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

Actual source code: baijsolvtran1.c

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

      4: PetscErrorCode MatSolveTranspose_SeqBAIJ_1(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    *rout,*cout,*r,*c,*adiag = a->diag,*ai = a->i,*aj = a->j,*vi;
     10:   PetscInt          i,n = a->mbs,j;
     11:   PetscInt          nz;
     12:   PetscScalar       *x,*tmp,s1;
     13:   const MatScalar   *aa = a->a,*v;
     14:   const PetscScalar *b;

     17:   VecGetArrayRead(bb,&b);
     18:   VecGetArray(xx,&x);
     19:   tmp  = 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:   for (i=0; i<n; i++) tmp[i] = b[c[i]];

     27:   /* forward solve the U^T */
     28:   for (i=0; i<n; i++) {
     29:     v   = aa + adiag[i+1] + 1;
     30:     vi  = aj + adiag[i+1] + 1;
     31:     nz  = adiag[i] - adiag[i+1] - 1;
     32:     s1  = tmp[i];
     33:     s1 *= v[nz];  /* multiply by inverse of diagonal entry */
     34:     for (j=0; j<nz; j++) tmp[vi[j]] -= s1*v[j];
     35:     tmp[i] = s1;
     36:   }

     38:   /* backward solve the L^T */
     39:   for (i=n-1; i>=0; i--) {
     40:     v  = aa + ai[i];
     41:     vi = aj + ai[i];
     42:     nz = ai[i+1] - ai[i];
     43:     s1 = tmp[i];
     44:     for (j=0; j<nz; j++) tmp[vi[j]] -= s1*v[j];
     45:   }

     47:   /* copy tmp into x according to permutation */
     48:   for (i=0; i<n; i++) x[r[i]] = tmp[i];

     50:   ISRestoreIndices(isrow,&rout);
     51:   ISRestoreIndices(iscol,&cout);
     52:   VecRestoreArrayRead(bb,&b);
     53:   VecRestoreArray(xx,&x);

     55:   PetscLogFlops(2.0*a->nz-A->cmap->n);
     56:   return(0);
     57: }

     59: PetscErrorCode MatSolveTranspose_SeqBAIJ_1_inplace(Mat A,Vec bb,Vec xx)
     60: {
     61:   Mat_SeqBAIJ       *a   =(Mat_SeqBAIJ*)A->data;
     62:   IS                iscol=a->col,isrow=a->row;
     63:   PetscErrorCode    ierr;
     64:   const PetscInt    *r,*c,*rout,*cout;
     65:   const PetscInt    *diag=a->diag,n=a->mbs,*vi,*ai=a->i,*aj=a->j;
     66:   PetscInt          i,nz;
     67:   const MatScalar   *aa=a->a,*v;
     68:   PetscScalar       s1,*x,*t;
     69:   const PetscScalar *b;

     72:   VecGetArrayRead(bb,&b);
     73:   VecGetArray(xx,&x);
     74:   t    = a->solve_work;

     76:   ISGetIndices(isrow,&rout); r = rout;
     77:   ISGetIndices(iscol,&cout); c = cout;

     79:   /* copy the b into temp work space according to permutation */
     80:   for (i=0; i<n; i++) t[i] = b[c[i]];

     82:   /* forward solve the U^T */
     83:   for (i=0; i<n; i++) {

     85:     v = aa + diag[i];
     86:     /* multiply by the inverse of the block diagonal */
     87:     s1 = (*v++)*t[i];
     88:     vi = aj + diag[i] + 1;
     89:     nz = ai[i+1] - diag[i] - 1;
     90:     while (nz--) {
     91:       t[*vi++] -= (*v++)*s1;
     92:     }
     93:     t[i] = s1;
     94:   }
     95:   /* backward solve the L^T */
     96:   for (i=n-1; i>=0; i--) {
     97:     v  = aa + diag[i] - 1;
     98:     vi = aj + diag[i] - 1;
     99:     nz = diag[i] - ai[i];
    100:     s1 = t[i];
    101:     while (nz--) {
    102:       t[*vi--] -=  (*v--)*s1;
    103:     }
    104:   }

    106:   /* copy t into x according to permutation */
    107:   for (i=0; i<n; i++) x[r[i]] = t[i];

    109:   ISRestoreIndices(isrow,&rout);
    110:   ISRestoreIndices(iscol,&cout);
    111:   VecRestoreArrayRead(bb,&b);
    112:   VecRestoreArray(xx,&x);
    113:   PetscLogFlops(2.0*(a->nz) - A->cmap->n);
    114:   return(0);
    115: }