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: {
28: PetscFunctionBegin;
29: PetscFunctionReturn(PETSC_SUCCESS);
30: }
32: /*------------------------------------------------------------*/
34: static PetscErrorCode TaoShellSolve_SoftThreshold(Tao tao)
35: {
36: PetscReal lambda, mu;
37: AppCtx *user;
38: Vec out, work, y, x;
39: Tao admm_tao, misfit;
41: PetscFunctionBegin;
42: user = NULL;
43: mu = 0;
44: PetscCall(TaoGetADMMParentTao(tao, &admm_tao));
45: PetscCall(TaoADMMGetMisfitSubsolver(admm_tao, &misfit));
46: PetscCall(TaoADMMGetSpectralPenalty(admm_tao, &mu));
47: PetscCall(TaoShellGetContext(tao, &user));
49: lambda = user->lambda;
50: work = user->workN;
51: PetscCall(TaoGetSolution(tao, &out));
52: PetscCall(TaoGetSolution(misfit, &x));
53: PetscCall(TaoADMMGetDualVector(admm_tao, &y));
55: /* Dx + y/mu */
56: PetscCall(MatMult(user->D, x, work));
57: PetscCall(VecAXPY(work, 1 / mu, y));
59: /* soft thresholding */
60: PetscCall(TaoSoftThreshold(work, -lambda / mu, lambda / mu, out));
61: PetscFunctionReturn(PETSC_SUCCESS);
62: }
64: /*------------------------------------------------------------*/
66: PetscErrorCode MisfitObjectiveAndGradient(Tao tao, Vec X, PetscReal *f, Vec g, void *ptr)
67: {
68: AppCtx *user = (AppCtx *)ptr;
70: PetscFunctionBegin;
71: /* Objective 0.5*||Ax-b||_2^2 */
72: PetscCall(MatMult(user->A, X, user->workM));
73: PetscCall(VecAXPY(user->workM, -1, user->b));
74: PetscCall(VecDot(user->workM, user->workM, f));
75: *f *= 0.5;
76: /* Gradient. ATAx-ATb */
77: PetscCall(MatMult(user->ATA, X, user->workN));
78: PetscCall(MatMultTranspose(user->A, user->b, user->workN2));
79: PetscCall(VecWAXPY(g, -1., user->workN2, user->workN));
80: PetscFunctionReturn(PETSC_SUCCESS);
81: }
83: /*------------------------------------------------------------*/
85: PetscErrorCode RegularizerObjectiveAndGradient1(Tao tao, Vec X, PetscReal *f_reg, Vec G_reg, void *ptr)
86: {
87: AppCtx *user = (AppCtx *)ptr;
89: PetscFunctionBegin;
90: /* compute regularizer objective
91: * f = f + lambda*sum(sqrt(y.^2+epsilon^2) - epsilon), where y = D*x */
92: PetscCall(VecCopy(X, user->workN2));
93: PetscCall(VecPow(user->workN2, 2.));
94: PetscCall(VecShift(user->workN2, user->eps * user->eps));
95: PetscCall(VecSqrtAbs(user->workN2));
96: PetscCall(VecCopy(user->workN2, user->workN3));
97: PetscCall(VecShift(user->workN2, -user->eps));
98: PetscCall(VecSum(user->workN2, f_reg));
99: *f_reg *= user->lambda;
100: /* compute regularizer gradient = lambda*x */
101: PetscCall(VecPointwiseDivide(G_reg, X, user->workN3));
102: PetscCall(VecScale(G_reg, user->lambda));
103: PetscFunctionReturn(PETSC_SUCCESS);
104: }
106: /*------------------------------------------------------------*/
108: PetscErrorCode RegularizerObjectiveAndGradient2(Tao tao, Vec X, PetscReal *f_reg, Vec G_reg, void *ptr)
109: {
110: AppCtx *user = (AppCtx *)ptr;
111: PetscReal temp;
113: PetscFunctionBegin;
114: /* compute regularizer objective = lambda*|z|_2^2 */
115: PetscCall(VecDot(X, X, &temp));
116: *f_reg = 0.5 * user->lambda * temp;
117: /* compute regularizer gradient = lambda*z */
118: PetscCall(VecCopy(X, G_reg));
119: PetscCall(VecScale(G_reg, user->lambda));
120: PetscFunctionReturn(PETSC_SUCCESS);
121: }
123: /*------------------------------------------------------------*/
125: static PetscErrorCode HessianMisfit(Tao tao, Vec x, Mat H, Mat Hpre, void *ptr)
126: {
127: PetscFunctionBegin;
128: PetscFunctionReturn(PETSC_SUCCESS);
129: }
131: /*------------------------------------------------------------*/
133: static PetscErrorCode HessianReg(Tao tao, Vec x, Mat H, Mat Hpre, void *ptr)
134: {
135: AppCtx *user = (AppCtx *)ptr;
137: PetscFunctionBegin;
138: PetscCall(MatMult(user->D, x, user->workN));
139: PetscCall(VecPow(user->workN2, 2.));
140: PetscCall(VecShift(user->workN2, user->eps * user->eps));
141: PetscCall(VecSqrtAbs(user->workN2));
142: PetscCall(VecShift(user->workN2, -user->eps));
143: PetscCall(VecReciprocal(user->workN2));
144: PetscCall(VecScale(user->workN2, user->eps * user->eps));
145: PetscCall(MatDiagonalSet(H, user->workN2, INSERT_VALUES));
146: PetscFunctionReturn(PETSC_SUCCESS);
147: }
149: /*------------------------------------------------------------*/
151: PetscErrorCode FullObjGrad(Tao tao, Vec X, PetscReal *f, Vec g, void *ptr)
152: {
153: AppCtx *user = (AppCtx *)ptr;
154: PetscReal f_reg;
156: PetscFunctionBegin;
157: /* Objective 0.5*||Ax-b||_2^2 + lambda*||x||_2^2*/
158: PetscCall(MatMult(user->A, X, user->workM));
159: PetscCall(VecAXPY(user->workM, -1, user->b));
160: PetscCall(VecDot(user->workM, user->workM, f));
161: PetscCall(VecNorm(X, NORM_2, &f_reg));
162: *f *= 0.5;
163: *f += user->lambda * f_reg * f_reg;
164: /* Gradient. ATAx-ATb + 2*lambda*x */
165: PetscCall(MatMult(user->ATA, X, user->workN));
166: PetscCall(MatMultTranspose(user->A, user->b, user->workN2));
167: PetscCall(VecWAXPY(g, -1., user->workN2, user->workN));
168: PetscCall(VecAXPY(g, 2 * user->lambda, X));
169: PetscFunctionReturn(PETSC_SUCCESS);
170: }
171: /*------------------------------------------------------------*/
173: static PetscErrorCode HessianFull(Tao tao, Vec x, Mat H, Mat Hpre, void *ptr)
174: {
175: PetscFunctionBegin;
176: PetscFunctionReturn(PETSC_SUCCESS);
177: }
178: /*------------------------------------------------------------*/
180: PetscErrorCode InitializeUserData(AppCtx *user)
181: {
182: 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". */
183: PetscViewer fd; /* used to load data from file */
184: PetscInt k, n;
185: PetscScalar v;
187: PetscFunctionBegin;
188: /* Load the A matrix, b vector, and xGT vector from a binary file. */
189: PetscCall(PetscViewerBinaryOpen(PETSC_COMM_WORLD, dataFile, FILE_MODE_READ, &fd));
190: PetscCall(MatCreate(PETSC_COMM_WORLD, &user->A));
191: PetscCall(MatSetType(user->A, MATAIJ));
192: PetscCall(MatLoad(user->A, fd));
193: PetscCall(VecCreate(PETSC_COMM_WORLD, &user->b));
194: PetscCall(VecLoad(user->b, fd));
195: PetscCall(VecCreate(PETSC_COMM_WORLD, &user->xGT));
196: PetscCall(VecLoad(user->xGT, fd));
197: PetscCall(PetscViewerDestroy(&fd));
199: PetscCall(MatGetSize(user->A, &user->M, &user->N));
201: PetscCall(MatCreate(PETSC_COMM_WORLD, &user->D));
202: PetscCall(MatSetSizes(user->D, PETSC_DECIDE, PETSC_DECIDE, user->N, user->N));
203: PetscCall(MatSetFromOptions(user->D));
204: PetscCall(MatSetUp(user->D));
205: for (k = 0; k < user->N; k++) {
206: v = 1.0;
207: n = k + 1;
208: if (k < user->N - 1) PetscCall(MatSetValues(user->D, 1, &k, 1, &n, &v, INSERT_VALUES));
209: v = -1.0;
210: PetscCall(MatSetValues(user->D, 1, &k, 1, &k, &v, INSERT_VALUES));
211: }
212: PetscCall(MatAssemblyBegin(user->D, MAT_FINAL_ASSEMBLY));
213: PetscCall(MatAssemblyEnd(user->D, MAT_FINAL_ASSEMBLY));
215: PetscCall(MatTransposeMatMult(user->D, user->D, MAT_INITIAL_MATRIX, PETSC_DEFAULT, &user->DTD));
217: PetscCall(MatCreate(PETSC_COMM_WORLD, &user->Hz));
218: PetscCall(MatSetSizes(user->Hz, PETSC_DECIDE, PETSC_DECIDE, user->N, user->N));
219: PetscCall(MatSetFromOptions(user->Hz));
220: PetscCall(MatSetUp(user->Hz));
221: PetscCall(MatAssemblyBegin(user->Hz, MAT_FINAL_ASSEMBLY));
222: PetscCall(MatAssemblyEnd(user->Hz, MAT_FINAL_ASSEMBLY));
224: PetscCall(VecCreate(PETSC_COMM_WORLD, &(user->x)));
225: PetscCall(VecCreate(PETSC_COMM_WORLD, &(user->workM)));
226: PetscCall(VecCreate(PETSC_COMM_WORLD, &(user->workN)));
227: PetscCall(VecCreate(PETSC_COMM_WORLD, &(user->workN2)));
228: PetscCall(VecSetSizes(user->x, PETSC_DECIDE, user->N));
229: PetscCall(VecSetSizes(user->workM, PETSC_DECIDE, user->M));
230: PetscCall(VecSetSizes(user->workN, PETSC_DECIDE, user->N));
231: PetscCall(VecSetSizes(user->workN2, PETSC_DECIDE, user->N));
232: PetscCall(VecSetFromOptions(user->x));
233: PetscCall(VecSetFromOptions(user->workM));
234: PetscCall(VecSetFromOptions(user->workN));
235: PetscCall(VecSetFromOptions(user->workN2));
237: PetscCall(VecDuplicate(user->workN, &(user->workN3)));
238: PetscCall(VecDuplicate(user->x, &(user->xlb)));
239: PetscCall(VecDuplicate(user->x, &(user->xub)));
240: PetscCall(VecDuplicate(user->x, &(user->c)));
241: PetscCall(VecSet(user->xlb, 0.0));
242: PetscCall(VecSet(user->c, 0.0));
243: PetscCall(VecSet(user->xub, PETSC_INFINITY));
245: PetscCall(MatTransposeMatMult(user->A, user->A, MAT_INITIAL_MATRIX, PETSC_DEFAULT, &(user->ATA)));
246: PetscCall(MatTransposeMatMult(user->A, user->A, MAT_INITIAL_MATRIX, PETSC_DEFAULT, &(user->Hx)));
247: PetscCall(MatTransposeMatMult(user->A, user->A, MAT_INITIAL_MATRIX, PETSC_DEFAULT, &(user->HF)));
249: PetscCall(MatAssemblyBegin(user->ATA, MAT_FINAL_ASSEMBLY));
250: PetscCall(MatAssemblyEnd(user->ATA, MAT_FINAL_ASSEMBLY));
251: PetscCall(MatAssemblyBegin(user->Hx, MAT_FINAL_ASSEMBLY));
252: PetscCall(MatAssemblyEnd(user->Hx, MAT_FINAL_ASSEMBLY));
253: PetscCall(MatAssemblyBegin(user->HF, MAT_FINAL_ASSEMBLY));
254: PetscCall(MatAssemblyEnd(user->HF, MAT_FINAL_ASSEMBLY));
256: user->lambda = 1.e-8;
257: user->eps = 1.e-3;
258: user->reg = 2;
259: user->mumin = 5.e-6;
261: PetscOptionsBegin(PETSC_COMM_WORLD, NULL, "Configure separable objection example", "tomographyADMM.c");
262: PetscCall(PetscOptionsInt("-reg", "Regularization scheme for z solver (1,2)", "tomographyADMM.c", user->reg, &(user->reg), NULL));
263: PetscCall(PetscOptionsReal("-lambda", "The regularization multiplier. 1 default", "tomographyADMM.c", user->lambda, &(user->lambda), NULL));
264: PetscCall(PetscOptionsReal("-eps", "L1 norm epsilon padding", "tomographyADMM.c", user->eps, &(user->eps), NULL));
265: PetscCall(PetscOptionsReal("-mumin", "Minimum value for ADMM spectral penalty", "tomographyADMM.c", user->mumin, &(user->mumin), NULL));
266: PetscOptionsEnd();
267: PetscFunctionReturn(PETSC_SUCCESS);
268: }
270: /*------------------------------------------------------------*/
272: PetscErrorCode DestroyContext(AppCtx *user)
273: {
274: PetscFunctionBegin;
275: PetscCall(MatDestroy(&user->A));
276: PetscCall(MatDestroy(&user->ATA));
277: PetscCall(MatDestroy(&user->Hx));
278: PetscCall(MatDestroy(&user->Hz));
279: PetscCall(MatDestroy(&user->HF));
280: PetscCall(MatDestroy(&user->D));
281: PetscCall(MatDestroy(&user->DTD));
282: PetscCall(VecDestroy(&user->xGT));
283: PetscCall(VecDestroy(&user->xlb));
284: PetscCall(VecDestroy(&user->xub));
285: PetscCall(VecDestroy(&user->b));
286: PetscCall(VecDestroy(&user->x));
287: PetscCall(VecDestroy(&user->c));
288: PetscCall(VecDestroy(&user->workN3));
289: PetscCall(VecDestroy(&user->workN2));
290: PetscCall(VecDestroy(&user->workN));
291: PetscCall(VecDestroy(&user->workM));
292: PetscFunctionReturn(PETSC_SUCCESS);
293: }
295: /*------------------------------------------------------------*/
297: int main(int argc, char **argv)
298: {
299: Tao tao, misfit, reg;
300: PetscReal v1, v2;
301: AppCtx *user;
302: PetscViewer fd;
303: char resultFile[] = "tomographyResult_x";
305: PetscFunctionBeginUser;
306: PetscCall(PetscInitialize(&argc, &argv, (char *)0, help));
307: PetscCall(PetscNew(&user));
308: PetscCall(InitializeUserData(user));
310: PetscCall(TaoCreate(PETSC_COMM_WORLD, &tao));
311: PetscCall(TaoSetType(tao, TAOADMM));
312: PetscCall(TaoSetSolution(tao, user->x));
313: /* f(x) + g(x) for parent tao */
314: PetscCall(TaoADMMSetSpectralPenalty(tao, 1.));
315: PetscCall(TaoSetObjectiveAndGradient(tao, NULL, FullObjGrad, (void *)user));
316: PetscCall(MatShift(user->HF, user->lambda));
317: PetscCall(TaoSetHessian(tao, user->HF, user->HF, HessianFull, (void *)user));
319: /* f(x) for misfit tao */
320: PetscCall(TaoADMMSetMisfitObjectiveAndGradientRoutine(tao, MisfitObjectiveAndGradient, (void *)user));
321: PetscCall(TaoADMMSetMisfitHessianRoutine(tao, user->Hx, user->Hx, HessianMisfit, (void *)user));
322: PetscCall(TaoADMMSetMisfitHessianChangeStatus(tao, PETSC_FALSE));
323: PetscCall(TaoADMMSetMisfitConstraintJacobian(tao, user->D, user->D, NullJacobian, (void *)user));
325: /* g(x) for regularizer tao */
326: if (user->reg == 1) {
327: PetscCall(TaoADMMSetRegularizerObjectiveAndGradientRoutine(tao, RegularizerObjectiveAndGradient1, (void *)user));
328: PetscCall(TaoADMMSetRegularizerHessianRoutine(tao, user->Hz, user->Hz, HessianReg, (void *)user));
329: PetscCall(TaoADMMSetRegHessianChangeStatus(tao, PETSC_TRUE));
330: } else if (user->reg == 2) {
331: PetscCall(TaoADMMSetRegularizerObjectiveAndGradientRoutine(tao, RegularizerObjectiveAndGradient2, (void *)user));
332: PetscCall(MatShift(user->Hz, 1));
333: PetscCall(MatScale(user->Hz, user->lambda));
334: PetscCall(TaoADMMSetRegularizerHessianRoutine(tao, user->Hz, user->Hz, HessianMisfit, (void *)user));
335: PetscCall(TaoADMMSetRegHessianChangeStatus(tao, PETSC_TRUE));
336: } else PetscCheck(user->reg == 3, PETSC_COMM_WORLD, PETSC_ERR_ARG_UNKNOWN_TYPE, "Incorrect Reg type"); /* TaoShell case */
338: /* Set type for the misfit solver */
339: PetscCall(TaoADMMGetMisfitSubsolver(tao, &misfit));
340: PetscCall(TaoADMMGetRegularizationSubsolver(tao, ®));
341: PetscCall(TaoSetType(misfit, TAONLS));
342: if (user->reg == 3) {
343: PetscCall(TaoSetType(reg, TAOSHELL));
344: PetscCall(TaoShellSetContext(reg, (void *)user));
345: PetscCall(TaoShellSetSolve(reg, TaoShellSolve_SoftThreshold));
346: } else {
347: PetscCall(TaoSetType(reg, TAONLS));
348: }
349: PetscCall(TaoSetVariableBounds(misfit, user->xlb, user->xub));
351: /* Soft Thresholding solves the ADMM problem with the L1 regularizer lambda*||z||_1 and the x-z=0 constraint */
352: PetscCall(TaoADMMSetRegularizerCoefficient(tao, user->lambda));
353: PetscCall(TaoADMMSetRegularizerConstraintJacobian(tao, NULL, NULL, NullJacobian, (void *)user));
354: PetscCall(TaoADMMSetMinimumSpectralPenalty(tao, user->mumin));
356: PetscCall(TaoADMMSetConstraintVectorRHS(tao, user->c));
357: PetscCall(TaoSetFromOptions(tao));
358: PetscCall(TaoSolve(tao));
360: /* Save x (reconstruction of object) vector to a binary file, which maybe read from Matlab and convert to a 2D image for comparison. */
361: PetscCall(PetscViewerBinaryOpen(PETSC_COMM_WORLD, resultFile, FILE_MODE_WRITE, &fd));
362: PetscCall(VecView(user->x, fd));
363: PetscCall(PetscViewerDestroy(&fd));
365: /* compute the error */
366: PetscCall(VecAXPY(user->x, -1, user->xGT));
367: PetscCall(VecNorm(user->x, NORM_2, &v1));
368: PetscCall(VecNorm(user->xGT, NORM_2, &v2));
369: PetscCall(PetscPrintf(PETSC_COMM_WORLD, "relative reconstruction error: ||x-xGT||/||xGT|| = %6.4e.\n", (double)(v1 / v2)));
371: /* Free TAO data structures */
372: PetscCall(TaoDestroy(&tao));
373: PetscCall(DestroyContext(user));
374: PetscCall(PetscFree(user));
375: PetscCall(PetscFinalize());
376: return 0;
377: }
379: /*TEST
381: build:
382: requires: !complex !single !__float128 !defined(PETSC_USE_64BIT_INDICES)
384: test:
385: suffix: 1
386: localrunfiles: tomographyData_A_b_xGT
387: args: -lambda 1.e-8 -tao_monitor -tao_type nls -tao_nls_pc_type icc
389: test:
390: suffix: 2
391: localrunfiles: tomographyData_A_b_xGT
392: 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
394: test:
395: suffix: 3
396: localrunfiles: tomographyData_A_b_xGT
397: 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
399: test:
400: suffix: 4
401: localrunfiles: tomographyData_A_b_xGT
402: 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
404: test:
405: suffix: 5
406: localrunfiles: tomographyData_A_b_xGT
407: 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
409: test:
410: suffix: 6
411: localrunfiles: tomographyData_A_b_xGT
412: 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
414: TEST*/