Actual source code: dgefa5.c

  1: /*$Id: dgefa5.c,v 1.15 2001/04/07 15:44:07 bsmith Exp $*/
  2: /*
  3:       Inverts 5 by 5 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 5.

 13: */
 14:  #include petsc.h

 16: int Kernel_A_gets_inverse_A_5(MatScalar *a)
 17: {
 18:     int        i__2,i__3,kp1,j,k,l,ll,i,ipvt[5],kb,k3;
 19:     int        k4,j3;
 20:     MatScalar  *aa,*ax,*ay,work[25],stmp;
 21:     MatReal    tmp,max;

 23: /*     gaussian elimination with partial pivoting */

 26:     /* Parameter adjustments */
 27:     a       -= 6;

 29:     for (k = 1; k <= 4; ++k) {
 30:         kp1 = k + 1;
 31:         k3  = 5*k;
 32:         k4  = k3 + k;
 33: /*        find l = pivot index */

 35:         i__2 = 5 - k;
 36:         aa = &a[k4];
 37:         max = PetscAbsScalar(aa[0]);
 38:         l = 1;
 39:         for (ll=1; ll<i__2; ll++) {
 40:           tmp = PetscAbsScalar(aa[ll]);
 41:           if (tmp > max) { max = tmp; l = ll+1;}
 42:         }
 43:         l       += k - 1;
 44:         ipvt[k-1] = l;

 46:         if (a[l + k3] == 0.) {
 47:           SETERRQ(k,"Zero pivot");
 48:         }

 50: /*           interchange if necessary */

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

 58: /*           compute multipliers */

 60:         stmp = -1. / a[k4];
 61:         i__2 = 5 - k;
 62:         aa = &a[1 + k4];
 63:         for (ll=0; ll<i__2; ll++) {
 64:           aa[ll] *= stmp;
 65:         }

 67: /*           row elimination with column indexing */

 69:         ax = &a[k4+1];
 70:         for (j = kp1; j <= 5; ++j) {
 71:             j3   = 5*j;
 72:             stmp = a[l + j3];
 73:             if (l != k) {
 74:               a[l + j3] = a[k + j3];
 75:               a[k + j3] = stmp;
 76:             }

 78:             i__3 = 5 - k;
 79:             ay = &a[1+k+j3];
 80:             for (ll=0; ll<i__3; ll++) {
 81:               ay[ll] += stmp*ax[ll];
 82:             }
 83:         }
 84:     }
 85:     ipvt[4] = 5;
 86:     if (a[30] == 0.) {
 87:         SETERRQ(3,"Zero pivot,final row");
 88:     }

 90:     /*
 91:          Now form the inverse 
 92:     */

 94:    /*     compute inverse(u) */

 96:     for (k = 1; k <= 5; ++k) {
 97:         k3    = 5*k;
 98:         k4    = k3 + k;
 99:         a[k4] = 1.0 / a[k4];
100:         stmp  = -a[k4];
101:         i__2  = k - 1;
102:         aa    = &a[k3 + 1];
103:         for (ll=0; ll<i__2; ll++) aa[ll] *= stmp;
104:         kp1 = k + 1;
105:         if (5 < kp1) continue;
106:         ax = aa;
107:         for (j = kp1; j <= 5; ++j) {
108:             j3        = 5*j;
109:             stmp      = a[k + j3];
110:             a[k + j3] = 0.0;
111:             ay        = &a[j3 + 1];
112:             for (ll=0; ll<k; ll++) {
113:               ay[ll] += stmp*ax[ll];
114:             }
115:         }
116:     }

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

120:     for (kb = 1; kb <= 4; ++kb) {
121:         k   = 5 - kb;
122:         k3  = 5*k;
123:         kp1 = k + 1;
124:         aa  = a + k3;
125:         for (i = kp1; i <= 5; ++i) {
126:             work[i-1] = aa[i];
127:             aa[i]   = 0.0;
128:         }
129:         for (j = kp1; j <= 5; ++j) {
130:             stmp  = work[j-1];
131:             ax    = &a[5*j + 1];
132:             ay    = &a[k3 + 1];
133:             ay[0] += stmp*ax[0];
134:             ay[1] += stmp*ax[1];
135:             ay[2] += stmp*ax[2];
136:             ay[3] += stmp*ax[3];
137:             ay[4] += stmp*ax[4];
138:         }
139:         l = ipvt[k-1];
140:         if (l != k) {
141:             ax = &a[k3 + 1];
142:             ay = &a[5*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:             stmp = ax[2]; ax[2] = ay[2]; ay[2] = stmp;
146:             stmp = ax[3]; ax[3] = ay[3]; ay[3] = stmp;
147:             stmp = ax[4]; ax[4] = ay[4]; ay[4] = stmp;
148:         }
149:     }
150:     return(0);
151: }