Actual source code: ex51.c

slepc-main 2024-11-15
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  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*/