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: 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) {
 50:             SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_MAT_LU_ZRPVT,"Zero pivot, row %D",k-1);
 51:             } else {
 52:             /* SHIFT is applied to SINGLE diagonal entry; does this make any sense? */
 53:               a[l + k3] = shift;
 54:             }
 55:         }

 57: /*           interchange if necessary */

 59:         if (l != k) {
 60:           stmp      = a[l + k3];
 61:           a[l + k3] = a[k4];
 62:           a[k4]     = stmp;
 63:         }

 65: /*           compute multipliers */

 67:         stmp = -1. / a[k4];
 68:         i__2 = 7 - k;
 69:         aa = &a[1 + k4];
 70:         for (ll=0; ll<i__2; ll++) {
 71:           aa[ll] *= stmp;
 72:         }

 74: /*           row elimination with column indexing */

 76:         ax = &a[k4+1];
 77:         for (j = kp1; j <= 7; ++j) {
 78:             j3   = 7*j;
 79:             stmp = a[l + j3];
 80:             if (l != k) {
 81:               a[l + j3] = a[k + j3];
 82:               a[k + j3] = stmp;
 83:             }

 85:             i__3 = 7 - k;
 86:             ay = &a[1+k+j3];
 87:             for (ll=0; ll<i__3; ll++) {
 88:               ay[ll] += stmp*ax[ll];
 89:             }
 90:         }
 91:     }
 92:     ipvt[6] = 7;
 93:     if (a[56] == 0.0) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_MAT_LU_ZRPVT,"Zero pivot, row %D",6);

 95:     /*
 96:          Now form the inverse 
 97:     */

 99:    /*     compute inverse(u) */

101:     for (k = 1; k <= 7; ++k) {
102:         k3    = 7*k;
103:         k4    = k3 + k;
104:         a[k4] = 1.0 / a[k4];
105:         stmp  = -a[k4];
106:         i__2  = k - 1;
107:         aa    = &a[k3 + 1];
108:         for (ll=0; ll<i__2; ll++) aa[ll] *= stmp;
109:         kp1 = k + 1;
110:         if (7 < kp1) continue;
111:         ax = aa;
112:         for (j = kp1; j <= 7; ++j) {
113:             j3        = 7*j;
114:             stmp      = a[k + j3];
115:             a[k + j3] = 0.0;
116:             ay        = &a[j3 + 1];
117:             for (ll=0; ll<k; ll++) {
118:               ay[ll] += stmp*ax[ll];
119:             }
120:         }
121:     }

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

125:     for (kb = 1; kb <= 6; ++kb) {
126:         k   = 7 - kb;
127:         k3  = 7*k;
128:         kp1 = k + 1;
129:         aa  = a + k3;
130:         for (i = kp1; i <= 7; ++i) {
131:             work[i-1] = aa[i];
132:             aa[i]   = 0.0;
133:         }
134:         for (j = kp1; j <= 7; ++j) {
135:             stmp  = work[j-1];
136:             ax    = &a[7*j + 1];
137:             ay    = &a[k3 + 1];
138:             ay[0] += stmp*ax[0];
139:             ay[1] += stmp*ax[1];
140:             ay[2] += stmp*ax[2];
141:             ay[3] += stmp*ax[3];
142:             ay[4] += stmp*ax[4];
143:             ay[5] += stmp*ax[5];
144:             ay[6] += stmp*ax[6];
145:         }
146:         l = ipvt[k-1];
147:         if (l != k) {
148:             ax = &a[k3 + 1];
149:             ay = &a[7*l + 1];
150:             stmp = ax[0]; ax[0] = ay[0]; ay[0] = stmp;
151:             stmp = ax[1]; ax[1] = ay[1]; ay[1] = stmp;
152:             stmp = ax[2]; ax[2] = ay[2]; ay[2] = stmp;
153:             stmp = ax[3]; ax[3] = ay[3]; ay[3] = stmp;
154:             stmp = ax[4]; ax[4] = ay[4]; ay[4] = stmp;
155:             stmp = ax[5]; ax[5] = ay[5]; ay[5] = stmp;
156:             stmp = ax[6]; ax[6] = ay[6]; ay[6] = stmp;
157:         }
158:     }
159:     return(0);
160: }