Actual source code: agmresdeflation.c
1: /*
2: This file computes data for the deflated restarting in the Newton-basis GMRES.
3: At each restart (or at each detected stagnation in the adaptive strategy), a basis of an
4: (approximated)invariant subspace corresponding to the smallest eigenvalues is extracted from the Krylov subspace.
5: It is then used to augment the Newton basis.
6: */
8: #include <../src/ksp/ksp/impls/gmres/agmres/agmresimpl.h>
10: /* Quicksort algorithm to sort the eigenvalues in increasing orders
11: val_r - real part of eigenvalues, unchanged on exit.
12: val_i - Imaginary part of eigenvalues unchanged on exit.
13: size - Number of eigenvalues (with complex conjugates)
14: perm - contains on exit the permutation vector to reorder the vectors val_r and val_i.
15: */
16: #define DEPTH 500
17: static PetscErrorCode KSPAGMRESQuickSort(PetscScalar *val_r, PetscScalar *val_i, PetscInt size, PetscInt *perm)
18: {
19: PetscInt deb[DEPTH], fin[DEPTH];
20: PetscInt ipivot;
21: PetscScalar pivot_r, pivot_i;
22: PetscInt i, L, R, j;
23: PetscScalar abs_pivot;
24: PetscScalar abs_val;
26: PetscFunctionBegin;
27: /* initialize perm vector */
28: for (j = 0; j < size; j++) perm[j] = j;
30: deb[0] = 0;
31: fin[0] = size;
32: i = 0;
33: while (i >= 0) {
34: L = deb[i];
35: R = fin[i] - 1;
36: if (L < R) {
37: pivot_r = val_r[L];
38: pivot_i = val_i[L];
39: abs_pivot = PetscSqrtReal(pivot_r * pivot_r + pivot_i * pivot_i);
40: ipivot = perm[L];
41: PetscCheck(i != DEPTH - 1, PETSC_COMM_SELF, PETSC_ERR_MEM, "Could cause stack overflow: Try to increase the value of DEPTH ");
42: while (L < R) {
43: abs_val = PetscSqrtReal(val_r[R] * val_r[R] + val_i[R] * val_i[R]);
44: while (abs_val >= abs_pivot && L < R) {
45: R--;
46: abs_val = PetscSqrtReal(val_r[R] * val_r[R] + val_i[R] * val_i[R]);
47: }
48: if (L < R) {
49: val_r[L] = val_r[R];
50: val_i[L] = val_i[R];
51: perm[L] = perm[R];
52: L += 1;
53: }
54: abs_val = PetscSqrtReal(val_r[L] * val_r[L] + val_i[L] * val_i[L]);
55: while (abs_val <= abs_pivot && L < R) {
56: L++;
57: abs_val = PetscSqrtReal(val_r[L] * val_r[L] + val_i[L] * val_i[L]);
58: }
59: if (L < R) {
60: val_r[R] = val_r[L];
61: val_i[R] = val_i[L];
62: perm[R] = perm[L];
63: R -= 1;
64: }
65: }
66: val_r[L] = pivot_r;
67: val_i[L] = pivot_i;
68: perm[L] = ipivot;
69: deb[i + 1] = L + 1;
70: fin[i + 1] = fin[i];
71: fin[i] = L;
72: i += 1;
73: PetscCheck(i != DEPTH - 1, PETSC_COMM_SELF, PETSC_ERR_MEM, "Could cause stack overflow: Try to increase the value of DEPTH ");
74: } else i--;
75: }
76: PetscFunctionReturn(PETSC_SUCCESS);
77: }
79: /*
80: Compute the Schur vectors from the generalized eigenvalue problem A.u =\lambda.B.u
81: KspSize - rank of the matrices A and B, size of the current Krylov basis
82: A - Left matrix
83: B - Right matrix
84: ldA - first dimension of A as declared in the calling program
85: ldB - first dimension of B as declared in the calling program
86: IsReduced - specifies if the matrices are already in the reduced form,
87: i.e A is a Hessenberg matrix and B is upper triangular.
88: Sr - on exit, the extracted Schur vectors corresponding
89: the smallest eigenvalues (with complex conjugates)
90: CurNeig - Number of extracted eigenvalues
91: */
92: static PetscErrorCode KSPAGMRESSchurForm(KSP ksp, PetscBLASInt KspSize, PetscScalar *A, PetscBLASInt ldA, PetscScalar *B, PetscBLASInt ldB, PetscBool IsReduced, PetscScalar *Sr, PetscInt *CurNeig)
93: {
94: KSP_AGMRES *agmres = (KSP_AGMRES *)ksp->data;
95: PetscInt max_k = agmres->max_k;
96: PetscBLASInt r;
97: PetscInt neig = agmres->neig;
98: PetscScalar *wr = agmres->wr;
99: PetscScalar *wi = agmres->wi;
100: PetscScalar *beta = agmres->beta;
101: PetscScalar *Q = agmres->Q;
102: PetscScalar *Z = agmres->Z;
103: PetscScalar *work = agmres->work;
104: PetscBLASInt *select = agmres->select;
105: PetscInt *perm = agmres->perm;
106: PetscBLASInt sdim = 0;
107: PetscInt i, j;
108: PetscBLASInt info;
109: PetscBLASInt *iwork = agmres->iwork;
110: PetscBLASInt N = (PetscBLASInt)MAXKSPSIZE;
111: PetscBLASInt lwork, liwork;
112: PetscBLASInt ilo;
113: PetscBLASInt ijob, wantQ, wantZ;
114: PetscScalar Dif[2];
116: PetscFunctionBegin;
117: ijob = 2;
118: wantQ = 1;
119: wantZ = 1;
120: PetscCall(PetscBLASIntCast(PetscMax(8 * N + 16, 4 * neig * (N - neig)), &lwork));
121: PetscCall(PetscBLASIntCast(2 * N * neig, &liwork));
122: ilo = 1;
124: /* Compute the Schur form */
125: if (IsReduced) { /* The eigenvalue problem is already in reduced form, meaning that A is upper Hessenberg and B is triangular */
126: PetscCallBLAS("LAPACKhgeqz", LAPACKhgeqz_("S", "I", "I", &KspSize, &ilo, &KspSize, A, &ldA, B, &ldB, wr, wi, beta, Q, &N, Z, &N, work, &lwork, &info));
127: PetscCheck(!info, PetscObjectComm((PetscObject)ksp), PETSC_ERR_PLIB, "Error while calling LAPACK routine xhgeqz_");
128: } else {
129: PetscCallBLAS("LAPACKgges", LAPACKgges_("V", "V", "N", NULL, &KspSize, A, &ldA, B, &ldB, &sdim, wr, wi, beta, Q, &N, Z, &N, work, &lwork, NULL, &info));
130: PetscCheck(!info, PetscObjectComm((PetscObject)ksp), PETSC_ERR_PLIB, "Error while calling LAPACK routine xgges_");
131: }
133: /* We should avoid computing these ratio... */
134: for (i = 0; i < KspSize; i++) {
135: if (beta[i] != 0.0) {
136: wr[i] /= beta[i];
137: wi[i] /= beta[i];
138: }
139: }
141: /* Sort the eigenvalues to extract the smallest ones */
142: PetscCall(KSPAGMRESQuickSort(wr, wi, KspSize, perm));
144: /* Count the number of extracted eigenvalues (with complex conjugates) */
145: r = 0;
146: while (r < neig) {
147: if (wi[r] != 0) r += 2;
148: else r += 1;
149: }
150: /* Reorder the Schur decomposition so that the cluster of smallest/largest eigenvalues appears in the leading diagonal blocks of A (and B)*/
151: PetscCall(PetscArrayzero(select, N));
152: if (!agmres->GreatestEig) {
153: for (j = 0; j < r; j++) select[perm[j]] = 1;
154: } else {
155: for (j = 0; j < r; j++) select[perm[KspSize - j - 1]] = 1;
156: }
157: PetscCallBLAS("LAPACKtgsen", LAPACKtgsen_(&ijob, &wantQ, &wantZ, select, &KspSize, A, &ldA, B, &ldB, wr, wi, beta, Q, &N, Z, &N, &r, NULL, NULL, &Dif[0], work, &lwork, iwork, &liwork, &info));
158: PetscCheck(info != 1, PetscObjectComm((PetscObject)ksp), PETSC_ERR_PLIB, "UNABLE TO REORDER THE EIGENVALUES WITH THE LAPACK ROUTINE : ILL-CONDITIONED PROBLEM");
159: /* Extract the Schur vectors associated to the r smallest eigenvalues */
160: PetscCall(PetscArrayzero(Sr, (N + 1) * r));
161: for (j = 0; j < r; j++) {
162: for (i = 0; i < KspSize; i++) Sr[j * (N + 1) + i] = Z[j * N + i];
163: }
165: /* Broadcast Sr to all other processes to have consistent data;
166: * FIXME should investigate how to get unique Schur vectors (unique QR factorization, probably the sign of rotations) */
167: PetscCallMPI(MPI_Bcast(Sr, (N + 1) * r, MPIU_SCALAR, agmres->First, PetscObjectComm((PetscObject)ksp)));
168: /* Update the Shift values for the Newton basis. This is surely necessary when applying the DeflationPrecond */
169: if (agmres->DeflPrecond) PetscCall(KSPAGMRESLejaOrdering(wr, wi, agmres->Rshift, agmres->Ishift, max_k));
170: *CurNeig = r; /* Number of extracted eigenvalues */
171: PetscFunctionReturn(PETSC_SUCCESS);
172: }
174: /*
175: Forms the matrices for the generalized eigenvalue problem,
176: it then compute the Schur vectors needed to augment the Newton basis.
177: */
178: PetscErrorCode KSPAGMRESComputeDeflationData(KSP ksp)
179: {
180: KSP_AGMRES *agmres = (KSP_AGMRES *)ksp->data;
181: Vec *U = agmres->U;
182: Vec *TmpU = agmres->TmpU;
183: PetscScalar *MatEigL = agmres->MatEigL;
184: PetscScalar *MatEigR = agmres->MatEigR;
185: PetscScalar *Sr = agmres->Sr;
186: PetscScalar alpha, beta;
187: PetscInt i, j;
188: PetscInt max_k = agmres->max_k; /* size of the non - augmented subspace */
189: PetscInt CurNeig; /* Current number of extracted eigenvalues */
190: PetscInt N = MAXKSPSIZE;
191: PetscBLASInt bN, iKspSize;
192: PetscInt lC = N + 1;
193: PetscInt KspSize = KSPSIZE;
194: PetscBLASInt blC, bKspSize;
195: PetscInt PrevNeig = agmres->r;
197: PetscFunctionBegin;
198: PetscCall(PetscLogEventBegin(KSP_AGMRESComputeDeflationData, ksp, 0, 0, 0));
199: if (agmres->neig <= 1) PetscFunctionReturn(PETSC_SUCCESS);
200: /* Explicitly form MatEigL = H^T*H, It can also be formed as H^T+h_{N+1,N}H^-1e^T */
201: alpha = 1.0;
202: beta = 0.0;
203: PetscCall(PetscBLASIntCast(KspSize, &bKspSize));
204: PetscCall(PetscBLASIntCast(lC, &blC));
205: PetscCall(PetscBLASIntCast(N, &bN));
206: PetscCallBLAS("BLASgemm", BLASgemm_("T", "N", &bKspSize, &bKspSize, &blC, &alpha, agmres->hes_origin, &blC, agmres->hes_origin, &blC, &beta, MatEigL, &bN));
207: if (!agmres->ritz) {
208: /* Form TmpU = V*H where V is the Newton basis orthogonalized with roddec*/
209: for (j = 0; j < KspSize; j++) {
210: /* Apply the elementary reflectors (stored in Qloc) on H */
211: PetscCall(KSPAGMRESRodvec(ksp, KspSize + 1, &agmres->hes_origin[j * lC], TmpU[j]));
212: }
213: /* Now form MatEigR = TmpU^T*W where W is [VEC_V(1:max_k); U] */
214: for (j = 0; j < max_k; j++) PetscCall(VecMDot(VEC_V(j), KspSize, TmpU, &MatEigR[j * N]));
215: for (j = max_k; j < KspSize; j++) PetscCall(VecMDot(U[j - max_k], KspSize, TmpU, &MatEigR[j * N]));
216: } else { /* Form H^T */
217: for (j = 0; j < N; j++) {
218: for (i = 0; i < N; i++) MatEigR[j * N + i] = agmres->hes_origin[i * lC + j];
219: }
220: }
221: /* Obtain the Schur form of the generalized eigenvalue problem MatEigL*y = \lambda*MatEigR*y */
222: PetscCall(PetscBLASIntCast(KspSize, &iKspSize));
223: if (agmres->DeflPrecond) {
224: PetscCall(KSPAGMRESSchurForm(ksp, iKspSize, agmres->hes_origin, blC, agmres->Rloc, blC, PETSC_TRUE, Sr, &CurNeig));
225: } else {
226: PetscCall(KSPAGMRESSchurForm(ksp, iKspSize, MatEigL, bN, MatEigR, bN, PETSC_FALSE, Sr, &CurNeig));
227: }
229: if (agmres->DeflPrecond) { /* Switch to DGMRES to improve the basis of the invariant subspace associated to the deflation */
230: agmres->HasSchur = PETSC_TRUE;
231: PetscCall(KSPDGMRESComputeDeflationData(ksp, &CurNeig));
232: PetscFunctionReturn(PETSC_SUCCESS);
233: }
234: /* Form the Schur vectors in the entire subspace: U = W * Sr where W = [VEC_V(1:max_k); U]*/
235: for (j = 0; j < PrevNeig; j++) { /* First, copy U to a temporary place */
236: PetscCall(VecCopy(U[j], TmpU[j]));
237: }
239: for (j = 0; j < CurNeig; j++) {
240: PetscCall(VecMAXPBY(U[j], max_k, &Sr[j * (N + 1)], 0, &VEC_V(0)));
241: PetscCall(VecMAXPY(U[j], PrevNeig, &Sr[j * (N + 1) + max_k], TmpU));
242: }
243: agmres->r = CurNeig;
244: PetscCall(PetscLogEventEnd(KSP_AGMRESComputeDeflationData, ksp, 0, 0, 0));
245: PetscFunctionReturn(PETSC_SUCCESS);
246: }