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. ]])