2: /*
  3:       Inverts 5 by 5 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 5.

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

 16: PETSC_EXTERN PetscErrorCode PetscKernel_A_gets_inverse_A_5(MatScalar *a,PetscInt *ipvt,MatScalar *work,PetscReal shift)
 17: {
 18:   PetscInt  i__2,i__3,kp1,j,k,l,ll,i,kb,k3;
 19:   PetscInt  k4,j3;
 20:   MatScalar *aa,*ax,*ay,stmp;
 21:   MatReal   tmp,max;

 23: /*     gaussian elimination with partial pivoting */

 26:   shift = .25*shift*(1.e-12 + PetscAbsScalar(a[0]) + PetscAbsScalar(a[6]) + PetscAbsScalar(a[12]) + PetscAbsScalar(a[18]) + PetscAbsScalar(a[24]));
 27:   /* Parameter adjustments */
 28:   a -= 6;

 30:   for (k = 1; k <= 4; ++k) {
 31:     kp1 = k + 1;
 32:     k3  = 5*k;
 33:     k4  = k3 + k;
 34: /*        find l = pivot index */

 36:     i__2 = 6 - 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 = 5 - 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 <= 5; ++j) {
 74:       j3   = 5*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 = 5 - k;
 82:       ay   = &a[1+k+j3];
 83:       for (ll=0; ll<i__3; ll++) ay[ll] += stmp*ax[ll];
 84:     }
 85:   }
 86:   ipvt[4] = 5;
 87:   if (a[30] == 0.0) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_MAT_LU_ZRPVT,"Zero pivot, row %D",4);

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

 93:   /*     compute inverse(u) */

 95:   for (k = 1; k <= 5; ++k) {
 96:     k3    = 5*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 (5 < kp1) continue;
105:     ax = aa;
106:     for (j = kp1; j <= 5; ++j) {
107:       j3        = 5*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 <= 4; ++kb) {
118:     k   = 5 - kb;
119:     k3  = 5*k;
120:     kp1 = k + 1;
121:     aa  = a + k3;
122:     for (i = kp1; i <= 5; ++i) {
123:       work[i-1] = aa[i];
124:       aa[i]     = 0.0;
125:     }
126:     for (j = kp1; j <= 5; ++j) {
127:       stmp   = work[j-1];
128:       ax     = &a[5*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:       ay[4] += stmp*ax[4];
135:     }
136:     l = ipvt[k-1];
137:     if (l != k) {
138:       ax   = &a[k3 + 1];
139:       ay   = &a[5*l + 1];
140:       stmp = ax[0]; ax[0] = ay[0]; ay[0] = stmp;
141:       stmp = ax[1]; ax[1] = ay[1]; ay[1] = stmp;
142:       stmp = ax[2]; ax[2] = ay[2]; ay[2] = stmp;
143:       stmp = ax[3]; ax[3] = ay[3]; ay[3] = stmp;
144:       stmp = ax[4]; ax[4] = ay[4]; ay[4] = stmp;
145:     }
146:   }
147:   return(0);
148: }