Defining Global Variables in the function
Hi. MATLAB Community. I am trying to get the following code to work. I’m working on a toy example that I hope to get running correctly before applying it to a larger numerical project. The issue I’m facing is that the values of k and rho_0 are not updating properly when I Area_Integral from the command window for different values of k and rho_0 (I am selecting k and rho_0 values so it stays in the if loop of the Area_Integral file. I uploaded the code for the various scripts I am using. When I write this in the command window, Area_Integral (1,0.4) and then Area_Integral (1.5,0.4) the value of k is not updated for the later case.
function out = Area_Integral(k, rho_0)
global k rho_0
if k>=1-rho_0^2
theta_array = linspace(0,pi/2,101);
root = zeros(size(theta_array));
for ii = 1:length(theta_array)
theta = theta_array(ii);
root(ii) = mnhf_secant(@poly4,[0.4 0.8],1e-8,0); %% Note: values of k, r0 and theta must be made accessible to poly4
end
out = 2*trapz(theta_array,root);
else
r_upperlim = sqrt(1+rho_0^2+sqrt(k^2+4*rho_0^2));
r_lowerlim = sqrt(1+rho_0^2-sqrt(k^2+4*rho_0^2));
fun_A2 = @(r) acos((r.^4+(1-rho_0^2)^2-k^2)./2./r.^2-rho_0^2).*r;
out = integral(fun_A2,r_lowerlim,r_upperlim);
end
if rho_0 == 1 && k <= 1e-12
out = pi;
end
end
function f = poly4(x)
global k rho_0 theta
disp([‘Values: k=’ num2str(k) ‘, rho_0=’ num2str(rho_0) ‘, theta=’ num2str(theta) ‘, x=’ num2str(x)])
disp([‘size(x): ‘ num2str(size(x))])
disp([‘size(k): ‘ num2str(size(k))])
disp([‘size(rho_0): ‘ num2str(size(rho_0))])
disp([‘size(theta): ‘ num2str(size(theta))])
k
%Equation B3 from Shuo and Li (LF20B)
f = (x.^2-2.*x.*cos(theta)+1-rho_0^2).*(x.^2-2.*x.*cos(theta+pi)+1-rho_0^2)-k.^2;
disp([‘f = ‘ num2str(f)])
end
function r=mnhf_secant(Fun,x,tol,trace)
%MNHF_SECANT finds the root of "Fun" using secant scheme.
%
% Fun – name of the external function
% x – vector of length 2, (initial guesses)
% tol – tolerance
% trace – print intermediate results
%
% Usage mnhf_secant(@poly1,[-0.5 2.0],1e-8,1)
% poly1 is the name of the external function.
% [-0.5 2.0] are the initial guesses for the root.
% Check inputs.
if nargin < 4, trace = 1; end
if nargin < 3, tol = 1e-8; end
if (length(x) ~= 2)
error(‘Please provide two initial guesses’)
end
f = feval(Fun,x); % Fun is assumed to accept a vector
for i = 1:100
x3 = x(1)-f(1)*(x(2)-x(1))/(f(2)-f(1)); % Update the guess.
f3 = feval(Fun,x3); % Function evaluation.
if trace, fprintf(1,’%3i %12.5f %12.5fn’, i,x3,f3); end
if abs(f3) < tol % Check for convergenece.
r = x3;
return
else % Reset values for x(1), x(2), f(1) and f(2).
x(1) = x(2); f(1) = f(2); x(2) = x3; f(2) = f3;
end
end
r = NaN;Hi. MATLAB Community. I am trying to get the following code to work. I’m working on a toy example that I hope to get running correctly before applying it to a larger numerical project. The issue I’m facing is that the values of k and rho_0 are not updating properly when I Area_Integral from the command window for different values of k and rho_0 (I am selecting k and rho_0 values so it stays in the if loop of the Area_Integral file. I uploaded the code for the various scripts I am using. When I write this in the command window, Area_Integral (1,0.4) and then Area_Integral (1.5,0.4) the value of k is not updated for the later case.
function out = Area_Integral(k, rho_0)
global k rho_0
if k>=1-rho_0^2
theta_array = linspace(0,pi/2,101);
root = zeros(size(theta_array));
for ii = 1:length(theta_array)
theta = theta_array(ii);
root(ii) = mnhf_secant(@poly4,[0.4 0.8],1e-8,0); %% Note: values of k, r0 and theta must be made accessible to poly4
end
out = 2*trapz(theta_array,root);
else
r_upperlim = sqrt(1+rho_0^2+sqrt(k^2+4*rho_0^2));
r_lowerlim = sqrt(1+rho_0^2-sqrt(k^2+4*rho_0^2));
fun_A2 = @(r) acos((r.^4+(1-rho_0^2)^2-k^2)./2./r.^2-rho_0^2).*r;
out = integral(fun_A2,r_lowerlim,r_upperlim);
end
if rho_0 == 1 && k <= 1e-12
out = pi;
end
end
function f = poly4(x)
global k rho_0 theta
disp([‘Values: k=’ num2str(k) ‘, rho_0=’ num2str(rho_0) ‘, theta=’ num2str(theta) ‘, x=’ num2str(x)])
disp([‘size(x): ‘ num2str(size(x))])
disp([‘size(k): ‘ num2str(size(k))])
disp([‘size(rho_0): ‘ num2str(size(rho_0))])
disp([‘size(theta): ‘ num2str(size(theta))])
k
%Equation B3 from Shuo and Li (LF20B)
f = (x.^2-2.*x.*cos(theta)+1-rho_0^2).*(x.^2-2.*x.*cos(theta+pi)+1-rho_0^2)-k.^2;
disp([‘f = ‘ num2str(f)])
end
function r=mnhf_secant(Fun,x,tol,trace)
%MNHF_SECANT finds the root of "Fun" using secant scheme.
%
% Fun – name of the external function
% x – vector of length 2, (initial guesses)
% tol – tolerance
% trace – print intermediate results
%
% Usage mnhf_secant(@poly1,[-0.5 2.0],1e-8,1)
% poly1 is the name of the external function.
% [-0.5 2.0] are the initial guesses for the root.
% Check inputs.
if nargin < 4, trace = 1; end
if nargin < 3, tol = 1e-8; end
if (length(x) ~= 2)
error(‘Please provide two initial guesses’)
end
f = feval(Fun,x); % Fun is assumed to accept a vector
for i = 1:100
x3 = x(1)-f(1)*(x(2)-x(1))/(f(2)-f(1)); % Update the guess.
f3 = feval(Fun,x3); % Function evaluation.
if trace, fprintf(1,’%3i %12.5f %12.5fn’, i,x3,f3); end
if abs(f3) < tol % Check for convergenece.
r = x3;
return
else % Reset values for x(1), x(2), f(1) and f(2).
x(1) = x(2); f(1) = f(2); x(2) = x3; f(2) = f3;
end
end
r = NaN; Hi. MATLAB Community. I am trying to get the following code to work. I’m working on a toy example that I hope to get running correctly before applying it to a larger numerical project. The issue I’m facing is that the values of k and rho_0 are not updating properly when I Area_Integral from the command window for different values of k and rho_0 (I am selecting k and rho_0 values so it stays in the if loop of the Area_Integral file. I uploaded the code for the various scripts I am using. When I write this in the command window, Area_Integral (1,0.4) and then Area_Integral (1.5,0.4) the value of k is not updated for the later case.
function out = Area_Integral(k, rho_0)
global k rho_0
if k>=1-rho_0^2
theta_array = linspace(0,pi/2,101);
root = zeros(size(theta_array));
for ii = 1:length(theta_array)
theta = theta_array(ii);
root(ii) = mnhf_secant(@poly4,[0.4 0.8],1e-8,0); %% Note: values of k, r0 and theta must be made accessible to poly4
end
out = 2*trapz(theta_array,root);
else
r_upperlim = sqrt(1+rho_0^2+sqrt(k^2+4*rho_0^2));
r_lowerlim = sqrt(1+rho_0^2-sqrt(k^2+4*rho_0^2));
fun_A2 = @(r) acos((r.^4+(1-rho_0^2)^2-k^2)./2./r.^2-rho_0^2).*r;
out = integral(fun_A2,r_lowerlim,r_upperlim);
end
if rho_0 == 1 && k <= 1e-12
out = pi;
end
end
function f = poly4(x)
global k rho_0 theta
disp([‘Values: k=’ num2str(k) ‘, rho_0=’ num2str(rho_0) ‘, theta=’ num2str(theta) ‘, x=’ num2str(x)])
disp([‘size(x): ‘ num2str(size(x))])
disp([‘size(k): ‘ num2str(size(k))])
disp([‘size(rho_0): ‘ num2str(size(rho_0))])
disp([‘size(theta): ‘ num2str(size(theta))])
k
%Equation B3 from Shuo and Li (LF20B)
f = (x.^2-2.*x.*cos(theta)+1-rho_0^2).*(x.^2-2.*x.*cos(theta+pi)+1-rho_0^2)-k.^2;
disp([‘f = ‘ num2str(f)])
end
function r=mnhf_secant(Fun,x,tol,trace)
%MNHF_SECANT finds the root of "Fun" using secant scheme.
%
% Fun – name of the external function
% x – vector of length 2, (initial guesses)
% tol – tolerance
% trace – print intermediate results
%
% Usage mnhf_secant(@poly1,[-0.5 2.0],1e-8,1)
% poly1 is the name of the external function.
% [-0.5 2.0] are the initial guesses for the root.
% Check inputs.
if nargin < 4, trace = 1; end
if nargin < 3, tol = 1e-8; end
if (length(x) ~= 2)
error(‘Please provide two initial guesses’)
end
f = feval(Fun,x); % Fun is assumed to accept a vector
for i = 1:100
x3 = x(1)-f(1)*(x(2)-x(1))/(f(2)-f(1)); % Update the guess.
f3 = feval(Fun,x3); % Function evaluation.
if trace, fprintf(1,’%3i %12.5f %12.5fn’, i,x3,f3); end
if abs(f3) < tol % Check for convergenece.
r = x3;
return
else % Reset values for x(1), x(2), f(1) and f(2).
x(1) = x(2); f(1) = f(2); x(2) = x3; f(2) = f3;
end
end
r = NaN; global variables MATLAB Answers — New Questions
