NaN with GPMR on certain systems

geoffroyleconte commented 2 years ago

Hi, I have an issue with GPMR when solving some systems (I provided one in the above zip file with the code to read it):

using SparseArrays, LinearAlgebra, Krylov, DelimitedFiles, MatrixMarket
read_path = raw"C:\Users\Geoffroy Leconte\Documents\doctorat\code\bugs\bug gpmr"
A = MatrixMarket.mmread(string(read_path, "/A.mtx"))
E = readdlm(string(read_path, "/E.rhs"), Float64)[:]
δ = readdlm(string(read_path, "/delta.rhs"), Float64)[:][1]
ξ1 = readdlm(string(read_path, "/xi1.rhs"), Float64)[:]
ξ2 = readdlm(string(read_path, "/xi2.rhs"), Float64)[:]

(x, y, stats) = gpmr(A', A, ξ1, ξ2, 
                      C = inv(Diagonal(sqrt.(E))), E = inv(Diagonal(sqrt.(E))), 
                      D = (1.0 / sqrt(δ)) .* I,  F = (1.0 / sqrt(δ)) .* I, λ = -1.0)

This leads to NaN. I don't know if it is supposed to fail on such a system but if it is, it would be convenient to have something that terminates the algorithm and returns an error.

Since this is a saddle-point system I can solve it with TRIMR or TRICG (and it works):

(x, y, stats) = tricg(A', ξ1, ξ2, M = inv(Diagonal(E)), N = (1.0 / δ) .* I, flip=true)

amontoison commented 2 years ago

Thanks @geoffroyleconte ! It's an excellent example of breakdown and it helps us to better understand the orthogonal tridiagonalization process and our new orthogonal Hessenberg reduction process.

amontoison commented 2 years ago

@dpo The SSY process is still working if βₖ₊₁ = 0 or γₖ₊₁ = 0 ! This issue answers our question of monday about it.

TriMR: system of 9806 equations in 9806 variables
    k     ‖rₖ‖        αₖ     βₖ₊₁     γₖ₊₁
    0  3.7e+03   ✗ ✗ ✗ ✗  2.7e+03  2.4e+03
    1  2.4e+03   0.0e+00  1.7e+02  0.0e+00
    2  1.1e+03   0.0e+00  0.0e+00  8.5e+01
    3  1.1e+03   0.0e+00  1.4e+02  0.0e+00
    4  7.8e+02   0.0e+00  0.0e+00  1.2e+02
    5  7.8e+02   0.0e+00  1.1e+02  0.0e+00
    6  6.7e+02   0.0e+00  0.0e+00  1.3e+02
    7  6.7e+02   0.0e+00  9.9e+01  0.0e+00
    8  6.1e+02   0.0e+00  0.0e+00  1.2e+02
    9  6.1e+02   0.0e+00  1.2e+02  0.0e+00
   10  5.7e+02   0.0e+00  0.0e+00  1.2e+02
   11  5.7e+02   0.0e+00  1.1e+02  0.0e+00
   12  5.4e+02   0.0e+00  0.0e+00  1.3e+02
   13  5.4e+02   0.0e+00  1.0e+02  0.0e+00
   14  5.3e+02   0.0e+00  0.0e+00  1.3e+02
   15  5.3e+02   0.0e+00  1.1e+02  0.0e+00
   16  5.2e+02   0.0e+00  0.0e+00  1.2e+02
   17  5.2e+02   0.0e+00  1.1e+02  0.0e+00
   18  5.1e+02   0.0e+00  0.0e+00  1.2e+02
   19  5.1e+02   0.0e+00  1.2e+02  0.0e+00
   20  5.0e+02   0.0e+00  0.0e+00  1.1e+02
   21  5.0e+02   0.0e+00  1.2e+02  0.0e+00
   22  4.9e+02   0.0e+00  0.0e+00  1.2e+02
   23  4.9e+02   0.0e+00  1.1e+02  0.0e+00
   24  4.8e+02   0.0e+00  0.0e+00  1.2e+02
   25  4.8e+02   0.0e+00  1.2e+02  0.0e+00
   26  4.7e+02   0.0e+00  0.0e+00  1.2e+02
   27  4.7e+02   0.0e+00  1.1e+02  0.0e+00
   28  4.7e+02   0.0e+00  0.0e+00  1.3e+02
   29  4.7e+02   0.0e+00  1.1e+02  0.0e+00
   30  4.6e+02   0.0e+00  0.0e+00  1.2e+02
   31  4.6e+02   0.0e+00  1.2e+02  0.0e+00
   32  4.6e+02   0.0e+00  0.0e+00  1.1e+02
   33  4.6e+02   0.0e+00  1.2e+02  0.0e+00
   34  4.5e+02   0.0e+00  0.0e+00  1.1e+02
   35  4.5e+02   0.0e+00  1.2e+02  0.0e+00
   36  4.5e+02   0.0e+00  0.0e+00  1.1e+02
   37  4.5e+02   0.0e+00  1.2e+02  0.0e+00
   38  4.4e+02   0.0e+00  0.0e+00  1.1e+02
   39  4.4e+02   0.0e+00  1.2e+02  0.0e+00
   40  4.4e+02   0.0e+00  0.0e+00  1.1e+02
   41  4.4e+02   0.0e+00  1.2e+02  0.0e+00
   42  4.3e+02   0.0e+00  0.0e+00  1.1e+02
   43  4.3e+02   0.0e+00  1.3e+02  0.0e+00
   44  4.2e+02   0.0e+00  0.0e+00  1.1e+02
   45  4.2e+02   0.0e+00  1.1e+02  0.0e+00
   46  4.2e+02   0.0e+00  0.0e+00  1.2e+02
   47  4.2e+02   0.0e+00  1.2e+02  0.0e+00
   48  4.1e+02   0.0e+00  0.0e+00  1.2e+02
   49  4.1e+02   0.0e+00  1.1e+02  0.0e+00
   50  4.0e+02   0.0e+00  0.0e+00  1.2e+02
   51  4.0e+02   0.0e+00  1.2e+02  0.0e+00
   52  4.0e+02   0.0e+00  0.0e+00  1.1e+02
   53  4.0e+02   0.0e+00  1.2e+02  0.0e+00
   54  3.9e+02   0.0e+00  0.0e+00  1.2e+02
   55  3.9e+02   0.0e+00  1.1e+02  0.0e+00
   56  3.9e+02   0.0e+00  0.0e+00  1.2e+02
   57  3.9e+02   0.0e+00  1.2e+02  0.0e+00
   58  3.8e+02   0.0e+00  0.0e+00  1.1e+02
   59  3.8e+02   0.0e+00  1.3e+02  0.0e+00
   60  3.7e+02   0.0e+00  0.0e+00  1.1e+02
   61  3.7e+02   0.0e+00  1.2e+02  0.0e+00
   62  3.6e+02   0.0e+00  0.0e+00  1.1e+02
   63  3.6e+02   0.0e+00  1.2e+02  0.0e+00
   64  3.6e+02   0.0e+00  0.0e+00  1.2e+02
   65  3.6e+02   0.0e+00  1.1e+02  0.0e+00
   66  3.5e+02   0.0e+00  0.0e+00  1.1e+02
   67  3.5e+02   0.0e+00  1.2e+02  0.0e+00
   68  3.4e+02   0.0e+00  0.0e+00  1.1e+02
   69  3.4e+02   0.0e+00  1.2e+02  0.0e+00
   70  3.4e+02   0.0e+00  0.0e+00  1.1e+02
   71  3.3e+02   0.0e+00  1.2e+02  0.0e+00
   72  3.3e+02   0.0e+00  0.0e+00  1.1e+02
   73  3.3e+02   0.0e+00  1.1e+02  0.0e+00
   74  3.2e+02   0.0e+00  0.0e+00  1.3e+02
   75  3.2e+02   0.0e+00  1.1e+02  0.0e+00
   76  3.2e+02   0.0e+00  0.0e+00  1.3e+02
   77  3.1e+02   0.0e+00  1.1e+02  0.0e+00
   78  3.1e+02   0.0e+00  0.0e+00  1.2e+02
   79  3.1e+02   0.0e+00  1.2e+02  0.0e+00
   80  3.1e+02   0.0e+00  0.0e+00  1.1e+02
   81  3.1e+02   0.0e+00  1.2e+02  0.0e+00
   82  3.0e+02   0.0e+00  0.0e+00  1.1e+02
   83  3.0e+02   0.0e+00  1.2e+02  0.0e+00
   84  3.0e+02   0.0e+00  0.0e+00  1.2e+02
   85  3.0e+02   0.0e+00  1.1e+02  0.0e+00
   86  2.9e+02   0.0e+00  0.0e+00  1.2e+02
   87  2.9e+02   0.0e+00  1.1e+02  0.0e+00
   88  2.9e+02   0.0e+00  0.0e+00  1.2e+02
   89  2.9e+02   0.0e+00  1.2e+02  0.0e+00
   90  2.8e+02   0.0e+00  0.0e+00  1.2e+02
   91  2.8e+02   0.0e+00  1.1e+02  0.0e+00
   92  2.8e+02   0.0e+00  0.0e+00  1.2e+02
   93  2.8e+02   0.0e+00  1.1e+02  0.0e+00
   94  2.8e+02   0.0e+00  0.0e+00  1.3e+02
   95  2.8e+02   0.0e+00  1.1e+02  0.0e+00
   96  2.8e+02   0.0e+00  0.0e+00  1.3e+02
   97  2.7e+02   0.0e+00  1.0e+02  0.0e+00
   98  2.7e+02   0.0e+00  0.0e+00  1.3e+02
   99  2.7e+02   0.0e+00  1.1e+02  0.0e+00
  100  2.7e+02   0.0e+00  0.0e+00  1.3e+02
  101  2.7e+02   0.0e+00  1.1e+02  0.0e+00
  102  2.7e+02   0.0e+00  0.0e+00  1.2e+02
  103  2.7e+02   0.0e+00  1.1e+02  0.0e+00
  104  2.6e+02   0.0e+00  0.0e+00  1.2e+02
  105  2.6e+02   0.0e+00  1.1e+02  0.0e+00
  106  2.6e+02   0.0e+00  0.0e+00  1.2e+02
  107  2.6e+02   0.0e+00  1.2e+02  0.0e+00
  108  2.6e+02   0.0e+00  0.0e+00  1.1e+02
  109  2.6e+02   0.0e+00  1.2e+02  0.0e+00
  110  2.6e+02   0.0e+00  0.0e+00  1.1e+02
  111  2.5e+02   0.0e+00  1.3e+02  0.0e+00
  112  2.5e+02   0.0e+00  0.0e+00  1.0e+02
  113  2.5e+02   0.0e+00  1.3e+02  0.0e+00
  114  2.5e+02   0.0e+00  0.0e+00  1.1e+02
  115  2.5e+02   0.0e+00  1.2e+02  0.0e+00
  116  2.5e+02   0.0e+00  0.0e+00  1.1e+02
  117  2.5e+02   0.0e+00  1.2e+02  0.0e+00
  118  2.5e+02   0.0e+00  0.0e+00  1.1e+02
  119  2.5e+02   0.0e+00  1.2e+02  0.0e+00
  120  2.4e+02   0.0e+00  0.0e+00  1.2e+02
  121  2.4e+02   0.0e+00  1.0e+02  0.0e+00
  122  2.4e+02   0.0e+00  0.0e+00  1.3e+02
  123  2.4e+02   0.0e+00  1.1e+02  0.0e+00
  124  2.4e+02   0.0e+00  0.0e+00  1.3e+02
  125  2.4e+02   0.0e+00  1.1e+02  0.0e+00
  126  2.4e+02   0.0e+00  0.0e+00  1.2e+02
  127  2.4e+02   0.0e+00  1.1e+02  0.0e+00
  128  2.3e+02   0.0e+00  0.0e+00  1.3e+02
  129  2.3e+02   0.0e+00  9.9e+01  0.0e+00
  130  2.3e+02   0.0e+00  0.0e+00  1.3e+02
  131  2.3e+02   0.0e+00  1.1e+02  0.0e+00
  132  2.3e+02   0.0e+00  0.0e+00  1.2e+02
  133  2.2e+02   0.0e+00  1.1e+02  0.0e+00
  134  2.2e+02   0.0e+00  0.0e+00  1.2e+02
  135  2.1e+02   0.0e+00  1.1e+02  0.0e+00
  136  2.1e+02   0.0e+00  0.0e+00  1.3e+02
  137  2.0e+02   0.0e+00  1.1e+02  0.0e+00
  138  2.0e+02   0.0e+00  0.0e+00  1.2e+02
  139  2.0e+02   0.0e+00  1.1e+02  0.0e+00
  140  2.0e+02   0.0e+00  0.0e+00  1.2e+02
  141  1.9e+02   0.0e+00  1.2e+02  0.0e+00
  142  1.9e+02   0.0e+00  0.0e+00  1.1e+02
  143  1.8e+02   0.0e+00  1.3e+02  0.0e+00
  144  1.8e+02   0.0e+00  0.0e+00  1.1e+02
  145  1.8e+02   0.0e+00  1.3e+02  0.0e+00
  146  1.8e+02   0.0e+00  0.0e+00  1.0e+02
  147  1.8e+02   0.0e+00  1.3e+02  0.0e+00
  148  1.8e+02   0.0e+00  0.0e+00  1.1e+02
  149  1.8e+02   0.0e+00  1.2e+02  0.0e+00
  150  1.7e+02   0.0e+00  0.0e+00  1.2e+02
  151  1.7e+02   0.0e+00  1.2e+02  0.0e+00
  152  1.7e+02   0.0e+00  0.0e+00  1.2e+02
  153  1.7e+02   0.0e+00  1.2e+02  0.0e+00
  154  1.7e+02   0.0e+00  0.0e+00  1.1e+02
  155  1.7e+02   0.0e+00  1.2e+02  0.0e+00
  156  1.7e+02   0.0e+00  0.0e+00  1.1e+02
  157  1.7e+02   0.0e+00  1.2e+02  0.0e+00
  158  1.7e+02   0.0e+00  0.0e+00  1.1e+02
  159  1.7e+02   0.0e+00  1.2e+02  0.0e+00
  160  1.7e+02   0.0e+00  0.0e+00  1.1e+02
  161  1.7e+02   0.0e+00  1.2e+02  0.0e+00
  162  1.6e+02   0.0e+00  0.0e+00  1.1e+02
  163  1.6e+02   0.0e+00  1.2e+02  0.0e+00
  164  1.6e+02   0.0e+00  0.0e+00  1.1e+02
  165  1.6e+02   0.0e+00  1.3e+02  0.0e+00
  166  1.6e+02   0.0e+00  0.0e+00  1.1e+02
  167  1.6e+02   0.0e+00  1.2e+02  0.0e+00
  168  1.6e+02   0.0e+00  0.0e+00  1.2e+02
  169  1.6e+02   0.0e+00  1.1e+02  0.0e+00
  170  1.6e+02   0.0e+00  0.0e+00  1.2e+02
  171  1.6e+02   0.0e+00  1.0e+02  0.0e+00
  172  1.6e+02   0.0e+00  0.0e+00  1.3e+02
  173  1.5e+02   0.0e+00  1.0e+02  0.0e+00
  174  1.5e+02   0.0e+00  0.0e+00  1.3e+02
  175  1.5e+02   0.0e+00  9.7e+01  0.0e+00
  176  1.5e+02   0.0e+00  0.0e+00  1.3e+02
  177  1.5e+02   0.0e+00  1.0e+02  0.0e+00
  178  1.5e+02   0.0e+00  0.0e+00  1.3e+02
  179  1.5e+02   0.0e+00  1.0e+02  0.0e+00
  180  1.5e+02   0.0e+00  0.0e+00  1.2e+02
  181  1.4e+02   0.0e+00  1.1e+02  0.0e+00
  182  1.4e+02   0.0e+00  0.0e+00  1.2e+02
  183  1.4e+02   0.0e+00  1.1e+02  0.0e+00
  184  1.4e+02   0.0e+00  0.0e+00  1.2e+02
  185  1.4e+02   0.0e+00  1.2e+02  0.0e+00
  186  1.4e+02   0.0e+00  0.0e+00  1.2e+02
  187  1.3e+02   0.0e+00  1.1e+02  0.0e+00
  188  1.3e+02   0.0e+00  0.0e+00  1.2e+02
  189  1.3e+02   0.0e+00  1.1e+02  0.0e+00
  190  1.3e+02   0.0e+00  0.0e+00  1.2e+02
  191  1.3e+02   0.0e+00  1.2e+02  0.0e+00
  192  1.3e+02   0.0e+00  0.0e+00  1.1e+02
  193  1.3e+02   0.0e+00  1.2e+02  0.0e+00
  194  1.2e+02   0.0e+00  0.0e+00  1.1e+02
  195  1.2e+02   0.0e+00  1.2e+02  0.0e+00
  196  1.2e+02   0.0e+00  0.0e+00  1.1e+02
  197  1.2e+02   0.0e+00  1.2e+02  0.0e+00
  198  1.2e+02   0.0e+00  0.0e+00  1.1e+02
  199  1.2e+02   0.0e+00  1.2e+02  0.0e+00
  200  1.2e+02   0.0e+00  0.0e+00  1.2e+02
  201  1.2e+02   0.0e+00  1.1e+02  0.0e+00
  202  1.2e+02   0.0e+00  0.0e+00  1.2e+02
  203  1.2e+02   0.0e+00  1.1e+02  0.0e+00
  204  1.2e+02   0.0e+00  0.0e+00  1.2e+02
  205  1.1e+02   0.0e+00  1.1e+02  0.0e+00
  206  1.1e+02   0.0e+00  0.0e+00  1.2e+02
  207  1.1e+02   0.0e+00  1.2e+02  0.0e+00
  208  1.1e+02   0.0e+00  0.0e+00  1.2e+02
  209  1.1e+02   0.0e+00  1.1e+02  0.0e+00
  210  1.1e+02   0.0e+00  0.0e+00  1.2e+02
  211  1.1e+02   0.0e+00  1.1e+02  0.0e+00
  212  1.1e+02   0.0e+00  0.0e+00  1.2e+02
  213  1.0e+02   0.0e+00  1.2e+02  0.0e+00
  214  1.0e+02   0.0e+00  0.0e+00  1.1e+02
  215  1.0e+02   0.0e+00  1.2e+02  0.0e+00
  216  1.0e+02   0.0e+00  0.0e+00  1.1e+02
  217  1.0e+02   0.0e+00  1.3e+02  0.0e+00
  218  1.0e+02   0.0e+00  0.0e+00  1.1e+02
  219  1.0e+02   0.0e+00  1.3e+02  0.0e+00
  220  1.0e+02   0.0e+00  0.0e+00  1.0e+02
  221  1.0e+02   0.0e+00  1.4e+02  0.0e+00
  222  9.9e+01   0.0e+00  0.0e+00  9.9e+01
  223  9.9e+01   0.0e+00  1.4e+02  0.0e+00
  224  9.8e+01   0.0e+00  0.0e+00  1.0e+02
  225  9.8e+01   0.0e+00  1.3e+02  0.0e+00
  226  9.6e+01   0.0e+00  0.0e+00  1.0e+02
  227  9.6e+01   0.0e+00  1.4e+02  0.0e+00
  228  9.2e+01   0.0e+00  0.0e+00  9.5e+01
  229  9.2e+01   0.0e+00  1.4e+02  0.0e+00
  230  8.7e+01   0.0e+00  0.0e+00  1.0e+02
  231  8.7e+01   0.0e+00  1.3e+02  0.0e+00
  232  7.8e+01   0.0e+00  0.0e+00  9.7e+01
  233  7.8e+01   0.0e+00  1.4e+02  0.0e+00
  234  6.7e+01   0.0e+00  0.0e+00  9.8e+01
  235  6.7e+01   0.0e+00  1.4e+02  0.0e+00
  236  5.4e+01   0.0e+00  0.0e+00  9.6e+01
  237  5.4e+01   0.0e+00  1.4e+02  0.0e+00
  238  4.1e+01   0.0e+00  0.0e+00  9.3e+01
  239  4.0e+01   0.0e+00  1.4e+02  0.0e+00
  240  2.9e+01   0.0e+00  0.0e+00  9.3e+01
  241  2.9e+01   0.0e+00  1.4e+02  0.0e+00
  242  1.9e+01   0.0e+00  0.0e+00  9.2e+01
  243  1.9e+01   0.0e+00  1.4e+02  0.0e+00
  244  1.3e+01   0.0e+00  0.0e+00  9.1e+01
  245  1.2e+01   0.0e+00  1.4e+02  0.0e+00
  246  8.2e+00   0.0e+00  0.0e+00  9.4e+01
  247  8.2e+00   0.0e+00  1.4e+02  0.0e+00
  248  5.3e+00   0.0e+00  0.0e+00  9.3e+01
  249  5.3e+00   0.0e+00  1.3e+02  0.0e+00
  250  3.7e+00   0.0e+00  0.0e+00  9.7e+01
  251  3.7e+00   0.0e+00  1.4e+02  0.0e+00
  252  2.5e+00   0.0e+00  0.0e+00  8.9e+01
  253  2.5e+00   0.0e+00  1.4e+02  0.0e+00
  254  1.7e+00   0.0e+00  0.0e+00  9.5e+01
  255  1.7e+00   0.0e+00  1.4e+02  0.0e+00
  256  1.2e+00   0.0e+00  0.0e+00  1.0e+02
  257  1.2e+00   0.0e+00  1.3e+02  0.0e+00
  258  8.5e-01   0.0e+00  0.0e+00  9.9e+01
  259  8.5e-01   0.0e+00  1.4e+02  0.0e+00
  260  6.2e-01   0.0e+00  0.0e+00  1.0e+02
  261  6.2e-01   0.0e+00  1.3e+02  0.0e+00
  262  4.8e-01   0.0e+00  0.0e+00  1.1e+02
  263  4.8e-01   0.0e+00  1.2e+02  0.0e+00
  264  3.8e-01   0.0e+00  0.0e+00  1.0e+02
  265  3.8e-01   0.0e+00  1.3e+02  0.0e+00
  266  3.1e-01   0.0e+00  0.0e+00  1.0e+02
  267  3.1e-01   0.0e+00  1.4e+02  0.0e+00
  268  2.4e-01   0.0e+00  0.0e+00  9.7e+01
  269  2.4e-01   0.0e+00  1.4e+02  0.0e+00
  270  1.7e-01   0.0e+00  0.0e+00  9.0e+01
  271  1.7e-01   0.0e+00  1.5e+02  0.0e+00
  272  1.1e-01   0.0e+00  0.0e+00  9.1e+01
  273  1.1e-01   0.0e+00  1.4e+02  0.0e+00
  274  7.6e-02   0.0e+00  0.0e+00  9.9e+01
  275  7.6e-02   0.0e+00  1.3e+02  0.0e+00
  276  5.5e-02   0.0e+00  0.0e+00  9.8e+01
  277  5.5e-02   0.0e+00  1.4e+02  0.0e+00
  278  4.0e-02   0.0e+00  0.0e+00  9.9e+01
  279  4.0e-02   0.0e+00  1.4e+02  0.0e+00
  280  2.9e-02   0.0e+00  0.0e+00  9.6e+01
  281  2.9e-02   0.0e+00  1.4e+02  0.0e+00
  282  2.0e-02   0.0e+00  0.0e+00  9.5e+01
  283  2.0e-02   0.0e+00  1.4e+02  0.0e+00
  284  1.4e-02   0.0e+00  0.0e+00  9.3e+01
  285  1.4e-02   0.0e+00  1.4e+02  0.0e+00
  286  9.1e-03   0.0e+00  0.0e+00  8.8e+01
  287  9.1e-03   0.0e+00  1.4e+02  0.0e+00
  288  5.8e-03   0.0e+00  0.0e+00  9.2e+01
  289  5.8e-03   0.0e+00  1.4e+02  0.0e+00
  290  4.0e-03   0.0e+00  0.0e+00  1.0e+02
  291  4.0e-03   0.0e+00  1.3e+02  0.0e+00
  292  3.0e-03   0.0e+00  0.0e+00  1.0e+02
  293  3.0e-03   0.0e+00  1.3e+02  0.0e+00
  294  2.2e-03   0.0e+00  0.0e+00  9.9e+01
  295  2.2e-03   0.0e+00  1.4e+02  0.0e+00
  296  1.6e-03   0.0e+00  0.0e+00  9.5e+01
  297  1.6e-03   0.0e+00  1.4e+02  0.0e+00
  298  1.1e-03   0.0e+00  0.0e+00  9.3e+01
  299  1.1e-03   0.0e+00  1.4e+02  0.0e+00
  300  7.9e-04   0.0e+00  0.0e+00  9.7e+01
  301  7.9e-04   0.0e+00  1.4e+02  0.0e+00
  302  5.6e-04   0.0e+00  0.0e+00  9.9e+01
  303  5.6e-04   0.0e+00  1.3e+02  0.0e+00
  304  4.1e-04   0.0e+00  0.0e+00  9.9e+01
  305  4.1e-04   0.0e+00  1.4e+02  0.0e+00
  306  2.8e-04   0.0e+00  0.0e+00  9.1e+01
  307  2.8e-04   0.0e+00  1.4e+02  0.0e+00
  308  1.8e-04   0.0e+00  0.0e+00  8.9e+01
  309  1.8e-04   0.0e+00  1.4e+02  0.0e+00
  310  1.2e-04   0.0e+00  0.0e+00  9.2e+01
  311  1.2e-04   0.0e+00  1.4e+02  0.0e+00
  312  7.7e-05   0.0e+00  0.0e+00  9.2e+01
  313  7.7e-05   0.0e+00  1.4e+02  0.0e+00
  314  5.0e-05   0.0e+00  0.0e+00  8.8e+01

JuliaSmoothOptimizers / Krylov.jl

NaN with GPMR on certain systems #466