Is there a way to vpasolve elementwise?

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John Moseley 2015-8-29

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评论： Star Strider 2015-8-30

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Hello,

I am hoping someone can point me in the right direction with regards to the following problem. I have an equation with two variables, x and y, and an unknown c, and I'd like to solve the equation for c over a range of x and y values. The equation cannot be solved for c analytically. Eventually, I'd like to plot the solutions for c as function of x and y in a contour plot. Below is the code that I thought would work for a much simplified example of the actual problem; this may help define the problem.

x = 1:5;
y = 1:5;
[X,Y] = meshgrid(x,y);
syms c
sol = vpasolve(X + c*Y - 3 == 0,c);

Obviously, this did not work. I'm sure I'm thinking about this wrong way. Any helpful ideas are welcome.

Thank you, John.

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Star Strider 2015-8-29

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The contour plot is actually the solution. Solving a two-variable problem like that is one of its hidden benefits.

I’m not quite sure what you want to do, but I solved for ‘c’ here, and then had contour provide the (x,y) coordinates for that over the grid you gave it. Here, I asked it for the coordinates corresponding to c=0:

x = 1:5;
y = 1:5;
[X,Y] = meshgrid(x,y);
F = (3-X)./Y;
sol = contour(X, Y, F, [0 0]);
xy = sol(:,2:end)

The ‘xy’ matrix are the coordinates, x = xy(1,:) and y = xy(2,:). I refer you to the documentation on contour for the details. Substitute other values for the fourth argument to define other values of ‘c’.