mtlb_var

Arguments

x

a real or a complex vector or matrix.

s

a real scalar or real vector.

• If x is a vector, s is the variance of x.

• If x is a matrix, s is a row vector containing the variance of each column of x.

w

type of normalization to use. Valid values are, depending on the number of columns m of x :

• w = 0 : normalizes with m-1, provides the best unbiased estimator of the variance (this is the default).

• w = 1: normalizes with m, this provides the second moment around the mean.

dim

the dimension along which the variance is computed (default is 1, i.e. column by column). If dim is 2, the variance is computed row by row.

Description

This function computes the variance of the values of a vector or matrix x. It provides the same service as Octave and Matlab. It differs from Scilab's variance primitive:

• mtlb_var returns a real (i.e. with a zero imaginary part) variance, even if x is a complex vector or matrix. The Scilab variance primitive returns a complex value if the input vector x is complex and if no option additional is used.

• Whatever the type of the input data x (i.e. vector or matrix), mtlb_var computes the variance either on dimension 1 or on dimension 2 while, if no option is passed to the Scilab's variance primitive, the variance is computed on all dimension at once.

Examples

The following 3 examples illustrates the use of the mtlb_var function. In the first case, a column vector is passed to the function, which returns the value 750. In the second case, a matrix is passed to the function, which returns the row vector [0.16 0.09]. In the third case, a complex column vector is passed to the function, which returns a value close to 2.

x = [10; 20; 30; 40; 50; 60; 70; 80; 90];
computed = mtlb_var(x);

x = [0.9    0.7
    0.1    0.1
    0.5    0.4];
computed = mtlb_var(x);

N=1000;
x = grand(N,1,'nor',0,1) + %i*grand(N,1,'nor',0,1);
computed = mtlb_var(x);

See also

• variance — variance d'un vecteur, matrice (voire hypermatrice) de nombres réels ou complexes