mf_toeplitz.hlp

是一个经济学管理应用软件 很难找的 但是经济学学生又必须用到

{smcl}
{* 07apr2005}{...}
{bf:help mata Toeplitz()}
{hline}
{* index Toeplitz()}{...}

{title:Title}

{p 4 4 2}
{bf:[M-5] Toeplitz() -- Toeplitz matrices}


{title:Syntax}

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{it:numeric matrix} 
{cmd:Toeplitz(}{it:numeric colvector c1}{cmd:,}
{it:numeric rowvector r1}{cmd:)}


{title:Description}

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{cmd:Toeplitz(}{it:c1}{cmd:,} {it:r1}{cmd:)}
returns the Toeplitz matrix defined by {it:c1} being its first 
column and {it:r1} being its first row.  A Toeplitz matrix {it:T} is
characterized by {it:T}[{it:i},{it:j}] = {it:T}[{it:i}-1,{it:j}-1], 
{it:i, j} > 1.
In a Toeplitz matrix, each diagonal is constant.

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Vectors {it:c1} and {it:r1} specify the first column and first row of {it:T}.


{title:Remarks}

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{it:c1}[1] is used to fill {it:T}[1,1] and {it:r1}[1] is not used.

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To obtain the symmetric (Hermitian) Toeplitz matrix, code
{cmd:Toeplitz(}{it:v}{cmd:,} {it:v}{cmd:')} 
(if {it:v} is a column vector), or
{cmd:Toeplitz(}{it:v}{cmd:',} {it:v}{cmd:)} if {it:v} is a row vector.


{title:Conformability}

    {cmd:Toeplitz(}{it:c1}{cmd:,} {it:r1}{cmd:)}:
	       {it:c1}:  {it:r x} 1
	       {it:r1}:  1 {it:x} c
	   {it:result}:  {it:r x c}


{title:Diagnostics}

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None.  Note that the top left element is defined by {it:c1}[1] and 
that {it:r1}[1] is not used.


{title:Source code}

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{view toeplitz.mata, adopath asis:toeplitz.mata}
    

{title:Also see}

{p 4 13 2}
Manual:  {hi:[M-5] Toeplitz()}

{p 4 13 2}
Online:  help for 
{bf:{help m4_matrix:[M-4] matrix}}
{p_end}