Actual source code: sbaijfact8.c

  1: /*$Id: sbaijfact8.c,v 1.4 2001/06/21 21:17:00 bsmith Exp $*/
 2:  #include src/mat/impls/sbaij/seq/sbaij.h
 3:  #include src/inline/ilu.h

  5: /*
  6:       Version for when blocks are 5 by 5 Using natural ordering
  7: */
  8: int MatCholeskyFactorNumeric_SeqSBAIJ_5_NaturalOrdering(Mat A,Mat *B)
  9: {
 10:   Mat                C = *B;
 11:   Mat_SeqSBAIJ       *a = (Mat_SeqSBAIJ*)A->data,*b = (Mat_SeqSBAIJ *)C->data;
 12:   int                ierr,i,j,mbs=a->mbs,*bi=b->i,*bj=b->j;
 13:   int                *ai,*aj,k,k1,jmin,jmax,*jl,*il,vj,nexti,ili;
 14:   MatScalar          *ba = b->a,*aa,*ap,*dk,*uik;
 15:   MatScalar          *u,*d,*rtmp,*rtmp_ptr;

 18: 
 19:   /* initialization */
 20:   PetscMalloc(25*mbs*sizeof(MatScalar),&rtmp);
 21:   PetscMemzero(rtmp,25*mbs*sizeof(MatScalar));
 22:   PetscMalloc(2*mbs*sizeof(int),&il);
 23:   jl = il + mbs;
 24:   for (i=0; i<mbs; i++) {
 25:     jl[i] = mbs; il[0] = 0;
 26:   }
 27:   PetscMalloc(50*sizeof(MatScalar),&dk);
 28:   uik  = dk + 25;

 30:   ai = a->i; aj = a->j; aa = a->a;

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

 35:     /*initialize k-th row with elements nonzero in row k of A */
 36:     jmin = ai[k]; jmax = ai[k+1];
 37:     if (jmin < jmax) {
 38:       ap = aa + jmin*25;
 39:       for (j = jmin; j < jmax; j++){
 40:         vj = aj[j];         /* block col. index */
 41:         rtmp_ptr = rtmp + vj*25;
 42:         for (i=0; i<25; i++) *rtmp_ptr++ = *ap++;
 43:       }
 44:     }

 46:     /* modify k-th row by adding in those rows i with U(i,k) != 0 */
 47:     PetscMemcpy(dk,rtmp+k*25,25*sizeof(MatScalar));
 48:     i = jl[k]; /* first row to be added to k_th row  */

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

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

 56:       /* uik = -inv(Di)*U_bar(i,k) */
 57:       d = ba + i*25;
 58:       u    = ba + ili*25;

 60:       uik[0] = -(d[0]*u[0] + d[5]*u[1] + d[10]*u[2] + d[15]*u[3] + d[20]*u[4]);
 61:       uik[1] = -(d[1]*u[0] + d[6]*u[1] + d[11]*u[2] + d[16]*u[3] + d[21]*u[4]);
 62:       uik[2] = -(d[2]*u[0] + d[7]*u[1] + d[12]*u[2] + d[17]*u[3] + d[22]*u[4]);
 63:       uik[3] = -(d[3]*u[0] + d[8]*u[1] + d[13]*u[2] + d[18]*u[3] + d[23]*u[4]);
 64:       uik[4] = -(d[4]*u[0] + d[9]*u[1] + d[14]*u[2] + d[19]*u[3] + d[24]*u[4]);

 66:       uik[5] = -(d[0]*u[5] + d[5]*u[6] + d[10]*u[7] + d[15]*u[8] + d[20]*u[9]);
 67:       uik[6] = -(d[1]*u[5] + d[6]*u[6] + d[11]*u[7] + d[16]*u[8] + d[21]*u[9]);
 68:       uik[7] = -(d[2]*u[5] + d[7]*u[6] + d[12]*u[7] + d[17]*u[8] + d[22]*u[9]);
 69:       uik[8] = -(d[3]*u[5] + d[8]*u[6] + d[13]*u[7] + d[18]*u[8] + d[23]*u[9]);
 70:       uik[9] = -(d[4]*u[5] + d[9]*u[6] + d[14]*u[7] + d[19]*u[8] + d[24]*u[9]);

 72:       uik[10]= -(d[0]*u[10] + d[5]*u[11] + d[10]*u[12] + d[15]*u[13] + d[20]*u[14]);
 73:       uik[11]= -(d[1]*u[10] + d[6]*u[11] + d[11]*u[12] + d[16]*u[13] + d[21]*u[14]);
 74:       uik[12]= -(d[2]*u[10] + d[7]*u[11] + d[12]*u[12] + d[17]*u[13] + d[22]*u[14]);
 75:       uik[13]= -(d[3]*u[10] + d[8]*u[11] + d[13]*u[12] + d[18]*u[13] + d[23]*u[14]);
 76:       uik[14]= -(d[4]*u[10] + d[9]*u[11] + d[14]*u[12] + d[19]*u[13] + d[24]*u[14]);

 78:       uik[15]= -(d[0]*u[15] + d[5]*u[16] + d[10]*u[17] + d[15]*u[18] + d[20]*u[19]);
 79:       uik[16]= -(d[1]*u[15] + d[6]*u[16] + d[11]*u[17] + d[16]*u[18] + d[21]*u[19]);
 80:       uik[17]= -(d[2]*u[15] + d[7]*u[16] + d[12]*u[17] + d[17]*u[18] + d[22]*u[19]);
 81:       uik[18]= -(d[3]*u[15] + d[8]*u[16] + d[13]*u[17] + d[18]*u[18] + d[23]*u[19]);
 82:       uik[19]= -(d[4]*u[15] + d[9]*u[16] + d[14]*u[17] + d[19]*u[18] + d[24]*u[19]);

 84:       uik[20]= -(d[0]*u[20] + d[5]*u[21] + d[10]*u[22] + d[15]*u[23] + d[20]*u[24]);
 85:       uik[21]= -(d[1]*u[20] + d[6]*u[21] + d[11]*u[22] + d[16]*u[23] + d[21]*u[24]);
 86:       uik[22]= -(d[2]*u[20] + d[7]*u[21] + d[12]*u[22] + d[17]*u[23] + d[22]*u[24]);
 87:       uik[23]= -(d[3]*u[20] + d[8]*u[21] + d[13]*u[22] + d[18]*u[23] + d[23]*u[24]);
 88:       uik[24]= -(d[4]*u[20] + d[9]*u[21] + d[14]*u[22] + d[19]*u[23] + d[24]*u[24]);


 91:       /* update D(k) += -U(i,k)^T * U_bar(i,k) */
 92:       dk[0] +=  uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2] + uik[3]*u[3] + uik[4]*u[4];
 93:       dk[1] +=  uik[5]*u[0] + uik[6]*u[1] + uik[7]*u[2] + uik[8]*u[3] + uik[9]*u[4];
 94:       dk[2] += uik[10]*u[0]+ uik[11]*u[1]+ uik[12]*u[2]+ uik[13]*u[3]+ uik[14]*u[4];
 95:       dk[3] += uik[15]*u[0]+ uik[16]*u[1]+ uik[17]*u[2]+ uik[18]*u[3]+ uik[19]*u[4];
 96:       dk[4] += uik[20]*u[0]+ uik[21]*u[1]+ uik[22]*u[2]+ uik[23]*u[3]+ uik[24]*u[4];

 98:       dk[5] +=  uik[0]*u[5] + uik[1]*u[6] + uik[2]*u[7] + uik[3]*u[8] + uik[4]*u[9];
 99:       dk[6] +=  uik[5]*u[5] + uik[6]*u[6] + uik[7]*u[7] + uik[8]*u[8] + uik[9]*u[9];
100:       dk[7] += uik[10]*u[5]+ uik[11]*u[6]+ uik[12]*u[7]+ uik[13]*u[8]+ uik[14]*u[9];
101:       dk[8] += uik[15]*u[5]+ uik[16]*u[6]+ uik[17]*u[7]+ uik[18]*u[8]+ uik[19]*u[9];
102:       dk[9] += uik[20]*u[5]+ uik[21]*u[6]+ uik[22]*u[7]+ uik[23]*u[8]+ uik[24]*u[9];

104:       dk[10] +=  uik[0]*u[10] + uik[1]*u[11] + uik[2]*u[12] + uik[3]*u[13] + uik[4]*u[14];
105:       dk[11] +=  uik[5]*u[10] + uik[6]*u[11] + uik[7]*u[12] + uik[8]*u[13] + uik[9]*u[14];
106:       dk[12] += uik[10]*u[10]+ uik[11]*u[11]+ uik[12]*u[12]+ uik[13]*u[13]+ uik[14]*u[14];
107:       dk[13] += uik[15]*u[10]+ uik[16]*u[11]+ uik[17]*u[12]+ uik[18]*u[13]+ uik[19]*u[14];
108:       dk[14] += uik[20]*u[10]+ uik[21]*u[11]+ uik[22]*u[12]+ uik[23]*u[13]+ uik[24]*u[14];

110:       dk[15] +=  uik[0]*u[15] + uik[1]*u[16] + uik[2]*u[17] + uik[3]*u[18] + uik[4]*u[19];
111:       dk[16] +=  uik[5]*u[15] + uik[6]*u[16] + uik[7]*u[17] + uik[8]*u[18] + uik[9]*u[19];
112:       dk[17] += uik[10]*u[15]+ uik[11]*u[16]+ uik[12]*u[17]+ uik[13]*u[18]+ uik[14]*u[19];
113:       dk[18] += uik[15]*u[15]+ uik[16]*u[16]+ uik[17]*u[17]+ uik[18]*u[18]+ uik[19]*u[19];
114:       dk[19] += uik[20]*u[15]+ uik[21]*u[16]+ uik[22]*u[17]+ uik[23]*u[18]+ uik[24]*u[19];

116:       dk[20] +=  uik[0]*u[20] + uik[1]*u[21] + uik[2]*u[22] + uik[3]*u[23] + uik[4]*u[24];
117:       dk[21] +=  uik[5]*u[20] + uik[6]*u[21] + uik[7]*u[22] + uik[8]*u[23] + uik[9]*u[24];
118:       dk[22] += uik[10]*u[20]+ uik[11]*u[21]+ uik[12]*u[22]+ uik[13]*u[23]+ uik[14]*u[24];
119:       dk[23] += uik[15]*u[20]+ uik[16]*u[21]+ uik[17]*u[22]+ uik[18]*u[23]+ uik[19]*u[24];
120:       dk[24] += uik[20]*u[20]+ uik[21]*u[21]+ uik[22]*u[22]+ uik[23]*u[23]+ uik[24]*u[24];

122:       /* update -U(i,k) */
123:       PetscMemcpy(ba+ili*25,uik,25*sizeof(MatScalar));

125:       /* add multiple of row i to k-th row ... */
126:       jmin = ili + 1; jmax = bi[i+1];
127:       if (jmin < jmax){
128:         for (j=jmin; j<jmax; j++) {
129:           /* rtmp += -U(i,k)^T * U_bar(i,j) */
130:           rtmp_ptr = rtmp + bj[j]*25;
131:           u = ba + j*25;
132:           rtmp_ptr[0] +=  uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2] + uik[3]*u[3] + uik[4]*u[4];
133:           rtmp_ptr[1] +=  uik[5]*u[0] + uik[6]*u[1] + uik[7]*u[2] + uik[8]*u[3] + uik[9]*u[4];
134:           rtmp_ptr[2] += uik[10]*u[0]+ uik[11]*u[1]+ uik[12]*u[2]+ uik[13]*u[3]+ uik[14]*u[4];
135:           rtmp_ptr[3] += uik[15]*u[0]+ uik[16]*u[1]+ uik[17]*u[2]+ uik[18]*u[3]+ uik[19]*u[4];
136:           rtmp_ptr[4] += uik[20]*u[0]+ uik[21]*u[1]+ uik[22]*u[2]+ uik[23]*u[3]+ uik[24]*u[4];

138:           rtmp_ptr[5] +=  uik[0]*u[5] + uik[1]*u[6] + uik[2]*u[7] + uik[3]*u[8] + uik[4]*u[9];
139:           rtmp_ptr[6] +=  uik[5]*u[5] + uik[6]*u[6] + uik[7]*u[7] + uik[8]*u[8] + uik[9]*u[9];
140:           rtmp_ptr[7] += uik[10]*u[5]+ uik[11]*u[6]+ uik[12]*u[7]+ uik[13]*u[8]+ uik[14]*u[9];
141:           rtmp_ptr[8] += uik[15]*u[5]+ uik[16]*u[6]+ uik[17]*u[7]+ uik[18]*u[8]+ uik[19]*u[9];
142:           rtmp_ptr[9] += uik[20]*u[5]+ uik[21]*u[6]+ uik[22]*u[7]+ uik[23]*u[8]+ uik[24]*u[9];

144:           rtmp_ptr[10] +=  uik[0]*u[10] + uik[1]*u[11] + uik[2]*u[12] + uik[3]*u[13] + uik[4]*u[14];
145:           rtmp_ptr[11] +=  uik[5]*u[10] + uik[6]*u[11] + uik[7]*u[12] + uik[8]*u[13] + uik[9]*u[14];
146:           rtmp_ptr[12] += uik[10]*u[10]+ uik[11]*u[11]+ uik[12]*u[12]+ uik[13]*u[13]+ uik[14]*u[14];
147:           rtmp_ptr[13] += uik[15]*u[10]+ uik[16]*u[11]+ uik[17]*u[12]+ uik[18]*u[13]+ uik[19]*u[14];
148:           rtmp_ptr[14] += uik[20]*u[10]+ uik[21]*u[11]+ uik[22]*u[12]+ uik[23]*u[13]+ uik[24]*u[14];

150:           rtmp_ptr[15] +=  uik[0]*u[15] + uik[1]*u[16] + uik[2]*u[17] + uik[3]*u[18] + uik[4]*u[19];
151:           rtmp_ptr[16] +=  uik[5]*u[15] + uik[6]*u[16] + uik[7]*u[17] + uik[8]*u[18] + uik[9]*u[19];
152:           rtmp_ptr[17] += uik[10]*u[15]+ uik[11]*u[16]+ uik[12]*u[17]+ uik[13]*u[18]+ uik[14]*u[19];
153:           rtmp_ptr[18] += uik[15]*u[15]+ uik[16]*u[16]+ uik[17]*u[17]+ uik[18]*u[18]+ uik[19]*u[19];
154:           rtmp_ptr[19] += uik[20]*u[15]+ uik[21]*u[16]+ uik[22]*u[17]+ uik[23]*u[18]+ uik[24]*u[19];

156:           rtmp_ptr[20] +=  uik[0]*u[20] + uik[1]*u[21] + uik[2]*u[22] + uik[3]*u[23] + uik[4]*u[24];
157:           rtmp_ptr[21] +=  uik[5]*u[20] + uik[6]*u[21] + uik[7]*u[22] + uik[8]*u[23] + uik[9]*u[24];
158:           rtmp_ptr[22] += uik[10]*u[20]+ uik[11]*u[21]+ uik[12]*u[22]+ uik[13]*u[23]+ uik[14]*u[24];
159:           rtmp_ptr[23] += uik[15]*u[20]+ uik[16]*u[21]+ uik[17]*u[22]+ uik[18]*u[23]+ uik[19]*u[24];
160:           rtmp_ptr[24] += uik[20]*u[20]+ uik[21]*u[21]+ uik[22]*u[22]+ uik[23]*u[23]+ uik[24]*u[24];
161:         }
162: 
163:         /* ... add i to row list for next nonzero entry */
164:         il[i] = jmin;             /* update il(i) in column k+1, ... mbs-1 */
165:         j     = bj[jmin];
166:         jl[i] = jl[j]; jl[j] = i; /* update jl */
167:       }
168:       i = nexti;
169:     }

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

173:     /* invert diagonal block */
174:     d = ba+k*25;
175:     PetscMemcpy(d,dk,25*sizeof(MatScalar));
176:     Kernel_A_gets_inverse_A_5(d);
177: 
178:     jmin = bi[k]; jmax = bi[k+1];
179:     if (jmin < jmax) {
180:       for (j=jmin; j<jmax; j++){
181:          vj = bj[j];           /* block col. index of U */
182:          u   = ba + j*25;
183:          rtmp_ptr = rtmp + vj*25;
184:          for (k1=0; k1<25; k1++){
185:            *u++        = *rtmp_ptr;
186:            *rtmp_ptr++ = 0.0;
187:          }
188:       }
189: 
190:       /* ... add k to row list for first nonzero entry in k-th row */
191:       il[k] = jmin;
192:       i     = bj[jmin];
193:       jl[k] = jl[i]; jl[i] = k;
194:     }
195:   }

197:   PetscFree(rtmp);
198:   PetscFree(il);
199:   PetscFree(dk);

201:   C->factor    = FACTOR_CHOLESKY;
202:   C->assembled = PETSC_TRUE;
203:   C->preallocated = PETSC_TRUE;
204:   PetscLogFlops(1.3333*125*b->mbs); /* from inverting diagonal blocks */
205:   return(0);
206: }