Date: 2016-07-24T16:54:49+00:00

Actual source code: dgefa4.c
petsc-3.7.3 2016-07-24
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      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