Actual source code: dgefa4.c
petsc-3.14.6 2021-03-30
2: /*
3: Inverts 4 by 4 matrix using gaussian elimination with partial pivoting.
5: Used by the sparse factorization routines in
6: src/mat/impls/baij/seq
8: This is a combination of the Linpack routines
9: dgefa() and dgedi() specialized for a size of 4.
11: */
12: #include <petscsys.h>
14: PETSC_EXTERN PetscErrorCode PetscKernel_A_gets_inverse_A_4(MatScalar *a,PetscReal shift,PetscBool allowzeropivot,PetscBool *zeropivotdetected)
15: {
16: PetscInt i__2,i__3,kp1,j,k,l,ll,i,ipvt[4],kb,k3;
17: PetscInt k4,j3;
18: MatScalar *aa,*ax,*ay,work[16],stmp;
19: MatReal tmp,max;
22: if (zeropivotdetected) *zeropivotdetected = PETSC_FALSE;
23: shift = .25*shift*(1.e-12 + PetscAbsScalar(a[0]) + PetscAbsScalar(a[5]) + PetscAbsScalar(a[10]) + PetscAbsScalar(a[15]));
25: /* Parameter adjustments */
26: a -= 5;
28: for (k = 1; k <= 3; ++k) {
29: kp1 = k + 1;
30: k3 = 4*k;
31: k4 = k3 + k;
33: /* find l = pivot index */
34: i__2 = 5 - k;
35: aa = &a[k4];
36: max = PetscAbsScalar(aa[0]);
37: l = 1;
38: for (ll=1; ll<i__2; ll++) {
39: tmp = PetscAbsScalar(aa[ll]);
40: if (tmp > max) { max = tmp; l = ll+1;}
41: }
42: l += k - 1;
43: ipvt[k-1] = l;
45: if (a[l + k3] == 0.0) {
46: if (shift == 0.0) {
47: if (allowzeropivot) {
49: PetscInfo1(NULL,"Zero pivot, row %D\n",k-1);
50: if (zeropivotdetected) *zeropivotdetected = PETSC_TRUE;
51: } else SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_MAT_LU_ZRPVT,"Zero pivot, row %D",k-1);
52: } else {
53: /* SHIFT is applied to SINGLE diagonal entry; does this make any sense? */
54: a[l + k3] = shift;
55: }
56: }
58: /* interchange if necessary */
59: if (l != k) {
60: stmp = a[l + k3];
61: a[l + k3] = a[k4];
62: a[k4] = stmp;
63: }
65: /* compute multipliers */
66: stmp = -1. / a[k4];
67: i__2 = 4 - k;
68: aa = &a[1 + k4];
69: for (ll=0; ll<i__2; ll++) aa[ll] *= stmp;
71: /* row elimination with column indexing */
72: ax = &a[k4+1];
73: for (j = kp1; j <= 4; ++j) {
74: j3 = 4*j;
75: stmp = a[l + j3];
76: if (l != k) {
77: a[l + j3] = a[k + j3];
78: a[k + j3] = stmp;
79: }
81: i__3 = 4 - k;
82: ay = &a[1+k+j3];
83: for (ll=0; ll<i__3; ll++) ay[ll] += stmp*ax[ll];
84: }
85: }
86: ipvt[3] = 4;
87: if (a[20] == 0.0) {
88: if (allowzeropivot) {
90: PetscInfo1(NULL,"Zero pivot, row %D\n",3);
91: if (zeropivotdetected) *zeropivotdetected = PETSC_TRUE;
92: } else SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_MAT_LU_ZRPVT,"Zero pivot, row %D",3);
93: }
95: /* Now form the inverse */
96: /* compute inverse(u) */
97: for (k = 1; k <= 4; ++k) {
98: k3 = 4*k;
99: k4 = k3 + k;
100: a[k4] = 1.0 / a[k4];
101: stmp = -a[k4];
102: i__2 = k - 1;
103: aa = &a[k3 + 1];
104: for (ll=0; ll<i__2; ll++) aa[ll] *= stmp;
105: kp1 = k + 1;
106: if (4 < kp1) continue;
107: ax = aa;
108: for (j = kp1; j <= 4; ++j) {
109: j3 = 4*j;
110: stmp = a[k + j3];
111: a[k + j3] = 0.0;
112: ay = &a[j3 + 1];
113: for (ll=0; ll<k; ll++) ay[ll] += stmp*ax[ll];
114: }
115: }
117: /* form inverse(u)*inverse(l) */
118: for (kb = 1; kb <= 3; ++kb) {
119: k = 4 - kb;
120: k3 = 4*k;
121: kp1 = k + 1;
122: aa = a + k3;
123: for (i = kp1; i <= 4; ++i) {
124: work[i-1] = aa[i];
125: aa[i] = 0.0;
126: }
127: for (j = kp1; j <= 4; ++j) {
128: stmp = work[j-1];
129: ax = &a[4*j + 1];
130: ay = &a[k3 + 1];
131: ay[0] += stmp*ax[0];
132: ay[1] += stmp*ax[1];
133: ay[2] += stmp*ax[2];
134: ay[3] += stmp*ax[3];
135: }
136: l = ipvt[k-1];
137: if (l != k) {
138: ax = &a[k3 + 1];
139: ay = &a[4*l + 1];
140: stmp = ax[0]; ax[0] = ay[0]; ay[0] = stmp;
141: stmp = ax[1]; ax[1] = ay[1]; ay[1] = stmp;
142: stmp = ax[2]; ax[2] = ay[2]; ay[2] = stmp;
143: stmp = ax[3]; ax[3] = ay[3]; ay[3] = stmp;
144: }
145: }
146: return(0);
147: }
149: #if defined(PETSC_HAVE_SSE)
150: #include PETSC_HAVE_SSE
152: PETSC_EXTERN PetscErrorCode PetscKernel_A_gets_inverse_A_4_SSE(float *a)
153: {
154: /*
155: This routine is converted from Intel's Small Matrix Library.
156: See: Streaming SIMD Extensions -- Inverse of 4x4 Matrix
157: Order Number: 245043-001
158: March 1999
159: https://www.intel.com/content/www/us/en/homepage.html
161: Inverse of a 4x4 matrix via Kramer's Rule:
162: bool Invert4x4(SMLXMatrix &);
163: */
165: SSE_SCOPE_BEGIN;
166: SSE_INLINE_BEGIN_1(a)
168: /* ----------------------------------------------- */
170: SSE_LOADL_PS(SSE_ARG_1,FLOAT_0,XMM0)
171: SSE_LOADH_PS(SSE_ARG_1,FLOAT_4,XMM0)
173: SSE_LOADL_PS(SSE_ARG_1,FLOAT_8,XMM5)
174: SSE_LOADH_PS(SSE_ARG_1,FLOAT_12,XMM5)
176: SSE_COPY_PS(XMM3,XMM0)
177: SSE_SHUFFLE(XMM3,XMM5,0x88)
179: SSE_SHUFFLE(XMM5,XMM0,0xDD)
181: SSE_LOADL_PS(SSE_ARG_1,FLOAT_2,XMM0)
182: SSE_LOADH_PS(SSE_ARG_1,FLOAT_6,XMM0)
184: SSE_LOADL_PS(SSE_ARG_1,FLOAT_10,XMM6)
185: SSE_LOADH_PS(SSE_ARG_1,FLOAT_14,XMM6)
187: SSE_COPY_PS(XMM4,XMM0)
188: SSE_SHUFFLE(XMM4,XMM6,0x88)
190: SSE_SHUFFLE(XMM6,XMM0,0xDD)
192: /* ----------------------------------------------- */
194: SSE_COPY_PS(XMM7,XMM4)
195: SSE_MULT_PS(XMM7,XMM6)
197: SSE_SHUFFLE(XMM7,XMM7,0xB1)
199: SSE_COPY_PS(XMM0,XMM5)
200: SSE_MULT_PS(XMM0,XMM7)
202: SSE_COPY_PS(XMM2,XMM3)
203: SSE_MULT_PS(XMM2,XMM7)
205: SSE_SHUFFLE(XMM7,XMM7,0x4E)
207: SSE_COPY_PS(XMM1,XMM5)
208: SSE_MULT_PS(XMM1,XMM7)
209: SSE_SUB_PS(XMM1,XMM0)
211: SSE_MULT_PS(XMM7,XMM3)
212: SSE_SUB_PS(XMM7,XMM2)
214: SSE_SHUFFLE(XMM7,XMM7,0x4E)
215: SSE_STORE_PS(SSE_ARG_1,FLOAT_4,XMM7)
217: /* ----------------------------------------------- */
219: SSE_COPY_PS(XMM0,XMM5)
220: SSE_MULT_PS(XMM0,XMM4)
222: SSE_SHUFFLE(XMM0,XMM0,0xB1)
224: SSE_COPY_PS(XMM2,XMM6)
225: SSE_MULT_PS(XMM2,XMM0)
226: SSE_ADD_PS(XMM2,XMM1)
228: SSE_COPY_PS(XMM7,XMM3)
229: SSE_MULT_PS(XMM7,XMM0)
231: SSE_SHUFFLE(XMM0,XMM0,0x4E)
233: SSE_COPY_PS(XMM1,XMM6)
234: SSE_MULT_PS(XMM1,XMM0)
235: SSE_SUB_PS(XMM2,XMM1)
237: SSE_MULT_PS(XMM0,XMM3)
238: SSE_SUB_PS(XMM0,XMM7)
240: SSE_SHUFFLE(XMM0,XMM0,0x4E)
241: SSE_STORE_PS(SSE_ARG_1,FLOAT_12,XMM0)
243: /* ----------------------------------------------- */
245: SSE_COPY_PS(XMM7,XMM5)
246: SSE_SHUFFLE(XMM7,XMM5,0x4E)
247: SSE_MULT_PS(XMM7,XMM6)
249: SSE_SHUFFLE(XMM7,XMM7,0xB1)
251: SSE_SHUFFLE(XMM4,XMM4,0x4E)
253: SSE_COPY_PS(XMM0,XMM4)
254: SSE_MULT_PS(XMM0,XMM7)
255: SSE_ADD_PS(XMM0,XMM2)
257: SSE_COPY_PS(XMM2,XMM3)
258: SSE_MULT_PS(XMM2,XMM7)
260: SSE_SHUFFLE(XMM7,XMM7,0x4E)
262: SSE_COPY_PS(XMM1,XMM4)
263: SSE_MULT_PS(XMM1,XMM7)
264: SSE_SUB_PS(XMM0,XMM1)
265: SSE_STORE_PS(SSE_ARG_1,FLOAT_0,XMM0)
267: SSE_MULT_PS(XMM7,XMM3)
268: SSE_SUB_PS(XMM7,XMM2)
270: SSE_SHUFFLE(XMM7,XMM7,0x4E)
272: /* ----------------------------------------------- */
274: SSE_COPY_PS(XMM1,XMM3)
275: SSE_MULT_PS(XMM1,XMM5)
277: SSE_SHUFFLE(XMM1,XMM1,0xB1)
279: SSE_COPY_PS(XMM0,XMM6)
280: SSE_MULT_PS(XMM0,XMM1)
281: SSE_ADD_PS(XMM0,XMM7)
283: SSE_COPY_PS(XMM2,XMM4)
284: SSE_MULT_PS(XMM2,XMM1)
285: SSE_SUB_PS_M(XMM2,SSE_ARG_1,FLOAT_12)
287: SSE_SHUFFLE(XMM1,XMM1,0x4E)
289: SSE_COPY_PS(XMM7,XMM6)
290: SSE_MULT_PS(XMM7,XMM1)
291: SSE_SUB_PS(XMM7,XMM0)
293: SSE_MULT_PS(XMM1,XMM4)
294: SSE_SUB_PS(XMM2,XMM1)
295: SSE_STORE_PS(SSE_ARG_1,FLOAT_12,XMM2)
297: /* ----------------------------------------------- */
299: SSE_COPY_PS(XMM1,XMM3)
300: SSE_MULT_PS(XMM1,XMM6)
302: SSE_SHUFFLE(XMM1,XMM1,0xB1)
304: SSE_COPY_PS(XMM2,XMM4)
305: SSE_MULT_PS(XMM2,XMM1)
306: SSE_LOAD_PS(SSE_ARG_1,FLOAT_4,XMM0)
307: SSE_SUB_PS(XMM0,XMM2)
309: SSE_COPY_PS(XMM2,XMM5)
310: SSE_MULT_PS(XMM2,XMM1)
311: SSE_ADD_PS(XMM2,XMM7)
313: SSE_SHUFFLE(XMM1,XMM1,0x4E)
315: SSE_COPY_PS(XMM7,XMM4)
316: SSE_MULT_PS(XMM7,XMM1)
317: SSE_ADD_PS(XMM7,XMM0)
319: SSE_MULT_PS(XMM1,XMM5)
320: SSE_SUB_PS(XMM2,XMM1)
322: /* ----------------------------------------------- */
324: SSE_MULT_PS(XMM4,XMM3)
326: SSE_SHUFFLE(XMM4,XMM4,0xB1)
328: SSE_COPY_PS(XMM1,XMM6)
329: SSE_MULT_PS(XMM1,XMM4)
330: SSE_ADD_PS(XMM1,XMM7)
332: SSE_COPY_PS(XMM0,XMM5)
333: SSE_MULT_PS(XMM0,XMM4)
334: SSE_LOAD_PS(SSE_ARG_1,FLOAT_12,XMM7)
335: SSE_SUB_PS(XMM7,XMM0)
337: SSE_SHUFFLE(XMM4,XMM4,0x4E)
339: SSE_MULT_PS(XMM6,XMM4)
340: SSE_SUB_PS(XMM1,XMM6)
342: SSE_MULT_PS(XMM5,XMM4)
343: SSE_ADD_PS(XMM5,XMM7)
345: /* ----------------------------------------------- */
347: SSE_LOAD_PS(SSE_ARG_1,FLOAT_0,XMM0)
348: SSE_MULT_PS(XMM3,XMM0)
350: SSE_COPY_PS(XMM4,XMM3)
351: SSE_SHUFFLE(XMM4,XMM3,0x4E)
352: SSE_ADD_PS(XMM4,XMM3)
354: SSE_COPY_PS(XMM6,XMM4)
355: SSE_SHUFFLE(XMM6,XMM4,0xB1)
356: SSE_ADD_SS(XMM6,XMM4)
358: SSE_COPY_PS(XMM3,XMM6)
359: SSE_RECIP_SS(XMM3,XMM6)
360: SSE_COPY_SS(XMM4,XMM3)
361: SSE_ADD_SS(XMM4,XMM3)
362: SSE_MULT_SS(XMM3,XMM3)
363: SSE_MULT_SS(XMM6,XMM3)
364: SSE_SUB_SS(XMM4,XMM6)
366: SSE_SHUFFLE(XMM4,XMM4,0x00)
368: SSE_MULT_PS(XMM0,XMM4)
369: SSE_STOREL_PS(SSE_ARG_1,FLOAT_0,XMM0)
370: SSE_STOREH_PS(SSE_ARG_1,FLOAT_2,XMM0)
372: SSE_MULT_PS(XMM1,XMM4)
373: SSE_STOREL_PS(SSE_ARG_1,FLOAT_4,XMM1)
374: SSE_STOREH_PS(SSE_ARG_1,FLOAT_6,XMM1)
376: SSE_MULT_PS(XMM2,XMM4)
377: SSE_STOREL_PS(SSE_ARG_1,FLOAT_8,XMM2)
378: SSE_STOREH_PS(SSE_ARG_1,FLOAT_10,XMM2)
380: SSE_MULT_PS(XMM4,XMM5)
381: SSE_STOREL_PS(SSE_ARG_1,FLOAT_12,XMM4)
382: SSE_STOREH_PS(SSE_ARG_1,FLOAT_14,XMM4)
384: /* ----------------------------------------------- */
386: SSE_INLINE_END_1;
387: SSE_SCOPE_END;
388: return(0);
389: }
391: #endif