Actual source code: baijfact9.c
1: #define PETSCMAT_DLL
3: /*
4: Factorization code for BAIJ format.
5: */
6: #include ../src/mat/impls/baij/seq/baij.h
7: #include ../src/mat/blockinvert.h
9: /* ------------------------------------------------------------*/
10: /*
11: Version for when blocks are 5 by 5
12: */
15: PetscErrorCode MatLUFactorNumeric_SeqBAIJ_5_inplace(Mat C,Mat A,const MatFactorInfo *info)
16: {
17: Mat_SeqBAIJ *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ *)C->data;
18: IS isrow = b->row,isicol = b->icol;
19: PetscErrorCode ierr;
20: const PetscInt *r,*ic,*bi = b->i,*bj = b->j,*ajtmpold,*ajtmp;
21: PetscInt i,j,n = a->mbs,nz,row,idx,ipvt[5];
22: const PetscInt *diag_offset = b->diag,*ai=a->i,*aj=a->j,*pj;
23: MatScalar *w,*pv,*rtmp,*x,*pc;
24: const MatScalar *v,*aa = a->a;
25: MatScalar p1,p2,p3,p4,m1,m2,m3,m4,m5,m6,m7,m8,m9,x1,x2,x3,x4;
26: MatScalar p5,p6,p7,p8,p9,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16;
27: MatScalar x17,x18,x19,x20,x21,x22,x23,x24,x25,p10,p11,p12,p13,p14;
28: MatScalar p15,p16,p17,p18,p19,p20,p21,p22,p23,p24,p25,m10,m11,m12;
29: MatScalar m13,m14,m15,m16,m17,m18,m19,m20,m21,m22,m23,m24,m25;
30: MatScalar *ba = b->a,work[25];
31: PetscReal shift = info->shiftamount;
34: ISGetIndices(isrow,&r);
35: ISGetIndices(isicol,&ic);
36: PetscMalloc(25*(n+1)*sizeof(MatScalar),&rtmp);
38: #define PETSC_USE_MEMZERO 1
39: #define PETSC_USE_MEMCPY 1
41: for (i=0; i<n; i++) {
42: nz = bi[i+1] - bi[i];
43: ajtmp = bj + bi[i];
44: for (j=0; j<nz; j++) {
45: #if defined(PETSC_USE_MEMZERO)
46: PetscMemzero(rtmp+25*ajtmp[j],25*sizeof(PetscScalar));
47: #else
48: x = rtmp+25*ajtmp[j];
49: x[0] = x[1] = x[2] = x[3] = x[4] = x[5] = x[6] = x[7] = x[8] = x[9] = 0.0;
50: x[10] = x[11] = x[12] = x[13] = x[14] = x[15] = x[16] = x[17] = 0.0;
51: x[18] = x[19] = x[20] = x[21] = x[22] = x[23] = x[24] = 0.0;
52: #endif
53: }
54: /* load in initial (unfactored row) */
55: idx = r[i];
56: nz = ai[idx+1] - ai[idx];
57: ajtmpold = aj + ai[idx];
58: v = aa + 25*ai[idx];
59: for (j=0; j<nz; j++) {
60: #if defined(PETSC_USE_MEMCPY)
61: PetscMemcpy(rtmp+25*ic[ajtmpold[j]],v,25*sizeof(PetscScalar));
62: #else
63: x = rtmp+25*ic[ajtmpold[j]];
64: x[0] = v[0]; x[1] = v[1]; x[2] = v[2]; x[3] = v[3];
65: x[4] = v[4]; x[5] = v[5]; x[6] = v[6]; x[7] = v[7]; x[8] = v[8];
66: x[9] = v[9]; x[10] = v[10]; x[11] = v[11]; x[12] = v[12]; x[13] = v[13];
67: x[14] = v[14]; x[15] = v[15]; x[16] = v[16]; x[17] = v[17];
68: x[18] = v[18]; x[19] = v[19]; x[20] = v[20]; x[21] = v[21];
69: x[22] = v[22]; x[23] = v[23]; x[24] = v[24];
70: #endif
71: v += 25;
72: }
73: row = *ajtmp++;
74: while (row < i) {
75: pc = rtmp + 25*row;
76: p1 = pc[0]; p2 = pc[1]; p3 = pc[2]; p4 = pc[3];
77: p5 = pc[4]; p6 = pc[5]; p7 = pc[6]; p8 = pc[7]; p9 = pc[8];
78: p10 = pc[9]; p11 = pc[10]; p12 = pc[11]; p13 = pc[12]; p14 = pc[13];
79: p15 = pc[14]; p16 = pc[15]; p17 = pc[16]; p18 = pc[17]; p19 = pc[18];
80: p20 = pc[19]; p21 = pc[20]; p22 = pc[21]; p23 = pc[22]; p24 = pc[23];
81: p25 = pc[24];
82: if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0 || p5 != 0.0 ||
83: p6 != 0.0 || p7 != 0.0 || p8 != 0.0 || p9 != 0.0 || p10 != 0.0 ||
84: p11 != 0.0 || p12 != 0.0 || p13 != 0.0 || p14 != 0.0 || p15 != 0.0
85: || p16 != 0.0 || p17 != 0.0 || p18 != 0.0 || p19 != 0.0 ||
86: p20 != 0.0 || p21 != 0.0 || p22 != 0.0 || p23 != 0.0 ||
87: p24 != 0.0 || p25 != 0.0) {
88: pv = ba + 25*diag_offset[row];
89: pj = bj + diag_offset[row] + 1;
90: x1 = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3];
91: x5 = pv[4]; x6 = pv[5]; x7 = pv[6]; x8 = pv[7]; x9 = pv[8];
92: x10 = pv[9]; x11 = pv[10]; x12 = pv[11]; x13 = pv[12]; x14 = pv[13];
93: x15 = pv[14]; x16 = pv[15]; x17 = pv[16]; x18 = pv[17];
94: x19 = pv[18]; x20 = pv[19]; x21 = pv[20]; x22 = pv[21];
95: x23 = pv[22]; x24 = pv[23]; x25 = pv[24];
96: pc[0] = m1 = p1*x1 + p6*x2 + p11*x3 + p16*x4 + p21*x5;
97: pc[1] = m2 = p2*x1 + p7*x2 + p12*x3 + p17*x4 + p22*x5;
98: pc[2] = m3 = p3*x1 + p8*x2 + p13*x3 + p18*x4 + p23*x5;
99: pc[3] = m4 = p4*x1 + p9*x2 + p14*x3 + p19*x4 + p24*x5;
100: pc[4] = m5 = p5*x1 + p10*x2 + p15*x3 + p20*x4 + p25*x5;
102: pc[5] = m6 = p1*x6 + p6*x7 + p11*x8 + p16*x9 + p21*x10;
103: pc[6] = m7 = p2*x6 + p7*x7 + p12*x8 + p17*x9 + p22*x10;
104: pc[7] = m8 = p3*x6 + p8*x7 + p13*x8 + p18*x9 + p23*x10;
105: pc[8] = m9 = p4*x6 + p9*x7 + p14*x8 + p19*x9 + p24*x10;
106: pc[9] = m10 = p5*x6 + p10*x7 + p15*x8 + p20*x9 + p25*x10;
108: pc[10] = m11 = p1*x11 + p6*x12 + p11*x13 + p16*x14 + p21*x15;
109: pc[11] = m12 = p2*x11 + p7*x12 + p12*x13 + p17*x14 + p22*x15;
110: pc[12] = m13 = p3*x11 + p8*x12 + p13*x13 + p18*x14 + p23*x15;
111: pc[13] = m14 = p4*x11 + p9*x12 + p14*x13 + p19*x14 + p24*x15;
112: pc[14] = m15 = p5*x11 + p10*x12 + p15*x13 + p20*x14 + p25*x15;
114: pc[15] = m16 = p1*x16 + p6*x17 + p11*x18 + p16*x19 + p21*x20;
115: pc[16] = m17 = p2*x16 + p7*x17 + p12*x18 + p17*x19 + p22*x20;
116: pc[17] = m18 = p3*x16 + p8*x17 + p13*x18 + p18*x19 + p23*x20;
117: pc[18] = m19 = p4*x16 + p9*x17 + p14*x18 + p19*x19 + p24*x20;
118: pc[19] = m20 = p5*x16 + p10*x17 + p15*x18 + p20*x19 + p25*x20;
120: pc[20] = m21 = p1*x21 + p6*x22 + p11*x23 + p16*x24 + p21*x25;
121: pc[21] = m22 = p2*x21 + p7*x22 + p12*x23 + p17*x24 + p22*x25;
122: pc[22] = m23 = p3*x21 + p8*x22 + p13*x23 + p18*x24 + p23*x25;
123: pc[23] = m24 = p4*x21 + p9*x22 + p14*x23 + p19*x24 + p24*x25;
124: pc[24] = m25 = p5*x21 + p10*x22 + p15*x23 + p20*x24 + p25*x25;
126: nz = bi[row+1] - diag_offset[row] - 1;
127: pv += 25;
128: for (j=0; j<nz; j++) {
129: x1 = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3];
130: x5 = pv[4]; x6 = pv[5]; x7 = pv[6]; x8 = pv[7]; x9 = pv[8];
131: x10 = pv[9]; x11 = pv[10]; x12 = pv[11]; x13 = pv[12];
132: x14 = pv[13]; x15 = pv[14]; x16 = pv[15]; x17 = pv[16];
133: x18 = pv[17]; x19 = pv[18]; x20 = pv[19]; x21 = pv[20];
134: x22 = pv[21]; x23 = pv[22]; x24 = pv[23]; x25 = pv[24];
135: x = rtmp + 25*pj[j];
136: x[0] -= m1*x1 + m6*x2 + m11*x3 + m16*x4 + m21*x5;
137: x[1] -= m2*x1 + m7*x2 + m12*x3 + m17*x4 + m22*x5;
138: x[2] -= m3*x1 + m8*x2 + m13*x3 + m18*x4 + m23*x5;
139: x[3] -= m4*x1 + m9*x2 + m14*x3 + m19*x4 + m24*x5;
140: x[4] -= m5*x1 + m10*x2 + m15*x3 + m20*x4 + m25*x5;
142: x[5] -= m1*x6 + m6*x7 + m11*x8 + m16*x9 + m21*x10;
143: x[6] -= m2*x6 + m7*x7 + m12*x8 + m17*x9 + m22*x10;
144: x[7] -= m3*x6 + m8*x7 + m13*x8 + m18*x9 + m23*x10;
145: x[8] -= m4*x6 + m9*x7 + m14*x8 + m19*x9 + m24*x10;
146: x[9] -= m5*x6 + m10*x7 + m15*x8 + m20*x9 + m25*x10;
148: x[10] -= m1*x11 + m6*x12 + m11*x13 + m16*x14 + m21*x15;
149: x[11] -= m2*x11 + m7*x12 + m12*x13 + m17*x14 + m22*x15;
150: x[12] -= m3*x11 + m8*x12 + m13*x13 + m18*x14 + m23*x15;
151: x[13] -= m4*x11 + m9*x12 + m14*x13 + m19*x14 + m24*x15;
152: x[14] -= m5*x11 + m10*x12 + m15*x13 + m20*x14 + m25*x15;
154: x[15] -= m1*x16 + m6*x17 + m11*x18 + m16*x19 + m21*x20;
155: x[16] -= m2*x16 + m7*x17 + m12*x18 + m17*x19 + m22*x20;
156: x[17] -= m3*x16 + m8*x17 + m13*x18 + m18*x19 + m23*x20;
157: x[18] -= m4*x16 + m9*x17 + m14*x18 + m19*x19 + m24*x20;
158: x[19] -= m5*x16 + m10*x17 + m15*x18 + m20*x19 + m25*x20;
160: x[20] -= m1*x21 + m6*x22 + m11*x23 + m16*x24 + m21*x25;
161: x[21] -= m2*x21 + m7*x22 + m12*x23 + m17*x24 + m22*x25;
162: x[22] -= m3*x21 + m8*x22 + m13*x23 + m18*x24 + m23*x25;
163: x[23] -= m4*x21 + m9*x22 + m14*x23 + m19*x24 + m24*x25;
164: x[24] -= m5*x21 + m10*x22 + m15*x23 + m20*x24 + m25*x25;
166: pv += 25;
167: }
168: PetscLogFlops(250.0*nz+225.0);
169: }
170: row = *ajtmp++;
171: }
172: /* finished row so stick it into b->a */
173: pv = ba + 25*bi[i];
174: pj = bj + bi[i];
175: nz = bi[i+1] - bi[i];
176: for (j=0; j<nz; j++) {
177: #if defined(PETSC_USE_MEMCPY)
178: PetscMemcpy(pv,rtmp+25*pj[j],25*sizeof(PetscScalar));
179: #else
180: x = rtmp+25*pj[j];
181: pv[0] = x[0]; pv[1] = x[1]; pv[2] = x[2]; pv[3] = x[3];
182: pv[4] = x[4]; pv[5] = x[5]; pv[6] = x[6]; pv[7] = x[7]; pv[8] = x[8];
183: pv[9] = x[9]; pv[10] = x[10]; pv[11] = x[11]; pv[12] = x[12];
184: pv[13] = x[13]; pv[14] = x[14]; pv[15] = x[15]; pv[16] = x[16];
185: pv[17] = x[17]; pv[18] = x[18]; pv[19] = x[19]; pv[20] = x[20];
186: pv[21] = x[21]; pv[22] = x[22]; pv[23] = x[23]; pv[24] = x[24];
187: #endif
188: pv += 25;
189: }
190: /* invert diagonal block */
191: w = ba + 25*diag_offset[i];
192: Kernel_A_gets_inverse_A_5(w,ipvt,work,shift);
193: }
195: PetscFree(rtmp);
196: ISRestoreIndices(isicol,&ic);
197: ISRestoreIndices(isrow,&r);
198: C->ops->solve = MatSolve_SeqBAIJ_5_inplace;
199: C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_5_inplace;
200: C->assembled = PETSC_TRUE;
201: PetscLogFlops(1.333333333333*5*5*5*b->mbs); /* from inverting diagonal blocks */
202: return(0);
203: }
205: /* MatLUFactorNumeric_SeqBAIJ_5 -
206: copied from MatLUFactorNumeric_SeqBAIJ_N_inplace() and manually re-implemented
207: Kernel_A_gets_A_times_B()
208: Kernel_A_gets_A_minus_B_times_C()
209: Kernel_A_gets_inverse_A()
210: */
214: PetscErrorCode MatLUFactorNumeric_SeqBAIJ_5(Mat B,Mat A,const MatFactorInfo *info)
215: {
216: Mat C=B;
217: Mat_SeqBAIJ *a=(Mat_SeqBAIJ*)A->data,*b=(Mat_SeqBAIJ *)C->data;
218: IS isrow = b->row,isicol = b->icol;
220: const PetscInt *r,*ic,*ics;
221: PetscInt i,j,k,nz,nzL,row;
222: const PetscInt n=a->mbs,*ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j;
223: const PetscInt *ajtmp,*bjtmp,*bdiag=b->diag,*pj,bs2=a->bs2;
224: MatScalar *rtmp,*pc,*mwork,*v,*pv,*aa=a->a,work[25];
225: PetscInt flg,ipvt[5];
226: PetscReal shift = info->shiftamount;
229: ISGetIndices(isrow,&r);
230: ISGetIndices(isicol,&ic);
232: /* generate work space needed by the factorization */
233: PetscMalloc2(bs2*n,MatScalar,&rtmp,bs2,MatScalar,&mwork);
234: PetscMemzero(rtmp,bs2*n*sizeof(MatScalar));
235: ics = ic;
237: for (i=0; i<n; i++){
238: /* zero rtmp */
239: /* L part */
240: nz = bi[i+1] - bi[i];
241: bjtmp = bj + bi[i];
242: for (j=0; j<nz; j++){
243: PetscMemzero(rtmp+bs2*bjtmp[j],bs2*sizeof(MatScalar));
244: }
246: /* U part */
247: nz = bdiag[i] - bdiag[i+1];
248: bjtmp = bj + bdiag[i+1]+1;
249: for (j=0; j<nz; j++){
250: PetscMemzero(rtmp+bs2*bjtmp[j],bs2*sizeof(MatScalar));
251: }
252:
253: /* load in initial (unfactored row) */
254: nz = ai[r[i]+1] - ai[r[i]];
255: ajtmp = aj + ai[r[i]];
256: v = aa + bs2*ai[r[i]];
257: for (j=0; j<nz; j++) {
258: PetscMemcpy(rtmp+bs2*ic[ajtmp[j]],v+bs2*j,bs2*sizeof(MatScalar));
259: }
261: /* elimination */
262: bjtmp = bj + bi[i];
263: nzL = bi[i+1] - bi[i];
264: for(k=0;k < nzL;k++) {
265: row = bjtmp[k];
266: pc = rtmp + bs2*row;
267: for (flg=0,j=0; j<bs2; j++) { if (pc[j]!=0.0) { flg = 1; break; }}
268: if (flg) {
269: pv = b->a + bs2*bdiag[row];
270: /* Kernel_A_gets_A_times_B(bs,pc,pv,mwork); *pc = *pc * (*pv); */
271: Kernel_A_gets_A_times_B_5(pc,pv,mwork);
272:
273: pj = b->j + bdiag[row+1]+1; /* begining of U(row,:) */
274: pv = b->a + bs2*(bdiag[row+1]+1);
275: nz = bdiag[row] - bdiag[row+1] - 1; /* num of entries inU(row,:), excluding diag */
276: for (j=0; j<nz; j++) {
277: /* Kernel_A_gets_A_minus_B_times_C(bs,rtmp+bs2*pj[j],pc,pv+bs2*j); */
278: /* rtmp+bs2*pj[j] = rtmp+bs2*pj[j] - (*pc)*(pv+bs2*j) */
279: v = rtmp + bs2*pj[j];
280: Kernel_A_gets_A_minus_B_times_C_5(v,pc,pv);
281: pv += bs2;
282: }
283: PetscLogFlops(250*nz+225); /* flops = 2*bs^3*nz + 2*bs^3 - bs2) */
284: }
285: }
287: /* finished row so stick it into b->a */
288: /* L part */
289: pv = b->a + bs2*bi[i] ;
290: pj = b->j + bi[i] ;
291: nz = bi[i+1] - bi[i];
292: for (j=0; j<nz; j++) {
293: PetscMemcpy(pv+bs2*j,rtmp+bs2*pj[j],bs2*sizeof(MatScalar));
294: }
296: /* Mark diagonal and invert diagonal for simplier triangular solves */
297: pv = b->a + bs2*bdiag[i];
298: pj = b->j + bdiag[i];
299: PetscMemcpy(pv,rtmp+bs2*pj[0],bs2*sizeof(MatScalar));
300: /* Kernel_A_gets_inverse_A(bs,pv,v_pivots,v_work); */
301: Kernel_A_gets_inverse_A_5(pv,ipvt,work,shift);
302:
303: /* U part */
304: pv = b->a + bs2*(bdiag[i+1]+1);
305: pj = b->j + bdiag[i+1]+1;
306: nz = bdiag[i] - bdiag[i+1] - 1;
307: for (j=0; j<nz; j++){
308: PetscMemcpy(pv+bs2*j,rtmp+bs2*pj[j],bs2*sizeof(MatScalar));
309: }
310: }
312: PetscFree2(rtmp,mwork);
313: ISRestoreIndices(isicol,&ic);
314: ISRestoreIndices(isrow,&r);
315: C->ops->solve = MatSolve_SeqBAIJ_5;
316: C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_5;
317: C->assembled = PETSC_TRUE;
318: PetscLogFlops(1.333333333333*5*5*5*n); /* from inverting diagonal blocks */
319: return(0);
320: }
322: /*
323: Version for when blocks are 5 by 5 Using natural ordering
324: */
327: PetscErrorCode MatLUFactorNumeric_SeqBAIJ_5_NaturalOrdering_inplace(Mat C,Mat A,const MatFactorInfo *info)
328: {
329: Mat_SeqBAIJ *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ *)C->data;
331: PetscInt i,j,n = a->mbs,*bi = b->i,*bj = b->j,ipvt[5];
332: PetscInt *ajtmpold,*ajtmp,nz,row;
333: PetscInt *diag_offset = b->diag,*ai=a->i,*aj=a->j,*pj;
334: MatScalar *pv,*v,*rtmp,*pc,*w,*x;
335: MatScalar x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15;
336: MatScalar x16,x17,x18,x19,x20,x21,x22,x23,x24,x25;
337: MatScalar p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11,p12,p13,p14,p15;
338: MatScalar p16,p17,p18,p19,p20,p21,p22,p23,p24,p25;
339: MatScalar m1,m2,m3,m4,m5,m6,m7,m8,m9,m10,m11,m12,m13,m14,m15;
340: MatScalar m16,m17,m18,m19,m20,m21,m22,m23,m24,m25;
341: MatScalar *ba = b->a,*aa = a->a,work[25];
342: PetscReal shift = info->shiftamount;
345: PetscMalloc(25*(n+1)*sizeof(MatScalar),&rtmp);
346: for (i=0; i<n; i++) {
347: nz = bi[i+1] - bi[i];
348: ajtmp = bj + bi[i];
349: for (j=0; j<nz; j++) {
350: x = rtmp+25*ajtmp[j];
351: x[0] = x[1] = x[2] = x[3] = x[4] = x[5] = x[6] = x[7] = x[8] = x[9] = 0.0;
352: x[10] = x[11] = x[12] = x[13] = x[14] = x[15] = 0.0;
353: x[16] = x[17] = x[18] = x[19] = x[20] = x[21] = x[22] = x[23] = x[24] = 0.0;
354: }
355: /* load in initial (unfactored row) */
356: nz = ai[i+1] - ai[i];
357: ajtmpold = aj + ai[i];
358: v = aa + 25*ai[i];
359: for (j=0; j<nz; j++) {
360: x = rtmp+25*ajtmpold[j];
361: x[0] = v[0]; x[1] = v[1]; x[2] = v[2]; x[3] = v[3];
362: x[4] = v[4]; x[5] = v[5]; x[6] = v[6]; x[7] = v[7]; x[8] = v[8];
363: x[9] = v[9]; x[10] = v[10]; x[11] = v[11]; x[12] = v[12]; x[13] = v[13];
364: x[14] = v[14]; x[15] = v[15]; x[16] = v[16]; x[17] = v[17]; x[18] = v[18];
365: x[19] = v[19]; x[20] = v[20]; x[21] = v[21]; x[22] = v[22]; x[23] = v[23];
366: x[24] = v[24];
367: v += 25;
368: }
369: row = *ajtmp++;
370: while (row < i) {
371: pc = rtmp + 25*row;
372: p1 = pc[0]; p2 = pc[1]; p3 = pc[2]; p4 = pc[3];
373: p5 = pc[4]; p6 = pc[5]; p7 = pc[6]; p8 = pc[7]; p9 = pc[8];
374: p10 = pc[9]; p11 = pc[10]; p12 = pc[11]; p13 = pc[12]; p14 = pc[13];
375: p15 = pc[14]; p16 = pc[15]; p17 = pc[16]; p18 = pc[17];
376: p19 = pc[18]; p20 = pc[19]; p21 = pc[20]; p22 = pc[21]; p23 = pc[22];
377: p24 = pc[23]; p25 = pc[24];
378: if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0 || p5 != 0.0 ||
379: p6 != 0.0 || p7 != 0.0 || p8 != 0.0 || p9 != 0.0 || p10 != 0.0 ||
380: p11 != 0.0 || p12 != 0.0 || p13 != 0.0 || p14 != 0.0 || p15 != 0.0
381: || p16 != 0.0 || p17 != 0.0 || p18 != 0.0 || p19 != 0.0 || p20 != 0.0
382: || p21 != 0.0 || p22 != 0.0 || p23 != 0.0 || p24 != 0.0 || p25 != 0.0) {
383: pv = ba + 25*diag_offset[row];
384: pj = bj + diag_offset[row] + 1;
385: x1 = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3];
386: x5 = pv[4]; x6 = pv[5]; x7 = pv[6]; x8 = pv[7]; x9 = pv[8];
387: x10 = pv[9]; x11 = pv[10]; x12 = pv[11]; x13 = pv[12]; x14 = pv[13];
388: x15 = pv[14]; x16 = pv[15]; x17 = pv[16]; x18 = pv[17]; x19 = pv[18];
389: x20 = pv[19]; x21 = pv[20]; x22 = pv[21]; x23 = pv[22]; x24 = pv[23];
390: x25 = pv[24];
391: pc[0] = m1 = p1*x1 + p6*x2 + p11*x3 + p16*x4 + p21*x5;
392: pc[1] = m2 = p2*x1 + p7*x2 + p12*x3 + p17*x4 + p22*x5;
393: pc[2] = m3 = p3*x1 + p8*x2 + p13*x3 + p18*x4 + p23*x5;
394: pc[3] = m4 = p4*x1 + p9*x2 + p14*x3 + p19*x4 + p24*x5;
395: pc[4] = m5 = p5*x1 + p10*x2 + p15*x3 + p20*x4 + p25*x5;
397: pc[5] = m6 = p1*x6 + p6*x7 + p11*x8 + p16*x9 + p21*x10;
398: pc[6] = m7 = p2*x6 + p7*x7 + p12*x8 + p17*x9 + p22*x10;
399: pc[7] = m8 = p3*x6 + p8*x7 + p13*x8 + p18*x9 + p23*x10;
400: pc[8] = m9 = p4*x6 + p9*x7 + p14*x8 + p19*x9 + p24*x10;
401: pc[9] = m10 = p5*x6 + p10*x7 + p15*x8 + p20*x9 + p25*x10;
403: pc[10] = m11 = p1*x11 + p6*x12 + p11*x13 + p16*x14 + p21*x15;
404: pc[11] = m12 = p2*x11 + p7*x12 + p12*x13 + p17*x14 + p22*x15;
405: pc[12] = m13 = p3*x11 + p8*x12 + p13*x13 + p18*x14 + p23*x15;
406: pc[13] = m14 = p4*x11 + p9*x12 + p14*x13 + p19*x14 + p24*x15;
407: pc[14] = m15 = p5*x11 + p10*x12 + p15*x13 + p20*x14 + p25*x15;
409: pc[15] = m16 = p1*x16 + p6*x17 + p11*x18 + p16*x19 + p21*x20;
410: pc[16] = m17 = p2*x16 + p7*x17 + p12*x18 + p17*x19 + p22*x20;
411: pc[17] = m18 = p3*x16 + p8*x17 + p13*x18 + p18*x19 + p23*x20;
412: pc[18] = m19 = p4*x16 + p9*x17 + p14*x18 + p19*x19 + p24*x20;
413: pc[19] = m20 = p5*x16 + p10*x17 + p15*x18 + p20*x19 + p25*x20;
415: pc[20] = m21 = p1*x21 + p6*x22 + p11*x23 + p16*x24 + p21*x25;
416: pc[21] = m22 = p2*x21 + p7*x22 + p12*x23 + p17*x24 + p22*x25;
417: pc[22] = m23 = p3*x21 + p8*x22 + p13*x23 + p18*x24 + p23*x25;
418: pc[23] = m24 = p4*x21 + p9*x22 + p14*x23 + p19*x24 + p24*x25;
419: pc[24] = m25 = p5*x21 + p10*x22 + p15*x23 + p20*x24 + p25*x25;
421: nz = bi[row+1] - diag_offset[row] - 1;
422: pv += 25;
423: for (j=0; j<nz; j++) {
424: x1 = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3];
425: x5 = pv[4]; x6 = pv[5]; x7 = pv[6]; x8 = pv[7]; x9 = pv[8];
426: x10 = pv[9]; x11 = pv[10]; x12 = pv[11]; x13 = pv[12];
427: x14 = pv[13]; x15 = pv[14]; x16 = pv[15]; x17 = pv[16]; x18 = pv[17];
428: x19 = pv[18]; x20 = pv[19]; x21 = pv[20]; x22 = pv[21]; x23 = pv[22];
429: x24 = pv[23]; x25 = pv[24];
430: x = rtmp + 25*pj[j];
431: x[0] -= m1*x1 + m6*x2 + m11*x3 + m16*x4 + m21*x5;
432: x[1] -= m2*x1 + m7*x2 + m12*x3 + m17*x4 + m22*x5;
433: x[2] -= m3*x1 + m8*x2 + m13*x3 + m18*x4 + m23*x5;
434: x[3] -= m4*x1 + m9*x2 + m14*x3 + m19*x4 + m24*x5;
435: x[4] -= m5*x1 + m10*x2 + m15*x3 + m20*x4 + m25*x5;
437: x[5] -= m1*x6 + m6*x7 + m11*x8 + m16*x9 + m21*x10;
438: x[6] -= m2*x6 + m7*x7 + m12*x8 + m17*x9 + m22*x10;
439: x[7] -= m3*x6 + m8*x7 + m13*x8 + m18*x9 + m23*x10;
440: x[8] -= m4*x6 + m9*x7 + m14*x8 + m19*x9 + m24*x10;
441: x[9] -= m5*x6 + m10*x7 + m15*x8 + m20*x9 + m25*x10;
443: x[10] -= m1*x11 + m6*x12 + m11*x13 + m16*x14 + m21*x15;
444: x[11] -= m2*x11 + m7*x12 + m12*x13 + m17*x14 + m22*x15;
445: x[12] -= m3*x11 + m8*x12 + m13*x13 + m18*x14 + m23*x15;
446: x[13] -= m4*x11 + m9*x12 + m14*x13 + m19*x14 + m24*x15;
447: x[14] -= m5*x11 + m10*x12 + m15*x13 + m20*x14 + m25*x15;
449: x[15] -= m1*x16 + m6*x17 + m11*x18 + m16*x19 + m21*x20;
450: x[16] -= m2*x16 + m7*x17 + m12*x18 + m17*x19 + m22*x20;
451: x[17] -= m3*x16 + m8*x17 + m13*x18 + m18*x19 + m23*x20;
452: x[18] -= m4*x16 + m9*x17 + m14*x18 + m19*x19 + m24*x20;
453: x[19] -= m5*x16 + m10*x17 + m15*x18 + m20*x19 + m25*x20;
455: x[20] -= m1*x21 + m6*x22 + m11*x23 + m16*x24 + m21*x25;
456: x[21] -= m2*x21 + m7*x22 + m12*x23 + m17*x24 + m22*x25;
457: x[22] -= m3*x21 + m8*x22 + m13*x23 + m18*x24 + m23*x25;
458: x[23] -= m4*x21 + m9*x22 + m14*x23 + m19*x24 + m24*x25;
459: x[24] -= m5*x21 + m10*x22 + m15*x23 + m20*x24 + m25*x25;
460: pv += 25;
461: }
462: PetscLogFlops(250.0*nz+225.0);
463: }
464: row = *ajtmp++;
465: }
466: /* finished row so stick it into b->a */
467: pv = ba + 25*bi[i];
468: pj = bj + bi[i];
469: nz = bi[i+1] - bi[i];
470: for (j=0; j<nz; j++) {
471: x = rtmp+25*pj[j];
472: pv[0] = x[0]; pv[1] = x[1]; pv[2] = x[2]; pv[3] = x[3];
473: pv[4] = x[4]; pv[5] = x[5]; pv[6] = x[6]; pv[7] = x[7]; pv[8] = x[8];
474: pv[9] = x[9]; pv[10] = x[10]; pv[11] = x[11]; pv[12] = x[12];
475: pv[13] = x[13]; pv[14] = x[14]; pv[15] = x[15]; pv[16] = x[16]; pv[17] = x[17];
476: pv[18] = x[18]; pv[19] = x[19]; pv[20] = x[20]; pv[21] = x[21]; pv[22] = x[22];
477: pv[23] = x[23]; pv[24] = x[24];
478: pv += 25;
479: }
480: /* invert diagonal block */
481: w = ba + 25*diag_offset[i];
482: Kernel_A_gets_inverse_A_5(w,ipvt,work,shift);
483: }
485: PetscFree(rtmp);
486: C->ops->solve = MatSolve_SeqBAIJ_5_NaturalOrdering_inplace;
487: C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_5_NaturalOrdering_inplace;
488: C->assembled = PETSC_TRUE;
489: PetscLogFlops(1.333333333333*5*5*5*b->mbs); /* from inverting diagonal blocks */
490: return(0);
491: }
495: PetscErrorCode MatLUFactorNumeric_SeqBAIJ_5_NaturalOrdering(Mat B,Mat A,const MatFactorInfo *info)
496: {
497: Mat C=B;
498: Mat_SeqBAIJ *a=(Mat_SeqBAIJ*)A->data,*b=(Mat_SeqBAIJ *)C->data;
500: PetscInt i,j,k,nz,nzL,row;
501: const PetscInt n=a->mbs,*ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j;
502: const PetscInt *ajtmp,*bjtmp,*bdiag=b->diag,*pj,bs2=a->bs2;
503: MatScalar *rtmp,*pc,*mwork,*v,*vv,*pv,*aa=a->a,work[25];
504: PetscInt flg,ipvt[5];
505: PetscReal shift = info->shiftamount;
508: /* generate work space needed by the factorization */
509: PetscMalloc2(bs2*n,MatScalar,&rtmp,bs2,MatScalar,&mwork);
510: PetscMemzero(rtmp,bs2*n*sizeof(MatScalar));
512: for (i=0; i<n; i++){
513: /* zero rtmp */
514: /* L part */
515: nz = bi[i+1] - bi[i];
516: bjtmp = bj + bi[i];
517: for (j=0; j<nz; j++){
518: PetscMemzero(rtmp+bs2*bjtmp[j],bs2*sizeof(MatScalar));
519: }
521: /* U part */
522: nz = bdiag[i] - bdiag[i+1];
523: bjtmp = bj + bdiag[i+1]+1;
524: for (j=0; j<nz; j++){
525: PetscMemzero(rtmp+bs2*bjtmp[j],bs2*sizeof(MatScalar));
526: }
527:
528: /* load in initial (unfactored row) */
529: nz = ai[i+1] - ai[i];
530: ajtmp = aj + ai[i];
531: v = aa + bs2*ai[i];
532: for (j=0; j<nz; j++) {
533: PetscMemcpy(rtmp+bs2*ajtmp[j],v+bs2*j,bs2*sizeof(MatScalar));
534: }
536: /* elimination */
537: bjtmp = bj + bi[i];
538: nzL = bi[i+1] - bi[i];
539: for(k=0;k < nzL;k++) {
540: row = bjtmp[k];
541: pc = rtmp + bs2*row;
542: for (flg=0,j=0; j<bs2; j++) { if (pc[j]!=0.0) { flg = 1; break; }}
543: if (flg) {
544: pv = b->a + bs2*bdiag[row];
545: /* Kernel_A_gets_A_times_B(bs,pc,pv,mwork); *pc = *pc * (*pv); */
546: Kernel_A_gets_A_times_B_5(pc,pv,mwork);
547:
548: pj = b->j + bdiag[row+1]+1; /* begining of U(row,:) */
549: pv = b->a + bs2*(bdiag[row+1]+1);
550: nz = bdiag[row] - bdiag[row+1] - 1; /* num of entries inU(row,:), excluding diag */
551: for (j=0; j<nz; j++) {
552: /* Kernel_A_gets_A_minus_B_times_C(bs,rtmp+bs2*pj[j],pc,pv+bs2*j); */
553: /* rtmp+bs2*pj[j] = rtmp+bs2*pj[j] - (*pc)*(pv+bs2*j) */
554: vv = rtmp + bs2*pj[j];
555: Kernel_A_gets_A_minus_B_times_C_5(vv,pc,pv);
556: pv += bs2;
557: }
558: PetscLogFlops(250*nz+225); /* flops = 2*bs^3*nz + 2*bs^3 - bs2) */
559: }
560: }
562: /* finished row so stick it into b->a */
563: /* L part */
564: pv = b->a + bs2*bi[i] ;
565: pj = b->j + bi[i] ;
566: nz = bi[i+1] - bi[i];
567: for (j=0; j<nz; j++) {
568: PetscMemcpy(pv+bs2*j,rtmp+bs2*pj[j],bs2*sizeof(MatScalar));
569: }
570:
571: /* Mark diagonal and invert diagonal for simplier triangular solves */
572: pv = b->a + bs2*bdiag[i];
573: pj = b->j + bdiag[i];
574: PetscMemcpy(pv,rtmp+bs2*pj[0],bs2*sizeof(MatScalar));
575: /* Kernel_A_gets_inverse_A(bs,pv,v_pivots,v_work); */
576: Kernel_A_gets_inverse_A_5(pv,ipvt,work,shift);
577:
578: /* U part */
579: pv = b->a + bs2*(bdiag[i+1]+1);
580: pj = b->j + bdiag[i+1]+1;
581: nz = bdiag[i] - bdiag[i+1] - 1;
582: for (j=0; j<nz; j++){
583: PetscMemcpy(pv+bs2*j,rtmp+bs2*pj[j],bs2*sizeof(MatScalar));
584: }
585: }
586: PetscFree2(rtmp,mwork);
587: C->ops->solve = MatSolve_SeqBAIJ_5_NaturalOrdering;
588: C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_5_NaturalOrdering;
589: C->assembled = PETSC_TRUE;
590: PetscLogFlops(1.333333333333*5*5*5*n); /* from inverting diagonal blocks */
591: return(0);
592: }