How to evaluate a polynomial p at each point in y?

How to evaluate a polynomial p at each point in y? I know polyval(p,x) makes the same but for each point in x, but I would like to know if there exist something similar for y.

Thanks!

Answer 1

[Ameer Hamza]

You can use fzero(). For example

p = [1 0 0]; % polynomial y = x.^2
y = 4; % value of y
x_sol = fzero(@(x) polyval(p, x)-y, rand()); % corresponding value of x

Result

>> x_sol
x_sol =
     2

[Angelavtc]

@Ameer Hamza thanks for your answer, it was really useful. But what if I want to do the same for a set of values x,y like the ones I am uploading here.

Lets say for the specific value y=0

I have seen that fzero only works for functions. What to do then?

Thanks in advance!

[Ameer Hamza]

There can be several ways, but I would use interpolation to convert the series of 'x' and 'y' points into a continuous function and then apply fzero()

fun = @(xq) interp1(x, y, xq);
x_sol = fzero(@(xq) fun(xq)-0, mean(x)); % mean(x) so that initial point is within 'x' vector

Answer 2

[Rik]

As far as I'm aware, this is not directly possible. If you rewrite the p-factors you can still use polyval.

y=p(1)*x+p(2)
x=(y-p(2))/p(1)=1/p(1)*y + -p(2)/p(1)
%so for numel(p)==2:
p_=[1 -p(2)]/p(1);
x=polyval(p_,y)

I haven't bothered to write a general inverter for p, but I suspect that isn't very hard.

Edit: I realised this is quite tricky for any order beyond 1, luckily you can empirically estimate the parameters:

%this requires a reasonable range of x:
p_=polyfit(polyval(p,x),x,numel(p)-1);

Answer 3

[Steven Lord]

For the simple case of a polynomial, you can use roots. For example if you want to find a value of x for which is equal to 50:

pOrig = [1 3 3 1];
p = pOrig; % Make a copy so we can use the original for checking later on
p(end) = p(end)-50;
r = roots(p);
check = polyval(pOrig, r) % Each element of check should be very close to 50

To check this graphically:

f = @(x) polyval(pOrig, x);
fplot(f); % Plot the polynomial
yline(50); % Draw the line y = 50
hold on
realroot = r(imag(r) == 0); % Find the real root for plotting
plot(realroot, f(realroot), 'o') % Indicate where the polynomial crosses the horizontal line

For a more general function you can use fzero as Ameer Hamza suggested.