NAG Library Manual, Mark 31
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NAG AD Library Introduction
Example description

 F03BN_A1W_F Example Program Results

 Array A after factorization
             1          2          3
 1      1.0000     0.0000    -5.0000
        1.0000     3.0000    14.0000
 
 2      1.0000     0.0000    -3.0000
        0.0000     2.0000     6.0000
 
 3      0.5000     0.2500    -0.2500
       -0.5000     0.2500    -0.2500

 Pivots
              2             3             3

 D = (      0.06250,      0.00000), ID = (4, 0)

 Value of determinant = (  0.10000E+01,  0.00000E+00)

  Derivatives calculated: First order adjoints
  Computational mode    : algorithmic

  Derivatives of scaled determinant of A w.r.t. A

    d(dreal)/da
          1       2       3
 1   0.6250  0.5625 -0.1250
    -0.0625  0.1875 -0.1250
 
 2  -0.1250  0.0000 -0.0625
    -0.3750 -0.5000  0.1250
 
 3  -0.1875 -0.1875  0.0625
     0.1250  0.1250  0.0000

    d(dimag)/da
          1       2       3
 1   0.0625 -0.1875  0.1250
     0.6250  0.5625 -0.1250
 
 2   0.3750  0.5000 -0.1250
    -0.1250  0.0000 -0.0625
 
 3  -0.1250 -0.1250  0.0000
    -0.1875 -0.1875  0.0625