- rearranged array with symmetry operations
- new subroutine "math_misorientation" which calculates misorientations (based on old subroutine "misorientation", which was not used previously) - rendered some functions pure
This commit is contained in:
Christoph Kords
parent
6e1c731175
commit
596b7f3727
528
code/math.f90
528
code/math.f90
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@ -65,143 +65,143 @@
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! Symmetry operators for 3 different materials
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! Symmetry Operations for 3 different materials
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! 24 for cubic, 12 for hexagonal, 8 for tetragonal (24+12+8)x3=132
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real(pReal), dimension(132,3), parameter :: sym = &
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reshape((/&
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1.0_pReal,0.0_pReal,0.0_pReal, &
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0.0_pReal,1.0_pReal,0.0_pReal, &
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||||
0.0_pReal,0.0_pReal,1.0_pReal, &
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0.0_pReal,0.0_pReal,1.0_pReal, &
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1.0_pReal,0.0_pReal,0.0_pReal, &
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0.0_pReal,1.0_pReal,0.0_pReal, &
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0.0_pReal,1.0_pReal,0.0_pReal, &
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0.0_pReal,0.0_pReal,1.0_pReal, &
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1.0_pReal,0.0_pReal,0.0_pReal, &
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0.0_pReal,-1.0_pReal,0.0_pReal, &
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0.0_pReal,0.0_pReal,1.0_pReal, &
|
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-1.0_pReal,0.0_pReal,0.0_pReal, &
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0.0_pReal,-1.0_pReal,0.0_pReal, &
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||||
0.0_pReal,0.0_pReal,-1.0_pReal, &
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1.0_pReal,0.0_pReal,0.0_pReal, &
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0.0_pReal,1.0_pReal,0.0_pReal, &
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0.0_pReal,0.0_pReal,-1.0_pReal, &
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-1.0_pReal,0.0_pReal,0.0_pReal, &
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0.0_pReal,0.0_pReal,-1.0_pReal, &
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||||
1.0_pReal,0.0_pReal,0.0_pReal, &
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0.0_pReal,-1.0_pReal,0.0_pReal, &
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0.0_pReal,0.0_pReal,-1.0_pReal, &
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-1.0_pReal,0.0_pReal,0.0_pReal, &
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0.0_pReal,1.0_pReal,0.0_pReal, &
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||||
0.0_pReal,0.0_pReal,1.0_pReal, &
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-1.0_pReal,0.0_pReal,0.0_pReal, &
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||||
0.0_pReal,-1.0_pReal,0.0_pReal, &
|
||||
-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, &
|
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-1.0_pReal,0.0_pReal,0.0_pReal, &
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0.0_pReal,-1.0_pReal,0.0_pReal, &
|
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0.0_pReal,0.0_pReal,1.0_pReal, &
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1.0_pReal,0.0_pReal,0.0_pReal, &
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0.0_pReal,-1.0_pReal,0.0_pReal, &
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0.0_pReal,0.0_pReal,-1.0_pReal, &
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0.0_pReal,0.0_pReal,-1.0_pReal, &
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0.0_pReal,-1.0_pReal,0.0_pReal, &
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-1.0_pReal,0.0_pReal,0.0_pReal, &
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0.0_pReal,0.0_pReal,1.0_pReal, &
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0.0_pReal,-1.0_pReal,0.0_pReal, &
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1.0_pReal,0.0_pReal,0.0_pReal, &
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0.0_pReal,0.0_pReal,1.0_pReal, &
|
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0.0_pReal,1.0_pReal,0.0_pReal, &
|
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-1.0_pReal,0.0_pReal,0.0_pReal, &
|
||||
0.0_pReal,0.0_pReal,-1.0_pReal, &
|
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0.0_pReal,1.0_pReal,0.0_pReal, &
|
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1.0_pReal,0.0_pReal,0.0_pReal, &
|
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-1.0_pReal,0.0_pReal,0.0_pReal, &
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0.0_pReal,0.0_pReal,-1.0_pReal, &
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0.0_pReal,-1.0_pReal,0.0_pReal, &
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1.0_pReal,0.0_pReal,0.0_pReal, &
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0.0_pReal,0.0_pReal,-1.0_pReal, &
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0.0_pReal,1.0_pReal,0.0_pReal, &
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1.0_pReal,0.0_pReal,0.0_pReal, &
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0.0_pReal,0.0_pReal,1.0_pReal, &
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0.0_pReal,-1.0_pReal,0.0_pReal, &
|
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-1.0_pReal,0.0_pReal,0.0_pReal, &
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0.0_pReal,0.0_pReal,1.0_pReal, &
|
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0.0_pReal,1.0_pReal,0.0_pReal, &
|
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0.0_pReal,-1.0_pReal,0.0_pReal, &
|
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-1.0_pReal,0.0_pReal,0.0_pReal, &
|
||||
0.0_pReal,0.0_pReal,-1.0_pReal, &
|
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0.0_pReal,1.0_pReal,0.0_pReal, &
|
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-1.0_pReal,0.0_pReal,0.0_pReal, &
|
||||
0.0_pReal,0.0_pReal,1.0_pReal, &
|
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0.0_pReal,1.0_pReal,0.0_pReal, &
|
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1.0_pReal,0.0_pReal,0.0_pReal, &
|
||||
0.0_pReal,0.0_pReal,-1.0_pReal, &
|
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0.0_pReal,-1.0_pReal,0.0_pReal, &
|
||||
1.0_pReal,0.0_pReal,0.0_pReal, &
|
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0.0_pReal,0.0_pReal,1.0_pReal, &
|
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1.0_pReal,0.0_pReal,0.0_pReal, &
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0.0_pReal,1.0_pReal,0.0_pReal, &
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0.0_pReal,0.0_pReal,1.0_pReal, &
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||||
-0.5_pReal,0.866025403_pReal,0.0_pReal, &
|
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-0.866025403_pReal,-0.5_pReal,0.0_pReal, &
|
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0.0_pReal,0.0_pReal,1.0_pReal, &
|
||||
-0.5_pReal,-0.866025403_pReal,0.0_pReal, &
|
||||
0.866025403_pReal,-0.5_pReal,0.0_pReal, &
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0.0_pReal,0.0_pReal,1.0_pReal, &
|
||||
0.5_pReal,0.866025403_pReal,0.0_pReal, &
|
||||
-0.866025403_pReal,0.5_pReal,0.0_pReal, &
|
||||
0.0_pReal,0.0_pReal,1.0_pReal, &
|
||||
-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, &
|
||||
0.5_pReal,-0.866025403_pReal,0.0_pReal, &
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||||
0.866025403_pReal,0.5_pReal,0.0_pReal, &
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0.0_pReal,0.0_pReal,1.0_pReal, &
|
||||
-0.5_pReal,-0.866025403_pReal,0.0_pReal, &
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||||
-0.866025403_pReal,0.5_pReal,0.0_pReal, &
|
||||
0.0_pReal,0.0_pReal,-1.0_pReal, &
|
||||
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, &
|
||||
-0.5_pReal,0.866025403_pReal,0.0_pReal, &
|
||||
0.866025403_pReal,0.5_pReal,0.0_pReal, &
|
||||
0.0_pReal,0.0_pReal,-1.0_pReal, &
|
||||
0.5_pReal,0.866025403_pReal,0.0_pReal, &
|
||||
0.866025403_pReal,-0.5_pReal,0.0_pReal, &
|
||||
0.0_pReal,0.0_pReal,-1.0_pReal, &
|
||||
-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, &
|
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0.5_pReal,-0.866025403_pReal,0.0_pReal, &
|
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-0.866025403_pReal,-0.5_pReal,0.0_pReal, &
|
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0.0_pReal,0.0_pReal,-1.0_pReal, &
|
||||
1.0_pReal,0.0_pReal,0.0_pReal, &
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0.0_pReal,1.0_pReal,0.0_pReal, &
|
||||
0.0_pReal,0.0_pReal,1.0_pReal, &
|
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-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, &
|
||||
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, &
|
||||
-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, &
|
||||
0.0_pReal,1.0_pReal,0.0_pReal, &
|
||||
-1.0_pReal,0.0_pReal,0.0_pReal, &
|
||||
0.0_pReal,0.0_pReal,1.0_pReal, &
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0.0_pReal,-1.0_pReal,0.0_pReal, &
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1.0_pReal,0.0_pReal,0.0_pReal, &
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0.0_pReal,0.0_pReal,1.0_pReal, &
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0.0_pReal,1.0_pReal,0.0_pReal, &
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||||
1.0_pReal,0.0_pReal,0.0_pReal, &
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0.0_pReal,0.0_pReal,-1.0_pReal, &
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0.0_pReal,-1.0_pReal,0.0_pReal, &
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-1.0_pReal,0.0_pReal,0.0_pReal, &
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0.0_pReal,0.0_pReal,-1.0_pReal &
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/),(/132,3/))
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real(pReal), dimension(3,3,44), parameter :: symOperations = &
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reshape((/&
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1.0_pReal, 0.0_pReal, 0.0_pReal, &
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0.0_pReal, 1.0_pReal, 0.0_pReal, &
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0.0_pReal, 0.0_pReal, 1.0_pReal, &
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||||
0.0_pReal, 0.0_pReal, 1.0_pReal, &
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||||
1.0_pReal, 0.0_pReal, 0.0_pReal, &
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0.0_pReal, 1.0_pReal, 0.0_pReal, &
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0.0_pReal, 1.0_pReal, 0.0_pReal, &
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0.0_pReal, 0.0_pReal, 1.0_pReal, &
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1.0_pReal, 0.0_pReal, 0.0_pReal, &
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||||
0.0_pReal, -1.0_pReal, 0.0_pReal, &
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0.0_pReal, 0.0_pReal, 1.0_pReal, &
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||||
-1.0_pReal, 0.0_pReal, 0.0_pReal, &
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||||
0.0_pReal, -1.0_pReal, 0.0_pReal, &
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||||
0.0_pReal, 0.0_pReal, -1.0_pReal, &
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||||
1.0_pReal, 0.0_pReal, 0.0_pReal, &
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||||
0.0_pReal, 1.0_pReal, 0.0_pReal, &
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||||
0.0_pReal, 0.0_pReal, -1.0_pReal, &
|
||||
-1.0_pReal, 0.0_pReal, 0.0_pReal, &
|
||||
0.0_pReal, 0.0_pReal, -1.0_pReal, &
|
||||
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, &
|
||||
-1.0_pReal, 0.0_pReal, 0.0_pReal, &
|
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0.0_pReal, 1.0_pReal, 0.0_pReal, &
|
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0.0_pReal, 0.0_pReal, 1.0_pReal, &
|
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-1.0_pReal, 0.0_pReal, 0.0_pReal, &
|
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0.0_pReal, -1.0_pReal, 0.0_pReal, &
|
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-1.0_pReal, 0.0_pReal, 0.0_pReal, &
|
||||
0.0_pReal, 1.0_pReal, 0.0_pReal, &
|
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0.0_pReal, 0.0_pReal, -1.0_pReal, &
|
||||
-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, &
|
||||
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, &
|
||||
0.0_pReal, 0.0_pReal, -1.0_pReal, &
|
||||
0.0_pReal, -1.0_pReal, 0.0_pReal, &
|
||||
-1.0_pReal, 0.0_pReal, 0.0_pReal, &
|
||||
0.0_pReal, 0.0_pReal, 1.0_pReal, &
|
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0.0_pReal, -1.0_pReal, 0.0_pReal, &
|
||||
1.0_pReal, 0.0_pReal, 0.0_pReal, &
|
||||
0.0_pReal, 0.0_pReal, 1.0_pReal, &
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||||
0.0_pReal, 1.0_pReal, 0.0_pReal, &
|
||||
-1.0_pReal, 0.0_pReal, 0.0_pReal, &
|
||||
0.0_pReal, 0.0_pReal, -1.0_pReal, &
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0.0_pReal, 1.0_pReal, 0.0_pReal, &
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1.0_pReal, 0.0_pReal, 0.0_pReal, &
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-1.0_pReal, 0.0_pReal, 0.0_pReal, &
|
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0.0_pReal, 0.0_pReal, -1.0_pReal, &
|
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0.0_pReal, -1.0_pReal, 0.0_pReal, &
|
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1.0_pReal, 0.0_pReal, 0.0_pReal, &
|
||||
0.0_pReal, 0.0_pReal, -1.0_pReal, &
|
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0.0_pReal, 1.0_pReal, 0.0_pReal, &
|
||||
1.0_pReal, 0.0_pReal, 0.0_pReal, &
|
||||
0.0_pReal, 0.0_pReal, 1.0_pReal, &
|
||||
0.0_pReal, -1.0_pReal, 0.0_pReal, &
|
||||
-1.0_pReal, 0.0_pReal, 0.0_pReal, &
|
||||
0.0_pReal, 0.0_pReal, 1.0_pReal, &
|
||||
0.0_pReal, 1.0_pReal, 0.0_pReal, &
|
||||
0.0_pReal, -1.0_pReal, 0.0_pReal, &
|
||||
-1.0_pReal, 0.0_pReal, 0.0_pReal, &
|
||||
0.0_pReal, 0.0_pReal, -1.0_pReal, &
|
||||
0.0_pReal, 1.0_pReal, 0.0_pReal, &
|
||||
-1.0_pReal, 0.0_pReal, 0.0_pReal, &
|
||||
0.0_pReal, 0.0_pReal, 1.0_pReal, &
|
||||
0.0_pReal, 1.0_pReal, 0.0_pReal, &
|
||||
1.0_pReal, 0.0_pReal, 0.0_pReal, &
|
||||
0.0_pReal, 0.0_pReal, -1.0_pReal, &
|
||||
0.0_pReal, -1.0_pReal, 0.0_pReal, &
|
||||
1.0_pReal, 0.0_pReal, 0.0_pReal, &
|
||||
0.0_pReal, 0.0_pReal, 1.0_pReal, &
|
||||
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, &
|
||||
-0.5_pReal, 0.866025403_pReal, 0.0_pReal, &
|
||||
-0.866025403_pReal, -0.5_pReal, 0.0_pReal, &
|
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0.0_pReal, 0.0_pReal, 1.0_pReal, &
|
||||
-0.5_pReal, -0.866025403_pReal, 0.0_pReal, &
|
||||
0.866025403_pReal, -0.5_pReal, 0.0_pReal, &
|
||||
0.0_pReal, 0.0_pReal, 1.0_pReal, &
|
||||
0.5_pReal, 0.866025403_pReal, 0.0_pReal, &
|
||||
-0.866025403_pReal, 0.5_pReal, 0.0_pReal, &
|
||||
0.0_pReal, 0.0_pReal, 1.0_pReal, &
|
||||
-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, &
|
||||
0.5_pReal, -0.866025403_pReal, 0.0_pReal, &
|
||||
0.866025403_pReal, 0.5_pReal, 0.0_pReal, &
|
||||
0.0_pReal, 0.0_pReal, 1.0_pReal, &
|
||||
-0.5_pReal, -0.866025403_pReal, 0.0_pReal, &
|
||||
-0.866025403_pReal, 0.5_pReal, 0.0_pReal, &
|
||||
0.0_pReal, 0.0_pReal, -1.0_pReal, &
|
||||
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, &
|
||||
-0.5_pReal, 0.866025403_pReal, 0.0_pReal, &
|
||||
0.866025403_pReal, 0.5_pReal, 0.0_pReal, &
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0.0_pReal, 0.0_pReal, -1.0_pReal, &
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0.5_pReal, 0.866025403_pReal, 0.0_pReal, &
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0.866025403_pReal, -0.5_pReal, 0.0_pReal, &
|
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0.0_pReal, 0.0_pReal, -1.0_pReal, &
|
||||
-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, &
|
||||
0.5_pReal, -0.866025403_pReal, 0.0_pReal, &
|
||||
-0.866025403_pReal, -0.5_pReal, 0.0_pReal, &
|
||||
0.0_pReal, 0.0_pReal, -1.0_pReal, &
|
||||
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, &
|
||||
-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, &
|
||||
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, &
|
||||
-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, &
|
||||
0.0_pReal, 1.0_pReal, 0.0_pReal, &
|
||||
-1.0_pReal, 0.0_pReal, 0.0_pReal, &
|
||||
0.0_pReal, 0.0_pReal, 1.0_pReal, &
|
||||
0.0_pReal, -1.0_pReal, 0.0_pReal, &
|
||||
1.0_pReal, 0.0_pReal, 0.0_pReal, &
|
||||
0.0_pReal, 0.0_pReal, 1.0_pReal, &
|
||||
0.0_pReal, 1.0_pReal, 0.0_pReal, &
|
||||
1.0_pReal, 0.0_pReal, 0.0_pReal, &
|
||||
0.0_pReal, 0.0_pReal, -1.0_pReal, &
|
||||
0.0_pReal, -1.0_pReal, 0.0_pReal, &
|
||||
-1.0_pReal, 0.0_pReal, 0.0_pReal, &
|
||||
0.0_pReal, 0.0_pReal, -1.0_pReal &
|
||||
/),(/3,3,44/))
|
||||
|
||||
|
||||
|
||||
|
|
@ -241,128 +241,111 @@ real(pReal), dimension(132,3), parameter :: sym = &
|
|||
|
||||
|
||||
|
||||
!**************************************************************************
|
||||
! calculates the misorientation for 2 orientations C1 and C2
|
||||
!**************************************************************************
|
||||
subroutine math_misorientation(axis, angle, rot, ori1, ori2, symmetryType)
|
||||
|
||||
|
||||
! This subroutine calculates the misorientation
|
||||
! INPUTS:
|
||||
! g1: 1st orientation
|
||||
! g2: 2nd orientation
|
||||
! typ: Type of crystal symmetry; 1:cubic, 2:hexagonal, 3:tetragonal
|
||||
! OUTPUTS:
|
||||
! uvw: Misorientation axis
|
||||
! ang: Misorientation angle (in degrees)
|
||||
! dg: net rotation
|
||||
! USES:
|
||||
! Vars: cubsym,tetsym,hcpsym
|
||||
! Consts: pi
|
||||
subroutine misorientation(g1,g2,typ,uvw,ang,dg)
|
||||
implicit none
|
||||
real(8) g1(3,3),g2(3,3),uvw(3),ang,dg(3,3)
|
||||
integer typ,nosym,s1,s2
|
||||
real(8) g11(3,3),g22(3,3),dg1(3,3),dg2(3,3),sq,x1,x2,x3
|
||||
real(8) trace,temp_ang
|
||||
real(8), allocatable :: symop(:,:,:)
|
||||
integer i,j
|
||||
|
||||
|
||||
if (typ==1) then
|
||||
nosym=24
|
||||
allocate(symop(nosym,3,3))
|
||||
do i=1,nosym
|
||||
do j=1,3
|
||||
symop(i,j,:)=sym(i*j,:)
|
||||
enddo
|
||||
enddo
|
||||
elseif (typ==2) then
|
||||
nosym=12
|
||||
allocate(symop(nosym,3,3))
|
||||
do i=1,nosym
|
||||
do j=1,3
|
||||
symop(i,j,:)=sym(72+(i*j),:)
|
||||
enddo
|
||||
enddo
|
||||
else
|
||||
nosym=8
|
||||
allocate(symop(nosym,3,3))
|
||||
do i=1,nosym
|
||||
do j=1,3
|
||||
symop(i,j,:)=sym(108+(i*j),:)
|
||||
enddo
|
||||
enddo
|
||||
endif
|
||||
|
||||
! Initially set the angle to be maximum
|
||||
ang=2*pi
|
||||
|
||||
! 1: Crystal Symmetry to 1st orientation
|
||||
do s1=1,nosym
|
||||
g11=matmul(symop(s1,:,:),g1)
|
||||
! 2: Crystal Symmetry to 2nd orientation
|
||||
do s2=1,nosym
|
||||
g22=matmul(symop(s2,:,:),g2)
|
||||
! 3: Net rotations (g2*inv(g1)=g2*transpose(g1))
|
||||
dg1=matmul(g2,transpose(g11))
|
||||
dg2=matmul(g1,transpose(g22))
|
||||
|
||||
! 5. CHECK IF THE MISORIENTATION IS IN FUNDAMENTAL ZONE
|
||||
! 5.a. For 1st result: (dg1)
|
||||
sq=dsqrt((dg1(2,3)-dg1(3,2))**2+(dg1(1,3)-dg1(3,1))**2+&
|
||||
(dg1(2,1)-dg1(1,2))**2)
|
||||
x1=(dg1(2,3)-dg1(3,2))/sq
|
||||
x2=(dg1(3,1)-dg1(1,3))/sq
|
||||
x3=(dg1(1,2)-dg1(2,1))/sq
|
||||
if (x1>=0) then
|
||||
if (x2>=0) then
|
||||
if (x3>=0) then
|
||||
if (x1<=x2) then
|
||||
if (x2<=x3) then
|
||||
trace=dg1(1,1)+dg1(2,2)+dg1(3,3)
|
||||
temp_ang=acos((trace-1)/2)
|
||||
if (abs(temp_ang).lt.ang) then
|
||||
ang=temp_ang
|
||||
dg=dg1
|
||||
uvw(1)=x1;uvw(2)=x2;uvw(3)=x3;
|
||||
endif
|
||||
endif
|
||||
endif
|
||||
endif
|
||||
endif
|
||||
endif
|
||||
|
||||
! 5.a. For the 2nd result: (dg2)
|
||||
sq=dsqrt((dg2(2,3)-dg2(3,2))**2+(dg2(1,3)-dg2(3,1))**2+&
|
||||
(dg2(2,1)-dg2(1,2))**2)
|
||||
x1=(dg2(2,3)-dg2(3,2))/sq
|
||||
x2=(dg2(3,1)-dg2(1,3))/sq
|
||||
x3=(dg2(1,2)-dg2(2,1))/sq
|
||||
if (x1>=0) then
|
||||
if (x2>=0) then
|
||||
if (x3>=0) then
|
||||
if (x1<=x2) then
|
||||
if (x2<=x3) then
|
||||
trace=dg2(1,1)+dg2(2,2)+dg2(3,3)
|
||||
temp_ang=acos((trace-1)/2)
|
||||
if (abs(temp_ang).lt.ang) then
|
||||
ang=temp_ang
|
||||
dg=dg2
|
||||
uvw(1)=x1;uvw(2)=x2;uvw(3)=x3;
|
||||
endif
|
||||
endif
|
||||
endif
|
||||
endif
|
||||
endif
|
||||
endif
|
||||
enddo
|
||||
use prec, only: pReal, pInt
|
||||
use IO, only: IO_warning
|
||||
implicit none
|
||||
|
||||
!*** input variables
|
||||
real(pReal), dimension(3,3), intent(in) :: ori1, & ! 1st orientation
|
||||
ori2 ! 2nd orientation
|
||||
integer(pInt), intent(in) :: symmetryType ! Type of crystal symmetry; 1:cubic, 2:hexagonal, 3:tetragonal
|
||||
|
||||
!*** output variables
|
||||
real(pReal), intent(out) :: angle ! misorientation angle in degrees
|
||||
real(pReal), dimension(3), intent(out) :: axis ! rotation axis of misorientation
|
||||
real(pReal), dimension(3,3), intent(out) :: rot ! net rotation of the misorientation
|
||||
|
||||
!*** local variables
|
||||
real(pReal) this_angle ! candidate for misorientation angle
|
||||
real(pReal), dimension(3) :: this_axis ! candidate for rotation axis
|
||||
real(pReal), dimension(3,3,2) :: these_rots ! 2 candidates for net rotation
|
||||
real(pReal), dimension(3,3) :: ori1sym, ori2sym ! symmetrical counterpart of 1st and 2nd orientation respectively
|
||||
real(pReal) invNorm
|
||||
integer(pInt) NsymOperations, & ! number of possible symmetry operations
|
||||
startindex, endindex, &
|
||||
s1, s2, &
|
||||
i
|
||||
real(pReal), dimension(:,:,:), allocatable :: mySymOperations ! symmetry Operations for my crystal symmetry
|
||||
|
||||
|
||||
axis = 0.0_pReal
|
||||
angle = 0.0_pReal
|
||||
rot = 0.0_pReal
|
||||
|
||||
! choose my symmetry operations according to my crystal symetry
|
||||
if (symmetryType == 1_pInt) then
|
||||
NsymOperations = 24_pInt
|
||||
startindex = 1_pInt
|
||||
elseif (symmetryType == 2_pInt) then
|
||||
NsymOperations = 12_pInt
|
||||
startindex = 25_pInt
|
||||
elseif (symmetryType == 3_pInt) then
|
||||
NsymOperations = 8_pInt
|
||||
startindex = 37_pInt
|
||||
else
|
||||
call IO_warning(700)
|
||||
return
|
||||
endif
|
||||
allocate(mySymOperations(NsymOperations,3,3))
|
||||
endindex = startindex + NsymOperations - 1_pInt
|
||||
mySymOperations = symOperations(:,:,startindex:endindex)
|
||||
|
||||
|
||||
! Initially set the orientation angle to maximum
|
||||
angle = 2.0_pReal * pi
|
||||
|
||||
! apply symmetry operation to 1st orientation
|
||||
do s1 = 1,NsymOperations
|
||||
ori1sym = math_mul33x33(mySymOperations(:,:,s1), ori1)
|
||||
|
||||
! apply symmetry operation to 2nd orientation
|
||||
do s2 = 1,NsymOperations
|
||||
ori2sym = math_mul33x33(mySymOperations(:,:,s2), ori2)
|
||||
|
||||
! calculate 2 possible net rotations
|
||||
these_rots(:,:,1) = math_mul33x33(ori2, transpose(ori1sym))
|
||||
these_rots(:,:,2) = math_mul33x33(ori1, transpose(ori2sym))
|
||||
|
||||
! store smallest misorientation for an axis inside standard orientation triangle
|
||||
do i = 1,2
|
||||
|
||||
! calculate rotation axis
|
||||
invNorm = ( (these_rots(1,2,i) - these_rots(2,1,i))**2.0_pReal &
|
||||
+ (these_rots(2,3,i) - these_rots(3,2,i))**2.0_pReal &
|
||||
+ (these_rots(3,1,i) - these_rots(1,3,i))**2.0_pReal ) ** (-0.5_pReal)
|
||||
this_axis(1) = (these_rots(2,3,i) - these_rots(3,2,i)) * invNorm
|
||||
this_axis(2) = (these_rots(3,1,i) - these_rots(1,3,i)) * invNorm
|
||||
this_axis(3) = (these_rots(1,2,i) - these_rots(2,1,i)) * invNorm
|
||||
|
||||
if ( (this_axis(1) >= 0.0_pReal) .and. (this_axis(2) >= 0.0_pReal) .and. (this_axis(3) >= 0.0_pReal) &
|
||||
.and. (this_axis(1) <= this_axis(2)) .and. (this_axis(2) <= this_axis(3)) ) then
|
||||
|
||||
! calculate rotation angle
|
||||
this_angle = acos(0.5_pReal * (ori1sym(1,1) + ori1sym(2,2) + ori1sym(3,3) - 1.0_pReal))
|
||||
|
||||
if (abs(this_angle) < angle) then
|
||||
angle = this_angle
|
||||
rot = these_rots(:,:,i)
|
||||
axis = this_axis
|
||||
endif
|
||||
|
||||
endif
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
|
||||
ang=ang*180/pi
|
||||
return
|
||||
|
||||
! convert angle to degrees
|
||||
angle = angle * inDeg
|
||||
|
||||
endsubroutine
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
!**************************************************************************
|
||||
! Quicksort algorithm for two-dimensional integer arrays
|
||||
!
|
||||
|
|
@ -449,12 +432,13 @@ endsubroutine
|
|||
!**************************************************************************
|
||||
! second rank identity tensor of specified dimension
|
||||
!**************************************************************************
|
||||
FUNCTION math_identity2nd(dimen)
|
||||
PURE FUNCTION math_identity2nd(dimen)
|
||||
|
||||
use prec, only: pReal, pInt
|
||||
implicit none
|
||||
|
||||
integer(pInt) i,dimen
|
||||
integer(pInt), intent(in) :: dimen
|
||||
integer(pInt) i
|
||||
real(pReal), dimension(dimen,dimen) :: math_identity2nd
|
||||
|
||||
math_identity2nd = 0.0_pReal
|
||||
|
|
@ -469,13 +453,13 @@ endsubroutine
|
|||
! e_ijk = -1 if odd permutation of ijk
|
||||
! e_ijk = 0 otherwise
|
||||
!**************************************************************************
|
||||
FUNCTION math_civita(i,j,k) ! change its name from math_permut
|
||||
PURE FUNCTION math_civita(i,j,k) ! change its name from math_permut
|
||||
! to math_civita <<<updated 31.07.2009>>>
|
||||
|
||||
use prec, only: pReal, pInt
|
||||
implicit none
|
||||
|
||||
integer(pInt) i,j,k
|
||||
integer(pInt), intent(in) :: i,j,k
|
||||
real(pReal) math_civita
|
||||
|
||||
math_civita = 0.0_pReal
|
||||
|
|
@ -494,12 +478,12 @@ endsubroutine
|
|||
! d_ij = 1 if i = j
|
||||
! d_ij = 0 otherwise
|
||||
!**************************************************************************
|
||||
FUNCTION math_delta(i,j)
|
||||
PURE FUNCTION math_delta(i,j)
|
||||
|
||||
use prec, only: pReal, pInt
|
||||
implicit none
|
||||
|
||||
integer(pInt) i,j
|
||||
integer(pInt), intent (in) :: i,j
|
||||
real(pReal) math_delta
|
||||
|
||||
math_delta = 0.0_pReal
|
||||
|
|
@ -714,7 +698,7 @@ endsubroutine
|
|||
!**************************************************************************
|
||||
! transposition of a 3x3 matrix
|
||||
!**************************************************************************
|
||||
function math_transpose3x3(A)
|
||||
pure function math_transpose3x3(A)
|
||||
|
||||
use prec, only: pReal,pInt
|
||||
implicit none
|
||||
|
|
@ -732,7 +716,7 @@ function math_transpose3x3(A)
|
|||
!**************************************************************************
|
||||
! Cramer inversion of 3x3 matrix (function)
|
||||
!**************************************************************************
|
||||
function math_inv3x3(A)
|
||||
pure function math_inv3x3(A)
|
||||
|
||||
! direct Cramer inversion of matrix A.
|
||||
! returns all zeroes if not possible, i.e. if det close to zero
|
||||
|
|
@ -773,7 +757,7 @@ function math_transpose3x3(A)
|
|||
!**************************************************************************
|
||||
! Cramer inversion of 3x3 matrix (subroutine)
|
||||
!**************************************************************************
|
||||
SUBROUTINE math_invert3x3(A, InvA, DetA, error)
|
||||
PURE SUBROUTINE math_invert3x3(A, InvA, DetA, error)
|
||||
|
||||
! Bestimmung der Determinanten und Inversen einer 3x3-Matrix
|
||||
! A = Matrix A
|
||||
|
|
@ -820,7 +804,7 @@ function math_transpose3x3(A)
|
|||
!**************************************************************************
|
||||
! Gauss elimination to invert 6x6 matrix
|
||||
!**************************************************************************
|
||||
SUBROUTINE math_invert(dimen,A, InvA, AnzNegEW, error)
|
||||
PURE SUBROUTINE math_invert(dimen,A, InvA, AnzNegEW, error)
|
||||
|
||||
! Invertieren einer dimen x dimen - Matrix
|
||||
! A = Matrix A
|
||||
|
|
@ -853,7 +837,7 @@ function math_transpose3x3(A)
|
|||
|
||||
! ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
|
||||
! ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
|
||||
SUBROUTINE Gauss (dimen,A,B,LogAbsDetA,NegHDK,error)
|
||||
PURE SUBROUTINE Gauss (dimen,A,B,LogAbsDetA,NegHDK,error)
|
||||
|
||||
! Loesung eines linearen Gleichungsssystem A * X = B mit Hilfe des
|
||||
! GAUSS-Algorithmus
|
||||
|
|
@ -1578,14 +1562,16 @@ math_sampleFiberOri = math_RtoEuler(math_mul33x33(pRot,math_mul33x33(fRot,oRot))
|
|||
|
||||
|
||||
!****************************************************************
|
||||
subroutine math_pDecomposition(FE,U,R,error)
|
||||
pure subroutine math_pDecomposition(FE,U,R,error)
|
||||
!-----FE=RU
|
||||
!****************************************************************
|
||||
use prec, only: pReal, pInt
|
||||
implicit none
|
||||
|
||||
logical error
|
||||
real(pReal) FE(3,3),R(3,3),U(3,3),CE(3,3),EW1,EW2,EW3,EB1(3,3),EB2(3,3),EB3(3,3),UI(3,3),det
|
||||
real(pReal), intent(in) :: FE(3,3)
|
||||
real(pReal), intent(out) :: R(3,3), U(3,3)
|
||||
logical, intent(out) :: error
|
||||
real(pReal) CE(3,3),EW1,EW2,EW3,EB1(3,3),EB2(3,3),EB3(3,3),UI(3,3),det
|
||||
|
||||
error = .false.
|
||||
ce = math_mul33x33(transpose(FE),FE)
|
||||
|
|
@ -1601,13 +1587,14 @@ math_sampleFiberOri = math_RtoEuler(math_mul33x33(pRot,math_mul33x33(fRot,oRot))
|
|||
|
||||
|
||||
!**********************************************************************
|
||||
subroutine math_spectral1(M,EW1,EW2,EW3,EB1,EB2,EB3)
|
||||
pure subroutine math_spectral1(M,EW1,EW2,EW3,EB1,EB2,EB3)
|
||||
!**** EIGENWERTE UND EIGENWERTBASIS DER SYMMETRISCHEN 3X3 MATRIX M
|
||||
|
||||
use prec, only: pReal, pInt
|
||||
implicit none
|
||||
|
||||
real(pReal) M(3,3),EB1(3,3),EB2(3,3),EB3(3,3),EW1,EW2,EW3
|
||||
real(pReal), intent(in) :: M(3,3)
|
||||
real(pReal), intent(out) :: EB1(3,3),EB2(3,3),EB3(3,3),EW1,EW2,EW3
|
||||
real(pReal) HI1M,HI2M,HI3M,TOL,R,S,T,P,Q,RHO,PHI,Y1,Y2,Y3,D1,D2,D3
|
||||
real(pReal) C1,C2,C3,M1(3,3),M2(3,3),M3(3,3),arg
|
||||
TOL=1.e-14_pReal
|
||||
|
|
@ -1698,11 +1685,12 @@ math_sampleFiberOri = math_RtoEuler(math_mul33x33(pRot,math_mul33x33(fRot,oRot))
|
|||
!**********************************************************************
|
||||
!**** HAUPTINVARIANTEN HI1M, HI2M, HI3M DER 3X3 MATRIX M
|
||||
|
||||
SUBROUTINE math_hi(M,HI1M,HI2M,HI3M)
|
||||
PURE SUBROUTINE math_hi(M,HI1M,HI2M,HI3M)
|
||||
use prec, only: pReal, pInt
|
||||
implicit none
|
||||
|
||||
real(pReal) M(3,3),HI1M,HI2M,HI3M
|
||||
real(pReal), intent(in) :: M(3,3)
|
||||
real(pReal), intent(out) :: HI1M, HI2M, HI3M
|
||||
|
||||
HI1M=M(1,1)+M(2,2)+M(3,3)
|
||||
HI2M=HI1M**2/2.0_pReal-(M(1,1)**2+M(2,2)**2+M(3,3)**2)/2.0_pReal-M(1,2)*M(2,1)-M(1,3)*M(3,1)-M(2,3)*M(3,2)
|
||||
|
|
|
|||
Loading…
Reference in New Issue