CODEWITHSUNDEEP
pythonmatrixsage
S.B.
S.B.

Reputation: 165

How to create vector circulant matrix in Sage?

Given the first row vector R0 = [a0,a1,...,a(n-1)] and a specific vector V, I would like to create a "vector circulant matrix" in SAGE, which will be constructed as follows.

The rows of the matrix will be 

R0=R0; R1=p(R0); R2=p(R1), ..., R(n-1)=p(R(n-2))

where p is a map which takes, for example row Ri = [r0,r1,...,r(n-1)] and makes it [0, r0, r1,...,r(n-2)]+r(n-1)*V

Note that I tried to write everything in the language of Sage. And this is not like the classical circulant, Toeplitz or Hankel matrix constructions.

(n, R0, and the vector V will be defined by the user at the beginning)

How to write a simple program that will give me the matrix defined above?

Upvotes: 1

Views: 454

Answers (1)

Samuel Lelièvre
Samuel Lelièvre

Reputation: 3453

Here is a function:

def f(r,v):
    def p(x):
        return vector([0]+list(x[:-1r])) + x[-1r]*v
    m = [r]
    for _ in xrange(len(r)-1r):
        m.append(p(m[-1r]))
    return matrix(m)

Example:

sage: r = vector(ZZ,(0, 1, 2, 3,))
sage: v = vector(ZZ,(3, 5, 7, 9,))
sage: f(r,v)
[   0    1    2    3]
[   9   15   22   29]
[  87  154  218  283]
[ 849 1502 2135 2765]

Upvotes: 1

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