xref: /petsc/src/mat/impls/baij/seq/dgefa2.c (revision d4bf62d159b4eec940d9872c577cf78ea329f539) !
1 #define PETSCMAT_DLL
2 
3 /*
4      Inverts 2 by 2 matrix using partial pivoting.
5 
6        Used by the sparse factorization routines in
7      src/mat/impls/baij/seq
8 
9 
10        This is a combination of the Linpack routines
11     dgefa() and dgedi() specialized for a size of 2.
12 
13 */
14 #include "petsc.h"
15 
16 #undef __FUNCT__
17 #define __FUNCT__ "Kernel_A_gets_inverse_A_2"
18 PetscErrorCode Kernel_A_gets_inverse_A_2(MatScalar *a,PetscReal shift)
19 {
20     PetscInt   i__2,i__3,kp1,j,k,l,ll,i,ipvt[2],k3;
21     PetscInt   k4,j3;
22     MatScalar  *aa,*ax,*ay,work[4],stmp;
23     MatReal    tmp,max;
24 
25 /*     gaussian elimination with partial pivoting */
26 
27     PetscFunctionBegin;
28     /* Parameter adjustments */
29     a       -= 3;
30 
31     /*for (k = 1; k <= 1; ++k) {*/
32         k   = 1;
33 	kp1 = k + 1;
34         k3  = 2*k;
35         k4  = k3 + k;
36 /*        find l = pivot index */
37 
38 	i__2 = 3 - k;
39         aa = &a[k4];
40         max = PetscAbsScalar(aa[0]);
41         l = 1;
42         for (ll=1; ll<i__2; ll++) {
43           tmp = PetscAbsScalar(aa[ll]);
44           if (tmp > max) { max = tmp; l = ll+1;}
45         }
46         l       += k - 1;
47 	ipvt[k-1] = l;
48 
49 	if (a[l + k3] == 0.0) {
50 	  SETERRQ1(PETSC_ERR_MAT_LU_ZRPVT,"Zero pivot, row %D",k-1);
51 	}
52 
53 /*           interchange if necessary */
54 
55 	if (l != k) {
56 	  stmp      = a[l + k3];
57 	  a[l + k3] = a[k4];
58 	  a[k4]     = stmp;
59         }
60 
61 /*           compute multipliers */
62 
63 	stmp = -1. / a[k4];
64 	i__2 = 2 - k;
65         aa = &a[1 + k4];
66         for (ll=0; ll<i__2; ll++) {
67           aa[ll] *= stmp;
68         }
69 
70 /*           row elimination with column indexing */
71 
72 	ax = &a[k4+1];
73         for (j = kp1; j <= 2; ++j) {
74             j3   = 2*j;
75 	    stmp = a[l + j3];
76 	    if (l != k) {
77 	      a[l + j3] = a[k + j3];
78 	      a[k + j3] = stmp;
79             }
80 
81 	    i__3 = 2 - k;
82             ay = &a[1+k+j3];
83             for (ll=0; ll<i__3; ll++) {
84               ay[ll] += stmp*ax[ll];
85             }
86 	}
87     /*}*/
88     ipvt[1] = 2;
89     if (a[6] == 0.0) {
90       SETERRQ1(PETSC_ERR_MAT_LU_ZRPVT,"Zero pivot, row %D",1);
91     }
92 
93     /*
94          Now form the inverse
95     */
96 
97    /*     compute inverse(u) */
98 
99     for (k = 1; k <= 2; ++k) {
100         k3    = 2*k;
101         k4    = k3 + k;
102 	a[k4] = 1.0 / a[k4];
103 	stmp  = -a[k4];
104 	i__2  = k - 1;
105         aa    = &a[k3 + 1];
106         for (ll=0; ll<i__2; ll++) aa[ll] *= stmp;
107 	kp1 = k + 1;
108 	if (2 < kp1) continue;
109         ax = aa;
110         for (j = kp1; j <= 2; ++j) {
111             j3        = 2*j;
112 	    stmp      = a[k + j3];
113 	    a[k + j3] = 0.0;
114             ay        = &a[j3 + 1];
115             for (ll=0; ll<k; ll++) {
116               ay[ll] += stmp*ax[ll];
117             }
118 	}
119     }
120 
121    /*    form inverse(u)*inverse(l) */
122 
123     /*for (kb = 1; kb <= 1; ++kb) {*/
124 
125 	k   = 1;
126         k3  = 2*k;
127 	kp1 = k + 1;
128         aa  = a + k3;
129 	for (i = kp1; i <= 2; ++i) {
130             work[i-1] = aa[i];
131 	    aa[i]   = 0.0;
132 	}
133 	for (j = kp1; j <= 2; ++j) {
134 	    stmp  = work[j-1];
135             ax    = &a[2*j + 1];
136             ay    = &a[k3 + 1];
137             ay[0] += stmp*ax[0];
138             ay[1] += stmp*ax[1];
139 	}
140 	l = ipvt[k-1];
141 	if (l != k) {
142             ax = &a[k3 + 1];
143             ay = &a[2*l + 1];
144             stmp = ax[0]; ax[0] = ay[0]; ay[0] = stmp;
145             stmp = ax[1]; ax[1] = ay[1]; ay[1] = stmp;
146 	}
147 
148     PetscFunctionReturn(0);
149 }
150 
151 #undef __FUNCT__
152 #define __FUNCT__ "Kernel_A_gets_inverse_A_9"
153 PetscErrorCode Kernel_A_gets_inverse_A_9(MatScalar *a,PetscReal shift)
154 {
155     PetscInt   i__2,i__3,kp1,j,k,l,ll,i,ipvt[9],kb,k3;
156     PetscInt   k4,j3;
157     MatScalar  *aa,*ax,*ay,work[81],stmp;
158     MatReal    tmp,max;
159 
160 /*     gaussian elimination with partial pivoting */
161 
162     PetscFunctionBegin;
163     /* Parameter adjustments */
164     a       -= 10;
165 
166     for (k = 1; k <= 8; ++k) {
167 	kp1 = k + 1;
168         k3  = 9*k;
169         k4  = k3 + k;
170 /*        find l = pivot index */
171 
172 	i__2 = 10 - k;
173         aa = &a[k4];
174         max = PetscAbsScalar(aa[0]);
175         l = 1;
176         for (ll=1; ll<i__2; ll++) {
177           tmp = PetscAbsScalar(aa[ll]);
178           if (tmp > max) { max = tmp; l = ll+1;}
179         }
180         l       += k - 1;
181 	ipvt[k-1] = l;
182 
183 	if (a[l + k3] == 0.0) {
184 	  SETERRQ1(PETSC_ERR_MAT_LU_ZRPVT,"Zero pivot, row %D",k-1);
185 	}
186 
187 /*           interchange if necessary */
188 
189 	if (l != k) {
190 	  stmp      = a[l + k3];
191 	  a[l + k3] = a[k4];
192 	  a[k4]     = stmp;
193         }
194 
195 /*           compute multipliers */
196 
197 	stmp = -1. / a[k4];
198 	i__2 = 9 - k;
199         aa = &a[1 + k4];
200         for (ll=0; ll<i__2; ll++) {
201           aa[ll] *= stmp;
202         }
203 
204 /*           row elimination with column indexing */
205 
206 	ax = &a[k4+1];
207         for (j = kp1; j <= 9; ++j) {
208             j3   = 9*j;
209 	    stmp = a[l + j3];
210 	    if (l != k) {
211 	      a[l + j3] = a[k + j3];
212 	      a[k + j3] = stmp;
213             }
214 
215 	    i__3 = 9 - k;
216             ay = &a[1+k+j3];
217             for (ll=0; ll<i__3; ll++) {
218               ay[ll] += stmp*ax[ll];
219             }
220 	}
221     }
222     ipvt[8] = 9;
223     if (a[90] == 0.0) {
224       SETERRQ1(PETSC_ERR_MAT_LU_ZRPVT,"Zero pivot, row %D",6);
225     }
226 
227     /*
228          Now form the inverse
229     */
230 
231    /*     compute inverse(u) */
232 
233     for (k = 1; k <= 9; ++k) {
234         k3    = 9*k;
235         k4    = k3 + k;
236 	a[k4] = 1.0 / a[k4];
237 	stmp  = -a[k4];
238 	i__2  = k - 1;
239         aa    = &a[k3 + 1];
240         for (ll=0; ll<i__2; ll++) aa[ll] *= stmp;
241 	kp1 = k + 1;
242 	if (9 < kp1) continue;
243         ax = aa;
244         for (j = kp1; j <= 9; ++j) {
245             j3        = 9*j;
246 	    stmp      = a[k + j3];
247 	    a[k + j3] = 0.0;
248             ay        = &a[j3 + 1];
249             for (ll=0; ll<k; ll++) {
250               ay[ll] += stmp*ax[ll];
251             }
252 	}
253     }
254 
255    /*    form inverse(u)*inverse(l) */
256 
257     for (kb = 1; kb <= 8; ++kb) {
258 	k   = 9 - kb;
259         k3  = 9*k;
260 	kp1 = k + 1;
261         aa  = a + k3;
262 	for (i = kp1; i <= 9; ++i) {
263             work[i-1] = aa[i];
264 	    aa[i]   = 0.0;
265 	}
266 	for (j = kp1; j <= 9; ++j) {
267 	    stmp  = work[j-1];
268             ax    = &a[9*j + 1];
269             ay    = &a[k3 + 1];
270             ay[0] += stmp*ax[0];
271             ay[1] += stmp*ax[1];
272             ay[2] += stmp*ax[2];
273             ay[3] += stmp*ax[3];
274             ay[4] += stmp*ax[4];
275             ay[5] += stmp*ax[5];
276             ay[6] += stmp*ax[6];
277             ay[7] += stmp*ax[7];
278             ay[8] += stmp*ax[8];
279 	}
280 	l = ipvt[k-1];
281 	if (l != k) {
282             ax = &a[k3 + 1];
283             ay = &a[9*l + 1];
284             stmp = ax[0]; ax[0] = ay[0]; ay[0] = stmp;
285             stmp = ax[1]; ax[1] = ay[1]; ay[1] = stmp;
286             stmp = ax[2]; ax[2] = ay[2]; ay[2] = stmp;
287             stmp = ax[3]; ax[3] = ay[3]; ay[3] = stmp;
288             stmp = ax[4]; ax[4] = ay[4]; ay[4] = stmp;
289             stmp = ax[5]; ax[5] = ay[5]; ay[5] = stmp;
290             stmp = ax[6]; ax[6] = ay[6]; ay[6] = stmp;
291             stmp = ax[7]; ax[7] = ay[7]; ay[7] = stmp;
292             stmp = ax[8]; ax[8] = ay[8]; ay[8] = stmp;
293 	}
294     }
295     PetscFunctionReturn(0);
296 }
297 
298