Actual source code: sbaijfact5.c

petsc-3.12.2 2019-11-22
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  2:  #include <../src/mat/impls/sbaij/seq/sbaij.h>
  3:  #include <petsc/private/kernels/blockinvert.h>

  5: /*
  6:       Version for when blocks are 4 by 4 Using natural ordering
  7: */
  8: PetscErrorCode MatCholeskyFactorNumeric_SeqSBAIJ_4_NaturalOrdering(Mat C,Mat A,const MatFactorInfo *info)
  9: {
 10:   Mat_SeqSBAIJ   *a = (Mat_SeqSBAIJ*)A->data,*b = (Mat_SeqSBAIJ*)C->data;
 12:   PetscInt       i,j,mbs=a->mbs,*bi=b->i,*bj=b->j;
 13:   PetscInt       *ai,*aj,k,k1,jmin,jmax,*jl,*il,vj,nexti,ili;
 14:   MatScalar      *ba = b->a,*aa,*ap,*dk,*uik;
 15:   MatScalar      *u,*diag,*rtmp,*rtmp_ptr;
 16:   PetscBool      pivotinblocks = b->pivotinblocks;
 17:   PetscReal      shift         = info->shiftamount;
 18:   PetscBool      allowzeropivot,zeropivotdetected=PETSC_FALSE;

 21:   /* initialization */
 22:   allowzeropivot = PetscNot(A->erroriffailure);
 23:   PetscCalloc1(16*mbs,&rtmp);
 24:   PetscMalloc2(mbs,&il,mbs,&jl);
 25:   il[0] = 0;
 26:   for (i=0; i<mbs; i++) jl[i] = mbs;
 27: 
 28:   PetscMalloc2(16,&dk,16,&uik);
 29:   ai   = a->i; aj = a->j; aa = a->a;

 31:   /* for each row k */
 32:   for (k = 0; k<mbs; k++) {

 34:     /*initialize k-th row with elements nonzero in row k of A */
 35:     jmin = ai[k]; jmax = ai[k+1];
 36:     if (jmin < jmax) {
 37:       ap = aa + jmin*16;
 38:       for (j = jmin; j < jmax; j++) {
 39:         vj       = aj[j];   /* block col. index */
 40:         rtmp_ptr = rtmp + vj*16;
 41:         for (i=0; i<16; i++) *rtmp_ptr++ = *ap++;
 42:       }
 43:     }

 45:     /* modify k-th row by adding in those rows i with U(i,k) != 0 */
 46:     PetscArraycpy(dk,rtmp+k*16,16);
 47:     i    = jl[k]; /* first row to be added to k_th row  */

 49:     while (i < mbs) {
 50:       nexti = jl[i]; /* next row to be added to k_th row */

 52:       /* compute multiplier */
 53:       ili = il[i];  /* index of first nonzero element in U(i,k:bms-1) */

 55:       /* uik = -inv(Di)*U_bar(i,k) */
 56:       diag = ba + i*16;
 57:       u    = ba + ili*16;

 59:       uik[0] = -(diag[0]*u[0] + diag[4]*u[1] + diag[8]*u[2] + diag[12]*u[3]);
 60:       uik[1] = -(diag[1]*u[0] + diag[5]*u[1] + diag[9]*u[2] + diag[13]*u[3]);
 61:       uik[2] = -(diag[2]*u[0] + diag[6]*u[1] + diag[10]*u[2]+ diag[14]*u[3]);
 62:       uik[3] = -(diag[3]*u[0] + diag[7]*u[1] + diag[11]*u[2]+ diag[15]*u[3]);

 64:       uik[4] = -(diag[0]*u[4] + diag[4]*u[5] + diag[8]*u[6] + diag[12]*u[7]);
 65:       uik[5] = -(diag[1]*u[4] + diag[5]*u[5] + diag[9]*u[6] + diag[13]*u[7]);
 66:       uik[6] = -(diag[2]*u[4] + diag[6]*u[5] + diag[10]*u[6]+ diag[14]*u[7]);
 67:       uik[7] = -(diag[3]*u[4] + diag[7]*u[5] + diag[11]*u[6]+ diag[15]*u[7]);

 69:       uik[8] = -(diag[0]*u[8] + diag[4]*u[9] + diag[8]*u[10] + diag[12]*u[11]);
 70:       uik[9] = -(diag[1]*u[8] + diag[5]*u[9] + diag[9]*u[10] + diag[13]*u[11]);
 71:       uik[10]= -(diag[2]*u[8] + diag[6]*u[9] + diag[10]*u[10]+ diag[14]*u[11]);
 72:       uik[11]= -(diag[3]*u[8] + diag[7]*u[9] + diag[11]*u[10]+ diag[15]*u[11]);

 74:       uik[12]= -(diag[0]*u[12] + diag[4]*u[13] + diag[8]*u[14] + diag[12]*u[15]);
 75:       uik[13]= -(diag[1]*u[12] + diag[5]*u[13] + diag[9]*u[14] + diag[13]*u[15]);
 76:       uik[14]= -(diag[2]*u[12] + diag[6]*u[13] + diag[10]*u[14]+ diag[14]*u[15]);
 77:       uik[15]= -(diag[3]*u[12] + diag[7]*u[13] + diag[11]*u[14]+ diag[15]*u[15]);

 79:       /* update D(k) += -U(i,k)^T * U_bar(i,k) */
 80:       dk[0] += uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2] + uik[3]*u[3];
 81:       dk[1] += uik[4]*u[0] + uik[5]*u[1] + uik[6]*u[2] + uik[7]*u[3];
 82:       dk[2] += uik[8]*u[0] + uik[9]*u[1] + uik[10]*u[2]+ uik[11]*u[3];
 83:       dk[3] += uik[12]*u[0]+ uik[13]*u[1]+ uik[14]*u[2]+ uik[15]*u[3];

 85:       dk[4] += uik[0]*u[4] + uik[1]*u[5] + uik[2]*u[6] + uik[3]*u[7];
 86:       dk[5] += uik[4]*u[4] + uik[5]*u[5] + uik[6]*u[6] + uik[7]*u[7];
 87:       dk[6] += uik[8]*u[4] + uik[9]*u[5] + uik[10]*u[6]+ uik[11]*u[7];
 88:       dk[7] += uik[12]*u[4]+ uik[13]*u[5]+ uik[14]*u[6]+ uik[15]*u[7];

 90:       dk[8] += uik[0]*u[8] + uik[1]*u[9] + uik[2]*u[10] + uik[3]*u[11];
 91:       dk[9] += uik[4]*u[8] + uik[5]*u[9] + uik[6]*u[10] + uik[7]*u[11];
 92:       dk[10]+= uik[8]*u[8] + uik[9]*u[9] + uik[10]*u[10]+ uik[11]*u[11];
 93:       dk[11]+= uik[12]*u[8]+ uik[13]*u[9]+ uik[14]*u[10]+ uik[15]*u[11];

 95:       dk[12]+= uik[0]*u[12] + uik[1]*u[13] + uik[2]*u[14] + uik[3]*u[15];
 96:       dk[13]+= uik[4]*u[12] + uik[5]*u[13] + uik[6]*u[14] + uik[7]*u[15];
 97:       dk[14]+= uik[8]*u[12] + uik[9]*u[13] + uik[10]*u[14]+ uik[11]*u[15];
 98:       dk[15]+= uik[12]*u[12]+ uik[13]*u[13]+ uik[14]*u[14]+ uik[15]*u[15];

100:       PetscLogFlops(64.0*4.0);

102:       /* update -U(i,k) */
103:       PetscArraycpy(ba+ili*16,uik,16);

105:       /* add multiple of row i to k-th row ... */
106:       jmin = ili + 1; jmax = bi[i+1];
107:       if (jmin < jmax) {
108:         for (j=jmin; j<jmax; j++) {
109:           /* rtmp += -U(i,k)^T * U_bar(i,j) */
110:           rtmp_ptr     = rtmp + bj[j]*16;
111:           u            = ba + j*16;
112:           rtmp_ptr[0] += uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2] + uik[3]*u[3];
113:           rtmp_ptr[1] += uik[4]*u[0] + uik[5]*u[1] + uik[6]*u[2] + uik[7]*u[3];
114:           rtmp_ptr[2] += uik[8]*u[0] + uik[9]*u[1] + uik[10]*u[2]+ uik[11]*u[3];
115:           rtmp_ptr[3] += uik[12]*u[0]+ uik[13]*u[1]+ uik[14]*u[2]+ uik[15]*u[3];

117:           rtmp_ptr[4] += uik[0]*u[4] + uik[1]*u[5] + uik[2]*u[6] + uik[3]*u[7];
118:           rtmp_ptr[5] += uik[4]*u[4] + uik[5]*u[5] + uik[6]*u[6] + uik[7]*u[7];
119:           rtmp_ptr[6] += uik[8]*u[4] + uik[9]*u[5] + uik[10]*u[6]+ uik[11]*u[7];
120:           rtmp_ptr[7] += uik[12]*u[4]+ uik[13]*u[5]+ uik[14]*u[6]+ uik[15]*u[7];

122:           rtmp_ptr[8] += uik[0]*u[8] + uik[1]*u[9] + uik[2]*u[10] + uik[3]*u[11];
123:           rtmp_ptr[9] += uik[4]*u[8] + uik[5]*u[9] + uik[6]*u[10] + uik[7]*u[11];
124:           rtmp_ptr[10]+= uik[8]*u[8] + uik[9]*u[9] + uik[10]*u[10]+ uik[11]*u[11];
125:           rtmp_ptr[11]+= uik[12]*u[8]+ uik[13]*u[9]+ uik[14]*u[10]+ uik[15]*u[11];

127:           rtmp_ptr[12]+= uik[0]*u[12] + uik[1]*u[13] + uik[2]*u[14] + uik[3]*u[15];
128:           rtmp_ptr[13]+= uik[4]*u[12] + uik[5]*u[13] + uik[6]*u[14] + uik[7]*u[15];
129:           rtmp_ptr[14]+= uik[8]*u[12] + uik[9]*u[13] + uik[10]*u[14]+ uik[11]*u[15];
130:           rtmp_ptr[15]+= uik[12]*u[12]+ uik[13]*u[13]+ uik[14]*u[14]+ uik[15]*u[15];
131:         }
132:         PetscLogFlops(2.0*64.0*(jmax-jmin));

134:         /* ... add i to row list for next nonzero entry */
135:         il[i] = jmin;             /* update il(i) in column k+1, ... mbs-1 */
136:         j     = bj[jmin];
137:         jl[i] = jl[j]; jl[j] = i; /* update jl */
138:       }
139:       i = nexti;
140:     }

142:     /* save nonzero entries in k-th row of U ... */

144:     /* invert diagonal block */
145:     diag = ba+k*16;
146:     PetscArraycpy(diag,dk,16);
147:     if (pivotinblocks) {
148:       PetscKernel_A_gets_inverse_A_4(diag,shift,allowzeropivot,&zeropivotdetected);
149:       if (zeropivotdetected) C->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
150:     } else {
151:       PetscKernel_A_gets_inverse_A_4_nopivot(diag);
152:     }

154:     jmin = bi[k]; jmax = bi[k+1];
155:     if (jmin < jmax) {
156:       for (j=jmin; j<jmax; j++) {
157:         vj       = bj[j];      /* block col. index of U */
158:         u        = ba + j*16;
159:         rtmp_ptr = rtmp + vj*16;
160:         for (k1=0; k1<16; k1++) {
161:           *u++        = *rtmp_ptr;
162:           *rtmp_ptr++ = 0.0;
163:         }
164:       }

166:       /* ... add k to row list for first nonzero entry in k-th row */
167:       il[k] = jmin;
168:       i     = bj[jmin];
169:       jl[k] = jl[i]; jl[i] = k;
170:     }
171:   }

173:   PetscFree(rtmp);
174:   PetscFree2(il,jl);
175:   PetscFree2(dk,uik);

177:   C->ops->solve          = MatSolve_SeqSBAIJ_4_NaturalOrdering_inplace;
178:   C->ops->solvetranspose = MatSolve_SeqSBAIJ_4_NaturalOrdering_inplace;
179:   C->ops->forwardsolve   = MatForwardSolve_SeqSBAIJ_4_NaturalOrdering_inplace;
180:   C->ops->backwardsolve  = MatBackwardSolve_SeqSBAIJ_4_NaturalOrdering_inplace;

182:   C->assembled    = PETSC_TRUE;
183:   C->preallocated = PETSC_TRUE;

185:   PetscLogFlops(1.3333*64*b->mbs); /* from inverting diagonal blocks */
186:   return(0);
187: }