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
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
|
(* ocamlgsl - OCaml interface to GSL *)
(* Copyright () 2002, 2003 - Olivier Andrieu, Paul Pelzl *)
(* distributed under the terms of the GPL version 2 *)
type complex = Complex.t =
{ re : float ; im : float }
let complex ~re ~im =
{ re = re ; im = im }
type complex_array = float array
let set a i c =
a.(2*i) <- c.re ;
a.(2*i + 1) <- c.im
let get a i =
{ re = a.(2*i); im = a.(2*i+1) }
let unpack ca =
let len = Array.length ca in
if len mod 2 <> 0
then invalid_arg "unpack_complex_array" ;
Array.init (len / 2) (get ca)
let pack a =
let len = Array.length a in
let ca = Array.make (2 * len) 0. in
for i=0 to pred len do
ca.(2*i) <- a.(i).re ;
ca.(2*i+1) <- a.(i).im
done ;
ca
let mult a b =
if Array.length a mod 2 <> 0
then invalid_arg "mult: not a complex array" ;
let len = (Array.length a) / 2 in
for i = 0 to pred len do
let re = a.(2*i) *. b.(2*i) -. a.(2*i+1) *. b.(2*i+1) in
let im = a.(2*i) *. b.(2*i+1) +. a.(2*i+1) *. b.(2*i) in
a.(2*i) <- re ;
a.(2*i+1) <- im
done
(* added by Paul Pelzl, 2003/12/25 *)
let rect x y = {re = x; im = y}
let polar = Complex.polar
let arg = Complex.arg
let abs = Complex.norm
let abs2 = Complex.norm2
external logabs : complex -> float
= "ml_gsl_complex_logabs"
let add = Complex.add
let sub = Complex.sub
let mul = Complex.mul
let div = Complex.div
let add_real a x = {re = a.re +. x; im = a.im}
let sub_real a x = {re = a.re -. x; im = a.im}
let mul_real a x = {re = a.re *. x; im = a.im *. x}
let div_real a x = {re = a.re /. x; im = a.im /. x}
let add_imag a y = {re = a.re; im = a.im +. y}
let sub_imag a y = {re = a.re; im = a.im -. y}
let mul_imag a y = {re = a.im *. (~-. y); im = a.re *. y}
let div_imag a y = {re = a.im /. y; im = a.re /. (~-. y)}
let conjugate = Complex.conj
let inverse = Complex.inv
let negative = Complex.neg
(* elementary complex functions *)
external sqrt : complex -> complex
= "ml_gsl_complex_sqrt"
external sqrt_real : float -> complex
= "ml_gsl_complex_sqrt_real"
external pow : complex -> complex -> complex
= "ml_gsl_complex_pow"
external pow_real : complex -> float -> complex
= "ml_gsl_complex_pow_real"
external exp : complex -> complex
= "ml_gsl_complex_exp"
external log : complex -> complex
= "ml_gsl_complex_log"
external log10 : complex -> complex
= "ml_gsl_complex_log10"
external log_b : complex -> complex -> complex
= "ml_gsl_complex_log_b"
(* complex trigonometric functions *)
external sin : complex -> complex
= "ml_gsl_complex_sin"
external cos : complex -> complex
= "ml_gsl_complex_cos"
external tan : complex -> complex
= "ml_gsl_complex_tan"
external sec : complex -> complex
= "ml_gsl_complex_sec"
external csc : complex -> complex
= "ml_gsl_complex_csc"
external cot : complex -> complex
= "ml_gsl_complex_cot"
(* inverse complex trigonometric functions *)
external arcsin : complex -> complex
= "ml_gsl_complex_arcsin"
external arcsin_real : float -> complex
= "ml_gsl_complex_arcsin_real"
external arccos : complex -> complex
= "ml_gsl_complex_arccos"
external arccos_real : float -> complex
= "ml_gsl_complex_arccos_real"
external arctan : complex -> complex
= "ml_gsl_complex_arctan"
external arcsec : complex -> complex
= "ml_gsl_complex_arcsec"
external arcsec_real : float -> complex
= "ml_gsl_complex_arcsec_real"
external arccsc : complex -> complex
= "ml_gsl_complex_arccsc"
external arccsc_real : float -> complex
= "ml_gsl_complex_arccsc_real"
external arccot : complex -> complex
= "ml_gsl_complex_arccot"
(* complex hyperbolic functions *)
external sinh : complex -> complex
= "ml_gsl_complex_sinh"
external cosh : complex -> complex
= "ml_gsl_complex_cosh"
external tanh : complex -> complex
= "ml_gsl_complex_tanh"
external sech : complex -> complex
= "ml_gsl_complex_sech"
external csch : complex -> complex
= "ml_gsl_complex_csch"
external coth : complex -> complex
= "ml_gsl_complex_coth"
(* inverse complex hyperbolic functions *)
external arcsinh : complex -> complex
= "ml_gsl_complex_arcsinh"
external arccosh : complex -> complex
= "ml_gsl_complex_arccosh"
external arccosh_real : float -> complex
= "ml_gsl_complex_arccosh_real"
external arctanh : complex -> complex
= "ml_gsl_complex_arctanh"
external arctanh_real : float -> complex
= "ml_gsl_complex_arctanh_real"
external arcsech : complex -> complex
= "ml_gsl_complex_arcsech"
external arccsch : complex -> complex
= "ml_gsl_complex_arccsch"
external arccoth : complex -> complex
= "ml_gsl_complex_arccoth"
|
