How to get fzero to work on an array?

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Daniel Beeson on 24 May 2020
Answered: Walter Roberson on 8 Dec 2021
I'm trying to solve fzero for each value of x in an array, and I get theis error:
Operands to the || and && operators must be convertible to logical scalar values.
Error in fzero (line 444)
while fb ~= 0 && a ~= b
Error in hw5_code (line 14)
mach = fzero(eqn,[.16 2]);
x = .2:.1:.6;
r = .3 + 3.*((x-.5).^2);
g = 1.4;
p0 = 7576;
t0 = 1033;
pb = 100;
a = pi.*r.^2;
a_star = pi.*(.3^2);
eqn = @(m) (a./a_star).^2 - (1./m.^2 .*((2./(g+1)) .* (1 + (((g-1)./2) .* m.^2))).^((g+1)./(g-1)));
mach = fzero(eqn,[.16 2]);
t = t0 .* ((1+ (((g-1)/2) .* mach.^2)).^-1);
p = p0 .* (1+ (((g-1)/2) .* mach.^2)).^-(g/(g-1));
rho = p./(287.*t);
air = sqrt(g.*287.*t);
v = mach.*air;
m_dot = rho .* v .* a;
a1 = 1 + ((2.*g)./(1+g)).*((mach.^2) -1);
a2 = (2 + (g-1).*(mach.^2))./((g+1).*(mach.^2));
change_entropy = log(a1.*a2) - (((g-1)/g).*log(a1));
Stephen on 24 May 2020
"Why are you passing a 1x2 vector as an initial guess to fzero()?"
The fzero documentation states that x0 may be scalar or a 2-element vector, in which case "fzero checks that fun(x0(1)) and fun(x0(2)) have opposite signs, and errors if they do not. It then iteratively shrinks the interval where fun changes sign to reach a solution." This is clearly very useful when the bracketing range is known.

Alan Weiss on 26 May 2020
I don't know if this is what you wanted, but I got it to work by making a loop for fzero:
x = .2:.1:.6;
r = .3 + 3.*((x-.5).^2);
g = 1.4;
p0 = 7576;
t0 = 1033;
pb = 100;
a = pi.*r.^2;
a_star = pi.*(.3^2);
eqn = @(m) (a./a_star).^2 - (1./m.^2 .*((2./(g+1)) .* (1 + (((g-1)./2) .* m.^2))).^((g+1)./(g-1)));
%%
% mach = fzero(eqn,[.16 2]);
mach = zeros(size(eqn(.16)));
for i = 1:length(mach)
tp = zeros(size(mach));
tp(i) = 1;
mach(i) = fzero(@(x)dot(tp,eqn(x)),[0.15 1]);
end
%%
t = t0 .* ((1+ (((g-1)/2) .* mach.^2)).^-1);
p = p0 .* (1+ (((g-1)/2) .* mach.^2)).^-(g/(g-1));
rho = p./(287.*t);
air = sqrt(g.*287.*t);
v = mach.*air;
m_dot = rho .* v .* a;
a1 = 1 + ((2.*g)./(1+g)).*((mach.^2) -1);
a2 = (2 + (g-1).*(mach.^2))./((g+1).*(mach.^2));
change_entropy = log(a1.*a2) - (((g-1)/g).*log(a1));
Alan Weiss
MATLAB mathematical toolbox documentation
Alan Weiss on 8 Dec 2021
I suggest that you use the debugger and put a break point before the loop that contains the fzero call. Check to see whether the function values have different signs at the interval endpoints. Adjust your code so that they always do.
Alan Weiss
MATLAB mathematical toolbox documentation

Walter Roberson on 8 Dec 2021
I'm trying to solve fzero for each value of x in an array, and I get theis error:
Don't Do That.
fzero() is defined as only accepting scalar equations of one variable. It cannot in itself be used to solve at multiple x values simultaneously
You need to loop through the different x values, constructing the other values such as a or r as you go.
If you make a and r into functions of the current x value, then you can probably arrayfun() the fzero() call.