MATLAB: Matlab floating point arithmetic and sensitive dependence

doubleMATLABmatrices

As part of a larger project, I have the following simple matrix multiplication:
c = a* b;
Where a is:
 Columns 1 through 7
 1.000000000000000   0.778800783071405   0.367879441171442   0.105399224561864   0.018315638888734   0.778800783071405   
 0.606530659712633
 Columns 8 through 14
 0.286504796860190   0.082084998623899   0.014264233908999   0.367879441171442   0.286504796860190   0.135335283236613   
 0.038774207831722
 Column 15
 0.006737946999085
and b is:
1.0e+02 *
     1.681770403629075
    -3.848571335694688
     4.372852859312935
    -3.552127988829399
     4.433852194145209
    -1.091783715227434
     2.219644313019083
    -1.858966831671062
     0.917816691444462
    -2.715630209256668
     1.794744879202224
    -4.126306698348984
     4.755107353594159
    -3.930478238870790
     4.574731559033815
Giving the result for c:
    -3.064215547965432e-14
However when I try to replicate this with the following test:
 a = [1, 0.778800783071405, 0.367879441171442, 0.105399224561864, 0.018315638888734, 0.778800783071405, 0.606530659712633, 0.28650479686019, 0.082084998623899, 0.014264233908999, 0.367879441171442, 0.28650479686019, 0.135335283236612, 0.038774207831722, 0.006737946999085];
  
 b = [168.1770403629075; -384.8571335694688; 437.2852859312935; -355.2127988829399; 443.3852194145209; -109.1783715227434; 221.9644313019083; -185.8966831671062; 91.7816691444462; -271.5630209256668; 179.4744879202224; -412.6306698348984; 475.5107353594159; -393.0478238870790; 457.4731559033815];
 c = a* b;
My result for c is:
   -5.813127756937320e-13
I assume this has something to do with floating point arithmetic and despite having the MatLab console set to format long I'm perhaps not seeing the full values of the data I'm then pasting in to my test code. If this is the case how does one work around it?
Thanks in advance

Best Answer

The only problem is concealed in the sentence:
 However when I try to replicate this with the following test: ...
Even with format long g the output to the command window is not exact. A conversion to the decimal output as text, than copy&pasting the data and converting them back to binary form can cause differences. So better post the values as MAT file and do not copy&paste inputs or outputs to compare the results.
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