Actual source code: ex51.c
slepc-main 2024-11-09
1: /*
2: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
3: SLEPc - Scalable Library for Eigenvalue Problem Computations
4: Copyright (c) 2002-, Universitat Politecnica de Valencia, Spain
6: This file is part of SLEPc.
7: SLEPc is distributed under a 2-clause BSD license (see LICENSE).
8: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
9: */
11: static char help[] = "Computes a partial GSVD of two matrices from IR Tools example.\n"
12: "The command line options are:\n"
13: " -n <n>, where <n> = number of grid subdivisions in x and y dimensions.\n\n";
15: #include <slepcsvd.h>
17: /* LookUp: returns an index i such that X(i) <= y < X(i+1), where X = linspace(0,1,N).
18: Only elements start..end-1 are considered */
19: PetscErrorCode LookUp(PetscInt N,PetscInt start,PetscInt end,PetscReal y,PetscInt *i)
20: {
21: PetscInt n=end-start,j=n/2;
22: PetscReal h=1.0/(N-1);
24: PetscFunctionBeginUser;
25: if (y<(start+j)*h) PetscCall(LookUp(N,start,start+j,y,i));
26: else if (y<(start+j+1)*h) *i = start+j;
27: else PetscCall(LookUp(N,start+j,end,y,i));
28: PetscFunctionReturn(PETSC_SUCCESS);
29: }
31: /*
32: PermuteMatrices - Symmetric permutation of A using MatPartitioning, then permute
33: columns of B in the same way.
34: */
35: PetscErrorCode PermuteMatrices(Mat *A,Mat *B)
36: {
37: MatPartitioning part;
38: IS isn,is,id;
39: PetscInt *nlocal,Istart,Iend;
40: PetscMPIInt size,rank;
41: MPI_Comm comm;
42: Mat in=*A,out;
44: PetscFunctionBegin;
45: PetscCall(PetscObjectGetComm((PetscObject)in,&comm));
46: PetscCallMPI(MPI_Comm_size(comm,&size));
47: PetscCallMPI(MPI_Comm_rank(comm,&rank));
48: PetscCall(MatPartitioningCreate(comm,&part));
49: PetscCall(MatPartitioningSetAdjacency(part,in));
50: PetscCall(MatPartitioningSetFromOptions(part));
51: PetscCall(MatPartitioningApply(part,&is)); /* get owner of each vertex */
52: PetscCall(ISPartitioningToNumbering(is,&isn)); /* get new global number of each vertex */
53: PetscCall(PetscMalloc1(size,&nlocal));
54: PetscCall(ISPartitioningCount(is,size,nlocal)); /* count vertices assigned to each process */
55: PetscCall(ISDestroy(&is));
57: /* get old global number of each new global number */
58: PetscCall(ISInvertPermutation(isn,nlocal[rank],&is));
59: PetscCall(PetscFree(nlocal));
60: PetscCall(ISDestroy(&isn));
61: PetscCall(MatPartitioningDestroy(&part));
63: /* symmetric permutation of A */
64: PetscCall(MatCreateSubMatrix(in,is,is,MAT_INITIAL_MATRIX,&out));
65: PetscCall(MatDestroy(A));
66: *A = out;
68: /* column permutation of B */
69: PetscCall(MatGetOwnershipRange(*B,&Istart,&Iend));
70: PetscCall(ISCreateStride(comm,Iend-Istart,Istart,1,&id));
71: PetscCall(ISSetIdentity(id));
72: PetscCall(MatCreateSubMatrix(*B,id,is,MAT_INITIAL_MATRIX,&out));
73: PetscCall(MatDestroy(B));
74: *B = out;
75: PetscCall(ISDestroy(&id));
76: PetscCall(ISDestroy(&is));
77: PetscFunctionReturn(PETSC_SUCCESS);
78: }
80: int main(int argc,char **argv)
81: {
82: Mat A,B; /* operator matrices */
83: SVD svd; /* singular value problem solver context */
84: KSP ksp;
85: PetscInt n=32,N,i,i2,j,k,xidx,yidx,bl,Istart,Iend,col[3];
86: PetscScalar vals[] = { 1, -2, 1 },X,Y;
87: PetscBool flg,terse,permute=PETSC_FALSE;
88: PetscRandom rctx;
90: PetscFunctionBeginUser;
91: PetscCall(SlepcInitialize(&argc,&argv,NULL,help));
93: PetscCall(PetscOptionsGetInt(NULL,NULL,"-n",&n,&flg));
94: N = n*n;
95: PetscCall(PetscPrintf(PETSC_COMM_WORLD,"\nGSVD of inverse interpolation problem, (%" PetscInt_FMT "+%" PetscInt_FMT ")x%" PetscInt_FMT "\n\n",N,2*N,N));
97: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
98: Build the matrices
99: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
101: PetscCall(PetscRandomCreate(PETSC_COMM_WORLD,&rctx));
102: PetscCall(PetscRandomSetInterval(rctx,0,1));
103: PetscCall(PetscRandomSetFromOptions(rctx));
105: PetscCall(MatCreate(PETSC_COMM_WORLD,&A));
106: PetscCall(MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,N,N));
107: PetscCall(MatSetFromOptions(A));
108: PetscCall(MatGetOwnershipRange(A,&Istart,&Iend));
110: /* make sure that the matrix is the same irrespective of the number of MPI processes */
111: PetscCall(PetscRandomSetSeed(rctx,0x12345678));
112: PetscCall(PetscRandomSeed(rctx));
113: for (k=0;k<Istart;k++) {
114: PetscCall(PetscRandomGetValue(rctx,&X));
115: PetscCall(PetscRandomGetValue(rctx,&Y));
116: }
118: for (k=0;k<Iend-Istart;k++) {
119: PetscCall(PetscRandomGetValue(rctx,&X));
120: PetscCall(LookUp(n,0,n,PetscRealPart(X),&xidx));
121: X = X*(n-1)-xidx; /* scale value to a 1-spaced grid */
122: PetscCall(PetscRandomGetValue(rctx,&Y));
123: PetscCall(LookUp(n,0,n,PetscRealPart(Y),&yidx));
124: Y = Y*(n-1)-yidx; /* scale value to a 1-spaced grid */
125: for (j=0;j<n;j++) {
126: for (i=0;i<n;i++) {
127: if (i<n-1 && j<n-1 && xidx==j && yidx==i) PetscCall(MatSetValue(A,Istart+k,i+j*n,1.0-X-Y+X*Y,ADD_VALUES));
128: if (i<n-1 && j>0 && xidx==j-1 && yidx==i) PetscCall(MatSetValue(A,Istart+k,i+j*n,X-X*Y,ADD_VALUES));
129: if (i>0 && j<n-1 && xidx==j && yidx==i-1) PetscCall(MatSetValue(A,Istart+k,i+j*n,Y-X*Y,ADD_VALUES));
130: if (i>0 && j>0 && xidx==j-1 && yidx==i-1) PetscCall(MatSetValue(A,Istart+k,i+j*n,X*Y,ADD_VALUES));
131: }
132: }
133: }
134: PetscCall(MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY));
135: PetscCall(MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY));
136: PetscCall(PetscRandomDestroy(&rctx));
138: PetscCall(MatCreate(PETSC_COMM_WORLD,&B));
139: PetscCall(MatSetSizes(B,PETSC_DECIDE,PETSC_DECIDE,2*N,N));
140: PetscCall(MatSetFromOptions(B));
142: for (i=Istart;i<Iend;i++) {
143: /* upper block: kron(speye(n),T1) where T1 is tridiagonal */
144: i2 = i+Istart;
145: if (i%n==0) PetscCall(MatSetValue(B,i2,i,1.0,INSERT_VALUES));
146: else if (i%n==n-1) {
147: PetscCall(MatSetValue(B,i2,i-1,-1.0,INSERT_VALUES));
148: PetscCall(MatSetValue(B,i2,i,1.0,INSERT_VALUES));
149: } else {
150: col[0]=i-1; col[1]=i; col[2]=i+1;
151: PetscCall(MatSetValues(B,1,&i2,3,col,vals,INSERT_VALUES));
152: }
153: /* lower block: kron(T2,speye(n)) where T2 is tridiagonal */
154: i2 = i+Iend;
155: bl = i/n; /* index of block */
156: j = i-bl*n; /* index within block */
157: if (bl==0 || bl==n-1) PetscCall(MatSetValue(B,i2,i,1.0,INSERT_VALUES));
158: else {
159: col[0]=i-n; col[1]=i; col[2]=i+n;
160: PetscCall(MatSetValues(B,1,&i2,3,col,vals,INSERT_VALUES));
161: }
162: }
163: PetscCall(MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY));
164: PetscCall(MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY));
166: PetscCall(PetscOptionsGetBool(NULL,NULL,"-permute",&permute,NULL));
167: if (permute) {
168: PetscCall(PetscPrintf(PETSC_COMM_WORLD," Permuting to optimize parallel matvec\n"));
169: PetscCall(PermuteMatrices(&A,&B));
170: }
172: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
173: Create the singular value solver and set various options
174: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
176: PetscCall(SVDCreate(PETSC_COMM_WORLD,&svd));
177: PetscCall(SVDSetOperators(svd,A,B));
178: PetscCall(SVDSetProblemType(svd,SVD_GENERALIZED));
180: PetscCall(SVDSetType(svd,SVDTRLANCZOS));
181: PetscCall(SVDSetDimensions(svd,6,PETSC_DETERMINE,PETSC_DETERMINE));
182: PetscCall(SVDTRLanczosSetExplicitMatrix(svd,PETSC_TRUE));
183: PetscCall(SVDTRLanczosSetScale(svd,-10));
184: PetscCall(SVDTRLanczosGetKSP(svd,&ksp));
185: PetscCall(KSPSetTolerances(ksp,1e-12,PETSC_CURRENT,PETSC_CURRENT,PETSC_CURRENT));
187: PetscCall(SVDSetFromOptions(svd));
189: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
190: Solve the problem and print solution
191: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
193: PetscCall(SVDSolve(svd));
195: /* show detailed info unless -terse option is given by user */
196: PetscCall(PetscOptionsHasName(NULL,NULL,"-terse",&terse));
197: if (terse) PetscCall(SVDErrorView(svd,SVD_ERROR_NORM,NULL));
198: else {
199: PetscCall(PetscViewerPushFormat(PETSC_VIEWER_STDOUT_WORLD,PETSC_VIEWER_ASCII_INFO_DETAIL));
200: PetscCall(SVDConvergedReasonView(svd,PETSC_VIEWER_STDOUT_WORLD));
201: PetscCall(SVDErrorView(svd,SVD_ERROR_NORM,PETSC_VIEWER_STDOUT_WORLD));
202: PetscCall(PetscViewerPopFormat(PETSC_VIEWER_STDOUT_WORLD));
203: }
204: PetscCall(SVDDestroy(&svd));
205: PetscCall(MatDestroy(&A));
206: PetscCall(MatDestroy(&B));
207: PetscCall(SlepcFinalize());
208: return 0;
209: }
211: /*TEST
213: testset:
214: args: -n 16 -terse
215: requires: double
216: output_file: output/ex51_1.out
217: test:
218: args: -svd_trlanczos_gbidiag {{upper lower}} -svd_trlanczos_oneside
219: suffix: 1
220: test:
221: suffix: 2
222: nsize: 2
223: args: -permute
224: filter: grep -v Permuting
226: TEST*/