On Feb 18, 12:24 pm, Thomas Arildsen <thomasarild...@gmail.com> wrote:
> Does Sage have functions for building matrices corresponding to the
> Matlab functions toeplitz and/or hankel?
>
> Thomas Arildsen

Hi Thomas

Sage wraps numpy, and numpy has support. Matrix arrays can be
exchanged, too. Note, that you have to specify the type with dtype
since there is a preparser - otherwise append an "r" to each number.

first import:

sage: import numpy as np
sage: import scipy.linalg as la

matlab examples from the help:

sage: c = np.r_[1:4]
sage: r = np.r_[7:11]
sage: la.hankel(c,r)
Warning: column and row values don't agree; column value used.

array([[ 1,  2,  3,  8],
       [ 2,  3,  8,  9],
       [ 3,  8,  9, 10]])



sage: c = np.array([1 , 2 , 3 , 4 , 5], dtype=float);
sage: r = np.array([1.5 , 2.5 , 3.5,  4.5,  5.5], dtype=float);
sage: a = la.toeplitz(c,r); a
Warning: column and row values don't agree; column value used.

array([[ 1. ,  2.5,  3.5,  4.5,  5.5],
       [ 2. ,  1. ,  2.5,  3.5,  4.5],
       [ 3. ,  2. ,  1. ,  2.5,  3.5],
       [ 4. ,  3. ,  2. ,  1. ,  2.5],
       [ 5. ,  4. ,  3. ,  2. ,  1. ]])


matrix as a sage type (variable a above):

sage: type(matrix(a))
<type 'sage.matrix.matrix_integer_dense.Matrix_integer_dense'>

h



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