Date: 2022-03-04T17:37:50+00:00

Actual source code: baijsolvtran3.c

      1: #include <../src/mat/impls/baij/seq/baij.h>
      2: #include <petsc/private/kernels/blockinvert.h>

      4: PetscErrorCode MatSolveTranspose_SeqBAIJ_3_inplace(Mat A,Vec bb,Vec xx)
      5: {
      6:   Mat_SeqBAIJ       *a   =(Mat_SeqBAIJ*)A->data;
      7:   IS                iscol=a->col,isrow=a->row;
      8:   PetscErrorCode    ierr;
      9:   const PetscInt    *r,*c,*rout,*cout;
     10:   const PetscInt    *diag=a->diag,n=a->mbs,*vi,*ai=a->i,*aj=a->j;
     11:   PetscInt          i,nz,idx,idt,ii,ic,ir,oidx;
     12:   const MatScalar   *aa=a->a,*v;
     13:   PetscScalar       s1,s2,s3,x1,x2,x3,*x,*t;
     14:   const PetscScalar *b;

     17:   VecGetArrayRead(bb,&b);
     18:   VecGetArray(xx,&x);
     19:   t    = a->solve_work;

     21:   ISGetIndices(isrow,&rout); r = rout;
     22:   ISGetIndices(iscol,&cout); c = cout;

     24:   /* copy the b into temp work space according to permutation */
     25:   ii = 0;
     26:   for (i=0; i<n; i++) {
     27:     ic      = 3*c[i];
     28:     t[ii]   = b[ic];
     29:     t[ii+1] = b[ic+1];
     30:     t[ii+2] = b[ic+2];
     31:     ii     += 3;
     32:   }

     34:   /* forward solve the U^T */
     35:   idx = 0;
     36:   for (i=0; i<n; i++) {

     38:     v = aa + 9*diag[i];
     39:     /* multiply by the inverse of the block diagonal */
     40:     x1 = t[idx];   x2 = t[1+idx]; x3    = t[2+idx];
     41:     s1 = v[0]*x1  +  v[1]*x2 +  v[2]*x3;
     42:     s2 = v[3]*x1  +  v[4]*x2 +  v[5]*x3;
     43:     s3 = v[6]*x1  +  v[7]*x2 + v[8]*x3;
     44:     v += 9;

     46:     vi = aj + diag[i] + 1;
     47:     nz = ai[i+1] - diag[i] - 1;
     48:     while (nz--) {
     49:       oidx       = 3*(*vi++);
     50:       t[oidx]   -= v[0]*s1  +  v[1]*s2 +  v[2]*s3;
     51:       t[oidx+1] -= v[3]*s1  +  v[4]*s2 +  v[5]*s3;
     52:       t[oidx+2] -= v[6]*s1 + v[7]*s2 + v[8]*s3;
     53:       v         += 9;
     54:     }
     55:     t[idx] = s1;t[1+idx] = s2; t[2+idx] = s3;
     56:     idx   += 3;
     57:   }
     58:   /* backward solve the L^T */
     59:   for (i=n-1; i>=0; i--) {
     60:     v   = aa + 9*diag[i] - 9;
     61:     vi  = aj + diag[i] - 1;
     62:     nz  = diag[i] - ai[i];
     63:     idt = 3*i;
     64:     s1  = t[idt];  s2 = t[1+idt]; s3 = t[2+idt];
     65:     while (nz--) {
     66:       idx       = 3*(*vi--);
     67:       t[idx]   -=  v[0]*s1 +  v[1]*s2 +  v[2]*s3;
     68:       t[idx+1] -=  v[3]*s1 +  v[4]*s2 +  v[5]*s3;
     69:       t[idx+2] -= v[6]*s1 + v[7]*s2 + v[8]*s3;
     70:       v        -= 9;
     71:     }
     72:   }

     74:   /* copy t into x according to permutation */
     75:   ii = 0;
     76:   for (i=0; i<n; i++) {
     77:     ir      = 3*r[i];
     78:     x[ir]   = t[ii];
     79:     x[ir+1] = t[ii+1];
     80:     x[ir+2] = t[ii+2];
     81:     ii     += 3;
     82:   }

     84:   ISRestoreIndices(isrow,&rout);
     85:   ISRestoreIndices(iscol,&cout);
     86:   VecRestoreArrayRead(bb,&b);
     87:   VecRestoreArray(xx,&x);
     88:   PetscLogFlops(2.0*9*(a->nz) - 3.0*A->cmap->n);
     89:   return(0);
     90: }

     92: PetscErrorCode MatSolveTranspose_SeqBAIJ_3(Mat A,Vec bb,Vec xx)
     93: {
     94:   Mat_SeqBAIJ       *a=(Mat_SeqBAIJ*)A->data;
     95:   PetscErrorCode    ierr;
     96:   IS                iscol=a->col,isrow=a->row;
     97:   const PetscInt    n    =a->mbs,*vi,*ai=a->i,*aj=a->j,*diag=a->diag;
     98:   const PetscInt    *r,*c,*rout,*cout;
     99:   PetscInt          nz,idx,idt,j,i,oidx,ii,ic,ir;
    100:   const PetscInt    bs =A->rmap->bs,bs2=a->bs2;
    101:   const MatScalar   *aa=a->a,*v;
    102:   PetscScalar       s1,s2,s3,x1,x2,x3,*x,*t;
    103:   const PetscScalar *b;

    106:   VecGetArrayRead(bb,&b);
    107:   VecGetArray(xx,&x);
    108:   t    = a->solve_work;

    110:   ISGetIndices(isrow,&rout); r = rout;
    111:   ISGetIndices(iscol,&cout); c = cout;

    113:   /* copy b into temp work space according to permutation */
    114:   for (i=0; i<n; i++) {
    115:     ii    = bs*i; ic = bs*c[i];
    116:     t[ii] = b[ic]; t[ii+1] = b[ic+1]; t[ii+2] = b[ic+2];
    117:   }

    119:   /* forward solve the U^T */
    120:   idx = 0;
    121:   for (i=0; i<n; i++) {
    122:     v = aa + bs2*diag[i];
    123:     /* multiply by the inverse of the block diagonal */
    124:     x1 = t[idx];   x2 = t[1+idx]; x3    = t[2+idx];
    125:     s1 = v[0]*x1  +  v[1]*x2 +  v[2]*x3;
    126:     s2 = v[3]*x1  +  v[4]*x2 +  v[5]*x3;
    127:     s3 = v[6]*x1  +  v[7]*x2 + v[8]*x3;
    128:     v -= bs2;

    130:     vi = aj + diag[i] - 1;
    131:     nz = diag[i] - diag[i+1] - 1;
    132:     for (j=0; j>-nz; j--) {
    133:       oidx       = bs*vi[j];
    134:       t[oidx]   -= v[0]*s1  +  v[1]*s2 +  v[2]*s3;
    135:       t[oidx+1] -= v[3]*s1  +  v[4]*s2 +  v[5]*s3;
    136:       t[oidx+2] -= v[6]*s1 + v[7]*s2 + v[8]*s3;
    137:       v         -= bs2;
    138:     }
    139:     t[idx] = s1;t[1+idx] = s2;  t[2+idx] = s3;
    140:     idx   += bs;
    141:   }
    142:   /* backward solve the L^T */
    143:   for (i=n-1; i>=0; i--) {
    144:     v   = aa + bs2*ai[i];
    145:     vi  = aj + ai[i];
    146:     nz  = ai[i+1] - ai[i];
    147:     idt = bs*i;
    148:     s1  = t[idt];  s2 = t[1+idt];  s3 = t[2+idt];
    149:     for (j=0; j<nz; j++) {
    150:       idx       = bs*vi[j];
    151:       t[idx]   -= v[0]*s1  +  v[1]*s2 +  v[2]*s3;
    152:       t[idx+1] -= v[3]*s1  +  v[4]*s2 +  v[5]*s3;
    153:       t[idx+2] -= v[6]*s1 + v[7]*s2 + v[8]*s3;
    154:       v        += bs2;
    155:     }
    156:   }

    158:   /* copy t into x according to permutation */
    159:   for (i=0; i<n; i++) {
    160:     ii    = bs*i;  ir = bs*r[i];
    161:     x[ir] = t[ii];  x[ir+1] = t[ii+1]; x[ir+2] = t[ii+2];
    162:   }

    164:   ISRestoreIndices(isrow,&rout);
    165:   ISRestoreIndices(iscol,&cout);
    166:   VecRestoreArrayRead(bb,&b);
    167:   VecRestoreArray(xx,&x);
    168:   PetscLogFlops(2.0*bs2*(a->nz) - bs*A->cmap->n);
    169:   return(0);
    170: }