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! Copyright 2011 Max-Planck-Institut für Eisenforschung GmbH
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!
! This file is part of DAMASK,
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! the Düsseldorf Advanced MAterial Simulation Kit.
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!
! DAMASK is free software: you can redistribute it and/or modify
! it under the terms of the GNU General Public License as published by
! the Free Software Foundation, either version 3 of the License, or
! (at your option) any later version.
!
! DAMASK is distributed in the hope that it will be useful,
! but WITHOUT ANY WARRANTY; without even the implied warranty of
! MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
! GNU General Public License for more details.
!
! You should have received a copy of the GNU General Public License
! along with DAMASK. If not, see <http://www.gnu.org/licenses/>.
!
!##############################################################
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!* $Id$
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!##############################################################
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#ifdef Spectral
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#include "kdtree2.f90"
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#endif
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module math
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!##############################################################
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use , intrinsic :: iso_c_binding
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use prec , only : pReal , pInt
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implicit none
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real ( pReal ) , parameter , public :: PI = 3.14159265358979323846264338327950288419716939937510_pReal
real ( pReal ) , parameter , public :: INDEG = 18 0.0_pReal / pi
real ( pReal ) , parameter , public :: INRAD = pi / 18 0.0_pReal
complex ( pReal ) , parameter , public :: TWOPIIMG = ( 0.0_pReal , 2.0_pReal ) * pi
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! *** 3x3 Identity ***
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real ( pReal ) , dimension ( 3 , 3 ) , parameter , public :: &
math_I3 = reshape ( [ &
1.0_pReal , 0.0_pReal , 0.0_pReal , &
0.0_pReal , 1.0_pReal , 0.0_pReal , &
0.0_pReal , 0.0_pReal , 1.0_pReal &
] , [ 3 , 3 ] )
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! *** Mandel notation ***
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integer ( pInt ) , dimension ( 2 , 6 ) , parameter , private :: &
mapMandel = reshape ( [ &
1_pInt , 1_pInt , &
2_pInt , 2_pInt , &
3_pInt , 3_pInt , &
1_pInt , 2_pInt , &
2_pInt , 3_pInt , &
1_pInt , 3_pInt &
] , [ 2 , 6 ] )
real ( pReal ) , dimension ( 6 ) , parameter , private :: &
nrmMandel = [ &
1.0_pReal , 1.0_pReal , 1.0_pReal , &
1.414213562373095_pReal , 1.414213562373095_pReal , 1.414213562373095_pReal ]
real ( pReal ) , dimension ( 6 ) , parameter , public :: &
invnrmMandel = [ &
1.0_pReal , 1.0_pReal , 1.0_pReal , &
0.7071067811865476_pReal , 0.7071067811865476_pReal , 0.7071067811865476_pReal ]
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! *** Voigt notation ***
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integer ( pInt ) , dimension ( 2 , 6 ) , parameter , private :: &
mapVoigt = reshape ( [ &
1_pInt , 1_pInt , &
2_pInt , 2_pInt , &
3_pInt , 3_pInt , &
2_pInt , 3_pInt , &
1_pInt , 3_pInt , &
1_pInt , 2_pInt &
] , [ 2 , 6 ] )
real ( pReal ) , dimension ( 6 ) , parameter , private :: &
nrmVoigt = 1.0_pReal , &
invnrmVoigt = 1.0_pReal
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! *** Plain notation ***
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integer ( pInt ) , dimension ( 2 , 9 ) , parameter , private :: &
mapPlain = reshape ( [ &
1_pInt , 1_pInt , &
1_pInt , 2_pInt , &
1_pInt , 3_pInt , &
2_pInt , 1_pInt , &
2_pInt , 2_pInt , &
2_pInt , 3_pInt , &
3_pInt , 1_pInt , &
3_pInt , 2_pInt , &
3_pInt , 3_pInt &
] , [ 2 , 9 ] )
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! Symmetry operations as quaternions
! 24 for cubic, 12 for hexagonal = 36
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integer ( pInt ) , dimension ( 2 ) , parameter , private :: &
math_NsymOperations = [ 24_pInt , 12_pInt ]
real ( pReal ) , dimension ( 4 , 36 ) , parameter , private :: &
math_symOperations = reshape ( [ &
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1.0_pReal , 0.0_pReal , 0.0_pReal , 0.0_pReal , & ! cubic symmetry operations
0.0_pReal , 0.0_pReal , 0.7071067811865476_pReal , 0.7071067811865476_pReal , & ! 2-fold symmetry
0.0_pReal , 0.7071067811865476_pReal , 0.0_pReal , 0.7071067811865476_pReal , &
0.0_pReal , 0.7071067811865476_pReal , 0.7071067811865476_pReal , 0.0_pReal , &
0.0_pReal , 0.0_pReal , 0.7071067811865476_pReal , - 0.7071067811865476_pReal , &
0.0_pReal , - 0.7071067811865476_pReal , 0.0_pReal , 0.7071067811865476_pReal , &
0.0_pReal , 0.7071067811865476_pReal , - 0.7071067811865476_pReal , 0.0_pReal , &
0.5_pReal , 0.5_pReal , 0.5_pReal , 0.5_pReal , & ! 3-fold symmetry
- 0.5_pReal , 0.5_pReal , 0.5_pReal , 0.5_pReal , &
0.5_pReal , - 0.5_pReal , 0.5_pReal , 0.5_pReal , &
- 0.5_pReal , - 0.5_pReal , 0.5_pReal , 0.5_pReal , &
0.5_pReal , 0.5_pReal , - 0.5_pReal , 0.5_pReal , &
- 0.5_pReal , 0.5_pReal , - 0.5_pReal , 0.5_pReal , &
0.5_pReal , 0.5_pReal , 0.5_pReal , - 0.5_pReal , &
- 0.5_pReal , 0.5_pReal , 0.5_pReal , - 0.5_pReal , &
0.7071067811865476_pReal , 0.7071067811865476_pReal , 0.0_pReal , 0.0_pReal , & ! 4-fold symmetry
0.0_pReal , 1.0_pReal , 0.0_pReal , 0.0_pReal , &
- 0.7071067811865476_pReal , 0.7071067811865476_pReal , 0.0_pReal , 0.0_pReal , &
0.7071067811865476_pReal , 0.0_pReal , 0.7071067811865476_pReal , 0.0_pReal , &
0.0_pReal , 0.0_pReal , 1.0_pReal , 0.0_pReal , &
- 0.7071067811865476_pReal , 0.0_pReal , 0.7071067811865476_pReal , 0.0_pReal , &
0.7071067811865476_pReal , 0.0_pReal , 0.0_pReal , 0.7071067811865476_pReal , &
0.0_pReal , 0.0_pReal , 0.0_pReal , 1.0_pReal , &
- 0.7071067811865476_pReal , 0.0_pReal , 0.0_pReal , 0.7071067811865476_pReal , &
1.0_pReal , 0.0_pReal , 0.0_pReal , 0.0_pReal , & ! hexagonal symmetry operations
0.0_pReal , 1.0_pReal , 0.0_pReal , 0.0_pReal , & ! 2-fold symmetry
0.0_pReal , 0.0_pReal , 1.0_pReal , 0.0_pReal , &
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0.0_pReal , 0.5_pReal , 0.866025403784439_pReal , 0.0_pReal , &
0.0_pReal , - 0.5_pReal , 0.866025403784439_pReal , 0.0_pReal , &
0.0_pReal , 0.866025403784439_pReal , 0.5_pReal , 0.0_pReal , &
0.0_pReal , - 0.866025403784439_pReal , 0.5_pReal , 0.0_pReal , &
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0.866025403784439_pReal , 0.0_pReal , 0.0_pReal , 0.5_pReal , & ! 6-fold symmetry
- 0.866025403784439_pReal , 0.0_pReal , 0.0_pReal , 0.5_pReal , &
0.5_pReal , 0.0_pReal , 0.0_pReal , 0.866025403784439_pReal , &
- 0.5_pReal , 0.0_pReal , 0.0_pReal , 0.866025403784439_pReal , &
0.0_pReal , 0.0_pReal , 0.0_pReal , 1.0_pReal &
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] , [ 4 , 36 ] )
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#ifdef Spectral
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include 'fftw3.f03'
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#endif
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public :: math_init , &
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qsort , &
math_range , &
math_identity2nd , &
math_civita
private :: math_partition , &
math_delta , &
Gauss
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contains
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!**************************************************************************
! initialization of module
!**************************************************************************
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subroutine math_init
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use , intrinsic :: iso_fortran_env ! to get compiler_version and compiler_options (at least for gfortran 4.6 at the moment)
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use prec , only : tol_math_check
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use numerics , only : fixedSeed
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use IO , only : IO_error
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implicit none
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integer ( pInt ) :: i
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real ( pReal ) , dimension ( 3 , 3 ) :: R , R2
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real ( pReal ) , dimension ( 3 ) :: Eulers
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real ( pReal ) , dimension ( 4 ) :: q , q2 , axisangle , randTest
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! the following variables are system dependend and shound NOT be pInt
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integer :: randSize ! gfortran requires a variable length to compile
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integer , dimension ( : ) , allocatable :: randInit ! if recalculations of former randomness (with given seed) is necessary
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! comment the first random_seed call out, set randSize to 1, and use ifort
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character ( len = 64 ) :: error_msg
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openmp parallelization working again (at least for j2 and nonlocal constitutive model).
In order to keep it like that, please follow these simple rules:
DON'T use implicit array subscripts:
example: real, dimension(3,3) :: A,B
A(:,2) = B(:,1) <--- DON'T USE
A(1:3,2) = B(1:3,1) <--- BETTER USE
In many cases the use of explicit array subscripts is inevitable for parallelization. Additionally, it is an easy means to prevent memory leaks.
Enclose all write statements with the following:
!$OMP CRITICAL (write2out)
<your write statement>
!$OMP END CRITICAL (write2out)
Whenever you change something in the code and are not sure if it affects parallelization and leads to nonconforming behavior, please ask me and/or Franz to check this.
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!$OMP CRITICAL (write2out)
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write ( 6 , * ) ''
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write ( 6 , * ) '<<<+- math init -+>>>'
write ( 6 , * ) '$Id$'
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#include "compilation_info.f90"
openmp parallelization working again (at least for j2 and nonlocal constitutive model).
In order to keep it like that, please follow these simple rules:
DON'T use implicit array subscripts:
example: real, dimension(3,3) :: A,B
A(:,2) = B(:,1) <--- DON'T USE
A(1:3,2) = B(1:3,1) <--- BETTER USE
In many cases the use of explicit array subscripts is inevitable for parallelization. Additionally, it is an easy means to prevent memory leaks.
Enclose all write statements with the following:
!$OMP CRITICAL (write2out)
<your write statement>
!$OMP END CRITICAL (write2out)
Whenever you change something in the code and are not sure if it affects parallelization and leads to nonconforming behavior, please ask me and/or Franz to check this.
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!$OMP END CRITICAL (write2out)
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call random_seed ( size = randSize )
allocate ( randInit ( randSize ) )
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if ( fixedSeed > 0_pInt ) then
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randInit ( 1 : randSize ) = int ( fixedSeed ) ! fixedSeed is of type pInt, randInit not
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call random_seed ( put = randInit )
else
call random_seed ( )
endif
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call random_seed ( get = randInit )
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do i = 1_pInt , 4_pInt
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call random_number ( randTest ( i ) )
enddo
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!$OMP CRITICAL (write2out)
! this critical block did cause trouble at IWM
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write ( 6 , * ) 'value of random seed: ' , randInit ( 1 )
write ( 6 , * ) 'size of random seed: ' , randSize
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write ( 6 , '(a,4(/,26x,f17.14))' ) ' start of random sequence: ' , randTest
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write ( 6 , * ) ''
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!$OMP END CRITICAL (write2out)
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call random_seed ( put = randInit )
call random_seed ( get = randInit )
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call halton_seed_set ( int ( randInit ( 1 ) , pInt ) )
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call halton_ndim_set ( 3_pInt )
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! --- check rotation dictionary ---
! +++ q -> a -> q +++
q = math_qRnd ( ) ;
axisangle = math_QuaternionToAxisAngle ( q ) ;
q2 = math_AxisAngleToQuaternion ( axisangle ( 1 : 3 ) , axisangle ( 4 ) )
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if ( any ( abs ( q - q2 ) > tol_math_check ) . and . &
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any ( abs ( - q - q2 ) > tol_math_check ) ) then
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write ( error_msg , '(a,e14.6)' ) 'maximum deviation ' , min ( maxval ( abs ( q - q2 ) ) , maxval ( abs ( - q - q2 ) ) )
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call IO_error ( 401_pInt , ext_msg = error_msg )
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endif
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! +++ q -> R -> q +++
R = math_QuaternionToR ( q ) ;
q2 = math_RToQuaternion ( R )
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if ( any ( abs ( q - q2 ) > tol_math_check ) . and . &
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any ( abs ( - q - q2 ) > tol_math_check ) ) then
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write ( error_msg , '(a,e14.6)' ) 'maximum deviation ' , min ( maxval ( abs ( q - q2 ) ) , maxval ( abs ( - q - q2 ) ) )
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call IO_error ( 402_pInt , ext_msg = error_msg )
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endif
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! +++ q -> euler -> q +++
Eulers = math_QuaternionToEuler ( q ) ;
q2 = math_EulerToQuaternion ( Eulers )
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if ( any ( abs ( q - q2 ) > tol_math_check ) . and . &
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any ( abs ( - q - q2 ) > tol_math_check ) ) then
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write ( error_msg , '(a,e14.6)' ) 'maximum deviation ' , min ( maxval ( abs ( q - q2 ) ) , maxval ( abs ( - q - q2 ) ) )
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call IO_error ( 403_pInt , ext_msg = error_msg )
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endif
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! +++ R -> euler -> R +++
Eulers = math_RToEuler ( R ) ;
R2 = math_EulerToR ( Eulers )
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if ( any ( abs ( R - R2 ) > tol_math_check ) ) then
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write ( error_msg , '(a,e14.6)' ) 'maximum deviation ' , maxval ( abs ( R - R2 ) )
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call IO_error ( 404_pInt , ext_msg = error_msg )
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endif
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end subroutine math_init
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!**************************************************************************
! Quicksort algorithm for two-dimensional integer arrays
!
! Sorting is done with respect to array(1,:)
! and keeps array(2:N,:) linked to it.
!**************************************************************************
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recursive subroutine qsort ( a , istart , iend )
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implicit none
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integer ( pInt ) , dimension ( : , : ) , intent ( inout ) :: a
integer ( pInt ) , intent ( in ) :: istart , iend
integer ( pInt ) :: ipivot
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if ( istart < iend ) then
ipivot = math_partition ( a , istart , iend )
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call qsort ( a , istart , ipivot - 1_pInt )
call qsort ( a , ipivot + 1_pInt , iend )
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endif
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end subroutine qsort
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!**************************************************************************
! Partitioning required for quicksort
!**************************************************************************
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integer ( pInt ) function math_partition ( a , istart , iend )
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implicit none
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integer ( pInt ) , dimension ( : , : ) , intent ( inout ) :: a
integer ( pInt ) , intent ( in ) :: istart , iend
integer ( pInt ) :: d , i , j , k , x , tmp
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d = int ( size ( a , 1_pInt ) , pInt ) ! number of linked data
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! set the starting and ending points, and the pivot point
i = istart
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j = iend
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x = a ( 1 , istart )
do
! find the first element on the right side less than or equal to the pivot point
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do j = j , istart , - 1_pInt
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if ( a ( 1 , j ) < = x ) exit
enddo
! find the first element on the left side greater than the pivot point
do i = i , iend
if ( a ( 1 , i ) > x ) exit
enddo
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if ( i < j ) then ! if the indexes do not cross, exchange values
do k = 1_pInt , d
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tmp = a ( k , i )
a ( k , i ) = a ( k , j )
a ( k , j ) = tmp
enddo
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else ! if they do cross, exchange left value with pivot and return with the partition index
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do k = 1_pInt , d
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tmp = a ( k , istart )
a ( k , istart ) = a ( k , j )
a ( k , j ) = tmp
enddo
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math_partition = j
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return
endif
enddo
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end function math_partition
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!**************************************************************************
! range of integers starting at one
!**************************************************************************
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pure function math_range ( N )
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implicit none
integer ( pInt ) , intent ( in ) :: N
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integer ( pInt ) :: i
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integer ( pInt ) , dimension ( N ) :: math_range
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forall ( i = 1_pInt : N ) math_range ( i ) = i
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end function math_range
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!**************************************************************************
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! second rank identity tensor of specified dimension
!**************************************************************************
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pure function math_identity2nd ( dimen )
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implicit none
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integer ( pInt ) , intent ( in ) :: dimen
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integer ( pInt ) :: i
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real ( pReal ) , dimension ( dimen , dimen ) :: math_identity2nd
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math_identity2nd = 0.0_pReal
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forall ( i = 1_pInt : dimen ) math_identity2nd ( i , i ) = 1.0_pReal
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end function math_identity2nd
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!**************************************************************************
! permutation tensor e_ijk used for computing cross product of two tensors
! e_ijk = 1 if even permutation of ijk
! e_ijk = -1 if odd permutation of ijk
! e_ijk = 0 otherwise
!**************************************************************************
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pure function math_civita ( i , j , k )
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implicit none
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integer ( pInt ) , intent ( in ) :: i , j , k
2009-07-31 17:32:20 +05:30
real ( pReal ) math_civita
2008-03-26 19:05:01 +05:30
2009-07-31 17:32:20 +05:30
math_civita = 0.0_pReal
2011-12-01 17:31:13 +05:30
if ( ( ( i == 1_pInt ) . and . ( j == 2_pInt ) . and . ( k == 3_pInt ) ) . or . &
( ( i == 2_pInt ) . and . ( j == 3_pInt ) . and . ( k == 1_pInt ) ) . or . &
( ( i == 3_pInt ) . and . ( j == 1_pInt ) . and . ( k == 2_pInt ) ) ) math_civita = 1.0_pReal
if ( ( ( i == 1_pInt ) . and . ( j == 3_pInt ) . and . ( k == 2_pInt ) ) . or . &
( ( i == 2_pInt ) . and . ( j == 1_pInt ) . and . ( k == 3_pInt ) ) . or . &
( ( i == 3_pInt ) . and . ( j == 2_pInt ) . and . ( k == 1_pInt ) ) ) math_civita = - 1.0_pReal
2008-03-27 17:24:34 +05:30
2012-03-09 01:55:28 +05:30
end function math_civita
2008-03-27 17:24:34 +05:30
2011-12-01 17:31:13 +05:30
2008-03-27 17:24:34 +05:30
!**************************************************************************
! kronecker delta function d_ij
! d_ij = 1 if i = j
! d_ij = 0 otherwise
!**************************************************************************
2012-03-09 01:55:28 +05:30
pure function math_delta ( i , j )
2008-03-27 17:24:34 +05:30
implicit none
2009-12-14 16:32:10 +05:30
integer ( pInt ) , intent ( in ) :: i , j
2011-12-01 17:31:13 +05:30
real ( pReal ) :: math_delta
2008-03-27 17:24:34 +05:30
math_delta = 0.0_pReal
if ( i == j ) math_delta = 1.0_pReal
2012-03-09 01:55:28 +05:30
end function math_delta
2007-03-29 21:02:52 +05:30
2011-12-01 17:31:13 +05:30
2007-03-29 21:02:52 +05:30
!**************************************************************************
! fourth rank identity tensor of specified dimension
!**************************************************************************
2012-03-09 01:55:28 +05:30
pure function math_identity4th ( dimen )
2007-03-29 21:02:52 +05:30
implicit none
2009-01-20 00:40:58 +05:30
integer ( pInt ) , intent ( in ) :: dimen
2011-12-01 17:31:13 +05:30
integer ( pInt ) :: i , j , k , l
2007-04-11 15:34:22 +05:30
real ( pReal ) , dimension ( dimen , dimen , dimen , dimen ) :: math_identity4th
2007-03-29 21:02:52 +05:30
2011-12-01 17:31:13 +05:30
forall ( i = 1_pInt : dimen , j = 1_pInt : dimen , k = 1_pInt : dimen , l = 1_pInt : dimen ) math_identity4th ( i , j , k , l ) = &
2010-09-22 17:34:43 +05:30
0.5_pReal * ( math_I3 ( i , k ) * math_I3 ( j , k ) + math_I3 ( i , l ) * math_I3 ( j , k ) )
2007-03-29 21:02:52 +05:30
2012-03-09 01:55:28 +05:30
end function math_identity4th
2008-02-15 18:12:27 +05:30
2011-12-01 17:31:13 +05:30
2009-01-20 00:40:58 +05:30
!**************************************************************************
! vector product a x b
!**************************************************************************
2012-03-09 01:55:28 +05:30
pure function math_vectorproduct ( A , B )
2009-01-20 00:40:58 +05:30
implicit none
real ( pReal ) , dimension ( 3 ) , intent ( in ) :: A , B
real ( pReal ) , dimension ( 3 ) :: math_vectorproduct
math_vectorproduct ( 1 ) = A ( 2 ) * B ( 3 ) - A ( 3 ) * B ( 2 )
math_vectorproduct ( 2 ) = A ( 3 ) * B ( 1 ) - A ( 1 ) * B ( 3 )
math_vectorproduct ( 3 ) = A ( 1 ) * B ( 2 ) - A ( 2 ) * B ( 1 )
2012-03-09 01:55:28 +05:30
end function math_vectorproduct
2009-01-20 00:40:58 +05:30
2009-03-05 20:07:59 +05:30
2009-03-17 20:43:17 +05:30
!**************************************************************************
! tensor product a \otimes b
!**************************************************************************
2012-03-09 01:55:28 +05:30
pure function math_tensorproduct ( A , B )
2009-03-17 20:43:17 +05:30
implicit none
real ( pReal ) , dimension ( 3 ) , intent ( in ) :: A , B
real ( pReal ) , dimension ( 3 , 3 ) :: math_tensorproduct
2011-12-01 17:31:13 +05:30
integer ( pInt ) :: i , j
2009-03-17 20:43:17 +05:30
2011-12-01 17:31:13 +05:30
forall ( i = 1_pInt : 3_pInt , j = 1_pInt : 3_pInt ) math_tensorproduct ( i , j ) = A ( i ) * B ( j )
2009-03-17 20:43:17 +05:30
2012-03-09 01:55:28 +05:30
end function math_tensorproduct
2009-03-17 20:43:17 +05:30
2009-03-05 20:07:59 +05:30
!**************************************************************************
! matrix multiplication 3x3 = 1
!**************************************************************************
2012-03-09 01:55:28 +05:30
pure function math_mul3x3 ( A , B )
2009-03-05 20:07:59 +05:30
implicit none
2011-12-01 17:31:13 +05:30
integer ( pInt ) :: i
2009-03-05 20:07:59 +05:30
real ( pReal ) , dimension ( 3 ) , intent ( in ) :: A , B
2010-09-30 15:02:49 +05:30
real ( pReal ) , dimension ( 3 ) :: C
2011-12-01 17:31:13 +05:30
real ( pReal ) :: math_mul3x3
2009-03-05 20:07:59 +05:30
2011-12-01 17:31:13 +05:30
forall ( i = 1_pInt : 3_pInt ) C ( i ) = A ( i ) * B ( i )
2009-03-05 20:07:59 +05:30
math_mul3x3 = sum ( C )
2012-03-09 01:55:28 +05:30
end function math_mul3x3
2009-03-05 20:07:59 +05:30
!**************************************************************************
! matrix multiplication 6x6 = 1
!**************************************************************************
2012-03-09 01:55:28 +05:30
pure function math_mul6x6 ( A , B )
2009-03-05 20:07:59 +05:30
implicit none
2011-12-01 17:31:13 +05:30
integer ( pInt ) :: i
2009-03-05 20:07:59 +05:30
real ( pReal ) , dimension ( 6 ) , intent ( in ) :: A , B
2010-09-30 15:02:49 +05:30
real ( pReal ) , dimension ( 6 ) :: C
2011-12-01 17:31:13 +05:30
real ( pReal ) :: math_mul6x6
2009-03-05 20:07:59 +05:30
2011-12-01 17:31:13 +05:30
forall ( i = 1_pInt : 6_pInt ) C ( i ) = A ( i ) * B ( i )
2009-03-05 20:07:59 +05:30
math_mul6x6 = sum ( C )
2012-03-09 01:55:28 +05:30
end function math_mul6x6
2009-01-20 00:40:58 +05:30
2009-08-11 22:01:57 +05:30
2010-09-30 15:02:49 +05:30
!**************************************************************************
! matrix multiplication 33x33 = 1 (double contraction --> ij * ij)
!**************************************************************************
2012-03-09 01:55:28 +05:30
pure function math_mul33xx33 ( A , B )
2010-09-30 15:02:49 +05:30
implicit none
2011-12-01 17:31:13 +05:30
integer ( pInt ) :: i , j
2010-09-30 15:02:49 +05:30
real ( pReal ) , dimension ( 3 , 3 ) , intent ( in ) :: A , B
real ( pReal ) , dimension ( 3 , 3 ) :: C
2011-12-01 17:31:13 +05:30
real ( pReal ) :: math_mul33xx33
2010-09-30 15:02:49 +05:30
2011-12-01 17:31:13 +05:30
forall ( i = 1_pInt : 3_pInt , j = 1_pInt : 3_pInt ) C ( i , j ) = A ( i , j ) * B ( i , j )
2010-09-30 15:02:49 +05:30
math_mul33xx33 = sum ( C )
2012-03-09 01:55:28 +05:30
end function math_mul33xx33
2010-09-30 15:02:49 +05:30
2011-12-01 17:31:13 +05:30
2010-10-13 21:34:44 +05:30
!**************************************************************************
! matrix multiplication 3333x33 = 33 (double contraction --> ijkl *kl = ij)
!**************************************************************************
2012-03-09 01:55:28 +05:30
pure function math_mul3333xx33 ( A , B )
2010-10-13 21:34:44 +05:30
implicit none
2011-12-01 17:31:13 +05:30
integer ( pInt ) :: i , j
2010-10-13 21:34:44 +05:30
real ( pReal ) , dimension ( 3 , 3 , 3 , 3 ) , intent ( in ) :: A
real ( pReal ) , dimension ( 3 , 3 ) , intent ( in ) :: B
2011-04-13 19:46:22 +05:30
real ( pReal ) , dimension ( 3 , 3 ) :: math_mul3333xx33
2010-10-13 21:34:44 +05:30
2012-02-13 19:38:07 +05:30
forall ( i = 1_pInt : 3_pInt , j = 1_pInt : 3_pInt ) &
math_mul3333xx33 ( i , j ) = sum ( A ( i , j , 1 : 3 , 1 : 3 ) * B ( 1 : 3 , 1 : 3 ) )
2012-03-09 01:55:28 +05:30
end function math_mul3333xx33
2010-10-13 21:34:44 +05:30
2010-09-30 15:02:49 +05:30
2012-02-23 01:41:09 +05:30
!**************************************************************************
! matrix multiplication 3333x3333 = 3333 (ijkl *klmn = ijmn)
!**************************************************************************
2012-03-09 01:55:28 +05:30
pure function math_mul3333xx3333 ( A , B )
2012-02-23 01:41:09 +05:30
implicit none
integer ( pInt ) :: i , j , k , l
real ( pReal ) , dimension ( 3 , 3 , 3 , 3 ) , intent ( in ) :: A
real ( pReal ) , dimension ( 3 , 3 , 3 , 3 ) , intent ( in ) :: B
real ( pReal ) , dimension ( 3 , 3 , 3 , 3 ) :: math_mul3333xx3333
do i = 1_pInt , 3_pInt
do j = 1_pInt , 3_pInt
do k = 1_pInt , 3_pInt
do l = 1_pInt , 3_pInt
math_mul3333xx3333 ( i , j , k , l ) = sum ( A ( i , j , 1 : 3 , 1 : 3 ) * B ( 1 : 3 , 1 : 3 , k , l ) )
enddo ; enddo ; enddo ; enddo
2012-03-09 01:55:28 +05:30
end function math_mul3333xx3333
2012-02-23 01:41:09 +05:30
2009-01-20 00:40:58 +05:30
!**************************************************************************
2012-01-26 19:20:00 +05:30
! matrix multiplication 33x33 = 33
2010-09-30 14:16:58 +05:30
!**************************************************************************
2012-03-09 01:55:28 +05:30
pure function math_mul33x33 ( A , B )
2009-01-20 00:40:58 +05:30
implicit none
2011-12-01 17:31:13 +05:30
integer ( pInt ) :: i , j
2009-01-20 00:40:58 +05:30
real ( pReal ) , dimension ( 3 , 3 ) , intent ( in ) :: A , B
real ( pReal ) , dimension ( 3 , 3 ) :: math_mul33x33
2011-12-01 17:31:13 +05:30
forall ( i = 1_pInt : 3_pInt , j = 1_pInt : 3_pInt ) math_mul33x33 ( i , j ) = &
2009-01-20 00:40:58 +05:30
A ( i , 1 ) * B ( 1 , j ) + A ( i , 2 ) * B ( 2 , j ) + A ( i , 3 ) * B ( 3 , j )
2012-03-09 01:55:28 +05:30
end function math_mul33x33
2009-01-20 00:40:58 +05:30
2008-07-09 01:08:22 +05:30
!**************************************************************************
2012-01-26 19:20:00 +05:30
! matrix multiplication 66x66 = 66
2008-07-09 01:08:22 +05:30
!**************************************************************************
2012-03-09 01:55:28 +05:30
pure function math_mul66x66 ( A , B )
2008-07-09 01:08:22 +05:30
implicit none
2011-12-01 17:31:13 +05:30
integer ( pInt ) :: i , j
2009-01-20 00:40:58 +05:30
real ( pReal ) , dimension ( 6 , 6 ) , intent ( in ) :: A , B
real ( pReal ) , dimension ( 6 , 6 ) :: math_mul66x66
2008-07-09 01:08:22 +05:30
2011-12-01 17:31:13 +05:30
forall ( i = 1_pInt : 6_pInt , j = 1_pInt : 6_pInt ) math_mul66x66 ( i , j ) = &
2008-07-09 01:08:22 +05:30
A ( i , 1 ) * B ( 1 , j ) + A ( i , 2 ) * B ( 2 , j ) + A ( i , 3 ) * B ( 3 , j ) + &
A ( i , 4 ) * B ( 4 , j ) + A ( i , 5 ) * B ( 5 , j ) + A ( i , 6 ) * B ( 6 , j )
2012-03-09 01:55:28 +05:30
end function math_mul66x66
2008-07-09 01:08:22 +05:30
2009-08-11 22:01:57 +05:30
!**************************************************************************
2012-01-26 19:20:00 +05:30
! matrix multiplication 99x99 = 99
2009-08-11 22:01:57 +05:30
!**************************************************************************
2012-03-09 01:55:28 +05:30
pure function math_mul99x99 ( A , B )
2009-08-11 22:01:57 +05:30
use prec , only : pReal , pInt
2012-03-30 01:24:31 +05:30
implicit none
2009-08-11 22:01:57 +05:30
integer ( pInt ) i , j
real ( pReal ) , dimension ( 9 , 9 ) , intent ( in ) :: A , B
real ( pReal ) , dimension ( 9 , 9 ) :: math_mul99x99
2011-12-01 17:31:13 +05:30
forall ( i = 1_pInt : 9_pInt , j = 1_pInt : 9_pInt ) math_mul99x99 ( i , j ) = &
2009-08-11 22:01:57 +05:30
A ( i , 1 ) * B ( 1 , j ) + A ( i , 2 ) * B ( 2 , j ) + A ( i , 3 ) * B ( 3 , j ) + &
A ( i , 4 ) * B ( 4 , j ) + A ( i , 5 ) * B ( 5 , j ) + A ( i , 6 ) * B ( 6 , j ) + &
A ( i , 7 ) * B ( 7 , j ) + A ( i , 8 ) * B ( 8 , j ) + A ( i , 9 ) * B ( 9 , j )
2012-03-09 01:55:28 +05:30
end function math_mul99x99
2009-01-20 00:40:58 +05:30
2009-08-11 22:01:57 +05:30
!**************************************************************************
! matrix multiplication 33x3 = 3
!**************************************************************************
2012-03-09 01:55:28 +05:30
pure function math_mul33x3 ( A , B )
2009-08-11 22:01:57 +05:30
implicit none
2011-12-01 17:31:13 +05:30
integer ( pInt ) :: i
2009-08-11 22:01:57 +05:30
real ( pReal ) , dimension ( 3 , 3 ) , intent ( in ) :: A
real ( pReal ) , dimension ( 3 ) , intent ( in ) :: B
real ( pReal ) , dimension ( 3 ) :: math_mul33x3
2012-01-25 20:01:21 +05:30
forall ( i = 1_pInt : 3_pInt ) math_mul33x3 ( i ) = sum ( A ( i , 1 : 3 ) * B )
2009-08-11 22:01:57 +05:30
2012-03-09 01:55:28 +05:30
end function math_mul33x3
2010-09-22 17:34:43 +05:30
!**************************************************************************
! matrix multiplication complex(33) x real(3) = complex(3)
!**************************************************************************
2012-03-09 01:55:28 +05:30
pure function math_mul33x3_complex ( A , B )
2010-09-22 17:34:43 +05:30
implicit none
2011-12-01 17:31:13 +05:30
integer ( pInt ) :: i
2010-09-22 17:34:43 +05:30
complex ( pReal ) , dimension ( 3 , 3 ) , intent ( in ) :: A
real ( pReal ) , dimension ( 3 ) , intent ( in ) :: B
complex ( pReal ) , dimension ( 3 ) :: math_mul33x3_complex
2012-02-10 16:54:53 +05:30
forall ( i = 1_pInt : 3_pInt ) math_mul33x3_complex ( i ) = sum ( A ( i , 1 : 3 ) * cmplx ( B , 0.0_pReal , pReal ) )
2010-09-22 17:34:43 +05:30
2012-03-09 01:55:28 +05:30
end function math_mul33x3_complex
2009-08-11 22:01:57 +05:30
2009-01-20 00:40:58 +05:30
!**************************************************************************
2009-03-05 20:07:59 +05:30
! matrix multiplication 66x6 = 6
2009-01-20 00:40:58 +05:30
!**************************************************************************
2012-03-09 01:55:28 +05:30
pure function math_mul66x6 ( A , B )
2009-01-20 00:40:58 +05:30
implicit none
2011-12-01 17:31:13 +05:30
integer ( pInt ) :: i
2009-01-20 00:40:58 +05:30
real ( pReal ) , dimension ( 6 , 6 ) , intent ( in ) :: A
real ( pReal ) , dimension ( 6 ) , intent ( in ) :: B
real ( pReal ) , dimension ( 6 ) :: math_mul66x6
2011-12-01 17:31:13 +05:30
forall ( i = 1_pInt : 6_pInt ) math_mul66x6 ( i ) = &
2009-01-20 00:40:58 +05:30
A ( i , 1 ) * B ( 1 ) + A ( i , 2 ) * B ( 2 ) + A ( i , 3 ) * B ( 3 ) + &
A ( i , 4 ) * B ( 4 ) + A ( i , 5 ) * B ( 5 ) + A ( i , 6 ) * B ( 6 )
2012-03-09 01:55:28 +05:30
end function math_mul66x6
2010-05-06 19:37:21 +05:30
!**************************************************************************
! random quaternion
!**************************************************************************
2012-03-09 01:55:28 +05:30
function math_qRnd ( )
2010-05-06 19:37:21 +05:30
implicit none
real ( pReal ) , dimension ( 4 ) :: math_qRnd
real ( pReal ) , dimension ( 3 ) :: rnd
2012-02-09 21:28:15 +05:30
call halton ( 3_pInt , rnd )
2011-02-25 14:55:53 +05:30
math_qRnd ( 1 ) = cos ( 2.0_pReal * pi * rnd ( 1 ) ) * sqrt ( rnd ( 3 ) )
math_qRnd ( 2 ) = sin ( 2.0_pReal * pi * rnd ( 2 ) ) * sqrt ( 1.0_pReal - rnd ( 3 ) )
math_qRnd ( 3 ) = cos ( 2.0_pReal * pi * rnd ( 2 ) ) * sqrt ( 1.0_pReal - rnd ( 3 ) )
math_qRnd ( 4 ) = sin ( 2.0_pReal * pi * rnd ( 1 ) ) * sqrt ( rnd ( 3 ) )
2010-05-06 19:37:21 +05:30
2012-03-09 01:55:28 +05:30
end function math_qRnd
2009-01-20 00:40:58 +05:30
2008-07-09 01:08:22 +05:30
2010-03-18 17:53:17 +05:30
!**************************************************************************
! quaternion multiplication q1xq2 = q12
!**************************************************************************
2012-03-09 01:55:28 +05:30
pure function math_qMul ( A , B )
2010-03-18 17:53:17 +05:30
implicit none
real ( pReal ) , dimension ( 4 ) , intent ( in ) :: A , B
real ( pReal ) , dimension ( 4 ) :: math_qMul
math_qMul ( 1 ) = A ( 1 ) * B ( 1 ) - A ( 2 ) * B ( 2 ) - A ( 3 ) * B ( 3 ) - A ( 4 ) * B ( 4 )
math_qMul ( 2 ) = A ( 1 ) * B ( 2 ) + A ( 2 ) * B ( 1 ) + A ( 3 ) * B ( 4 ) - A ( 4 ) * B ( 3 )
math_qMul ( 3 ) = A ( 1 ) * B ( 3 ) - A ( 2 ) * B ( 4 ) + A ( 3 ) * B ( 1 ) + A ( 4 ) * B ( 2 )
math_qMul ( 4 ) = A ( 1 ) * B ( 4 ) + A ( 2 ) * B ( 3 ) - A ( 3 ) * B ( 2 ) + A ( 4 ) * B ( 1 )
2012-03-09 01:55:28 +05:30
end function math_qMul
2010-03-18 17:53:17 +05:30
!**************************************************************************
! quaternion dotproduct
!**************************************************************************
2012-03-09 01:55:28 +05:30
pure function math_qDot ( A , B )
2010-03-18 17:53:17 +05:30
implicit none
real ( pReal ) , dimension ( 4 ) , intent ( in ) :: A , B
2011-12-01 17:31:13 +05:30
real ( pReal ) :: math_qDot
2010-03-18 17:53:17 +05:30
math_qDot = A ( 1 ) * B ( 1 ) + A ( 2 ) * B ( 2 ) + A ( 3 ) * B ( 3 ) + A ( 4 ) * B ( 4 )
2012-03-09 01:55:28 +05:30
end function math_qDot
2010-03-18 17:53:17 +05:30
!**************************************************************************
! quaternion conjugation
!**************************************************************************
2012-03-09 01:55:28 +05:30
pure function math_qConj ( Q )
2010-03-18 17:53:17 +05:30
implicit none
real ( pReal ) , dimension ( 4 ) , intent ( in ) :: Q
real ( pReal ) , dimension ( 4 ) :: math_qConj
math_qConj ( 1 ) = Q ( 1 )
math_qConj ( 2 : 4 ) = - Q ( 2 : 4 )
2012-03-09 01:55:28 +05:30
end function math_qConj
2010-03-18 17:53:17 +05:30
!**************************************************************************
! quaternion norm
!**************************************************************************
2012-03-09 01:55:28 +05:30
pure function math_qNorm ( Q )
2010-03-18 17:53:17 +05:30
implicit none
real ( pReal ) , dimension ( 4 ) , intent ( in ) :: Q
2011-12-01 17:31:13 +05:30
real ( pReal ) :: math_qNorm
2010-03-18 17:53:17 +05:30
2011-02-25 14:55:53 +05:30
math_qNorm = sqrt ( max ( 0.0_pReal , Q ( 1 ) * Q ( 1 ) + Q ( 2 ) * Q ( 2 ) + Q ( 3 ) * Q ( 3 ) + Q ( 4 ) * Q ( 4 ) ) )
2010-03-18 17:53:17 +05:30
2012-03-09 01:55:28 +05:30
end function math_qNorm
2010-03-18 17:53:17 +05:30
!**************************************************************************
! quaternion inversion
!**************************************************************************
2012-03-09 01:55:28 +05:30
pure function math_qInv ( Q )
2010-03-18 17:53:17 +05:30
implicit none
real ( pReal ) , dimension ( 4 ) , intent ( in ) :: Q
real ( pReal ) , dimension ( 4 ) :: math_qInv
2011-12-01 17:31:13 +05:30
real ( pReal ) :: squareNorm
2010-03-18 17:53:17 +05:30
math_qInv = 0.0_pReal
squareNorm = math_qDot ( Q , Q )
if ( squareNorm > tiny ( squareNorm ) ) &
math_qInv = math_qConj ( Q ) / squareNorm
2012-03-09 01:55:28 +05:30
end function math_qInv
2010-03-18 17:53:17 +05:30
!**************************************************************************
2010-09-30 14:16:58 +05:30
! action of a quaternion on a vector (rotate vector v with Q)
2010-03-18 17:53:17 +05:30
!**************************************************************************
2012-03-09 01:55:28 +05:30
pure function math_qRot ( Q , v )
2010-03-18 17:53:17 +05:30
implicit none
real ( pReal ) , dimension ( 4 ) , intent ( in ) :: Q
real ( pReal ) , dimension ( 3 ) , intent ( in ) :: v
real ( pReal ) , dimension ( 3 ) :: math_qRot
real ( pReal ) , dimension ( 4 , 4 ) :: T
2011-12-01 17:31:13 +05:30
integer ( pInt ) :: i , j
2010-03-18 17:53:17 +05:30
2011-12-01 17:31:13 +05:30
do i = 1_pInt , 4_pInt
do j = 1_pInt , i
2010-03-18 17:53:17 +05:30
T ( i , j ) = Q ( i ) * Q ( j )
enddo
enddo
math_qRot ( 1 ) = - v ( 1 ) * ( T ( 3 , 3 ) + T ( 4 , 4 ) ) + v ( 2 ) * ( T ( 3 , 2 ) - T ( 4 , 1 ) ) + v ( 3 ) * ( T ( 4 , 2 ) + T ( 3 , 1 ) )
math_qRot ( 2 ) = v ( 1 ) * ( T ( 3 , 2 ) + T ( 4 , 1 ) ) - v ( 2 ) * ( T ( 2 , 2 ) + T ( 4 , 4 ) ) + v ( 3 ) * ( T ( 4 , 3 ) - T ( 2 , 1 ) )
math_qRot ( 3 ) = v ( 1 ) * ( T ( 4 , 2 ) - T ( 3 , 1 ) ) + v ( 2 ) * ( T ( 4 , 3 ) + T ( 2 , 1 ) ) - v ( 3 ) * ( T ( 2 , 2 ) + T ( 3 , 3 ) )
math_qRot = 2.0_pReal * math_qRot + v
2012-03-09 01:55:28 +05:30
end function math_qRot
2010-03-18 17:53:17 +05:30
2008-07-09 01:08:22 +05:30
!**************************************************************************
2012-01-26 19:20:00 +05:30
! transposition of a 33 matrix
2008-07-09 01:08:22 +05:30
!**************************************************************************
2012-01-26 19:20:00 +05:30
pure function math_transpose33 ( A )
2008-07-09 01:08:22 +05:30
implicit none
2009-08-11 22:01:57 +05:30
real ( pReal ) , dimension ( 3 , 3 ) , intent ( in ) :: A
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real ( pReal ) , dimension ( 3 , 3 ) :: math_transpose33
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integer ( pInt ) :: i , j
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forall ( i = 1_pInt : 3_pInt , j = 1_pInt : 3_pInt ) math_transpose33 ( i , j ) = A ( j , i )
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end function math_transpose33
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!**************************************************************************
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! Cramer inversion of 33 matrix (function)
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!**************************************************************************
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pure function math_inv33 ( A )
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! direct Cramer inversion of matrix A.
! returns all zeroes if not possible, i.e. if det close to zero
implicit none
real ( pReal ) , dimension ( 3 , 3 ) , intent ( in ) :: A
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real ( pReal ) :: DetA
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real ( pReal ) , dimension ( 3 , 3 ) :: math_inv33
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math_inv33 = 0.0_pReal
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DetA = A ( 1 , 1 ) * ( A ( 2 , 2 ) * A ( 3 , 3 ) - A ( 2 , 3 ) * A ( 3 , 2 ) ) &
- A ( 1 , 2 ) * ( A ( 2 , 1 ) * A ( 3 , 3 ) - A ( 2 , 3 ) * A ( 3 , 1 ) ) &
+ A ( 1 , 3 ) * ( A ( 2 , 1 ) * A ( 3 , 2 ) - A ( 2 , 2 ) * A ( 3 , 1 ) )
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if ( abs ( DetA ) > tiny ( abs ( DetA ) ) ) then
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math_inv33 ( 1 , 1 ) = ( A ( 2 , 2 ) * A ( 3 , 3 ) - A ( 2 , 3 ) * A ( 3 , 2 ) ) / DetA
math_inv33 ( 2 , 1 ) = ( - A ( 2 , 1 ) * A ( 3 , 3 ) + A ( 2 , 3 ) * A ( 3 , 1 ) ) / DetA
math_inv33 ( 3 , 1 ) = ( A ( 2 , 1 ) * A ( 3 , 2 ) - A ( 2 , 2 ) * A ( 3 , 1 ) ) / DetA
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math_inv33 ( 1 , 2 ) = ( - A ( 1 , 2 ) * A ( 3 , 3 ) + A ( 1 , 3 ) * A ( 3 , 2 ) ) / DetA
math_inv33 ( 2 , 2 ) = ( A ( 1 , 1 ) * A ( 3 , 3 ) - A ( 1 , 3 ) * A ( 3 , 1 ) ) / DetA
math_inv33 ( 3 , 2 ) = ( - A ( 1 , 1 ) * A ( 3 , 2 ) + A ( 1 , 2 ) * A ( 3 , 1 ) ) / DetA
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math_inv33 ( 1 , 3 ) = ( A ( 1 , 2 ) * A ( 2 , 3 ) - A ( 1 , 3 ) * A ( 2 , 2 ) ) / DetA
math_inv33 ( 2 , 3 ) = ( - A ( 1 , 1 ) * A ( 2 , 3 ) + A ( 1 , 3 ) * A ( 2 , 1 ) ) / DetA
math_inv33 ( 3 , 3 ) = ( A ( 1 , 1 ) * A ( 2 , 2 ) - A ( 1 , 2 ) * A ( 2 , 1 ) ) / DetA
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endif
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end function math_inv33
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!**************************************************************************
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! Cramer inversion of 33 matrix (subroutine)
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!**************************************************************************
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pure subroutine math_invert33 ( A , InvA , DetA , error )
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! Bestimmung der Determinanten und Inversen einer 33-Matrix
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! A = Matrix A
! InvA = Inverse of A
! DetA = Determinant of A
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! error = logical
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implicit none
logical , intent ( out ) :: error
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real ( pReal ) , dimension ( 3 , 3 ) , intent ( in ) :: A
real ( pReal ) , dimension ( 3 , 3 ) , intent ( out ) :: InvA
real ( pReal ) , intent ( out ) :: DetA
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DetA = A ( 1 , 1 ) * ( A ( 2 , 2 ) * A ( 3 , 3 ) - A ( 2 , 3 ) * A ( 3 , 2 ) ) &
- A ( 1 , 2 ) * ( A ( 2 , 1 ) * A ( 3 , 3 ) - A ( 2 , 3 ) * A ( 3 , 1 ) ) &
+ A ( 1 , 3 ) * ( A ( 2 , 1 ) * A ( 3 , 2 ) - A ( 2 , 2 ) * A ( 3 , 1 ) )
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if ( abs ( DetA ) < = tiny ( abs ( DetA ) ) ) then
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error = . true .
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else
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InvA ( 1 , 1 ) = ( A ( 2 , 2 ) * A ( 3 , 3 ) - A ( 2 , 3 ) * A ( 3 , 2 ) ) / DetA
InvA ( 2 , 1 ) = ( - A ( 2 , 1 ) * A ( 3 , 3 ) + A ( 2 , 3 ) * A ( 3 , 1 ) ) / DetA
InvA ( 3 , 1 ) = ( A ( 2 , 1 ) * A ( 3 , 2 ) - A ( 2 , 2 ) * A ( 3 , 1 ) ) / DetA
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InvA ( 1 , 2 ) = ( - A ( 1 , 2 ) * A ( 3 , 3 ) + A ( 1 , 3 ) * A ( 3 , 2 ) ) / DetA
InvA ( 2 , 2 ) = ( A ( 1 , 1 ) * A ( 3 , 3 ) - A ( 1 , 3 ) * A ( 3 , 1 ) ) / DetA
InvA ( 3 , 2 ) = ( - A ( 1 , 1 ) * A ( 3 , 2 ) + A ( 1 , 2 ) * A ( 3 , 1 ) ) / DetA
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InvA ( 1 , 3 ) = ( A ( 1 , 2 ) * A ( 2 , 3 ) - A ( 1 , 3 ) * A ( 2 , 2 ) ) / DetA
InvA ( 2 , 3 ) = ( - A ( 1 , 1 ) * A ( 2 , 3 ) + A ( 1 , 3 ) * A ( 2 , 1 ) ) / DetA
InvA ( 3 , 3 ) = ( A ( 1 , 1 ) * A ( 2 , 2 ) - A ( 1 , 2 ) * A ( 2 , 1 ) ) / DetA
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error = . false .
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endif
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end subroutine math_invert33
!**************************************************************************
! Inversion of symmetriced 3x3x3x3 tensor.
!**************************************************************************
function math_invSym3333 ( A )
use IO , only : IO_error
implicit none
real ( pReal ) , dimension ( 3 , 3 , 3 , 3 ) :: math_invSym3333
real ( pReal ) , dimension ( 3 , 3 , 3 , 3 ) , intent ( in ) :: A
integer ( pInt ) :: ierr1 , ierr2
integer ( pInt ) , dimension ( 6 ) :: ipiv6
real ( pReal ) , dimension ( 6 , 6 ) :: temp66_Real
real ( pReal ) , dimension ( 6 ) :: work6
temp66_real = math_Mandel3333to66 ( A )
call dgetrf ( 6 , 6 , temp66_real , 6 , ipiv6 , ierr1 )
call dgetri ( 6 , temp66_real , 6 , ipiv6 , work6 , 6 , ierr2 )
if ( ierr1 * ierr2 == 0_pInt ) then
math_invSym3333 = math_Mandel66to3333 ( temp66_real )
else
call IO_error ( 400_pInt , ext_msg = 'math_invSym3333' )
endif
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2012-03-09 01:55:28 +05:30
end function math_invSym3333
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!**************************************************************************
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! Gauss elimination to invert matrix of arbitrary dimension
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!**************************************************************************
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pure subroutine math_invert ( dimen , A , InvA , AnzNegEW , error )
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! Invertieren einer dimen x dimen - Matrix
! A = Matrix A
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! InvA = Inverse of A
! AnzNegEW = Number of negative Eigenvalues of A
! error = false: Inversion done.
! = true: Inversion stopped in SymGauss because of dimishing
! Pivotelement
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implicit none
integer ( pInt ) , intent ( in ) :: dimen
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real ( pReal ) , dimension ( dimen , dimen ) , intent ( in ) :: A
real ( pReal ) , dimension ( dimen , dimen ) , intent ( out ) :: InvA
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integer ( pInt ) , intent ( out ) :: AnzNegEW
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logical , intent ( out ) :: error
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real ( pReal ) :: LogAbsDetA
real ( pReal ) , dimension ( dimen , dimen ) :: B
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InvA = math_identity2nd ( dimen )
B = A
CALL Gauss ( dimen , B , InvA , LogAbsDetA , AnzNegEW , error )
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end subroutine math_invert
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! ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
! ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
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pure subroutine Gauss ( dimen , A , B , LogAbsDetA , NegHDK , error )
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! Solves a linear EQS A * X = B with the GAUSS-Algorithm
! For numerical stabilization using a pivot search in rows and columns
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!
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! input parameters
! A(dimen,dimen) = matrix A
! B(dimen,dimen) = right side B
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!
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! output parameters
! B(dimen,dimen) = Matrix containing unknown vectors X
! LogAbsDetA = 10-Logarithm of absolute value of determinatns of A
! NegHDK = Number of negative Maindiagonal coefficients resulting
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! Vorwaertszerlegung
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! error = false: EQS is solved
! = true : Matrix A is singular.
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!
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! A and B will be changed!
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implicit none
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logical , intent ( out ) :: error
integer ( pInt ) , intent ( in ) :: dimen
integer ( pInt ) , intent ( out ) :: NegHDK
real ( pReal ) , intent ( out ) :: LogAbsDetA
real ( pReal ) , intent ( inout ) , dimension ( dimen , dimen ) :: A , B
logical :: SortX
integer ( pInt ) :: PivotZeile , PivotSpalte , StoreI , I , IP1 , J , K , L
integer ( pInt ) , dimension ( dimen ) :: XNr
real ( pReal ) :: AbsA , PivotWert , EpsAbs , Quote
real ( pReal ) , dimension ( dimen ) :: StoreA , StoreB
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error = . true . ; NegHDK = 1_pInt ; SortX = . false .
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! Unbekanntennumerierung
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DO I = 1_pInt , dimen
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XNr ( I ) = I
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ENDDO
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! Genauigkeitsschranke und Bestimmung des groessten Pivotelementes
PivotWert = ABS ( A ( 1 , 1 ) )
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PivotZeile = 1_pInt
PivotSpalte = 1_pInt
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do I = 1_pInt , dimen ; do J = 1_pInt , dimen
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AbsA = ABS ( A ( I , J ) )
IF ( AbsA . GT . PivotWert ) THEN
PivotWert = AbsA
PivotZeile = I
PivotSpalte = J
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ENDIF
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enddo ; enddo
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IF ( PivotWert . LT . 0.0000001_pReal ) RETURN ! Pivotelement = 0?
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EpsAbs = PivotWert * 0.1_pReal ** PRECISION ( 1.0_pReal )
! V O R W A E R T S T R I A N G U L A T I O N
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DO I = 1_pInt , dimen - 1_pInt
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! Zeilentausch?
IF ( PivotZeile . NE . I ) THEN
StoreA ( I : dimen ) = A ( I , I : dimen )
A ( I , I : dimen ) = A ( PivotZeile , I : dimen )
A ( PivotZeile , I : dimen ) = StoreA ( I : dimen )
StoreB ( 1 : dimen ) = B ( I , 1 : dimen )
B ( I , 1 : dimen ) = B ( PivotZeile , 1 : dimen )
B ( PivotZeile , 1 : dimen ) = StoreB ( 1 : dimen )
SortX = . TRUE .
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ENDIF
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! Spaltentausch?
IF ( PivotSpalte . NE . I ) THEN
StoreA ( 1 : dimen ) = A ( 1 : dimen , I )
A ( 1 : dimen , I ) = A ( 1 : dimen , PivotSpalte )
A ( 1 : dimen , PivotSpalte ) = StoreA ( 1 : dimen )
StoreI = XNr ( I )
XNr ( I ) = XNr ( PivotSpalte )
XNr ( PivotSpalte ) = StoreI
SortX = . TRUE .
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ENDIF
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! Triangulation
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DO J = I + 1_pInt , dimen
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Quote = A ( J , I ) / A ( I , I )
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DO K = I + 1_pInt , dimen
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A ( J , K ) = A ( J , K ) - Quote * A ( I , K )
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ENDDO
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DO K = 1_pInt , dimen
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B ( J , K ) = B ( J , K ) - Quote * B ( I , K )
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ENDDO
ENDDO
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! Bestimmung des groessten Pivotelementes
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IP1 = I + 1_pInt
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PivotWert = ABS ( A ( IP1 , IP1 ) )
PivotZeile = IP1
PivotSpalte = IP1
DO J = IP1 , dimen
DO K = IP1 , dimen
AbsA = ABS ( A ( J , K ) )
IF ( AbsA . GT . PivotWert ) THEN
PivotWert = AbsA
PivotZeile = J
PivotSpalte = K
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ENDIF
ENDDO
ENDDO
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IF ( PivotWert . LT . EpsAbs ) RETURN ! Pivotelement = 0?
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ENDDO
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! R U E C K W A E R T S A U F L O E S U N G
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DO I = dimen , 1_pInt , - 1_pInt
DO L = 1_pInt , dimen
DO J = I + 1_pInt , dimen
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B ( I , L ) = B ( I , L ) - A ( I , J ) * B ( J , L )
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ENDDO
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B ( I , L ) = B ( I , L ) / A ( I , I )
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ENDDO
ENDDO
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! Sortieren der Unbekanntenvektoren?
IF ( SortX ) THEN
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DO L = 1_pInt , dimen
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StoreA ( 1 : dimen ) = B ( 1 : dimen , L )
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DO I = 1_pInt , dimen
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J = XNr ( I )
B ( J , L ) = StoreA ( I )
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ENDDO
ENDDO
ENDIF
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! Determinante
LogAbsDetA = 0.0_pReal
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NegHDK = 0_pInt
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DO I = 1_pInt , dimen
IF ( A ( I , I ) . LT . 0.0_pReal ) NegHDK = NegHDK + 1_pInt
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AbsA = ABS ( A ( I , I ) )
LogAbsDetA = LogAbsDetA + LOG10 ( AbsA )
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ENDDO
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error = . false .
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end subroutine Gauss
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!********************************************************************
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! symmetrize a 33 matrix
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!********************************************************************
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function math_symmetric33 ( m )
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implicit none
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real ( pReal ) , dimension ( 3 , 3 ) :: math_symmetric33
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real ( pReal ) , dimension ( 3 , 3 ) , intent ( in ) :: m
integer ( pInt ) :: i , j
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forall ( i = 1_pInt : 3_pInt , j = 1_pInt : 3_pInt ) math_symmetric33 ( i , j ) = 0.5_pReal * ( m ( i , j ) + m ( j , i ) )
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end function math_symmetric33
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!********************************************************************
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! symmetrize a 66 matrix
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!********************************************************************
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pure function math_symmetric66 ( m )
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implicit none
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integer ( pInt ) :: i , j
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real ( pReal ) , dimension ( 6 , 6 ) , intent ( in ) :: m
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real ( pReal ) , dimension ( 6 , 6 ) :: math_symmetric66
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2012-01-26 19:20:00 +05:30
forall ( i = 1_pInt : 6_pInt , j = 1_pInt : 6_pInt ) math_symmetric66 ( i , j ) = 0.5_pReal * ( m ( i , j ) + m ( j , i ) )
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end function math_symmetric66
2008-02-15 18:12:27 +05:30
2012-01-25 16:00:39 +05:30
!********************************************************************
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! skew part of a 33 matrix
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!********************************************************************
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pure function math_skew33 ( m )
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implicit none
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real ( pReal ) , dimension ( 3 , 3 ) :: math_skew33
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real ( pReal ) , dimension ( 3 , 3 ) , intent ( in ) :: m
integer ( pInt ) :: i , j
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forall ( i = 1_pInt : 3_pInt , j = 1_pInt : 3_pInt ) math_skew33 ( i , j ) = m ( i , j ) - 0.5_pReal * ( m ( i , j ) + m ( j , i ) )
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end function math_skew33
2008-02-15 18:12:27 +05:30
2012-01-25 16:00:39 +05:30
2012-01-26 19:20:00 +05:30
!********************************************************************
! deviatoric part of a 33 matrix
!********************************************************************
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pure function math_deviatoric33 ( m )
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2012-02-09 21:28:15 +05:30
implicit none
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2012-02-09 21:28:15 +05:30
real ( pReal ) , dimension ( 3 , 3 ) :: math_deviatoric33
real ( pReal ) , dimension ( 3 , 3 ) , intent ( in ) :: m
integer ( pInt ) :: i
real ( pReal ) :: hydrostatic
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hydrostatic = ( m ( 1 , 1 ) + m ( 2 , 2 ) + m ( 3 , 3 ) ) / 3.0_pReal
math_deviatoric33 = m
forall ( i = 1_pInt : 3_pInt ) math_deviatoric33 ( i , i ) = m ( i , i ) - hydrostatic
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end function math_deviatoric33
2012-01-26 19:20:00 +05:30
2010-03-24 18:50:12 +05:30
!********************************************************************
! equivalent scalar quantity of a full strain tensor
!********************************************************************
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pure function math_equivStrain33 ( m )
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implicit none
real ( pReal ) , dimension ( 3 , 3 ) , intent ( in ) :: m
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real ( pReal ) :: math_equivStrain33 , e11 , e22 , e33 , s12 , s23 , s31
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e11 = ( 2.0_pReal * m ( 1 , 1 ) - m ( 2 , 2 ) - m ( 3 , 3 ) ) / 3.0_pReal
e22 = ( 2.0_pReal * m ( 2 , 2 ) - m ( 3 , 3 ) - m ( 1 , 1 ) ) / 3.0_pReal
e33 = ( 2.0_pReal * m ( 3 , 3 ) - m ( 1 , 1 ) - m ( 2 , 2 ) ) / 3.0_pReal
s12 = 2.0_pReal * m ( 1 , 2 )
s23 = 2.0_pReal * m ( 2 , 3 )
s31 = 2.0_pReal * m ( 3 , 1 )
math_equivStrain33 = 2.0_pReal * ( 1.50_pReal * ( e11 ** 2.0_pReal + e22 ** 2.0_pReal + e33 ** 2.0_pReal ) + &
0.75_pReal * ( s12 ** 2.0_pReal + s23 ** 2.0_pReal + s31 ** 2.0_pReal ) ) ** ( 0.5_pReal ) / 3.0_pReal
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end function math_equivStrain33
2010-03-24 18:50:12 +05:30
2011-12-01 17:31:13 +05:30
!********************************************************************
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subroutine math_equivStrain33_field ( res , tensor , vm )
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!********************************************************************
!calculate von Mises equivalent of tensor field
!
implicit none
! input variables
integer ( pInt ) , intent ( in ) , dimension ( 3 ) :: res
real ( pReal ) , intent ( in ) , dimension ( res ( 1 ) , res ( 2 ) , res ( 3 ) , 3 , 3 ) :: tensor
! output variables
real ( pReal ) , intent ( out ) , dimension ( res ( 1 ) , res ( 2 ) , res ( 3 ) ) :: vm
! other variables
integer ( pInt ) :: i , j , k
real ( pReal ) , dimension ( 3 , 3 ) :: deviator , delta = 0.0_pReal
real ( pReal ) :: J_2
delta ( 1 , 1 ) = 1.0_pReal
delta ( 2 , 2 ) = 1.0_pReal
delta ( 3 , 3 ) = 1.0_pReal
do k = 1_pInt , res ( 3 ) ; do j = 1_pInt , res ( 2 ) ; do i = 1_pInt , res ( 1 )
deviator = tensor ( i , j , k , 1 : 3 , 1 : 3 ) - 1.0_pReal / 3.0_pReal * tensor ( i , j , k , 1 , 1 ) * tensor ( i , j , k , 2 , 2 ) * tensor ( i , j , k , 3 , 3 ) * delta
J_2 = deviator ( 1 , 1 ) * deviator ( 2 , 2 ) &
+ deviator ( 2 , 2 ) * deviator ( 3 , 3 ) &
+ deviator ( 1 , 1 ) * deviator ( 3 , 3 ) &
- ( deviator ( 1 , 2 ) ) ** 2.0_pReal &
- ( deviator ( 2 , 3 ) ) ** 2.0_pReal &
- ( deviator ( 1 , 3 ) ) ** 2.0_pReal
vm ( i , j , k ) = sqrt ( 3.0_pReal * J_2 )
enddo ; enddo ; enddo
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end subroutine math_equivStrain33_field
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2011-07-29 21:27:39 +05:30
2007-03-21 15:50:25 +05:30
!********************************************************************
2012-01-26 19:20:00 +05:30
! determinant of a 33 matrix
2007-03-21 15:50:25 +05:30
!********************************************************************
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pure function math_det33 ( m )
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implicit none
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2009-01-16 20:57:13 +05:30
real ( pReal ) , dimension ( 3 , 3 ) , intent ( in ) :: m
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real ( pReal ) :: math_det33
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2012-01-26 19:20:00 +05:30
math_det33 = m ( 1 , 1 ) * ( m ( 2 , 2 ) * m ( 3 , 3 ) - m ( 2 , 3 ) * m ( 3 , 2 ) ) &
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- m ( 1 , 2 ) * ( m ( 2 , 1 ) * m ( 3 , 3 ) - m ( 2 , 3 ) * m ( 3 , 1 ) ) &
+ m ( 1 , 3 ) * ( m ( 2 , 1 ) * m ( 3 , 2 ) - m ( 2 , 2 ) * m ( 3 , 1 ) )
2007-03-20 19:25:22 +05:30
2012-03-09 01:55:28 +05:30
end function math_det33
2007-03-21 15:50:25 +05:30
2009-08-11 22:01:57 +05:30
2011-07-29 21:27:39 +05:30
!********************************************************************
2012-01-26 19:20:00 +05:30
! norm of a 33 matrix
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!********************************************************************
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pure function math_norm33 ( m )
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implicit none
real ( pReal ) , dimension ( 3 , 3 ) , intent ( in ) :: m
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real ( pReal ) :: math_norm33
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math_norm33 = sqrt ( sum ( m ** 2.0_pReal ) )
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end function
2011-07-29 21:27:39 +05:30
2009-08-11 22:01:57 +05:30
!********************************************************************
2012-01-26 19:20:00 +05:30
! euclidic norm of a 3 vector
2009-08-11 22:01:57 +05:30
!********************************************************************
2012-03-09 01:55:28 +05:30
pure function math_norm3 ( v )
2007-03-21 15:50:25 +05:30
2009-08-11 22:01:57 +05:30
implicit none
2010-03-18 17:53:17 +05:30
real ( pReal ) , dimension ( 3 ) , intent ( in ) :: v
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real ( pReal ) :: math_norm3
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2011-02-25 14:55:53 +05:30
math_norm3 = sqrt ( v ( 1 ) * v ( 1 ) + v ( 2 ) * v ( 2 ) + v ( 3 ) * v ( 3 ) )
2009-08-11 22:01:57 +05:30
2012-03-09 01:55:28 +05:30
end function math_norm3
2009-08-11 22:01:57 +05:30
2008-02-15 18:12:27 +05:30
!********************************************************************
2012-01-26 19:20:00 +05:30
! convert 33 matrix into vector 9
2008-02-15 18:12:27 +05:30
!********************************************************************
2012-03-09 01:55:28 +05:30
pure function math_Plain33to9 ( m33 )
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implicit none
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real ( pReal ) , dimension ( 3 , 3 ) , intent ( in ) :: m33
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real ( pReal ) , dimension ( 9 ) :: math_Plain33to9
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integer ( pInt ) :: i
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2011-12-01 17:31:13 +05:30
forall ( i = 1_pInt : 9_pInt ) math_Plain33to9 ( i ) = m33 ( mapPlain ( 1 , i ) , mapPlain ( 2 , i ) )
2008-02-15 18:12:27 +05:30
2012-03-09 01:55:28 +05:30
end function math_Plain33to9
2011-08-26 19:36:37 +05:30
2008-02-15 18:12:27 +05:30
!********************************************************************
2012-01-26 19:20:00 +05:30
! convert Plain 9 back to 33 matrix
2008-02-15 18:12:27 +05:30
!********************************************************************
2012-03-09 01:55:28 +05:30
pure function math_Plain9to33 ( v9 )
2008-02-15 18:12:27 +05:30
implicit none
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real ( pReal ) , dimension ( 9 ) , intent ( in ) :: v9
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real ( pReal ) , dimension ( 3 , 3 ) :: math_Plain9to33
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integer ( pInt ) :: i
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2011-12-01 17:31:13 +05:30
forall ( i = 1_pInt : 9_pInt ) math_Plain9to33 ( mapPlain ( 1 , i ) , mapPlain ( 2 , i ) ) = v9 ( i )
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2012-03-09 01:55:28 +05:30
end function math_Plain9to33
2008-02-15 18:12:27 +05:30
2007-03-28 12:51:47 +05:30
!********************************************************************
2012-01-26 19:20:00 +05:30
! convert symmetric 33 matrix into Mandel vector 6
2007-03-28 12:51:47 +05:30
!********************************************************************
2012-03-09 01:55:28 +05:30
pure function math_Mandel33to6 ( m33 )
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implicit none
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real ( pReal ) , dimension ( 3 , 3 ) , intent ( in ) :: m33
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real ( pReal ) , dimension ( 6 ) :: math_Mandel33to6
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integer ( pInt ) :: i
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2011-12-01 17:31:13 +05:30
forall ( i = 1_pInt : 6_pInt ) math_Mandel33to6 ( i ) = nrmMandel ( i ) * m33 ( mapMandel ( 1 , i ) , mapMandel ( 2 , i ) )
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2012-03-09 01:55:28 +05:30
end function math_Mandel33to6
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!********************************************************************
2012-01-26 19:20:00 +05:30
! convert Mandel 6 back to symmetric 33 matrix
2007-03-28 12:51:47 +05:30
!********************************************************************
2012-03-09 01:55:28 +05:30
pure function math_Mandel6to33 ( v6 )
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implicit none
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real ( pReal ) , dimension ( 6 ) , intent ( in ) :: v6
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real ( pReal ) , dimension ( 3 , 3 ) :: math_Mandel6to33
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integer ( pInt ) :: i
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forall ( i = 1_pInt : 6_pInt )
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math_Mandel6to33 ( mapMandel ( 1 , i ) , mapMandel ( 2 , i ) ) = invnrmMandel ( i ) * v6 ( i )
math_Mandel6to33 ( mapMandel ( 2 , i ) , mapMandel ( 1 , i ) ) = invnrmMandel ( i ) * v6 ( i )
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end forall
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end function math_Mandel6to33
2007-03-28 12:51:47 +05:30
2008-02-15 18:12:27 +05:30
!********************************************************************
2012-01-26 19:20:00 +05:30
! convert 3333 tensor into plain matrix 99
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!********************************************************************
2012-03-09 01:55:28 +05:30
pure function math_Plain3333to99 ( m3333 )
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implicit none
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real ( pReal ) , dimension ( 3 , 3 , 3 , 3 ) , intent ( in ) :: m3333
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real ( pReal ) , dimension ( 9 , 9 ) :: math_Plain3333to99
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integer ( pInt ) :: i , j
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2011-12-01 17:31:13 +05:30
forall ( i = 1_pInt : 9_pInt , j = 1_pInt : 9_pInt ) math_Plain3333to99 ( i , j ) = &
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m3333 ( mapPlain ( 1 , i ) , mapPlain ( 2 , i ) , mapPlain ( 1 , j ) , mapPlain ( 2 , j ) )
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end function math_Plain3333to99
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!********************************************************************
2012-01-26 19:20:00 +05:30
! plain matrix 99 into 3333 tensor
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!********************************************************************
2012-03-09 01:55:28 +05:30
pure function math_Plain99to3333 ( m99 )
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implicit none
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2010-09-22 17:34:43 +05:30
real ( pReal ) , dimension ( 9 , 9 ) , intent ( in ) :: m99
real ( pReal ) , dimension ( 3 , 3 , 3 , 3 ) :: math_Plain99to3333
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integer ( pInt ) :: i , j
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2011-12-01 17:31:13 +05:30
forall ( i = 1_pInt : 9_pInt , j = 1_pInt : 9_pInt ) math_Plain99to3333 ( mapPlain ( 1 , i ) , mapPlain ( 2 , i ) , &
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mapPlain ( 1 , j ) , mapPlain ( 2 , j ) ) = m99 ( i , j )
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end function math_Plain99to3333
2008-02-15 18:12:27 +05:30
2011-07-29 21:27:39 +05:30
!********************************************************************
2012-01-26 19:20:00 +05:30
! convert Mandel matrix 66 into Plain matrix 66
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!********************************************************************
2012-03-09 01:55:28 +05:30
pure function math_Mandel66toPlain66 ( m66 )
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implicit none
real ( pReal ) , dimension ( 6 , 6 ) , intent ( in ) :: m66
real ( pReal ) , dimension ( 6 , 6 ) :: math_Mandel66toPlain66
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integer ( pInt ) :: i , j
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2011-12-01 17:31:13 +05:30
forall ( i = 1_pInt : 6_pInt , j = 1_pInt : 6_pInt ) &
2011-07-29 21:27:39 +05:30
math_Mandel66toPlain66 ( i , j ) = invnrmMandel ( i ) * invnrmMandel ( j ) * m66 ( i , j )
return
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end function
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!********************************************************************
2012-01-26 19:20:00 +05:30
! convert Plain matrix 66 into Mandel matrix 66
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!********************************************************************
2012-03-09 01:55:28 +05:30
pure function math_Plain66toMandel66 ( m66 )
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implicit none
real ( pReal ) , dimension ( 6 , 6 ) , intent ( in ) :: m66
real ( pReal ) , dimension ( 6 , 6 ) :: math_Plain66toMandel66
integer ( pInt ) i , j
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forall ( i = 1_pInt : 6_pInt , j = 1_pInt : 6_pInt ) &
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math_Plain66toMandel66 ( i , j ) = nrmMandel ( i ) * nrmMandel ( j ) * m66 ( i , j )
return
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end function
2011-07-29 21:27:39 +05:30
2007-03-28 12:51:47 +05:30
!********************************************************************
2012-01-26 19:20:00 +05:30
! convert symmetric 3333 tensor into Mandel matrix 66
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!********************************************************************
2012-03-09 01:55:28 +05:30
pure function math_Mandel3333to66 ( m3333 )
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implicit none
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real ( pReal ) , dimension ( 3 , 3 , 3 , 3 ) , intent ( in ) :: m3333
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real ( pReal ) , dimension ( 6 , 6 ) :: math_Mandel3333to66
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integer ( pInt ) :: i , j
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2011-12-01 17:31:13 +05:30
forall ( i = 1_pInt : 6_pInt , j = 1_pInt : 6_pInt ) math_Mandel3333to66 ( i , j ) = &
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nrmMandel ( i ) * nrmMandel ( j ) * m3333 ( mapMandel ( 1 , i ) , mapMandel ( 2 , i ) , mapMandel ( 1 , j ) , mapMandel ( 2 , j ) )
2007-03-28 12:51:47 +05:30
2012-03-09 01:55:28 +05:30
end function math_Mandel3333to66
2010-05-06 19:37:21 +05:30
2011-12-01 17:31:13 +05:30
2008-02-15 18:12:27 +05:30
!********************************************************************
2012-01-26 19:20:00 +05:30
! convert Mandel matrix 66 back to symmetric 3333 tensor
2008-02-15 18:12:27 +05:30
!********************************************************************
2012-03-09 01:55:28 +05:30
pure function math_Mandel66to3333 ( m66 )
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implicit none
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real ( pReal ) , dimension ( 6 , 6 ) , intent ( in ) :: m66
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real ( pReal ) , dimension ( 3 , 3 , 3 , 3 ) :: math_Mandel66to3333
2011-12-01 17:31:13 +05:30
integer ( pInt ) :: i , j
2008-02-15 18:12:27 +05:30
2011-12-01 17:31:13 +05:30
forall ( i = 1_pInt : 6_pInt , j = 1_pInt : 6_pInt )
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math_Mandel66to3333 ( mapMandel ( 1 , i ) , mapMandel ( 2 , i ) , mapMandel ( 1 , j ) , mapMandel ( 2 , j ) ) = invnrmMandel ( i ) * invnrmMandel ( j ) * m66 ( i , j )
math_Mandel66to3333 ( mapMandel ( 2 , i ) , mapMandel ( 1 , i ) , mapMandel ( 1 , j ) , mapMandel ( 2 , j ) ) = invnrmMandel ( i ) * invnrmMandel ( j ) * m66 ( i , j )
math_Mandel66to3333 ( mapMandel ( 1 , i ) , mapMandel ( 2 , i ) , mapMandel ( 2 , j ) , mapMandel ( 1 , j ) ) = invnrmMandel ( i ) * invnrmMandel ( j ) * m66 ( i , j )
math_Mandel66to3333 ( mapMandel ( 2 , i ) , mapMandel ( 1 , i ) , mapMandel ( 2 , j ) , mapMandel ( 1 , j ) ) = invnrmMandel ( i ) * invnrmMandel ( j ) * m66 ( i , j )
end forall
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end function math_Mandel66to3333
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!********************************************************************
2012-01-26 19:20:00 +05:30
! convert Voigt matrix 66 back to symmetric 3333 tensor
2008-02-15 18:12:27 +05:30
!********************************************************************
2012-03-09 01:55:28 +05:30
pure function math_Voigt66to3333 ( m66 )
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implicit none
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real ( pReal ) , dimension ( 6 , 6 ) , intent ( in ) :: m66
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real ( pReal ) , dimension ( 3 , 3 , 3 , 3 ) :: math_Voigt66to3333
2011-12-01 17:31:13 +05:30
integer ( pInt ) :: i , j
2008-02-15 18:12:27 +05:30
2011-12-01 17:31:13 +05:30
forall ( i = 1_pInt : 6_pInt , j = 1_pInt : 6_pInt )
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math_Voigt66to3333 ( mapVoigt ( 1 , i ) , mapVoigt ( 2 , i ) , mapVoigt ( 1 , j ) , mapVoigt ( 2 , j ) ) = invnrmVoigt ( i ) * invnrmVoigt ( j ) * m66 ( i , j )
math_Voigt66to3333 ( mapVoigt ( 2 , i ) , mapVoigt ( 1 , i ) , mapVoigt ( 1 , j ) , mapVoigt ( 2 , j ) ) = invnrmVoigt ( i ) * invnrmVoigt ( j ) * m66 ( i , j )
math_Voigt66to3333 ( mapVoigt ( 1 , i ) , mapVoigt ( 2 , i ) , mapVoigt ( 2 , j ) , mapVoigt ( 1 , j ) ) = invnrmVoigt ( i ) * invnrmVoigt ( j ) * m66 ( i , j )
math_Voigt66to3333 ( mapVoigt ( 2 , i ) , mapVoigt ( 1 , i ) , mapVoigt ( 2 , j ) , mapVoigt ( 1 , j ) ) = invnrmVoigt ( i ) * invnrmVoigt ( j ) * m66 ( i , j )
end forall
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end function math_Voigt66to3333
2008-02-15 18:12:27 +05:30
2007-03-21 15:50:25 +05:30
!********************************************************************
2010-05-06 19:37:21 +05:30
! Euler angles (in radians) from rotation matrix
2007-03-21 15:50:25 +05:30
!********************************************************************
2012-03-09 01:55:28 +05:30
pure function math_RtoEuler ( R )
2007-03-20 19:25:22 +05:30
implicit none
2009-01-20 00:40:58 +05:30
2009-01-16 20:57:13 +05:30
real ( pReal ) , dimension ( 3 , 3 ) , intent ( in ) :: R
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real ( pReal ) , dimension ( 3 ) :: math_RtoEuler
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real ( pReal ) :: sqhkl , squvw , sqhk , myVal
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sqhkl = sqrt ( R ( 1 , 3 ) * R ( 1 , 3 ) + R ( 2 , 3 ) * R ( 2 , 3 ) + R ( 3 , 3 ) * R ( 3 , 3 ) )
squvw = sqrt ( R ( 1 , 1 ) * R ( 1 , 1 ) + R ( 2 , 1 ) * R ( 2 , 1 ) + R ( 3 , 1 ) * R ( 3 , 1 ) )
sqhk = sqrt ( R ( 1 , 3 ) * R ( 1 , 3 ) + R ( 2 , 3 ) * R ( 2 , 3 ) )
! calculate PHI
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myVal = R ( 3 , 3 ) / sqhkl
2007-03-29 21:02:52 +05:30
2012-03-09 01:55:28 +05:30
if ( myVal > 1.0_pReal ) myVal = 1.0_pReal
if ( myVal < - 1.0_pReal ) myVal = - 1.0_pReal
2007-03-29 21:02:52 +05:30
2012-03-09 01:55:28 +05:30
math_RtoEuler ( 2 ) = acos ( myVal )
2007-03-21 15:50:25 +05:30
2010-05-26 21:22:54 +05:30
if ( math_RtoEuler ( 2 ) < 1.0e-8_pReal ) then
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! calculate phi2
math_RtoEuler ( 3 ) = 0.0_pReal
! calculate phi1
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myVal = R ( 1 , 1 ) / squvw
if ( myVal > 1.0_pReal ) myVal = 1.0_pReal
if ( myVal < - 1.0_pReal ) myVal = - 1.0_pReal
2007-03-29 21:02:52 +05:30
2012-03-09 01:55:28 +05:30
math_RtoEuler ( 1 ) = acos ( myVal )
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if ( R ( 2 , 1 ) > 0.0_pReal ) math_RtoEuler ( 1 ) = 2.0_pReal * pi - math_RtoEuler ( 1 )
else
! calculate phi2
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myVal = R ( 2 , 3 ) / sqhk
if ( myVal > 1.0_pReal ) myVal = 1.0_pReal
if ( myVal < - 1.0_pReal ) myVal = - 1.0_pReal
2007-03-29 21:02:52 +05:30
2012-03-09 01:55:28 +05:30
math_RtoEuler ( 3 ) = acos ( myVal )
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if ( R ( 1 , 3 ) < 0.0 ) math_RtoEuler ( 3 ) = 2.0_pReal * pi - math_RtoEuler ( 3 )
! calculate phi1
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myVal = - R ( 3 , 2 ) / sin ( math_RtoEuler ( 2 ) )
if ( myVal > 1.0_pReal ) myVal = 1.0_pReal
if ( myVal < - 1.0_pReal ) myVal = - 1.0_pReal
2007-03-29 21:02:52 +05:30
2012-03-09 01:55:28 +05:30
math_RtoEuler ( 1 ) = acos ( myVal )
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if ( R ( 3 , 1 ) < 0.0 ) math_RtoEuler ( 1 ) = 2.0_pReal * pi - math_RtoEuler ( 1 )
end if
2012-03-09 01:55:28 +05:30
end function math_RtoEuler
2010-05-06 19:37:21 +05:30
!********************************************************************
! quaternion (w+ix+jy+kz) from orientation matrix
!********************************************************************
2011-12-01 17:31:13 +05:30
! math adopted from http://code.google.com/p/mtex/source/browse/trunk/geometry/geometry_tools/mat2quat.m
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pure function math_RtoQuaternion ( R )
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implicit none
real ( pReal ) , dimension ( 3 , 3 ) , intent ( in ) :: R
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real ( pReal ) , dimension ( 4 ) :: absQ , math_RtoQuaternion
real ( pReal ) :: max_absQ
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integer , dimension ( 1 ) :: largest !no pInt, maxloc returns integer default
2010-05-26 21:22:54 +05:30
2011-03-03 16:17:07 +05:30
absQ ( 1 ) = 1.0_pReal + R ( 1 , 1 ) + R ( 2 , 2 ) + R ( 3 , 3 )
absQ ( 2 ) = 1.0_pReal + R ( 1 , 1 ) - R ( 2 , 2 ) - R ( 3 , 3 )
absQ ( 3 ) = 1.0_pReal - R ( 1 , 1 ) + R ( 2 , 2 ) - R ( 3 , 3 )
absQ ( 4 ) = 1.0_pReal - R ( 1 , 1 ) - R ( 2 , 2 ) + R ( 3 , 3 )
2011-12-01 17:31:13 +05:30
math_RtoQuaternion = 0.0_pReal
2011-03-03 16:17:07 +05:30
2010-05-26 21:22:54 +05:30
largest = maxloc ( absQ )
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max_absQ = 0.5_pReal * sqrt ( absQ ( largest ( 1 ) ) )
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select case ( largest ( 1 ) )
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case ( 1_pInt )
!1----------------------------------
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math_RtoQuaternion ( 2 ) = R ( 2 , 3 ) - R ( 3 , 2 )
math_RtoQuaternion ( 3 ) = R ( 3 , 1 ) - R ( 1 , 3 )
math_RtoQuaternion ( 4 ) = R ( 1 , 2 ) - R ( 2 , 1 )
2011-12-01 17:31:13 +05:30
case ( 2_pInt )
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math_RtoQuaternion ( 1 ) = R ( 2 , 3 ) - R ( 3 , 2 )
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!2----------------------------------
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math_RtoQuaternion ( 3 ) = R ( 1 , 2 ) + R ( 2 , 1 )
math_RtoQuaternion ( 4 ) = R ( 3 , 1 ) + R ( 1 , 3 )
2011-12-01 17:31:13 +05:30
case ( 3_pInt )
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math_RtoQuaternion ( 1 ) = R ( 3 , 1 ) - R ( 1 , 3 )
math_RtoQuaternion ( 2 ) = R ( 1 , 2 ) + R ( 2 , 1 )
2011-12-01 17:31:13 +05:30
!3----------------------------------
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math_RtoQuaternion ( 4 ) = R ( 2 , 3 ) + R ( 3 , 2 )
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case ( 4_pInt )
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math_RtoQuaternion ( 1 ) = R ( 1 , 2 ) - R ( 2 , 1 )
math_RtoQuaternion ( 2 ) = R ( 3 , 1 ) + R ( 1 , 3 )
math_RtoQuaternion ( 3 ) = R ( 3 , 2 ) + R ( 2 , 3 )
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!4----------------------------------
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end select
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math_RtoQuaternion = math_RtoQuaternion * 0.25_pReal / max_absQ
math_RtoQuaternion ( largest ( 1 ) ) = max_absQ
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2012-03-09 01:55:28 +05:30
end function math_RtoQuaternion
2007-03-21 15:50:25 +05:30
2010-03-18 17:53:17 +05:30
!****************************************************************
2010-05-06 19:37:21 +05:30
! rotation matrix from Euler angles (in radians)
2010-03-18 17:53:17 +05:30
!****************************************************************
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pure function math_EulerToR ( Euler )
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implicit none
real ( pReal ) , dimension ( 3 ) , intent ( in ) :: Euler
real ( pReal ) , dimension ( 3 , 3 ) :: math_EulerToR
real ( pReal ) c1 , c , c2 , s1 , s , s2
2011-02-25 14:55:53 +05:30
C1 = cos ( Euler ( 1 ) )
C = cos ( Euler ( 2 ) )
C2 = cos ( Euler ( 3 ) )
S1 = sin ( Euler ( 1 ) )
S = sin ( Euler ( 2 ) )
S2 = sin ( Euler ( 3 ) )
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2010-03-18 17:53:17 +05:30
math_EulerToR ( 1 , 1 ) = C1 * C2 - S1 * S2 * C
math_EulerToR ( 1 , 2 ) = S1 * C2 + C1 * S2 * C
math_EulerToR ( 1 , 3 ) = S2 * S
math_EulerToR ( 2 , 1 ) = - C1 * S2 - S1 * C2 * C
math_EulerToR ( 2 , 2 ) = - S1 * S2 + C1 * C2 * C
math_EulerToR ( 2 , 3 ) = C2 * S
math_EulerToR ( 3 , 1 ) = S1 * S
math_EulerToR ( 3 , 2 ) = - C1 * S
math_EulerToR ( 3 , 3 ) = C
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end function math_EulerToR
2011-12-01 17:31:13 +05:30
2010-03-18 17:53:17 +05:30
!********************************************************************
2010-05-06 19:37:21 +05:30
! quaternion (w+ix+jy+kz) from 3-1-3 Euler angles (in radians)
2010-03-18 17:53:17 +05:30
!********************************************************************
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pure function math_EulerToQuaternion ( eulerangles )
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implicit none
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real ( pReal ) , dimension ( 3 ) , intent ( in ) :: eulerangles
real ( pReal ) , dimension ( 4 ) :: math_EulerToQuaternion
real ( pReal ) , dimension ( 3 ) :: halfangles
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real ( pReal ) :: c , s
2010-03-18 17:53:17 +05:30
2010-05-06 19:37:21 +05:30
halfangles = 0.5_pReal * eulerangles
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2011-02-25 14:55:53 +05:30
c = cos ( halfangles ( 2 ) )
s = sin ( halfangles ( 2 ) )
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2011-02-25 14:55:53 +05:30
math_EulerToQuaternion ( 1 ) = cos ( halfangles ( 1 ) + halfangles ( 3 ) ) * c
math_EulerToQuaternion ( 2 ) = cos ( halfangles ( 1 ) - halfangles ( 3 ) ) * s
math_EulerToQuaternion ( 3 ) = sin ( halfangles ( 1 ) - halfangles ( 3 ) ) * s
math_EulerToQuaternion ( 4 ) = sin ( halfangles ( 1 ) + halfangles ( 3 ) ) * c
2010-05-06 19:37:21 +05:30
2012-03-09 01:55:28 +05:30
end function math_EulerToQuaternion
2010-03-18 17:53:17 +05:30
2010-05-06 19:37:21 +05:30
!****************************************************************
! rotation matrix from axis and angle (in radians)
!****************************************************************
2012-03-09 01:55:28 +05:30
pure function math_AxisAngleToR ( axis , omega )
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implicit none
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real ( pReal ) , dimension ( 3 ) , intent ( in ) :: axis
real ( pReal ) , intent ( in ) :: omega
real ( pReal ) , dimension ( 3 ) :: axisNrm
real ( pReal ) , dimension ( 3 , 3 ) :: math_AxisAngleToR
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real ( pReal ) :: norm , s , c , c1
integer ( pInt ) :: i
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2011-02-25 14:55:53 +05:30
norm = sqrt ( math_mul3x3 ( axis , axis ) )
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if ( norm > 1.0e-8_pReal ) then ! non-zero rotation
forall ( i = 1_pInt : 3_pInt ) axisNrm ( i ) = axis ( i ) / norm ! normalize axis to be sure
2010-05-06 19:37:21 +05:30
2011-02-25 14:55:53 +05:30
s = sin ( omega )
c = cos ( omega )
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c1 = 1.0_pReal - c
! formula for active rotation taken from http://mathworld.wolfram.com/RodriguesRotationFormula.html
! below is transposed form to get passive rotation
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math_AxisAngleToR ( 1 , 1 ) = c + c1 * axisNrm ( 1 ) ** 2.0_pReal
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math_AxisAngleToR ( 2 , 1 ) = - s * axisNrm ( 3 ) + c1 * axisNrm ( 1 ) * axisNrm ( 2 )
math_AxisAngleToR ( 3 , 1 ) = s * axisNrm ( 2 ) + c1 * axisNrm ( 1 ) * axisNrm ( 3 )
math_AxisAngleToR ( 1 , 2 ) = s * axisNrm ( 3 ) + c1 * axisNrm ( 2 ) * axisNrm ( 1 )
2011-12-01 17:31:13 +05:30
math_AxisAngleToR ( 2 , 2 ) = c + c1 * axisNrm ( 2 ) ** 2.0_pReal
2010-05-06 19:37:21 +05:30
math_AxisAngleToR ( 3 , 2 ) = - s * axisNrm ( 1 ) + c1 * axisNrm ( 2 ) * axisNrm ( 3 )
math_AxisAngleToR ( 1 , 3 ) = - s * axisNrm ( 2 ) + c1 * axisNrm ( 3 ) * axisNrm ( 1 )
math_AxisAngleToR ( 2 , 3 ) = s * axisNrm ( 1 ) + c1 * axisNrm ( 3 ) * axisNrm ( 2 )
2011-12-01 17:31:13 +05:30
math_AxisAngleToR ( 3 , 3 ) = c + c1 * axisNrm ( 3 ) ** 2.0_pReal
2010-05-06 19:37:21 +05:30
else
math_AxisAngleToR = math_I3
endif
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2010-05-06 19:37:21 +05:30
2012-03-09 01:55:28 +05:30
end function math_AxisAngleToR
2010-05-06 19:37:21 +05:30
!****************************************************************
! quaternion (w+ix+jy+kz) from axis and angle (in radians)
!****************************************************************
2012-03-09 01:55:28 +05:30
pure function math_AxisAngleToQuaternion ( axis , omega )
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implicit none
real ( pReal ) , dimension ( 3 ) , intent ( in ) :: axis
real ( pReal ) , intent ( in ) :: omega
real ( pReal ) , dimension ( 3 ) :: axisNrm
real ( pReal ) , dimension ( 4 ) :: math_AxisAngleToQuaternion
2011-12-01 17:31:13 +05:30
real ( pReal ) :: s , c , norm
integer ( pInt ) :: i
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2011-02-25 14:55:53 +05:30
norm = sqrt ( math_mul3x3 ( axis , axis ) )
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if ( norm > 1.0e-8_pReal ) then ! non-zero rotation
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forall ( i = 1_pInt : 3_pInt ) axisNrm ( i ) = axis ( i ) / norm ! normalize axis to be sure
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! formula taken from http://en.wikipedia.org/wiki/Rotation_representation_%28mathematics%29#Rodrigues_parameters
2011-02-25 14:55:53 +05:30
s = sin ( omega / 2.0_pReal )
c = cos ( omega / 2.0_pReal )
2010-05-06 19:37:21 +05:30
math_AxisAngleToQuaternion ( 1 ) = c
math_AxisAngleToQuaternion ( 2 : 4 ) = s * axisNrm ( 1 : 3 )
else
math_AxisAngleToQuaternion = ( / 1.0_pReal , 0.0_pReal , 0.0_pReal , 0.0_pReal / ) ! no rotation
endif
2012-03-09 01:55:28 +05:30
end function math_AxisAngleToQuaternion
2010-03-18 17:53:17 +05:30
!********************************************************************
! orientation matrix from quaternion (w+ix+jy+kz)
!********************************************************************
2012-03-09 01:55:28 +05:30
pure function math_QuaternionToR ( Q )
2010-03-18 17:53:17 +05:30
implicit none
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real ( pReal ) , dimension ( 4 ) , intent ( in ) :: Q
real ( pReal ) , dimension ( 3 , 3 ) :: math_QuaternionToR , T , S
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integer ( pInt ) :: i , j
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2011-12-01 17:31:13 +05:30
forall ( i = 1_pInt : 3_pInt , j = 1_pInt : 3_pInt ) &
T ( i , j ) = Q ( i + 1_pInt ) * Q ( j + 1_pInt )
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S = reshape ( ( / 0.0_pReal , Q ( 4 ) , - Q ( 3 ) , &
- Q ( 4 ) , 0.0_pReal , + Q ( 2 ) , &
Q ( 3 ) , - Q ( 2 ) , 0.0_pReal / ) , ( / 3 , 3 / ) ) ! notation is transposed!
math_QuaternionToR = ( 2.0_pReal * Q ( 1 ) * Q ( 1 ) - 1.0_pReal ) * math_I3 + &
2.0_pReal * T - &
2.0_pReal * Q ( 1 ) * S
2011-12-01 17:31:13 +05:30
2012-03-09 01:55:28 +05:30
end function math_QuaternionToR
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!********************************************************************
2010-05-06 19:37:21 +05:30
! 3-1-3 Euler angles (in radians) from quaternion (w+ix+jy+kz)
2010-03-18 17:53:17 +05:30
!********************************************************************
2012-03-09 01:55:28 +05:30
pure function math_QuaternionToEuler ( Q )
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implicit none
real ( pReal ) , dimension ( 4 ) , intent ( in ) :: Q
real ( pReal ) , dimension ( 3 ) :: math_QuaternionToEuler
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real ( pReal ) :: acos_arg
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2011-02-25 14:55:53 +05:30
math_QuaternionToEuler ( 2 ) = acos ( 1.0_pReal - 2.0_pReal * ( Q ( 2 ) * Q ( 2 ) + Q ( 3 ) * Q ( 3 ) ) )
2010-05-06 19:37:21 +05:30
2011-02-25 14:55:53 +05:30
if ( abs ( math_QuaternionToEuler ( 2 ) ) < 1.0e-3_pReal ) then
2011-03-03 19:53:39 +05:30
acos_arg = Q ( 1 )
if ( acos_arg > 1.0_pReal ) acos_arg = 1.0_pReal
if ( acos_arg < - 1.0_pReal ) acos_arg = - 1.0_pReal
math_QuaternionToEuler ( 1 ) = 2.0_pReal * acos ( acos_arg )
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math_QuaternionToEuler ( 3 ) = 0.0_pReal
else
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math_QuaternionToEuler ( 1 ) = atan2 ( Q ( 1 ) * Q ( 3 ) + Q ( 2 ) * Q ( 4 ) , Q ( 1 ) * Q ( 2 ) - Q ( 3 ) * Q ( 4 ) )
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if ( math_QuaternionToEuler ( 1 ) < 0.0_pReal ) &
math_QuaternionToEuler ( 1 ) = math_QuaternionToEuler ( 1 ) + 2.0_pReal * pi
2011-02-25 14:55:53 +05:30
math_QuaternionToEuler ( 3 ) = atan2 ( - Q ( 1 ) * Q ( 3 ) + Q ( 2 ) * Q ( 4 ) , Q ( 1 ) * Q ( 2 ) + Q ( 3 ) * Q ( 4 ) )
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if ( math_QuaternionToEuler ( 3 ) < 0.0_pReal ) &
math_QuaternionToEuler ( 3 ) = math_QuaternionToEuler ( 3 ) + 2.0_pReal * pi
endif
2010-03-19 21:41:53 +05:30
if ( math_QuaternionToEuler ( 2 ) < 0.0_pReal ) &
math_QuaternionToEuler ( 2 ) = math_QuaternionToEuler ( 2 ) + pi
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end function math_QuaternionToEuler
2010-03-18 17:53:17 +05:30
2010-04-12 16:37:25 +05:30
!********************************************************************
2010-05-06 19:37:21 +05:30
! axis-angle (x, y, z, ang in radians) from quaternion (w+ix+jy+kz)
2010-04-12 16:37:25 +05:30
!********************************************************************
2012-03-09 01:55:28 +05:30
pure function math_QuaternionToAxisAngle ( Q )
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implicit none
real ( pReal ) , dimension ( 4 ) , intent ( in ) :: Q
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real ( pReal ) :: halfAngle , sinHalfAngle
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real ( pReal ) , dimension ( 4 ) :: math_QuaternionToAxisAngle
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halfAngle = acos ( max ( - 1.0_pReal , min ( 1.0_pReal , Q ( 1 ) ) ) ) ! limit to [-1,1] --> 0 to 180 deg
sinHalfAngle = sin ( halfAngle )
2010-04-29 15:31:09 +05:30
2010-05-06 19:37:21 +05:30
if ( sinHalfAngle < = 1.0e-4_pReal ) then ! very small rotation angle?
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math_QuaternionToAxisAngle = 0.0_pReal
else
math_QuaternionToAxisAngle ( 1 : 3 ) = Q ( 2 : 4 ) / sinHalfAngle
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math_QuaternionToAxisAngle ( 4 ) = halfAngle * 2.0_pReal
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endif
2011-08-01 15:41:32 +05:30
2012-03-09 01:55:28 +05:30
end function math_QuaternionToAxisAngle
2010-05-06 19:37:21 +05:30
2010-04-12 16:37:25 +05:30
2010-04-28 22:49:58 +05:30
!********************************************************************
2010-05-06 19:37:21 +05:30
! Rodrigues vector (x, y, z) from unit quaternion (w+ix+jy+kz)
2010-04-28 22:49:58 +05:30
!********************************************************************
2012-03-09 01:55:28 +05:30
pure function math_QuaternionToRodrig ( Q )
2010-04-28 22:49:58 +05:30
2011-12-01 17:31:13 +05:30
use prec , only : DAMASK_NaN
2010-04-28 22:49:58 +05:30
implicit none
real ( pReal ) , dimension ( 4 ) , intent ( in ) :: Q
real ( pReal ) , dimension ( 3 ) :: math_QuaternionToRodrig
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if ( Q ( 1 ) / = 0.0_pReal ) then ! unless rotation by 180 deg
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math_QuaternionToRodrig = Q ( 2 : 4 ) / Q ( 1 )
else
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math_QuaternionToRodrig = DAMASK_NaN ! NaN since Rodrig is unbound for 180 deg...
2010-04-28 22:49:58 +05:30
endif
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end function math_QuaternionToRodrig
2007-03-20 19:25:22 +05:30
2007-03-29 21:02:52 +05:30
!**************************************************************************
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! misorientation angle between two sets of Euler angles
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!**************************************************************************
2012-03-09 01:55:28 +05:30
pure function math_EulerMisorientation ( EulerA , EulerB )
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2007-03-20 19:25:22 +05:30
implicit none
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real ( pReal ) , dimension ( 3 ) , intent ( in ) :: EulerA , EulerB
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real ( pReal ) , dimension ( 3 , 3 ) :: r
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real ( pReal ) :: math_EulerMisorientation , tr
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2008-07-23 18:19:40 +05:30
r = math_mul33x33 ( math_EulerToR ( EulerB ) , transpose ( math_EulerToR ( EulerA ) ) )
2008-07-09 01:08:22 +05:30
2007-03-29 21:02:52 +05:30
tr = ( r ( 1 , 1 ) + r ( 2 , 2 ) + r ( 3 , 3 ) - 1.0_pReal ) * 0.4999999_pReal
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math_EulerMisorientation = abs ( 0.5_pReal * pi - asin ( tr ) )
2007-03-20 19:25:22 +05:30
2012-03-09 01:55:28 +05:30
end function math_EulerMisorientation
2010-05-06 19:37:21 +05:30
2007-03-20 19:25:22 +05:30
2010-04-28 22:49:58 +05:30
!**************************************************************************
2010-05-06 19:37:21 +05:30
! figures whether unit quat falls into stereographic standard triangle
2010-04-28 22:49:58 +05:30
!**************************************************************************
pure function math_QuaternionInSST ( Q , symmetryType )
implicit none
!*** input variables
real ( pReal ) , dimension ( 4 ) , intent ( in ) :: Q ! orientation
integer ( pInt ) , intent ( in ) :: symmetryType ! Type of crystal symmetry; 1:cubic, 2:hexagonal
!*** output variables
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logical :: math_QuaternionInSST
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!*** local variables
real ( pReal ) , dimension ( 3 ) :: Rodrig ! Rodrigues vector of Q
Rodrig = math_QuaternionToRodrig ( Q )
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if ( any ( Rodrig / = Rodrig ) ) then
math_QuaternionInSST = . false .
else
select case ( symmetryType )
case ( 1_pInt )
math_QuaternionInSST = Rodrig ( 1 ) > Rodrig ( 2 ) . and . &
Rodrig ( 2 ) > Rodrig ( 3 ) . and . &
Rodrig ( 3 ) > 0.0_pReal
case ( 2_pInt )
math_QuaternionInSST = Rodrig ( 1 ) > sqrt ( 3.0_pReal ) * Rodrig ( 2 ) . and . &
Rodrig ( 2 ) > 0.0_pReal . and . &
Rodrig ( 3 ) > 0.0_pReal
case default
math_QuaternionInSST = . true .
end select
endif
2010-04-28 22:49:58 +05:30
2012-03-09 01:55:28 +05:30
end function math_QuaternionInSST
2010-04-28 22:49:58 +05:30
2010-05-04 18:24:13 +05:30
2010-04-28 22:49:58 +05:30
!**************************************************************************
2010-05-06 19:37:21 +05:30
! calculates the disorientation for 2 unit quaternions
2010-04-28 22:49:58 +05:30
!**************************************************************************
2010-05-04 21:32:05 +05:30
function math_QuaternionDisorientation ( Q1 , Q2 , symmetryType )
2010-04-28 22:49:58 +05:30
2010-05-04 21:32:05 +05:30
use IO , only : IO_error
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implicit none
!*** input variables
real ( pReal ) , dimension ( 4 ) , intent ( in ) :: Q1 , & ! 1st orientation
Q2 ! 2nd orientation
integer ( pInt ) , intent ( in ) :: symmetryType ! Type of crystal symmetry; 1:cubic, 2:hexagonal
!*** output variables
real ( pReal ) , dimension ( 4 ) :: math_QuaternionDisorientation ! disorientation
!*** local variables
real ( pReal ) , dimension ( 4 ) :: dQ , dQsymA , mis
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integer ( pInt ) :: i , j , k , s
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dQ = math_qMul ( math_qConj ( Q1 ) , Q2 )
math_QuaternionDisorientation = dQ
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select case ( symmetryType )
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case ( 0_pInt )
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if ( math_QuaternionDisorientation ( 1 ) < 0.0_pReal ) &
math_QuaternionDisorientation = - math_QuaternionDisorientation ! keep omega within 0 to 180 deg
2010-05-04 18:24:13 +05:30
2011-12-01 17:31:13 +05:30
case ( 1_pInt , 2_pInt )
s = sum ( math_NsymOperations ( 1 : symmetryType - 1_pInt ) )
do i = 1_pInt , 2_pInt
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dQ = math_qConj ( dQ ) ! switch order of "from -- to"
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do j = 1_pInt , math_NsymOperations ( symmetryType ) ! run through first crystal's symmetries
dQsymA = math_qMul ( math_symOperations ( 1 : 4 , s + j ) , dQ ) ! apply sym
do k = 1_pInt , math_NsymOperations ( symmetryType ) ! run through 2nd crystal's symmetries
mis = math_qMul ( dQsymA , math_symOperations ( 1 : 4 , s + k ) ) ! apply sym
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if ( mis ( 1 ) < 0.0_pReal ) & ! want positive angle
mis = - mis
if ( mis ( 1 ) - math_QuaternionDisorientation ( 1 ) > - 1e-8_pReal . and . &
math_QuaternionInSST ( mis , symmetryType ) ) &
math_QuaternionDisorientation = mis ! found better one
enddo ; enddo ; enddo
2010-05-04 18:24:13 +05:30
case default
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call IO_error ( 450_pInt , symmetryType ) ! complain about unknown symmetry
2010-05-04 18:24:13 +05:30
end select
2010-04-28 22:49:58 +05:30
2012-03-09 01:55:28 +05:30
end function math_QuaternionDisorientation
2010-04-28 22:49:58 +05:30
2007-03-21 15:50:25 +05:30
!********************************************************************
2007-03-29 21:02:52 +05:30
! draw a random sample from Euler space
2007-03-21 15:50:25 +05:30
!********************************************************************
2012-03-09 01:55:28 +05:30
function math_sampleRandomOri ( )
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2007-03-20 19:25:22 +05:30
implicit none
2007-03-21 15:50:25 +05:30
2007-03-29 21:02:52 +05:30
real ( pReal ) , dimension ( 3 ) :: math_sampleRandomOri , rnd
2007-03-21 15:50:25 +05:30
2011-12-01 17:31:13 +05:30
call halton ( 3_pInt , rnd )
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math_sampleRandomOri ( 1 ) = rnd ( 1 ) * 2.0_pReal * pi
math_sampleRandomOri ( 2 ) = acos ( 2.0_pReal * rnd ( 2 ) - 1.0_pReal )
math_sampleRandomOri ( 3 ) = rnd ( 3 ) * 2.0_pReal * pi
2007-03-20 19:25:22 +05:30
2012-03-09 01:55:28 +05:30
end function math_sampleRandomOri
2007-03-20 19:25:22 +05:30
2007-03-29 21:02:52 +05:30
!********************************************************************
! draw a random sample from Gauss component
! with noise (in radians) half-width
!********************************************************************
2012-03-09 01:55:28 +05:30
function math_sampleGaussOri ( center , noise )
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2007-03-20 19:25:22 +05:30
implicit none
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2007-03-29 21:02:52 +05:30
real ( pReal ) , dimension ( 3 ) :: math_sampleGaussOri , center , disturb
real ( pReal ) , dimension ( 3 ) , parameter :: origin = ( / 0.0_pReal , 0.0_pReal , 0.0_pReal / )
real ( pReal ) , dimension ( 5 ) :: rnd
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real ( pReal ) :: noise , scatter , cosScatter
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integer ( pInt ) i
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if ( noise == 0.0_pReal ) then
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math_sampleGaussOri = center
return
endif
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! Helming uses different distribution with Bessel functions
! therefore the gauss scatter width has to be scaled differently
scatter = 0.95_pReal * noise
cosScatter = cos ( scatter )
do
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call halton ( 5_pInt , rnd )
forall ( i = 1_pInt : 3_pInt ) rnd ( i ) = 2.0_pReal * rnd ( i ) - 1.0_pReal ! expand 1:3 to range [-1,+1]
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disturb ( 1 ) = scatter * rnd ( 1 ) ! phi1
disturb ( 2 ) = sign ( 1.0_pReal , rnd ( 2 ) ) * acos ( cosScatter + ( 1.0_pReal - cosScatter ) * rnd ( 4 ) ) ! Phi
disturb ( 3 ) = scatter * rnd ( 2 ) ! phi2
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if ( rnd ( 5 ) < = exp ( - 1.0_pReal * ( math_EulerMisorientation ( origin , disturb ) / scatter ) ** 2_pReal ) ) exit
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enddo
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math_sampleGaussOri = math_RtoEuler ( math_mul33x33 ( math_EulerToR ( disturb ) , math_EulerToR ( center ) ) )
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end function math_sampleGaussOri
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2007-03-29 21:02:52 +05:30
!********************************************************************
! draw a random sample from Fiber component
! with noise (in radians)
!********************************************************************
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function math_sampleFiberOri ( alpha , beta , noise )
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2007-03-20 19:25:22 +05:30
implicit none
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real ( pReal ) , dimension ( 3 ) :: math_sampleFiberOri , fiberInC , fiberInS , axis
real ( pReal ) , dimension ( 2 ) :: alpha , beta , rnd
real ( pReal ) , dimension ( 3 , 3 ) :: oRot , fRot , pRot
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real ( pReal ) :: noise , scatter , cos2Scatter , angle
integer ( pInt ) , dimension ( 2 , 3 ) , parameter :: rotMap = reshape ( ( / 2_pInt , 3_pInt , &
3_pInt , 1_pInt , &
1_pInt , 2_pInt / ) , ( / 2 , 3 / ) )
integer ( pInt ) :: i
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2007-03-29 21:02:52 +05:30
! Helming uses different distribution with Bessel functions
! therefore the gauss scatter width has to be scaled differently
scatter = 0.95_pReal * noise
cos2Scatter = cos ( 2.0_pReal * scatter )
! fiber axis in crystal coordinate system
fiberInC ( 1 ) = sin ( alpha ( 1 ) ) * cos ( alpha ( 2 ) )
fiberInC ( 2 ) = sin ( alpha ( 1 ) ) * sin ( alpha ( 2 ) )
fiberInC ( 3 ) = cos ( alpha ( 1 ) )
! fiber axis in sample coordinate system
fiberInS ( 1 ) = sin ( beta ( 1 ) ) * cos ( beta ( 2 ) )
fiberInS ( 2 ) = sin ( beta ( 1 ) ) * sin ( beta ( 2 ) )
fiberInS ( 3 ) = cos ( beta ( 1 ) )
! ---# rotation matrix from sample to crystal system #---
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angle = - acos ( dot_product ( fiberInC , fiberInS ) )
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if ( angle / = 0.0_pReal ) then
! rotation axis between sample and crystal system (cross product)
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forall ( i = 1_pInt : 3_pInt ) axis ( i ) = fiberInC ( rotMap ( 1 , i ) ) * fiberInS ( rotMap ( 2 , i ) ) - fiberInC ( rotMap ( 2 , i ) ) * fiberInS ( rotMap ( 1 , i ) )
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oRot = math_AxisAngleToR ( math_vectorproduct ( fiberInC , fiberInS ) , angle )
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else
oRot = math_I3
end if
! ---# rotation matrix about fiber axis (random angle) #---
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call halton ( 1_pInt , rnd )
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fRot = math_AxisAngleToR ( fiberInS , rnd ( 1 ) * 2.0_pReal * pi )
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! ---# rotation about random axis perpend to fiber #---
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! random axis pependicular to fiber axis
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call halton ( 2_pInt , axis )
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if ( fiberInS ( 3 ) / = 0.0_pReal ) then
axis ( 3 ) = - ( axis ( 1 ) * fiberInS ( 1 ) + axis ( 2 ) * fiberInS ( 2 ) ) / fiberInS ( 3 )
else if ( fiberInS ( 2 ) / = 0.0_pReal ) then
axis ( 3 ) = axis ( 2 )
axis ( 2 ) = - ( axis ( 1 ) * fiberInS ( 1 ) + axis ( 3 ) * fiberInS ( 3 ) ) / fiberInS ( 2 )
else if ( fiberInS ( 1 ) / = 0.0_pReal ) then
axis ( 3 ) = axis ( 1 )
axis ( 1 ) = - ( axis ( 2 ) * fiberInS ( 2 ) + axis ( 3 ) * fiberInS ( 3 ) ) / fiberInS ( 1 )
end if
! scattered rotation angle
do
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call halton ( 2_pInt , rnd )
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angle = acos ( cos2Scatter + ( 1.0_pReal - cos2Scatter ) * rnd ( 1 ) )
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if ( rnd ( 2 ) < = exp ( - 1.0_pReal * ( angle / scatter ) ** 2.0_pReal ) ) exit
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enddo
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call halton ( 1_pInt , rnd )
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if ( rnd ( 1 ) < = 0.5 ) angle = - angle
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pRot = math_AxisAngleToR ( axis , angle )
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! ---# apply the three rotations #---
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math_sampleFiberOri = math_RtoEuler ( math_mul33x33 ( pRot , math_mul33x33 ( fRot , oRot ) ) )
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end function math_sampleFiberOri
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!********************************************************************
! symmetric Euler angles for given symmetry string
! 'triclinic' or '', 'monoclinic', 'orthotropic'
!********************************************************************
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pure function math_symmetricEulers ( sym , Euler )
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implicit none
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integer ( pInt ) , intent ( in ) :: sym
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real ( pReal ) , dimension ( 3 ) , intent ( in ) :: Euler
real ( pReal ) , dimension ( 3 , 3 ) :: math_symmetricEulers
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integer ( pInt ) :: i , j
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math_symmetricEulers ( 1 , 1 ) = pi + Euler ( 1 )
math_symmetricEulers ( 2 , 1 ) = Euler ( 2 )
math_symmetricEulers ( 3 , 1 ) = Euler ( 3 )
math_symmetricEulers ( 1 , 2 ) = pi - Euler ( 1 )
math_symmetricEulers ( 2 , 2 ) = pi - Euler ( 2 )
math_symmetricEulers ( 3 , 2 ) = pi + Euler ( 3 )
math_symmetricEulers ( 1 , 3 ) = 2.0_pReal * pi - Euler ( 1 )
math_symmetricEulers ( 2 , 3 ) = pi - Euler ( 2 )
math_symmetricEulers ( 3 , 3 ) = pi + Euler ( 3 )
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forall ( i = 1_pInt : 3_pInt , j = 1_pInt : 3_pInt ) math_symmetricEulers ( j , i ) = modulo ( math_symmetricEulers ( j , i ) , 2.0_pReal * pi )
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select case ( sym )
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case ( 4_pInt ) ! all done
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2011-12-01 17:31:13 +05:30
case ( 2_pInt ) ! return only first
math_symmetricEulers ( 1 : 3 , 2 : 3 ) = 0.0_pReal
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case default ! return blank
math_symmetricEulers = 0.0_pReal
end select
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end function math_symmetricEulers
2008-02-15 18:12:27 +05:30
2011-02-04 21:11:32 +05:30
!********************************************************************
! draw a random sample from Gauss variable
!********************************************************************
function math_sampleGaussVar ( meanvalue , stddev , width )
implicit none
!*** input variables
real ( pReal ) , intent ( in ) :: meanvalue , & ! meanvalue of gauss distribution
stddev ! standard deviation of gauss distribution
real ( pReal ) , intent ( in ) , optional :: width ! width of considered values as multiples of standard deviation
!*** output variables
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real ( pReal ) :: math_sampleGaussVar
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!*** local variables
real ( pReal ) , dimension ( 2 ) :: rnd ! random numbers
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real ( pReal ) :: scatter , & ! normalized scatter around meanvalue
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myWidth
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if ( stddev == 0.0_pReal ) then
2011-02-04 21:11:32 +05:30
math_sampleGaussVar = meanvalue
return
endif
if ( present ( width ) ) then
myWidth = width
else
myWidth = 3.0_pReal ! use +-3*sigma as default value for scatter
endif
do
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call halton ( 2_pInt , rnd )
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scatter = myWidth * ( 2.0_pReal * rnd ( 1 ) - 1.0_pReal )
if ( rnd ( 2 ) < = exp ( - 0.5_pReal * scatter ** 2.0_pReal ) ) & ! test if scattered value is drawn
exit
enddo
math_sampleGaussVar = scatter * stddev
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end function math_sampleGaussVar
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!****************************************************************
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subroutine math_spectralDecompositionSym33 ( M , values , vectors , error )
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!****************************************************************
implicit none
real ( pReal ) , dimension ( 3 , 3 ) , intent ( in ) :: M
real ( pReal ) , dimension ( 3 ) , intent ( out ) :: values
real ( pReal ) , dimension ( 3 , 3 ) , intent ( out ) :: vectors
logical , intent ( out ) :: error
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integer ( pInt ) :: info
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real ( pReal ) , dimension ( ( 64 + 2 ) * 3 ) :: work ! block size of 64 taken from http://www.netlib.org/lapack/double/dsyev.f
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2011-09-14 18:56:00 +05:30
vectors = M ! copy matrix to input (doubles as output) array
call DSYEV ( 'V' , 'U' , 3 , vectors , 3 , values , work , ( 64 + 2 ) * 3 , info )
error = ( info == 0_pInt )
end subroutine
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2007-03-21 15:50:25 +05:30
!****************************************************************
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pure subroutine math_pDecomposition ( FE , U , R , error )
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!-----FE = R.U
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!****************************************************************
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implicit none
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real ( pReal ) , intent ( in ) , dimension ( 3 , 3 ) :: FE
real ( pReal ) , intent ( out ) , dimension ( 3 , 3 ) :: R , U
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logical , intent ( out ) :: error
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real ( pReal ) , dimension ( 3 , 3 ) :: CE , EB1 , EB2 , EB3 , UI
real ( pReal ) :: EW1 , EW2 , EW3 , det
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error = . false .
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ce = math_mul33x33 ( math_transpose33 ( FE ) , FE )
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CALL math_spectral1 ( CE , EW1 , EW2 , EW3 , EB1 , EB2 , EB3 )
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U = sqrt ( EW1 ) * EB1 + sqrt ( EW2 ) * EB2 + sqrt ( EW3 ) * EB3
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call math_invert33 ( U , UI , det , error )
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if ( . not . error ) R = math_mul33x33 ( FE , UI )
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2012-03-09 01:55:28 +05:30
end subroutine math_pDecomposition
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!**********************************************************************
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pure subroutine math_spectral1 ( M , EW1 , EW2 , EW3 , EB1 , EB2 , EB3 )
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!**** EIGENWERTE UND EIGENWERTBASIS DER SYMMETRISCHEN 3X3 MATRIX M
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implicit none
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real ( pReal ) , dimension ( 3 , 3 ) , intent ( in ) :: M
real ( pReal ) , dimension ( 3 , 3 ) , intent ( out ) :: EB1 , EB2 , EB3
real ( pReal ) , intent ( out ) :: EW1 , EW2 , EW3
real ( pReal ) HI1M , HI2M , HI3M , R , S , T , P , Q , RHO , PHI , Y1 , Y2 , Y3 , D1 , D2 , D3
real ( pReal ) , parameter :: TOL = 1.e-14_pReal
real ( pReal ) , dimension ( 3 , 3 ) :: M1 , M2 , M3
real ( pReal ) C1 , C2 , C3 , arg
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CALL math_hi ( M , HI1M , HI2M , HI3M )
R = - HI1M
S = HI2M
T = - HI3M
P = S - R ** 2.0_pReal / 3.0_pReal
Q = 2.0_pReal / 2 7.0_pReal * R ** 3.0_pReal - R * S / 3.0_pReal + T
EB1 = 0.0_pReal
EB2 = 0.0_pReal
EB3 = 0.0_pReal
IF ( ( ABS ( P ) . LT . TOL ) . AND . ( ABS ( Q ) . LT . TOL ) ) THEN
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! DREI GLEICHE EIGENWERTE
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EW1 = HI1M / 3.0_pReal
EW2 = EW1
EW3 = EW1
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! this is not really correct, but this way U is calculated
! correctly in PDECOMPOSITION (correct is EB?=I)
2007-03-20 19:25:22 +05:30
EB1 ( 1 , 1 ) = 1.0_pReal
EB2 ( 2 , 2 ) = 1.0_pReal
EB3 ( 3 , 3 ) = 1.0_pReal
ELSE
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RHO = sqrt ( - 3.0_pReal * P ** 3.0_pReal ) / 9.0_pReal
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arg = - Q / RHO / 2.0_pReal
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if ( arg . GT . 1.0_pReal ) arg = 1.0_pReal
if ( arg . LT . - 1.0_pReal ) arg = - 1.0_pReal
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PHI = acos ( arg )
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Y1 = 2.0_pReal * RHO ** ( 1.0_pReal / 3.0_pReal ) * cos ( PHI / 3.0_pReal )
Y2 = 2.0_pReal * RHO ** ( 1.0_pReal / 3.0_pReal ) * cos ( PHI / 3.0_pReal + 2.0_pReal / 3.0_pReal * PI )
Y3 = 2.0_pReal * RHO ** ( 1.0_pReal / 3.0_pReal ) * cos ( PHI / 3.0_pReal + 4.0_pReal / 3.0_pReal * PI )
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EW1 = Y1 - R / 3.0_pReal
EW2 = Y2 - R / 3.0_pReal
EW3 = Y3 - R / 3.0_pReal
C1 = ABS ( EW1 - EW2 )
C2 = ABS ( EW2 - EW3 )
C3 = ABS ( EW3 - EW1 )
IF ( C1 . LT . TOL ) THEN
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! EW1 is equal to EW2
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D3 = 1.0_pReal / ( EW3 - EW1 ) / ( EW3 - EW2 )
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M1 = M - EW1 * math_I3
M2 = M - EW2 * math_I3
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EB3 = math_mul33x33 ( M1 , M2 ) * D3
2008-07-09 01:08:22 +05:30
2007-03-27 20:43:08 +05:30
EB1 = math_I3 - EB3
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! both EB2 and EW2 are set to zero so that they do not
! contribute to U in PDECOMPOSITION
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EW2 = 0.0_pReal
ELSE IF ( C2 . LT . TOL ) THEN
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! EW2 is equal to EW3
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D1 = 1.0_pReal / ( EW1 - EW2 ) / ( EW1 - EW3 )
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M2 = M - math_I3 * EW2
M3 = M - math_I3 * EW3
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EB1 = math_mul33x33 ( M2 , M3 ) * D1
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EB2 = math_I3 - EB1
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! both EB3 and EW3 are set to zero so that they do not
! contribute to U in PDECOMPOSITION
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EW3 = 0.0_pReal
ELSE IF ( C3 . LT . TOL ) THEN
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! EW1 is equal to EW3
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D2 = 1.0_pReal / ( EW2 - EW1 ) / ( EW2 - EW3 )
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M1 = M - math_I3 * EW1
M3 = M - math_I3 * EW3
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EB2 = math_mul33x33 ( M1 , M3 ) * D2
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EB1 = math_I3 - EB2
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! both EB3 and EW3 are set to zero so that they do not
! contribute to U in PDECOMPOSITION
2007-03-20 19:25:22 +05:30
EW3 = 0.0_pReal
ELSE
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! all three eigenvectors are different
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D1 = 1.0_pReal / ( EW1 - EW2 ) / ( EW1 - EW3 )
D2 = 1.0_pReal / ( EW2 - EW1 ) / ( EW2 - EW3 )
D3 = 1.0_pReal / ( EW3 - EW1 ) / ( EW3 - EW2 )
2007-03-27 20:43:08 +05:30
M1 = M - EW1 * math_I3
M2 = M - EW2 * math_I3
M3 = M - EW3 * math_I3
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EB1 = math_mul33x33 ( M2 , M3 ) * D1
EB2 = math_mul33x33 ( M1 , M3 ) * D2
EB3 = math_mul33x33 ( M1 , M2 ) * D3
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2007-03-20 19:25:22 +05:30
END IF
END IF
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2012-03-09 01:55:28 +05:30
end subroutine math_spectral1
2007-03-20 19:25:22 +05:30
2011-12-01 17:31:13 +05:30
2011-08-26 19:36:37 +05:30
!**********************************************************************
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function math_eigenvalues33 ( M )
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!**** Eigenvalues of symmetric 3X3 matrix M
implicit none
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real ( pReal ) , intent ( in ) , dimension ( 3 , 3 ) :: M
real ( pReal ) , dimension ( 3 , 3 ) :: EB1 = 0.0_pReal , EB2 = 0.0_pReal , EB3 = 0.0_pReal
2012-01-26 19:20:00 +05:30
real ( pReal ) , dimension ( 3 ) :: math_eigenvalues33
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real ( pReal ) :: HI1M , HI2M , HI3M , R , S , T , P , Q , RHO , PHI , Y1 , Y2 , Y3 , arg
real ( pReal ) , parameter :: TOL = 1.e-14_pReal
2011-08-26 19:36:37 +05:30
CALL math_hi ( M , HI1M , HI2M , HI3M )
R = - HI1M
S = HI2M
T = - HI3M
P = S - R ** 2.0_pReal / 3.0_pReal
Q = 2.0_pReal / 2 7.0_pReal * R ** 3.0_pReal - R * S / 3.0_pReal + T
2011-12-01 17:31:13 +05:30
2011-08-26 19:36:37 +05:30
if ( ( abs ( P ) < TOL ) . and . ( abs ( Q ) < TOL ) ) THEN
! three equivalent eigenvalues
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math_eigenvalues33 ( 1 ) = HI1M / 3.0_pReal
math_eigenvalues33 ( 2 ) = math_eigenvalues33 ( 1 )
math_eigenvalues33 ( 3 ) = math_eigenvalues33 ( 1 )
2011-08-26 19:36:37 +05:30
! this is not really correct, but this way U is calculated
! correctly in PDECOMPOSITION (correct is EB?=I)
EB1 ( 1 , 1 ) = 1.0_pReal
EB2 ( 2 , 2 ) = 1.0_pReal
EB3 ( 3 , 3 ) = 1.0_pReal
else
RHO = sqrt ( - 3.0_pReal * P ** 3.0_pReal ) / 9.0_pReal
arg = - Q / RHO / 2.0_pReal
2011-12-01 17:31:13 +05:30
if ( arg . GT . 1.0_pReal ) arg = 1.0_pReal
if ( arg . LT . - 1.0_pReal ) arg = - 1.0_pReal
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PHI = acos ( arg )
Y1 = 2 * RHO ** ( 1.0_pReal / 3.0_pReal ) * cos ( PHI / 3.0_pReal )
Y2 = 2 * RHO ** ( 1.0_pReal / 3.0_pReal ) * cos ( PHI / 3.0_pReal + 2.0_pReal / 3.0_pReal * PI )
Y3 = 2 * RHO ** ( 1.0_pReal / 3.0_pReal ) * cos ( PHI / 3.0_pReal + 4.0_pReal / 3.0_pReal * PI )
2012-01-26 19:20:00 +05:30
math_eigenvalues33 ( 1 ) = Y1 - R / 3.0_pReal
math_eigenvalues33 ( 2 ) = Y2 - R / 3.0_pReal
math_eigenvalues33 ( 3 ) = Y3 - R / 3.0_pReal
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endif
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end function math_eigenvalues33
2007-03-20 19:25:22 +05:30
2011-12-01 17:31:13 +05:30
2007-03-21 15:50:25 +05:30
!**********************************************************************
!**** HAUPTINVARIANTEN HI1M, HI2M, HI3M DER 3X3 MATRIX M
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pure subroutine math_hi ( M , HI1M , HI2M , HI3M )
2011-12-01 17:31:13 +05:30
2007-03-20 19:25:22 +05:30
implicit none
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2009-12-14 16:32:10 +05:30
real ( pReal ) , intent ( in ) :: M ( 3 , 3 )
real ( pReal ) , intent ( out ) :: HI1M , HI2M , HI3M
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HI1M = M ( 1 , 1 ) + M ( 2 , 2 ) + M ( 3 , 3 )
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HI2M = HI1M ** 2.0_pReal / 2.0_pReal - ( M ( 1 , 1 ) ** 2.0_pReal + M ( 2 , 2 ) ** 2.0_pReal + M ( 3 , 3 ) ** 2.0_pReal ) &
/ 2.0_pReal - M ( 1 , 2 ) * M ( 2 , 1 ) - M ( 1 , 3 ) * M ( 3 , 1 ) - M ( 2 , 3 ) * M ( 3 , 2 )
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HI3M = math_det33 ( M )
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! QUESTION: is 3rd equiv det(M) ?? if yes, use function math_det !agreed on YES
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end subroutine math_hi
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!*******************************************************************************
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! GET_SEED returns a seed for the random number generator.
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!
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! The seed depends on the current time, and ought to be (slightly)
! different every millisecond. Once the seed is obtained, a random
! number generator should be called a few times to further process
! the seed.
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!
! Parameters:
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! Output, integer SEED, a pseudorandom seed value.
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!
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! Modified: 27 June 2000
! Author: John Burkardt
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!
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! Modified: 29 April 2005
! Author: Franz Roters
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!
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subroutine get_seed ( seed )
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implicit none
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integer ( pInt ) :: seed
real ( pReal ) :: temp = 0.0_pReal
character ( len = 10 ) :: time
character ( len = 8 ) :: today
integer ( pInt ) :: values ( 8 )
character ( len = 5 ) :: zone
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call date_and_time ( today , time , zone , values )
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temp = temp + real ( values ( 2 ) - 1_pInt , pReal ) / 1 1.0_pReal
temp = temp + real ( values ( 3 ) - 1_pInt , pReal ) / 3 0.0_pReal
temp = temp + real ( values ( 5 ) , pReal ) / 2 3.0_pReal
temp = temp + real ( values ( 6 ) , pReal ) / 5 9.0_pReal
temp = temp + real ( values ( 7 ) , pReal ) / 5 9.0_pReal
temp = temp + real ( values ( 8 ) , pReal ) / 99 9.0_pReal
temp = temp / 6.0_pReal
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if ( temp < = 0.0_pReal ) then
temp = 1.0_pReal / 3.0_pReal
else if ( 1.0_pReal < = temp ) then
temp = 2.0_pReal / 3.0_pReal
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end if
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seed = int ( real ( huge ( 1_pInt ) , pReal ) * temp , pInt )
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!
! Never use a seed of 0 or maximum integer.
!
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if ( seed == 0_pInt ) then
seed = 1_pInt
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end if
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if ( seed == huge ( 1_pInt ) ) then
seed = seed - 1_pInt
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end if
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end subroutine get_seed
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!*******************************************************************************
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! HALTON computes the next element in the Halton sequence.
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!
! Parameters:
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! Input, integer NDIM, the dimension of the element.
! Output, real R(NDIM), the next element of the current Halton sequence.
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!
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! Modified: 09 March 2003
! Author: John Burkardt
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!
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! Modified: 29 April 2005
! Author: Franz Roters
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!
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subroutine halton ( ndim , r )
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implicit none
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integer ( pInt ) , intent ( in ) :: ndim
real ( pReal ) , intent ( out ) , dimension ( ndim ) :: r
integer ( pInt ) , dimension ( ndim ) :: base
integer ( pInt ) :: seed
integer ( pInt ) , dimension ( 1 ) :: value_halton
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call halton_memory ( 'GET' , 'SEED' , 1_pInt , value_halton )
seed = value_halton ( 1 )
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call halton_memory ( 'GET' , 'BASE' , ndim , base )
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call i_to_halton ( seed , base , ndim , r )
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value_halton ( 1 ) = 1_pInt
call halton_memory ( 'INC' , 'SEED' , 1_pInt , value_halton )
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end subroutine halton
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!*******************************************************************************
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! HALTON_MEMORY sets or returns quantities associated with the Halton sequence.
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!
! Parameters:
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! Input, character (len = *) action_halton, the desired action.
! 'GET' means get the value of a particular quantity.
! 'SET' means set the value of a particular quantity.
! 'INC' means increment the value of a particular quantity.
! (Only the SEED can be incremented.)
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!
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! Input, character (len = *) name_halton, the name of the quantity.
! 'BASE' means the Halton base or bases.
! 'NDIM' means the spatial dimension.
! 'SEED' means the current Halton seed.
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!
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! Input/output, integer NDIM, the dimension of the quantity.
! If action_halton is 'SET' and action_halton is 'BASE', then NDIM is input, and
! is the number of entries in value_halton to be put into BASE.
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!
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! Input/output, integer value_halton(NDIM), contains a value.
! If action_halton is 'SET', then on input, value_halton contains values to be assigned
! to the internal variable.
! If action_halton is 'GET', then on output, value_halton contains the values of
! the specified internal variable.
! If action_halton is 'INC', then on input, value_halton contains the increment to
! be added to the specified internal variable.
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!
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! Modified: 09 March 2003
! Author: John Burkardt
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!
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! Modified: 29 April 2005
! Author: Franz Roters
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subroutine halton_memory ( action_halton , name_halton , ndim , value_halton )
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implicit none
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character ( len = * ) , intent ( in ) :: action_halton , name_halton
integer ( pInt ) , dimension ( * ) , intent ( inout ) :: value_halton
integer ( pInt ) , allocatable , save , dimension ( : ) :: base
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logical , save :: first_call = . true .
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integer ( pInt ) , intent ( in ) :: ndim
integer ( pInt ) :: i
integer ( pInt ) , save :: ndim_save = 0_pInt , seed = 1_pInt
if ( first_call ) then
ndim_save = 1_pInt
allocate ( base ( ndim_save ) )
base ( 1 ) = 2_pInt
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first_call = . false .
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endif
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!
! Set
!
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if ( action_halton ( 1 : 1 ) == 'S' . or . action_halton ( 1 : 1 ) == 's' ) then
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if ( name_halton ( 1 : 1 ) == 'B' . or . name_halton ( 1 : 1 ) == 'b' ) then
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if ( ndim_save / = ndim ) then
deallocate ( base )
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ndim_save = ndim
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allocate ( base ( ndim_save ) )
endif
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base ( 1 : ndim ) = value_halton ( 1 : ndim )
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elseif ( name_halton ( 1 : 1 ) == 'N' . or . name_halton ( 1 : 1 ) == 'n' ) then
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if ( ndim_save / = value_halton ( 1 ) ) then
deallocate ( base )
ndim_save = value_halton ( 1 )
allocate ( base ( ndim_save ) )
do i = 1_pInt , ndim_save
base ( i ) = prime ( i )
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enddo
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else
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ndim_save = value_halton ( 1 )
endif
elseif ( name_halton ( 1 : 1 ) == 'S' . or . name_halton ( 1 : 1 ) == 's' ) then
seed = value_halton ( 1 )
endif
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!
! Get
!
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elseif ( action_halton ( 1 : 1 ) == 'G' . or . action_halton ( 1 : 1 ) == 'g' ) then
if ( name_halton ( 1 : 1 ) == 'B' . or . name_halton ( 1 : 1 ) == 'b' ) then
if ( ndim / = ndim_save ) then
deallocate ( base )
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ndim_save = ndim
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allocate ( base ( ndim_save ) )
do i = 1_pInt , ndim_save
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base ( i ) = prime ( i )
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enddo
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endif
value_halton ( 1 : ndim_save ) = base ( 1 : ndim_save )
elseif ( name_halton ( 1 : 1 ) == 'N' . or . name_halton ( 1 : 1 ) == 'n' ) then
value_halton ( 1 ) = ndim_save
elseif ( name_halton ( 1 : 1 ) == 'S' . or . name_halton ( 1 : 1 ) == 's' ) then
value_halton ( 1 ) = seed
endif
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!
! Increment
!
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elseif ( action_halton ( 1 : 1 ) == 'I' . or . action_halton ( 1 : 1 ) == 'i' ) then
if ( name_halton ( 1 : 1 ) == 'S' . or . name_halton ( 1 : 1 ) == 's' ) then
seed = seed + value_halton ( 1 )
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end if
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endif
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end subroutine halton_memory
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!*******************************************************************************
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! HALTON_NDIM_SET sets the dimension for a Halton sequence.
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!
! Parameters:
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! Input, integer NDIM, the dimension of the Halton vectors.
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!
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! Modified: 26 February 2001
! Author: John Burkardt
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!
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! Modified: 29 April 2005
! Author: Franz Roters
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!
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subroutine halton_ndim_set ( ndim )
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implicit none
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integer ( pInt ) , intent ( in ) :: ndim
integer ( pInt ) :: value_halton ( 1 )
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value_halton ( 1 ) = ndim
call halton_memory ( 'SET' , 'NDIM' , 1_pInt , value_halton )
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end subroutine halton_ndim_set
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!*******************************************************************************
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! HALTON_SEED_SET sets the "seed" for the Halton sequence.
!
! Calling HALTON repeatedly returns the elements of the
! Halton sequence in order, starting with element number 1.
! An internal counter, called SEED, keeps track of the next element
! to return. Each time the routine is called, the SEED-th element
! is computed, and then SEED is incremented by 1.
!
! To restart the Halton sequence, it is only necessary to reset
! SEED to 1. It might also be desirable to reset SEED to some other value.
! This routine allows the user to specify any value of SEED.
!
! The default value of SEED is 1, which restarts the Halton sequence.
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!
! Parameters:
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! Input, integer SEED, the seed for the Halton sequence.
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!
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! Modified: 26 February 2001
! Author: John Burkardt
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!
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! Modified: 29 April 2005
! Author: Franz Roters
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!
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subroutine halton_seed_set ( seed )
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implicit none
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integer ( pInt ) , parameter :: ndim = 1_pInt
integer ( pInt ) , intent ( in ) :: seed
integer ( pInt ) :: value_halton ( ndim )
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value_halton ( 1 ) = seed
call halton_memory ( 'SET' , 'SEED' , ndim , value_halton )
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end subroutine halton_seed_set
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!*******************************************************************************
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! I_TO_HALTON computes an element of a Halton sequence.
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!
! Reference:
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! J H Halton: On the efficiency of certain quasi-random sequences of points
! in evaluating multi-dimensional integrals, Numerische Mathematik, Volume 2, pages 84-90, 1960.
!
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! Parameters:
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! Input, integer SEED, the index of the desired element.
! Only the absolute value of SEED is considered. SEED = 0 is allowed,
! and returns R = 0.
!
! Input, integer BASE(NDIM), the Halton bases, which should be
! distinct prime numbers. This routine only checks that each base
! is greater than 1.
!
! Input, integer NDIM, the dimension of the sequence.
!
! Output, real R(NDIM), the SEED-th element of the Halton sequence
! for the given bases.
!
! Modified: 26 February 2001
! Author: John Burkardt
!
! Modified: 29 April 2005
! Author: Franz RotersA
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subroutine i_to_halton ( seed , base , ndim , r )
use IO , only : IO_error
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implicit none
integer ( pInt ) , intent ( in ) :: ndim
integer ( pInt ) , intent ( in ) , dimension ( ndim ) :: base
real ( pReal ) , dimension ( ndim ) :: base_inv
integer ( pInt ) , dimension ( ndim ) :: digit
real ( pReal ) , dimension ( ndim ) , intent ( out ) :: r
integer ( pInt ) :: seed
integer ( pInt ) , dimension ( ndim ) :: seed2
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seed2 ( 1 : ndim ) = abs ( seed )
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r ( 1 : ndim ) = 0.0_pReal
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if ( any ( base ( 1 : ndim ) < = 1_pInt ) ) call IO_error ( error_ID = 405_pInt )
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base_inv ( 1 : ndim ) = 1.0_pReal / real ( base ( 1 : ndim ) , pReal )
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do while ( any ( seed2 ( 1 : ndim ) / = 0_pInt ) )
digit ( 1 : ndim ) = mod ( seed2 ( 1 : ndim ) , base ( 1 : ndim ) )
r ( 1 : ndim ) = r ( 1 : ndim ) + real ( digit ( 1 : ndim ) , pReal ) * base_inv ( 1 : ndim )
base_inv ( 1 : ndim ) = base_inv ( 1 : ndim ) / real ( base ( 1 : ndim ) , pReal )
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seed2 ( 1 : ndim ) = seed2 ( 1 : ndim ) / base ( 1 : ndim )
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enddo
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end subroutine i_to_halton
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!*******************************************************************************
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! PRIME returns any of the first PRIME_MAX prime numbers.
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!
! Note:
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! PRIME_MAX is 1500, and the largest prime stored is 12553.
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! Reference:
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! Milton Abramowitz and Irene Stegun: Handbook of Mathematical Functions,
! US Department of Commerce, 1964, pages 870-873.
!
! Daniel Zwillinger: CRC Standard Mathematical Tables and Formulae,
! 30th Edition, CRC Press, 1996, pages 95-98.
!
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! Parameters:
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! Input, integer N, the index of the desired prime number.
! N = -1 returns PRIME_MAX, the index of the largest prime available.
! N = 0 is legal, returning PRIME = 1.
! It should generally be true that 0 <= N <= PRIME_MAX.
!
! Output, integer PRIME, the N-th prime. If N is out of range, PRIME
! is returned as 0.
!
! Modified: 21 June 2002
! Author: John Burkardt
!
! Modified: 29 April 2005
! Author: Franz Roters
!
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function prime ( n )
use IO , only : IO_error
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implicit none
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integer ( pInt ) , parameter :: prime_max = 1500_pInt
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integer ( pInt ) , save :: icall = 0_pInt
integer ( pInt ) , intent ( in ) :: n
integer ( pInt ) , save , dimension ( prime_max ) :: npvec
integer ( pInt ) prime
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if ( icall == 0_pInt ) then
icall = 1_pInt
npvec ( 1 : 100 ) = ( / &
2_pInt , 3_pInt , 5_pInt , 7_pInt , 11_pInt , 13_pInt , 17_pInt , 19_pInt , 23_pInt , 29_pInt , &
31_pInt , 37_pInt , 41_pInt , 43_pInt , 47_pInt , 53_pInt , 59_pInt , 61_pInt , 67_pInt , 71_pInt , &
73_pInt , 79_pInt , 83_pInt , 89_pInt , 97_pInt , 101_pInt , 103_pInt , 107_pInt , 109_pInt , 113_pInt , &
127_pInt , 131_pInt , 137_pInt , 139_pInt , 149_pInt , 151_pInt , 157_pInt , 163_pInt , 167_pInt , 173_pInt , &
179_pInt , 181_pInt , 191_pInt , 193_pInt , 197_pInt , 199_pInt , 211_pInt , 223_pInt , 227_pInt , 229_pInt , &
233_pInt , 239_pInt , 241_pInt , 251_pInt , 257_pInt , 263_pInt , 269_pInt , 271_pInt , 277_pInt , 281_pInt , &
283_pInt , 293_pInt , 307_pInt , 311_pInt , 313_pInt , 317_pInt , 331_pInt , 337_pInt , 347_pInt , 349_pInt , &
353_pInt , 359_pInt , 367_pInt , 373_pInt , 379_pInt , 383_pInt , 389_pInt , 397_pInt , 401_pInt , 409_pInt , &
419_pInt , 421_pInt , 431_pInt , 433_pInt , 439_pInt , 443_pInt , 449_pInt , 457_pInt , 461_pInt , 463_pInt , &
467_pInt , 479_pInt , 487_pInt , 491_pInt , 499_pInt , 503_pInt , 509_pInt , 521_pInt , 523_pInt , 541_pInt / )
npvec ( 101 : 200 ) = ( / &
547_pInt , 557_pInt , 563_pInt , 569_pInt , 571_pInt , 577_pInt , 587_pInt , 593_pInt , 599_pInt , 601_pInt , &
607_pInt , 613_pInt , 617_pInt , 619_pInt , 631_pInt , 641_pInt , 643_pInt , 647_pInt , 653_pInt , 659_pInt , &
661_pInt , 673_pInt , 677_pInt , 683_pInt , 691_pInt , 701_pInt , 709_pInt , 719_pInt , 727_pInt , 733_pInt , &
739_pInt , 743_pInt , 751_pInt , 757_pInt , 761_pInt , 769_pInt , 773_pInt , 787_pInt , 797_pInt , 809_pInt , &
811_pInt , 821_pInt , 823_pInt , 827_pInt , 829_pInt , 839_pInt , 853_pInt , 857_pInt , 859_pInt , 863_pInt , &
877_pInt , 881_pInt , 883_pInt , 887_pInt , 907_pInt , 911_pInt , 919_pInt , 929_pInt , 937_pInt , 941_pInt , &
947_pInt , 953_pInt , 967_pInt , 971_pInt , 977_pInt , 983_pInt , 991_pInt , 997_pInt , 1009_pInt , 1013_pInt , &
1019_pInt , 1021_pInt , 1031_pInt , 1033_pInt , 1039_pInt , 1049_pInt , 1051_pInt , 1061_pInt , 1063_pInt , 1069_pInt , &
1087_pInt , 1091_pInt , 1093_pInt , 1097_pInt , 1103_pInt , 1109_pInt , 1117_pInt , 1123_pInt , 1129_pInt , 1151_pInt , &
1153_pInt , 1163_pInt , 1171_pInt , 1181_pInt , 1187_pInt , 1193_pInt , 1201_pInt , 1213_pInt , 1217_pInt , 1223_pInt / )
npvec ( 201 : 300 ) = ( / &
1229_pInt , 1231_pInt , 1237_pInt , 1249_pInt , 1259_pInt , 1277_pInt , 1279_pInt , 1283_pInt , 1289_pInt , 1291_pInt , &
1297_pInt , 1301_pInt , 1303_pInt , 1307_pInt , 1319_pInt , 1321_pInt , 1327_pInt , 1361_pInt , 1367_pInt , 1373_pInt , &
1381_pInt , 1399_pInt , 1409_pInt , 1423_pInt , 1427_pInt , 1429_pInt , 1433_pInt , 1439_pInt , 1447_pInt , 1451_pInt , &
1453_pInt , 1459_pInt , 1471_pInt , 1481_pInt , 1483_pInt , 1487_pInt , 1489_pInt , 1493_pInt , 1499_pInt , 1511_pInt , &
1523_pInt , 1531_pInt , 1543_pInt , 1549_pInt , 1553_pInt , 1559_pInt , 1567_pInt , 1571_pInt , 1579_pInt , 1583_pInt , &
1597_pInt , 1601_pInt , 1607_pInt , 1609_pInt , 1613_pInt , 1619_pInt , 1621_pInt , 1627_pInt , 1637_pInt , 1657_pInt , &
1663_pInt , 1667_pInt , 1669_pInt , 1693_pInt , 1697_pInt , 1699_pInt , 1709_pInt , 1721_pInt , 1723_pInt , 1733_pInt , &
1741_pInt , 1747_pInt , 1753_pInt , 1759_pInt , 1777_pInt , 1783_pInt , 1787_pInt , 1789_pInt , 1801_pInt , 1811_pInt , &
1823_pInt , 1831_pInt , 1847_pInt , 1861_pInt , 1867_pInt , 1871_pInt , 1873_pInt , 1877_pInt , 1879_pInt , 1889_pInt , &
1901_pInt , 1907_pInt , 1913_pInt , 1931_pInt , 1933_pInt , 1949_pInt , 1951_pInt , 1973_pInt , 1979_pInt , 1987_pInt / )
npvec ( 301 : 400 ) = ( / &
1993_pInt , 1997_pInt , 1999_pInt , 2003_pInt , 2011_pInt , 2017_pInt , 2027_pInt , 2029_pInt , 2039_pInt , 2053_pInt , &
2063_pInt , 2069_pInt , 2081_pInt , 2083_pInt , 2087_pInt , 2089_pInt , 2099_pInt , 2111_pInt , 2113_pInt , 2129_pInt , &
2131_pInt , 2137_pInt , 2141_pInt , 2143_pInt , 2153_pInt , 2161_pInt , 2179_pInt , 2203_pInt , 2207_pInt , 2213_pInt , &
2221_pInt , 2237_pInt , 2239_pInt , 2243_pInt , 2251_pInt , 2267_pInt , 2269_pInt , 2273_pInt , 2281_pInt , 2287_pInt , &
2293_pInt , 2297_pInt , 2309_pInt , 2311_pInt , 2333_pInt , 2339_pInt , 2341_pInt , 2347_pInt , 2351_pInt , 2357_pInt , &
2371_pInt , 2377_pInt , 2381_pInt , 2383_pInt , 2389_pInt , 2393_pInt , 2399_pInt , 2411_pInt , 2417_pInt , 2423_pInt , &
2437_pInt , 2441_pInt , 2447_pInt , 2459_pInt , 2467_pInt , 2473_pInt , 2477_pInt , 2503_pInt , 2521_pInt , 2531_pInt , &
2539_pInt , 2543_pInt , 2549_pInt , 2551_pInt , 2557_pInt , 2579_pInt , 2591_pInt , 2593_pInt , 2609_pInt , 2617_pInt , &
2621_pInt , 2633_pInt , 2647_pInt , 2657_pInt , 2659_pInt , 2663_pInt , 2671_pInt , 2677_pInt , 2683_pInt , 2687_pInt , &
2689_pInt , 2693_pInt , 2699_pInt , 2707_pInt , 2711_pInt , 2713_pInt , 2719_pInt , 2729_pInt , 2731_pInt , 2741_pInt / )
npvec ( 401 : 500 ) = ( / &
2749_pInt , 2753_pInt , 2767_pInt , 2777_pInt , 2789_pInt , 2791_pInt , 2797_pInt , 2801_pInt , 2803_pInt , 2819_pInt , &
2833_pInt , 2837_pInt , 2843_pInt , 2851_pInt , 2857_pInt , 2861_pInt , 2879_pInt , 2887_pInt , 2897_pInt , 2903_pInt , &
2909_pInt , 2917_pInt , 2927_pInt , 2939_pInt , 2953_pInt , 2957_pInt , 2963_pInt , 2969_pInt , 2971_pInt , 2999_pInt , &
3001_pInt , 3011_pInt , 3019_pInt , 3023_pInt , 3037_pInt , 3041_pInt , 3049_pInt , 3061_pInt , 3067_pInt , 3079_pInt , &
3083_pInt , 3089_pInt , 3109_pInt , 3119_pInt , 3121_pInt , 3137_pInt , 3163_pInt , 3167_pInt , 3169_pInt , 3181_pInt , &
3187_pInt , 3191_pInt , 3203_pInt , 3209_pInt , 3217_pInt , 3221_pInt , 3229_pInt , 3251_pInt , 3253_pInt , 3257_pInt , &
3259_pInt , 3271_pInt , 3299_pInt , 3301_pInt , 3307_pInt , 3313_pInt , 3319_pInt , 3323_pInt , 3329_pInt , 3331_pInt , &
3343_pInt , 3347_pInt , 3359_pInt , 3361_pInt , 3371_pInt , 3373_pInt , 3389_pInt , 3391_pInt , 3407_pInt , 3413_pInt , &
3433_pInt , 3449_pInt , 3457_pInt , 3461_pInt , 3463_pInt , 3467_pInt , 3469_pInt , 3491_pInt , 3499_pInt , 3511_pInt , &
3517_pInt , 3527_pInt , 3529_pInt , 3533_pInt , 3539_pInt , 3541_pInt , 3547_pInt , 3557_pInt , 3559_pInt , 3571_pInt / )
npvec ( 501 : 600 ) = ( / &
3581_pInt , 3583_pInt , 3593_pInt , 3607_pInt , 3613_pInt , 3617_pInt , 3623_pInt , 3631_pInt , 3637_pInt , 3643_pInt , &
3659_pInt , 3671_pInt , 3673_pInt , 3677_pInt , 3691_pInt , 3697_pInt , 3701_pInt , 3709_pInt , 3719_pInt , 3727_pInt , &
3733_pInt , 3739_pInt , 3761_pInt , 3767_pInt , 3769_pInt , 3779_pInt , 3793_pInt , 3797_pInt , 3803_pInt , 3821_pInt , &
3823_pInt , 3833_pInt , 3847_pInt , 3851_pInt , 3853_pInt , 3863_pInt , 3877_pInt , 3881_pInt , 3889_pInt , 3907_pInt , &
3911_pInt , 3917_pInt , 3919_pInt , 3923_pInt , 3929_pInt , 3931_pInt , 3943_pInt , 3947_pInt , 3967_pInt , 3989_pInt , &
4001_pInt , 4003_pInt , 4007_pInt , 4013_pInt , 4019_pInt , 4021_pInt , 4027_pInt , 4049_pInt , 4051_pInt , 4057_pInt , &
4073_pInt , 4079_pInt , 4091_pInt , 4093_pInt , 4099_pInt , 4111_pInt , 4127_pInt , 4129_pInt , 4133_pInt , 4139_pInt , &
4153_pInt , 4157_pInt , 4159_pInt , 4177_pInt , 4201_pInt , 4211_pInt , 4217_pInt , 4219_pInt , 4229_pInt , 4231_pInt , &
4241_pInt , 4243_pInt , 4253_pInt , 4259_pInt , 4261_pInt , 4271_pInt , 4273_pInt , 4283_pInt , 4289_pInt , 4297_pInt , &
4327_pInt , 4337_pInt , 4339_pInt , 4349_pInt , 4357_pInt , 4363_pInt , 4373_pInt , 4391_pInt , 4397_pInt , 4409_pInt / )
npvec ( 601 : 700 ) = ( / &
4421_pInt , 4423_pInt , 4441_pInt , 4447_pInt , 4451_pInt , 4457_pInt , 4463_pInt , 4481_pInt , 4483_pInt , 4493_pInt , &
4507_pInt , 4513_pInt , 4517_pInt , 4519_pInt , 4523_pInt , 4547_pInt , 4549_pInt , 4561_pInt , 4567_pInt , 4583_pInt , &
4591_pInt , 4597_pInt , 4603_pInt , 4621_pInt , 4637_pInt , 4639_pInt , 4643_pInt , 4649_pInt , 4651_pInt , 4657_pInt , &
4663_pInt , 4673_pInt , 4679_pInt , 4691_pInt , 4703_pInt , 4721_pInt , 4723_pInt , 4729_pInt , 4733_pInt , 4751_pInt , &
4759_pInt , 4783_pInt , 4787_pInt , 4789_pInt , 4793_pInt , 4799_pInt , 4801_pInt , 4813_pInt , 4817_pInt , 4831_pInt , &
4861_pInt , 4871_pInt , 4877_pInt , 4889_pInt , 4903_pInt , 4909_pInt , 4919_pInt , 4931_pInt , 4933_pInt , 4937_pInt , &
4943_pInt , 4951_pInt , 4957_pInt , 4967_pInt , 4969_pInt , 4973_pInt , 4987_pInt , 4993_pInt , 4999_pInt , 5003_pInt , &
5009_pInt , 5011_pInt , 5021_pInt , 5023_pInt , 5039_pInt , 5051_pInt , 5059_pInt , 5077_pInt , 5081_pInt , 5087_pInt , &
5099_pInt , 5101_pInt , 5107_pInt , 5113_pInt , 5119_pInt , 5147_pInt , 5153_pInt , 5167_pInt , 5171_pInt , 5179_pInt , &
5189_pInt , 5197_pInt , 5209_pInt , 5227_pInt , 5231_pInt , 5233_pInt , 5237_pInt , 5261_pInt , 5273_pInt , 5279_pInt / )
npvec ( 701 : 800 ) = ( / &
5281_pInt , 5297_pInt , 5303_pInt , 5309_pInt , 5323_pInt , 5333_pInt , 5347_pInt , 5351_pInt , 5381_pInt , 5387_pInt , &
5393_pInt , 5399_pInt , 5407_pInt , 5413_pInt , 5417_pInt , 5419_pInt , 5431_pInt , 5437_pInt , 5441_pInt , 5443_pInt , &
5449_pInt , 5471_pInt , 5477_pInt , 5479_pInt , 5483_pInt , 5501_pInt , 5503_pInt , 5507_pInt , 5519_pInt , 5521_pInt , &
5527_pInt , 5531_pInt , 5557_pInt , 5563_pInt , 5569_pInt , 5573_pInt , 5581_pInt , 5591_pInt , 5623_pInt , 5639_pInt , &
5641_pInt , 5647_pInt , 5651_pInt , 5653_pInt , 5657_pInt , 5659_pInt , 5669_pInt , 5683_pInt , 5689_pInt , 5693_pInt , &
5701_pInt , 5711_pInt , 5717_pInt , 5737_pInt , 5741_pInt , 5743_pInt , 5749_pInt , 5779_pInt , 5783_pInt , 5791_pInt , &
5801_pInt , 5807_pInt , 5813_pInt , 5821_pInt , 5827_pInt , 5839_pInt , 5843_pInt , 5849_pInt , 5851_pInt , 5857_pInt , &
5861_pInt , 5867_pInt , 5869_pInt , 5879_pInt , 5881_pInt , 5897_pInt , 5903_pInt , 5923_pInt , 5927_pInt , 5939_pInt , &
5953_pInt , 5981_pInt , 5987_pInt , 6007_pInt , 6011_pInt , 6029_pInt , 6037_pInt , 6043_pInt , 6047_pInt , 6053_pInt , &
6067_pInt , 6073_pInt , 6079_pInt , 6089_pInt , 6091_pInt , 6101_pInt , 6113_pInt , 6121_pInt , 6131_pInt , 6133_pInt / )
npvec ( 801 : 900 ) = ( / &
6143_pInt , 6151_pInt , 6163_pInt , 6173_pInt , 6197_pInt , 6199_pInt , 6203_pInt , 6211_pInt , 6217_pInt , 6221_pInt , &
6229_pInt , 6247_pInt , 6257_pInt , 6263_pInt , 6269_pInt , 6271_pInt , 6277_pInt , 6287_pInt , 6299_pInt , 6301_pInt , &
6311_pInt , 6317_pInt , 6323_pInt , 6329_pInt , 6337_pInt , 6343_pInt , 6353_pInt , 6359_pInt , 6361_pInt , 6367_pInt , &
6373_pInt , 6379_pInt , 6389_pInt , 6397_pInt , 6421_pInt , 6427_pInt , 6449_pInt , 6451_pInt , 6469_pInt , 6473_pInt , &
6481_pInt , 6491_pInt , 6521_pInt , 6529_pInt , 6547_pInt , 6551_pInt , 6553_pInt , 6563_pInt , 6569_pInt , 6571_pInt , &
6577_pInt , 6581_pInt , 6599_pInt , 6607_pInt , 6619_pInt , 6637_pInt , 6653_pInt , 6659_pInt , 6661_pInt , 6673_pInt , &
6679_pInt , 6689_pInt , 6691_pInt , 6701_pInt , 6703_pInt , 6709_pInt , 6719_pInt , 6733_pInt , 6737_pInt , 6761_pInt , &
6763_pInt , 6779_pInt , 6781_pInt , 6791_pInt , 6793_pInt , 6803_pInt , 6823_pInt , 6827_pInt , 6829_pInt , 6833_pInt , &
6841_pInt , 6857_pInt , 6863_pInt , 6869_pInt , 6871_pInt , 6883_pInt , 6899_pInt , 6907_pInt , 6911_pInt , 6917_pInt , &
6947_pInt , 6949_pInt , 6959_pInt , 6961_pInt , 6967_pInt , 6971_pInt , 6977_pInt , 6983_pInt , 6991_pInt , 6997_pInt / )
npvec ( 901 : 1000 ) = ( / &
7001_pInt , 7013_pInt , 7019_pInt , 7027_pInt , 7039_pInt , 7043_pInt , 7057_pInt , 7069_pInt , 7079_pInt , 7103_pInt , &
7109_pInt , 7121_pInt , 7127_pInt , 7129_pInt , 7151_pInt , 7159_pInt , 7177_pInt , 7187_pInt , 7193_pInt , 7207_pInt , &
7211_pInt , 7213_pInt , 7219_pInt , 7229_pInt , 7237_pInt , 7243_pInt , 7247_pInt , 7253_pInt , 7283_pInt , 7297_pInt , &
7307_pInt , 7309_pInt , 7321_pInt , 7331_pInt , 7333_pInt , 7349_pInt , 7351_pInt , 7369_pInt , 7393_pInt , 7411_pInt , &
7417_pInt , 7433_pInt , 7451_pInt , 7457_pInt , 7459_pInt , 7477_pInt , 7481_pInt , 7487_pInt , 7489_pInt , 7499_pInt , &
7507_pInt , 7517_pInt , 7523_pInt , 7529_pInt , 7537_pInt , 7541_pInt , 7547_pInt , 7549_pInt , 7559_pInt , 7561_pInt , &
7573_pInt , 7577_pInt , 7583_pInt , 7589_pInt , 7591_pInt , 7603_pInt , 7607_pInt , 7621_pInt , 7639_pInt , 7643_pInt , &
7649_pInt , 7669_pInt , 7673_pInt , 7681_pInt , 7687_pInt , 7691_pInt , 7699_pInt , 7703_pInt , 7717_pInt , 7723_pInt , &
7727_pInt , 7741_pInt , 7753_pInt , 7757_pInt , 7759_pInt , 7789_pInt , 7793_pInt , 7817_pInt , 7823_pInt , 7829_pInt , &
7841_pInt , 7853_pInt , 7867_pInt , 7873_pInt , 7877_pInt , 7879_pInt , 7883_pInt , 7901_pInt , 7907_pInt , 7919_pInt / )
npvec ( 1001 : 1100 ) = ( / &
7927_pInt , 7933_pInt , 7937_pInt , 7949_pInt , 7951_pInt , 7963_pInt , 7993_pInt , 8009_pInt , 8011_pInt , 8017_pInt , &
8039_pInt , 8053_pInt , 8059_pInt , 8069_pInt , 8081_pInt , 8087_pInt , 8089_pInt , 8093_pInt , 8101_pInt , 8111_pInt , &
8117_pInt , 8123_pInt , 8147_pInt , 8161_pInt , 8167_pInt , 8171_pInt , 8179_pInt , 8191_pInt , 8209_pInt , 8219_pInt , &
8221_pInt , 8231_pInt , 8233_pInt , 8237_pInt , 8243_pInt , 8263_pInt , 8269_pInt , 8273_pInt , 8287_pInt , 8291_pInt , &
8293_pInt , 8297_pInt , 8311_pInt , 8317_pInt , 8329_pInt , 8353_pInt , 8363_pInt , 8369_pInt , 8377_pInt , 8387_pInt , &
8389_pInt , 8419_pInt , 8423_pInt , 8429_pInt , 8431_pInt , 8443_pInt , 8447_pInt , 8461_pInt , 8467_pInt , 8501_pInt , &
8513_pInt , 8521_pInt , 8527_pInt , 8537_pInt , 8539_pInt , 8543_pInt , 8563_pInt , 8573_pInt , 8581_pInt , 8597_pInt , &
8599_pInt , 8609_pInt , 8623_pInt , 8627_pInt , 8629_pInt , 8641_pInt , 8647_pInt , 8663_pInt , 8669_pInt , 8677_pInt , &
8681_pInt , 8689_pInt , 8693_pInt , 8699_pInt , 8707_pInt , 8713_pInt , 8719_pInt , 8731_pInt , 8737_pInt , 8741_pInt , &
8747_pInt , 8753_pInt , 8761_pInt , 8779_pInt , 8783_pInt , 8803_pInt , 8807_pInt , 8819_pInt , 8821_pInt , 8831_pInt / )
npvec ( 1101 : 1200 ) = ( / &
8837_pInt , 8839_pInt , 8849_pInt , 8861_pInt , 8863_pInt , 8867_pInt , 8887_pInt , 8893_pInt , 8923_pInt , 8929_pInt , &
8933_pInt , 8941_pInt , 8951_pInt , 8963_pInt , 8969_pInt , 8971_pInt , 8999_pInt , 9001_pInt , 9007_pInt , 9011_pInt , &
9013_pInt , 9029_pInt , 9041_pInt , 9043_pInt , 9049_pInt , 9059_pInt , 9067_pInt , 9091_pInt , 9103_pInt , 9109_pInt , &
9127_pInt , 9133_pInt , 9137_pInt , 9151_pInt , 9157_pInt , 9161_pInt , 9173_pInt , 9181_pInt , 9187_pInt , 9199_pInt , &
9203_pInt , 9209_pInt , 9221_pInt , 9227_pInt , 9239_pInt , 9241_pInt , 9257_pInt , 9277_pInt , 9281_pInt , 9283_pInt , &
9293_pInt , 9311_pInt , 9319_pInt , 9323_pInt , 9337_pInt , 9341_pInt , 9343_pInt , 9349_pInt , 9371_pInt , 9377_pInt , &
9391_pInt , 9397_pInt , 9403_pInt , 9413_pInt , 9419_pInt , 9421_pInt , 9431_pInt , 9433_pInt , 9437_pInt , 9439_pInt , &
9461_pInt , 9463_pInt , 9467_pInt , 9473_pInt , 9479_pInt , 9491_pInt , 9497_pInt , 9511_pInt , 9521_pInt , 9533_pInt , &
9539_pInt , 9547_pInt , 9551_pInt , 9587_pInt , 9601_pInt , 9613_pInt , 9619_pInt , 9623_pInt , 9629_pInt , 9631_pInt , &
9643_pInt , 9649_pInt , 9661_pInt , 9677_pInt , 9679_pInt , 9689_pInt , 9697_pInt , 9719_pInt , 9721_pInt , 9733_pInt / )
npvec ( 1201 : 1300 ) = ( / &
9739_pInt , 9743_pInt , 9749_pInt , 9767_pInt , 9769_pInt , 9781_pInt , 9787_pInt , 9791_pInt , 9803_pInt , 9811_pInt , &
9817_pInt , 9829_pInt , 9833_pInt , 9839_pInt , 9851_pInt , 9857_pInt , 9859_pInt , 9871_pInt , 9883_pInt , 9887_pInt , &
9901_pInt , 9907_pInt , 9923_pInt , 9929_pInt , 9931_pInt , 9941_pInt , 9949_pInt , 9967_pInt , 9973_pInt , 10007_pInt , &
10009_pInt , 10037_pInt , 10039_pInt , 10061_pInt , 10067_pInt , 10069_pInt , 10079_pInt , 10091_pInt , 10093_pInt , 10099_pInt , &
10103_pInt , 10111_pInt , 10133_pInt , 10139_pInt , 10141_pInt , 10151_pInt , 10159_pInt , 10163_pInt , 10169_pInt , 10177_pInt , &
10181_pInt , 10193_pInt , 10211_pInt , 10223_pInt , 10243_pInt , 10247_pInt , 10253_pInt , 10259_pInt , 10267_pInt , 10271_pInt , &
10273_pInt , 10289_pInt , 10301_pInt , 10303_pInt , 10313_pInt , 10321_pInt , 10331_pInt , 10333_pInt , 10337_pInt , 10343_pInt , &
10357_pInt , 10369_pInt , 10391_pInt , 10399_pInt , 10427_pInt , 10429_pInt , 10433_pInt , 10453_pInt , 10457_pInt , 10459_pInt , &
10463_pInt , 10477_pInt , 10487_pInt , 10499_pInt , 10501_pInt , 10513_pInt , 10529_pInt , 10531_pInt , 10559_pInt , 10567_pInt , &
10589_pInt , 10597_pInt , 10601_pInt , 10607_pInt , 10613_pInt , 10627_pInt , 10631_pInt , 10639_pInt , 10651_pInt , 10657_pInt / )
npvec ( 1301 : 1400 ) = ( / &
10663_pInt , 10667_pInt , 10687_pInt , 10691_pInt , 10709_pInt , 10711_pInt , 10723_pInt , 10729_pInt , 10733_pInt , 10739_pInt , &
10753_pInt , 10771_pInt , 10781_pInt , 10789_pInt , 10799_pInt , 10831_pInt , 10837_pInt , 10847_pInt , 10853_pInt , 10859_pInt , &
10861_pInt , 10867_pInt , 10883_pInt , 10889_pInt , 10891_pInt , 10903_pInt , 10909_pInt , 19037_pInt , 10939_pInt , 10949_pInt , &
10957_pInt , 10973_pInt , 10979_pInt , 10987_pInt , 10993_pInt , 11003_pInt , 11027_pInt , 11047_pInt , 11057_pInt , 11059_pInt , &
11069_pInt , 11071_pInt , 11083_pInt , 11087_pInt , 11093_pInt , 11113_pInt , 11117_pInt , 11119_pInt , 11131_pInt , 11149_pInt , &
11159_pInt , 11161_pInt , 11171_pInt , 11173_pInt , 11177_pInt , 11197_pInt , 11213_pInt , 11239_pInt , 11243_pInt , 11251_pInt , &
11257_pInt , 11261_pInt , 11273_pInt , 11279_pInt , 11287_pInt , 11299_pInt , 11311_pInt , 11317_pInt , 11321_pInt , 11329_pInt , &
11351_pInt , 11353_pInt , 11369_pInt , 11383_pInt , 11393_pInt , 11399_pInt , 11411_pInt , 11423_pInt , 11437_pInt , 11443_pInt , &
11447_pInt , 11467_pInt , 11471_pInt , 11483_pInt , 11489_pInt , 11491_pInt , 11497_pInt , 11503_pInt , 11519_pInt , 11527_pInt , &
11549_pInt , 11551_pInt , 11579_pInt , 11587_pInt , 11593_pInt , 11597_pInt , 11617_pInt , 11621_pInt , 11633_pInt , 11657_pInt / )
npvec ( 1401 : 1500 ) = ( / &
11677_pInt , 11681_pInt , 11689_pInt , 11699_pInt , 11701_pInt , 11717_pInt , 11719_pInt , 11731_pInt , 11743_pInt , 11777_pInt , &
11779_pInt , 11783_pInt , 11789_pInt , 11801_pInt , 11807_pInt , 11813_pInt , 11821_pInt , 11827_pInt , 11831_pInt , 11833_pInt , &
11839_pInt , 11863_pInt , 11867_pInt , 11887_pInt , 11897_pInt , 11903_pInt , 11909_pInt , 11923_pInt , 11927_pInt , 11933_pInt , &
11939_pInt , 11941_pInt , 11953_pInt , 11959_pInt , 11969_pInt , 11971_pInt , 11981_pInt , 11987_pInt , 12007_pInt , 12011_pInt , &
12037_pInt , 12041_pInt , 12043_pInt , 12049_pInt , 12071_pInt , 12073_pInt , 12097_pInt , 12101_pInt , 12107_pInt , 12109_pInt , &
12113_pInt , 12119_pInt , 12143_pInt , 12149_pInt , 12157_pInt , 12161_pInt , 12163_pInt , 12197_pInt , 12203_pInt , 12211_pInt , &
12227_pInt , 12239_pInt , 12241_pInt , 12251_pInt , 12253_pInt , 12263_pInt , 12269_pInt , 12277_pInt , 12281_pInt , 12289_pInt , &
12301_pInt , 12323_pInt , 12329_pInt , 12343_pInt , 12347_pInt , 12373_pInt , 12377_pInt , 12379_pInt , 12391_pInt , 12401_pInt , &
12409_pInt , 12413_pInt , 12421_pInt , 12433_pInt , 12437_pInt , 12451_pInt , 12457_pInt , 12473_pInt , 12479_pInt , 12487_pInt , &
12491_pInt , 12497_pInt , 12503_pInt , 12511_pInt , 12517_pInt , 12527_pInt , 12539_pInt , 12541_pInt , 12547_pInt , 12553_pInt / )
2007-03-20 19:25:22 +05:30
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endif
2007-03-20 19:25:22 +05:30
2011-12-01 17:31:13 +05:30
if ( n == - 1_pInt ) then
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prime = prime_max
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else if ( n == 0_pInt ) then
prime = 1_pInt
else if ( n < = prime_max ) then
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prime = npvec ( n )
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else
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call IO_error ( error_ID = 406_pInt )
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end if
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end function prime
2007-03-20 19:25:22 +05:30
2011-12-01 17:31:13 +05:30
2009-01-20 00:40:58 +05:30
!**************************************************************************
! volume of tetrahedron given by four vertices
!**************************************************************************
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pure function math_volTetrahedron ( v1 , v2 , v3 , v4 )
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implicit none
real ( pReal ) math_volTetrahedron
real ( pReal ) , dimension ( 3 ) , intent ( in ) :: v1 , v2 , v3 , v4
real ( pReal ) , dimension ( 3 , 3 ) :: m
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m ( 1 : 3 , 1 ) = v1 - v2
m ( 1 : 3 , 2 ) = v2 - v3
m ( 1 : 3 , 3 ) = v3 - v4
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2012-01-26 19:20:00 +05:30
math_volTetrahedron = math_det33 ( m ) / 6.0_pReal
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end function math_volTetrahedron
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2011-12-01 17:31:13 +05:30
2011-10-24 23:56:34 +05:30
!**************************************************************************
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! rotate 33 tensor forward
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!**************************************************************************
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pure function math_rotate_forward33 ( tensor , rot_tensor )
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implicit none
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real ( pReal ) , dimension ( 3 , 3 ) :: math_rotate_forward33
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real ( pReal ) , dimension ( 3 , 3 ) , intent ( in ) :: tensor , rot_tensor
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math_rotate_forward33 = math_mul33x33 ( rot_tensor , &
math_mul33x33 ( tensor , math_transpose33 ( rot_tensor ) ) )
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end function math_rotate_forward33
2011-10-24 23:56:34 +05:30
2011-12-01 17:31:13 +05:30
2011-10-24 23:56:34 +05:30
!**************************************************************************
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! rotate 33 tensor backward
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!**************************************************************************
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pure function math_rotate_backward33 ( tensor , rot_tensor )
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implicit none
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real ( pReal ) , dimension ( 3 , 3 ) :: math_rotate_backward33
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real ( pReal ) , dimension ( 3 , 3 ) , intent ( in ) :: tensor , rot_tensor
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math_rotate_backward33 = math_mul33x33 ( math_transpose33 ( rot_tensor ) , &
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math_mul33x33 ( tensor , rot_tensor ) )
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end function math_rotate_backward33
2011-10-24 23:56:34 +05:30
2011-12-01 17:31:13 +05:30
2011-10-24 23:56:34 +05:30
!**************************************************************************
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! rotate 3333 tensor
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! C'_ijkl=g_im*g_jn*g_ko*g_lp*C_mnop
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!**************************************************************************
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pure function math_rotate_forward3333 ( tensor , rot_tensor )
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implicit none
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real ( pReal ) , dimension ( 3 , 3 , 3 , 3 ) :: math_rotate_forward3333
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real ( pReal ) , dimension ( 3 , 3 ) , intent ( in ) :: rot_tensor
real ( pReal ) , dimension ( 3 , 3 , 3 , 3 ) , intent ( in ) :: tensor
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integer ( pInt ) :: i , j , k , l , m , n , o , p
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math_rotate_forward3333 = 0.0_pReal
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do i = 1_pInt , 3_pInt ; do j = 1_pInt , 3_pInt ; do k = 1_pInt , 3_pInt ; do l = 1_pInt , 3_pInt
do m = 1_pInt , 3_pInt ; do n = 1_pInt , 3_pInt ; do o = 1_pInt , 3_pInt ; do p = 1_pInt , 3_pInt
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math_rotate_forward3333 ( i , j , k , l ) = tensor ( i , j , k , l ) + rot_tensor ( m , i ) * rot_tensor ( n , j ) * &
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rot_tensor ( o , k ) * rot_tensor ( p , l ) * tensor ( m , n , o , p )
enddo ; enddo ; enddo ; enddo ; enddo ; enddo ; enddo ; enddo
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end function math_rotate_forward3333
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2011-12-01 17:31:13 +05:30
!+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
!+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
! Functions below are taken from the old postprocessingMath.f90
! mostly they are used in combination with f2py to build fortran
!+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
! put the next two funtions into mesh?
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function mesh_location ( idx , resolution )
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! small helper functions for indexing
! CAREFULL, index and location runs from 0 to N-1 (python style)
integer ( pInt ) , intent ( in ) :: idx
integer ( pInt ) , intent ( in ) , dimension ( 3 ) :: resolution
integer ( pInt ) , dimension ( 3 ) :: mesh_location
mesh_location = ( / modulo ( idx / resolution ( 3 ) / resolution ( 2 ) , resolution ( 1 ) ) , &
modulo ( idx / resolution ( 3 ) , resolution ( 2 ) ) , &
modulo ( idx , resolution ( 3 ) ) / )
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end function mesh_location
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function mesh_index ( location , resolution )
! small helper functions for indexing
! CAREFULL, index and location runs from 0 to N-1 (python style)
integer ( pInt ) , intent ( in ) , dimension ( 3 ) :: resolution , location
integer ( pInt ) :: mesh_index
mesh_index = modulo ( location ( 3 ) , resolution ( 3 ) ) + &
( modulo ( location ( 2 ) , resolution ( 2 ) ) ) * resolution ( 3 ) + &
( modulo ( location ( 1 ) , resolution ( 1 ) ) ) * resolution ( 3 ) * resolution ( 2 )
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end function mesh_index
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!+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
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subroutine volume_compare ( res , geomdim , defgrad , nodes , volume_mismatch )
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!+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
! Routine to calculate the mismatch between volume of reconstructed (compatible
! cube and determinant of defgrad at the FP
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use debug , only : debug_math , &
debug_what , &
debug_levelBasic
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implicit none
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! input variables
integer ( pInt ) , intent ( in ) , dimension ( 3 ) :: res
real ( pReal ) , intent ( in ) , dimension ( 3 ) :: geomdim
real ( pReal ) , intent ( in ) , dimension ( res ( 1 ) , res ( 2 ) , res ( 3 ) , 3 , 3 ) :: defgrad
real ( pReal ) , intent ( in ) , dimension ( res ( 1 ) + 1_pInt , res ( 2 ) + 1_pInt , res ( 3 ) + 1_pInt , 3 ) :: nodes
! output variables
real ( pReal ) , intent ( out ) , dimension ( res ( 1 ) , res ( 2 ) , res ( 3 ) ) :: volume_mismatch
! other variables
real ( pReal ) , dimension ( 8 , 3 ) :: coords
integer ( pInt ) i , j , k
real ( pReal ) vol_initial
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if ( iand ( debug_what ( debug_math ) , debug_levelBasic ) / = 0_pInt ) then
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print * , 'Calculating volume mismatch'
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print '(a,3(e12.5))' , ' Dimension: ' , geomdim
print '(a,3(i5))' , ' Resolution:' , res
2012-01-13 21:48:16 +05:30
endif
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vol_initial = geomdim ( 1 ) * geomdim ( 2 ) * geomdim ( 3 ) / ( real ( res ( 1 ) * res ( 2 ) * res ( 3 ) , pReal ) )
do k = 1_pInt , res ( 3 )
do j = 1_pInt , res ( 2 )
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do i = 1_pInt , res ( 1 )
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coords ( 1 , 1 : 3 ) = nodes ( i , j , k , 1 : 3 )
coords ( 2 , 1 : 3 ) = nodes ( i + 1_pInt , j , k , 1 : 3 )
coords ( 3 , 1 : 3 ) = nodes ( i + 1_pInt , j + 1_pInt , k , 1 : 3 )
coords ( 4 , 1 : 3 ) = nodes ( i , j + 1_pInt , k , 1 : 3 )
coords ( 5 , 1 : 3 ) = nodes ( i , j , k + 1_pInt , 1 : 3 )
coords ( 6 , 1 : 3 ) = nodes ( i + 1_pInt , j , k + 1_pInt , 1 : 3 )
coords ( 7 , 1 : 3 ) = nodes ( i + 1_pInt , j + 1_pInt , k + 1_pInt , 1 : 3 )
coords ( 8 , 1 : 3 ) = nodes ( i , j + 1_pInt , k + 1_pInt , 1 : 3 )
volume_mismatch ( i , j , k ) = abs ( math_volTetrahedron ( coords ( 7 , 1 : 3 ) , coords ( 1 , 1 : 3 ) , coords ( 8 , 1 : 3 ) , coords ( 4 , 1 : 3 ) ) ) &
+ abs ( math_volTetrahedron ( coords ( 7 , 1 : 3 ) , coords ( 1 , 1 : 3 ) , coords ( 8 , 1 : 3 ) , coords ( 5 , 1 : 3 ) ) ) &
+ abs ( math_volTetrahedron ( coords ( 7 , 1 : 3 ) , coords ( 1 , 1 : 3 ) , coords ( 3 , 1 : 3 ) , coords ( 4 , 1 : 3 ) ) ) &
+ abs ( math_volTetrahedron ( coords ( 7 , 1 : 3 ) , coords ( 1 , 1 : 3 ) , coords ( 3 , 1 : 3 ) , coords ( 2 , 1 : 3 ) ) ) &
+ abs ( math_volTetrahedron ( coords ( 7 , 1 : 3 ) , coords ( 5 , 1 : 3 ) , coords ( 2 , 1 : 3 ) , coords ( 6 , 1 : 3 ) ) ) &
+ abs ( math_volTetrahedron ( coords ( 7 , 1 : 3 ) , coords ( 5 , 1 : 3 ) , coords ( 2 , 1 : 3 ) , coords ( 1 , 1 : 3 ) ) )
2012-01-26 19:20:00 +05:30
volume_mismatch ( i , j , k ) = volume_mismatch ( i , j , k ) / math_det33 ( defgrad ( i , j , k , 1 : 3 , 1 : 3 ) )
2011-12-01 17:31:13 +05:30
enddo ; enddo ; enddo
volume_mismatch = volume_mismatch / vol_initial
end subroutine volume_compare
!+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
subroutine shape_compare ( res , geomdim , defgrad , nodes , centroids , shape_mismatch )
!+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
! Routine to calculate the mismatch between the vectors from the central point to
! the corners of reconstructed (combatible) volume element and the vectors calculated by deforming
! the initial volume element with the current deformation gradient
2012-01-13 21:48:16 +05:30
2012-03-09 01:55:28 +05:30
use debug , only : debug_math , &
debug_what , &
debug_levelBasic
2011-12-01 17:31:13 +05:30
implicit none
! input variables
integer ( pInt ) , intent ( in ) , dimension ( 3 ) :: res
real ( pReal ) , intent ( in ) , dimension ( 3 ) :: geomdim
real ( pReal ) , intent ( in ) , dimension ( res ( 1 ) , res ( 2 ) , res ( 3 ) , 3 , 3 ) :: defgrad
real ( pReal ) , intent ( in ) , dimension ( res ( 1 ) + 1_pInt , res ( 2 ) + 1_pInt , res ( 3 ) + 1_pInt , 3 ) :: nodes
real ( pReal ) , intent ( in ) , dimension ( res ( 1 ) , res ( 2 ) , res ( 3 ) , 3 ) :: centroids
! output variables
real ( pReal ) , intent ( out ) , dimension ( res ( 1 ) , res ( 2 ) , res ( 3 ) ) :: shape_mismatch
! other variables
real ( pReal ) , dimension ( 8 , 3 ) :: coords_initial
integer ( pInt ) i , j , k
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if ( iand ( debug_what ( debug_math ) , debug_levelBasic ) / = 0_pInt ) then
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print * , 'Calculating shape mismatch'
2012-02-10 16:54:53 +05:30
print '(a,3(e12.5))' , ' Dimension: ' , geomdim
print '(a,3(i5))' , ' Resolution:' , res
2012-01-13 21:48:16 +05:30
endif
2011-12-01 17:31:13 +05:30
coords_initial ( 1 , 1 : 3 ) = ( / - geomdim ( 1 ) / 2.0_pReal / real ( res ( 1 ) , pReal ) , &
- geomdim ( 2 ) / 2.0_pReal / real ( res ( 2 ) , pReal ) , &
- geomdim ( 3 ) / 2.0_pReal / real ( res ( 3 ) , pReal ) / )
coords_initial ( 2 , 1 : 3 ) = ( / + geomdim ( 1 ) / 2.0_pReal / real ( res ( 1 ) , pReal ) , &
- geomdim ( 2 ) / 2.0_pReal / real ( res ( 2 ) , pReal ) , &
- geomdim ( 3 ) / 2.0_pReal / real ( res ( 3 ) , pReal ) / )
coords_initial ( 3 , 1 : 3 ) = ( / + geomdim ( 1 ) / 2.0_pReal / real ( res ( 1 ) , pReal ) , &
+ geomdim ( 2 ) / 2.0_pReal / real ( res ( 2 ) , pReal ) , &
- geomdim ( 3 ) / 2.0_pReal / real ( res ( 3 ) , pReal ) / )
coords_initial ( 4 , 1 : 3 ) = ( / - geomdim ( 1 ) / 2.0_pReal / real ( res ( 1 ) , pReal ) , &
+ geomdim ( 2 ) / 2.0_pReal / real ( res ( 2 ) , pReal ) , &
- geomdim ( 3 ) / 2.0_pReal / real ( res ( 3 ) , pReal ) / )
coords_initial ( 5 , 1 : 3 ) = ( / - geomdim ( 1 ) / 2.0_pReal / real ( res ( 1 ) , pReal ) , &
- geomdim ( 2 ) / 2.0_pReal / real ( res ( 2 ) , pReal ) , &
+ geomdim ( 3 ) / 2.0_pReal / real ( res ( 3 ) , pReal ) / )
coords_initial ( 6 , 1 : 3 ) = ( / + geomdim ( 1 ) / 2.0_pReal / real ( res ( 1 ) , pReal ) , &
- geomdim ( 2 ) / 2.0_pReal / real ( res ( 2 ) , pReal ) , &
+ geomdim ( 3 ) / 2.0_pReal / real ( res ( 3 ) , pReal ) / )
coords_initial ( 7 , 1 : 3 ) = ( / + geomdim ( 1 ) / 2.0_pReal / real ( res ( 1 ) , pReal ) , &
+ geomdim ( 2 ) / 2.0_pReal / real ( res ( 2 ) , pReal ) , &
+ geomdim ( 3 ) / 2.0_pReal / real ( res ( 3 ) , pReal ) / )
coords_initial ( 8 , 1 : 3 ) = ( / - geomdim ( 1 ) / 2.0_pReal / real ( res ( 1 ) , pReal ) , &
+ geomdim ( 2 ) / 2.0_pReal / real ( res ( 2 ) , pReal ) , &
+ geomdim ( 3 ) / 2.0_pReal / real ( res ( 3 ) , pReal ) / )
do i = 1_pInt , 8_pInt
enddo
do k = 1_pInt , res ( 3 )
do j = 1_pInt , res ( 2 )
do i = 1_pInt , res ( 1 )
shape_mismatch ( i , j , k ) = &
sqrt ( sum ( ( nodes ( i , j , k , 1 : 3 ) - centroids ( i , j , k , 1 : 3 ) &
- matmul ( defgrad ( i , j , k , 1 : 3 , 1 : 3 ) , coords_initial ( 1 , 1 : 3 ) ) ) ** 2.0_pReal ) ) &
+ sqrt ( sum ( ( nodes ( i + 1_pInt , j , k , 1 : 3 ) - centroids ( i , j , k , 1 : 3 ) &
- matmul ( defgrad ( i , j , k , 1 : 3 , 1 : 3 ) , coords_initial ( 2 , 1 : 3 ) ) ) ** 2.0_pReal ) ) &
+ sqrt ( sum ( ( nodes ( i + 1_pInt , j + 1_pInt , k , 1 : 3 ) - centroids ( i , j , k , 1 : 3 ) &
- matmul ( defgrad ( i , j , k , 1 : 3 , 1 : 3 ) , coords_initial ( 3 , 1 : 3 ) ) ) ** 2.0_pReal ) ) &
+ sqrt ( sum ( ( nodes ( i , j + 1_pInt , k , 1 : 3 ) - centroids ( i , j , k , 1 : 3 ) &
- matmul ( defgrad ( i , j , k , 1 : 3 , 1 : 3 ) , coords_initial ( 4 , 1 : 3 ) ) ) ** 2.0_pReal ) ) &
+ sqrt ( sum ( ( nodes ( i , j , k + 1_pInt , 1 : 3 ) - centroids ( i , j , k , 1 : 3 ) &
- matmul ( defgrad ( i , j , k , 1 : 3 , 1 : 3 ) , coords_initial ( 5 , 1 : 3 ) ) ) ** 2.0_pReal ) ) &
+ sqrt ( sum ( ( nodes ( i + 1_pInt , j , k + 1_pInt , 1 : 3 ) - centroids ( i , j , k , 1 : 3 ) &
- matmul ( defgrad ( i , j , k , 1 : 3 , 1 : 3 ) , coords_initial ( 6 , 1 : 3 ) ) ) ** 2.0_pReal ) ) &
+ sqrt ( sum ( ( nodes ( i + 1_pInt , j + 1_pInt , k + 1_pInt , 1 : 3 ) - centroids ( i , j , k , 1 : 3 ) &
- matmul ( defgrad ( i , j , k , 1 : 3 , 1 : 3 ) , coords_initial ( 7 , 1 : 3 ) ) ) ** 2.0_pReal ) ) &
+ sqrt ( sum ( ( nodes ( i , j + 1_pInt , k + 1_pInt , 1 : 3 ) - centroids ( i , j , k , 1 : 3 ) &
- matmul ( defgrad ( i , j , k , 1 : 3 , 1 : 3 ) , coords_initial ( 8 , 1 : 3 ) ) ) ** 2.0_pReal ) )
enddo ; enddo ; enddo
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end subroutine shape_compare
2011-12-01 17:31:13 +05:30
!+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
subroutine mesh_regular_grid ( res , geomdim , defgrad_av , centroids , nodes )
!+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
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! Routine to build mesh of (distorted) cubes for given coordinates (= center of the cubes)
2011-12-01 17:31:13 +05:30
!
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use debug , only : debug_math , &
debug_what , &
debug_levelBasic
2011-12-01 17:31:13 +05:30
implicit none
! input variables
integer ( pInt ) , intent ( in ) , dimension ( 3 ) :: res
real ( pReal ) , intent ( in ) , dimension ( 3 ) :: geomdim
real ( pReal ) , intent ( in ) , dimension ( 3 , 3 ) :: defgrad_av
real ( pReal ) , intent ( in ) , dimension ( res ( 1 ) , res ( 2 ) , res ( 3 ) , 3 ) :: centroids
! output variables
real ( pReal ) , intent ( out ) , dimension ( res ( 1 ) + 1_pInt , res ( 2 ) + 1_pInt , res ( 3 ) + 1_pInt , 3 ) :: nodes
! variables with dimension depending on input
real ( pReal ) , dimension ( res ( 1 ) + 2_pInt , res ( 2 ) + 2_pInt , res ( 3 ) + 2_pInt , 3 ) :: wrappedCentroids
! other variables
integer ( pInt ) :: i , j , k , n
2011-12-06 23:16:33 +05:30
integer ( pInt ) , dimension ( 3 ) , parameter :: diag = 1_pInt
integer ( pInt ) , dimension ( 3 ) :: shift = 0_pInt , lookup = 0_pInt , me = 0_pInt
2011-12-01 17:31:13 +05:30
integer ( pInt ) , dimension ( 3 , 8 ) :: neighbor = reshape ( ( / &
0_pInt , 0_pInt , 0_pInt , &
1_pInt , 0_pInt , 0_pInt , &
1_pInt , 1_pInt , 0_pInt , &
0_pInt , 1_pInt , 0_pInt , &
0_pInt , 0_pInt , 1_pInt , &
1_pInt , 0_pInt , 1_pInt , &
1_pInt , 1_pInt , 1_pInt , &
0_pInt , 1_pInt , 1_pInt &
/ ) , &
( / 3 , 8 / ) )
2012-01-25 16:00:39 +05:30
2012-03-09 01:55:28 +05:30
if ( iand ( debug_what ( debug_math ) , debug_levelBasic ) / = 0_pInt ) then
2012-01-13 21:48:16 +05:30
print * , 'Meshing cubes around centroids'
2012-02-10 16:54:53 +05:30
print '(a,3(e12.5))' , ' Dimension: ' , geomdim
print '(a,3(i5))' , ' Resolution:' , res
2012-01-13 21:48:16 +05:30
endif
2011-12-01 17:31:13 +05:30
nodes = 0.0_pReal
wrappedCentroids = 0.0_pReal
wrappedCentroids ( 2_pInt : res ( 1 ) + 1_pInt , 2_pInt : res ( 2 ) + 1_pInt , 2_pInt : res ( 3 ) + 1_pInt , 1 : 3 ) = centroids
do k = 0_pInt , res ( 3 ) + 1_pInt
do j = 0_pInt , res ( 2 ) + 1_pInt
do i = 0_pInt , res ( 1 ) + 1_pInt
if ( k == 0_pInt . or . k == res ( 3 ) + 1_pInt . or . & ! z skin
j == 0_pInt . or . j == res ( 2 ) + 1_pInt . or . & ! y skin
i == 0_pInt . or . i == res ( 1 ) + 1_pInt ) then ! x skin
me = ( / i , j , k / ) ! me on skin
shift = sign ( abs ( res + diag - 2_pInt * me ) / ( res + diag ) , res + diag - 2_pInt * me )
lookup = me - diag + shift * res
2011-12-06 22:28:17 +05:30
wrappedCentroids ( i + 1_pInt , j + 1_pInt , k + 1_pInt , 1 : 3 ) = &
centroids ( lookup ( 1 ) + 1_pInt , lookup ( 2 ) + 1_pInt , lookup ( 3 ) + 1_pInt , 1 : 3 ) - &
2011-12-01 17:31:13 +05:30
matmul ( defgrad_av , shift * geomdim )
endif
enddo ; enddo ; enddo
do k = 0_pInt , res ( 3 )
do j = 0_pInt , res ( 2 )
do i = 0_pInt , res ( 1 )
do n = 1_pInt , 8_pInt
2011-12-06 22:28:17 +05:30
nodes ( i + 1_pInt , j + 1_pInt , k + 1_pInt , 1 : 3 ) = &
2011-12-06 23:16:33 +05:30
nodes ( i + 1_pInt , j + 1_pInt , k + 1_pInt , 1 : 3 ) + wrappedCentroids ( i + 1_pInt + neighbor ( 1_pInt , n ) , &
j + 1_pInt + neighbor ( 2 , n ) , &
k + 1_pInt + neighbor ( 3 , n ) , 1 : 3 )
2011-12-01 17:31:13 +05:30
enddo ; enddo ; enddo ; enddo
nodes = nodes / 8.0_pReal
end subroutine mesh_regular_grid
!+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
subroutine deformed_linear ( res , geomdim , defgrad_av , defgrad , coord_avgCorner )
!+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
! Routine to calculate coordinates in current configuration for given defgrad
! using linear interpolation (blurres out high frequency defomation)
!
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use debug , only : debug_math , &
debug_what , &
debug_levelBasic
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implicit none
! input variables
integer ( pInt ) , intent ( in ) , dimension ( 3 ) :: res
real ( pReal ) , intent ( in ) , dimension ( 3 ) :: geomdim
real ( pReal ) , intent ( in ) , dimension ( 3 , 3 ) :: defgrad_av
real ( pReal ) , intent ( in ) , dimension ( res ( 1 ) , res ( 2 ) , res ( 3 ) , 3 , 3 ) :: defgrad
! output variables
real ( pReal ) , intent ( out ) , dimension ( res ( 1 ) , res ( 2 ) , res ( 3 ) , 3 ) :: coord_avgCorner
! variables with dimension depending on input
real ( pReal ) , dimension ( 8 , 6 , res ( 1 ) , res ( 2 ) , res ( 3 ) , 3 ) :: coord
real ( pReal ) , dimension ( 8 , res ( 1 ) , res ( 2 ) , res ( 3 ) , 3 ) :: coord_avgOrder
! other variables
real ( pReal ) , dimension ( 3 ) :: myStep , fones = 1.0_pReal , parameter_coords , negative , positive
integer ( pInt ) , dimension ( 3 ) :: rear , init , ones = 1_pInt , oppo , me
integer ( pInt ) i , j , k , s , o
integer ( pInt ) , dimension ( 3 , 8 ) :: corner = reshape ( ( / &
0_pInt , 0_pInt , 0_pInt , &
1_pInt , 0_pInt , 0_pInt , &
1_pInt , 1_pInt , 0_pInt , &
0_pInt , 1_pInt , 0_pInt , &
1_pInt , 1_pInt , 1_pInt , &
0_pInt , 1_pInt , 1_pInt , &
0_pInt , 0_pInt , 1_pInt , &
1_pInt , 0_pInt , 1_pInt &
/ ) , &
( / 3 , 8 / ) )
integer ( pInt ) , dimension ( 3 , 8 ) :: step = reshape ( ( / &
1_pInt , 1_pInt , 1_pInt , &
- 1_pInt , 1_pInt , 1_pInt , &
- 1_pInt , - 1_pInt , 1_pInt , &
1_pInt , - 1_pInt , 1_pInt , &
- 1_pInt , - 1_pInt , - 1_pInt , &
1_pInt , - 1_pInt , - 1_pInt , &
1_pInt , 1_pInt , - 1_pInt , &
- 1_pInt , 1_pInt , - 1_pInt &
/ ) , &
( / 3 , 8 / ) )
integer ( pInt ) , dimension ( 3 , 6 ) :: order = reshape ( ( / &
1_pInt , 2_pInt , 3_pInt , &
1_pInt , 3_pInt , 2_pInt , &
2_pInt , 1_pInt , 3_pInt , &
2_pInt , 3_pInt , 1_pInt , &
3_pInt , 1_pInt , 2_pInt , &
3_pInt , 2_pInt , 1_pInt &
/ ) , &
( / 3 , 6 / ) )
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if ( iand ( debug_what ( debug_math ) , debug_levelBasic ) / = 0_pInt ) then
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print * , 'Restore geometry using linear integration'
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print '(a,3(e12.5))' , ' Dimension: ' , geomdim
print '(a,3(i5))' , ' Resolution:' , res
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endif
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coord_avgOrder = 0.0_pReal
do s = 0_pInt , 7_pInt ! corners (from 0 to 7)
init = corner ( : , s + 1_pInt ) * ( res - ones ) + ones
oppo = corner ( : , mod ( ( s + 4_pInt ) , 8_pInt ) + 1_pInt ) * ( res - ones ) + ones
do o = 1_pInt , 6_pInt ! orders (from 1 to 6)
do k = init ( order ( 3 , o ) ) , oppo ( order ( 3 , o ) ) , step ( order ( 3 , o ) , s + 1_pInt )
rear ( order ( 2 , o ) ) = init ( order ( 2 , o ) )
do j = init ( order ( 2 , o ) ) , oppo ( order ( 2 , o ) ) , step ( order ( 2 , o ) , s + 1_pInt )
rear ( order ( 1 , o ) ) = init ( order ( 1 , o ) )
do i = init ( order ( 1 , o ) ) , oppo ( order ( 1 , o ) ) , step ( order ( 1 , o ) , s + 1_pInt )
me ( order ( 1 , o ) ) = i
me ( order ( 2 , o ) ) = j
me ( order ( 3 , o ) ) = k
if ( ( me ( 1 ) == init ( 1 ) ) . and . ( me ( 2 ) == init ( 2 ) ) . and . ( me ( 3 ) == init ( 3 ) ) ) then
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coord ( s + 1_pInt , o , me ( 1 ) , me ( 2 ) , me ( 3 ) , 1 : 3 ) = geomdim * ( matmul ( defgrad_av , real ( corner ( 1 : 3 , s + 1 ) , pReal ) ) + &
matmul ( defgrad ( me ( 1 ) , me ( 2 ) , me ( 3 ) , 1 : 3 , 1 : 3 ) , 0.5_pReal * real ( step ( 1 : 3 , s + 1_pInt ) / res , pReal ) ) )
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else
myStep = ( me - rear ) * geomdim / res
coord ( s + 1_pInt , o , me ( 1 ) , me ( 2 ) , me ( 3 ) , 1 : 3 ) = coord ( s + 1_pInt , o , rear ( 1 ) , rear ( 2 ) , rear ( 3 ) , 1 : 3 ) + &
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0.5_pReal * matmul ( defgrad ( me ( 1 ) , me ( 2 ) , me ( 3 ) , 1 : 3 , 1 : 3 ) + &
defgrad ( rear ( 1 ) , rear ( 2 ) , rear ( 3 ) , 1 : 3 , 1 : 3 ) , myStep )
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endif
rear = me
enddo ; enddo ; enddo ; enddo
do i = 1_pInt , 6_pInt
coord_avgOrder ( s + 1_pInt , 1 : res ( 1 ) , 1 : res ( 2 ) , 1 : res ( 3 ) , 1 : 3 ) = coord_avgOrder ( s + 1_pInt , 1 : res ( 1 ) , 1 : res ( 2 ) , 1 : res ( 3 ) , 1 : 3 ) &
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+ coord ( s + 1_pInt , i , 1 : res ( 1 ) , 1 : res ( 2 ) , 1 : res ( 3 ) , 1 : 3 ) / 6.0_pReal
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enddo
enddo
do k = 0_pInt , res ( 3 ) - 1_pInt
do j = 0_pInt , res ( 2 ) - 1_pInt
do i = 0_pInt , res ( 1 ) - 1_pInt
parameter_coords = ( 2.0_pReal * ( / real ( i , pReal ) + 0.0_pReal , real ( j , pReal ) + 0.0_pReal , real ( k , pReal ) + 0.0_pReal / ) &
- real ( res , pReal ) + fones ) / ( real ( res , pReal ) - fones )
positive = fones + parameter_coords
negative = fones - parameter_coords
coord_avgCorner ( i + 1_pInt , j + 1_pInt , k + 1_pInt , 1 : 3 ) &
= ( coord_avgOrder ( 1 , i + 1_pInt , j + 1_pInt , k + 1_pInt , 1 : 3 ) * negative ( 1 ) * negative ( 2 ) * negative ( 3 ) &
+ coord_avgOrder ( 2 , i + 1_pInt , j + 1_pInt , k + 1_pInt , 1 : 3 ) * positive ( 1 ) * negative ( 2 ) * negative ( 3 ) &
+ coord_avgOrder ( 3 , i + 1_pInt , j + 1_pInt , k + 1_pInt , 1 : 3 ) * positive ( 1 ) * positive ( 2 ) * negative ( 3 ) &
+ coord_avgOrder ( 4 , i + 1_pInt , j + 1_pInt , k + 1_pInt , 1 : 3 ) * negative ( 1 ) * positive ( 2 ) * negative ( 3 ) &
+ coord_avgOrder ( 5 , i + 1_pInt , j + 1_pInt , k + 1_pInt , 1 : 3 ) * positive ( 1 ) * positive ( 2 ) * positive ( 3 ) &
+ coord_avgOrder ( 6 , i + 1_pInt , j + 1_pInt , k + 1_pInt , 1 : 3 ) * negative ( 1 ) * positive ( 2 ) * positive ( 3 ) &
+ coord_avgOrder ( 7 , i + 1_pInt , j + 1_pInt , k + 1_pInt , 1 : 3 ) * negative ( 1 ) * negative ( 2 ) * positive ( 3 ) &
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+ coord_avgOrder ( 8 , i + 1_pInt , j + 1_pInt , k + 1_pInt , 1 : 3 ) * positive ( 1 ) * negative ( 2 ) * positive ( 3 ) ) * 0.125_pReal
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enddo ; enddo ; enddo
end subroutine deformed_linear
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#ifdef Spectral
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!+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
subroutine deformed_fft ( res , geomdim , defgrad_av , scaling , defgrad , coords )
!+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
! Routine to calculate coordinates in current configuration for given defgrad
! using integration in Fourier space (more accurate than deformed(...))
!
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use IO , only : IO_error
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use numerics , only : fftw_timelimit , fftw_planner_flag
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use debug , only : debug_math , &
debug_what , &
debug_levelBasic
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implicit none
! input variables
integer ( pInt ) , intent ( in ) , dimension ( 3 ) :: res
real ( pReal ) , intent ( in ) , dimension ( 3 ) :: geomdim
real ( pReal ) , intent ( in ) , dimension ( 3 , 3 ) :: defgrad_av
real ( pReal ) , intent ( in ) :: scaling
real ( pReal ) , intent ( in ) , dimension ( res ( 1 ) , res ( 2 ) , res ( 3 ) , 3 , 3 ) :: defgrad
! output variables
real ( pReal ) , intent ( out ) , dimension ( res ( 1 ) , res ( 2 ) , res ( 3 ) , 3 ) :: coords
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! allocatable arrays for fftw c routines
type ( C_PTR ) :: fftw_forth , fftw_back
type ( C_PTR ) :: coords_fftw , defgrad_fftw
real ( pReal ) , dimension ( : , : , : , : , : ) , pointer :: defgrad_real
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complex ( pReal ) , dimension ( : , : , : , : , : ) , pointer :: defgrad_fourier
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real ( pReal ) , dimension ( : , : , : , : ) , pointer :: coords_real
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complex ( pReal ) , dimension ( : , : , : , : ) , pointer :: coords_fourier
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! other variables
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integer ( pInt ) :: i , j , k , m , res1_red
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integer ( pInt ) , dimension ( 3 ) :: k_s
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real ( pReal ) , dimension ( 3 ) :: step , offset_coords , integrator
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integrator = geomdim / 2.0_pReal / pi ! see notes where it is used
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if ( iand ( debug_what ( debug_math ) , debug_levelBasic ) / = 0_pInt ) then
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print * , 'Restore geometry using FFT-based integration'
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print '(a,3(e12.5))' , ' Dimension: ' , geomdim
print '(a,3(i5))' , ' Resolution:' , res
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endif
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res1_red = res ( 1 ) / 2_pInt + 1_pInt ! size of complex array in first dimension (c2r, r2c)
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step = geomdim / real ( res , pReal )
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if ( pReal / = C_DOUBLE . or . pInt / = C_INT ) call IO_error ( error_ID = 808_pInt )
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call fftw_set_timelimit ( fftw_timelimit )
defgrad_fftw = fftw_alloc_complex ( int ( res1_red * res ( 2 ) * res ( 3 ) * 9_pInt , C_SIZE_T ) ) !C_SIZE_T is of type integer(8)
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call c_f_pointer ( defgrad_fftw , defgrad_real , [ res ( 1 ) + 2_pInt , res ( 2 ) , res ( 3 ) , 3_pInt , 3_pInt ] )
call c_f_pointer ( defgrad_fftw , defgrad_fourier , [ res1_red , res ( 2 ) , res ( 3 ) , 3_pInt , 3_pInt ] )
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coords_fftw = fftw_alloc_complex ( int ( res1_red * res ( 2 ) * res ( 3 ) * 3_pInt , C_SIZE_T ) ) !C_SIZE_T is of type integer(8)
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call c_f_pointer ( coords_fftw , coords_real , [ res ( 1 ) + 2_pInt , res ( 2 ) , res ( 3 ) , 3_pInt ] )
call c_f_pointer ( coords_fftw , coords_fourier , [ res1_red , res ( 2 ) , res ( 3 ) , 3_pInt ] )
fftw_forth = fftw_plan_many_dft_r2c ( 3_pInt , ( / res ( 3 ) , res ( 2 ) , res ( 1 ) / ) , 9_pInt , & ! dimensions , length in each dimension in reversed order
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defgrad_real , ( / res ( 3 ) , res ( 2 ) , res ( 1 ) + 2_pInt / ) , & ! input data , physical length in each dimension in reversed order
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1_pInt , res ( 3 ) * res ( 2 ) * ( res ( 1 ) + 2_pInt ) , & ! striding , product of physical lenght in the 3 dimensions
defgrad_fourier , ( / res ( 3 ) , res ( 2 ) , res1_red / ) , &
1_pInt , res ( 3 ) * res ( 2 ) * res1_red , fftw_planner_flag )
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fftw_back = fftw_plan_many_dft_c2r ( 3_pInt , ( / res ( 3 ) , res ( 2 ) , res ( 1 ) / ) , 3_pInt , &
coords_fourier , ( / res ( 3 ) , res ( 2 ) , res1_red / ) , &
1_pInt , res ( 3 ) * res ( 2 ) * res1_red , &
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coords_real , ( / res ( 3 ) , res ( 2 ) , res ( 1 ) + 2_pInt / ) , &
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1_pInt , res ( 3 ) * res ( 2 ) * ( res ( 1 ) + 2_pInt ) , fftw_planner_flag )
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do k = 1_pInt , res ( 3 ) ; do j = 1_pInt , res ( 2 ) ; do i = 1_pInt , res ( 1 )
defgrad_real ( i , j , k , 1 : 3 , 1 : 3 ) = defgrad ( i , j , k , 1 : 3 , 1 : 3 ) ! ensure that data is aligned properly (fftw_alloc)
enddo ; enddo ; enddo
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call fftw_execute_dft_r2c ( fftw_forth , defgrad_real , defgrad_fourier )
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!remove highest frequency in each direction
if ( res ( 1 ) > 1_pInt ) &
defgrad_fourier ( res ( 1 ) / 2_pInt + 1_pInt , 1 : res ( 2 ) , 1 : res ( 3 ) , &
1 : 3 , 1 : 3 ) = cmplx ( 0.0_pReal , 0.0_pReal , pReal )
if ( res ( 2 ) > 1_pInt ) &
defgrad_fourier ( 1 : res1_red , res ( 2 ) / 2_pInt + 1_pInt , 1 : res ( 3 ) , &
1 : 3 , 1 : 3 ) = cmplx ( 0.0_pReal , 0.0_pReal , pReal )
if ( res ( 3 ) > 1_pInt ) &
defgrad_fourier ( 1 : res1_red , 1 : res ( 2 ) , res ( 3 ) / 2_pInt + 1_pInt , &
1 : 3 , 1 : 3 ) = cmplx ( 0.0_pReal , 0.0_pReal , pReal )
coords_fourier = cmplx ( 0.0_pReal , 0.0_pReal , pReal )
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do k = 1_pInt , res ( 3 )
k_s ( 3 ) = k - 1_pInt
if ( k > res ( 3 ) / 2_pInt + 1_pInt ) k_s ( 3 ) = k_s ( 3 ) - res ( 3 )
do j = 1_pInt , res ( 2 )
k_s ( 2 ) = j - 1_pInt
if ( j > res ( 2 ) / 2_pInt + 1_pInt ) k_s ( 2 ) = k_s ( 2 ) - res ( 2 )
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do i = 1_pInt , res1_red
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k_s ( 1 ) = i - 1_pInt
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do m = 1_pInt , 3_pInt
coords_fourier ( i , j , k , m ) = sum ( defgrad_fourier ( i , j , k , m , 1 : 3 ) * cmplx ( 0.0_pReal , real ( k_s , pReal ) * integrator , pReal ) )
enddo
if ( k_s ( 3 ) / = 0_pInt . or . k_s ( 2 ) / = 0_pInt . or . k_s ( 1 ) / = 0_pInt ) &
coords_fourier ( i , j , k , 1 : 3 ) = coords_fourier ( i , j , k , 1 : 3 ) / real ( - sum ( k_s * k_s ) , pReal )
! if(i/=1_pInt) coords_fourier(i,j,k,1:3) = coords_fourier(i,j,k,1:3)& ! substituting division by (on the fly calculated) xi * 2pi * img by multiplication with reversed img/real part
! - defgrad_fourier(i,j,k,1:3,1)*cmplx(0.0_pReal,integrator(1)/real(k_s(1),pReal),pReal)
! if(j/=1_pInt) coords_fourier(i,j,k,1:3) = coords_fourier(i,j,k,1:3)&
! - defgrad_fourier(i,j,k,1:3,2)*cmplx(0.0_pReal,integrator(2)/real(k_s(2),pReal),pReal)
! if(k/=1_pInt) coords_fourier(i,j,k,1:3) = coords_fourier(i,j,k,1:3)&
! - defgrad_fourier(i,j,k,1:3,3)*cmplx(0.0_pReal,integrator(3)/real(k_s(3),pReal),pReal)
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enddo ; enddo ; enddo
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call fftw_execute_dft_c2r ( fftw_back , coords_fourier , coords_real )
coords_real = coords_real / real ( res ( 1 ) * res ( 2 ) * res ( 3 ) , pReal )
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do k = 1_pInt , res ( 3 ) ; do j = 1_pInt , res ( 2 ) ; do i = 1_pInt , res ( 1 )
coords ( i , j , k , 1 : 3 ) = coords_real ( i , j , k , 1 : 3 ) ! ensure that data is aligned properly (fftw_alloc)
enddo ; enddo ; enddo
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offset_coords = matmul ( defgrad ( 1 , 1 , 1 , 1 : 3 , 1 : 3 ) , step / 2.0_pReal ) - scaling * coords ( 1 , 1 , 1 , 1 : 3 )
do k = 1_pInt , res ( 3 ) ; do j = 1_pInt , res ( 2 ) ; do i = 1_pInt , res ( 1 )
coords ( i , j , k , 1 : 3 ) = scaling * coords ( i , j , k , 1 : 3 ) + offset_coords + matmul ( defgrad_av , &
( / step ( 1 ) * real ( i - 1_pInt , pReal ) , &
step ( 2 ) * real ( j - 1_pInt , pReal ) , &
step ( 3 ) * real ( k - 1_pInt , pReal ) / ) )
enddo ; enddo ; enddo
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call fftw_destroy_plan ( fftw_forth ) ; call fftw_destroy_plan ( fftw_back )
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call c_f_pointer ( C_NULL_PTR , defgrad_real , [ res ( 1 ) + 2_pInt , res ( 2 ) , res ( 3 ) , 3_pInt , 3_pInt ] ) ! let all pointers point on NULL-Type
call c_f_pointer ( C_NULL_PTR , defgrad_fourier , [ res1_red , res ( 2 ) , res ( 3 ) , 3_pInt , 3_pInt ] )
call c_f_pointer ( C_NULL_PTR , coords_real , [ res ( 1 ) + 2_pInt , res ( 2 ) , res ( 3 ) , 3_pInt ] )
call c_f_pointer ( C_NULL_PTR , coords_fourier , [ res1_red , res ( 2 ) , res ( 3 ) , 3_pInt ] )
if ( . not . ( c_associated ( C_LOC ( defgrad_real ( 1 , 1 , 1 , 1 , 1 ) ) ) . and . c_associated ( C_LOC ( defgrad_fourier ( 1 , 1 , 1 , 1 , 1 ) ) ) ) ) & ! Check if pointers are deassociated and free memory
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call fftw_free ( defgrad_fftw ) ! This procedure ensures that optimization do not mix-up lines, because a
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if ( . not . ( c_associated ( C_LOC ( coords_real ( 1 , 1 , 1 , 1 ) ) ) . and . c_associated ( C_LOC ( coords_fourier ( 1 , 1 , 1 , 1 ) ) ) ) ) & ! simple fftw_free(field_fftw) could be done immediately after the last line where field_fftw appears, e.g:
call fftw_free ( coords_fftw ) ! call c_f_pointer(field_fftw, field_fourier, [res1_red ,res(2),res(3),vec_tens,3])
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end subroutine deformed_fft
!+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
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subroutine curl_fft ( res , geomdim , vec_tens , field , curl )
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!+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
! calculates curl field using differentation in Fourier space
! use vec_tens to decide if tensor (3) or vector (1)
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use IO , only : IO_error
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use numerics , only : fftw_timelimit , fftw_planner_flag
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use debug , only : debug_math , &
debug_what , &
debug_levelBasic
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implicit none
! input variables
integer ( pInt ) , intent ( in ) , dimension ( 3 ) :: res
real ( pReal ) , intent ( in ) , dimension ( 3 ) :: geomdim
integer ( pInt ) , intent ( in ) :: vec_tens
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real ( pReal ) , intent ( in ) , dimension ( res ( 1 ) , res ( 2 ) , res ( 3 ) , vec_tens , 3 ) :: field
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! output variables
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real ( pReal ) , intent ( out ) , dimension ( res ( 1 ) , res ( 2 ) , res ( 3 ) , vec_tens , 3 ) :: curl
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! variables with dimension depending on input
real ( pReal ) , dimension ( res ( 1 ) / 2_pInt + 1_pInt , res ( 2 ) , res ( 3 ) , 3 ) :: xi
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! allocatable arrays for fftw c routines
type ( C_PTR ) :: fftw_forth , fftw_back
type ( C_PTR ) :: field_fftw , curl_fftw
real ( pReal ) , dimension ( : , : , : , : , : ) , pointer :: field_real
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complex ( pReal ) , dimension ( : , : , : , : , : ) , pointer :: field_fourier
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real ( pReal ) , dimension ( : , : , : , : , : ) , pointer :: curl_real
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complex ( pReal ) , dimension ( : , : , : , : , : ) , pointer :: curl_fourier
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! other variables
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integer ( pInt ) i , j , k , l , res1_red
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integer ( pInt ) , dimension ( 3 ) :: k_s
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real ( pReal ) :: wgt
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if ( iand ( debug_what ( debug_math ) , debug_levelBasic ) / = 0_pInt ) then
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print * , 'Calculating curl of vector/tensor field'
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print '(a,3(e12.5))' , ' Dimension: ' , geomdim
print '(a,3(i5))' , ' Resolution:' , res
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endif
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wgt = 1.0_pReal / real ( res ( 1 ) * res ( 2 ) * res ( 3 ) , pReal )
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res1_red = res ( 1 ) / 2_pInt + 1_pInt ! size of complex array in first dimension (c2r, r2c)
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if ( pReal / = C_DOUBLE . or . pInt / = C_INT ) call IO_error ( error_ID = 808_pInt )
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call fftw_set_timelimit ( fftw_timelimit )
field_fftw = fftw_alloc_complex ( int ( res1_red * res ( 2 ) * res ( 3 ) * vec_tens * 3_pInt , C_SIZE_T ) ) !C_SIZE_T is of type integer(8)
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call c_f_pointer ( field_fftw , field_real , [ res ( 1 ) + 2_pInt , res ( 2 ) , res ( 3 ) , vec_tens , 3_pInt ] )
call c_f_pointer ( field_fftw , field_fourier , [ res1_red , res ( 2 ) , res ( 3 ) , vec_tens , 3_pInt ] )
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curl_fftw = fftw_alloc_complex ( int ( res1_red * res ( 2 ) * res ( 3 ) * vec_tens * 3_pInt , C_SIZE_T ) ) !C_SIZE_T is of type integer(8)
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call c_f_pointer ( curl_fftw , curl_real , [ res ( 1 ) + 2_pInt , res ( 2 ) , res ( 3 ) , vec_tens , 3_pInt ] )
call c_f_pointer ( curl_fftw , curl_fourier , [ res1_red , res ( 2 ) , res ( 3 ) , vec_tens , 3_pInt ] )
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fftw_forth = fftw_plan_many_dft_r2c ( 3_pInt , ( / res ( 3 ) , res ( 2 ) , res ( 1 ) / ) , vec_tens * 3_pInt , & ! dimensions , length in each dimension in reversed order
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field_real , ( / res ( 3 ) , res ( 2 ) , res ( 1 ) + 2_pInt / ) , & ! input data , physical length in each dimension in reversed order
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1_pInt , res ( 3 ) * res ( 2 ) * ( res ( 1 ) + 2_pInt ) , & ! striding , product of physical lenght in the 3 dimensions
field_fourier , ( / res ( 3 ) , res ( 2 ) , res1_red / ) , &
1_pInt , res ( 3 ) * res ( 2 ) * res1_red , fftw_planner_flag )
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fftw_back = fftw_plan_many_dft_c2r ( 3_pInt , ( / res ( 3 ) , res ( 2 ) , res ( 1 ) / ) , vec_tens * 3_pInt , &
curl_fourier , ( / res ( 3 ) , res ( 2 ) , res1_red / ) , &
1_pInt , res ( 3 ) * res ( 2 ) * res1_red , &
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curl_real , ( / res ( 3 ) , res ( 2 ) , res ( 1 ) + 2_pInt / ) , &
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1_pInt , res ( 3 ) * res ( 2 ) * ( res ( 1 ) + 2_pInt ) , fftw_planner_flag )
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do k = 1_pInt , res ( 3 ) ; do j = 1_pInt , res ( 2 ) ; do i = 1_pInt , res ( 1 )
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field_real ( i , j , k , 1 : vec_tens , 1 : 3 ) = field ( i , j , k , 1 : vec_tens , 1 : 3 ) ! ensure that data is aligned properly (fftw_alloc)
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enddo ; enddo ; enddo
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call fftw_execute_dft_r2c ( fftw_forth , field_real , field_fourier )
!remove highest frequency in each direction
if ( res ( 1 ) > 1_pInt ) &
field_fourier ( res ( 1 ) / 2_pInt + 1_pInt , 1 : res ( 2 ) , 1 : res ( 3 ) , &
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1 : vec_tens , 1 : 3 ) = cmplx ( 0.0_pReal , 0.0_pReal , pReal )
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if ( res ( 2 ) > 1_pInt ) &
field_fourier ( 1 : res1_red , res ( 2 ) / 2_pInt + 1_pInt , 1 : res ( 3 ) , &
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1 : vec_tens , 1 : 3 ) = cmplx ( 0.0_pReal , 0.0_pReal , pReal )
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if ( res ( 3 ) > 1_pInt ) &
field_fourier ( 1 : res1_red , 1 : res ( 2 ) , res ( 3 ) / 2_pInt + 1_pInt , &
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1 : vec_tens , 1 : 3 ) = cmplx ( 0.0_pReal , 0.0_pReal , pReal )
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do k = 1_pInt , res ( 3 ) ! calculation of discrete angular frequencies, ordered as in FFTW (wrap around)
k_s ( 3 ) = k - 1_pInt
if ( k > res ( 3 ) / 2_pInt + 1_pInt ) k_s ( 3 ) = k_s ( 3 ) - res ( 3 )
do j = 1_pInt , res ( 2 )
k_s ( 2 ) = j - 1_pInt
if ( j > res ( 2 ) / 2_pInt + 1_pInt ) k_s ( 2 ) = k_s ( 2 ) - res ( 2 )
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do i = 1_pInt , res1_red
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k_s ( 1 ) = i - 1_pInt
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xi ( i , j , k , 1 : 3 ) = real ( k_s , pReal ) / geomdim
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enddo ; enddo ; enddo
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do k = 1_pInt , res ( 3 ) ; do j = 1_pInt , res ( 2 ) ; do i = 1_pInt , res1_red
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do l = 1_pInt , vec_tens
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curl_fourier ( i , j , k , l , 1 ) = ( field_fourier ( i , j , k , l , 3 ) * xi ( i , j , k , 2 ) &
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- field_fourier ( i , j , k , l , 2 ) * xi ( i , j , k , 3 ) ) * TWOPIIMG
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curl_fourier ( i , j , k , l , 2 ) = ( - field_fourier ( i , j , k , l , 3 ) * xi ( i , j , k , 1 ) &
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+ field_fourier ( i , j , k , l , 1 ) * xi ( i , j , k , 3 ) ) * TWOPIIMG
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curl_fourier ( i , j , k , l , 3 ) = ( field_fourier ( i , j , k , l , 2 ) * xi ( i , j , k , 1 ) &
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- field_fourier ( i , j , k , l , 1 ) * xi ( i , j , k , 2 ) ) * TWOPIIMG
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enddo
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enddo ; enddo ; enddo
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call fftw_execute_dft_c2r ( fftw_back , curl_fourier , curl_real )
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do k = 1_pInt , res ( 3 ) ; do j = 1_pInt , res ( 2 ) ; do i = 1_pInt , res ( 1 )
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curl ( i , j , k , 1 : vec_tens , 1 : 3 ) = curl_real ( i , j , k , 1 : vec_tens , 1 : 3 ) ! ensure that data is aligned properly (fftw_alloc)
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enddo ; enddo ; enddo
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curl = curl * wgt
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call fftw_destroy_plan ( fftw_forth ) ; call fftw_destroy_plan ( fftw_back )
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call c_f_pointer ( C_NULL_PTR , field_real , [ res ( 1 ) + 2_pInt , res ( 2 ) , res ( 3 ) , vec_tens , 3_pInt ] ) ! let all pointers point on NULL-Type
call c_f_pointer ( C_NULL_PTR , field_fourier , [ res1_red , res ( 2 ) , res ( 3 ) , vec_tens , 3_pInt ] )
call c_f_pointer ( C_NULL_PTR , curl_real , [ res ( 1 ) + 2_pInt , res ( 2 ) , res ( 3 ) , vec_tens , 3_pInt ] )
call c_f_pointer ( C_NULL_PTR , curl_fourier , [ res1_red , res ( 2 ) , res ( 3 ) , vec_tens , 3_pInt ] )
if ( . not . ( c_associated ( C_LOC ( field_real ( 1 , 1 , 1 , 1 , 1 ) ) ) . and . c_associated ( C_LOC ( field_fourier ( 1 , 1 , 1 , 1 , 1 ) ) ) ) ) & ! Check if pointers are deassociated and free memory
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call fftw_free ( field_fftw ) ! This procedure ensures that optimization do not mix-up lines, because a
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if ( . not . ( c_associated ( C_LOC ( curl_real ( 1 , 1 , 1 , 1 , 1 ) ) ) . and . c_associated ( C_LOC ( curl_fourier ( 1 , 1 , 1 , 1 , 1 ) ) ) ) ) & ! simple fftw_free(field_fftw) could be done immediately after the last line where field_fftw appears, e.g:
call fftw_free ( curl_fftw ) ! call c_f_pointer(field_fftw, field_fourier, [res1_red ,res(2),res(3),vec_tens,3])
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end subroutine curl_fft
!+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
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subroutine divergence_fft ( res , geomdim , vec_tens , field , divergence )
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!+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
! calculates divergence field using integration in Fourier space
! use vec_tens to decide if tensor (3) or vector (1)
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use IO , only : IO_error
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use numerics , only : fftw_timelimit , fftw_planner_flag
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use debug , only : debug_math , &
debug_what , &
debug_levelBasic
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implicit none
! input variables
integer ( pInt ) , intent ( in ) , dimension ( 3 ) :: res
real ( pReal ) , intent ( in ) , dimension ( 3 ) :: geomdim
integer ( pInt ) , intent ( in ) :: vec_tens
real ( pReal ) , intent ( in ) , dimension ( res ( 1 ) , res ( 2 ) , res ( 3 ) , vec_tens , 3 ) :: field
! output variables
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real ( pReal ) , intent ( out ) , dimension ( res ( 1 ) , res ( 2 ) , res ( 3 ) , vec_tens ) :: divergence
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! variables with dimension depending on input
real ( pReal ) , dimension ( res ( 1 ) / 2_pInt + 1_pInt , res ( 2 ) , res ( 3 ) , 3 ) :: xi
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! allocatable arrays for fftw c routines
type ( C_PTR ) :: fftw_forth , fftw_back
type ( C_PTR ) :: field_fftw , divergence_fftw
real ( pReal ) , dimension ( : , : , : , : , : ) , pointer :: field_real
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complex ( pReal ) , dimension ( : , : , : , : , : ) , pointer :: field_fourier
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real ( pReal ) , dimension ( : , : , : , : ) , pointer :: divergence_real
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complex ( pReal ) , dimension ( : , : , : , : ) , pointer :: divergence_fourier
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! other variables
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integer ( pInt ) :: i , j , k , l , res1_red
real ( pReal ) :: wgt
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integer ( pInt ) , dimension ( 3 ) :: k_s
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if ( iand ( debug_what ( debug_math ) , debug_levelBasic ) / = 0_pInt ) then
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print '(a)' , 'Calculating divergence of tensor/vector field using FFT'
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print '(a,3(e12.5))' , ' Dimension: ' , geomdim
print '(a,3(i5))' , ' Resolution:' , res
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endif
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res1_red = res ( 1 ) / 2_pInt + 1_pInt ! size of complex array in first dimension (c2r, r2c)
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wgt = 1.0_pReal / real ( res ( 1 ) * res ( 2 ) * res ( 3 ) , pReal )
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if ( pReal / = C_DOUBLE . or . pInt / = C_INT ) call IO_error ( error_ID = 808_pInt )
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call fftw_set_timelimit ( fftw_timelimit )
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field_fftw = fftw_alloc_complex ( int ( res1_red * res ( 2 ) * res ( 3 ) * vec_tens * 3_pInt , C_SIZE_T ) ) !C_SIZE_T is of type integer(8)
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call c_f_pointer ( field_fftw , field_real , [ res ( 1 ) + 2_pInt , res ( 2 ) , res ( 3 ) , vec_tens , 3_pInt ] )
call c_f_pointer ( field_fftw , field_fourier , [ res1_red , res ( 2 ) , res ( 3 ) , vec_tens , 3_pInt ] )
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divergence_fftw = fftw_alloc_complex ( int ( res1_red * res ( 2 ) * res ( 3 ) * vec_tens , C_SIZE_T ) )
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call c_f_pointer ( divergence_fftw , divergence_real , [ res ( 1 ) + 2_pInt , res ( 2 ) , res ( 3 ) , vec_tens ] )
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call c_f_pointer ( divergence_fftw , divergence_fourier , [ res1_red , res ( 2 ) , res ( 3 ) , vec_tens ] )
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fftw_forth = fftw_plan_many_dft_r2c ( 3_pInt , ( / res ( 3 ) , res ( 2 ) , res ( 1 ) / ) , vec_tens * 3_pInt , & ! dimensions , length in each dimension in reversed order
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field_real , ( / res ( 3 ) , res ( 2 ) , res ( 1 ) + 2_pInt / ) , & ! input data , physical length in each dimension in reversed order
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1_pInt , res ( 3 ) * res ( 2 ) * ( res ( 1 ) + 2_pInt ) , & ! striding , product of physical lenght in the 3 dimensions
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field_fourier , ( / res ( 3 ) , res ( 2 ) , res1_red / ) , &
1_pInt , res ( 3 ) * res ( 2 ) * res1_red , fftw_planner_flag )
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fftw_back = fftw_plan_many_dft_c2r ( 3_pInt , ( / res ( 3 ) , res ( 2 ) , res ( 1 ) / ) , vec_tens , &
divergence_fourier , ( / res ( 3 ) , res ( 2 ) , res1_red / ) , &
1_pInt , res ( 3 ) * res ( 2 ) * res1_red , &
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divergence_real , ( / res ( 3 ) , res ( 2 ) , res ( 1 ) + 2_pInt / ) , &
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1_pInt , res ( 3 ) * res ( 2 ) * ( res ( 1 ) + 2_pInt ) , fftw_planner_flag ) ! padding
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do k = 1_pInt , res ( 3 ) ; do j = 1_pInt , res ( 2 ) ; do i = 1_pInt , res ( 1 )
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field_real ( i , j , k , 1 : vec_tens , 1 : 3 ) = field ( i , j , k , 1 : vec_tens , 1 : 3 ) ! ensure that data is aligned properly (fftw_alloc)
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enddo ; enddo ; enddo
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call fftw_execute_dft_r2c ( fftw_forth , field_real , field_fourier )
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do k = 1_pInt , res ( 3 ) ! calculation of discrete angular frequencies, ordered as in FFTW (wrap around)
k_s ( 3 ) = k - 1_pInt
if ( k > res ( 3 ) / 2_pInt + 1_pInt ) k_s ( 3 ) = k_s ( 3 ) - res ( 3 )
do j = 1_pInt , res ( 2 )
k_s ( 2 ) = j - 1_pInt
if ( j > res ( 2 ) / 2_pInt + 1_pInt ) k_s ( 2 ) = k_s ( 2 ) - res ( 2 )
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do i = 1_pInt , res1_red
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k_s ( 1 ) = i - 1_pInt
xi ( i , j , k , 1 : 3 ) = real ( k_s , pReal ) / geomdim
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enddo ; enddo ; enddo
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!remove highest frequency in each direction
if ( res ( 1 ) > 1_pInt ) &
field_fourier ( res ( 1 ) / 2_pInt + 1_pInt , 1 : res ( 2 ) , 1 : res ( 3 ) , &
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1 : vec_tens , 1 : 3 ) = cmplx ( 0.0_pReal , 0.0_pReal , pReal )
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if ( res ( 2 ) > 1_pInt ) &
field_fourier ( 1 : res1_red , res ( 2 ) / 2_pInt + 1_pInt , 1 : res ( 3 ) , &
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1 : vec_tens , 1 : 3 ) = cmplx ( 0.0_pReal , 0.0_pReal , pReal )
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if ( res ( 3 ) > 1_pInt ) &
field_fourier ( 1 : res1_red , 1 : res ( 2 ) , res ( 3 ) / 2_pInt + 1_pInt , &
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1 : vec_tens , 1 : 3 ) = cmplx ( 0.0_pReal , 0.0_pReal , pReal )
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do k = 1_pInt , res ( 3 ) ; do j = 1_pInt , res ( 2 ) ; do i = 1_pInt , res1_red
do l = 1_pInt , vec_tens
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divergence_fourier ( i , j , k , l ) = sum ( field_fourier ( i , j , k , l , 1 : 3 ) * cmplx ( xi ( i , j , k , 1 : 3 ) , 0.0_pReal , pReal ) ) &
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* TWOPIIMG
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enddo
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enddo ; enddo ; enddo
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call fftw_execute_dft_c2r ( fftw_back , divergence_fourier , divergence_real )
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do k = 1_pInt , res ( 3 ) ; do j = 1_pInt , res ( 2 ) ; do i = 1_pInt , res ( 1 )
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divergence ( i , j , k , 1 : vec_tens ) = divergence_real ( i , j , k , 1 : vec_tens ) ! ensure that data is aligned properly (fftw_alloc)
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enddo ; enddo ; enddo
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divergence = divergence * wgt
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call fftw_destroy_plan ( fftw_forth ) ; call fftw_destroy_plan ( fftw_back )
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call c_f_pointer ( C_NULL_PTR , field_real , [ res ( 1 ) + 2_pInt , res ( 2 ) , res ( 3 ) , vec_tens , 3_pInt ] ) ! let all pointers point on NULL-Type
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call c_f_pointer ( C_NULL_PTR , field_fourier , [ res1_red , res ( 2 ) , res ( 3 ) , vec_tens , 3_pInt ] )
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call c_f_pointer ( C_NULL_PTR , divergence_real , [ res ( 1 ) + 2_pInt , res ( 2 ) , res ( 3 ) , vec_tens ] )
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call c_f_pointer ( C_NULL_PTR , divergence_fourier , [ res1_red , res ( 2 ) , res ( 3 ) , vec_tens ] )
if ( . not . ( c_associated ( C_LOC ( field_real ( 1 , 1 , 1 , 1 , 1 ) ) ) . and . c_associated ( C_LOC ( field_fourier ( 1 , 1 , 1 , 1 , 1 ) ) ) ) ) & ! Check if pointers are deassociated and free memory
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call fftw_free ( field_fftw ) ! This procedure ensures that optimization do not mix-up lines, because a
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if ( . not . ( c_associated ( C_LOC ( divergence_real ( 1 , 1 , 1 , 1 ) ) ) . and . c_associated ( C_LOC ( divergence_fourier ( 1 , 1 , 1 , 1 ) ) ) ) ) & ! simple fftw_free(field_fftw) could be done immediately after the last line where field_fftw appears, e.g:
call fftw_free ( divergence_fftw ) ! call c_f_pointer(field_fftw, field_fourier, [res1_red ,res(2),res(3),vec_tens,3])
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end subroutine divergence_fft
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!+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
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subroutine divergence_fdm ( res , geomdim , vec_tens , order , field , divergence )
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!+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
! calculates divergence field using FDM with variable accuracy
! use vec_tes to decide if tensor (3) or vector (1)
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use debug , only : debug_math , &
debug_what , &
debug_levelBasic
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implicit none
integer ( pInt ) , intent ( in ) , dimension ( 3 ) :: res
integer ( pInt ) , intent ( in ) :: vec_tens
integer ( pInt ) , intent ( inout ) :: order
real ( pReal ) , intent ( in ) , dimension ( 3 ) :: geomdim
real ( pReal ) , intent ( in ) , dimension ( res ( 1 ) , res ( 2 ) , res ( 3 ) , vec_tens , 3 ) :: field
! output variables
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real ( pReal ) , intent ( out ) , dimension ( res ( 1 ) , res ( 2 ) , res ( 3 ) , vec_tens ) :: divergence
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! other variables
integer ( pInt ) , dimension ( 6 , 3 ) :: coordinates
integer ( pInt ) i , j , k , m , l
real ( pReal ) , dimension ( 4 , 4 ) , parameter :: FDcoefficient = reshape ( ( / &
1.0_pReal / 2.0_pReal , 0.0_pReal , 0.0_pReal , 0.0_pReal , & !from http://en.wikipedia.org/wiki/Finite_difference_coefficients
2.0_pReal / 3.0_pReal , - 1.0_pReal / 1 2.0_pReal , 0.0_pReal , 0.0_pReal , &
3.0_pReal / 4.0_pReal , - 3.0_pReal / 2 0.0_pReal , 1.0_pReal / 6 0.0_pReal , 0.0_pReal , &
4.0_pReal / 5.0_pReal , - 1.0_pReal / 5.0_pReal , 4.0_pReal / 10 5.0_pReal , - 1.0_pReal / 28 0.0_pReal / ) , &
( / 4 , 4 / ) )
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if ( iand ( debug_what ( debug_math ) , debug_levelBasic ) / = 0_pInt ) then
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print * , 'Calculating divergence of tensor/vector field using FDM'
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print '(a,3(e12.5))' , ' Dimension: ' , geomdim
print '(a,3(i5))' , ' Resolution:' , res
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endif
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divergence = 0.0_pReal
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order = order + 1_pInt
do k = 0_pInt , res ( 3 ) - 1_pInt ; do j = 0_pInt , res ( 2 ) - 1_pInt ; do i = 0_pInt , res ( 1 ) - 1_pInt
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do m = 1_pInt , order
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coordinates ( 1 , 1 : 3 ) = mesh_location ( mesh_index ( ( / i + m , j , k / ) , ( / res ( 1 ) , res ( 2 ) , res ( 3 ) / ) ) , ( / res ( 1 ) , res ( 2 ) , res ( 3 ) / ) ) &
+ ( / 1_pInt , 1_pInt , 1_pInt / )
coordinates ( 2 , 1 : 3 ) = mesh_location ( mesh_index ( ( / i - m , j , k / ) , ( / res ( 1 ) , res ( 2 ) , res ( 3 ) / ) ) , ( / res ( 1 ) , res ( 2 ) , res ( 3 ) / ) ) &
+ ( / 1_pInt , 1_pInt , 1_pInt / )
coordinates ( 3 , 1 : 3 ) = mesh_location ( mesh_index ( ( / i , j + m , k / ) , ( / res ( 1 ) , res ( 2 ) , res ( 3 ) / ) ) , ( / res ( 1 ) , res ( 2 ) , res ( 3 ) / ) ) &
+ ( / 1_pInt , 1_pInt , 1_pInt / )
coordinates ( 4 , 1 : 3 ) = mesh_location ( mesh_index ( ( / i , j - m , k / ) , ( / res ( 1 ) , res ( 2 ) , res ( 3 ) / ) ) , ( / res ( 1 ) , res ( 2 ) , res ( 3 ) / ) ) &
+ ( / 1_pInt , 1_pInt , 1_pInt / )
coordinates ( 5 , 1 : 3 ) = mesh_location ( mesh_index ( ( / i , j , k + m / ) , ( / res ( 1 ) , res ( 2 ) , res ( 3 ) / ) ) , ( / res ( 1 ) , res ( 2 ) , res ( 3 ) / ) ) &
+ ( / 1_pInt , 1_pInt , 1_pInt / )
coordinates ( 6 , 1 : 3 ) = mesh_location ( mesh_index ( ( / i , j , k - m / ) , ( / res ( 1 ) , res ( 2 ) , res ( 3 ) / ) ) , ( / res ( 1 ) , res ( 2 ) , res ( 3 ) / ) ) &
+ ( / 1_pInt , 1_pInt , 1_pInt / )
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do l = 1_pInt , vec_tens
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divergence ( i + 1_pInt , j + 1_pInt , k + 1_pInt , l ) = divergence ( i + 1_pInt , j + 1_pInt , k + 1_pInt , l ) + FDcoefficient ( m , order ) * &
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( ( field ( coordinates ( 1 , 1 ) , coordinates ( 1 , 2 ) , coordinates ( 1 , 3 ) , l , 1 ) - &
field ( coordinates ( 2 , 1 ) , coordinates ( 2 , 2 ) , coordinates ( 2 , 3 ) , l , 1 ) ) * real ( res ( 1 ) , pReal ) / geomdim ( 1 ) + &
( field ( coordinates ( 3 , 1 ) , coordinates ( 3 , 2 ) , coordinates ( 3 , 3 ) , l , 2 ) - &
field ( coordinates ( 4 , 1 ) , coordinates ( 4 , 2 ) , coordinates ( 4 , 3 ) , l , 2 ) ) * real ( res ( 2 ) , pReal ) / geomdim ( 2 ) + &
( field ( coordinates ( 5 , 1 ) , coordinates ( 5 , 2 ) , coordinates ( 5 , 3 ) , l , 3 ) - &
field ( coordinates ( 6 , 1 ) , coordinates ( 6 , 2 ) , coordinates ( 6 , 3 ) , l , 3 ) ) * real ( res ( 3 ) , pReal ) / geomdim ( 3 ) )
enddo
enddo
enddo ; enddo ; enddo
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end subroutine divergence_fdm
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#endif
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!+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
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subroutine tensor_avg ( res , tensor , avg )
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!+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
!calculate average of tensor field
!
implicit none
! input variables
integer ( pInt ) , intent ( in ) , dimension ( 3 ) :: res
real ( pReal ) , intent ( in ) , dimension ( res ( 1 ) , res ( 2 ) , res ( 3 ) , 3 , 3 ) :: tensor
! output variables
real ( pReal ) , intent ( out ) , dimension ( 3 , 3 ) :: avg
! other variables
real ( pReal ) wgt
integer ( pInt ) m , n
wgt = 1.0_pReal / real ( res ( 1 ) * res ( 2 ) * res ( 3 ) , pReal )
do m = 1_pInt , 3_pInt ; do n = 1_pInt , 3_pInt
avg ( m , n ) = sum ( tensor ( 1 : res ( 1 ) , 1 : res ( 2 ) , 1 : res ( 3 ) , m , n ) ) * wgt
enddo ; enddo
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end subroutine tensor_avg
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!+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
subroutine logstrain_spat ( res , defgrad , logstrain_field )
!+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
!calculate logarithmic strain in spatial configuration for given defgrad field
!
implicit none
! input variables
integer ( pInt ) , intent ( in ) , dimension ( 3 ) :: res
real ( pReal ) , intent ( in ) , dimension ( res ( 1 ) , res ( 2 ) , res ( 3 ) , 3 , 3 ) :: defgrad
! output variables
real ( pReal ) , intent ( out ) , dimension ( res ( 1 ) , res ( 2 ) , res ( 3 ) , 3 , 3 ) :: logstrain_field
! other variables
real ( pReal ) , dimension ( 3 , 3 ) :: temp33_Real , temp33_Real2
real ( pReal ) , dimension ( 3 , 3 , 3 ) :: eigenvectorbasis
real ( pReal ) , dimension ( 3 ) :: eigenvalue
integer ( pInt ) :: i , j , k
logical :: errmatinv
do k = 1_pInt , res ( 3 ) ; do j = 1_pInt , res ( 2 ) ; do i = 1_pInt , res ( 1 )
call math_pDecomposition ( defgrad ( i , j , k , 1 : 3 , 1 : 3 ) , temp33_Real2 , temp33_Real , errmatinv ) !store R in temp33_Real
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temp33_Real2 = math_inv33 ( temp33_Real )
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temp33_Real = math_mul33x33 ( defgrad ( i , j , k , 1 : 3 , 1 : 3 ) , temp33_Real2 ) ! v = F o inv(R), store in temp33_Real2
call math_spectral1 ( temp33_Real , eigenvalue ( 1 ) , eigenvalue ( 2 ) , eigenvalue ( 3 ) , &
eigenvectorbasis ( 1 , 1 : 3 , 1 : 3 ) , eigenvectorbasis ( 2 , 1 : 3 , 1 : 3 ) , eigenvectorbasis ( 3 , 1 : 3 , 1 : 3 ) )
eigenvalue = log ( sqrt ( eigenvalue ) )
logstrain_field ( i , j , k , 1 : 3 , 1 : 3 ) = eigenvalue ( 1 ) * eigenvectorbasis ( 1 , 1 : 3 , 1 : 3 ) + &
eigenvalue ( 2 ) * eigenvectorbasis ( 2 , 1 : 3 , 1 : 3 ) + &
eigenvalue ( 3 ) * eigenvectorbasis ( 3 , 1 : 3 , 1 : 3 )
enddo ; enddo ; enddo
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end subroutine logstrain_spat
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!+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
subroutine logstrain_mat ( res , defgrad , logstrain_field )
!+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
!calculate logarithmic strain in material configuration for given defgrad field
!
implicit none
! input variables
integer ( pInt ) , intent ( in ) , dimension ( 3 ) :: res
real ( pReal ) , intent ( in ) , dimension ( res ( 1 ) , res ( 2 ) , res ( 3 ) , 3 , 3 ) :: defgrad
! output variables
real ( pReal ) , intent ( out ) , dimension ( res ( 1 ) , res ( 2 ) , res ( 3 ) , 3 , 3 ) :: logstrain_field
! other variables
real ( pReal ) , dimension ( 3 , 3 ) :: temp33_Real , temp33_Real2
real ( pReal ) , dimension ( 3 , 3 , 3 ) :: eigenvectorbasis
real ( pReal ) , dimension ( 3 ) :: eigenvalue
integer ( pInt ) :: i , j , k
logical :: errmatinv
do k = 1_pInt , res ( 3 ) ; do j = 1_pInt , res ( 2 ) ; do i = 1_pInt , res ( 1 )
call math_pDecomposition ( defgrad ( i , j , k , 1 : 3 , 1 : 3 ) , temp33_Real , temp33_Real2 , errmatinv ) !store U in temp33_Real
call math_spectral1 ( temp33_Real , eigenvalue ( 1 ) , eigenvalue ( 2 ) , eigenvalue ( 3 ) , &
eigenvectorbasis ( 1 , 1 : 3 , 1 : 3 ) , eigenvectorbasis ( 2 , 1 : 3 , 1 : 3 ) , eigenvectorbasis ( 3 , 1 : 3 , 1 : 3 ) )
eigenvalue = log ( sqrt ( eigenvalue ) )
logstrain_field ( i , j , k , 1 : 3 , 1 : 3 ) = eigenvalue ( 1 ) * eigenvectorbasis ( 1 , 1 : 3 , 1 : 3 ) + &
eigenvalue ( 2 ) * eigenvectorbasis ( 2 , 1 : 3 , 1 : 3 ) + &
eigenvalue ( 3 ) * eigenvectorbasis ( 3 , 1 : 3 , 1 : 3 )
enddo ; enddo ; enddo
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end subroutine logstrain_mat
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!+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
subroutine calculate_cauchy ( res , defgrad , p_stress , c_stress )
!+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
!calculate cauchy stress for given PK1 stress and defgrad field
!
implicit none
! input variables
integer ( pInt ) , intent ( in ) , dimension ( 3 ) :: res
real ( pReal ) , intent ( in ) , dimension ( res ( 1 ) , res ( 2 ) , res ( 3 ) , 3 , 3 ) :: defgrad
real ( pReal ) , intent ( in ) , dimension ( res ( 1 ) , res ( 2 ) , res ( 3 ) , 3 , 3 ) :: p_stress
! output variables
real ( pReal ) , intent ( out ) , dimension ( res ( 1 ) , res ( 2 ) , res ( 3 ) , 3 , 3 ) :: c_stress
! other variables
real ( pReal ) :: jacobi
integer ( pInt ) :: i , j , k
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c_stress = 0.0_pReal
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do k = 1_pInt , res ( 3 ) ; do j = 1_pInt , res ( 2 ) ; do i = 1_pInt , res ( 1 )
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jacobi = math_det33 ( defgrad ( i , j , k , 1 : 3 , 1 : 3 ) )
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c_stress ( i , j , k , 1 : 3 , 1 : 3 ) = matmul ( p_stress ( i , j , k , 1 : 3 , 1 : 3 ) , transpose ( defgrad ( i , j , k , 1 : 3 , 1 : 3 ) ) ) / jacobi
enddo ; enddo ; enddo
end subroutine calculate_cauchy
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#ifdef Spectral
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!+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
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subroutine math_nearestNeighborSearch ( spatialDim , Favg , geomdim , queryPoints , domainPoints , querySet , domainSet , indices )
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!+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
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! Obtain the nearest neighbor in domain set for all points in querySet
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!
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use kdtree2_module
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use IO , only : &
IO_error
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implicit none
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! input variables
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integer ( pInt ) , intent ( in ) :: spatialDim
real ( pReal ) , dimension ( 3 , 3 ) , intent ( in ) :: Favg
real ( pReal ) , dimension ( 3 ) , intent ( in ) :: geomdim
integer ( pInt ) , intent ( in ) :: domainPoints
integer ( pInt ) , intent ( in ) :: queryPoints
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real ( pReal ) , dimension ( spatialDim , queryPoints ) , intent ( in ) :: querySet
real ( pReal ) , dimension ( spatialDim , domainPoints ) , intent ( in ) :: domainSet
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! output variable
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integer ( pInt ) , dimension ( queryPoints ) , intent ( out ) :: indices
! other variables depending on input
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real ( pReal ) , dimension ( spatialDim , ( 3_pInt ** spatialDim ) * domainPoints ) :: domainSetLarge
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! other variables
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integer ( pInt ) :: i , j , l , m , n
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type ( kdtree2 ) , pointer :: tree
type ( kdtree2_result ) , dimension ( 1 ) :: Results
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if ( size ( querySet ( : , 1 ) ) / = spatialDim ) call IO_error ( 407_pInt , ext_msg = 'query set' )
if ( size ( domainSet ( : , 1 ) ) / = spatialDim ) call IO_error ( 407_pInt , ext_msg = 'domain set' )
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i = 0_pInt
if ( spatialDim == 2_pInt ) then
do j = 1_pInt , domainPoints
do l = - 1_pInt , 1_pInt ; do m = - 1_pInt , 1_pInt
i = i + 1_pInt
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domainSetLarge ( 1 : 2 , i ) = domainSet ( 1 : 2 , j ) + matmul ( Favg ( 1 : 2 , 1 : 2 ) , real ( [ l , m ] , pReal ) * geomdim ( 1 : 2 ) )
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enddo ; enddo
enddo
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else
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do j = 1_pInt , domainPoints
do l = - 1_pInt , 1_pInt ; do m = - 1_pInt , 1_pInt ; do n = - 1_pInt , 1_pInt
i = i + 1_pInt
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domainSetLarge ( 1 : 3 , i ) = domainSet ( 1 : 3 , j ) + math_mul33x3 ( Favg , real ( [ l , m , n ] , pReal ) * geomdim )
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enddo ; enddo ; enddo
enddo
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endif
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tree = > kdtree2_create ( domainSetLarge , sort = . true . , rearrange = . true . )
do j = 1_pInt , queryPoints
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call kdtree2_n_nearest ( tp = tree , qv = querySet ( 1 : spatialDim , j ) , nn = 1_pInt , results = Results )
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indices ( j ) = Results ( 1 ) % idx
enddo
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indices = indices - 1_pInt ! let them run from 0 to domainPoints -1
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end subroutine math_nearestNeighborSearch
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#endif
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end module math