This is an example of a QR decomposition using Gramp Schmidt 
and the VSIPL core library. No VSIPL QR functions are used.

To compile you need to build the library in src_core, and in src_VU.

The example matrices (An.data) are from chapter 5 of the book
Liner Algebra by Richard Bronson (Academic Press)

Bronsons results are below.
/********************************************/
qrdex 3 3 A1.data

A1 is 1 0 1
      1 1 0
      0 1 1

Q is 1/sqrt(2)   -1/sqrt(6)    1/sqrt(3)
     1/sqrt(2)    1/sqrt(6)   -1/sqrt(3)
        0         2/sqrt(6)    1/sqrt(3)

R is sqrt(2)    1/sqrt(2)   1/sqrt(2)
       0        sqrt(2/3)   1/sqrt(6)
       0           0        2/sqrt(3)
/********************************************/
qrdex 4 4 A2.data

A2 is 1 1 0 1
      1 2 1 0
      0 1 2 1
      1 0 1 1 

Q is 0.5774 0.0000 -0.3651  0.7303
     0.5774 0.5774 -0.1826 -0.5477
     0.0000 0.5774  0.7303  0.3651
     0.5774 0.5774  0.5477 -0.1826

R is  1.7321  1.7321  1.1547  1.1547
         0    1.7321  1.1547  0.0000
         0       0    1.8257  0.9129
         0       0      0     0.9129
/********************************************/
qrdex 3 2 A3.data

A3 is 1 2
      2 2
      2 1

Q is 1/3  10/sqrt(153)
     2/3   2/sqrt(153)
     2/3  -7/sqrt(153)

R is 3      8/3
     0  sqrt(153)/9
/********************************************/
