MATLAB: Replacing variables with dumthe variables

substitution of variables

Hello everyone,

I have obtained a really long equation in Matlab containing a lot of variables. Is there a function in Matlab that can find N suitable dummy variables in which it can compress the found combinations of the actual variables?

Forex:

y(x) = A*log(x)+A*B*sin(x)+C*e^x

Where:

A = 2*a+b+5*c+2*d

B = c+d/a

C = a^2+c^4/b+b/2

(the actual equation is much longer)

Thanks in advance!

Best Answer

The only one that I can think of is the Symbolic Math Toolbox coeffs (link) function. Others, such as simplify (link), and related functions linked to on that page, could also be useful.

Related Solutions

MATLAB: I have to construct a 3D plot and contour plot of the following equation which will result in rouge waves i have attached a pic of it .i have tried it several times but i am getting nothing.please help me with the task.any help would be appreciated

By converting the exp() into sin and cos, you can extract the imaginary part of z, getting

IMZ = sin(T)+(-192*sin(T)*(5*T^4+6*T^2*X^2+(9/2)*T^2+X^4+(3/2)*X^2-3/16)-192*cos(T)*(2*T^5+4*T^3*X^2+T^3+2*T*X^4-3*T*X^2-(15/8)*T))/(64*T^6+192*T^4*X^2+192*T^2*X^4+64*X^6+432*T^4-288*T^2*X^2+48*X^4+396*T^2+108*X^2+9)

In order to be able to plot z, this imaginary part IMZ must be 0.

You can attempt to solve IMZ for T, but there is no useful closed form solution for it.

You can solve IMZ for X, which will give you a set of 6 closed form solutions. For each of those, the expression is real valued for parts of the range T = -2 to +2; if there are real-valued solutions outside [-2, +2] then they would have to be quite close to the boundary (that is, the plots I did showed no obvious real solutions outside of [-2, +2] but my plots might not have been accurate enough to be sure.) One solution, for example, is

X = -(1/2)*(-tan(T)*(-48*tan(T)^3*T^4+72*tan(T)^3*T^2+192*tan(T)^2*T^3+3^(1/2)*(768*tan(T)^4*T^8-6912*tan(T)^4*T^6-6144*tan(T)^3*T^7-2016*tan(T)^4*T^4+9216*tan(T)^3*T^5+3072*tan(T)^2*T^6-2048*tan(T)*T^7-432*tan(T)^4*T^2+1152*tan(T)^3*T^3-4608*tan(T)^2*T^4+3072*tan(T)*T^5+2048*T^6-45*tan(T)^4-576*tan(T)^2*T^2+384*tan(T)*T^3-1536*T^4)^(1/2)*tan(T)+9*tan(T)^3+64*T^3)^(1/3)*(-(24*I)*3^(1/2)*tan(T)^2*T^2+I*(-48*tan(T)^3*T^4+72*tan(T)^3*T^2+192*tan(T)^2*T^3+3^(1/2)*(768*tan(T)^4*T^8-6912*tan(T)^4*T^6-6144*tan(T)^3*T^7-2016*tan(T)^4*T^4+9216*tan(T)^3*T^5+3072*tan(T)^2*T^6-2048*tan(T)*T^7-432*tan(T)^4*T^2+1152*tan(T)^3*T^3-4608*tan(T)^2*T^4+3072*tan(T)*T^5+2048*T^6-45*tan(T)^4-576*tan(T)^2*T^2+384*tan(T)*T^3-1536*T^4)^(1/2)*tan(T)+9*tan(T)^3+64*T^3)^(2/3)*3^(1/2)-(6*I)*3^(1/2)*tan(T)^2-(16*I)*3^(1/2)*T^2+4*(-48*tan(T)^3*T^4+72*tan(T)^3*T^2+192*tan(T)^2*T^3+3^(1/2)*(768*tan(T)^4*T^8-6912*tan(T)^4*T^6-6144*tan(T)^3*T^7-2016*tan(T)^4*T^4+9216*tan(T)^3*T^5+3072*tan(T)^2*T^6-2048*tan(T)*T^7-432*tan(T)^4*T^2+1152*tan(T)^3*T^3-4608*tan(T)^2*T^4+3072*tan(T)*T^5+2048*T^6-45*tan(T)^4-576*tan(T)^2*T^2+384*tan(T)*T^3-1536*T^4)^(1/2)*tan(T)+9*tan(T)^3+64*T^3)^(1/3)*tan(T)*T^2+24*tan(T)^2*T^2+(-48*tan(T)^3*T^4+72*tan(T)^3*T^2+192*tan(T)^2*T^3+3^(1/2)*(768*tan(T)^4*T^8-6912*tan(T)^4*T^6-6144*tan(T)^3*T^7-2016*tan(T)^4*T^4+9216*tan(T)^3*T^5+3072*tan(T)^2*T^6-2048*tan(T)*T^7-432*tan(T)^4*T^2+1152*tan(T)^3*T^3-4608*tan(T)^2*T^4+3072*tan(T)*T^5+2048*T^6-45*tan(T)^4-576*tan(T)^2*T^2+384*tan(T)*T^3-1536*T^4)^(1/2)*tan(T)+9*tan(T)^3+64*T^3)^(2/3)-3*tan(T)*(-48*tan(T)^3*T^4+72*tan(T)^3*T^2+192*tan(T)^2*T^3+3^(1/2)*(768*tan(T)^4*T^8-6912*tan(T)^4*T^6-6144*tan(T)^3*T^7-2016*tan(T)^4*T^4+9216*tan(T)^3*T^5+3072*tan(T)^2*T^6-2048*tan(T)*T^7-432*tan(T)^4*T^2+1152*tan(T)^3*T^3-4608*tan(T)^2*T^4+3072*tan(T)*T^5+2048*T^6-45*tan(T)^4-576*tan(T)^2*T^2+384*tan(T)*T^3-1536*T^4)^(1/2)*tan(T)+9*tan(T)^3+64*T^3)^(1/3)-8*(-48*tan(T)^3*T^4+72*tan(T)^3*T^2+192*tan(T)^2*T^3+3^(1/2)*(768*tan(T)^4*T^8-6912*tan(T)^4*T^6-6144*tan(T)^3*T^7-2016*tan(T)^4*T^4+9216*tan(T)^3*T^5+3072*tan(T)^2*T^6-2048*tan(T)*T^7-432*tan(T)^4*T^2+1152*tan(T)^3*T^3-4608*tan(T)^2*T^4+3072*tan(T)*T^5+2048*T^6-45*tan(T)^4-576*tan(T)^2*T^2+384*tan(T)*T^3-1536*T^4)^(1/2)*tan(T)+9*tan(T)^3+64*T^3)^(1/3)*T+6*tan(T)^2+16*T^2))^(1/2)/(tan(T)*(-48*tan(T)^3*T^4+72*tan(T)^3*T^2+192*tan(T)^2*T^3+3^(1/2)*(768*tan(T)^4*T^8-6912*tan(T)^4*T^6-6144*tan(T)^3*T^7-2016*tan(T)^4*T^4+9216*tan(T)^3*T^5+3072*tan(T)^2*T^6-2048*tan(T)*T^7-432*tan(T)^4*T^2+1152*tan(T)^3*T^3-4608*tan(T)^2*T^4+3072*tan(T)*T^5+2048*T^6-45*tan(T)^4-576*tan(T)^2*T^2+384*tan(T)*T^3-1536*T^4)^(1/2)*tan(T)+9*tan(T)^3+64*T^3)^(1/3))

It appears that for any given non-zero T value in [-2, +2], that there are either 2 or 4 X values at which the imaginary part of z disappears.

Therefore, like for your other question, there is no surface to draw: there are some lines of solution. If you were evaluating numerically, you would probably not happen to discover the lines of solution, so the entire plot would probably appear empty. You would need to do a symbolic solution and plot that.

MATLAB: Eigenvalues corresponds to eigenvectors

Absolutely standard: L(k,k) ~ V(:,k).

You can check it with the code:

for k=1:size(h,1)
disp(strcat('k=',num2str(k),'; h*v-lambda*v=',num2str(double(norm(simplify(h*V(:,k) - L(k,k)*V(:,k)))))));
end

Best Answer

Related Solutions

MATLAB: I have to construct a 3D plot and contour plot of the following equation which will result in rouge waves i have attached a pic of it .i have tried it several times but i am getting nothing.please help me with the task.any help would be appreciated

MATLAB: Eigenvalues corresponds to eigenvectors

Related Question