Actual source code: dgefa2.c
1: #define PETSCMAT_DLL
3: /*
4: Inverts 2 by 2 matrix using partial pivoting.
6: Used by the sparse factorization routines in
7: src/mat/impls/baij/seq
9: See also src/inline/ilu.h
11: This is a combination of the Linpack routines
12: dgefa() and dgedi() specialized for a size of 2.
14: */
15: #include petsc.h
19: PetscErrorCode Kernel_A_gets_inverse_A_2(MatScalar *a,PetscReal shift)
20: {
21: PetscInt i__2,i__3,kp1,j,k,l,ll,i,ipvt[2],k3;
22: PetscInt k4,j3;
23: MatScalar *aa,*ax,*ay,work[4],stmp;
24: MatReal tmp,max;
26: /* gaussian elimination with partial pivoting */
29: /* Parameter adjustments */
30: a -= 3;
32: /*for (k = 1; k <= 1; ++k) {*/
33: k = 1;
34: kp1 = k + 1;
35: k3 = 2*k;
36: k4 = k3 + k;
37: /* find l = pivot index */
39: i__2 = 3 - k;
40: aa = &a[k4];
41: max = PetscAbsScalar(aa[0]);
42: l = 1;
43: for (ll=1; ll<i__2; ll++) {
44: tmp = PetscAbsScalar(aa[ll]);
45: if (tmp > max) { max = tmp; l = ll+1;}
46: }
47: l += k - 1;
48: ipvt[k-1] = l;
50: if (a[l + k3] == 0.0) {
51: SETERRQ1(PETSC_ERR_MAT_LU_ZRPVT,"Zero pivot, row %D",k-1);
52: }
54: /* interchange if necessary */
56: if (l != k) {
57: stmp = a[l + k3];
58: a[l + k3] = a[k4];
59: a[k4] = stmp;
60: }
62: /* compute multipliers */
64: stmp = -1. / a[k4];
65: i__2 = 2 - k;
66: aa = &a[1 + k4];
67: for (ll=0; ll<i__2; ll++) {
68: aa[ll] *= stmp;
69: }
71: /* row elimination with column indexing */
73: ax = &a[k4+1];
74: for (j = kp1; j <= 2; ++j) {
75: j3 = 2*j;
76: stmp = a[l + j3];
77: if (l != k) {
78: a[l + j3] = a[k + j3];
79: a[k + j3] = stmp;
80: }
82: i__3 = 2 - k;
83: ay = &a[1+k+j3];
84: for (ll=0; ll<i__3; ll++) {
85: ay[ll] += stmp*ax[ll];
86: }
87: }
88: /*}*/
89: ipvt[1] = 2;
90: if (a[6] == 0.0) {
91: SETERRQ1(PETSC_ERR_MAT_LU_ZRPVT,"Zero pivot, row %D",1);
92: }
94: /*
95: Now form the inverse
96: */
98: /* compute inverse(u) */
100: for (k = 1; k <= 2; ++k) {
101: k3 = 2*k;
102: k4 = k3 + k;
103: a[k4] = 1.0 / a[k4];
104: stmp = -a[k4];
105: i__2 = k - 1;
106: aa = &a[k3 + 1];
107: for (ll=0; ll<i__2; ll++) aa[ll] *= stmp;
108: kp1 = k + 1;
109: if (2 < kp1) continue;
110: ax = aa;
111: for (j = kp1; j <= 2; ++j) {
112: j3 = 2*j;
113: stmp = a[k + j3];
114: a[k + j3] = 0.0;
115: ay = &a[j3 + 1];
116: for (ll=0; ll<k; ll++) {
117: ay[ll] += stmp*ax[ll];
118: }
119: }
120: }
122: /* form inverse(u)*inverse(l) */
124: /*for (kb = 1; kb <= 1; ++kb) {*/
125:
126: k = 1;
127: k3 = 2*k;
128: kp1 = k + 1;
129: aa = a + k3;
130: for (i = kp1; i <= 2; ++i) {
131: work[i-1] = aa[i];
132: aa[i] = 0.0;
133: }
134: for (j = kp1; j <= 2; ++j) {
135: stmp = work[j-1];
136: ax = &a[2*j + 1];
137: ay = &a[k3 + 1];
138: ay[0] += stmp*ax[0];
139: ay[1] += stmp*ax[1];
140: }
141: l = ipvt[k-1];
142: if (l != k) {
143: ax = &a[k3 + 1];
144: ay = &a[2*l + 1];
145: stmp = ax[0]; ax[0] = ay[0]; ay[0] = stmp;
146: stmp = ax[1]; ax[1] = ay[1]; ay[1] = stmp;
147: }
148:
149: return(0);
150: }
154: PetscErrorCode Kernel_A_gets_inverse_A_9(MatScalar *a,PetscReal shift)
155: {
156: PetscInt i__2,i__3,kp1,j,k,l,ll,i,ipvt[9],kb,k3;
157: PetscInt k4,j3;
158: MatScalar *aa,*ax,*ay,work[81],stmp;
159: MatReal tmp,max;
161: /* gaussian elimination with partial pivoting */
164: /* Parameter adjustments */
165: a -= 10;
167: for (k = 1; k <= 8; ++k) {
168: kp1 = k + 1;
169: k3 = 9*k;
170: k4 = k3 + k;
171: /* find l = pivot index */
173: i__2 = 10 - k;
174: aa = &a[k4];
175: max = PetscAbsScalar(aa[0]);
176: l = 1;
177: for (ll=1; ll<i__2; ll++) {
178: tmp = PetscAbsScalar(aa[ll]);
179: if (tmp > max) { max = tmp; l = ll+1;}
180: }
181: l += k - 1;
182: ipvt[k-1] = l;
184: if (a[l + k3] == 0.0) {
185: SETERRQ1(PETSC_ERR_MAT_LU_ZRPVT,"Zero pivot, row %D",k-1);
186: }
188: /* interchange if necessary */
190: if (l != k) {
191: stmp = a[l + k3];
192: a[l + k3] = a[k4];
193: a[k4] = stmp;
194: }
196: /* compute multipliers */
198: stmp = -1. / a[k4];
199: i__2 = 9 - k;
200: aa = &a[1 + k4];
201: for (ll=0; ll<i__2; ll++) {
202: aa[ll] *= stmp;
203: }
205: /* row elimination with column indexing */
207: ax = &a[k4+1];
208: for (j = kp1; j <= 9; ++j) {
209: j3 = 9*j;
210: stmp = a[l + j3];
211: if (l != k) {
212: a[l + j3] = a[k + j3];
213: a[k + j3] = stmp;
214: }
216: i__3 = 9 - k;
217: ay = &a[1+k+j3];
218: for (ll=0; ll<i__3; ll++) {
219: ay[ll] += stmp*ax[ll];
220: }
221: }
222: }
223: ipvt[8] = 9;
224: if (a[90] == 0.0) {
225: SETERRQ1(PETSC_ERR_MAT_LU_ZRPVT,"Zero pivot, row %D",6);
226: }
228: /*
229: Now form the inverse
230: */
232: /* compute inverse(u) */
234: for (k = 1; k <= 9; ++k) {
235: k3 = 9*k;
236: k4 = k3 + k;
237: a[k4] = 1.0 / a[k4];
238: stmp = -a[k4];
239: i__2 = k - 1;
240: aa = &a[k3 + 1];
241: for (ll=0; ll<i__2; ll++) aa[ll] *= stmp;
242: kp1 = k + 1;
243: if (9 < kp1) continue;
244: ax = aa;
245: for (j = kp1; j <= 9; ++j) {
246: j3 = 9*j;
247: stmp = a[k + j3];
248: a[k + j3] = 0.0;
249: ay = &a[j3 + 1];
250: for (ll=0; ll<k; ll++) {
251: ay[ll] += stmp*ax[ll];
252: }
253: }
254: }
256: /* form inverse(u)*inverse(l) */
258: for (kb = 1; kb <= 8; ++kb) {
259: k = 9 - kb;
260: k3 = 9*k;
261: kp1 = k + 1;
262: aa = a + k3;
263: for (i = kp1; i <= 9; ++i) {
264: work[i-1] = aa[i];
265: aa[i] = 0.0;
266: }
267: for (j = kp1; j <= 9; ++j) {
268: stmp = work[j-1];
269: ax = &a[9*j + 1];
270: ay = &a[k3 + 1];
271: ay[0] += stmp*ax[0];
272: ay[1] += stmp*ax[1];
273: ay[2] += stmp*ax[2];
274: ay[3] += stmp*ax[3];
275: ay[4] += stmp*ax[4];
276: ay[5] += stmp*ax[5];
277: ay[6] += stmp*ax[6];
278: ay[7] += stmp*ax[7];
279: ay[8] += stmp*ax[8];
280: }
281: l = ipvt[k-1];
282: if (l != k) {
283: ax = &a[k3 + 1];
284: ay = &a[9*l + 1];
285: stmp = ax[0]; ax[0] = ay[0]; ay[0] = stmp;
286: stmp = ax[1]; ax[1] = ay[1]; ay[1] = stmp;
287: stmp = ax[2]; ax[2] = ay[2]; ay[2] = stmp;
288: stmp = ax[3]; ax[3] = ay[3]; ay[3] = stmp;
289: stmp = ax[4]; ax[4] = ay[4]; ay[4] = stmp;
290: stmp = ax[5]; ax[5] = ay[5]; ay[5] = stmp;
291: stmp = ax[6]; ax[6] = ay[6]; ay[6] = stmp;
292: stmp = ax[7]; ax[7] = ay[7]; ay[7] = stmp;
293: stmp = ax[8]; ax[8] = ay[8]; ay[8] = stmp;
294: }
295: }
296: return(0);
297: }