RALFit
RALFit copied to clipboard
ralna
evaltensor_f
Under the context of Tensor-Newton Subproblem.
Multiple redundant calls to eval_HF when eval_HP is present
Problem
In the recursive call to evaltensor_hf there is a redundant call to eval_hf at x=params%x that does not change withing a recursive call to nlls_solve.
Fix
Add flag to avoid calling uneccesarily eval_hf within evaltensor_hf...
Showcase
Lanczos.f90 with or without eval_hp call back
16 5.8309E-08 7.62945E-05 2.23415E-01 1.64E+06 9.18E-01 STRC 358 1.9E-01 TR Ok 1.00
---------------------------------------------------------------------------------------------------
0 5.8309E-08 7.62945E-05 2.23415E-01 1.00E+02 -1.00E+00 --I-
EVALUATION Hf @ x= 0.25892606574455329 1.5139338761396632 1.8028587114687327 4.0864347691744571 0.45168112936543126 6.0083834535144192
1 5.7811E-08 4.47801E-07 1.31694E-03 2.00E+02 1.00E+00 SNI- 3.0E-04 TR Ok 1.00
2 5.7643E-08 2.20741E-06 6.50120E-03 4.00E+02 9.98E-01 SYI- 4.5E-03 TR Ok 1.00
EVALUATION Hf @ x= 0.25892606574455329 1.5139338761396632 1.8028587114687327 4.0864347691744571 0.45168112936543126 6.0083834535144192
3 5.7642E-08 7.82994E-08 2.30607E-04 8.00E+02 1.00E+00 SNI- 1.9E-05 TR Ok 1.00
4 5.7369E-08 5.09497E-06 1.50414E-02 1.60E+03 9.94E-01 SYI- 7.2E-03 TR Ok 1.00
EVALUATION Hf @ x= 0.25892606574455329 1.5139338761396632 1.8028587114687327 4.0864347691744571 0.45168112936543126 6.0083834535144192
5 5.7364E-08 7.30301E-08 2.15610E-04 3.20E+03 1.00E+00 SNI- 6.6E-05 TR Ok 1.00
6 5.6852E-08 1.59537E-05 4.73121E-02 6.40E+03 9.70E-01 SYI- 1.4E-02 TR Ok 1.00
EVALUATION Hf @ x= 0.25892606574455329 1.5139338761396632 1.8028587114687327 4.0864347691744571 0.45168112936543126 6.0083834535144192
7 5.6823E-08 7.21911E-08 2.14144E-04 1.28E+04 1.00E+00 SNI- 2.5E-04 TR Ok 1.00
8 5.6041E-08 5.53252E-05 1.65256E-01 1.28E+04 8.02E-01 SYI- 2.6E-02 TR Ok 1.00
EVALUATION Hf @ x= 0.25892606574455329 1.5139338761396632 1.8028587114687327 4.0864347691744571 0.45168112936543126 6.0083834535144192
9 5.5820E-08 6.48920E-08 1.94214E-04 2.56E+04 1.00E+00 SNI- 4.0E-04 TR Ok 1.00
10 5.5153E-08 8.99576E-05 2.70855E-01 2.56E+04 5.69E-01 SYI- 3.3E-02 TR Ok 1.00
EVALUATION Hf @ x= 0.25892606574455329 1.5139338761396632 1.8028587114687327 4.0864347691744571 0.45168112936543126 6.0083834535144192
11 5.4592E-08 5.74673E-08 1.73917E-04 5.12E+04 1.00E+00 SNI- 7.2E-04 TR Ok 1.00
12 5.4359E-08 1.26257E-04 3.82916E-01 5.12E+04 1.91E-01 SYI- 4.0E-02 TR Ok 1.00
EVALUATION Hf @ x= 0.25892606574455329 1.5139338761396632 1.8028587114687327 4.0864347691744571 0.45168112936543126 6.0083834535144192
13 5.3273E-08 5.57465E-08 1.70784E-04 1.02E+05 1.00E+00 SNI- 1.2E-03 TR Ok 1.00
14 5.12E+04 -1.47E-01 UYI-
14 5.2840E-08 8.05000E-05 2.47627E-01 5.12E+04 5.42E-01 SYI- 3.3E-02 TR Ok 1.00
EVALUATION Hf @ x= 0.25892606574455329 1.5139338761396632 1.8028587114687327 4.0864347691744571 0.45168112936543126 6.0083834535144192
---------------------------------------------------------------------------------------------------
Iter | error | optim | rel optim | Delta | rho |S2IF| inn it| step | loop|LS| tau
---------------------------------------------------------------------------------------------------
15 5.2388E-08 3.63556E-08 1.12316E-04 1.02E+05 1.00E+00 SNI- 9.4E-04 TR Ok 1.00
16 5.2150E-08 7.90295E-05 2.44708E-01 1.02E+05 4.18E-01 SYI- 3.4E-02 TR Ok 1.00
EVALUATION Hf @ x= 0.25892606574455329 1.5139338761396632 1.8028587114687327 4.0864347691744571 0.45168112936543126 6.0083834535144192
17 5.1713E-08 3.68390E-08 1.14549E-04 2.05E+05 1.00E+00 SNI- 1.3E-03 TR Ok 1.00
18 5.1539E-08 4.75545E-05 1.48118E-01 2.05E+05 6.69E-01 SYI- 2.7E-02 TR Ok 1.00
EVALUATION Hf @ x= 0.25892606574455329 1.5139338761396632 1.8028587114687327 4.0864347691744571 0.45168112936543126 6.0083834535144192
19 5.1375E-08 8.87601E-08 2.76902E-04 4.10E+05 1.00E+00 SNI- 1.4E-03 TR Ok 1.00
20 5.1296E-08 1.44657E-05 4.51628E-02 8.19E+05 1.16E+00 SYI- 1.6E-02 TR Ok 1.00
EVALUATION Hf @ x= 0.25892606574455329 1.5139338761396632 1.8028587114687327 4.0864347691744571 0.45168112936543126 6.0083834535144192
21 5.1273E-08 3.62754E-07 1.13280E-03 1.64E+06 9.94E-01 SNI- 2.4E-03 TR Ok 1.00
22 5.1260E-08 1.99739E-06 6.23819E-03 3.28E+06 1.40E+00 SYI- 6.0E-03 TR Ok 1.00
EVALUATION Hf @ x= 0.25892606574455329 1.5139338761396632 1.8028587114687327 4.0864347691744571 0.45168112936543126 6.0083834535144192
23 5.1257E-08 3.54128E-07 1.10603E-03 6.55E+06 9.49E-01 SNI- 2.4E-03 TR Ok 1.00
EVALUATION Hf @ x= 0.25892606574455329 1.5139338761396632 1.8028587114687327 4.0864347691744571 0.45168112936543126 6.0083834535144192
24 5.1257E-08 8.25167E-08 2.57722E-04 1.31E+07 1.42E+00 SYI- 1.3E-03 TR Ok 1.00
EVALUATION Hf @ x= 0.25892606574455329 1.5139338761396632 1.8028587114687327 4.0864347691744571 0.45168112936543126 6.0083834535144192
25 5.1257E-08 1.85295E-08 5.78727E-05 2.62E+07 1.43E+00 SYI- 5.6E-04 TR Ok 1.00
EVALUATION Hf @ x= 0.25892606574455329 1.5139338761396632 1.8028587114687327 4.0864347691744571 0.45168112936543126 6.0083834535144192
26 5.1257E-08 3.52720E-09 1.10164E-05 5.24E+07 1.44E+00 SYI- 2.5E-04 TR Ok 1.00
EVALUATION Hf @ x= 0.25892606574455329 1.5139338761396632 1.8028587114687327 4.0864347691744571 0.45168112936543126 6.0083834535144192
27 5.1257E-08 6.72223E-10 2.09953E-06 1.00E+08 1.44E+00 SYI- 1.1E-04 TR Ok 1.00
EVALUATION Hf @ x= 0.25892606574455329 1.5139338761396632 1.8028587114687327 4.0864347691744571 0.45168112936543126 6.0083834535144192
28 5.1257E-08 1.28500E-10 4.01340E-07 1.00E+08 1.00E+00 SYI- 4.7E-05 TR Ok 1.00
EVALUATION Hf @ x= 0.25892606574455329 1.5139338761396632 1.8028587114687327 4.0864347691744571 0.45168112936543126 6.0083834535144192
29 5.1257E-08 2.48728E-11 7.76846E-08 1.00E+08 1.00E+00 SYI- 2.1E-05 TR Ok 1.00
EVALUATION Hf @ x= 0.25892606574455329 1.5139338761396632 1.8028587114687327 4.0864347691744571 0.45168112936543126 6.0083834535144192
30 5.1257E-08 5.09597E-12 1.59161E-08 1.00E+08 1.00E+00 SYI- 9.0E-06 TR Ok 1.00
EVALUATION Hf @ x= 0.25892606574455329 1.5139338761396632 1.8028587114687327 4.0864347691744571 0.45168112936543126 6.0083834535144192
31 5.1257E-08 1.26741E-12 3.95847E-09 1.00E+08 1.00E+00 SYI- 3.9E-06 TR Ok 1.00
EVALUATION Hf @ x= 0.25892606574455329 1.5139338761396632 1.8028587114687327 4.0864347691744571 0.45168112936543126 6.0083834535144192
32 5.1257E-08 4.29920E-13 1.34276E-09 1.00E+08 1.00E+00 SYI- 1.7E-06 TR Ok 1.00
EVALUATION Hf @ x= 0.25892606574455329 1.5139338761396632 1.8028587114687327 4.0864347691744571 0.45168112936543126 6.0083834535144192
33 5.1257E-08 1.75667E-13 5.48656E-10 1.00E+08 1.00E+00 SYI- 7.5E-07 TR Ok 1.00
EVALUATION Hf @ x= 0.25892606574455329 1.5139338761396632 1.8028587114687327 4.0864347691744571 0.45168112936543126 6.0083834535144192
34 5.1257E-08 7.57051E-14 2.36447E-10 1.00E+08 1.00E+00 SYI- 3.3E-07 TR Ok 1.00
EVALUATION Hf @ x= 0.25892606574455329 1.5139338761396632 1.8028587114687327 4.0864347691744571 0.45168112936543126 6.0083834535144192
35 5.1257E-08 3.29861E-14 1.03025E-10 1.00E+08 1.00E+00 SYI- 1.4E-07 TR Ok 1.00
EVALUATION Hf @ x= 0.25892606574455329 1.5139338761396632 1.8028587114687327 4.0864347691744571 0.45168112936543126 6.0083834535144192
36 5.1257E-08 1.44034E-14 4.49858E-11 1.00E+08 1.00E+00 SYI- 6.2E-08 TR Ok 1.00
---------------------------------------------------------------------------------------------------
EVALUATION Hf @ x= 0.24610105492175122 1.4851846891680101 1.7053653236113633 4.0085490010973119 0.56199265759382211 5.8198897602272197
17 5.0828E-08 1.75838E-04 5.51500E-01 1.64E+06 7.22E-01 STRC 394 2.5E-01 TR Ok 1.00
...
...
...
----------------------------------------------------------
Status: converged, an optimal solution was found
----------------------------------------------------------
Norm of error 8.05672E-09
Norm of gradient 1.42339E-13
Norm of scaled gradient 1.12132E-09
Iteration count 30
Trust region step 30 (100.0%)
LS step 0 ( 0.0%)
PG step 0 ( 0.0%)
Function evaluations 31
Trust region step 31 (100.0%)
LS step 0 ( 0.0%)
PG step 0 ( 0.0%)
Gradient evaluations 31
Trust region step 31 (100.0%)
LS step 0 ( 0.0%)
PG step 0 ( 0.0%)
Hessian evaluations (eval_hf) 628 <----- this number should be 31
Hessian evaluations (eval_hp) 958
Multiple redundant calls to eval_HP
At every inner iteration 0, the nlls_iterate is started with s=x0=0.0, which will trigger an expensive call to eval_HP or or m matrix-vector products with zero-vector y
that ultimately will return a zero matrix...
Either check if all(y==0) at the entry of calculate_sHs. A good option is to not call tensoreval_f when we already have the answer s=0 then f(s) = r_k
