Problem with for loop plotting a graph

Question

Alexander Kimbley 2018-12-6

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/434249-problem-with-for-loop-plotting-a-graph

评论： Star Strider 2019-2-7

Hi I'm really new to Matlab so you'll have to bare with me. I'm trying to plot a graph using the for function but to no avail.

I'm using the following code:

>> for a=2.0:-0.02:0.0

p=[f(a),g(a),h(a),r(a),t(a)] (where f,g,h,r,t are complicated functions of a I don't fancy writing down.)

R=roots(p)

C=imag(R)

c=C(1,1)

....

end

I'm looking to plot the complex part of the first root of each polynomial against each value of a or if its possible plotting the complex part of every root against a for every a on the same graph with different colours representing each root.

Thanks, sorry if the problem is ill described.

2 个评论
显示无隐藏无

madhan ravi 2018-12-6

编辑：madhan ravi 2018-12-6

attach the script file and the relevent function files

Alexander Kimbley 2018-12-6

script.m

Thanks, this is the entire polynomial.

请先登录，再进行评论。

请先登录，再回答此问题。

Answer 1

Star Strider 2018-12-6

1
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/434249-problem-with-for-loop-plotting-a-graph#answer_350920

在 MATLAB Online 中打开

The Symbolic Math Toolbox is inefficient for this sort of problem.

Try this:

U = 1;
B = 0.1;
H = 0.5;
pfcn = @(a) [2*exp(2*a*(1-H)).*(1 - tanh(a*H)), -6*U*(1 + tanh(a*H)).*exp(2*a*(1 - H)) + 2*U*(1 - tanh(a*H)),(7*U^2 *(1 + tanh(a*H)) - 2*B^2 *tanh(a*H)).*exp(2*a*(1 - H)) - 5*U^2 *(1 - tanh(a*H)), exp(2*a*(1 - H)).*(2*U*B^2 *tanh(a*H) - 4*U^3 *(1 + tanh(a*H))) - (2*U*B^2 *tanh(a*H) - 4*U^3 *(1 + tanh(a*H))), U^2 *(U^2 *(1 + tanh(a*H)) - B^2 *tanh(a*H)).*exp(2*a*(1 - H)) - U^2 *(U^2 *(1 - tanh(a*H)) - B^2 *tanh(a*H))];
a=2.0:-0.02:0.0;
for k1 = 1:numel(a)
    p = pfcn(a);
    R = roots(p);
    C(:,k1) = imag(R);
end
figure
plot(a, C, '.')
grid
figure
meshc(C)
grid on

That should tell you all you need to know about the imaginary roots of your function at each ‘a’ value.

14 个评论
显示 12更早的评论隐藏 12更早的评论

Star Strider 2019-2-4

在 MATLAB Online 中打开

There should be six roots, but there is only one. You appear to be doing a straghtforward multiplication rather than doing a colvolution:

B = rand;

a = rand;

H = rand;

pfcn = @(x) [B^2+exp(2*a*H)*(B^2-2*x.^2)].*[B^2-(1-x).^2].*[((1-x).^2)*(1+tanh(a*(1-H)))-B^2-a*(((1-x).^2).*(1-tanh(a*(1-H)))-B^2)]-(B^2-2*x.^2)*(B^2-a*(B^2-2*x.^2)).*[((1-x).^2)*(1+tanh(a*(1-H)))-B^2+exp(-2*a*H)*(((1-x).^2)*(1-tanh(a*(1-H)))-B^2)];

rts = fsolve(pfcn, (rand+1i*rand));

You need to convolve the various factors to produce the polynomial you want. You likely only need to do this once, and the Symbolic Math Toolbox may be the best approach. One option would be:

syms x a b c 
r1 = x + a;
r2 = x + b;
r3 = x + c;
p(x) = expand(r1 * r2 * r3);
p = collect(p, x)

producing:

p(x) =
x^3 + (a + b + c)*x^2 + (a*b + a*c + b*c)*x + a*b*c

Using it with the matlabFunction function would produce an anonymous function for ‘pfcn’:

pfcn = matlabFunction(p)

producing:

pfcn =
  function_handle with value:
    @(x,a,b,c)x.^3+(a+b+c).*x.^2+(a.*b+a.*c+b.*c).*x+a.*b.*c

or more simply (after a bit of editing):

pfcn = @(x,a,b,c)x.^3+(a+b+c).*x.^2+(a.*b+a.*c+b.*c).*x+a.*b.*c;

The coefficients would not need to be expressly used as part of the argument list if you wanted ‘pfcn’ to inherit them from your workspace.

Star Strider 2019-2-5

在 MATLAB Online 中打开

As always, my pleasure.

This now works, and produces interesting plots:

B=0.5;
H=0.2;
pfcn = @(a) [((4*exp(2*H*a) - 2*exp(4*H*a) - (2*tanh(H*a))/(tanh(H*a)*tanh(a) - 1) + (2*tanh(a))/(tanh(H*a)*tanh(a) - 1) - (4*exp(2*H*a)*tanh(a))/(tanh(H*a)*tanh(a) - 1) - (2*exp(4*H*a)*tanh(a))/(tanh(H*a)*tanh(a) - 1) + (4*exp(2*H*a)*tanh(H*a))/(tanh(H*a)*tanh(a) - 1) + (2*exp(4*H*a)*tanh(H*a))/(tanh(H*a)*tanh(a) - 1) + 2) + (8*exp(4*H*a) - 12*exp(2*H*a) + (4*tanh(H*a))/(tanh(H*a)*tanh(a) - 1) - (4*tanh(a))/(tanh(H*a)*tanh(a) - 1) + (12*exp(2*H*a)*tanh(a))/(tanh(H*a)*tanh(a) - 1) + (8*exp(4*H*a)*tanh(a))/(tanh(H*a)*tanh(a) - 1) - (12*exp(2*H*a)*tanh(H*a))/(tanh(H*a)*tanh(a) - 1) - (8*exp(4*H*a)*tanh(H*a))/(tanh(H*a)*tanh(a) - 1) - 4));
    + ((14*exp(2*H*a) - 12*exp(4*H*a) - (2*tanh(H*a))/(tanh(H*a)*tanh(a) - 1) + B^2*exp(-2*H*a) - 9*B^2*exp(2*H*a) + 5*B^2*exp(4*H*a) - 5*B^2 + (2*tanh(a))/(tanh(H*a)*tanh(a) - 1) - (14*exp(2*H*a)*tanh(a))/(tanh(H*a)*tanh(a) - 1) - (12*exp(4*H*a)*tanh(a))/(tanh(H*a)*tanh(a) - 1) - (3*B^2*tanh(a))/(tanh(H*a)*tanh(a) - 1) + (14*exp(2*H*a)*tanh(H*a))/(tanh(H*a)*tanh(a) - 1) + (12*exp(4*H*a)*tanh(H*a))/(tanh(H*a)*tanh(a) - 1) + (3*B^2*tanh(H*a))/(tanh(H*a)*tanh(a) - 1) - (B^2*exp(-2*H*a)*tanh(H*a))/(tanh(H*a)*tanh(a) - 1) - (7*B^2*exp(2*H*a)*tanh(H*a))/(tanh(H*a)*tanh(a) - 1) - (3*B^2*exp(4*H*a)*tanh(H*a))/(tanh(H*a)*tanh(a) - 1) + (B^2*exp(-2*H*a)*tanh(a))/(tanh(H*a)*tanh(a) - 1) + (7*B^2*exp(2*H*a)*tanh(a))/(tanh(H*a)*tanh(a) - 1) + (3*B^2*exp(4*H*a)*tanh(a))/(tanh(H*a)*tanh(a) - 1) + 2));
    + ((8*exp(4*H*a) - 8*exp(2*H*a) - 2*B^2*exp(-2*H*a) + 14*B^2*exp(2*H*a) - 12*B^2*exp(4*H*a) + 8*B^2 + (8*exp(2*H*a)*tanh(a))/(tanh(H*a)*tanh(a) - 1) + (8*exp(4*H*a)*tanh(a))/(tanh(H*a)*tanh(a) - 1) + (4*B^2*tanh(a))/(tanh(H*a)*tanh(a) - 1) - (8*exp(2*H*a)*tanh(H*a))/(tanh(H*a)*tanh(a) - 1) - (8*exp(4*H*a)*tanh(H*a))/(tanh(H*a)*tanh(a) - 1) - (4*B^2*tanh(H*a))/(tanh(H*a)*tanh(a) - 1) + (2*B^2*exp(-2*H*a)*tanh(H*a))/(tanh(H*a)*tanh(a) - 1) + (18*B^2*exp(2*H*a)*tanh(H*a))/(tanh(H*a)*tanh(a) - 1) + (8*B^2*exp(4*H*a)*tanh(H*a))/(tanh(H*a)*tanh(a) - 1) - (2*B^2*exp(-2*H*a)*tanh(a))/(tanh(H*a)*tanh(a) - 1) - (18*B^2*exp(2*H*a)*tanh(a))/(tanh(H*a)*tanh(a) - 1) - (8*B^2*exp(4*H*a)*tanh(a))/(tanh(H*a)*tanh(a) - 1)));
    + ((2*exp(2*H*a) - 2*exp(4*H*a) + B^2*exp(-2*H*a) - 7*B^2*exp(2*H*a) + 10*B^2*exp(4*H*a) - 2*B^4*exp(-2*H*a) + 6*B^4*exp(2*H*a) - 4*B^4*exp(4*H*a) - 8*B^2 + 4*B^4 - (2*exp(2*H*a)*tanh(a))/(tanh(H*a)*tanh(a) - 1) - (2*exp(4*H*a)*tanh(a))/(tanh(H*a)*tanh(a) - 1) + (2*B^2*tanh(a))/(tanh(H*a)*tanh(a) - 1) + (B^4*tanh(a))/(tanh(H*a)*tanh(a) - 1) + (2*exp(2*H*a)*tanh(H*a))/(tanh(H*a)*tanh(a) - 1) + (2*exp(4*H*a)*tanh(H*a))/(tanh(H*a)*tanh(a) - 1) - (2*B^2*tanh(H*a))/(tanh(H*a)*tanh(a) - 1) - (B^4*tanh(H*a))/(tanh(H*a)*tanh(a) - 1) - (B^2*exp(-2*H*a)*tanh(H*a))/(tanh(H*a)*tanh(a) - 1) - (17*B^2*exp(2*H*a)*tanh(H*a))/(tanh(H*a)*tanh(a) - 1) - (8*B^2*exp(4*H*a)*tanh(H*a))/(tanh(H*a)*tanh(a) - 1) + (B^4*exp(-2*H*a)*tanh(H*a))/(tanh(H*a)*tanh(a) - 1) + (3*B^4*exp(2*H*a)*tanh(H*a))/(tanh(H*a)*tanh(a) - 1) + (B^4*exp(4*H*a)*tanh(H*a))/(tanh(H*a)*tanh(a) - 1) + (B^2*exp(-2*H*a)*tanh(a))/(tanh(H*a)*tanh(a) - 1) + (17*B^2*exp(2*H*a)*tanh(a))/(tanh(H*a)*tanh(a) - 1) + (8*B^2*exp(4*H*a)*tanh(a))/(tanh(H*a)*tanh(a) - 1) - (B^4*exp(-2*H*a)*tanh(a))/(tanh(H*a)*tanh(a) - 1) - (3*B^4*exp(2*H*a)*tanh(a))/(tanh(H*a)*tanh(a) - 1) - (B^4*exp(4*H*a)*tanh(a))/(tanh(H*a)*tanh(a) - 1)));
    + ((2*B^4*exp(-2*H*a) - 4*B^2*exp(4*H*a) - 2*B^4*exp(2*H*a) + 4*B^4*exp(4*H*a) + 4*B^2 - 4*B^4 - (4*B^2*tanh(a))/(tanh(H*a)*tanh(a) - 1) - (2*B^4*tanh(a))/(tanh(H*a)*tanh(a) - 1) + (4*B^2*tanh(H*a))/(tanh(H*a)*tanh(a) - 1) + (2*B^4*tanh(H*a))/(tanh(H*a)*tanh(a) - 1) + (8*B^2*exp(2*H*a)*tanh(H*a))/(tanh(H*a)*tanh(a) - 1) + (4*B^2*exp(4*H*a)*tanh(H*a))/(tanh(H*a)*tanh(a) - 1) - (2*B^4*exp(-2*H*a)*tanh(H*a))/(tanh(H*a)*tanh(a) - 1) - (6*B^4*exp(2*H*a)*tanh(H*a))/(tanh(H*a)*tanh(a) - 1) - (2*B^4*exp(4*H*a)*tanh(H*a))/(tanh(H*a)*tanh(a) - 1) - (8*B^2*exp(2*H*a)*tanh(a))/(tanh(H*a)*tanh(a) - 1) - (4*B^2*exp(4*H*a)*tanh(a))/(tanh(H*a)*tanh(a) - 1) + (2*B^4*exp(-2*H*a)*tanh(a))/(tanh(H*a)*tanh(a) - 1) + (6*B^4*exp(2*H*a)*tanh(a))/(tanh(H*a)*tanh(a) - 1) + (2*B^4*exp(4*H*a)*tanh(a))/(tanh(H*a)*tanh(a) - 1)));
    + (B^2*exp(4*H*a) - B^4*exp(-2*H*a) + B^4*exp(2*H*a) - 2*B^4*exp(4*H*a) + B^6*exp(-2*H*a) - B^6*exp(2*H*a) + B^6*exp(4*H*a) - B^2 + 2*B^4 - B^6 + (B^2*tanh(a))/(tanh(H*a)*tanh(a) - 1) + (B^4*tanh(a))/(tanh(H*a)*tanh(a) - 1) - (B^2*tanh(H*a))/(tanh(H*a)*tanh(a) - 1) - (B^4*tanh(H*a))/(tanh(H*a)*tanh(a) - 1) - (2*B^2*exp(2*H*a)*tanh(H*a))/(tanh(H*a)*tanh(a) - 1) - (B^2*exp(4*H*a)*tanh(H*a))/(tanh(H*a)*tanh(a) - 1) + (B^4*exp(-2*H*a)*tanh(H*a))/(tanh(H*a)*tanh(a) - 1) + (3*B^4*exp(2*H*a)*tanh(H*a))/(tanh(H*a)*tanh(a) - 1) + (B^4*exp(4*H*a)*tanh(H*a))/(tanh(H*a)*tanh(a) - 1) + (2*B^2*exp(2*H*a)*tanh(a))/(tanh(H*a)*tanh(a) - 1) + (B^2*exp(4*H*a)*tanh(a))/(tanh(H*a)*tanh(a) - 1) - (B^4*exp(-2*H*a)*tanh(a))/(tanh(H*a)*tanh(a) - 1) - (3*B^4*exp(2*H*a)*tanh(a))/(tanh(H*a)*tanh(a) - 1) - (B^4*exp(4*H*a)*tanh(a))/(tanh(H*a)*tanh(a) - 1))];
a=10.0:-0.001:0.0;
for k1 = 1:numel(a)
    p = pfcn(a(k1));
    R = roots(p);
    C(:,k1) = imag(R);
end
figure
plot(a, C, '.')
grid
figure
meshc(C)
grid on

The problem was that you had some commas and periods in what appear to be inappropriate places, and also concatenation errors created by the spaces between the terms and operators in each line. (The solution for the concatenation errors is to remove the commas and periods, and for the spaces, to put parentheses around each complete line.)

Alexander Kimbley 2019-2-7

Thanks a lot! You've been such a godsend!

Star Strider 2019-2-7

As always, my pleasure! Thank you!

请先登录，再进行评论。

Problem with for loop plotting a graph

2 个评论
显示无隐藏无

采纳的回答

14 个评论
显示 12更早的评论隐藏 12更早的评论

更多回答（0 个）

另请参阅

类别

标签

Community Treasure Hunt

Problem with for loop plotting a graph

2 个评论 显示 无隐藏 无

采纳的回答

14 个评论 显示 12更早的评论隐藏 12更早的评论

更多回答（0 个）

另请参阅

类别

标签

Community Treasure Hunt

2 个评论
显示无隐藏无

14 个评论
显示 12更早的评论隐藏 12更早的评论