Date: 2015-10-02T22:12:36+00:00

Actual source code: spectral.c
petsc-3.6.2 2015-10-02
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      1: #include <petscmat.h> /*I <petscmat.h> I*/
      2: #include <petscblaslapack.h>

      6: /*@
      7:   MatCreateLaplacian - Create the matrix Laplacian, with all values in the matrix less than the tolerance set to zero

      9:   Input Parameters:
     10: + A   - The matrix
     11: . tol - The zero tolerance
     12: - weighted - Flag for using edge weights

     14:   Output Parameters:
     15: . L - The graph Laplacian matrix

     17:   Level: intermediate

     19: .seealso: MatChop()
     20:  @*/
     21: PetscErrorCode MatCreateLaplacian(Mat A, PetscReal tol, PetscBool weighted, Mat *L)
     22: {
     23:   PetscScalar   *newVals;
     24:   PetscInt      *newCols;
     25:   PetscInt       rStart, rEnd, r, colMax = 0;
     26:   PetscInt      *dnnz, *onnz;
     27:   PetscInt       m, n, M, N;

     31:   if (weighted) SETERRQ(PetscObjectComm((PetscObject) A), PETSC_ERR_SUP, "Will get to this soon");
     32:   MatCreate(PetscObjectComm((PetscObject) A), L);
     33:   MatGetSize(A, &M, &N);
     34:   MatGetLocalSize(A, &m, &n);
     35:   MatSetSizes(*L, m, n, M, N);
     36:   MatGetOwnershipRange(A, &rStart, &rEnd);
     37:   PetscMalloc2(m,&dnnz,m,&onnz);
     38:   for (r = rStart; r < rEnd; ++r) {
     39:     const PetscScalar *vals;
     40:     const PetscInt    *cols;
     41:     PetscInt           ncols, newcols, c;
     42:     PetscBool          hasdiag = PETSC_FALSE;

     44:     dnnz[r-rStart] = onnz[r-rStart] = 0;
     45:     MatGetRow(A, r, &ncols, &cols, &vals);
     46:     for (c = 0, newcols = 0; c < ncols; ++c) {
     47:       if (cols[c] == r) {
     48:         ++newcols;
     49:         hasdiag = PETSC_TRUE;
     50:         ++dnnz[r-rStart];
     51:       } else if (PetscAbsScalar(vals[c]) >= tol) {
     52:         if ((cols[c] >= rStart) && (cols[c] < rEnd)) ++dnnz[r-rStart];
     53:         else                                         ++onnz[r-rStart];
     54:         ++newcols;
     55:       }
     56:     }
     57:     if (!hasdiag) {++newcols; ++dnnz[r-rStart];}
     58:     colMax = PetscMax(colMax, newcols);
     59:     MatRestoreRow(A, r, &ncols, &cols, &vals);
     60:   }
     61:   MatSetFromOptions(*L);
     62:   MatXAIJSetPreallocation(*L, 1, dnnz, onnz, NULL, NULL);
     63:   MatSetUp(*L);
     64:   PetscMalloc2(colMax,&newCols,colMax,&newVals);
     65:   for (r = rStart; r < rEnd; ++r) {
     66:     const PetscScalar *vals;
     67:     const PetscInt    *cols;
     68:     PetscInt           ncols, newcols, c;
     69:     PetscBool          hasdiag = PETSC_FALSE;

     71:     MatGetRow(A, r, &ncols, &cols, &vals);
     72:     for (c = 0, newcols = 0; c < ncols; ++c) {
     73:       if (cols[c] == r) {
     74:         newCols[newcols] = cols[c];
     75:         newVals[newcols] = dnnz[r-rStart]+onnz[r-rStart]-1;
     76:         ++newcols;
     77:         hasdiag = PETSC_TRUE;
     78:       } else if (PetscAbsScalar(vals[c]) >= tol) {
     79:         newCols[newcols] = cols[c];
     80:         newVals[newcols] = -1.0;
     81:         ++newcols;
     82:       }
     83:       if (newcols > colMax) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Overran work space");
     84:     }
     85:     if (!hasdiag) {
     86:       newCols[newcols] = r;
     87:       newVals[newcols] = dnnz[r-rStart]+onnz[r-rStart]-1;
     88:       ++newcols;
     89:     }
     90:     MatRestoreRow(A, r, &ncols, &cols, &vals);
     91:     MatSetValues(*L, 1, &r, newcols, newCols, newVals, INSERT_VALUES);
     92:   }
     93:   PetscFree2(dnnz,onnz);
     94:   MatAssemblyBegin(*L, MAT_FINAL_ASSEMBLY);
     95:   MatAssemblyEnd(*L, MAT_FINAL_ASSEMBLY);
     96:   PetscFree2(newCols,newVals);
     97:   return(0);
     98: }

    100: /*
    101:   MatGetOrdering_Spectral - Find the symmetric reordering of the graph by .
    102: */
    105: PETSC_EXTERN PetscErrorCode MatGetOrdering_Spectral(Mat A, MatOrderingType type, IS *row, IS *col)
    106: {
    107:   Mat             L;
    108:   PetscInt       *perm, tmp;
    109:   const PetscReal eps = 1.0e-12;
    110:   PetscErrorCode  ierr;

    113:   MatCreateLaplacian(A, eps, PETSC_FALSE, &L);
    114:   {
    115:     /* Check Laplacian */
    116:     PetscReal norm;
    117:     Vec       x, y;

    119:     MatCreateVecs(L, &x, NULL);
    120:     VecDuplicate(x, &y);
    121:     VecSet(x, 1.0);
    122:     MatMult(L, x, y);
    123:     VecNorm(y, NORM_INFINITY, &norm);
    124:     if (norm > 1.0e-10) SETERRQ(PetscObjectComm((PetscObject) y), PETSC_ERR_PLIB, "Invalid graph Laplacian");
    125:     VecDestroy(&x);
    126:     VecDestroy(&y);
    127:   }
    128:   /* Compute Fiedler vector (right now, all eigenvectors) */
    129:   {
    130:     Mat          LD;
    131:     PetscScalar *a;
    132:     PetscReal   *realpart, *imagpart, *eigvec, *work;
    133: #ifndef PETSC_USE_COMPLEX
    134:     PetscReal    sdummy;
    135: #endif
    136:     PetscBLASInt bn, bN, lwork, lierr, idummy;
    137:     PetscInt     n, i, evInd;

    139:     MatConvert(L, MATDENSE, MAT_INITIAL_MATRIX, &LD);
    140:     MatGetLocalSize(LD, &n, NULL);
    141:     MatDenseGetArray(LD, &a);
    142:     PetscBLASIntCast(n, &bn);
    143:     PetscBLASIntCast(n, &bN);
    144:     PetscBLASIntCast(5*n,&lwork);
    145:     PetscBLASIntCast(1,&idummy);
    146:     PetscMalloc4(n,&realpart,n,&imagpart,n*n,&eigvec,lwork,&work);
    147:     PetscFPTrapPush(PETSC_FP_TRAP_OFF);
    148: #ifdef PETSC_USE_COMPLEX
    149:     SETERRQ(PetscObjectComm((PetscObject) A), PETSC_ERR_SUP, "Spectral partitioning does not support complex numbers");
    150: #elif defined(PETSC_HAVE_ESSL)
    151:     SETERRQ(PetscObjectComm((PetscObject) A), PETSC_ERR_SUP, "Spectral partitioning does not support ESSL Lapack Routines");
    152: #else
    153:     PetscStackCall("LAPACKgeev", LAPACKgeev_("N","V",&bn,a,&bN,realpart,imagpart,&sdummy,&idummy,eigvec,&bN,work,&lwork,&lierr));
    154: #endif
    155:     if (lierr) SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_LIB, "Error in LAPACK routine %d", (int) lierr);
    156:     PetscFPTrapPop();
    157:     MatDenseRestoreArray(LD,&a);
    158:     MatDestroy(&LD);
    159:     /* Check lowest eigenvalue and eigenvector */
    160:     PetscMalloc1(n, &perm);
    161:     for (i = 0; i < n; ++i) perm[i] = i;
    162:     PetscSortRealWithPermutation(n,realpart,perm);
    163:     evInd = perm[0];
    164:     if ((realpart[evInd] > 1.0e-12) || (imagpart[evInd] > 1.0e-12)) SETERRQ(PetscObjectComm((PetscObject) L), PETSC_ERR_PLIB, "Graph Laplacian must have lowest eigenvalue 0");
    165:     evInd = perm[1];
    166:     if ((realpart[evInd] < 1.0e-12) && (imagpart[evInd] < 1.0e-12)) SETERRQ(PetscObjectComm((PetscObject) L), PETSC_ERR_PLIB, "Graph Laplacian must have only one zero eigenvalue");
    167:     evInd = perm[0];
    168:     for (i = 0; i < n; ++i) {
    169:       if (fabs(eigvec[evInd*n+i] - eigvec[evInd*n+0]) > 1.0e-10) SETERRQ3(PetscObjectComm((PetscObject) L), PETSC_ERR_PLIB, "Graph Laplacian must have constant lowest eigenvector ev_%d %g != ev_0 %g", i, eigvec[evInd*n+i], eigvec[evInd*n+0]);
    170:     }
    171:     /* Construct Fiedler partition */
    172:     evInd = perm[1];
    173:     for (i = 0; i < n; ++i) perm[i] = i;
    174:     PetscSortRealWithPermutation(n, &eigvec[evInd*n], perm);
    175:     for (i = 0; i < n/2; ++i) {
    176:       tmp          = perm[n-1-i];
    177:       perm[n-1-i] = perm[i];
    178:       perm[i]     = tmp;
    179:     }
    180:     ISCreateGeneral(PETSC_COMM_SELF, n, perm, PETSC_OWN_POINTER, row);
    181:     PetscObjectReference((PetscObject) *row);
    182:     *col = *row;

    184:     PetscFree4(realpart,imagpart,eigvec,work);
    185:     MatDestroy(&L);
    186:   }
    187:   return(0);
    188: }