MATLAB: How to find x-values when y-function equals a set value

x values when the function equals=n

Hi, there!

New to matlab.. I have a dilema trying to find the x-values for a function =0.7(see figure). And I should be able to find both values of x when the bell-curve changes.

Big help, please! I've tried fzero, and other functions and mostly does't work or it will just give me one single value of x. there should always be 2.

Thank you in advance!

x=[0.46 0.7]

f=(a1*exp(-((x-b1)/c1).^2))=0.7

The a1, b1 and c1 values are known.

Best Answer

Try this:

x = linspace(0.54, 0.61);                                           % Create Data

y = exp(-(x-0.58).^2*1E+4);                                         % Create Data
idx = find(diff(sign(y-0.7)));
for k = 1:numel(idx)
    idxrng = [-1 1]+idx(k);
    x7(k) = interp1(y(idxrng), x(idxrng), 0.7);                     % Interpolate To Find Intersection ‘x’-Value
end
figure
plot(x, y)
hold on
plot(xlim, [1 1]*0.7, ':k', 'LineWidth',1)                          % Reference Line
plot(x7, [1 1]*0.7, 'pg','MarkerFaceColor','g','MarkerSize',10)     % Intersections
plot([1 1]*x7(1), [min(ylim) 0.7], ':k')
plot([1 1]*x7(2), [min(ylim) 0.7], ':k')
hold off
legend('Data','Reference','Intersections', 'Location','NW')

Use your own function for ‘y’. I would have used it, however the parameters are nowhere to be found.

EDIT — (18 Oct 2020 at 19:37)

Added plot image —

Related Solutions

MATLAB: [Using the fit funcion type smoothingspline] How to get the peaks of a fiting curve found by the command ‘fit’

Data=load('Held_Roll_T15_D147_BK2Y90_a2_1.txt');
X=Data(:,1);
Y=Data(:,2);
[X_axis,Index]=unique(X,'rows');
X_axis(end)- X_axis(end-1);
Y_axis=Y(Index);
figure()
f = fit(X_axis,Y_axis,'smoothingspline','SmoothingParam',0.9999907449908739);
%
y = f(X_axis) ; 
plot(X_axis,Y_axis,'.b') 
hold on
plot(X_axis,y,'r') ;
legend({'data'; 'fit'})
% Find peaks
[pks,idx] = findpeaks(y);
figure
hold on
plot(X_axis,y,'r') ;
plot(X_axis(idx),y(idx),'V')
legend({'fit', 'peaks'}) ;

MATLAB: Find the intersection points

Add these ines:

curv_dif = um - um2;                                        % Subtract Curves

idx = find(diff(sign(curv_dif)));                           % Indicex Of Sign Changes

for k = 1:numel(idx)
    idxrng = [-1 0 1]+idx(k);
    xint(k) = interp1(curv_dif(idxrng), Ac(idxrng), 0);     % ‘x’ At Intersection

    yint(k) = interp1(Ac, um, xint(k));                     % ‘y’ At Intersection

end

so the complete revised code is now:

a0 = 1;
Ab = 5.21e6;
kenex = 1.05;
f = 0.1;
Lc = 1700;
T = 12.42*3600;
g = 9.81;
sigma = 2*pi/T;
Ck = 0.86;
% Hydraulic Curve
Ac = [1:1:2e3];
Rc = sqrt(Ac/20);
F = kenex + f*Lc./(4*Rc);
beta = F*Ab./(2*Lc*Ac)*a0;
alpha = (Lc*Ab./(g*Ac)).^0.5*sigma;
mu = 16*alpha.^2.*beta/(3*pi);
um_prime = ((((1-alpha.^2).^4 + mu.^2).^0.5 - (1-alpha.^2).^2)./(0.5*mu.^2)).^0.5;
um = um_prime*2*pi*a0/T.*Ab./Ac;
% Sedimentary Curve
P = (Ac/1.58e-4).^(1/0.95);
um2 = P*pi*Ck./(T*Ac);
figure(1);
semilogx(Ac,um)
xlabel('Channel Area (m^2)')
ylabel('u_m (m/s)')
grid on
hold on
semilogx(Ac,um2);
curv_dif = um - um2;                                        % Subtract Curves
idx = find(diff(sign(curv_dif)));                           % Indicex Of Sign Changes
for k = 1:numel(idx)
    idxrng = [-1 0 1]+idx(k);
    xint(k) = interp1(curv_dif(idxrng), Ac(idxrng), 0);     % ‘x’ At Intersection
    yint(k) = interp1(Ac, um, xint(k));                     % ‘y’ At Intersection
end
plot(xint, yint, 'xr')
hold off
legend('Hydraulic Curve','Sedimentary Curve','Intersections','Location','best')

EDIT — (12 Jun 2020 at 21:24)

Added plot figure —

Best Answer

Related Solutions

MATLAB: [Using the fit funcion type smoothingspline] How to get the peaks of a fiting curve found by the command ‘fit’

MATLAB: Find the intersection points

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