matrix.cpp

opencv实现的人体运动跟踪源码

                s[kk-1]=-s[kk-1];
              }
            if (n>=kk+1)
              { for (j=kk+1; j<=n; j++)
                  { if ((kk<=k)&&(s[kk-1]!=0.0))
                      { d=0.0;
                        for (i=kk; i<=m; i++)
                          { ix=(i-1)*n+kk-1;
                            iy=(i-1)*n+j-1;
                            d=d+a[ix]*a[iy];
                          }
                        d=-d/a[(kk-1)*n+kk-1];
                        for (i=kk; i<=m; i++)
                          { ix=(i-1)*n+j-1;
                            iy=(i-1)*n+kk-1;
                            a[ix]=a[ix]+d*a[iy];
                          }
                      }
                    e[j-1]=a[(kk-1)*n+j-1];
                  }
              }
            if (kk<=k)
              { for (i=kk; i<=m; i++)
                  { ix=(i-1)*m+kk-1; iy=(i-1)*n+kk-1;
                    u[ix]=a[iy];
                  }
              }
            if (kk<=l)
              { d=0.0;
                for (i=kk+1; i<=n; i++)
                  d=d+e[i-1]*e[i-1];
                e[kk-1]=sqrt(d);
                if (e[kk-1]!=0.0)
                  { if (e[kk]!=0.0)
                      { e[kk-1]=fabs(e[kk-1]);
                        if (e[kk]<0.0) e[kk-1]=-e[kk-1];
                      }
                    for (i=kk+1; i<=n; i++)
                      e[i-1]=e[i-1]/e[kk-1];
                    e[kk]=1.0+e[kk];
                  }
                e[kk-1]=-e[kk-1];
                if ((kk+1<=m)&&(e[kk-1]!=0.0))
                  { for (i=kk+1; i<=m; i++) w[i-1]=0.0;
                    for (j=kk+1; j<=n; j++)
                      for (i=kk+1; i<=m; i++)
                        w[i-1]=w[i-1]+e[j-1]*a[(i-1)*n+j-1];
                    for (j=kk+1; j<=n; j++)
                      for (i=kk+1; i<=m; i++)
                        { ix=(i-1)*n+j-1;
                          a[ix]=a[ix]-w[i-1]*e[j-1]/e[kk];
                        }
                  }
                for (i=kk+1; i<=n; i++)
                  v[(i-1)*n+kk-1]=e[i-1];
              }
          }
      }
    mm=n;
    if (m+1<n) mm=m+1;
    if (k<n) s[k]=a[k*n+k];
    if (m<mm) s[mm-1]=0.0;
    if (l+1<mm) e[l]=a[l*n+mm-1];
    e[mm-1]=0.0;
    nn=m;
    if (m>n) nn=n;
    if (nn>=k+1)
      { for (j=k+1; j<=nn; j++)
          { for (i=1; i<=m; i++)
              u[(i-1)*m+j-1]=0.0;
            u[(j-1)*m+j-1]=1.0;
          }
      }
    if (k>=1)
      { for (ll=1; ll<=k; ll++)
          { kk=k-ll+1; iz=(kk-1)*m+kk-1;
            if (s[kk-1]!=0.0)
              { if (nn>=kk+1)
                  for (j=kk+1; j<=nn; j++)
                    { d=0.0;
                      for (i=kk; i<=m; i++)
                        { ix=(i-1)*m+kk-1;
                          iy=(i-1)*m+j-1;
                          d=d+u[ix]*u[iy]/u[iz];
                        }
                      d=-d;
                      for (i=kk; i<=m; i++)
                        { ix=(i-1)*m+j-1;
                          iy=(i-1)*m+kk-1;
                          u[ix]=u[ix]+d*u[iy];
                        }
                    }
                  for (i=kk; i<=m; i++)
                    { ix=(i-1)*m+kk-1; u[ix]=-u[ix];}
                  u[iz]=1.0+u[iz];
                  if (kk-1>=1)
                    for (i=1; i<=kk-1; i++)
                      u[(i-1)*m+kk-1]=0.0;
              }
            else
              { for (i=1; i<=m; i++)
                  u[(i-1)*m+kk-1]=0.0;
                u[(kk-1)*m+kk-1]=1.0;
              }
          }
      }
    for (ll=1; ll<=n; ll++)
      { kk=n-ll+1; iz=kk*n+kk-1;
        if ((kk<=l)&&(e[kk-1]!=0.0))
          { for (j=kk+1; j<=n; j++)
              { d=0.0;
                for (i=kk+1; i<=n; i++)
                  { ix=(i-1)*n+kk-1; iy=(i-1)*n+j-1;
                    d=d+v[ix]*v[iy]/v[iz];
                  }
                d=-d;
                for (i=kk+1; i<=n; i++)
                  { ix=(i-1)*n+j-1; iy=(i-1)*n+kk-1;
                    v[ix]=v[ix]+d*v[iy];
                  }
              }
          }
        for (i=1; i<=n; i++)
          v[(i-1)*n+kk-1]=0.0;
        v[iz-n]=1.0;
      }
    for (i=1; i<=m; i++)
    for (j=1; j<=n; j++)
      a[(i-1)*n+j-1]=0.0;
    m1=mm; it=60;
    while (1==1)
      { if (mm==0)
          { ppp(a,e,s,v,m,n);
            delete [] s; 
			delete [] e; 
			delete [] w;
			return true;
          }
        if (it==0)
          { ppp(a,e,s,v,m,n);
            delete [] s; 
			delete [] e; 
			delete [] w;
			return false;
          }
        kk=mm-1;
	while ((kk!=0)&&(fabs(e[kk-1])!=0.0))
          { d=fabs(s[kk-1])+fabs(s[kk]);
            dd=fabs(e[kk-1]);
            if (dd>eps*d) kk=kk-1;
            else e[kk-1]=0.0;
          }
        if (kk==mm-1)
          { kk=kk+1;
            if (s[kk-1]<0.0)
              { s[kk-1]=-s[kk-1];
                for (i=1; i<=n; i++)
                  { ix=(i-1)*n+kk-1; v[ix]=-v[ix];}
              }
            while ((kk!=m1)&&(s[kk-1]<s[kk]))
              { d=s[kk-1]; s[kk-1]=s[kk]; s[kk]=d;
                if (kk<n)
                  for (i=1; i<=n; i++)
                    { ix=(i-1)*n+kk-1; iy=(i-1)*n+kk;
                      d=v[ix]; v[ix]=v[iy]; v[iy]=d;
                    }
                if (kk<m)
                  for (i=1; i<=m; i++)
                    { ix=(i-1)*m+kk-1; iy=(i-1)*m+kk;
                      d=u[ix]; u[ix]=u[iy]; u[iy]=d;
                    }
                kk=kk+1;
              }
            it=60;
            mm=mm-1;
          }
        else
          { ks=mm;
            while ((ks>kk)&&(fabs(s[ks-1])!=0.0))
              { d=0.0;
                if (ks!=mm) d=d+fabs(e[ks-1]);
                if (ks!=kk+1) d=d+fabs(e[ks-2]);
                dd=fabs(s[ks-1]);
                if (dd>eps*d) ks=ks-1;
                else s[ks-1]=0.0;
              }
            if (ks==kk)
              { kk=kk+1;
                d=fabs(s[mm-1]);
                t=fabs(s[mm-2]);
                if (t>d) d=t;
                t=fabs(e[mm-2]);
                if (t>d) d=t;
                t=fabs(s[kk-1]);
                if (t>d) d=t;
                t=fabs(e[kk-1]);
                if (t>d) d=t;
                sm=s[mm-1]/d; sm1=s[mm-2]/d;
                em1=e[mm-2]/d;
                sk=s[kk-1]/d; ek=e[kk-1]/d;
                b=((sm1+sm)*(sm1-sm)+em1*em1)/2.0;
                c=sm*em1; c=c*c; shh=0.0;
                if ((b!=0.0)||(c!=0.0))
                  { shh=sqrt(b*b+c);
                    if (b<0.0) shh=-shh;
                    shh=c/(b+shh);
                  }
                fg[0]=(sk+sm)*(sk-sm)-shh;
                fg[1]=sk*ek;
                for (i=kk; i<=mm-1; i++)
                  { sss(fg,cs);
                    if (i!=kk) e[i-2]=fg[0];
                    fg[0]=cs[0]*s[i-1]+cs[1]*e[i-1];
                    e[i-1]=cs[0]*e[i-1]-cs[1]*s[i-1];
                    fg[1]=cs[1]*s[i];
                    s[i]=cs[0]*s[i];
                    if ((cs[0]!=1.0)||(cs[1]!=0.0))
                      for (j=1; j<=n; j++)
                        { ix=(j-1)*n+i-1;
                          iy=(j-1)*n+i;
                          d=cs[0]*v[ix]+cs[1]*v[iy];
                          v[iy]=-cs[1]*v[ix]+cs[0]*v[iy];
                          v[ix]=d;
                        }
                    sss(fg,cs);
                    s[i-1]=fg[0];
                    fg[0]=cs[0]*e[i-1]+cs[1]*s[i];
                    s[i]=-cs[1]*e[i-1]+cs[0]*s[i];
                    fg[1]=cs[1]*e[i];
                    e[i]=cs[0]*e[i];
                    if (i<m)
                      if ((cs[0]!=1.0)||(cs[1]!=0.0))
                        for (j=1; j<=m; j++)
                          { ix=(j-1)*m+i-1;
                            iy=(j-1)*m+i;
                            d=cs[0]*u[ix]+cs[1]*u[iy];
                            u[iy]=-cs[1]*u[ix]+cs[0]*u[iy];
                            u[ix]=d;
                          }
                  }
                e[mm-2]=fg[0];
                it=it-1;
              }
            else
              { if (ks==mm)
                  { kk=kk+1;
                    fg[1]=e[mm-2]; e[mm-2]=0.0;
                    for (ll=kk; ll<=mm-1; ll++)
                      { i=mm+kk-ll-1;
                        fg[0]=s[i-1];
                        sss(fg,cs);
                        s[i-1]=fg[0];
                        if (i!=kk)
                          { fg[1]=-cs[1]*e[i-2];
                            e[i-2]=cs[0]*e[i-2];
                          }
                        if ((cs[0]!=1.0)||(cs[1]!=0.0))
                          for (j=1; j<=n; j++)
                            { ix=(j-1)*n+i-1;
                              iy=(j-1)*n+mm-1;
                              d=cs[0]*v[ix]+cs[1]*v[iy];
                              v[iy]=-cs[1]*v[ix]+cs[0]*v[iy];
                              v[ix]=d;
                            }
                      }
                  }
                else
                  { kk=ks+1;
                    fg[1]=e[kk-2];
                    e[kk-2]=0.0;
                    for (i=kk; i<=mm; i++)
                      { fg[0]=s[i-1];
                        sss(fg,cs);
                        s[i-1]=fg[0];
                        fg[1]=-cs[1]*e[i-1];
                        e[i-1]=cs[0]*e[i-1];
                        if ((cs[0]!=1.0)||(cs[1]!=0.0))
                          for (j=1; j<=m; j++)
                            { ix=(j-1)*m+i-1;
                              iy=(j-1)*m+kk-2;
                              d=cs[0]*u[ix]+cs[1]*u[iy];
                              u[iy]=-cs[1]*u[ix]+cs[0]*u[iy];
                              u[ix]=d;
                            }
                      }
                  }
              }
          }
      }
    return true;

}

void CMatrix::ppp(double *a, double *e, double *s, double *v,int m, int n)
{ 
	int i,j,p,q;
    double d;
    if (m>=n) i=n;
    else i=m;
    for (j=1; j<=i-1; j++)
      { a[(j-1)*n+j-1]=s[j-1];
        a[(j-1)*n+j]=e[j-1];
      }
    a[(i-1)*n+i-1]=s[i-1];
    if (m<n) a[(i-1)*n+i]=e[i-1];
    for (i=1; i<=n-1; i++)
    for (j=i+1; j<=n; j++)
      { p=(i-1)*n+j-1; q=(j-1)*n+i-1;
        d=v[p]; v[p]=v[q]; v[q]=d;
      }
    return;
}

void CMatrix::sss(double fg[2], double cs[2])
{ 
	double r,d;
    if ((fabs(fg[0])+fabs(fg[1]))==0.0)
      { cs[0]=1.0; cs[1]=0.0; d=0.0;}
    else 
      { d=sqrt(fg[0]*fg[0]+fg[1]*fg[1]);
        if (fabs(fg[0])>fabs(fg[1]))
          { d=fabs(d);
            if (fg[0]<0.0) d=-d;
          }
        if (fabs(fg[1])>=fabs(fg[0]))
          { d=fabs(d);
            if (fg[1]<0.0) d=-d;
          }
        cs[0]=fg[0]/d; cs[1]=fg[1]/d;
      }
    r=1.0;
    if (fabs(fg[0])>fabs(fg[1])) r=cs[1];
    else
      if (cs[0]!=0.0) r=1.0/cs[0];
    fg[0]=d; fg[1]=r;
    return;
}
        
BOOL CMatrix::InvertNew(double *src, int matrSize, double *des)
{
  	int n = matrSize;
	double *a = new double[n * n];
	memcpy(a, src, sizeof(double) * n * n);

	int i,j,k,m;
    double w,g,*b;
    b=new double[n];

    for (k=0; k<=n-1; k++)
      { w=a[0];

        if (fabs(w)+1.0==1.0)
        { delete [] b; 
		    return false;
		}
        m=n-k-1;
        for (i=1; i<=n-1; i++)
          { g=a[i*n]; b[i]=g/w;
            if (i<=m) b[i]=-b[i];
            for (j=1; j<=i; j++)
              a[(i-1)*n+j-1]=a[i*n+j]+g*b[j];
          }
        a[n*n-1]=1.0/w;
        for (i=1; i<=n-1; i++)
          a[(n-1)*n+i-1]=b[i];
      }
    for (i=0; i<=n-2; i++)
    for (j=i+1; j<=n-1; j++)
      a[i*n+j]=a[j*n+i];
    
	memcpy(des, a, sizeof(double) * n * n);

	delete [] b;
	delete [] a;

	return true;
}  
//---------------------均值向量---------------------------------------------
BOOL CMatrix::Average(double *src, int height ,int width,double *dest){
	if( src == NULL ||dest == NULL || width <= 0 || height <= 0)
		return false;
	for(int i = 0 ;i < height ; i++){
		for(int j = 0 ;j < width ; j++){
			dest[i] += * (src + i * width + j); 
		}
		dest[i] /=width;
	}
	return true;
}  
//--------------------协方差矩阵------------------------------------------
BOOL CMatrix::CovMatrix(double *src, int height ,int width,double *dest ){
	if( src == NULL ||dest == NULL ||width <= 0 || height <= 0)
		return false;
	double * average  =  new double   [height];  //height*1
	double * disperse =  new double   [height]; //height *1
	double * transpose = new double   [height]; // 1* height
	double * tempdest =  new double   [height*height];

	memset( average,   0, height * sizeof( double ));
	memset( disperse,  0, height * sizeof( double ));
	memset( transpose, 0, height * sizeof( double ));
	memset( tempdest,  0, height *height * sizeof( double ));

    Average(src, height ,width ,average);
	for(int i = 0 ; i< width ; i++){
		//symmetric
		for(int j = 0 ;j < height ; j++){
			disperse[j] = *(src+ i + j * width) - *(average+j);
		}
		Transpose(disperse, height, 1, transpose);
		Mul(disperse, height, 1, transpose, 1, height, tempdest);
		Add(dest, tempdest, dest, height, height);
	}
	Scale(dest , dest , 1.0 /( width -1 ), height ,height);
	return true;
}   

//--------------------------逆矩阵--------------------------------------------
//求pMatrix的逆矩阵，并存结果于矩阵_pMatrix中
void CMatrix:: ContraryMatrix(double *pMatrix, double * _pMatrix, int dim)
{ 
    double *tMatrix = new double[2*dim*dim];
    for (int i=0; i<dim; i++){
        for (int j=0; j<dim; j++)
            tMatrix[i*dim*2+j] = pMatrix[i*dim+j];        
    }
    for (i=0; i<dim; i++){
        for (int j=dim; j<dim*2; j++)
            tMatrix[i*dim*2+j] = 0.0;
        tMatrix[i*dim*2+dim+i]  = 1.0;        
    }
    //Initialization over!
    for (i=0; i<dim; i++)//Process Cols
    {
        double base = tMatrix[i*dim*2+i];
        if (fabs(base) < 1E-300){
            AfxMessageBox("求逆矩阵过程中被零除，无法求解!" );
            exit(0);
        }
        for (int j=0; j<dim; j++)//row
        {
            if (j == i) continue;
            double times = tMatrix[j*dim*2+i]/base;
            for (int k=0; k<dim*2; k++)//col
            {        
                tMatrix[j*dim*2+k] = tMatrix[j*dim*2+k] - times*tMatrix[i*dim*2+k];
            }
        }        
        for (int k=0; k<dim*2; k++){
            tMatrix[i*dim*2+k] /= base;
        }
    }
    for (i=0; i<dim; i++)
    {
        for (int j=0; j<dim; j++)
            _pMatrix[i*dim+j] = tMatrix[i*dim*2+j+dim];        
    }    
    delete[] tMatrix;
}