Actual source code: dgefa3.c

  1: #define PETSCMAT_DLL

  3: /*
  4:      Inverts 3 by 3 matrix using partial pivoting.

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

  9:        See also src/inline/ilu.h

 11:        This is a combination of the Linpack routines
 12:     dgefa() and dgedi() specialized for a size of 3.

 14: */
 15:  #include petsc.h

 19: PetscErrorCode Kernel_A_gets_inverse_A_3(MatScalar *a)
 20: {
 21:     PetscInt   i__2,i__3,kp1,j,k,l,ll,i,ipvt[3],kb,k3;
 22:     PetscInt   k4,j3;
 23:     MatScalar  *aa,*ax,*ay,work[9],stmp;
 24:     MatReal    tmp,max;

 26: /*     gaussian elimination with partial pivoting */

 29:     /* Parameter adjustments */
 30:     a       -= 4;

 32:     for (k = 1; k <= 2; ++k) {
 33:         kp1 = k + 1;
 34:         k3  = 3*k;
 35:         k4  = k3 + k;
 36: /*        find l = pivot index */

 38:         i__2 = 4 - 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] == 0.0) {
 50:           SETERRQ1(PETSC_ERR_MAT_LU_ZRPVT,"Zero pivot, row %D",k-1);
 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 = 3 - 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 <= 3; ++j) {
 74:             j3   = 3*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 = 3 - 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[2] = 3;
 89:     if (a[12] == 0.0) {
 90:       SETERRQ1(PETSC_ERR_MAT_LU_ZRPVT,"Zero pivot, row %D",2);
 91:     }

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

 97:    /*     compute inverse(u) */

 99:     for (k = 1; k <= 3; ++k) {
100:         k3    = 3*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 (3 < kp1) continue;
109:         ax = aa;
110:         for (j = kp1; j <= 3; ++j) {
111:             j3        = 3*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 <= 2; ++kb) {
124:         k   = 3 - kb;
125:         k3  = 3*k;
126:         kp1 = k + 1;
127:         aa  = a + k3;
128:         for (i = kp1; i <= 3; ++i) {
129:             work[i-1] = aa[i];
130:             aa[i]   = 0.0;
131:         }
132:         for (j = kp1; j <= 3; ++j) {
133:             stmp  = work[j-1];
134:             ax    = &a[3*j + 1];
135:             ay    = &a[k3 + 1];
136:             ay[0] += stmp*ax[0];
137:             ay[1] += stmp*ax[1];
138:             ay[2] += stmp*ax[2];
139:         }
140:         l = ipvt[k-1];
141:         if (l != k) {
142:             ax = &a[k3 + 1];
143:             ay = &a[3*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:             stmp = ax[2]; ax[2] = ay[2]; ay[2] = stmp;
147:         }
148:     }
149:     return(0);
150: }