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Module « scipy.linalg »

Fonction leslie - module scipy.linalg

Signature de la fonction leslie

def leslie(f, s) 

Description

help(scipy.linalg.leslie)

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. The length of each slice of `s` (along the last
    axis) 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`.
    For 1-D input, the data-type of the array will be the data-type of
    ``f[0]+s[0]``.

Notes
-----
.. versionadded:: 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.

N-dimensional input are treated as a batches of coefficient arrays: each
slice along the last axis of the input arrays is a 1-D coefficient array,
and each slice along the last two dimensions of the output is the
corresponding Leslie matrix.

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

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