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: }