Maxima Function
global_variances (matrix)
global_variances(matrix,logical_value)
Function global_variances returns a list of global variance measures:
total variance: trace(S_1),
mean variance: trace(S_1)/p,
generalized variance: determinant(S_1),
generalized standard deviation: sqrt(determinant(S_1)),
efective variance determinant(S_1)^(1/p), (defined in: Pen D. (2002) aAn de datos multivariantes; McGraw-Hill, Madrid.)
efective standard deviation: determinant(S_1)^(1/(2*p)).
where p is the dimension of the multivariate random variable and S_1 the covariance matrix returned by cov1.
Example:
(%i1) load (descriptive)$ (%i2) load (numericalio)$ (%i3) s2 : read_matrix (file_search ("wind.data"))$ (%i4) global_variances (s2); (%o4) [105.338342060606, 21.06766841212119, 12874.34690469686, 113.4651792608502, 6.636590811800794, 2.576158149609762]
Function global_variances has an optional logical argument: global_variances(x,true) tells Maxima that x is the data matrix, making the same as global_variances(x). On the other hand, global_variances(x,false) means that x is not the data matrix, but the covariance matrix, avoiding its recalculation,