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EST_multistats.cc
/*************************************************************************/
/* */
/* Centre for Speech Technology Research */
/* University of Edinburgh, UK */
/* Copyright (c) 1995,1996 */
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/* the following conditions: */
/* 1. The code must retain the above copyright notice, this list of */
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/*************************************************************************/
/* Author : Paul Taylor */
/* Date : July 1995 */
/*-----------------------------------------------------------------------*/
/* Basic Multivariate Statistical Functions */
/* */
/*=======================================================================*/
#include <cmath>
#include "EST_multistats.h"
float mean(EST_FVector &v)
{
int i;
float u = 0.0;
for (i = 0; i < v.n(); ++i)
u += v(i);
return u / v.n();
}
float sum(EST_FVector &v)
{
int i;
float u = 0.0;
for (i = 0; i < v.n(); ++i)
u += v(i);
return u;
}
EST_FVector mean(EST_FMatrix &m)
{
EST_FVector u(m.num_columns());
int i, j;
for (i = 0; i < m.num_columns(); ++i)
{
u[i] = 0.0;
for (j = 0; j < m.num_rows(); ++j)
u[i] += m(j, i);
u[i] /= m.num_rows();
}
return u;
}
EST_FVector sample_variance(EST_FMatrix &m)
{
EST_FVector v(m.num_columns());
EST_FVector u(m.num_columns());
int i, j;
u = mean(m);
for (j = 0; j < m.num_columns(); ++j)
{
v[j] = 0.0;
for (i = 0; i < m.num_rows(); ++i)
v[j] += pow(m(i, j) - u(j), float(2.0));
v[j] /= m.num_rows() - 1; // sample variance
}
return v;
}
EST_FVector sample_stdev(EST_FMatrix &m)
{
EST_FVector v;
v = sample_variance(m);
int j;
for (j = 0; j < v.n(); ++j)
v[j] = sqrt(v(j));
return v;
}
EST_FMatrix sample_covariance(EST_FMatrix &m)
{
EST_FVector u(m.num_columns());
EST_FMatrix c(m.num_columns(), m.num_columns());
int i, j, k;
u = mean(m);
for (j = 0; j < m.num_columns(); ++j)
for (k = 0; k < m.num_columns(); ++k)
{
c(j, k) = 0.0;
for (i = 0; i < m.num_rows(); ++i)
c(j, k) += (m(i, j) - u(j)) * (m(i, k) - u(k));
c(j, k) /= m.num_rows();
}
return c;
}
EST_FMatrix sample_correlation(EST_FMatrix &m)
{
EST_FMatrix r(m.num_columns(), m.num_columns());
EST_FVector s = sample_stdev(m);
EST_FMatrix c = sample_covariance(m);
int j, k;
for (j = 0; j < m.num_columns(); ++j)
for (k = 0; k < m.num_columns(); ++k)
r(j, k) = c(j, k)/(s(j) * s(k));
return r;
}
EST_FMatrix euclidean_distance(EST_FMatrix &m)
{
// nowt yet
return m;
}
// normalise matrix m, by subtracting vector "sub" from each column and
// then dividing each column by vector div;
EST_FMatrix normalise(EST_FMatrix &m, EST_FVector &sub, EST_FVector &div)
{
int i, j;
EST_FMatrix z(m.num_rows(), m.num_columns());
for (j = 0; j < m.num_columns(); ++j)
for (i = 0; i < m.num_rows(); ++i)
z(i, j) = (m(i, j) - sub(j)) / div(j);
return z;
}
// calculate penrose distance for matrix of means gu of p variables
// (columns) in g populations (columns), and variance gv.
EST_FMatrix penrose_distance(EST_FMatrix &gu, EST_FVector &gv)
{
int i, j, k;
int p = gu.num_columns();
int n = gu.num_rows();
EST_FMatrix P(n, n);
cout << "pop mean " << gu;
for (i = 0; i < n; ++i)
for (j = 0; j < n; ++j)
{
P(i, j) = 0.0;
for (k = 0; k < p; ++k)
P(i, j) += pow(gu(i, k) - gu(j, k), float(2.0)) / gv(k);
P(i, j) /= p;
}
return P;
}
float single_mahal(EST_FMatrix &ui, EST_FMatrix &uj, EST_FMatrix &invv)
{
float e;
EST_FMatrix a, b,c,d;
a = ui - uj;
transpose(a,b);
multiply(b,invv,c);
multiply(c,a,d);
e = d(0,0);
return e;
}
EST_FMatrix mahalanobis_distance(EST_FMatrix &gu, EST_FMatrix &covar)
{
int i, j;
int n = gu.num_rows();
EST_FMatrix P(n, n), invv, ui, uj;
inverse(covar,invv); // should be inverse!!
for (i = 0; i < n; ++i)
for (j = 0; j < n; ++j)
{
transpose(row(gu, i),ui);
transpose(row(gu, j),uj);
P(i, j) = single_mahal(ui, uj, invv);
}
return P;
}
float simple_penrose(EST_FVector &ui, EST_FVector &uj, EST_FVector &v)
{
int k;
int n = uj.n();
float P = 0.0;
for (k = 0; k < n; ++k)
P += pow(ui(k) - uj(k), float(2.0)) / v(k);
P /= n;
return P;
}
EST_FMatrix population_mean(EST_FMatrix *in, int num_pop)
{
int i, k;
EST_FMatrix pmean(num_pop, in[0].num_columns());
EST_FVector u(in[0].num_columns());
for (i = 0; i < num_pop; ++i)
{
u = mean(in[i]);
for (k =0; k < in[i].num_columns(); ++k)
pmean(i, k) = u(k);
}
return pmean;
}
EST_FMatrix add_populations(EST_FMatrix *in, int num_pop)
{
int i, j, k, l, n;
l = 0;
for (i = 0; i < num_pop; ++i)
l += in[i].num_rows();
n = in[0].num_columns();
EST_FMatrix msum(l, n);
for (k = l = 0; k < num_pop; ++k)
for (j =0; j < n; ++j, ++l)
for (i = 0; i < in[i].num_rows(); ++i)
msum(l, j) = in[k](i, j);
return msum;
}
EST_FMatrix
Definition EST_FMatrix.h:56
EST_FVector
Definition EST_FMatrix.h:114
EST_TMatrix::num_columns
int num_columns() const
return number of columns
Definition EST_TMatrix.h:181
EST_TMatrix::num_rows
int num_rows() const
return number of rows
Definition EST_TMatrix.h:179
EST_TVector::n
INLINE int n() const
number of items in vector.
Definition EST_TVector.h:254