scipy.linalg.leslie

scipy.linalg.leslie(f, s)

Create a Leslie matrix.

Given the length n array of fecundity coefficients f and the length n-1 array of survival coefficients s, return the associated Leslie matrix.

Parameters

f(N,) array_like

The “fecundity” coefficients.

s(N-1,) array_like

The “survival” coefficients, has to be 1-D. 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 sub-diagonal, which is s. The data-type of the array will be the data-type of f[0]+s[0].

Notes

New in version 0.8.0.

The Leslie matrix is used to model discrete-time, age-structured 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 per-capita produced by each age class, and the n - 1 “survival coefficients”, which give the per-capita 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. ]])