NAG Library Manual, Mark 28.7
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NAG AD Library Introduction
Example description

 F08KP_A1W_F Example Program Results

 Singular values
     3.9994  3.0003  1.9944  0.9995
 Left singular vectors
          1       2       3       4       5       6
 1  -0.5634 -0.2687  0.2451  0.3787  0.0139 -0.1493
     0.0016 -0.2749  0.4657  0.2987 -0.0003 -0.0514
 
 2   0.1205 -0.2909  0.4329 -0.0182  0.0254 -0.0369
    -0.6108  0.1085 -0.1758 -0.0437 -0.5033 -0.2003
 
 3  -0.0816 -0.1660 -0.4667 -0.0800  0.2141 -0.2871
     0.1613  0.3885  0.3821 -0.2276 -0.4801 -0.0903
 
 4   0.1441  0.1984 -0.0034  0.2608 -0.2664 -0.3808
    -0.1532 -0.1737  0.1555 -0.5382  0.2516 -0.4744
 
 5  -0.2487  0.6253  0.2643  0.1002  0.5720 -0.0462
    -0.0926  0.3304 -0.0194  0.0140  0.0720 -0.1202
 
 6  -0.3758 -0.0307  0.1266 -0.4175 -0.0516  0.6051
     0.0793 -0.0816  0.1747 -0.4058 -0.0153 -0.3004

 Right singular vectors by row
          1       2       3       4
 1  -0.6971 -0.0867  0.0560 -0.1878
    -0.0000 -0.3548 -0.5400 -0.2253
 
 2   0.2403  0.0725 -0.2477  0.7026
     0.0000 -0.2336 -0.5291  0.2177
 
 3  -0.5123 -0.3030  0.0678  0.4418
     0.0000 -0.1735  0.5162  0.3864
 
 4  -0.4403  0.5294 -0.3027  0.1667
     0.0000  0.6361 -0.0346  0.0258

  Derivatives calculated: First order adjoints
  Computational mode    : algorithmic

  Derivatives of S w.r.t. first column of A:
          1       2       3       4       5       6
 1   0.3928 -0.0840  0.0569 -0.1004  0.1734  0.2620
    -0.0011  0.4258 -0.1125  0.1068  0.0646 -0.0553
 
 2  -0.0646 -0.0699 -0.0399  0.0477  0.1502 -0.0074
    -0.0660  0.0261  0.0933 -0.0417  0.0794 -0.0196
 
 3  -0.1256 -0.2218  0.2391  0.0017 -0.1354 -0.0648
    -0.2386  0.0901 -0.1958 -0.0796  0.0099 -0.0895
 
 4  -0.1668  0.0080  0.0352 -0.1148 -0.0441  0.1838
    -0.1315  0.0193  0.1002  0.2370 -0.0062  0.1787