csparse_helper.cpp

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// HOG-Man - Hierarchical Optimization for Pose Graphs on Manifolds
// Copyright (C) 2010 G. Grisetti, R. Kümmerle, C. Stachniss
// 
// HOG-Man is free software: you can redistribute it and/or modify
// it under the terms of the GNU Lesser General Public License as published
// by the Free Software Foundation, either version 3 of the License, or
// (at your option) any later version.
// 
// HOG-Man is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
// GNU Lesser General Public License for more details.
// 
// You should have received a copy of the GNU Lesser General Public License
// along with this program.  If not, see <http://www.gnu.org/licenses/>.

#include "csparse_helper.h"

#include <cassert>

namespace AISNavigation {

int cs_cholsolsymb(const cs *A, double *b, const css* S, double* x, int* work)
{
  csn *N ;
  int n, ok ;
  if (!CS_CSC (A) || !b || ! S || !x) {
    fprintf(stderr, "%s: No valid input!\n", __PRETTY_FUNCTION__);
    assert(0); // get a backtrace in debug mode
    return (0) ;     /* check inputs */
  }
  n = A->n ;
  N = cs_chol_workspace (A, S, work, x) ;                    /* numeric Cholesky factorization */
  if (!N) {
    fprintf(stderr, "%s: cholesky failed!\n", __PRETTY_FUNCTION__);
    /*assert(0);*/
  }
  ok = (N != NULL) ;
  if (ok)
  {
    cs_ipvec (S->pinv, b, x, n) ;   /* x = P*b */
    cs_lsolve (N->L, x) ;           /* x = L\x */
    cs_ltsolve (N->L, x) ;          /* x = L'\x */
    cs_pvec (S->pinv, x, b, n) ;    /* b = P'*x */
  }
  cs_nfree (N) ;
  return (ok) ;
}

int cs_cholsolinvblocksymb(const cs *A, double **block, int r1, int c1, int r2,int c2, double* y, const css* S, double* x, double* b, double* temp, int* work)
{
  csn *N ;
  int n, ok, i, j ;
  if (!CS_CSC (A) || !block || !y || !x || !b || !temp) return (0) ;     /* check inputs */
  n = A->n ;
  if(r2<=r1||c2<=c1) return (0);
  if(c1<0 || c2>n)
    return 0;
  if(r1<0 || r2>n)
    return 0;

  N = cs_chol_workspace (A, S, work, x) ;                    /* numeric Cholesky factorization */
  ok = (N != NULL) ;
  if (ok)
  {
    // solve the system
    cs_ipvec (S->pinv, y, x, n) ;   /* x = P*y */
    cs_lsolve (N->L, x) ;           /* x = L\x */
    cs_ltsolve (N->L, x) ;          /* x = L'\x */
    cs_pvec (S->pinv, x, y, n) ;    /* b = P'*x */
    // solve the inverse

    for (i=0; i<n; i++){
      b[i]=0.;
    }
    for (i=c1; i<c2; i++){
      b[i]=1.;

      cs_ipvec (S->pinv, b, x, n) ;   /* x = P*b */
      cs_lsolve (N->L, x) ;           /* x = L\x */
      cs_ltsolve (N->L, x) ;          /* x = L'\x */
      cs_pvec (S->pinv, x, temp, n) ;    /* b = P'*x */
      for (j=r1; j<r2; j++){
        block[j-r1][i-c1]=temp[j];
      }
      b[i]=0.;
    }
  } 
  cs_nfree (N) ;
  return (ok) ;
}

/* L = chol (A, [pinv parent cp]), pinv is optional */
csn* cs_chol_workspace (const cs *A, const css *S, int* cin, double* xin)
{
    double d, lki, *Lx, *x, *Cx ;
    int top, i, p, k, n, *Li, *Lp, *cp, *pinv, *s, *c, *parent, *Cp, *Ci ;
    cs *L, *C, *E ;
    csn *N ;
    if (!CS_CSC (A) || !S || !S->cp || !S->parent) return (NULL) ;
    n = A->n ;
    N = (csn*) cs_calloc (1, sizeof (csn)) ;       /* allocate result */
    c = cin ;     /* get int workspace */
    x = xin ;    /* get double workspace */
    cp = S->cp ; pinv = S->pinv ; parent = S->parent ;
    C = pinv ? cs_symperm (A, pinv, 1) : ((cs *) A) ;
    E = pinv ? C : NULL ;           /* E is alias for A, or a copy E=A(p,p) */
    if (!N || !c || !x || !C) return (cs_ndone (N, E, NULL, NULL, 0)) ;
    s = c + n ;
    Cp = C->p ; Ci = C->i ; Cx = C->x ;
    N->L = L = cs_spalloc (n, n, cp [n], 1, 0) ;    /* allocate result */
    if (!L) return (cs_ndone (N, E, NULL, NULL, 0)) ;
    Lp = L->p ; Li = L->i ; Lx = L->x ;
    for (k = 0 ; k < n ; k++) Lp [k] = c [k] = cp [k] ;
    for (k = 0 ; k < n ; k++)       /* compute L(k,:) for L*L' = C */
    {
        /* --- Nonzero pattern of L(k,:) ------------------------------------ */
        top = cs_ereach (C, k, parent, s, c) ;      /* find pattern of L(k,:) */
        x [k] = 0 ;                                 /* x (0:k) is now zero */
        for (p = Cp [k] ; p < Cp [k+1] ; p++)       /* x = full(triu(C(:,k))) */
        {
            if (Ci [p] <= k) x [Ci [p]] = Cx [p] ;
        }
        d = x [k] ;                     /* d = C(k,k) */
        x [k] = 0 ;                     /* clear x for k+1st iteration */
        /* --- Triangular solve --------------------------------------------- */
        for ( ; top < n ; top++)    /* solve L(0:k-1,0:k-1) * x = C(:,k) */
        {
            i = s [top] ;               /* s [top..n-1] is pattern of L(k,:) */
            lki = x [i] / Lx [Lp [i]] ; /* L(k,i) = x (i) / L(i,i) */
            x [i] = 0 ;                 /* clear x for k+1st iteration */
            for (p = Lp [i] + 1 ; p < c [i] ; p++)
            {
                x [Li [p]] -= Lx [p] * lki ;
            }
            d -= lki * lki ;            /* d = d - L(k,i)*L(k,i) */
            p = c [i]++ ;
            Li [p] = k ;                /* store L(k,i) in column i */
            Lx [p] = lki ;
        }
        /* --- Compute L(k,k) ----------------------------------------------- */
        if (d <= 0) return (cs_ndone (N, E, NULL, NULL, 0)) ; /* not pos def */
        p = c [k]++ ;
        Li [p] = k ;                /* store L(k,k) = sqrt (d) in column k */
        Lx [p] = sqrt (d) ;
    }
    Lp [n] = cp [n] ;               /* finalize L */
    return (cs_ndone (N, E, NULL, NULL, 1)) ; /* success: free E,s,x; return N */
}

} // end namespace