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
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
|
include <mach.h>
include "lsqfit.h"
# LL_RLSQF1 -- Given an initial fit reject points outside of the low and
# high cut rejections parameters.
procedure ll_rlsqf1 (x, y, xerr, yerr, weight, npts, maxiter, answers, nreject,
locut, hicut)
real x[ARB] #I the input vector
real y[ARB] #I the reference vector
real xerr[ARB] #I the input vector errors squared
real yerr[ARB] #I the reference vector errors squared
real weight[ARB] #I the input weight array
int npts #I the number of points
int maxiter #I the number of iterations
real answers[ARB] #I/O the answers array
int nreject #I the max number of rejection cycles
real locut #I the low side rejection parameter
real hicut #I the high side rejection parameter
int i, niter, nrej
real loval, hival, resid
begin
if ((IS_INDEFR(locut) && IS_INDEFR(hicut)) || npts <= 2)
return
if (RMS[answers] <= 0.0 || IS_INDEFR(CHI[answers]))
return
niter = 0
repeat {
if (IS_INDEFR(locut))
loval = -MAX_REAL
else
loval = -locut * RMS[answers]
if (IS_INDEFR(hicut))
hival = MAX_REAL
else
hival = hicut * RMS[answers]
nrej = 0
do i = 1, npts {
if (weight[i] <= 0.0)
next
resid = y[i] - (SLOPE[answers] * x[i] + YINCPT[answers])
if (resid >= loval && resid <= hival)
next
weight[i] = 0.0
nrej = nrej + 1
}
if (nrej <= 0)
break
call ll_lsqf1 (x, y, xerr, yerr, weight, npts, maxiter, answers)
if (IS_INDEFR(CHI[answers]))
break
if (RMS[answers] <= 0.0)
break
niter = niter + 1
} until (niter >= nreject)
end
# LL_LSQF1 -- Compute the slope and intercept of the equation y = a * x + b
# using error arrays in both x and y.
procedure ll_lsqf1 (x, y, xerr, yerr, weight, npts, niter, answers)
real x[ARB] #I the input vector
real y[ARB] #I the reference vector
real xerr[ARB] #I the input vector errors squared
real yerr[ARB] #I the reference vector errors squared
real weight[ARB] #I the input weight array
int npts #I the number of points
int niter #I the number of iterations
real answers[ARB] #I/O the answers array
int i, j
pointer bufr, bufx, bufw
real slope, yintrcpt, me1, msq, wt, dm, db
begin
# Peform the initial fit.
call ll_0lsqf1 (x, y, weight, npts, answers)
if (IS_INDEFR(CHI[answers]))
return
# Allocate working space.
call malloc (bufr, npts, TY_REAL)
call malloc (bufx, npts, TY_REAL)
call malloc (bufw, npts, TY_REAL)
# Initialize the iterations.
slope = SLOPE[answers]
yintrcpt = YINCPT[answers]
me1 = CHI[answers]
# Iterate on the fit.
do i = 1, niter {
msq = slope * slope
do j = 1, npts {
if (weight[j] <= 0.0) {
Memr[bufr+j-1] = 0.0
Memr[bufw+j-1] = 0.0
Memr[bufx+j-1] = 0.0
} else {
wt = yerr[j] + msq * xerr[j]
if (wt <= 0.0)
wt = 1.0
else
wt = 1.0 / wt
Memr[bufr+j-1] = y[j] - (slope * x[j] + yintrcpt)
Memr[bufw+j-1] = weight[j] * wt
Memr[bufx+j-1] = x[j] + Memr[bufr+j-1] * slope * xerr[j] *
wt
}
}
call ll_0lsqf1 (Memr[bufx], Memr[bufr], Memr[bufw], npts, answers)
if (IS_INDEFR(CHI[answers]))
break
if (abs ((me1 - CHI[answers]) / CHI[answers]) < 1.0e-5)
break
dm = SLOPE[answers]
db = YINCPT[answers]
me1 = CHI[answers]
slope = slope + dm
yintrcpt = yintrcpt + db
}
# Compute the final answers.
SLOPE[answers] = slope
YINCPT[answers] = yintrcpt
call mfree (bufr, TY_REAL)
call mfree (bufx, TY_REAL)
call mfree (bufw, TY_REAL)
end
# LL_0LSQF1: Compute the slope and intercept of the equation y = a * x + b
# using errors in y only.
procedure ll_0lsqf1 (x, y, w, npts, answers)
real x[ARB] #I the input vector
real y[ARB] #I the reference vector
real w[ARB] #I the weight vector
int npts #I the number of points
real answers[ARB] #I the answers
int i, ngood
double sumyy, sumxx, sumxy, sumx, sumy, sumw
double a, b, det
real wressq, ressq
bool fp_equald()
double ll_dsum1(), ll_dsum2(), ll_dsum3()
begin
# Compute the determinant.
sumyy = ll_dsum3 (y, y, w, npts)
sumxx = ll_dsum3 (x, x, w, npts)
sumxy = ll_dsum3 (x, y, w, npts)
sumy = ll_dsum2 (y, w, npts)
sumx = ll_dsum2 (x, w, npts)
sumw = ll_dsum1 (w, npts)
det = sumw * sumxx - sumx * sumx
if (fp_equald (0.0d0, det)) {
SLOPE[answers] = INDEFR
YINCPT[answers] = INDEFR
ESLOPE[answers] = INDEFR
EYINCPT[answers] = INDEFR
CHI[answers] = INDEFR
RMS[answers] = INDEFR
} else {
a = (sumw * sumxy - sumx * sumy) / det
b = (sumxx * sumy - sumx * sumxy) / det
ngood = 0.0
ressq = 0.0
do i = 1, npts {
if (w[i] > 0.0) {
ngood = ngood + 1
ressq = ressq + (y[i] - (a * x[i] + b)) ** 2
}
}
SLOPE[answers] = a
YINCPT[answers] = b
wressq = sumyy + a * (a * sumxx + 2. * (b * sumx - sumxy)) +
b * (b * sumw - 2.0 * sumy)
if (ngood <= 2) {
CHI[answers] = 0.0
ESLOPE[answers] = 0.0
EYINCPT[answers] = 0.0
RMS[answers] = 0.0
} else if (wressq >= 0.0) {
CHI[answers] = sqrt (wressq / (ngood - 2))
ESLOPE[answers] = CHI[answers] * sqrt (real (sumw / abs(det)))
EYINCPT[answers] = CHI[answers] * sqrt (real (sumxx / abs(det)))
RMS[answers] = sqrt (ressq / (ngood - 2))
} else {
CHI[answers] = 0.0
ESLOPE[answers] = 0.0
EYINCPT[answers] = 0.0
RMS[answers] = 0.0
}
}
end
## GET_LSQF2: iterate LSq Fit to z=ax+by+c for errors in x, y and z.
## NB: xerr, yerr, zerr are errors SQUARED.
##
#
#procedure get_lsqf2 (x, y, z, xerr, yerr, zerr, weight, npts, niter, stats)
#
#real x[npts], y[npts], z[npts] # data vectors
#real xerr[npts], yerr[npts], zerr[npts] # error ** 2 vectors
#real weight[npts] # additional weight factors
#int npts # vector lengths
#int niter # no. of iterations
#real stats[NFITPAR] # returned fit params
#
#int i, j
#real a, b, c, me1
#pointer bufr, bufx, bufy, bufw
#real asq, bsq, res, wt, da, db, dc
#
#begin
# call malloc (bufr, npts, TY_REAL)
# call malloc (bufx, npts, TY_REAL)
# call malloc (bufy, npts, TY_REAL)
# call malloc (bufw, npts, TY_REAL)
#
## initial fit; NB needs expansion
# call get_0lsqf2 (x, y, z, weight, npts, stats)
# a = SLOPE1[stats]
# b = SLOPE2[stats]
# c = OFFSET[stats]
# me1 = CHI[stats]
## call printf ("iteration: %2d a=%7.4f b=%7.4f off=%6.2f (%7.3f) \n")
## call pargi (0)
## call pargr (a)
## call pargr (b)
## call pargr (c)
## call pargr (me1)
#
## iterate
# do i = 1, niter {
# asq = a * a
# bsq = b * b
# do j = 1, npts {
# res = z[j] - (a * x[j] + b * y[j] + c)
# wt = 1. / (zerr[j] + asq * xerr[j] + bsq * yerr[j])
# Memr[bufr+j-1] = res
# Memr[bufw+j-1] = weight[j] * wt
# Memr[bufx+j-1] = x[j] + res * a * xerr[j] * wt
# Memr[bufy+j-1] = y[j] + res * b * yerr[j] * wt
# }
# call get_0lsqf2 (Memr[bufx], Memr[bufy], Memr[bufr], Memr[bufw], npts, stats)
# da = SLOPE1[stats]
# db = SLOPE2[stats]
# dc = OFFSET[stats]
# me1 = CHI[stats]
# a = a + da
# b = b + db
# c = c + dc
## call printf ("iteration: %2d a=%7.4f b=%7.4f off=%6.2f (%7.3f) \n")
## call pargi (i)
## call pargr (a)
## call pargr (b)
## call pargr (c)
## call pargr (me1)
# }
#
# SLOPE1[stats] = a
# SLOPE2[stats] = b
# OFFSET[stats] = c
#
# call mfree (bufr, TY_REAL)
# call mfree (bufx, TY_REAL)
# call mfree (bufy, TY_REAL)
# call mfree (bufw, TY_REAL)
#end
#
##
## GET_0LSQF2 -- calculate the zeroth order LLSq Fit for 2 independent variables,
## assumming errors in z only
##
#
# procedure get_0lsqf2 (x, y, z, w, npt, stats)
#
#real x[npt], y[npt] # input coords
#real z[npt] # ref. coord.
#real w[npt] # weights
#int npt # number of points
#real stats[NFITPAR] # fit info struct
#
#real ga[4, 3]
#
#double dsum1(), dsum2(), dsum3()
#
#begin
# ga[1,1] = dsum3 (x, x, w, npt)
# ga[2,1] = dsum3 (x, y, w, npt)
# ga[2,2] = dsum3 (y, y, w, npt)
# ga[3,1] = dsum2 (x, w, npt)
# ga[3,2] = dsum2 (y, w, npt)
# ga[4,1] = dsum3 (x, z, w, npt)
# ga[4,2] = dsum3 (y, z, w, npt)
# ga[4,3] = dsum2 (z, w, npt)
# ga[3,3] = dsum1 (w, npt)
#
# ga[1,2] = ga[2,1]
# ga[1,3] = ga[3,1]
# ga[2,3] = ga[3,2]
#
# call g_elim(ga, 3)
#
# SLOPE1[stats] = ga[4,1]
# SLOPE2[stats] = ga[4,2]
# OFFSET[stats] = ga[4,3]
##need to define errors, me1
# EOFFSET[stats] = INDEF
# ESLOPE1[stats] = INDEF
# ESLOPE2[stats] = INDEF
# CHI[stats] = INDEF
#end
#
# LL_LLSQF0 -- Compute the offset b in the equation y - x = b using error
# arrays in both x and y.
#procedure ll_lsqf0 (x, y, xerr, yerr, w, npts, answers)
#real x[ARB] #I the input vector
#real y[ARB] #I the reference vector
#real xerr[ARB] #I the input vector errors squared
#real yerr[ARB] #I the reference vector errors squared
#real w[ARB] #I the input weight vector
#int npts #I the number of points
#real answers[ARB] #I the answer vector
#double sumxx, sumx, sumw
#pointer bufr, bufw
#double ll_dsum1(), ll_dsum2(), ll_dsum3()
#begin
# # Allocate working space.
# call malloc (bufr, npts, TY_REAL)
# call malloc (bufw, npts, TY_REAL)
#
# call asubr (y, x, Memr[bufr], npts)
# call aaddr (yerr, xerr, Memr[bufw], npts)
# call adivr (w, Memr[bufw], Memr[bufw], npts)
#
# sumxx = ll_dsum3 (Memr[bufr], Memr[bufr], Memr[bufw], npts)
# sumx = ll_dsum2 (Memr[bufr], Memr[bufw], npts)
# sumw = ll_dsum1 (Memr[bufw], npts)
#
# if (sumw <= 0.0d0) {
# OFFSET[answers] = INDEFR
# EOFFSET[answers] = INDEFR
# CHI[answers] = INDEFR
# } else {
# OFFSET[answers] = sumx / sumw
# if (npts > 1) {
# CHI[answers] = sqrt (real ((sumxx - sumx * sumx / sumw) /
# (npts - 1)))
# EOFFSET[answers] = CHI[answers] / sqrt (real (sumw))
# } else {
# CHI[answers] = 0.0
# EOFFSET[answers] = 0.0
# }
# }
#
# # Free working space.
# call mfree (bufr, TY_REAL)
# call mfree (bufw, TY_REAL)
#end
# LL_DSUM1 -- Compute a double precision vector sum.
double procedure ll_dsum1 (a, n)
real a[ARB] #I the input vector
int n #I the number of points
double sum
int i
begin
sum = 0.0d0
do i = 1, n
sum = sum + a[i]
return (sum)
end
# LL_DSUM2 -- Compute a double precision vector product.
double procedure ll_dsum2 (a, b, n)
real a[n] #I the input vector
real b[n] #I the weight vector
int n #I the number of points
double sum
int i
begin
sum = 0.0d0
do i = 1, n {
if (b[i] > 0.0)
sum = sum + a[i] * b[i]
}
return (sum)
end
# LL_DSUM3 -- Compute a double precision weighted dot product.
double procedure ll_dsum3 (a, b, c, n)
real a[n] #I first input vector
real b[n] #I second input vector
real c[n] #I input weight vector
int n #I the number of points
double sum
int i
begin
sum = 0.0d0
do i = 1, n
if (c[i] > 0.0)
sum = sum + a[i] * b[i] * c[i]
return (sum)
end
|
