Matrix Output displays Incorrectly

Alright folks, so I'm brand new here and to matlab so this may be a dumb question. Anyway, I've created the following code to solve a nonlinear equation w/ the secant method. and I can't get mymatrix "ansdat" to display properly:

function f2 = BBSecantSolve()

%initial guesses vm is v_i-1 and v is v_i
vm = 0.05;
v = 0.02;
iter = 0;

disp('  itteration   v(i-1)    v(i)     v(i+1)    err        f(v)     f(vm)');
ansdat=[];

%for loop used to limit iterations to <= 100,000
for i=1:100000

      iter = iter + 1; %counter for output

      %eval f(vi) and f(vi-1) only once each loop
      fv = BB(v);
      fvm = BB(vm); 

      vp = v - fv *(v-vm)/(fv-fvm);% find vp according to secant formula
      err = abs((vp - v)/vp);%find absolute standard error

      ansdat=[ansdat;iter vm v vp err fv fvm];%add current values to output matrix

      if err < 1e-4 %exit loop when the standard error is less than 0.0001
          format short;%numerical output format
          disp(ansdat);%show the matrix with all iteration values
          f2 = vp;%give final answer
          return
      end

      %set next loop values for vm and v
      vm = v;
      v = vp;
  end
  %error message in the case loop reaches 100,000 iterations
  disp('maximum iterations reached, try a different initial guess');

function f = BB(vol)
%Beattie-Bridgman constants specific to CO2
A0 = 507.2836;
a = 0.07132;
B0 = 0.10476;
b = 0.07235;
c = 660000;

%Other System Variables
Ru = 8.314; %kPa * m^3 / (kmol * K)
P = 10132.5; %kPa
T = 300; %K
m = 0.001; %kmol
f = Ru*T/(vol^2)*(1-c/(vol*T^3))*(vol+B0*(1-b/vol))-(A0*(1-a/vol))/vol^2-P;
end
end

using the debugging tools I get the value of 'ansdat' right before my disp(ansdat) line to be (fyi this looks like the values I expect with the counter in the left most column increasing by one each iteration):

1.000   0.050   0.020   0.051   0.605   3596341.147     78007.417
2.000   0.020   0.051   0.051   0.012   73362.643       3596341.147
3.000  0.051  0.051  0.062  0.171  69193.920  73362.643
4.000  0.051  0.062  0.069  0.101  27424.121  69193.920
5.000  0.062  0.069  0.078  0.112  15248.698  27424.121
6.000  0.069  0.078  0.085  0.089  7092.634  15248.698
7.000  0.078  0.085  0.092  0.070  3246.279  7092.634
8.000  0.085  0.092  0.096  0.042  1254.512  3246.279
9.000  0.092  0.096  0.097  0.017  368.021          1254.512
10.000  0.096  0.097  0.098  0.003  61.533          368.021
11.000  0.097  0.098  0.098  0.000  3.753          61.533
12.000  0.098  0.098  0.098  0.000  0.041          3.753

However, the output that prints is:

0.0000    0.0000    0.0000    0.0000    0.0000    3.5963    0.0780
0.0000    0.0000    0.0000    0.0000    0.0000    0.0734    3.5963
0.0000    0.0000    0.0000    0.0000    0.0000    0.0692    0.0734
0.0000    0.0000    0.0000    0.0000    0.0000    0.0274    0.0692
0.0000    0.0000    0.0000    0.0000    0.0000    0.0152    0.0274
0.0000    0.0000    0.0000    0.0000    0.0000    0.0071    0.0152
0.0000    0.0000    0.0000    0.0000    0.0000    0.0032    0.0071
0.0000    0.0000    0.0000    0.0000    0.0000    0.0013    0.0032
0.0000    0.0000    0.0000    0.0000    0.0000    0.0004    0.0013
0.0000    0.0000    0.0000    0.0000    0.0000    0.0001    0.0004
0.0000    0.0000    0.0000    0.0000    0.0000    0.0000    0.0001
0.0000    0.0000    0.0000    0.0000    0.0000    0.0000    0.0000

Can anyone tell me what in the world is going on!?

Thanks in advance

Answer 1

[Kelly Kearney]

At the top of that matrix output, I'm guessing you'll find a

1.0e+06 *

You specify short format display, but due to the range in your data, Matlab needs a multiplier to show the largest numbers. At only 4 decimal points, your smaller numbers are truncated. Change the line to

format shortg

or something similar, and you should see the expected output.

[Kevin]

Thanks Kelly, the shortg format worked perfectly.

[dpb]

Ahhhh...I was just coming back to add an ADDENDUM...

Answer 2

[dpb]

...
ansdat=[ansdat;iter vm v vp err fv fvm];
if err < 1e-4              %exit error is less than 0.0001
  format short;            %numerical output format
  disp(ansdat);            %show the matrix with all iteration values
  ...

You've placed all the data in the single array so Matlab by default will scale disparate ranges of exponents; if you'll note on the display there will be a header line that say something like

1.0e-06 *

above the data which when multiplied by the values gives the correct numbers. Of course, there's the problem of not enough significant digits to show the same precision across a wide range of exponents in the same array.

To make the data fit, you need to use fprintf() with an appropriate format string for the values you have.

fmt=[repmat('%14.3f',1,7) '\n'];
fprintf(fmt,ansdat')

NB the ' transpose operator to output the internally column-major storage order by row.