| 1 |
#include <assert.h> |
| 2 |
#include <stdio.h> |
| 3 |
#include <stdlib.h> |
| 4 |
#include "gsl/gsl_vector.h" |
| 5 |
#include "gsl/gsl_multiroots.h" |
| 6 |
#include "gsl/gsl_permutation.h" |
| 7 |
#include "gsl/gsl_linalg.h" |
| 8 |
|
| 9 |
/* #undef USE_DERIVATIVES */ |
| 10 |
/* #define SOLVER gsl_multiroot_fsolver_hybrids */ |
| 11 |
/* #define SOLVER gsl_multiroot_fsolver_hybrid */ |
| 12 |
/* #define SOLVER gsl_multiroot_fsolver_dnewton */ |
| 13 |
#define USE_DERIVATIVES |
| 14 |
/* #define SOLVER gsl_multiroot_fdfsolver_hybridsj */ |
| 15 |
/* #define SOLVER gsl_multiroot_fdfsolver_hybridj */ |
| 16 |
/* #define SOLVER gsl_multiroot_fdfsolver_newton */ |
| 17 |
#define SOLVER gsl_multiroot_fdfsolver_gnewton |
| 18 |
|
| 19 |
#define CONSTANT INT_MAX |
| 20 |
|
| 21 |
/** |
| 22 |
* trigrid_data -- parameters and results for a triangular grid fitting |
| 23 |
*/ |
| 24 |
|
| 25 |
struct trigrid_data { |
| 26 |
/* parameters */ |
| 27 |
unsigned int X, Y; |
| 28 |
double * A; |
| 29 |
|
| 30 |
/* results */ |
| 31 |
int status; |
| 32 |
unsigned int iter; |
| 33 |
#ifdef USE_DERIVATIVES |
| 34 |
gsl_multiroot_fdfsolver * s; |
| 35 |
#else |
| 36 |
gsl_multiroot_fsolver * s; |
| 37 |
#endif |
| 38 |
unsigned int xs_start, ys_start; |
| 39 |
gsl_vector * xs; |
| 40 |
}; |
| 41 |
|
| 42 |
|
| 43 |
void trigrid_fit(struct trigrid_data * data); |
| 44 |
int trigrid_f(const gsl_vector * xs, void * params, gsl_vector * f); |
| 45 |
int trigrid_df(const gsl_vector * xs, void * params, gsl_matrix * J); |
| 46 |
int trigrid_fdf(const gsl_vector * xs, void * params, gsl_vector * f, gsl_matrix * J); |
| 47 |
double trigrid_get_x(const struct trigrid_data * data, const gsl_vector * xs, |
| 48 |
unsigned int x, unsigned int y); |
| 49 |
double trigrid_get_y(const struct trigrid_data * data, const gsl_vector * xs, |
| 50 |
unsigned int x, unsigned int y); |
| 51 |
unsigned int trigrid_offset_x(const struct trigrid_data * data, |
| 52 |
unsigned int x, unsigned int y); |
| 53 |
unsigned int trigrid_offset_y(const struct trigrid_data * data, |
| 54 |
unsigned int x, unsigned int y); |
| 55 |
int main(void); |
| 56 |
void trigrid_print(struct trigrid_data * data); |
| 57 |
|
| 58 |
|
| 59 |
/** |
| 60 |
* trigrid_fit -- create a triangular grid with triangle areas A |
| 61 |
* |
| 62 |
* p struct trigrid_data with the following fields filled in: |
| 63 |
* X number of pairs of triangles in a row |
| 64 |
* Y number of rows of triangles |
| 65 |
* A target areas from bottom left by row, 2 * X * Y values |
| 66 |
* |
| 67 |
* p is updated with the result, which can be conveniently accessed |
| 68 |
* using trigrid_get_x and trigrid_get_y |
| 69 |
*/ |
| 70 |
|
| 71 |
void trigrid_fit(struct trigrid_data * data) |
| 72 |
{ |
| 73 |
unsigned int X = data->X, Y = data->Y; |
| 74 |
const size_t n = X * Y * 2; |
| 75 |
unsigned int x, y, i; |
| 76 |
|
| 77 |
int status; |
| 78 |
size_t iter = 0; |
| 79 |
|
| 80 |
|
| 81 |
#ifdef USE_DERIVATIVES |
| 82 |
gsl_multiroot_function_fdf f = {&trigrid_f, &trigrid_df, &trigrid_fdf, n, data}; |
| 83 |
#else |
| 84 |
gsl_multiroot_function f = {&trigrid_f, n, data}; |
| 85 |
#endif |
| 86 |
|
| 87 |
gsl_vector * xs = gsl_vector_alloc(n); |
| 88 |
data->xs = xs; |
| 89 |
|
| 90 |
i = 0; |
| 91 |
data->xs_start = i; |
| 92 |
for (y = 0; y != Y + 1; y++) |
| 93 |
for (x = 1; x != X; x++) |
| 94 |
gsl_vector_set(xs, i++, x + 0.1 * ((double) rand() / RAND_MAX - 0.5)); |
| 95 |
gsl_vector_set(xs, i++, X + 0.1 * ((double) rand() / RAND_MAX - 0.5)); |
| 96 |
data->ys_start = i; |
| 97 |
for (x = 0; x != X + 1; x++) |
| 98 |
for (y = 1; y != Y; y++) |
| 99 |
gsl_vector_set(xs, i++, y + 0.1 * ((double) rand() / RAND_MAX - 0.5)); |
| 100 |
gsl_vector_set(xs, i++, Y + 0.1 * ((double) rand() / RAND_MAX - 0.5)); |
| 101 |
assert(i == n); |
| 102 |
|
| 103 |
#ifdef USE_DERIVATIVES |
| 104 |
data->s = gsl_multiroot_fdfsolver_alloc(SOLVER, n); |
| 105 |
gsl_multiroot_fdfsolver_set(data->s, &f, xs); |
| 106 |
#else |
| 107 |
data->s = gsl_multiroot_fsolver_alloc(SOLVER, n); |
| 108 |
gsl_multiroot_fsolver_set(data->s, &f, xs); |
| 109 |
#endif |
| 110 |
|
| 111 |
/* trigrid_print(data); */ |
| 112 |
|
| 113 |
do { |
| 114 |
iter++; |
| 115 |
fprintf(stderr, "iter = %3u\n", iter); |
| 116 |
|
| 117 |
#ifdef USE_DERIVATIVES |
| 118 |
status = gsl_multiroot_fdfsolver_iterate(data->s); |
| 119 |
#else |
| 120 |
status = gsl_multiroot_fsolver_iterate(data->s); |
| 121 |
#endif |
| 122 |
|
| 123 |
/* trigrid_print(data); */ |
| 124 |
|
| 125 |
if (status) |
| 126 |
break; |
| 127 |
|
| 128 |
status = gsl_multiroot_test_residual(data->s->f, 0.01); |
| 129 |
} while (status == GSL_CONTINUE && iter != 1000); |
| 130 |
|
| 131 |
fprintf(stderr, "status = %s\n", gsl_strerror(status)); |
| 132 |
|
| 133 |
data->status = status; |
| 134 |
data->iter = iter; |
| 135 |
} |
| 136 |
|
| 137 |
|
| 138 |
/** |
| 139 |
* trigrid_f -- function evaluator for triangular grid fitter |
| 140 |
*/ |
| 141 |
|
| 142 |
int trigrid_f(const gsl_vector * xs, void * params, gsl_vector * f) |
| 143 |
{ |
| 144 |
unsigned int x, y, X, Y, i; |
| 145 |
struct trigrid_data * data = (struct trigrid_data *) params; |
| 146 |
|
| 147 |
X = data->X; |
| 148 |
Y = data->Y; |
| 149 |
|
| 150 |
for (i = 0, y = 0; y != Y; y++) { |
| 151 |
for (x = 0; x != X; x++) { |
| 152 |
double A, v; |
| 153 |
double ax, ay, bx, by, cx, cy, dx, dy; |
| 154 |
|
| 155 |
ax = trigrid_get_x(data, xs, x, y); |
| 156 |
ay = trigrid_get_y(data, xs, x, y); |
| 157 |
bx = trigrid_get_x(data, xs, x + 1, y + 1); |
| 158 |
by = trigrid_get_y(data, xs, x + 1, y + 1); |
| 159 |
cx = trigrid_get_x(data, xs, x, y + 1); |
| 160 |
cy = trigrid_get_y(data, xs, x, y + 1); |
| 161 |
dx = trigrid_get_x(data, xs, x + 1, y); |
| 162 |
dy = trigrid_get_y(data, xs, x + 1, y); |
| 163 |
|
| 164 |
/* printf("x = %u, y = %u, a = %g %g, b = %g %g, c = %g %g, d = %g %g\n", */ |
| 165 |
/* x, y, ax, ay, bx, by, cx, cy, dx, dy); */ |
| 166 |
|
| 167 |
/* upper triangle */ |
| 168 |
A = data->A[i]; |
| 169 |
v = 0.5 * (ax * (by - cy) + bx * (cy - ay) + cx * (ay - by)); |
| 170 |
/* printf("upper A = %g, v = %g\n", A, v); */ |
| 171 |
|
| 172 |
gsl_vector_set(f, i++, v - A); |
| 173 |
|
| 174 |
/* lower triangle */ |
| 175 |
A = data->A[i]; |
| 176 |
v = 0.5 * (ax * (dy - by) + dx * (by - ay) + bx * (ay - dy)); |
| 177 |
/* printf("lower A = %g, v = %g\n\n", A, v); */ |
| 178 |
|
| 179 |
gsl_vector_set(f, i++, v - A); |
| 180 |
} |
| 181 |
} |
| 182 |
|
| 183 |
return GSL_SUCCESS; |
| 184 |
} |
| 185 |
|
| 186 |
|
| 187 |
/** |
| 188 |
* trigrid_df -- function derivative evaluator for triangular grid fitter |
| 189 |
*/ |
| 190 |
|
| 191 |
int trigrid_df(const gsl_vector * xs, void * params, gsl_matrix * J) |
| 192 |
{ |
| 193 |
unsigned int x, y, X, Y, i; |
| 194 |
struct trigrid_data * data = (struct trigrid_data *) params; |
| 195 |
|
| 196 |
X = data->X; |
| 197 |
Y = data->Y; |
| 198 |
gsl_matrix_set_zero(J); |
| 199 |
|
| 200 |
/* printf("xs =\n"); */ |
| 201 |
/* gsl_vector_fprintf(stdout, xs, "%g"); */ |
| 202 |
|
| 203 |
for (i = 0, y = 0; y != Y; y++) { |
| 204 |
for (x = 0; x != X; x++) { |
| 205 |
double ax, ay, bx, by, cx, cy, dx, dy; |
| 206 |
unsigned int axo, ayo, bxo, byo, cxo, cyo, dxo, dyo; |
| 207 |
|
| 208 |
ax = trigrid_get_x(data, xs, x, y); |
| 209 |
ay = trigrid_get_y(data, xs, x, y); |
| 210 |
bx = trigrid_get_x(data, xs, x + 1, y + 1); |
| 211 |
by = trigrid_get_y(data, xs, x + 1, y + 1); |
| 212 |
cx = trigrid_get_x(data, xs, x, y + 1); |
| 213 |
cy = trigrid_get_y(data, xs, x, y + 1); |
| 214 |
dx = trigrid_get_x(data, xs, x + 1, y); |
| 215 |
dy = trigrid_get_y(data, xs, x + 1, y); |
| 216 |
|
| 217 |
axo = trigrid_offset_x(data, x, y); |
| 218 |
ayo = trigrid_offset_y(data, x, y); |
| 219 |
bxo = trigrid_offset_x(data, x + 1, y + 1); |
| 220 |
byo = trigrid_offset_y(data, x + 1, y + 1); |
| 221 |
cxo = trigrid_offset_x(data, x, y + 1); |
| 222 |
cyo = trigrid_offset_y(data, x, y + 1); |
| 223 |
dxo = trigrid_offset_x(data, x + 1, y); |
| 224 |
dyo = trigrid_offset_y(data, x + 1, y); |
| 225 |
|
| 226 |
/* printf("x = %u, y = %u, a = %g %g, b = %g %g, c = %g %g, d = %g %g\n", */ |
| 227 |
/* x, y, ax, ay, bx, by, cx, cy, dx, dy); */ |
| 228 |
|
| 229 |
/* upper triangle */ |
| 230 |
/* v = 0.5 * (ax * (by - cy) + bx * (cy - ay) + cx * (ay - by)); */ |
| 231 |
|
| 232 |
if (axo != CONSTANT) gsl_matrix_set(J, i, axo, 0.5 * (by - cy)); |
| 233 |
if (ayo != CONSTANT) gsl_matrix_set(J, i, ayo, 0.5 * (cx - bx)); |
| 234 |
if (bxo != CONSTANT) gsl_matrix_set(J, i, bxo, 0.5 * (cy - ay)); |
| 235 |
if (byo != CONSTANT) gsl_matrix_set(J, i, byo, 0.5 * (ax - cx)); |
| 236 |
if (cxo != CONSTANT) gsl_matrix_set(J, i, cxo, 0.5 * (ay - by)); |
| 237 |
if (cyo != CONSTANT) gsl_matrix_set(J, i, cyo, 0.5 * (bx - ax)); |
| 238 |
|
| 239 |
i++; |
| 240 |
|
| 241 |
/* lower triangle */ |
| 242 |
/* v = 0.5 * (ax * (dy - by) + dx * (by - ay) + bx * (ay - dy)); */ |
| 243 |
|
| 244 |
if (axo != CONSTANT) gsl_matrix_set(J, i, axo, 0.5 * (dy - by)); |
| 245 |
if (ayo != CONSTANT) gsl_matrix_set(J, i, ayo, 0.5 * (bx - dx)); |
| 246 |
if (dxo != CONSTANT) gsl_matrix_set(J, i, dxo, 0.5 * (by - ay)); |
| 247 |
if (dyo != CONSTANT) gsl_matrix_set(J, i, dyo, 0.5 * (ax - bx)); |
| 248 |
if (bxo != CONSTANT) gsl_matrix_set(J, i, bxo, 0.5 * (ay - dy)); |
| 249 |
if (byo != CONSTANT) gsl_matrix_set(J, i, byo, 0.5 * (dx - ax)); |
| 250 |
|
| 251 |
i++; |
| 252 |
} |
| 253 |
} |
| 254 |
|
| 255 |
/* printf("J =\n"); |
| 256 |
gsl_matrix_fprintf(stdout, J, "%f"); |
| 257 |
printf("\n"); |
| 258 |
*/ |
| 259 |
{ |
| 260 |
gsl_matrix * JJ = gsl_matrix_alloc(2 * data->X * data->Y, 2 * data->X * data->Y); |
| 261 |
gsl_permutation * p = gsl_permutation_alloc(2 * data->X * data->Y); |
| 262 |
int signum; |
| 263 |
|
| 264 |
gsl_matrix_memcpy(JJ, J); |
| 265 |
gsl_linalg_LU_decomp(JJ, p, &signum); |
| 266 |
fprintf(stderr, "det = %g\n", gsl_linalg_LU_det(JJ, signum)); |
| 267 |
} |
| 268 |
|
| 269 |
return GSL_SUCCESS; |
| 270 |
} |
| 271 |
|
| 272 |
|
| 273 |
int trigrid_fdf(const gsl_vector * xs, void * params, gsl_vector * f, gsl_matrix * J) |
| 274 |
{ |
| 275 |
trigrid_f(xs, params, f); |
| 276 |
trigrid_df(xs, params, J); |
| 277 |
|
| 278 |
return GSL_SUCCESS; |
| 279 |
} |
| 280 |
|
| 281 |
|
| 282 |
/** |
| 283 |
* trigrid_get_[xy] -- extract grid coordinates from a struct trigrid_data |
| 284 |
*/ |
| 285 |
|
| 286 |
double trigrid_get_x(const struct trigrid_data * data, const gsl_vector * xs, |
| 287 |
unsigned int x, unsigned int y) |
| 288 |
{ |
| 289 |
unsigned int i = trigrid_offset_x(data, x, y); |
| 290 |
if (i != CONSTANT) |
| 291 |
return gsl_vector_get(xs, i); |
| 292 |
if (x == 0) |
| 293 |
return 0; |
| 294 |
if (x == data->X) |
| 295 |
return data->X; |
| 296 |
assert(0); |
| 297 |
} |
| 298 |
|
| 299 |
unsigned int trigrid_offset_x(const struct trigrid_data * data, |
| 300 |
unsigned int x, unsigned int y) |
| 301 |
{ |
| 302 |
if ((x == data->X) && (y == data->Y)) |
| 303 |
/* top right corner */ |
| 304 |
return data->ys_start - 1; |
| 305 |
if (x == 0) |
| 306 |
return CONSTANT; |
| 307 |
if (x == data->X) |
| 308 |
return CONSTANT; |
| 309 |
return data->xs_start + y * (data->X - 1) + x - 1; |
| 310 |
} |
| 311 |
|
| 312 |
double trigrid_get_y(const struct trigrid_data * data, const gsl_vector * xs, |
| 313 |
unsigned int x, unsigned int y) |
| 314 |
{ |
| 315 |
unsigned int i = trigrid_offset_y(data, x, y); |
| 316 |
if (i != CONSTANT) |
| 317 |
return gsl_vector_get(xs, i); |
| 318 |
if (y == 0) |
| 319 |
return 0; |
| 320 |
if (y == data->Y) |
| 321 |
return data->Y; |
| 322 |
assert(0); |
| 323 |
} |
| 324 |
|
| 325 |
unsigned int trigrid_offset_y(const struct trigrid_data * data, |
| 326 |
unsigned int x, unsigned int y) |
| 327 |
{ |
| 328 |
if ((x == data->X) && (y == data->Y)) |
| 329 |
/* top right corner */ |
| 330 |
return data->ys_start + (data->X + 1) * (data->Y - 1); |
| 331 |
if (y == 0) |
| 332 |
return CONSTANT; |
| 333 |
if (y == data->Y) |
| 334 |
return CONSTANT; |
| 335 |
return data->ys_start + x * (data->Y - 1) + y - 1; |
| 336 |
} |
| 337 |
|
| 338 |
|
| 339 |
|
| 340 |
|
| 341 |
|
| 342 |
|
| 343 |
int main(void) |
| 344 |
{ |
| 345 |
unsigned int X = 10, Y = 10; |
| 346 |
double A[] = { |
| 347 |
0.5,0.5, 0.5,0.5, 0.5,0.5, 0.5,0.5, 0.5,0.5, 0.5,0.5, 0.5,0.5, 0.5,0.5, 0.5,0.5, 0.5,0.5, |
| 348 |
0.5,0.5, 0.5,0.5, 0.5,0.5, 0.5,0.5, 0.5,0.5, 0.5,0.5, 0.5,0.5, 0.5,0.5, 0.5,0.5, 0.5,0.5, |
| 349 |
0.5,0.5, 0.5,0.5, 0.5,0.5, 0.5,0.5, 0.5,0.5, 0.5,0.5, 0.5,0.5, 0.5,0.5, 0.5,0.5, 0.5,0.5, |
| 350 |
0.5,0.5, 0.5,0.5, 0.5,0.5, 0.5,0.5, 0.7,0.7, 0.7,0.7, 0.5,0.5, 0.5,0.5, 0.5,0.5, 0.5,0.5, |
| 351 |
0.5,0.5, 0.5,0.5, 0.5,0.5, 0.5,0.5, 0.7,0.7, 0.7,0.7, 0.5,0.5, 0.5,0.5, 0.5,0.5, 0.5,0.5, |
| 352 |
|
| 353 |
0.5,0.5, 0.5,0.5, 0.5,0.5, 0.5,0.5, 0.7,0.7, 0.7,0.7, 0.5,0.5, 0.5,0.5, 0.5,0.5, 0.5,0.5, |
| 354 |
0.5,0.5, 0.5,0.5, 0.5,0.5, 0.5,0.5, 0.7,0.7, 0.7,0.7, 0.5,0.5, 0.5,0.5, 0.5,0.5, 0.5,0.5, |
| 355 |
0.5,0.5, 0.5,0.5, 0.5,0.5, 0.5,0.5, 0.5,0.5, 0.5,0.5, 0.5,0.5, 0.5,0.5, 0.5,0.5, 0.5,0.5, |
| 356 |
0.1,0.1, 0.1,0.1, 0.5,0.5, 0.5,0.5, 0.5,0.5, 0.5,0.5, 0.5,0.5, 0.5,0.5, 0.5,0.5, 0.5,0.5, |
| 357 |
0.1,0.1, 0.1,0.1, 0.5,0.5, 0.5,0.5, 0.5,0.5, 0.5,0.5, 0.5,0.5, 0.5,0.5, 0.5,0.5, 0.5,0.5 |
| 358 |
}; |
| 359 |
|
| 360 |
struct trigrid_data data = {X, Y, A, 0, 0, 0, 0, 0, 0}; |
| 361 |
trigrid_fit(&data); |
| 362 |
trigrid_print(&data); |
| 363 |
|
| 364 |
return 0; |
| 365 |
} |
| 366 |
|
| 367 |
|
| 368 |
void trigrid_print(struct trigrid_data * data) |
| 369 |
{ |
| 370 |
unsigned int x, y, i = 0; |
| 371 |
#ifdef USE_DERIVATIVES |
| 372 |
gsl_vector * root = gsl_multiroot_fdfsolver_root(data->s); |
| 373 |
#else |
| 374 |
gsl_vector * root = gsl_multiroot_fsolver_root(data->s); |
| 375 |
#endif |
| 376 |
|
| 377 |
fprintf(stderr, "root =\n"); |
| 378 |
gsl_vector_fprintf(stderr, root, "%g"); |
| 379 |
fprintf(stderr, "\n"); |
| 380 |
|
| 381 |
fprintf(stderr, "f =\n"); |
| 382 |
gsl_vector_fprintf(stderr, data->s->f, "%g"); |
| 383 |
fprintf(stderr, "\n"); |
| 384 |
|
| 385 |
printf("PROCClosedLines\n\n"); |
| 386 |
printf("PROCFont(\"Corpus.Medium\", 5, 80)\n"); |
| 387 |
|
| 388 |
for (y = 0; y != data->Y; y++) { |
| 389 |
for (x = 0; x != data->X; x++) { |
| 390 |
double ax, ay, bx, by, cx, cy, dx, dy; |
| 391 |
|
| 392 |
ax = trigrid_get_x(data, root, x, y); |
| 393 |
ay = trigrid_get_y(data, root, x, y); |
| 394 |
bx = trigrid_get_x(data, root, x + 1, y + 1); |
| 395 |
by = trigrid_get_y(data, root, x + 1, y + 1); |
| 396 |
cx = trigrid_get_x(data, root, x, y + 1); |
| 397 |
cy = trigrid_get_y(data, root, x, y + 1); |
| 398 |
dx = trigrid_get_x(data, root, x + 1, y); |
| 399 |
dy = trigrid_get_y(data, root, x + 1, y); |
| 400 |
|
| 401 |
/* printf("%.3f %.3f ", ax, ay);*/ |
| 402 |
|
| 403 |
printf("PROCGroup\n"); |
| 404 |
printf("PROCMove(%g, %g)\n", ax, ay); |
| 405 |
printf("PROCDraw(%g, %g)\n", bx, by); |
| 406 |
printf("PROCDraw(%g, %g)\n", cx, cy); |
| 407 |
printf("PROCPrint(\"%.3f\", %g, %g)\n", |
| 408 |
/*data->A[i] +*/ gsl_vector_get(data->s->f, i), |
| 409 |
(ax + bx + cx) / 3, (ay + by + cy) / 3); |
| 410 |
printf("PROCEndGroup\n\n"); |
| 411 |
i++; |
| 412 |
|
| 413 |
printf("PROCGroup\n"); |
| 414 |
printf("PROCMove(%g, %g)\n", ax, ay); |
| 415 |
printf("PROCDraw(%g, %g)\n", dx, dy); |
| 416 |
printf("PROCDraw(%g, %g)\n", bx, by); |
| 417 |
printf("PROCPrint(\"%.3f\", %g, %g)\n", |
| 418 |
/*data->A[i] +*/ gsl_vector_get(data->s->f, i), |
| 419 |
(ax + dx + bx) / 3, (ay + dy + by) / 3); |
| 420 |
printf("PROCEndGroup\n\n"); |
| 421 |
i++; |
| 422 |
} |
| 423 |
printf("\n"); |
| 424 |
} |
| 425 |
printf("\n"); |
| 426 |
|
| 427 |
printf("PROCPrint(\"'%s' solver, %u iterations, end status '%s'\", 0, %u)\n", |
| 428 |
#ifdef USE_DERIVATIVES |
| 429 |
gsl_multiroot_fdfsolver_name(data->s), |
| 430 |
#else |
| 431 |
gsl_multiroot_fsolver_name(data->s), |
| 432 |
#endif |
| 433 |
data->iter, |
| 434 |
gsl_strerror(data->status), |
| 435 |
data->Y + 1); |
| 436 |
} |
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