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

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

 25: /*     gaussian elimination with partial pivoting */

 28:     /* Parameter adjustments */
 29:     a       -= 3;

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

 38:         i__2 = 2 - k;
 39:         aa = &a[k4];
 40:         max = PetscAbsScalar(aa[0]);
 41:         l = 1;
 42:         for (ll=1; ll<i__2; ll++) {
 43:           tmp = PetscAbsScalar(aa[ll]);
 44:           if (tmp > max) { max = tmp; l = ll+1;}
 45:         }
 46:         l       += k - 1;
 47:         ipvt[k-1] = l;

 49:         if (a[l + k3] == 0.) {
 50:           SETERRQ(k,"Zero pivot");
 51:         }

 53: /*           interchange if necessary */

 55:         if (l != k) {
 56:           stmp      = a[l + k3];
 57:           a[l + k3] = a[k4];
 58:           a[k4]     = stmp;
 59:         }

 61: /*           compute multipliers */

 63:         stmp = -1. / a[k4];
 64:         i__2 = 2 - k;
 65:         aa = &a[1 + k4];
 66:         for (ll=0; ll<i__2; ll++) {
 67:           aa[ll] *= stmp;
 68:         }

 70: /*           row elimination with column indexing */

 72:         ax = &a[k4+1];
 73:         for (j = kp1; j <= 2; ++j) {
 74:             j3   = 2*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 = 2 - k;
 82:             ay = &a[1+k+j3];
 83:             for (ll=0; ll<i__3; ll++) {
 84:               ay[ll] += stmp*ax[ll];
 85:             }
 86:         }
 87:     /*}*/
 88:     ipvt[1] = 2;
 89:     if (a[6] == 0.) {
 90:         SETERRQ(3,"Zero pivot,final row");
 91:     }

 93:     /*
 94:          Now form the inverse 
 95:     */

 97:    /*     compute inverse(u) */

 99:     for (k = 1; k <= 2; ++k) {
100:         k3    = 2*k;
101:         k4    = k3 + k;
102:         a[k4] = 1.0 / a[k4];
103:         stmp  = -a[k4];
104:         i__2  = k - 1;
105:         aa    = &a[k3 + 1];
106:         for (ll=0; ll<i__2; ll++) aa[ll] *= stmp;
107:         kp1 = k + 1;
108:         if (2 < kp1) continue;
109:         ax = aa;
110:         for (j = kp1; j <= 2; ++j) {
111:             j3        = 2*j;
112:             stmp      = a[k + j3];
113:             a[k + j3] = 0.0;
114:             ay        = &a[j3 + 1];
115:             for (ll=0; ll<k; ll++) {
116:               ay[ll] += stmp*ax[ll];
117:             }
118:         }
119:     }

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

123:     /*for (kb = 1; kb <= 1; ++kb) {*/
124: 
125:         k   = 1;
126:         k3  = 2*k;
127:         kp1 = k + 1;
128:         aa  = a + k3;
129:         for (i = kp1; i <= 2; ++i) {
130:             work[i-1] = aa[i];
131:             aa[i]   = 0.0;
132:         }
133:         for (j = kp1; j <= 2; ++j) {
134:             stmp  = work[j-1];
135:             ax    = &a[2*j + 1];
136:             ay    = &a[k3 + 1];
137:             ay[0] += stmp*ax[0];
138:             ay[1] += stmp*ax[1];
139:         }
140:         l = ipvt[k-1];
141:         if (l != k) {
142:             ax = &a[k3 + 1];
143:             ay = &a[2*l + 1];
144:             stmp = ax[0]; ax[0] = ay[0]; ay[0] = stmp;
145:             stmp = ax[1]; ax[1] = ay[1]; ay[1] = stmp;
146:         }
147: 
148:     return(0);
149: }