GCC Code Coverage Report

Directory: ./
File: src/sys/classes/rg/impls/polygon/rgpolygon.c
Date: 2026-02-22 03:58:10
Exec Total Coverage
Lines: 246 252 97.6%
Functions: 13 13 100.0%
Branches: 408 788 51.8%
Line Branch Exec Source
1 /*
2 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
3 SLEPc - Scalable Library for Eigenvalue Problem Computations
4 Copyright (c) 2002-, Universitat Politecnica de Valencia, Spain
5
6 This file is part of SLEPc.
7 SLEPc is distributed under a 2-clause BSD license (see LICENSE).
8 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
9 */
10 /*
11 Polygonal region defined by a set of vertices
12 */
13
14 #include <slepc/private/rgimpl.h> /*I "slepcrg.h" I*/
15 #include <petscdraw.h>
16
17 #define VERTMAX 30
18
19 typedef struct {
20 PetscInt n; /* number of vertices */
21 PetscScalar *vr,*vi; /* array of vertices (vi not used in complex scalars) */
22 } RG_POLYGON;
23
24 static PetscErrorCode RGComputeBoundingBox_Polygon(RG,PetscReal*,PetscReal*,PetscReal*,PetscReal*);
25
26 #if !defined(PETSC_USE_COMPLEX)
27 10 static PetscBool CheckSymmetry(PetscInt n,PetscScalar *vr,PetscScalar *vi)
28 {
29 10 PetscInt i,j,k;
30 /* find change of sign in imaginary part */
31 10 j = vi[0]!=0.0? 0: 1;
32
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 10 for (k=j+1;k<n;k++) {
33
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 10 if (vi[k]!=0.0) {
34
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 10 if (vi[k]*vi[j]<0.0) break;
35 ✗ j++;
36 }
37 }
38
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 10 if (k==n) return (j==1)? PETSC_TRUE: PETSC_FALSE;
39 /* check pairing vertices */
40
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 40 for (i=0;i<n/2;i++) {
41
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 30 if (vr[k]!=vr[j] || vi[k]!=-vi[j]) return PETSC_FALSE;
42 30 k = (k+1)%n;
43 30 j = (j-1+n)%n;
44 }
45 return PETSC_TRUE;
46 }
47 #endif
48
49 24 static PetscErrorCode RGPolygonSetVertices_Polygon(RG rg,PetscInt n,PetscScalar *vr,PetscScalar *vi)
50 {
51 24 PetscInt i;
52 24 RG_POLYGON *ctx = (RG_POLYGON*)rg->data;
53
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 24 PetscFunctionBegin;
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 24 PetscCheck(n>2,PetscObjectComm((PetscObject)rg),PETSC_ERR_ARG_OUTOFRANGE,"At least 3 vertices required, you provided %" PetscInt_FMT,n);
56
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 24 PetscCheck(n<=VERTMAX,PetscObjectComm((PetscObject)rg),PETSC_ERR_ARG_OUTOFRANGE,"Too many points, maximum allowed is %d",VERTMAX);
57 #if !defined(PETSC_USE_COMPLEX)
58
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 10 PetscCheck(CheckSymmetry(n,vr,vi),PetscObjectComm((PetscObject)rg),PETSC_ERR_ARG_WRONG,"In real scalars the region must be symmetric wrt real axis");
59 #endif
60
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 24 if (ctx->n) {
61 ✗ PetscCall(PetscFree(ctx->vr));
62 #if !defined(PETSC_USE_COMPLEX)
63 ✗ PetscCall(PetscFree(ctx->vi));
64 #endif
65 }
66 24 ctx->n = n;
67
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 24 PetscCall(PetscMalloc1(n,&ctx->vr));
68 #if !defined(PETSC_USE_COMPLEX)
69
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 10 PetscCall(PetscMalloc1(n,&ctx->vi));
70 #endif
71
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 183 for (i=0;i<n;i++) {
72 159 ctx->vr[i] = vr[i];
73 #if !defined(PETSC_USE_COMPLEX)
74 70 ctx->vi[i] = vi[i];
75 #endif
76 }
77
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 5 PetscFunctionReturn(PETSC_SUCCESS);
78 }
79
80 /*@
81 RGPolygonSetVertices - Sets the vertices that define the polygon region.
82
83 Logically Collective
84
85 Input Parameters:
86 + rg - the region context
87 . n - number of vertices
88 . vr - array of vertices
89 - vi - array of vertices (imaginary part)
90
91 Options Database Keys:
92 + -rg_polygon_vertices <vr1,vr2,...> - comma-separated list of vertices
93 - -rg_polygon_verticesi <vi1,vi2,...> - comma-separated list of vertices (imaginary part)
94
95 Notes:
96 In the case of complex scalars, only argument `vr` is used, containing
97 the complex vertices; the list of vertices can be provided in the
98 command line with a comma-separated list of complex values
99 `[+/-][realnumber][+/-]realnumberi` with no spaces.
100
101 When PETSc is built with real scalars, the real and imaginary parts of
102 the vertices must be provided in two separate arrays (or two lists in
103 the command line). In this case, the region must be symmetric with
104 respect to the real axis.
105
106 Level: advanced
107
108 .seealso: [](sec:rg), `RGPOLYGON`, `RGPolygonGetVertices()`
109 @*/
110 24 PetscErrorCode RGPolygonSetVertices(RG rg,PetscInt n,PetscScalar vr[],PetscScalar vi[])
111 {
112
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 24 PetscFunctionBegin;
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 24 PetscValidHeaderSpecific(rg,RG_CLASSID,1);
114
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 24 PetscValidLogicalCollectiveInt(rg,n,2);
115
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 24 PetscAssertPointer(vr,3);
116 #if !defined(PETSC_USE_COMPLEX)
117
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 10 PetscAssertPointer(vi,4);
118 #endif
119
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 24 PetscTryMethod(rg,"RGPolygonSetVertices_C",(RG,PetscInt,PetscScalar*,PetscScalar*),(rg,n,vr,vi));
120
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 24 PetscFunctionReturn(PETSC_SUCCESS);
121 }
122
123 16 static PetscErrorCode RGPolygonGetVertices_Polygon(RG rg,PetscInt *n,PetscScalar *vr[],PetscScalar *vi[])
124 {
125 16 RG_POLYGON *ctx = (RG_POLYGON*)rg->data;
126 16 PetscInt i;
127
128
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 16 PetscFunctionBegin;
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 16 if (n) *n = ctx->n;
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 16 if (vr) {
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 16 if (!ctx->n) *vr = NULL;
132 else {
133
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 16 PetscCall(PetscMalloc1(ctx->n,vr));
134
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 128 for (i=0;i<ctx->n;i++) (*vr)[i] = ctx->vr[i];
135 }
136 }
137 #if !defined(PETSC_USE_COMPLEX)
138
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 8 if (vi) {
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 8 if (!ctx->n) *vi = NULL;
140 else {
141
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 8 PetscCall(PetscMalloc1(ctx->n,vi));
142
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 64 for (i=0;i<ctx->n;i++) (*vi)[i] = ctx->vi[i];
143 }
144 }
145 #endif
146
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 4 PetscFunctionReturn(PETSC_SUCCESS);
147 }
148
149 /*@C
150 RGPolygonGetVertices - Gets the vertices that define the polygon region.
151
152 Not Collective
153
154 Input Parameter:
155 . rg - the region context
156
157 Output Parameters:
158 + n - number of vertices
159 . vr - array of vertices
160 - vi - array of vertices (imaginary part)
161
162 Notes:
163 The values passed by user with `RGPolygonSetVertices()` are returned (or `NULL`
164 pointers otherwise).
165 The returned arrays should be freed by the user when no longer needed.
166
167 Level: advanced
168
169 .seealso: [](sec:rg), `RGPOLYGON`, `RGPolygonSetVertices()`
170 @*/
171 16 PetscErrorCode RGPolygonGetVertices(RG rg,PetscInt *n,PetscScalar *vr[],PetscScalar *vi[]) PeNS
172 {
173
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 16 PetscFunctionBegin;
174
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 16 PetscValidHeaderSpecific(rg,RG_CLASSID,1);
175
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 16 PetscUseMethod(rg,"RGPolygonGetVertices_C",(RG,PetscInt*,PetscScalar**,PetscScalar**),(rg,n,vr,vi));
176
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 16 PetscFunctionReturn(PETSC_SUCCESS);
177 }
178
179 29 static PetscErrorCode RGView_Polygon(RG rg,PetscViewer viewer)
180 {
181 29 RG_POLYGON *ctx = (RG_POLYGON*)rg->data;
182 29 PetscBool isdraw,isascii;
183 29 int winw,winh;
184 29 PetscDraw draw;
185 29 PetscDrawAxis axis;
186 29 PetscReal a,b,c,d,ab,cd,lx,ly,w,x0,y0,x1,y1,scale=1.2;
187 29 PetscInt i;
188 29 char str[50];
189
190
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 29 PetscFunctionBegin;
191
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 29 PetscCall(PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERDRAW,&isdraw));
192
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 29 PetscCall(PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&isascii));
193
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 29 if (isascii) {
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 21 PetscCall(PetscViewerASCIIPrintf(viewer," vertices: "));
195
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 21 PetscCall(PetscViewerASCIIUseTabs(viewer,PETSC_FALSE));
196
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 168 for (i=0;i<ctx->n;i++) {
197 #if defined(PETSC_USE_COMPLEX)
198
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 77 PetscCall(SlepcSNPrintfScalar(str,sizeof(str),ctx->vr[i],PETSC_FALSE));
199 #else
200
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 70 if (ctx->vi[i]!=0.0) PetscCall(PetscSNPrintf(str,sizeof(str),"%g%+gi",(double)ctx->vr[i],(double)ctx->vi[i]));
201
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 10 else PetscCall(PetscSNPrintf(str,sizeof(str),"%g",(double)ctx->vr[i]));
202 #endif
203
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 168 PetscCall(PetscViewerASCIIPrintf(viewer,"%s%s",str,(i<ctx->n-1)?", ":""));
204 }
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 21 PetscCall(PetscViewerASCIIPrintf(viewer,"\n"));
206
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 21 PetscCall(PetscViewerASCIIUseTabs(viewer,PETSC_TRUE));
207
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 8 } else if (isdraw) {
208
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 8 PetscCall(PetscViewerDrawGetDraw(viewer,0,&draw));
209
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 8 PetscCall(PetscDrawCheckResizedWindow(draw));
210
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 8 PetscCall(PetscDrawGetWindowSize(draw,&winw,&winh));
211 8 winw = PetscMax(winw,1); winh = PetscMax(winh,1);
212
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 8 PetscCall(PetscDrawClear(draw));
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 8 PetscCall(PetscDrawSetTitle(draw,"Polygonal region"));
214
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 8 PetscCall(PetscDrawAxisCreate(draw,&axis));
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 8 PetscCall(RGComputeBoundingBox_Polygon(rg,&a,&b,&c,&d));
216 8 a *= rg->sfactor;
217 8 b *= rg->sfactor;
218 8 c *= rg->sfactor;
219 8 d *= rg->sfactor;
220 8 lx = b-a;
221 8 ly = d-c;
222 8 ab = (a+b)/2;
223 8 cd = (c+d)/2;
224
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 8 w = scale*PetscMax(lx/winw,ly/winh)/2;
225
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 8 PetscCall(PetscDrawAxisSetLimits(axis,ab-w*winw,ab+w*winw,cd-w*winh,cd+w*winh));
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 8 PetscCall(PetscDrawAxisDraw(axis));
227
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 8 PetscCall(PetscDrawAxisDestroy(&axis));
228
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 64 for (i=0;i<ctx->n;i++) {
229 #if defined(PETSC_USE_COMPLEX)
230 28 x0 = PetscRealPart(ctx->vr[i]); y0 = PetscImaginaryPart(ctx->vr[i]);
231
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 28 if (i<ctx->n-1) {
232 24 x1 = PetscRealPart(ctx->vr[i+1]); y1 = PetscImaginaryPart(ctx->vr[i+1]);
233 } else {
234 4 x1 = PetscRealPart(ctx->vr[0]); y1 = PetscImaginaryPart(ctx->vr[0]);
235 }
236 #else
237 28 x0 = ctx->vr[i]; y0 = ctx->vi[i];
238
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 28 if (i<ctx->n-1) {
239 24 x1 = ctx->vr[i+1]; y1 = ctx->vi[i+1];
240 } else {
241 4 x1 = ctx->vr[0]; y1 = ctx->vi[0];
242 }
243 #endif
244
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 56 PetscCall(PetscDrawLine(draw,x0*rg->sfactor,y0*rg->sfactor,x1*rg->sfactor,y1*rg->sfactor,PETSC_DRAW_MAGENTA));
245 }
246
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 8 PetscCall(PetscDrawFlush(draw));
247
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 8 PetscCall(PetscDrawSave(draw));
248
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 8 PetscCall(PetscDrawPause(draw));
249 }
250
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 6 PetscFunctionReturn(PETSC_SUCCESS);
251 }
252
253 50 static PetscErrorCode RGIsTrivial_Polygon(RG rg,PetscBool *trivial)
254 {
255 50 RG_POLYGON *ctx = (RG_POLYGON*)rg->data;
256
257
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 50 PetscFunctionBegin;
258 50 *trivial = PetscNot(ctx->n);
259
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 50 PetscFunctionReturn(PETSC_SUCCESS);
260 }
261
262 19 static PetscErrorCode RGComputeContour_Polygon(RG rg,PetscInt n,PetscScalar *ucr,PetscScalar *uci)
263 {
264 19 RG_POLYGON *ctx = (RG_POLYGON*)rg->data;
265 19 PetscReal length,h,d,rem=0.0;
266 19 PetscInt k=1,idx=ctx->n-1,i;
267 19 PetscBool ini=PETSC_FALSE;
268 19 PetscScalar incr,*cr=ucr,*ci=uci;
269 #if !defined(PETSC_USE_COMPLEX)
270 8 PetscScalar inci;
271 #endif
272
273
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 19 PetscFunctionBegin;
274
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 19 PetscCheck(ctx->n,PetscObjectComm((PetscObject)rg),PETSC_ERR_ARG_WRONGSTATE,"No vertices have been set yet");
275 19 length = SlepcAbsEigenvalue(ctx->vr[0]-ctx->vr[ctx->n-1],ctx->vi[0]-ctx->vi[ctx->n-1]);
276
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 132 for (i=0;i<ctx->n-1;i++) length += SlepcAbsEigenvalue(ctx->vr[i]-ctx->vr[i+1],ctx->vi[i]-ctx->vi[i+1]);
277 19 h = length/n;
278
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 19 if (!ucr) PetscCall(PetscMalloc1(n,&cr));
279
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 19 if (!uci) PetscCall(PetscMalloc1(n,&ci));
280 19 cr[0] = ctx->vr[0];
281 #if !defined(PETSC_USE_COMPLEX)
282 8 ci[0] = ctx->vi[0];
283 #endif
284 19 incr = ctx->vr[ctx->n-1]-ctx->vr[0];
285 #if !defined(PETSC_USE_COMPLEX)
286 8 inci = ctx->vi[ctx->n-1]-ctx->vi[0];
287 #endif
288 19 d = SlepcAbsEigenvalue(incr,inci);
289 19 incr /= d;
290 #if !defined(PETSC_USE_COMPLEX)
291 8 inci /= d;
292 #endif
293
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 565 while (k<n) {
294
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 546 if (ini) {
295 105 incr = ctx->vr[idx]-ctx->vr[idx+1];
296 #if !defined(PETSC_USE_COMPLEX)
297 48 inci = ctx->vi[idx]-ctx->vi[idx+1];
298 #endif
299 105 d = SlepcAbsEigenvalue(incr,inci);
300 105 incr /= d;
301 #if !defined(PETSC_USE_COMPLEX)
302 48 inci /= d;
303 #endif
304
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 105 if (rem+d>h) {
305 105 cr[k] = ctx->vr[idx+1]+incr*(h-rem);
306 #if !defined(PETSC_USE_COMPLEX)
307 48 ci[k] = ctx->vi[idx+1]+inci*(h-rem);
308 #endif
309 105 k++;
310 105 ini = PETSC_FALSE;
311 ✗ } else {rem += d; idx--;}
312 } else {
313 #if !defined(PETSC_USE_COMPLEX)
314 72 rem = SlepcAbsEigenvalue(ctx->vr[idx]-cr[k-1],ctx->vi[idx]-ci[k-1]);
315 #else
316 369 rem = PetscAbsScalar(ctx->vr[idx]-cr[k-1]);
317 #endif
318
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 441 if (rem>h) {
319 336 cr[k] = cr[k-1]+incr*h;
320 #if !defined(PETSC_USE_COMPLEX)
321 24 ci[k] = ci[k-1]+inci*h;
322 #endif
323 336 k++;
324 105 } else {ini = PETSC_TRUE; idx--;}
325 }
326 }
327
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 19 if (!ucr) PetscCall(PetscFree(cr));
328
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 19 if (!uci) PetscCall(PetscFree(ci));
329
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 5 PetscFunctionReturn(PETSC_SUCCESS);
330 }
331
332 24 static PetscErrorCode RGComputeBoundingBox_Polygon(RG rg,PetscReal *a,PetscReal *b,PetscReal *c,PetscReal *d)
333 {
334 24 RG_POLYGON *ctx = (RG_POLYGON*)rg->data;
335 24 PetscInt i;
336
337
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 24 PetscFunctionBegin;
338
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 24 if (a) *a = PETSC_MAX_REAL;
339
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 24 if (b) *b = -PETSC_MAX_REAL;
340
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 24 if (c) *c = PETSC_MAX_REAL;
341
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 24 if (d) *d = -PETSC_MAX_REAL;
342
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 192 for (i=0;i<ctx->n;i++) {
343 #if defined(PETSC_USE_COMPLEX)
344
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 96 if (a) *a = PetscMin(*a,PetscRealPart(ctx->vr[i]));
345
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 96 if (b) *b = PetscMax(*b,PetscRealPart(ctx->vr[i]));
346
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 120 if (c) *c = PetscMin(*c,PetscImaginaryPart(ctx->vr[i]));
347
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 132 if (d) *d = PetscMax(*d,PetscImaginaryPart(ctx->vr[i]));
348 #else
349
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 108 if (a) *a = PetscMin(*a,ctx->vr[i]);
350
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 120 if (b) *b = PetscMax(*b,ctx->vr[i]);
351
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 120 if (c) *c = PetscMin(*c,ctx->vi[i]);
352
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 156 if (d) *d = PetscMax(*d,ctx->vi[i]);
353 #endif
354 }
355
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 24 PetscFunctionReturn(PETSC_SUCCESS);
356 }
357
358 17853 static PetscErrorCode RGCheckInside_Polygon(RG rg,PetscReal px,PetscReal py,PetscInt *inout)
359 {
360 17853 RG_POLYGON *ctx = (RG_POLYGON*)rg->data;
361 17853 PetscReal val,x[VERTMAX],y[VERTMAX];
362 17853 PetscBool mx,my,nx,ny;
363 17853 PetscInt i,j;
364
365
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 17853 PetscFunctionBegin;
366
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 89328 for (i=0;i<ctx->n;i++) {
367 #if defined(PETSC_USE_COMPLEX)
368 71405 x[i] = PetscRealPart(ctx->vr[i])-px;
369 71405 y[i] = PetscImaginaryPart(ctx->vr[i])-py;
370 #else
371 70 x[i] = ctx->vr[i]-px;
372 70 y[i] = ctx->vi[i]-py;
373 #endif
374 }
375 17853 *inout = -1;
376
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 89328 for (i=0;i<ctx->n;i++) {
377 71475 j = (i+1)%ctx->n;
378 71475 mx = PetscNot(x[i]<0.0);
379 71475 nx = PetscNot(x[j]<0.0);
380 71475 my = PetscNot(y[i]<0.0);
381 71475 ny = PetscNot(y[j]<0.0);
382
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 71475 if (!((my||ny) && (mx||nx)) || (mx&&nx)) continue;
383
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 6811 if (((my && ny && (mx||nx)) && (!(mx&&nx)))) {
384 5876 *inout = -*inout;
385 5876 continue;
386 }
387 935 val = (y[i]*x[j]-x[i]*y[j])/(x[j]-x[i]);
388
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 935 if (PetscAbs(val)<10*PETSC_MACHINE_EPSILON) {
389 ✗ *inout = 0;
390 ✗ PetscFunctionReturn(PETSC_SUCCESS);
391
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 935 } else if (val>0.0) *inout = -*inout;
392 }
393
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 5948 PetscFunctionReturn(PETSC_SUCCESS);
394 }
395
396 24 static PetscErrorCode RGSetFromOptions_Polygon(RG rg,PetscOptionItems PetscOptionsObject)
397 {
398 24 PetscScalar array[VERTMAX];
399 24 PetscInt i,k;
400 24 PetscBool flg,flgi=PETSC_FALSE;
401 #if !defined(PETSC_USE_COMPLEX)
402 10 PetscScalar arrayi[VERTMAX];
403 10 PetscInt ki;
404 #else
405 14 PetscScalar *arrayi=NULL;
406 #endif
407
408
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 24 PetscFunctionBegin;
409
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 24 PetscOptionsHeadBegin(PetscOptionsObject,"RG Polygon Options");
410
411 24 k = VERTMAX;
412
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 744 for (i=0;i<k;i++) array[i] = 0;
413
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 24 PetscCall(PetscOptionsScalarArray("-rg_polygon_vertices","Vertices of polygon","RGPolygonSetVertices",array,&k,&flg));
414 #if !defined(PETSC_USE_COMPLEX)
415 10 ki = VERTMAX;
416
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 310 for (i=0;i<ki;i++) arrayi[i] = 0;
417
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 10 PetscCall(PetscOptionsScalarArray("-rg_polygon_verticesi","Vertices of polygon (imaginary part)","RGPolygonSetVertices",arrayi,&ki,&flgi));
418
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 10 PetscCheck(ki==k,PetscObjectComm((PetscObject)rg),PETSC_ERR_ARG_SIZ,"The number of real %" PetscInt_FMT " and imaginary %" PetscInt_FMT " parts do not match",k,ki);
419 #endif
420
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 24 if (flg || flgi) PetscCall(RGPolygonSetVertices(rg,k,array,arrayi));
421
422
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 24 PetscOptionsHeadEnd();
423
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 5 PetscFunctionReturn(PETSC_SUCCESS);
424 }
425
426 24 static PetscErrorCode RGDestroy_Polygon(RG rg)
427 {
428 24 RG_POLYGON *ctx = (RG_POLYGON*)rg->data;
429
430
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 24 PetscFunctionBegin;
431
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 24 if (ctx->n) {
432
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 24 PetscCall(PetscFree(ctx->vr));
433 #if !defined(PETSC_USE_COMPLEX)
434
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 10 PetscCall(PetscFree(ctx->vi));
435 #endif
436 }
437
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 24 PetscCall(PetscFree(rg->data));
438
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 24 PetscCall(PetscObjectComposeFunction((PetscObject)rg,"RGPolygonSetVertices_C",NULL));
439
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 24 PetscCall(PetscObjectComposeFunction((PetscObject)rg,"RGPolygonGetVertices_C",NULL));
440
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 5 PetscFunctionReturn(PETSC_SUCCESS);
441 }
442
443 /*MC
444 RGPOLYGON - RGPOLYGON = "polygon" - A polygonal region defined by its
445 vertices, given via `RGPolygonSetVertices()`.
446
447 Note:
448 The following figure shows an example of a polygonal region.
449
450 ![Polygonal region](../../_static/images/manual/svg/fig-rg-polygon.svg)
451
452 Level: beginner
453
454 .seealso: [](sec:rg), `RG`, `RGType`, `RGSetType()`, `RGPolygonSetVertices()`
455 M*/
456
457 24 SLEPC_EXTERN PetscErrorCode RGCreate_Polygon(RG rg)
458 {
459 24 RG_POLYGON *polygon;
460
461
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 24 PetscFunctionBegin;
462
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 24 PetscCall(PetscNew(&polygon));
463 24 rg->data = (void*)polygon;
464
465 24 rg->ops->istrivial = RGIsTrivial_Polygon;
466 24 rg->ops->computecontour = RGComputeContour_Polygon;
467 24 rg->ops->computebbox = RGComputeBoundingBox_Polygon;
468 24 rg->ops->checkinside = RGCheckInside_Polygon;
469 24 rg->ops->setfromoptions = RGSetFromOptions_Polygon;
470 24 rg->ops->view = RGView_Polygon;
471 24 rg->ops->destroy = RGDestroy_Polygon;
472
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 24 PetscCall(PetscObjectComposeFunction((PetscObject)rg,"RGPolygonSetVertices_C",RGPolygonSetVertices_Polygon));
473
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 24 PetscCall(PetscObjectComposeFunction((PetscObject)rg,"RGPolygonGetVertices_C",RGPolygonGetVertices_Polygon));
474
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 5 PetscFunctionReturn(PETSC_SUCCESS);
475 }
476