Actual source code: tomographyADMM.c
1: #include <petsctao.h>
2: /*
3: Description: ADMM tomography reconstruction example .
4: 0.5*||Ax-b||^2 + lambda*g(x)
5: Reference: BRGN Tomography Example
6: */
8: static char help[] = "Finds the ADMM solution to the under constraint linear model Ax = b, with regularizer. \n\
9: A is a M*N real matrix (M<N), x is sparse. A good regularizer is an L1 regularizer. \n\
10: We first split the operator into 0.5*||Ax-b||^2, f(x), and lambda*||x||_1, g(z), where lambda is user specified weight. \n\
11: g(z) could be either ||z||_1, or ||z||_2^2. Default closed form solution for NORM1 would be soft-threshold, which is \n\
12: natively supported in admm.c with -tao_admm_regularizer_type soft-threshold. Or user can use regular TAO solver for \n\
13: either NORM1 or NORM2 or TAOSHELL, with -reg {1,2,3} \n\
14: Then, we augment both f and g, and solve it via ADMM. \n\
15: D is the M*N transform matrix so that D*x is sparse. \n";
17: typedef struct {
18: PetscInt M,N,K,reg;
19: PetscReal lambda,eps,mumin;
20: Mat A,ATA,H,Hx,D,Hz,DTD,HF;
21: Vec c,xlb,xub,x,b,workM,workN,workN2,workN3,xGT; /* observation b, ground truth xGT, the lower bound and upper bound of x*/
22: } AppCtx;
24: /*------------------------------------------------------------*/
26: PetscErrorCode NullJacobian(Tao tao,Vec X,Mat J,Mat Jpre,void *ptr)
27: {
29: return(0);
30: }
32: /*------------------------------------------------------------*/
34: static PetscErrorCode TaoShellSolve_SoftThreshold(Tao tao)
35: {
37: PetscReal lambda, mu;
38: AppCtx *user;
39: Vec out,work,y,x;
40: Tao admm_tao,misfit;
43: user = NULL;
44: mu = 0;
45: TaoGetADMMParentTao(tao,&admm_tao);
46: TaoADMMGetMisfitSubsolver(admm_tao, &misfit);
47: TaoADMMGetSpectralPenalty(admm_tao,&mu);
48: TaoShellGetContext(tao,&user);
50: lambda = user->lambda;
51: work = user->workN;
52: TaoGetSolutionVector(tao, &out);
53: TaoGetSolutionVector(misfit, &x);
54: TaoADMMGetDualVector(admm_tao, &y);
56: /* Dx + y/mu */
57: MatMult(user->D,x,work);
58: VecAXPY(work,1/mu,y);
60: /* soft thresholding */
61: TaoSoftThreshold(work, -lambda/mu, lambda/mu, out);
62: return(0);
63: }
65: /*------------------------------------------------------------*/
67: PetscErrorCode MisfitObjectiveAndGradient(Tao tao,Vec X,PetscReal *f,Vec g,void *ptr)
68: {
69: AppCtx *user = (AppCtx*)ptr;
73: /* Objective 0.5*||Ax-b||_2^2 */
74: MatMult(user->A,X,user->workM);
75: VecAXPY(user->workM,-1,user->b);
76: VecDot(user->workM,user->workM,f);
77: *f *= 0.5;
78: /* Gradient. ATAx-ATb */
79: MatMult(user->ATA,X,user->workN);
80: MatMultTranspose(user->A,user->b,user->workN2);
81: VecWAXPY(g,-1.,user->workN2,user->workN);
82: return(0);
83: }
85: /*------------------------------------------------------------*/
87: PetscErrorCode RegularizerObjectiveAndGradient1(Tao tao,Vec X,PetscReal *f_reg,Vec G_reg,void *ptr)
88: {
89: AppCtx *user = (AppCtx*)ptr;
93: /* compute regularizer objective
94: * f = f + lambda*sum(sqrt(y.^2+epsilon^2) - epsilon), where y = D*x */
95: VecCopy(X,user->workN2);
96: VecPow(user->workN2,2.);
97: VecShift(user->workN2,user->eps*user->eps);
98: VecSqrtAbs(user->workN2);
99: VecCopy(user->workN2, user->workN3);
100: VecShift(user->workN2,-user->eps);
101: VecSum(user->workN2,f_reg);
102: *f_reg *= user->lambda;
103: /* compute regularizer gradient = lambda*x */
104: VecPointwiseDivide(G_reg,X,user->workN3);
105: VecScale(G_reg,user->lambda);
106: return(0);
107: }
109: /*------------------------------------------------------------*/
111: PetscErrorCode RegularizerObjectiveAndGradient2(Tao tao,Vec X,PetscReal *f_reg,Vec G_reg,void *ptr)
112: {
113: AppCtx *user = (AppCtx*)ptr;
115: PetscReal temp;
118: /* compute regularizer objective = lambda*|z|_2^2 */
119: VecDot(X,X,&temp);
120: *f_reg = 0.5*user->lambda*temp;
121: /* compute regularizer gradient = lambda*z */
122: VecCopy(X,G_reg);
123: VecScale(G_reg,user->lambda);
124: return(0);
125: }
127: /*------------------------------------------------------------*/
129: static PetscErrorCode HessianMisfit(Tao tao, Vec x, Mat H, Mat Hpre, void *ptr)
130: {
132: return(0);
133: }
135: /*------------------------------------------------------------*/
137: static PetscErrorCode HessianReg(Tao tao, Vec x, Mat H, Mat Hpre, void *ptr)
138: {
139: AppCtx *user = (AppCtx*)ptr;
143: MatMult(user->D,x,user->workN);
144: VecPow(user->workN2,2.);
145: VecShift(user->workN2,user->eps*user->eps);
146: VecSqrtAbs(user->workN2);
147: VecShift(user->workN2,-user->eps);
148: VecReciprocal(user->workN2);
149: VecScale(user->workN2,user->eps*user->eps);
150: MatDiagonalSet(H,user->workN2,INSERT_VALUES);
151: return(0);
152: }
154: /*------------------------------------------------------------*/
156: PetscErrorCode FullObjGrad(Tao tao,Vec X,PetscReal *f,Vec g,void *ptr)
157: {
158: AppCtx *user = (AppCtx*)ptr;
160: PetscReal f_reg;
163: /* Objective 0.5*||Ax-b||_2^2 + lambda*||x||_2^2*/
164: MatMult(user->A,X,user->workM);
165: VecAXPY(user->workM,-1,user->b);
166: VecDot(user->workM,user->workM,f);
167: VecNorm(X,NORM_2,&f_reg);
168: *f *= 0.5;
169: *f += user->lambda*f_reg*f_reg;
170: /* Gradient. ATAx-ATb + 2*lambda*x */
171: MatMult(user->ATA,X,user->workN);
172: MatMultTranspose(user->A,user->b,user->workN2);
173: VecWAXPY(g,-1.,user->workN2,user->workN);
174: VecAXPY(g,2*user->lambda,X);
175: return(0);
176: }
177: /*------------------------------------------------------------*/
179: static PetscErrorCode HessianFull(Tao tao, Vec x, Mat H, Mat Hpre, void *ptr)
180: {
182: return(0);
183: }
184: /*------------------------------------------------------------*/
186: PetscErrorCode InitializeUserData(AppCtx *user)
187: {
188: 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". */
189: PetscViewer fd; /* used to load data from file */
191: PetscInt k,n;
192: PetscScalar v;
195: /* Load the A matrix, b vector, and xGT vector from a binary file. */
196: PetscViewerBinaryOpen(PETSC_COMM_WORLD,dataFile,FILE_MODE_READ,&fd);
197: MatCreate(PETSC_COMM_WORLD,&user->A);
198: MatSetType(user->A,MATAIJ);
199: MatLoad(user->A,fd);
200: VecCreate(PETSC_COMM_WORLD,&user->b);
201: VecLoad(user->b,fd);
202: VecCreate(PETSC_COMM_WORLD,&user->xGT);
203: VecLoad(user->xGT,fd);
204: PetscViewerDestroy(&fd);
206: MatGetSize(user->A,&user->M,&user->N);
208: MatCreate(PETSC_COMM_WORLD,&user->D);
209: MatSetSizes(user->D,PETSC_DECIDE,PETSC_DECIDE,user->N,user->N);
210: MatSetFromOptions(user->D);
211: MatSetUp(user->D);
212: for (k=0; k<user->N; k++) {
213: v = 1.0;
214: n = k+1;
215: if (k< user->N -1) {
216: MatSetValues(user->D,1,&k,1,&n,&v,INSERT_VALUES);
217: }
218: v = -1.0;
219: MatSetValues(user->D,1,&k,1,&k,&v,INSERT_VALUES);
220: }
221: MatAssemblyBegin(user->D,MAT_FINAL_ASSEMBLY);
222: MatAssemblyEnd(user->D,MAT_FINAL_ASSEMBLY);
224: MatTransposeMatMult(user->D,user->D,MAT_INITIAL_MATRIX,PETSC_DEFAULT,&user->DTD);
226: MatCreate(PETSC_COMM_WORLD,&user->Hz);
227: MatSetSizes(user->Hz,PETSC_DECIDE,PETSC_DECIDE,user->N,user->N);
228: MatSetFromOptions(user->Hz);
229: MatSetUp(user->Hz);
230: MatAssemblyBegin(user->Hz,MAT_FINAL_ASSEMBLY);
231: MatAssemblyEnd(user->Hz,MAT_FINAL_ASSEMBLY);
233: VecCreate(PETSC_COMM_WORLD,&(user->x));
234: VecCreate(PETSC_COMM_WORLD,&(user->workM));
235: VecCreate(PETSC_COMM_WORLD,&(user->workN));
236: VecCreate(PETSC_COMM_WORLD,&(user->workN2));
237: VecSetSizes(user->x,PETSC_DECIDE,user->N);
238: VecSetSizes(user->workM,PETSC_DECIDE,user->M);
239: VecSetSizes(user->workN,PETSC_DECIDE,user->N);
240: VecSetSizes(user->workN2,PETSC_DECIDE,user->N);
241: VecSetFromOptions(user->x);
242: VecSetFromOptions(user->workM);
243: VecSetFromOptions(user->workN);
244: VecSetFromOptions(user->workN2);
246: VecDuplicate(user->workN,&(user->workN3));
247: VecDuplicate(user->x,&(user->xlb));
248: VecDuplicate(user->x,&(user->xub));
249: VecDuplicate(user->x,&(user->c));
250: VecSet(user->xlb,0.0);
251: VecSet(user->c,0.0);
252: VecSet(user->xub,PETSC_INFINITY);
254: MatTransposeMatMult(user->A,user->A, MAT_INITIAL_MATRIX, PETSC_DEFAULT, &(user->ATA));
255: MatTransposeMatMult(user->A,user->A, MAT_INITIAL_MATRIX, PETSC_DEFAULT, &(user->Hx));
256: MatTransposeMatMult(user->A,user->A, MAT_INITIAL_MATRIX, PETSC_DEFAULT, &(user->HF));
258: MatAssemblyBegin(user->ATA,MAT_FINAL_ASSEMBLY);
259: MatAssemblyEnd(user->ATA,MAT_FINAL_ASSEMBLY);
260: MatAssemblyBegin(user->Hx,MAT_FINAL_ASSEMBLY);
261: MatAssemblyEnd(user->Hx,MAT_FINAL_ASSEMBLY);
262: MatAssemblyBegin(user->HF,MAT_FINAL_ASSEMBLY);
263: MatAssemblyEnd(user->HF,MAT_FINAL_ASSEMBLY);
265: user->lambda = 1.e-8;
266: user->eps = 1.e-3;
267: user->reg = 2;
268: user->mumin = 5.e-6;
270: PetscOptionsBegin(PETSC_COMM_WORLD, NULL, "Configure separable objection example", "tomographyADMM.c");
271: PetscOptionsInt("-reg","Regularization scheme for z solver (1,2)", "tomographyADMM.c", user->reg, &(user->reg), NULL);
272: PetscOptionsReal("-lambda", "The regularization multiplier. 1 default", "tomographyADMM.c", user->lambda, &(user->lambda), NULL);
273: PetscOptionsReal("-eps", "L1 norm epsilon padding", "tomographyADMM.c", user->eps, &(user->eps), NULL);
274: PetscOptionsReal("-mumin", "Minimum value for ADMM spectral penalty", "tomographyADMM.c", user->mumin, &(user->mumin), NULL);
275: PetscOptionsEnd();
276: return(0);
277: }
279: /*------------------------------------------------------------*/
281: PetscErrorCode DestroyContext(AppCtx *user)
282: {
286: MatDestroy(&user->A);
287: MatDestroy(&user->ATA);
288: MatDestroy(&user->Hx);
289: MatDestroy(&user->Hz);
290: MatDestroy(&user->HF);
291: MatDestroy(&user->D);
292: MatDestroy(&user->DTD);
293: VecDestroy(&user->xGT);
294: VecDestroy(&user->xlb);
295: VecDestroy(&user->xub);
296: VecDestroy(&user->b);
297: VecDestroy(&user->x);
298: VecDestroy(&user->c);
299: VecDestroy(&user->workN3);
300: VecDestroy(&user->workN2);
301: VecDestroy(&user->workN);
302: VecDestroy(&user->workM);
303: return(0);
304: }
306: /*------------------------------------------------------------*/
308: int main(int argc,char **argv)
309: {
311: Tao tao,misfit,reg;
312: PetscReal v1,v2;
313: AppCtx* user;
314: PetscViewer fd;
315: char resultFile[] = "tomographyResult_x";
317: PetscInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr;
318: PetscNew(&user);
319: InitializeUserData(user);
321: TaoCreate(PETSC_COMM_WORLD, &tao);
322: TaoSetType(tao, TAOADMM);
323: TaoSetInitialVector(tao, user->x);
324: /* f(x) + g(x) for parent tao */
325: TaoADMMSetSpectralPenalty(tao,1.);
326: TaoSetObjectiveAndGradientRoutine(tao, FullObjGrad, (void*)user);
327: MatShift(user->HF,user->lambda);
328: TaoSetHessianRoutine(tao, user->HF, user->HF, HessianFull, (void*)user);
330: /* f(x) for misfit tao */
331: TaoADMMSetMisfitObjectiveAndGradientRoutine(tao, MisfitObjectiveAndGradient, (void*)user);
332: TaoADMMSetMisfitHessianRoutine(tao, user->Hx, user->Hx, HessianMisfit, (void*)user);
333: TaoADMMSetMisfitHessianChangeStatus(tao,PETSC_FALSE);
334: TaoADMMSetMisfitConstraintJacobian(tao,user->D,user->D,NullJacobian,(void*)user);
336: /* g(x) for regularizer tao */
337: if (user->reg == 1) {
338: TaoADMMSetRegularizerObjectiveAndGradientRoutine(tao, RegularizerObjectiveAndGradient1, (void*)user);
339: TaoADMMSetRegularizerHessianRoutine(tao, user->Hz, user->Hz, HessianReg, (void*)user);
340: TaoADMMSetRegHessianChangeStatus(tao,PETSC_TRUE);
341: } else if (user->reg == 2) {
342: TaoADMMSetRegularizerObjectiveAndGradientRoutine(tao, RegularizerObjectiveAndGradient2, (void*)user);
343: MatShift(user->Hz,1);
344: MatScale(user->Hz,user->lambda);
345: TaoADMMSetRegularizerHessianRoutine(tao, user->Hz, user->Hz, HessianMisfit, (void*)user);
346: TaoADMMSetRegHessianChangeStatus(tao,PETSC_TRUE);
347: } else if (user->reg != 3) SETERRQ(PETSC_COMM_WORLD, PETSC_ERR_ARG_UNKNOWN_TYPE, "Incorrect Reg type"); /* TaoShell case */
349: /* Set type for the misfit solver */
350: TaoADMMGetMisfitSubsolver(tao, &misfit);
351: TaoADMMGetRegularizationSubsolver(tao, ®);
352: TaoSetType(misfit,TAONLS);
353: if (user->reg == 3) {
354: TaoSetType(reg,TAOSHELL);
355: TaoShellSetContext(reg, (void*) user);
356: TaoShellSetSolve(reg, TaoShellSolve_SoftThreshold);
357: } else {
358: TaoSetType(reg,TAONLS);
359: }
360: TaoSetVariableBounds(misfit,user->xlb,user->xub);
362: /* Soft Thresholding solves the ADMM problem with the L1 regularizer lambda*||z||_1 and the x-z=0 constraint */
363: TaoADMMSetRegularizerCoefficient(tao, user->lambda);
364: TaoADMMSetRegularizerConstraintJacobian(tao,NULL,NULL,NullJacobian,(void*)user);
365: TaoADMMSetMinimumSpectralPenalty(tao,user->mumin);
367: TaoADMMSetConstraintVectorRHS(tao,user->c);
368: TaoSetFromOptions(tao);
369: TaoSolve(tao);
371: /* Save x (reconstruction of object) vector to a binary file, which maybe read from Matlab and convert to a 2D image for comparison. */
372: PetscViewerBinaryOpen(PETSC_COMM_WORLD,resultFile,FILE_MODE_WRITE,&fd);
373: VecView(user->x,fd);
374: PetscViewerDestroy(&fd);
376: /* compute the error */
377: VecAXPY(user->x,-1,user->xGT);
378: VecNorm(user->x,NORM_2,&v1);
379: VecNorm(user->xGT,NORM_2,&v2);
380: PetscPrintf(PETSC_COMM_WORLD, "relative reconstruction error: ||x-xGT||/||xGT|| = %6.4e.\n", (double)(v1/v2));
382: /* Free TAO data structures */
383: TaoDestroy(&tao);
384: DestroyContext(user);
385: PetscFree(user);
386: PetscFinalize();
387: return ierr;
388: }
390: /*TEST
392: build:
393: requires: !complex !single !__float128 !defined(PETSC_USE_64BIT_INDICES)
395: test:
396: suffix: 1
397: localrunfiles: tomographyData_A_b_xGT
398: args: -lambda 1.e-8 -tao_monitor -tao_type nls -tao_nls_pc_type icc
400: test:
401: suffix: 2
402: localrunfiles: tomographyData_A_b_xGT
403: args: -reg 2 -lambda 1.e-8 -tao_admm_dual_update update_basic -tao_admm_regularizer_type regularizer_user -tao_max_it 20 -tao_monitor -tao_admm_tolerance_update_factor 1.e-8 -misfit_tao_nls_pc_type icc -misfit_tao_monitor -reg_tao_monitor
405: test:
406: suffix: 3
407: localrunfiles: tomographyData_A_b_xGT
408: args: -lambda 1.e-8 -tao_admm_dual_update update_basic -tao_admm_regularizer_type regularizer_soft_thresh -tao_max_it 20 -tao_monitor -tao_admm_tolerance_update_factor 1.e-8 -misfit_tao_nls_pc_type icc -misfit_tao_monitor
410: test:
411: suffix: 4
412: localrunfiles: tomographyData_A_b_xGT
413: args: -lambda 1.e-8 -tao_admm_dual_update update_adaptive -tao_admm_regularizer_type regularizer_soft_thresh -tao_max_it 20 -tao_monitor -misfit_tao_monitor -misfit_tao_nls_pc_type icc
415: test:
416: suffix: 5
417: localrunfiles: tomographyData_A_b_xGT
418: args: -reg 2 -lambda 1.e-8 -tao_admm_dual_update update_adaptive -tao_admm_regularizer_type regularizer_user -tao_max_it 20 -tao_monitor -tao_admm_tolerance_update_factor 1.e-8 -misfit_tao_monitor -reg_tao_monitor -misfit_tao_nls_pc_type icc
420: test:
421: suffix: 6
422: localrunfiles: tomographyData_A_b_xGT
423: args: -reg 3 -lambda 1.e-8 -tao_admm_dual_update update_adaptive -tao_admm_regularizer_type regularizer_user -tao_max_it 20 -tao_monitor -tao_admm_tolerance_update_factor 1.e-8 -misfit_tao_monitor -reg_tao_monitor -misfit_tao_nls_pc_type icc
425: TEST*/