
 A=Q*R, MATRIX A:
   0.500   0.000  -0.500
   0.500   0.000  -1.500
   0.500  -1.000   0.500
   0.500  -1.000  -0.500
 

 MATRIX Q:
   0.500   0.500   0.500
   0.500   0.500  -0.500
   0.500  -0.500   0.500
   0.500  -0.500  -0.500
 

 MATRIX R:
   1.000  -1.000  -1.000
   0.000   1.000  -1.000
   0.000   0.000   1.000
 

 DELETE COLUMN 2 OF A AND UPDATE Q AND R BY DDELC
 ON RETURN FROM DDELC INFO=0
 COLUMN RECOMPUTED BY DDELC:   0.000   0.000  -1.000  -1.000

 UPDATED MATRIX Q:
   0.500   0.000
   0.500   0.707
   0.500  -0.707
   0.500   0.000
 

 UPDATED MATRIX R: 
   1.000  -1.000
   0.000  -1.414
 
 ABS( ELEMENT OF LARGEST MAGNITUDE OF A-Q*R ):  0.0E+00
 ABS( ELEMENT OF LARGEST MAGNITUDE OF Q'*Q-I ): 0.2E-15


 DELETE ROW 3 OF A AND UPDATE Q AND R BY DDELR
 ON RETURN FROM DDELR INFO=0
 ROW RECOMPUTED BY DDELR:    0.500   0.500

 UPDATED MATRIX Q:
  -0.577   0.408
  -0.577  -0.816
  -0.577   0.408
 

 UPDATED MATRIX R:
  -0.866   1.443
   0.000   0.816
 
 ABS( ELEMENT OF LARGEST MAGNITUDE OF A-Q*R ):  0.2E-15
 ABS( ELEMENT OF LARGEST MAGNITUDE OF Q'*Q-I ): 0.6E-16


 NEW 1ST COLUMN TO BE INSERTED INTO A BY DINSC:   1.000   2.000   3.000
 ON RETURN FROM DINSC INFO=0
 COMPUTED RECIPROCAL CONDITION NUMBER BY DINSC: 0.2E+00

 UPDATED MATRIX Q:
  -0.267   0.873   0.408
  -0.535   0.218  -0.816
  -0.802  -0.436   0.408
 

 UPDATED MATRIX R:
  -3.742  -0.802   1.336
   0.000   0.327  -0.546
   0.000   0.000   0.816
 
 ABS( ELEMENT OF LARGEST MAGNITUDE OF A-Q*R ):  0.4E-15
 ABS( ELEMENT OF LARGEST MAGNITUDE OF Q'*Q-I ): 0.1E-15


 NEW 3RD ROW TO BE INSERTED INTO A BY DINSR:   1.000   2.000   3.000
 ON RETURN FROM DINSR INFO=0

 UPDATED MATRIX Q:
  -0.258   0.095  -0.470
  -0.516  -0.095  -0.671
  -0.258   0.949   0.146
  -0.775  -0.285   0.555
 

 UPDATED MATRIX R:
  -3.873  -1.291   0.516
   0.000   1.756   3.085
   0.000   0.000   1.403
 
 ABS( ELEMENT OF LARGEST MAGNITUDE OF A-Q*R ):  0.4E-15
 ABS( ELEMENT OF LARGEST MAGNITUDE OF Q'*Q-I ): 0.2E-15


 RANK ONE MATRIX V*U' ADDED TO A, Q AND R UPDATED BY DRNK1

 VECTOR V:   0.500   0.500   2.000   0.500
 VECTOR U:   1.000  -1.000   1.000

 ON RETURN FROM DRNK1 INFO=1

 UPDATED MATRIX Q:
  -0.275   0.470   0.007
  -0.458   0.671  -0.256
  -0.550  -0.146   0.816
  -0.642  -0.555  -0.519
 

 UPDATED MATRIX R:
  -5.454   0.000  -2.292
   0.000   0.000  -1.403
   0.000   0.000   4.334
 
 ABS( ELEMENT OF LARGEST MAGNITUDE OF A-Q*R ):  0.9E-15
 ABS( ELEMENT OF LARGEST MAGNITUDE OF Q'*Q-I ): 0.4E-15


 RANK REVEALING QR FACTORIZATION BY DRRPM
 ON RETURN FROM DRRPM INFO=0
 DELTA ON EXIT FROM DRRPM: 0.3E-16
 POSITION OF ELEMENTS OF MAX MAGNITUDE OF SUCCESSIVELY COMPUTED
 SINGULAR VECTORS BY DRRPM:  2  2  2
 DRRPM DETERMINED QR FACTORIZATION OF MATRIX A(*,IP(J)), WHERE
  IP(1), IP(2), ... =   1  3  2

 MATRIX Q FOR COLUMN PERMUTED MATRIX A:
  -0.275   0.138  -0.449
  -0.458   0.450  -0.559
  -0.550  -0.821  -0.112
  -0.642   0.323   0.688
 

 MATRIX R FOR COLUMN PERMUTED MATRIX A:
  -5.454  -2.292   0.000
   0.000  -4.555   0.000
   0.000   0.000   0.000
 
 ABS( ELEMENT OF LARGEST MAGNITUDE OF A-Q*R ):  0.9E-15
 ABS( ELEMENT OF LARGEST MAGNITUDE OF Q'*Q-I ): 0.2E-15


 MATRIX A AFTER COLUMN PERMUTATION:
   1.500   0.000   0.000
   2.500  -1.000   0.000
   3.000   5.000   0.000
   3.500   0.000   0.000
 
