On 18 April 2018 at 23:52, Matthew Knepley <knep...@gmail.com> wrote:
> On Wed, Apr 18, 2018 at 5:52 PM, Sepideh Kavousi <skav...@lsu.edu> wrote: > >> Mathew and Dave, >> >> Thank you so much it is working perfectly now. >> > > Excellent. > > If you want your name to appear on the next PETSc release as a > contributor, you > can make a PR with this change :) > Here is a URL describing the PR's protocol for PETSc contribs: https://bitbucket.org/petsc/petsc/wiki/pull-request-instructions-git > > Thanks, > > Matt > > >> Sepideh >> ------------------------------ >> *From:* Dave May <dave.mayhe...@gmail.com> >> *Sent:* Wednesday, April 18, 2018 3:13:33 PM >> *To:* Sepideh Kavousi >> *Cc:* Matthew Knepley; petsc-users@mcs.anl.gov >> *Subject:* Re: [petsc-users] error running parallel on cluster >> >> >> >> On 18 April 2018 at 21:06, Sepideh Kavousi <skav...@lsu.edu> wrote: >> >> Mathew >> >> I added the lines and I still have the same issue. It may be a silly >> question but should I configure and install petsc again using this new >> lines added? or changing the line is enough? the highlighted lines are the >> lines I modified. >> >> >> PetscErrorCode ierr; >> DM dm; >> DMTS_DA *dmdats = (DMTS_DA*)ctx; >> DMDALocalInfo info; >> Vec Xloc,Xdotloc; >> void *x,*f,*xdot; >> >> PetscFunctionBegin; >> PetscValidHeaderSpecific(ts,TS_CLASSID,1); >> PetscValidHeaderSpecific(X,VEC_CLASSID,2); >> PetscValidHeaderSpecific(F,VEC_CLASSID,3); >> if (!dmdats->ifunctionlocal) SETERRQ(PetscObjectComm((Petsc >> Object)ts),PETSC_ERR_PLIB,"Corrupt context"); >> ierr = TSGetDM(ts,&dm);CHKERRQ(ierr); >> ierr = DMGetLocalVector(dm,&Xdotloc);CHKERRQ(ierr); >> ierr = DMGlobalToLocalBegin(dm,Xdot,INSERT_VALUES,Xdotloc);CHKERRQ( >> ierr); >> ierr = DMGlobalToLocalEnd(dm,Xdot,INSERT_VALUES,Xdotloc);CHKERRQ(ierr); >> >> ierr = DMGetLocalVector(dm,&Xloc);CHKERRQ(ierr); >> ierr = DMGlobalToLocalBegin(dm,X,INSERT_VALUES,Xloc);CHKERRQ(ierr); >> ierr = DMGlobalToLocalEnd(dm,X,INSERT_VALUES,Xloc);CHKERRQ(ierr); >> ierr = DMDAGetLocalInfo(dm,&info);CHKERRQ(ierr); >> ierr = DMDAVecGetArray(dm,Xloc,&x);CHKERRQ(ierr); >> ierr = DMDAVecGetArray(dm,Xdotloc,&xdot);CHKERRQ(ierr); >> >> >> Don't forget to include these calls (in this order) after you are done >> with the Xdotloc vector >> >> ierr = DMDAVecRestoreArray(dm,Xdotloc,&xdot);CHKERRQ(ierr); >> ierr = DMRestoreLocalVector(dm,&Xdotloc);CHKERRQ(ierr); >> >> Failure to do so will result in a memory leak. >> >> >> >> Thanks, >> >> Sepideh >> ------------------------------ >> *From:* Matthew Knepley <knep...@gmail.com> >> *Sent:* Tuesday, April 17, 2018 5:59:12 PM >> >> *To:* Sepideh Kavousi >> *Cc:* petsc-users@mcs.anl.gov >> *Subject:* Re: [petsc-users] error running parallel on cluster >> >> On Tue, Apr 17, 2018 at 3:07 PM, Sepideh Kavousi <skav...@lsu.edu> wrote: >> >> The reason I can not use your method is that the input arguments of >> SetIFunctionLocal are the arrays of x,x_t instead of x,x_t vectors. In your >> method which was: >> >> ierr *=* DMGetLocalVector(dm,*&*Xdotloc);CHKERRQ(ierr); ierr *=* >> DMGlobalToLocalBegin(dm,Xdot,INSERT_VALUES,Xdotloc);CHKERRQ(ierr); ierr *=* >> DMGlobalToLocalEnd(dm,Xdot,INSERT_VALUES,Xdotloc);CHKERRQ(ierr); >> ierr *=* DMDAVecGetArray(dm,Xdotloc,*&*xdot);CHKERRQ(ierr); >> >> >> You misunderstand my suggestion. I mean stick this code in right here in >> PETSc >> >> https://bitbucket.org/petsc/petsc/annotate/be3efd428a942676a >> 0189b3273b3c582694ff011/src/ts/utils/dmdats.c?at=master&file >> viewer=file-view-default#dmdats.c-68 >> >> Then the X_t array you get in your local function will be ghosted. >> >> Matt >> >> >> I need to have the vector of Xdot, not the array. So I think I should use >> SetIFunction instead of SetIFunctionLocal. >> >> >> Sepideh >> ------------------------------ >> *From:* Matthew Knepley <knep...@gmail.com> >> *Sent:* Tuesday, April 17, 2018 1:22:53 PM >> *To:* Sepideh Kavousi >> *Cc:* petsc-users@mcs.anl.gov >> *Subject:* Re: [petsc-users] error running parallel on cluster >> >> On Tue, Apr 17, 2018 at 1:50 PM, Sepideh Kavousi <skav...@lsu.edu> wrote: >> >> Mathew, >> I previously use DMDATSSetIFunctionLocal(user.d >> a,INSERT_VALUES,(DMDATSIFunctionLocal) FormFunction,&user) in my code. >> If I want to use your solution I can not use it because in the FormFunction >> definition I must use arrays, not vectors.So to solve this issue I followed >> two methods where none were able to solve it. >> 1- in first method I decided to use TSSetIFunction instead of >> DMDATSSetIFunctionLocal >> >> for this means first in the main function, I use TSSetDM and my form >> function variables were as: >> PetscErrorCode FormFunction(TS ts,PetscScalar t,Vec Y,Vec Ydot,Vec F, >> struct VAR_STRUCT *user) { >> . >> . >> . >> . >> ierr = TSGetDM(ts,&dmda);CHKERRQ(ierr); >> ierr= DMDAGetLocalInfo(dmda,&info2) ;CHKERRQ(ierr); >> >> ierr = DMGetLocalVector(dmda,&Ydot_local);CHKERRQ(ierr); >> ierr = DMGlobalToLocalBegin(dmda,Ydot,INSERT_VALUES,Ydot_local);CHK >> ERRQ(ierr); >> ierr = DMGlobalToLocalEnd(dmda,Ydot,INSERT_VALUES,Ydot_local);CHKER >> RQ(ierr); >> . >> . >> . >> >> } >> But still, it does not consider vectors y,ydot,f related to dmda (problem >> executing DMDAVecGetArray) >> >> >> We cannot help you if you do not show full error messages. >> >> Why not fix the code with SetIFunctionLocal(), as I said in my last >> email. I will fix PETSc proper in branch at the end of the week. I >> have a proposal due tomorrow, so I cannot do it right now. >> >> Thanks, >> >> Matt >> >> >> 2- in second method I decided to use DMTSSetIFunction >> but still, FormFunction is in form of TSIFunction where we do not define >> dm object and I think it does not understand dm and da are connected, >> although I have used TSSetDM in the main function. >> >> Can you please help me what should I do? >> Regards, >> Sepideh >> >> >> >> >> ------------------------------ >> *From:* Matthew Knepley <knep...@gmail.com> >> *Sent:* Monday, April 16, 2018 9:34:01 PM >> >> *To:* Sepideh Kavousi >> *Cc:* petsc-users@mcs.anl.gov >> *Subject:* Re: [petsc-users] error running parallel on cluster >> >> On Mon, Apr 16, 2018 at 10:22 PM, Sepideh Kavousi <skav...@lsu.edu> >> wrote: >> >> I run with valgrind with the following command: >> >> /work/skavou1/petsc/debug/bin/mpiexec -np 2 valgrind --tool=memcheck -q >> --num-callers=20 --log-file=valgrind.log.%p ./one.out -malloc off >> -ts_monitor -snes_fd_color -ts_max_snes_failures -1 -ts_type beuler >> -pc_type bjacobi -snes_linesearch_type nleqerr -snes_type newtontr >> -ksp_gmres_restart 31 -sub_pc_type ilu -snes_monitor -snes_converged_reason >> -ksp_monitor >> >> >> Okay, I think this is coded wrong. The DMDA stuff ignores DMLocal and >> only chooses to ghost the input vector X and not X_t >> >> https://bitbucket.org/petsc/petsc/annotate/be3efd428a942676a >> 0189b3273b3c582694ff011/src/ts/utils/dmdats.c?at=master&file >> viewer=file-view-default#dmdats.c-68 >> >> Unfortunately, this was done by Peter in 2012 and he is gone, so we can't >> blame him. >> It is true that very few people use spatial derivatives of X_t, but it >> does make sense. >> Right there, you want to add >> >> ierr = DMGetLocalVector(dm,&Xdotloc);CHKERRQ(ierr); ierr = >> DMGlobalToLocalBegin(dm,Xdot,INSERT_VALUES,Xdotloc);CHKERRQ(ierr); ierr = >> DMGlobalToLocalEnd(dm,Xdot,INSERT_VALUES,Xdotloc);CHKERRQ(ierr); >> >> ierr = DMDAVecGetArray(dm,Xdotloc,&xdot);CHKERRQ(ierr); >> >> >> and it should work. >> >> Matt >> >> >> the valgringoutput is as following: >> >> ==39396== Invalid read of size 8 >> ==39396== at 0x402679: FormFunction (one.c:212) >> ==39396== by 0x611AA5F: TSComputeIFunction_DMDA (dmdats.c:79) >> ==39396== by 0x61349BD: TSComputeIFunction (ts.c:830) >> ==39396== by 0x623DD1C: SNESTSFormFunction_Theta (theta.c:649) >> ==39396== by 0x615E599: SNESTSFormFunction (ts.c:4569) >> ==39396== by 0x600C84E: SNESComputeFunction (snes.c:2203) >> ==39396== by 0x60A34B6: SNESSolve_NEWTONTR (tr.c:105) >> ==39396== by 0x60246C0: SNESSolve (snes.c:4312) >> ==39396== by 0x6237346: TSTheta_SNESSolve (theta.c:176) >> ==39396== by 0x6237CA8: TSStep_Theta (theta.c:216) >> ==39396== by 0x6153380: TSStep (ts.c:3548) >> ==39396== by 0x615559D: TSSolve (ts.c:3731) >> ==39396== by 0x403C95: main (one.c:303) >> ==39396== Address 0x83f5158 is 8 bytes before a block of size 7,200 >> alloc'd >> ==39396== at 0x4A05588: memalign (vg_replace_malloc.c:727) >> ==39396== by 0x4D87516: PetscMallocAlign (mal.c:42) >> ==39396== by 0x4D88DE0: PetscMallocA (mal.c:397) >> ==39396== by 0x50AB230: VecGetArray2d (rvector.c:2167) >> ==39396== by 0x589437E: DMDAVecGetArray (dagetarray.c:73) >> ==39396== by 0x611A8ED: TSComputeIFunction_DMDA (dmdats.c:74) >> ==39396== by 0x61349BD: TSComputeIFunction (ts.c:830) >> ==39396== by 0x623DD1C: SNESTSFormFunction_Theta (theta.c:649) >> ==39396== by 0x615E599: SNESTSFormFunction (ts.c:4569) >> ==39396== by 0x600C84E: SNESComputeFunction (snes.c:2203) >> ==39396== by 0x60A34B6: SNESSolve_NEWTONTR (tr.c:105) >> ==39396== by 0x60246C0: SNESSolve (snes.c:4312) >> ==39396== by 0x6237346: TSTheta_SNESSolve (theta.c:176) >> ==39396== by 0x6237CA8: TSStep_Theta (theta.c:216) >> ==39396== by 0x6153380: TSStep (ts.c:3548) >> ==39396== by 0x615559D: TSSolve (ts.c:3731) >> ==39396== by 0x403C95: main (one.c:303) >> ==39396== >> ==39396== Invalid read of size 8 >> ==39396== at 0x402689: FormFunction (one.c:212) >> ==39396== by 0x611AA5F: TSComputeIFunction_DMDA (dmdats.c:79) >> ==39396== by 0x61349BD: TSComputeIFunction (ts.c:830) >> ==39396== by 0x623DD1C: SNESTSFormFunction_Theta (theta.c:649) >> ==39396== by 0x615E599: SNESTSFormFunction (ts.c:4569) >> ==39396== by 0x600C84E: SNESComputeFunction (snes.c:2203) >> ==39396== by 0x60A34B6: SNESSolve_NEWTONTR (tr.c:105) >> ==39396== by 0x60246C0: SNESSolve (snes.c:4312) >> ==39396== by 0x6237346: TSTheta_SNESSolve (theta.c:176) >> ==39396== by 0x6237CA8: TSStep_Theta (theta.c:216) >> ==39396== by 0x6153380: TSStep (ts.c:3548) >> ==39396== by 0x615559D: TSSolve (ts.c:3731) >> ==39396== by 0x403C95: main (one.c:303) >> ==39396== Address 0x18 is not stack'd, malloc'd or (recently) free'd >> ==39396== >> >> Thanks, >> >> Sepideh >> ------------------------------ >> *From:* Matthew Knepley <knep...@gmail.com> >> *Sent:* Monday, April 16, 2018 8:44:43 PM >> *To:* Sepideh Kavousi >> *Cc:* petsc-users@mcs.anl.gov >> *Subject:* Re: [petsc-users] error running parallel on cluster >> >> On Mon, Apr 16, 2018 at 9:39 PM, Sepideh Kavousi <skav...@lsu.edu> wrote: >> >> this is not used forghost points . my code is : >> >> >> 1) You are using ghost points, since you use i-1 as an index >> >> 2) I was wrong. X_t should also be ghosted. >> >> Run under valgrind. >> >> Thanks, >> >> Matt >> >> >> for (j=info2->ys;j<info2->ys+info2->ym;j++){ >> for (i=info2->xs;i<info2->xs+info2->xm;i++){ >> if (i==0) {aF[j][i].U=aY[j][i+1].U-aY[j][i].U ; >> aF[j][i].p=aY[j][i+1].p-aY[j][i].p ;} >> else if (i==info2->mx-1) {aF[j][i].U=aY[j][i-1].U-aY[j][i].U >> ; aF[j][i].p=aY[j][i].p-aY[j][i-1].p ;} >> else if (j==0) {aF[j][i].U=aY[j+1][i].U-aY[j][i].U; >> aF[j][i].p=aY[j+1][i].p-aY[j][i].p ;} >> else if (j==info2->my-1) {aF[j][i].U=aY[j-1][i].U-aY[j][i].U >> ; aF[j][i].p=aY[j][i].p-aY[j-1][i].p ;} >> else { >> //derivatives of U and p >> Px=(aY[j][i+1].p-aY[j][i-1].p)/(2.0*user->hx); >> Py=(aY[j+1][i].p-aY[j-1][i].p)/(2.0*user->hy); >> Pxx=((aY[j][i+1].p+aY[j][i-1].p-2.0*aY[j][i].p)/(hx2)); >> Pxy=((aY[j+1][i+1].p+aY[j-1][ >> i-1].p-aY[j+1][i-1].p-aY[j-1][i+1].p)/(4.0*hxy)); >> Pyy=((aY[j+1][i].p+aY[j-1][i].p-2.0*aY[j][i].p)/hy2); >> Pxt=(aYdot[j][i+1].p-aYdot[j][i-1].p)/(2.0*user->hx); >> Pyt=(aYdot[j+1][i].p-aYdot[j-1][i].p)/(2.0*user->hy); >> >> >> if (((Px*Px)+(Py*Py))>0.0 ) { // >> theta=PetscAtanReal(Py/Px); >> thetax=(Px*Pxy-Py*Pxx)/((Px*Px)+(Py*Py)); >> thetay=(Px*Pyy-Py*Pxy)/((Px*Px)+(Py*Py)); >> } >> else { >> theta=PETSC_PI*0.5; >> thetax=0.0; >> thetay=0.0; >> } >> e=(1.0+user->epsilon*cos(4.0*theta));; >> ep=-(4.0*user->epsilon*sin(4.0*theta)); >> epp=-(4.0*user->epsilon*4.0*cos(4.0*theta)); >> >> >> >> Ux=(aY[j][i+1].U-aY[j][i-1].U)/(2.0*user->hx); >> Uy=(aY[j+1][i].U-aY[j-1][i].U)/(2.0*user->hy); >> Uxx=((aY[j][i+1].U+aY[j][i-1].U-2.0*aY[j][i].U)/(hx2)); >> Uyy=((aY[j+1][i].U+aY[j-1][i].U-2.0*aY[j][i].U)/hy2); >> >> U1=user->D*user->tau_0/(user->W*user->W); >> U2= ((Px*Px+Py*Py)>0.0) ? user->a_p/sqrt(Px*Px+Py*Py) : >> 0.0 ; >> //U2=0.0; >> P1= (user->W*user->hy*j-user->Vp*user->tau_0*t)/user->lT; >> >> aF[j][i].U=(U1*(-0.5*(Ux*Px+U >> y*Py)+0.5*(1-aY[j][i].p)*(Uxx+Uyy))+U2*(1+(1-user->k)*aY[j][ >> i].U)*(Pxt*Px+Pyt*Py+aYdot[j][i].p*(Pxx+Pyy))+U2*(1-user->k) >> *aYdot[j][i].p*(Ux*Px+Uy*Py)+0.5*(1+(1-user->k)*aY[j][i].U)* >> aYdot[j][i].p-0.5*(1+user->k-(1-user->k)*aY[j][i].p)*aYdot[j][i].U)*hx2; >> >> aF[j][i].p=( e*e*(Pxx+Pyy)+2.0*e*ep*(thetax >> *Px+thetay*Py)+(e*epp+ep*ep)*(thetay*Px-thetax*Py)+(aY[j][i] >> .p-aY[j][i].p*aY[j][i].p*aY[j][i].p)-user->lambda*(aY[j][i]. >> p*aY[j][i].p-1)*(aY[j][i].p*aY[j][i].p-1)*(aY[j][i].U+P1)-(1 >> -(1-user->k)*P1)*(1.0+4.0*user->epsilon*cos(4.0*theta))*(1.0 >> +4.0*user->epsilon*cos(4.0*theta))*aYdot[j][i].p )*hx2 ; >> >> } >> } >> >> Sepideh >> ------------------------------ >> *From:* Matthew Knepley <knep...@gmail.com> >> *Sent:* Monday, April 16, 2018 8:36:37 PM >> *To:* Sepideh Kavousi >> *Cc:* petsc-users@mcs.anl.gov >> *Subject:* Re: [petsc-users] error running parallel on cluster >> >> On Mon, Apr 16, 2018 at 9:20 PM, Sepideh Kavousi <skav...@lsu.edu> wrote: >> >> Hello, >> I am solving a PDE where I have the spacial derivtive of the time >> derivative of a variable. In the DMDATSSetIFunctionLocal function I >> defined d(dY/dt)/dx as: >> (aYdot[j][i+1].p-aYdot[j][i-1].p)/(2.0*user->hx) >> >> >> I do not think that you get ghosted Ydot in that function. >> >> Matt >> >> >> on my workstation, it is working but on the cluster it gives an error. I >> can not run with debugger on the cluster but I have checked and the error >> is related to this part and I do not have any problem on cluster when >> running in series. Can you please help me about it. >> >> the error is: >> 0]PETSC ERROR: Caught signal number 11 SEGV: Segmentation Violation, >> probably memory access out of range >> [0]PETSC ERROR: Try option -start_in_debugger or -on_error_attach_debugger >> [0]PETSC ERROR: or see http://www.mcs.anl.gov/petsc/d >> ocumentation/faq.html#valgrind >> [0]PETSC ERROR: or try http://valgrind.org on GNU/linux and Apple Mac OS >> X to find memory corruption errors >> [0]PETSC ERROR: likely location of problem given in stack below >> [0]PETSC ERROR: --------------------- Stack Frames >> ------------------------------------ >> [0]PETSC ERROR: Note: The EXACT line numbers in the stack are not >> available, >> [0]PETSC ERROR: INSTEAD the line number of the start of the function >> [0]PETSC ERROR: is given. >> [0]PETSC ERROR: [0] TSComputeIFunction_DMDA line 63 >> /ddnB/work/skavou1/petsc/src/ts/utils/dmdats.c >> [0]PETSC ERROR: [0] TS user implicit function line 829 >> /ddnB/work/skavou1/petsc/src/ts/interface/ts.c >> [0]PETSC ERROR: [0] TSComputeIFunction line 815 >> /ddnB/work/skavou1/petsc/src/ts/interface/ts.c >> [0]PETSC ERROR: [0] SNESTSFormFunction_Theta line 640 >> /ddnB/work/skavou1/petsc/src/ts/impls/implicit/theta/theta.c >> [0]PETSC ERROR: [0] SNESTSFormFunction line 4564 >> /ddnB/work/skavou1/petsc/src/ts/interface/ts.c >> [0]PETSC ERROR: [0] SNES user function line 2202 >> /ddnB/work/skavou1/petsc/src/snes/interface/snes.c >> [0]PETSC ERROR: [0] SNESComputeFunction line 2187 >> /ddnB/work/skavou1/petsc/src/snes/interface/snes.c >> [0]PETSC ERROR: [0] SNESSolve_NEWTONTR line 90 >> /ddnB/work/skavou1/petsc/src/snes/impls/tr/tr.c >> [0]PETSC ERROR: [0] SNESSolve line 4203 /ddnB/work/skavou1/petsc/src/s >> nes/interface/snes.c >> [0]PETSC ERROR: [0] TSTheta_SNESSolve line 175 >> /ddnB/work/skavou1/petsc/src/ts/impls/implicit/theta/theta.c >> [0]PETSC ERROR: [0] TSStep_Theta line 191 /ddnB/work/skavou1/petsc/src/t >> s/impls/implicit/theta/theta.c >> [0]PETSC ERROR: [0] TSStep line 3526 /ddnB/work/skavou1/petsc/src/t >> s/interface/ts.c >> [0]PETSC ERROR: [0] TSSolve line 3668 /ddnB/work/skavou1/petsc/src/t >> s/interface/ts.c >> [0]PETSC ERROR: --------------------- Error Message >> -------------------------------------------------------------- >> [0]PETSC ERROR: Signal received >> [0]PETSC ERROR: See http://www.mcs.anl.gov/petsc/documentation/faq.html >> for trouble shooting. >> [0]PETSC ERROR: Petsc Release Version 3.9.0, unknown >> [0]PETSC ERROR: ./one.out on a debug named mike1 by skavou1 Mon Apr 16 >> 20:11:44 2018 >> [0]PETSC ERROR: Configure options --with-cc=gcc --with-cxx=g++ >> --with-fc=gfortran --download-mpich --download-fblaslapack >> [0]PETSC ERROR: #1 User provided function() line 0 in unknown file >> application called MPI_Abort(MPI_COMM_WORLD, 59) - process 0 >> ==29057== >> ==29057== HEAP SUMMARY: >> ==29057== in use at exit: 560,151 bytes in 383 blocks >> ==29057== total heap usage: 8,734 allocs, 8,351 frees, 4,449,350 bytes >> allocated >> ==29057== >> ==29057== LEAK SUMMARY: >> ==29057== definitely lost: 0 bytes in 0 blocks >> ==29057== indirectly lost: 0 bytes in 0 blocks >> ==29057== possibly lost: 0 bytes in 0 blocks >> ==29057== still reachable: 560,151 bytes in 383 blocks >> ==29057== suppressed: 0 bytes in 0 blocks >> ==29057== Rerun with --leak-check=full to see details of leaked memory >> ==29057== >> ==29057== For counts of detected and suppressed errors, rerun with: -v >> ==29057== ERROR SUMMARY: 0 errors from 0 contexts (suppressed: 8 from 6) >> >> >> >> >> Thanks, >> Sepideh >> >> >> >> >> -- >> 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/> >> >> >> >> >> -- >> 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/> >> >> >> >> >> -- >> 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/> >> >> >> >> >> -- >> 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/> >> >> >> >> >> -- >> 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/> >> >> >> > > > -- > 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/> >
