1 /* XH: todo add cs1f.F90 and asjust makefile */ 2 /* 3 Include "petsctao.h" so that we can use TAO solvers. Note that this 4 file automatically includes libraries such as: 5 petsc.h - base PETSc routines petscvec.h - vectors 6 petscsys.h - system routines petscmat.h - matrices 7 petscis.h - index sets petscksp.h - Krylov subspace methods 8 petscviewer.h - viewers petscpc.h - preconditioners 9 10 */ 11 12 #include <petsctao.h> 13 14 /* 15 Description: Compressive sensing test example 1. 16 0.5*||Ax-b||^2 + lambda*||D*x||_1 17 Xiang Huang: Nov 19, 2018 18 19 Reference: None 20 */ 21 22 static char help[] = "Finds the least-squares solution to the under constraint linear model Ax = b, with L1-norm regularizer. \n\ 23 A is a M*N real matrix (M<N), x is sparse. \n\ 24 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\ 25 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"; 26 27 #define M 3 28 #define N 5 29 #define K 4 30 31 /* User-defined application context */ 32 typedef struct { 33 /* Working space. linear least square: f(x) = A*x - b */ 34 PetscReal A[M][N]; /* array of coefficients */ 35 PetscReal b[M]; /* array of observations */ 36 PetscReal xGT[M]; /* array of ground truth object, which can be used to compare the reconstruction result */ 37 PetscReal D[K][N]; /* array of coefficients for 0.5*||Ax-b||^2 + lambda*||D*x||_1 */ 38 PetscReal J[M][N]; /* dense jacobian matrix array. For linear least square, J = A. For nonlinear least square, it is different from A */ 39 PetscInt idm[M]; /* Matrix row, column indices for jacobian and dictionary */ 40 PetscInt idn[N]; 41 PetscInt idk[K]; 42 } AppCtx; 43 44 /* User provided Routines */ 45 PetscErrorCode InitializeUserData(AppCtx *); 46 PetscErrorCode FormStartingPoint(Vec); 47 PetscErrorCode FormDictionaryMatrix(Mat, AppCtx *); 48 PetscErrorCode EvaluateFunction(Tao, Vec, Vec, void *); 49 PetscErrorCode EvaluateJacobian(Tao, Vec, Mat, Mat, void *); 50 51 /*--------------------------------------------------------------------*/ 52 int main(int argc, char **argv) { 53 Vec x, f; /* solution, function f(x) = A*x-b */ 54 Mat J, D; /* Jacobian matrix, Transform matrix */ 55 Tao tao; /* Tao solver context */ 56 PetscInt i; /* iteration information */ 57 PetscReal hist[100], resid[100]; 58 PetscInt lits[100]; 59 AppCtx user; /* user-defined work context */ 60 61 PetscFunctionBeginUser; 62 PetscCall(PetscInitialize(&argc, &argv, (char *)0, help)); 63 64 /* Allocate solution and vector function vectors */ 65 PetscCall(VecCreateSeq(PETSC_COMM_SELF, N, &x)); 66 PetscCall(VecCreateSeq(PETSC_COMM_SELF, M, &f)); 67 68 /* Allocate Jacobian and Dictionary matrix. */ 69 PetscCall(MatCreateSeqDense(PETSC_COMM_SELF, M, N, NULL, &J)); 70 PetscCall(MatCreateSeqDense(PETSC_COMM_SELF, K, N, NULL, &D)); /* XH: TODO: dense -> sparse/dense/shell etc, do it on fly */ 71 72 for (i = 0; i < M; i++) user.idm[i] = i; 73 for (i = 0; i < N; i++) user.idn[i] = i; 74 for (i = 0; i < K; i++) user.idk[i] = i; 75 76 /* Create TAO solver and set desired solution method */ 77 PetscCall(TaoCreate(PETSC_COMM_SELF, &tao)); 78 PetscCall(TaoSetType(tao, TAOBRGN)); 79 80 /* User set application context: A, D matrice, and b vector. */ 81 PetscCall(InitializeUserData(&user)); 82 83 /* Set initial guess */ 84 PetscCall(FormStartingPoint(x)); 85 86 /* Fill the content of matrix D from user application Context */ 87 PetscCall(FormDictionaryMatrix(D, &user)); 88 89 /* Bind x to tao->solution. */ 90 PetscCall(TaoSetSolution(tao, x)); 91 /* Bind D to tao->data->D */ 92 PetscCall(TaoBRGNSetDictionaryMatrix(tao, D)); 93 94 /* Set the function and Jacobian routines. */ 95 PetscCall(TaoSetResidualRoutine(tao, f, EvaluateFunction, (void *)&user)); 96 PetscCall(TaoSetJacobianResidualRoutine(tao, J, J, EvaluateJacobian, (void *)&user)); 97 98 /* Check for any TAO command line arguments */ 99 PetscCall(TaoSetFromOptions(tao)); 100 101 PetscCall(TaoSetConvergenceHistory(tao, hist, resid, 0, lits, 100, PETSC_TRUE)); 102 103 /* Perform the Solve */ 104 PetscCall(TaoSolve(tao)); 105 106 /* XH: Debug: View the result, function and Jacobian. */ 107 PetscCall(PetscPrintf(PETSC_COMM_SELF, "-------- result x, residual f=A*x-b, and Jacobian=A. -------- \n")); 108 PetscCall(VecView(x, PETSC_VIEWER_STDOUT_SELF)); 109 PetscCall(VecView(f, PETSC_VIEWER_STDOUT_SELF)); 110 PetscCall(MatView(J, PETSC_VIEWER_STDOUT_SELF)); 111 PetscCall(MatView(D, PETSC_VIEWER_STDOUT_SELF)); 112 113 /* Free TAO data structures */ 114 PetscCall(TaoDestroy(&tao)); 115 116 /* Free PETSc data structures */ 117 PetscCall(VecDestroy(&x)); 118 PetscCall(VecDestroy(&f)); 119 PetscCall(MatDestroy(&J)); 120 PetscCall(MatDestroy(&D)); 121 122 PetscCall(PetscFinalize()); 123 return 0; 124 } 125 126 /*--------------------------------------------------------------------*/ 127 PetscErrorCode EvaluateFunction(Tao tao, Vec X, Vec F, void *ptr) { 128 AppCtx *user = (AppCtx *)ptr; 129 PetscInt m, n; 130 const PetscReal *x; 131 PetscReal *b = user->b, *f; 132 133 PetscFunctionBegin; 134 PetscCall(VecGetArrayRead(X, &x)); 135 PetscCall(VecGetArray(F, &f)); 136 137 /* Even for linear least square, we do not direct use matrix operation f = A*x - b now, just for future modification and compatibility for nonlinear least square */ 138 for (m = 0; m < M; m++) { 139 f[m] = -b[m]; 140 for (n = 0; n < N; n++) { f[m] += user->A[m][n] * x[n]; } 141 } 142 PetscCall(VecRestoreArrayRead(X, &x)); 143 PetscCall(VecRestoreArray(F, &f)); 144 PetscLogFlops(2.0 * M * N); 145 PetscFunctionReturn(0); 146 } 147 148 /*------------------------------------------------------------*/ 149 /* J[m][n] = df[m]/dx[n] */ 150 PetscErrorCode EvaluateJacobian(Tao tao, Vec X, Mat J, Mat Jpre, void *ptr) { 151 AppCtx *user = (AppCtx *)ptr; 152 PetscInt m, n; 153 const PetscReal *x; 154 155 PetscFunctionBegin; 156 PetscCall(VecGetArrayRead(X, &x)); /* not used for linear least square, but keep for future nonlinear least square) */ 157 /* XH: TODO: For linear least square, we can just set J=A fixed once, instead of keep update it! Maybe just create a function getFixedJacobian? 158 For nonlinear least square, we require x to compute J, keep codes here for future nonlinear least square*/ 159 for (m = 0; m < M; ++m) { 160 for (n = 0; n < N; ++n) { user->J[m][n] = user->A[m][n]; } 161 } 162 163 PetscCall(MatSetValues(J, M, user->idm, N, user->idn, (PetscReal *)user->J, INSERT_VALUES)); 164 PetscCall(MatAssemblyBegin(J, MAT_FINAL_ASSEMBLY)); 165 PetscCall(MatAssemblyEnd(J, MAT_FINAL_ASSEMBLY)); 166 167 PetscCall(VecRestoreArrayRead(X, &x)); /* not used for linear least square, but keep for future nonlinear least square) */ 168 PetscLogFlops(0); /* 0 for linear least square, >0 for nonlinear least square */ 169 PetscFunctionReturn(0); 170 } 171 172 /* ------------------------------------------------------------ */ 173 /* Currently fixed matrix, in future may be dynamic for D(x)? */ 174 PetscErrorCode FormDictionaryMatrix(Mat D, AppCtx *user) { 175 PetscFunctionBegin; 176 PetscCall(MatSetValues(D, K, user->idk, N, user->idn, (PetscReal *)user->D, INSERT_VALUES)); 177 PetscCall(MatAssemblyBegin(D, MAT_FINAL_ASSEMBLY)); 178 PetscCall(MatAssemblyEnd(D, MAT_FINAL_ASSEMBLY)); 179 180 PetscLogFlops(0); /* 0 for fixed dictionary matrix, >0 for varying dictionary matrix */ 181 PetscFunctionReturn(0); 182 } 183 184 /* ------------------------------------------------------------ */ 185 PetscErrorCode FormStartingPoint(Vec X) { 186 PetscFunctionBegin; 187 PetscCall(VecSet(X, 0.0)); 188 PetscFunctionReturn(0); 189 } 190 191 /* ---------------------------------------------------------------------- */ 192 PetscErrorCode InitializeUserData(AppCtx *user) { 193 PetscReal *b = user->b; /* **A=user->A, but we don't kown the dimension of A in this way, how to fix? */ 194 PetscInt m, n, k; /* loop index for M,N,K dimension. */ 195 196 PetscFunctionBegin; 197 /* b = A*x while x = [0;0;1;0;0] here*/ 198 m = 0; 199 b[m++] = 0.28; 200 b[m++] = 0.55; 201 b[m++] = 0.96; 202 203 /* matlab generated random matrix, uniformly distributed in [0,1] with 2 digits accuracy. rng(0); A = rand(M, N); A = round(A*100)/100; 204 A = [0.81 0.91 0.28 0.96 0.96 205 0.91 0.63 0.55 0.16 0.49 206 0.13 0.10 0.96 0.97 0.80] 207 */ 208 m = 0; 209 n = 0; 210 user->A[m][n++] = 0.81; 211 user->A[m][n++] = 0.91; 212 user->A[m][n++] = 0.28; 213 user->A[m][n++] = 0.96; 214 user->A[m][n++] = 0.96; 215 ++m; 216 n = 0; 217 user->A[m][n++] = 0.91; 218 user->A[m][n++] = 0.63; 219 user->A[m][n++] = 0.55; 220 user->A[m][n++] = 0.16; 221 user->A[m][n++] = 0.49; 222 ++m; 223 n = 0; 224 user->A[m][n++] = 0.13; 225 user->A[m][n++] = 0.10; 226 user->A[m][n++] = 0.96; 227 user->A[m][n++] = 0.97; 228 user->A[m][n++] = 0.80; 229 230 /* initialize to 0 */ 231 for (k = 0; k < K; k++) { 232 for (n = 0; n < N; n++) { user->D[k][n] = 0.0; } 233 } 234 /* Choice I: set D to identity matrix of size N*N for testing */ 235 /* for (k=0; k<K; k++) user->D[k][k] = 1.0; */ 236 /* Choice II: set D to Backward difference matrix of size (N-1)*N, with zero extended boundary assumption */ 237 for (k = 0; k < K; k++) { 238 user->D[k][k] = -1.0; 239 user->D[k][k + 1] = 1.0; 240 } 241 242 PetscFunctionReturn(0); 243 } 244 245 /*TEST 246 247 build: 248 requires: !complex !single !quad !defined(PETSC_USE_64BIT_INDICES) 249 250 test: 251 localrunfiles: cs1Data_A_b_xGT 252 args: -tao_smonitor -tao_max_it 100 -tao_type pounders -tao_gatol 1.e-6 253 254 test: 255 suffix: 2 256 localrunfiles: cs1Data_A_b_xGT 257 args: -tao_monitor -tao_max_it 100 -tao_type brgn -tao_brgn_regularization_type l2prox -tao_brgn_regularizer_weight 1e-8 -tao_gatol 1.e-6 -tao_brgn_subsolver_tao_bnk_ksp_converged_reason 258 259 test: 260 suffix: 3 261 localrunfiles: cs1Data_A_b_xGT 262 args: -tao_monitor -tao_max_it 100 -tao_type brgn -tao_brgn_regularization_type l1dict -tao_brgn_regularizer_weight 1e-8 -tao_brgn_l1_smooth_epsilon 1e-6 -tao_gatol 1.e-6 263 264 test: 265 suffix: 4 266 localrunfiles: cs1Data_A_b_xGT 267 args: -tao_monitor -tao_max_it 100 -tao_type brgn -tao_brgn_regularization_type l2pure -tao_brgn_regularizer_weight 1e-8 -tao_gatol 1.e-6 268 269 test: 270 suffix: 5 271 localrunfiles: cs1Data_A_b_xGT 272 args: -tao_monitor -tao_max_it 100 -tao_type brgn -tao_brgn_regularization_type lm -tao_gatol 1.e-6 -tao_brgn_subsolver_tao_type bnls 273 274 TEST*/ 275