harmean
harmonic mean : inverse of the inverses average (without zeros)
Syntax
hm = harmean(x) hm = harmean(x, orientation)
Arguments
- x
vector, matrix, or hypermatrix of real or complex numbers or polynomials. Rationals not supported.
- orientation
index of the dimension along which the harmean is computed. It can be either
- a character
"*"
(default),"r"
,"c"
or"m"
. "m" is equivalent tofind(size(x)>1,1)
. - a positive integer. 1 is equivalent to "r" and 2 is equivalent to "c".
- a character
- hm
scalar, or row (if
"r"
is used), or column (if"c"
is used). Ifx
are polynomials,hm
is of rational type.
Description
This function computes the harmonic mean of input values = inverse of the average of inversed non-zero values.
hm = harmean(x)
or hm = harmean(x, '*')
returns
in scalar hm
the harmonic mean of all the entries.
hm = harmean(x,'r')
(or, equivalently,
hm = harmean(x, 1)
) returns in each entry of
the row vector hm
the harmonic mean of each
column of x
.
hm = harmean(x,'c')
(or, equivalently,
hm = harmean(x, 2)
) returns in each entry
of the column vector hm
the harmonic mean of
each row of x
.
If x is an hypermatrix and a
"r", 1, "c", 2 flag is used, an error occurs. |
Examples
harmean(1:10) // Returns 1 / mean(1 ./(1:10)) h = harmean([1 1 0 1 0 1]) // returns 1: zeros are not considered 1 / mean(1./[1 1 0 1 0 1]) // returns 0, as soon as a zero is present x = grand(3, 4, "uin",-10, 10) harmean(x) harmean(x, "r") harmean(x, 2) // Hypermatrix x = grand(3,4,2, "uin",-10, 10) harmean(x) // warning: harmean(x, "r") and harmean(x, 3) generate one error: not supported ! harmean([%z 0]) harmean([%z %z/2]) harmean([%z %i+%z]) harmean([%z %i+%z]) == 1 / ((1/%z + 1/(%i+%z))/2)
Bibliography
Wonacott, T.H. & Wonacott, R.J.; Introductory Statistics, fifth edition, J.Wiley & Sons, 1990.
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