MATLAB error using fzero function

2023 1 23
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更新时间：2023 1 27
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My following code generates the plot of V and D values in figure 1. In the graph, the parabolas and straight lines intersect, and I need to find the roots from the plot. So I tried to use fzero function, but the error appeared: Operands to the logical AND (&&) and OR (||) operators must be convertible to logical scalar values. Use the ANY or ALL functions to reduce operands to logical scalar values.
Error in fzero (line 326) elseif ~isfinite(fx) || ~isreal(fx)
Error in HW1 (line 35) x=fzero(fun,1);
My code is:
clear all; close all
W = 10000; %[N]
S = 40; %[m^2]
AR = 7;
cd0 = 0.01;
k = 1 / pi / AR;
clalpha = 2*pi;
Tsl=800;
figure(1);hold on; xlabel('V');ylabel('D')
for h=0:1:8;
i=0;
for alpha = 1:0.25:12
i=i+1;
rho(i)=1.2*exp(-h/10.4);
cl(i) = clalpha * alpha * pi/180;
V(i) = sqrt(2*W/rho(i)/S/cl(i));
L(i) = 0.5 * rho(i) * V(i) * V(i) * S * cl(i);
cd(i) = cd0 + k * cl(i) * cl(i);
D(i) = 0.5 * rho(i) * V(i) * V(i) * S * cd(i);
clcd(i) = cl(i)/cd(i);
p(i) = D(i)*V(i);
ang(i) = alpha;
T(i)=Tsl*(rho(i)/1.2).^0.75;
end
figure(1); plot(V,D); hold on
plot(V,T);
end
fun = @(V) 0.5*V.*V.*rho.*S.*cd-T;
x=fzero(fun,1);
Operands to the logical AND (&&) and OR (||) operators must be convertible to logical scalar values. Use the ANY or ALL functions to reduce operands to logical scalar values.

Error in fzero (line 326)
elseif ~isfinite(fx) || ~isreal(fx)
Probably, I should not use the fzero function, but the task is to find the roots of V from a plot (figure 1). There are parabolas and straight lines respectively.

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Star Strider
Star Strider 2023-1-23
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1 个投票

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I have no idea what intersections you want to find, so this is a guess.
It should at least get you started —
% clear all; close all
W = 10000; %[N]
S = 40; %[m^2]
AR = 7;
cd0 = 0.01;
k = 1 / pi / AR;
clalpha = 2*pi;
Tsl=800;
figure(1);hold on; xlabel('V');ylabel('D')
hv=0:1:8;
alphav = 1:0.25:12;
for k1 = 1:numel(hv)
h = hv(k1);
i=0;
for alpha = 1:0.25:12
i=i+1;
rho(i)=1.2*exp(-h/10.4);
cl(i) = clalpha * alpha * pi/180;
V(i) = sqrt(2*W/rho(i)/S/cl(i));
L(i) = 0.5 * rho(i) * V(i) * V(i) * S * cl(i);
cd(i) = cd0 + k * cl(i) * cl(i);
D(i) = 0.5 * rho(i) * V(i) * V(i) * S * cd(i);
clcd(i) = cl(i)/cd(i);
p(i) = D(i)*V(i);
ang(i) = alpha;
T(i)=Tsl*(rho(i)/1.2).^0.75;
end
Vm(k1,:) = V; % Save Results
Dm(k1,:) = D; % Save Results
Tm(k1,:) = T; % Save Results
xix = find(diff(sign(0.5*V.*V.*rho.*S.*cd-T))); % Approximate Indices Of Intersections
if ~isempty(xix) % Skip If Empty
for k3 = 1:numel(xix)
idxrng = max(xix(k3)-1,1) : min(numel(V),xix(k3)+1);
xv(k3) = interp1(D(idxrng)-T(idxrng), V(idxrng), 0);
yv(k3) = interp1(V(idxrng),D(idxrng), xv(k3));
Xm{k1,k3} = xv(k3); % Intersection X-Matrix
Ym{k1,k3} = yv(k3); % Intersection Y-Matrix
end
end
figure(1)
plot(V,D, 'DisplayName',sprintf('D_{%d}',k1))
hold on
plot(V,T, 'DisplayName',sprintf('T_{%d}',k1))
plot(xv, yv, 's', 'DisplayName',sprintf('Intersections %d',k1)) % Plot Intersections (Optional)
end
legend('Location','eastoutside','NumColumns',2)
Intersections = cell2table(cat(2,Xm,Ym), 'VariableNames',{'X1','X2','Y1','Y2'})
Intersections = 9×4 table
X1 X2 Y1 Y2 ______ ____________ ______ ____________ 55.445 {0×0 double} 800 {0×0 double} 55.654 {0×0 double} 744.34 {0×0 double} 55.885 {0×0 double} 692.55 {0×0 double} 55.914 {[ 21.1789]} 644.37 {[644.3652]} 55.866 {[ 23.3517]} 599.53 {[599.5325]} 55.586 {[ 25.8488]} 557.82 {[557.8191]} 54.967 {[ 28.7803]} 519.01 {[519.0081]} 53.781 {[ 32.3659]} 482.9 {[482.8973]} 51.479 {[ 37.2235]} 449.3 {[449.2990]}
% Vm
% Dm
% Tm
% fun = @(V) 0.5*V.*V.*rho.*S.*cd-T;
% x=fzero(fun,1);
See the documentation on interp1 to understand the intersections calculations.
.

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Star Strider
Star Strider 2023-1-23
My pleasure!
If my Answer helped you solve your problem, please Accept it!
.
Alina Abdikadyr
Alina Abdikadyr 2023-1-26
Hello!
I modified the code and tried to use interp1 command. In the graph the intersections are displayed correctly, but in the table, only two intersections are displayed.
clear all; close all
W = 10000;
S = 40;
AR = 7;
cd0 = 0.01;
k = 1 / pi / AR;
clalpha = 2*pi;
Tsl=800;
figure(1);hold on; xlabel('V');ylabel('D')
for rho = 1.2:-0.15:0.6
k1=numel(rho);
h=rho(k1);
i=0;
for alpha = 1:0.25:15
i=i+1;
cl(i) = clalpha * alpha * pi/180;
V(i) = sqrt(2*W/rho/S/cl(i));
L(i) = 0.5 * rho * V(i) * V(i) * S * cl(i);
cd(i) = cd0 + k * cl(i) * cl(i);
D(i) = 0.5 * rho * V(i) * V(i) * S * cd(i);
clcd(i) = cl(i)/cd(i);
p(i) = D(i)*V(i);
ang(i) = alpha;
T(i)=Tsl*(rho/1.2).^0.75;
end
Vm(k1,:) = V; % Save Results
Dm(k1,:) = D; % Save Results
Tm(k1,:) = T; % Save Results
xix = find(diff(sign(0.5*V.*V.*rho.*S.*cd-T))); % Approximate Indices Of Intersections
if ~isempty(xix) % Skip If Empty
for k3 = 1:numel(xix)
idxrng = max(xix(k3)-1,1) : min(numel(V),xix(k3)+1);
xv(k3) = interp1(D(idxrng)-T(idxrng), V(idxrng), 0);
yv(k3) = interp1(V(idxrng),D(idxrng), xv(k3));
Xm{k1,k3} = xv(k3); % Intersection X-Matrix
Ym{k1,k3} = yv(k3); % Intersection Y-Matrix
end
end
figure(1)
plot(V,D, 'DisplayName',sprintf('D_{%d}',k1))
hold on
plot(V,T, 'DisplayName',sprintf('T_{%d}',k1))
xlim([0 100])
ylim([0 1000])
plot(xv, yv, 's', 'DisplayName',sprintf('Intersections %d',k1)) % Plot Intersections (Optional)
end
%legend('Location','eastoutside','NumColumns',2)
Intersections = cell2table(cat(2,Xm,Ym), 'VariableNames',{'Xmax','Xmin','Y1','Y2'})
Star Strider
Star Strider 2023-1-26
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Ran in:
It was modified a bit too much, and eliminated the ‘k1’ loop count variable. That was the essential problem.
Creating:
rhov = 1.2:-0.15:0.6;
and then using:
for k1 = 1:numel(rhov);
rho = rhov(k1);
<REST OF THE LOOP CODE>
end
restored the original code architecture.
It now works as the orignal version did —
W = 10000;
S = 40;
AR = 7;
cd0 = 0.01;
k = 1 / pi / AR;
clalpha = 2*pi;
Tsl=800;
rhov = 1.2:-0.15:0.6;
figure(1);hold on; xlabel('V');ylabel('D')
for k1 = 1:numel(rhov);
rho = rhov(k1);
i=0;
for alpha = 1:0.25:15
i=i+1;
cl(i) = clalpha * alpha * pi/180;
V(i) = sqrt(2*W/rho/S/cl(i));
L(i) = 0.5 * rho * V(i) * V(i) * S * cl(i);
cd(i) = cd0 + k * cl(i) * cl(i);
D(i) = 0.5 * rho * V(i) * V(i) * S * cd(i);
clcd(i) = cl(i)/cd(i);
p(i) = D(i)*V(i);
ang(i) = alpha;
T(i)=Tsl*(rho/1.2).^0.75;
end
Vm(k1,:) = V; % Save Results
Dm(k1,:) = D; % Save Results
Tm(k1,:) = T; % Save Results
xix = find(diff(sign(0.5*V.*V.*rho.*S.*cd-T))); % Approximate Indices Of Intersections
if ~isempty(xix) % Skip If Empty
for k3 = 1:numel(xix)
idxrng = max(xix(k3)-1,1) : min(numel(V),xix(k3)+1);
xv(k3) = interp1(D(idxrng)-T(idxrng), V(idxrng), 0);
yv(k3) = interp1(V(idxrng),D(idxrng), xv(k3));
Xm{k1,k3} = xv(k3); % Intersection X-Matrix
Ym{k1,k3} = yv(k3); % Intersection Y-Matrix
end
end
figure(1)
plot(V,D, 'DisplayName',sprintf('D_{%d}',k1))
hold on
plot(V,T, 'DisplayName',sprintf('T_{%d}',k1))
xlim([0 100])
ylim([0 1000])
plot(xv, yv, 's', 'DisplayName',sprintf('Intersections %d',k1)) % Plot Intersections (Optional)
end
% Q = cat(1,Xm,Ym)
legend('Location','eastoutside','NumColumns',1)
Intersections = cell2table(cat(2,Xm,Ym), 'VariableNames',{'Xmax','Xmin','Y1','Y2'})
Intersections = 5×4 table
Xmax Xmin Y1 Y2 ______ ______ ______ ______ 55.445 16.019 800 800 55.735 18.193 723.76 723.76 55.914 21.162 644.74 644.74 55.614 25.551 562.34 562.34 53.429 33.237 475.68 475.68
The rest of the code is essentialy unchanged.
.
Alina Abdikadyr
Alina Abdikadyr 2023-1-26
Thank you very much!
Could you please help me how could I find a minimum point from each parabola?
Star Strider
Star Strider 2023-1-26
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Ran in:
As always, my pleasure!
The easiest approach would simply to use the min function in this instance.
Adding:
[Dmin,idx] = min(D);
minD(k1,:) = Dmin;
VminD(k1,:) = V(idx);
and the appropriate table entries using the addvars function returns their values and ‘V’ coordinate values in the ‘Intersections’ table —
W = 10000;
S = 40;
AR = 7;
cd0 = 0.01;
k = 1 / pi / AR;
clalpha = 2*pi;
Tsl=800;
rhov = 1.2:-0.15:0.6;
figure(1);hold on; xlabel('V');ylabel('D')
for k1 = 1:numel(rhov);
rho = rhov(k1);
i=0;
for alpha = 1:0.25:15
i=i+1;
cl(i) = clalpha * alpha * pi/180;
V(i) = sqrt(2*W/rho/S/cl(i));
L(i) = 0.5 * rho * V(i) * V(i) * S * cl(i);
cd(i) = cd0 + k * cl(i) * cl(i);
D(i) = 0.5 * rho * V(i) * V(i) * S * cd(i);
clcd(i) = cl(i)/cd(i);
p(i) = D(i)*V(i);
ang(i) = alpha;
T(i)=Tsl*(rho/1.2).^0.75;
end
Vm(k1,:) = V; % Save Results
Dm(k1,:) = D; % Save Results
Tm(k1,:) = T; % Save Results
xix = find(diff(sign(0.5*V.*V.*rho.*S.*cd-T))); % Approximate Indices Of Intersections
if ~isempty(xix) % Skip If Empty
for k3 = 1:numel(xix)
idxrng = max(xix(k3)-1,1) : min(numel(V),xix(k3)+1);
xv(k3) = interp1(D(idxrng)-T(idxrng), V(idxrng), 0);
yv(k3) = interp1(V(idxrng),D(idxrng), xv(k3));
Xm{k1,k3} = xv(k3); % Intersection X-Matrix
Ym{k1,k3} = yv(k3); % Intersection Y-Matrix
end
end
figure(1)
plot(V,D, 'DisplayName',sprintf('D_{%d}',k1))
hold on
plot(V,T, 'DisplayName',sprintf('T_{%d}',k1))
xlim([0 100])
ylim([0 1000])
plot(xv, yv, 's', 'DisplayName',sprintf('Intersections %d',k1)) % Plot Intersections (Optional)
[Dmin,idx] = min(D);
minD(k1,:) = Dmin;
VminD(k1,:) = V(idx);
end
% Q = cat(1,Xm,Ym)
legend('Location','eastoutside','NumColumns',1)
Intersections = cell2table(cat(2,Xm,Ym), 'VariableNames',{'Xmax','Xmin','Y1','Y2'});
Intersections = addvars(Intersections, minD,VminD, 'After','Y2')
Intersections = 5×6 table
Xmax Xmin Y1 Y2 minD VminD ______ ______ ______ ______ _____ ______ 55.445 16.019 800 800 426.5 29.9 55.735 18.193 723.76 723.76 426.5 31.964 55.914 21.162 644.74 644.74 426.5 34.526 55.614 25.551 562.34 562.34 426.5 37.821 53.429 33.237 475.68 475.68 426.5 42.285
All the minima appear to have the same magnitude, however their ‘V’ coordinates (‘VminD’) differ.
.
Alina Abdikadyr
Alina Abdikadyr 2023-1-27
Thank you very much!
I'm trying to modify the code.
Sorry for asking so many questions, but if in the intersections table, I get {0×0 double} values.
And I try to convert cell arrays using cell2mat, but the error appears.
Vmax Vmin Pmax Pmin
______ ____________ _____ ______________
56.013 {0×0 double} 25000 {0×0 double }
55.822 {0×0 double} 22198 {0×0 double }
55.235 {0×0 double} 19710 {0×0 double }
53.92 {0×0 double} 17501 {0×0 double }
51.119 {[ 23.8756]} 15539 {[1.5539e+04]}
39.638 {[ 39.6377]} 13798 {[1.3798e+04]}
My code is:
clear all; close all
W = 10000;
S = 40;
AR = 7;
cd0 = 0.005;
k = 1 / pi / AR;
clalpha = 2*pi;
Psl=25000;
figure(1);hold on; xlabel('V');ylabel('P')
hv=0:1.6484:8.242;
for k1 = 1:numel(hv)
h = hv(k1);
i=0;
for alpha = 1:0.25:15
i=i+1;
rho(i)=1.225*exp(-h/10.4);
cl(i) = clalpha * alpha * pi/180;
V(i) = sqrt(2*W/rho(i)/S/cl(i));
L(i) = 0.5 * rho(i)* V(i) * V(i) * S * cl(i);
cd(i) = cd0 + k * cl(i) * cl(i);
D(i) = 0.5 * rho(i) * V(i) * V(i) * S * cd(i);
clcd(i) = cl(i)/cd(i);
P(i) = D(i)*V(i);
ang(i) = alpha;
Ph(i)=Psl*(rho(i)/1.225).^0.75;
end
Vm(k1,:) = V;
Pm(k1,:) = P;
Pmh(k1,:) = Ph;
xix = find(diff(sign(D.*V-Ph)));
if ~isempty(xix)
for k3 = 1:numel(xix)
idxrng = max(xix(k3)-1,1) : min(numel(V),xix(k3)+1);
xv(k3) = interp1(P(idxrng)-Ph(idxrng), V(idxrng), 0);
yv(k3) = interp1(V(idxrng),P(idxrng), xv(k3));
Xm{k1,k3} = xv(k3); % Intersection X-Matrix
Ym{k1,k3} = yv(k3); % Intersection Y-Matrix
end
end
figure(1)
plot(V,P)
hold on
plot(V,Ph)
xlim([0 90])
ylim([0 45000])
plot(xv, yv, 's', 'DisplayName',sprintf('Intersections %d',k1)) % Plot Intersections (Optional)
end
%legend('Location','eastoutside','NumColumns',2)
Intersections = cell2table(cat(2,Xm,Ym), 'VariableNames',{'Vmax','Vmin','Pmax','Pmin'})
Xm1=cell2mat(Xm);
Star Strider
Star Strider 2023-1-27
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You omitted the ‘Pmax’ and ‘Pmin’ calculations.
Adding them back —
W = 10000;
S = 40;
AR = 7;
cd0 = 0.005;
k = 1 / pi / AR;
clalpha = 2*pi;
Psl=25000;
figure(1);hold on; xlabel('V');ylabel('P')
hv=0:1.6484:8.242;
for k1 = 1:numel(hv)
h = hv(k1);
i=0;
for alpha = 1:0.25:15
i=i+1;
rho(i)=1.225*exp(-h/10.4);
cl(i) = clalpha * alpha * pi/180;
V(i) = sqrt(2*W/rho(i)/S/cl(i));
L(i) = 0.5 * rho(i)* V(i) * V(i) * S * cl(i);
cd(i) = cd0 + k * cl(i) * cl(i);
D(i) = 0.5 * rho(i) * V(i) * V(i) * S * cd(i);
clcd(i) = cl(i)/cd(i);
P(i) = D(i)*V(i);
ang(i) = alpha;
Ph(i)=Psl*(rho(i)/1.225).^0.75;
end
Vm(k1,:) = V;
Pm(k1,:) = P;
Pmh(k1,:) = Ph;
xix = find(diff(sign(D.*V-Ph)));
if ~isempty(xix)
for k3 = 1:numel(xix)
idxrng = max(xix(k3)-1,1) : min(numel(V),xix(k3)+1);
xv(k3) = interp1(P(idxrng)-Ph(idxrng), V(idxrng), 0);
yv(k3) = interp1(V(idxrng),P(idxrng), xv(k3));
Xm{k1,k3} = xv(k3); % Intersection X-Matrix
Ym{k1,k3} = yv(k3); % Intersection Y-Matrix
end
end
figure(1)
plot(V,P)
hold on
plot(V,Ph)
xlim([0 90])
ylim([0 45000])
plot(xv, yv, 's', 'DisplayName',sprintf('Intersections %d',k1)) % Plot Intersections (Optional)
[maxP,idx] = max(P);
[minP,idx] = min(P);
Pmax(k1,:) = maxP;
Pmin(k1,:) = minP;
[maxV,idx] = max(V);
[minV,idx] = min(V);
Vmax(k1,:) = maxV;
Vmin(k1,:) = minV;
end
%legend('Location','eastoutside','NumColumns',2)
Intersections = cell2table(cat(2,Xm,Ym), 'VariableNames',{'Xmax','Xmin','Y1','Y2'});
Intersections = addvars(Intersections, Pmax,Pmin,Vmax,Vmin, 'After','Y2')
Intersections = 6×8 table
Xmax Xmin Y1 Y2 Pmax Pmin Vmax Vmin ______ ____________ _____ ______________ _____ ______ ______ ______ 56.013 {0×0 double} 25000 {0×0 double } 30859 9283.1 61.008 15.752 55.822 {0×0 double} 22198 {0×0 double } 33404 10049 66.04 17.051 55.235 {0×0 double} 19710 {0×0 double } 36159 10878 71.486 18.458 53.92 {0×0 double} 17501 {0×0 double } 39141 11775 77.382 19.98 51.119 {[ 23.8756]} 15539 {[1.5539e+04]} 42369 12746 83.764 21.628 39.638 {[ 39.6377]} 13798 {[1.3798e+04]} 45863 13797 90.673 23.412
% Xm1=cell2mat(Xm);
Please always include the intersection arrays ‘Xm’ and ‘Ym’ in the ‘Intersections’ table. (The ‘Xm’ and ‘Ym’ arrays are the intersection coordinates.) Some ‘P’ and ‘Ph’ vectors have one intersection and some have two intersections. Those that have only one intersection have empty cells for the second intersection. (This is to be expected.)
I assume ‘Pmax’, ‘Pmin’, ‘Vmax’ and ‘Vmin’ are calculated as you want them to be. I corrected the ‘Intersections’ table to include all of them. It is easiest to calculate them in the plotting loop, and then add them with the addvars call.
It would be straightforward to include the maxima and minima of the ‘Ph’ vectors as well, if you want to. Add their calculations in the existing loop, and then add their names to the addvars argument list.
.
Alina Abdikadyr
Alina Abdikadyr 2023-1-27
Sorry, but in the table, there are Vmax and Vmin, how could I find a corresponding values of P for calculated Vmax and Vmin
The table gives Pmax and Pmin from a plot, but how to get P values for Vmax and Vmin?
Xmax Xmin Y1 Y2 Pmax Pmin Vmax Vmin
______ ____________ _____ ______________ _____ ______ ______ ______
56.013 {0×0 double} 25000 {0×0 double } 30859 9283.1 61.008 15.752
55.822 {0×0 double} 22198 {0×0 double } 33404 10049 66.04 17.051
55.235 {0×0 double} 19710 {0×0 double } 36159 10878 71.486 18.458
53.92 {0×0 double} 17501 {0×0 double } 39141 11775 77.382 19.98
51.119 {[ 23.8756]} 15539 {[1.5539e+04]} 42369 12746 83.764 21.628
39.638 {[ 39.6377]} 13798 {[1.3798e+04]} 45863 13797 90.673 23.412
Star Strider
Star Strider 2023-1-27
Ran in:
Ran in:
Use the returned indices to refer to them.
I calculated them as:
PmaxV(k1,:) = P(Vxidx);
PminV(k1,:) = P(Vnidx);
where ‘Vxidx’ and ‘Vnidx’ are returned from:
[maxV,Vxidx] = max(V);
[minV,Vnidx] = min(V);
And added them to the ‘Intersections’ table as well —
W = 10000;
S = 40;
AR = 7;
cd0 = 0.005;
k = 1 / pi / AR;
clalpha = 2*pi;
Psl=25000;
figure(1);hold on; xlabel('V');ylabel('P')
hv=0:1.6484:8.242;
for k1 = 1:numel(hv)
h = hv(k1);
i=0;
for alpha = 1:0.25:15
i=i+1;
rho(i)=1.225*exp(-h/10.4);
cl(i) = clalpha * alpha * pi/180;
V(i) = sqrt(2*W/rho(i)/S/cl(i));
L(i) = 0.5 * rho(i)* V(i) * V(i) * S * cl(i);
cd(i) = cd0 + k * cl(i) * cl(i);
D(i) = 0.5 * rho(i) * V(i) * V(i) * S * cd(i);
clcd(i) = cl(i)/cd(i);
P(i) = D(i)*V(i);
ang(i) = alpha;
Ph(i)=Psl*(rho(i)/1.225).^0.75;
end
Vm(k1,:) = V;
Pm(k1,:) = P;
Pmh(k1,:) = Ph;
xix = find(diff(sign(D.*V-Ph)));
if ~isempty(xix)
for k3 = 1:numel(xix)
idxrng = max(xix(k3)-1,1) : min(numel(V),xix(k3)+1);
xv(k3) = interp1(P(idxrng)-Ph(idxrng), V(idxrng), 0);
yv(k3) = interp1(V(idxrng),P(idxrng), xv(k3));
Xm{k1,k3} = xv(k3); % Intersection X-Matrix
Ym{k1,k3} = yv(k3); % Intersection Y-Matrix
end
end
figure(1)
plot(V,P)
hold on
plot(V,Ph)
xlim([0 90])
ylim([0 45000])
plot(xv, yv, 's', 'DisplayName',sprintf('Intersections %d',k1)) % Plot Intersections (Optional)
[maxP,idx] = max(P);
[minP,idx] = min(P);
Pmax(k1,:) = maxP;
Pmin(k1,:) = minP;
[maxV,Vxidx] = max(V);
[minV,Vnidx] = min(V);
Vmax(k1,:) = maxV;
Vmin(k1,:) = minV;
PmaxV(k1,:) = P(Vxidx);
PminV(k1,:) = P(Vnidx);
end
%legend('Location','eastoutside','NumColumns',2)
Intersections = cell2table(cat(2,Xm,Ym), 'VariableNames',{'Xmax','Xmin','Y1','Y2'});
Intersections = addvars(Intersections, Pmax,Pmin,Vmax,Vmin,PmaxV,PminV, 'After','Y2')
Intersections = 6×10 table
Xmax Xmin Y1 Y2 Pmax Pmin Vmax Vmin PmaxV PminV ______ ____________ _____ ______________ _____ ______ ______ ______ _____ _____ 56.013 {0×0 double} 25000 {0×0 double } 30859 9283.1 61.008 15.752 30859 12261 55.822 {0×0 double} 22198 {0×0 double } 33404 10049 66.04 17.051 33404 13273 55.235 {0×0 double} 19710 {0×0 double } 36159 10878 71.486 18.458 36159 14367 53.92 {0×0 double} 17501 {0×0 double } 39141 11775 77.382 19.98 39141 15552 51.119 {[ 23.8756]} 15539 {[1.5539e+04]} 42369 12746 83.764 21.628 42369 16835 39.638 {[ 39.6377]} 13798 {[1.3798e+04]} 45863 13797 90.673 23.412 45863 18223
% Xm1=cell2mat(Xm);
.

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更多回答（1 个）

John D'Errico
John D'Errico 2023-1-23
编辑：John D'Errico 2023-1-23

0 个投票

You cannot use fzero on a vector. A vector of elements is NOT a function. It is just a list of numbers. And while you may think of it as a function, it is not. Essentially, a vector of numbers is just a picture of a function.
Suppose you were not feeling well today, so you decided to visit your doctor. But rather than appearing for an examination, you decided to just send your doctor a picture of yourself. Would that be sufficient to solve your problem? Rather than bring your car in for an oil change, would you just send a picture of your car to the JiffyLube place? Fzero needs a function, not just a list of numbers.
Instead, you will need to use tools to identify where the curves cross, perhaps using methods of interpolation. Or, better yet, you could use the actual functions themselves, now as true functions that fzero can evaluate at any point.

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