MATLAB: Variable ‘a’ is undefined on some execution paths.

simulation

when I start simulation, an error message 'Variable 'a_p' is undefined on some execution paths' arise and terminate simulation. I define the variable 'a_p' in that subsystem as following

for j = 1:J
  if j==1; 
      a_p=[3,4,5,9,10]; 
  else 
      if j==2;
          a_p= [1,2,6,7,8,14,15]; 
      else 
          if j==3;
              a_p=[11 12 13 19 20]; 
          else 
              if j==4;
                  a_p=[16 17 18 25];
              else 
                  if j==5;
                      a_p=[21 22 23 24];
                  end
              end
          end
      end
  end
end

It would be appreciated if you could help me on simulation running

Best Answer

Both Geoff Hayes and Grieg have made some good points about simplifying the if statements, but it seems no one has addressed the point of the loop itself: if J is five for example this loop will run five times, and calls if a total of fifteen times, and yet the end result is simply that of j=5. This is slow and pointless.

Rather than doing this in unnecessary loops, why not use simpler, neater and faster code? switch would be the obvious choice:

switch J
   case 1
      a_p = [3,4,5,9,10]; 
   case 2
      a_p = [1,2,6,7,8,14,15];
   case 3
      a_p = [11,12,13,19,20];
   case 4
      a_p = [16,17,18,25];
   case 5
      a_p = [21,22,23,24];
   otherwise
      % error(...)  ?
      % a_p = [...] ?
end

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: FFT code on time series

hi Sam,

in case you have verified the properties of the signal in the above comment,we can proceed as the following :

We have a signal of length L=3950 taken every 12 hours for 2563.5 days. So formally the sampling rate is Fs= 3950/2563 =~1.54 Hz .

For these types of times series , the range is dynamically changing therefore we plot the frequency in dB to expand the low values and compress the high ones :

1)Solution 1:

Fs=1.55; %  
L=length(Thermocline);
N=ceil(log2(L));
FFTherm=fft(Thermocline,2^N);
f=(Fs/2^N)*(0:2^(N-1)-1);
Power=FFTherm.*conj(FFTherm);
figure,
semilogy(f,Power(1:2^(N-1)))
xlabel('  Frequency (Hz)'), ylabel(' Magnitude (w)'),
title('  Power Spectral Density'), grid on;

2) Solution : 2

 % Directly you type in the C.P :
  psd(Thermocline)

So the frequency is in the range [0,...,0.1] Hz. To see if this result, physically, makes sens, try to check :

"Stochastic climate models, Part I1, Application to sea-surface temperature anomalies and thermocline variability" by CLAUDE FRA NKIG NOUL :

And another paper: "MEAN AND EDDY DYNAMICS OF THE MAIN THERMOCLINE" by GEOFFREY K. VALLIS

http://www.princeton.edu/~gkv/papers/thermocline.pdf

These two papers give a general idea on how much an estimate of the frequency must be .

I hope this helps .

KHMOU Youssef.

Best Answer

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

MATLAB: FFT code on time series

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