1

If we take for example a vector of one line 

>>m = linspace(0,100,11)
>>J = exp(m.^0.25)

we get

J =

  Columns 1 through 4

    1.0000    5.9197    8.2875   10.3848

  Columns 5 through 8

   12.3650   14.2841   16.1700   18.0385

  Columns 9 through 11

   19.8996   21.7599   23.6243

We get the right result in the first entry of the output matrix which is e^(0^0.25) = e^0 = 1

But if we take

>> J = exp(m.^2.5)

We get

J =

  1.0e+137 *

  Columns 1 through 4

    0.0000    2.1676       Inf       Inf

  Columns 5 through 8

       Inf       Inf       Inf       Inf

  Columns 9 through 11

       Inf       Inf       Inf

But e^(0^2.5) = e^0 = 1

I did not use matlab for a long time I don't have a good idea how this works, I first thought it could be a round off or a truncation or both, I looked up what the operation was and some documentation of the formats, I found that it does show the right result within the vector using the format longE :

>>format longE

which returns 1.000000000000000e+00

but then I checked the first matrix with the enry 0 ( Default format short) by using 

>>J(1)

And it returned 1.

So the value in that entry is correct but it shows 0 , and a factor outside the matrix 1.0e+137 *
I don't get what is happening, why it shows a 0 ?

phi
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2 Answers2

4

When displaying a matrix in format long, MATLAB chooses a factor which is suitable for all entries. An example for the purpose of explanation:

k=10.^[1:10]

k =

   1.0e+10 *

    0.0000    0.0000    0.0000    0.0000    0.0000    0.0001    0.0010    0.0100    0.1000    1.0000

The first entry is a 10, but because of the factor of 10 000 000 000 it is not displayed. When you instead type in k(1) matlab will choose a format suitable for that number:

>> k(1)

ans =

    10

The standard output is "usually" good where all numbers in a similar magnitude. A workaround is to use mat2str.

>> mat2str([pi,10.^[1:20]])

ans =

    '[3.14159265358979 10 100 1000 10000 100000 1000000 10000000 100000000 1000000000 10000000000 100000000000 1000000000000 10000000000000 100000000000000 1e+15 1e+16 1e+17 1e+18 1e+19 1e+20]'

It displays up to 15 digits which is usually enough, but 17 digits would be required to display a double in full accuracy (further information)

Daniel
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2

The numerical output format in MATLAB's Command Window is under user control which you can change from the MATLAB Command Window Preferences.

What you are observing is the default behavior.

>> k=10.^[1:10];
>> k
k =
  1.0e+10 *
    0.0000  0.0000  0.0000  0.0000  0.0000  0.0001  0.0010  0.0100  0.1000  1.0000

However, you can change the output format to use the floating point format:

>> format short e
>> k
k =
1.0000e+01   1.0000e+02   1.0000e+03   1.0000e+04   1.0000e+05   1.0000e+06   
1.0000e+07   1.0000e+08   1.0000e+09   1.0000e+10

You can also change it to use the "best of fixed or floating point format":

>> format short g
>> k
k =
10     100     1000    10000    1e+05    1e+06    1e+07    1e+08    1e+09    1e+10

See the format command on other available options. Explicitly printing your variables (using the mat2str command etc.) to see their full precision is not necessary, nor is it used by most MATLAB users. If you really want full precision you can use format long e or format long g.

Kavka
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