; IDL Version 7.1.1 (linux x86_64 m64)
; Journal File for mats@sally
; Working directory: /home/mats/idl/develop/matrixalgebra
; Date: Thu Apr  5 16:19:19 2012
 
;The QRfac routine makes sense (for the ## convention)
;if we realize that QRfac should be called with the
;transpose of the matrix we want to factorize. Here
;with the example from the qrfac.pro documentation.
; 
;------ |A| (op:##) [3x2] ------
; 9.00  4.00
; 2.00  8.00
; 6.00  7.00
;-------------------------------
; 
;------ |AT=transpose(A)| (op:##) [2x3] ------
; 9.00  2.00  6.00
; 4.00  8.00  7.00
;---------------------------------------------
; 
;Now call "QRFAC, AT, R1, QMATRIX = Q"
; 
; 
;The R matrix returned is properly upper-right triangular
;with the ## conventions:
; 
;------ |R1| (op:##) [2x2] ------
; -11.000   -8.545
;   0.000   -7.482
;--------------------------------
; 
;QRfac calculates a "thin" QR factorization, where both the
;returned R and Q matrices are square. Q1 is the partition
;of Q that matches R1:
; 
;------ |Q| (op:##) [3x3] ------
;  -0.818    0.400   -0.413
;  -0.182   -0.862   -0.474
;  -0.545   -0.313    0.778
;-------------------------------
; 
;------ |Q1| (op:##) [3x2] ------
;  -0.818    0.400
;  -0.182   -0.862
;  -0.545   -0.313
;--------------------------------
; 
;Now we just need to make sure the product actually is
;equal to the original matrix:
; 
;------ |Q1 ## R1| (op:##) [3x2] ------
;   9.000    4.000
;   2.000    8.000
;   6.000    7.000
;--------------------------------------
; 
;------ |A| (op:##) [3x2] ------
;   9.000    4.000
;   2.000    8.000
;   6.000    7.000
;-------------------------------
; 
;------ |A - (Q1 ## R1)| (op:##) [3x2] ------
;   0.000    0.000
;   0.000    0.000
;   0.000    0.000
;--------------------------------------------