Date: 2022-11-02T11:47:16+00:00

Actual source code: ex51.c
slepc-3.18.1 2022-11-02
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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);

     25:   if (y<(start+j)*h) LookUp(N,start,start+j,y,i);
     26:   else if (y<(start+j+1)*h) *i = start+j;
     27:   else LookUp(N,start+j,end,y,i);
     28:   return 0;
     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:   PetscObjectGetComm((PetscObject)in,&comm);
     45:   MPI_Comm_size(comm,&size);
     46:   MPI_Comm_rank(comm,&rank);
     47:   MatPartitioningCreate(comm,&part);
     48:   MatPartitioningSetAdjacency(part,in);
     49:   MatPartitioningSetFromOptions(part);
     50:   MatPartitioningApply(part,&is); /* get owner of each vertex */
     51:   ISPartitioningToNumbering(is,&isn); /* get new global number of each vertex */
     52:   PetscMalloc1(size,&nlocal);
     53:   ISPartitioningCount(is,size,nlocal); /* count vertices assigned to each process */
     54:   ISDestroy(&is);

     56:   /* get old global number of each new global number */
     57:   ISInvertPermutation(isn,nlocal[rank],&is);
     58:   PetscFree(nlocal);
     59:   ISDestroy(&isn);
     60:   MatPartitioningDestroy(&part);

     62:   /* symmetric permutation of A */
     63:   MatCreateSubMatrix(in,is,is,MAT_INITIAL_MATRIX,&out);
     64:   MatDestroy(A);
     65:   *A = out;

     67:   /* column permutation of B */
     68:   MatGetOwnershipRange(*B,&Istart,&Iend);
     69:   ISCreateStride(comm,Iend-Istart,Istart,1,&id);
     70:   ISSetIdentity(id);
     71:   MatCreateSubMatrix(*B,id,is,MAT_INITIAL_MATRIX,&out);
     72:   MatDestroy(B);
     73:   *B = out;
     74:   ISDestroy(&id);
     75:   ISDestroy(&is);
     76:   return 0;
     77: }

     79: int main(int argc,char **argv)
     80: {
     81:   Mat            A,B;             /* operator matrices */
     82:   SVD            svd;             /* singular value problem solver context */
     83:   KSP            ksp;
     84:   PetscInt       n=32,N,i,i2,j,k,xidx,yidx,bl,Istart,Iend,col[3];
     85:   PetscScalar    vals[] = { 1, -2, 1 },X,Y;
     86:   PetscBool      flg,terse,permute=PETSC_FALSE;
     87:   PetscRandom    rctx;

     90:   SlepcInitialize(&argc,&argv,(char*)0,help);

     92:   PetscOptionsGetInt(NULL,NULL,"-n",&n,&flg);
     93:   N = n*n;
     94:   PetscPrintf(PETSC_COMM_WORLD,"\nGSVD of inverse interpolation problem, (%" PetscInt_FMT "+%" PetscInt_FMT ")x%" PetscInt_FMT "\n\n",N,2*N,N);

     96:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     97:                           Build the matrices
     98:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    100:   PetscRandomCreate(PETSC_COMM_WORLD,&rctx);
    101:   PetscRandomSetInterval(rctx,0,1);
    102:   PetscRandomSetFromOptions(rctx);

    104:   MatCreate(PETSC_COMM_WORLD,&A);
    105:   MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,N,N);
    106:   MatSetFromOptions(A);
    107:   MatSetUp(A);
    108:   MatGetOwnershipRange(A,&Istart,&Iend);

    110:   /* make sure that the matrix is the same irrespective of the number of MPI processes */
    111:   PetscRandomSetSeed(rctx,0x12345678);
    112:   PetscRandomSeed(rctx);
    113:   for (k=0;k<Istart;k++) {
    114:     PetscRandomGetValue(rctx,&X);
    115:     PetscRandomGetValue(rctx,&Y);
    116:   }

    118:   for (k=0;k<Iend-Istart;k++) {
    119:     PetscRandomGetValue(rctx,&X);
    120:     LookUp(n,0,n,PetscRealPart(X),&xidx);
    121:     X = X*(n-1)-xidx;   /* scale value to a 1-spaced grid */
    122:     PetscRandomGetValue(rctx,&Y);
    123:     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) 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) MatSetValue(A,Istart+k,i+j*n,X-X*Y,ADD_VALUES);
    129:         if (i>0 && j<n-1 && xidx==j && yidx==i-1) MatSetValue(A,Istart+k,i+j*n,Y-X*Y,ADD_VALUES);
    130:         if (i>0 && j>0 && xidx==j-1 && yidx==i-1) MatSetValue(A,Istart+k,i+j*n,X*Y,ADD_VALUES);
    131:       }
    132:     }
    133:   }
    134:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
    135:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
    136:   PetscRandomDestroy(&rctx);

    138:   MatCreate(PETSC_COMM_WORLD,&B);
    139:   MatSetSizes(B,PETSC_DECIDE,PETSC_DECIDE,2*N,N);
    140:   MatSetFromOptions(B);
    141:   MatSetUp(B);

    143:   for (i=Istart;i<Iend;i++) {
    144:     /* upper block: kron(speye(n),T1) where T1 is tridiagonal */
    145:     i2 = i+Istart;
    146:     if (i%n==0) MatSetValue(B,i2,i,1.0,INSERT_VALUES);
    147:     else if (i%n==n-1) {
    148:       MatSetValue(B,i2,i-1,-1.0,INSERT_VALUES);
    149:       MatSetValue(B,i2,i,1.0,INSERT_VALUES);
    150:     } else {
    151:       col[0]=i-1; col[1]=i; col[2]=i+1;
    152:       MatSetValues(B,1,&i2,3,col,vals,INSERT_VALUES);
    153:     }
    154:     /* lower block: kron(T2,speye(n)) where T2 is tridiagonal */
    155:     i2 = i+Iend;
    156:     bl = i/n;  /* index of block */
    157:     j = i-bl*n; /* index within block */
    158:     if (bl==0 || bl==n-1) MatSetValue(B,i2,i,1.0,INSERT_VALUES);
    159:     else {
    160:       col[0]=i-n; col[1]=i; col[2]=i+n;
    161:       MatSetValues(B,1,&i2,3,col,vals,INSERT_VALUES);
    162:     }
    163:   }
    164:   MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
    165:   MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);

    167:   PetscOptionsGetBool(NULL,NULL,"-permute",&permute,NULL);
    168:   if (permute) {
    169:     PetscPrintf(PETSC_COMM_WORLD," Permuting to optimize parallel matvec\n");
    170:     PermuteMatrices(&A,&B);
    171:   }

    173:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    174:           Create the singular value solver and set various options
    175:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    177:   SVDCreate(PETSC_COMM_WORLD,&svd);
    178:   SVDSetOperators(svd,A,B);
    179:   SVDSetProblemType(svd,SVD_GENERALIZED);

    181:   SVDSetType(svd,SVDTRLANCZOS);
    182:   SVDSetDimensions(svd,6,PETSC_DEFAULT,PETSC_DEFAULT);
    183:   SVDTRLanczosSetExplicitMatrix(svd,PETSC_TRUE);
    184:   SVDTRLanczosSetScale(svd,-10);
    185:   SVDTRLanczosGetKSP(svd,&ksp);
    186:   KSPSetTolerances(ksp,1e-12,PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT);

    188:   SVDSetFromOptions(svd);

    190:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    191:                       Solve the problem and print solution
    192:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    194:   SVDSolve(svd);

    196:   /* show detailed info unless -terse option is given by user */
    197:   PetscOptionsHasName(NULL,NULL,"-terse",&terse);
    198:   if (terse) SVDErrorView(svd,SVD_ERROR_NORM,NULL);
    199:   else {
    200:     PetscViewerPushFormat(PETSC_VIEWER_STDOUT_WORLD,PETSC_VIEWER_ASCII_INFO_DETAIL);
    201:     SVDConvergedReasonView(svd,PETSC_VIEWER_STDOUT_WORLD);
    202:     SVDErrorView(svd,SVD_ERROR_NORM,PETSC_VIEWER_STDOUT_WORLD);
    203:     PetscViewerPopFormat(PETSC_VIEWER_STDOUT_WORLD);
    204:   }
    205:   SVDDestroy(&svd);
    206:   MatDestroy(&A);
    207:   MatDestroy(&B);
    208:   SlepcFinalize();
    209:   return 0;
    210: }

    212: /*TEST

    214:    testset:
    215:       args: -n 16 -terse
    216:       requires: double
    217:       output_file: output/ex51_1.out
    218:       test:
    219:          args: -svd_trlanczos_gbidiag {{upper lower}} -svd_trlanczos_oneside
    220:          suffix: 1
    221:       test:
    222:          suffix: 2
    223:          nsize: 2
    224:          args: -permute
    225:          filter: grep -v Permuting

    227: TEST*/