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