# [petsc-users] Understanding the -ksp_monitor_true_residual output

Aulisa, Eugenio eugenio.aulisa at ttu.edu
Tue Apr 12 08:39:33 CDT 2016

```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.
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/
phone: (806) 834-6684
fax: (806) 742-1112

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