Actual source code: sbaijfact10.c
petsc-3.3-p7 2013-05-11
2: #include <../src/mat/impls/sbaij/seq/sbaij.h>
3: #include <../src/mat/blockinvert.h>
5: /*
6: Version for when blocks are 6 by 6 Using natural ordering
7: */
10: PetscErrorCode MatCholeskyFactorNumeric_SeqSBAIJ_6_NaturalOrdering(Mat C,Mat A,const MatFactorInfo *info)
11: {
12: Mat_SeqSBAIJ *a = (Mat_SeqSBAIJ*)A->data,*b = (Mat_SeqSBAIJ *)C->data;
14: PetscInt i,j,mbs=a->mbs,*bi=b->i,*bj=b->j;
15: PetscInt *ai,*aj,k,k1,jmin,jmax,*jl,*il,vj,nexti,ili;
16: MatScalar *ba = b->a,*aa,*ap,*dk,*uik;
17: MatScalar *u,*d,*w,*wp,u0,u1,u2,u3,u4,u5,u6,u7,u8,u9,u10,u11,u12;
18: MatScalar u13,u14,u15,u16,u17,u18,u19,u20,u21,u22,u23,u24,u25,u26,u27;
19: MatScalar u28,u29,u30,u31,u32,u33,u34,u35;
20: MatScalar d0,d1,d2,d3,d4,d5,d6,d7,d8,d9,d10,d11,d12;
21: MatScalar d13,d14,d15,d16,d17,d18,d19,d20,d21,d22,d23,d24,d25,d26,d27;
22: MatScalar d28,d29,d30,d31,d32,d33,d34,d35;
23: MatScalar m0,m1,m2,m3,m4,m5,m6,m7,m8,m9,m10,m11,m12;
24: MatScalar m13,m14,m15,m16,m17,m18,m19,m20,m21,m22,m23,m24,m25,m26,m27;
25: MatScalar m28,m29,m30,m31,m32,m33,m34,m35;
26: PetscReal shift = info->shiftamount;
27:
29: /* initialization */
30: PetscMalloc(36*mbs*sizeof(MatScalar),&w);
31: PetscMemzero(w,36*mbs*sizeof(MatScalar));
32: PetscMalloc2(mbs,PetscInt,&il,mbs,PetscInt,&jl);
33: for (i=0; i<mbs; i++) {
34: jl[i] = mbs; il[0] = 0;
35: }
36: PetscMalloc2(36,MatScalar,&dk,36,MatScalar,&uik);
37: ai = a->i; aj = a->j; aa = a->a;
39: /* for each row k */
40: for (k = 0; k<mbs; k++){
42: /*initialize k-th row with elements nonzero in row k of A */
43: jmin = ai[k]; jmax = ai[k+1];
44: if (jmin < jmax) {
45: ap = aa + jmin*36;
46: for (j = jmin; j < jmax; j++){
47: vj = aj[j]; /* block col. index */
48: wp = w + vj*36;
49: for (i=0; i<36; i++) *wp++ = *ap++;
50: }
51: }
53: /* modify k-th row by adding in those rows i with U(i,k) != 0 */
54: PetscMemcpy(dk,w+k*36,36*sizeof(MatScalar));
55: i = jl[k]; /* first row to be added to k_th row */
57: while (i < mbs){
58: nexti = jl[i]; /* next row to be added to k_th row */
60: /* compute multiplier */
61: ili = il[i]; /* index of first nonzero element in U(i,k:bms-1) */
63: /* uik = -inv(Di)*U_bar(i,k) */
64: d = ba + i*36;
65: u = ba + ili*36;
67: u0 = u[0]; u1 = u[1]; u2 = u[2]; u3 = u[3]; u4 = u[4]; u5 = u[5]; u6 = u[6];
68: u7 = u[7]; u8 = u[8]; u9 = u[9]; u10 = u[10]; u11 = u[11]; u12 = u[12]; u13 = u[13];
69: u14 = u[14]; u15 = u[15]; u16 = u[16]; u17 = u[17]; u18 = u[18]; u19 = u[19]; u20 = u[20];
70: u21 = u[21]; u22 = u[22]; u23 = u[23]; u24 = u[24]; u25 = u[25]; u26 = u[26]; u27 = u[27];
71: u28 = u[28]; u29 = u[29]; u30 = u[30]; u31 = u[31]; u32 = u[32]; u33 = u[33]; u34 = u[34];
72: u35 = u[35];
74: d0 = d[0]; d1 = d[1]; d2 = d[2]; d3 = d[3];
75: d4 = d[4]; d5 = d[5]; d6 = d[6]; d7 = d[7];
76: d8 = d[8]; d9 = d[9]; d10 = d[10]; d11 = d[11];
77: d12 = d[12]; d13 = d[13]; d14 = d[14]; d15 = d[15];
78: d16 = d[16]; d17 = d[17]; d18 = d[18]; d19 = d[19];
79: d20 = d[20]; d21 = d[21]; d22 = d[22]; d23 = d[23];
80: d24 = d[24]; d25 = d[25]; d26 = d[26]; d27 = d[27];
81: d28 = d[28]; d29 = d[29]; d30 = d[30]; d31 = d[31];
82: d32 = d[32]; d33 = d[33]; d34 = d[34]; d35 = d[35];
84: m0 = uik[0] = -(d0*u0 + d6*u1 + d12*u2 + d18*u3 + d24*u4 + d30*u5);
85: m1 = uik[1] = -(d1*u0 + d7*u1 + d13*u2 + d19*u3 + d25*u4 + d31*u5);
86: m2 = uik[2] = -(d2*u0 + d8*u1 + d14*u2 + d20*u3 + d26*u4 + d32*u5);
87: m3 = uik[3] = -(d3*u0 + d9*u1 + d15*u2 + d21*u3 + d27*u4 + d33*u5);
88: m4 = uik[4] = -(d4*u0+ d10*u1 + d16*u2 + d22*u3 + d28*u4 + d34*u5);
89: m5 = uik[5] = -(d5*u0+ d11*u1 + d17*u2 + d23*u3 + d29*u4 + d35*u5);
91: m6 = uik[6] = -(d0*u6 + d6*u7 + d12*u8 + d18*u9 + d24*u10 + d30*u11);
92: m7 = uik[7] = -(d1*u6 + d7*u7 + d13*u8 + d19*u9 + d25*u10 + d31*u11);
93: m8 = uik[8] = -(d2*u6 + d8*u7 + d14*u8 + d20*u9 + d26*u10 + d32*u11);
94: m9 = uik[9] = -(d3*u6 + d9*u7 + d15*u8 + d21*u9 + d27*u10 + d33*u11);
95: m10 = uik[10]= -(d4*u6+ d10*u7 + d16*u8 + d22*u9 + d28*u10 + d34*u11);
96: m11 = uik[11]= -(d5*u6+ d11*u7 + d17*u8 + d23*u9 + d29*u10 + d35*u11);
98: m12 = uik[12] = -(d0*u12 + d6*u13 + d12*u14 + d18*u15 + d24*u16 + d30*u17);
99: m13 = uik[13] = -(d1*u12 + d7*u13 + d13*u14 + d19*u15 + d25*u16 + d31*u17);
100: m14 = uik[14] = -(d2*u12 + d8*u13 + d14*u14 + d20*u15 + d26*u16 + d32*u17);
101: m15 = uik[15] = -(d3*u12 + d9*u13 + d15*u14 + d21*u15 + d27*u16 + d33*u17);
102: m16 = uik[16] = -(d4*u12+ d10*u13 + d16*u14 + d22*u15 + d28*u16 + d34*u17);
103: m17 = uik[17] = -(d5*u12+ d11*u13 + d17*u14 + d23*u15 + d29*u16 + d35*u17);
105: m18 = uik[18] = -(d0*u18 + d6*u19 + d12*u20 + d18*u21 + d24*u22 + d30*u23);
106: m19 = uik[19] = -(d1*u18 + d7*u19 + d13*u20 + d19*u21 + d25*u22 + d31*u23);
107: m20 = uik[20] = -(d2*u18 + d8*u19 + d14*u20 + d20*u21 + d26*u22 + d32*u23);
108: m21 = uik[21] = -(d3*u18 + d9*u19 + d15*u20 + d21*u21 + d27*u22 + d33*u23);
109: m22 = uik[22] = -(d4*u18+ d10*u19 + d16*u20 + d22*u21 + d28*u22 + d34*u23);
110: m23 = uik[23] = -(d5*u18+ d11*u19 + d17*u20 + d23*u21 + d29*u22 + d35*u23);
112: m24 = uik[24] = -(d0*u24 + d6*u25 + d12*u26 + d18*u27 + d24*u28 + d30*u29);
113: m25 = uik[25] = -(d1*u24 + d7*u25 + d13*u26 + d19*u27 + d25*u28 + d31*u29);
114: m26 = uik[26] = -(d2*u24 + d8*u25 + d14*u26 + d20*u27 + d26*u28 + d32*u29);
115: m27 = uik[27] = -(d3*u24 + d9*u25 + d15*u26 + d21*u27 + d27*u28 + d33*u29);
116: m28 = uik[28] = -(d4*u24+ d10*u25 + d16*u26 + d22*u27 + d28*u28 + d34*u29);
117: m29 = uik[29] = -(d5*u24+ d11*u25 + d17*u26 + d23*u27 + d29*u28 + d35*u29);
119: m30 = uik[30] = -(d0*u30 + d6*u31 + d12*u32 + d18*u33 + d24*u34 + d30*u35);
120: m31 = uik[31] = -(d1*u30 + d7*u31 + d13*u32 + d19*u33 + d25*u34 + d31*u35);
121: m32 = uik[32] = -(d2*u30 + d8*u31 + d14*u32 + d20*u33 + d26*u34 + d32*u35);
122: m33 = uik[33] = -(d3*u30 + d9*u31 + d15*u32 + d21*u33 + d27*u34 + d33*u35);
123: m34 = uik[34] = -(d4*u30+ d10*u31 + d16*u32 + d22*u33 + d28*u34 + d34*u35);
124: m35 = uik[35] = -(d5*u30+ d11*u31 + d17*u32 + d23*u33 + d29*u34 + d35*u35);
126: /* update D(k) += -U(i,k)^T * U_bar(i,k) */
127: dk[0] += m0*u0 + m1*u1 + m2*u2 + m3*u3 + m4*u4 + m5*u5;
128: dk[1] += m6*u0 + m7*u1 + m8*u2 + m9*u3+ m10*u4+ m11*u5;
129: dk[2] += m12*u0+ m13*u1+ m14*u2+ m15*u3+ m16*u4+ m17*u5;
130: dk[3] += m18*u0+ m19*u1+ m20*u2+ m21*u3+ m22*u4+ m23*u5;
131: dk[4] += m24*u0+ m25*u1+ m26*u2+ m27*u3+ m28*u4+ m29*u5;
132: dk[5] += m30*u0+ m31*u1+ m32*u2+ m33*u3+ m34*u4+ m35*u5;
134: dk[6] += m0*u6 + m1*u7 + m2*u8 + m3*u9 + m4*u10 + m5*u11;
135: dk[7] += m6*u6 + m7*u7 + m8*u8 + m9*u9+ m10*u10+ m11*u11;
136: dk[8] += m12*u6+ m13*u7+ m14*u8+ m15*u9+ m16*u10+ m17*u11;
137: dk[9] += m18*u6+ m19*u7+ m20*u8+ m21*u9+ m22*u10+ m23*u11;
138: dk[10]+= m24*u6+ m25*u7+ m26*u8+ m27*u9+ m28*u10+ m29*u11;
139: dk[11]+= m30*u6+ m31*u7+ m32*u8+ m33*u9+ m34*u10+ m35*u11;
141: dk[12]+= m0*u12 + m1*u13 + m2*u14 + m3*u15 + m4*u16 + m5*u17;
142: dk[13]+= m6*u12 + m7*u13 + m8*u14 + m9*u15+ m10*u16+ m11*u17;
143: dk[14]+= m12*u12+ m13*u13+ m14*u14+ m15*u15+ m16*u16+ m17*u17;
144: dk[15]+= m18*u12+ m19*u13+ m20*u14+ m21*u15+ m22*u16+ m23*u17;
145: dk[16]+= m24*u12+ m25*u13+ m26*u14+ m27*u15+ m28*u16+ m29*u17;
146: dk[17]+= m30*u12+ m31*u13+ m32*u14+ m33*u15+ m34*u16+ m35*u17;
148: dk[18]+= m0*u18 + m1*u19 + m2*u20 + m3*u21 + m4*u22 + m5*u23;
149: dk[19]+= m6*u18 + m7*u19 + m8*u20 + m9*u21+ m10*u22+ m11*u23;
150: dk[20]+= m12*u18+ m13*u19+ m14*u20+ m15*u21+ m16*u22+ m17*u23;
151: dk[21]+= m18*u18+ m19*u19+ m20*u20+ m21*u21+ m22*u22+ m23*u23;
152: dk[22]+= m24*u18+ m25*u19+ m26*u20+ m27*u21+ m28*u22+ m29*u23;
153: dk[23]+= m30*u18+ m31*u19+ m32*u20+ m33*u21+ m34*u22+ m35*u23;
155: dk[24]+= m0*u24 + m1*u25 + m2*u26 + m3*u27 + m4*u28 + m5*u29;
156: dk[25]+= m6*u24 + m7*u25 + m8*u26 + m9*u27+ m10*u28+ m11*u29;
157: dk[26]+= m12*u24+ m13*u25+ m14*u26+ m15*u27+ m16*u28+ m17*u29;
158: dk[27]+= m18*u24+ m19*u25+ m20*u26+ m21*u27+ m22*u28+ m23*u29;
159: dk[28]+= m24*u24+ m25*u25+ m26*u26+ m27*u27+ m28*u28+ m29*u29;
160: dk[29]+= m30*u24+ m31*u25+ m32*u26+ m33*u27+ m34*u28+ m35*u29;
162: dk[30]+= m0*u30 + m1*u31 + m2*u32 + m3*u33 + m4*u34 + m5*u35;
163: dk[31]+= m6*u30 + m7*u31 + m8*u32 + m9*u33+ m10*u34+ m11*u35;
164: dk[32]+= m12*u30+ m13*u31+ m14*u32+ m15*u33+ m16*u34+ m17*u35;
165: dk[33]+= m18*u30+ m19*u31+ m20*u32+ m21*u33+ m22*u34+ m23*u35;
166: dk[34]+= m24*u30+ m25*u31+ m26*u32+ m27*u33+ m28*u34+ m29*u35;
167: dk[35]+= m30*u30+ m31*u31+ m32*u32+ m33*u33+ m34*u34+ m35*u35;
169: PetscLogFlops(216.0*4.0);
170:
171: /* update -U(i,k) */
172: PetscMemcpy(ba+ili*36,uik,36*sizeof(MatScalar));
174: /* add multiple of row i to k-th row ... */
175: jmin = ili + 1; jmax = bi[i+1];
176: if (jmin < jmax){
177: for (j=jmin; j<jmax; j++) {
178: /* w += -U(i,k)^T * U_bar(i,j) */
179: wp = w + bj[j]*36;
180: u = ba + j*36;
182: u0 = u[0]; u1 = u[1]; u2 = u[2]; u3 = u[3]; u4 = u[4]; u5 = u[5]; u6 = u[6];
183: u7 = u[7]; u8 = u[8]; u9 = u[9]; u10 = u[10]; u11 = u[11]; u12 = u[12]; u13 = u[13];
184: u14 = u[14]; u15 = u[15]; u16 = u[16]; u17 = u[17]; u18 = u[18]; u19 = u[19]; u20 = u[20];
185: u21 = u[21]; u22 = u[22]; u23 = u[23]; u24 = u[24]; u25 = u[25]; u26 = u[26]; u27 = u[27];
186: u28 = u[28]; u29 = u[29]; u30 = u[30]; u31 = u[31]; u32 = u[32]; u33 = u[33]; u34 = u[34];
187: u35 = u[35];
189: wp[0] += m0*u0 + m1*u1 + m2*u2 + m3*u3 + m4*u4 + m5*u5;
190: wp[1] += m6*u0 + m7*u1 + m8*u2 + m9*u3+ m10*u4+ m11*u5;
191: wp[2] += m12*u0+ m13*u1+ m14*u2+ m15*u3+ m16*u4+ m17*u5;
192: wp[3] += m18*u0+ m19*u1+ m20*u2+ m21*u3+ m22*u4+ m23*u5;
193: wp[4] += m24*u0+ m25*u1+ m26*u2+ m27*u3+ m28*u4+ m29*u5;
194: wp[5] += m30*u0+ m31*u1+ m32*u2+ m33*u3+ m34*u4+ m35*u5;
196: wp[6] += m0*u6 + m1*u7 + m2*u8 + m3*u9 + m4*u10 + m5*u11;
197: wp[7] += m6*u6 + m7*u7 + m8*u8 + m9*u9+ m10*u10+ m11*u11;
198: wp[8] += m12*u6+ m13*u7+ m14*u8+ m15*u9+ m16*u10+ m17*u11;
199: wp[9] += m18*u6+ m19*u7+ m20*u8+ m21*u9+ m22*u10+ m23*u11;
200: wp[10]+= m24*u6+ m25*u7+ m26*u8+ m27*u9+ m28*u10+ m29*u11;
201: wp[11]+= m30*u6+ m31*u7+ m32*u8+ m33*u9+ m34*u10+ m35*u11;
203: wp[12]+= m0*u12 + m1*u13 + m2*u14 + m3*u15 + m4*u16 + m5*u17;
204: wp[13]+= m6*u12 + m7*u13 + m8*u14 + m9*u15+ m10*u16+ m11*u17;
205: wp[14]+= m12*u12+ m13*u13+ m14*u14+ m15*u15+ m16*u16+ m17*u17;
206: wp[15]+= m18*u12+ m19*u13+ m20*u14+ m21*u15+ m22*u16+ m23*u17;
207: wp[16]+= m24*u12+ m25*u13+ m26*u14+ m27*u15+ m28*u16+ m29*u17;
208: wp[17]+= m30*u12+ m31*u13+ m32*u14+ m33*u15+ m34*u16+ m35*u17;
210: wp[18]+= m0*u18 + m1*u19 + m2*u20 + m3*u21 + m4*u22 + m5*u23;
211: wp[19]+= m6*u18 + m7*u19 + m8*u20 + m9*u21+ m10*u22+ m11*u23;
212: wp[20]+= m12*u18+ m13*u19+ m14*u20+ m15*u21+ m16*u22+ m17*u23;
213: wp[21]+= m18*u18+ m19*u19+ m20*u20+ m21*u21+ m22*u22+ m23*u23;
214: wp[22]+= m24*u18+ m25*u19+ m26*u20+ m27*u21+ m28*u22+ m29*u23;
215: wp[23]+= m30*u18+ m31*u19+ m32*u20+ m33*u21+ m34*u22+ m35*u23;
217: wp[24]+= m0*u24 + m1*u25 + m2*u26 + m3*u27 + m4*u28 + m5*u29;
218: wp[25]+= m6*u24 + m7*u25 + m8*u26 + m9*u27+ m10*u28+ m11*u29;
219: wp[26]+= m12*u24+ m13*u25+ m14*u26+ m15*u27+ m16*u28+ m17*u29;
220: wp[27]+= m18*u24+ m19*u25+ m20*u26+ m21*u27+ m22*u28+ m23*u29;
221: wp[28]+= m24*u24+ m25*u25+ m26*u26+ m27*u27+ m28*u28+ m29*u29;
222: wp[29]+= m30*u24+ m31*u25+ m32*u26+ m33*u27+ m34*u28+ m35*u29;
224: wp[30]+= m0*u30 + m1*u31 + m2*u32 + m3*u33 + m4*u34 + m5*u35;
225: wp[31]+= m6*u30 + m7*u31 + m8*u32 + m9*u33+ m10*u34+ m11*u35;
226: wp[32]+= m12*u30+ m13*u31+ m14*u32+ m15*u33+ m16*u34+ m17*u35;
227: wp[33]+= m18*u30+ m19*u31+ m20*u32+ m21*u33+ m22*u34+ m23*u35;
228: wp[34]+= m24*u30+ m25*u31+ m26*u32+ m27*u33+ m28*u34+ m29*u35;
229: wp[35]+= m30*u30+ m31*u31+ m32*u32+ m33*u33+ m34*u34+ m35*u35;
230: }
231: PetscLogFlops(2.0*216.0*(jmax-jmin));
232:
233: /* ... add i to row list for next nonzero entry */
234: il[i] = jmin; /* update il(i) in column k+1, ... mbs-1 */
235: j = bj[jmin];
236: jl[i] = jl[j]; jl[j] = i; /* update jl */
237: }
238: i = nexti;
239: }
241: /* save nonzero entries in k-th row of U ... */
243: /* invert diagonal block */
244: d = ba+k*36;
245: PetscMemcpy(d,dk,36*sizeof(MatScalar));
246: PetscKernel_A_gets_inverse_A_6(d,shift);
247:
248: jmin = bi[k]; jmax = bi[k+1];
249: if (jmin < jmax) {
250: for (j=jmin; j<jmax; j++){
251: vj = bj[j]; /* block col. index of U */
252: u = ba + j*36;
253: wp = w + vj*36;
254: for (k1=0; k1<36; k1++){
255: *u++ = *wp;
256: *wp++ = 0.0;
257: }
258: }
259:
260: /* ... add k to row list for first nonzero entry in k-th row */
261: il[k] = jmin;
262: i = bj[jmin];
263: jl[k] = jl[i]; jl[i] = k;
264: }
265: }
267: PetscFree(w);
268: PetscFree2(il,jl);
269: PetscFree2(dk,uik);
271: C->ops->solve = MatSolve_SeqSBAIJ_6_NaturalOrdering_inplace;
272: C->ops->solvetranspose = MatSolve_SeqSBAIJ_6_NaturalOrdering_inplace;
273: C->ops->forwardsolve = MatForwardSolve_SeqSBAIJ_6_NaturalOrdering_inplace;
274: C->ops->backwardsolve = MatBackwardSolve_SeqSBAIJ_6_NaturalOrdering_inplace;
275: C->assembled = PETSC_TRUE;
276: C->preallocated = PETSC_TRUE;
277: PetscLogFlops(1.3333*216*b->mbs); /* from inverting diagonal blocks */
278: return(0);
279: }