[Date Prev][Date Next][Thread Prev][Thread Next][Date Index][Thread Index]
## Re: [Maxima-discuss] Z-Transforms

**From**: |
Mike Miller |

**Subject**: |
Re: [Maxima-discuss] Z-Transforms |

**Date**: |
Fri, 8 Jul 2016 12:22:27 -0700 |

**User-agent**: |
Mutt/1.6.0 (2016-04-01) |

On Fri, Jul 08, 2016 at 12:12:15 -0400, Przemek Klosowski wrote:
>* On 07/07/2016 03:11 PM, Stavros Macrakis (Σταῦρος Μακράκης) wrote:*
>* > a dozen-line Octave program to do what can be done in two lines in*
>* > Maxima. [...]*
>* > *
>* > T[n,k]:=if k < 1 or k > n then 0 elseif k = 1 or k = n then 1*
>* > else k*T[n-1,k]+(n-k+1)*T[n-1,k-1]$*
>* > *
>* > Then*
>* > *
>* > genmatrix(T,11,10) =>*
>* > *
>* > [ 1 0 0 0 0 0 0 0 0*
>* > 0 ]*
>* > [ ]*
>* > [ 1 1 0 0 0 0 0 0 0*
>* > 0 ]*
>* > [ ]*
>* > [ 1 4 1 0 0 0 0 0 0*
>* > 0 ]*
>* > [ ]*
>* > [ 1 11 11 1 0 0 0 0 0*
>* > 0 ]*
>* > [ ]*
>* > [ 1 26 66 26 1 0 0 0 0*
>* > 0 ]*
>* > [ ]*
>* > [ 1 57 302 302 57 1 0 0 0*
>* > 0 ]*
>* > [ ]*
>* > [ 1 120 1191 2416 1191 120 1 0 0*
>* > 0 ]*
>* > [ ]*
>* > [ 1 247 4293 15619 15619 4293 247 1 0*
>* > 0 ]*
>* > [ ]*
>* > [ 1 502 14608 88234 156190 88234 14608 502 1*
>* > 0 ]*
>* > [ ]*
>* > [ 1 1013 47840 455192 1310354 1310354 455192 47840 1013*
>* > 1 ]*
>* > [ ]*
>* > [ 1 2036 152637 2203488 9738114 15724248 9738114 2203488 152637*
>* > 2036 ]*
>* *
>* *
>* I thought "challenge accepted" and tried to write this in a vectorized*
>* shortcut, but I couldn't hack it. I start by*
>* *
>* T=eye(11,10);T(:,1)=1; *
>* repmat(1:10,11,1).*shift(T,1)+(repmat((1:11)',1,10)-repmat(1:10,11,1)+1).*shift(shift(T,1),1,2)*
>* *
>* but I couldn't see how to nicely write the rest without explicit loops. Can*
>* anyone suggest an approach?*
I don't have an expression, but I think it would involve rewriting that
nicely formulated recursive definition into a closed-form non-recursive
definition for each element of the array, because that's the way the
Octave language works.
So the first step would be to redefine the above so that one can compute
the value of T(n,k) in the lower triangle independently of any other
element of T.
As a non-mathematician, that looks harder than it's worth thinking
about, so I would just write the function in C++ and it becomes a fast
function call in Octave.
--
mike