On Mon, Oct 2, 2017 at 11:56 AM, Wenbo Zhao <zhaowenbo.n...@gmail.com> wrote:
> > > On Mon, Oct 2, 2017 at 11:49 PM, Mark Adams <mfad...@lbl.gov> wrote: > >> Whenbo, do you build your PETSc? >> >> Yes. > My configure option is listed below > ./configure --with-mpi=1 --with-shared-libraries=1 \ > --with-64-bit-indices=1 --with-debugging=1 > > And I set PETSC_DIR, PETSC_ARCH and SLEPC_DIR in my ~/.bashrc. > > > The Makefile for my problem is listed below, > > PETSC_ARCH = arch-linux2-c-debug > PETSC_DIR = /home/zhaowenbo/research/petsc/petsc_git > SLEPC_DIR = /home/zhaowenbo/research/slepc/slepc_git > #PETSC_DIR = /home/zhaowenbo/research/petsc/petsc-3.7.4 > #SLEPC_DIR = /home/zhaowenbo/research/slepc/slepc-3.7.3 > HYPRE_DIR = /usr/local/hypre > # > DEBUG_OPT = -g > COMP_FLAGS = -fPIC -Wall \ > -I${SLEPC_DIR}/include -I${SLEPC_DIR}/${PETSC_ARCH}/include \ > -I${PETSC_DIR}/include -I${PETSC_DIR}/${PETSC_ARCH}/include \ > -Isrc > > LINK_FLAGS = -fPIC -Wall \ > -Wl,-rpath,${SLEPC_DIR}/${PETSC_ARCH}/lib -L${SLEPC_DIR}/${PETSC_ARCH}/lib > -lslepc \ > -Wl,-rpath,${PETSC_DIR}/${PETSC_ARCH}/lib -L${PETSC_DIR}/${PETSC_ARCH}/lib > -lpetsc \ > -llapack -lblas -lhwloc -lm -lgfortran -lquadmath > > step-41: src/main.o src/readinp.o src/base.o src/sp3.o src/diffu.o > mpicxx -o step-41 $^ ${LINK_FLAGS} ${DEBUG_OPT} > > src/main.o: src/main.c > mpicxx -o src/main.o -c $^ ${COMP_FLAGS} ${DEBUG_OPT} > > src/readinp.o: src/readinp.c > mpicxx -o src/readinp.o -c $^ ${COMP_FLAGS} ${DEBUG_OPT} > > src/sp3.o: src/sp3.c > mpicxx -o src/sp3.o -c $^ ${COMP_FLAGS} ${DEBUG_OPT} > > src/diffu.o: src/diffu.c > mpicxx -o src/diffu.o -c $^ ${COMP_FLAGS} ${DEBUG_OPT} > > src/base.o: src/base.c > mpicxx -o src/base.o -c $^ ${COMP_FLAGS} ${DEBUG_OPT} > > > clean: > rm step-41 src/main.o src/readinp.o src/sp3.o src/diffu.o src/base.o > > runkr_smooth: > mpirun -n ${NCORE} ./step-41 \ > -st_ksp_type gmres -st_ksp_view -st_ksp_monitor \ > -st_pc_type gamg -st_pc_gamg_type agg -st_pc_gamg_agg_nsmooths 1 \ > -mata AMAT.dat -matb BMAT.dat \ > -st_gamg_est_ksp_view -st_gamg_est_ksp_monitor \ > -st_gamg_est_ksp_converged_reason \ > Add -st_gamg_est_ksp_error_if_not_converged 0 Thanks, Matt -eps_nev 1 -eps_ncv 10 -eps_monitor -log_view > log_smooth 2>&1 > > runkr_nonsmooth: > mpirun -n ${NCORE} ./step-41 \ > -st_ksp_type gmres -st_ksp_view -st_ksp_monitor \ > -st_pc_type gamg -st_pc_gamg_type agg -st_pc_gamg_agg_nsmooths 0 \ > -mata AMAT.dat -matb BMAT.dat \ > -st_gamg_est_ksp_view -st_gamg_est_ksp_monitor \ > -st_gamg_est_ksp_converged_reason \ > -eps_nev 1 -eps_ncv 10 -eps_monitor -log_view > log_nonsmooth 2>&1 > > > Thanks, > Wenbo > > > > >> On Mon, Oct 2, 2017 at 11:45 AM, Mark Adams <mfad...@lbl.gov> wrote: >> >>> This is normal: >>> >>> Linear st_gamg_est_ solve did not converge due to DIVERGED_ITS >>> iterations 10 >>> >>> It looks like ksp->errorifnotconverged got set somehow. If the default >>> changed in KSP then (SAGG) GAMG would not ever work. >>> >>> I assume you don't have a .petscrc file with more (crazy) options in it >>> ... >>> >>> >>> On Mon, Oct 2, 2017 at 11:39 AM, Wenbo Zhao <zhaowenbo.n...@gmail.com> >>> wrote: >>> >>>> >>>> >>>> On Mon, Oct 2, 2017 at 11:30 PM, Matthew Knepley <knep...@gmail.com> >>>> wrote: >>>> >>>>> On Mon, Oct 2, 2017 at 11:15 AM, Mark Adams <mfad...@lbl.gov> wrote: >>>>> >>>>>> non-smoothed aggregation is converging very fast. smoothed fails in >>>>>> the eigen estimator. >>>>>> >>>>>> Run this again with -st_gamg_est_ksp_view and >>>>>> -st_gamg_est_ksp_monitor, and see if you get more output (I'm not 100% >>>>>> sure >>>>>> about these args). >>>>>> >>>>> >>>>> I also want -st_gamg_est_ksp_converged_reason >>>>> >>>>> Thanks, >>>>> >>>>> Matt >>>>> >>>> $make NCORE=1 runkr_smooth >>>> mpirun -n 1 ./step-41 \ >>>> -st_ksp_type gmres -st_ksp_view -st_ksp_monitor \ >>>> -st_pc_type gamg -st_pc_gamg_type agg -st_pc_gamg_agg_nsmooths 1 \ >>>> -mata AMAT.dat -matb BMAT.dat \ >>>> -st_gamg_est_ksp_view -st_gamg_est_ksp_monitor \ >>>> -st_gamg_est_ksp_converged_reason \ >>>> -eps_nev 1 -eps_ncv 10 -eps_monitor -log_view > log_smooth 2>&1 >>>> makefile:43: recipe for target 'runkr_smooth' failed >>>> make: *** [runkr_smooth] Error 91 >>>> >>>> Thanks >>>> Wenbo >>>> >>>> >>>>> >>>>> >>>>>> >>>>>> On Mon, Oct 2, 2017 at 11:06 AM, Wenbo Zhao <zhaowenbo.n...@gmail.com >>>>>> > wrote: >>>>>> >>>>>>> Matt, >>>>>>> >>>>>>> Test 1 nonsmooth >>>>>>> zhaowenbo@ubuntu:~/test_slepc/SPARK/spark$ make NCORE=1 >>>>>>> runkr_nonsmooth >>>>>>> mpirun -n 1 ./step-41 \ >>>>>>> -st_ksp_type gmres -st_ksp_view -st_ksp_monitor \ >>>>>>> -st_pc_type gamg -st_pc_gamg_type agg -st_pc_gamg_agg_nsmooths 0 \ >>>>>>> -mata AMAT.dat -matb BMAT.dat \ >>>>>>> -eps_nev 1 -eps_ncv 10 -eps_monitor -log_view > log_nonsmooth >>>>>>> 2>&1 >>>>>>> >>>>>>> Test 2 smooth >>>>>>> zhaowenbo@ubuntu:~/test_slepc/SPARK/spark$ make NCORE=1 >>>>>>> runkr_smooth >>>>>>> mpirun -n 1 ./step-41 \ >>>>>>> -st_ksp_type gmres -st_ksp_view -st_ksp_monitor \ >>>>>>> -st_pc_type gamg -st_pc_gamg_type agg -st_pc_gamg_agg_nsmooths 1 \ >>>>>>> -mata AMAT.dat -matb BMAT.dat \ >>>>>>> -eps_nev 1 -eps_ncv 10 -eps_monitor -log_view > log_smooth 2>&1 >>>>>>> makefile:43: recipe for target 'runkr_smooth' failed >>>>>>> make: *** [runkr_smooth] Error 91 >>>>>>> >>>>>>> >>>>>>> Thanks, >>>>>>> >>>>>>> Wenbo >>>>>>> >>>>>>> On Mon, Oct 2, 2017 at 10:48 PM, Matthew Knepley <knep...@gmail.com> >>>>>>> wrote: >>>>>>> >>>>>>>> On Mon, Oct 2, 2017 at 10:43 AM, Wenbo Zhao < >>>>>>>> zhaowenbo.n...@gmail.com> wrote: >>>>>>>> >>>>>>>>> Mark, >>>>>>>>> >>>>>>>>> Thanks for your reply. >>>>>>>>> >>>>>>>>> On Mon, Oct 2, 2017 at 9:51 PM, Mark Adams <mfad...@lbl.gov> >>>>>>>>> wrote: >>>>>>>>> >>>>>>>>>> Please send the output with -st_ksp_view and -st_ksp_monitor and >>>>>>>>>> we can start to debug it. >>>>>>>>>> >>>>>>>>>> Test 1 with nonsmooth and preonly is OK >>>>>>>>> zhaowenbo@ubuntu:~/test_slepc/SPARK/spark$ make NCORE=1 >>>>>>>>> runkr_nonsmooth >>>>>>>>> mpirun -n 1 ./step-41 \ >>>>>>>>> -st_ksp_type gmres -st_ksp_view -st_ksp_monitor \ >>>>>>>>> -st_pc_type gamg -st_pc_gamg_type agg -st_pc_gamg_agg_nsmooths >>>>>>>>> 0 \ >>>>>>>>> -st_ksp_view -mata AMAT.dat -matb BMAT.dat \ >>>>>>>>> -st_mg_coarse_ksp_type preonly -st_mg_coarse_ksp_monitor \ >>>>>>>>> -eps_nev 1 -eps_ncv 10 -eps_monitor -log_view > log_nonsmooth >>>>>>>>> 2>&1 >>>>>>>>> >>>>>>>>> Test 2 smooth and preonly is not OK >>>>>>>>> zhaowenbo@ubuntu:~/test_slepc/SPARK/spark$ make NCORE=1 >>>>>>>>> runkr_smooth >>>>>>>>> mpirun -n 1 ./step-41 \ >>>>>>>>> -st_ksp_type gmres -st_ksp_view -st_ksp_monitor \ >>>>>>>>> -st_pc_type gamg -st_pc_gamg_type agg -st_pc_gamg_agg_nsmooths >>>>>>>>> 1 \ >>>>>>>>> -st_ksp_view -mata AMAT.dat -matb BMAT.dat \ >>>>>>>>> -st_mg_coarse_ksp_type preonly -st_mg_coarse_ksp_monitor \ >>>>>>>>> -eps_nev 1 -eps_ncv 10 -eps_monitor -log_view > log_smooth 2>&1 >>>>>>>>> makefile:43: recipe for target 'runkr_smooth' failed >>>>>>>>> make: *** [runkr_smooth] Error 91 >>>>>>>>> >>>>>>>>> Test 3 nonsmooth and gmres is not OK >>>>>>>>> zhaowenbo@ubuntu:~/test_slepc/SPARK/spark$ make NCORE=1 >>>>>>>>> runkr_gmres >>>>>>>>> mpirun -n 1 ./step-41 \ >>>>>>>>> -st_ksp_type gmres -st_ksp_view -st_ksp_monitor \ >>>>>>>>> -st_pc_type gamg -st_pc_gamg_type agg -st_pc_gamg_agg_nsmooths >>>>>>>>> 0 \ >>>>>>>>> -st_ksp_view -mata AMAT.dat -matb BMAT.dat \ >>>>>>>>> -st_mg_coarse_ksp_type gmres -st_mg_coarse_ksp_monitor >>>>>>>>> -st_mg_coarse_ksp_rtol 1.0e-6 \ >>>>>>>>> >>>>>>>> >>>>>>>> DO NOT DO THIS. Please send the output where you do NOTHING to the >>>>>>>> coarse solver. >>>>>>>> >>>>>>>> Thanks, >>>>>>>> >>>>>>>> Matt >>>>>>>> >>>>>>>> >>>>>>>>> -eps_nev 1 -eps_ncv 10 -eps_monitor -log_view > log_gmres 2>&1 >>>>>>>>> makefile:59: recipe for target 'runkr_gmres' failed >>>>>>>>> make: *** [runkr_gmres] Error 91 >>>>>>>>> >>>>>>>>> log-files is attached. >>>>>>>>> >>>>>>>>> >>>>>>>>> You mentioned that B is not symmetric. I assume it is elliptic >>>>>>>>>> (diffusion). Where does the asymmetry come from? >>>>>>>>>> >>>>>>>>>> >>>>>>>>> It is a two-group diffusion equations, where group denotes neutron >>>>>>>>> enegry discretisation. >>>>>>>>> Matrix B consists of neutron diffusion/leakage term, removal term >>>>>>>>> and minus neutron scatter source term between different energies, when >>>>>>>>> matrix A denotes neutron fission source. >>>>>>>>> >>>>>>>>> Diffusion term(Laplace operator) is elliptic and symmetric. >>>>>>>>> Removal term is diagonal only. However scatter term is asymmetry since >>>>>>>>> scatter term from high energy to low energy is far greater than the >>>>>>>>> term >>>>>>>>> from low to high. >>>>>>>>> >>>>>>>>> >>>>>>>>> Wenbo >>>>>>>>> >>>>>>>>> >>>>>>>>>> On Mon, Oct 2, 2017 at 9:39 AM, Wenbo Zhao < >>>>>>>>>> zhaowenbo.n...@gmail.com> wrote: >>>>>>>>>> >>>>>>>>>>> Matt, >>>>>>>>>>> Thanks for your reply. >>>>>>>>>>> For the defalt option doesnt work firstly( -st_ksp_type gmres >>>>>>>>>>> -st_pc_type gamg -st_pc_gamg_type agg -st_pc_gamg_agg_nsmooths 1), >>>>>>>>>>> I tried >>>>>>>>>>> to test those options. >>>>>>>>>>> >>>>>>>>>>> Wenbo >>>>>>>>>>> >>>>>>>>>>> On Mon, Oct 2, 2017 at 9:08 PM, Matthew Knepley < >>>>>>>>>>> knep...@gmail.com> wrote: >>>>>>>>>>> >>>>>>>>>>>> On Mon, Oct 2, 2017 at 8:30 AM, Wenbo Zhao < >>>>>>>>>>>> zhaowenbo.n...@gmail.com> wrote: >>>>>>>>>>>> >>>>>>>>>>>>> Matt >>>>>>>>>>>>> >>>>>>>>>>>>> Because I am not clear about what will happen using 'preonly' >>>>>>>>>>>>> for large scale problem. >>>>>>>>>>>>> >>>>>>>>>>>> >>>>>>>>>>>> The size of the problem has nothing to do with 'preonly'. All >>>>>>>>>>>> it means is to apply a preconditioner without a Krylov solver. >>>>>>>>>>>> >>>>>>>>>>>> >>>>>>>>>>>>> It seems to use a direct solver from below, >>>>>>>>>>>>> http://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/ >>>>>>>>>>>>> KSP/KSPPREONLY.html >>>>>>>>>>>>> >>>>>>>>>>>> >>>>>>>>>>>> However, I still cannot understand why you would change the >>>>>>>>>>>> default? >>>>>>>>>>>> >>>>>>>>>>>> Matt >>>>>>>>>>>> >>>>>>>>>>>> >>>>>>>>>>>>> >>>>>>>>>>>>> Thanks! >>>>>>>>>>>>> Wenbo >>>>>>>>>>>>> >>>>>>>>>>>>> On Mon, Oct 2, 2017 at 5:09 PM, Matthew Knepley < >>>>>>>>>>>>> knep...@gmail.com> wrote: >>>>>>>>>>>>> >>>>>>>>>>>>>> On Sun, Oct 1, 2017 at 9:53 PM, Wenbo Zhao < >>>>>>>>>>>>>> zhaowenbo.n...@gmail.com> wrote: >>>>>>>>>>>>>> >>>>>>>>>>>>>>> Matt, >>>>>>>>>>>>>>> Thanks for your reply. >>>>>>>>>>>>>>> It DOES make no sense for this problem. >>>>>>>>>>>>>>> But I am not clear about the 'preonly' option. Which solver >>>>>>>>>>>>>>> is used in preonly? I wonder if 'preonly' is suitable for large >>>>>>>>>>>>>>> scale >>>>>>>>>>>>>>> problem such as 400,000,000 unknowns. >>>>>>>>>>>>>>> So I tried 'gmres' option and found these error messages. >>>>>>>>>>>>>>> >>>>>>>>>>>>>> >>>>>>>>>>>>>> I mean, why are you setting this at all. Just do not set the >>>>>>>>>>>>>> coarse solver. The default should work fine. >>>>>>>>>>>>>> >>>>>>>>>>>>>> Thanks, >>>>>>>>>>>>>> >>>>>>>>>>>>>> Matt >>>>>>>>>>>>>> >>>>>>>>>>>>>> >>>>>>>>>>>>>>> Could you give me some suggestions? >>>>>>>>>>>>>>> >>>>>>>>>>>>>>> Thanks. >>>>>>>>>>>>>>> >>>>>>>>>>>>>>> Wenbo >>>>>>>>>>>>>>> >>>>>>>>>>>>>>> >>>>>>>>>>>>>>> On Mon, Oct 2, 2017 at 12:34 AM, Matthew Knepley < >>>>>>>>>>>>>>> knep...@gmail.com> wrote: >>>>>>>>>>>>>>> >>>>>>>>>>>>>>>> On Sun, Oct 1, 2017 at 6:49 AM, Wenbo Zhao < >>>>>>>>>>>>>>>> zhaowenbo.n...@gmail.com> wrote: >>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>> Hi, >>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>> I met some questions when I use PETSC/SLEPC to solve >>>>>>>>>>>>>>>>> two-group neutron diffusion equations with finite difference >>>>>>>>>>>>>>>>> method. The >>>>>>>>>>>>>>>>> grid is 3*3*3, when DOF on each points is 2. So the matrix >>>>>>>>>>>>>>>>> size is 54*54. >>>>>>>>>>>>>>>>> It is generalized eigenvalue problem Ax=\lamda Bx, where B >>>>>>>>>>>>>>>>> is diagonally dominant matrix but not symmetry. >>>>>>>>>>>>>>>>> EPS is set as below, >>>>>>>>>>>>>>>>> ierr = EPSSetProblemType(eps,EPS_GNHEP);CHKERRQ(ierr);¬ >>>>>>>>>>>>>>>>> ierr = EPSSetWhichEigenpairs(eps,EPS_ >>>>>>>>>>>>>>>>> LARGEST_REAL);CHKERRQ(ierr);¬ >>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>> Krylovschur is used as eps sovler. GAMG is used as PC. >>>>>>>>>>>>>>>>> I tried agg_nsmooths and mg_coarse_ksp_type. Only >>>>>>>>>>>>>>>>> non-smooths and preonly is OK. >>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>> Why are you setting the coarse solver. This makes no sense. >>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>> Thanks, >>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>> Matt >>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>> Test 1 >>>>>>>>>>>>>>>>> $ make NCORE=1 runkr_nonsmooth >>>>>>>>>>>>>>>>> mpirun -n 1 ./step-41 \ >>>>>>>>>>>>>>>>> -st_ksp_type gmres \ >>>>>>>>>>>>>>>>> -st_pc_type gamg -st_pc_gamg_type agg >>>>>>>>>>>>>>>>> -st_pc_gamg_agg_nsmooths 0 \ >>>>>>>>>>>>>>>>> -st_ksp_view -mata AMAT.dat -matb BMAT.dat \ >>>>>>>>>>>>>>>>> -st_mg_coarse_ksp_type preonly >>>>>>>>>>>>>>>>> -st_mg_coarse_ksp_monitor \ >>>>>>>>>>>>>>>>> -eps_nev 1 -eps_ncv 10 -eps_monitor -log_view > >>>>>>>>>>>>>>>>> log_nonsmooth 2>&1 >>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>> Test 2 >>>>>>>>>>>>>>>>> $ make NCORE=1 runkr_smooth >>>>>>>>>>>>>>>>> mpirun -n 1 ./step-41 \ >>>>>>>>>>>>>>>>> -st_ksp_type gmres \ >>>>>>>>>>>>>>>>> -st_pc_type gamg -st_pc_gamg_type agg >>>>>>>>>>>>>>>>> -st_pc_gamg_agg_nsmooths 1 \ >>>>>>>>>>>>>>>>> -st_ksp_view -mata AMAT.dat -matb BMAT.dat \ >>>>>>>>>>>>>>>>> -st_mg_coarse_ksp_type preonly >>>>>>>>>>>>>>>>> -st_mg_coarse_ksp_monitor \ >>>>>>>>>>>>>>>>> -eps_nev 1 -eps_ncv 10 -eps_monitor -log_view > >>>>>>>>>>>>>>>>> log_smooth 2>&1 >>>>>>>>>>>>>>>>> makefile:43: recipe for target 'runkr_smooth' failed >>>>>>>>>>>>>>>>> make: *** [runkr_smooth] Error 91 >>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>> Test 3 >>>>>>>>>>>>>>>>> $ make NCORE=1 runkr_gmres >>>>>>>>>>>>>>>>> mpirun -n 1 ./step-41 \ >>>>>>>>>>>>>>>>> -st_ksp_type gmres \ >>>>>>>>>>>>>>>>> -st_pc_type gamg -st_pc_gamg_type agg >>>>>>>>>>>>>>>>> -st_pc_gamg_agg_nsmooths 0 \ >>>>>>>>>>>>>>>>> -st_ksp_view -mata AMAT.dat -matb BMAT.dat \ >>>>>>>>>>>>>>>>> -st_mg_coarse_ksp_type gmres -st_mg_coarse_ksp_monitor >>>>>>>>>>>>>>>>> -st_mg_coarse_ksp_rtol 1.0e-6 \ >>>>>>>>>>>>>>>>> -eps_nev 1 -eps_ncv 10 -eps_monitor -log_view > >>>>>>>>>>>>>>>>> log_gmres 2>&1 >>>>>>>>>>>>>>>>> makefile:59: recipe for target 'runkr_gmres' failed >>>>>>>>>>>>>>>>> make: *** [runkr_gmres] Error 91 >>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>> Log files were attched. >>>>>>>>>>>>>>>>> The matrix file were also attched as AMAT.dat and BMAT.dat. >>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>> Is it correct? Or something wrong with my code or >>>>>>>>>>>>>>>>> commad-line? >>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>> Thanks! >>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>> Wenbo >>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>> -- >>>>>>>>>>>>>>>> What most experimenters take for granted before they begin >>>>>>>>>>>>>>>> their experiments is infinitely more interesting than any >>>>>>>>>>>>>>>> results to which >>>>>>>>>>>>>>>> their experiments lead. >>>>>>>>>>>>>>>> -- Norbert Wiener >>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>> https://www.cse.buffalo.edu/~knepley/ >>>>>>>>>>>>>>>> <http://www.caam.rice.edu/%7Emk51/> >>>>>>>>>>>>>>>> >>>>>>>>>>>>>>> >>>>>>>>>>>>>>> >>>>>>>>>>>>>> >>>>>>>>>>>>>> >>>>>>>>>>>>>> -- >>>>>>>>>>>>>> What most experimenters take for granted before they begin >>>>>>>>>>>>>> their experiments is infinitely more interesting than any >>>>>>>>>>>>>> results to which >>>>>>>>>>>>>> their experiments lead. >>>>>>>>>>>>>> -- Norbert Wiener >>>>>>>>>>>>>> >>>>>>>>>>>>>> https://www.cse.buffalo.edu/~knepley/ >>>>>>>>>>>>>> <http://www.caam.rice.edu/%7Emk51/> >>>>>>>>>>>>>> >>>>>>>>>>>>> >>>>>>>>>>>>> >>>>>>>>>>>> >>>>>>>>>>>> >>>>>>>>>>>> -- >>>>>>>>>>>> What most experimenters take for granted before they begin >>>>>>>>>>>> their experiments is infinitely more interesting than any results >>>>>>>>>>>> to which >>>>>>>>>>>> their experiments lead. >>>>>>>>>>>> -- Norbert Wiener >>>>>>>>>>>> >>>>>>>>>>>> https://www.cse.buffalo.edu/~knepley/ >>>>>>>>>>>> <http://www.caam.rice.edu/%7Emk51/> >>>>>>>>>>>> >>>>>>>>>>> >>>>>>>>>>> >>>>>>>>>> >>>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> -- >>>>>>>> What most experimenters take for granted before they begin their >>>>>>>> experiments is infinitely more interesting than any results to which >>>>>>>> their >>>>>>>> experiments lead. >>>>>>>> -- Norbert Wiener >>>>>>>> >>>>>>>> https://www.cse.buffalo.edu/~knepley/ >>>>>>>> <http://www.caam.rice.edu/%7Emk51/> >>>>>>>> >>>>>>> >>>>>>> >>>>>> >>>>> >>>>> >>>>> -- >>>>> What most experimenters take for granted before they begin their >>>>> experiments is infinitely more interesting than any results to which their >>>>> experiments lead. >>>>> -- Norbert Wiener >>>>> >>>>> https://www.cse.buffalo.edu/~knepley/ >>>>> <http://www.caam.rice.edu/%7Emk51/> >>>>> >>>> >>>> >>> >> > -- What most experimenters take for granted before they begin their experiments is infinitely more interesting than any results to which their experiments lead. -- Norbert Wiener https://www.cse.buffalo.edu/~knepley/ <http://www.caam.rice.edu/~mk51/>