convergence test

bb034a68 · niklas.baumgarten · f2973ad2 · bb034a68
Commit bb034a68 authored Apr 27, 2021 by niklas.baumgarten
--- a/notebooks/Elliptic Experiments 2.ipynb
+++ b/notebooks/Elliptic Experiments 2.ipynb
@@ -344,13 +344,13 @@
  },
  {
   "cell_type": "code",
-   "execution_count": 21,
+   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
-       "model_id": "556da193419043bab7cfa12697b76d80",
+       "model_id": "d36f279e4231454d82842c3e0ec27cbf",
       "version_major": 2,
       "version_minor": 0
      },
@@ -384,12 +384,54 @@
    "    p.add_vtu(\"Pressure.6.1.{}.vtu\".format(n), ax=p.ax4)   "
   ]
  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Convergence tests"
+   ]
+  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
-   "source": []
+   "source": [
+    "test_case = True\n",
+    "if test_case:\n",
+    "    mpp.kernels = 4\n",
+    "    mpp.mute = False\n",
+    "    kwargs = {\"epsilon\":          0.0,\n",
+    "              \"initLevels\":       [3, 4, 5, 6, 7],\n",
+    "              \"initSampleAmount\": [100, 100, 100, 100, 100],\n",
+    "              \"Problem\": \"StochasticLaplace2DTest\"}\n",
+    "    epsilons = [0.1, 0.03, 0.01, 0.003]\n",
+    "else:\n",
+    "    mpp.kernels = 32\n",
+    "    mpp.mute = True\n",
+    "    kwargs = {\"epsilon\":          0.0,\n",
+    "              \"initLevels\":       [3, 4, 5, 6, 7, 8, 9],\n",
+    "              \"initSampleAmount\": [500, 500, 500, 500, 500, 500, 500],\n",
+    "              \"Problem\": \"StochasticLaplace2DTest\"}\n",
+    "    epsilons = [0.1, 0.03, 0.01, 0.003, 0.001, 0.0003]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "scrolled": false
+   },
+   "outputs": [],
+   "source": [
+    "mpp.clean_data()\n",
+    "mpp.reset_data()\n",
+    "\n",
+    "mpp.run(config=\"mlmc_elliptic\", kwargs=kwargs)\n",
+    "mpp.parse_log()\n",
+    "\n",
+    "convergence_plot(mpp)"
+   ]
  }
 ],
 "metadata": {

 %% Cell type:code id: tags:

 ``` python
 import sys
 sys.path.append('..')

 import mpp.python.mppy as mppy
 import mpp.python.mppy.utilities as utils
 from python.mlmc_mppy import *

 import pandas as pd

 mpp = mppy.Mpp(project_name='MLMC',
               executable='MLMC-M++',
               kernels=4,
               mute=False)

 mpp.build()
 ```

 %% Output

    
    ================ running cmake ================
    
    -- Project directory= /home/niklas/CLionProjects/mlmc
    -- Mpp directory= /home/niklas/CLionProjects/mlmc/mpp
    -- Setting prepare commit message hook to mpp
       file: /home/niklas/CLionProjects/mlmc/mpp/doc/../../.git/modules/mpp/hooks/prepare-commit-msg
    -- Failed to find LLVM FileCheck
    -- git Version: v1.5.2-bf585a27
    -- Version: 1.5.2
    -- Performing Test HAVE_STD_REGEX -- success
    -- Performing Test HAVE_GNU_POSIX_REGEX -- failed to compile
    -- Performing Test HAVE_POSIX_REGEX -- success
    -- Performing Test HAVE_STEADY_CLOCK -- success
    -- A library with LAPACK API found.
    -- C Compiler optimization= -O3
    -- C++ version= 17
    -- Compiler version= c++
    -- Compiler optimization= -O0
    -- Suppress deprecated warnings= OFF
    -- Building space time library= OFF
    -- Time dimension= 0
    -- Using fftw library= ON
    -- Space dimension= 2
    -- Affine linear transformations= ON
    -- Geometric tolerance= 1e-10
    -- Near zero= 1e-15
    -- Very large= 1e30
    -- Infinity= 1e100
    -- Building mpp unit tests= OFF
    -- Building mpp interval arithmetic unit tests= OFF
    -- Configuring done
    -- Generating done
    -- Build files have been written to: /home/niklas/CLionProjects/mlmc/build
    
    ================ running  make ================
    
    [  1%] Built target gtest
    [  6%] Built target benchmark
    [ 10%] Built target LIB_BASIC
    [ 57%] Built target superlu
    [ 57%] Built target benchmark_main
    [ 58%] Built target gmock
    [ 58%] Built target gtest_main
    [ 59%] Built target gmock_main
    [ 62%] Built target LIB_MATH
    [ 63%] Built target LIB_TEST
    [ 68%] Built target LIB_MESH
    [ 71%] Built target LIB_DISC
    [ 75%] Built target LIB_VECTOR
    [ 80%] Built target LIB_ELEM
    [ 84%] Built target LIB_SOLVERS
    [ 84%] Built target MPP_LIBRARIES
    [ 84%] Built target BASICS
    [ 85%] Built target TestPlotting
    Scanning dependencies of target PDESOLVER
    [ 86%] Building CXX object mlmc/src/pdesolver/CMakeFiles/PDESOLVER.dir/PDESolverCreator.cpp.o
    [ 86%] Building CXX object mlmc/src/pdesolver/CMakeFiles/PDESOLVER.dir/assembling/MixedEllipticAssemble.cpp.o
    [ 86%] Building CXX object mlmc/src/pdesolver/CMakeFiles/PDESOLVER.dir/PDESolver.cpp.o
    [ 86%] Building CXX object mlmc/src/pdesolver/CMakeFiles/PDESOLVER.dir/assembling/LagrangeEllipticAssemble.cpp.o
    [ 86%] Building CXX object mlmc/src/pdesolver/CMakeFiles/PDESOLVER.dir/assembling/HybridEllipticAssemble.cpp.o
    [ 87%] Building CXX object mlmc/src/pdesolver/CMakeFiles/PDESOLVER.dir/assembling/DGEllipticAssemble.cpp.o
    [ 87%] Building CXX object mlmc/src/pdesolver/CMakeFiles/PDESOLVER.dir/assembling/PGReactionAssemble.cpp.o
    [ 87%] Building CXX object mlmc/src/pdesolver/CMakeFiles/PDESOLVER.dir/assembling/DGReactionAssemble.cpp.o
    [ 88%] Linking CXX static library libPDESOLVER.a
    [ 88%] Built target PDESOLVER
    Scanning dependencies of target PROBLEMS
    [ 88%] Building CXX object mlmc/src/problems/CMakeFiles/PROBLEMS.dir/StochasticEllipticProblem.cpp.o
    [ 89%] Linking CXX static library libPROBLEMS.a
    [ 89%] Built target PROBLEMS
    Scanning dependencies of target GENERATORS
    [ 89%] Building CXX object mlmc/src/generators/CMakeFiles/GENERATORS.dir/algorithms/HybridFluxGenerator.cpp.o
    [ 89%] Linking CXX static library libGENERATORS.a
    [ 91%] Built target GENERATORS
    [ 91%] Linking CXX executable TestNormalDistribution
    [ 91%] Linking CXX executable TestUniformDistribution
    [ 91%] Linking CXX executable TestCirculantEmbedding
    Scanning dependencies of target MONTECARLO
    [ 91%] Building CXX object mlmc/src/montecarlo/CMakeFiles/MONTECARLO.dir/MonteCarlo.cpp.o
    [ 91%] Built target TestUniformDistribution
    [ 91%] Linking CXX executable TestSymmetricCovariance
    [ 91%] Built target TestNormalDistribution
    Scanning dependencies of target TestPDESolverMPI
    [ 91%] Building CXX object mlmc/tests/CMakeFiles/TestPDESolverMPI.dir/pdesolver/TestPDESolver.cpp.o
    [ 91%] Built target TestCirculantEmbedding
    [ 91%] Building CXX object mlmc/src/montecarlo/CMakeFiles/MONTECARLO.dir/MultilevelMonteCarlo.cpp.o
    [ 92%] Built target TestSymmetricCovariance
    Scanning dependencies of target TestPDESolver
    [ 93%] Building CXX object mlmc/tests/CMakeFiles/TestPDESolver.dir/pdesolver/TestPDESolver.cpp.o
    [ 94%] Building CXX object mlmc/src/montecarlo/CMakeFiles/MONTECARLO.dir/datastructure/Errors.cpp.o
    [ 94%] Building CXX object mlmc/src/montecarlo/CMakeFiles/MONTECARLO.dir/datastructure/Exponents.cpp.o
    [ 94%] Linking CXX executable TestPDESolverMPI
    [ 94%] Building CXX object mlmc/src/montecarlo/CMakeFiles/MONTECARLO.dir/datastructure/EmpiricMeasureLevelMaps.cpp.o
    [ 94%] Linking CXX executable TestPDESolver
    [ 94%] Built target TestPDESolverMPI
    [ 94%] Built target TestPDESolver
    [ 95%] Linking CXX static library libMONTECARLO.a
    [ 95%] Built target MONTECARLO
    [ 95%] Linking CXX executable TestWelfordAggregateMPI
    Scanning dependencies of target MLMC-M++
    [ 96%] Building CXX object CMakeFiles/MLMC-M++.dir/mlmc/src/Main.cpp.o
    Scanning dependencies of target TestMonteCarloMPI
    Scanning dependencies of target TestMainMPI
    [ 96%] Building CXX object mlmc/tests/CMakeFiles/TestMainMPI.dir/TestMain.cpp.o
    [ 97%] Building CXX object mlmc/tests/CMakeFiles/TestMonteCarloMPI.dir/montecarlo/TestMonteCarlo.cpp.o
    [ 98%] Built target TestWelfordAggregateMPI
    Scanning dependencies of target TestEmpiricMeasureLevelMaps
    [ 99%] Building CXX object mlmc/tests/CMakeFiles/TestEmpiricMeasureLevelMaps.dir/montecarlo/datastructure/TestEmpiricMeasureLevelMaps.cpp.o
    [ 99%] Linking CXX executable MLMC-M++
    [ 99%] Linking CXX executable TestMonteCarloMPI
    [ 99%] Linking CXX executable TestMainMPI
    [ 99%] Linking CXX executable TestEmpiricMeasureLevelMaps
    [ 99%] Built target MLMC-M++
    Scanning dependencies of target TestExponents
    [100%] Building CXX object mlmc/tests/CMakeFiles/TestExponents.dir/montecarlo/datastructure/TestExponents.cpp.o
    [100%] Built target TestMonteCarloMPI
    Scanning dependencies of target TestErrors
    [100%] Building CXX object mlmc/tests/CMakeFiles/TestErrors.dir/montecarlo/datastructure/TestErrors.cpp.o
    [100%] Built target TestMainMPI
    [100%] Linking CXX executable TestSPRNG5MPI
    [100%] Built target TestEmpiricMeasureLevelMaps
    [100%] Built target TestSPRNG5MPI
    [100%] Linking CXX executable TestExponents
    [100%] Linking CXX executable TestErrors
    [100%] Built target TestExponents
    [100%] Built target TestErrors

    0

 %% Cell type:code id: tags:

 ``` python
 mpp.reset_data()
 mpp.clean_data()

 kwargs={"GeneratorPlotting": 1,
        "PDESolverPlotting": 1,
        "initLevels":        [4, 5, 6],
        "Problem": "StochasticLaplace2DTest"}

 mpp.run(4, config="mlmc_elliptic", kwargs=kwargs)
 ```

 %% Output

    
    ================ running  mpp ================
    
    start program on 4 procs at Tue Apr 27 13:38:15 2021
    Running on: niklas-ThinkPad-T470p
       Config Info:
         GeneratorVerbose: ......... 0
         NewtonVerbose: ............ 0
         PDESolverVerbose: ......... 0
         LinearVerbose: ............ 0
         MeshVerbose: .............. 1
         MainVerbose: .............. 1
         MCVerbose: ................ 1
         MLMCVerbose: .............. 1
         PDESolverPlotting: ........ 1
         GeneratorPlotting: ........ 1
         lambda: ................... [0.15, 0.15]
         Model: .................... LagrangeElliptic
         AssembleVerbose: .......... 0
         degree: ................... 1
         MCParallel: ............... false
         maxLevel: ................. 7
         Problem: .................. StochasticLaplace2DTest
         StochasticField: .......... LogNormal
         epsilon: .................. 0.01
         ConfigVerbose: ............ 1
         onlyFine: ................. false
         Mean: ..................... 0.0
         initLevels: ............... [4, 5, 6]
         smoothing: ................ 1.0
         Quantity: ................. L2
         initSampleAmount: ......... [12, 6, 3]
         sigma: .................... 1.0
    
       MLMC Experiment: Run
         MLMC Method: eps=0.010000
           MonteCarlo l=4: Start with: M=0 dM=12 Mcomm=0 dMcomm=12
           MonteCarlo l=4: MeanQ=0 MeanY=0 SVarQ=0 SVarY=0
           MonteCarlo l=4: End with: M=12 dM=12 Mcomm=0 dMcomm=0
           MonteCarlo l=4: MeanQ=0.57815467 MeanY=0.57815467 SVarQ=1.6015669e-05 SVarY=1.6015669e-05
           MonteCarlo l=4: Took 0.27 seconds
           MonteCarlo l=5: Start with: M=0 dM=6 Mcomm=0 dMcomm=6
           MonteCarlo l=5: MeanQ=0 MeanY=0 SVarQ=0 SVarY=0
           MonteCarlo l=5: End with: M=6 dM=6 Mcomm=0 dMcomm=0
           MonteCarlo l=5: MeanQ=0.57956002 MeanY=0.0027737227 SVarQ=1.3311143e-05 SVarY=4.9078869e-05
           MonteCarlo l=5: Took 0.75 seconds
           MonteCarlo l=6: Start with: M=0 dM=3 Mcomm=0 dMcomm=3
           MonteCarlo l=6: MeanQ=0 MeanY=0 SVarQ=0 SVarY=0
           MonteCarlo l=6: End with: M=3 dM=3 Mcomm=0 dMcomm=0
           MonteCarlo l=6: MeanQ=0.58015262 MeanY=0.0026051525 SVarQ=1.1962813e-05 SVarY=6.3081821e-05
           MonteCarlo l=6: Took 1.41 seconds
         MLMC Method: alpha=0.090455732 beta=-0.36212231 gamma=1.9138626
         MLMC Method: dM=[-8, -2, 0]
         MLMC Method: numErr=0.040261089
           MonteCarlo l=5: Start with: M=6 dM=3 Mcomm=0 dMcomm=3
           MonteCarlo l=5: MeanQ=0.57956002 MeanY=0.0027737227 SVarQ=1.3311143e-05 SVarY=4.9078869e-05
           MonteCarlo l=5: End with: M=9 dM=3 Mcomm=0 dMcomm=0
           MonteCarlo l=5: MeanQ=0.58005915 MeanY=0.0012960378 SVarQ=1.1520124e-05 SVarY=4.865392e-05
           MonteCarlo l=5: Took 0.36 seconds
           MonteCarlo l=6: Start with: M=3 dM=2 Mcomm=0 dMcomm=2
           MonteCarlo l=6: MeanQ=0.58015262 MeanY=0.0026051525 SVarQ=1.1962813e-05 SVarY=6.3081821e-05
           MonteCarlo l=6: End with: M=5 dM=2 Mcomm=0 dMcomm=0
           MonteCarlo l=6: MeanQ=0.57881206 MeanY=0.0016184985 SVarQ=1.2600565e-05 SVarY=5.2065491e-05
           MonteCarlo l=6: Took 0.95 seconds
           MonteCarlo l=7: Start with: M=0 dM=3 Mcomm=0 dMcomm=3
           MonteCarlo l=7: MeanQ=0 MeanY=0 SVarQ=0 SVarY=0
           MonteCarlo l=7: End with: M=3 dM=3 Mcomm=0 dMcomm=0
           MonteCarlo l=7: MeanQ=0.58015614 MeanY=0.0025882243 SVarQ=1.1985695e-05 SVarY=6.3513427e-05
           MonteCarlo l=7: Took 5.91 seconds
         MLMC Method: alpha=-0.49892745 beta=-0.19225278 gamma=1.934905
         MLMC Method: dM=[-3, -1, -1, 0]
         MLMC Method: numErr=0
         MLMC Method: statErr=0.0061907084
         MLMC Method:  9.81 seconds
       MLMC Experiment:  9.81 seconds
    
       MC Results Info:
         E(Qf-Qc): ................. [0.578155, 0.00129604, 0.0016185, 0.00258822]
         E(Qf): .................... [0.578155, 0.580059, 0.578812, 0.580156]
         V(Qf-Qc): ................. [1.60157e-05, 4.86539e-05, 5.20655e-05, 6.35134e-05]
         V(Qf): .................... [1.60157e-05, 1.15201e-05, 1.26006e-05, 1.19857e-05]
         kurtosis: ................. [1.742, 1.39489, 1.53131, 1.5]
         E(cost): .................. [81, 289, 1089, 4225]
         Used Levels: .............. [4, 5, 6, 7]
         Used Samples: ............. [12, 9, 5, 3]
    
       Exponents Info:
         Final alpha: .............. -0.49892745
         Final beta: ............... -0.19225278
         Final gamma: .............. 1.934905
    
       MLMC Results Info:
         Value: .................... 1.7508484
         Cost: ..................... 12827
         Epsilon: .................. 0.01
         Total Error: .............. 0.0061907084
         Statistical Error: ........ 0.0061907084
         Numerical Error: .......... 0
    
    end program after  9.91 seconds on 4 procs at Tue Apr 27 13:38:25 2021

    0

 %% Cell type:code id: tags:

 ``` python
 from mpp.python.mppy.utilities import VtkPlot
 from ipywidgets import interact, interactive, fixed, interact_manual
 import ipywidgets as widgets

 @interact(n=widgets.IntSlider(min=0, max=5, step=1, value=0))
 def plot_nth_frame(n):
    p = VtkPlot(figsize=(16, 12))
    plt.axis('off')
    gs = gridspec.GridSpec(2, 2)
    p.ax1 = p.fig.add_subplot(gs[0])
    #p.add_vtu("Kappa.5.0.{}.vtu".format(n), ax=p.ax1)
    p.add_quivers("Flux.5.0.{}.vtu".format(n), ax=p.ax1)
    p.ax2 = p.fig.add_subplot(gs[1])
    #p.add_vtu("Kappa.5.1.{}.vtu".format(n), ax=p.ax2)
    p.add_quivers("Flux.5.1.{}.vtu".format(n), ax=p.ax2)
    p.ax3 = p.fig.add_subplot(gs[2])
    p.add_vtu("Pressure.5.0.{}.vtu".format(n), ax=p.ax3)
    p.ax4 = p.fig.add_subplot(gs[3])
    p.add_vtu("Pressure.5.1.{}.vtu".format(n), ax=p.ax4)
 ```

 %% Output


 %% Cell type:code id: tags:

 ``` python
 from mpp.python.mppy.utilities import VtkPlot
 from ipywidgets import interact, interactive, fixed, interact_manual
 import ipywidgets as widgets

 @interact(n=widgets.IntSlider(min=0, max=2, step=1, value=0))
 def plot_nth_frame(n):
    p = VtkPlot(figsize=(16, 12))
    plt.axis('off')
    gs = gridspec.GridSpec(2, 2)
    p.ax1 = p.fig.add_subplot(gs[0])
    #p.add_vtu("Kappa.6.0.{}.vtu".format(n), ax=p.ax1)
    p.add_quivers("Flux.6.0.{}.vtu".format(n), ax=p.ax1)
    p.ax2 = p.fig.add_subplot(gs[1])
    #p.add_vtu("Kappa.6.1.{}.vtu".format(n), ax=p.ax2)
    p.add_quivers("Flux.6.1.{}.vtu".format(n), ax=p.ax2)
    p.ax3 = p.fig.add_subplot(gs[2])
    p.add_vtu("Pressure.6.0.{}.vtu".format(n), ax=p.ax3)
    p.ax4 = p.fig.add_subplot(gs[3])
    p.add_vtu("Pressure.6.1.{}.vtu".format(n), ax=p.ax4)
 ```

 %% Output


+%% Cell type:markdown id: tags:
+
+## Convergence tests
+
 %% Cell type:code id: tags:

 ``` python
+test_case = True
+if test_case:
+    mpp.kernels = 4
+    mpp.mute = False
+    kwargs = {"epsilon":          0.0,
+              "initLevels":       [3, 4, 5, 6, 7],
+              "initSampleAmount": [100, 100, 100, 100, 100],
+              "Problem": "StochasticLaplace2DTest"}
+    epsilons = [0.1, 0.03, 0.01, 0.003]
+else:
+    mpp.kernels = 32
+    mpp.mute = True
+    kwargs = {"epsilon":          0.0,
+              "initLevels":       [3, 4, 5, 6, 7, 8, 9],
+              "initSampleAmount": [500, 500, 500, 500, 500, 500, 500],
+              "Problem": "StochasticLaplace2DTest"}
+    epsilons = [0.1, 0.03, 0.01, 0.003, 0.001, 0.0003]
+```
+
+%% Cell type:code id: tags:
+
+``` python
+mpp.clean_data()
+mpp.reset_data()
+
+mpp.run(config="mlmc_elliptic", kwargs=kwargs)
+mpp.parse_log()
+
+convergence_plot(mpp)
 ```