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 '*' (default value), '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 — 配列要素の積
• harmean — 調和平均 : inverse of the inverses average (without zeros)

Bibliography

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