rterm)*s.*s+2*sqrt(6)*rterm*s+(1-rterm))./ ...
    (2*sqrt(2)*r*(s.*s+1)));
y = (cosh(x).^2-1/r/r).*exp(-2*alpha.*alpha/alpha0/alpha0);
end

Answer 1

[Jose Iglesias]

Thank you tremendously for all your guidance!!

[Voss]

No problem! How about you do me a favor and unaccept your answer and accept mine? I appreciate it!

Answer 2

[Voss]

As mentioned in the answer here (with plenty of reference links in it):

https://www.mathworks.com/matlabcentral/answers/301131-quad8-in-matlab-7#answer_232947

quad8() has been removed and replaced by quadl(), which was then replaced by integral().

Changing quad8 to integral and changing the first argument to a function handle - and fixing a couple of typos - seems to have gotten the code to run:

clear all;
close;
format long;
global r;
%
%Setup of the parameters
%
u=7.5e+3;              %speed of the plane
alpha0=2.5*pi/180;     %beam depth in radians
alpha_lim=1.5*alpha0;  %limit angle for integration
phi=45*pi/180;         %squinted angkle in radiians
theta=30*pi/180;       %vertial plotting anglein radians
%Finding the limit in the integration
%path in terms of relative Doppler frequency
%
c = cos(alpha_lim);
s = sin(alpha_lim);
fu = (8*c*c-7)/(-2*sqrt(14)*s+2*sqrt(2)*c)

fu = 
   0.413975431045285

fl = (8*c*c-7)/(2*sqrt(14)*s+2*sqrt(2)*c)

fl = 
   0.291617380244238

%
% Computing the power spectral density(psd)
%
fd = linspace(fu,fl,502);    % rrelative Doppler frequency
fr = 1./fd;                  % fr parameter
Num = length(fr);
psd = zeros(1,Num-2);        % We exclude the boundary points
                             % in the psd
footprint_u = zeros(1,Num-2);
footprint_l = zeros(1,Num-2);
footprint_f = zeros(1,Num-2);
for n = 2:Num-1,
    r = fr(n);
    
    t1 = sqrt(r*r-1);
    t2 = sqrt(7*(r*r-1)-(1-2*sqrt(2)*c*r)^2);
    t3 = 1+t1-2*sqrt(2)*c*r;
    
    su = (-sqrt(6)*t1-t2)/t3;
    sl = (-sqrt(6)*t1+t2)/t3;
    
    uu = log(su);
    ul = log(sl);
    footprint_u(n-1) = uu;
    footprint_l(n-1) = ul;
    footprint_f(n-1) = r;
%     psd(n-1) = quad8('f_int',ul,uu)/(sqrt(1-1/r/r))^3;
    psd(n-1) = integral(@f_int,ul,uu)/(sqrt(1-1/r/r))^3;
end
psd= psd/max(psd);
fd_plot = fd(2:Num-1);
plot(fd_plot,psd);
%semilogy(fd_plot,psd);
hold on
x_fl=[fd(1) fd(1)];
y_fl=[0 1];
plot(x_fl,y_fl,'k')
%semilogy(x_fl,y_fl,'k')
x_fu=[fd(Num) fd(Num)];
y_fu=[0 1];
plot(x_fu,y_fu,'k')
%semilogy(x_fu,y_fu,'k')
title('Fading Spectrum')
xlabel('f_{D}/f_{D_{0}}')
ylabel('PSD/PSD_{0}')
text(0.281,.5,'lowest f_{d}/f_{d_{0}}=0.292');
text(0.385,.5,'highest f_{d}/f_{d_{0}}=0.414');

%
% generating the Limit Isodops and
% The footprint
%
figure(2)
u_hyp=linspace(0,1,100);
x_hyp_low=cosh(u_hyp)./(sqrt((1/fu)^2-1));
% y_hyp_low_sinh(u_hyp);
y_hyp_low=sinh(u_hyp); % possible typo corrected
plot(x_hyp_low,y_hyp_low,'k--')
hold on;
x_hyp_up=cosh(u_hyp)./(sqrt((1/fl)^2-1));
y_hyp_up=sinh(u_hyp);
plot(x_hyp_up,y_hyp_up,'k--')
% The footprint
% Those point belong to thte isodops
% and for those points u=uu or ul
% 
u_footprint = zeros(1,2*Num-4);
f_footprint = zeros(1,2*Num-4);
for n = 1:Num-2,
    u_footprint1(n)=footprint_u(n);
%     u_footprint2(n)=footprint_1(n);
    u_footprint2(n)=footprint_l(n); % possible typo corrected
    f_footprint1(n)=footprint_f(n);
    f_footprint2(n)=footprint_f(n);
end
x_footprint1=cosh(u_footprint1)./(sqrt((f_footprint1).^2-1));
y_footprint1=sinh(u_footprint1);
plot(x_footprint1,y_footprint1);
x_footprint2=cosh(u_footprint2)./(sqrt((f_footprint2).^2-1));
y_footprint2=sinh(u_footprint2);
plot(x_footprint2,y_footprint2);
axis equal;
set(gca, 'xlim', [0 0.8], 'ylim', [0 0.8])
title('Footprint')
xlabel('X=x/h')
ylabel('Y=y/h')
grid on
text(0.25, 0.1, 'f_{d}/f_{d}_{0}=0.292')
text(0.5, 0.7, 'f_{d}/f_{d}_{0}=0.414')

%
% This is the integrand for the psd
%
function y = f_int(x)
global r
s = exp(x);
rterm = sqrt(r*r-1);
alpha0 = 2.5*pi/180;
alpha = acos(((1+rterm)*s.*s+2*sqrt(6)*rterm*s+(1-rterm))./ ...
    (2*sqrt(2)*r*(s.*s+1)));
y = (cosh(x).^2-1/r/r).*exp(-2*alpha.*alpha/alpha0/alpha0);
end

[Jose Iglesias]

I tried running it but I am getting an error message that says

Attempt to execute SCRIPT integral as a function:

Error in Untitled (line 47)

psd(n-1) = integral(@f_int,ul,uu)/(sqrt(1-1/r/r))^3;

I think what is going on is that you have the integral being called as a script before being called as a function.. I am currenlty sorting out info on mathworks website including renaming the script. I tried putting which <integral> -all but either I am putting that in the wrong location, or that is not the answer. Any suggestions on how I can have integral to be called as a function and not a script?

[Image Analyst]

What is the name of your m-file? Do you have an "integral.m" file? What does this say in the command window:

which -all integral

[Walter Roberson]

Gosh, quad8 was a long time ago!

[Voss]

@Jose Iglesias: As you can see, the code runs here and generates those beautiful plots. So most likely the problem is that you have a script called integral.m somewhere on your path taking precedence over the built-in MATLAB function integral.m. Please show the output of which -all integral and/or which integral -all (no <> around integral) as @Image Analyst requested.

@Walter Roberson: Yeah, I think quad8 was just a couple of years after Newton and Leibniz.

[Jose Iglesias]

When I type in which -all integral it says this

C:\Users\macaw\OneDrive - Arizona State University\Documents\MATLAB\Examples\R2020a\antenna\atx_pattern_custom\integral.m

C:\Program Files\MATLAB\R2020a\toolbox\matlab\funfun\integral.m

[Voss]

Thanks. Try renaming or removing the file at:

C:\Users\macaw\OneDrive - Arizona State University\Documents\MATLAB\Examples\R2020a\antenna\atx_pattern_custom\integral.m

Then run the code again and see if it works.

[Voss]

You could also edit your path so it doesn't include that directory.

[Jose Iglesias]

Thank you for all your help. I renamed the file and it works.