# How to plot vector valued function with single input.

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Niklas Kurz il 22 Dic 2020
Commentato: Walter Roberson il 23 Dic 2020
I wonder if this is even possible and the question itself is redundant. Normaly a vector valued function is plotted with 2 inputs:
[x,y] = meshgrid(-1:0.1:1);
fx = x.^2;
fy = 3.*y;
quiver(x,y,fx,fy)
in order that each (x,y) input in the coordinate plane is adressed to an output (I suppose). Probably that's rather a question for Mathstack, but while I'm at it: is it possible to plot a function that goes like f(phi) = [cos(phi); sin(phi)] ?
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Walter Roberson il 22 Dic 2020
syms phi real
f(phi) = [cos(phi); sin(phi)];
fplot(f)
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Niklas Kurz il 23 Dic 2020
But can't you plot it like f(phi,0) = [cos(phi); sin(phi)]. How to achieve this?
Walter Roberson il 23 Dic 2020
You cannot do that.
If f in that syntax were a numeric array or a cell array, then the 0 would be an invalid index.
If f in that syntax is a symbolic function name that you are defining, then the arguments to f() on the left side of a symbolic function definition must each be scalar symbolic variable names or row vectors of symbolic variable names (unless there is only a single parameter, in which case it is permitted to be a column vector of symbolic variable names.) 0 is not a valid symbolic variable name, so f(phi,0) cannot be defined.
It is not possible to define a symbolic function in parts. For example it is not possible to define
f(0,0) = -1
f(0,phi) = sin(phi)
f(theta,0) = theta^2
Each symbolic function can only be defined in a single statement -- though the statement can use piecewise():
f(theta,phi) = piecewise(theta==0 & phi == 0, -1, theta == 0, sin(phi), phi == 0, theta^2, etc)

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