How to convert symbolic output to numeric value in Symbolic Math Toolbox?

Question

상원 음 2023-2-7

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1907725-how-to-convert-symbolic-output-to-numeric-value-in-symbolic-math-toolbox

评论： 상원 음 2023-2-8

采纳的回答： Paul

在 MATLAB Online 中打开

Dear MATLAB users,

I tried to calculate following problem using Symbolic Math Toolbox.

Unfortunately, I have faced some problems using Symbolic Math Toolbox.

My code is as follows.

My problem is when i run this code, when the mu is small number, the P0, Pmu an Pc is calculated as numerical value.

But, starts from some points, the results are shown like 'round((513*vpasum(Inf/gamma(n + 181), n, 0, Inf))/2500)'.

When i tried to convert this kind of output to numerical value, it fails.

Therefore, is there any way to convert this kind of output to numerical value?

Thanks in advance!

syms n mu P0 Pmu Pc obj sigma lambda k
lambda=20
sigma=0.1
for mu=1:40
	an=symprod(lambda/(mu+(k*sigma)),k,1,n);
	P0=1/(1+symsum(an,n,1,Inf));
	Pmu=mu*P0_record*vpa(symsum(((lambda^n)*gamma(1+(mu/sigma)))/((sigma^n)*(mu+n*sigma)*gamma(1+n+(mu/sigma))),n,0,Inf));
	Pc=(1-P0)*(mu/(mu+sigma));
	obj=Pmu*Pc;
	P0_record(mu)=round(P0,4);
	Pmu_record(mu)=round(Pmu,4);
	Pc_record(mu)=round(Pc,4);
	obj_record(mu)=round(obj,4);
end

0 个评论
显示 -2更早的评论隐藏 -2更早的评论

请先登录，再进行评论。

请先登录，再回答此问题。

Answer 1

Paul 2023-2-7

0
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1907725-how-to-convert-symbolic-output-to-numeric-value-in-symbolic-math-toolbox#answer_1165525

编辑：Paul 2023-2-7

在 MATLAB Online 中打开

My first inclination was to stay symbolic all the way through and then compute numerical values at the end.

syms lambda mu sigma positive

syms n k integer

a_n = symprod(lambda/(mu + k*sigma),k,1,n);

a_n = simplify(a_n,10)

a_n =

P_0 = 1/(1 + symsum(a_n,n,1,inf));

P_0 = simplify(P_0,10)

P_0 =

P_n = P_0*a_n

P_n =

P_mu = symsum(P_n*(mu/(mu + n*sigma)),n,0,inf)

P_mu =

P_c = (1 - P_0)*(mu/(mu + sigma))

P_c =

Now evaluate using subs. For example

muval = (1:40).';
Pc_record  = subs(P_c,  [lambda sigma mu] , {20, 0.1 , muval});
Pmu_record = subs(P_mu, [lambda sigma mu] , {20, 0.1 , muval});
P0_record  = subs(P_0,  [lambda sigma mu] , {20, 0.1 , muval});

VPA to see the values. Need to increase digits to deal with very large terms in the expressions.

digits(100);
figure
h1 = subplot(211);hold on;plot(muval,real(vpa(Pc_record))),ylabel('real(Pc)')
h2 = subplot(212);hold on;plot(muval,imag(vpa(Pc_record))),ylabel('imag(Pc)');xlabel('mu')
figure
h3 = subplot(211);hold on;plot(muval,real(vpa(Pmu_record))),ylabel('real(Pmu)')
h4 = subplot(212);hold on;plot(muval,imag(vpa(Pmu_record))),ylabel('imag(Pmu)');xlabel('mu')
figure
h5 = subplot(211);hold on;plot(muval,real(vpa(P0_record))),ylabel('real(P0)')
h6 = subplot(212);hold on;plot(muval,imag(vpa(P0_record))),ylabel('imag(P0)'),xlabel('mu')

It looks like for large vaues of mu some error is creeping into the vpa calculations yielding a very, very, small imaginary component even with digits(100). I assume that imaginary part can be safely ignored. Or maybe use more digits? Or maybe the expressions can be further simplified symbolically before subbing in specific values. Sometimes that helps.

Alternatively, setting lambda and sigma ahead of the loop seems to work better, but slower. Couldn't run for all values of mu because it takes too long (takes much longer to run here than on my local machine)

digits(32) % reset to default
clear P0_record Pmu_record Pc_record
syms lambda mu sigma positive
syms n k integer
lambda = sym(20);
sigma = sym(0.1);

Can only use a few values of muval to stay under the Answers runtime limit

muval = [1:8:40 40];

for ii = 1:numel(muval)

mu = sym(muval(ii));

a_n = symprod(lambda/(mu + k*sigma),k,1,n);

a_n = simplify(a_n,10);

P_0 = 1/(1 + symsum(a_n,n,1,inf));

P_0 = simplify(P_0);

P_n = P_0*a_n;

P_mu = symsum(P_n*(mu/(mu + n*sigma)),n,0,inf);

P_c = (1 - P_0)*(mu/(mu + sigma));

Pc_record(ii) = double(P_c);

Pmu_record(ii) = double(P_mu);

P0_record(ii) = double(P_0);

end

plot(h1,muval,real(Pc_record),'-x'),grid

plot(h2,muval,imag(Pc_record),'-x'),grid

plot(h3,muval,real(Pmu_record),'-x'),grid

plot(h4,muval,imag(Pmu_record),'-x'),grid

plot(h5,muval,real(P0_record),'-x'),grid

plot(h6,muval,imag(P0_record),'-x'),grid

1 个评论
显示 -1更早的评论隐藏 -1更早的评论

상원 음 2023-2-8

Thank you for your consideration and detailed explanation! It help me a lot!!

请先登录，再进行评论。

Answer 2

KSSV 2023-2-7

0
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1907725-how-to-convert-symbolic-output-to-numeric-value-in-symbolic-math-toolbox#answer_1165210

Read about double, vpasolve.

1 个评论
显示 -1更早的评论隐藏 -1更早的评论

상원 음 2023-2-8

Thank you for guide! I will study that function.

请先登录，再进行评论。

Answer 3

Amal Raj 2023-2-7

0
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1907725-how-to-convert-symbolic-output-to-numeric-value-in-symbolic-math-toolbox#answer_1165225

在 MATLAB Online 中打开

Hi,

You can use the vpa function to convert the symbolic expression to a numerical value with a specified number of digits.

Then go on with the calculation.

P0=1/(1+symsum(an,n,1,Inf));
Pmu=mu*P0_record*vpa(symsum(((lambda^n)*gamma(1+(mu/sigma)))/((sigma^n)*(mu+n*sigma)*gamma(1+n+(mu/sigma))),n,0,Inf));
Pc=(1-P0)*(mu/(mu+sigma));
% 32 significat digits
P0=vpa(1/(1+symsum(an,n,1,Inf)),32);
Pmu=vpa(mu*P0_record*vpa(symsum(((lambda^n)*gamma(1+(mu/sigma)))/((sigma^n)*(mu+n*sigma)*gamma(1+n+(mu/sigma))),n,0,Inf)),32);
Pc=vpa((1-P0)*(mu/(mu+sigma)),32);