I need to construct a non linear matricial recursive system for the series of matrix Mk like the following one
Mk[i][j]=F(Mk−1[i][j],Mk−1[i][j]) for M0 given
I have read that for one dimension one can use Sympy rec. But is there a way to do it simply in Sagemath?
Define a function, either recursive or not, to do that.
Recursive version:
def Mk_rec(M0, k, F):
import numbers
if not isinstance(k, numbers.Integral) or k < 0:
raise ValueError(f'Expected non-negative integer k, got: {k}')
MS = M0.parent() # the matrix space
if k == 0:
return MS(M0)
M = Mk_rec(M0, k - 1, F)
FF = lambda a: F(a, a)
return MS(lambda i, j: FF(M[i, j]))Non-recursive version:
def Mk_nrec(M0, k, F):
import numbers
if not isinstance(k, numbers.Integral) or k < 0:
raise ValueError(f'Expected non-negative integer k, got: {k}')
MS = M0.parent() # the matrix space
M = MS(M0)
FF = lambda a: F(a, a)
for j in range(k):
M = MS(lambda i, j: FF(M[i, j]))
return MExamples:
sage: M0 = matrix([[0, 2], [1, -1]])
sage: F = lambda a, b: a + b
sage: Mk_nrec(M0, 2, F)
[ 0 8]
[ 4 -4]
sage: Mk_rec(M0, 2, F)
[ 0 8]
[ 4 -4]Asked: 4 years ago
Seen: 330 times
Last updated: Mar 09 '21
Copyright Sage, 2010. Some rights reserved under creative commons license. Content on this site is licensed under a Creative Commons Attribution Share Alike 3.0 license.
The problem as stated has nothing to do with matrices, since for any fixed i, j, it represents just a recurrence sequence of numbers. Why do you want to deal with matrices rather than with their individual elements?