Actual source code: baijsolvtran3.c

petsc-3.12.0 2019-09-29
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  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: }