Actual source code: baijfact9.c
petsc-3.3-p7 2013-05-11
2: /*
3: Factorization code for BAIJ format.
4: */
5: #include <../src/mat/impls/baij/seq/baij.h>
6: #include <../src/mat/blockinvert.h>
8: /* ------------------------------------------------------------*/
9: /*
10: Version for when blocks are 5 by 5
11: */
14: PetscErrorCode MatLUFactorNumeric_SeqBAIJ_5_inplace(Mat C,Mat A,const MatFactorInfo *info)
15: {
16: Mat_SeqBAIJ *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ *)C->data;
17: IS isrow = b->row,isicol = b->icol;
18: PetscErrorCode ierr;
19: const PetscInt *r,*ic,*bi = b->i,*bj = b->j,*ajtmpold,*ajtmp;
20: PetscInt i,j,n = a->mbs,nz,row,idx,ipvt[5];
21: const PetscInt *diag_offset = b->diag,*ai=a->i,*aj=a->j,*pj;
22: MatScalar *w,*pv,*rtmp,*x,*pc;
23: const MatScalar *v,*aa = a->a;
24: MatScalar p1,p2,p3,p4,m1,m2,m3,m4,m5,m6,m7,m8,m9,x1,x2,x3,x4;
25: MatScalar p5,p6,p7,p8,p9,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16;
26: MatScalar x17,x18,x19,x20,x21,x22,x23,x24,x25,p10,p11,p12,p13,p14;
27: MatScalar p15,p16,p17,p18,p19,p20,p21,p22,p23,p24,p25,m10,m11,m12;
28: MatScalar m13,m14,m15,m16,m17,m18,m19,m20,m21,m22,m23,m24,m25;
29: MatScalar *ba = b->a,work[25];
30: PetscReal shift = info->shiftamount;
33: ISGetIndices(isrow,&r);
34: ISGetIndices(isicol,&ic);
35: PetscMalloc(25*(n+1)*sizeof(MatScalar),&rtmp);
37: #define PETSC_USE_MEMZERO 1
38: #define PETSC_USE_MEMCPY 1
40: for (i=0; i<n; i++) {
41: nz = bi[i+1] - bi[i];
42: ajtmp = bj + bi[i];
43: for (j=0; j<nz; j++) {
44: #if defined(PETSC_USE_MEMZERO)
45: PetscMemzero(rtmp+25*ajtmp[j],25*sizeof(PetscScalar));
46: #else
47: x = rtmp+25*ajtmp[j];
48: x[0] = x[1] = x[2] = x[3] = x[4] = x[5] = x[6] = x[7] = x[8] = x[9] = 0.0;
49: x[10] = x[11] = x[12] = x[13] = x[14] = x[15] = x[16] = x[17] = 0.0;
50: x[18] = x[19] = x[20] = x[21] = x[22] = x[23] = x[24] = 0.0;
51: #endif
52: }
53: /* load in initial (unfactored row) */
54: idx = r[i];
55: nz = ai[idx+1] - ai[idx];
56: ajtmpold = aj + ai[idx];
57: v = aa + 25*ai[idx];
58: for (j=0; j<nz; j++) {
59: #if defined(PETSC_USE_MEMCPY)
60: PetscMemcpy(rtmp+25*ic[ajtmpold[j]],v,25*sizeof(PetscScalar));
61: #else
62: x = rtmp+25*ic[ajtmpold[j]];
63: x[0] = v[0]; x[1] = v[1]; x[2] = v[2]; x[3] = v[3];
64: x[4] = v[4]; x[5] = v[5]; x[6] = v[6]; x[7] = v[7]; x[8] = v[8];
65: x[9] = v[9]; x[10] = v[10]; x[11] = v[11]; x[12] = v[12]; x[13] = v[13];
66: x[14] = v[14]; x[15] = v[15]; x[16] = v[16]; x[17] = v[17];
67: x[18] = v[18]; x[19] = v[19]; x[20] = v[20]; x[21] = v[21];
68: x[22] = v[22]; x[23] = v[23]; x[24] = v[24];
69: #endif
70: v += 25;
71: }
72: row = *ajtmp++;
73: while (row < i) {
74: pc = rtmp + 25*row;
75: p1 = pc[0]; p2 = pc[1]; p3 = pc[2]; p4 = pc[3];
76: p5 = pc[4]; p6 = pc[5]; p7 = pc[6]; p8 = pc[7]; p9 = pc[8];
77: p10 = pc[9]; p11 = pc[10]; p12 = pc[11]; p13 = pc[12]; p14 = pc[13];
78: p15 = pc[14]; p16 = pc[15]; p17 = pc[16]; p18 = pc[17]; p19 = pc[18];
79: p20 = pc[19]; p21 = pc[20]; p22 = pc[21]; p23 = pc[22]; p24 = pc[23];
80: p25 = pc[24];
81: if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0 || p5 != 0.0 ||
82: p6 != 0.0 || p7 != 0.0 || p8 != 0.0 || p9 != 0.0 || p10 != 0.0 ||
83: p11 != 0.0 || p12 != 0.0 || p13 != 0.0 || p14 != 0.0 || p15 != 0.0
84: || p16 != 0.0 || p17 != 0.0 || p18 != 0.0 || p19 != 0.0 ||
85: p20 != 0.0 || p21 != 0.0 || p22 != 0.0 || p23 != 0.0 ||
86: p24 != 0.0 || p25 != 0.0) {
87: pv = ba + 25*diag_offset[row];
88: pj = bj + diag_offset[row] + 1;
89: x1 = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3];
90: x5 = pv[4]; x6 = pv[5]; x7 = pv[6]; x8 = pv[7]; x9 = pv[8];
91: x10 = pv[9]; x11 = pv[10]; x12 = pv[11]; x13 = pv[12]; x14 = pv[13];
92: x15 = pv[14]; x16 = pv[15]; x17 = pv[16]; x18 = pv[17];
93: x19 = pv[18]; x20 = pv[19]; x21 = pv[20]; x22 = pv[21];
94: x23 = pv[22]; x24 = pv[23]; x25 = pv[24];
95: pc[0] = m1 = p1*x1 + p6*x2 + p11*x3 + p16*x4 + p21*x5;
96: pc[1] = m2 = p2*x1 + p7*x2 + p12*x3 + p17*x4 + p22*x5;
97: pc[2] = m3 = p3*x1 + p8*x2 + p13*x3 + p18*x4 + p23*x5;
98: pc[3] = m4 = p4*x1 + p9*x2 + p14*x3 + p19*x4 + p24*x5;
99: pc[4] = m5 = p5*x1 + p10*x2 + p15*x3 + p20*x4 + p25*x5;
101: pc[5] = m6 = p1*x6 + p6*x7 + p11*x8 + p16*x9 + p21*x10;
102: pc[6] = m7 = p2*x6 + p7*x7 + p12*x8 + p17*x9 + p22*x10;
103: pc[7] = m8 = p3*x6 + p8*x7 + p13*x8 + p18*x9 + p23*x10;
104: pc[8] = m9 = p4*x6 + p9*x7 + p14*x8 + p19*x9 + p24*x10;
105: pc[9] = m10 = p5*x6 + p10*x7 + p15*x8 + p20*x9 + p25*x10;
107: pc[10] = m11 = p1*x11 + p6*x12 + p11*x13 + p16*x14 + p21*x15;
108: pc[11] = m12 = p2*x11 + p7*x12 + p12*x13 + p17*x14 + p22*x15;
109: pc[12] = m13 = p3*x11 + p8*x12 + p13*x13 + p18*x14 + p23*x15;
110: pc[13] = m14 = p4*x11 + p9*x12 + p14*x13 + p19*x14 + p24*x15;
111: pc[14] = m15 = p5*x11 + p10*x12 + p15*x13 + p20*x14 + p25*x15;
113: pc[15] = m16 = p1*x16 + p6*x17 + p11*x18 + p16*x19 + p21*x20;
114: pc[16] = m17 = p2*x16 + p7*x17 + p12*x18 + p17*x19 + p22*x20;
115: pc[17] = m18 = p3*x16 + p8*x17 + p13*x18 + p18*x19 + p23*x20;
116: pc[18] = m19 = p4*x16 + p9*x17 + p14*x18 + p19*x19 + p24*x20;
117: pc[19] = m20 = p5*x16 + p10*x17 + p15*x18 + p20*x19 + p25*x20;
119: pc[20] = m21 = p1*x21 + p6*x22 + p11*x23 + p16*x24 + p21*x25;
120: pc[21] = m22 = p2*x21 + p7*x22 + p12*x23 + p17*x24 + p22*x25;
121: pc[22] = m23 = p3*x21 + p8*x22 + p13*x23 + p18*x24 + p23*x25;
122: pc[23] = m24 = p4*x21 + p9*x22 + p14*x23 + p19*x24 + p24*x25;
123: pc[24] = m25 = p5*x21 + p10*x22 + p15*x23 + p20*x24 + p25*x25;
125: nz = bi[row+1] - diag_offset[row] - 1;
126: pv += 25;
127: for (j=0; j<nz; j++) {
128: x1 = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3];
129: x5 = pv[4]; x6 = pv[5]; x7 = pv[6]; x8 = pv[7]; x9 = pv[8];
130: x10 = pv[9]; x11 = pv[10]; x12 = pv[11]; x13 = pv[12];
131: x14 = pv[13]; x15 = pv[14]; x16 = pv[15]; x17 = pv[16];
132: x18 = pv[17]; x19 = pv[18]; x20 = pv[19]; x21 = pv[20];
133: x22 = pv[21]; x23 = pv[22]; x24 = pv[23]; x25 = pv[24];
134: x = rtmp + 25*pj[j];
135: x[0] -= m1*x1 + m6*x2 + m11*x3 + m16*x4 + m21*x5;
136: x[1] -= m2*x1 + m7*x2 + m12*x3 + m17*x4 + m22*x5;
137: x[2] -= m3*x1 + m8*x2 + m13*x3 + m18*x4 + m23*x5;
138: x[3] -= m4*x1 + m9*x2 + m14*x3 + m19*x4 + m24*x5;
139: x[4] -= m5*x1 + m10*x2 + m15*x3 + m20*x4 + m25*x5;
141: x[5] -= m1*x6 + m6*x7 + m11*x8 + m16*x9 + m21*x10;
142: x[6] -= m2*x6 + m7*x7 + m12*x8 + m17*x9 + m22*x10;
143: x[7] -= m3*x6 + m8*x7 + m13*x8 + m18*x9 + m23*x10;
144: x[8] -= m4*x6 + m9*x7 + m14*x8 + m19*x9 + m24*x10;
145: x[9] -= m5*x6 + m10*x7 + m15*x8 + m20*x9 + m25*x10;
147: x[10] -= m1*x11 + m6*x12 + m11*x13 + m16*x14 + m21*x15;
148: x[11] -= m2*x11 + m7*x12 + m12*x13 + m17*x14 + m22*x15;
149: x[12] -= m3*x11 + m8*x12 + m13*x13 + m18*x14 + m23*x15;
150: x[13] -= m4*x11 + m9*x12 + m14*x13 + m19*x14 + m24*x15;
151: x[14] -= m5*x11 + m10*x12 + m15*x13 + m20*x14 + m25*x15;
153: x[15] -= m1*x16 + m6*x17 + m11*x18 + m16*x19 + m21*x20;
154: x[16] -= m2*x16 + m7*x17 + m12*x18 + m17*x19 + m22*x20;
155: x[17] -= m3*x16 + m8*x17 + m13*x18 + m18*x19 + m23*x20;
156: x[18] -= m4*x16 + m9*x17 + m14*x18 + m19*x19 + m24*x20;
157: x[19] -= m5*x16 + m10*x17 + m15*x18 + m20*x19 + m25*x20;
159: x[20] -= m1*x21 + m6*x22 + m11*x23 + m16*x24 + m21*x25;
160: x[21] -= m2*x21 + m7*x22 + m12*x23 + m17*x24 + m22*x25;
161: x[22] -= m3*x21 + m8*x22 + m13*x23 + m18*x24 + m23*x25;
162: x[23] -= m4*x21 + m9*x22 + m14*x23 + m19*x24 + m24*x25;
163: x[24] -= m5*x21 + m10*x22 + m15*x23 + m20*x24 + m25*x25;
165: pv += 25;
166: }
167: PetscLogFlops(250.0*nz+225.0);
168: }
169: row = *ajtmp++;
170: }
171: /* finished row so stick it into b->a */
172: pv = ba + 25*bi[i];
173: pj = bj + bi[i];
174: nz = bi[i+1] - bi[i];
175: for (j=0; j<nz; j++) {
176: #if defined(PETSC_USE_MEMCPY)
177: PetscMemcpy(pv,rtmp+25*pj[j],25*sizeof(PetscScalar));
178: #else
179: x = rtmp+25*pj[j];
180: pv[0] = x[0]; pv[1] = x[1]; pv[2] = x[2]; pv[3] = x[3];
181: pv[4] = x[4]; pv[5] = x[5]; pv[6] = x[6]; pv[7] = x[7]; pv[8] = x[8];
182: pv[9] = x[9]; pv[10] = x[10]; pv[11] = x[11]; pv[12] = x[12];
183: pv[13] = x[13]; pv[14] = x[14]; pv[15] = x[15]; pv[16] = x[16];
184: pv[17] = x[17]; pv[18] = x[18]; pv[19] = x[19]; pv[20] = x[20];
185: pv[21] = x[21]; pv[22] = x[22]; pv[23] = x[23]; pv[24] = x[24];
186: #endif
187: pv += 25;
188: }
189: /* invert diagonal block */
190: w = ba + 25*diag_offset[i];
191: PetscKernel_A_gets_inverse_A_5(w,ipvt,work,shift);
192: }
194: PetscFree(rtmp);
195: ISRestoreIndices(isicol,&ic);
196: ISRestoreIndices(isrow,&r);
197: C->ops->solve = MatSolve_SeqBAIJ_5_inplace;
198: C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_5_inplace;
199: C->assembled = PETSC_TRUE;
200: PetscLogFlops(1.333333333333*5*5*5*b->mbs); /* from inverting diagonal blocks */
201: return(0);
202: }
204: /* MatLUFactorNumeric_SeqBAIJ_5 -
205: copied from MatLUFactorNumeric_SeqBAIJ_N_inplace() and manually re-implemented
206: PetscKernel_A_gets_A_times_B()
207: PetscKernel_A_gets_A_minus_B_times_C()
208: PetscKernel_A_gets_inverse_A()
209: */
213: PetscErrorCode MatLUFactorNumeric_SeqBAIJ_5(Mat B,Mat A,const MatFactorInfo *info)
214: {
215: Mat C=B;
216: Mat_SeqBAIJ *a=(Mat_SeqBAIJ*)A->data,*b=(Mat_SeqBAIJ *)C->data;
217: IS isrow = b->row,isicol = b->icol;
219: const PetscInt *r,*ic;
220: PetscInt i,j,k,nz,nzL,row;
221: const PetscInt n=a->mbs,*ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j;
222: const PetscInt *ajtmp,*bjtmp,*bdiag=b->diag,*pj,bs2=a->bs2;
223: MatScalar *rtmp,*pc,*mwork,*v,*pv,*aa=a->a,work[25];
224: PetscInt flg,ipvt[5];
225: PetscReal shift = info->shiftamount;
228: ISGetIndices(isrow,&r);
229: ISGetIndices(isicol,&ic);
231: /* generate work space needed by the factorization */
232: PetscMalloc2(bs2*n,MatScalar,&rtmp,bs2,MatScalar,&mwork);
233: PetscMemzero(rtmp,bs2*n*sizeof(MatScalar));
235: for (i=0; i<n; i++){
236: /* zero rtmp */
237: /* L part */
238: nz = bi[i+1] - bi[i];
239: bjtmp = bj + bi[i];
240: for (j=0; j<nz; j++){
241: PetscMemzero(rtmp+bs2*bjtmp[j],bs2*sizeof(MatScalar));
242: }
244: /* U part */
245: nz = bdiag[i] - bdiag[i+1];
246: bjtmp = bj + bdiag[i+1]+1;
247: for (j=0; j<nz; j++){
248: PetscMemzero(rtmp+bs2*bjtmp[j],bs2*sizeof(MatScalar));
249: }
250:
251: /* load in initial (unfactored row) */
252: nz = ai[r[i]+1] - ai[r[i]];
253: ajtmp = aj + ai[r[i]];
254: v = aa + bs2*ai[r[i]];
255: for (j=0; j<nz; j++) {
256: PetscMemcpy(rtmp+bs2*ic[ajtmp[j]],v+bs2*j,bs2*sizeof(MatScalar));
257: }
259: /* elimination */
260: bjtmp = bj + bi[i];
261: nzL = bi[i+1] - bi[i];
262: for(k=0;k < nzL;k++) {
263: row = bjtmp[k];
264: pc = rtmp + bs2*row;
265: for (flg=0,j=0; j<bs2; j++) { if (pc[j]!=0.0) { flg = 1; break; }}
266: if (flg) {
267: pv = b->a + bs2*bdiag[row];
268: /* PetscKernel_A_gets_A_times_B(bs,pc,pv,mwork); *pc = *pc * (*pv); */
269: PetscKernel_A_gets_A_times_B_5(pc,pv,mwork);
270:
271: pj = b->j + bdiag[row+1]+1; /* begining of U(row,:) */
272: pv = b->a + bs2*(bdiag[row+1]+1);
273: nz = bdiag[row] - bdiag[row+1] - 1; /* num of entries inU(row,:), excluding diag */
274: for (j=0; j<nz; j++) {
275: /* PetscKernel_A_gets_A_minus_B_times_C(bs,rtmp+bs2*pj[j],pc,pv+bs2*j); */
276: /* rtmp+bs2*pj[j] = rtmp+bs2*pj[j] - (*pc)*(pv+bs2*j) */
277: v = rtmp + bs2*pj[j];
278: PetscKernel_A_gets_A_minus_B_times_C_5(v,pc,pv);
279: pv += bs2;
280: }
281: PetscLogFlops(250*nz+225); /* flops = 2*bs^3*nz + 2*bs^3 - bs2) */
282: }
283: }
285: /* finished row so stick it into b->a */
286: /* L part */
287: pv = b->a + bs2*bi[i] ;
288: pj = b->j + bi[i] ;
289: nz = bi[i+1] - bi[i];
290: for (j=0; j<nz; j++) {
291: PetscMemcpy(pv+bs2*j,rtmp+bs2*pj[j],bs2*sizeof(MatScalar));
292: }
294: /* Mark diagonal and invert diagonal for simplier triangular solves */
295: pv = b->a + bs2*bdiag[i];
296: pj = b->j + bdiag[i];
297: PetscMemcpy(pv,rtmp+bs2*pj[0],bs2*sizeof(MatScalar));
298: /* PetscKernel_A_gets_inverse_A(bs,pv,v_pivots,v_work); */
299: PetscKernel_A_gets_inverse_A_5(pv,ipvt,work,shift);
300:
301: /* U part */
302: pv = b->a + bs2*(bdiag[i+1]+1);
303: pj = b->j + bdiag[i+1]+1;
304: nz = bdiag[i] - bdiag[i+1] - 1;
305: for (j=0; j<nz; j++){
306: PetscMemcpy(pv+bs2*j,rtmp+bs2*pj[j],bs2*sizeof(MatScalar));
307: }
308: }
310: PetscFree2(rtmp,mwork);
311: ISRestoreIndices(isicol,&ic);
312: ISRestoreIndices(isrow,&r);
313: C->ops->solve = MatSolve_SeqBAIJ_5;
314: C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_5;
315: C->assembled = PETSC_TRUE;
316: PetscLogFlops(1.333333333333*5*5*5*n); /* from inverting diagonal blocks */
317: return(0);
318: }
320: /*
321: Version for when blocks are 5 by 5 Using natural ordering
322: */
325: PetscErrorCode MatLUFactorNumeric_SeqBAIJ_5_NaturalOrdering_inplace(Mat C,Mat A,const MatFactorInfo *info)
326: {
327: Mat_SeqBAIJ *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ *)C->data;
329: PetscInt i,j,n = a->mbs,*bi = b->i,*bj = b->j,ipvt[5];
330: PetscInt *ajtmpold,*ajtmp,nz,row;
331: PetscInt *diag_offset = b->diag,*ai=a->i,*aj=a->j,*pj;
332: MatScalar *pv,*v,*rtmp,*pc,*w,*x;
333: MatScalar x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15;
334: MatScalar x16,x17,x18,x19,x20,x21,x22,x23,x24,x25;
335: MatScalar p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11,p12,p13,p14,p15;
336: MatScalar p16,p17,p18,p19,p20,p21,p22,p23,p24,p25;
337: MatScalar m1,m2,m3,m4,m5,m6,m7,m8,m9,m10,m11,m12,m13,m14,m15;
338: MatScalar m16,m17,m18,m19,m20,m21,m22,m23,m24,m25;
339: MatScalar *ba = b->a,*aa = a->a,work[25];
340: PetscReal shift = info->shiftamount;
343: PetscMalloc(25*(n+1)*sizeof(MatScalar),&rtmp);
344: for (i=0; i<n; i++) {
345: nz = bi[i+1] - bi[i];
346: ajtmp = bj + bi[i];
347: for (j=0; j<nz; j++) {
348: x = rtmp+25*ajtmp[j];
349: x[0] = x[1] = x[2] = x[3] = x[4] = x[5] = x[6] = x[7] = x[8] = x[9] = 0.0;
350: x[10] = x[11] = x[12] = x[13] = x[14] = x[15] = 0.0;
351: x[16] = x[17] = x[18] = x[19] = x[20] = x[21] = x[22] = x[23] = x[24] = 0.0;
352: }
353: /* load in initial (unfactored row) */
354: nz = ai[i+1] - ai[i];
355: ajtmpold = aj + ai[i];
356: v = aa + 25*ai[i];
357: for (j=0; j<nz; j++) {
358: x = rtmp+25*ajtmpold[j];
359: x[0] = v[0]; x[1] = v[1]; x[2] = v[2]; x[3] = v[3];
360: x[4] = v[4]; x[5] = v[5]; x[6] = v[6]; x[7] = v[7]; x[8] = v[8];
361: x[9] = v[9]; x[10] = v[10]; x[11] = v[11]; x[12] = v[12]; x[13] = v[13];
362: x[14] = v[14]; x[15] = v[15]; x[16] = v[16]; x[17] = v[17]; x[18] = v[18];
363: x[19] = v[19]; x[20] = v[20]; x[21] = v[21]; x[22] = v[22]; x[23] = v[23];
364: x[24] = v[24];
365: v += 25;
366: }
367: row = *ajtmp++;
368: while (row < i) {
369: pc = rtmp + 25*row;
370: p1 = pc[0]; p2 = pc[1]; p3 = pc[2]; p4 = pc[3];
371: p5 = pc[4]; p6 = pc[5]; p7 = pc[6]; p8 = pc[7]; p9 = pc[8];
372: p10 = pc[9]; p11 = pc[10]; p12 = pc[11]; p13 = pc[12]; p14 = pc[13];
373: p15 = pc[14]; p16 = pc[15]; p17 = pc[16]; p18 = pc[17];
374: p19 = pc[18]; p20 = pc[19]; p21 = pc[20]; p22 = pc[21]; p23 = pc[22];
375: p24 = pc[23]; p25 = pc[24];
376: if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0 || p5 != 0.0 ||
377: p6 != 0.0 || p7 != 0.0 || p8 != 0.0 || p9 != 0.0 || p10 != 0.0 ||
378: p11 != 0.0 || p12 != 0.0 || p13 != 0.0 || p14 != 0.0 || p15 != 0.0
379: || p16 != 0.0 || p17 != 0.0 || p18 != 0.0 || p19 != 0.0 || p20 != 0.0
380: || p21 != 0.0 || p22 != 0.0 || p23 != 0.0 || p24 != 0.0 || p25 != 0.0) {
381: pv = ba + 25*diag_offset[row];
382: pj = bj + diag_offset[row] + 1;
383: x1 = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3];
384: x5 = pv[4]; x6 = pv[5]; x7 = pv[6]; x8 = pv[7]; x9 = pv[8];
385: x10 = pv[9]; x11 = pv[10]; x12 = pv[11]; x13 = pv[12]; x14 = pv[13];
386: x15 = pv[14]; x16 = pv[15]; x17 = pv[16]; x18 = pv[17]; x19 = pv[18];
387: x20 = pv[19]; x21 = pv[20]; x22 = pv[21]; x23 = pv[22]; x24 = pv[23];
388: x25 = pv[24];
389: pc[0] = m1 = p1*x1 + p6*x2 + p11*x3 + p16*x4 + p21*x5;
390: pc[1] = m2 = p2*x1 + p7*x2 + p12*x3 + p17*x4 + p22*x5;
391: pc[2] = m3 = p3*x1 + p8*x2 + p13*x3 + p18*x4 + p23*x5;
392: pc[3] = m4 = p4*x1 + p9*x2 + p14*x3 + p19*x4 + p24*x5;
393: pc[4] = m5 = p5*x1 + p10*x2 + p15*x3 + p20*x4 + p25*x5;
395: pc[5] = m6 = p1*x6 + p6*x7 + p11*x8 + p16*x9 + p21*x10;
396: pc[6] = m7 = p2*x6 + p7*x7 + p12*x8 + p17*x9 + p22*x10;
397: pc[7] = m8 = p3*x6 + p8*x7 + p13*x8 + p18*x9 + p23*x10;
398: pc[8] = m9 = p4*x6 + p9*x7 + p14*x8 + p19*x9 + p24*x10;
399: pc[9] = m10 = p5*x6 + p10*x7 + p15*x8 + p20*x9 + p25*x10;
401: pc[10] = m11 = p1*x11 + p6*x12 + p11*x13 + p16*x14 + p21*x15;
402: pc[11] = m12 = p2*x11 + p7*x12 + p12*x13 + p17*x14 + p22*x15;
403: pc[12] = m13 = p3*x11 + p8*x12 + p13*x13 + p18*x14 + p23*x15;
404: pc[13] = m14 = p4*x11 + p9*x12 + p14*x13 + p19*x14 + p24*x15;
405: pc[14] = m15 = p5*x11 + p10*x12 + p15*x13 + p20*x14 + p25*x15;
407: pc[15] = m16 = p1*x16 + p6*x17 + p11*x18 + p16*x19 + p21*x20;
408: pc[16] = m17 = p2*x16 + p7*x17 + p12*x18 + p17*x19 + p22*x20;
409: pc[17] = m18 = p3*x16 + p8*x17 + p13*x18 + p18*x19 + p23*x20;
410: pc[18] = m19 = p4*x16 + p9*x17 + p14*x18 + p19*x19 + p24*x20;
411: pc[19] = m20 = p5*x16 + p10*x17 + p15*x18 + p20*x19 + p25*x20;
413: pc[20] = m21 = p1*x21 + p6*x22 + p11*x23 + p16*x24 + p21*x25;
414: pc[21] = m22 = p2*x21 + p7*x22 + p12*x23 + p17*x24 + p22*x25;
415: pc[22] = m23 = p3*x21 + p8*x22 + p13*x23 + p18*x24 + p23*x25;
416: pc[23] = m24 = p4*x21 + p9*x22 + p14*x23 + p19*x24 + p24*x25;
417: pc[24] = m25 = p5*x21 + p10*x22 + p15*x23 + p20*x24 + p25*x25;
419: nz = bi[row+1] - diag_offset[row] - 1;
420: pv += 25;
421: for (j=0; j<nz; j++) {
422: x1 = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3];
423: x5 = pv[4]; x6 = pv[5]; x7 = pv[6]; x8 = pv[7]; x9 = pv[8];
424: x10 = pv[9]; x11 = pv[10]; x12 = pv[11]; x13 = pv[12];
425: x14 = pv[13]; x15 = pv[14]; x16 = pv[15]; x17 = pv[16]; x18 = pv[17];
426: x19 = pv[18]; x20 = pv[19]; x21 = pv[20]; x22 = pv[21]; x23 = pv[22];
427: x24 = pv[23]; x25 = pv[24];
428: x = rtmp + 25*pj[j];
429: x[0] -= m1*x1 + m6*x2 + m11*x3 + m16*x4 + m21*x5;
430: x[1] -= m2*x1 + m7*x2 + m12*x3 + m17*x4 + m22*x5;
431: x[2] -= m3*x1 + m8*x2 + m13*x3 + m18*x4 + m23*x5;
432: x[3] -= m4*x1 + m9*x2 + m14*x3 + m19*x4 + m24*x5;
433: x[4] -= m5*x1 + m10*x2 + m15*x3 + m20*x4 + m25*x5;
435: x[5] -= m1*x6 + m6*x7 + m11*x8 + m16*x9 + m21*x10;
436: x[6] -= m2*x6 + m7*x7 + m12*x8 + m17*x9 + m22*x10;
437: x[7] -= m3*x6 + m8*x7 + m13*x8 + m18*x9 + m23*x10;
438: x[8] -= m4*x6 + m9*x7 + m14*x8 + m19*x9 + m24*x10;
439: x[9] -= m5*x6 + m10*x7 + m15*x8 + m20*x9 + m25*x10;
441: x[10] -= m1*x11 + m6*x12 + m11*x13 + m16*x14 + m21*x15;
442: x[11] -= m2*x11 + m7*x12 + m12*x13 + m17*x14 + m22*x15;
443: x[12] -= m3*x11 + m8*x12 + m13*x13 + m18*x14 + m23*x15;
444: x[13] -= m4*x11 + m9*x12 + m14*x13 + m19*x14 + m24*x15;
445: x[14] -= m5*x11 + m10*x12 + m15*x13 + m20*x14 + m25*x15;
447: x[15] -= m1*x16 + m6*x17 + m11*x18 + m16*x19 + m21*x20;
448: x[16] -= m2*x16 + m7*x17 + m12*x18 + m17*x19 + m22*x20;
449: x[17] -= m3*x16 + m8*x17 + m13*x18 + m18*x19 + m23*x20;
450: x[18] -= m4*x16 + m9*x17 + m14*x18 + m19*x19 + m24*x20;
451: x[19] -= m5*x16 + m10*x17 + m15*x18 + m20*x19 + m25*x20;
453: x[20] -= m1*x21 + m6*x22 + m11*x23 + m16*x24 + m21*x25;
454: x[21] -= m2*x21 + m7*x22 + m12*x23 + m17*x24 + m22*x25;
455: x[22] -= m3*x21 + m8*x22 + m13*x23 + m18*x24 + m23*x25;
456: x[23] -= m4*x21 + m9*x22 + m14*x23 + m19*x24 + m24*x25;
457: x[24] -= m5*x21 + m10*x22 + m15*x23 + m20*x24 + m25*x25;
458: pv += 25;
459: }
460: PetscLogFlops(250.0*nz+225.0);
461: }
462: row = *ajtmp++;
463: }
464: /* finished row so stick it into b->a */
465: pv = ba + 25*bi[i];
466: pj = bj + bi[i];
467: nz = bi[i+1] - bi[i];
468: for (j=0; j<nz; j++) {
469: x = rtmp+25*pj[j];
470: pv[0] = x[0]; pv[1] = x[1]; pv[2] = x[2]; pv[3] = x[3];
471: pv[4] = x[4]; pv[5] = x[5]; pv[6] = x[6]; pv[7] = x[7]; pv[8] = x[8];
472: pv[9] = x[9]; pv[10] = x[10]; pv[11] = x[11]; pv[12] = x[12];
473: pv[13] = x[13]; pv[14] = x[14]; pv[15] = x[15]; pv[16] = x[16]; pv[17] = x[17];
474: pv[18] = x[18]; pv[19] = x[19]; pv[20] = x[20]; pv[21] = x[21]; pv[22] = x[22];
475: pv[23] = x[23]; pv[24] = x[24];
476: pv += 25;
477: }
478: /* invert diagonal block */
479: w = ba + 25*diag_offset[i];
480: PetscKernel_A_gets_inverse_A_5(w,ipvt,work,shift);
481: }
483: PetscFree(rtmp);
484: C->ops->solve = MatSolve_SeqBAIJ_5_NaturalOrdering_inplace;
485: C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_5_NaturalOrdering_inplace;
486: C->assembled = PETSC_TRUE;
487: PetscLogFlops(1.333333333333*5*5*5*b->mbs); /* from inverting diagonal blocks */
488: return(0);
489: }
493: PetscErrorCode MatLUFactorNumeric_SeqBAIJ_5_NaturalOrdering(Mat B,Mat A,const MatFactorInfo *info)
494: {
495: Mat C=B;
496: Mat_SeqBAIJ *a=(Mat_SeqBAIJ*)A->data,*b=(Mat_SeqBAIJ *)C->data;
498: PetscInt i,j,k,nz,nzL,row;
499: const PetscInt n=a->mbs,*ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j;
500: const PetscInt *ajtmp,*bjtmp,*bdiag=b->diag,*pj,bs2=a->bs2;
501: MatScalar *rtmp,*pc,*mwork,*v,*vv,*pv,*aa=a->a,work[25];
502: PetscInt flg,ipvt[5];
503: PetscReal shift = info->shiftamount;
506: /* generate work space needed by the factorization */
507: PetscMalloc2(bs2*n,MatScalar,&rtmp,bs2,MatScalar,&mwork);
508: PetscMemzero(rtmp,bs2*n*sizeof(MatScalar));
510: for (i=0; i<n; i++){
511: /* zero rtmp */
512: /* L part */
513: nz = bi[i+1] - bi[i];
514: bjtmp = bj + bi[i];
515: for (j=0; j<nz; j++){
516: PetscMemzero(rtmp+bs2*bjtmp[j],bs2*sizeof(MatScalar));
517: }
519: /* U part */
520: nz = bdiag[i] - bdiag[i+1];
521: bjtmp = bj + bdiag[i+1]+1;
522: for (j=0; j<nz; j++){
523: PetscMemzero(rtmp+bs2*bjtmp[j],bs2*sizeof(MatScalar));
524: }
525:
526: /* load in initial (unfactored row) */
527: nz = ai[i+1] - ai[i];
528: ajtmp = aj + ai[i];
529: v = aa + bs2*ai[i];
530: for (j=0; j<nz; j++) {
531: PetscMemcpy(rtmp+bs2*ajtmp[j],v+bs2*j,bs2*sizeof(MatScalar));
532: }
534: /* elimination */
535: bjtmp = bj + bi[i];
536: nzL = bi[i+1] - bi[i];
537: for(k=0;k < nzL;k++) {
538: row = bjtmp[k];
539: pc = rtmp + bs2*row;
540: for (flg=0,j=0; j<bs2; j++) { if (pc[j]!=0.0) { flg = 1; break; }}
541: if (flg) {
542: pv = b->a + bs2*bdiag[row];
543: /* PetscKernel_A_gets_A_times_B(bs,pc,pv,mwork); *pc = *pc * (*pv); */
544: PetscKernel_A_gets_A_times_B_5(pc,pv,mwork);
545:
546: pj = b->j + bdiag[row+1]+1; /* begining of U(row,:) */
547: pv = b->a + bs2*(bdiag[row+1]+1);
548: nz = bdiag[row] - bdiag[row+1] - 1; /* num of entries inU(row,:), excluding diag */
549: for (j=0; j<nz; j++) {
550: /* PetscKernel_A_gets_A_minus_B_times_C(bs,rtmp+bs2*pj[j],pc,pv+bs2*j); */
551: /* rtmp+bs2*pj[j] = rtmp+bs2*pj[j] - (*pc)*(pv+bs2*j) */
552: vv = rtmp + bs2*pj[j];
553: PetscKernel_A_gets_A_minus_B_times_C_5(vv,pc,pv);
554: pv += bs2;
555: }
556: PetscLogFlops(250*nz+225); /* flops = 2*bs^3*nz + 2*bs^3 - bs2) */
557: }
558: }
560: /* finished row so stick it into b->a */
561: /* L part */
562: pv = b->a + bs2*bi[i] ;
563: pj = b->j + bi[i] ;
564: nz = bi[i+1] - bi[i];
565: for (j=0; j<nz; j++) {
566: PetscMemcpy(pv+bs2*j,rtmp+bs2*pj[j],bs2*sizeof(MatScalar));
567: }
568:
569: /* Mark diagonal and invert diagonal for simplier triangular solves */
570: pv = b->a + bs2*bdiag[i];
571: pj = b->j + bdiag[i];
572: PetscMemcpy(pv,rtmp+bs2*pj[0],bs2*sizeof(MatScalar));
573: /* PetscKernel_A_gets_inverse_A(bs,pv,v_pivots,v_work); */
574: PetscKernel_A_gets_inverse_A_5(pv,ipvt,work,shift);
575:
576: /* U part */
577: pv = b->a + bs2*(bdiag[i+1]+1);
578: pj = b->j + bdiag[i+1]+1;
579: nz = bdiag[i] - bdiag[i+1] - 1;
580: for (j=0; j<nz; j++){
581: PetscMemcpy(pv+bs2*j,rtmp+bs2*pj[j],bs2*sizeof(MatScalar));
582: }
583: }
584: PetscFree2(rtmp,mwork);
585: C->ops->solve = MatSolve_SeqBAIJ_5_NaturalOrdering;
586: C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_5_NaturalOrdering;
587: C->assembled = PETSC_TRUE;
588: PetscLogFlops(1.333333333333*5*5*5*n); /* from inverting diagonal blocks */
589: return(0);
590: }