Actual source code: baijfact9.c
petsc-3.7.3 2016-08-01
2: /*
3: Factorization code for BAIJ format.
4: */
5: #include <../src/mat/impls/baij/seq/baij.h>
6: #include <petsc/private/kernels/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;
31: PetscBool allowzeropivot,zeropivotdetected;
34: allowzeropivot = PetscNot(A->erroriffailure);
35: ISGetIndices(isrow,&r);
36: ISGetIndices(isicol,&ic);
37: PetscMalloc1(25*(n+1),&rtmp);
39: #define PETSC_USE_MEMZERO 1
40: #define PETSC_USE_MEMCPY 1
42: for (i=0; i<n; i++) {
43: nz = bi[i+1] - bi[i];
44: ajtmp = bj + bi[i];
45: for (j=0; j<nz; j++) {
46: #if defined(PETSC_USE_MEMZERO)
47: PetscMemzero(rtmp+25*ajtmp[j],25*sizeof(PetscScalar));
48: #else
49: x = rtmp+25*ajtmp[j];
50: x[0] = x[1] = x[2] = x[3] = x[4] = x[5] = x[6] = x[7] = x[8] = x[9] = 0.0;
51: x[10] = x[11] = x[12] = x[13] = x[14] = x[15] = x[16] = x[17] = 0.0;
52: x[18] = x[19] = x[20] = x[21] = x[22] = x[23] = x[24] = 0.0;
53: #endif
54: }
55: /* load in initial (unfactored row) */
56: idx = r[i];
57: nz = ai[idx+1] - ai[idx];
58: ajtmpold = aj + ai[idx];
59: v = aa + 25*ai[idx];
60: for (j=0; j<nz; j++) {
61: #if defined(PETSC_USE_MEMCPY)
62: PetscMemcpy(rtmp+25*ic[ajtmpold[j]],v,25*sizeof(PetscScalar));
63: #else
64: x = rtmp+25*ic[ajtmpold[j]];
65: x[0] = v[0]; x[1] = v[1]; x[2] = v[2]; x[3] = v[3];
66: x[4] = v[4]; x[5] = v[5]; x[6] = v[6]; x[7] = v[7]; x[8] = v[8];
67: x[9] = v[9]; x[10] = v[10]; x[11] = v[11]; x[12] = v[12]; x[13] = v[13];
68: x[14] = v[14]; x[15] = v[15]; x[16] = v[16]; x[17] = v[17];
69: x[18] = v[18]; x[19] = v[19]; x[20] = v[20]; x[21] = v[21];
70: x[22] = v[22]; x[23] = v[23]; x[24] = v[24];
71: #endif
72: v += 25;
73: }
74: row = *ajtmp++;
75: while (row < i) {
76: pc = rtmp + 25*row;
77: p1 = pc[0]; p2 = pc[1]; p3 = pc[2]; p4 = pc[3];
78: p5 = pc[4]; p6 = pc[5]; p7 = pc[6]; p8 = pc[7]; p9 = pc[8];
79: p10 = pc[9]; p11 = pc[10]; p12 = pc[11]; p13 = pc[12]; p14 = pc[13];
80: p15 = pc[14]; p16 = pc[15]; p17 = pc[16]; p18 = pc[17]; p19 = pc[18];
81: p20 = pc[19]; p21 = pc[20]; p22 = pc[21]; p23 = pc[22]; p24 = pc[23];
82: p25 = pc[24];
83: if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0 || p5 != 0.0 ||
84: p6 != 0.0 || p7 != 0.0 || p8 != 0.0 || p9 != 0.0 || p10 != 0.0 ||
85: p11 != 0.0 || p12 != 0.0 || p13 != 0.0 || p14 != 0.0 || p15 != 0.0
86: || p16 != 0.0 || p17 != 0.0 || p18 != 0.0 || p19 != 0.0 ||
87: p20 != 0.0 || p21 != 0.0 || p22 != 0.0 || p23 != 0.0 ||
88: p24 != 0.0 || p25 != 0.0) {
89: pv = ba + 25*diag_offset[row];
90: pj = bj + diag_offset[row] + 1;
91: x1 = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3];
92: x5 = pv[4]; x6 = pv[5]; x7 = pv[6]; x8 = pv[7]; x9 = pv[8];
93: x10 = pv[9]; x11 = pv[10]; x12 = pv[11]; x13 = pv[12]; x14 = pv[13];
94: x15 = pv[14]; x16 = pv[15]; x17 = pv[16]; x18 = pv[17];
95: x19 = pv[18]; x20 = pv[19]; x21 = pv[20]; x22 = pv[21];
96: x23 = pv[22]; x24 = pv[23]; x25 = pv[24];
97: pc[0] = m1 = p1*x1 + p6*x2 + p11*x3 + p16*x4 + p21*x5;
98: pc[1] = m2 = p2*x1 + p7*x2 + p12*x3 + p17*x4 + p22*x5;
99: pc[2] = m3 = p3*x1 + p8*x2 + p13*x3 + p18*x4 + p23*x5;
100: pc[3] = m4 = p4*x1 + p9*x2 + p14*x3 + p19*x4 + p24*x5;
101: pc[4] = m5 = p5*x1 + p10*x2 + p15*x3 + p20*x4 + p25*x5;
103: pc[5] = m6 = p1*x6 + p6*x7 + p11*x8 + p16*x9 + p21*x10;
104: pc[6] = m7 = p2*x6 + p7*x7 + p12*x8 + p17*x9 + p22*x10;
105: pc[7] = m8 = p3*x6 + p8*x7 + p13*x8 + p18*x9 + p23*x10;
106: pc[8] = m9 = p4*x6 + p9*x7 + p14*x8 + p19*x9 + p24*x10;
107: pc[9] = m10 = p5*x6 + p10*x7 + p15*x8 + p20*x9 + p25*x10;
109: pc[10] = m11 = p1*x11 + p6*x12 + p11*x13 + p16*x14 + p21*x15;
110: pc[11] = m12 = p2*x11 + p7*x12 + p12*x13 + p17*x14 + p22*x15;
111: pc[12] = m13 = p3*x11 + p8*x12 + p13*x13 + p18*x14 + p23*x15;
112: pc[13] = m14 = p4*x11 + p9*x12 + p14*x13 + p19*x14 + p24*x15;
113: pc[14] = m15 = p5*x11 + p10*x12 + p15*x13 + p20*x14 + p25*x15;
115: pc[15] = m16 = p1*x16 + p6*x17 + p11*x18 + p16*x19 + p21*x20;
116: pc[16] = m17 = p2*x16 + p7*x17 + p12*x18 + p17*x19 + p22*x20;
117: pc[17] = m18 = p3*x16 + p8*x17 + p13*x18 + p18*x19 + p23*x20;
118: pc[18] = m19 = p4*x16 + p9*x17 + p14*x18 + p19*x19 + p24*x20;
119: pc[19] = m20 = p5*x16 + p10*x17 + p15*x18 + p20*x19 + p25*x20;
121: pc[20] = m21 = p1*x21 + p6*x22 + p11*x23 + p16*x24 + p21*x25;
122: pc[21] = m22 = p2*x21 + p7*x22 + p12*x23 + p17*x24 + p22*x25;
123: pc[22] = m23 = p3*x21 + p8*x22 + p13*x23 + p18*x24 + p23*x25;
124: pc[23] = m24 = p4*x21 + p9*x22 + p14*x23 + p19*x24 + p24*x25;
125: pc[24] = m25 = p5*x21 + p10*x22 + p15*x23 + p20*x24 + p25*x25;
127: nz = bi[row+1] - diag_offset[row] - 1;
128: pv += 25;
129: for (j=0; j<nz; j++) {
130: x1 = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3];
131: x5 = pv[4]; x6 = pv[5]; x7 = pv[6]; x8 = pv[7]; x9 = pv[8];
132: x10 = pv[9]; x11 = pv[10]; x12 = pv[11]; x13 = pv[12];
133: x14 = pv[13]; x15 = pv[14]; x16 = pv[15]; x17 = pv[16];
134: x18 = pv[17]; x19 = pv[18]; x20 = pv[19]; x21 = pv[20];
135: x22 = pv[21]; x23 = pv[22]; x24 = pv[23]; x25 = pv[24];
136: x = rtmp + 25*pj[j];
137: x[0] -= m1*x1 + m6*x2 + m11*x3 + m16*x4 + m21*x5;
138: x[1] -= m2*x1 + m7*x2 + m12*x3 + m17*x4 + m22*x5;
139: x[2] -= m3*x1 + m8*x2 + m13*x3 + m18*x4 + m23*x5;
140: x[3] -= m4*x1 + m9*x2 + m14*x3 + m19*x4 + m24*x5;
141: x[4] -= m5*x1 + m10*x2 + m15*x3 + m20*x4 + m25*x5;
143: x[5] -= m1*x6 + m6*x7 + m11*x8 + m16*x9 + m21*x10;
144: x[6] -= m2*x6 + m7*x7 + m12*x8 + m17*x9 + m22*x10;
145: x[7] -= m3*x6 + m8*x7 + m13*x8 + m18*x9 + m23*x10;
146: x[8] -= m4*x6 + m9*x7 + m14*x8 + m19*x9 + m24*x10;
147: x[9] -= m5*x6 + m10*x7 + m15*x8 + m20*x9 + m25*x10;
149: x[10] -= m1*x11 + m6*x12 + m11*x13 + m16*x14 + m21*x15;
150: x[11] -= m2*x11 + m7*x12 + m12*x13 + m17*x14 + m22*x15;
151: x[12] -= m3*x11 + m8*x12 + m13*x13 + m18*x14 + m23*x15;
152: x[13] -= m4*x11 + m9*x12 + m14*x13 + m19*x14 + m24*x15;
153: x[14] -= m5*x11 + m10*x12 + m15*x13 + m20*x14 + m25*x15;
155: x[15] -= m1*x16 + m6*x17 + m11*x18 + m16*x19 + m21*x20;
156: x[16] -= m2*x16 + m7*x17 + m12*x18 + m17*x19 + m22*x20;
157: x[17] -= m3*x16 + m8*x17 + m13*x18 + m18*x19 + m23*x20;
158: x[18] -= m4*x16 + m9*x17 + m14*x18 + m19*x19 + m24*x20;
159: x[19] -= m5*x16 + m10*x17 + m15*x18 + m20*x19 + m25*x20;
161: x[20] -= m1*x21 + m6*x22 + m11*x23 + m16*x24 + m21*x25;
162: x[21] -= m2*x21 + m7*x22 + m12*x23 + m17*x24 + m22*x25;
163: x[22] -= m3*x21 + m8*x22 + m13*x23 + m18*x24 + m23*x25;
164: x[23] -= m4*x21 + m9*x22 + m14*x23 + m19*x24 + m24*x25;
165: x[24] -= m5*x21 + m10*x22 + m15*x23 + m20*x24 + m25*x25;
167: pv += 25;
168: }
169: PetscLogFlops(250.0*nz+225.0);
170: }
171: row = *ajtmp++;
172: }
173: /* finished row so stick it into b->a */
174: pv = ba + 25*bi[i];
175: pj = bj + bi[i];
176: nz = bi[i+1] - bi[i];
177: for (j=0; j<nz; j++) {
178: #if defined(PETSC_USE_MEMCPY)
179: PetscMemcpy(pv,rtmp+25*pj[j],25*sizeof(PetscScalar));
180: #else
181: x = rtmp+25*pj[j];
182: pv[0] = x[0]; pv[1] = x[1]; pv[2] = x[2]; pv[3] = x[3];
183: pv[4] = x[4]; pv[5] = x[5]; pv[6] = x[6]; pv[7] = x[7]; pv[8] = x[8];
184: pv[9] = x[9]; pv[10] = x[10]; pv[11] = x[11]; pv[12] = x[12];
185: pv[13] = x[13]; pv[14] = x[14]; pv[15] = x[15]; pv[16] = x[16];
186: pv[17] = x[17]; pv[18] = x[18]; pv[19] = x[19]; pv[20] = x[20];
187: pv[21] = x[21]; pv[22] = x[22]; pv[23] = x[23]; pv[24] = x[24];
188: #endif
189: pv += 25;
190: }
191: /* invert diagonal block */
192: w = ba + 25*diag_offset[i];
193: PetscKernel_A_gets_inverse_A_5(w,ipvt,work,shift,allowzeropivot,&zeropivotdetected);
194: if (zeropivotdetected) C->errortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
195: }
197: PetscFree(rtmp);
198: ISRestoreIndices(isicol,&ic);
199: ISRestoreIndices(isrow,&r);
201: C->ops->solve = MatSolve_SeqBAIJ_5_inplace;
202: C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_5_inplace;
203: C->assembled = PETSC_TRUE;
205: PetscLogFlops(1.333333333333*5*5*5*b->mbs); /* from inverting diagonal blocks */
206: return(0);
207: }
209: /* MatLUFactorNumeric_SeqBAIJ_5 -
210: copied from MatLUFactorNumeric_SeqBAIJ_N_inplace() and manually re-implemented
211: PetscKernel_A_gets_A_times_B()
212: PetscKernel_A_gets_A_minus_B_times_C()
213: PetscKernel_A_gets_inverse_A()
214: */
218: PetscErrorCode MatLUFactorNumeric_SeqBAIJ_5(Mat B,Mat A,const MatFactorInfo *info)
219: {
220: Mat C =B;
221: Mat_SeqBAIJ *a =(Mat_SeqBAIJ*)A->data,*b=(Mat_SeqBAIJ*)C->data;
222: IS isrow = b->row,isicol = b->icol;
224: const PetscInt *r,*ic;
225: PetscInt i,j,k,nz,nzL,row;
226: const PetscInt n=a->mbs,*ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j;
227: const PetscInt *ajtmp,*bjtmp,*bdiag=b->diag,*pj,bs2=a->bs2;
228: MatScalar *rtmp,*pc,*mwork,*v,*pv,*aa=a->a,work[25];
229: PetscInt flg,ipvt[5];
230: PetscReal shift = info->shiftamount;
231: PetscBool allowzeropivot,zeropivotdetected;
234: allowzeropivot = PetscNot(A->erroriffailure);
235: ISGetIndices(isrow,&r);
236: ISGetIndices(isicol,&ic);
238: /* generate work space needed by the factorization */
239: PetscMalloc2(bs2*n,&rtmp,bs2,&mwork);
240: PetscMemzero(rtmp,bs2*n*sizeof(MatScalar));
242: for (i=0; i<n; i++) {
243: /* zero rtmp */
244: /* L part */
245: nz = bi[i+1] - bi[i];
246: bjtmp = bj + bi[i];
247: for (j=0; j<nz; j++) {
248: PetscMemzero(rtmp+bs2*bjtmp[j],bs2*sizeof(MatScalar));
249: }
251: /* U part */
252: nz = bdiag[i] - bdiag[i+1];
253: bjtmp = bj + bdiag[i+1]+1;
254: for (j=0; j<nz; j++) {
255: PetscMemzero(rtmp+bs2*bjtmp[j],bs2*sizeof(MatScalar));
256: }
258: /* load in initial (unfactored row) */
259: nz = ai[r[i]+1] - ai[r[i]];
260: ajtmp = aj + ai[r[i]];
261: v = aa + bs2*ai[r[i]];
262: for (j=0; j<nz; j++) {
263: PetscMemcpy(rtmp+bs2*ic[ajtmp[j]],v+bs2*j,bs2*sizeof(MatScalar));
264: }
266: /* elimination */
267: bjtmp = bj + bi[i];
268: nzL = bi[i+1] - bi[i];
269: for (k=0; k < nzL; k++) {
270: row = bjtmp[k];
271: pc = rtmp + bs2*row;
272: for (flg=0,j=0; j<bs2; j++) {
273: if (pc[j]!=0.0) {
274: flg = 1;
275: break;
276: }
277: }
278: if (flg) {
279: pv = b->a + bs2*bdiag[row];
280: /* PetscKernel_A_gets_A_times_B(bs,pc,pv,mwork); *pc = *pc * (*pv); */
281: PetscKernel_A_gets_A_times_B_5(pc,pv,mwork);
283: pj = b->j + bdiag[row+1]+1; /* begining of U(row,:) */
284: pv = b->a + bs2*(bdiag[row+1]+1);
285: nz = bdiag[row] - bdiag[row+1] - 1; /* num of entries inU(row,:), excluding diag */
286: for (j=0; j<nz; j++) {
287: /* PetscKernel_A_gets_A_minus_B_times_C(bs,rtmp+bs2*pj[j],pc,pv+bs2*j); */
288: /* rtmp+bs2*pj[j] = rtmp+bs2*pj[j] - (*pc)*(pv+bs2*j) */
289: v = rtmp + bs2*pj[j];
290: PetscKernel_A_gets_A_minus_B_times_C_5(v,pc,pv);
291: pv += bs2;
292: }
293: PetscLogFlops(250*nz+225); /* flops = 2*bs^3*nz + 2*bs^3 - bs2) */
294: }
295: }
297: /* finished row so stick it into b->a */
298: /* L part */
299: pv = b->a + bs2*bi[i];
300: pj = b->j + bi[i];
301: nz = bi[i+1] - bi[i];
302: for (j=0; j<nz; j++) {
303: PetscMemcpy(pv+bs2*j,rtmp+bs2*pj[j],bs2*sizeof(MatScalar));
304: }
306: /* Mark diagonal and invert diagonal for simplier triangular solves */
307: pv = b->a + bs2*bdiag[i];
308: pj = b->j + bdiag[i];
309: PetscMemcpy(pv,rtmp+bs2*pj[0],bs2*sizeof(MatScalar));
310: PetscKernel_A_gets_inverse_A_5(pv,ipvt,work,shift,allowzeropivot,&zeropivotdetected);
311: if (zeropivotdetected) C->errortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
313: /* U part */
314: pv = b->a + bs2*(bdiag[i+1]+1);
315: pj = b->j + bdiag[i+1]+1;
316: nz = bdiag[i] - bdiag[i+1] - 1;
317: for (j=0; j<nz; j++) {
318: PetscMemcpy(pv+bs2*j,rtmp+bs2*pj[j],bs2*sizeof(MatScalar));
319: }
320: }
322: PetscFree2(rtmp,mwork);
323: ISRestoreIndices(isicol,&ic);
324: ISRestoreIndices(isrow,&r);
326: C->ops->solve = MatSolve_SeqBAIJ_5;
327: C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_5;
328: C->assembled = PETSC_TRUE;
330: PetscLogFlops(1.333333333333*5*5*5*n); /* from inverting diagonal blocks */
331: return(0);
332: }
334: /*
335: Version for when blocks are 5 by 5 Using natural ordering
336: */
339: PetscErrorCode MatLUFactorNumeric_SeqBAIJ_5_NaturalOrdering_inplace(Mat C,Mat A,const MatFactorInfo *info)
340: {
341: Mat_SeqBAIJ *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ*)C->data;
343: PetscInt i,j,n = a->mbs,*bi = b->i,*bj = b->j,ipvt[5];
344: PetscInt *ajtmpold,*ajtmp,nz,row;
345: PetscInt *diag_offset = b->diag,*ai=a->i,*aj=a->j,*pj;
346: MatScalar *pv,*v,*rtmp,*pc,*w,*x;
347: MatScalar x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15;
348: MatScalar x16,x17,x18,x19,x20,x21,x22,x23,x24,x25;
349: MatScalar p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11,p12,p13,p14,p15;
350: MatScalar p16,p17,p18,p19,p20,p21,p22,p23,p24,p25;
351: MatScalar m1,m2,m3,m4,m5,m6,m7,m8,m9,m10,m11,m12,m13,m14,m15;
352: MatScalar m16,m17,m18,m19,m20,m21,m22,m23,m24,m25;
353: MatScalar *ba = b->a,*aa = a->a,work[25];
354: PetscReal shift = info->shiftamount;
355: PetscBool allowzeropivot,zeropivotdetected;
358: allowzeropivot = PetscNot(A->erroriffailure);
359: PetscMalloc1(25*(n+1),&rtmp);
360: for (i=0; i<n; i++) {
361: nz = bi[i+1] - bi[i];
362: ajtmp = bj + bi[i];
363: for (j=0; j<nz; j++) {
364: x = rtmp+25*ajtmp[j];
365: x[0] = x[1] = x[2] = x[3] = x[4] = x[5] = x[6] = x[7] = x[8] = x[9] = 0.0;
366: x[10] = x[11] = x[12] = x[13] = x[14] = x[15] = 0.0;
367: x[16] = x[17] = x[18] = x[19] = x[20] = x[21] = x[22] = x[23] = x[24] = 0.0;
368: }
369: /* load in initial (unfactored row) */
370: nz = ai[i+1] - ai[i];
371: ajtmpold = aj + ai[i];
372: v = aa + 25*ai[i];
373: for (j=0; j<nz; j++) {
374: x = rtmp+25*ajtmpold[j];
375: x[0] = v[0]; x[1] = v[1]; x[2] = v[2]; x[3] = v[3];
376: x[4] = v[4]; x[5] = v[5]; x[6] = v[6]; x[7] = v[7]; x[8] = v[8];
377: x[9] = v[9]; x[10] = v[10]; x[11] = v[11]; x[12] = v[12]; x[13] = v[13];
378: x[14] = v[14]; x[15] = v[15]; x[16] = v[16]; x[17] = v[17]; x[18] = v[18];
379: x[19] = v[19]; x[20] = v[20]; x[21] = v[21]; x[22] = v[22]; x[23] = v[23];
380: x[24] = v[24];
381: v += 25;
382: }
383: row = *ajtmp++;
384: while (row < i) {
385: pc = rtmp + 25*row;
386: p1 = pc[0]; p2 = pc[1]; p3 = pc[2]; p4 = pc[3];
387: p5 = pc[4]; p6 = pc[5]; p7 = pc[6]; p8 = pc[7]; p9 = pc[8];
388: p10 = pc[9]; p11 = pc[10]; p12 = pc[11]; p13 = pc[12]; p14 = pc[13];
389: p15 = pc[14]; p16 = pc[15]; p17 = pc[16]; p18 = pc[17];
390: p19 = pc[18]; p20 = pc[19]; p21 = pc[20]; p22 = pc[21]; p23 = pc[22];
391: p24 = pc[23]; p25 = pc[24];
392: if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0 || p5 != 0.0 ||
393: p6 != 0.0 || p7 != 0.0 || p8 != 0.0 || p9 != 0.0 || p10 != 0.0 ||
394: p11 != 0.0 || p12 != 0.0 || p13 != 0.0 || p14 != 0.0 || p15 != 0.0
395: || p16 != 0.0 || p17 != 0.0 || p18 != 0.0 || p19 != 0.0 || p20 != 0.0
396: || p21 != 0.0 || p22 != 0.0 || p23 != 0.0 || p24 != 0.0 || p25 != 0.0) {
397: pv = ba + 25*diag_offset[row];
398: pj = bj + diag_offset[row] + 1;
399: x1 = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3];
400: x5 = pv[4]; x6 = pv[5]; x7 = pv[6]; x8 = pv[7]; x9 = pv[8];
401: x10 = pv[9]; x11 = pv[10]; x12 = pv[11]; x13 = pv[12]; x14 = pv[13];
402: x15 = pv[14]; x16 = pv[15]; x17 = pv[16]; x18 = pv[17]; x19 = pv[18];
403: x20 = pv[19]; x21 = pv[20]; x22 = pv[21]; x23 = pv[22]; x24 = pv[23];
404: x25 = pv[24];
405: pc[0] = m1 = p1*x1 + p6*x2 + p11*x3 + p16*x4 + p21*x5;
406: pc[1] = m2 = p2*x1 + p7*x2 + p12*x3 + p17*x4 + p22*x5;
407: pc[2] = m3 = p3*x1 + p8*x2 + p13*x3 + p18*x4 + p23*x5;
408: pc[3] = m4 = p4*x1 + p9*x2 + p14*x3 + p19*x4 + p24*x5;
409: pc[4] = m5 = p5*x1 + p10*x2 + p15*x3 + p20*x4 + p25*x5;
411: pc[5] = m6 = p1*x6 + p6*x7 + p11*x8 + p16*x9 + p21*x10;
412: pc[6] = m7 = p2*x6 + p7*x7 + p12*x8 + p17*x9 + p22*x10;
413: pc[7] = m8 = p3*x6 + p8*x7 + p13*x8 + p18*x9 + p23*x10;
414: pc[8] = m9 = p4*x6 + p9*x7 + p14*x8 + p19*x9 + p24*x10;
415: pc[9] = m10 = p5*x6 + p10*x7 + p15*x8 + p20*x9 + p25*x10;
417: pc[10] = m11 = p1*x11 + p6*x12 + p11*x13 + p16*x14 + p21*x15;
418: pc[11] = m12 = p2*x11 + p7*x12 + p12*x13 + p17*x14 + p22*x15;
419: pc[12] = m13 = p3*x11 + p8*x12 + p13*x13 + p18*x14 + p23*x15;
420: pc[13] = m14 = p4*x11 + p9*x12 + p14*x13 + p19*x14 + p24*x15;
421: pc[14] = m15 = p5*x11 + p10*x12 + p15*x13 + p20*x14 + p25*x15;
423: pc[15] = m16 = p1*x16 + p6*x17 + p11*x18 + p16*x19 + p21*x20;
424: pc[16] = m17 = p2*x16 + p7*x17 + p12*x18 + p17*x19 + p22*x20;
425: pc[17] = m18 = p3*x16 + p8*x17 + p13*x18 + p18*x19 + p23*x20;
426: pc[18] = m19 = p4*x16 + p9*x17 + p14*x18 + p19*x19 + p24*x20;
427: pc[19] = m20 = p5*x16 + p10*x17 + p15*x18 + p20*x19 + p25*x20;
429: pc[20] = m21 = p1*x21 + p6*x22 + p11*x23 + p16*x24 + p21*x25;
430: pc[21] = m22 = p2*x21 + p7*x22 + p12*x23 + p17*x24 + p22*x25;
431: pc[22] = m23 = p3*x21 + p8*x22 + p13*x23 + p18*x24 + p23*x25;
432: pc[23] = m24 = p4*x21 + p9*x22 + p14*x23 + p19*x24 + p24*x25;
433: pc[24] = m25 = p5*x21 + p10*x22 + p15*x23 + p20*x24 + p25*x25;
435: nz = bi[row+1] - diag_offset[row] - 1;
436: pv += 25;
437: for (j=0; j<nz; j++) {
438: x1 = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3];
439: x5 = pv[4]; x6 = pv[5]; x7 = pv[6]; x8 = pv[7]; x9 = pv[8];
440: x10 = pv[9]; x11 = pv[10]; x12 = pv[11]; x13 = pv[12];
441: x14 = pv[13]; x15 = pv[14]; x16 = pv[15]; x17 = pv[16]; x18 = pv[17];
442: x19 = pv[18]; x20 = pv[19]; x21 = pv[20]; x22 = pv[21]; x23 = pv[22];
443: x24 = pv[23]; x25 = pv[24];
444: x = rtmp + 25*pj[j];
445: x[0] -= m1*x1 + m6*x2 + m11*x3 + m16*x4 + m21*x5;
446: x[1] -= m2*x1 + m7*x2 + m12*x3 + m17*x4 + m22*x5;
447: x[2] -= m3*x1 + m8*x2 + m13*x3 + m18*x4 + m23*x5;
448: x[3] -= m4*x1 + m9*x2 + m14*x3 + m19*x4 + m24*x5;
449: x[4] -= m5*x1 + m10*x2 + m15*x3 + m20*x4 + m25*x5;
451: x[5] -= m1*x6 + m6*x7 + m11*x8 + m16*x9 + m21*x10;
452: x[6] -= m2*x6 + m7*x7 + m12*x8 + m17*x9 + m22*x10;
453: x[7] -= m3*x6 + m8*x7 + m13*x8 + m18*x9 + m23*x10;
454: x[8] -= m4*x6 + m9*x7 + m14*x8 + m19*x9 + m24*x10;
455: x[9] -= m5*x6 + m10*x7 + m15*x8 + m20*x9 + m25*x10;
457: x[10] -= m1*x11 + m6*x12 + m11*x13 + m16*x14 + m21*x15;
458: x[11] -= m2*x11 + m7*x12 + m12*x13 + m17*x14 + m22*x15;
459: x[12] -= m3*x11 + m8*x12 + m13*x13 + m18*x14 + m23*x15;
460: x[13] -= m4*x11 + m9*x12 + m14*x13 + m19*x14 + m24*x15;
461: x[14] -= m5*x11 + m10*x12 + m15*x13 + m20*x14 + m25*x15;
463: x[15] -= m1*x16 + m6*x17 + m11*x18 + m16*x19 + m21*x20;
464: x[16] -= m2*x16 + m7*x17 + m12*x18 + m17*x19 + m22*x20;
465: x[17] -= m3*x16 + m8*x17 + m13*x18 + m18*x19 + m23*x20;
466: x[18] -= m4*x16 + m9*x17 + m14*x18 + m19*x19 + m24*x20;
467: x[19] -= m5*x16 + m10*x17 + m15*x18 + m20*x19 + m25*x20;
469: x[20] -= m1*x21 + m6*x22 + m11*x23 + m16*x24 + m21*x25;
470: x[21] -= m2*x21 + m7*x22 + m12*x23 + m17*x24 + m22*x25;
471: x[22] -= m3*x21 + m8*x22 + m13*x23 + m18*x24 + m23*x25;
472: x[23] -= m4*x21 + m9*x22 + m14*x23 + m19*x24 + m24*x25;
473: x[24] -= m5*x21 + m10*x22 + m15*x23 + m20*x24 + m25*x25;
474: pv += 25;
475: }
476: PetscLogFlops(250.0*nz+225.0);
477: }
478: row = *ajtmp++;
479: }
480: /* finished row so stick it into b->a */
481: pv = ba + 25*bi[i];
482: pj = bj + bi[i];
483: nz = bi[i+1] - bi[i];
484: for (j=0; j<nz; j++) {
485: x = rtmp+25*pj[j];
486: pv[0] = x[0]; pv[1] = x[1]; pv[2] = x[2]; pv[3] = x[3];
487: pv[4] = x[4]; pv[5] = x[5]; pv[6] = x[6]; pv[7] = x[7]; pv[8] = x[8];
488: pv[9] = x[9]; pv[10] = x[10]; pv[11] = x[11]; pv[12] = x[12];
489: pv[13] = x[13]; pv[14] = x[14]; pv[15] = x[15]; pv[16] = x[16]; pv[17] = x[17];
490: pv[18] = x[18]; pv[19] = x[19]; pv[20] = x[20]; pv[21] = x[21]; pv[22] = x[22];
491: pv[23] = x[23]; pv[24] = x[24];
492: pv += 25;
493: }
494: /* invert diagonal block */
495: w = ba + 25*diag_offset[i];
496: PetscKernel_A_gets_inverse_A_5(w,ipvt,work,shift,allowzeropivot,&zeropivotdetected);
497: if (zeropivotdetected) C->errortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
498: }
500: PetscFree(rtmp);
502: C->ops->solve = MatSolve_SeqBAIJ_5_NaturalOrdering_inplace;
503: C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_5_NaturalOrdering_inplace;
504: C->assembled = PETSC_TRUE;
506: PetscLogFlops(1.333333333333*5*5*5*b->mbs); /* from inverting diagonal blocks */
507: return(0);
508: }
512: PetscErrorCode MatLUFactorNumeric_SeqBAIJ_5_NaturalOrdering(Mat B,Mat A,const MatFactorInfo *info)
513: {
514: Mat C =B;
515: Mat_SeqBAIJ *a=(Mat_SeqBAIJ*)A->data,*b=(Mat_SeqBAIJ*)C->data;
517: PetscInt i,j,k,nz,nzL,row;
518: const PetscInt n=a->mbs,*ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j;
519: const PetscInt *ajtmp,*bjtmp,*bdiag=b->diag,*pj,bs2=a->bs2;
520: MatScalar *rtmp,*pc,*mwork,*v,*vv,*pv,*aa=a->a,work[25];
521: PetscInt flg,ipvt[5];
522: PetscReal shift = info->shiftamount;
523: PetscBool allowzeropivot,zeropivotdetected;
526: allowzeropivot = PetscNot(A->erroriffailure);
528: /* generate work space needed by the factorization */
529: PetscMalloc2(bs2*n,&rtmp,bs2,&mwork);
530: PetscMemzero(rtmp,bs2*n*sizeof(MatScalar));
532: for (i=0; i<n; i++) {
533: /* zero rtmp */
534: /* L part */
535: nz = bi[i+1] - bi[i];
536: bjtmp = bj + bi[i];
537: for (j=0; j<nz; j++) {
538: PetscMemzero(rtmp+bs2*bjtmp[j],bs2*sizeof(MatScalar));
539: }
541: /* U part */
542: nz = bdiag[i] - bdiag[i+1];
543: bjtmp = bj + bdiag[i+1]+1;
544: for (j=0; j<nz; j++) {
545: PetscMemzero(rtmp+bs2*bjtmp[j],bs2*sizeof(MatScalar));
546: }
548: /* load in initial (unfactored row) */
549: nz = ai[i+1] - ai[i];
550: ajtmp = aj + ai[i];
551: v = aa + bs2*ai[i];
552: for (j=0; j<nz; j++) {
553: PetscMemcpy(rtmp+bs2*ajtmp[j],v+bs2*j,bs2*sizeof(MatScalar));
554: }
556: /* elimination */
557: bjtmp = bj + bi[i];
558: nzL = bi[i+1] - bi[i];
559: for (k=0; k < nzL; k++) {
560: row = bjtmp[k];
561: pc = rtmp + bs2*row;
562: for (flg=0,j=0; j<bs2; j++) {
563: if (pc[j]!=0.0) {
564: flg = 1;
565: break;
566: }
567: }
568: if (flg) {
569: pv = b->a + bs2*bdiag[row];
570: /* PetscKernel_A_gets_A_times_B(bs,pc,pv,mwork); *pc = *pc * (*pv); */
571: PetscKernel_A_gets_A_times_B_5(pc,pv,mwork);
573: pj = b->j + bdiag[row+1]+1; /* begining of U(row,:) */
574: pv = b->a + bs2*(bdiag[row+1]+1);
575: nz = bdiag[row] - bdiag[row+1] - 1; /* num of entries inU(row,:), excluding diag */
576: for (j=0; j<nz; j++) {
577: /* PetscKernel_A_gets_A_minus_B_times_C(bs,rtmp+bs2*pj[j],pc,pv+bs2*j); */
578: /* rtmp+bs2*pj[j] = rtmp+bs2*pj[j] - (*pc)*(pv+bs2*j) */
579: vv = rtmp + bs2*pj[j];
580: PetscKernel_A_gets_A_minus_B_times_C_5(vv,pc,pv);
581: pv += bs2;
582: }
583: PetscLogFlops(250*nz+225); /* flops = 2*bs^3*nz + 2*bs^3 - bs2) */
584: }
585: }
587: /* finished row so stick it into b->a */
588: /* L part */
589: pv = b->a + bs2*bi[i];
590: pj = b->j + bi[i];
591: nz = bi[i+1] - bi[i];
592: for (j=0; j<nz; j++) {
593: PetscMemcpy(pv+bs2*j,rtmp+bs2*pj[j],bs2*sizeof(MatScalar));
594: }
596: /* Mark diagonal and invert diagonal for simplier triangular solves */
597: pv = b->a + bs2*bdiag[i];
598: pj = b->j + bdiag[i];
599: PetscMemcpy(pv,rtmp+bs2*pj[0],bs2*sizeof(MatScalar));
600: PetscKernel_A_gets_inverse_A_5(pv,ipvt,work,shift,allowzeropivot,&zeropivotdetected);
601: if (zeropivotdetected) C->errortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
603: /* U part */
604: pv = b->a + bs2*(bdiag[i+1]+1);
605: pj = b->j + bdiag[i+1]+1;
606: nz = bdiag[i] - bdiag[i+1] - 1;
607: for (j=0; j<nz; j++) {
608: PetscMemcpy(pv+bs2*j,rtmp+bs2*pj[j],bs2*sizeof(MatScalar));
609: }
610: }
611: PetscFree2(rtmp,mwork);
613: C->ops->solve = MatSolve_SeqBAIJ_5_NaturalOrdering;
614: C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_5_NaturalOrdering;
615: C->assembled = PETSC_TRUE;
617: PetscLogFlops(1.333333333333*5*5*5*n); /* from inverting diagonal blocks */
618: return(0);
619: }