Actual source code: minsurf1.c
petsc-3.13.6 2020-09-29
1: #include <petsctao.h>
3: static char help[] =
4: "This example demonstrates use of the TAO package to\n\
5: solve an unconstrained system of equations. This example is based on a\n\
6: problem from the MINPACK-2 test suite. Given a rectangular 2-D domain and\n\
7: boundary values along the edges of the domain, the objective is to find the\n\
8: surface with the minimal area that satisfies the boundary conditions.\n\
9: This Section 1.5 Writing Application Codes with PETSc solves this problem using complimentarity -- We are actually\n\
10: solving the system (grad f)_i >= 0, if x_i == l_i \n\
11: (grad f)_i = 0, if l_i < x_i < u_i \n\
12: (grad f)_i <= 0, if x_i == u_i \n\
13: where f is the function to be minimized. \n\
14: \n\
15: The command line options are:\n\
16: -mx <xg>, where <xg> = number of grid points in the 1st coordinate direction\n\
17: -my <yg>, where <yg> = number of grid points in the 2nd coordinate direction\n\
18: -start <st>, where <st> =0 for zero vector, and an average of the boundary conditions otherwise \n\n";
20: /*T
21: Concepts: TAO^Solving a complementarity problem
22: Routines: TaoCreate(); TaoDestroy();
24: Processors: 1
25: T*/
30: /*
31: User-defined Section 1.5 Writing Application Codes with PETSc context - contains data needed by the
32: Section 1.5 Writing Application Codes with PETSc-provided call-back routines, FormFunctionGradient(),
33: FormHessian().
34: */
35: typedef struct {
36: PetscInt mx, my;
37: PetscReal *bottom, *top, *left, *right;
38: } AppCtx;
41: /* -------- User-defined Routines --------- */
43: static PetscErrorCode MSA_BoundaryConditions(AppCtx *);
44: static PetscErrorCode MSA_InitialPoint(AppCtx *, Vec);
45: PetscErrorCode FormConstraints(Tao, Vec, Vec, void *);
46: PetscErrorCode FormJacobian(Tao, Vec, Mat, Mat, void *);
48: int main(int argc, char **argv)
49: {
51: Vec x; /* solution vector */
52: Vec c; /* Constraints function vector */
53: Vec xl,xu; /* Bounds on the variables */
54: PetscBool flg; /* A return variable when checking for user options */
55: Tao tao; /* TAO solver context */
56: Mat J; /* Jacobian matrix */
57: PetscInt N; /* Number of elements in vector */
58: PetscScalar lb = PETSC_NINFINITY; /* lower bound constant */
59: PetscScalar ub = PETSC_INFINITY; /* upper bound constant */
60: AppCtx user; /* user-defined work context */
62: /* Initialize PETSc, TAO */
63: PetscInitialize(&argc, &argv, (char *)0, help );if (ierr) return ierr;
65: /* Specify default dimension of the problem */
66: user.mx = 4; user.my = 4;
68: /* Check for any command line arguments that override defaults */
69: PetscOptionsGetInt(NULL,NULL, "-mx", &user.mx, &flg);
70: PetscOptionsGetInt(NULL,NULL, "-my", &user.my, &flg);
72: /* Calculate any derived values from parameters */
73: N = user.mx*user.my;
75: PetscPrintf(PETSC_COMM_SELF,"\n---- Minimum Surface Area Problem -----\n");
76: PetscPrintf(PETSC_COMM_SELF,"mx:%D, my:%D\n", user.mx,user.my);
78: /* Create appropriate vectors and matrices */
79: VecCreateSeq(MPI_COMM_SELF, N, &x);
80: VecDuplicate(x, &c);
81: MatCreateSeqAIJ(MPI_COMM_SELF, N, N, 7, NULL, &J);
83: /* The TAO code begins here */
85: /* Create TAO solver and set desired solution method */
86: TaoCreate(PETSC_COMM_SELF,&tao);
87: TaoSetType(tao,TAOSSILS);
89: /* Set data structure */
90: TaoSetInitialVector(tao, x);
92: /* Set routines for constraints function and Jacobian evaluation */
93: TaoSetConstraintsRoutine(tao, c, FormConstraints, (void *)&user);
94: TaoSetJacobianRoutine(tao, J, J, FormJacobian, (void *)&user);
96: /* Set the variable bounds */
97: MSA_BoundaryConditions(&user);
99: /* Set initial solution guess */
100: MSA_InitialPoint(&user, x);
102: /* Set Bounds on variables */
103: VecDuplicate(x, &xl);
104: VecDuplicate(x, &xu);
105: VecSet(xl, lb);
106: VecSet(xu, ub);
107: TaoSetVariableBounds(tao,xl,xu);
109: /* Check for any tao command line options */
110: TaoSetFromOptions(tao);
112: /* Solve the Section 1.5 Writing Application Codes with PETSc */
113: TaoSolve(tao);
115: /* Free Tao data structures */
116: TaoDestroy(&tao);
118: /* Free PETSc data structures */
119: VecDestroy(&x);
120: VecDestroy(&xl);
121: VecDestroy(&xu);
122: VecDestroy(&c);
123: MatDestroy(&J);
125: /* Free user-created data structures */
126: PetscFree(user.bottom);
127: PetscFree(user.top);
128: PetscFree(user.left);
129: PetscFree(user.right);
131: PetscFinalize();
132: return ierr;
133: }
135: /* -------------------------------------------------------------------- */
137: /* FormConstraints - Evaluates gradient of f.
139: Input Parameters:
140: . tao - the TAO_APPLICATION context
141: . X - input vector
142: . ptr - optional user-defined context, as set by TaoSetConstraintsRoutine()
144: Output Parameters:
145: . G - vector containing the newly evaluated gradient
146: */
147: PetscErrorCode FormConstraints(Tao tao, Vec X, Vec G, void *ptr)
148: {
149: AppCtx *user = (AppCtx *) ptr;
151: PetscInt i,j,row;
152: PetscInt mx=user->mx, my=user->my;
153: PetscReal hx=1.0/(mx+1),hy=1.0/(my+1), hydhx=hy/hx, hxdhy=hx/hy;
154: PetscReal f1,f2,f3,f4,f5,f6,d1,d2,d3,d4,d5,d6,d7,d8,xc,xl,xr,xt,xb,xlt,xrb;
155: PetscReal df1dxc,df2dxc,df3dxc,df4dxc,df5dxc,df6dxc;
156: PetscScalar zero=0.0;
157: PetscScalar *g, *x;
160: /* Initialize vector to zero */
161: VecSet(G, zero);
163: /* Get pointers to vector data */
164: VecGetArray(X, &x);
165: VecGetArray(G, &g);
167: /* Compute function over the locally owned part of the mesh */
168: for (j=0; j<my; j++){
169: for (i=0; i< mx; i++){
170: row= j*mx + i;
172: xc = x[row];
173: xlt=xrb=xl=xr=xb=xt=xc;
175: if (i==0){ /* left side */
176: xl= user->left[j+1];
177: xlt = user->left[j+2];
178: } else {
179: xl = x[row-1];
180: }
182: if (j==0){ /* bottom side */
183: xb=user->bottom[i+1];
184: xrb = user->bottom[i+2];
185: } else {
186: xb = x[row-mx];
187: }
189: if (i+1 == mx){ /* right side */
190: xr=user->right[j+1];
191: xrb = user->right[j];
192: } else {
193: xr = x[row+1];
194: }
196: if (j+1==0+my){ /* top side */
197: xt=user->top[i+1];
198: xlt = user->top[i];
199: }else {
200: xt = x[row+mx];
201: }
203: if (i>0 && j+1<my){
204: xlt = x[row-1+mx];
205: }
206: if (j>0 && i+1<mx){
207: xrb = x[row+1-mx];
208: }
210: d1 = (xc-xl);
211: d2 = (xc-xr);
212: d3 = (xc-xt);
213: d4 = (xc-xb);
214: d5 = (xr-xrb);
215: d6 = (xrb-xb);
216: d7 = (xlt-xl);
217: d8 = (xt-xlt);
219: df1dxc = d1*hydhx;
220: df2dxc = ( d1*hydhx + d4*hxdhy );
221: df3dxc = d3*hxdhy;
222: df4dxc = ( d2*hydhx + d3*hxdhy );
223: df5dxc = d2*hydhx;
224: df6dxc = d4*hxdhy;
226: d1 /= hx;
227: d2 /= hx;
228: d3 /= hy;
229: d4 /= hy;
230: d5 /= hy;
231: d6 /= hx;
232: d7 /= hy;
233: d8 /= hx;
235: f1 = PetscSqrtScalar( 1.0 + d1*d1 + d7*d7);
236: f2 = PetscSqrtScalar( 1.0 + d1*d1 + d4*d4);
237: f3 = PetscSqrtScalar( 1.0 + d3*d3 + d8*d8);
238: f4 = PetscSqrtScalar( 1.0 + d3*d3 + d2*d2);
239: f5 = PetscSqrtScalar( 1.0 + d2*d2 + d5*d5);
240: f6 = PetscSqrtScalar( 1.0 + d4*d4 + d6*d6);
242: df1dxc /= f1;
243: df2dxc /= f2;
244: df3dxc /= f3;
245: df4dxc /= f4;
246: df5dxc /= f5;
247: df6dxc /= f6;
249: g[row] = (df1dxc+df2dxc+df3dxc+df4dxc+df5dxc+df6dxc )/2.0;
250: }
251: }
253: /* Restore vectors */
254: VecRestoreArray(X, &x);
255: VecRestoreArray(G, &g);
256: PetscLogFlops(67*mx*my);
257: return(0);
258: }
260: /* ------------------------------------------------------------------- */
261: /*
262: FormJacobian - Evaluates Jacobian matrix.
264: Input Parameters:
265: . tao - the TAO_APPLICATION context
266: . X - input vector
267: . ptr - optional user-defined context, as set by TaoSetJacobian()
269: Output Parameters:
270: . tH - Jacobian matrix
272: */
273: PetscErrorCode FormJacobian(Tao tao, Vec X, Mat H, Mat tHPre, void *ptr)
274: {
275: AppCtx *user = (AppCtx *) ptr;
276: PetscErrorCode ierr;
277: PetscInt i,j,k,row;
278: PetscInt mx=user->mx, my=user->my;
279: PetscInt col[7];
280: PetscReal hx=1.0/(mx+1), hy=1.0/(my+1), hydhx=hy/hx, hxdhy=hx/hy;
281: PetscReal f1,f2,f3,f4,f5,f6,d1,d2,d3,d4,d5,d6,d7,d8,xc,xl,xr,xt,xb,xlt,xrb;
282: PetscReal hl,hr,ht,hb,hc,htl,hbr;
283: const PetscScalar *x;
284: PetscScalar v[7];
285: PetscBool assembled;
287: /* Set various matrix options */
288: MatSetOption(H,MAT_IGNORE_OFF_PROC_ENTRIES,PETSC_TRUE);
289: MatAssembled(H,&assembled);
290: if (assembled){MatZeroEntries(H); }
292: /* Get pointers to vector data */
293: VecGetArrayRead(X, &x);
295: /* Compute Jacobian over the locally owned part of the mesh */
296: for (i=0; i< mx; i++){
297: for (j=0; j<my; j++){
298: row= j*mx + i;
300: xc = x[row];
301: xlt=xrb=xl=xr=xb=xt=xc;
303: /* Left side */
304: if (i==0){
305: xl = user->left[j+1];
306: xlt = user->left[j+2];
307: } else {
308: xl = x[row-1];
309: }
311: if (j==0){
312: xb = user->bottom[i+1];
313: xrb = user->bottom[i+2];
314: } else {
315: xb = x[row-mx];
316: }
318: if (i+1 == mx){
319: xr = user->right[j+1];
320: xrb = user->right[j];
321: } else {
322: xr = x[row+1];
323: }
325: if (j+1==my){
326: xt = user->top[i+1];
327: xlt = user->top[i];
328: }else {
329: xt = x[row+mx];
330: }
332: if (i>0 && j+1<my){
333: xlt = x[row-1+mx];
334: }
335: if (j>0 && i+1<mx){
336: xrb = x[row+1-mx];
337: }
340: d1 = (xc-xl)/hx;
341: d2 = (xc-xr)/hx;
342: d3 = (xc-xt)/hy;
343: d4 = (xc-xb)/hy;
344: d5 = (xrb-xr)/hy;
345: d6 = (xrb-xb)/hx;
346: d7 = (xlt-xl)/hy;
347: d8 = (xlt-xt)/hx;
349: f1 = PetscSqrtScalar( 1.0 + d1*d1 + d7*d7);
350: f2 = PetscSqrtScalar( 1.0 + d1*d1 + d4*d4);
351: f3 = PetscSqrtScalar( 1.0 + d3*d3 + d8*d8);
352: f4 = PetscSqrtScalar( 1.0 + d3*d3 + d2*d2);
353: f5 = PetscSqrtScalar( 1.0 + d2*d2 + d5*d5);
354: f6 = PetscSqrtScalar( 1.0 + d4*d4 + d6*d6);
357: hl = (-hydhx*(1.0+d7*d7)+d1*d7)/(f1*f1*f1)+(-hydhx*(1.0+d4*d4)+d1*d4)/(f2*f2*f2);
358: hr = (-hydhx*(1.0+d5*d5)+d2*d5)/(f5*f5*f5)+(-hydhx*(1.0+d3*d3)+d2*d3)/(f4*f4*f4);
359: ht = (-hxdhy*(1.0+d8*d8)+d3*d8)/(f3*f3*f3)+(-hxdhy*(1.0+d2*d2)+d2*d3)/(f4*f4*f4);
360: hb = (-hxdhy*(1.0+d6*d6)+d4*d6)/(f6*f6*f6)+(-hxdhy*(1.0+d1*d1)+d1*d4)/(f2*f2*f2);
362: hbr = -d2*d5/(f5*f5*f5) - d4*d6/(f6*f6*f6);
363: htl = -d1*d7/(f1*f1*f1) - d3*d8/(f3*f3*f3);
365: hc = hydhx*(1.0+d7*d7)/(f1*f1*f1) + hxdhy*(1.0+d8*d8)/(f3*f3*f3) + hydhx*(1.0+d5*d5)/(f5*f5*f5) + hxdhy*(1.0+d6*d6)/(f6*f6*f6) +
366: (hxdhy*(1.0+d1*d1)+hydhx*(1.0+d4*d4)-2*d1*d4)/(f2*f2*f2) + (hxdhy*(1.0+d2*d2)+hydhx*(1.0+d3*d3)-2*d2*d3)/(f4*f4*f4);
368: hl/=2.0; hr/=2.0; ht/=2.0; hb/=2.0; hbr/=2.0; htl/=2.0; hc/=2.0;
370: k=0;
371: if (j>0){
372: v[k]=hb; col[k]=row - mx; k++;
373: }
375: if (j>0 && i < mx -1){
376: v[k]=hbr; col[k]=row - mx+1; k++;
377: }
379: if (i>0){
380: v[k]= hl; col[k]=row - 1; k++;
381: }
383: v[k]= hc; col[k]=row; k++;
385: if (i < mx-1 ){
386: v[k]= hr; col[k]=row+1; k++;
387: }
389: if (i>0 && j < my-1 ){
390: v[k]= htl; col[k] = row+mx-1; k++;
391: }
393: if (j < my-1 ){
394: v[k]= ht; col[k] = row+mx; k++;
395: }
397: /*
398: Set matrix values using local numbering, which was defined
399: earlier, in the main routine.
400: */
401: MatSetValues(H,1,&row,k,col,v,INSERT_VALUES);
402: }
403: }
405: /* Restore vectors */
406: VecRestoreArrayRead(X,&x);
408: /* Assemble the matrix */
409: MatAssemblyBegin(H,MAT_FINAL_ASSEMBLY);
410: MatAssemblyEnd(H,MAT_FINAL_ASSEMBLY);
411: PetscLogFlops(199*mx*my);
412: return(0);
413: }
415: /* ------------------------------------------------------------------- */
416: /*
417: MSA_BoundaryConditions - Calculates the boundary conditions for
418: the region.
420: Input Parameter:
421: . user - user-defined Section 1.5 Writing Application Codes with PETSc context
423: Output Parameter:
424: . user - user-defined Section 1.5 Writing Application Codes with PETSc context
425: */
426: static PetscErrorCode MSA_BoundaryConditions(AppCtx * user)
427: {
428: PetscErrorCode ierr;
429: PetscInt i,j,k,limit=0,maxits=5;
430: PetscInt mx=user->mx,my=user->my;
431: PetscInt bsize=0, lsize=0, tsize=0, rsize=0;
432: PetscReal one=1.0, two=2.0, three=3.0, tol=1e-10;
433: PetscReal fnorm,det,hx,hy,xt=0,yt=0;
434: PetscReal u1,u2,nf1,nf2,njac11,njac12,njac21,njac22;
435: PetscReal b=-0.5, t=0.5, l=-0.5, r=0.5;
436: PetscReal *boundary;
439: bsize=mx+2; lsize=my+2; rsize=my+2; tsize=mx+2;
441: PetscMalloc1(bsize, &user->bottom);
442: PetscMalloc1(tsize, &user->top);
443: PetscMalloc1(lsize, &user->left);
444: PetscMalloc1(rsize, &user->right);
446: hx= (r-l)/(mx+1); hy=(t-b)/(my+1);
448: for (j=0; j<4; j++){
449: if (j==0){
450: yt=b;
451: xt=l;
452: limit=bsize;
453: boundary=user->bottom;
454: } else if (j==1){
455: yt=t;
456: xt=l;
457: limit=tsize;
458: boundary=user->top;
459: } else if (j==2){
460: yt=b;
461: xt=l;
462: limit=lsize;
463: boundary=user->left;
464: } else { /* if (j==3) */
465: yt=b;
466: xt=r;
467: limit=rsize;
468: boundary=user->right;
469: }
471: for (i=0; i<limit; i++){
472: u1=xt;
473: u2=-yt;
474: for (k=0; k<maxits; k++){
475: nf1=u1 + u1*u2*u2 - u1*u1*u1/three-xt;
476: nf2=-u2 - u1*u1*u2 + u2*u2*u2/three-yt;
477: fnorm=PetscSqrtScalar(nf1*nf1+nf2*nf2);
478: if (fnorm <= tol) break;
479: njac11=one+u2*u2-u1*u1;
480: njac12=two*u1*u2;
481: njac21=-two*u1*u2;
482: njac22=-one - u1*u1 + u2*u2;
483: det = njac11*njac22-njac21*njac12;
484: u1 = u1-(njac22*nf1-njac12*nf2)/det;
485: u2 = u2-(njac11*nf2-njac21*nf1)/det;
486: }
488: boundary[i]=u1*u1-u2*u2;
489: if (j==0 || j==1) {
490: xt=xt+hx;
491: } else { /* if (j==2 || j==3) */
492: yt=yt+hy;
493: }
494: }
495: }
496: return(0);
497: }
499: /* ------------------------------------------------------------------- */
500: /*
501: MSA_InitialPoint - Calculates the initial guess in one of three ways.
503: Input Parameters:
504: . user - user-defined Section 1.5 Writing Application Codes with PETSc context
505: . X - vector for initial guess
507: Output Parameters:
508: . X - newly computed initial guess
509: */
510: static PetscErrorCode MSA_InitialPoint(AppCtx * user, Vec X)
511: {
513: PetscInt start=-1,i,j;
514: PetscScalar zero=0.0;
515: PetscBool flg;
518: PetscOptionsGetInt(NULL,NULL,"-start",&start,&flg);
520: if (flg && start==0){ /* The zero vector is reasonable */
521: VecSet(X, zero);
522: } else { /* Take an average of the boundary conditions */
523: PetscInt row;
524: PetscInt mx=user->mx,my=user->my;
525: PetscScalar *x;
527: /* Get pointers to vector data */
528: VecGetArray(X,&x);
530: /* Perform local computations */
531: for (j=0; j<my; j++){
532: for (i=0; i< mx; i++){
533: row=(j)*mx + (i);
534: x[row] = ( ((j+1)*user->bottom[i+1]+(my-j+1)*user->top[i+1])/(my+2)+ ((i+1)*user->left[j+1]+(mx-i+1)*user->right[j+1])/(mx+2))/2.0;
535: }
536: }
538: /* Restore vectors */
539: VecRestoreArray(X,&x);
540: }
541: return(0);
542: }
545: /*TEST
547: build:
548: requires: !complex
550: test:
551: args: -tao_monitor -tao_view -tao_type ssils -tao_gttol 1.e-5
552: requires: !single
554: test:
555: suffix: 2
556: args: -tao_monitor -tao_view -tao_type ssfls -tao_gttol 1.e-5
558: TEST*/