Date: 2013-07-02T14:42:36+00:00

Actual source code: dgefa7.c
petsc-3.4.2 2013-07-02

      2: /*
      3:       Inverts 7 by 7 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 7.

     11: */
     12: #include <petscsys.h>

     16: PETSC_EXTERN PetscErrorCode PetscKernel_A_gets_inverse_A_7(MatScalar *a,PetscReal shift)
     17: {
     18:   PetscInt  i__2,i__3,kp1,j,k,l,ll,i,ipvt[7],kb,k3;
     19:   PetscInt  k4,j3;
     20:   MatScalar *aa,*ax,*ay,work[49],stmp;
     21:   MatReal   tmp,max;

     23: /*     gaussian elimination with partial pivoting */

     26:   shift = .25*shift*(1.e-12 + PetscAbsScalar(a[0]) + PetscAbsScalar(a[8]) + PetscAbsScalar(a[16]) + PetscAbsScalar(a[24]) + PetscAbsScalar(a[32]) + PetscAbsScalar(a[40]) + PetscAbsScalar(a[48]));

     28:   /* Parameter adjustments */
     29:   a -= 8;

     31:   for (k = 1; k <= 6; ++k) {
     32:     kp1 = k + 1;
     33:     k3  = 7*k;
     34:     k4  = k3 + k;
     35: /*        find l = pivot index */

     37:     i__2 = 8 - k;
     38:     aa   = &a[k4];
     39:     max  = PetscAbsScalar(aa[0]);
     40:     l    = 1;
     41:     for (ll=1; ll<i__2; ll++) {
     42:       tmp = PetscAbsScalar(aa[ll]);
     43:       if (tmp > max) { max = tmp; l = ll+1;}
     44:     }
     45:     l        += k - 1;
     46:     ipvt[k-1] = l;

     48:     if (a[l + k3] == 0.0) {
     49:       if (shift == 0.0) 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 = 7 - k;
     68:     aa   = &a[1 + k4];
     69:     for (ll=0; ll<i__2; ll++) aa[ll] *= stmp;

     71: /*           row elimination with column indexing */

     73:     ax = &a[k4+1];
     74:     for (j = kp1; j <= 7; ++j) {
     75:       j3   = 7*j;
     76:       stmp = a[l + j3];
     77:       if (l != k) {
     78:         a[l + j3] = a[k + j3];
     79:         a[k + j3] = stmp;
     80:       }

     82:       i__3 = 7 - k;
     83:       ay   = &a[1+k+j3];
     84:       for (ll=0; ll<i__3; ll++) ay[ll] += stmp*ax[ll];
     85:     }
     86:   }
     87:   ipvt[6] = 7;
     88:   if (a[56] == 0.0) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_MAT_LU_ZRPVT,"Zero pivot, row %D",6);

     90:   /*
     91:        Now form the inverse
     92:   */

     94:   /*     compute inverse(u) */

     96:   for (k = 1; k <= 7; ++k) {
     97:     k3    = 7*k;
     98:     k4    = k3 + k;
     99:     a[k4] = 1.0 / a[k4];
    100:     stmp  = -a[k4];
    101:     i__2  = k - 1;
    102:     aa    = &a[k3 + 1];
    103:     for (ll=0; ll<i__2; ll++) aa[ll] *= stmp;
    104:     kp1 = k + 1;
    105:     if (7 < kp1) continue;
    106:     ax = aa;
    107:     for (j = kp1; j <= 7; ++j) {
    108:       j3        = 7*j;
    109:       stmp      = a[k + j3];
    110:       a[k + j3] = 0.0;
    111:       ay        = &a[j3 + 1];
    112:       for (ll=0; ll<k; ll++) ay[ll] += stmp*ax[ll];
    113:     }
    114:   }

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

    118:   for (kb = 1; kb <= 6; ++kb) {
    119:     k   = 7 - kb;
    120:     k3  = 7*k;
    121:     kp1 = k + 1;
    122:     aa  = a + k3;
    123:     for (i = kp1; i <= 7; ++i) {
    124:       work[i-1] = aa[i];
    125:       aa[i]     = 0.0;
    126:     }
    127:     for (j = kp1; j <= 7; ++j) {
    128:       stmp   = work[j-1];
    129:       ax     = &a[7*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:       ay[4] += stmp*ax[4];
    136:       ay[5] += stmp*ax[5];
    137:       ay[6] += stmp*ax[6];
    138:     }
    139:     l = ipvt[k-1];
    140:     if (l != k) {
    141:       ax   = &a[k3 + 1];
    142:       ay   = &a[7*l + 1];
    143:       stmp = ax[0]; ax[0] = ay[0]; ay[0] = stmp;
    144:       stmp = ax[1]; ax[1] = ay[1]; ay[1] = stmp;
    145:       stmp = ax[2]; ax[2] = ay[2]; ay[2] = stmp;
    146:       stmp = ax[3]; ax[3] = ay[3]; ay[3] = stmp;
    147:       stmp = ax[4]; ax[4] = ay[4]; ay[4] = stmp;
    148:       stmp = ax[5]; ax[5] = ay[5]; ay[5] = stmp;
    149:       stmp = ax[6]; ax[6] = ay[6]; ay[6] = stmp;
    150:     }
    151:   }
    152:   return(0);
    153: }