Date: 2024-09-25T09:35:00+00:00

Actual source code: matutil.c
slepc-3.21.2 2024-09-25
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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: #include <slepc/private/slepcimpl.h>

     13: static PetscErrorCode MatCreateTile_Seq(PetscScalar a,Mat A,PetscScalar b,Mat B,PetscScalar c,Mat C,PetscScalar d,Mat D,Mat G)
     14: {
     15:   PetscInt          i,j,M1,M2,N1,N2,ncols,*scols;
     16:   PetscScalar       *svals,*buf;
     17:   const PetscInt    *cols;
     18:   const PetscScalar *vals;

     20:   PetscFunctionBegin;
     21:   PetscCall(MatGetSize(A,&M1,&N1));
     22:   PetscCall(MatGetSize(D,&M2,&N2));

     24:   PetscCall(PetscMalloc2(PetscMax(N1,N2),&buf,PetscMax(N1,N2),&scols));
     25:   /* Transfer A */
     26:   if (a!=0.0) {
     27:     for (i=0;i<M1;i++) {
     28:       PetscCall(MatGetRow(A,i,&ncols,&cols,&vals));
     29:       if (a!=1.0) {
     30:         svals=buf;
     31:         for (j=0;j<ncols;j++) svals[j] = vals[j]*a;
     32:       } else svals=(PetscScalar*)vals;
     33:       PetscCall(MatSetValues(G,1,&i,ncols,cols,svals,INSERT_VALUES));
     34:       PetscCall(MatRestoreRow(A,i,&ncols,&cols,&vals));
     35:     }
     36:   }
     37:   /* Transfer B */
     38:   if (b!=0.0) {
     39:     for (i=0;i<M1;i++) {
     40:       PetscCall(MatGetRow(B,i,&ncols,&cols,&vals));
     41:       if (b!=1.0) {
     42:         svals=buf;
     43:         for (j=0;j<ncols;j++) svals[j] = vals[j]*b;
     44:       } else svals=(PetscScalar*)vals;
     45:       for (j=0;j<ncols;j++) scols[j] = cols[j]+N1;
     46:       PetscCall(MatSetValues(G,1,&i,ncols,scols,svals,INSERT_VALUES));
     47:       PetscCall(MatRestoreRow(B,i,&ncols,&cols,&vals));
     48:     }
     49:   }
     50:   /* Transfer C */
     51:   if (c!=0.0) {
     52:     for (i=0;i<M2;i++) {
     53:       PetscCall(MatGetRow(C,i,&ncols,&cols,&vals));
     54:       if (c!=1.0) {
     55:         svals=buf;
     56:         for (j=0;j<ncols;j++) svals[j] = vals[j]*c;
     57:       } else svals=(PetscScalar*)vals;
     58:       j = i+M1;
     59:       PetscCall(MatSetValues(G,1,&j,ncols,cols,svals,INSERT_VALUES));
     60:       PetscCall(MatRestoreRow(C,i,&ncols,&cols,&vals));
     61:     }
     62:   }
     63:   /* Transfer D */
     64:   if (d!=0.0) {
     65:     for (i=0;i<M2;i++) {
     66:       PetscCall(MatGetRow(D,i,&ncols,&cols,&vals));
     67:       if (d!=1.0) {
     68:         svals=buf;
     69:         for (j=0;j<ncols;j++) svals[j] = vals[j]*d;
     70:       } else svals=(PetscScalar*)vals;
     71:       for (j=0;j<ncols;j++) scols[j] = cols[j]+N1;
     72:       j = i+M1;
     73:       PetscCall(MatSetValues(G,1,&j,ncols,scols,svals,INSERT_VALUES));
     74:       PetscCall(MatRestoreRow(D,i,&ncols,&cols,&vals));
     75:     }
     76:   }
     77:   PetscCall(PetscFree2(buf,scols));
     78:   PetscFunctionReturn(PETSC_SUCCESS);
     79: }

     81: static PetscErrorCode MatCreateTile_MPI(PetscScalar a,Mat A,PetscScalar b,Mat B,PetscScalar c,Mat C,PetscScalar d,Mat D,Mat G)
     82: {
     83:   PetscMPIInt       np;
     84:   PetscInt          p,i,j,N1,N2,m1,m2,*map1,*map2;
     85:   PetscInt          ncols,*scols,start,gstart;
     86:   PetscScalar       *svals,*buf;
     87:   const PetscInt    *cols,*mapptr1,*mapptr2;
     88:   const PetscScalar *vals;

     90:   PetscFunctionBegin;
     91:   PetscCall(MatGetSize(A,NULL,&N1));
     92:   PetscCall(MatGetLocalSize(A,&m1,NULL));
     93:   PetscCall(MatGetSize(D,NULL,&N2));
     94:   PetscCall(MatGetLocalSize(D,&m2,NULL));

     96:   /* Create mappings */
     97:   PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)G),&np));
     98:   PetscCall(MatGetOwnershipRangesColumn(A,&mapptr1));
     99:   PetscCall(MatGetOwnershipRangesColumn(B,&mapptr2));
    100:   PetscCall(PetscMalloc4(PetscMax(N1,N2),&buf,PetscMax(N1,N2),&scols,N1,&map1,N2,&map2));
    101:   for (p=0;p<np;p++) {
    102:     for (i=mapptr1[p];i<mapptr1[p+1];i++) map1[i] = i+mapptr2[p];
    103:   }
    104:   for (p=0;p<np;p++) {
    105:     for (i=mapptr2[p];i<mapptr2[p+1];i++) map2[i] = i+mapptr1[p+1];
    106:   }
    107:   PetscCall(MatGetOwnershipRange(G,&gstart,NULL));

    109:   /* Transfer A */
    110:   if (a!=0.0) {
    111:     PetscCall(MatGetOwnershipRange(A,&start,NULL));
    112:     for (i=0;i<m1;i++) {
    113:       PetscCall(MatGetRow(A,i+start,&ncols,&cols,&vals));
    114:       if (a!=1.0) {
    115:         svals=buf;
    116:         for (j=0;j<ncols;j++) svals[j] = vals[j]*a;
    117:       } else svals=(PetscScalar*)vals;
    118:       for (j=0;j<ncols;j++) scols[j] = map1[cols[j]];
    119:       j = gstart+i;
    120:       PetscCall(MatSetValues(G,1,&j,ncols,scols,svals,INSERT_VALUES));
    121:       PetscCall(MatRestoreRow(A,i+start,&ncols,&cols,&vals));
    122:     }
    123:   }
    124:   /* Transfer B */
    125:   if (b!=0.0) {
    126:     PetscCall(MatGetOwnershipRange(B,&start,NULL));
    127:     for (i=0;i<m1;i++) {
    128:       PetscCall(MatGetRow(B,i+start,&ncols,&cols,&vals));
    129:       if (b!=1.0) {
    130:         svals=buf;
    131:         for (j=0;j<ncols;j++) svals[j] = vals[j]*b;
    132:       } else svals=(PetscScalar*)vals;
    133:       for (j=0;j<ncols;j++) scols[j] = map2[cols[j]];
    134:       j = gstart+i;
    135:       PetscCall(MatSetValues(G,1,&j,ncols,scols,svals,INSERT_VALUES));
    136:       PetscCall(MatRestoreRow(B,i+start,&ncols,&cols,&vals));
    137:     }
    138:   }
    139:   /* Transfer C */
    140:   if (c!=0.0) {
    141:     PetscCall(MatGetOwnershipRange(C,&start,NULL));
    142:     for (i=0;i<m2;i++) {
    143:       PetscCall(MatGetRow(C,i+start,&ncols,&cols,&vals));
    144:       if (c!=1.0) {
    145:         svals=buf;
    146:         for (j=0;j<ncols;j++) svals[j] = vals[j]*c;
    147:       } else svals=(PetscScalar*)vals;
    148:       for (j=0;j<ncols;j++) scols[j] = map1[cols[j]];
    149:       j = gstart+m1+i;
    150:       PetscCall(MatSetValues(G,1,&j,ncols,scols,svals,INSERT_VALUES));
    151:       PetscCall(MatRestoreRow(C,i+start,&ncols,&cols,&vals));
    152:     }
    153:   }
    154:   /* Transfer D */
    155:   if (d!=0.0) {
    156:     PetscCall(MatGetOwnershipRange(D,&start,NULL));
    157:     for (i=0;i<m2;i++) {
    158:       PetscCall(MatGetRow(D,i+start,&ncols,&cols,&vals));
    159:       if (d!=1.0) {
    160:         svals=buf;
    161:         for (j=0;j<ncols;j++) svals[j] = vals[j]*d;
    162:       } else svals=(PetscScalar*)vals;
    163:       for (j=0;j<ncols;j++) scols[j] = map2[cols[j]];
    164:       j = gstart+m1+i;
    165:       PetscCall(MatSetValues(G,1,&j,ncols,scols,svals,INSERT_VALUES));
    166:       PetscCall(MatRestoreRow(D,i+start,&ncols,&cols,&vals));
    167:     }
    168:   }
    169:   PetscCall(PetscFree4(buf,scols,map1,map2));
    170:   PetscFunctionReturn(PETSC_SUCCESS);
    171: }

    173: /*@
    174:    MatCreateTile - Explicitly build a matrix from four blocks, G = [ a*A b*B; c*C d*D ].

    176:    Collective

    178:    Input Parameters:
    179: +  A - matrix for top-left block
    180: .  a - scaling factor for block A
    181: .  B - matrix for top-right block
    182: .  b - scaling factor for block B
    183: .  C - matrix for bottom-left block
    184: .  c - scaling factor for block C
    185: .  D - matrix for bottom-right block
    186: -  d - scaling factor for block D

    188:    Output Parameter:
    189: .  G  - the resulting matrix

    191:    Notes:
    192:    In the case of a parallel matrix, a permuted version of G is returned. The permutation
    193:    is a perfect shuffle such that the local parts of A, B, C, D remain in the local part of
    194:    G for the same process.

    196:    Matrix G must be destroyed by the user.

    198:    The blocks can be of different type. They can be either ConstantDiagonal, or a standard
    199:    type such as AIJ, or any other type provided that it supports the MatGetRow operation.
    200:    The type of the output matrix will be the same as the first block that is not
    201:    ConstantDiagonal (checked in the A,B,C,D order).

    203:    Level: developer

    205: .seealso: MatCreateNest()
    206: @*/
    207: PetscErrorCode MatCreateTile(PetscScalar a,Mat A,PetscScalar b,Mat B,PetscScalar c,Mat C,PetscScalar d,Mat D,Mat *G)
    208: {
    209:   PetscInt       i,k,M1,M2,N1,N2,M,N,m1,m2,n1,n2,m,n,bs;
    210:   PetscBool      diag[4];
    211:   Mat            block[4] = {A,B,C,D};
    212:   MatType        type[4];
    213:   PetscMPIInt    size;

    215:   PetscFunctionBegin;
    220:   PetscCheckSameTypeAndComm(A,2,B,4);
    221:   PetscCheckSameTypeAndComm(A,2,C,6);
    222:   PetscCheckSameTypeAndComm(A,2,D,8);
    227:   PetscAssertPointer(G,9);

    229:   /* check row 1 */
    230:   PetscCall(MatGetSize(A,&M1,NULL));
    231:   PetscCall(MatGetLocalSize(A,&m1,NULL));
    232:   PetscCall(MatGetSize(B,&M,NULL));
    233:   PetscCall(MatGetLocalSize(B,&m,NULL));
    234:   PetscCheck(M==M1 && m==m1,PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_INCOMP,"Incompatible dimensions");
    235:   /* check row 2 */
    236:   PetscCall(MatGetSize(C,&M2,NULL));
    237:   PetscCall(MatGetLocalSize(C,&m2,NULL));
    238:   PetscCall(MatGetSize(D,&M,NULL));
    239:   PetscCall(MatGetLocalSize(D,&m,NULL));
    240:   PetscCheck(M==M2 && m==m2,PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_INCOMP,"Incompatible dimensions");
    241:   /* check column 1 */
    242:   PetscCall(MatGetSize(A,NULL,&N1));
    243:   PetscCall(MatGetLocalSize(A,NULL,&n1));
    244:   PetscCall(MatGetSize(C,NULL,&N));
    245:   PetscCall(MatGetLocalSize(C,NULL,&n));
    246:   PetscCheck(N==N1 && n==n1,PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_INCOMP,"Incompatible dimensions");
    247:   /* check column 2 */
    248:   PetscCall(MatGetSize(B,NULL,&N2));
    249:   PetscCall(MatGetLocalSize(B,NULL,&n2));
    250:   PetscCall(MatGetSize(D,NULL,&N));
    251:   PetscCall(MatGetLocalSize(D,NULL,&n));
    252:   PetscCheck(N==N2 && n==n2,PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_INCOMP,"Incompatible dimensions");

    254:   /* check matrix types */
    255:   for (i=0;i<4;i++) {
    256:     PetscCall(MatGetType(block[i],&type[i]));
    257:     PetscCall(PetscStrcmp(type[i],MATCONSTANTDIAGONAL,&diag[i]));
    258:   }
    259:   for (k=0;k<4;k++) if (!diag[k]) break;
    260:   PetscCheck(k<4,PetscObjectComm((PetscObject)A),PETSC_ERR_SUP,"Not implemented for 4 diagonal blocks");

    262:   PetscCall(MatGetBlockSize(block[k],&bs));
    263:   PetscCall(MatCreate(PetscObjectComm((PetscObject)block[k]),G));
    264:   PetscCall(MatSetSizes(*G,m1+m2,n1+n2,M1+M2,N1+N2));
    265:   PetscCall(MatSetType(*G,type[k]));
    266:   PetscCall(MatSetBlockSize(*G,bs));
    267:   PetscCall(MatSetUp(*G));

    269:   PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)*G),&size));
    270:   if (size>1) PetscCall(MatCreateTile_MPI(a,A,b,B,c,C,d,D,*G));
    271:   else PetscCall(MatCreateTile_Seq(a,A,b,B,c,C,d,D,*G));
    272:   PetscCall(MatAssemblyBegin(*G,MAT_FINAL_ASSEMBLY));
    273:   PetscCall(MatAssemblyEnd(*G,MAT_FINAL_ASSEMBLY));
    274:   PetscFunctionReturn(PETSC_SUCCESS);
    275: }

    277: /*@C
    278:    MatCreateVecsEmpty - Get vector(s) compatible with the matrix, i.e. with the same
    279:    parallel layout, but without internal array.

    281:    Collective

    283:    Input Parameter:
    284: .  mat - the matrix

    286:    Output Parameters:
    287: +  right - (optional) vector that the matrix can be multiplied against
    288: -  left - (optional) vector that the matrix vector product can be stored in

    290:    Note:
    291:    This is similar to MatCreateVecs(), but the new vectors do not have an internal
    292:    array, so the intended usage is with VecPlaceArray().

    294:    Level: developer

    296: .seealso: VecDuplicateEmpty()
    297: @*/
    298: PetscErrorCode MatCreateVecsEmpty(Mat mat,Vec *right,Vec *left)
    299: {
    300:   PetscBool      standard,cuda=PETSC_FALSE,skip=PETSC_FALSE;
    301:   PetscInt       M,N,mloc,nloc,rbs,cbs;
    302:   PetscMPIInt    size;
    303:   Vec            v;

    305:   PetscFunctionBegin;

    309:   PetscCall(PetscObjectTypeCompareAny((PetscObject)mat,&standard,MATSEQAIJ,MATMPIAIJ,MATSEQBAIJ,MATMPIBAIJ,MATSEQSBAIJ,MATMPISBAIJ,MATSEQDENSE,MATMPIDENSE,""));
    310:   PetscCall(PetscObjectTypeCompareAny((PetscObject)mat,&cuda,MATSEQAIJCUSPARSE,MATMPIAIJCUSPARSE,""));
    311:   if (!standard && !cuda) {
    312:     PetscCall(MatCreateVecs(mat,right,left));
    313:     v = right? *right: *left;
    314:     if (v) {
    315:       PetscCall(PetscObjectTypeCompareAny((PetscObject)v,&standard,VECSEQ,VECMPI,""));
    316:       PetscCall(PetscObjectTypeCompareAny((PetscObject)v,&cuda,VECSEQCUDA,VECMPICUDA,""));
    317:     }
    318:     if (!standard && !cuda) skip = PETSC_TRUE;
    319:     else {
    320:       if (right) PetscCall(VecDestroy(right));
    321:       if (left) PetscCall(VecDestroy(left));
    322:     }
    323:   }
    324:   if (!skip) {
    325:     PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)mat),&size));
    326:     PetscCall(MatGetLocalSize(mat,&mloc,&nloc));
    327:     PetscCall(MatGetSize(mat,&M,&N));
    328:     PetscCall(MatGetBlockSizes(mat,&rbs,&cbs));
    329:     if (right) {
    330:       if (cuda) {
    331: #if defined(PETSC_HAVE_CUDA)
    332:         if (size>1) PetscCall(VecCreateMPICUDAWithArray(PetscObjectComm((PetscObject)mat),cbs,nloc,N,NULL,right));
    333:         else PetscCall(VecCreateSeqCUDAWithArray(PetscObjectComm((PetscObject)mat),cbs,N,NULL,right));
    334: #endif
    335:       } else {
    336:         if (size>1) PetscCall(VecCreateMPIWithArray(PetscObjectComm((PetscObject)mat),cbs,nloc,N,NULL,right));
    337:         else PetscCall(VecCreateSeqWithArray(PetscObjectComm((PetscObject)mat),cbs,N,NULL,right));
    338:       }
    339:     }
    340:     if (left) {
    341:       if (cuda) {
    342: #if defined(PETSC_HAVE_CUDA)
    343:         if (size>1) PetscCall(VecCreateMPICUDAWithArray(PetscObjectComm((PetscObject)mat),rbs,mloc,M,NULL,left));
    344:         else PetscCall(VecCreateSeqCUDAWithArray(PetscObjectComm((PetscObject)mat),rbs,M,NULL,left));
    345: #endif
    346:       } else {
    347:         if (size>1) PetscCall(VecCreateMPIWithArray(PetscObjectComm((PetscObject)mat),rbs,mloc,M,NULL,left));
    348:         else PetscCall(VecCreateSeqWithArray(PetscObjectComm((PetscObject)mat),rbs,M,NULL,left));
    349:       }
    350:     }
    351:   }
    352:   PetscFunctionReturn(PETSC_SUCCESS);
    353: }

    355: /*@C
    356:    MatNormEstimate - Estimate the 2-norm of a matrix.

    358:    Collective

    360:    Input Parameters:
    361: +  A   - the matrix
    362: .  vrn - random vector with normally distributed entries (can be NULL)
    363: -  w   - workspace vector (can be NULL)

    365:    Output Parameter:
    366: .  nrm - the norm estimate

    368:    Notes:
    369:    Does not need access to the matrix entries, just performs a matrix-vector product.
    370:    Based on work by I. Ipsen and coworkers https://ipsen.math.ncsu.edu/ps/slides_ima.pdf

    372:    The input vector vrn must have unit 2-norm.
    373:    If vrn is NULL, then it is created internally and filled with VecSetRandomNormal().

    375:    Level: developer

    377: .seealso: VecSetRandomNormal()
    378: @*/
    379: PetscErrorCode MatNormEstimate(Mat A,Vec vrn,Vec w,PetscReal *nrm)
    380: {
    381:   PetscInt       n;
    382:   Vec            vv=NULL,ww=NULL;

    384:   PetscFunctionBegin;
    389:   PetscAssertPointer(nrm,4);

    391:   if (!vrn) {
    392:     PetscCall(MatCreateVecs(A,&vv,NULL));
    393:     vrn = vv;
    394:     PetscCall(VecSetRandomNormal(vv,NULL,NULL,NULL));
    395:     PetscCall(VecNormalize(vv,NULL));
    396:   }
    397:   if (!w) {
    398:     PetscCall(MatCreateVecs(A,&ww,NULL));
    399:     w = ww;
    400:   }

    402:   PetscCall(MatGetSize(A,&n,NULL));
    403:   PetscCall(MatMult(A,vrn,w));
    404:   PetscCall(VecNorm(w,NORM_2,nrm));
    405:   *nrm *= PetscSqrtReal((PetscReal)n);

    407:   PetscCall(VecDestroy(&vv));
    408:   PetscCall(VecDestroy(&ww));
    409:   PetscFunctionReturn(PETSC_SUCCESS);
    410: }