Merge branch 'misc-improvements' into 'development'
polishing See merge request damask/DAMASK!497
This commit is contained in:
Franz Roters
commit
76fe2d2b36
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|
@ -45,7 +45,7 @@ variables:
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MPI_INTEL: "MPI/Intel/2022.0.1/IntelMPI/2021.5.0"
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# ++++++++++++ PETSc ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
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PETSC_GNU: "Libraries/PETSc/3.16.1/GNU-10-OpenMPI-4.1.1"
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PETSC_INTELLLVM: "Libraries/PETSc/3.16.2/oneAPI-2022.0.1-IntelMPI-2021.5.0"
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PETSC_INTELLLVM: "Libraries/PETSc/3.16.3/oneAPI-2022.0.1-IntelMPI-2021.5.0"
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PETSC_INTEL: "Libraries/PETSc/3.16.2/Intel-2022.0.1-IntelMPI-2021.5.0"
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# ++++++++++++ MSC Marc +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
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MSC: "FEM/MSC/2021.3.1"
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|
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@ -10,7 +10,7 @@ endif()
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# Dummy project to determine compiler names and version
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project(Prerequisites LANGUAGES)
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set(ENV{PKG_CONFIG_PATH} "$ENV{PETSC_DIR}/$ENV{PETSC_ARCH}/lib/pkgconfig")
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pkg_check_modules(PETSC REQUIRED PETSc>=3.12.0 PETSc<3.17.0)
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pkg_search_module(PETSC REQUIRED PETSc>=3.12.0 PETSc<3.17.0)
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pkg_get_variable(CMAKE_Fortran_COMPILER PETSc fcompiler)
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pkg_get_variable(CMAKE_C_COMPILER PETSc ccompiler)
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@ -88,16 +88,12 @@ else()
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message(FATAL_ERROR "Compiler type(CMAKE_Fortran_COMPILER_ID) not recognized")
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endif()
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file(STRINGS "$ENV{PETSC_DIR}/$ENV{PETSC_ARCH}/lib/petsc/conf/petscvariables" PETSC_EXTERNAL_LIB REGEX "PETSC_WITH_EXTERNAL_LIB = .*$?")
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string(REGEX MATCHALL "-[lLW]([^\" ]+)" PETSC_EXTERNAL_LIB "${PETSC_EXTERNAL_LIB}")
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list(REMOVE_DUPLICATES PETSC_EXTERNAL_LIB)
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string(REPLACE ";" " " PETSC_EXTERNAL_LIB "${PETSC_EXTERNAL_LIB}")
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file(STRINGS "$ENV{PETSC_DIR}/$ENV{PETSC_ARCH}/lib/petsc/conf/petscvariables" PETSC_EXTERNAL_LIB REGEX "PETSC_EXTERNAL_LIB_BASIC = .*$?")
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string(REPLACE "PETSC_EXTERNAL_LIB_BASIC = " "" PETSC_EXTERNAL_LIB "${PETSC_EXTERNAL_LIB}")
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message("PETSC_EXTERNAL_LIB:\n${PETSC_EXTERNAL_LIB}\n")
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file(STRINGS "$ENV{PETSC_DIR}/$ENV{PETSC_ARCH}/lib/petsc/conf/petscvariables" PETSC_INCLUDES REGEX "PETSC_FC_INCLUDES = .*$?")
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string(REGEX MATCHALL "-I([^\" ]+)" PETSC_INCLUDES "${PETSC_INCLUDES}")
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list(REMOVE_DUPLICATES PETSC_INCLUDES)
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string(REPLACE ";" " " PETSC_INCLUDES "${PETSC_INCLUDES}")
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string(REPLACE "PETSC_FC_INCLUDES = " "" PETSC_INCLUDES "${PETSC_INCLUDES}")
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message("PETSC_INCLUDES:\n${PETSC_INCLUDES}\n")
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set(CMAKE_Fortran_FLAGS_${CMAKE_BUILD_TYPE} "${BUILDCMD_PRE} ${OPENMP_FLAGS} ${STANDARD_CHECK} ${OPTIMIZATION_FLAGS} ${COMPILE_FLAGS} ${PRECISION_FLAGS}")
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@ -109,7 +105,7 @@ if(CMAKE_BUILD_TYPE STREQUAL "DEBUG")
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endif()
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set(CMAKE_Fortran_FLAGS_${CMAKE_BUILD_TYPE} "${CMAKE_Fortran_FLAGS_${CMAKE_BUILD_TYPE}} ${PETSC_INCLUDES} ${BUILDCMD_POST}")
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set(CMAKE_Fortran_LINK_EXECUTABLE "${CMAKE_Fortran_LINK_EXECUTABLE} <OBJECTS> -o <TARGET> <LINK_LIBRARIES> ${PETSC_EXTERNAL_LIB} -lz ${BUILDCMD_POST}")
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set(CMAKE_Fortran_LINK_EXECUTABLE "${CMAKE_Fortran_LINK_EXECUTABLE} <OBJECTS> -o <TARGET> <LINK_LIBRARIES> -L${PETSC_LIBRARY_DIRS} -lpetsc ${PETSC_EXTERNAL_LIB} -lz ${BUILDCMD_POST}")
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message("Fortran Compiler Flags:\n${CMAKE_Fortran_FLAGS_${CMAKE_BUILD_TYPE}}\n")
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message("C Compiler Flags:\n${CMAKE_C_FLAGS_${CMAKE_BUILD_TYPE}}\n")
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|
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6
Makefile
6
Makefile
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@ -10,14 +10,12 @@ all: grid mesh
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.PHONY: grid
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grid:
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@cmake -B build/grid -DDAMASK_SOLVER=grid -DCMAKE_INSTALL_PREFIX=${PWD} -DCMAKE_BUILD_TYPE=${BUILD_TYPE} -DBUILDCMD_POST=${BUILDCMD_POST} -DBUILDCMD_PRE=${BUILDCMD_PRE} -DOPTIMIZATION=${OPTIMIZATION} -DOPENMP=${OPENMP}
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@cmake --build build/grid --parallel
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@cmake --install build/grid
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@cmake --build build/grid --parallel --target install
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.PHONY: mesh
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mesh:
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@cmake -B build/mesh -DDAMASK_SOLVER=mesh -DCMAKE_INSTALL_PREFIX=${PWD} -DCMAKE_BUILD_TYPE=${BUILD_TYPE} -DBUILDCMD_POST=${BUILDCMD_POST} -DBUILDCMD_PRE=${BUILDCMD_PRE} -DOPTIMIZATION=${OPTIMIZATION} -DOPENMP=${OPENMP}
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@cmake --build build/mesh --parallel
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@cmake --install build/mesh
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@cmake --build build/mesh --parallel --target install
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.PHONY: clean
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clean:
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||||
|
|
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|||
|
|
@ -67,9 +67,7 @@ os.system(f'xvfb-run -a {executable} -compile {menu_file}')
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print('setting file access rights...')
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|
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files = (glob.glob(str(marc_root/f'marc{marc_version}/tools/*_damask*')) +
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glob.glob(str(marc_root/f'mentat{marc_version}/bin/kill[4-6]')) +
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glob.glob(str(marc_root/f'mentat{marc_version}/bin/submit[4-6]')))
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||||
|
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for file in files:
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for file in (glob.glob(str(marc_root/f'marc{marc_version}/tools/*_damask*')) +
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||||
glob.glob(str(marc_root/f'mentat{marc_version}/bin/kill[4-6]')) +
|
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glob.glob(str(marc_root/f'mentat{marc_version}/bin/submit[4-6]'))):
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os.chmod(file , 0o755)
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||||
|
|
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@ -1,71 +0,0 @@
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#!/usr/bin/env python3
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|
||||
import os
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import sys
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from io import StringIO
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from optparse import OptionParser
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|
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import damask
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|
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scriptName = os.path.splitext(os.path.basename(__file__))[0]
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scriptID = ' '.join([scriptName,damask.version])
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|
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# --------------------------------------------------------------------
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# MAIN
|
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# --------------------------------------------------------------------
|
||||
|
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parser = OptionParser(usage='%prog options [ASCIItable(s)]', description = """
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Add displacments resulting from deformation gradient field.
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Operates on periodic three-dimensional x,y,z-ordered data sets.
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Outputs at cell centers or cell nodes (into separate file).
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""", version = scriptID)
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|
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parser.add_option('-f',
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'--defgrad',
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||||
dest = 'f',
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metavar = 'string',
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help = 'label of deformation gradient [%default]')
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parser.add_option('-p',
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'--pos', '--position',
|
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dest = 'pos',
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metavar = 'string',
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help = 'label of coordinates [%default]')
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parser.add_option('--nodal',
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dest = 'nodal',
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action = 'store_true',
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help = 'output nodal (instead of cell-centered) displacements')
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|
||||
parser.set_defaults(f = 'f',
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pos = 'pos',
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||||
)
|
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|
||||
(options,filenames) = parser.parse_args()
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||||
|
||||
for name in filenames:
|
||||
damask.util.report(scriptName,name)
|
||||
|
||||
table = damask.Table.load(StringIO(''.join(sys.stdin.read())) if name is None else name)
|
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grid,size,origin = damask.grid_filters.cellsSizeOrigin_coordinates0_point(table.get(options.pos))
|
||||
|
||||
F = table.get(options.f).reshape(tuple(grid)+(-1,),order='F').reshape(tuple(grid)+(3,3))
|
||||
if options.nodal:
|
||||
damask.Table(damask.grid_filters.coordinates0_node(grid,size).reshape(-1,3,order='F'),
|
||||
{'pos':(3,)})\
|
||||
.add('avg({}).{}'.format(options.f,options.pos),
|
||||
damask.grid_filters.displacement_avg_node(size,F).reshape(-1,3,order='F'),
|
||||
scriptID+' '+' '.join(sys.argv[1:]))\
|
||||
.add('fluct({}).{}'.format(options.f,options.pos),
|
||||
damask.grid_filters.displacement_fluct_node(size,F).reshape(-1,3,order='F'),
|
||||
scriptID+' '+' '.join(sys.argv[1:]))\
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||||
.save((sys.stdout if name is None else os.path.splitext(name)[0]+'_nodal.txt'))
|
||||
else:
|
||||
table.add('avg({}).{}'.format(options.f,options.pos),
|
||||
damask.grid_filters.displacement_avg_point(size,F).reshape(-1,3,order='F'),
|
||||
scriptID+' '+' '.join(sys.argv[1:]))\
|
||||
.add('fluct({}).{}'.format(options.f,options.pos),
|
||||
damask.grid_filters.displacement_fluct_point(size,F).reshape(-1,3,order='F'),
|
||||
scriptID+' '+' '.join(sys.argv[1:]))\
|
||||
.save((sys.stdout if name is None else name))
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||||
|
|
@ -114,12 +114,13 @@ class Crystal():
|
|||
|
||||
def __repr__(self):
|
||||
"""Represent."""
|
||||
return '\n'.join([f'Crystal family {self.family}']
|
||||
+ ([] if self.lattice is None else [f'Bravais lattice {self.lattice}']+
|
||||
list(map(lambda x:f'{x[0]}: {x[1]:.5g}',
|
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zip(['a','b','c','α','β','γ',],
|
||||
self.parameters))))
|
||||
)
|
||||
family = f'Crystal family: {self.family}'
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||||
return family if self.lattice is None else \
|
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'\n'.join([family,
|
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f'Bravais lattice: {self.lattice}',
|
||||
'a={:.5g}m, b={:.5g}m, c={:.5g}m'.format(*self.parameters[:3]),
|
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'α={:.5g}°, β={:.5g}°, γ={:.5g}°'.format(*np.degrees(self.parameters[3:]))])
|
||||
|
||||
|
||||
def __eq__(self,other):
|
||||
"""
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||||
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|
@ -378,7 +379,7 @@ class Crystal():
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|||
"""
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||||
_kinematics = {
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||||
'cF': {
|
||||
'slip' :[np.array([
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'slip': [np.array([
|
||||
[+0,+1,-1, +1,+1,+1],
|
||||
[-1,+0,+1, +1,+1,+1],
|
||||
[+1,-1,+0, +1,+1,+1],
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|
|
@ -398,7 +399,7 @@ class Crystal():
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|||
[+1,+0,-1, +1,+0,+1],
|
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[+0,+1,+1, +0,+1,-1],
|
||||
[+0,+1,-1, +0,+1,+1]])],
|
||||
'twin' :[np.array([
|
||||
'twin': [np.array([
|
||||
[-2, 1, 1, 1, 1, 1],
|
||||
[ 1,-2, 1, 1, 1, 1],
|
||||
[ 1, 1,-2, 1, 1, 1],
|
||||
|
|
@ -413,7 +414,7 @@ class Crystal():
|
|||
[-1, 1, 2, -1, 1,-1]])]
|
||||
},
|
||||
'cI': {
|
||||
'slip' :[np.array([
|
||||
'slip': [np.array([
|
||||
[+1,-1,+1, +0,+1,+1],
|
||||
[-1,-1,+1, +0,+1,+1],
|
||||
[+1,+1,+1, +0,-1,+1],
|
||||
|
|
@ -464,7 +465,7 @@ class Crystal():
|
|||
[+1,+1,+1, -3,+2,+1],
|
||||
[+1,+1,-1, +3,-2,+1],
|
||||
[+1,-1,+1, +3,+2,-1]])],
|
||||
'twin' :[np.array([
|
||||
'twin': [np.array([
|
||||
[-1, 1, 1, 2, 1, 1],
|
||||
[ 1, 1, 1, -2, 1, 1],
|
||||
[ 1, 1,-1, 2,-1, 1],
|
||||
|
|
@ -479,7 +480,7 @@ class Crystal():
|
|||
[ 1, 1, 1, 1, 1,-2]])]
|
||||
},
|
||||
'hP': {
|
||||
'slip' :[np.array([
|
||||
'slip': [np.array([
|
||||
[+2,-1,-1,+0, +0,+0,+0,+1],
|
||||
[-1,+2,-1,+0, +0,+0,+0,+1],
|
||||
[-1,-1,+2,+0, +0,+0,+0,+1]]),
|
||||
|
|
@ -514,7 +515,7 @@ class Crystal():
|
|||
[+1,+1,-2,+3, -1,-1,+2,+2],
|
||||
[-1,+2,-1,+3, +1,-2,+1,+2],
|
||||
[-2,+1,+1,+3, +2,-1,-1,+2]])],
|
||||
'twin' :[np.array([
|
||||
'twin': [np.array([
|
||||
[-1, 0, 1, 1, 1, 0,-1, 2], # shear = (3-(c/a)^2)/(sqrt(3) c/a) <-10.1>{10.2}
|
||||
[ 0,-1, 1, 1, 0, 1,-1, 2],
|
||||
[ 1,-1, 0, 1, -1, 1, 0, 2],
|
||||
|
|
@ -542,7 +543,74 @@ class Crystal():
|
|||
[-1,-1, 2,-3, -1,-1, 2, 2],
|
||||
[ 1,-2, 1,-3, 1,-2, 1, 2],
|
||||
[ 2,-1,-1,-3, 2,-1,-1, 2]])]
|
||||
},
|
||||
},
|
||||
'tI': {
|
||||
'slip': [np.array([
|
||||
[+0,+0,+1, +1,+0,+0],
|
||||
[+0,+0,+1, +0,+1,+0]]),
|
||||
np.array([
|
||||
[+0,+0,+1, +1,+1,+0],
|
||||
[+0,+0,+1, -1,+1,+0]]),
|
||||
np.array([
|
||||
[+0,+1,+0, +1,+0,+0],
|
||||
[+1,+0,+0, +0,+1,+0]]),
|
||||
np.array([
|
||||
[+1,-1,+1, +1,+1,+0],
|
||||
[+1,-1,-1, +1,+1,+0],
|
||||
[-1,-1,-1, -1,+1,+0],
|
||||
[-1,-1,+1, -1,+1,+0]]),
|
||||
np.array([
|
||||
[+1,-1,+0, +1,+1,+0],
|
||||
[+1,+1,+0, +1,-1,+0]]),
|
||||
np.array([
|
||||
[+0,+1,+1, +1,+0,+0],
|
||||
[+0,-1,+1, +1,+0,+0],
|
||||
[-1,+0,+1, +0,+1,+0],
|
||||
[+1,+0,+1, +0,+1,+0]]),
|
||||
np.array([
|
||||
[+0,+1,+0, +0,+0,+1],
|
||||
[+1,+0,+0, +0,+0,+1]]),
|
||||
np.array([
|
||||
[+1,+1,+0, +0,+0,+1],
|
||||
[-1,+1,+0, +0,+0,+1]]),
|
||||
np.array([
|
||||
[+0,+1,-1, +0,+1,+1],
|
||||
[+0,-1,-1, +0,-1,+1],
|
||||
[-1,+0,-1, -1,+0,+1],
|
||||
[+1,+0,-1, +1,+0,+1]]),
|
||||
np.array([
|
||||
[+1,-1,+1, +0,+1,+1],
|
||||
[+1,+1,-1, +0,+1,+1],
|
||||
[+1,+1,+1, +0,+1,-1],
|
||||
[-1,+1,+1, +0,+1,-1],
|
||||
[+1,-1,-1, +1,+0,+1],
|
||||
[-1,-1,+1, +1,+0,+1],
|
||||
[+1,+1,+1, +1,+0,-1],
|
||||
[+1,-1,+1, +1,+0,-1]]),
|
||||
np.array([
|
||||
[+1,+0,+0, +0,+1,+1],
|
||||
[+1,+0,+0, +0,+1,-1],
|
||||
[+0,+1,+0, +1,+0,+1],
|
||||
[+0,+1,+0, +1,+0,-1]]),
|
||||
np.array([
|
||||
[+0,+1,-1, +2,+1,+1],
|
||||
[+0,-1,-1, +2,-1,+1],
|
||||
[+1,+0,-1, +1,+2,+1],
|
||||
[-1,+0,-1, -1,+2,+1],
|
||||
[+0,+1,-1, -2,+1,+1],
|
||||
[+0,-1,-1, -2,-1,+1],
|
||||
[-1,+0,-1, -1,-2,+1],
|
||||
[+1,+0,-1, +1,-2,+1]]),
|
||||
np.array([
|
||||
[-1,+1,+1, +2,+1,+1],
|
||||
[-1,-1,+1, +2,-1,+1],
|
||||
[+1,-1,+1, +1,+2,+1],
|
||||
[-1,-1,+1, -1,+2,+1],
|
||||
[+1,+1,+1, -2,+1,+1],
|
||||
[+1,-1,+1, -2,-1,+1],
|
||||
[-1,+1,+1, -1,-2,+1],
|
||||
[+1,+1,+1, +1,-2,+1]])]
|
||||
}
|
||||
}
|
||||
master = _kinematics[self.lattice][mode]
|
||||
if self.lattice == 'hP':
|
||||
|
|
|
|||
|
|
@ -514,6 +514,17 @@ class Orientation(Rotation,Crystal):
|
|||
[ 0.07359167 -0.36505797 0.92807163]]
|
||||
Bunge Eulers / deg: (11.40, 21.86, 0.60)
|
||||
|
||||
Plot a sample from the Mackenzie distribution.
|
||||
|
||||
>>> import matplotlib.pyplot as plt
|
||||
>>> import damask
|
||||
>>> N = 10000
|
||||
>>> a = damask.Orientation.from_random(shape=N,family='cubic')
|
||||
>>> b = damask.Orientation.from_random(shape=N,family='cubic')
|
||||
>>> d = a.disorientation(b).as_axis_angle(degrees=True,pair=True)[1]
|
||||
>>> plt.hist(d,25)
|
||||
>>> plt.show()
|
||||
|
||||
"""
|
||||
if self.family != other.family:
|
||||
raise NotImplementedError('disorientation between different crystal families')
|
||||
|
|
|
|||
|
|
@ -79,3 +79,23 @@ class TestCrystal:
|
|||
a=a,b=b,c=c,
|
||||
alpha=alpha,beta=beta,gamma=gamma)
|
||||
assert np.allclose(points,c.lattice_points)
|
||||
|
||||
@pytest.mark.parametrize('crystal,length',
|
||||
[(Crystal(lattice='cF'),[12,6]),
|
||||
(Crystal(lattice='cI'),[12,12,24]),
|
||||
(Crystal(lattice='hP'),[3,3,6,12,6]),
|
||||
(Crystal(lattice='tI',c=1.2),[2,2,2,4,2,4,2,2,4,8,4,8,8])
|
||||
])
|
||||
def test_N_slip(self,crystal,length):
|
||||
assert [len(s) for s in crystal.kinematics('slip')['direction']] == length
|
||||
assert [len(s) for s in crystal.kinematics('slip')['plane']] == length
|
||||
|
||||
@pytest.mark.parametrize('crystal,length',
|
||||
[(Crystal(lattice='cF'),[12]),
|
||||
(Crystal(lattice='cI'),[12]),
|
||||
(Crystal(lattice='hP'),[6,6,6,6]),
|
||||
])
|
||||
def test_N_twin(self,crystal,length):
|
||||
assert [len(s) for s in crystal.kinematics('twin')['direction']] == length
|
||||
assert [len(s) for s in crystal.kinematics('twin')['plane']] == length
|
||||
|
||||
|
|
|
|||
|
|
@ -2,6 +2,8 @@ import pytest
|
|||
import numpy as np
|
||||
|
||||
from damask import grid_filters
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from damask import Grid
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from damask import seeds
|
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class TestGridFilters:
|
||||
|
||||
|
|
@ -139,12 +141,19 @@ class TestGridFilters:
|
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else:
|
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function(unordered,mode)
|
||||
|
||||
def test_regrid(self):
|
||||
def test_regrid_identity(self):
|
||||
size = np.random.random(3)
|
||||
cells = np.random.randint(8,32,(3))
|
||||
F = np.broadcast_to(np.eye(3), tuple(cells)+(3,3))
|
||||
F = np.broadcast_to(np.eye(3), tuple(cells)+(3,3))
|
||||
assert all(grid_filters.regrid(size,F,cells) == np.arange(cells.prod()))
|
||||
|
||||
def test_regrid_double_cells(self):
|
||||
size = np.random.random(3)
|
||||
cells = np.random.randint(8,32,(3))
|
||||
g = Grid.from_Voronoi_tessellation(cells,size,seeds.from_random(size,10))
|
||||
F = np.broadcast_to(np.eye(3), tuple(cells)+(3,3))
|
||||
assert all(g.scale(cells*2).material.flatten() ==
|
||||
g.material.flatten()[grid_filters.regrid(size,F,cells*2)])
|
||||
|
||||
@pytest.mark.parametrize('differential_operator',[grid_filters.curl,
|
||||
grid_filters.divergence,
|
||||
|
|
|
|||
|
|
@ -30,7 +30,7 @@ module subroutine elastic_init(phases)
|
|||
phase, &
|
||||
mech, &
|
||||
elastic
|
||||
logical :: thermal_active
|
||||
|
||||
|
||||
print'(/,1x,a)', '<<<+- phase:mechanical:elastic init -+>>>'
|
||||
print'(/,1x,a)', '<<<+- phase:mechanical:elastic:Hooke init -+>>>'
|
||||
|
|
|
|||
|
|
@ -372,7 +372,7 @@ end function rotTensor4
|
|||
|
||||
|
||||
!---------------------------------------------------------------------------------------------------
|
||||
!> @brief Rotate a rank-4 tensor in Voigt 6x6 notation passively (default) or actively.
|
||||
!> @brief Rotate a rank-4 stiffness tensor in Voigt 6x6 notation passively (default) or actively.
|
||||
!> @details: https://scicomp.stackexchange.com/questions/35600
|
||||
!! ToDo: Need to check active/passive !!!
|
||||
!---------------------------------------------------------------------------------------------------
|
||||
|
|
@ -393,11 +393,11 @@ pure function rotStiffness(self,C,active) result(cRot)
|
|||
R = self%asMatrix()
|
||||
endif
|
||||
|
||||
M = reshape([R(1,1)**2.0_pReal, R(2,1)**2.0_pReal, R(3,1)**2.0_pReal, &
|
||||
M = reshape([R(1,1)**2, R(2,1)**2, R(3,1)**2, &
|
||||
R(2,1)*R(3,1), R(1,1)*R(3,1), R(1,1)*R(2,1), &
|
||||
R(1,2)**2.0_pReal, R(2,2)**2.0_pReal, R(3,2)**2.0_pReal, &
|
||||
R(1,2)**2, R(2,2)**2, R(3,2)**2, &
|
||||
R(2,2)*R(3,2), R(1,2)*R(3,2), R(1,2)*R(2,2), &
|
||||
R(1,3)**2.0_pReal, R(2,3)**2.0_pReal, R(3,3)**2.0_pReal, &
|
||||
R(1,3)**2, R(2,3)**2, R(3,3)**2, &
|
||||
R(2,3)*R(3,3), R(1,3)*R(3,3), R(1,3)*R(2,3), &
|
||||
2.0_pReal*R(1,2)*R(1,3), 2.0_pReal*R(2,2)*R(2,3), 2.0_pReal*R(3,2)*R(3,3), &
|
||||
R(2,2)*R(3,3)+R(2,3)*R(3,2), R(1,2)*R(3,3)+R(1,3)*R(3,2), R(1,2)*R(2,3)+R(1,3)*R(2,2), &
|
||||
|
|
|
|||
Loading…
Reference in New Issue