Actual source code: dgefa4.c
petsc-3.3-p7 2013-05-11
2: /*
3: Inverts 4 by 4 matrix using 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: PetscErrorCode PetscKernel_A_gets_inverse_A_4(MatScalar *a,PetscReal shift)
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;
23: /* gaussian elimination with partial pivoting */
26: 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;
34: /* 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: SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_MAT_LU_ZRPVT,"Zero pivot, row %D",k-1);
50: } else {
51: /* SHIFT is applied to SINGLE diagonal entry; does this make any sense? */
52: a[l + k3] = shift;
53: }
54: }
56: /* interchange if necessary */
58: if (l != k) {
59: stmp = a[l + k3];
60: a[l + k3] = a[k4];
61: a[k4] = stmp;
62: }
64: /* 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++) {
70: aa[ll] *= stmp;
71: }
73: /* row elimination with column indexing */
75: ax = &a[k4+1];
76: for (j = kp1; j <= 4; ++j) {
77: j3 = 4*j;
78: stmp = a[l + j3];
79: if (l != k) {
80: a[l + j3] = a[k + j3];
81: a[k + j3] = stmp;
82: }
84: i__3 = 4 - k;
85: ay = &a[1+k+j3];
86: for (ll=0; ll<i__3; ll++) {
87: ay[ll] += stmp*ax[ll];
88: }
89: }
90: }
91: ipvt[3] = 4;
92: if (a[20] == 0.0) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_MAT_LU_ZRPVT,"Zero pivot, row %D",3);
94: /*
95: Now form the inverse
96: */
98: /* compute inverse(u) */
100: for (k = 1; k <= 4; ++k) {
101: k3 = 4*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 (4 < kp1) continue;
110: ax = aa;
111: for (j = kp1; j <= 4; ++j) {
112: j3 = 4*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 <= 3; ++kb) {
125: k = 4 - kb;
126: k3 = 4*k;
127: kp1 = k + 1;
128: aa = a + k3;
129: for (i = kp1; i <= 4; ++i) {
130: work[i-1] = aa[i];
131: aa[i] = 0.0;
132: }
133: for (j = kp1; j <= 4; ++j) {
134: stmp = work[j-1];
135: ax = &a[4*j + 1];
136: ay = &a[k3 + 1];
137: ay[0] += stmp*ax[0];
138: ay[1] += stmp*ax[1];
139: ay[2] += stmp*ax[2];
140: ay[3] += stmp*ax[3];
141: }
142: l = ipvt[k-1];
143: if (l != k) {
144: ax = &a[k3 + 1];
145: ay = &a[4*l + 1];
146: stmp = ax[0]; ax[0] = ay[0]; ay[0] = stmp;
147: stmp = ax[1]; ax[1] = ay[1]; ay[1] = stmp;
148: stmp = ax[2]; ax[2] = ay[2]; ay[2] = stmp;
149: stmp = ax[3]; ax[3] = ay[3]; ay[3] = stmp;
150: }
151: }
152: return(0);
153: }
155: #if defined(PETSC_HAVE_SSE)
156: #include PETSC_HAVE_SSE
160: PetscErrorCode PetscKernel_A_gets_inverse_A_4_SSE(float *a)
161: {
162: /*
163: This routine is converted from Intel's Small Matrix Library.
164: See: Streaming SIMD Extensions -- Inverse of 4x4 Matrix
165: Order Number: 245043-001
166: March 1999
167: http://www.intel.com
169: Inverse of a 4x4 matrix via Kramer's Rule:
170: bool Invert4x4(SMLXMatrix &);
171: */
174: SSE_SCOPE_BEGIN;
175: SSE_INLINE_BEGIN_1(a)
177: /* ----------------------------------------------- */
179: SSE_LOADL_PS(SSE_ARG_1,FLOAT_0,XMM0)
180: SSE_LOADH_PS(SSE_ARG_1,FLOAT_4,XMM0)
182: SSE_LOADL_PS(SSE_ARG_1,FLOAT_8,XMM5)
183: SSE_LOADH_PS(SSE_ARG_1,FLOAT_12,XMM5)
185: SSE_COPY_PS(XMM3,XMM0)
186: SSE_SHUFFLE(XMM3,XMM5,0x88)
188: SSE_SHUFFLE(XMM5,XMM0,0xDD)
190: SSE_LOADL_PS(SSE_ARG_1,FLOAT_2,XMM0)
191: SSE_LOADH_PS(SSE_ARG_1,FLOAT_6,XMM0)
193: SSE_LOADL_PS(SSE_ARG_1,FLOAT_10,XMM6)
194: SSE_LOADH_PS(SSE_ARG_1,FLOAT_14,XMM6)
196: SSE_COPY_PS(XMM4,XMM0)
197: SSE_SHUFFLE(XMM4,XMM6,0x88)
199: SSE_SHUFFLE(XMM6,XMM0,0xDD)
201: /* ----------------------------------------------- */
203: SSE_COPY_PS(XMM7,XMM4)
204: SSE_MULT_PS(XMM7,XMM6)
206: SSE_SHUFFLE(XMM7,XMM7,0xB1)
208: SSE_COPY_PS(XMM0,XMM5)
209: SSE_MULT_PS(XMM0,XMM7)
211: SSE_COPY_PS(XMM2,XMM3)
212: SSE_MULT_PS(XMM2,XMM7)
214: SSE_SHUFFLE(XMM7,XMM7,0x4E)
216: SSE_COPY_PS(XMM1,XMM5)
217: SSE_MULT_PS(XMM1,XMM7)
218: SSE_SUB_PS(XMM1,XMM0)
220: SSE_MULT_PS(XMM7,XMM3)
221: SSE_SUB_PS(XMM7,XMM2)
223: SSE_SHUFFLE(XMM7,XMM7,0x4E)
224: SSE_STORE_PS(SSE_ARG_1,FLOAT_4,XMM7)
226: /* ----------------------------------------------- */
228: SSE_COPY_PS(XMM0,XMM5)
229: SSE_MULT_PS(XMM0,XMM4)
231: SSE_SHUFFLE(XMM0,XMM0,0xB1)
233: SSE_COPY_PS(XMM2,XMM6)
234: SSE_MULT_PS(XMM2,XMM0)
235: SSE_ADD_PS(XMM2,XMM1)
236:
237: SSE_COPY_PS(XMM7,XMM3)
238: SSE_MULT_PS(XMM7,XMM0)
240: SSE_SHUFFLE(XMM0,XMM0,0x4E)
242: SSE_COPY_PS(XMM1,XMM6)
243: SSE_MULT_PS(XMM1,XMM0)
244: SSE_SUB_PS(XMM2,XMM1)
246: SSE_MULT_PS(XMM0,XMM3)
247: SSE_SUB_PS(XMM0,XMM7)
249: SSE_SHUFFLE(XMM0,XMM0,0x4E)
250: SSE_STORE_PS(SSE_ARG_1,FLOAT_12,XMM0)
252: /* ----------------------------------------------- */
254: SSE_COPY_PS(XMM7,XMM5)
255: SSE_SHUFFLE(XMM7,XMM5,0x4E)
256: SSE_MULT_PS(XMM7,XMM6)
258: SSE_SHUFFLE(XMM7,XMM7,0xB1)
260: SSE_SHUFFLE(XMM4,XMM4,0x4E)
262: SSE_COPY_PS(XMM0,XMM4)
263: SSE_MULT_PS(XMM0,XMM7)
264: SSE_ADD_PS(XMM0,XMM2)
266: SSE_COPY_PS(XMM2,XMM3)
267: SSE_MULT_PS(XMM2,XMM7)
269: SSE_SHUFFLE(XMM7,XMM7,0x4E)
271: SSE_COPY_PS(XMM1,XMM4)
272: SSE_MULT_PS(XMM1,XMM7)
273: SSE_SUB_PS(XMM0,XMM1)
274: SSE_STORE_PS(SSE_ARG_1,FLOAT_0,XMM0)
276: SSE_MULT_PS(XMM7,XMM3)
277: SSE_SUB_PS(XMM7,XMM2)
279: SSE_SHUFFLE(XMM7,XMM7,0x4E)
281: /* ----------------------------------------------- */
283: SSE_COPY_PS(XMM1,XMM3)
284: SSE_MULT_PS(XMM1,XMM5)
286: SSE_SHUFFLE(XMM1,XMM1,0xB1)
288: SSE_COPY_PS(XMM0,XMM6)
289: SSE_MULT_PS(XMM0,XMM1)
290: SSE_ADD_PS(XMM0,XMM7)
291:
292: SSE_COPY_PS(XMM2,XMM4)
293: SSE_MULT_PS(XMM2,XMM1)
294: SSE_SUB_PS_M(XMM2,SSE_ARG_1,FLOAT_12)
296: SSE_SHUFFLE(XMM1,XMM1,0x4E)
298: SSE_COPY_PS(XMM7,XMM6)
299: SSE_MULT_PS(XMM7,XMM1)
300: SSE_SUB_PS(XMM7,XMM0)
302: SSE_MULT_PS(XMM1,XMM4)
303: SSE_SUB_PS(XMM2,XMM1)
304: SSE_STORE_PS(SSE_ARG_1,FLOAT_12,XMM2)
306: /* ----------------------------------------------- */
308: SSE_COPY_PS(XMM1,XMM3)
309: SSE_MULT_PS(XMM1,XMM6)
311: SSE_SHUFFLE(XMM1,XMM1,0xB1)
313: SSE_COPY_PS(XMM2,XMM4)
314: SSE_MULT_PS(XMM2,XMM1)
315: SSE_LOAD_PS(SSE_ARG_1,FLOAT_4,XMM0)
316: SSE_SUB_PS(XMM0,XMM2)
318: SSE_COPY_PS(XMM2,XMM5)
319: SSE_MULT_PS(XMM2,XMM1)
320: SSE_ADD_PS(XMM2,XMM7)
322: SSE_SHUFFLE(XMM1,XMM1,0x4E)
324: SSE_COPY_PS(XMM7,XMM4)
325: SSE_MULT_PS(XMM7,XMM1)
326: SSE_ADD_PS(XMM7,XMM0)
328: SSE_MULT_PS(XMM1,XMM5)
329: SSE_SUB_PS(XMM2,XMM1)
331: /* ----------------------------------------------- */
333: SSE_MULT_PS(XMM4,XMM3)
335: SSE_SHUFFLE(XMM4,XMM4,0xB1)
337: SSE_COPY_PS(XMM1,XMM6)
338: SSE_MULT_PS(XMM1,XMM4)
339: SSE_ADD_PS(XMM1,XMM7)
341: SSE_COPY_PS(XMM0,XMM5)
342: SSE_MULT_PS(XMM0,XMM4)
343: SSE_LOAD_PS(SSE_ARG_1,FLOAT_12,XMM7)
344: SSE_SUB_PS(XMM7,XMM0)
346: SSE_SHUFFLE(XMM4,XMM4,0x4E)
348: SSE_MULT_PS(XMM6,XMM4)
349: SSE_SUB_PS(XMM1,XMM6)
351: SSE_MULT_PS(XMM5,XMM4)
352: SSE_ADD_PS(XMM5,XMM7)
354: /* ----------------------------------------------- */
356: SSE_LOAD_PS(SSE_ARG_1,FLOAT_0,XMM0)
357: SSE_MULT_PS(XMM3,XMM0)
359: SSE_COPY_PS(XMM4,XMM3)
360: SSE_SHUFFLE(XMM4,XMM3,0x4E)
361: SSE_ADD_PS(XMM4,XMM3)
363: SSE_COPY_PS(XMM6,XMM4)
364: SSE_SHUFFLE(XMM6,XMM4,0xB1)
365: SSE_ADD_SS(XMM6,XMM4)
367: SSE_COPY_PS(XMM3,XMM6)
368: SSE_RECIP_SS(XMM3,XMM6)
369: SSE_COPY_SS(XMM4,XMM3)
370: SSE_ADD_SS(XMM4,XMM3)
371: SSE_MULT_SS(XMM3,XMM3)
372: SSE_MULT_SS(XMM6,XMM3)
373: SSE_SUB_SS(XMM4,XMM6)
375: SSE_SHUFFLE(XMM4,XMM4,0x00)
377: SSE_MULT_PS(XMM0,XMM4)
378: SSE_STOREL_PS(SSE_ARG_1,FLOAT_0,XMM0)
379: SSE_STOREH_PS(SSE_ARG_1,FLOAT_2,XMM0)
381: SSE_MULT_PS(XMM1,XMM4)
382: SSE_STOREL_PS(SSE_ARG_1,FLOAT_4,XMM1)
383: SSE_STOREH_PS(SSE_ARG_1,FLOAT_6,XMM1)
385: SSE_MULT_PS(XMM2,XMM4)
386: SSE_STOREL_PS(SSE_ARG_1,FLOAT_8,XMM2)
387: SSE_STOREH_PS(SSE_ARG_1,FLOAT_10,XMM2)
389: SSE_MULT_PS(XMM4,XMM5)
390: SSE_STOREL_PS(SSE_ARG_1,FLOAT_12,XMM4)
391: SSE_STOREH_PS(SSE_ARG_1,FLOAT_14,XMM4)
393: /* ----------------------------------------------- */
395: SSE_INLINE_END_1;
396: SSE_SCOPE_END;
398: return(0);
399: }
401: #endif