Link to the source code for this example:
Open optimization_ex1 in new tab.The console output of the program:
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* Running Example optimization_ex1:
* example-opt -tao_monitor -tao_view -tao_type nls
***************************************************************
Mesh Information:
elem_dimensions()={2}
spatial_dimension()=2
n_nodes()=441
n_local_nodes()=441
n_elem()=100
n_local_elem()=100
n_active_elem()=100
n_subdomains()=1
n_partitions()=1
n_processors()=1
n_threads()=1
processor_id()=0
EquationSystems
n_systems()=1
System #0, "Optimization"
Type "Optimization"
Variables="u"
Finite Element Types="LAGRANGE", "JACOBI_20_00"
Infinite Element Mapping="CARTESIAN"
Approximation Orders="SECOND", "THIRD"
n_dofs()=441
n_local_dofs()=441
n_constrained_dofs()=80
n_local_constrained_dofs()=80
n_vectors()=4
n_matrices()=2
DofMap Sparsity
Average On-Processor Bandwidth <= 14.8776
Average Off-Processor Bandwidth <= 0
Maximum On-Processor Bandwidth <= 25
Maximum Off-Processor Bandwidth <= 0
DofMap Constraints
Number of DoF Constraints = 80
Average DoF Constraint Length= 0
iter = 0, Function value: 0, Residual: 0.217778
iter = 1, Function value: -0.281146, Residual: 1.41941e-06
Tao Object: 1 MPI processes
type: nls
Rejected matrix updates: 0
Newton steps: 1
BFGS steps: 0
Scaled gradient steps: 0
Gradient steps: 0
nls ksp atol: 0
nls ksp rtol: 1
nls ksp ctol: 0
nls ksp negc: 0
nls ksp dtol: 0
nls ksp iter: 0
nls ksp othr: 0
TaoLineSearch Object: 1 MPI processes
type: more-thuente
KSP Object: 1 MPI processes
type: stcg
total KSP iterations: 28
convergence tolerances: fatol=1e-10, frtol=1e-10
convergence tolerances: gatol=1e-08, steptol=0, gttol=0
Residual in Function/Gradient:=1.41941e-06
Objective value=-0.281146
total number of iterations=1, (max: 50)
total number of function evaluations=7, max: 128
total number of gradient evaluations=2, max: 128
total number of Hessian evaluations=1
Solution converged: estimated f(x)-f(X*) <= fatol
Tao optimization solver convergence/divergence reason: CONVERGED_FATOL
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| Time: Wed Apr 13 09:41:07 2016 |
| OS: Darwin |
| HostName: peterson-laptop.local |
| OS Release: 15.0.0 |
| OS Version: Darwin Kernel Version 15.0.0: Sat Sep 19 15:53:46 PDT 2015; root:xnu-3247.10.11~1/RELEASE_X86_64 |
| Machine: x86_64 |
| Username: petejw |
| Configuration: ../configure 'INSTALL=/usr/bin/install -C' |
| '--with-methods=opt dbg' |
| '--prefix=/Users/petejw/projects/libmesh_git/installed' |
| '--enable-perflog' |
| '--enable-tracefiles' |
| '--disable-blocked-storage' |
| '--enable-default-comm-world' |
| '--enable-tecio' |
| '--enable-unique-ptr' |
| '--enable-ifem' |
| 'PETSC_DIR=/opt/moose/petsc/mpich_petsc-3.6.1/clang-opt-superlu' |
| 'SLEPC_DIR=/opt/petejw/slepc/3.6.1' |
| 'CPPFLAGS= ' |
| 'LIBS= ' |
| 'CPPFLAGS= ' |
| 'LIBS= ' |
| '--disable-netcdf-4' |
| '--disable-testsets' |
| 'CXX=mpicxx' |
| 'CC=mpicc' |
| 'F77=mpif77' |
| 'FC=mpif90' |
| 'CPPFLAGS= ' |
| 'LIBS= ' |
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| libMesh Performance: Alive time=0.236581, Active time=0.01159 |
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| Event nCalls Total Time Avg Time Total Time Avg Time % of Active Time |
| w/o Sub w/o Sub With Sub With Sub w/o S With S |
|-----------------------------------------------------------------------------------------------------------------|
| |
| |
| DofMap |
| add_neighbors_to_send_list() 1 0.0000 0.000048 0.0000 0.000048 0.41 0.41 |
| build_constraint_matrix() 100 0.0001 0.000001 0.0001 0.000001 0.74 0.74 |
| build_sparsity() 1 0.0004 0.000395 0.0004 0.000435 3.41 3.75 |
| cnstrn_elem_mat_vec() 100 0.0001 0.000001 0.0001 0.000001 0.93 0.93 |
| create_dof_constraints() 1 0.0005 0.000500 0.0010 0.001025 4.31 8.84 |
| distribute_dofs() 1 0.0001 0.000083 0.0004 0.000434 0.72 3.74 |
| dof_indices() 400 0.0001 0.000000 0.0001 0.000000 1.26 1.26 |
| enforce_constraints_exactly() 10 0.0004 0.000037 0.0004 0.000037 3.16 3.16 |
| prepare_send_list() 2 0.0000 0.000000 0.0000 0.000000 0.00 0.00 |
| reinit() 1 0.0004 0.000351 0.0004 0.000351 3.03 3.03 |
| |
| EquationSystems |
| build_solution_vector() 1 0.0002 0.000233 0.0003 0.000283 2.01 2.44 |
| |
| ExodusII_IO |
| write_nodal_data() 1 0.0014 0.001368 0.0014 0.001368 11.80 11.80 |
| |
| FE |
| compute_shape_functions() 140 0.0003 0.000002 0.0003 0.000002 2.72 2.72 |
| init_shape_functions() 41 0.0000 0.000001 0.0000 0.000001 0.19 0.19 |
| inverse_map() 120 0.0001 0.000001 0.0001 0.000001 1.03 1.03 |
| |
| FEMap |
| compute_affine_map() 140 0.0001 0.000001 0.0001 0.000001 1.13 1.13 |
| compute_face_map() 40 0.0001 0.000002 0.0002 0.000005 0.72 1.86 |
| init_face_shape_functions() 40 0.0000 0.000001 0.0000 0.000001 0.19 0.19 |
| init_reference_to_physical_map() 41 0.0002 0.000004 0.0002 0.000004 1.33 1.33 |
| |
| Mesh |
| find_neighbors() 1 0.0003 0.000258 0.0003 0.000258 2.23 2.23 |
| renumber_nodes_and_elem() 2 0.0000 0.000005 0.0000 0.000005 0.09 0.09 |
| |
| MeshOutput |
| write_equation_systems() 1 0.0000 0.000018 0.0017 0.001669 0.16 14.40 |
| |
| MeshTools::Generation |
| build_cube() 1 0.0001 0.000131 0.0001 0.000131 1.13 1.13 |
| |
| OptimizationSystem |
| solve() 1 0.0022 0.002184 0.0070 0.007001 18.84 60.41 |
| |
| Parallel |
| allgather() 1 0.0000 0.000000 0.0000 0.000000 0.00 0.00 |
| |
| Partitioner |
| single_partition() 1 0.0000 0.000012 0.0000 0.000012 0.10 0.10 |
| |
| TaoOptimizationSolver |
| gradient() 2 0.0001 0.000040 0.0001 0.000070 0.69 1.21 |
| hessian() 1 0.0003 0.000297 0.0003 0.000328 2.56 2.83 |
| objective() 7 0.0004 0.000056 0.0007 0.000096 3.40 5.81 |
| solve() 1 0.0037 0.003674 0.0048 0.004817 31.70 41.56 |
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| Totals: 1200 0.0116 100.00 |
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***************************************************************
* Done Running Example optimization_ex1:
* example-opt -tao_monitor -tao_view -tao_type nls
***************************************************************