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
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
//
// GENERATED FILE
//
use super::*;
use crate::SpiceContext;
use f2rust_std::*;
const DX: i32 = 1;
const DY: i32 = 2;
const DZ: i32 = 3;
const DR: i32 = 1;
const DCOLAT: i32 = 2;
const DLON: i32 = 3;
/// Derivative of rectangular w.r.t. spherical
///
/// Compute the Jacobian matrix of the transformation from spherical
/// to rectangular coordinates.
///
/// # Brief I/O
///
/// ```text
/// VARIABLE I/O DESCRIPTION
/// -------- --- --------------------------------------------------
/// R I Distance of a point from the origin.
/// COLAT I Angle of the point from the positive Z-axis.
/// SLON I Angle of the point from the XY plane.
/// JACOBI O Matrix of partial derivatives.
/// ```
///
/// # Detailed Input
///
/// ```text
/// R is the distance of a point from the origin.
///
/// COLAT is the angle between the point and the positive
/// Z-axis, in radians.
///
/// SLON is the angle of the point from the XZ plane in
/// radians. The angle increases in the counterclockwise
/// sense about the +Z axis.
/// ```
///
/// # Detailed Output
///
/// ```text
/// JACOBI is the matrix of partial derivatives of the conversion
/// between spherical and rectangular coordinates,
/// evaluated at the input coordinates. This matrix has
/// the form
///
/// .- -.
/// | DX/DR DX/DCOLAT DX/DSLON |
/// | |
/// | DY/DR DY/DCOLAT DY/DSLON |
/// | |
/// | DZ/DR DZ/DCOLAT DZ/DSLON |
/// `- -'
///
/// evaluated at the input values of R, SLON and LAT.
/// Here X, Y, and Z are given by the familiar formulae
///
/// X = R*COS(SLON)*SIN(COLAT)
/// Y = R*SIN(SLON)*SIN(COLAT)
/// Z = R*COS(COLAT)
/// ```
///
/// # Exceptions
///
/// ```text
/// Error free.
/// ```
///
/// # Particulars
///
/// ```text
/// It is often convenient to describe the motion of an object in
/// the spherical coordinate system. However, when performing
/// vector computations its hard to beat rectangular coordinates.
///
/// To transform states given with respect to spherical coordinates
/// to states with respect to rectangular coordinates, one makes use
/// of the Jacobian of the transformation between the two systems.
///
/// Given a state in spherical coordinates
///
/// ( r, colat, slon, dr, dcolat, dslon )
///
/// the velocity in rectangular coordinates is given by the matrix
/// equation:
/// t | t
/// (dx, dy, dz) = JACOBI| * (dr, dcolat, dslon)
/// |(r,colat,slon)
///
/// This routine computes the matrix
///
/// |
/// JACOBI|
/// |(r,colat,slon)
/// ```
///
/// # Examples
///
/// ```text
/// The numerical results shown for this example may differ across
/// platforms. The results depend on the SPICE kernels used as
/// input, the compiler and supporting libraries, and the machine
/// specific arithmetic implementation.
///
/// 1) Find the spherical state of the Earth as seen from
/// Mars in the IAU_MARS reference frame at January 1, 2005 TDB.
/// Map this state back to rectangular coordinates as a check.
///
/// Use the meta-kernel shown below to load the required SPICE
/// kernels.
///
///
/// KPL/MK
///
/// File name: drdsph_ex1.tm
///
/// This meta-kernel is intended to support operation of SPICE
/// example programs. The kernels shown here should not be
/// assumed to contain adequate or correct versions of data
/// required by SPICE-based user applications.
///
/// In order for an application to use this meta-kernel, the
/// kernels referenced here must be present in the user's
/// current working directory.
///
/// The names and contents of the kernels referenced
/// by this meta-kernel are as follows:
///
/// File name Contents
/// --------- --------
/// de421.bsp Planetary ephemeris
/// pck00010.tpc Planet orientation and
/// radii
/// naif0009.tls Leapseconds
///
///
/// \begindata
///
/// KERNELS_TO_LOAD = ( 'de421.bsp',
/// 'pck00010.tpc',
/// 'naif0009.tls' )
///
/// \begintext
///
/// End of meta-kernel
///
///
/// Example code begins here.
///
///
/// PROGRAM DRDSPH_EX1
/// IMPLICIT NONE
///
/// C
/// C SPICELIB functions
/// C
/// DOUBLE PRECISION RPD
///
/// C
/// C Local parameters
/// C
/// CHARACTER*(*) FMT1
/// PARAMETER ( FMT1 = '(A,E18.8)' )
/// C
/// C Local variables
/// C
/// DOUBLE PRECISION COLAT
/// DOUBLE PRECISION DRECTN ( 3 )
/// DOUBLE PRECISION ET
/// DOUBLE PRECISION JACOBI ( 3, 3 )
/// DOUBLE PRECISION LT
/// DOUBLE PRECISION SPHVEL ( 3 )
/// DOUBLE PRECISION RECTAN ( 3 )
/// DOUBLE PRECISION R
/// DOUBLE PRECISION SLON
/// DOUBLE PRECISION STATE ( 6 )
///
/// C
/// C Load SPK, PCK and LSK kernels, use a meta kernel for
/// C convenience.
/// C
/// CALL FURNSH ( 'drdsph_ex1.tm' )
///
/// C
/// C Look up the apparent state of earth as seen from Mars at
/// C January 1, 2005 TDB, relative to the IAU_MARS reference
/// C frame.
/// C
/// CALL STR2ET ( 'January 1, 2005 TDB', ET )
///
/// CALL SPKEZR ( 'Earth', ET, 'IAU_MARS', 'LT+S',
/// . 'Mars', STATE, LT )
///
/// C
/// C Convert position to spherical coordinates.
/// C
/// CALL RECSPH ( STATE, R, COLAT, SLON )
///
/// C
/// C Convert velocity to spherical coordinates.
/// C
///
/// CALL DSPHDR ( STATE(1), STATE(2), STATE(3), JACOBI )
///
/// CALL MXV ( JACOBI, STATE(4), SPHVEL )
///
/// C
/// C As a check, convert the spherical state back to
/// C rectangular coordinates.
/// C
/// CALL SPHREC ( R, COLAT, SLON, RECTAN )
///
/// CALL DRDSPH ( R, COLAT, SLON, JACOBI )
///
/// CALL MXV ( JACOBI, SPHVEL, DRECTN )
///
///
/// WRITE(*,*) ' '
/// WRITE(*,*) 'Rectangular coordinates:'
/// WRITE(*,*) ' '
/// WRITE(*,FMT1) ' X (km) = ', STATE(1)
/// WRITE(*,FMT1) ' Y (km) = ', STATE(2)
/// WRITE(*,FMT1) ' Z (km) = ', STATE(3)
/// WRITE(*,*) ' '
/// WRITE(*,*) 'Rectangular velocity:'
/// WRITE(*,*) ' '
/// WRITE(*,FMT1) ' dX/dt (km/s) = ', STATE(4)
/// WRITE(*,FMT1) ' dY/dt (km/s) = ', STATE(5)
/// WRITE(*,FMT1) ' dZ/dt (km/s) = ', STATE(6)
/// WRITE(*,*) ' '
/// WRITE(*,*) 'Spherical coordinates:'
/// WRITE(*,*) ' '
/// WRITE(*,FMT1) ' Radius (km) = ', R
/// WRITE(*,FMT1) ' Colatitude (deg) = ',
/// . COLAT/RPD()
/// WRITE(*,FMT1) ' Longitude (deg) = ', SLON/RPD()
/// WRITE(*,*) ' '
/// WRITE(*,*) 'Spherical velocity:'
/// WRITE(*,*) ' '
/// WRITE(*,FMT1) ' d Radius/dt (km/s) = ', SPHVEL(1)
/// WRITE(*,FMT1) ' d Colatitude/dt (deg/s) = ',
/// . SPHVEL(2)/RPD()
/// WRITE(*,FMT1) ' d Longitude/dt (deg/s) = ',
/// . SPHVEL(3)/RPD()
/// WRITE(*,*) ' '
/// WRITE(*,*) 'Rectangular coordinates from inverse ' //
/// . 'mapping:'
/// WRITE(*,*) ' '
/// WRITE(*,FMT1) ' X (km) = ', RECTAN(1)
/// WRITE(*,FMT1) ' Y (km) = ', RECTAN(2)
/// WRITE(*,FMT1) ' Z (km) = ', RECTAN(3)
/// WRITE(*,*) ' '
/// WRITE(*,*) 'Rectangular velocity from inverse mapping:'
/// WRITE(*,*) ' '
/// WRITE(*,FMT1) ' dX/dt (km/s) = ', DRECTN(1)
/// WRITE(*,FMT1) ' dY/dt (km/s) = ', DRECTN(2)
/// WRITE(*,FMT1) ' dZ/dt (km/s) = ', DRECTN(3)
/// WRITE(*,*) ' '
/// END
///
///
/// When this program was executed on a Mac/Intel/gfortran/64-bit
/// platform, the output was:
///
///
/// Rectangular coordinates:
///
/// X (km) = -0.76096183E+08
/// Y (km) = 0.32436380E+09
/// Z (km) = 0.47470484E+08
///
/// Rectangular velocity:
///
/// dX/dt (km/s) = 0.22952075E+05
/// dY/dt (km/s) = 0.53760111E+04
/// dZ/dt (km/s) = -0.20881149E+02
///
/// Spherical coordinates:
///
/// Radius (km) = 0.33653522E+09
/// Colatitude (deg) = 0.81891013E+02
/// Longitude (deg) = 0.10320290E+03
///
/// Spherical velocity:
///
/// d Radius/dt (km/s) = -0.11211601E+02
/// d Colatitude/dt (deg/s) = 0.33189930E-05
/// d Longitude/dt (deg/s) = -0.40539288E-02
///
/// Rectangular coordinates from inverse mapping:
///
/// X (km) = -0.76096183E+08
/// Y (km) = 0.32436380E+09
/// Z (km) = 0.47470484E+08
///
/// Rectangular velocity from inverse mapping:
///
/// dX/dt (km/s) = 0.22952075E+05
/// dY/dt (km/s) = 0.53760111E+04
/// dZ/dt (km/s) = -0.20881149E+02
/// ```
///
/// # Author and Institution
///
/// ```text
/// J. Diaz del Rio (ODC Space)
/// W.L. Taber (JPL)
/// I.M. Underwood (JPL)
/// ```
///
/// # Version
///
/// ```text
/// - SPICELIB Version 1.1.0, 26-OCT-2021 (JDR)
///
/// Edited the header to comply with NAIF standard.
/// Added complete code example.
///
/// Changed the argument name LONG to SLON for consistency with
/// other routines.
///
/// - SPICELIB Version 1.0.0, 20-JUL-2001 (WLT) (IMU)
/// ```
pub fn drdsph(r: f64, colat: f64, slon: f64, jacobi: &mut [[f64; 3]; 3]) {
DRDSPH(r, colat, slon, jacobi.as_flattened_mut());
}
//$Procedure DRDSPH ( Derivative of rectangular w.r.t. spherical )
pub fn DRDSPH(R: f64, COLAT: f64, SLON: f64, JACOBI: &mut [f64]) {
let mut JACOBI = DummyArrayMut2D::new(JACOBI, 1..=3, 1..=3);
let mut CCOLAT: f64 = 0.0;
let mut CLONG: f64 = 0.0;
let mut SCOLAT: f64 = 0.0;
let mut SLONG: f64 = 0.0;
//
// Local parameters
//
//
// Local variables
//
CCOLAT = f64::cos(COLAT);
SCOLAT = f64::sin(COLAT);
CLONG = f64::cos(SLON);
SLONG = f64::sin(SLON);
JACOBI[[DX, DR]] = (CLONG * SCOLAT);
JACOBI[[DY, DR]] = (SLONG * SCOLAT);
JACOBI[[DZ, DR]] = CCOLAT;
JACOBI[[DX, DCOLAT]] = ((R * CLONG) * CCOLAT);
JACOBI[[DY, DCOLAT]] = ((R * SLONG) * CCOLAT);
JACOBI[[DZ, DCOLAT]] = -(R * SCOLAT);
JACOBI[[DX, DLON]] = -((R * SLONG) * SCOLAT);
JACOBI[[DY, DLON]] = ((R * CLONG) * SCOLAT);
JACOBI[[DZ, DLON]] = 0.0;
}