matmath_c.txt

LM算法的实现并不难,这里给出了LM算法C语言实现

/*  matmath.c

    This is a roughly self-contained code module for matrix
    math, which started with the Numerical Recipes in C code
    and matrix representations.

    J. Watlington, 11/15/95

    Modified:
*/

#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include "matmath.h"

#define NR_END 1
#define FREE_ARG char*

/**********************************************************

     Vector Math Functions

*/

void vec_copy( m_elem *src, m_elem *dst, int num_elements )
{
  int  i;

  for( i = 1; i <= num_elements; i++ )
    dst[ i ] = src[ i ];
}

void vec_add( m_elem *a, m_elem *b, m_elem *c, int n )
{
  int i;
  m_elem  *a_ptr, *b_ptr, *c_ptr;

  a_ptr = a + 1;
  b_ptr = b + 1;
  c_ptr = c + 1;

  for( i = 1; i <= n; i++)
    *c_ptr++ = *a_ptr++ + *b_ptr++;
}

/* vec_sub()
   This function computes C = A - B, for vectors of size n  */

void vec_sub( m_elem *a, m_elem *b, m_elem *c, int n )
{
  int i;
  m_elem  *a_ptr, *b_ptr, *c_ptr;

  a_ptr = a + 1;
  b_ptr = b + 1;
  c_ptr = c + 1;

  for( i = 1; i <= n; i++)
    *c_ptr++ = *a_ptr++ - *b_ptr++;
}


/**********************************************************

  Matrix math functions

*/

void mat_add( m_elem **a, m_elem **b, m_elem **c, int m, int n )
{
  int i,j;
  m_elem  *a_ptr, *b_ptr, *c_ptr;

  for( j = 1; j <= m; j++)
    {
      a_ptr = &a[j][1];
      b_ptr = &b[j][1];
      c_ptr = &c[j][1];

      for( i = 1; i <= n; i++)
	*c_ptr++ = *a_ptr++ + *b_ptr++;
    }
}


/* mat_sub()
   This function computes C = A - B, for matrices of size m x n  */

void mat_sub( m_elem **a, m_elem **b, m_elem **c, int m, int n )
{
  int i,j;
  m_elem  *a_ptr, *b_ptr, *c_ptr;

  for( j = 1; j <= m; j++)
    {
      a_ptr = &a[j][1];
      b_ptr = &b[j][1];
      c_ptr = &c[j][1];

      for( i = 1; i <= n; i++)
	*c_ptr++ = *a_ptr++ - *b_ptr++;
    }
}

/*  mat_mult
    This function performs a matrix multiplication.
*/
void mat_mult( m_elem **a, m_elem **b, m_elem **c,
	      int a_rows, int a_cols, int b_cols )
{
  int i, j, k;
  m_elem  *a_ptr;
  m_elem  temp;

  for( i = 1; i <= a_rows; i++)
    {
      a_ptr = &a[i][0];
      for( j = 1; j <= b_cols; j++ )
	{
	  temp = 0.0;
	  for( k = 1; k <= a_cols; k++ )
	    temp = temp + (a_ptr[k] * b[k][j]); 
	  c[i][j] = temp;
	}
    }
}


/*  mat_mult_vector
    This function performs a matrix x vector multiplication.
*/
void mat_mult_vector( m_elem **a, m_elem *b, m_elem *c,
	      int a_rows, int a_cols )
{
  int i, j, k;
  m_elem  *a_ptr, *b_ptr;
  m_elem  temp;

  for( i = 1; i <= a_rows; i++)
    {
      a_ptr = &a[i][0];
      b_ptr = &b[1];
      temp = 0.0;

      for( k = 1; k <= a_cols; k++ )
	temp += a_ptr[ k ] * *b_ptr++;

      c[i] = temp;
    }
}


/*  mat_mult_transpose
    This function performs a matrix multiplication of A x transpose B.
*/
void mat_mult_transpose( m_elem **a, m_elem **b, m_elem **c,
	      int a_rows, int a_cols, int b_cols )
{
  int i, j, k;
  m_elem  *a_ptr, *b_ptr;
  m_elem  temp;

  for( i = 1; i <= a_rows; i++)
    {
      a_ptr = &a[i][0];
      for( j = 1; j <= b_cols; j++ )
	{
	  b_ptr = &b[j][1];

	  temp = (m_elem)0;

	  for( k = 1; k <= a_cols; k++ )
	    temp += a_ptr[ k ] * *b_ptr++;

	  c[i][j] = temp;
	}
    }
}

/*  mat_transpose_mult
    This function performs a matrix multiplication of transpose A x B.
    a_rows refers to the transposed A, is a_cols in actual A storage
    a_cols is same, is a_rows in actual A storage
*/
void mat_transpose_mult( m_elem **A, m_elem **B, m_elem **C,
	      int a_rows, int a_cols, int b_cols )
{
  int i, j, k;
  m_elem  temp;

  for( i = 1; i <= a_rows; i++)
    {
      for( j = 1; j <= b_cols; j++ )
	{
	  temp = 0.0;

	  for( k = 1; k <= a_cols; k++ )
	    temp += A[ k ][ i ] * B[ k ][ j ];

	  C[ i ][ j ] = temp;
	}
    }
}

void mat_copy( m_elem **src, m_elem **dst, int num_rows, int num_cols )
{
  int  i, j;

  for( i = 1; i <= num_rows; i++ )
    for( j = 1; j <= num_cols; j++ )
      dst[ i ][ j ] = src[ i ][ j ];
}


/* gaussj()
   This function performs gauss-jordan elimination to solve a set
   of linear equations, at the same time generating the inverse of
   the A matrix.

   (C) Copr. 1986-92 Numerical Recipes Software `2$m.1.9-153.
*/

#define SWAP(a,b) {temp=(a);(a)=(b);(b)=temp;}

void gaussj(m_elem **a, int n, m_elem **b, int m)
{
  int *indxc,*indxr,*ipiv;
  int i,icol,irow,j,k,l,ll;
  m_elem big,dum,pivinv,temp;

  indxc=ivector(1,n);
  indxr=ivector(1,n);
  ipiv=ivector(1,n);
  for (j=1;j<=n;j++) ipiv[j]=0;
  for (i=1;i<=n;i++) {
    big=0.0;
    for (j=1;j<=n;j++)
      if (ipiv[j] != 1)
	for (k=1;k<=n;k++) {
	  if (ipiv[k] == 0) {
	    if (fabs(a[j][k]) >= big) {
	      big=fabs(a[j][k]);
	      irow=j;
	      icol=k;
	    }
	  } else if (ipiv[k] > 1) nrerror("gaussj: Singular Matrix-1");
	}
    ++(ipiv[icol]);
    if (irow != icol) {
      for (l=1;l<=n;l++) SWAP(a[irow][l],a[icol][l])
	for (l=1;l<=m;l++) SWAP(b[irow][l],b[icol][l])
    }
    indxr[i]=irow;
    indxc[i]=icol;
    if (a[icol][icol] == 0.0) nrerror("gaussj: Singular Matrix-2");
    pivinv=1.0/a[icol][icol];
    a[icol][icol]=1.0;
    for (l=1;l<=n;l++) a[icol][l] *= pivinv;
    for (l=1;l<=m;l++) b[icol][l] *= pivinv;
    for (ll=1;ll<=n;ll++)
      if (ll != icol) {
	dum=a[ll][icol];
	a[ll][icol]=0.0;
	for (l=1;l<=n;l++) a[ll][l] -= a[icol][l]*dum;
	for (l=1;l<=m;l++) b[ll][l] -= b[icol][l]*dum;
      }
  }
  for (l=n;l>=1;l--) {
    if (indxr[l] != indxc[l])
      for (k=1;k<=n;k++)
	SWAP(a[k][indxr[l]],a[k][indxc[l]]);
  }

  free_ivector(ipiv,1,n);
  free_ivector(indxr,1,n);
  free_ivector(indxc,1,n);
}
#undef SWAP


/**********************************************************

  Quaternion math

  A quaternion is a four vector used to represent rotation in
  three-space.  The representation being used here is from
  Ali Azarbayejani.

  It is stored in components 0 through 3 of the vector.
*/

m_elem *quaternion( void )
{
  m_elem  *v;

  v = vector( 0, 3 );
  v[0] = (m_elem)1.0;  v[1] = (m_elem)0.0;
  v[2] = (m_elem)0.0;  v[3] = (m_elem)0.0;
}

void quaternion_update( m_elem *quat, m_elem wx,
		       m_elem wy, m_elem wz )
{
  int           i;
  m_elem  temp;
  m_elem  delta[QUATERNION_SIZE], new[QUATERNION_SIZE];

  /*  First, define a quaternion from the angular velocities  */

  temp = wx*wx + wy*wy + wz*wz;
  delta[0] = sqrt( 1 - (temp * 0.25) );
  temp = 1.0 / 2.0;
  delta[1] = wx * temp;
  delta[2] = wy * temp;
  delta[3] = wz * temp;

  /*  Now multiply it with the input quaternion, to update it. */

  new[0] = quat[0]*delta[0] - quat[1]*delta[1] - quat[2]*delta[2]
    - quat[3]*delta[3];
  new[1] = quat[1]*delta[0] + quat[0]*delta[1] - quat[3]*delta[2]
    + quat[2]*delta[3];
  new[2] = quat[2]*delta[0] + quat[3]*delta[1] + quat[0]*delta[2]
    - quat[1]*delta[3];
  new[3] = quat[3]*delta[0] - quat[2]*delta[1] + quat[1]*delta[2]
    + quat[0]*delta[3];

  /*  Finally, normalize the quaternion and copy it back  */

  temp = new[0]*new[0] + new[1]*new[1] + new[2]*new[2] + new[3]*new[3];
  if( temp < MIN_QUATERNION_MAGNITUDE )
    {
      quat[0] = 1.0;
      quat[1] = 0.0; quat[2] = 0.0; quat[3] = 0.0;
      return;
    }

  temp = 1.0 / (m_elem)sqrt( (double)temp );
  if( temp != 1.0 )
    {
      for( i = 0; i < QUATERNION_SIZE; i++ )
	quat[i] = new[i] * temp;
    }
  else
    for( i = 0; i < QUATERNION_SIZE; i++ )
      quat[i] = new[i];
}

/*  quaternion_to_rotation
    This function takes pointers to a quaternion input, and a rotation
    matrix for the results.  It calculates the 3D rotation matrix that
    is equivalent to the quaternion.
*/
void quaternion_to_rotation( m_elem *quat, m_elem **rot )
{
  m_elem  q01 = quat[0] * quat[1];
  m_elem  q02 = quat[0] * quat[2];
  m_elem  q03 = quat[0] * quat[3];
  m_elem  q11 = quat[1] * quat[1];
  m_elem  q12 = quat[1] * quat[2];
  m_elem  q13 = quat[1] * quat[3];
  m_elem  q22 = quat[2] * quat[2];
  m_elem  q23 = quat[2] * quat[3];
  m_elem  q33 = quat[3] * quat[3];