Actual source code: sbaijfact5.c
1: #define PETSCMAT_DLL
3: #include src/mat/impls/sbaij/seq/sbaij.h
4: #include src/inline/ilu.h
6: /*
7: Version for when blocks are 4 by 4 Using natural ordering
8: */
11: PetscErrorCode MatCholeskyFactorNumeric_SeqSBAIJ_4_NaturalOrdering(Mat A,MatFactorInfo *info,Mat *B)
12: {
13: Mat C = *B;
14: Mat_SeqSBAIJ *a = (Mat_SeqSBAIJ*)A->data,*b = (Mat_SeqSBAIJ *)C->data;
16: PetscInt i,j,mbs=a->mbs,*bi=b->i,*bj=b->j;
17: PetscInt *ai,*aj,k,k1,jmin,jmax,*jl,*il,vj,nexti,ili;
18: MatScalar *ba = b->a,*aa,*ap,*dk,*uik;
19: MatScalar *u,*diag,*rtmp,*rtmp_ptr;
20: PetscTruth pivotinblocks = b->pivotinblocks;
23:
24: /* initialization */
25: PetscMalloc(16*mbs*sizeof(MatScalar),&rtmp);
26: PetscMemzero(rtmp,16*mbs*sizeof(MatScalar));
27: PetscMalloc(2*mbs*sizeof(PetscInt),&il);
28: jl = il + mbs;
29: for (i=0; i<mbs; i++) {
30: jl[i] = mbs; il[0] = 0;
31: }
32: PetscMalloc(32*sizeof(MatScalar),&dk);
33: uik = dk + 16;
35: ai = a->i; aj = a->j; aa = a->a;
37: /* for each row k */
38: for (k = 0; k<mbs; k++){
40: /*initialize k-th row with elements nonzero in row k of A */
41: jmin = ai[k]; jmax = ai[k+1];
42: if (jmin < jmax) {
43: ap = aa + jmin*16;
44: for (j = jmin; j < jmax; j++){
45: vj = aj[j]; /* block col. index */
46: rtmp_ptr = rtmp + vj*16;
47: for (i=0; i<16; i++) *rtmp_ptr++ = *ap++;
48: }
49: }
51: /* modify k-th row by adding in those rows i with U(i,k) != 0 */
52: PetscMemcpy(dk,rtmp+k*16,16*sizeof(MatScalar));
53: i = jl[k]; /* first row to be added to k_th row */
55: while (i < mbs){
56: nexti = jl[i]; /* next row to be added to k_th row */
58: /* compute multiplier */
59: ili = il[i]; /* index of first nonzero element in U(i,k:bms-1) */
61: /* uik = -inv(Di)*U_bar(i,k) */
62: diag = ba + i*16;
63: u = ba + ili*16;
65: uik[0] = -(diag[0]*u[0] + diag[4]*u[1] + diag[8]*u[2] + diag[12]*u[3]);
66: uik[1] = -(diag[1]*u[0] + diag[5]*u[1] + diag[9]*u[2] + diag[13]*u[3]);
67: uik[2] = -(diag[2]*u[0] + diag[6]*u[1] + diag[10]*u[2]+ diag[14]*u[3]);
68: uik[3] = -(diag[3]*u[0] + diag[7]*u[1] + diag[11]*u[2]+ diag[15]*u[3]);
70: uik[4] = -(diag[0]*u[4] + diag[4]*u[5] + diag[8]*u[6] + diag[12]*u[7]);
71: uik[5] = -(diag[1]*u[4] + diag[5]*u[5] + diag[9]*u[6] + diag[13]*u[7]);
72: uik[6] = -(diag[2]*u[4] + diag[6]*u[5] + diag[10]*u[6]+ diag[14]*u[7]);
73: uik[7] = -(diag[3]*u[4] + diag[7]*u[5] + diag[11]*u[6]+ diag[15]*u[7]);
75: uik[8] = -(diag[0]*u[8] + diag[4]*u[9] + diag[8]*u[10] + diag[12]*u[11]);
76: uik[9] = -(diag[1]*u[8] + diag[5]*u[9] + diag[9]*u[10] + diag[13]*u[11]);
77: uik[10]= -(diag[2]*u[8] + diag[6]*u[9] + diag[10]*u[10]+ diag[14]*u[11]);
78: uik[11]= -(diag[3]*u[8] + diag[7]*u[9] + diag[11]*u[10]+ diag[15]*u[11]);
80: uik[12]= -(diag[0]*u[12] + diag[4]*u[13] + diag[8]*u[14] + diag[12]*u[15]);
81: uik[13]= -(diag[1]*u[12] + diag[5]*u[13] + diag[9]*u[14] + diag[13]*u[15]);
82: uik[14]= -(diag[2]*u[12] + diag[6]*u[13] + diag[10]*u[14]+ diag[14]*u[15]);
83: uik[15]= -(diag[3]*u[12] + diag[7]*u[13] + diag[11]*u[14]+ diag[15]*u[15]);
85: /* update D(k) += -U(i,k)^T * U_bar(i,k) */
86: dk[0] += uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2] + uik[3]*u[3];
87: dk[1] += uik[4]*u[0] + uik[5]*u[1] + uik[6]*u[2] + uik[7]*u[3];
88: dk[2] += uik[8]*u[0] + uik[9]*u[1] + uik[10]*u[2]+ uik[11]*u[3];
89: dk[3] += uik[12]*u[0]+ uik[13]*u[1]+ uik[14]*u[2]+ uik[15]*u[3];
91: dk[4] += uik[0]*u[4] + uik[1]*u[5] + uik[2]*u[6] + uik[3]*u[7];
92: dk[5] += uik[4]*u[4] + uik[5]*u[5] + uik[6]*u[6] + uik[7]*u[7];
93: dk[6] += uik[8]*u[4] + uik[9]*u[5] + uik[10]*u[6]+ uik[11]*u[7];
94: dk[7] += uik[12]*u[4]+ uik[13]*u[5]+ uik[14]*u[6]+ uik[15]*u[7];
96: dk[8] += uik[0]*u[8] + uik[1]*u[9] + uik[2]*u[10] + uik[3]*u[11];
97: dk[9] += uik[4]*u[8] + uik[5]*u[9] + uik[6]*u[10] + uik[7]*u[11];
98: dk[10]+= uik[8]*u[8] + uik[9]*u[9] + uik[10]*u[10]+ uik[11]*u[11];
99: dk[11]+= uik[12]*u[8]+ uik[13]*u[9]+ uik[14]*u[10]+ uik[15]*u[11];
101: dk[12]+= uik[0]*u[12] + uik[1]*u[13] + uik[2]*u[14] + uik[3]*u[15];
102: dk[13]+= uik[4]*u[12] + uik[5]*u[13] + uik[6]*u[14] + uik[7]*u[15];
103: dk[14]+= uik[8]*u[12] + uik[9]*u[13] + uik[10]*u[14]+ uik[11]*u[15];
104: dk[15]+= uik[12]*u[12]+ uik[13]*u[13]+ uik[14]*u[14]+ uik[15]*u[15];
106: PetscLogFlops(64*4);
107:
108: /* update -U(i,k) */
109: PetscMemcpy(ba+ili*16,uik,16*sizeof(MatScalar));
111: /* add multiple of row i to k-th row ... */
112: jmin = ili + 1; jmax = bi[i+1];
113: if (jmin < jmax){
114: for (j=jmin; j<jmax; j++) {
115: /* rtmp += -U(i,k)^T * U_bar(i,j) */
116: rtmp_ptr = rtmp + bj[j]*16;
117: u = ba + j*16;
118: rtmp_ptr[0] += uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2] + uik[3]*u[3];
119: rtmp_ptr[1] += uik[4]*u[0] + uik[5]*u[1] + uik[6]*u[2] + uik[7]*u[3];
120: rtmp_ptr[2] += uik[8]*u[0] + uik[9]*u[1] + uik[10]*u[2]+ uik[11]*u[3];
121: rtmp_ptr[3] += uik[12]*u[0]+ uik[13]*u[1]+ uik[14]*u[2]+ uik[15]*u[3];
123: rtmp_ptr[4] += uik[0]*u[4] + uik[1]*u[5] + uik[2]*u[6] + uik[3]*u[7];
124: rtmp_ptr[5] += uik[4]*u[4] + uik[5]*u[5] + uik[6]*u[6] + uik[7]*u[7];
125: rtmp_ptr[6] += uik[8]*u[4] + uik[9]*u[5] + uik[10]*u[6]+ uik[11]*u[7];
126: rtmp_ptr[7] += uik[12]*u[4]+ uik[13]*u[5]+ uik[14]*u[6]+ uik[15]*u[7];
128: rtmp_ptr[8] += uik[0]*u[8] + uik[1]*u[9] + uik[2]*u[10] + uik[3]*u[11];
129: rtmp_ptr[9] += uik[4]*u[8] + uik[5]*u[9] + uik[6]*u[10] + uik[7]*u[11];
130: rtmp_ptr[10]+= uik[8]*u[8] + uik[9]*u[9] + uik[10]*u[10]+ uik[11]*u[11];
131: rtmp_ptr[11]+= uik[12]*u[8]+ uik[13]*u[9]+ uik[14]*u[10]+ uik[15]*u[11];
133: rtmp_ptr[12]+= uik[0]*u[12] + uik[1]*u[13] + uik[2]*u[14] + uik[3]*u[15];
134: rtmp_ptr[13]+= uik[4]*u[12] + uik[5]*u[13] + uik[6]*u[14] + uik[7]*u[15];
135: rtmp_ptr[14]+= uik[8]*u[12] + uik[9]*u[13] + uik[10]*u[14]+ uik[11]*u[15];
136: rtmp_ptr[15]+= uik[12]*u[12]+ uik[13]*u[13]+ uik[14]*u[14]+ uik[15]*u[15];
137: }
138: PetscLogFlops(2*64*(jmax-jmin));
139:
140: /* ... add i to row list for next nonzero entry */
141: il[i] = jmin; /* update il(i) in column k+1, ... mbs-1 */
142: j = bj[jmin];
143: jl[i] = jl[j]; jl[j] = i; /* update jl */
144: }
145: i = nexti;
146: }
148: /* save nonzero entries in k-th row of U ... */
150: /* invert diagonal block */
151: diag = ba+k*16;
152: PetscMemcpy(diag,dk,16*sizeof(MatScalar));
153: if (pivotinblocks) {
154: Kernel_A_gets_inverse_A_4(diag);
155: } else {
156: Kernel_A_gets_inverse_A_4_nopivot(diag);
157: }
158:
159: jmin = bi[k]; jmax = bi[k+1];
160: if (jmin < jmax) {
161: for (j=jmin; j<jmax; j++){
162: vj = bj[j]; /* block col. index of U */
163: u = ba + j*16;
164: rtmp_ptr = rtmp + vj*16;
165: for (k1=0; k1<16; k1++){
166: *u++ = *rtmp_ptr;
167: *rtmp_ptr++ = 0.0;
168: }
169: }
170:
171: /* ... add k to row list for first nonzero entry in k-th row */
172: il[k] = jmin;
173: i = bj[jmin];
174: jl[k] = jl[i]; jl[i] = k;
175: }
176: }
178: PetscFree(rtmp);
179: PetscFree(il);
180: PetscFree(dk);
181:
182: C->factor = FACTOR_CHOLESKY;
183: C->assembled = PETSC_TRUE;
184: C->preallocated = PETSC_TRUE;
185: PetscLogFlops(1.3333*64*b->mbs); /* from inverting diagonal blocks */
186: return(0);
187: }