geomean

Arguments

X

Vector, matrix or hypermatrix of real or complex numbers.

orien

Dimension accross which the geometric average is computed. The value must be among 'r', 1, 'c', 2, .. ndims(X). Values 'r' (rows) and 1 are equivalent, as 'c' (columns) and 2 are.

gm

Scalar number: the geometric mean gm = prod(X)^(1/N), where N = length(X) is the number of components in X.

GM

Vector, matrix or hypermatrix of numbers. s = size(GM) is equal to size(X), except that s(orien) is set to 1 (due to the projected application of geomean() over components along the orien dimension).

If X is a matrix, we have:

• GM = geomean(X,1) => GM(1,j) = geomean(X(:,j))
• GM = geomean(X,2) => GM(i,1) = geomean(X(i,:))

Description

geomean(X,..) computes the geometric mean of values stored in X.

If X stores only positive or null values, gm or GM are real. Otherwise they are most often complex.

If X is sparse-encoded, then it is reencoded in full format before being processed. gm is always full-encoded. GM is sparse-encoded as well.

Examples

geomean(1:10) // Returns factorial(10)^(1/10) = 4.5287286881167648

// Projected geomean:
// -----------------
m = grand(4,5, "uin", 1, 100);
m(3,2) = 0; m(2,4) = %inf; m(4,5) =  %nan
geomean(m, "r")
geomean(m, 2)
h = grand(3,5,2, "uin",1,100)
geomean(h,3)

--> m = grand(4,5, "uin", 1, 100);
--> m(3,2) = 0; m(2,4) = %inf; m(4,5) =  %nan
 m  =
   13.   5.    99.   41.   20.
   3.    92.   4.    Inf   5.
   35.   0.    36.   40.   98.
   86.   86.   66.   21.   Nan

--> geomean(m, "r")
 ans  =
   18.510058   0.   31.14479   Inf   Nan

--> geomean(m, 2)
 ans  =
   22.104082
   Inf
   0.
   Nan

--> h = grand(3,5,2, "uin",1,100)
 h  =
(:,:,1)
   10.   40.   37.   72.   30.
   10.   47.   54.   13.   19.
   44.   27.   61.   10.   27.
(:,:,2)
   96.   88.   7.    98.   35.
   54.   29.   96.   77.   8.
   94.   45.   21.   46.   3.

--> geomean(h,3)
 ans  =
   16.522712   43.150898   23.2379     36.91883    72.
   14.142136   13.747727   64.311741   34.85685    35.79106
   12.247449   30.983867   59.329588   16.093477   84.

// APPLICATION: Average growing rate
// ---------------------------------
// During 8 years, we measure the diameter D(i=1:8) of the trunc of a tree.
D = [10 14 18 26 33 42 51 70];          // in mm

// The growing rate gr(i) for year #i+1 wrt year #i is, in %:
gr = (D(2:$)./D(1:$-1) - 1)*100

// The average yearly growing rate is then, in %:
mgr = (geomean(1+gr/100)-1)*100

// If this tree had a constant growing rate, its diameter would have been:
D(1)*(1+mgr/100)^(0:7)

--> gr = (D(2:$)./D(1:$-1) - 1)*100
 gr  =
   40.   28.57   44.44   26.92   27.27   21.43   37.25

--> mgr = (geomean(1+gr/100)-1)*100
 mgr  =
   32.05

--> D(1)*(1+mgr/100)^(0:7)
 ans  =
   10.   13.2   17.44   23.02   30.4   40.15   53.01   70.

See also

• prod — produto
• harmean — harmonic mean : inverse of the inverses average (without zeros)

Bibliography

Wonacott, T.H. & Wonacott, R.J.; Introductory Statistics, fifth edition, J.Wiley & Sons, 1990.