How do I make my symbolic function into a matrix?

I have the following function:

Grow= 1/(15.69892467*(2*3.14159).^.5)*(2.82718).^(-(.5*((y-(.879*x+5.682))/15.69892467).^2))

where I defined x and y using syms x y

The graph represents the growth kernel of an integral projection model for a grass species. I can graph it just fine using mesh(x,y,Grow, [1, 500]) but now I need to make a matrix of the data so that I can find the eigenvalues and eigenvectors.

I want the matrix to be a square matrix that represents the different combination of x and y values. So row one would be the solution to the equation when y=1 and x = 1, 2,...to 500 and row 2 would be y=2, x=1,2... to 500 etc. I'd like to make a 500 by 500 matrix.

I would appreciate any advice you can give me. I have the feeling this should be a simple operation but I can't figure it out. I tried making two vectors x and y but because of the nature of matrix subtraction, I just ended up with another vector.

Answer 1

[Walter Roberson]

[x, y] = ndgrid(1:500,1:500);
Grow = 1/(15.69892467*sqrt(2*pi)) * (2.82718).^(-(.5*((y-(0.879*x+5.682))/15.69892467).^2));

Note: rank(Grow) says 79... and I suspect that the greatest part of it is numeric nonsense)

[Heather G]

Thank you, that seems to work for that specific equation, but I am coming across a problem when I implement this strategy with the other half of my equation. I have the equation:

Fec1=(0.1485*log(x)+ 0.0643)*(((61.8411*y-855.048)*(1-.017))).^(-.33)*(0.14348*(2.72818).^(-0.0646743*(-3.07+1).^2)) When I graph it with the symbolic variables, I get this graph:

However, once I convert it to a matrix it becomes a complex double, which I can't graph normally. You have definitely solved my initial problem, but do you have any suggestions for what to do now?

I have tried graphing Rep=real(Fec1) but that seems to scale the graph strangely while maintaining the same shape.

[Walter Roberson]

When you plot using symbolic variables, the portion of the plot that is complex is silently omitted.

Your Fec1 is complex when 61.8411*y-855.048 is negative. The boundary for that is y = 13.8265328398104 at which point you have a division by 0, so it approaches infinity from above y = 13.8265328398104 . You should therefore only plot at values above that for y.

Your Fec1 has log(0) at x = 0 which leads to negative infinity near x = 0. It is negative below x = 1/exp(643/1485) which is about 0.6485 . You should avoid plotting for x <= 0 but you can get close to 0 if you want.

You made a small transcription error when you converted to MATLAB from symbolic. You have

Fec1=(0.1485*log(x)+ 0.0643)*(((61.8411*y-855.048)*(1-.017))).^(-.33)*(0.14348*(2.72818).^(-0.0646743*(-3.07+1).^2));

but you need

Fec1=(0.1485*log(x)+ 0.0643).*(((61.8411*y-855.048)*(1-.017))).^(-.33)*(0.14348*(2.72818).^(-0.0646743*(-3.07+1).^2));

which is to say you need .* instead of * between the x and the y parts.

If you put the two together and use (for example)

[x,y] = ndgrid(linspace(1/10,500), linspace(13.9, 500));
Fec1=(0.1485*log(x)+ 0.0643).*(((61.8411*y-855.048)*(1-.017))).^(-.33)*(0.14348*(2.72818).^(-0.0646743*(-3.07+1).^2));
surf(x, y, Fec1, 'edgecolor', 'none')

then you will get a reasonable plot.

[Heather G]

Thank you so much for answering my questions!

Everything looks great now :)