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Re: [Help-gsl] Find variance - covariance matrix of a matrix

From: Francesco Abbate
Subject: Re: [Help-gsl] Find variance - covariance matrix of a matrix
Date: Tue, 9 Mar 2010 11:20:45 +0100

2010/3/9 Srimal Jayawardena <address@hidden>:
> Hi
> Is there a simple function/method for me to obtain the variance -
> covariance matrix of a given matrix.
> I'm looking for the  equivalent of 'cov' in MATLAB

Here what the Matlab documentation says:

C = cov(x) where x is a vector returns the variance of the vector
elements. For matrices where each row is an observation and each
column a variable, cov(x) is the covariance matrix. diag(cov(x)) is a
vector of variances for each column, and sqrt(diag(cov(x))) is a
vector of standard deviations.

So actually what Matlab calculates is the covariance between each of
the column vectors.

Here a simple routine that, given a matrix m, calculates the
covariance matrix by in the matrix r.

cov_calculate(gsl_matrix *r, gsl_matrix *m)
  gsl_vector_view a, b;
  size_t i, j;

  for (i = 0; i < m->size1; i++) {
    for (j = 0; j < m->size2; j++) {
      double v;
      a = gsl_matrix_column (m, i);
      b = gsl_matrix_column (m, j);
      v = gsl_stats_covariance (, a.vector.stride,, b.vector.stride, a.vector.size);
      gsl_matrix_set (r, i, j, v);

Note that the function gsl_stats_covariance does not works with
vectors or matrices but only with double pointer. This is why we need
to take directly the "data" field of the vector struct.

Best regards,

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