scipy.linalg.leslie¶

scipy.linalg.
leslie
(f, s)[source]¶ Create a Leslie matrix.
Given the length n array of fecundity coefficients f and the length n1 array of survival coefficients s, return the associated Leslie matrix.
Parameters:  f : (N,) array_like
The “fecundity” coefficients.
 s : (N1,) array_like
The “survival” coefficients, has to be 1D. The length of s must be one less than the length of f, and it must be at least 1.
Returns:  L : (N, N) ndarray
The array is zero except for the first row, which is f, and the first subdiagonal, which is s. The datatype of the array will be the datatype of
f[0]+s[0]
.
Notes
New in version 0.8.0.
The Leslie matrix is used to model discretetime, agestructured population growth [1] [2]. In a population with n age classes, two sets of parameters define a Leslie matrix: the n “fecundity coefficients”, which give the number of offspring percapita produced by each age class, and the n  1 “survival coefficients”, which give the percapita survival rate of each age class.
References
[1] (1, 2) P. H. Leslie, On the use of matrices in certain population mathematics, Biometrika, Vol. 33, No. 3, 183–212 (Nov. 1945) [2] (1, 2) P. H. Leslie, Some further notes on the use of matrices in population mathematics, Biometrika, Vol. 35, No. 3/4, 213–245 (Dec. 1948) Examples
>>> from scipy.linalg import leslie >>> leslie([0.1, 2.0, 1.0, 0.1], [0.2, 0.8, 0.7]) array([[ 0.1, 2. , 1. , 0.1], [ 0.2, 0. , 0. , 0. ], [ 0. , 0.8, 0. , 0. ], [ 0. , 0. , 0.7, 0. ]])