Actual source code: dgefa2.c

  1: /*$Id: dgefa2.c,v 1.10 2001/04/07 15:47:07 bsmith Exp $*/
  2: /*
  3:      Inverts 2 by 2 matrix using partial pivoting.

  5:        Used by the sparse factorization routines in 
  6:      src/mat/impls/baij/seq and src/mat/impls/bdiag/seq

  8:        See also src/inline/ilu.h

 10:        This is a combination of the Linpack routines
 11:     dgefa() and dgedi() specialized for a size of 2.

 13: */
 14:  #include petsc.h

 16: int Kernel_A_gets_inverse_A_2(MatScalar *a)
 17: {
 18:     int        i__2,i__3,kp1,j,k,l,ll,i,ipvt[2],k3;
 19:     int        k4,j3;
 20:     MatScalar  *aa,*ax,*ay,work[4],stmp;
 21:     MatReal    tmp,max;

 23: /*     gaussian elimination with partial pivoting */

 26:     /* Parameter adjustments */
 27:     a       -= 3;

 29:     /*for (k = 1; k <= 1; ++k) {*/
 30:         k   = 1;
 31:         kp1 = k + 1;
 32:         k3  = 2*k;
 33:         k4  = k3 + k;
 34: /*        find l = pivot index */

 36:         i__2 = 2 - 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.) {
 48:           SETERRQ(k,"Zero pivot");
 49:         }

 51: /*           interchange if necessary */

 53:         if (l != k) {
 54:           stmp      = a[l + k3];
 55:           a[l + k3] = a[k4];
 56:           a[k4]     = stmp;
 57:         }

 59: /*           compute multipliers */

 61:         stmp = -1. / a[k4];
 62:         i__2 = 2 - k;
 63:         aa = &a[1 + k4];
 64:         for (ll=0; ll<i__2; ll++) {
 65:           aa[ll] *= stmp;
 66:         }

 68: /*           row elimination with column indexing */

 70:         ax = &a[k4+1];
 71:         for (j = kp1; j <= 2; ++j) {
 72:             j3   = 2*j;
 73:             stmp = a[l + j3];
 74:             if (l != k) {
 75:               a[l + j3] = a[k + j3];
 76:               a[k + j3] = stmp;
 77:             }

 79:             i__3 = 2 - k;
 80:             ay = &a[1+k+j3];
 81:             for (ll=0; ll<i__3; ll++) {
 82:               ay[ll] += stmp*ax[ll];
 83:             }
 84:         }
 85:     /*}*/
 86:     ipvt[1] = 2;
 87:     if (a[6] == 0.) {
 88:         SETERRQ(3,"Zero pivot,final row");
 89:     }

 91:     /*
 92:          Now form the inverse 
 93:     */

 95:    /*     compute inverse(u) */

 97:     for (k = 1; k <= 2; ++k) {
 98:         k3    = 2*k;
 99:         k4    = k3 + k;
100:         a[k4] = 1.0 / a[k4];
101:         stmp  = -a[k4];
102:         i__2  = k - 1;
103:         aa    = &a[k3 + 1];
104:         for (ll=0; ll<i__2; ll++) aa[ll] *= stmp;
105:         kp1 = k + 1;
106:         if (2 < kp1) continue;
107:         ax = aa;
108:         for (j = kp1; j <= 2; ++j) {
109:             j3        = 2*j;
110:             stmp      = a[k + j3];
111:             a[k + j3] = 0.0;
112:             ay        = &a[j3 + 1];
113:             for (ll=0; ll<k; ll++) {
114:               ay[ll] += stmp*ax[ll];
115:             }
116:         }
117:     }

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

121:     /*for (kb = 1; kb <= 1; ++kb) {*/
122: 
123:         k   = 1;
124:         k3  = 2*k;
125:         kp1 = k + 1;
126:         aa  = a + k3;
127:         for (i = kp1; i <= 2; ++i) {
128:             work[i-1] = aa[i];
129:             aa[i]   = 0.0;
130:         }
131:         for (j = kp1; j <= 2; ++j) {
132:             stmp  = work[j-1];
133:             ax    = &a[2*j + 1];
134:             ay    = &a[k3 + 1];
135:             ay[0] += stmp*ax[0];
136:             ay[1] += stmp*ax[1];
137:         }
138:         l = ipvt[k-1];
139:         if (l != k) {
140:             ax = &a[k3 + 1];
141:             ay = &a[2*l + 1];
142:             stmp = ax[0]; ax[0] = ay[0]; ay[0] = stmp;
143:             stmp = ax[1]; ax[1] = ay[1]; ay[1] = stmp;
144:         }
145: 
146:     return(0);
147: }