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fvn_sparse/UMFPACK/Source/umf_lsolve.c 4.12 KB
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422234dc3   daniau   git-svn-id: https... 
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  /* ========================================================================== */
  /* === UMF_lsolve =========================================================== */
  /* ========================================================================== */
  
  /* -------------------------------------------------------------------------- */
  /* 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 Lx = 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 UMF_lsolve
  (
      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, *Lip, llen, lp, newLchain,
  	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 ;
      n1 = Numeric->n1 ;
  
  #ifndef NDEBUG
      DEBUG4 (("Lsolve start:
  ")) ;
      for (j = 0 ; j < Numeric->n_row ; j++)
      {
  	DEBUG4 (("Lsolve start "ID": ", j)) ;
  	EDEBUG4 (X [j]) ;
  	DEBUG4 (("
  ")) ;
      }
  #endif
  
      /* ---------------------------------------------------------------------- */
      /* singletons */
      /* ---------------------------------------------------------------------- */
  
      for (k = 0 ; k < n1 ; k++)
      {
  	DEBUG4 (("Singleton k "ID"
  ", k)) ;
  	xk = X [k] ;
  	deg = Lilen [k] ;
  	if (deg > 0 && IS_NONZERO (xk))
  	{
  	    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 (("
  ")) ;
  		/* X [Li [j]] -= xk * Lval [j] ; */
  		MULT_SUB (X [Li [j]], xk, Lval [j]) ;
  	    }
  	}
      }
  
      /* ---------------------------------------------------------------------- */
      /* rest of L */
      /* ---------------------------------------------------------------------- */
  
      deg = 0 ;
  
      for (k = n1 ; k < npiv ; k++)
      {
  
  	/* ------------------------------------------------------------------ */
  	/* make column of L in Pattern [0..deg-1] */
  	/* ------------------------------------------------------------------ */
  
  	lp = Lip [k] ;
  	newLchain = (lp < 0) ;
  	if (newLchain)
  	{
  	    lp = -lp ;
  	    deg = 0 ;
  	    DEBUG4 (("start of chain for column of L
  ")) ;
  	}
  
  	/* remove pivot row */
  	pos = Lpos [k] ;
  	if (pos != EMPTY)
  	{
  	    DEBUG4 (("  k "ID" removing row "ID" at position "ID"
  ",
  	    k, Pattern [pos], pos)) ;
  	    ASSERT (!newLchain) ;
  	    ASSERT (deg > 0) ;
  	    ASSERT (pos >= 0 && pos < deg) ;
  	    ASSERT (Pattern [pos] == k) ;
  	    Pattern [pos] = Pattern [--deg] ;
  	}
  
  	/* concatenate the pattern */
  	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 ;
  	}
  
  	/* ------------------------------------------------------------------ */
  	/* use column k of L */
  	/* ------------------------------------------------------------------ */
  
  	xk = X [k] ;
  	if (IS_NONZERO (xk))
  	{
  	    xp = (Entry *) (Numeric->Memory + lp + UNITS (Int, llen)) ;
  	    for (j = 0 ; j < deg ; j++)
  	    {
  		DEBUG4 (("  row "ID"  k "ID" value", Pattern [j], k)) ;
  		EDEBUG4 (*xp) ;
  		DEBUG4 (("
  ")) ;
  		/* X [Pattern [j]] -= xk * (*xp) ; */
  		MULT_SUB (X [Pattern [j]], xk, *xp) ;
  		xp++ ;
  	    }
  	}
      }
  
  #ifndef NDEBUG
      for (j = 0 ; j < Numeric->n_row ; j++)
      {
  	DEBUG4 (("Lsolve done "ID": ", j)) ;
  	EDEBUG4 (X [j]) ;
  	DEBUG4 (("
  ")) ;
      }
      DEBUG4 (("Lsolve done.
  ")) ;
  #endif
  
      return (MULTSUB_FLOPS * ((double) Numeric->lnz)) ;
  }