Display Results as nicely formatted table

in this codes, how do I get the resalts as a nice table showing step by step iterations clarifying more collums would be

itteration, lower, upper, f(lower), f(upper), f(xc), f(c), xupper-xlower

function y = f(x) y = x.^3 - 2;

exists. Then:

>> format long
>> eps_abs = 1e-5;
>> eps_step = 1e-5;
>> a = 0.0;
>> b = 2.0;
>> while (b - a >= eps_step || ( abs( f(a) ) >= eps_abs && abs( f(b) )  >= eps_abs ) )
    c = (a + b)/2;
    if ( f(c) == 0 )
       break;
    elseif ( f(a)*f(c) < 0 )
       b = c;
    else
       a = c;
    end
end
>> [a b]
ans = 1.259918212890625  1.259925842285156
>> abs(f(a))
ans =    0.0000135103601622
>> abs(f(b))
ans =    0.0000228224229404

[Tadashi]

If your MATLAB version is R2013b or newer, you can use table command.

Answer 1

[Paulo Silva]

I have no idea what f(xc) is so I didn't included it, don't use the following code to benchmark your function because it's slower (datasave isn't preallocated), use it only to get a nice table of values and have another function that doesn't make the table for benchmarks (tic toc or profiler).

Using the format short:

clc
fprintf('  itteration   lower    upper    f(lower)  f(upper)    f(c)  xupper-xlower\n')
clear
f=@(x) x.^3 - 2;
format short
eps_abs = 1e-5;
eps_step = 1e-5;
a = 0;
b = 2.0;
iter=0;
datasave=[];
while (b - a >= eps_step || ( abs( f(a) ) >= eps_abs && abs( f(b) )  >= eps_abs ) )
    iter=iter+1;
    c = (a + b)/2;
    datasave=[datasave; iter a b f(a) f(b) f(c) b-a];
    if ( f(c) == 0 )
       break;
    elseif ( f(a)*f(c) < 0 )
       b = c;
    else
       a = c;
    end
end

disp(datasave)

The output looks like this:

   itteration   lower    upper    f(lower)  f(upper)    f(c)  xupper-xlower
      1.0000         0    2.0000   -2.0000    6.0000       NaN    2.0000
      2.0000    1.0000    2.0000   -1.0000    6.0000   -1.0000    1.0000
      3.0000    1.0000    1.5000   -1.0000    1.3750    1.3750    0.5000
      4.0000    1.2500    1.5000   -0.0469    1.3750   -0.0469    0.2500
      5.0000    1.2500    1.3750   -0.0469    0.5996    0.5996    0.1250
      6.0000    1.2500    1.3125   -0.0469    0.2610    0.2610    0.0625
      7.0000    1.2500    1.2813   -0.0469    0.1033    0.1033    0.0313
      8.0000    1.2500    1.2656   -0.0469    0.0273    0.0273    0.0156
      9.0000    1.2578    1.2656   -0.0100    0.0273   -0.0100    0.0078
     10.0000    1.2578    1.2617   -0.0100    0.0086    0.0086    0.0039
     11.0000    1.2598    1.2617   -0.0007    0.0086   -0.0007    0.0020
     12.0000    1.2598    1.2607   -0.0007    0.0039    0.0039    0.0010
     13.0000    1.2598    1.2603   -0.0007    0.0016    0.0016    0.0005
     14.0000    1.2598    1.2600   -0.0007    0.0004    0.0004    0.0002
     15.0000    1.2599    1.2600   -0.0002    0.0004   -0.0002    0.0001
     16.0000    1.2599    1.2599   -0.0002    0.0001    0.0001    0.0001
     17.0000    1.2599    1.2599   -0.0000    0.0001   -0.0000    0.0000
     18.0000    1.2599    1.2599   -0.0000    0.0001    0.0001    0.0000
     19.0000    1.2599    1.2599   -0.0000    0.0000    0.0000    0.0000

Using the format long:

clc
fprintf('       itteration              lower             upper             f(lower)            f(upper)               f(c)           xupper-xlower\n')
clear
f=@(x) x.^3 - 2;
format long
eps_abs = 1e-5;
eps_step = 1e-5;
a = 0;
b = 2.0;
iter=0;
datasave=[];
while (b - a >= eps_step || ( abs( f(a) ) >= eps_abs && abs( f(b) )  >= eps_abs ) )
    iter=iter+1;
    c = (a + b)/2;
    datasave=[datasave; iter a b f(a) f(b) f(c) b-a];
    if ( f(c) == 0 )
       break;
    elseif ( f(a)*f(c) < 0 )
       b = c;
    else
       a = c;
    end
end

disp(datasave)

The output looks like this:

     itteration              lower             upper             f(lower)            f(upper)               f(c)           xupper-xlower
     1.000000000000000                   0   2.000000000000000  -2.000000000000000   6.000000000000000                 NaN   2.000000000000000
     2.000000000000000   1.000000000000000   2.000000000000000  -1.000000000000000   6.000000000000000  -1.000000000000000   1.000000000000000
     3.000000000000000   1.000000000000000   1.500000000000000  -1.000000000000000   1.375000000000000   1.375000000000000   0.500000000000000
     4.000000000000000   1.250000000000000   1.500000000000000  -0.046875000000000   1.375000000000000  -0.046875000000000   0.250000000000000
     5.000000000000000   1.250000000000000   1.375000000000000  -0.046875000000000   0.599609375000000   0.599609375000000   0.125000000000000
     6.000000000000000   1.250000000000000   1.312500000000000  -0.046875000000000   0.260986328125000   0.260986328125000   0.062500000000000
     7.000000000000000   1.250000000000000   1.281250000000000  -0.046875000000000   0.103302001953125   0.103302001953125   0.031250000000000
     8.000000000000000   1.250000000000000   1.265625000000000  -0.046875000000000   0.027286529541016   0.027286529541016   0.015625000000000
     9.000000000000000   1.257812500000000   1.265625000000000  -0.010024547576904   0.027286529541016  -0.010024547576904   0.007812500000000
    10.000000000000000   1.257812500000000   1.261718750000000  -0.010024547576904   0.008573234081268   0.008573234081268   0.003906250000000
    11.000000000000000   1.259765625000000   1.261718750000000  -0.000740073621273   0.008573234081268  -0.000740073621273   0.001953125000000
    12.000000000000000   1.259765625000000   1.260742187500000  -0.000740073621273   0.003912973217666   0.003912973217666   0.000976562500000
    13.000000000000000   1.259765625000000   1.260253906250000  -0.000740073621273   0.001585548394360   0.001585548394360   0.000488281250000
    14.000000000000000   1.259765625000000   1.260009765625000  -0.000740073621273   0.000422512079240   0.000422512079240   0.000244140625000
    15.000000000000000   1.259887695312500   1.260009765625000  -0.000158837092386   0.000422512079240  -0.000158837092386   0.000122070312500
    16.000000000000000   1.259887695312500   1.259948730468750  -0.000158837092386   0.000131823412403   0.000131823412403   0.000061035156250
    17.000000000000000   1.259918212890625   1.259948730468750  -0.000013510360162   0.000131823412403  -0.000013510360162   0.000030517578125
    18.000000000000000   1.259918212890625   1.259933471679688  -0.000013510360162   0.000059155646067   0.000059155646067   0.000015258789063
    19.000000000000000   1.259918212890625   1.259925842285156  -0.000013510360162   0.000022822422940   0.000022822422940   0.000007629394531

[Paulo Silva]

The ouput looks bad here but should look good if you can copy the spaces to your matlab, if not just adjust the space in the fprintf, also the size of the command line window should be big enough to show all the data.

[buxZED]

lifesaver

can i ask a really stupid question?

in the code "if ( f(c) == 0 )"

whay two "=" signs ?

[Paulo Silva]

one = means assignement and two means compare, try it like this

a=5;a %you get the number 5 because you %assign 5 to a

b=2;a==b %you get the logic value 0, it means %not equal

b=5;a==b %you get the logic value 1, it means %the variables are equal

[buxZED]

Thank you very much for clarifying

Like to thank you on behalf of me and my friends

We do really appreciate the time and effort

[Paulo Silva]

Just a small correction, you might want to change the lines

datasave=[datasave; iter a b f(a) f(b) f(c) b-a];

c = (a + b)/2;

to

c = (a + b)/2;

datasave=[datasave; iter a b f(a) f(b) f(c) b-a];

and remove the c=nan; from the code

So you don't have NaN in the first f(c) value

[Paulo Silva]

I fixed the code, now the f(c) column is correct.

[buxZED]

clc

fprintf(' Iteration XL XR f(XL) f(XR) f(XC) |XR-XL|\n')

clear

stu_id=0.2529;

f=@(x) (2.8*x.^3)-(3.5*x.^2)+(1.5*x)-(0.15+(0.1*stu_id));

format long

eps_abs = 1e-5;

eps_step = 1e-5;

XL = 0;

XR = 1.0;

XC=(XL+XR)/2;

iter=0;

datasave=[];

while (XR - XL >= eps_step || ( abs( f(XL) ) >= eps_abs && abs( f(XR) ) >= eps_abs ) )

iter=iter+1;

datasave=[datasave; iter XL XR f(XL) f(XR) f(XC) XR-XL];

XC = (XL + XR)/2;

if ( f(XC) == 0 )

break;

elseif ( f(XL)*f(XC) < 0 )

XR = XC;

else

XL = XC;

end

end

disp(datasave)

how do I add "c" to the table

have i done anything wrong?

Answer 2

[Omar Alsaidi]

fprintf('Celsius equivalent of a Fahrenheit temperature:\t\t Fahrenheit equivalent of a Celsius temperature:\n\n \t Celsius\tFahrenheit \t\t \t\tFahrenheit\tCelsius\n')

c=[0:2:100];

f=[32:2:212];

function [C] = Celsius(f)

C=(f-32) *5/9;

end

function [F]=Fahrenheit(c)

F =9/5*c+32;

end

Answer 3

[Abhay]

X=11/3 Format long Display (X)