linearSystemCSR.cpp

// Gmsh - Copyright (C) 1997-2010 C. Geuzaine, J.-F. Remacle
//
// See the LICENSE.txt file for license information. Please report all
// bugs and problems to <gmsh@geuz.org>.

#include <stdlib.h>
#include <stdio.h>
#include <string.h>
#include "GmshConfig.h"
#include "GmshMessage.h"
#include "linearSystemCSR.h"
#include "OS.h"

#define SWAP(a, b)  temp = (a); (a) = (b); (b) = temp;
#define SWAPI(a, b) tempi = (a); (a) = (b); (b) = tempi;

static void *CSRMalloc(size_t size)
{
  void *ptr;
  if (!size) return(NULL);
  ptr = malloc(size);
  return(ptr);
}

static void *CSRRealloc(void *ptr, size_t size)
{
  if (!size) return(NULL);
  ptr = realloc(ptr, size);
  return(ptr);
}

static void CSRList_Realloc(CSRList_T *liste, int n)
{
  char *temp;
  if (n <= 0) return;
  if (liste->array == NULL) {
    liste->nmax = ((n - 1) / liste->incr + 1) * liste->incr;
    liste->array = (char *)CSRMalloc(liste->nmax * liste->size);
  }
  else {
    if (n > liste->nmax) {
      liste->nmax = ((n - 1) / liste->incr + 1) * liste->incr;
      temp = (char *)CSRRealloc(liste->array, liste->nmax * liste->size);
      liste->array = temp;
    }
  }
}

static CSRList_T *CSRList_Create(int n, int incr, int size)
{
  CSRList_T *liste;

  if (n <= 0) n = 1 ;
  if (incr <= 0) incr = 1;

  liste = (CSRList_T *)CSRMalloc(sizeof(CSRList_T));

  liste->nmax    = 0;
  liste->incr    = incr;
  liste->size    = size;
  liste->n       = 0;
  liste->isorder = 0;
  liste->array   = NULL;

  CSRList_Realloc(liste, n);
  return(liste);
}

static void CSRList_Delete(CSRList_T *liste)
{
  if (liste != 0) {
    free(liste->array);
    free(liste);
  }
}

void CSRList_Add(CSRList_T *liste, void *data)
{
  liste->n++;
  CSRList_Realloc(liste, liste->n);
  liste->isorder = 0;
  memcpy(&liste->array[(liste->n - 1) * liste->size], data, liste->size);
}

int CSRList_Nbr(CSRList_T *liste)
{
  return(liste->n);
}

template<>
void linearSystemCSR<double>::allocate(int nbRows)
{
  if(_a) {
    CSRList_Delete(_a);
    CSRList_Delete(_ai);
    CSRList_Delete(_ptr);
    CSRList_Delete(_jptr);
    delete _x;
    delete _b;
    delete[] something;
  }

  if(nbRows == 0){
    _a = 0;
    _ai = 0;
    _ptr = 0;
    _jptr = 0;
    _b = 0;
    _x = 0;
    sorted = false;
    something = 0;
    return;
  }

  _a    = CSRList_Create(nbRows, nbRows, sizeof(double));
  _ai   = CSRList_Create(nbRows, nbRows, sizeof(INDEX_TYPE));
  _ptr  = CSRList_Create(nbRows, nbRows, sizeof(INDEX_TYPE));
  _jptr = CSRList_Create(nbRows + 1, nbRows, sizeof(INDEX_TYPE));

  something = new char[nbRows];

  for (int i = 0; i < nbRows; i++) something[i] = 0;

  _b = new std::vector<double>(nbRows);
  _x = new std::vector<double>(nbRows);
}

const int NSTACK = 50;
const unsigned int M_sort2 = 7;

static void free_ivector(int *v, long nl, long nh)
{
  // free an int vector allocated with ivector() 
  free((char*)(v + nl - 1));
}

static int *ivector(long nl, long nh)
{
  // allocate an int vector with subscript range v[nl..nh]
  int *v;
  v = (int *)malloc((size_t) ((nh - nl + 2) * sizeof(int)));
  if (!v) fprintf(stderr, "allocation failure in ivector()\n");
  return v - nl + 1;
}

static int cmpij(INDEX_TYPE ai, INDEX_TYPE aj, INDEX_TYPE bi, INDEX_TYPE bj)
{
  if(ai < bi) return -1;
  if(ai > bi) return 1;
  if(aj < bj) return -1;
  if(aj > bj) return 1;
  return 0;
}

template <class scalar>
static void _sort2_xkws(unsigned long n, double arr[], INDEX_TYPE ai[], INDEX_TYPE aj[])
{
  unsigned long i, ir = n, j, k, l = 1;
  int *istack, jstack = 0;
  INDEX_TYPE tempi;
  scalar a, temp;
  int b, c;

  istack = ivector(1, NSTACK);
  for (;;) {
    if (ir - l < M_sort2) {
      for (j = l + 1; j <= ir; j++) {
        a = arr[j -1];
        b = ai[j -1];
        c = aj[j -1];
        for (i = j - 1; i >= 1; i--) {
          if (cmpij(ai[i - 1], aj[i - 1], b, c) <= 0) break;
          arr[i + 1 - 1] = arr[i - 1];
          ai[i + 1 - 1] = ai[i - 1];
          aj[i + 1 - 1] = aj[i - 1];
        }
        arr[i + 1 - 1] = a;
        ai[i + 1 - 1] = b;
        aj[i + 1 - 1] = c;
      }
      if (!jstack) {
        free_ivector(istack, 1, NSTACK);
        return;
      }
      ir = istack[jstack];
      l = istack[jstack - 1];
      jstack -= 2;
    }
    else {
      k = (l + ir) >> 1;
      SWAP(arr[k - 1], arr[l + 1 - 1])
      SWAPI(ai[k - 1], ai[l + 1 - 1])
      SWAPI(aj[k - 1], aj[l + 1 - 1])
      if (cmpij(ai[l + 1 - 1], aj[l + 1 - 1], ai[ir - 1], aj[ir - 1]) > 0){
        SWAP(arr[l + 1 - 1], arr[ir - 1])
        SWAPI(ai[l + 1 - 1], ai[ir - 1])
        SWAPI(aj[l + 1 - 1], aj[ir - 1])
      }
      if (cmpij(ai[l - 1], aj[l - 1], ai[ir - 1], aj[ir - 1]) > 0){
        SWAP(arr[l - 1], arr[ir - 1])
        SWAPI(ai[l - 1], ai[ir - 1])
        SWAPI(aj[l - 1], aj[ir - 1])
      }
      if (cmpij(ai[l + 1 - 1], aj[l + 1 - 1], ai[l - 1], aj[l - 1]) > 0){
        SWAP(arr[l + 1 - 1], arr[l - 1])
        SWAPI(ai[l + 1 - 1], ai[l - 1])
        SWAPI(aj[l + 1 - 1], aj[l - 1])
      }
      i = l + 1;
      j = ir;
      a = arr[l - 1];
      b = ai[l - 1];
      c = aj[l - 1];
      for (;;) {
        do i++; while (cmpij(ai[i -1], aj[i -1], b, c) < 0);
        do j--; while (cmpij(ai[j -1], aj[j -1], b, c) > 0);
        if (j < i) break;
        SWAP(arr[i - 1], arr[j - 1])
        SWAPI(ai[i - 1], ai[j - 1])
        SWAPI(aj[i - 1], aj[j - 1])
      }
      arr[l - 1] = arr[j - 1];
      arr[j - 1] = a;
      ai[l - 1] = ai[j - 1];
      ai[j - 1] = b;
      aj[l - 1] = aj[j - 1];
      aj[j - 1] = c;
      jstack += 2;
      if (jstack > NSTACK) {
        Msg::Fatal("NSTACK too small while sorting the columns of the matrix");
        throw;
      }
      if (ir - i + 1 >= j - l) {
        istack[jstack] = ir;
        istack[jstack - 1] = i;
        ir = j - 1;
      }
      else {
        istack[jstack] = j - 1;
        istack[jstack - 1] = l;
        l = i;
      }
    }
  }
}

template <class scalar>
void sortColumns_(int NbLines,
                  int nnz,
                  INDEX_TYPE *ptr,
                  INDEX_TYPE *jptr,
                  INDEX_TYPE *ai,
                  scalar *a)
{
  // replace pointers by lines
  int *count = new int[NbLines];

  for(int i = 0; i < NbLines; i++){
    count[i] = 0;
    INDEX_TYPE _position = jptr[i];
    while(1){
      count[i]++;
      INDEX_TYPE _position_temp = _position;
      _position = ptr[_position];
      ptr[_position_temp] = i;
      if (_position == 0) break;
    }
  }
  _sort2_xkws<double>(nnz, a, ptr, ai);
  jptr[0] = 0;
  for(int i = 1; i <= NbLines; i++){
    jptr[i] = jptr[i - 1] + count[i - 1];
  }

  for(int i = 0; i < NbLines; i++){
    for (int j = jptr[i]; j < jptr[i + 1] - 1; j++){
      ptr[j] = j + 1;
    }
    ptr[jptr[i + 1]] = 0;
  }

  delete[] count;
}

#if defined(HAVE_GMM)

#include "gmm.h"

template<>
int linearSystemCSRGmm<double>::systemSolve()
{
  if (!sorted)
    sortColumns_(_b->size(),
                CSRList_Nbr(_a),
                (INDEX_TYPE *) _ptr->array,
                (INDEX_TYPE *) _jptr->array,
                (INDEX_TYPE *) _ai->array,
                (double*) _a->array);
  sorted = true;

  gmm::csr_matrix_ref<double*, INDEX_TYPE *, INDEX_TYPE *, 0>
    ref((double*)_a->array, (INDEX_TYPE *) _ai->array,
        (INDEX_TYPE *)_jptr->array, _b->size(), _b->size());
  gmm::csr_matrix<double, 0> M;
  M.init_with(ref);

  gmm::ildltt_precond<gmm::csr_matrix<double, 0> > P(M, 10, 1.e-10);
  gmm::iteration iter(_prec);
  iter.set_noisy(_noisy);
  if(_gmres) gmm::gmres(M, *_x, *_b, P, 100, iter);
  else gmm::cg(M, *_x, *_b, P, iter);
  return 1;
}

#endif

#if defined(HAVE_TAUCS)

extern "C" {
#include "taucs.h"
}

template<>
int linearSystemCSRTaucs<double>::systemSolve()
{
  if(!sorted){
    sortColumns_(_b->size(),
                CSRList_Nbr(_a),
                (INDEX_TYPE *) _ptr->array,
                (INDEX_TYPE *) _jptr->array,
                (INDEX_TYPE *) _ai->array,
                (double*) _a->array);
  }
  sorted = true;

  taucs_ccs_matrix myVeryCuteTaucsMatrix;
  myVeryCuteTaucsMatrix.n = myVeryCuteTaucsMatrix.m = _b->size();
  //myVeryCuteTaucsMatrix.rowind = (INDEX_TYPE*)_ptr->array;
  //myVeryCuteTaucsMatrix.colptr = (INDEX_TYPE*)_ai->array;
  myVeryCuteTaucsMatrix.rowind = (INDEX_TYPE*)_ai->array;
  myVeryCuteTaucsMatrix.colptr = (INDEX_TYPE*)_jptr->array;
  myVeryCuteTaucsMatrix.values.d = (double*)_a->array;
  myVeryCuteTaucsMatrix.flags = TAUCS_SYMMETRIC | TAUCS_LOWER | TAUCS_DOUBLE;

  char* options[] = { "taucs.factor.LLT=true", NULL };
  double t1 = Cpu();
  int result = taucs_linsolve(&myVeryCuteTaucsMatrix,
                              NULL,
                              1,
                              &(*_x)[0],
                              &(*_b)[0],
                              options,
                              NULL);
  double t2 = Cpu();
  Msg::Debug("TAUCS has solved %d unknowns in %8.3f seconds", _b->size(), t2 - t1);
  if (result != TAUCS_SUCCESS){
    Msg::Error("Taucs Was Not Successfull %d", result);
  }
  return 1;
}

#endif