Actual source code: sbaijfact7.c
2: #include <../src/mat/impls/sbaij/seq/sbaij.h>
3: #include <petsc/private/kernels/blockinvert.h>
5: /* Version for when blocks are 5 by 5 */
6: PetscErrorCode MatCholeskyFactorNumeric_SeqSBAIJ_5(Mat C,Mat A,const MatFactorInfo *info)
7: {
8: Mat_SeqSBAIJ *a = (Mat_SeqSBAIJ*)A->data,*b = (Mat_SeqSBAIJ*)C->data;
9: IS perm = b->row;
10: const PetscInt *ai,*aj,*perm_ptr,mbs=a->mbs,*bi=b->i,*bj=b->j;
11: PetscInt i,j,*a2anew,k,k1,jmin,jmax,*jl,*il,vj,nexti,ili,ipvt[5];
12: MatScalar *ba = b->a,*aa,*ap,*dk,*uik;
13: MatScalar *u,*d,*rtmp,*rtmp_ptr,work[25];
14: PetscReal shift = info->shiftamount;
15: PetscBool allowzeropivot,zeropivotdetected;
17: /* initialization */
18: allowzeropivot = PetscNot(A->erroriffailure);
19: PetscCalloc1(25*mbs,&rtmp);
20: PetscMalloc2(mbs,&il,mbs,&jl);
21: il[0] = 0;
22: for (i=0; i<mbs; i++) jl[i] = mbs;
24: PetscMalloc2(25,&dk,25,&uik);
25: ISGetIndices(perm,&perm_ptr);
27: /* check permutation */
28: if (!a->permute) {
29: ai = a->i; aj = a->j; aa = a->a;
30: } else {
31: ai = a->inew; aj = a->jnew;
32: PetscMalloc1(25*ai[mbs],&aa);
33: PetscArraycpy(aa,a->a,25*ai[mbs]);
34: PetscMalloc1(ai[mbs],&a2anew);
35: PetscArraycpy(a2anew,a->a2anew,ai[mbs]);
37: for (i=0; i<mbs; i++) {
38: jmin = ai[i]; jmax = ai[i+1];
39: for (j=jmin; j<jmax; j++) {
40: while (a2anew[j] != j) {
41: k = a2anew[j]; a2anew[j] = a2anew[k]; a2anew[k] = k;
42: for (k1=0; k1<25; k1++) {
43: dk[k1] = aa[k*25+k1];
44: aa[k*25+k1] = aa[j*25+k1];
45: aa[j*25+k1] = dk[k1];
46: }
47: }
48: /* transform columnoriented blocks that lie in the lower triangle to roworiented blocks */
49: if (i > aj[j]) {
50: /* printf("change orientation, row: %d, col: %d\n",i,aj[j]); */
51: ap = aa + j*25; /* ptr to the beginning of j-th block of aa */
52: for (k=0; k<25; k++) dk[k] = ap[k]; /* dk <- j-th block of aa */
53: for (k=0; k<5; k++) { /* j-th block of aa <- dk^T */
54: for (k1=0; k1<5; k1++) *ap++ = dk[k + 5*k1];
55: }
56: }
57: }
58: }
59: PetscFree(a2anew);
60: }
62: /* for each row k */
63: for (k = 0; k<mbs; k++) {
65: /*initialize k-th row with elements nonzero in row perm(k) of A */
66: jmin = ai[perm_ptr[k]]; jmax = ai[perm_ptr[k]+1];
67: if (jmin < jmax) {
68: ap = aa + jmin*25;
69: for (j = jmin; j < jmax; j++) {
70: vj = perm_ptr[aj[j]]; /* block col. index */
71: rtmp_ptr = rtmp + vj*25;
72: for (i=0; i<25; i++) *rtmp_ptr++ = *ap++;
73: }
74: }
76: /* modify k-th row by adding in those rows i with U(i,k) != 0 */
77: PetscArraycpy(dk,rtmp+k*25,25);
78: i = jl[k]; /* first row to be added to k_th row */
80: while (i < mbs) {
81: nexti = jl[i]; /* next row to be added to k_th row */
83: /* compute multiplier */
84: ili = il[i]; /* index of first nonzero element in U(i,k:bms-1) */
86: /* uik = -inv(Di)*U_bar(i,k) */
87: d = ba + i*25;
88: u = ba + ili*25;
90: uik[0] = -(d[0]*u[0] + d[5]*u[1] + d[10]*u[2] + d[15]*u[3] + d[20]*u[4]);
91: uik[1] = -(d[1]*u[0] + d[6]*u[1] + d[11]*u[2] + d[16]*u[3] + d[21]*u[4]);
92: uik[2] = -(d[2]*u[0] + d[7]*u[1] + d[12]*u[2] + d[17]*u[3] + d[22]*u[4]);
93: uik[3] = -(d[3]*u[0] + d[8]*u[1] + d[13]*u[2] + d[18]*u[3] + d[23]*u[4]);
94: uik[4] = -(d[4]*u[0] + d[9]*u[1] + d[14]*u[2] + d[19]*u[3] + d[24]*u[4]);
96: uik[5] = -(d[0]*u[5] + d[5]*u[6] + d[10]*u[7] + d[15]*u[8] + d[20]*u[9]);
97: uik[6] = -(d[1]*u[5] + d[6]*u[6] + d[11]*u[7] + d[16]*u[8] + d[21]*u[9]);
98: uik[7] = -(d[2]*u[5] + d[7]*u[6] + d[12]*u[7] + d[17]*u[8] + d[22]*u[9]);
99: uik[8] = -(d[3]*u[5] + d[8]*u[6] + d[13]*u[7] + d[18]*u[8] + d[23]*u[9]);
100: uik[9] = -(d[4]*u[5] + d[9]*u[6] + d[14]*u[7] + d[19]*u[8] + d[24]*u[9]);
102: uik[10]= -(d[0]*u[10] + d[5]*u[11] + d[10]*u[12] + d[15]*u[13] + d[20]*u[14]);
103: uik[11]= -(d[1]*u[10] + d[6]*u[11] + d[11]*u[12] + d[16]*u[13] + d[21]*u[14]);
104: uik[12]= -(d[2]*u[10] + d[7]*u[11] + d[12]*u[12] + d[17]*u[13] + d[22]*u[14]);
105: uik[13]= -(d[3]*u[10] + d[8]*u[11] + d[13]*u[12] + d[18]*u[13] + d[23]*u[14]);
106: uik[14]= -(d[4]*u[10] + d[9]*u[11] + d[14]*u[12] + d[19]*u[13] + d[24]*u[14]);
108: uik[15]= -(d[0]*u[15] + d[5]*u[16] + d[10]*u[17] + d[15]*u[18] + d[20]*u[19]);
109: uik[16]= -(d[1]*u[15] + d[6]*u[16] + d[11]*u[17] + d[16]*u[18] + d[21]*u[19]);
110: uik[17]= -(d[2]*u[15] + d[7]*u[16] + d[12]*u[17] + d[17]*u[18] + d[22]*u[19]);
111: uik[18]= -(d[3]*u[15] + d[8]*u[16] + d[13]*u[17] + d[18]*u[18] + d[23]*u[19]);
112: uik[19]= -(d[4]*u[15] + d[9]*u[16] + d[14]*u[17] + d[19]*u[18] + d[24]*u[19]);
114: uik[20]= -(d[0]*u[20] + d[5]*u[21] + d[10]*u[22] + d[15]*u[23] + d[20]*u[24]);
115: uik[21]= -(d[1]*u[20] + d[6]*u[21] + d[11]*u[22] + d[16]*u[23] + d[21]*u[24]);
116: uik[22]= -(d[2]*u[20] + d[7]*u[21] + d[12]*u[22] + d[17]*u[23] + d[22]*u[24]);
117: uik[23]= -(d[3]*u[20] + d[8]*u[21] + d[13]*u[22] + d[18]*u[23] + d[23]*u[24]);
118: uik[24]= -(d[4]*u[20] + d[9]*u[21] + d[14]*u[22] + d[19]*u[23] + d[24]*u[24]);
120: /* update D(k) += -U(i,k)^T * U_bar(i,k) */
121: dk[0] += uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2] + uik[3]*u[3] + uik[4]*u[4];
122: dk[1] += uik[5]*u[0] + uik[6]*u[1] + uik[7]*u[2] + uik[8]*u[3] + uik[9]*u[4];
123: dk[2] += uik[10]*u[0]+ uik[11]*u[1]+ uik[12]*u[2]+ uik[13]*u[3]+ uik[14]*u[4];
124: dk[3] += uik[15]*u[0]+ uik[16]*u[1]+ uik[17]*u[2]+ uik[18]*u[3]+ uik[19]*u[4];
125: dk[4] += uik[20]*u[0]+ uik[21]*u[1]+ uik[22]*u[2]+ uik[23]*u[3]+ uik[24]*u[4];
127: dk[5] += uik[0]*u[5] + uik[1]*u[6] + uik[2]*u[7] + uik[3]*u[8] + uik[4]*u[9];
128: dk[6] += uik[5]*u[5] + uik[6]*u[6] + uik[7]*u[7] + uik[8]*u[8] + uik[9]*u[9];
129: dk[7] += uik[10]*u[5]+ uik[11]*u[6]+ uik[12]*u[7]+ uik[13]*u[8]+ uik[14]*u[9];
130: dk[8] += uik[15]*u[5]+ uik[16]*u[6]+ uik[17]*u[7]+ uik[18]*u[8]+ uik[19]*u[9];
131: dk[9] += uik[20]*u[5]+ uik[21]*u[6]+ uik[22]*u[7]+ uik[23]*u[8]+ uik[24]*u[9];
133: dk[10] += uik[0]*u[10] + uik[1]*u[11] + uik[2]*u[12] + uik[3]*u[13] + uik[4]*u[14];
134: dk[11] += uik[5]*u[10] + uik[6]*u[11] + uik[7]*u[12] + uik[8]*u[13] + uik[9]*u[14];
135: dk[12] += uik[10]*u[10]+ uik[11]*u[11]+ uik[12]*u[12]+ uik[13]*u[13]+ uik[14]*u[14];
136: dk[13] += uik[15]*u[10]+ uik[16]*u[11]+ uik[17]*u[12]+ uik[18]*u[13]+ uik[19]*u[14];
137: dk[14] += uik[20]*u[10]+ uik[21]*u[11]+ uik[22]*u[12]+ uik[23]*u[13]+ uik[24]*u[14];
139: dk[15] += uik[0]*u[15] + uik[1]*u[16] + uik[2]*u[17] + uik[3]*u[18] + uik[4]*u[19];
140: dk[16] += uik[5]*u[15] + uik[6]*u[16] + uik[7]*u[17] + uik[8]*u[18] + uik[9]*u[19];
141: dk[17] += uik[10]*u[15]+ uik[11]*u[16]+ uik[12]*u[17]+ uik[13]*u[18]+ uik[14]*u[19];
142: dk[18] += uik[15]*u[15]+ uik[16]*u[16]+ uik[17]*u[17]+ uik[18]*u[18]+ uik[19]*u[19];
143: dk[19] += uik[20]*u[15]+ uik[21]*u[16]+ uik[22]*u[17]+ uik[23]*u[18]+ uik[24]*u[19];
145: dk[20] += uik[0]*u[20] + uik[1]*u[21] + uik[2]*u[22] + uik[3]*u[23] + uik[4]*u[24];
146: dk[21] += uik[5]*u[20] + uik[6]*u[21] + uik[7]*u[22] + uik[8]*u[23] + uik[9]*u[24];
147: dk[22] += uik[10]*u[20]+ uik[11]*u[21]+ uik[12]*u[22]+ uik[13]*u[23]+ uik[14]*u[24];
148: dk[23] += uik[15]*u[20]+ uik[16]*u[21]+ uik[17]*u[22]+ uik[18]*u[23]+ uik[19]*u[24];
149: dk[24] += uik[20]*u[20]+ uik[21]*u[21]+ uik[22]*u[22]+ uik[23]*u[23]+ uik[24]*u[24];
151: PetscLogFlops(125.0*4.0);
153: /* update -U(i,k) */
154: PetscArraycpy(ba+ili*25,uik,25);
156: /* add multiple of row i to k-th row ... */
157: jmin = ili + 1; jmax = bi[i+1];
158: if (jmin < jmax) {
159: for (j=jmin; j<jmax; j++) {
160: /* rtmp += -U(i,k)^T * U_bar(i,j) */
161: rtmp_ptr = rtmp + bj[j]*25;
162: u = ba + j*25;
163: rtmp_ptr[0] += uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2] + uik[3]*u[3] + uik[4]*u[4];
164: rtmp_ptr[1] += uik[5]*u[0] + uik[6]*u[1] + uik[7]*u[2] + uik[8]*u[3] + uik[9]*u[4];
165: rtmp_ptr[2] += uik[10]*u[0]+ uik[11]*u[1]+ uik[12]*u[2]+ uik[13]*u[3]+ uik[14]*u[4];
166: rtmp_ptr[3] += uik[15]*u[0]+ uik[16]*u[1]+ uik[17]*u[2]+ uik[18]*u[3]+ uik[19]*u[4];
167: rtmp_ptr[4] += uik[20]*u[0]+ uik[21]*u[1]+ uik[22]*u[2]+ uik[23]*u[3]+ uik[24]*u[4];
169: rtmp_ptr[5] += uik[0]*u[5] + uik[1]*u[6] + uik[2]*u[7] + uik[3]*u[8] + uik[4]*u[9];
170: rtmp_ptr[6] += uik[5]*u[5] + uik[6]*u[6] + uik[7]*u[7] + uik[8]*u[8] + uik[9]*u[9];
171: rtmp_ptr[7] += uik[10]*u[5]+ uik[11]*u[6]+ uik[12]*u[7]+ uik[13]*u[8]+ uik[14]*u[9];
172: rtmp_ptr[8] += uik[15]*u[5]+ uik[16]*u[6]+ uik[17]*u[7]+ uik[18]*u[8]+ uik[19]*u[9];
173: rtmp_ptr[9] += uik[20]*u[5]+ uik[21]*u[6]+ uik[22]*u[7]+ uik[23]*u[8]+ uik[24]*u[9];
175: rtmp_ptr[10] += uik[0]*u[10] + uik[1]*u[11] + uik[2]*u[12] + uik[3]*u[13] + uik[4]*u[14];
176: rtmp_ptr[11] += uik[5]*u[10] + uik[6]*u[11] + uik[7]*u[12] + uik[8]*u[13] + uik[9]*u[14];
177: rtmp_ptr[12] += uik[10]*u[10]+ uik[11]*u[11]+ uik[12]*u[12]+ uik[13]*u[13]+ uik[14]*u[14];
178: rtmp_ptr[13] += uik[15]*u[10]+ uik[16]*u[11]+ uik[17]*u[12]+ uik[18]*u[13]+ uik[19]*u[14];
179: rtmp_ptr[14] += uik[20]*u[10]+ uik[21]*u[11]+ uik[22]*u[12]+ uik[23]*u[13]+ uik[24]*u[14];
181: rtmp_ptr[15] += uik[0]*u[15] + uik[1]*u[16] + uik[2]*u[17] + uik[3]*u[18] + uik[4]*u[19];
182: rtmp_ptr[16] += uik[5]*u[15] + uik[6]*u[16] + uik[7]*u[17] + uik[8]*u[18] + uik[9]*u[19];
183: rtmp_ptr[17] += uik[10]*u[15]+ uik[11]*u[16]+ uik[12]*u[17]+ uik[13]*u[18]+ uik[14]*u[19];
184: rtmp_ptr[18] += uik[15]*u[15]+ uik[16]*u[16]+ uik[17]*u[17]+ uik[18]*u[18]+ uik[19]*u[19];
185: rtmp_ptr[19] += uik[20]*u[15]+ uik[21]*u[16]+ uik[22]*u[17]+ uik[23]*u[18]+ uik[24]*u[19];
187: rtmp_ptr[20] += uik[0]*u[20] + uik[1]*u[21] + uik[2]*u[22] + uik[3]*u[23] + uik[4]*u[24];
188: rtmp_ptr[21] += uik[5]*u[20] + uik[6]*u[21] + uik[7]*u[22] + uik[8]*u[23] + uik[9]*u[24];
189: rtmp_ptr[22] += uik[10]*u[20]+ uik[11]*u[21]+ uik[12]*u[22]+ uik[13]*u[23]+ uik[14]*u[24];
190: rtmp_ptr[23] += uik[15]*u[20]+ uik[16]*u[21]+ uik[17]*u[22]+ uik[18]*u[23]+ uik[19]*u[24];
191: rtmp_ptr[24] += uik[20]*u[20]+ uik[21]*u[21]+ uik[22]*u[22]+ uik[23]*u[23]+ uik[24]*u[24];
192: }
193: PetscLogFlops(2.0*125.0*(jmax-jmin));
195: /* ... add i to row list for next nonzero entry */
196: il[i] = jmin; /* update il(i) in column k+1, ... mbs-1 */
197: j = bj[jmin];
198: jl[i] = jl[j]; jl[j] = i; /* update jl */
199: }
200: i = nexti;
201: }
203: /* save nonzero entries in k-th row of U ... */
205: /* invert diagonal block */
206: d = ba+k*25;
207: PetscArraycpy(d,dk,25);
208: PetscKernel_A_gets_inverse_A_5(d,ipvt,work,shift,allowzeropivot,&zeropivotdetected);
209: if (zeropivotdetected) C->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
211: jmin = bi[k]; jmax = bi[k+1];
212: if (jmin < jmax) {
213: for (j=jmin; j<jmax; j++) {
214: vj = bj[j]; /* block col. index of U */
215: u = ba + j*25;
216: rtmp_ptr = rtmp + vj*25;
217: for (k1=0; k1<25; k1++) {
218: *u++ = *rtmp_ptr;
219: *rtmp_ptr++ = 0.0;
220: }
221: }
223: /* ... add k to row list for first nonzero entry in k-th row */
224: il[k] = jmin;
225: i = bj[jmin];
226: jl[k] = jl[i]; jl[i] = k;
227: }
228: }
230: PetscFree(rtmp);
231: PetscFree2(il,jl);
232: PetscFree2(dk,uik);
233: if (a->permute) {
234: PetscFree(aa);
235: }
237: ISRestoreIndices(perm,&perm_ptr);
239: C->ops->solve = MatSolve_SeqSBAIJ_5_inplace;
240: C->ops->solvetranspose = MatSolve_SeqSBAIJ_5_inplace;
241: C->assembled = PETSC_TRUE;
242: C->preallocated = PETSC_TRUE;
244: PetscLogFlops(1.3333*125*b->mbs); /* from inverting diagonal blocks */
245: return 0;
246: }