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:   const PetscInt    *r,*c,*rout,*cout;
  9:   const PetscInt    *diag=a->diag,n=a->mbs,*vi,*ai=a->i,*aj=a->j;
 10:   PetscInt          i,nz,idx,idt,ii,ic,ir,oidx;
 11:   const MatScalar   *aa=a->a,*v;
 12:   PetscScalar       s1,s2,s3,x1,x2,x3,*x,*t;
 13:   const PetscScalar *b;

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

 19:   ISGetIndices(isrow,&rout); r = rout;
 20:   ISGetIndices(iscol,&cout); c = cout;

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

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

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

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

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

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

 90: PetscErrorCode MatSolveTranspose_SeqBAIJ_3(Mat A,Vec bb,Vec xx)
 91: {
 92:   Mat_SeqBAIJ       *a=(Mat_SeqBAIJ*)A->data;
 93:   IS                iscol=a->col,isrow=a->row;
 94:   const PetscInt    n    =a->mbs,*vi,*ai=a->i,*aj=a->j,*diag=a->diag;
 95:   const PetscInt    *r,*c,*rout,*cout;
 96:   PetscInt          nz,idx,idt,j,i,oidx,ii,ic,ir;
 97:   const PetscInt    bs =A->rmap->bs,bs2=a->bs2;
 98:   const MatScalar   *aa=a->a,*v;
 99:   PetscScalar       s1,s2,s3,x1,x2,x3,*x,*t;
100:   const PetscScalar *b;

102:   VecGetArrayRead(bb,&b);
103:   VecGetArray(xx,&x);
104:   t    = a->solve_work;

106:   ISGetIndices(isrow,&rout); r = rout;
107:   ISGetIndices(iscol,&cout); c = cout;

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

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

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

154:   /* copy t into x according to permutation */
155:   for (i=0; i<n; i++) {
156:     ii    = bs*i;  ir = bs*r[i];
157:     x[ir] = t[ii];  x[ir+1] = t[ii+1]; x[ir+2] = t[ii+2];
158:   }

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