pca_hao.cpp

VC 6.0下的主成分分析代码

}

/**  Variance-covariance matrix: creation  *****************************/

void covcol(data, n, m, symmat)
float **data, **symmat;
int n, m;
/* Create m * m covariance matrix from given n * m data matrix. */
{
float *mean, *vector();
int i, j, j1, j2;

/* Allocate storage for mean vector */

mean = vector(m);

/* Determine mean of column vectors of input data matrix */

for (j = 1; j <= m; j++)
    {
    mean[j] = 0.0;
    for (i = 1; i <= n; i++)
        {
        mean[j] += data[i][j];
        }
    mean[j] /= (float)n;
    }

printf("\nMeans of column vectors:\n");
for (j = 1; j <= m; j++)  {
    printf("%7.1f",mean[j]);  }   printf("\n");

/* Center the column vectors. */

for (i = 1; i <= n; i++)
    {
    for (j = 1; j <= m; j++)
        {
        data[i][j] -= mean[j];
        }
    }

/* Calculate the m * m covariance matrix. */
for (j1 = 1; j1 <= m; j1++)
    {
    for (j2 = j1; j2 <= m; j2++)
        {
        symmat[j1][j2] = 0.0;
        for (i = 1; i <= n; i++)
            {
            symmat[j1][j2] += data[i][j1] * data[i][j2];
            }
        symmat[j2][j1] = symmat[j1][j2];
        }
    }

return;

}

/**  Sums-of-squares-and-cross-products matrix: creation  **************/

void scpcol(data, n, m, symmat)
float **data, **symmat;
int n, m;
/* Create m * m sums-of-cross-products matrix from n * m data matrix. */
{
int i, j1, j2;

/* Calculate the m * m sums-of-squares-and-cross-products matrix. */

for (j1 = 1; j1 <= m; j1++)
    {
    for (j2 = j1; j2 <= m; j2++)
        {
        symmat[j1][j2] = 0.0;
        for (i = 1; i <= n; i++)
            {
            symmat[j1][j2] += data[i][j1] * data[i][j2];
            }
        symmat[j2][j1] = symmat[j1][j2];
        }
    }

return;

}

/**  Error handler  **************************************************/

void erhand(err_msg)
char err_msg[];
/* Error handler */
{
    fprintf(stderr,"Run-time error:\n");
    fprintf(stderr,"%s\n", err_msg);
    fprintf(stderr,"Exiting to system.\n");
    exit(1);
}

/**  Allocation of vector storage  ***********************************/

float *vector(n)
int n;
/* Allocates a float vector with range [1..n]. */
{

    float *v;

    v = (float *) malloc ((unsigned) n*sizeof(float));
    if (!v) erhand("Allocation failure in vector().");
    return v-1;

}

/**  Allocation of float matrix storage  *****************************/

float **matrix(n,m)
int n, m;
/* Allocate a float matrix with range [1..n][1..m]. */
{
    int i;
    float **mat;

    /* Allocate pointers to rows. */
    mat = (float **) malloc((unsigned) (n)*sizeof(float*));
    if (!mat) erhand("Allocation failure 1 in matrix().");
    mat -= 1;

    /* Allocate rows and set pointers to them. */
    for (i = 1; i <= n; i++)
        {
        mat[i] = (float *) malloc((unsigned) (m)*sizeof(float));
        if (!mat[i]) erhand("Allocation failure 2 in matrix().");
        mat[i] -= 1;
        }

     /* Return pointer to array of pointers to rows. */
     return mat;

}

/**  Deallocate vector storage  *********************************/

void free_vector(v,n)
float *v;
int n;
/* Free a float vector allocated by vector(). */
{
   free((char*) (v+1));
}

/**  Deallocate float matrix storage  ***************************/

void free_matrix(mat,n,m)
float **mat;
int n, m;
/* Free a float matrix allocated by matrix(). */
{
   int i;

   for (i = n; i >= 1; i--)
       {
       free ((char*) (mat[i]+1));
       }
   free ((char*) (mat+1));
}

/**  Reduce a real, symmetric matrix to a symmetric, tridiag. matrix. */

void tred2(a, n, d, e)
float **a, *d, *e;
/* float **a, d[], e[]; */
int n;
/* Householder reduction of matrix a to tridiagonal form.
   Algorithm: Martin et al., Num. Math. 11, 181-195, 1968.
   Ref: Smith et al., Matrix Eigensystem Routines -- EISPACK Guide
        Springer-Verlag, 1976, pp. 489-494.
        W H Press et al., Numerical Recipes in C, Cambridge U P,
        1988, pp. 373-374.  */
{
int l, k, j, i;
float scale, hh, h, g, f;

for (i = n; i >= 2; i--)
    {
    l = i - 1;
    h = scale = 0.0;
    if (l > 1)
       {
       for (k = 1; k <= l; k++)
           scale += fabs(a[i][k]);
       if (scale == 0.0)
          e[i] = a[i][l];
       else
          {
          for (k = 1; k <= l; k++)
              {
              a[i][k] /= scale;
              h += a[i][k] * a[i][k];
              }
          f = a[i][l];
          g = f>0 ? -sqrt(h) : sqrt(h);
          e[i] = scale * g;
          h -= f * g;
          a[i][l] = f - g;
          f = 0.0;
          for (j = 1; j <= l; j++)
              {
              a[j][i] = a[i][j]/h;
              g = 0.0;
              for (k = 1; k <= j; k++)
                  g += a[j][k] * a[i][k];
              for (k = j+1; k <= l; k++)
                  g += a[k][j] * a[i][k];
              e[j] = g / h;
              f += e[j] * a[i][j];
              }
          hh = f / (h + h);
          for (j = 1; j <= l; j++)
              {
              f = a[i][j];
              e[j] = g = e[j] - hh * f;
              for (k = 1; k <= j; k++)
                  a[j][k] -= (f * e[k] + g * a[i][k]);
              }
         }
    }
    else
        e[i] = a[i][l];
    d[i] = h;
    }
d[1] = 0.0;
e[1] = 0.0;
for (i = 1; i <= n; i++)
    {
    l = i - 1;
    if (d[i])
       {
       for (j = 1; j <= l; j++)
           {
           g = 0.0;
           for (k = 1; k <= l; k++)
               g += a[i][k] * a[k][j];
           for (k = 1; k <= l; k++)
               a[k][j] -= g * a[k][i];
           }
       }
       d[i] = a[i][i];
       a[i][i] = 1.0;
       for (j = 1; j <= l; j++)
           a[j][i] = a[i][j] = 0.0;
    }
}

/**  Tridiagonal QL algorithm -- Implicit  **********************/

void tqli(d, e, n, z)
float d[], e[], **z;
int n;
{
int m, l, iter, i, k;
float s, r, p, g, f, dd, c, b;
void erhand();

for (i = 2; i <= n; i++)
    e[i-1] = e[i];
e[n] = 0.0;
for (l = 1; l <= n; l++)
    {
    iter = 0;
    do
      {
      for (m = l; m <= n-1; m++)
          {
          dd = fabs(d[m]) + fabs(d[m+1]);
          if (fabs(e[m]) + dd == dd) break;
          }
          if (m != l)
             {
             if (iter++ == 30) erhand("No convergence in TLQI.");
             g = (d[l+1] - d[l]) / (2.0 * e[l]);
             r = sqrt((g * g) + 1.0);
             g = d[m] - d[l] + e[l] / (g + SIGN(r, g));
             s = c = 1.0;
             p = 0.0;
             for (i = m-1; i >= l; i--)
                 {
                 f = s * e[i];
                 b = c * e[i];
                 if (fabs(f) >= fabs(g))
                    {
                    c = g / f;
                    r = sqrt((c * c) + 1.0);
                    e[i+1] = f * r;
                    c *= (s = 1.0/r);
                    }
                 else
                    {
                    s = f / g;
                    r = sqrt((s * s) + 1.0);
                    e[i+1] = g * r;
                    s *= (c = 1.0/r);
                    }
                 g = d[i+1] - p;
                 r = (d[i] - g) * s + 2.0 * c * b;
                 p = s * r;
                 d[i+1] = g + p;
                 g = c * r - b;
                 for (k = 1; k <= n; k++)
                     {
                     f = z[k][i+1];
                     z[k][i+1] = s * z[k][i] + c * f;
                     z[k][i] = c * z[k][i] - s * f;
                     }
                 }
                 d[l] = d[l] - p;
                 e[l] = g;
                 e[m] = 0.0;
             }
          }  while (m != l);
      }
 }