[ADOL-C] Possible bugs in ADOL-C

[Christian Wolf]

Hello,

I am trying to build/use ADOL-C and I am running into the following issues:

1. I built colpack with MPI (--enable-openmp) support. To allow ADOL-C 
to compile I have to use
 > LIBS=-lgopm ./configure ....
2. The documentation seems (at least with respect to the sparse driver) 
a bit outdated/buggy.
3. (The main bug (?)) As far as I understand things the compresses 
hessian matrix (called for example "B") must fullfill the equation B = H 
S where S is the seed matrix. Please correct me if this is not correct.

I tried with various builds (2.4.1 and trunk) to compile and run the 
program ADOL-C/examples/additional_examples/sparse/sparse_hessian. Just 
by looking at the output (no modifications to the SVN version) of the 
default output I get

Sparsity pattern of Hessian:
  0:  0  1
  1:  0  1  4
  2:  2  5
  3:  3
  4:  1  4  5
  5:  2  4  5

  Seed matrix

  0:      1.0000      0.0000      0.0000      0.0000
  1:      0.0000      1.0000      0.0000      0.0000
  2:      1.0000      0.0000      0.0000      0.0000
  3:      1.0000      0.0000      0.0000      0.0000
  4:      1.0000      0.0000      0.0000      0.0000
  5:      0.0000      0.0000      1.0000      0.0000

<snip>

  H

  0:      1.0000      0.0000      0.0000      0.0000      0.0000 0.0000
  1:      5.0000      3.5787      0.0000      0.0000      0.0000 0.0000
  2:      0.0000      0.0000      1.8000      0.0000      0.0000 0.0000
  3:      0.0000      0.0000      0.0000     -0.9602      0.0000 0.0000
  4:      0.0000     -0.5820      0.0000      0.0000     95.4314 0.0000
  5:      0.0000      0.0000  22026.4658      0.0000     79.4007 88169.4721

compressed H: (Here called B)

  0:      1.0000      5.0000      0.0000      0.0000
  1:      4.4180      3.5787      0.0000      0.0000
  2:      1.8000      0.0000  22026.4658      0.0000
  3:     -0.9602      0.0000      0.0000      0.0000
  4:     95.4314     -0.5820     79.4007      0.0000
  5:  22105.8665      0.0000  88169.4721      0.0000

Clearly the sparsity pattern is correct (while H shows only the lower 
triangle). On manually evaluating the value B[1][0] I get a value of 5.

In [1] the author writes that there are several ways to choose the seed 
matrtix. At the moment it seems to be constructed that the i-th row of B 
and the j-th column of the seed matrix must be multiplyed (matrix or 
scalar product) to obtain H[i][j]. This is (as far as I think) related 
to the fact that at the moment the direct approach is used (only 
permutation of identy matrix).
Can I rely on this fact that there will be no change in the future to 
the default behavior?

Thanks a lot
Christian


[1] "Computing Sparse Hessians with Automatic Differentiation" from 
ANDREA WALTHER at the Institute of Scientific Computing, Technische 
Universität Dresden