[petsc-users] Understanding the -ksp_monitor_true_residual output

Aulisa, Eugenio eugenio.aulisa at ttu.edu
Tue Apr 12 12:45:17 CDT 2016 

Thanks


Eugenio Aulisa

Department of Mathematics and Statistics,
Texas Tech University
Lubbock TX, 79409-1042
room: 226
http://www.math.ttu.edu/~eaulisa/
phone: (806) 834-6684
fax: (806) 742-1112



________________________________
From: Dave May [dave.mayhem23 at gmail.com]
Sent: Tuesday, April 12, 2016 12:21 PM
To: Aulisa, Eugenio
Cc: PETSc users list ‎[petsc-users at mcs.anl.gov]‎
Subject: Re: [petsc-users] Understanding the -ksp_monitor_true_residual output



On 12 April 2016 at 15:39, Aulisa, Eugenio <eugenio.aulisa at ttu.edu<redir.aspx?REF=k9Dky_5pfrz4XgZAG7gWOu7bSuApwoto-LQVifvGmKF7qysu-mLTCAFtYWlsdG86ZXVnZW5pby5hdWxpc2FAdHR1LmVkdQ..>> wrote:
Hi,

I am trying to understand better the meaning of
the output obtained using the option

-ksp_monitor_true_residual

For this particular ksp gmres solver I used

KSPSetTolerances( ksp, 1.0e-4, 1.0e-20, 1.0e50, 60);

Below I am reporting the output for 5 different solutions

In each of them the convergence reason is 2, the relative tolerance.

If I well understood the manual I would expect the solver to exit when the
output of the third column ||r(i)||/||b|| would fall below 1.0e-04, but it is not.

By default, GMRES uses left preconditioning,
thus iterations are terminated when || P^{-1} r_i || / || P^{-1} b || < 1e-4
With GMRES, you can change the side of the preconditioning via
  -ksp_pc_side right
(note that not all methods support both left and right preconditioning)

FGMRES and GCR use right preconditioning by default


Thanks,
  Dave

Only in the last solution this is the case.
So probably I did not understood well the manual, and there is a rescaling involved.

Can anybody clarify?

Thanks,
Eugenio Aulisa



   ********* solution 1 *********
  0 KSP preconditioned resid norm 3.410562043865e+01 true resid norm 2.677893657847e-02 ||r(i)||/||b|| 3.993927934126e+00
  1 KSP preconditioned resid norm 5.824255715066e+00 true resid norm 1.393228808527e-02 ||r(i)||/||b|| 2.077922489826e+00
  2 KSP preconditioned resid norm 2.044834259922e+00 true resid norm 9.998998076659e-03 ||r(i)||/||b|| 1.491294384100e+00
  3 KSP preconditioned resid norm 7.983786718994e-01 true resid norm 7.993995927780e-03 ||r(i)||/||b|| 1.192259578632e+00
  4 KSP preconditioned resid norm 5.088731995172e-01 true resid norm 8.593150583543e-03 ||r(i)||/||b|| 1.281620129208e+00
  5 KSP preconditioned resid norm 4.857006661570e-01 true resid norm 9.145941228163e-03 ||r(i)||/||b|| 1.364065748018e+00
  6 KSP preconditioned resid norm 4.709624056986e-01 true resid norm 8.186977687270e-03 ||r(i)||/||b|| 1.221041723798e+00
  7 KSP preconditioned resid norm 3.220045108449e-01 true resid norm 4.352636436074e-03 ||r(i)||/||b|| 6.491712692992e-01
  8 KSP preconditioned resid norm 2.317017366518e-01 true resid norm 3.068984741076e-03 ||r(i)||/||b|| 4.577218311441e-01
  9 KSP preconditioned resid norm 1.910797150631e-01 true resid norm 2.564718555990e-03 ||r(i)||/||b|| 3.825133628412e-01
 10 KSP preconditioned resid norm 1.729613253747e-01 true resid norm 2.555884137267e-03 ||r(i)||/||b|| 3.811957589244e-01
 11 KSP preconditioned resid norm 1.708323617518e-01 true resid norm 2.699641560429e-03 ||r(i)||/||b|| 4.026363708929e-01
 12 KSP preconditioned resid norm 1.606003434286e-01 true resid norm 2.148175491821e-03 ||r(i)||/||b|| 3.203883051534e-01
 13 KSP preconditioned resid norm 1.205953154320e-01 true resid norm 1.319733567910e-03 ||r(i)||/||b|| 1.968308467752e-01
 14 KSP preconditioned resid norm 6.473668392252e-02 true resid norm 7.750007977497e-04 ||r(i)||/||b|| 1.155870146685e-01
 15 KSP preconditioned resid norm 4.210976512647e-02 true resid norm 3.627137178803e-04 ||r(i)||/||b|| 5.409671312704e-02
 16 KSP preconditioned resid norm 2.167079981806e-02 true resid norm 1.885937330161e-04 ||r(i)||/||b|| 2.812769567181e-02
       *************** MG linear solver time: 1.710646e+01
       *************** Number of outer ksp solver iterations = 16
       *************** Convergence reason = 2
       *************** Residual norm =  0.0216708





   ********* solution 2 *********
   ********* Level Max 4 MG PROJECTION MATRICES TIME:   1.199155
   ********* Level Max 4 MGINIT TIME:   0.691589
   ********* Level Max 4 ASSEMBLY TIME: 11.470600
     ********* Linear Cycle + Residual Update iteration 1
       *************** Linear iteration 1 ***********
  0 KSP preconditioned resid norm 5.264510580035e+01 true resid norm 4.446470526095e-03 ||r(i)||/||b|| 1.343097318343e+00
  1 KSP preconditioned resid norm 1.194632734776e+00 true resid norm 2.650838633150e-03 ||r(i)||/||b|| 8.007101899472e-01
  2 KSP preconditioned resid norm 2.514505382950e-01 true resid norm 8.961867887367e-04 ||r(i)||/||b|| 2.707014621199e-01
  3 KSP preconditioned resid norm 4.126701684642e-02 true resid norm 2.828561525607e-04 ||r(i)||/||b|| 8.543930242012e-02
  4 KSP preconditioned resid norm 2.990078801994e-02 true resid norm 3.012123557665e-04 ||r(i)||/||b|| 9.098396242766e-02
  5 KSP preconditioned resid norm 2.498986435717e-02 true resid norm 3.492907889867e-04 ||r(i)||/||b|| 1.055064953780e-01
  6 KSP preconditioned resid norm 2.212280334220e-02 true resid norm 2.649097730890e-04 ||r(i)||/||b|| 8.001843344081e-02
  7 KSP preconditioned resid norm 1.270611663385e-02 true resid norm 1.114378752133e-04 ||r(i)||/||b|| 3.366083514611e-02
       *************** MG linear solver time: 1.032488e+01
       *************** Number of outer ksp solver iterations = 7
       *************** Convergence reason = 2
       *************** Residual norm = 0.012706117




   ********* solution 3 *********
  0 KSP preconditioned resid norm 8.243929775966e-02 true resid norm 1.154408051359e-04 ||r(i)||/||b|| 1.020198211331e+00
  1 KSP preconditioned resid norm 9.646734506593e-03 true resid norm 1.275532346161e-04 ||r(i)||/||b|| 1.127240767696e+00
  2 KSP preconditioned resid norm 9.036645252734e-03 true resid norm 1.308042358485e-04 ||r(i)||/||b|| 1.155971212173e+00
  3 KSP preconditioned resid norm 9.031542604401e-03 true resid norm 1.291290364679e-04 ||r(i)||/||b|| 1.141166781368e+00
  4 KSP preconditioned resid norm 5.171448589573e-03 true resid norm 8.206502754373e-05 ||r(i)||/||b|| 7.252426402812e-01
  5 KSP preconditioned resid norm 2.891929663032e-03 true resid norm 7.598041857685e-05 ||r(i)||/||b|| 6.714704305557e-01
  6 KSP preconditioned resid norm 2.343001795062e-03 true resid norm 7.025844324392e-05 ||r(i)||/||b|| 6.209029644586e-01
  7 KSP preconditioned resid norm 2.185509183830e-03 true resid norm 6.344926688255e-05 ||r(i)||/||b|| 5.607274525472e-01
  8 KSP preconditioned resid norm 2.058441165493e-03 true resid norm 5.444619590411e-05 ||r(i)||/||b|| 4.811635851791e-01
  9 KSP preconditioned resid norm 1.932842861175e-03 true resid norm 4.852637232344e-05 ||r(i)||/||b|| 4.288476521667e-01
 10 KSP preconditioned resid norm 1.898825969952e-03 true resid norm 4.918129150547e-05 ||r(i)||/||b|| 4.346354442501e-01
 11 KSP preconditioned resid norm 1.891602735935e-03 true resid norm 4.710536993558e-05 ||r(i)||/||b|| 4.162896654766e-01
 12 KSP preconditioned resid norm 1.781187329134e-03 true resid norm 3.777014072473e-05 ||r(i)||/||b|| 3.337903782266e-01
 13 KSP preconditioned resid norm 1.099066136430e-03 true resid norm 1.424597383325e-05 ||r(i)||/||b|| 1.258975715410e-01
 14 KSP preconditioned resid norm 6.280243703281e-04 true resid norm 5.012017417525e-06 ||r(i)||/||b|| 4.429327392944e-02
 15 KSP preconditioned resid norm 3.076374051756e-04 true resid norm 2.605020117635e-06 ||r(i)||/||b|| 2.302164179611e-02
 16 KSP preconditioned resid norm 1.368303935548e-04 true resid norm 1.393123702916e-06 ||r(i)||/||b|| 1.231161120372e-02
 17 KSP preconditioned resid norm 7.228043655761e-05 true resid norm 7.895171494272e-07 ||r(i)||/||b|| 6.977290072715e-03
 18 KSP preconditioned resid norm 3.866647775994e-05 true resid norm 4.528577419728e-07 ||r(i)||/||b|| 4.002091442486e-03
       *************** MG linear solver time: 1.798489e+01
       *************** Number of outer ksp solver iterations = 18
       *************** Convergence reason = 2
       *************** Residual norm = 3.8666478e-05




   ********* solution 4 *********
  0 KSP preconditioned resid norm 1.580191013568e-04 true resid norm 4.329063484560e-07 ||r(i)||/||b|| 9.556132759754e-01
  1 KSP preconditioned resid norm 3.193492170557e-05 true resid norm 3.833183963598e-07 ||r(i)||/||b|| 8.461510204077e-01
  2 KSP preconditioned resid norm 1.771193813393e-05 true resid norm 3.779057891921e-07 ||r(i)||/||b|| 8.342030337691e-01
  3 KSP preconditioned resid norm 1.457271790528e-05 true resid norm 3.908277498762e-07 ||r(i)||/||b|| 8.627274414739e-01
  4 KSP preconditioned resid norm 1.450745561248e-05 true resid norm 3.973502432864e-07 ||r(i)||/||b|| 8.771254315185e-01
  5 KSP preconditioned resid norm 1.413655961039e-05 true resid norm 3.690661275865e-07 ||r(i)||/||b|| 8.146900420664e-01
  6 KSP preconditioned resid norm 1.250367472770e-05 true resid norm 2.896966438369e-07 ||r(i)||/||b|| 6.394869464109e-01
  7 KSP preconditioned resid norm 8.752862209538e-06 true resid norm 1.583120202644e-07 ||r(i)||/||b|| 3.494637324001e-01
  8 KSP preconditioned resid norm 5.705999073439e-06 true resid norm 9.765760786693e-08 ||r(i)||/||b|| 2.155729684041e-01
  9 KSP preconditioned resid norm 4.192178998873e-06 true resid norm 8.201685117361e-08 ||r(i)||/||b|| 1.810469911442e-01
 10 KSP preconditioned resid norm 3.787794183624e-06 true resid norm 8.005205894911e-08 ||r(i)||/||b|| 1.767098370670e-01
 11 KSP preconditioned resid norm 3.786646339736e-06 true resid norm 8.038622787957e-08 ||r(i)||/||b|| 1.774474937623e-01
 12 KSP preconditioned resid norm 3.485518782082e-06 true resid norm 6.939667236683e-08 ||r(i)||/||b|| 1.531887477714e-01
 13 KSP preconditioned resid norm 2.521214592414e-06 true resid norm 4.378155291157e-08 ||r(i)||/||b|| 9.664499805635e-02
 14 KSP preconditioned resid norm 1.284994591466e-06 true resid norm 2.240582241084e-08 ||r(i)||/||b|| 4.945943027010e-02
 15 KSP preconditioned resid norm 6.133028069300e-07 true resid norm 1.361309969809e-08 ||r(i)||/||b|| 3.005005319295e-02
 16 KSP preconditioned resid norm 3.455523081821e-07 true resid norm 9.658743967776e-09 ||r(i)||/||b|| 2.132106400789e-02
 17 KSP preconditioned resid norm 2.505109883585e-07 true resid norm 6.870409301721e-09 ||r(i)||/||b|| 1.516599228338e-02
 18 KSP preconditioned resid norm 1.443203299992e-07 true resid norm 2.920265170395e-09 ||r(i)||/||b|| 6.446299935659e-03
 19 KSP preconditioned resid norm 6.636071800703e-08 true resid norm 8.697314690164e-10 ||r(i)||/||b|| 1.919876992541e-03
 20 KSP preconditioned resid norm 2.714859523602e-08 true resid norm 3.148984178618e-10 ||r(i)||/||b|| 6.951182623347e-04
 21 KSP preconditioned resid norm 1.117207550910e-08 true resid norm 9.396722225928e-11 ||r(i)||/||b|| 2.074266765035e-04
       *************** MG linear solver time: 2.005832e+01
       *************** Number of outer ksp solver iterations = 21
       *************** Convergence reason = 2
       *************** Residual norm = 1.1172076e-08




   ********* solution 5 *********
  0 KSP preconditioned resid norm 8.454401619840e-09 true resid norm 8.452738510071e-11 ||r(i)||/||b|| 8.995416179570e-01
  1 KSP preconditioned resid norm 4.580659647172e-09 true resid norm 8.265563180408e-11 ||r(i)||/||b|| 8.796223931180e-01
  2 KSP preconditioned resid norm 4.256081515265e-09 true resid norm 8.549582845321e-11 ||r(i)||/||b|| 9.098478056991e-01
  3 KSP preconditioned resid norm 3.976359790239e-09 true resid norm 8.007959832870e-11 ||r(i)||/||b|| 8.522082087375e-01
  4 KSP preconditioned resid norm 2.913165841066e-09 true resid norm 6.211100493580e-11 ||r(i)||/||b|| 6.609861857942e-01
  5 KSP preconditioned resid norm 2.130900661500e-09 true resid norm 4.739159015704e-11 ||r(i)||/||b|| 5.043419672409e-01
  6 KSP preconditioned resid norm 1.606110624311e-09 true resid norm 3.793019756253e-11 ||r(i)||/||b|| 4.036536945295e-01
  7 KSP preconditioned resid norm 1.194061891991e-09 true resid norm 3.460284393549e-11 ||r(i)||/||b|| 3.682439505559e-01
  8 KSP preconditioned resid norm 1.116001295092e-09 true resid norm 3.338332136751e-11 ||r(i)||/||b|| 3.552657742805e-01
  9 KSP preconditioned resid norm 1.101694508395e-09 true resid norm 3.242096748193e-11 ||r(i)||/||b|| 3.450243907306e-01
 10 KSP preconditioned resid norm 1.101137265122e-09 true resid norm 3.225308396705e-11 ||r(i)||/||b|| 3.432377720103e-01
 11 KSP preconditioned resid norm 1.100600624436e-09 true resid norm 3.226535049788e-11 ||r(i)||/||b|| 3.433683126034e-01
 12 KSP preconditioned resid norm 1.092907627060e-09 true resid norm 3.134764252264e-11 ||r(i)||/||b|| 3.336020514577e-01
 13 KSP preconditioned resid norm 9.870087224964e-10 true resid norm 2.277199172927e-11 ||r(i)||/||b|| 2.423398554190e-01
 14 KSP preconditioned resid norm 6.855374335133e-10 true resid norm 8.872613630455e-12 ||r(i)||/||b|| 9.442247871666e-02
 15 KSP preconditioned resid norm 3.960223027036e-10 true resid norm 3.394176790592e-12 ||r(i)||/||b|| 3.612087701758e-02
 16 KSP preconditioned resid norm 1.977336550448e-10 true resid norm 1.661499967555e-12 ||r(i)||/||b|| 1.768170596156e-02
 17 KSP preconditioned resid norm 8.560605344251e-11 true resid norm 7.411831253461e-13 ||r(i)||/||b|| 7.887681216944e-03
 18 KSP preconditioned resid norm 3.819157888961e-11 true resid norm 4.556531922343e-13 ||r(i)||/||b|| 4.849067663472e-03
 19 KSP preconditioned resid norm 2.031569059250e-11 true resid norm 2.030960472074e-13 ||r(i)||/||b|| 2.161350983329e-03
 20 KSP preconditioned resid norm 9.966436828718e-12 true resid norm 9.192887548370e-14 ||r(i)||/||b|| 9.783083824378e-04
 21 KSP preconditioned resid norm 4.416012066006e-12 true resid norm 4.607062767741e-14 ||r(i)||/||b|| 4.902842660027e-04
 22 KSP preconditioned resid norm 1.740999775043e-12 true resid norm 1.452842765632e-14 ||r(i)||/||b|| 1.546117309173e-04
 23 KSP preconditioned resid norm 6.762885582183e-13 true resid norm 3.253813922193e-15 ||r(i)||/||b|| 3.462713340314e-05
       *************** MG linear solver time: 2.151817e+01
       *************** Number of outer ksp solver iterations = 23
       *************** Convergence reason = 2
       *************** Residual norm = 6.7628856e-13






Eugenio Aulisa

Department of Mathematics and Statistics,
Texas Tech University
Lubbock TX, 79409-1042
room: 226
http://www.math.ttu.edu/~eaulisa/<redir.aspx?REF=yu-ijEuhcgO8zsqYqUc7eIeAFdyQ6entoqb8OcAcstR7qysu-mLTCAFodHRwOi8vd3d3Lm1hdGgudHR1LmVkdS9-ZWF1bGlzYS8.>
phone: (806) 834-6684<tel:%28806%29%20834-6684>
fax: (806) 742-1112<tel:%28806%29%20742-1112>




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