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
|
# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
include <math/gsurfit.h>
include "gsurfitdef.h"
# GSDER -- Procedure to calculate a new surface which is a derivative of
# the previous surface
procedure gsder (sf1, x, y, zfit, npts, nxd, nyd)
pointer sf1 # pointer to the previous surface
real x[npts] # x values
real y[npts] # y values
real zfit[npts] # fitted values
int npts # number of points
int nxd, nyd # order of the derivatives in x and y
real norm
int ncoeff, nxder, nyder, i, j
int order, maxorder1, maxorder2, nmove1, nmove2
pointer sf2, sp, coeff, ptr1, ptr2
begin
if (sf1 == NULL)
return
if (nxd < 0 || nyd < 0)
call error (0, "GSDER: Order of derivatives cannot be < 0")
if (nxd == 0 && nyd == 0) {
call gsvector (sf1, x, y, zfit, npts)
return
}
# allocate space for new surface
call calloc (sf2, LEN_GSSTRUCT, TY_STRUCT)
# check the order of the derivatives and return 0 if the order is
# high
nxder = min (nxd, GS_NXCOEFF(sf1))
nyder = min (nyd, GS_NYCOEFF(sf1))
if (nxder >= GS_NXCOEFF(sf1) && nyder >= GS_NYCOEFF(sf1))
call amovkr (real(0.0), zfit, npts)
# set up new surface
GS_TYPE(sf2) = GS_TYPE(sf1)
# set the derivative surface parameters
switch (GS_TYPE(sf2)) {
case GS_LEGENDRE, GS_CHEBYSHEV, GS_POLYNOMIAL:
GS_XTERMS(sf2) = GS_XTERMS(sf1)
# find the order of the new surface
switch (GS_XTERMS(sf2)) {
case GS_XNONE:
if (nxder > 0 && nyder > 0) {
GS_NXCOEFF(sf2) = 1
GS_XORDER(sf2) = 1
GS_NYCOEFF(sf2) = 1
GS_YORDER(sf2) = 1
GS_NCOEFF(sf2) = 1
} else if (nxder > 0) {
GS_NXCOEFF(sf2) = max (1, GS_NXCOEFF(sf1) - nxder)
GS_XORDER(sf2) = max (1, GS_NXCOEFF(sf1) - nxder)
GS_NYCOEFF(sf2) = 1
GS_YORDER(sf2) = 1
GS_NCOEFF(sf2) = GS_NXCOEFF(sf2)
} else if (nyder > 0) {
GS_NXCOEFF(sf2) = 1
GS_XORDER(sf2) = 1
GS_NYCOEFF(sf2) = max (1, GS_NYCOEFF(sf1) - nyder)
GS_YORDER(sf2) = max (1, GS_NYCOEFF(sf1) - nyder)
GS_NCOEFF(sf2) = GS_NYCOEFF(sf2)
}
case GS_XHALF:
if ((nxder >= GS_NXCOEFF(sf1)) || (nyder >= GS_NYCOEFF(sf1)) ||
(nxder + nyder) >= max (GS_NXCOEFF(sf1),
GS_NYCOEFF(sf1))) {
GS_NXCOEFF(sf2) = 1
GS_XORDER(sf2) = 1
GS_NYCOEFF(sf2) = 1
GS_YORDER(sf2) = 1
GS_NCOEFF(sf2) = 1
} else {
maxorder1 = max (GS_XORDER(sf1) + 1, GS_YORDER(sf1) + 1)
order = max (1, min (maxorder1 - 1 - nyder - nxder,
GS_NXCOEFF(sf1) - nxder))
GS_NXCOEFF(sf2) = order
GS_XORDER(sf2) = order
order = max (1, min (maxorder1 - 1 - nyder - nxder,
GS_NYCOEFF(sf1) - nyder))
GS_NYCOEFF(sf2) = order
GS_YORDER(sf2) = order
order = min (GS_XORDER(sf2), GS_YORDER(sf2))
GS_NCOEFF(sf2) = GS_NXCOEFF(sf2) * GS_NYCOEFF(sf2) -
order * (order - 1) / 2
}
default:
if (nxder >= GS_NXCOEFF(sf1) || nyder >= GS_NYCOEFF(sf1)) {
GS_NXCOEFF(sf2) = 1
GS_XORDER(sf2) = 1
GS_NYCOEFF(sf2) = 1
GS_YORDER(sf2) = 1
GS_NCOEFF(sf2) = 1
} else {
GS_NXCOEFF(sf2) = max (1, GS_NXCOEFF(sf1) - nxder)
GS_XORDER(sf2) = max (1, GS_XORDER(sf1) - nxder)
GS_NYCOEFF(sf2) = max (1, GS_NYCOEFF(sf1) - nyder)
GS_YORDER(sf2) = max (1, GS_YORDER(sf1) - nyder)
GS_NCOEFF(sf2) = GS_NXCOEFF(sf2) * GS_NYCOEFF(sf2)
}
}
# define the data limits
GS_XMIN(sf2) = GS_XMIN(sf1)
GS_XMAX(sf2) = GS_XMAX(sf1)
GS_XRANGE(sf2) = GS_XRANGE(sf1)
GS_XMAXMIN(sf2) = GS_XMAXMIN(sf1)
GS_YMIN(sf2) = GS_YMIN(sf1)
GS_YMAX(sf2) = GS_YMAX(sf1)
GS_YRANGE(sf2) = GS_YRANGE(sf1)
GS_YMAXMIN(sf2) = GS_YMAXMIN(sf1)
default:
call error (0, "GSDER: Unknown surface type.")
}
# set remaining surface pointers to NULL
GS_XBASIS(sf2) = NULL
GS_YBASIS(sf2) = NULL
GS_MATRIX(sf2) = NULL
GS_CHOFAC(sf2) = NULL
GS_VECTOR(sf2) = NULL
GS_COEFF(sf2) = NULL
GS_WZ(sf2) = NULL
# allocate space for coefficients
call calloc (GS_COEFF(sf2), GS_NCOEFF(sf2), TY_REAL)
# get coefficients
call smark (sp)
call salloc (coeff, GS_NCOEFF(sf1), TY_REAL)
call gscoeff (sf1, Memr[coeff], ncoeff)
# compute the new coefficients
switch (GS_XTERMS(sf2)) {
case GS_XFULL:
if (nxder >= GS_NXCOEFF(sf1) || nyder >= GS_NYCOEFF(sf1))
COEFF(GS_COEFF(sf2)) = 0.
else {
ptr2 = GS_COEFF(sf2) + (GS_NYCOEFF(sf2) - 1) * GS_NXCOEFF(sf2)
ptr1 = coeff + (GS_NYCOEFF(sf1) - 1) * GS_NXCOEFF(sf1)
do i = GS_NYCOEFF(sf1), nyder + 1, -1 {
call amovr (Memr[ptr1+nxder], COEFF(ptr2),
GS_NXCOEFF(sf2))
ptr2 = ptr2 - GS_NXCOEFF(sf2)
ptr1 = ptr1 - GS_NXCOEFF(sf1)
}
}
case GS_XHALF:
if ((nxder >= GS_NXCOEFF(sf1)) || (nyder >= GS_NYCOEFF(sf1)) ||
(nxder + nyder) >= max (GS_NXCOEFF(sf1), GS_NYCOEFF(sf1)))
COEFF(GS_COEFF(sf2)) = 0.
else {
maxorder1 = max (GS_XORDER(sf1) + 1, GS_YORDER(sf1) + 1)
maxorder2 = max (GS_XORDER(sf2) + 1, GS_YORDER(sf2) + 1)
ptr2 = GS_COEFF(sf2) + GS_NCOEFF(sf2)
ptr1 = coeff + GS_NCOEFF(sf1)
do i = GS_NYCOEFF(sf1), nyder + 1, -1 {
nmove1 = max (0, min (maxorder1 - i, GS_NXCOEFF(sf1)))
nmove2 = max (0, min (maxorder2 - i + nyder,
GS_NXCOEFF(sf2)))
ptr1 = ptr1 - nmove1
ptr2 = ptr2 - nmove2
call amovr (Memr[ptr1+nxder], COEFF(ptr2), nmove2)
}
}
default:
if (nxder > 0 && nyder > 0)
COEFF(GS_COEFF(sf2)) = 0.
else if (nxder > 0) {
if (nxder >= GS_NXCOEFF(sf1))
COEFF(GS_COEFF(sf2)) = 0.
else {
ptr1 = coeff
ptr2 = GS_COEFF(sf2) + GS_NCOEFF(sf2) - 1
do j = GS_NXCOEFF(sf1), nxder + 1, -1 {
COEFF(ptr2) = Memr[ptr1+j-1]
ptr2 = ptr2 - 1
}
}
} else if (nyder > 0) {
if (nyder >= GS_NYCOEFF(sf1))
COEFF(GS_COEFF(sf2)) = 0.
else {
ptr1 = coeff + GS_NCOEFF(sf1) - 1
ptr2 = GS_COEFF(sf2)
do i = GS_NYCOEFF(sf1), nyder + 1, -1
ptr1 = ptr1 - 1
call amovr (Memr[ptr1+1], COEFF(ptr2), GS_NCOEFF(sf2))
}
}
}
# evaluate the derivatives
switch (GS_TYPE(sf2)) {
case GS_POLYNOMIAL:
call rgs_derpoly (COEFF(GS_COEFF(sf2)), x, y, zfit, npts,
GS_XTERMS(sf2), GS_XORDER(sf2), GS_YORDER(sf2), nxder,
nyder, GS_XMAXMIN(sf2), GS_XRANGE(sf2), GS_YMAXMIN(sf2),
GS_YRANGE(sf2))
case GS_CHEBYSHEV:
call rgs_dercheb (COEFF(GS_COEFF(sf2)), x, y, zfit, npts,
GS_XTERMS(sf2), GS_XORDER(sf2), GS_YORDER(sf2), nxder,
nyder, GS_XMAXMIN(sf2), GS_XRANGE(sf2), GS_YMAXMIN(sf2),
GS_YRANGE(sf2))
case GS_LEGENDRE:
call rgs_derleg (COEFF(GS_COEFF(sf2)), x, y, zfit, npts,
GS_XTERMS(sf2), GS_XORDER(sf2), GS_YORDER(sf2), nxder,
nyder, GS_XMAXMIN(sf2), GS_XRANGE(sf2), GS_YMAXMIN(sf2),
GS_YRANGE(sf2))
default:
call error (0, "GSVECTOR: Unknown surface type.")
}
# Normalize.
if (GS_TYPE(sf2) != GS_POLYNOMIAL) {
norm = (2. / (GS_XMAX(sf2) - GS_XMIN(sf2))) ** nxder * (2. /
(GS_YMAX(sf2) - GS_YMIN(sf2))) ** nyder
call amulkr (zfit, norm, zfit, npts)
}
# free the space
call gsfree (sf2)
call sfree (sp)
end
|
