Please note that the recommended version of Scilab is 6.1.1. This page might be outdated.
However, this page did not exist in the previous stable version.
geomean
geometric mean
Syntax
gm = geomean(X) GM = geomean(X, orien) // orien: 'r'1'c'2..ndims(X)
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) and1
are equivalent, as'c'
(columns) and2
are. gm
Scalar number: the geometric mean
gm = prod(X)^(1/N)
, whereN = length(X)
is the number of components inX
. GM
Vector, matrix or hypermatrix of numbers.
s = size(GM)
is equal tosize(X)
, except thats(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 sparseencoded, then

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
Bibliography
Wonacott, T.H. & Wonacott, R.J.; Introductory Statistics, fifth edition, J.Wiley & Sons, 1990.
Comments
Add a comment:
Please login to comment this page.