-
Notifications
You must be signed in to change notification settings - Fork 3
/
Hankel_Transform.F90
179 lines (168 loc) · 10.5 KB
/
Hankel_Transform.F90
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
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
! Reference:
! Guptasarma D. and Singh, 1997. New digital linear filters for Hankel J_0
! and J_1 tranforms. Geophysical Prospecting, 45, 745-762.
module Hankel_Transform
! Hankel transform, i.e. equation (1) in (Guptasarma and Singh, 1997):
! $ f(r) = \int_0^\infty K(\lambda) J_i(r \lambda) d\lambda $
implicit none
public
integer, parameter, private :: KV = kind(1.0d0)
contains
real(kind = KV) function HankelJ0TransformFast(extFunc, r) result(f)
! eqations (2) and (3), and table 1 in (Guptasarma and Singh, 1997)
real(kind = KV) :: extFunc
real(kind = KV), intent(in) :: r
integer :: i
integer, parameter :: n = 61
real(kind = KV) :: lambda, K(n)
real(kind = KV) :: a = -5.08250000000d+00, s = 1.16638303862d-01
real(kind = KV) :: W(n) = [ &
& 3.30220475766d-04, -1.18223623458d-03, 2.01879495264d-03, -2.13218719891d-03, &
& 1.60839063172d-03, -9.09156346708d-04, 4.37889252738d-04, -1.55298878782d-04, &
& 7.98411962729d-05, 4.37268394072d-06, 3.94253441247d-05, 4.02675924344d-05, &
& 5.66053344653d-05, 7.25774926389d-05, 9.55412535465d-05, 1.24699163157d-04, &
& 1.63262166579d-04, 2.13477133718d-04, 2.79304232173d-04, 3.65312787897d-04, &
& 4.77899413107d-04, 6.25100170825d-04, 8.17726956451d-04, 1.06961339341d-03, &
& 1.39920928148d-03, 1.83020380399d-03, 2.39417015791d-03, 3.13158560774d-03, &
& 4.09654426763d-03, 5.35807925630d-03, 7.00889482693d-03, 9.16637526490d-03, &
& 1.19891721272d-02, 1.56755740646d-02, 2.04953856060d-02, 2.67778388247d-02, &
& 3.49719672729d-02, 4.55975312615d-02, 5.93498881451d-02, 7.69179091244d-02, &
& 9.91094769804d-02, 1.26166963993d-01, 1.57616825575d-01, 1.89707800260d-01, &
& 2.13804195282d-01, 2.08669340316d-01, 1.40250562745d-01, -3.65385242807d-02, &
& -2.98004010732d-01, -4.21898149249d-01, 5.94373771266d-02, 5.29621428353d-01, &
& -4.41362405166d-01, 1.90355040550d-01, -6.19966386785d-02, 1.87255115744d-02, &
& -5.68736766738d-03, 1.68263510609d-03, -4.38587145792d-04, 8.59117336292d-05, &
& -9.15853765160d-06 &
& ]
do i = 1, n, 1
lambda = 10.0d0**(a + (i - 1)*s)/r
K(i) = extFunc("lambda", lambda)
end do
f = dot_product(K, W)/r
end function HankelJ0TransformFast
real(kind = KV) function HankelJ0Transform(extFunc, r) result(f)
! eqations (2) and (3), and table 2 in (Guptasarma and Singh, 1997)
real(kind = KV) :: extFunc
real(kind = KV), intent(in) :: r
integer :: i
integer, parameter :: n = 120
real(kind = KV) :: lambda, K(n)
real(kind = KV) :: a = -8.38850000000d+00, s = 9.0422646867d-02
real(kind = KV) :: W(n) = [ &
& 9.62801364263d-07, -5.02069203805d-06, 1.25268783953d-05, -1.99324417376d-05, &
& 2.29149033546d-05, -2.04737583809d-05, 1.49952002937d-05, -9.37502840980d-06, &
& 5.20156955323d-06, -2.62939890538d-06, 1.26550848081d-06, -5.73156151923d-07, &
& 2.76281274155d-07, -1.09963734387d-07, 7.38038330280d-08, -9.31614600001d-09, &
& 3.87247135578d-08, 2.10303178461d-08, 4.10556513877d-08, 4.13077946246d-08, &
& 5.68828741789d-08, 6.59543638130d-08, 8.40811858728d-08, 1.01532550003d-07, &
& 1.26437360082d-07, 1.54733678097d-07, 1.91218582499d-07, 2.35008851918d-07, &
& 2.89750329490d-07, 3.56550504341d-07, 4.39299297826d-07, 5.40794544880d-07, &
& 6.66136379541d-07, 8.20175040653d-07, 1.01015545059d-06, 1.24384500153d-06, &
& 1.53187399787d-06, 1.88633707689d-06, 2.32307100992d-06, 2.86067883258d-06, &
& 3.52293208580d-06, 4.33827546442d-06, 5.34253613351d-06, 6.57906223200d-06, &
& 8.10198829111d-06, 9.97723263578d-06, 1.22867312381d-05, 1.51305855976d-05, &
& 1.86329431672d-05, 2.29456891669d-05, 2.82570465155d-05, 3.47973610445d-05, &
& 4.28521099371d-05, 5.27705217882d-05, 6.49856943660d-05, 8.00269662180d-05, &
& 9.85515408752d-05, 1.21361571831d-04, 1.49454562334d-04, 1.84045784500d-04, &
& 2.26649641428d-04, 2.79106748890d-04, 3.43716968725d-04, 4.23267056591d-04, &
& 5.21251001943d-04, 6.41886194381d-04, 7.90483105615d-04, 9.73420647376d-04, &
& 1.19877439042d-03, 1.47618560844d-03, 1.81794224454d-03, 2.23860214971d-03, &
& 2.75687537633d-03, 3.39471308297d-03, 4.18062141752d-03, 5.14762977308d-03, &
& 6.33918155348d-03, 7.80480111772d-03, 9.61064602702d-03, 1.18304971234d-02, &
& 1.45647517743d-02, 1.79219149417d-02, 2.20527911163d-02, 2.71124775541d-02, &
& 3.33214363101d-02, 4.08864842127d-02, 5.01074356716d-02, 6.12084049407d-02, &
& 7.45146949048d-02, 9.00780900611d-02, 1.07940155413d-01, 1.27267746478d-01, &
& 1.46676027814d-01, 1.62254276550d-01, 1.68045766353d-01, 1.52383204788d-01, &
& 1.01214136498d-01, -2.44389126667d-03, -1.54078468398d-01, -3.03214415655d-01, &
& -2.97674373379d-01, 7.93541259524d-03, 4.26273267393d-01, 1.00032384844d-01, &
& -4.94117404043d-01, 3.92604878741d-01, -1.90111691178d-01, 7.43654896362d-02, &
& -2.78508428343d-02, 1.09992061155d-02, -4.69798719697d-03, 2.12587632706d-03, &
& -9.81986734159d-04, 4.44992546836d-04, -1.89983519162d-04, 7.31024164292d-05, &
& -2.40057837293d-05, 6.23096824846d-06, -1.12363896552d-06, 1.04470606055d-07 &
& ]
do i = 1, n, 1
lambda = 10.0d0**(a + (i - 1)*s)/r
K(i) = extFunc("lambda", lambda)
end do
f = dot_product(K, W)/r
end function HankelJ0Transform
real(kind = KV) function HankelJ1TransformFast(extFunc, r) result(f)
! eqations (2) and (3), and table 3 in (Guptasarma and Singh, 1997)
real(kind = KV) :: extFunc
real(kind = KV), intent(in) :: r
integer :: i
integer, parameter :: n = 47
real(kind = KV) :: lambda, K(n)
real(kind = KV) :: a = -3.05078187595d+00, s = 1.10599010095d-01
real(kind = KV) :: W(n) = [ &
& 3.17926147465d-06, -9.73811660718d-06, 1.64866227408d-05, -1.81501261160d-05, &
& 1.87556556369d-05, -1.46550406038d-05, 1.53799733803d-05, -6.95628273934d-06, &
& 1.41881555665d-05, 3.41445665537d-06, 2.13941715512d-05, 2.34962369042d-05, &
& 4.84340283290d-05, 7.33732978590d-05, 1.27703784430d-04, 2.08120025730d-04, &
& 3.49803898913d-04, 5.79107814687d-04, 9.65887918451d-04, 1.60401273703d-03, &
& 2.66903777685d-03, 4.43111590040d-03, 7.35631696247d-03, 1.21782796293d-02, &
& 2.01097829218d-02, 3.30096953061d-02, 5.37143591532d-02, 8.60516613299d-02, &
& 1.34267607144d-01, 2.00125033067d-01, 2.74027505792d-01, 3.18168749246d-01, &
& 2.41655667461d-01, -5.40549161658d-02, -4.46912952135d-01, -1.92231885629d-01, &
& 5.52376753950d-01, -3.57429049025d-01, 1.41510519002d-01, -4.61421935309d-02, &
& 1.48273761923d-02, -5.07479209193d-03, 1.83829713749d-03, -6.67742804324d-04, &
& 2.21277518118d-04, -5.66248732755d-05, 7.88229202853d-06 &
& ]
do i = 1, n, 1
lambda = 10.0d0**(a + (i - 1)*s)/r
K(i) = extFunc("lambda", lambda)
end do
f = dot_product(K, W)/r
end function HankelJ1TransformFast
real(kind = KV) function HankelJ1Transform(extFunc, r) result(f)
! eqations (2) and (3), and table 4 in (Guptasarma and Singh, 1997)
real(kind = KV) :: extFunc
real(kind = KV), intent(in) :: r
integer :: i
integer, parameter :: n = 140
real(kind = KV) :: lambda, K(n)
real(kind = KV) :: a = -7.91001919000d+00, s = 8.7967143957d-02
real(kind = KV) :: W(n) = [ &
& -6.76671159511d-14, 3.39808396836d-13, -7.43411889153d-13, 8.93613024469d-13, &
& -5.47341591896d-13, -5.84920181906d-14, 5.20780672883d-13, -6.92656254606d-13, &
& 6.88908045074d-13, -6.39910528298d-13, 5.82098912530d-13, -4.84912700478d-13, &
& 3.54684337858d-13, -2.10855291368d-13, 1.00452749275d-13, 5.58449957721d-15, &
& -5.67206735175d-14, 1.09107856853d-13, -6.04067500756d-14, 8.84512134731d-14, &
& 2.22321981827d-14, 8.38072239207d-14, 1.23647835900d-13, 1.44351787234d-13, &
& 2.94276480713d-13, 3.39965995918d-13, 6.17024672340d-13, 8.25310217692d-13, &
& 1.32560792613d-12, 1.90949961267d-12, 2.93458179767d-12, 4.33454210095d-12, &
& 6.55863288798d-12, 9.78324910827d-12, 1.47126365223d-11, 2.20240108708d-11, &
& 3.30577485691d-11, 4.95377381480d-11, 7.43047574433d-11, 1.11400535181d-10, &
& 1.67052734516d-10, 2.50470107577d-10, 3.75597211630d-10, 5.63165204681d-10, &
& 8.44458166896d-10, 1.26621795331d-09, 1.89866561359d-09, 2.84693620927d-09, &
& 4.26886170263d-09, 6.40104325574d-09, 9.59798498616d-09, 1.43918931885d-08, &
& 2.15798696769d-08, 3.23584600810d-08, 4.85195105813d-08, 7.27538583183d-08, &
& 1.09090191748d-07, 1.63577866557d-07, 2.45275193920d-07, 3.67784458730d-07, &
& 5.51470341585d-07, 8.26916206192d-07, 1.23991037294d-06, 1.85921554669d-06, &
& 2.78777669034d-06, 4.18019870272d-06, 6.26794044911d-06, 9.39858833064d-06, &
& 1.40925408889d-05, 2.11312291505d-05, 3.16846342900d-05, 4.75093313246d-05, &
& 7.12354794719d-05, 1.06810848460d-04, 1.60146590551d-04, 2.40110903628d-04, &
& 3.59981158972d-04, 5.39658308918d-04, 8.08925141201d-04, 1.21234066243d-03, &
& 1.81650387595d-03, 2.72068483151d-03, 4.07274689463d-03, 6.09135552241d-03, &
& 9.09940027636d-03, 1.35660714813d-02, 2.01692550906d-02, 2.98534800308d-02, &
& 4.39060697220d-02, 6.39211368217d-02, 9.16763946228d-02, 1.28368795114d-01, &
& 1.73241920046d-01, 2.19830379079d-01, 2.51193131178d-01, 2.32380049895d-01, &
& 1.17121080205d-01, -1.17252913088d-01, -3.52148528535d-01, -2.71162871370d-01, &
& 2.91134747110d-01, 3.17192840623d-01, -4.93075681595d-01, 3.11223091821d-01, &
& -1.36044122543d-01, 5.12141261934d-02, -1.90806300761d-02, 7.57044398633d-03, &
& -3.25432753751d-03, 1.49774676371d-03, -7.24569558272d-04, 3.62792644965d-04, &
& -1.85907973641d-04, 9.67201396593d-05, -5.07744171678d-05, 2.67510121456d-05, &
& -1.40667136728d-05, 7.33363699547d-06, -3.75638767050d-06, 1.86344211280d-06, &
& -8.71623576811d-07, 3.61028200288d-07, -1.05847108097d-07, -1.51569361490d-08, &
& 6.67633241420d-08, -8.33741579804d-08, 8.31065906136d-08, -7.53457009758d-08, &
& 6.48057680299d-08, -5.37558016587d-08, 4.32436265303d-08, -3.37262648712d-08, &
& 2.53558687098d-08, -1.81287021528d-08, 1.20228328586d-08, -7.10898040664d-09, &
& 3.53667004588d-09, -1.36030600198d-09, 3.52544249042d-10, -4.53719284366d-11 &
& ]
do i = 1, n, 1
lambda = 10.0d0**(a + (i - 1)*s)/r
K(i) = extFunc("lambda", lambda)
end do
f = dot_product(K, W)/r
end function HankelJ1Transform
end module Hankel_Transform