Actual source code: tomography.c

petsc-master 2020-11-30
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```  1: /* XH:
2:     Todo: add cs1f.F90 and adjust makefile.
3:     Todo: maybe provide code template to generate 1D/2D/3D gradient, DCT transform matrix for D etc.
4: */
5: /*
6:    Include "petsctao.h" so that we can use TAO solvers.  Note that this
7:    file automatically includes libraries such as:
8:      petsc.h       - base PETSc routines   petscvec.h - vectors
9:      petscsys.h    - sysem routines        petscmat.h - matrices
10:      petscis.h     - index sets            petscksp.h - Krylov subspace methods
11:      petscviewer.h - viewers               petscpc.h  - preconditioners

13: */

15: #include <petsctao.h>

17: /*
18: Description:   BRGN tomography reconstruction example .
19:                0.5*||Ax-b||^2 + lambda*g(x)
20: Reference:     None
21: */

23: static char help[] = "Finds the least-squares solution to the under constraint linear model Ax = b, with regularizer. \n\
24:             A is a M*N real matrix (M<N), x is sparse. A good regularizer is an L1 regularizer. \n\
25:             We find the sparse solution by solving 0.5*||Ax-b||^2 + lambda*||D*x||_1, where lambda (by default 1e-4) is a user specified weight.\n\
26:             D is the K*N transform matrix so that D*x is sparse. By default D is identity matrix, so that D*x = x.\n";
27: /*T
28:    Concepts: TAO^Solving a system of nonlinear equations, nonlinear least squares
29:    Routines: TaoCreate();
30:    Routines: TaoSetType();
31:    Routines: TaoSetSeparableObjectiveRoutine();
32:    Routines: TaoSetJacobianRoutine();
33:    Routines: TaoSetInitialVector();
34:    Routines: TaoSetFromOptions();
35:    Routines: TaoSetConvergenceHistory(); TaoGetConvergenceHistory();
36:    Routines: TaoSolve();
37:    Routines: TaoView(); TaoDestroy();
38:    Processors: 1
39: T*/

41: /* User-defined application context */
42: typedef struct {
43:   /* Working space. linear least square:  res(x) = A*x - b */
44:   PetscInt  M,N,K;            /* Problem dimension: A is M*N Matrix, D is K*N Matrix */
45:   Mat       A,D;              /* Coefficients, Dictionary Transform of size M*N and K*N respectively. For linear least square, Jacobian Matrix J = A. For nonlinear least square, it is different from A */
46:   Vec       b,xGT,xlb,xub;    /* observation b, ground truth xGT, the lower bound and upper bound of x*/
47: } AppCtx;

49: /* User provided Routines */
50: PetscErrorCode InitializeUserData(AppCtx *);
51: PetscErrorCode FormStartingPoint(Vec,AppCtx *);
52: PetscErrorCode EvaluateResidual(Tao,Vec,Vec,void *);
53: PetscErrorCode EvaluateJacobian(Tao,Vec,Mat,Mat,void *);
54: PetscErrorCode EvaluateRegularizerObjectiveAndGradient(Tao,Vec,PetscReal *,Vec,void*);
55: PetscErrorCode EvaluateRegularizerHessian(Tao,Vec,Mat,void*);
56: PetscErrorCode EvaluateRegularizerHessianProd(Mat,Vec,Vec);

58: /*--------------------------------------------------------------------*/
59: int main(int argc,char **argv)
60: {
62:   Vec            x,res;              /* solution, function res(x) = A*x-b */
63:   Mat            Hreg;               /* regularizer Hessian matrix for user specified regularizer*/
64:   Tao            tao;                /* Tao solver context */
65:   PetscReal      hist[100],resid[100],v1,v2;
66:   PetscInt       lits[100];
67:   AppCtx         user;               /* user-defined work context */
68:   PetscViewer    fd;   /* used to save result to file */
69:   char           resultFile[] = "tomographyResult_x";  /* Debug: change from "tomographyResult_x" to "cs1Result_x" */

71:   PetscInitialize(&argc,&argv,(char *)0,help);if (ierr) return ierr;

73:   /* Create TAO solver and set desired solution method */
74:   TaoCreate(PETSC_COMM_SELF,&tao);
75:   TaoSetType(tao,TAOBRGN);

77:   /* User set application context: A, D matrice, and b vector. */
78:   InitializeUserData(&user);

80:   /* Allocate solution vector x,  and function vectors Ax-b, */
81:   VecCreateSeq(PETSC_COMM_SELF,user.N,&x);
82:   VecCreateSeq(PETSC_COMM_SELF,user.M,&res);

84:   /* Set initial guess */
85:   FormStartingPoint(x,&user);

87:   /* Bind x to tao->solution. */
88:   TaoSetInitialVector(tao,x);
89:   /* Sets the upper and lower bounds of x */
90:   TaoSetVariableBounds(tao,user.xlb,user.xub);

92:   /* Bind user.D to tao->data->D */
93:   TaoBRGNSetDictionaryMatrix(tao,user.D);

95:   /* Set the residual function and Jacobian routines for least squares. */
96:   TaoSetResidualRoutine(tao,res,EvaluateResidual,(void*)&user);
97:   /* Jacobian matrix fixed as user.A for Linear least sqaure problem. */
98:   TaoSetJacobianResidualRoutine(tao,user.A,user.A,EvaluateJacobian,(void*)&user);

100:   /* User set the regularizer objective, gradient, and hessian. Set it the same as using l2prox choice, for testing purpose.  */
101:   TaoBRGNSetRegularizerObjectiveAndGradientRoutine(tao,EvaluateRegularizerObjectiveAndGradient,(void*)&user);
102:   /* User defined regularizer Hessian setup, here is identiy shell matrix */
103:   MatCreate(PETSC_COMM_SELF,&Hreg);
104:   MatSetSizes(Hreg,PETSC_DECIDE,PETSC_DECIDE,user.N,user.N);
105:   MatSetType(Hreg,MATSHELL);
106:   MatSetUp(Hreg);
107:   MatShellSetOperation(Hreg,MATOP_MULT,(void (*)(void))EvaluateRegularizerHessianProd);
108:   TaoBRGNSetRegularizerHessianRoutine(tao,Hreg,EvaluateRegularizerHessian,(void*)&user);

110:   /* Check for any TAO command line arguments */
111:   TaoSetFromOptions(tao);

113:   TaoSetConvergenceHistory(tao,hist,resid,0,lits,100,PETSC_TRUE);

115:   /* Perform the Solve */
116:   TaoSolve(tao);

118:   /* Save x (reconstruction of object) vector to a binary file, which maybe read from Matlab and convert to a 2D image for comparison. */
119:   PetscViewerBinaryOpen(PETSC_COMM_SELF,resultFile,FILE_MODE_WRITE,&fd);
120:   VecView(x,fd);
121:   PetscViewerDestroy(&fd);

123:   /* compute the error */
124:   VecAXPY(x,-1,user.xGT);
125:   VecNorm(x,NORM_2,&v1);
126:   VecNorm(user.xGT,NORM_2,&v2);
127:   PetscPrintf(PETSC_COMM_SELF, "relative reconstruction error: ||x-xGT||/||xGT|| = %6.4e.\n", (double)(v1/v2));

129:   /* Free TAO data structures */
130:   TaoDestroy(&tao);

132:    /* Free PETSc data structures */
133:   VecDestroy(&x);
134:   VecDestroy(&res);
135:   MatDestroy(&Hreg);
136:   /* Free user data structures */
137:   MatDestroy(&user.A);
138:   MatDestroy(&user.D);
139:   VecDestroy(&user.b);
140:   VecDestroy(&user.xGT);
141:   VecDestroy(&user.xlb);
142:   VecDestroy(&user.xub);
143:   PetscFinalize();
144:   return ierr;
145: }

147: /*--------------------------------------------------------------------*/
148: /* Evaluate residual function A(x)-b in least square problem ||A(x)-b||^2 */
149: PetscErrorCode EvaluateResidual(Tao tao,Vec X,Vec F,void *ptr)
150: {
151:   AppCtx         *user = (AppCtx *)ptr;

155:   /* Compute Ax - b */
156:   MatMult(user->A,X,F);
157:   VecAXPY(F,-1,user->b);
158:   PetscLogFlops(2.0*user->M*user->N);
159:   return(0);
160: }

162: /*------------------------------------------------------------*/
163: PetscErrorCode EvaluateJacobian(Tao tao,Vec X,Mat J,Mat Jpre,void *ptr)
164: {
165:   /* Jacobian is not changing here, so use a empty dummy function here.  J[m][n] = df[m]/dx[n] = A[m][n] for linear least square */
167:   return(0);
168: }

170: /* ------------------------------------------------------------ */
171: PetscErrorCode EvaluateRegularizerObjectiveAndGradient(Tao tao,Vec X,PetscReal *f_reg,Vec G_reg,void *ptr)
172: {

176:   /* compute regularizer objective = 0.5*x'*x */
177:   VecDot(X,X,f_reg);
178:   *f_reg *= 0.5;
179:   /* compute regularizer gradient = x */
180:   VecCopy(X,G_reg);
181:   return(0);
182: }

184: PetscErrorCode EvaluateRegularizerHessianProd(Mat Hreg,Vec in,Vec out)
185: {
188:   VecCopy(in,out);
189:   return(0);
190: }

192: /* ------------------------------------------------------------ */
193: PetscErrorCode EvaluateRegularizerHessian(Tao tao,Vec X,Mat Hreg,void *ptr)
194: {
195:   /* Hessian for regularizer objective = 0.5*x'*x is identity matrix, and is not changing*/
197:   return(0);
198: }

200: /* ------------------------------------------------------------ */
201: PetscErrorCode FormStartingPoint(Vec X,AppCtx *user)
202: {
205:   VecSet(X,0.0);
206:   return(0);
207: }

209: /* ---------------------------------------------------------------------- */
210: PetscErrorCode InitializeUserData(AppCtx *user)
211: {
212:   PetscInt       k,n; /* indices for row and columns of D. */
213:   char           dataFile[] = "tomographyData_A_b_xGT";   /* Matrix A and vectors b, xGT(ground truth) binary files generated by Matlab. Debug: change from "tomographyData_A_b_xGT" to "cs1Data_A_b_xGT". */
214:   PetscInt       dictChoice = 1; /* choose from 0:identity, 1:gradient1D, 2:gradient2D, 3:DCT etc */
215:   PetscViewer    fd;   /* used to load data from file */
217:   PetscReal      v;

221:   /*
222:   Matrix Vector read and write refer to:
223:   https://www.mcs.anl.gov/petsc/petsc-current/src/mat/tutorials/ex10.c
224:   https://www.mcs.anl.gov/petsc/petsc-current/src/mat/tutorials/ex12.c
225:  */
226:   /* Load the A matrix, b vector, and xGT vector from a binary file. */
227:   PetscViewerBinaryOpen(PETSC_COMM_WORLD,dataFile,FILE_MODE_READ,&fd);
228:   MatCreate(PETSC_COMM_WORLD,&user->A);
229:   MatSetType(user->A,MATSEQAIJ);
230:   MatLoad(user->A,fd);
231:   VecCreate(PETSC_COMM_WORLD,&user->b);
232:   VecLoad(user->b,fd);
233:   VecCreate(PETSC_COMM_WORLD,&user->xGT);
234:   VecLoad(user->xGT,fd);
235:   PetscViewerDestroy(&fd);
236:   VecDuplicate(user->xGT,&(user->xlb));
237:   VecSet(user->xlb,0.0);
238:   VecDuplicate(user->xGT,&(user->xub));
239:   VecSet(user->xub,PETSC_INFINITY);

241:   /* Specify the size */
242:   MatGetSize(user->A,&user->M,&user->N);

244:   /* shortcut, when D is identity matrix, we may just specify it as NULL, and brgn will treat D*x as x without actually computing D*x.
245:   if (dictChoice == 0) {
246:     user->D = NULL;
247:     return(0);
248:   }
249:   */

251:   /* Speficy D */
252:   /* (1) Specify D Size */
253:   switch (dictChoice) {
254:     case 0: /* 0:identity */
255:       user->K = user->N;
256:       break;
257:     case 1: /* 1:gradient1D */
258:       user->K = user->N-1;
259:       break;
260:   }

262:   MatCreate(PETSC_COMM_SELF,&user->D);
263:   MatSetSizes(user->D,PETSC_DECIDE,PETSC_DECIDE,user->K,user->N);
264:   MatSetFromOptions(user->D);
265:   MatSetUp(user->D);

267:   /* (2) Specify D Content */
268:   switch (dictChoice) {
269:     case 0: /* 0:identity */
270:       for (k=0; k<user->K; k++) {
271:         v = 1.0;
272:         MatSetValues(user->D,1,&k,1,&k,&v,INSERT_VALUES);
273:       }
274:       break;
275:     case 1: /* 1:gradient1D.  [-1, 1, 0,...; 0, -1, 1, 0, ...] */
276:       for (k=0; k<user->K; k++) {
277:         v = 1.0;
278:         n = k+1;
279:         MatSetValues(user->D,1,&k,1,&n,&v,INSERT_VALUES);
280:         v = -1.0;
281:         MatSetValues(user->D,1,&k,1,&k,&v,INSERT_VALUES);
282:       }
283:       break;
284:   }
285:   MatAssemblyBegin(user->D,MAT_FINAL_ASSEMBLY);
286:   MatAssemblyEnd(user->D,MAT_FINAL_ASSEMBLY);

288:   return(0);
289: }

291: /*TEST

293:    build:
294:       requires: !complex !single !__float128 !define(PETSC_USE_64BIT_INDICES)

296:    test:
297:       localrunfiles: tomographyData_A_b_xGT
298:       args: -tao_max_it 1000 -tao_brgn_regularization_type l1dict -tao_brgn_regularizer_weight 1e-8 -tao_brgn_l1_smooth_epsilon 1e-6 -tao_gatol 1.e-8

300:    test:
301:       suffix: 2
302:       localrunfiles: tomographyData_A_b_xGT
303:       args: -tao_monitor -tao_max_it 1000 -tao_brgn_regularization_type l2prox -tao_brgn_regularizer_weight 1e-8 -tao_gatol 1.e-6

305:    test:
306:       suffix: 3
307:       localrunfiles: tomographyData_A_b_xGT
308:       args: -tao_monitor -tao_max_it 1000 -tao_brgn_regularization_type user -tao_brgn_regularizer_weight 1e-8 -tao_gatol 1.e-6

310: TEST*/
```