How can I save and plot all values of x and y for each value of V? x and y values are in the vertical axis and V in the horizontal axis in the graphic

V=[1,2,3,4];

i=1;

while i<=4

syms x y

eqn1 = V(i)*x + y == 2;

eqn2 = -x + y == 3;

sol = solve([eqn1, eqn2], [x, y]);

xSol = double(sol.x);

ySol = double(sol.y);

end

Answer 1

[Star Strider]

Try this instead:

V=[1,2,3,4];

for k = 1:numel(V)
    xy(:,k) = [V(k) 1; -1 1] \ [2; 3]; 
end

figure
plot3(xy(1,:), xy(2,:), V, '-p')
grid
view(30, 30)
xlabel('x')
ylabel('y')
zlabel('V')
axis([-0.6  -0.1    2.4  2.9    0  5])
text(xy(1,:), xy(2,:), V, compose('V = %.1f',V),  'HorizontalAlignment','right', 'VerticalAlignment','middle')

producing:

EDIT — (26 Jan 2021 at 13:54)

Added plot image.

[Pablo Zarco]

Can it be using the function solve?

[Star Strider]

You can use the Symbolic Math Toolbox functions if you want to, however that is inefficient. There is no reason to use solve for such a simple, linear probllem.

Using the mldivide,\ function/operator here is much more efficient, and provides the correct result.

[Pablo Zarco]

I know but for other more complex equation systems i need to use that function. So if I understand this simple one with that function I will be able to do it with other more complicated ones.

[Star Strider]

As I mentioned, you can certainly use solve.

There could easily be other functions (such as fsolve) that would be more efficient that the Symbolic Toolbox Functions for interative operations such as those you are doing. It depends on what they are, and the values they return.

For example, your problem could be coded with fsolve as:

V=[1,2,3,4];

xyfcn = @(b,Vv) [(Vv*b(1) + b(2) - 2); (-b(1) + b(2) - 3)]; 

for k = 1:numel(V)
    xy(:,k) = fsolve(@(b)xyfcn(b,V(k)), rand(2,1)); 
end

returning the same values, with ‘x’ being defined as ‘b(1)’ and ‘y’ as ‘b(2)’.

This is much more efficient that using the Symbolic Math Toolbox for the same essential problem.

[Pablo Zarco]

There is an error on the line of xy that says: the variable xy appears to change size on every loop iteration, how can I solve this? Thank you very much by the way!

[Star Strider]

That is not an error. That is simply a warning.

The ‘fix’ for it is to preallocate ‘xy’ by putting:

xy = zeros(2,numel(V));

just before the loop.

This should work for all problems with 2 solutions, regardless of the number of elements that vector ‘V’ has.

[Pablo Zarco]

ok Thank you very much, this is helping me a lot. One more last question, if there was another 2 vectors like Vv multipling the y's like this:

Vv*x + Pp*y = 2;

-x + Qqy = 3

it will be like this right?

V=[1,2,3,4];

Q=[1,5,7,4];

P=[1,6,3,9];

xyfcn = @(b,Vv) [(Vv*b(1) + Pp*b(2) - 2); (-b(1) + Qq*b(2) - 3)]

for k = 1:numel(V)

xy(:,k) = fsolve(@(b)xyfcn(b,V(k),P(k),Q(k)), rand(2,1));

end

[Star Strider]

As always, my pleasure!

That would work, however ‘syfcn’ would need to be changed slightrly to accommodate the additional arguments:

xyfcn = @(b,Vv,Pp,Qq) [(Vv*b(1) + Pp*b(2) - 2); (-b(1) + Qq*b(2) - 3)];

and then this works:

V=[1,2,3,4];
Q=[1,5,7,4];
P=[1,6,3,9];
xyfcn = @(b,Vv,Pp,Qq) [(Vv*b(1) + Pp*b(2) - 2); (-b(1) + Qq*b(2) - 3)]
xy = zeros(2, numel(V));
for k = 1:numel(V)
    xy(:,k) = fsolve(@(b)xyfcn(b,V(k),P(k),Q(k)), rand(2,1));
end

figure
plot3(xy(1,:), xy(2,:), V, '-p')
grid
view(150, 30)
xlabel('x')
ylabel('y')
zlabel('V')
% axis([-0.6  -0.1    2.4  2.9    0  5])
text(xy(1,:), xy(2,:), V, compose('(V = %.1f, Q = %.1f, P = %.1f)',[V; Q; P]'),  'HorizontalAlignment','center', 'VerticalAlignment','bottom', 'FontSize',8)

However plotting it against the other argument vectors would be a problem, since a 3D plot is the limit. It would still be possible to plot it aginst one of them, possibly using the text call to speecify the othe variables, that I expanded from the original version here.