/*! @file dpivotgrowth.c * \brief Computes the reciprocal pivot growth factor * *
* -- SuperLU routine (version 2.0) -- * Univ. of California Berkeley, Xerox Palo Alto Research Center, * and Lawrence Berkeley National Lab. * November 15, 1997 **/ #include
* Purpose * ======= * * Compute the reciprocal pivot growth factor of the leading ncols columns * of the matrix, using the formula: * min_j ( max_i(abs(A_ij)) / max_i(abs(U_ij)) ) * * Arguments * ========= * * ncols (input) int * The number of columns of matrices A, L and U. * * A (input) SuperMatrix* * Original matrix A, permuted by columns, of dimension * (A->nrow, A->ncol). The type of A can be: * Stype = NC; Dtype = SLU_D; Mtype = GE. * * L (output) SuperMatrix* * The factor L from the factorization Pr*A=L*U; use compressed row * subscripts storage for supernodes, i.e., L has type: * Stype = SC; Dtype = SLU_D; Mtype = TRLU. * * U (output) SuperMatrix* * The factor U from the factorization Pr*A*Pc=L*U. Use column-wise * storage scheme, i.e., U has types: Stype = NC; * Dtype = SLU_D; Mtype = TRU. **/ double dPivotGrowth(int ncols, SuperMatrix *A, int *perm_c, SuperMatrix *L, SuperMatrix *U) { NCformat *Astore; SCformat *Lstore; NCformat *Ustore; double *Aval, *Lval, *Uval; int fsupc, nsupr, luptr, nz_in_U; int i, j, k, oldcol; int *inv_perm_c; double rpg, maxaj, maxuj; double smlnum; double *luval; /* Get machine constants. */ smlnum = dlamch_("S"); rpg = 1. / smlnum; Astore = A->Store; Lstore = L->Store; Ustore = U->Store; Aval = Astore->nzval; Lval = Lstore->nzval; Uval = Ustore->nzval; inv_perm_c = (int *) SUPERLU_MALLOC(A->ncol*sizeof(int)); for (j = 0; j < A->ncol; ++j) inv_perm_c[perm_c[j]] = j; for (k = 0; k <= Lstore->nsuper; ++k) { fsupc = L_FST_SUPC(k); nsupr = L_SUB_START(fsupc+1) - L_SUB_START(fsupc); luptr = L_NZ_START(fsupc); luval = &Lval[luptr]; nz_in_U = 1; for (j = fsupc; j < L_FST_SUPC(k+1) && j < ncols; ++j) { maxaj = 0.; oldcol = inv_perm_c[j]; for (i = Astore->colptr[oldcol]; i < Astore->colptr[oldcol+1]; ++i) maxaj = SUPERLU_MAX( maxaj, fabs(Aval[i]) ); maxuj = 0.; for (i = Ustore->colptr[j]; i < Ustore->colptr[j+1]; i++) maxuj = SUPERLU_MAX( maxuj, fabs(Uval[i]) ); /* Supernode */ for (i = 0; i < nz_in_U; ++i) maxuj = SUPERLU_MAX( maxuj, fabs(luval[i]) ); ++nz_in_U; luval += nsupr; if ( maxuj == 0. ) rpg = SUPERLU_MIN( rpg, 1.); else rpg = SUPERLU_MIN( rpg, maxaj / maxuj ); } if ( j >= ncols ) break; } SUPERLU_FREE(inv_perm_c); return (rpg); }