public Array <float> Fit(Array <float> X, bool center = true)
{
var m = X.Shape[0];
var n = X.Shape[1];
var k = Math.Min(m, n);
this.means = NN.Mean(X, axis: 0);
if (center)
{
X -= means;
}
var copy = (float[])X.Values.Clone();
var s = new float[k];
var u = NN.Zeros <float>(m, m);
components_ = NN.Zeros <float>(n, n);
var superb = new float[k - 1];
BlasNet.Lapack.gesvd('A', 'A', m, n, copy, n, s, u.Values, m, components_.Values, n, superb);
var components = nComponents == 0 ? k : Math.Min(k, nComponents);
SVDFlip(u, components);
return(X);
}
public static Array <Real> Cov(Array <Real> m, int ddof = 1, Array <Real> result = null)
{
// Estimate a covariance matrix, given data.
// Covariance indicates the level to which two variables vary together.
// If we examine N-dimensional samples, :math:`X = [x_1, x_2, ... x_N]^T`,
// then the covariance matrix element :math:`C_{ij}` is the covariance of
// :math:`x_i` and :math:`x_j`. The element :math:`C_{ii}` is the variance
// of :math:`x_i`.
// Parameters
// ----------
// m : array_like
// A 1-D or 2-D array containing multiple variables and observations.
// Each row of `m` represents a variable, and each column a single
// observation of all those variables. Also see `rowvar` below.
// ddof : int, optional
// .. versionadded:: 1.5
// If not ``None`` normalization is by ``(N - ddof)``, where ``N`` is
// the number of observations; this overrides the value implied by
// ``bias``. The default value is ``None``.
// Returns
// -------
// out : ndarray
// The covariance matrix of the variables.
// See Also
// --------
// corrcoef : Normalized covariance matrix
// Examples
// --------
// Consider two variables, :math:`x_0` and :math:`x_1`, which
// correlate perfectly, but in opposite directions:
// >>> x = np.array([[0, 2], [1, 1], [2, 0]]).T
// >>> x
// array([[0, 1, 2],
// [2, 1, 0]])
// Note how :math:`x_0` increases while :math:`x_1` decreases. The covariance
// matrix shows this clearly:
// >>> np.cov(x)
// array([[ 1., -1.],
// [-1., 1.]])
// Note that element :math:`C_{0,1}`, which shows the correlation between
// :math:`x_0` and :math:`x_1`, is negative.
// Further, note how `x` and `y` are combined:
// >>> x = [-2.1, -1, 4.3]
// >>> y = [3, 1.1, 0.12]
// >>> X = np.vstack((x,y))
// >>> print np.cov(X)
// [[ 11.71 -4.286 ]
// [ -4.286 2.14413333]]
// >>> print np.cov(x, y)
// [[ 11.71 -4.286 ]
// [ -4.286 2.14413333]]
// >>> print np.cov(x)
// 11.71
var fact = (Real)(m.Shape[1] - ddof);
if (fact <= 0)
{
throw new ArgumentException("Degrees of freedom <= 0 for slice");
}
var X = m - NN.Mean(m, axis: 1, keepdims: true);
//result = X.T.Dot(X, result: result);
result = X.Dot(X.T, result: result);
result.Scale((Real)1.0 / fact, result: result);
return(result);
}
