summaryrefslogtreecommitdiff
path: root/rspl/rspl1.c
blob: dc3588bb8aa5e012a3ab9cd8ed90a623b1631b39 (plain)
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

 /* Single dimension regularized spline data structure */

/* 
 * Argyll Color Correction System
 * Author: Graeme W. Gill
 * Date:   2000/10/29
 *
 * Copyright 1996 - 2010 Graeme W. Gill
 * All rights reserved.
 *
 * This material is licenced under the GNU GENERAL PUBLIC LICENSE Version 2 or later :-
 * see the License2.txt file for licencing details.
 *
 * This is a simple 1D version of rspl, useful for standalone purposes.
 *
 */

#include <stdio.h>
#include <stdlib.h>
#include <stdarg.h>
#include <math.h>
#include "numsup.h"
#include "rspl1.h"

#undef DEBUG

#ifdef DEBUG
# define DBGA g_log, 0 		/* First argument to DBGF() */
# define DBGF(xx)	a1logd xx
#else
# define DBGF(xx)
#endif


/* Do an interpolation based on the grid */
/* Use a linear interp between grid points. */
/* If the input is outside the grid range, it will */
/* be clamped to the nearest grid point. */
static int interp(
rspl *t,
co *p
) {
	int rv = 0;
	double x, y, xx, w1;
	int i;

	x = p->p[0];

	if (x < t->gl) {
		x = t->gl;
		rv = 1;
	} else if (x > t->gh) {
		x = t->gh;
		rv = 1;
	}

	xx = (x - t->gl)/t->gw;			/* Grid location of point */
	i = (int)floor(xx);				/* Lower grid of point */
	if (i >= (t->nig-2))
		i = t->nig-2;

	w1 = xx - (double)i;			/* Weight to upper grid point */

	y = ((1.0 - w1) * t->x[i]) + (w1 * t->x[i+1]);

	p->v[0] = y * t->vw + t->vl;	/* Rescale the data */

	return rv;
}

/* Destructor */
static void del_rspl(rspl *t) {
	if (t != NULL) {
		if (t->x != NULL)
			free_dvector(t->x, 0, t->nig);
	free(t);
	}
}

/* Initialise the regular spline from scattered data */
/* Return nz on error */
static int fit_rspl_imp(
	struct _rspl *t,/* this */
	int flags,		/* (Not used) */
	void *d,		/* Array holding position and function values of data points */
	int dtp,		/* Flag indicating data type, 0 = (co *), 1 = (cow *), 2 = (coww *) */
	int ndp,		/* Number of data points */
	datai glow,		/* Grid low scale - will expand to enclose data, NULL = default 0.0 */
	datai ghigh,	/* Grid high scale - will expand to enclose data, NULL = default 1.0 */
	int    *gres,	/* Spline grid resolution, ncells = gres-1 */
	datao vlow,		/* Data value low normalize, NULL = default 0.0 */
	datao vhigh,	/* Data value high normalize - NULL = default 1.0 */
	double smooth,	/* Smoothing factor, 0.0 = default 1.0 */
	double *avgdev, /* (Not used) */
	double **ipos 	/* (not used) */
) {
	int n;
	double cw;

	DBGF((DBGA, "rspl1:fit_rspl_imp() with %d points called, dtp = %d\n",ndp,dtp));

	/* Allocate space for interpolation grid */
	t->nig = *gres;

	if ((t->x   = dvector(0, t->nig)) == NULL) {
		DBGF((DBGA, "rspl1:Malloc of vector x failed\n"));
		return 1;
	}

	/* Normalize curve weight to grid resolution. */
	cw = 0.0000005 * smooth * pow((t->nig-1),4.0) / (t->nig - 2);
	DBGF((DBGA, "rspl1:cw = %e\n",cw));

	/* cw is multiplied by the sum of grid curvature errors squared to keep */
	/* the same ratio with the sum of data position errors squared */

	/* Determine the data range */
	t->xl = 1e300;
	t->xh = -1e300;
	t->dl = 1e300;
	t->dh = -1e300;
	if (dtp == 0) {
		co *dd = (co *)d;

		for (n = 0; n < ndp; n++) {
			if (dd[n].p[0] < t->xl)
				t->xl = dd[n].p[0];
			if (dd[n].p[0] > t->xh)
				t->xh = dd[n].p[0];
			if (dd[n].v[0] < t->dl)
				t->dl = dd[n].v[0];
			if (dd[n].v[0] > t->dh)
				t->dh = dd[n].v[0];

			DBGF((DBGA, "rspl1:Point %d = %f, %f\n",n,dd[n].p[0],dd[n].v[0]));
		}
	} else if (dtp == 1) {
		cow *dd = (cow *)d;

		for (n = 0; n < ndp; n++) {
			if (dd[n].p[0] < t->xl)
				t->xl = dd[n].p[0];
			if (dd[n].p[0] > t->xh)
				t->xh = dd[n].p[0];
			if (dd[n].v[0] < t->dl)
				t->dl = dd[n].v[0];
			if (dd[n].v[0] > t->dh)
				t->dh = dd[n].v[0];
			DBGF((DBGA, "rspl1:Point %d = %f, %f (%f)\n",n,dd[n].p[0],dd[n].v[0],dd[n].w));
		}
	} else {
		DBGF((DBGA, "rspl1:Internal error, unknown dtp value %d\n",dtp));
		return 1;
	}

	t->gl = glow != NULL ? *glow : 0.0;
	t->gh = ghigh != NULL ? *ghigh : 1.0;

	/* adjust input ranges to encompass data */ 
	if (t->xl < t->gl)
		t->gl = t->xl;
	if (t->xh > t->gh)
		t->gh = t->xh;

	/* Set the input and output scaling */
	t->gw  = (t->gh - t->gl)/(double)(t->nig-1);

	t->vl  = vlow != NULL ? *vlow : 0.0;
	t->vw  = ((vhigh != NULL ? *vhigh : 1.0) - t->vl);

	DBGF((DBGA, "rspl1:gl %f, gh %f, gw %f, vl %f, vw %f\n",t->gl,t->gh,t->gw,t->vl,t->vw));

	/* create smoothed grid data */
	{
		int n,i,k;
		double **A;		/* A matrix of interpoint weights */
		double *b;		/* b vector for RHS of simultabeous equation */

		/* We just store the diagonal of the A matrix */
		if ((A = dmatrix(0, t->nig, 0, 2)) == NULL) {
			DBGF((DBGA, "rspl1:Malloc of matrix A failed\n"));
			return 1;
		}

		if ((b = dvector(0,t->nig)) == NULL) {
			free_dvector(b,0,t->nig);
			DBGF((DBGA, "rspl1:Malloc of vector b failed\n"));
			return 1;
		}

		/* Initialize the A and b matricies */
		for (i = 0; i < t->nig; i++) {
			for (k = 0; k < 3; k++) 
				A[i][k] = 0.0;
			t->x[i] = b[i] = 0.0;
		}
	
		/* Accumulate data dependent factors */
		for (n = 0; n < ndp; n++) {
			double bf, cbf;
			double xv, yv, wv;

			if (dtp == 0) {
				co *dd = (co *)d;

				xv = dd[n].p[0];
				yv = dd[n].v[0];
				wv = 1.0;
			} else if (dtp == 1) {
				cow *dd = (cow *)d;

				xv = dd[n].p[0];
				yv = dd[n].v[0];
				wv = dd[n].w;
			} else {
				DBGF((DBGA, "rspl1:Internal error, unknown dtp value %d\n",dtp));
				return 1;
			}
			yv = (yv - t->vl)/t->vw;	/* Normalize the value */

			/* Figure out which grid cell data is in */
			i = (int)((xv - t->gl)/t->gw);	/* Index of next lowest data point */

			bf = ((((double)(i+1) * t->gw) + t->gl) - xv)/t->gw; /* weight to lower grid point */
			cbf = 1.0 - bf;						/* weight to upper grid point */

			b[i]    -= 2.0 * bf * -yv * wv;			/* dui component due to dn */
			A[i][0] += 2.0 * bf * bf * wv;			/* dui component due to ui */
			A[i][1] += 2.0 * bf * cbf * wv;			/* dui component due to ui+1 */

			if ((i+1) < t->nig) {
				b[i+1]     -= 2.0 * cbf * -yv * wv;	/* dui component due to dn */
				A[i+1][0]  += 2.0 * cbf * cbf * wv;	/* dui component due to ui */
			}
		}
	
		/* Accumulate curvature dependent factors */
		for (i = 0; i < t->nig; i++) {

			if ((i-2) >= 0) {					/* Curvature of cell below */
				A[i][0] +=  2.0 * cw;
			}

			if ((i-1) >= 0 && (i+1) < t->nig) {	/* Curvature of t cell */
				A[i][0] +=  8.0 * cw;
				A[i][1] += -4.0 * cw;
			}
			if ((i+2) < t->nig) {					/* Curvature of cell above */
				A[i][0] +=  2.0 * cw;
				A[i][1] += -4.0 * cw;
				A[i][2] +=  2.0 * cw;
			}
		}

#ifdef DEBUG
		DBGF((DBGA, "A matrix:\n"));
		for (i = 0; i < t->nig; i++) {
			for (k = 0; k < 3; k++)
				DBGF((DBGA, "A[%d][%d] = %f\n",i,k,A[i][k]));
		}
		DBGF((DBGA, "b vector:\n"));
		for (i = 0; i < t->nig; i++)
			DBGF((DBGA, "b[%d] = %f\n",i,b[i]));
#endif /* DEBUG */

		/* Apply Cholesky decomposition to A[][] to create L[][] */
		for (i = 0; i < t->nig; i++) {
			double sm;
			for (n = 0; n < 3; n++) {
				sm = A[i][n];
				for (k = 1; (n+k) < 3 && (i-k) >=0; k++) {
					sm -= A[i-k][n+k] * A[i-k][k];
				}
				if (n == 0) {
					if (sm <= 0.0) {
						free_dvector(b,0,t->nig);
						free_dmatrix(A,0,t->nig,0,2);
						DBGF((DBGA, "rspl1:Sum is -ve - loss of accuracy ?\n"));
						return 1;
					}
					A[i][0] = sqrt(sm);
				} else {
					A[i][n] = sm/A[i][0];
				}
			}
		}

		/* Solve L . y = b, storing y in x */
		for (i = 0; i < t->nig; i++) {
			double sm;
			sm = b[i];
			for (k = 1; k < 3 && (i-k) >= 0; k++) {
				sm -= A[i-k][k] * t->x[i-k];
			}
			t->x[i] = sm/A[i][0];
		}

		/* Solve LT . x = y */
		for (i = t->nig-1; i >= 0; i--) {
			double sm;
			sm = t->x[i];
			for (k = 1; k < 3 && (i+k) < t->nig; k++) {
				sm -= A[i][k] * t->x[i+k];
			}
			t->x[i] = sm/A[i][0];
		}
#ifdef DEBUG
		DBGF((DBGA, "Solution vector:\n"));
		for (i = 0; i < t->nig; i++) {
			DBGF((DBGA, "x[%d] = %f\n",i,t->x[i]));
		}
#endif /* DEBUG */

		free_dvector(b,0,t->nig);
		free_dmatrix(A,0,t->nig,0,2);
	}
	return 0;
}

/* Initialise from scattered data. */
/* Return nz on error */
static int fit_rspl(
	struct _rspl *t,/* this */
	int flags,		/* (Not used) */
	co *d,			/* Array holding position and function values of data points */
	int ndp,		/* Number of data points */
	datai glow,		/* Grid low scale - will expand to enclose data, NULL = default 0.0 */
	datai ghigh,	/* Grid high scale - will expand to enclose data, NULL = default 1.0 */
	int *gres,		/* Spline grid resolution, ncells = gres-1 */
	datao vlow,		/* Data value low normalize, NULL = default 0.0 */
	datao vhigh,	/* Data value high normalize - NULL = default 1.0 */
	double smooth,	/* Smoothing factor, 0.0 = default 1.0 */
	double *avgdev, /* (Not used) */
	double **ipos 	/* (not used) */
) {
	/* Call implementation with (co *) data */
	return fit_rspl_imp(t, flags, (void *)d, 0, ndp, glow, ghigh, gres, vlow, vhigh,
	                    smooth, avgdev, ipos);
}

/* Initialise the regular spline from scattered data with weights */
/* Return nz on error */
static int
fit_rspl_w(
	rspl *t,		/* this */
	int flags,		/* Combination of flags */
	cow *d,			/* Array holding position, function and weight values of data points */
	int dno,		/* Number of data points */
	ratai glow,		/* Grid low scale - will be expanded to enclose data, NULL = default 0.0 */
	ratai ghigh,	/* Grid high scale - will be expanded to enclose data, NULL = default 1.0 */
	int *gres,		/* Spline grid resolution */
	ratao vlow,		/* Data value low normalize, NULL = default 0.0 */
	ratao vhigh,	/* Data value high normalize - NULL = default 1.0 */
	double smooth,	/* Smoothing factor, 0.0 = default 1.0 */
	double *avgdev, /* (Not used) */
	double **ipos 	/* (not used) */
) {
	/* Call implementation with (cow *) data */
	return fit_rspl_imp(t, flags, (void *)d, 1, dno, glow, ghigh, gres, vlow, vhigh,
	                    smooth, avgdev, ipos);
}

/* Construct an empty rspl1 */
/* Return NULL if something goes wrong. */
rspl *new_rspl(int flags, int di, int fdi) {
	rspl *t;	/* this */

	if (flags != RSPL_NOFLAGS || di != 1 || fdi != 1) {
		DBGF((DBGA, "rspl1:Can't handle general rspl: flags %d, di %d, do %d\n",flags,di,fdi));
		return NULL;
	}

	if ((t = (rspl *)calloc(1, sizeof(rspl))) == NULL) {
		DBGF((DBGA, "rspl1:Malloc of structure failed\n"));
		return NULL;
	}

	/* Initialise the classes methods */
	t->interp     = interp;
	t->fit_rspl   = fit_rspl; 
	t->fit_rspl_w = fit_rspl_w; 
	t->del        = del_rspl;

	return t;
}