Actual source code: baijsolvtran7.c

petsc-3.12.1 2019-10-22
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  1:  #include <../src/mat/impls/baij/seq/baij.h>
  2:  #include <petsc/private/kernels/blockinvert.h>

  4: PetscErrorCode MatSolveTranspose_SeqBAIJ_7_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,s7,x1,x2,x3,x4,x5,x6,x7,*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      = 7*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:     t[ii+6] = b[ic+6];
 35:     ii     += 7;
 36:   }

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

 42:     v = aa + 49*diag[i];
 43:     /* multiply by the inverse of the block diagonal */
 44:     x1 = t[idx];   x2 = t[1+idx]; x3    = t[2+idx]; x4 = t[3+idx]; x5 = t[4+idx];
 45:     x6 = t[5+idx]; x7 = t[6+idx];
 46:     s1 = v[0]*x1  +  v[1]*x2 +  v[2]*x3 +  v[3]*x4 +  v[4]*x5 +  v[5]*x6 +  v[6]*x7;
 47:     s2 = v[7]*x1  +  v[8]*x2 +  v[9]*x3 + v[10]*x4 + v[11]*x5 + v[12]*x6 + v[13]*x7;
 48:     s3 = v[14]*x1 + v[15]*x2 + v[16]*x3 + v[17]*x4 + v[18]*x5 + v[19]*x6 + v[20]*x7;
 49:     s4 = v[21]*x1 + v[22]*x2 + v[23]*x3 + v[24]*x4 + v[25]*x5 + v[26]*x6 + v[27]*x7;
 50:     s5 = v[28]*x1 + v[29]*x2 + v[30]*x3 + v[31]*x4 + v[32]*x5 + v[33]*x6 + v[34]*x7;
 51:     s6 = v[35]*x1 + v[36]*x2 + v[37]*x3 + v[38]*x4 + v[39]*x5 + v[40]*x6 + v[41]*x7;
 52:     s7 = v[42]*x1 + v[43]*x2 + v[44]*x3 + v[45]*x4 + v[46]*x5 + v[47]*x6 + v[48]*x7;
 53:     v += 49;

 55:     vi = aj + diag[i] + 1;
 56:     nz = ai[i+1] - diag[i] - 1;
 57:     while (nz--) {
 58:       oidx       = 7*(*vi++);
 59:       t[oidx]   -= v[0]*s1  +  v[1]*s2 +  v[2]*s3 +  v[3]*s4 +  v[4]*s5 +  v[5]*s6 +  v[6]*s7;
 60:       t[oidx+1] -= v[7]*s1  +  v[8]*s2 +  v[9]*s3 + v[10]*s4 + v[11]*s5 + v[12]*s6 + v[13]*s7;
 61:       t[oidx+2] -= v[14]*s1 + v[15]*s2 + v[16]*s3 + v[17]*s4 + v[18]*s5 + v[19]*s6 + v[20]*s7;
 62:       t[oidx+3] -= v[21]*s1 + v[22]*s2 + v[23]*s3 + v[24]*s4 + v[25]*s5 + v[26]*s6 + v[27]*s7;
 63:       t[oidx+4] -= v[28]*s1 + v[29]*s2 + v[30]*s3 + v[31]*s4 + v[32]*s5 + v[33]*s6 + v[34]*s7;
 64:       t[oidx+5] -= v[35]*s1 + v[36]*s2 + v[37]*s3 + v[38]*s4 + v[39]*s5 + v[40]*s6 + v[41]*s7;
 65:       t[oidx+6] -= v[42]*s1 + v[43]*s2 + v[44]*s3 + v[45]*s4 + v[46]*s5 + v[47]*s6 + v[48]*s7;
 66:       v         += 49;
 67:     }
 68:     t[idx]   = s1;t[1+idx] = s2; t[2+idx] = s3;t[3+idx] = s4; t[4+idx] = s5;
 69:     t[5+idx] = s6;t[6+idx] = s7;
 70:     idx     += 7;
 71:   }
 72:   /* backward solve the L^T */
 73:   for (i=n-1; i>=0; i--) {
 74:     v   = aa + 49*diag[i] - 49;
 75:     vi  = aj + diag[i] - 1;
 76:     nz  = diag[i] - ai[i];
 77:     idt = 7*i;
 78:     s1  = t[idt];  s2 = t[1+idt]; s3 = t[2+idt];s4 = t[3+idt]; s5 = t[4+idt];
 79:     s6  = t[5+idt];s7 = t[6+idt];
 80:     while (nz--) {
 81:       idx       = 7*(*vi--);
 82:       t[idx]   -=  v[0]*s1 +  v[1]*s2 +  v[2]*s3 +  v[3]*s4 +  v[4]*s5 +  v[5]*s6 +  v[6]*s7;
 83:       t[idx+1] -=  v[7]*s1 +  v[8]*s2 +  v[9]*s3 + v[10]*s4 + v[11]*s5 + v[12]*s6 + v[13]*s7;
 84:       t[idx+2] -= v[14]*s1 + v[15]*s2 + v[16]*s3 + v[17]*s4 + v[18]*s5 + v[19]*s6 + v[20]*s7;
 85:       t[idx+3] -= v[21]*s1 + v[22]*s2 + v[23]*s3 + v[24]*s4 + v[25]*s5 + v[26]*s6 + v[27]*s7;
 86:       t[idx+4] -= v[28]*s1 + v[29]*s2 + v[30]*s3 + v[31]*s4 + v[32]*s5 + v[33]*s6 + v[34]*s7;
 87:       t[idx+5] -= v[35]*s1 + v[36]*s2 + v[37]*s3 + v[38]*s4 + v[39]*s5 + v[40]*s6 + v[41]*s7;
 88:       t[idx+6] -= v[42]*s1 + v[43]*s2 + v[44]*s3 + v[45]*s4 + v[46]*s5 + v[47]*s6 + v[48]*s7;
 89:       v        -= 49;
 90:     }
 91:   }

 93:   /* copy t into x according to permutation */
 94:   ii = 0;
 95:   for (i=0; i<n; i++) {
 96:     ir      = 7*r[i];
 97:     x[ir]   = t[ii];
 98:     x[ir+1] = t[ii+1];
 99:     x[ir+2] = t[ii+2];
100:     x[ir+3] = t[ii+3];
101:     x[ir+4] = t[ii+4];
102:     x[ir+5] = t[ii+5];
103:     x[ir+6] = t[ii+6];
104:     ii     += 7;
105:   }

107:   ISRestoreIndices(isrow,&rout);
108:   ISRestoreIndices(iscol,&cout);
109:   VecRestoreArrayRead(bb,&b);
110:   VecRestoreArray(xx,&x);
111:   PetscLogFlops(2.0*49*(a->nz) - 7.0*A->cmap->n);
112:   return(0);
113: }
114: PetscErrorCode MatSolveTranspose_SeqBAIJ_7(Mat A,Vec bb,Vec xx)
115: {
116:   Mat_SeqBAIJ       *a=(Mat_SeqBAIJ*)A->data;
117:   PetscErrorCode    ierr;
118:   IS                iscol=a->col,isrow=a->row;
119:   const PetscInt    n    =a->mbs,*vi,*ai=a->i,*aj=a->j,*diag=a->diag;
120:   const PetscInt    *r,*c,*rout,*cout;
121:   PetscInt          nz,idx,idt,j,i,oidx,ii,ic,ir;
122:   const PetscInt    bs =A->rmap->bs,bs2=a->bs2;
123:   const MatScalar   *aa=a->a,*v;
124:   PetscScalar       s1,s2,s3,s4,s5,s6,s7,x1,x2,x3,x4,x5,x6,x7,*x,*t;
125:   const PetscScalar *b;

128:   VecGetArrayRead(bb,&b);
129:   VecGetArray(xx,&x);
130:   t    = a->solve_work;

132:   ISGetIndices(isrow,&rout); r = rout;
133:   ISGetIndices(iscol,&cout); c = cout;

135:   /* copy b into temp work space according to permutation */
136:   for (i=0; i<n; i++) {
137:     ii      = bs*i; ic = bs*c[i];
138:     t[ii]   = b[ic]; t[ii+1] = b[ic+1]; t[ii+2] = b[ic+2]; t[ii+3] = b[ic+3];
139:     t[ii+4] = b[ic+4];  t[ii+5] = b[ic+5];  t[ii+6] = b[ic+6];
140:   }

142:   /* forward solve the U^T */
143:   idx = 0;
144:   for (i=0; i<n; i++) {
145:     v = aa + bs2*diag[i];
146:     /* multiply by the inverse of the block diagonal */
147:     x1 = t[idx];   x2 = t[1+idx]; x3    = t[2+idx]; x4 = t[3+idx]; x5 = t[4+idx];
148:     x6 = t[5+idx]; x7 = t[6+idx];
149:     s1 = v[0]*x1  +  v[1]*x2 +  v[2]*x3 +  v[3]*x4 +  v[4]*x5 +  v[5]*x6 +  v[6]*x7;
150:     s2 = v[7]*x1  +  v[8]*x2 +  v[9]*x3 + v[10]*x4 + v[11]*x5 + v[12]*x6 + v[13]*x7;
151:     s3 = v[14]*x1 + v[15]*x2 + v[16]*x3 + v[17]*x4 + v[18]*x5 + v[19]*x6 + v[20]*x7;
152:     s4 = v[21]*x1 + v[22]*x2 + v[23]*x3 + v[24]*x4 + v[25]*x5 + v[26]*x6 + v[27]*x7;
153:     s5 = v[28]*x1 + v[29]*x2 + v[30]*x3 + v[31]*x4 + v[32]*x5 + v[33]*x6 + v[34]*x7;
154:     s6 = v[35]*x1 + v[36]*x2 + v[37]*x3 + v[38]*x4 + v[39]*x5 + v[40]*x6 + v[41]*x7;
155:     s7 = v[42]*x1 + v[43]*x2 + v[44]*x3 + v[45]*x4 + v[46]*x5 + v[47]*x6 + v[48]*x7;
156:     v -= bs2;

158:     vi = aj + diag[i] - 1;
159:     nz = diag[i] - diag[i+1] - 1;
160:     for (j=0; j>-nz; j--) {
161:       oidx       = bs*vi[j];
162:       t[oidx]   -= v[0]*s1  +  v[1]*s2 +  v[2]*s3 +  v[3]*s4 +  v[4]*s5 +  v[5]*s6 +  v[6]*s7;
163:       t[oidx+1] -= v[7]*s1  +  v[8]*s2 +  v[9]*s3 + v[10]*s4 + v[11]*s5 + v[12]*s6 + v[13]*s7;
164:       t[oidx+2] -= v[14]*s1 + v[15]*s2 + v[16]*s3 + v[17]*s4 + v[18]*s5 + v[19]*s6 + v[20]*s7;
165:       t[oidx+3] -= v[21]*s1 + v[22]*s2 + v[23]*s3 + v[24]*s4 + v[25]*s5 + v[26]*s6 + v[27]*s7;
166:       t[oidx+4] -= v[28]*s1 + v[29]*s2 + v[30]*s3 + v[31]*s4 + v[32]*s5 + v[33]*s6 + v[34]*s7;
167:       t[oidx+5] -= v[35]*s1 + v[36]*s2 + v[37]*s3 + v[38]*s4 + v[39]*s5 + v[40]*s6 + v[41]*s7;
168:       t[oidx+6] -= v[42]*s1 + v[43]*s2 + v[44]*s3 + v[45]*s4 + v[46]*s5 + v[47]*s6 + v[48]*s7;
169:       v         -= bs2;
170:     }
171:     t[idx]   = s1;t[1+idx] = s2;  t[2+idx] = s3;  t[3+idx] = s4; t[4+idx] =s5;
172:     t[5+idx] = s6;  t[6+idx] = s7;
173:     idx     += bs;
174:   }
175:   /* backward solve the L^T */
176:   for (i=n-1; i>=0; i--) {
177:     v   = aa + bs2*ai[i];
178:     vi  = aj + ai[i];
179:     nz  = ai[i+1] - ai[i];
180:     idt = bs*i;
181:     s1  = t[idt];  s2 = t[1+idt];  s3 = t[2+idt];  s4 = t[3+idt]; s5 = t[4+idt];
182:     s6  = t[5+idt];  s7 = t[6+idt];
183:     for (j=0; j<nz; j++) {
184:       idx       = bs*vi[j];
185:       t[idx]   -=  v[0]*s1 +  v[1]*s2 +  v[2]*s3 +  v[3]*s4 +  v[4]*s5 +  v[5]*s6 +  v[6]*s7;
186:       t[idx+1] -=  v[7]*s1 +  v[8]*s2 +  v[9]*s3 + v[10]*s4 + v[11]*s5 + v[12]*s6 + v[13]*s7;
187:       t[idx+2] -= v[14]*s1 + v[15]*s2 + v[16]*s3 + v[17]*s4 + v[18]*s5 + v[19]*s6 + v[20]*s7;
188:       t[idx+3] -= v[21]*s1 + v[22]*s2 + v[23]*s3 + v[24]*s4 + v[25]*s5 + v[26]*s6 + v[27]*s7;
189:       t[idx+4] -= v[28]*s1 + v[29]*s2 + v[30]*s3 + v[31]*s4 + v[32]*s5 + v[33]*s6 + v[34]*s7;
190:       t[idx+5] -= v[35]*s1 + v[36]*s2 + v[37]*s3 + v[38]*s4 + v[39]*s5 + v[40]*s6 + v[41]*s7;
191:       t[idx+6] -= v[42]*s1 + v[43]*s2 + v[44]*s3 + v[45]*s4 + v[46]*s5 + v[47]*s6 + v[48]*s7;
192:       v        += bs2;
193:     }
194:   }

196:   /* copy t into x according to permutation */
197:   for (i=0; i<n; i++) {
198:     ii      = bs*i;  ir = bs*r[i];
199:     x[ir]   = t[ii];  x[ir+1] = t[ii+1]; x[ir+2] = t[ii+2];  x[ir+3] = t[ii+3];
200:     x[ir+4] = t[ii+4];  x[ir+5] = t[ii+5];  x[ir+6] = t[ii+6];
201:   }

203:   ISRestoreIndices(isrow,&rout);
204:   ISRestoreIndices(iscol,&cout);
205:   VecRestoreArrayRead(bb,&b);
206:   VecRestoreArray(xx,&x);
207:   PetscLogFlops(2.0*bs2*(a->nz) - bs*A->cmap->n);
208:   return(0);
209: }