Added solvers for one-dimensional root finding
This commit is contained in:
J.A. de Jong @ vulgaris
parent
a13fa4c5ad
commit
4fd249ec52
@ -69,7 +69,7 @@ set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -O2 -march=native -mtune=native")
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# For importing find directives for Cmake
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set(CMAKE_MODULE_PATH ${CMAKE_MODULE_PATH} ${PROJECT_SOURCE_DIR}/common/cmake_tools)
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set(CMAKE_MODULE_PATH ${CMAKE_MODULE_PATH} ${PROJECT_SOURCE_DIR}/cmake_tools)
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# ##########################
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# Python #####################
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@ -91,20 +91,6 @@ MESSAGE("Python major version: ${TaSMET_PY_MAJOR_VERSION}")
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# Find the site_packages directory of python
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execute_process(COMMAND python${TaSMET_PY_MAJOR_VERSION} -c "from distutils.sysconfig import get_python_lib; print(get_python_lib())" OUTPUT_VARIABLE PYTHON_SITE_PACKAGES OUTPUT_STRIP_TRAILING_WHITESPACE)
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# ################################
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# Initialize swig
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# ################################
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find_package(SWIG REQUIRED)
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include(${SWIG_USE_FILE})
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SET(CMAKE_SWIG_FLAGS -Wall -DSWIG_PYTHON)
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if(${TaSMET_PY_MAJOR_VERSION}=="3")
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SET(CMAKE_SWIG_FLAGS ${CMAKE_SWIG_FLAGS} -py${TaSMET_PY_MAJOR_VERSION})
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endif(${TaSMET_PY_MAJOR_VERSION}=="3")
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include_directories(common/src)
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# Armadillo
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find_package(Armadillo REQUIRED)
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add_definitions(-DARMA_USE_SUPERLU -DARMA_USE_CXX11)
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@ -114,26 +100,13 @@ add_definitions(-DARMA_USE_SUPERLU -DARMA_USE_CXX11)
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# This is the common code (gas and solid libs, etc)
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# link_directories(common)
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aux_source_directory(common/src/gas gas)
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include_directories(
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${PYTHON_INCLUDE_DIRS}
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common/src/swig
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common/src/gas
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src
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src/solver
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src/material
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)
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# Add the code subdirectory
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add_subdirectory(src)
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add_subdirectory(testing)
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# set_source_files_properties( ${swig_generated_file_fullname}
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# PROPERTIES COMPILE_FLAGS "${SWIG_COMMON_COMPILE_FLAGS} ")
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# ================================== Installation
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# Install common files
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install(FILES ${PROJECT_SOURCE_DIR}/common/__init__.py
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DESTINATION ${PYTHON_SITE_PACKAGES}/${PROJECT_NAME}/common)
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install(FILES ${PROJECT_SOURCE_DIR}/common/common.py
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DESTINATION ${PYTHON_SITE_PACKAGES}/${PROJECT_NAME}/common)
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# Rest of the files is installed from src/CMakeLists.txt
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130
doc/usg.lyx
130
doc/usg.lyx
@ -1881,6 +1881,7 @@ Create a PhaseConstraint object:
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\end_layout
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\begin_layout Verbatim
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pc=PhaseConstraint(Varnr, freqnr, left)
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\end_layout
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@ -1889,6 +1890,7 @@ Apply this contraint to a segment which can accept them, for example a Tube:
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\end_layout
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\begin_layout Verbatim
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t1.setPhaseConstraint(pc)
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\end_layout
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@ -3768,10 +3770,54 @@ Momentum equation (prescribes pressure
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\end_layout
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\begin_layout Standard
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And
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And the boundary condition for the temperature is computed assuming adiabatic
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compression-expansion.
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Currently, this is implemented for thermally perfect gases only:
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\end_layout
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\begin_layout Standard
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\begin_inset Formula
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\begin{equation}
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T_{p}=T_{0}\left(\frac{p_{0}+p_{p}}{p_{0}}\right)^{\frac{\gamma_{0}-1}{\gamma_{0}}}
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c_{p}\left(T\right)\mathrm{d}T=\frac{\mathrm{d}p}{\rho}
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\end{equation}
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\end_inset
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FIlling in the perfect gas law and a bit of bookkeeping results in
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\end_layout
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\begin_layout Standard
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\begin_inset Formula
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\begin{equation}
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\frac{1}{R_{s}}\int\limits _{T_{0}}^{T_{p}}\frac{c_{p}\left(T\right)}{T}\mathrm{d}T-\ln\left(\frac{p_{p}-p_{0}}{p_{0}}\right)=0
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\end{equation}
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\end_inset
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Note that in general, to solve this equation for the temperature requires
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a numerical integration, however for the currently implemented gases,
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\begin_inset Formula $c_{p}$
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\end_inset
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is a polynomial function of
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\begin_inset Formula $T$
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\end_inset
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:
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\begin_inset Formula
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\begin{equation}
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c_{p}(T)=\sum_{i=0}^{N_{c_{p}}}c_{p,i}T^{i}
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\end{equation}
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\end_inset
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In that case
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\end_layout
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\begin_layout Standard
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\begin_inset Formula
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\begin{equation}
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\frac{1}{R_{s}}\left(c_{p,0}\ln\left(\frac{T_{p}}{T_{0}}\right)+\sum_{i=1}^{N_{c_{p}}}\frac{c_{p,i}\left(T_{p}-T_{0}\right)^{i}}{i}\right)-\ln\left(\frac{p_{p}-p_{0}}{p_{0}}\right)=0.\label{eq:T-p-adiabatic}
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\end{equation}
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\end_inset
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@ -3779,6 +3825,47 @@ T_{p}=T_{0}\left(\frac{p_{0}+p_{p}}{p_{0}}\right)^{\frac{\gamma_{0}-1}{\gamma_{0
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\end_layout
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\begin_layout Standard
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Equation
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\begin_inset CommandInset ref
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LatexCommand ref
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reference "eq:T-p-adiabatic"
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\end_inset
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is solved using a one-dimensional root finding algorithm (see Section
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\begin_inset CommandInset ref
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LatexCommand ref
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reference "sec:One-dimensional-function-solvers"
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\end_inset
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).
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Note that for an ideal gas an explicit formula is available:
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\end_layout
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\begin_layout Standard
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\begin_inset Formula
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\begin{equation}
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T_{p,\mathrm{ideal}}=T_{0}\left(\frac{p_{0}+p_{p}}{p_{0}}\right)^{\frac{\gamma_{0}-1}{\gamma_{0}}}.\label{eq:ideal-gas-isentropic-p-T}
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\end{equation}
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\end_inset
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Looking closely at Equation
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\begin_inset CommandInset ref
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LatexCommand ref
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reference "eq:ideal-gas-isentropic-p-T"
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\end_inset
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, we find that
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\begin_inset Formula $T_{p,\mathrm{ideal}}$
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\end_inset
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provides a good guess for the final solution.
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\end_layout
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\begin_layout Subsection
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AdiabaticWall
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\end_layout
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@ -5044,8 +5131,45 @@ Minor loss
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Systems
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\end_layout
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\begin_layout Section
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\begin_layout Chapter
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Solvers
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\end_layout
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\begin_layout Section
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One-dimensional function solvers
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\begin_inset CommandInset label
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LatexCommand label
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name "sec:One-dimensional-function-solvers"
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\end_inset
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\end_layout
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\begin_layout Subsection
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Gradient-based
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\end_layout
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\begin_layout Subsection
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Gradient free
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\begin_inset CommandInset label
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LatexCommand label
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name "subsec:Gradient-free"
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\end_inset
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\end_layout
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\begin_layout Standard
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As a gradient free one-dimensional function solver, we use Brent's mehhod.
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Brent's method combines root bracketing, bisection and inverse quadratic
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interpolation to find the root of the function without using the gradient.
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See Wikipedia for more information.
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\end_layout
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\begin_layout Section
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Minimizers
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\end_layout
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\end_body
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@ -18,7 +18,8 @@ include_directories(
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# python
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# seg
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# sol
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# sys
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sys
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solver
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# var
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# volume
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)
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@ -28,19 +29,25 @@ add_subdirectory(material)
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# add_subdirectory(duct)
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# add_subdirectory(mech)
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# add_subdirectory(seg)
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# add_subdirectory(sol)
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add_subdirectory(solver)
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add_subdirectory(sys)
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# add_subdirectory(var)
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add_library(tasmet_src tasmet_tracer.cpp tasmet_exception.cpp tasmet_assert.cpp)
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target_link_libraries(tasmet_src
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# duct
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# mech
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# seg
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# sol
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# sys
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# var
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add_library(tasmet_src_src
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tasmet_tracer.cpp
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tasmet_exception.cpp
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tasmet_assert.cpp
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)
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add_library(tasmet_src)
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target_link_libraries(tasmet_src
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funcs
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material
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solver
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sys
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# This one should be last as other parts link to these utilities
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tasmet_src_src
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)
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# set_source_files_properties(swig/nonlin.i
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# PROPERTIES CPLUSPLUS ON)
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@ -8,47 +8,24 @@
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#include "air.h"
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namespace {
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// Air-specific data
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d kappac[]={-0.00227583562,1.15480022E-4, \
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-7.90252856E-8,4.11702505E-11, \
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-7.43864331E-15};
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d cpc[]={1047.63657,-0.372589265, \
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9.45304214E-4,-6.02409443E-7, \
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1.2858961E-10};
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d muc[]={-8.38278E-7,8.35717342E-8, \
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-7.69429583E-11,4.6437266E-14, \
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-1.06585607E-17};
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} // namespace
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d Air::h(d T,d p) const {
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return cpc[0]*T+0.5*cpc[1]*pow(T,2)+(1/3.0)*cpc[2]*pow(T,3)+cpc[3]*0.25*pow(T,4)+cpc[4]*(0.2)*pow(T,5);
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}
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vd Air::h(const vd& T,const vd& p) const {
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return cpc[0]*T+0.5*cpc[1]*pow(T,2)+(1/3.0)*cpc[2]*pow(T,3)+cpc[3]*0.25*pow(T,4)+cpc[4]*(0.2)*pow(T,5);
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}
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vd Air::cp(const vd& T,const vd& p) const {
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return cpc[0]+cpc[1]*T+cpc[2]*pow(T,2)+cpc[3]*pow(T,3)+cpc[4]*pow(T,4);
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}
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d Air::cp(d T,d p) const {
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return cpc[0]+cpc[1]*T+cpc[2]*pow(T,2)+cpc[3]*pow(T,3)+cpc[4]*pow(T,4);
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}
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vd Air::kappa(const vd& T,const vd& p) const {
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return kappac[0]+kappac[1]*T+kappac[2]*pow(T,2)+kappac[3]*pow(T,3)+kappac[4]*pow(T,4);
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}
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d Air::kappa(d T,d p) const {
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return kappac[0]+kappac[1]*T+kappac[2]*pow(T,2)+kappac[3]*pow(T,3)+kappac[4]*pow(T,4);
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}
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vd Air::mu(const vd& T,const vd& p) const {
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return muc[1]*T+muc[2]*pow(T,2)+muc[3]*pow(T,3)+muc[4]*pow(T,4)+muc[0];
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us nfac = _kappac.size();
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vd powfac(nfac);
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for(us i=0;i<nfac;i++)
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powfac(i) = pow(T,i);
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return dot(_kappac,powfac);
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}
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d Air::mu(d T,d p) const {
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return muc[1]*T+muc[2]*pow(T,2)+muc[3]*pow(T,3)+muc[4]*pow(T,4)+muc[0];
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us nfac = _muc.size();
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vd powfac(nfac);
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for(us i=0;i<nfac;i++)
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powfac(i) = pow(T,i);
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return dot(_muc,powfac);
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}
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//////////////////////////////////////////////////////////////////////
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@ -12,18 +12,26 @@
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class Air : public PerfectGas {
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vdi<5> _cpc = {1047.63657,-0.372589265, \
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9.45304214E-4,-6.02409443E-7, \
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1.2858961E-10};
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vdi<5> _kappac = {-0.00227583562,1.15480022E-4, \
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-7.90252856E-8,4.11702505E-11, \
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-7.43864331E-15};
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vdi<5> _muc = {-8.38278E-7,8.35717342E-8, \
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-7.69429583E-11,4.6437266E-14, \
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-1.06585607E-17};
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protected:
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d Rs() const {return 287;}
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public:
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Air(d T0,d p0):PerfectGas(air,T0,p0){}
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const vd& cpc() const {return _cpc;}
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d cp(d T,d p) const;
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vd cp(const vd& T,const vd& p) const;
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d h(d T,d p) const;
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vd h(const vd& T,const vd& p) const;
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d mu(d T,d p) const;
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vd mu(const vd& T,const vd& p) const;
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d kappa(d T,d p) const;
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vd kappa(const vd& T,const vd& p) const;
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~Air(){}
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};
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@ -14,6 +14,11 @@
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#include "tasmet_types.h"
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#include "tasmet_constants.h"
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#define element_wise(varname) \
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vd varname_(T.size()); \
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for(us i=0;i<T.size();i++) \
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varname_ = varname(T(i),p(i));\
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return varname_
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class Gas{
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public:
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@ -50,7 +55,9 @@ public:
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// Specific heat ratio
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d gamma(d T,d p) const {return cp(T,p)/cv(T,p);}
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vd gamma(const vd& T,const vd& p) const {return cp(T,p)/cv(T,p);}
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vd gamma(const vd& T,const vd& p) const {
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element_wise(gamma);
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}
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// Prandtl number
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vd pr(const vd& T,const vd& p) const {return mu(T,p)%cp(T,p)/kappa(T,p);}
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@ -59,49 +66,55 @@ public:
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// Virtuals that are part of the interface
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// Density [kg/m^3]
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virtual d rho(d T,d p) const=0;
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virtual vd rho(const vd& T,const vd& p) const=0;
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vd rho(const vd& T,const vd& p) const {
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element_wise(rho);
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}
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// Adiabatic speed of sound
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virtual d cm(d T,d p) const=0;
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virtual vd cm(const vd& T,const vd& p) const=0;
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vd cm(const vd& T,const vd& p) const {
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element_wise(cm);
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}
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// Internal energy [J/kg]
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virtual d e(d T,d p) const=0;
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virtual vd e(const vd& T,const vd& p) const=0;
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vd e(const vd& T,const vd& p) const {
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element_wise(e);
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}
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// Static enthalpy [J/kg]
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virtual d h(d T,d p) const=0;
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virtual vd h(const vd& T,const vd& p) const=0;
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vd h(const vd& T,const vd& p) const {
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element_wise(h);
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}
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// Specific heat at constant pressure
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virtual d cp(d T,d p) const=0;
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virtual vd cp(const vd& T,const vd& p) const=0;
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vd cp(const vd& T,const vd& p) const {
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element_wise(cp);
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}
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// Specific heat at constant density
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virtual d cv(d T,d p) const=0;
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virtual vd cv(const vd& T,const vd& p) const=0;
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virtual d beta(d T,d p) const=0;
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virtual vd beta(const vd& T,const vd& p) const=0;
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vd cv(const vd& T,const vd& p) const {
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element_wise(cv);
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}
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// Dynamic viscosity [Pa*s]
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virtual d mu(d T,d p) const=0;
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virtual vd mu(const vd& T,const vd& p) const=0;
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vd mu(const vd& T,const vd& p) const {
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element_wise(mu);
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}
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// Thermal conductivity [W/mK]
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virtual d kappa(d T,d p) const=0;
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virtual vd kappa(const vd& T,const vd& p) const=0;
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vd kappa(const vd& T,const vd& p) const {
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element_wise(kappa);
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}
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};
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#undef element_wise
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#endif // GAS_H
|
||||
|
||||
@ -9,25 +9,12 @@
|
||||
#include "helium.h"
|
||||
|
||||
|
||||
vd Helium::cp(const vd& T,const vd& p) const {
|
||||
return cp(0.0,0.0)*arma::ones(T.size());
|
||||
}
|
||||
vd Helium::h(const vd& T,const vd& p) const {
|
||||
return cp(T,p)%T;
|
||||
}
|
||||
d Helium::mu(d T,d p) const {
|
||||
return 0.412e-6*pow(T,0.68014);
|
||||
}
|
||||
d Helium::kappa(d T,d p) const {
|
||||
return 0.0025672*pow(T,0.716);
|
||||
}
|
||||
vd Helium::mu(const vd& T,const vd& p) const {
|
||||
return 0.412e-6*pow(T,0.68014);
|
||||
}
|
||||
vd Helium::kappa(const vd& T,const vd& p) const {
|
||||
return 0.0025672*pow(T,0.716);
|
||||
}
|
||||
|
||||
|
||||
|
||||
//////////////////////////////////////////////////////////////////////
|
||||
|
||||
@ -11,22 +11,18 @@
|
||||
#include "perfectgas.h"
|
||||
|
||||
class Helium :public PerfectGas {
|
||||
vdi<1> _cpc = {5195};
|
||||
protected:
|
||||
d Rs() const {return 2070;}
|
||||
public:
|
||||
Helium(d T0,d p0):PerfectGas(helium,T0,p0){}
|
||||
|
||||
d cp(d T,d p) const { return 5195;}
|
||||
vd cp(const vd& T,const vd& p) const;
|
||||
|
||||
d h(d T,d p) const {return cp(0.0,0.0)*T;}
|
||||
vd h(const vd& T,const vd& p) const;
|
||||
const vd& cpc() const { return _cpc; }
|
||||
d cp(d T,d p) const { return _cpc(0);}
|
||||
|
||||
d mu(d T,d p) const;
|
||||
vd mu(const vd& T,const vd& p) const;
|
||||
|
||||
d kappa(d T,d p) const;
|
||||
vd kappa(const vd& T,const vd& p) const;
|
||||
|
||||
virtual ~Helium(){}
|
||||
};
|
||||
|
||||
@ -8,42 +8,13 @@
|
||||
|
||||
#include "nitrogen.h"
|
||||
|
||||
namespace {
|
||||
// Nitrogen-specific data
|
||||
d cpc[]={3.29868,0.00140824, \
|
||||
-3.96322e-6,5.64152e-9, \
|
||||
-2.44486e-12};
|
||||
|
||||
d kappavals[]={6.995e-3,0.0631e-3};
|
||||
} // namespace
|
||||
|
||||
d Nitrogen::h(d T,d p) const {
|
||||
return Rs()*(cpc[0]*T+0.5*cpc[1]*pow(T,2)+(1/3.0)*cpc[2]*pow(T,3)+cpc[3]*0.25*pow(T,4)+cpc[4]*(0.2)*pow(T,5));
|
||||
}
|
||||
vd Nitrogen::h(const vd& T,const vd& p) const {
|
||||
return Rs()*(cpc[0]*T+0.5*cpc[1]*pow(T,2)+(1/3.0)*cpc[2]*pow(T,3)+cpc[3]*0.25*pow(T,4)+cpc[4]*(0.2)*pow(T,5));
|
||||
}
|
||||
vd Nitrogen::cp(const vd& T,const vd& p) const {
|
||||
return Rs()*(cpc[0]+cpc[1]*T+cpc[2]*pow(T,2)+cpc[3]*pow(T,3)+cpc[4]*pow(T,4));
|
||||
}
|
||||
d Nitrogen::cp(d T,d p) const {
|
||||
return Rs()*(cpc[0]+cpc[1]*T+cpc[2]*pow(T,2)+cpc[3]*pow(T,3)+cpc[4]*pow(T,4));
|
||||
}
|
||||
// Document Mina
|
||||
vd Nitrogen::kappa(const vd& T,const vd& p) const {
|
||||
return kappavals[1]*T+kappavals[0];
|
||||
}
|
||||
d Nitrogen::kappa(d T,d p) const {
|
||||
return kappavals[1]*T+kappavals[0];
|
||||
}
|
||||
// http://www.lmnoeng.com/Flow/GasViscosity.php
|
||||
vd Nitrogen::mu(const vd& T,const vd& p) const {
|
||||
return (0.01781/1000)*(411.55/(T+111))%pow(T/300.55,1.5);
|
||||
return _kappac(1)*T+_kappac(0);
|
||||
}
|
||||
|
||||
d Nitrogen::mu(d T,d p) const {
|
||||
return (0.01781/1000)*(411.55/(T+111))*pow(T/300.55,1.5);
|
||||
}
|
||||
|
||||
|
||||
|
||||
//////////////////////////////////////////////////////////////////////
|
||||
|
||||
@ -13,20 +13,22 @@
|
||||
|
||||
|
||||
class Nitrogen : public PerfectGas {
|
||||
vdi<5> _cpc={3.29868,0.00140824,
|
||||
-3.96322e-6,
|
||||
5.64152e-9,
|
||||
-2.44486e-12};
|
||||
|
||||
vdi<2> _kappac={6.995e-3,0.0631e-3};
|
||||
|
||||
protected:
|
||||
d Rs() const {return 297;}
|
||||
public:
|
||||
Nitrogen(d T0,d p0):PerfectGas(nitrogen,T0,p0){}
|
||||
|
||||
d cp(d T,d p) const;
|
||||
vd cp(const vd& T,const vd& p) const;
|
||||
d h(d T,d p) const;
|
||||
vd h(const vd& T,const vd& p) const;
|
||||
const vd& cpc() const { return _cpc; }
|
||||
d mu(d T,d p) const;
|
||||
vd mu(const vd& T,const vd& p) const;
|
||||
d kappa(d T,d p) const;
|
||||
vd kappa(const vd& T,const vd& p) const;
|
||||
~Nitrogen(){}
|
||||
|
||||
};
|
||||
|
||||
|
||||
|
||||
@ -2,8 +2,11 @@
|
||||
//
|
||||
// Author: J.A. de Jong
|
||||
//
|
||||
// Description:
|
||||
//
|
||||
// Description: A thermally perfect gas obeys the ideal-gas law
|
||||
// equation of state (p=rho*R*T) but has TEMPERATURE-DEPENDENT and
|
||||
// PRESSURE-DEPENDENT specific heat constants. Our definition of a
|
||||
// perfect gas has only temperature-dependent specific heat, viscosity
|
||||
// and thermal conductivity values.
|
||||
//////////////////////////////////////////////////////////////////////
|
||||
#pragma once
|
||||
#ifndef PERFECTGAS_H
|
||||
@ -28,33 +31,33 @@ protected:
|
||||
// Not implemented for a perfect gas:
|
||||
// mu, kappa, h, cp, Rs
|
||||
|
||||
public:
|
||||
virtual d Rs() const=0;
|
||||
|
||||
public:
|
||||
// Vector of polynomial coefficients to compute the
|
||||
// specific heat at constant pressure
|
||||
virtual const vd& cpc() const=0;
|
||||
|
||||
~PerfectGas(){}
|
||||
|
||||
vd rho(const vd&T,const vd&p) const {
|
||||
checkzero(T);
|
||||
return p/Rs()/T;
|
||||
d h(d T,d p) const {
|
||||
const vd& cpc_ = this->cpc();
|
||||
us nfac = cpc_.size();
|
||||
vd powfac(nfac);
|
||||
|
||||
for(us i=0;i<nfac;i++)
|
||||
powfac(i) = pow(T,i)/(1+i);
|
||||
|
||||
return dot(cpc_,powfac);
|
||||
}
|
||||
vd p(const vd& T,const vd& rho) const {
|
||||
return rho%(Rs()*T);
|
||||
}
|
||||
vd cv(const vd& T,const vd& p) const {
|
||||
return cp(T,p)-Rs();
|
||||
}
|
||||
vd e(const vd& T,const vd& p) const {
|
||||
return h(T,p)-Rs()*T;
|
||||
}
|
||||
d beta(d T,d p) const {
|
||||
checkzero(T);
|
||||
return 1/T;
|
||||
}
|
||||
vd beta(const vd& T,const vd& p) const {
|
||||
return 1/T;
|
||||
}
|
||||
vd cm(const vd& T,const vd& p) const {
|
||||
return sqrt(gamma(T,p)*Rs()%T);
|
||||
d cp(d T,d p) const {
|
||||
const vd& cpc_ = this->cpc();
|
||||
us nfac = cpc_.size();
|
||||
vd powfac(nfac);
|
||||
|
||||
for(us i=0;i<nfac;i++)
|
||||
powfac(i) = pow(T,i);
|
||||
return dot(cpc_,powfac);
|
||||
}
|
||||
d rho(d T,d p) const {
|
||||
checkzero(T);
|
||||
@ -73,6 +76,7 @@ public:
|
||||
|
||||
};
|
||||
|
||||
|
||||
#endif // PERFECTGAS_H
|
||||
//////////////////////////////////////////////////////////////////////
|
||||
|
||||
|
||||
7
src/solver/CMakeLists.txt
Normal file
7
src/solver/CMakeLists.txt
Normal file
@ -0,0 +1,7 @@
|
||||
include_directories(${PROJECT_SOURCE_DIR}/src/solver)
|
||||
add_library(solver
|
||||
solver.cpp
|
||||
system.cpp
|
||||
newton_raphson.cpp
|
||||
brent.cpp
|
||||
)
|
||||
91
src/solver/bracket_root.h
Normal file
91
src/solver/bracket_root.h
Normal file
@ -0,0 +1,91 @@
|
||||
// bracket_lin.h
|
||||
//
|
||||
// Author: J.A. de Jong
|
||||
//
|
||||
// Description: Bracket a function's root given a guess value, returns
|
||||
// another guess where the solution has the opposite sign
|
||||
//////////////////////////////////////////////////////////////////////
|
||||
#pragma once
|
||||
#ifndef BRACKET_LIN_H
|
||||
#define BRACKET_LIN_H
|
||||
#include "system.h"
|
||||
#include "tasmet_tracer.h"
|
||||
#include <limits>
|
||||
|
||||
inline int sign(d& x){
|
||||
return x < 0? -1: 1;
|
||||
}
|
||||
const us maxiter = 100;
|
||||
|
||||
inline std::pair<d,d> bracket_root(NoGradientNonlinearSystem<d>& sys,const d guess) {
|
||||
|
||||
TRACE(10,"bracket_root()");
|
||||
|
||||
d xa = guess;
|
||||
d fa = sys.residual(xa);
|
||||
|
||||
d fb = fa;
|
||||
// We add here a small amount, such that, in case the first guess
|
||||
// is 0, we
|
||||
d xb = xa+std::numeric_limits<d>::epsilon();
|
||||
|
||||
d factor = 1.001;
|
||||
d delta = xa/10 + std::numeric_limits<d>::epsilon();
|
||||
|
||||
us iter = 0;
|
||||
|
||||
int step = 64;
|
||||
|
||||
bool switched = false;
|
||||
|
||||
while (iter < maxiter) {
|
||||
|
||||
VARTRACE(5,xb);
|
||||
|
||||
xb += delta*factor;
|
||||
|
||||
fb = sys.residual(xb);
|
||||
|
||||
if(sign(fa) != sign(fb)) {
|
||||
// Found it!
|
||||
VARTRACE(5,xa);
|
||||
VARTRACE(5,xb);
|
||||
VARTRACE(5,fa);
|
||||
VARTRACE(5,fb);
|
||||
return std::make_pair(xa,xb);
|
||||
}
|
||||
|
||||
if (abs(fb) < abs(fa)){
|
||||
// We found a point which is closer to the real root
|
||||
xa = xb;
|
||||
fa = fb;
|
||||
}
|
||||
else if(!switched) {
|
||||
TRACE(5,"Switching search direction");
|
||||
switched = true;
|
||||
// We searched in the wrong direction
|
||||
factor*=-1;
|
||||
}
|
||||
|
||||
// Heuristic: normally it's best not to increase the step sizes as we'll just end up
|
||||
// with a really wide range to search for the root. However, if the initial guess was *really*
|
||||
// bad then we need to speed up the search otherwise we'll take forever if we're orders of
|
||||
// magnitude out. This happens most often if the guess is a small value (say 1) and the result
|
||||
// we're looking for is close to std::numeric_limits<T>::min().
|
||||
//
|
||||
|
||||
if((10000 - iter) % step == 0) {
|
||||
factor *=2;
|
||||
if(step > 1) step/=2;
|
||||
}
|
||||
|
||||
iter++;
|
||||
}
|
||||
|
||||
WARN("Failed to bracket root");
|
||||
|
||||
return std::make_pair(xa,xb);
|
||||
|
||||
}
|
||||
#endif // BRACKET_LIN_H
|
||||
//////////////////////////////////////////////////////////////////////
|
||||
173
src/solver/brent.cpp
Normal file
173
src/solver/brent.cpp
Normal file
@ -0,0 +1,173 @@
|
||||
// brent.cpp
|
||||
//
|
||||
// last-edit-by: J.A. de Jong
|
||||
//
|
||||
// Description:
|
||||
// Brent's root finding algorithm as implemented from Wikipedia:
|
||||
// https://en.wikipedia.org/wiki/Brent's_method
|
||||
//////////////////////////////////////////////////////////////////////
|
||||
|
||||
#include "brent.h"
|
||||
#include "tasmet_tracer.h"
|
||||
#include "tasmet_exception.h"
|
||||
#include <limits>
|
||||
#include "tasmet_constants.h"
|
||||
#include <algorithm> // std::swap
|
||||
#include "bracket_root.h"
|
||||
|
||||
const d eps = std::numeric_limits<d>::epsilon();
|
||||
|
||||
Brent::Brent(const NoGradientNonlinearSystem<d>& sys,us maxiter,d reltol):
|
||||
Solver(sys),
|
||||
_reltol(reltol),
|
||||
_maxiter(maxiter)
|
||||
{
|
||||
|
||||
TRACE(15,"Brent::Brent");
|
||||
#ifdef TASMET_DEBUG
|
||||
bool ok=true;
|
||||
ok&=(maxiter>0);
|
||||
ok&=(reltol >= eps);
|
||||
|
||||
if(!ok){
|
||||
throw TaSMETError("Brent: invalid arguments");
|
||||
}
|
||||
#endif
|
||||
}
|
||||
namespace {
|
||||
inline bool is_between(d x,d a,d b) {
|
||||
const d& mi = std::min(a,b);
|
||||
const d& ma = std::max(a,b);
|
||||
return ((mi <= x) && (x <=ma));
|
||||
}
|
||||
}
|
||||
|
||||
void Brent::start_implementation(NoGradientNonlinearSystem<d>& system,
|
||||
progress_callback* callback) {
|
||||
|
||||
TRACE(15,"Brent::start_implementation");
|
||||
|
||||
us niter = 0;
|
||||
|
||||
d a = system.getSolution();
|
||||
|
||||
std::pair<d,d> brackets = bracket_root(system,a);
|
||||
a = brackets.first;
|
||||
d b = brackets.second;
|
||||
|
||||
d fa = system.residual(a);
|
||||
d fb = system.residual(b);
|
||||
|
||||
d c = a;
|
||||
d fc = fa;
|
||||
|
||||
d s; // Test point
|
||||
d fs; // Function at test point
|
||||
|
||||
d t,u,v;
|
||||
d d_;
|
||||
|
||||
if(fa*fb>=0){
|
||||
WARN("Brent solver failed: root is not bracketed");
|
||||
return;
|
||||
}
|
||||
|
||||
if(abs(fa) < abs(fb)) {
|
||||
std::swap(a,b);
|
||||
std::swap(fa,fb);
|
||||
}
|
||||
|
||||
bool mflag = true;
|
||||
bool bisec_flag;
|
||||
SolverProgress progress;
|
||||
|
||||
while(_running && progress.iteration <=_maxiter) {
|
||||
|
||||
if((fa!=fc) && (fb!=fc)){
|
||||
// Inverse quadratic interpolation
|
||||
TRACE(15,"IQI");
|
||||
t = a*fb*fc/((fa-fb)*(fa-fc));
|
||||
u = b*fa*fc/((fb-fa)*(fb-fc));
|
||||
v = c*fa*fb/((fc-fa)*(fc-fb));
|
||||
|
||||
s = t+u+v;
|
||||
}
|
||||
else {
|
||||
// Secant method
|
||||
TRACE(15,"Secant");
|
||||
s = b-fb*(b-a)/(fb-fa);
|
||||
}
|
||||
|
||||
bisec_flag = false;
|
||||
|
||||
d abssmb = abs(s-b);
|
||||
d absbmc = abs(b-c);
|
||||
d abscmd = abs(c-d_);
|
||||
|
||||
VARTRACE(15,s);
|
||||
|
||||
if((bisec_flag |= (!is_between(s,(3*a+b)/4,b)))) goto bflag;
|
||||
TRACE(15,"Survived 1");
|
||||
if(bisec_flag |= (mflag && (abssmb >= absbmc/2))) goto bflag;
|
||||
TRACE(15,"Survived 2");
|
||||
if(bisec_flag |= ((!mflag) && (abssmb >= abscmd/2))) goto bflag;
|
||||
TRACE(15,"Survived 3");
|
||||
if(bisec_flag |= (mflag && (absbmc < abs(_reltol)))) goto bflag;;
|
||||
TRACE(15,"Survived 4");
|
||||
bflag:
|
||||
if(bisec_flag || ((!mflag) && (abscmd < abs(_reltol)))) {
|
||||
TRACE(15,"Bisection");
|
||||
s = (a+b)/2;
|
||||
mflag = true;
|
||||
}
|
||||
else {
|
||||
mflag = false;
|
||||
}
|
||||
|
||||
fs = system.residual(s);
|
||||
d_ = c;
|
||||
|
||||
if(fa*fs < 0) {
|
||||
c = b;
|
||||
fc = fb;
|
||||
b=s;
|
||||
fb = fs;
|
||||
}
|
||||
else {
|
||||
c = a;
|
||||
fc = fa;
|
||||
a = s;
|
||||
fa = fs;
|
||||
}
|
||||
if(abs(fa)<abs(fb)) {
|
||||
std::swap(a,b);
|
||||
std::swap(fa,fb);
|
||||
}
|
||||
|
||||
progress.fun_err = abs(fs);
|
||||
progress.rel_err = abs(b-a);
|
||||
progress.iteration++;
|
||||
|
||||
VARTRACE(15,s);
|
||||
VARTRACE(15,a);
|
||||
VARTRACE(15,b);
|
||||
VARTRACE(15,c);
|
||||
VARTRACE(15,fa);
|
||||
VARTRACE(15,fb);
|
||||
VARTRACE(15,fc);
|
||||
VARTRACE(15,fs);
|
||||
|
||||
SolverAction action = (*callback)(progress);
|
||||
|
||||
if(action==Stop){
|
||||
break;
|
||||
}
|
||||
|
||||
|
||||
}
|
||||
|
||||
system.updateSolution(b);
|
||||
}
|
||||
|
||||
|
||||
//////////////////////////////////////////////////////////////////////
|
||||
24
src/solver/brent.h
Normal file
24
src/solver/brent.h
Normal file
@ -0,0 +1,24 @@
|
||||
// brent.h
|
||||
//
|
||||
// Author: J.A. de Jong
|
||||
//
|
||||
// Description:
|
||||
// Brent's root finding algorithm
|
||||
//////////////////////////////////////////////////////////////////////
|
||||
#pragma once
|
||||
#ifndef BRENT_H
|
||||
#define BRENT_H
|
||||
#include "solver.h"
|
||||
|
||||
class Brent: public Solver<NoGradientNonlinearSystem<d>,d> {
|
||||
d _reltol;
|
||||
us _maxiter;
|
||||
public:
|
||||
Brent(const NoGradientNonlinearSystem<d>& sys,us maxiter=10000,d reltol=1e-6);
|
||||
protected:
|
||||
void start_implementation(NoGradientNonlinearSystem<d>& sys,progress_callback*);
|
||||
};
|
||||
|
||||
|
||||
#endif // BRENT_H
|
||||
//////////////////////////////////////////////////////////////////////
|
||||
57
src/solver/newton_raphson.cpp
Normal file
57
src/solver/newton_raphson.cpp
Normal file
@ -0,0 +1,57 @@
|
||||
// newton_raphson.cpp
|
||||
//
|
||||
// last-edit-by: J.A. de Jong
|
||||
//
|
||||
// Description:
|
||||
//
|
||||
//////////////////////////////////////////////////////////////////////
|
||||
|
||||
#include "newton_raphson.h"
|
||||
#include "tasmet_tracer.h"
|
||||
|
||||
void NewtonRaphson::start_implementation(GradientNonlinearSystem& system,
|
||||
progress_callback* callback) {
|
||||
|
||||
assert(callback);
|
||||
|
||||
us niter = 0;
|
||||
|
||||
// Relative error, function error
|
||||
d reler,funer;
|
||||
|
||||
vd guess = system.getSolution();
|
||||
|
||||
vd residual=system.residual();
|
||||
|
||||
SolverProgress progress;
|
||||
SolverAction action;
|
||||
|
||||
while (_running && progress.iteration<=_maxiter) {
|
||||
|
||||
sdmat jac=system.jacobian();
|
||||
|
||||
assert(jac.n_cols==residual.size());
|
||||
assert(jac.n_rows==residual.size());
|
||||
|
||||
vd dx = -1*_dampfac*arma::spsolve(jac,residual,"superlu");
|
||||
|
||||
guess += dx;
|
||||
|
||||
system.updateSolution(guess);
|
||||
|
||||
residual = system.residual();
|
||||
|
||||
progress.rel_err = norm(dx);
|
||||
progress.fun_err = norm(residual);
|
||||
progress.iteration++;
|
||||
|
||||
action = (*callback)(progress);
|
||||
|
||||
if(action==Stop){
|
||||
break;
|
||||
}
|
||||
|
||||
}
|
||||
|
||||
}
|
||||
//////////////////////////////////////////////////////////////////////
|
||||
30
src/solver/newton_raphson.h
Normal file
30
src/solver/newton_raphson.h
Normal file
@ -0,0 +1,30 @@
|
||||
// newton_raphson.h
|
||||
//
|
||||
// Author: J.A. de Jong
|
||||
//
|
||||
// Description:
|
||||
// Implementation of the Newton-Raphson method
|
||||
//////////////////////////////////////////////////////////////////////
|
||||
#pragma once
|
||||
#ifndef NEWTON_RAPHSON_H
|
||||
#define NEWTON_RAPHSON_H
|
||||
#include "solver.h"
|
||||
|
||||
class NewtonRaphson: public Solver<GradientNonlinearSystem,vd> {
|
||||
|
||||
d _dampfac = 1.0;
|
||||
d _maxiter = 10000;
|
||||
public:
|
||||
NewtonRaphson(const GradientNonlinearSystem&sys,d dampfac,us maxiter):
|
||||
Solver(sys),
|
||||
_dampfac(dampfac),
|
||||
_maxiter(maxiter){}
|
||||
|
||||
protected:
|
||||
void start_implementation(GradientNonlinearSystem& system,progress_callback* callback);
|
||||
|
||||
};
|
||||
|
||||
|
||||
#endif // NEWTON_RAPHSON_H
|
||||
//////////////////////////////////////////////////////////////////////
|
||||
101
src/solver/solver.cpp
Normal file
101
src/solver/solver.cpp
Normal file
@ -0,0 +1,101 @@
|
||||
// solver.cpp
|
||||
//
|
||||
// last-edit-by: J.A. de Jong
|
||||
//
|
||||
// Description:
|
||||
//
|
||||
//////////////////////////////////////////////////////////////////////
|
||||
|
||||
#include "solver.h"
|
||||
#include "tasmet_exception.h"
|
||||
#include <chrono>
|
||||
|
||||
template<typename system_T,typename result_T>
|
||||
static void SolverThread(Solver<system_T,result_T>* solver,
|
||||
system_T* system,
|
||||
progress_callback* callback);
|
||||
|
||||
|
||||
template<typename system_T,typename result_T>
|
||||
Solver<system_T,result_T>::Solver(const system_T& sys){
|
||||
_sys = sys.copy();
|
||||
if(!_sys)
|
||||
throw TasMETBadAlloc();
|
||||
_running = false;
|
||||
}
|
||||
|
||||
template<typename system_T,typename result_T>
|
||||
Solver<system_T,result_T>::~Solver(){
|
||||
|
||||
stop();
|
||||
assert(!_running);
|
||||
assert(!_solver_thread);
|
||||
delete _sys;
|
||||
|
||||
}
|
||||
|
||||
template<typename system_T,typename result_T>
|
||||
void Solver<system_T,result_T>::start(progress_callback* callback,bool wait){
|
||||
|
||||
if(_running){
|
||||
assert(_solver_thread);
|
||||
throw TaSMETError("Solver already running");
|
||||
}
|
||||
|
||||
assert(_solver_thread == nullptr);
|
||||
|
||||
this->_solver_thread = new std::thread(SolverThread<system_T,result_T>,
|
||||
this,
|
||||
_sys,
|
||||
callback);
|
||||
if(!_solver_thread)
|
||||
throw TasMETBadAlloc();
|
||||
|
||||
if(wait){
|
||||
while (_running){
|
||||
std::this_thread::sleep_for(std::chrono::milliseconds(1));
|
||||
}
|
||||
// Cleanup resources
|
||||
stop();
|
||||
}
|
||||
}
|
||||
|
||||
template<typename system_T,typename result_T>
|
||||
void Solver<system_T,result_T>::stop() {
|
||||
|
||||
_running = false;
|
||||
if(_solver_thread){
|
||||
|
||||
_solver_thread->join();
|
||||
delete _solver_thread;
|
||||
_solver_thread = nullptr;
|
||||
|
||||
}
|
||||
}
|
||||
template<typename system_T,typename result_T>
|
||||
result_T Solver<system_T,result_T>::getSolution() const{
|
||||
if(_running){
|
||||
throw TaSMETError("Solver is running");
|
||||
}
|
||||
// Cleanup thread resources
|
||||
stop();
|
||||
return _sys->getSolution();
|
||||
}
|
||||
template<typename system_T,typename result_T>
|
||||
void SolverThread(Solver<system_T,result_T>* solver,system_T* system,progress_callback* callback) {
|
||||
assert(system);
|
||||
|
||||
solver->_running = true;
|
||||
|
||||
solver->start_implementation(*system,callback);
|
||||
|
||||
solver->_running = false;
|
||||
|
||||
}
|
||||
|
||||
|
||||
// Explicit instantiation for a
|
||||
template class Solver<NoGradientNonlinearSystem<vd>,vd>;
|
||||
template class Solver<GradientNonlinearSystem,vd>;
|
||||
template class Solver<NoGradientNonlinearSystem<d>,d>;
|
||||
//////////////////////////////////////////////////////////////////////
|
||||
64
src/solver/solver.h
Normal file
64
src/solver/solver.h
Normal file
@ -0,0 +1,64 @@
|
||||
// solver.h
|
||||
//
|
||||
// Author: J.A. de Jong
|
||||
//
|
||||
// Description:
|
||||
// When solve() is called, a copy of itself is created on the heap,
|
||||
// for which a thread will be run. After the thread is done, the
|
||||
// updated (solved) TaSystem will overwrite the old one.
|
||||
//////////////////////////////////////////////////////////////////////
|
||||
#pragma once
|
||||
#ifndef SOLVER_H
|
||||
#define SOLVER_H
|
||||
#include <functional>
|
||||
#include <thread>
|
||||
#include <atomic>
|
||||
|
||||
#include "tasmet_types.h"
|
||||
#include "tasmet_assert.h"
|
||||
#include "system.h"
|
||||
|
||||
struct SolverProgress
|
||||
{
|
||||
size_t iteration = 0;
|
||||
d fun_err;
|
||||
d rel_err;
|
||||
bool done = false;
|
||||
};
|
||||
|
||||
enum SolverAction{
|
||||
Continue=0,
|
||||
Stop = 1
|
||||
};
|
||||
|
||||
typedef std::function<SolverAction(SolverProgress)> progress_callback;
|
||||
|
||||
template<typename system_T,typename result_T>
|
||||
class Solver {
|
||||
|
||||
protected:
|
||||
system_T* _sys = nullptr;
|
||||
std::thread* _solver_thread = nullptr;
|
||||
std::atomic<bool> _running;
|
||||
public:
|
||||
Solver(const system_T& sys);
|
||||
Solver(const Solver&)=delete;
|
||||
Solver& operator=(const Solver&)=delete;
|
||||
|
||||
void start(progress_callback* callback=nullptr,bool wait=true);
|
||||
void stop(); // Stops the solver
|
||||
|
||||
// Returns the solution of the problem
|
||||
result_T getSolution() const;
|
||||
|
||||
virtual ~Solver();
|
||||
template<typename Y,typename rT>
|
||||
friend void SolverThread(Solver<Y,rT>*,Y*,progress_callback*);
|
||||
protected:
|
||||
virtual void start_implementation(system_T& sys,progress_callback*)=0;
|
||||
};
|
||||
|
||||
|
||||
#endif /* _SOLVER_H_ */
|
||||
|
||||
//////////////////////////////////////////////////////////////////////
|
||||
61
src/solver/system.cpp
Normal file
61
src/solver/system.cpp
Normal file
@ -0,0 +1,61 @@
|
||||
// system.cpp
|
||||
//
|
||||
// last-edit-by: J.A. de Jong
|
||||
//
|
||||
// Description: Instantiations for the SingleDofNoGradient class for
|
||||
// the float and complex type
|
||||
//////////////////////////////////////////////////////////////////////
|
||||
|
||||
#include "system.h"
|
||||
|
||||
|
||||
template<typename T>
|
||||
SingleDofNoGradient<T>::SingleDofNoGradient(const NoGradientNonlinearSystem<T>& wrapped_system) {
|
||||
|
||||
this->wrapped_system = wrapped_system.copy();
|
||||
}
|
||||
template<typename T>
|
||||
SingleDofNoGradient<T>::~SingleDofNoGradient(){
|
||||
delete this->wrapped_system;
|
||||
}
|
||||
template<typename T>
|
||||
SingleDofNoGradient<T>* SingleDofNoGradient<T>::copy() const {
|
||||
return new SingleDofNoGradient<T>(*wrapped_system);
|
||||
}
|
||||
|
||||
template<>
|
||||
vd SingleDofNoGradient<d>::residual() const {
|
||||
d val = wrapped_system->residual();
|
||||
return vd({val});
|
||||
}
|
||||
template<>
|
||||
vd SingleDofNoGradient<c>::residual() const {
|
||||
c val = wrapped_system->residual();
|
||||
return vd({val.real(),val.imag()});
|
||||
}
|
||||
template<>
|
||||
vd SingleDofNoGradient<d>::getSolution() const {
|
||||
d val = wrapped_system->getSolution();
|
||||
return vd({val});
|
||||
}
|
||||
template<>
|
||||
vd SingleDofNoGradient<c>::getSolution() const {
|
||||
c val = wrapped_system->getSolution();
|
||||
return vd({val.real(),val.imag()});
|
||||
}
|
||||
|
||||
template<>
|
||||
void SingleDofNoGradient<d>::updateSolution(const vd& new_guess){
|
||||
assert(new_guess.size()==1);
|
||||
wrapped_system->updateSolution(new_guess(0));
|
||||
}
|
||||
template<>
|
||||
void SingleDofNoGradient<c>::updateSolution(const vd& new_guess){
|
||||
assert(new_guess.size()==2);
|
||||
wrapped_system->updateSolution(c(new_guess(0),new_guess(1)));
|
||||
}
|
||||
|
||||
// Explicit intantiation for float-type and complex-type
|
||||
template class SingleDofNoGradient<d>;
|
||||
template class SingleDofNoGradient<c>;
|
||||
//////////////////////////////////////////////////////////////////////
|
||||
74
src/solver/system.h
Normal file
74
src/solver/system.h
Normal file
@ -0,0 +1,74 @@
|
||||
// system.h
|
||||
//
|
||||
// Author: J.A. de Jong
|
||||
//
|
||||
// Description:
|
||||
// This header file describes an interface to a system of equations
|
||||
// that can be solved using a (non)linear solver.
|
||||
//////////////////////////////////////////////////////////////////////
|
||||
#pragma once
|
||||
#ifndef SYSTEM_H
|
||||
#define SYSTEM_H
|
||||
#include "tasmet_types.h"
|
||||
#include "tasmet_assert.h"
|
||||
|
||||
template<typename T>
|
||||
class NoGradientNonlinearSystem{
|
||||
// A nonlinear system for which the gradient of the residual to
|
||||
// the solution vector cannot be obtained.
|
||||
public:
|
||||
virtual T residual() const=0;
|
||||
|
||||
virtual T residual(const T& guess) { updateSolution(guess); return residual();}
|
||||
|
||||
// Obtain an initial guess of the solution
|
||||
virtual T getSolution() const=0;
|
||||
|
||||
// Create a copy of the system
|
||||
virtual NoGradientNonlinearSystem* copy() const=0;
|
||||
|
||||
virtual void updateSolution(const T& new_guess)=0;
|
||||
|
||||
virtual ~NoGradientNonlinearSystem(){}
|
||||
};
|
||||
|
||||
|
||||
// Wrapper around a vector-valued system, such that a solver for a
|
||||
// multi-dimensional system can be called for a single-DOF system
|
||||
template <typename T>
|
||||
class SingleDofNoGradient: public NoGradientNonlinearSystem<vd> {
|
||||
|
||||
static_assert(is_same<T,d>::value || is_same<T,c>::value,"Instaniation must be complex or double");
|
||||
|
||||
NoGradientNonlinearSystem<T>* wrapped_system = nullptr;
|
||||
|
||||
public:
|
||||
|
||||
SingleDofNoGradient(const NoGradientNonlinearSystem<T>& wrapped_system);
|
||||
|
||||
virtual vd residual() const;
|
||||
|
||||
virtual vd getSolution() const;
|
||||
|
||||
// Create a copy of the system
|
||||
virtual SingleDofNoGradient<T>* copy() const;
|
||||
|
||||
virtual void updateSolution(const vd& new_guess);
|
||||
|
||||
~SingleDofNoGradient();
|
||||
|
||||
};
|
||||
|
||||
class GradientNonlinearSystem: public NoGradientNonlinearSystem<vd> {
|
||||
|
||||
public:
|
||||
|
||||
virtual sdmat jacobian() const=0;
|
||||
|
||||
GradientNonlinearSystem* copy() const=0;
|
||||
};
|
||||
|
||||
|
||||
|
||||
#endif // SYSTEM_H
|
||||
//////////////////////////////////////////////////////////////////////
|
||||
@ -8,12 +8,21 @@
|
||||
#pragma once
|
||||
#ifndef TASMET_ASSERT_H
|
||||
#define TASMET_ASSERT_H
|
||||
|
||||
#ifndef TASMET_DEBUG
|
||||
#include <type_traits>
|
||||
#ifndef TASMET_DEBUG
|
||||
|
||||
static_assert(false, "TASMET_DEBUG macro not defined. Please set it to 1 or 0");
|
||||
|
||||
#endif
|
||||
|
||||
// Compile-time type checking for template instantiation.
|
||||
template<class T, class U>
|
||||
struct is_same : std::false_type {};
|
||||
|
||||
template<class T>
|
||||
struct is_same<T, T> : std::true_type {};
|
||||
|
||||
|
||||
#if TASMET_DEBUG == 1
|
||||
#include <cassert>
|
||||
#include "tasmet_io.h"
|
||||
|
||||
@ -8,6 +8,6 @@
|
||||
|
||||
#include "tasmet_tracer.h"
|
||||
|
||||
|
||||
int tasmet_tracer_level = MAXTRACELEVEL;
|
||||
|
||||
//////////////////////////////////////////////////////////////////////
|
||||
|
||||
@ -29,7 +29,7 @@ typedef size_t us; /* Size type I always use */
|
||||
// To change the whole code to 32-bit floating points, change this to
|
||||
// float.
|
||||
#if TASMET_FLOAT == 32
|
||||
// typedef float d; /* Shortcut for double */
|
||||
typedef float d; /* Shortcut for double */
|
||||
#elif TASMET_FLOAT == 64
|
||||
typedef double d; /* Shortcut for double */
|
||||
#else
|
||||
@ -67,6 +67,10 @@ const c sqmI=sqrt(-1.0*I);
|
||||
const c minI(0,-1); //Minus complex unity
|
||||
const d number_pi=arma::datum::pi; // The number 3.14159265359..
|
||||
|
||||
template<size_t i>
|
||||
using vdi = arma::Col<d>::fixed<i>;
|
||||
template<size_t i>
|
||||
using vci = arma::Col<c>::fixed<i>;
|
||||
|
||||
typedef arma::Col<d> vd; /* Column vector of doubles */
|
||||
typedef arma::Col<c> vc; /* Column vector of complex numbers */
|
||||
|
||||
1
testing/CMakeLists.txt
Normal file
1
testing/CMakeLists.txt
Normal file
@ -0,0 +1 @@
|
||||
add_subdirectory(solver)
|
||||
4
testing/solver/CMakeLists.txt
Normal file
4
testing/solver/CMakeLists.txt
Normal file
@ -0,0 +1,4 @@
|
||||
add_executable(newton_raphson_test newton_raphson_test.cpp)
|
||||
add_executable(brent_test brent_test.cpp)
|
||||
target_link_libraries(brent_test tasmet_src armadillo openblas pthread)
|
||||
target_link_libraries(newton_raphson_test tasmet_src armadillo openblas pthread)
|
||||
69
testing/solver/brent_test.cpp
Normal file
69
testing/solver/brent_test.cpp
Normal file
@ -0,0 +1,69 @@
|
||||
// newton_raphson_test.cpp
|
||||
//
|
||||
// last-edit-by: J.A. de Jong
|
||||
//
|
||||
// Description:
|
||||
// Test program to test the Newton-Raphson solver implementation
|
||||
//////////////////////////////////////////////////////////////////////
|
||||
#include "system.h"
|
||||
#include "brent.h"
|
||||
#include "tasmet_io.h"
|
||||
#include "tasmet_tracer.h"
|
||||
#include "helium.h"
|
||||
#include "nitrogen.h"
|
||||
#include "air.h"
|
||||
|
||||
SolverAction solver_callback(SolverProgress p){
|
||||
|
||||
cout << "Iteration: " << p.iteration << ". Function error: " << p.fun_err <<". Relative error: " << p.rel_err << endl;
|
||||
if(p.fun_err < 1e-7){
|
||||
TRACE(9, "Returning stop");
|
||||
return Stop;
|
||||
}
|
||||
else {
|
||||
TRACE(9, "Returning continue");
|
||||
return Continue;
|
||||
}
|
||||
}
|
||||
|
||||
class TestFunction: public NoGradientNonlinearSystem<d> {
|
||||
d cur_sol;
|
||||
public:
|
||||
TestFunction(d guess){cur_sol = guess;}
|
||||
d residual() const {
|
||||
return pow(cur_sol,2)-3;
|
||||
}
|
||||
|
||||
void updateSolution(const d& res){ cur_sol = res;}
|
||||
d getSolution() const { return cur_sol;}
|
||||
TestFunction* copy() const {return new TestFunction(cur_sol);}
|
||||
sdmat jacobian() const {
|
||||
sdmat res(1,1);
|
||||
res(0,0) = 2*cur_sol;
|
||||
return res;
|
||||
}
|
||||
};
|
||||
|
||||
int main(){
|
||||
|
||||
INITTRACE(5);
|
||||
|
||||
TestFunction t(100);
|
||||
Brent solver(t);
|
||||
|
||||
std::function<SolverAction(SolverProgress)> p = solver_callback;
|
||||
solver.start(&p);
|
||||
|
||||
d res = solver.getSolution();
|
||||
|
||||
cout << "Final solution: x = " << res << endl;
|
||||
|
||||
Nitrogen nit(293.15,101325);
|
||||
Air air(293.15,101325);
|
||||
|
||||
|
||||
}
|
||||
|
||||
|
||||
|
||||
//////////////////////////////////////////////////////////////////////
|
||||
62
testing/solver/newton_raphson_test.cpp
Normal file
62
testing/solver/newton_raphson_test.cpp
Normal file
@ -0,0 +1,62 @@
|
||||
// newton_raphson_test.cpp
|
||||
//
|
||||
// last-edit-by: J.A. de Jong
|
||||
//
|
||||
// Description:
|
||||
// Test program to test the Newton-Raphson solver implementation
|
||||
//////////////////////////////////////////////////////////////////////
|
||||
#include "system.h"
|
||||
#include "newton_raphson.h"
|
||||
#include "tasmet_io.h"
|
||||
#include "tasmet_tracer.h"
|
||||
|
||||
SolverAction solver_callback(SolverProgress p){
|
||||
|
||||
cout << "Iteration: " << p.iteration << ". Function error: " << p.fun_err << endl;
|
||||
if(p.fun_err < 1e-7){
|
||||
TRACE(9, "Returning stop");
|
||||
return Stop;
|
||||
}
|
||||
else {
|
||||
TRACE(9, "Returning continue");
|
||||
return Continue;
|
||||
}
|
||||
}
|
||||
|
||||
class TestFunction: public GradientNonlinearSystem {
|
||||
d cur_sol;
|
||||
public:
|
||||
TestFunction(d guess){cur_sol = guess;}
|
||||
vd residual() const {
|
||||
d val = pow(cur_sol,2)-3;
|
||||
return vd({val});
|
||||
}
|
||||
|
||||
void updateSolution(const vd& res){ cur_sol = res(0);}
|
||||
vd getSolution() const { return vd({cur_sol});}
|
||||
TestFunction* copy() const {return new TestFunction(cur_sol);}
|
||||
sdmat jacobian() const {
|
||||
sdmat res(1,1);
|
||||
res(0,0) = 2*cur_sol;
|
||||
return res;
|
||||
}
|
||||
};
|
||||
|
||||
int main(){
|
||||
|
||||
INITTRACE(10);
|
||||
|
||||
TestFunction t(100);
|
||||
NewtonRaphson solver(t,1.0,1000);
|
||||
|
||||
std::function<SolverAction(SolverProgress)> p = solver_callback;
|
||||
solver.start(&p);
|
||||
solver.stop();
|
||||
|
||||
cout << "Final solution: x = " << solver.getSolution();
|
||||
|
||||
}
|
||||
|
||||
|
||||
|
||||
//////////////////////////////////////////////////////////////////////
|
||||
Loading…
Reference in New Issue
Block a user