Actual source code: tomography.c

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

 70:   PetscInitialize(&argc,&argv,(char *)0,help);

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

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

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

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

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

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

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

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

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

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

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

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

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

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

131:    /* Free PETSc data structures */
132:   VecDestroy(&x);
133:   VecDestroy(&res);
134:   MatDestroy(&Hreg);
135:   /* Free user data structures */
136:   MatDestroy(&user.A);
137:   MatDestroy(&user.D);
138:   VecDestroy(&user.b);
139:   VecDestroy(&user.xGT);
140:   VecDestroy(&user.xlb);
141:   VecDestroy(&user.xub);
142:   PetscFinalize();
143:   return 0;
144: }

146: /*--------------------------------------------------------------------*/
147: /* Evaluate residual function A(x)-b in least square problem ||A(x)-b||^2 */
148: PetscErrorCode EvaluateResidual(Tao tao,Vec X,Vec F,void *ptr)
149: {
150:   AppCtx         *user = (AppCtx *)ptr;

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

159: /*------------------------------------------------------------*/
160: PetscErrorCode EvaluateJacobian(Tao tao,Vec X,Mat J,Mat Jpre,void *ptr)
161: {
162:   /* 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 */
163:   return 0;
164: }

166: /* ------------------------------------------------------------ */
167: PetscErrorCode EvaluateRegularizerObjectiveAndGradient(Tao tao,Vec X,PetscReal *f_reg,Vec G_reg,void *ptr)
168: {
169:   /* compute regularizer objective = 0.5*x'*x */
170:   VecDot(X,X,f_reg);
171:   *f_reg *= 0.5;
172:   /* compute regularizer gradient = x */
173:   VecCopy(X,G_reg);
174:   return 0;
175: }

177: PetscErrorCode EvaluateRegularizerHessianProd(Mat Hreg,Vec in,Vec out)
178: {
179:   VecCopy(in,out);
180:   return 0;
181: }

183: /* ------------------------------------------------------------ */
184: PetscErrorCode EvaluateRegularizerHessian(Tao tao,Vec X,Mat Hreg,void *ptr)
185: {
186:   /* Hessian for regularizer objective = 0.5*x'*x is identity matrix, and is not changing*/
187:   return 0;
188: }

190: /* ------------------------------------------------------------ */
191: PetscErrorCode FormStartingPoint(Vec X,AppCtx *user)
192: {
193:   VecSet(X,0.0);
194:   return 0;
195: }

197: /* ---------------------------------------------------------------------- */
198: PetscErrorCode InitializeUserData(AppCtx *user)
199: {
200:   PetscInt       k,n; /* indices for row and columns of D. */
201:   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". */
202:   PetscInt       dictChoice = 1; /* choose from 0:identity, 1:gradient1D, 2:gradient2D, 3:DCT etc */
203:   PetscViewer    fd;   /* used to load data from file */
204:   PetscReal      v;


207:   /*
208:   Matrix Vector read and write refer to:
209:   https://petsc.org/release/src/mat/tutorials/ex10.c
210:   https://petsc.org/release/src/mat/tutorials/ex12.c
211:  */
212:   /* Load the A matrix, b vector, and xGT vector from a binary file. */
213:   PetscViewerBinaryOpen(PETSC_COMM_WORLD,dataFile,FILE_MODE_READ,&fd);
214:   MatCreate(PETSC_COMM_WORLD,&user->A);
215:   MatSetType(user->A,MATSEQAIJ);
216:   MatLoad(user->A,fd);
217:   VecCreate(PETSC_COMM_WORLD,&user->b);
218:   VecLoad(user->b,fd);
219:   VecCreate(PETSC_COMM_WORLD,&user->xGT);
220:   VecLoad(user->xGT,fd);
221:   PetscViewerDestroy(&fd);
222:   VecDuplicate(user->xGT,&(user->xlb));
223:   VecSet(user->xlb,0.0);
224:   VecDuplicate(user->xGT,&(user->xub));
225:   VecSet(user->xub,PETSC_INFINITY);

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

230:   /* 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.
231:   if (dictChoice == 0) {
232:     user->D = NULL;
233:     return 0;
234:   }
235:   */

237:   /* Speficy D */
238:   /* (1) Specify D Size */
239:   switch (dictChoice) {
240:     case 0: /* 0:identity */
241:       user->K = user->N;
242:       break;
243:     case 1: /* 1:gradient1D */
244:       user->K = user->N-1;
245:       break;
246:   }

248:   MatCreate(PETSC_COMM_SELF,&user->D);
249:   MatSetSizes(user->D,PETSC_DECIDE,PETSC_DECIDE,user->K,user->N);
250:   MatSetFromOptions(user->D);
251:   MatSetUp(user->D);

253:   /* (2) Specify D Content */
254:   switch (dictChoice) {
255:     case 0: /* 0:identity */
256:       for (k=0; k<user->K; k++) {
257:         v = 1.0;
258:         MatSetValues(user->D,1,&k,1,&k,&v,INSERT_VALUES);
259:       }
260:       break;
261:     case 1: /* 1:gradient1D.  [-1, 1, 0,...; 0, -1, 1, 0, ...] */
262:       for (k=0; k<user->K; k++) {
263:         v = 1.0;
264:         n = k+1;
265:         MatSetValues(user->D,1,&k,1,&n,&v,INSERT_VALUES);
266:         v = -1.0;
267:         MatSetValues(user->D,1,&k,1,&k,&v,INSERT_VALUES);
268:       }
269:       break;
270:   }
271:   MatAssemblyBegin(user->D,MAT_FINAL_ASSEMBLY);
272:   MatAssemblyEnd(user->D,MAT_FINAL_ASSEMBLY);

274:   return 0;
275: }

277: /*TEST

279:    build:
280:       requires: !complex !single !__float128 !defined(PETSC_USE_64BIT_INDICES)

282:    test:
283:       localrunfiles: tomographyData_A_b_xGT
284:       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

286:    test:
287:       suffix: 2
288:       localrunfiles: tomographyData_A_b_xGT
289:       args: -tao_monitor -tao_max_it 1000 -tao_brgn_regularization_type l2prox -tao_brgn_regularizer_weight 1e-8 -tao_gatol 1.e-6

291:    test:
292:       suffix: 3
293:       localrunfiles: tomographyData_A_b_xGT
294:       args: -tao_monitor -tao_max_it 1000 -tao_brgn_regularization_type user -tao_brgn_regularizer_weight 1e-8 -tao_gatol 1.e-6

296: TEST*/