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fvn_sparse/UMFPACK/Source/umf_ltsolve.c
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/* ========================================================================== */ /* === UMF_ltsolve ========================================================== */ /* ========================================================================== */ /* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ /* Solves L'x = b or L.'x=b, where L is the lower triangular factor of a */ /* matrix. B is overwritten with the solution X. */ /* Returns the floating point operation count */ #include "umf_internal.h" GLOBAL double #ifdef CONJUGATE_SOLVE UMF_lhsolve /* solve L'x=b (complex conjugate transpose) */ #else UMF_ltsolve /* solve L.'x=b (array transpose) */ #endif ( NumericType *Numeric, Entry X [ ], /* b on input, solution x on output */ Int Pattern [ ] /* a work array of size n */ ) { Entry xk ; Entry *xp, *Lval ; Int k, deg, *ip, j, row, *Lpos, *Lilen, kstart, kend, *Lip, llen, lp, pos, npiv, n1, *Li ; /* ---------------------------------------------------------------------- */ if (Numeric->n_row != Numeric->n_col) return (0.) ; npiv = Numeric->npiv ; Lpos = Numeric->Lpos ; Lilen = Numeric->Lilen ; Lip = Numeric->Lip ; kstart = npiv ; n1 = Numeric->n1 ; #ifndef NDEBUG DEBUG4 (("Ltsolve start: ")) ; for (j = 0 ; j < Numeric->n_row ; j++) { DEBUG4 (("Ltsolve start "ID": ", j)) ; EDEBUG4 (X [j]) ; DEBUG4 ((" ")) ; } #endif /* ---------------------------------------------------------------------- */ /* non-singletons */ /* ---------------------------------------------------------------------- */ for (kend = npiv-1 ; kend >= n1 ; kend = kstart-1) { /* ------------------------------------------------------------------ */ /* find the start of this Lchain */ /* ------------------------------------------------------------------ */ /* for (kstart = kend ; kstart >= 0 && Lip [kstart] > 0 ; kstart--) ; */ kstart = kend ; while (kstart >= 0 && Lip [kstart] > 0) { kstart-- ; } /* the Lchain goes from kstart to kend */ /* ------------------------------------------------------------------ */ /* scan the whole chain to find the pattern of the last column of L */ /* ------------------------------------------------------------------ */ deg = 0 ; DEBUG4 (("start of chain for column of L ")) ; for (k = kstart ; k <= kend ; k++) { ASSERT (k >= 0 && k < npiv) ; /* -------------------------------------------------------------- */ /* make column k of L in Pattern [0..deg-1] */ /* -------------------------------------------------------------- */ /* remove pivot row */ pos = Lpos [k] ; if (pos != EMPTY) { DEBUG4 ((" k "ID" removing row "ID" at position "ID" ", k, Pattern [pos], pos)) ; ASSERT (k != kstart) ; ASSERT (deg > 0) ; ASSERT (pos >= 0 && pos < deg) ; ASSERT (Pattern [pos] == k) ; Pattern [pos] = Pattern [--deg] ; } /* concatenate the pattern */ lp = Lip [k] ; if (k == kstart) { lp = -lp ; } ASSERT (lp > 0) ; ip = (Int *) (Numeric->Memory + lp) ; llen = Lilen [k] ; for (j = 0 ; j < llen ; j++) { row = *ip++ ; DEBUG4 ((" row "ID" k "ID" ", row, k)) ; ASSERT (row > k) ; Pattern [deg++] = row ; } } /* Pattern [0..deg-1] is now the pattern of column kend */ /* ------------------------------------------------------------------ */ /* solve using this chain, in reverse order */ /* ------------------------------------------------------------------ */ DEBUG4 (("Unwinding Lchain ")) ; for (k = kend ; k >= kstart ; k--) { /* -------------------------------------------------------------- */ /* use column k of L */ /* -------------------------------------------------------------- */ ASSERT (k >= 0 && k < npiv) ; lp = Lip [k] ; if (k == kstart) { lp = -lp ; } ASSERT (lp > 0) ; llen = Lilen [k] ; xp = (Entry *) (Numeric->Memory + lp + UNITS (Int, llen)) ; xk = X [k] ; for (j = 0 ; j < deg ; j++) { DEBUG4 ((" row "ID" k "ID" value", Pattern [j], k)) ; EDEBUG4 (*xp) ; DEBUG4 ((" ")) ; #ifdef CONJUGATE_SOLVE /* xk -= X [Pattern [j]] * conjugate (*xp) ; */ MULT_SUB_CONJ (xk, X [Pattern [j]], *xp) ; #else /* xk -= X [Pattern [j]] * (*xp) ; */ MULT_SUB (xk, X [Pattern [j]], *xp) ; #endif xp++ ; } X [k] = xk ; /* -------------------------------------------------------------- */ /* construct column k-1 of L */ /* -------------------------------------------------------------- */ /* un-concatenate the pattern */ deg -= llen ; /* add pivot row */ pos = Lpos [k] ; if (pos != EMPTY) { DEBUG4 ((" k "ID" adding row "ID" at position "ID" ", k, k, pos)) ; ASSERT (k != kstart) ; ASSERT (pos >= 0 && pos <= deg) ; Pattern [deg++] = Pattern [pos] ; Pattern [pos] = k ; } } } /* ---------------------------------------------------------------------- */ /* singletons */ /* ---------------------------------------------------------------------- */ for (k = n1 - 1 ; k >= 0 ; k--) { DEBUG4 (("Singleton k "ID" ", k)) ; deg = Lilen [k] ; if (deg > 0) { xk = X [k] ; lp = Lip [k] ; Li = (Int *) (Numeric->Memory + lp) ; lp += UNITS (Int, deg) ; Lval = (Entry *) (Numeric->Memory + lp) ; for (j = 0 ; j < deg ; j++) { DEBUG4 ((" row "ID" k "ID" value", Li [j], k)) ; EDEBUG4 (Lval [j]) ; DEBUG4 ((" ")) ; #ifdef CONJUGATE_SOLVE /* xk -= X [Li [j]] * conjugate (Lval [j]) ; */ MULT_SUB_CONJ (xk, X [Li [j]], Lval [j]) ; #else /* xk -= X [Li [j]] * Lval [j] ; */ MULT_SUB (xk, X [Li [j]], Lval [j]) ; #endif } X [k] = xk ; } } #ifndef NDEBUG for (j = 0 ; j < Numeric->n_row ; j++) { DEBUG4 (("Ltsolve done "ID": ", j)) ; EDEBUG4 (X [j]) ; DEBUG4 ((" ")) ; } DEBUG4 (("Ltsolve done. ")) ; #endif return (MULTSUB_FLOPS * ((double) Numeric->lnz)) ; } |