Date: 2013-07-02T14:42:35+00:00

Actual source code: dgefa4.c
petsc-3.4.2 2013-07-02

      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: PETSC_EXTERN 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) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_MAT_LU_ZRPVT,"Zero pivot, row %D",k-1);
     49:       else {
     50:         /* SHIFT is applied to SINGLE diagonal entry; does this make any sense? */
     51:         a[l + k3] = shift;
     52:       }
     53:     }

     55: /*           interchange if necessary */

     57:     if (l != k) {
     58:       stmp      = a[l + k3];
     59:       a[l + k3] = a[k4];
     60:       a[k4]     = stmp;
     61:     }

     63: /*           compute multipliers */

     65:     stmp = -1. / a[k4];
     66:     i__2 = 4 - k;
     67:     aa   = &a[1 + k4];
     68:     for (ll=0; ll<i__2; ll++) aa[ll] *= stmp;

     70: /*           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) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_MAT_LU_ZRPVT,"Zero pivot, row %D",3);

     89:   /*
     90:         Now form the inverse
     91:   */

     93:   /*     compute inverse(u) */

     95:   for (k = 1; k <= 4; ++k) {
     96:     k3    = 4*k;
     97:     k4    = k3 + k;
     98:     a[k4] = 1.0 / a[k4];
     99:     stmp  = -a[k4];
    100:     i__2  = k - 1;
    101:     aa    = &a[k3 + 1];
    102:     for (ll=0; ll<i__2; ll++) aa[ll] *= stmp;
    103:     kp1 = k + 1;
    104:     if (4 < kp1) continue;
    105:     ax = aa;
    106:     for (j = kp1; j <= 4; ++j) {
    107:       j3        = 4*j;
    108:       stmp      = a[k + j3];
    109:       a[k + j3] = 0.0;
    110:       ay        = &a[j3 + 1];
    111:       for (ll=0; ll<k; ll++) ay[ll] += stmp*ax[ll];
    112:     }
    113:   }

    115:   /*    form inverse(u)*inverse(l) */

    117:   for (kb = 1; kb <= 3; ++kb) {
    118:     k   = 4 - kb;
    119:     k3  = 4*k;
    120:     kp1 = k + 1;
    121:     aa  = a + k3;
    122:     for (i = kp1; i <= 4; ++i) {
    123:       work[i-1] = aa[i];
    124:       aa[i]     = 0.0;
    125:     }
    126:     for (j = kp1; j <= 4; ++j) {
    127:       stmp   = work[j-1];
    128:       ax     = &a[4*j + 1];
    129:       ay     = &a[k3 + 1];
    130:       ay[0] += stmp*ax[0];
    131:       ay[1] += stmp*ax[1];
    132:       ay[2] += stmp*ax[2];
    133:       ay[3] += stmp*ax[3];
    134:     }
    135:     l = ipvt[k-1];
    136:     if (l != k) {
    137:       ax   = &a[k3 + 1];
    138:       ay   = &a[4*l + 1];
    139:       stmp = ax[0]; ax[0] = ay[0]; ay[0] = stmp;
    140:       stmp = ax[1]; ax[1] = ay[1]; ay[1] = stmp;
    141:       stmp = ax[2]; ax[2] = ay[2]; ay[2] = stmp;
    142:       stmp = ax[3]; ax[3] = ay[3]; ay[3] = stmp;
    143:     }
    144:   }
    145:   return(0);
    146: }

    148: #if defined(PETSC_HAVE_SSE)
    149: #include PETSC_HAVE_SSE

    153: PETSC_EXTERN PetscErrorCode PetscKernel_A_gets_inverse_A_4_SSE(float *a)
    154: {
    155:   /*
    156:      This routine is converted from Intel's Small Matrix Library.
    157:      See: Streaming SIMD Extensions -- Inverse of 4x4 Matrix
    158:      Order Number: 245043-001
    159:      March 1999
    160:      http://www.intel.com

    162:      Inverse of a 4x4 matrix via Kramer's Rule:
    163:      bool Invert4x4(SMLXMatrix &);
    164:   */
    166:   SSE_SCOPE_BEGIN;
    167:   SSE_INLINE_BEGIN_1(a)

    169: /* ----------------------------------------------- */

    171:   SSE_LOADL_PS(SSE_ARG_1,FLOAT_0,XMM0)
    172:   SSE_LOADH_PS(SSE_ARG_1,FLOAT_4,XMM0)

    174:   SSE_LOADL_PS(SSE_ARG_1,FLOAT_8,XMM5)
    175:   SSE_LOADH_PS(SSE_ARG_1,FLOAT_12,XMM5)

    177:   SSE_COPY_PS(XMM3,XMM0)
    178:   SSE_SHUFFLE(XMM3,XMM5,0x88)

    180:   SSE_SHUFFLE(XMM5,XMM0,0xDD)

    182:   SSE_LOADL_PS(SSE_ARG_1,FLOAT_2,XMM0)
    183:   SSE_LOADH_PS(SSE_ARG_1,FLOAT_6,XMM0)

    185:   SSE_LOADL_PS(SSE_ARG_1,FLOAT_10,XMM6)
    186:   SSE_LOADH_PS(SSE_ARG_1,FLOAT_14,XMM6)

    188:   SSE_COPY_PS(XMM4,XMM0)
    189:   SSE_SHUFFLE(XMM4,XMM6,0x88)

    191:   SSE_SHUFFLE(XMM6,XMM0,0xDD)

    193: /* ----------------------------------------------- */

    195:   SSE_COPY_PS(XMM7,XMM4)
    196:   SSE_MULT_PS(XMM7,XMM6)

    198:   SSE_SHUFFLE(XMM7,XMM7,0xB1)

    200:   SSE_COPY_PS(XMM0,XMM5)
    201:   SSE_MULT_PS(XMM0,XMM7)

    203:   SSE_COPY_PS(XMM2,XMM3)
    204:   SSE_MULT_PS(XMM2,XMM7)

    206:   SSE_SHUFFLE(XMM7,XMM7,0x4E)

    208:   SSE_COPY_PS(XMM1,XMM5)
    209:   SSE_MULT_PS(XMM1,XMM7)
    210:   SSE_SUB_PS(XMM1,XMM0)

    212:   SSE_MULT_PS(XMM7,XMM3)
    213:   SSE_SUB_PS(XMM7,XMM2)

    215:   SSE_SHUFFLE(XMM7,XMM7,0x4E)
    216:   SSE_STORE_PS(SSE_ARG_1,FLOAT_4,XMM7)

    218: /* ----------------------------------------------- */

    220:   SSE_COPY_PS(XMM0,XMM5)
    221:   SSE_MULT_PS(XMM0,XMM4)

    223:   SSE_SHUFFLE(XMM0,XMM0,0xB1)

    225:   SSE_COPY_PS(XMM2,XMM6)
    226:   SSE_MULT_PS(XMM2,XMM0)
    227:   SSE_ADD_PS(XMM2,XMM1)

    229:   SSE_COPY_PS(XMM7,XMM3)
    230:   SSE_MULT_PS(XMM7,XMM0)

    232:   SSE_SHUFFLE(XMM0,XMM0,0x4E)

    234:   SSE_COPY_PS(XMM1,XMM6)
    235:   SSE_MULT_PS(XMM1,XMM0)
    236:   SSE_SUB_PS(XMM2,XMM1)

    238:   SSE_MULT_PS(XMM0,XMM3)
    239:   SSE_SUB_PS(XMM0,XMM7)

    241:   SSE_SHUFFLE(XMM0,XMM0,0x4E)
    242:   SSE_STORE_PS(SSE_ARG_1,FLOAT_12,XMM0)

    244:   /* ----------------------------------------------- */

    246:   SSE_COPY_PS(XMM7,XMM5)
    247:   SSE_SHUFFLE(XMM7,XMM5,0x4E)
    248:   SSE_MULT_PS(XMM7,XMM6)

    250:   SSE_SHUFFLE(XMM7,XMM7,0xB1)

    252:   SSE_SHUFFLE(XMM4,XMM4,0x4E)

    254:   SSE_COPY_PS(XMM0,XMM4)
    255:   SSE_MULT_PS(XMM0,XMM7)
    256:   SSE_ADD_PS(XMM0,XMM2)

    258:   SSE_COPY_PS(XMM2,XMM3)
    259:   SSE_MULT_PS(XMM2,XMM7)

    261:   SSE_SHUFFLE(XMM7,XMM7,0x4E)

    263:   SSE_COPY_PS(XMM1,XMM4)
    264:   SSE_MULT_PS(XMM1,XMM7)
    265:   SSE_SUB_PS(XMM0,XMM1)
    266:   SSE_STORE_PS(SSE_ARG_1,FLOAT_0,XMM0)

    268:   SSE_MULT_PS(XMM7,XMM3)
    269:   SSE_SUB_PS(XMM7,XMM2)

    271:   SSE_SHUFFLE(XMM7,XMM7,0x4E)

    273:   /* ----------------------------------------------- */

    275:   SSE_COPY_PS(XMM1,XMM3)
    276:   SSE_MULT_PS(XMM1,XMM5)

    278:   SSE_SHUFFLE(XMM1,XMM1,0xB1)

    280:   SSE_COPY_PS(XMM0,XMM6)
    281:   SSE_MULT_PS(XMM0,XMM1)
    282:   SSE_ADD_PS(XMM0,XMM7)

    284:   SSE_COPY_PS(XMM2,XMM4)
    285:   SSE_MULT_PS(XMM2,XMM1)
    286:   SSE_SUB_PS_M(XMM2,SSE_ARG_1,FLOAT_12)

    288:   SSE_SHUFFLE(XMM1,XMM1,0x4E)

    290:   SSE_COPY_PS(XMM7,XMM6)
    291:   SSE_MULT_PS(XMM7,XMM1)
    292:   SSE_SUB_PS(XMM7,XMM0)

    294:   SSE_MULT_PS(XMM1,XMM4)
    295:   SSE_SUB_PS(XMM2,XMM1)
    296:   SSE_STORE_PS(SSE_ARG_1,FLOAT_12,XMM2)

    298:   /* ----------------------------------------------- */

    300:   SSE_COPY_PS(XMM1,XMM3)
    301:   SSE_MULT_PS(XMM1,XMM6)

    303:   SSE_SHUFFLE(XMM1,XMM1,0xB1)

    305:   SSE_COPY_PS(XMM2,XMM4)
    306:   SSE_MULT_PS(XMM2,XMM1)
    307:   SSE_LOAD_PS(SSE_ARG_1,FLOAT_4,XMM0)
    308:   SSE_SUB_PS(XMM0,XMM2)

    310:   SSE_COPY_PS(XMM2,XMM5)
    311:   SSE_MULT_PS(XMM2,XMM1)
    312:   SSE_ADD_PS(XMM2,XMM7)

    314:   SSE_SHUFFLE(XMM1,XMM1,0x4E)

    316:   SSE_COPY_PS(XMM7,XMM4)
    317:   SSE_MULT_PS(XMM7,XMM1)
    318:   SSE_ADD_PS(XMM7,XMM0)

    320:   SSE_MULT_PS(XMM1,XMM5)
    321:   SSE_SUB_PS(XMM2,XMM1)

    323:   /* ----------------------------------------------- */

    325:   SSE_MULT_PS(XMM4,XMM3)

    327:   SSE_SHUFFLE(XMM4,XMM4,0xB1)

    329:   SSE_COPY_PS(XMM1,XMM6)
    330:   SSE_MULT_PS(XMM1,XMM4)
    331:   SSE_ADD_PS(XMM1,XMM7)

    333:   SSE_COPY_PS(XMM0,XMM5)
    334:   SSE_MULT_PS(XMM0,XMM4)
    335:   SSE_LOAD_PS(SSE_ARG_1,FLOAT_12,XMM7)
    336:   SSE_SUB_PS(XMM7,XMM0)

    338:   SSE_SHUFFLE(XMM4,XMM4,0x4E)

    340:   SSE_MULT_PS(XMM6,XMM4)
    341:   SSE_SUB_PS(XMM1,XMM6)

    343:   SSE_MULT_PS(XMM5,XMM4)
    344:   SSE_ADD_PS(XMM5,XMM7)

    346:   /* ----------------------------------------------- */

    348:   SSE_LOAD_PS(SSE_ARG_1,FLOAT_0,XMM0)
    349:   SSE_MULT_PS(XMM3,XMM0)

    351:   SSE_COPY_PS(XMM4,XMM3)
    352:   SSE_SHUFFLE(XMM4,XMM3,0x4E)
    353:   SSE_ADD_PS(XMM4,XMM3)

    355:   SSE_COPY_PS(XMM6,XMM4)
    356:   SSE_SHUFFLE(XMM6,XMM4,0xB1)
    357:   SSE_ADD_SS(XMM6,XMM4)

    359:   SSE_COPY_PS(XMM3,XMM6)
    360:   SSE_RECIP_SS(XMM3,XMM6)
    361:   SSE_COPY_SS(XMM4,XMM3)
    362:   SSE_ADD_SS(XMM4,XMM3)
    363:   SSE_MULT_SS(XMM3,XMM3)
    364:   SSE_MULT_SS(XMM6,XMM3)
    365:   SSE_SUB_SS(XMM4,XMM6)

    367:   SSE_SHUFFLE(XMM4,XMM4,0x00)

    369:   SSE_MULT_PS(XMM0,XMM4)
    370:   SSE_STOREL_PS(SSE_ARG_1,FLOAT_0,XMM0)
    371:   SSE_STOREH_PS(SSE_ARG_1,FLOAT_2,XMM0)

    373:   SSE_MULT_PS(XMM1,XMM4)
    374:   SSE_STOREL_PS(SSE_ARG_1,FLOAT_4,XMM1)
    375:   SSE_STOREH_PS(SSE_ARG_1,FLOAT_6,XMM1)

    377:   SSE_MULT_PS(XMM2,XMM4)
    378:   SSE_STOREL_PS(SSE_ARG_1,FLOAT_8,XMM2)
    379:   SSE_STOREH_PS(SSE_ARG_1,FLOAT_10,XMM2)

    381:   SSE_MULT_PS(XMM4,XMM5)
    382:   SSE_STOREL_PS(SSE_ARG_1,FLOAT_12,XMM4)
    383:   SSE_STOREH_PS(SSE_ARG_1,FLOAT_14,XMM4)

    385:   /* ----------------------------------------------- */

    387:   SSE_INLINE_END_1;
    388:   SSE_SCOPE_END;
    389:   return(0);
    390: }

    392: #endif