Ransac.h

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#ifndef Ransac_h
#define Ransac_h

#include <math.h>

namespace Isis {
  //functions for solving the normal equations
  int choleski_solve(double *a, double *b, int nsize, int flag);  //solves the normal
  int inverse (double *a, int nsize);          //inverses ata (only to be used after ata has been choleski decomposed by choleski_sovle)
  int isymp(int row, int col);  //used for memory optimized symetric matricies, returns the single dimensional array location equivalent to the 2D location in the symetric matrix

  int indeces_from_set(int *indeces,int set, int set_size,int n);
  int binomial_coeficient(int n, int k);

  inline int isymp(int row, int col)
  {
    /* returns the index position of ellement [i][j] in the memory optimized symetric matrix a
       row -> row in square symetric matrix
       col -> column in square symetric matrix
     */
    int k;
    ++row;
    ++col;
    if(row < col)  k= row + col *(col -1)/2;
    else      k= col + row * (row - 1)/2;
    --k;
    return k;

  }

  inline int binomial_coeficient(int n, int k)
  {
    if( k > n)
      return 0;

    if( n < 1)
      return 0;

    int i,j,bc;
    bc=1;
    j=k;

    for(i=k-1;i>0;i--)
    {
      j *= i;
    }


    for(i=n-k+1;i<=n;i++)
      bc *=i;

    bc/=j;

    return bc;
  }


  /*  given a desired set size, and the number of items in the population this function returns the indeces
      of set number set.  For example:

      set_size = 3  n=5

      Set  Index0  Index1  Index2
      1  0  1  2
      2  0  1  3
      3  0  1  4
      4  0  1  5
      5  0  2  3
      6  0  2  4
      7  0  2  5
      8  0  3  4
      9  0  3  5
      so indeces_from_set(  , 5, 3, 6) would return 0, 2, 3

      set    -> the number of the set starting from 1
      set_size-> how many are in each set
      n    -> the population size
      indeces <-  the set_size indeces for set number set

      return 1 if successfuly, otherwise -1

   */
  inline int indeces_from_set(int *indeces,int set, int set_size,int n)
  {
    //frist set_size must not be greater than n
    if( set_size > n)
      return -1;

    //set must be >= 0
    if( set < 0)
      return -1;

    //set must also be less than or equal to the number of possible sets
    if( set > binomial_coeficient(n, set_size) )
      return -1;

    int i,j,k;

    for( i =0,j=0;i<set_size-1;i++,j=indeces[i-1]+1)
    {
      k = binomial_coeficient( n - j - 1, set_size - i - 1);
      while( set > k)
      {
        j++;
        set -= k;
        k = binomial_coeficient( n - j - 1, set_size - i - 1);
      }
      indeces[i] = j;
    }

    indeces[i] = j+set-1;

    return 1;
  }


  int decompose (double *, int);
  int foresub (double *,double *, int);
  int backsub (double *,double *, int);

#define SOLVED 1
#define NOT_SOLVABLE 0
#define NO_ERRORS -1


  inline int choleski_solve (double *a, double *b, int nsize, int flag)
  {
    /* solves the set of linear equations square_matrix(a)delta = b
       a   <-> positive definite symetric matrix a becomes L of the LLt choleski decomposition or the inverse of a (a symetric matrix still in memory optimized mode)
       b   <-> array of doubles of size nsize, the constant part of the system of linear equations
       nsize -> number of unkowns, also lenght of b, also square(a) is nsize x nsize
       flag  -> type of solutions sought: 1 decomposition only, 2 decomposition and solve, 3 decompose solve and inverse a
     */

    if (flag < 1 && flag > 3)
      return NOT_SOLVABLE;

    /*************** STEP 1:  DECOMPOSE THE A MATRIX ***************/
    if (! decompose (a, nsize)) return NOT_SOLVABLE;

    if (flag == 1) return SOLVED;

    /*************** STEP 2:  FORWARD SUBSTITUTION *****************/
    if (! foresub (a, b, nsize)) return NOT_SOLVABLE;


    /*************** STEP 2:  BACKWARD SUBSTITUTION ****************/
    if (! backsub (a, b, nsize)) return NOT_SOLVABLE;

    if (flag == 2) return SOLVED;

    /*************** STEP 4:  INVERSE THE A MATRIX *****************/
    inverse (a, nsize);
    return SOLVED;
  }

  /*******************************************************************
    FUNCTION DECOMPOSE
   *******************************************************************/
  inline int decompose (double *a, int nsize)
  {
    /* decomposes the memory optimized symetric matirx a into LLt (Choleski decomposition)
       a <-> positive definite symetric matrix a becomes L of the LLt choleski decomposition
       n  -> size of the square matrix a represents or number of unknowns
     */
    double sum;
    double *ap1 = a - 1;
    double *ap2;
    double *ap3;
    double *ap4;
    double *ap5;
    double *ap6 = a;
    double *ap7;
    int i, j, k, m, n = 2;

    ap7 = a;
    for (k = 0; k < nsize; k++)
    {
      ap2 = a;
      ap3 = ap7 + 1;
      ap4 = a -1;
      m = 2;
      for (i = 0; i < k; i++)
      {
        sum = 0.0;
        ap5 = ap1 + 1;
        ap4++;
        for (j = 0; j < i; j++)
        {
          sum += *ap4++ * *ap5++;
        }
        if (*ap2 == 0.0)
          return NOT_SOLVABLE;
        *ap3 = (*ap3 - sum) / *ap2;ap3++;
        ap2 += m++;
      }
      sum = 0.0;
      ap1++;
      for (j = 0; j < k; j++)
      {
        sum += *ap1 * *ap1;ap1++;
      }
      /*if ((*ap6 - sum) <= 0.0)
        return (errcode (06));
       *ap6  = sqrt(*ap6 - sum);*/


      //if ((*ap6 - sum) <= 1e-20)
      if ((*ap6 - sum) <= 0)
        *ap6 = sqrt(-(*ap6 - sum));
      else
        *ap6  = sqrt(*ap6 - sum);


      ap7  = ap6;
      ap6 += n++;
    }
    return SOLVED;
  }

  /*******************************************************************
    FUNCTION FORESUB
   *******************************************************************/
  inline int foresub (double *a,double *b,int nsize)
  {
    int i, j;
    double sum;
    double *ap1 = a;
    double *bp1 = b;
    double *bp2;

    if (*ap1 == 0.0)
      return NOT_SOLVABLE;
    *bp1++ /= *ap1++;
    for (i = 1; i < nsize; i++)
    {
      sum = 0.0;
      for (j = 0, bp2 = b; j < i; j++)
      {
        sum += *ap1++ * *bp2++;
      }
      if (*ap1 == 0.0)
        return NOT_SOLVABLE;
      *bp1 = (*bp1 - sum) / *ap1;bp1++;ap1++;
    }
    return SOLVED;
  }

  /*******************************************************************
    FUNCTION BACKSUB
   *******************************************************************/
  inline int backsub (double *a,double *b,int nsize)
    //double *a,*b;
    //int nsize;
  {
    int i,j;
    int k = nsize - 1;
    int m = nsize;
    int n;
    double sum;
    double *ap1 = a + (k + k * (k + 1) / 2);
    double *ap2 = ap1 - 1;
    double *ap3;
    double *bp1 = b + k;
    double *bp2 = bp1;
    double *bp3;

    if (*ap1 == 0.0)
      return NOT_SOLVABLE;
    *bp1 = *bp1 / *ap1;bp1--;
    for (i = k - 1; i >= 0; i--)
    {
      sum = 0.0;
      n = nsize - 1;
      for (j = nsize - 1, ap3 = ap2--, bp3 = bp2; j >= i + 1; j--)
      {
        sum += *ap3 * *bp3--;
        ap3 -= n--;
      }
      ap1 -= m--;
      if (*ap1 == 0.0)
        return NOT_SOLVABLE;
      *bp1 = (*bp1 - sum) / *ap1;bp1--;
    }
    return SOLVED;
  }

  /*******************************************************************
    FUNCTION INVERSE
   *******************************************************************/
  inline int inverse (double *a, int nsize)
    //double *a;
    //int nsize;
  {
    int i, j, k, m, n;
    double sum;
    double *ap1 = a;
    double *ap2;
    double *ap3;
    double *ap4;
    double *ap5;

    /* FIRST INVERSE ALL DIAGONAL ELEMENTS */
    m = 2;
    while (ap1 < (a + (nsize * (nsize + 1)/2)))
    {
      *ap1  = 1. / *ap1;
      ap1 += m++;
    }

    /* DO FIRST SET OF MANIPULATIONS */
    ap5 = a + 1;
    for (i = 1; i < nsize; i++)
    {
      ap4 = ap5 - 1;
      m = i + 1;
      n = i;
      for (j = m; j <= nsize; j++)
      {
        ap1 = ap5 - 1;
        ap2 = ap3 = ap4 + i;
        sum = 0.0;
        for (k = i; k <= n;)
        {
          sum += *ap1 * *ap2++;
          ap1 += k++;
        }
        ap4 += j;
        *ap3 = -(*ap4) * sum;
        n = j;
      }
      ap5 += m;
    }

    /* DO SECOND SET OF MANIPULATIONS */
    n = 0;
    ap1 = ap2 = ap3 = ap4 = a;
    for (i = 0; i < nsize;)
    {
      ap5 = ap4;
      m = 0;
      for (j = i; j < nsize;)
      {
        ap5 += j;
        ap1 = ap3 = ap5 + i + n;
        ap2 = ap5 + m++;
        sum = 0.0;
        for (k = j; k < nsize;)
        {
          sum += *ap1 * *ap2;
          ap1 += ++k;
          ap2 += k;
        }
        *ap3 = sum;
        j++;
      }
      ap4 += ++i;
      n--;
    }
    return SOLVED;
  }
}

#endif