1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
|
*DECK MCGDYA
SUBROUTINE MCGDYA(NMU,ZMU,WZMU,NANGL,CAZ1,CAZ2,IL,IM,ILP,IMP,MM)
*
*-----------------------------------------------------------------------
*
*Purpose:
* Returns the dyadic matrix of Eq. (43).
*
*Copyright:
* Copyright (C) 2015 Ecole Polytechnique de Montreal
* This library is free software; you can redistribute it and/or
* modify it under the terms of the GNU Lesser General Public
* License as published by the Free Software Foundation; either
* version 2.1 of the License, or (at your option) any later version.
*
*Author(s): A. Hebert
*
*Parameters: input
* NMU number of polar angles.
* ZMU polar quadrature set in 2D.
* WZMU polar quadrature set in 2D.
* NANGL number of azimuthal angles.
* CAZ1 first azimuthal cosines.
* CAZ2 second azimuthal cosines.
* IL spherical harmonics index.
* IM spherical harmonics index.
* ILP spherical harmonics index.
* IMP spherical harmonics index.
*
*Parameters: output
* MM dyadic matrix.
*
*-----------------------------------------------------------------------
*
IMPLICIT DOUBLE PRECISION(A-H,O-Z)
*----
* SUBROUTINE ARGUMENTS
*----
INTEGER NMU, IL, IM, ILP, IMP
REAL ZMU(NMU),WZMU(NMU)
DOUBLE PRECISION CAZ1(NANGL),CAZ2(NANGL),MM(2,2)
*
REAL PNSH
DOUBLE PRECISION DYAD(2,2)
REAL, DIMENSION(:), ALLOCATABLE :: WW, MU, ETA, XI
DOUBLE PRECISION, PARAMETER :: PI=3.14159265358979323846264338328
*
ALLOCATE(WW(2*NMU*NANGL), MU(2*NMU*NANGL), ETA(2*NMU*NANGL),
> XI(2*NMU*NANGL))
DO IANGLE=1,NANGL
DO IMU=1,NMU
MU((IANGLE-1)*NMU+IMU)=SQRT(1.0-1.0/ZMU(IMU)**2)
ETA((IANGLE-1)*NMU+IMU)=REAL(CAZ1(IANGLE)/ZMU(IMU))
XI((IANGLE-1)*NMU+IMU)=REAL(CAZ2(IANGLE)/ZMU(IMU))
WW((IANGLE-1)*NMU+IMU)=WZMU(IMU)*MU((IANGLE-1)*NMU+IMU)
MU((NANGL+IANGLE-1)*NMU+IMU)=-MU((IANGLE-1)*NMU+IMU)
ETA((NANGL+IANGLE-1)*NMU+IMU)=-ETA((IANGLE-1)*NMU+IMU)
XI((NANGL+IANGLE-1)*NMU+IMU)=-XI((IANGLE-1)*NMU+IMU)
WW((NANGL+IANGLE-1)*NMU+IMU)=WW((IANGLE-1)*NMU+IMU)
ENDDO
ENDDO
MM(:,:)=0.0D0 ; WSUM=0.0D0 ;
DO IANGLE=1,2*NMU*NANGL
DYAD=MATMUL(RESHAPE((/ ETA(IANGLE), XI(IANGLE) /),(/ 2, 1 /)),
> RESHAPE((/ ETA(IANGLE), XI(IANGLE) /),(/ 1, 2 /)))
RLM=PNSH(IL,IM,MU(IANGLE),ETA(IANGLE),XI(IANGLE))
RLMP=PNSH(ILP,IMP,MU(IANGLE),ETA(IANGLE),XI(IANGLE))
WSUM=WSUM+WW(IANGLE)
MM=MM+WW(IANGLE)*RLM*RLMP*DYAD
ENDDO
MM=(2.0D0*ILP+1.0D0)/WSUM*MM
DEALLOCATE(WW, MU, ETA, XI)
RETURN
END
|
