Actual source code: dgefa4.c
petsc-3.7.3 2016-08-01
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>
16: PETSC_EXTERN PetscErrorCode PetscKernel_A_gets_inverse_A_4(MatScalar *a,PetscReal shift,PetscBool allowzeropivot,PetscBool *zeropivotdetected)
17: {
18: PetscInt i__2,i__3,kp1,j,k,l,ll,i,ipvt[4],kb,k3;
19: PetscInt k4,j3;
20: MatScalar *aa,*ax,*ay,work[16],stmp;
21: MatReal tmp,max;
24: if (zeropivotdetected) *zeropivotdetected = PETSC_FALSE;
25: shift = .25*shift*(1.e-12 + PetscAbsScalar(a[0]) + PetscAbsScalar(a[5]) + PetscAbsScalar(a[10]) + PetscAbsScalar(a[15]));
27: /* Parameter adjustments */
28: a -= 5;
30: for (k = 1; k <= 3; ++k) {
31: kp1 = k + 1;
32: k3 = 4*k;
33: k4 = k3 + k;
35: /* find l = pivot index */
36: i__2 = 5 - k;
37: aa = &a[k4];
38: max = PetscAbsScalar(aa[0]);
39: l = 1;
40: for (ll=1; ll<i__2; ll++) {
41: tmp = PetscAbsScalar(aa[ll]);
42: if (tmp > max) { max = tmp; l = ll+1;}
43: }
44: l += k - 1;
45: ipvt[k-1] = l;
47: if (a[l + k3] == 0.0) {
48: if (shift == 0.0) {
49: if (allowzeropivot) {
51: PetscInfo1(NULL,"Zero pivot, row %D\n",k-1);
52: if (zeropivotdetected) *zeropivotdetected = PETSC_TRUE;
53: } else SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_MAT_LU_ZRPVT,"Zero pivot, row %D",k-1);
54: } else {
55: /* SHIFT is applied to SINGLE diagonal entry; does this make any sense? */
56: a[l + k3] = shift;
57: }
58: }
60: /* interchange if necessary */
61: if (l != k) {
62: stmp = a[l + k3];
63: a[l + k3] = a[k4];
64: a[k4] = stmp;
65: }
67: /* compute multipliers */
68: stmp = -1. / a[k4];
69: i__2 = 4 - k;
70: aa = &a[1 + k4];
71: for (ll=0; ll<i__2; ll++) aa[ll] *= stmp;
73: /* row elimination with column indexing */
74: ax = &a[k4+1];
75: for (j = kp1; j <= 4; ++j) {
76: j3 = 4*j;
77: stmp = a[l + j3];
78: if (l != k) {
79: a[l + j3] = a[k + j3];
80: a[k + j3] = stmp;
81: }
83: i__3 = 4 - k;
84: ay = &a[1+k+j3];
85: for (ll=0; ll<i__3; ll++) ay[ll] += stmp*ax[ll];
86: }
87: }
88: ipvt[3] = 4;
89: if (a[20] == 0.0) {
90: if (allowzeropivot) {
92: PetscInfo1(NULL,"Zero pivot, row %D\n",3);
93: if (zeropivotdetected) *zeropivotdetected = PETSC_TRUE;
94: } else SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_MAT_LU_ZRPVT,"Zero pivot, row %D",3);
95: }
97: /* Now form the inverse */
98: /* compute inverse(u) */
99: for (k = 1; k <= 4; ++k) {
100: k3 = 4*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 (4 < kp1) continue;
109: ax = aa;
110: for (j = kp1; j <= 4; ++j) {
111: j3 = 4*j;
112: stmp = a[k + j3];
113: a[k + j3] = 0.0;
114: ay = &a[j3 + 1];
115: for (ll=0; ll<k; ll++) ay[ll] += stmp*ax[ll];
116: }
117: }
119: /* form inverse(u)*inverse(l) */
120: for (kb = 1; kb <= 3; ++kb) {
121: k = 4 - kb;
122: k3 = 4*k;
123: kp1 = k + 1;
124: aa = a + k3;
125: for (i = kp1; i <= 4; ++i) {
126: work[i-1] = aa[i];
127: aa[i] = 0.0;
128: }
129: for (j = kp1; j <= 4; ++j) {
130: stmp = work[j-1];
131: ax = &a[4*j + 1];
132: ay = &a[k3 + 1];
133: ay[0] += stmp*ax[0];
134: ay[1] += stmp*ax[1];
135: ay[2] += stmp*ax[2];
136: ay[3] += stmp*ax[3];
137: }
138: l = ipvt[k-1];
139: if (l != k) {
140: ax = &a[k3 + 1];
141: ay = &a[4*l + 1];
142: stmp = ax[0]; ax[0] = ay[0]; ay[0] = stmp;
143: stmp = ax[1]; ax[1] = ay[1]; ay[1] = stmp;
144: stmp = ax[2]; ax[2] = ay[2]; ay[2] = stmp;
145: stmp = ax[3]; ax[3] = ay[3]; ay[3] = stmp;
146: }
147: }
148: return(0);
149: }
151: #if defined(PETSC_HAVE_SSE)
152: #include PETSC_HAVE_SSE
156: PETSC_EXTERN PetscErrorCode PetscKernel_A_gets_inverse_A_4_SSE(float *a)
157: {
158: /*
159: This routine is converted from Intel's Small Matrix Library.
160: See: Streaming SIMD Extensions -- Inverse of 4x4 Matrix
161: Order Number: 245043-001
162: March 1999
163: http://www.intel.com
165: Inverse of a 4x4 matrix via Kramer's Rule:
166: bool Invert4x4(SMLXMatrix &);
167: */
169: SSE_SCOPE_BEGIN;
170: SSE_INLINE_BEGIN_1(a)
172: /* ----------------------------------------------- */
174: SSE_LOADL_PS(SSE_ARG_1,FLOAT_0,XMM0)
175: SSE_LOADH_PS(SSE_ARG_1,FLOAT_4,XMM0)
177: SSE_LOADL_PS(SSE_ARG_1,FLOAT_8,XMM5)
178: SSE_LOADH_PS(SSE_ARG_1,FLOAT_12,XMM5)
180: SSE_COPY_PS(XMM3,XMM0)
181: SSE_SHUFFLE(XMM3,XMM5,0x88)
183: SSE_SHUFFLE(XMM5,XMM0,0xDD)
185: SSE_LOADL_PS(SSE_ARG_1,FLOAT_2,XMM0)
186: SSE_LOADH_PS(SSE_ARG_1,FLOAT_6,XMM0)
188: SSE_LOADL_PS(SSE_ARG_1,FLOAT_10,XMM6)
189: SSE_LOADH_PS(SSE_ARG_1,FLOAT_14,XMM6)
191: SSE_COPY_PS(XMM4,XMM0)
192: SSE_SHUFFLE(XMM4,XMM6,0x88)
194: SSE_SHUFFLE(XMM6,XMM0,0xDD)
196: /* ----------------------------------------------- */
198: SSE_COPY_PS(XMM7,XMM4)
199: SSE_MULT_PS(XMM7,XMM6)
201: SSE_SHUFFLE(XMM7,XMM7,0xB1)
203: SSE_COPY_PS(XMM0,XMM5)
204: SSE_MULT_PS(XMM0,XMM7)
206: SSE_COPY_PS(XMM2,XMM3)
207: SSE_MULT_PS(XMM2,XMM7)
209: SSE_SHUFFLE(XMM7,XMM7,0x4E)
211: SSE_COPY_PS(XMM1,XMM5)
212: SSE_MULT_PS(XMM1,XMM7)
213: SSE_SUB_PS(XMM1,XMM0)
215: SSE_MULT_PS(XMM7,XMM3)
216: SSE_SUB_PS(XMM7,XMM2)
218: SSE_SHUFFLE(XMM7,XMM7,0x4E)
219: SSE_STORE_PS(SSE_ARG_1,FLOAT_4,XMM7)
221: /* ----------------------------------------------- */
223: SSE_COPY_PS(XMM0,XMM5)
224: SSE_MULT_PS(XMM0,XMM4)
226: SSE_SHUFFLE(XMM0,XMM0,0xB1)
228: SSE_COPY_PS(XMM2,XMM6)
229: SSE_MULT_PS(XMM2,XMM0)
230: SSE_ADD_PS(XMM2,XMM1)
232: SSE_COPY_PS(XMM7,XMM3)
233: SSE_MULT_PS(XMM7,XMM0)
235: SSE_SHUFFLE(XMM0,XMM0,0x4E)
237: SSE_COPY_PS(XMM1,XMM6)
238: SSE_MULT_PS(XMM1,XMM0)
239: SSE_SUB_PS(XMM2,XMM1)
241: SSE_MULT_PS(XMM0,XMM3)
242: SSE_SUB_PS(XMM0,XMM7)
244: SSE_SHUFFLE(XMM0,XMM0,0x4E)
245: SSE_STORE_PS(SSE_ARG_1,FLOAT_12,XMM0)
247: /* ----------------------------------------------- */
249: SSE_COPY_PS(XMM7,XMM5)
250: SSE_SHUFFLE(XMM7,XMM5,0x4E)
251: SSE_MULT_PS(XMM7,XMM6)
253: SSE_SHUFFLE(XMM7,XMM7,0xB1)
255: SSE_SHUFFLE(XMM4,XMM4,0x4E)
257: SSE_COPY_PS(XMM0,XMM4)
258: SSE_MULT_PS(XMM0,XMM7)
259: SSE_ADD_PS(XMM0,XMM2)
261: SSE_COPY_PS(XMM2,XMM3)
262: SSE_MULT_PS(XMM2,XMM7)
264: SSE_SHUFFLE(XMM7,XMM7,0x4E)
266: SSE_COPY_PS(XMM1,XMM4)
267: SSE_MULT_PS(XMM1,XMM7)
268: SSE_SUB_PS(XMM0,XMM1)
269: SSE_STORE_PS(SSE_ARG_1,FLOAT_0,XMM0)
271: SSE_MULT_PS(XMM7,XMM3)
272: SSE_SUB_PS(XMM7,XMM2)
274: SSE_SHUFFLE(XMM7,XMM7,0x4E)
276: /* ----------------------------------------------- */
278: SSE_COPY_PS(XMM1,XMM3)
279: SSE_MULT_PS(XMM1,XMM5)
281: SSE_SHUFFLE(XMM1,XMM1,0xB1)
283: SSE_COPY_PS(XMM0,XMM6)
284: SSE_MULT_PS(XMM0,XMM1)
285: SSE_ADD_PS(XMM0,XMM7)
287: SSE_COPY_PS(XMM2,XMM4)
288: SSE_MULT_PS(XMM2,XMM1)
289: SSE_SUB_PS_M(XMM2,SSE_ARG_1,FLOAT_12)
291: SSE_SHUFFLE(XMM1,XMM1,0x4E)
293: SSE_COPY_PS(XMM7,XMM6)
294: SSE_MULT_PS(XMM7,XMM1)
295: SSE_SUB_PS(XMM7,XMM0)
297: SSE_MULT_PS(XMM1,XMM4)
298: SSE_SUB_PS(XMM2,XMM1)
299: SSE_STORE_PS(SSE_ARG_1,FLOAT_12,XMM2)
301: /* ----------------------------------------------- */
303: SSE_COPY_PS(XMM1,XMM3)
304: SSE_MULT_PS(XMM1,XMM6)
306: SSE_SHUFFLE(XMM1,XMM1,0xB1)
308: SSE_COPY_PS(XMM2,XMM4)
309: SSE_MULT_PS(XMM2,XMM1)
310: SSE_LOAD_PS(SSE_ARG_1,FLOAT_4,XMM0)
311: SSE_SUB_PS(XMM0,XMM2)
313: SSE_COPY_PS(XMM2,XMM5)
314: SSE_MULT_PS(XMM2,XMM1)
315: SSE_ADD_PS(XMM2,XMM7)
317: SSE_SHUFFLE(XMM1,XMM1,0x4E)
319: SSE_COPY_PS(XMM7,XMM4)
320: SSE_MULT_PS(XMM7,XMM1)
321: SSE_ADD_PS(XMM7,XMM0)
323: SSE_MULT_PS(XMM1,XMM5)
324: SSE_SUB_PS(XMM2,XMM1)
326: /* ----------------------------------------------- */
328: SSE_MULT_PS(XMM4,XMM3)
330: SSE_SHUFFLE(XMM4,XMM4,0xB1)
332: SSE_COPY_PS(XMM1,XMM6)
333: SSE_MULT_PS(XMM1,XMM4)
334: SSE_ADD_PS(XMM1,XMM7)
336: SSE_COPY_PS(XMM0,XMM5)
337: SSE_MULT_PS(XMM0,XMM4)
338: SSE_LOAD_PS(SSE_ARG_1,FLOAT_12,XMM7)
339: SSE_SUB_PS(XMM7,XMM0)
341: SSE_SHUFFLE(XMM4,XMM4,0x4E)
343: SSE_MULT_PS(XMM6,XMM4)
344: SSE_SUB_PS(XMM1,XMM6)
346: SSE_MULT_PS(XMM5,XMM4)
347: SSE_ADD_PS(XMM5,XMM7)
349: /* ----------------------------------------------- */
351: SSE_LOAD_PS(SSE_ARG_1,FLOAT_0,XMM0)
352: SSE_MULT_PS(XMM3,XMM0)
354: SSE_COPY_PS(XMM4,XMM3)
355: SSE_SHUFFLE(XMM4,XMM3,0x4E)
356: SSE_ADD_PS(XMM4,XMM3)
358: SSE_COPY_PS(XMM6,XMM4)
359: SSE_SHUFFLE(XMM6,XMM4,0xB1)
360: SSE_ADD_SS(XMM6,XMM4)
362: SSE_COPY_PS(XMM3,XMM6)
363: SSE_RECIP_SS(XMM3,XMM6)
364: SSE_COPY_SS(XMM4,XMM3)
365: SSE_ADD_SS(XMM4,XMM3)
366: SSE_MULT_SS(XMM3,XMM3)
367: SSE_MULT_SS(XMM6,XMM3)
368: SSE_SUB_SS(XMM4,XMM6)
370: SSE_SHUFFLE(XMM4,XMM4,0x00)
372: SSE_MULT_PS(XMM0,XMM4)
373: SSE_STOREL_PS(SSE_ARG_1,FLOAT_0,XMM0)
374: SSE_STOREH_PS(SSE_ARG_1,FLOAT_2,XMM0)
376: SSE_MULT_PS(XMM1,XMM4)
377: SSE_STOREL_PS(SSE_ARG_1,FLOAT_4,XMM1)
378: SSE_STOREH_PS(SSE_ARG_1,FLOAT_6,XMM1)
380: SSE_MULT_PS(XMM2,XMM4)
381: SSE_STOREL_PS(SSE_ARG_1,FLOAT_8,XMM2)
382: SSE_STOREH_PS(SSE_ARG_1,FLOAT_10,XMM2)
384: SSE_MULT_PS(XMM4,XMM5)
385: SSE_STOREL_PS(SSE_ARG_1,FLOAT_12,XMM4)
386: SSE_STOREH_PS(SSE_ARG_1,FLOAT_14,XMM4)
388: /* ----------------------------------------------- */
390: SSE_INLINE_END_1;
391: SSE_SCOPE_END;
392: return(0);
393: }
395: #endif