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

Actual source code: baijsolvnat2.c

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

      4: /*
      5:       Special case where the matrix was ILU(0) factored in the natural
      6:    ordering. This eliminates the need for the column and row permutation.
      7: */
      8: PetscErrorCode MatSolve_SeqBAIJ_2_NaturalOrdering_inplace(Mat A,Vec bb,Vec xx)
      9: {
     10:   Mat_SeqBAIJ       *a = (Mat_SeqBAIJ*)A->data;
     11:   const PetscInt    n  =a->mbs,*vi,*ai=a->i,*aj=a->j,*diag=a->diag;
     12:   PetscErrorCode    ierr;
     13:   const MatScalar   *aa=a->a,*v;
     14:   PetscScalar       *x,s1,s2,x1,x2;
     15:   const PetscScalar *b;
     16:   PetscInt          jdx,idt,idx,nz,i;

     19:   VecGetArrayRead(bb,&b);
     20:   VecGetArray(xx,&x);

     22:   /* forward solve the lower triangular */
     23:   idx  = 0;
     24:   x[0] = b[0]; x[1] = b[1];
     25:   for (i=1; i<n; i++) {
     26:     v    =  aa      + 4*ai[i];
     27:     vi   =  aj      + ai[i];
     28:     nz   =  diag[i] - ai[i];
     29:     idx +=  2;
     30:     s1   =  b[idx];s2 = b[1+idx];
     31:     while (nz--) {
     32:       jdx = 2*(*vi++);
     33:       x1  = x[jdx];x2 = x[1+jdx];
     34:       s1 -= v[0]*x1 + v[2]*x2;
     35:       s2 -= v[1]*x1 + v[3]*x2;
     36:       v  += 4;
     37:     }
     38:     x[idx]   = s1;
     39:     x[1+idx] = s2;
     40:   }
     41:   /* backward solve the upper triangular */
     42:   for (i=n-1; i>=0; i--) {
     43:     v   = aa + 4*diag[i] + 4;
     44:     vi  = aj + diag[i] + 1;
     45:     nz  = ai[i+1] - diag[i] - 1;
     46:     idt = 2*i;
     47:     s1  = x[idt];  s2 = x[1+idt];
     48:     while (nz--) {
     49:       idx = 2*(*vi++);
     50:       x1  = x[idx];   x2 = x[1+idx];
     51:       s1 -= v[0]*x1 + v[2]*x2;
     52:       s2 -= v[1]*x1 + v[3]*x2;
     53:       v  += 4;
     54:     }
     55:     v        = aa +  4*diag[i];
     56:     x[idt]   = v[0]*s1 + v[2]*s2;
     57:     x[1+idt] = v[1]*s1 + v[3]*s2;
     58:   }

     60:   VecRestoreArrayRead(bb,&b);
     61:   VecRestoreArray(xx,&x);
     62:   PetscLogFlops(2.0*4*(a->nz) - 2.0*A->cmap->n);
     63:   return(0);
     64: }

     66: PetscErrorCode MatSolve_SeqBAIJ_2_NaturalOrdering(Mat A,Vec bb,Vec xx)
     67: {
     68:   Mat_SeqBAIJ       *a = (Mat_SeqBAIJ*)A->data;
     69:   const PetscInt    n  = a->mbs,*vi,*ai=a->i,*aj=a->j,*adiag=a->diag;
     70:   PetscInt          i,k,nz,idx,idt,jdx;
     71:   PetscErrorCode    ierr;
     72:   const MatScalar   *aa=a->a,*v;
     73:   PetscScalar       *x,s1,s2,x1,x2;
     74:   const PetscScalar *b;

     77:   VecGetArrayRead(bb,&b);
     78:   VecGetArray(xx,&x);
     79:   /* forward solve the lower triangular */
     80:   idx  = 0;
     81:   x[0] = b[idx]; x[1] = b[1+idx];
     82:   for (i=1; i<n; i++) {
     83:     v   = aa + 4*ai[i];
     84:     vi  = aj + ai[i];
     85:     nz  = ai[i+1] - ai[i];
     86:     idx = 2*i;
     87:     s1  = b[idx];s2 = b[1+idx];
     88:     PetscPrefetchBlock(vi+nz,nz,0,PETSC_PREFETCH_HINT_NTA);
     89:     PetscPrefetchBlock(v+4*nz,4*nz,0,PETSC_PREFETCH_HINT_NTA);
     90:     for (k=0; k<nz; k++) {
     91:       jdx = 2*vi[k];
     92:       x1  = x[jdx];x2 = x[1+jdx];
     93:       s1 -= v[0]*x1 + v[2]*x2;
     94:       s2 -= v[1]*x1 + v[3]*x2;
     95:       v  +=  4;
     96:     }
     97:     x[idx]   = s1;
     98:     x[1+idx] = s2;
     99:   }

    101:   /* backward solve the upper triangular */
    102:   for (i=n-1; i>=0; i--) {
    103:     v   = aa + 4*(adiag[i+1]+1);
    104:     vi  = aj + adiag[i+1]+1;
    105:     nz  = adiag[i] - adiag[i+1]-1;
    106:     idt = 2*i;
    107:     s1  = x[idt];  s2 = x[1+idt];
    108:     PetscPrefetchBlock(vi+nz,nz,0,PETSC_PREFETCH_HINT_NTA);
    109:     PetscPrefetchBlock(v+4*nz,4*nz,0,PETSC_PREFETCH_HINT_NTA);
    110:     for (k=0; k<nz; k++) {
    111:       idx = 2*vi[k];
    112:       x1  = x[idx];   x2 = x[1+idx];
    113:       s1 -= v[0]*x1 + v[2]*x2;
    114:       s2 -= v[1]*x1 + v[3]*x2;
    115:       v  += 4;
    116:     }
    117:     /* x = inv_diagonal*x */
    118:     x[idt]   = v[0]*s1 + v[2]*s2;
    119:     x[1+idt] = v[1]*s1 + v[3]*s2;
    120:   }

    122:   VecRestoreArrayRead(bb,&b);
    123:   VecRestoreArray(xx,&x);
    124:   PetscLogFlops(2.0*4*(a->nz) - 2.0*A->cmap->n);
    125:   return(0);
    126: }

    128: PetscErrorCode MatForwardSolve_SeqBAIJ_2_NaturalOrdering(Mat A,Vec bb,Vec xx)
    129: {
    130:   Mat_SeqBAIJ       *a = (Mat_SeqBAIJ*)A->data;
    131:   const PetscInt    n  = a->mbs,*vi,*ai=a->i,*aj=a->j;
    132:   PetscInt          i,k,nz,idx,jdx;
    133:   PetscErrorCode    ierr;
    134:   const MatScalar   *aa=a->a,*v;
    135:   PetscScalar       *x,s1,s2,x1,x2;
    136:   const PetscScalar *b;

    139:   VecGetArrayRead(bb,&b);
    140:   VecGetArray(xx,&x);
    141:   /* forward solve the lower triangular */
    142:   idx  = 0;
    143:   x[0] = b[idx]; x[1] = b[1+idx];
    144:   for (i=1; i<n; i++) {
    145:     v   = aa + 4*ai[i];
    146:     vi  = aj + ai[i];
    147:     nz  = ai[i+1] - ai[i];
    148:     idx = 2*i;
    149:     s1  = b[idx];s2 = b[1+idx];
    150:     PetscPrefetchBlock(vi+nz,nz,0,PETSC_PREFETCH_HINT_NTA);
    151:     PetscPrefetchBlock(v+4*nz,4*nz,0,PETSC_PREFETCH_HINT_NTA);
    152:     for (k=0; k<nz; k++) {
    153:       jdx = 2*vi[k];
    154:       x1  = x[jdx];x2 = x[1+jdx];
    155:       s1 -= v[0]*x1 + v[2]*x2;
    156:       s2 -= v[1]*x1 + v[3]*x2;
    157:       v  +=  4;
    158:     }
    159:     x[idx]   = s1;
    160:     x[1+idx] = s2;
    161:   }

    163:   VecRestoreArrayRead(bb,&b);
    164:   VecRestoreArray(xx,&x);
    165:   PetscLogFlops(4.0*(a->nz) - A->cmap->n);
    166:   return(0);
    167: }

    169: PetscErrorCode MatBackwardSolve_SeqBAIJ_2_NaturalOrdering(Mat A,Vec bb,Vec xx)
    170: {
    171:   Mat_SeqBAIJ       *a = (Mat_SeqBAIJ*)A->data;
    172:   const PetscInt    n  = a->mbs,*vi,*aj=a->j,*adiag=a->diag;
    173:   PetscInt          i,k,nz,idx,idt;
    174:   PetscErrorCode    ierr;
    175:   const MatScalar   *aa=a->a,*v;
    176:   PetscScalar       *x,s1,s2,x1,x2;
    177:   const PetscScalar *b;

    180:   VecGetArrayRead(bb,&b);
    181:   VecGetArray(xx,&x);

    183:   /* backward solve the upper triangular */
    184:   for (i=n-1; i>=0; i--) {
    185:     v   = aa + 4*(adiag[i+1]+1);
    186:     vi  = aj + adiag[i+1]+1;
    187:     nz  = adiag[i] - adiag[i+1]-1;
    188:     idt = 2*i;
    189:     s1  = b[idt];  s2 = b[1+idt];
    190:     PetscPrefetchBlock(vi+nz,nz,0,PETSC_PREFETCH_HINT_NTA);
    191:     PetscPrefetchBlock(v+4*nz,4*nz,0,PETSC_PREFETCH_HINT_NTA);
    192:     for (k=0; k<nz; k++) {
    193:       idx = 2*vi[k];
    194:       x1  = x[idx];   x2 = x[1+idx];
    195:       s1 -= v[0]*x1 + v[2]*x2;
    196:       s2 -= v[1]*x1 + v[3]*x2;
    197:       v  += 4;
    198:     }
    199:     /* x = inv_diagonal*x */
    200:     x[idt]   = v[0]*s1 + v[2]*s2;
    201:     x[1+idt] = v[1]*s1 + v[3]*s2;
    202:   }

    204:   VecRestoreArrayRead(bb,&b);
    205:   VecRestoreArray(xx,&x);
    206:   PetscLogFlops(4.0*a->nz - A->cmap->n);
    207:   return(0);
    208: }