Actual source code: dgefa2.c

  1: /*
  2:      Inverts 2 by 2 matrix using partial pivoting.

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

  7:        See also src/inline/ilu.h

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

 12: */
 13:  #include petsc.h

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

 24: /*     gaussian elimination with partial pivoting */

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

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

 37:         i__2 = 2 - 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:           SETERRQ1(PETSC_ERR_MAT_LU_ZRPVT,"Zero pivot, row %D",k-1);
 50:         }

 52: /*           interchange if necessary */

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

 60: /*           compute multipliers */

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

 69: /*           row elimination with column indexing */

 71:         ax = &a[k4+1];
 72:         for (j = kp1; j <= 2; ++j) {
 73:             j3   = 2*j;
 74:             stmp = a[l + j3];
 75:             if (l != k) {
 76:               a[l + j3] = a[k + j3];
 77:               a[k + j3] = stmp;
 78:             }

 80:             i__3 = 2 - k;
 81:             ay = &a[1+k+j3];
 82:             for (ll=0; ll<i__3; ll++) {
 83:               ay[ll] += stmp*ax[ll];
 84:             }
 85:         }
 86:     /*}*/
 87:     ipvt[1] = 2;
 88:     if (a[6] == 0.0) {
 89:       SETERRQ1(PETSC_ERR_MAT_LU_ZRPVT,"Zero pivot, row %D",1);
 90:     }

 92:     /*
 93:          Now form the inverse 
 94:     */

 96:    /*     compute inverse(u) */

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

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

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