Actual source code: eige.c
1: #include <petsc/private/kspimpl.h>
2: #include <petscdm.h>
3: #include <petscblaslapack.h>
5: typedef struct {
6: KSP ksp;
7: Vec work;
8: } Mat_KSP;
10: static PetscErrorCode MatCreateVecs_KSP(Mat A, Vec *X, Vec *Y)
11: {
12: Mat_KSP *ctx;
13: Mat M;
15: PetscFunctionBegin;
16: PetscCall(MatShellGetContext(A, &ctx));
17: PetscCall(KSPGetOperators(ctx->ksp, &M, NULL));
18: PetscCall(MatCreateVecs(M, X, Y));
19: PetscFunctionReturn(PETSC_SUCCESS);
20: }
22: static PetscErrorCode MatMult_KSP(Mat A, Vec X, Vec Y)
23: {
24: Mat_KSP *ctx;
26: PetscFunctionBegin;
27: PetscCall(MatShellGetContext(A, &ctx));
28: PetscCall(KSP_PCApplyBAorAB(ctx->ksp, X, Y, ctx->work));
29: PetscFunctionReturn(PETSC_SUCCESS);
30: }
32: /*@C
33: KSPComputeOperator - Computes the explicit preconditioned operator, including diagonal scaling and null
34: space removal if applicable.
36: Collective
38: Input Parameters:
39: + ksp - the Krylov subspace context
40: - mattype - the matrix type to be used
42: Output Parameter:
43: . mat - the explicit preconditioned operator
45: Level: advanced
47: Notes:
48: This computation is done by applying the operators to columns of the
49: identity matrix.
51: Currently, this routine uses a dense matrix format for the output operator if `mattype` is `NULL`.
52: This routine is costly in general, and is recommended for use only with relatively small systems.
54: .seealso: [](ch_ksp), `KSP`, `KSPSetOperators()`, `KSPComputeEigenvaluesExplicitly()`, `PCComputeOperator()`, `KSPSetDiagonalScale()`, `KSPSetNullSpace()`, `MatType`
55: @*/
56: PetscErrorCode KSPComputeOperator(KSP ksp, MatType mattype, Mat *mat)
57: {
58: PetscInt N, M, m, n;
59: Mat_KSP ctx;
60: Mat A, Aksp;
62: PetscFunctionBegin;
64: PetscAssertPointer(mat, 3);
65: PetscCall(KSPGetOperators(ksp, &A, NULL));
66: PetscCall(MatGetLocalSize(A, &m, &n));
67: PetscCall(MatGetSize(A, &M, &N));
68: PetscCall(MatCreateShell(PetscObjectComm((PetscObject)ksp), m, n, M, N, &ctx, &Aksp));
69: PetscCall(MatShellSetOperation(Aksp, MATOP_MULT, (void (*)(void))MatMult_KSP));
70: PetscCall(MatShellSetOperation(Aksp, MATOP_CREATE_VECS, (void (*)(void))MatCreateVecs_KSP));
71: ctx.ksp = ksp;
72: PetscCall(MatCreateVecs(A, &ctx.work, NULL));
73: PetscCall(MatComputeOperator(Aksp, mattype, mat));
74: PetscCall(VecDestroy(&ctx.work));
75: PetscCall(MatDestroy(&Aksp));
76: PetscFunctionReturn(PETSC_SUCCESS);
77: }
79: /*@
80: KSPComputeEigenvaluesExplicitly - Computes all of the eigenvalues of the
81: preconditioned operator using LAPACK.
83: Collective
85: Input Parameters:
86: + ksp - iterative context obtained from `KSPCreate()`
87: - nmax - size of arrays `r` and `c`
89: Output Parameters:
90: + r - real part of computed eigenvalues, provided by user with a dimension at least of `n`
91: - c - complex part of computed eigenvalues, provided by user with a dimension at least of `n`
93: Level: advanced
95: Notes:
96: This approach is very slow but will generally provide accurate eigenvalue
97: estimates. This routine explicitly forms a dense matrix representing
98: the preconditioned operator, and thus will run only for relatively small
99: problems, say `n` < 500.
101: Many users may just want to use the monitoring routine
102: `KSPMonitorSingularValue()` (which can be set with option -ksp_monitor_singular_value)
103: to print the singular values at each iteration of the linear solve.
105: The preconditioner operator, rhs vector, and solution vectors should be
106: set before this routine is called. i.e use `KSPSetOperators()`, `KSPSolve()`
108: .seealso: [](ch_ksp), `KSP`, `KSPComputeEigenvalues()`, `KSPMonitorSingularValue()`, `KSPComputeExtremeSingularValues()`, `KSPSetOperators()`, `KSPSolve()`
109: @*/
110: PetscErrorCode KSPComputeEigenvaluesExplicitly(KSP ksp, PetscInt nmax, PetscReal r[], PetscReal c[])
111: {
112: Mat BA;
113: PetscMPIInt size, rank;
114: MPI_Comm comm;
115: PetscScalar *array;
116: Mat A;
117: PetscInt m, row, nz, i, n, dummy;
118: const PetscInt *cols;
119: const PetscScalar *vals;
121: PetscFunctionBegin;
122: PetscCall(PetscObjectGetComm((PetscObject)ksp, &comm));
123: PetscCall(KSPComputeOperator(ksp, MATDENSE, &BA));
124: PetscCallMPI(MPI_Comm_size(comm, &size));
125: PetscCallMPI(MPI_Comm_rank(comm, &rank));
127: PetscCall(MatGetSize(BA, &n, &n));
128: if (size > 1) { /* assemble matrix on first processor */
129: PetscCall(MatCreate(PetscObjectComm((PetscObject)ksp), &A));
130: if (rank == 0) {
131: PetscCall(MatSetSizes(A, n, n, n, n));
132: } else {
133: PetscCall(MatSetSizes(A, 0, 0, n, n));
134: }
135: PetscCall(MatSetType(A, MATMPIDENSE));
136: PetscCall(MatMPIDenseSetPreallocation(A, NULL));
138: PetscCall(MatGetOwnershipRange(BA, &row, &dummy));
139: PetscCall(MatGetLocalSize(BA, &m, &dummy));
140: for (i = 0; i < m; i++) {
141: PetscCall(MatGetRow(BA, row, &nz, &cols, &vals));
142: PetscCall(MatSetValues(A, 1, &row, nz, cols, vals, INSERT_VALUES));
143: PetscCall(MatRestoreRow(BA, row, &nz, &cols, &vals));
144: row++;
145: }
147: PetscCall(MatAssemblyBegin(A, MAT_FINAL_ASSEMBLY));
148: PetscCall(MatAssemblyEnd(A, MAT_FINAL_ASSEMBLY));
149: PetscCall(MatDenseGetArray(A, &array));
150: } else {
151: PetscCall(MatDenseGetArray(BA, &array));
152: }
154: #if !defined(PETSC_USE_COMPLEX)
155: if (rank == 0) {
156: PetscScalar *work;
157: PetscReal *realpart, *imagpart;
158: PetscBLASInt idummy, lwork;
159: PetscInt *perm;
161: idummy = n;
162: lwork = 5 * n;
163: PetscCall(PetscMalloc2(n, &realpart, n, &imagpart));
164: PetscCall(PetscMalloc1(5 * n, &work));
165: {
166: PetscBLASInt lierr;
167: PetscScalar sdummy;
168: PetscBLASInt bn;
170: PetscCall(PetscBLASIntCast(n, &bn));
171: PetscCall(PetscFPTrapPush(PETSC_FP_TRAP_OFF));
172: PetscCallBLAS("LAPACKgeev", LAPACKgeev_("N", "N", &bn, array, &bn, realpart, imagpart, &sdummy, &idummy, &sdummy, &idummy, work, &lwork, &lierr));
173: PetscCheck(!lierr, PETSC_COMM_SELF, PETSC_ERR_LIB, "Error in LAPACK routine %d", (int)lierr);
174: PetscCall(PetscFPTrapPop());
175: }
176: PetscCall(PetscFree(work));
177: PetscCall(PetscMalloc1(n, &perm));
179: for (i = 0; i < n; i++) perm[i] = i;
180: PetscCall(PetscSortRealWithPermutation(n, realpart, perm));
181: for (i = 0; i < n; i++) {
182: r[i] = realpart[perm[i]];
183: c[i] = imagpart[perm[i]];
184: }
185: PetscCall(PetscFree(perm));
186: PetscCall(PetscFree2(realpart, imagpart));
187: }
188: #else
189: if (rank == 0) {
190: PetscScalar *work, *eigs;
191: PetscReal *rwork;
192: PetscBLASInt idummy, lwork;
193: PetscInt *perm;
195: idummy = n;
196: lwork = 5 * n;
197: PetscCall(PetscMalloc1(5 * n, &work));
198: PetscCall(PetscMalloc1(2 * n, &rwork));
199: PetscCall(PetscMalloc1(n, &eigs));
200: {
201: PetscBLASInt lierr;
202: PetscScalar sdummy;
203: PetscBLASInt nb;
204: PetscCall(PetscBLASIntCast(n, &nb));
205: PetscCall(PetscFPTrapPush(PETSC_FP_TRAP_OFF));
206: PetscCallBLAS("LAPACKgeev", LAPACKgeev_("N", "N", &nb, array, &nb, eigs, &sdummy, &idummy, &sdummy, &idummy, work, &lwork, rwork, &lierr));
207: PetscCheck(!lierr, PETSC_COMM_SELF, PETSC_ERR_LIB, "Error in LAPACK routine %d", (int)lierr);
208: PetscCall(PetscFPTrapPop());
209: }
210: PetscCall(PetscFree(work));
211: PetscCall(PetscFree(rwork));
212: PetscCall(PetscMalloc1(n, &perm));
213: for (i = 0; i < n; i++) perm[i] = i;
214: for (i = 0; i < n; i++) r[i] = PetscRealPart(eigs[i]);
215: PetscCall(PetscSortRealWithPermutation(n, r, perm));
216: for (i = 0; i < n; i++) {
217: r[i] = PetscRealPart(eigs[perm[i]]);
218: c[i] = PetscImaginaryPart(eigs[perm[i]]);
219: }
220: PetscCall(PetscFree(perm));
221: PetscCall(PetscFree(eigs));
222: }
223: #endif
224: if (size > 1) {
225: PetscCall(MatDenseRestoreArray(A, &array));
226: PetscCall(MatDestroy(&A));
227: } else {
228: PetscCall(MatDenseRestoreArray(BA, &array));
229: }
230: PetscCall(MatDestroy(&BA));
231: PetscFunctionReturn(PETSC_SUCCESS);
232: }
234: static PetscErrorCode PolyEval(PetscInt nroots, const PetscReal *r, const PetscReal *c, PetscReal x, PetscReal y, PetscReal *px, PetscReal *py)
235: {
236: PetscInt i;
237: PetscReal rprod = 1, iprod = 0;
239: PetscFunctionBegin;
240: for (i = 0; i < nroots; i++) {
241: PetscReal rnew = rprod * (x - r[i]) - iprod * (y - c[i]);
242: PetscReal inew = rprod * (y - c[i]) + iprod * (x - r[i]);
243: rprod = rnew;
244: iprod = inew;
245: }
246: *px = rprod;
247: *py = iprod;
248: PetscFunctionReturn(PETSC_SUCCESS);
249: }
251: #include <petscdraw.h>
252: /* Collective */
253: PetscErrorCode KSPPlotEigenContours_Private(KSP ksp, PetscInt neig, const PetscReal *r, const PetscReal *c)
254: {
255: PetscReal xmin, xmax, ymin, ymax, *xloc, *yloc, *value, px0, py0, rscale, iscale;
256: PetscInt M, N, i, j;
257: PetscMPIInt rank;
258: PetscViewer viewer;
259: PetscDraw draw;
260: PetscDrawAxis drawaxis;
262: PetscFunctionBegin;
263: PetscCallMPI(MPI_Comm_rank(PetscObjectComm((PetscObject)ksp), &rank));
264: if (rank) PetscFunctionReturn(PETSC_SUCCESS);
265: M = 80;
266: N = 80;
267: xmin = r[0];
268: xmax = r[0];
269: ymin = c[0];
270: ymax = c[0];
271: for (i = 1; i < neig; i++) {
272: xmin = PetscMin(xmin, r[i]);
273: xmax = PetscMax(xmax, r[i]);
274: ymin = PetscMin(ymin, c[i]);
275: ymax = PetscMax(ymax, c[i]);
276: }
277: PetscCall(PetscMalloc3(M, &xloc, N, &yloc, M * N, &value));
278: for (i = 0; i < M; i++) xloc[i] = xmin - 0.1 * (xmax - xmin) + 1.2 * (xmax - xmin) * i / (M - 1);
279: for (i = 0; i < N; i++) yloc[i] = ymin - 0.1 * (ymax - ymin) + 1.2 * (ymax - ymin) * i / (N - 1);
280: PetscCall(PolyEval(neig, r, c, 0, 0, &px0, &py0));
281: rscale = px0 / (PetscSqr(px0) + PetscSqr(py0));
282: iscale = -py0 / (PetscSqr(px0) + PetscSqr(py0));
283: for (j = 0; j < N; j++) {
284: for (i = 0; i < M; i++) {
285: PetscReal px, py, tx, ty, tmod;
286: PetscCall(PolyEval(neig, r, c, xloc[i], yloc[j], &px, &py));
287: tx = px * rscale - py * iscale;
288: ty = py * rscale + px * iscale;
289: tmod = PetscSqr(tx) + PetscSqr(ty); /* modulus of the complex polynomial */
290: if (tmod > 1) tmod = 1.0;
291: if (tmod > 0.5 && tmod < 1) tmod = 0.5;
292: if (tmod > 0.2 && tmod < 0.5) tmod = 0.2;
293: if (tmod > 0.05 && tmod < 0.2) tmod = 0.05;
294: if (tmod < 1e-3) tmod = 1e-3;
295: value[i + j * M] = PetscLogReal(tmod) / PetscLogReal(10.0);
296: }
297: }
298: PetscCall(PetscViewerDrawOpen(PETSC_COMM_SELF, NULL, "Iteratively Computed Eigen-contours", PETSC_DECIDE, PETSC_DECIDE, 450, 450, &viewer));
299: PetscCall(PetscViewerDrawGetDraw(viewer, 0, &draw));
300: PetscCall(PetscDrawTensorContour(draw, M, N, NULL, NULL, value));
301: if (0) {
302: PetscCall(PetscDrawAxisCreate(draw, &drawaxis));
303: PetscCall(PetscDrawAxisSetLimits(drawaxis, xmin, xmax, ymin, ymax));
304: PetscCall(PetscDrawAxisSetLabels(drawaxis, "Eigen-counters", "real", "imag"));
305: PetscCall(PetscDrawAxisDraw(drawaxis));
306: PetscCall(PetscDrawAxisDestroy(&drawaxis));
307: }
308: PetscCall(PetscViewerDestroy(&viewer));
309: PetscCall(PetscFree3(xloc, yloc, value));
310: PetscFunctionReturn(PETSC_SUCCESS);
311: }