Actual source code: baijsolvtran6.c

petsc-master 2019-12-13
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  1:  #include <../src/mat/impls/baij/seq/baij.h>
  2:  #include <petsc/private/kernels/blockinvert.h>

  4: PetscErrorCode MatSolveTranspose_SeqBAIJ_6_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,s4,s5,s6,x1,x2,x3,x4,x5,x6,*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      = 6*c[i];
 28:     t[ii]   = b[ic];
 29:     t[ii+1] = b[ic+1];
 30:     t[ii+2] = b[ic+2];
 31:     t[ii+3] = b[ic+3];
 32:     t[ii+4] = b[ic+4];
 33:     t[ii+5] = b[ic+5];
 34:     ii     += 6;
 35:   }

 37:   /* forward solve the U^T */
 38:   idx = 0;
 39:   for (i=0; i<n; i++) {

 41:     v = aa + 36*diag[i];
 42:     /* multiply by the inverse of the block diagonal */
 43:     x1 = t[idx];   x2 = t[1+idx]; x3    = t[2+idx]; x4 = t[3+idx]; x5 = t[4+idx];
 44:     x6 = t[5+idx];
 45:     s1 = v[0]*x1  +  v[1]*x2 +  v[2]*x3 +  v[3]*x4 +  v[4]*x5 +  v[5]*x6;
 46:     s2 = v[6]*x1  +  v[7]*x2 +  v[8]*x3 +  v[9]*x4 + v[10]*x5 + v[11]*x6;
 47:     s3 = v[12]*x1 + v[13]*x2 + v[14]*x3 + v[15]*x4 + v[16]*x5 + v[17]*x6;
 48:     s4 = v[18]*x1 + v[19]*x2 + v[20]*x3 + v[21]*x4 + v[22]*x5 + v[23]*x6;
 49:     s5 = v[24]*x1 + v[25]*x2 + v[26]*x3 + v[27]*x4 + v[28]*x5 + v[29]*x6;
 50:     s6 = v[30]*x1 + v[31]*x2 + v[32]*x3 + v[33]*x4 + v[34]*x5 + v[35]*x6;
 51:     v += 36;

 53:     vi = aj + diag[i] + 1;
 54:     nz = ai[i+1] - diag[i] - 1;
 55:     while (nz--) {
 56:       oidx       = 6*(*vi++);
 57:       t[oidx]   -= v[0]*s1  +  v[1]*s2 +  v[2]*s3 +  v[3]*s4 +  v[4]*s5 +  v[5]*s6;
 58:       t[oidx+1] -= v[6]*s1  +  v[7]*s2 +  v[8]*s3 +  v[9]*s4 + v[10]*s5 + v[11]*s6;
 59:       t[oidx+2] -= v[12]*s1 + v[13]*s2 + v[14]*s3 + v[15]*s4 + v[16]*s5 + v[17]*s6;
 60:       t[oidx+3] -= v[18]*s1 + v[19]*s2 + v[20]*s3 + v[21]*s4 + v[22]*s5 + v[23]*s6;
 61:       t[oidx+4] -= v[24]*s1 + v[25]*s2 + v[26]*s3 + v[27]*s4 + v[28]*s5 + v[29]*s6;
 62:       t[oidx+5] -= v[30]*s1 + v[31]*s2 + v[32]*s3 + v[33]*s4 + v[34]*s5 + v[35]*s6;
 63:       v         += 36;
 64:     }
 65:     t[idx]   = s1;t[1+idx] = s2; t[2+idx] = s3;t[3+idx] = s4; t[4+idx] = s5;
 66:     t[5+idx] = s6;
 67:     idx     += 6;
 68:   }
 69:   /* backward solve the L^T */
 70:   for (i=n-1; i>=0; i--) {
 71:     v   = aa + 36*diag[i] - 36;
 72:     vi  = aj + diag[i] - 1;
 73:     nz  = diag[i] - ai[i];
 74:     idt = 6*i;
 75:     s1  = t[idt];  s2 = t[1+idt]; s3 = t[2+idt];s4 = t[3+idt]; s5 = t[4+idt];
 76:     s6  = t[5+idt];
 77:     while (nz--) {
 78:       idx       = 6*(*vi--);
 79:       t[idx]   -=  v[0]*s1 +  v[1]*s2 +  v[2]*s3 +  v[3]*s4 +  v[4]*s5 +  v[5]*s6;
 80:       t[idx+1] -=  v[6]*s1 +  v[7]*s2 +  v[8]*s3 +  v[9]*s4 + v[10]*s5 + v[11]*s6;
 81:       t[idx+2] -= v[12]*s1 + v[13]*s2 + v[14]*s3 + v[15]*s4 + v[16]*s5 + v[17]*s6;
 82:       t[idx+3] -= v[18]*s1 + v[19]*s2 + v[20]*s3 + v[21]*s4 + v[22]*s5 + v[23]*s6;
 83:       t[idx+4] -= v[24]*s1 + v[25]*s2 + v[26]*s3 + v[27]*s4 + v[28]*s5 + v[29]*s6;
 84:       t[idx+5] -= v[30]*s1 + v[31]*s2 + v[32]*s3 + v[33]*s4 + v[34]*s5 + v[35]*s6;
 85:       v        -= 36;
 86:     }
 87:   }

 89:   /* copy t into x according to permutation */
 90:   ii = 0;
 91:   for (i=0; i<n; i++) {
 92:     ir      = 6*r[i];
 93:     x[ir]   = t[ii];
 94:     x[ir+1] = t[ii+1];
 95:     x[ir+2] = t[ii+2];
 96:     x[ir+3] = t[ii+3];
 97:     x[ir+4] = t[ii+4];
 98:     x[ir+5] = t[ii+5];
 99:     ii     += 6;
100:   }

102:   ISRestoreIndices(isrow,&rout);
103:   ISRestoreIndices(iscol,&cout);
104:   VecRestoreArrayRead(bb,&b);
105:   VecRestoreArray(xx,&x);
106:   PetscLogFlops(2.0*36*(a->nz) - 6.0*A->cmap->n);
107:   return(0);
108: }

110: PetscErrorCode MatSolveTranspose_SeqBAIJ_6(Mat A,Vec bb,Vec xx)
111: {
112:   Mat_SeqBAIJ       *a=(Mat_SeqBAIJ*)A->data;
113:   PetscErrorCode    ierr;
114:   IS                iscol=a->col,isrow=a->row;
115:   const PetscInt    n    =a->mbs,*vi,*ai=a->i,*aj=a->j,*diag=a->diag;
116:   const PetscInt    *r,*c,*rout,*cout;
117:   PetscInt          nz,idx,idt,j,i,oidx,ii,ic,ir;
118:   const PetscInt    bs =A->rmap->bs,bs2=a->bs2;
119:   const MatScalar   *aa=a->a,*v;
120:   PetscScalar       s1,s2,s3,s4,s5,s6,x1,x2,x3,x4,x5,x6,*x,*t;
121:   const PetscScalar *b;

124:   VecGetArrayRead(bb,&b);
125:   VecGetArray(xx,&x);
126:   t    = a->solve_work;

128:   ISGetIndices(isrow,&rout); r = rout;
129:   ISGetIndices(iscol,&cout); c = cout;

131:   /* copy b into temp work space according to permutation */
132:   for (i=0; i<n; i++) {
133:     ii      = bs*i; ic = bs*c[i];
134:     t[ii]   = b[ic]; t[ii+1] = b[ic+1]; t[ii+2] = b[ic+2]; t[ii+3] = b[ic+3];
135:     t[ii+4] = b[ic+4];  t[ii+5] = b[ic+5];
136:   }

138:   /* forward solve the U^T */
139:   idx = 0;
140:   for (i=0; i<n; i++) {
141:     v = aa + bs2*diag[i];
142:     /* multiply by the inverse of the block diagonal */
143:     x1 = t[idx];   x2 = t[1+idx]; x3    = t[2+idx]; x4 = t[3+idx]; x5 = t[4+idx];
144:     x6 = t[5+idx];
145:     s1 = v[0]*x1  +  v[1]*x2 +  v[2]*x3 +  v[3]*x4 +  v[4]*x5 +  v[5]*x6;
146:     s2 = v[6]*x1  +  v[7]*x2 +  v[8]*x3 +  v[9]*x4 + v[10]*x5 + v[11]*x6;
147:     s3 = v[12]*x1 + v[13]*x2 + v[14]*x3 + v[15]*x4 + v[16]*x5 + v[17]*x6;
148:     s4 = v[18]*x1 + v[19]*x2 + v[20]*x3 + v[21]*x4 + v[22]*x5 + v[23]*x6;
149:     s5 = v[24]*x1 + v[25]*x2 + v[26]*x3 + v[27]*x4 + v[28]*x5 + v[29]*x6;
150:     s6 = v[30]*x1 + v[31]*x2 + v[32]*x3 + v[33]*x4 + v[34]*x5 + v[35]*x6;
151:     v -= bs2;

153:     vi = aj + diag[i] - 1;
154:     nz = diag[i] - diag[i+1] - 1;
155:     for (j=0; j>-nz; j--) {
156:       oidx       = bs*vi[j];
157:       t[oidx]   -= v[0]*s1  +  v[1]*s2 +  v[2]*s3 +  v[3]*s4 +  v[4]*s5 +  v[5]*s6;
158:       t[oidx+1] -= v[6]*s1  +  v[7]*s2 +  v[8]*s3 +  v[9]*s4 + v[10]*s5 + v[11]*s6;
159:       t[oidx+2] -= v[12]*s1 + v[13]*s2 + v[14]*s3 + v[15]*s4 + v[16]*s5 + v[17]*s6;
160:       t[oidx+3] -= v[18]*s1 + v[19]*s2 + v[20]*s3 + v[21]*s4 + v[22]*s5 + v[23]*s6;
161:       t[oidx+4] -= v[24]*s1 + v[25]*s2 + v[26]*s3 + v[27]*s4 + v[28]*s5 + v[29]*s6;
162:       t[oidx+5] -= v[30]*s1 + v[31]*s2 + v[32]*s3 + v[33]*s4 + v[34]*s5 + v[35]*s6;
163:       v         -= bs2;
164:     }
165:     t[idx]   = s1;t[1+idx] = s2;  t[2+idx] = s3;  t[3+idx] = s4; t[4+idx] =s5;
166:     t[5+idx] = s6;
167:     idx     += bs;
168:   }
169:   /* backward solve the L^T */
170:   for (i=n-1; i>=0; i--) {
171:     v   = aa + bs2*ai[i];
172:     vi  = aj + ai[i];
173:     nz  = ai[i+1] - ai[i];
174:     idt = bs*i;
175:     s1  = t[idt];  s2 = t[1+idt];  s3 = t[2+idt];  s4 = t[3+idt]; s5 = t[4+idt];
176:     s6  = t[5+idt];
177:     for (j=0; j<nz; j++) {
178:       idx       = bs*vi[j];
179:       t[idx]   -= v[0]*s1  +  v[1]*s2 +  v[2]*s3 +  v[3]*s4 +  v[4]*s5 +  v[5]*s6;
180:       t[idx+1] -= v[6]*s1  +  v[7]*s2 +  v[8]*s3 +  v[9]*s4 + v[10]*s5 + v[11]*s6;
181:       t[idx+2] -= v[12]*s1 + v[13]*s2 + v[14]*s3 + v[15]*s4 + v[16]*s5 + v[17]*s6;
182:       t[idx+3] -= v[18]*s1 + v[19]*s2 + v[20]*s3 + v[21]*s4 + v[22]*s5 + v[23]*s6;
183:       t[idx+4] -= v[24]*s1 + v[25]*s2 + v[26]*s3 + v[27]*s4 + v[28]*s5 + v[29]*s6;
184:       t[idx+5] -= v[30]*s1 + v[31]*s2 + v[32]*s3 + v[33]*s4 + v[34]*s5 + v[35]*s6;
185:       v        += bs2;
186:     }
187:   }

189:   /* copy t into x according to permutation */
190:   for (i=0; i<n; i++) {
191:     ii      = bs*i;  ir = bs*r[i];
192:     x[ir]   = t[ii];  x[ir+1] = t[ii+1]; x[ir+2] = t[ii+2];  x[ir+3] = t[ii+3];
193:     x[ir+4] = t[ii+4];  x[ir+5] = t[ii+5];
194:   }

196:   ISRestoreIndices(isrow,&rout);
197:   ISRestoreIndices(iscol,&cout);
198:   VecRestoreArrayRead(bb,&b);
199:   VecRestoreArray(xx,&x);
200:   PetscLogFlops(2.0*bs2*(a->nz) - bs*A->cmap->n);
201:   return(0);
202: }