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 coefficents s, return the associated Leslie matrix.

Parameters :

f : array_like

The “fecundity” coefficients, has to be 1-D.

s : 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 : ndarray

Returns a 2-D ndarray of shape (n, n), where n is the length of f. 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 [R30] [R31]. 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

[R30]

(1, 2) P. H. Leslie, On the use of matrices in certain population mathematics, Biometrika, Vol. 33, No. 3, 183–212 (Nov. 1945)

[R31]

(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

>>> 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. ]])