MATLAB: Newbie question

variable plot script

Okay, so I've got a solution, which I've successfully turned into a script, so I can run it and change values as I want. But what if I want to make a plot of one of the variables against the solution? I've tried changing the variable in question into 1:10, or x, but then it just doesn't work. I can run it with a different value for the variable a few times and make comments based on that, but it'd be nicer just to have a plot showing how the variable affected the final answer.

Here's my script (I just copied and pasted it from the script editor window): –

f=500
c=340
wavelength=c/f
SB=30
BR=15
SG=2
RG=2
BG=5
pi=3.14159265358979
L_pR=67
L_pA=70
Rvalues=[45 45 45 45 sqrt(45^2+4^2) sqrt(45^2+4^2) sqrt(45^2+4^2) sqrt(45^2+4^2)]
Lvalues=[sqrt(SB^2+(BG-SG)^2)+sqrt(BR^2+(BG-RG)^2) sqrt(SB^2+(BG-SG)^2)+sqrt(BR^2+(BG+RG)^2) sqrt(SB^2+(BG+SG)^2)+sqrt(BR^2+(BG-RG)^2) sqrt(SB^2+(BG+SG)^2)+sqrt(BR^2+(BG+RG)^2) sqrt(SB^2+(BG-SG)^2)+sqrt(BR^2+(BG-RG)^2) sqrt(SB^2+(BG-SG)^2)+sqrt(BR^2+(BG+RG)^2) sqrt(SB^2+(BG+SG)^2)+sqrt(BR^2+(BG-RG)^2) sqrt(SB^2+(BG+SG)^2)+sqrt(BR^2+(BG+RG)^2)]
Nvalues=(2/wavelength)*(Lvalues-Rvalues)
Triangle_biValues=5+20*log10((sqrt(2*pi*Nvalues))./tanh(sqrt(2*pi*Nvalues)))
BeranekSecondHalfvalues=20*log10(Lvalues./Rvalues)
A_biValues=Triangle_biValues+BeranekSecondHalfvalues
A_biNEGdBValues=10.^(-A_biValues/10)
NR_b=10*log10(sum(A_biNEGdBValues))
L_pB=L_pR-((10*log10(10^(-0/10)+10^(-0/10)))-NR_b)

That didn't paste well, so I've put the script file in my public dropbox too – http://dl.dropbox.com/u/11341635/WideBarrierQ1a.m

I want to see how changing BG affects the solution as a plot.

Tom

Best Answer

pi is already defined; it is not a good idea to redefine it.

Remove your BG=5 line.

Immediately before you calculate Lvalues, add the line

BGs = [1 2 3 4 5 6 7 8 9 10];  %the list of values you want to use
L_pB = zeros(1,length(BGs));   %more efficient to preallocate
for K = 1 : length(BGs)
  BG = BGs(K);

Then, change your assignment that has L_pB on the left hand side, to instead of L_pB(:,K) on the left hand side. And then add the lines

end
plot(BGs, L_pB, 's')

right after that.

I have, though, not gone through the code to be sure that you only calculate a single L_pB value per BG value. If instead multiple values are calculated each time, change the 1 in the "zeros" line to be the number of items that are calculated each time (e.g., 7)

I did not join the points together in the plot because it is not clear to me that the points could be considered ordered or continuous.

Related Solutions

MATLAB: Can’t separate the two variables for which solution needs to be found

Well, you can reduce everything down to an expression in p and L, generating a 15th degree polynomial if solved for p, or a 12th degree polynomial if solved for L. There are, of course, no analytical roots for either of them.

To make the expression clearer, I will show it collected by p within L, and by L within p:

(-p^12 + (4*p^12-24*p^11+72*p^10-152*p^9+252*p^8-336*p^7+368*p^6-336*p^5+252*p^4-152*p^3+72*p^2-24*p+4)*L^11 + (-12*p^13+24*p^12+24*p^11-132*p^10+264*p^9-384*p^8+384*p^7-264*p^6+132*p^5-24*p^4-24*p^3+12*p^2)*L^10 + p^10 + (12*p^14+60*p^13-216*p^12+240*p^11-260*p^10+292*p^9-132*p^8+16*p^7+56*p^6-188*p^5+188*p^4-96*p^3+32*p^2-4*p)*L^9 + (-4*p^15-96*p^14-24*p^13+376*p^12-348*p^11+383*p^10-407*p^9+36*p^8+116*p^7-46*p^6-22*p^5+40*p^4-5*p^2+p)*L^8 + (36*p^15+252*p^14-240*p^13-120*p^12+39*p^11-138*p^10+276*p^9-312*p^8+194*p^7+48*p^6-52*p^5+16*p^4+3*p^3-2*p^2)*L^7 + (-108*p^15-204*p^14+332*p^13-175*p^12-105*p^11+150*p^10+98*p^9+22*p^8-62*p^7+63*p^6-p^5-12*p^4+2*p^3)*L^6 + (108*p^15-72*p^14-119*p^13+364*p^12-82*p^11-63*p^10+119*p^9+23*p^8-10*p^7-28*p^6+32*p^5-22*p^4+6*p^3)*L^5 + (108*p^14-54*p^13-37*p^12+166*p^11-43*p^10-29*p^9+18*p^8+26*p^7-45*p^6+16*p^5+3*p^4-p^3)*L^4 + (45*p^13-29*p^12-16*p^11+47*p^10-21*p^9-23*p^8+17*p^7+9*p^6-6*p^5+p^4)*L^3 + (p^13+17*p^12-20*p^11+3*p^10+11*p^9+5*p^8-9*p^7+3*p^6)*L^2 + (-3*p^13+3*p^12+3*p^11-2*p^10-4*p^9+3*p^8)*L) / ((p-1)*(p^4+(p^4-2*p^3+2*p^2-2*p+1)*L^3+p^3+(-p^5-2*p^4+2*p^3+p^2)*L^2+(3*p^5+p)*L)*(-p^2+(p-1)*L)^2*p^2)

Or alternately,

((-4*L^8+36*L^7-108*L^6+108*L^5)*p^15 + (12*L^9-96*L^8+252*L^7-204*L^6-72*L^5+108*L^4)*p^14 + (-12*L^10+60*L^9-24*L^8-240*L^7+332*L^6-119*L^5-54*L^4+45*L^3+L^2-3*L)*p^13 + (4*L^11+24*L^10-216*L^9+376*L^8-120*L^7-175*L^6+364*L^5-37*L^4-29*L^3+17*L^2+3*L-1)*p^12 + 4*L^11 + (-24*L^11+24*L^10+240*L^9-348*L^8+39*L^7-105*L^6-82*L^5+166*L^4-16*L^3-20*L^2+3*L)*p^11 + (72*L^11-132*L^10-260*L^9+383*L^8-138*L^7+150*L^6-63*L^5-43*L^4+47*L^3+3*L^2-2*L+1)*p^10 + (-152*L^11+264*L^10+292*L^9-407*L^8+276*L^7+98*L^6+119*L^5-29*L^4-21*L^3+11*L^2-4*L)*p^9 + (252*L^11-384*L^10-132*L^9+36*L^8-312*L^7+22*L^6+23*L^5+18*L^4-23*L^3+5*L^2+3*L)*p^8 + (-336*L^11+384*L^10+16*L^9+116*L^8+194*L^7-62*L^6-10*L^5+26*L^4+17*L^3-9*L^2)*p^7 + (368*L^11-264*L^10+56*L^9-46*L^8+48*L^7+63*L^6-28*L^5-45*L^4+9*L^3+3*L^2)*p^6 + (-336*L^11+132*L^10-188*L^9-22*L^8-52*L^7-L^6+32*L^5+16*L^4-6*L^3)*p^5 + (252*L^11-24*L^10+188*L^9+40*L^8+16*L^7-12*L^6-22*L^5+3*L^4+L^3)*p^4 + (-152*L^11-24*L^10-96*L^9+3*L^7+2*L^6+6*L^5-L^4)*p^3 + (72*L^11+12*L^10+32*L^9-5*L^8-2*L^7)*p^2 + (-24*L^11-4*L^9+L^8)*p) / ((p-1)*((-L^2+3*L)*p^5+(L^3-2*L^2+1)*p^4+L^3+(-2*L^3+2*L^2+1)*p^3+(2*L^3+L^2)*p^2+(-2*L^3+L)*p)*(L*p-p^2-L)^2*p^2)

Not so nice, either way you look at it.

If you examine the first variant, collected by L, and look at the denominator, you can see that the expression blows up for several cases -- p = 0, p = 1, p = L/2 +/- sqrt(L^2-4*L)/2, or p^4+(p^4-2*p^3+2*p^2-2*p+1)*L^3+p^3+(-p^5-2*p^4+2*p^3+p^2)*L^2+(3*p^5+p)*L = 0 which has 3 roots when solved for L.

The third of those conditions can be expressed as L = p^2/(p-1) which is real-valued for all p except p = 1, so no matter how the cubic behaves, there will be at least one non-solution for each p. In fact the cubic has a minimum of 1 real L root for each positive p (two real solutions beyond a point), and a minimum of two real L roots for each negative p. I believe that the cubic has three real roots for each negative p, but some fancy algebraic mangling would be necessary to prove that those vanishingly small imaginary components are necessarily zero.

Anyhow, for each p there are thus between 1 and 4 L for which x1 and x2 have no solution.

MATLAB: How do i solve the errors arising from this code

Please check whether this is what you want:

function main
  A_sb10 = 0;
  A_s0 = 1;
  A_10 = 0;
  A_sb20 = 0;
 A0 = [A_s0 A_10 A_sb10 A_sb20];
  [z,A] = ode45(@(t,y)odefcn(t,y(1),y(2),y(3),y(4)), [0 1], A0);
   A_sb1  = A(:,1); A_1 = A(:,3);
   A_s  = A(:,2);   A_sb2 = A(:,4);
   plot(z,real(A(:,4)))
  end
function dAdz = odefcn(t ,A_s, A_1, A_sb1, A_sb2)
  %parameters used inthe simulation.
  pi= 3.143; lambda_1 = 1536 ; lambda_2 = 1538; lambda_s = 1534; lambda_0 = 1535;
  lambda_c = (lambda_1 + lambda_2)/2;
  w_0 = (2*pi)/lambda_0;
  w_1 = (2*pi)/lambda_1;
  w_2 = (2*pi)/lambda_2;
  w_s = (2*pi)/lambda_s;
  w_c = (2*pi)/lambda_c;
  B_3 =2.881*10^-2;B_4 =-1.852*10^-4;P_1 = 1;P_2 =1 ;
  gamma =122.7*10^-3;
  B_2 = B_3*(w_c - w_0)^2 + (B_4/2)*(w_c - w_0);
  delta_w_p = (w_2 - w_1)/2;
  delta_w_s = w_s - w_c;
  w_sb1 = 2*delta_w_p - delta_w_s;
  %w_sb2 = 2*delta_w_p - delta_w_s;
  delta_w_sb = w_c - w_sb1;
  r = 2*gamma*sqrt(P_1*P_2);
dA_sb1dz = (1i/24)*A_sb1*(12*B_2*(delta_w_sb^2 - delta_w_p^2)... 
- 4*B_3*(delta_w_s^3-delta_w_p^3)+ B_4*(delta_w_sb^4 - delta_w_p^4))+1i*gamma...
*P_1*(A_sb1 + conj(A_s))+ 1i*r*(conj(A_sb1) + A_s);
dA_sdz = (1i/24)*A_s*(12*B_2*(delta_w_s^2 - delta_w_p^2)... 
- 4*B_3*(delta_w_s^3-delta_w_p^3)+ B_4*(delta_w_s^4 - delta_w_p^4))+ 1i*gamma...
*P_1*(conj(A_sb1) + A_s)+ 1i*r*(conj(A_1) + A_sb2);
dA_1dz = (1i/24)*A_1*(12*B_2*(delta_w_s^2 - delta_w_p^2)... 
+ 4*B_3*(delta_w_s^3-delta_w_p^3)+ B_4*(delta_w_s^4 - delta_w_p^4))+1i*gamma...
*P_2*(conj(A_sb2) + A_1)+ 1i*r*(conj(A_s) + A_sb1);
dA_sb2dz = (1i/24)*A_sb2*(12*B_2*(delta_w_sb^2 - delta_w_p^2)... 
+ 4*B_3*(delta_w_sb^3-delta_w_p^3)+ B_4*(delta_w_sb^4 - delta_w_p^4))+1i*gamma...
*P_2*(conj(A_1) + A_sb2)+ 1i*r*(conj(A_sb1) + A_s);
     dAdz = [dA_sb1dz; dA_sdz; dA_1dz; dA_sb2dz];
  end

Best Answer

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MATLAB: Can’t separate the two variables for which solution needs to be found

MATLAB: How do i solve the errors arising from this code

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