mf_vandermonde.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}
{* 28mar2005}{...}
{bf:help mata Vandermonde()}
{hline}
{* index Vandermonde()}{...}

{title:Title}

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


{title:Syntax}

{p 8 12 2}
{it:numeric matrix} 
{cmd:Vandermonde(}{it:numeric colvector x}{cmd:)}


{title:Description}

{p 4 4 2}
{cmd:Vandermonde(}{it:x}{cmd:)} returns the Vandermonde matrix 
containing the geometric progression of {it:x} in each row

		{c TLC}{c -}                                  {c -}{c TRC}
		{c |} 1  {it:x}_1  {it:x}_1^2  {it:x}_1^3  ...  {it:x}_1^{it:n}-1 {c |}
		{c |} 1  {it:x}_2  {it:x}_2^2  {it:x}_2^3  ...  {it:x}_2^{it:n}-1 {c |}
		{c |} .   .    .      .             .    {c |}
		{c |} .   .    .      .             .    {c |}
		{c |} .   .    .      .             .    {c |}
		{c |} 1  {it:x}_{it:n}  {it:x}_{it:n}^2  {it:x}_{it:n}^3  ...  {it:x}_{it:n}^{it:n}-1 {c |}
		{c BLC}{c -}                                  {c -}{c BRC}

{p 4 4 2}
where {it:n} = rows({it:x}).
Note that same authors use the transpose of the above matrix.


{title:Remarks}

{p 4 4 2}
Vandermonde matrices are useful in polynomial interpolation.


{title:Conformability}

    {cmd:Vandermonde(}{it:x}{cmd:)}:
		{it:x}:  {it:n x} 1
	   {it:result}:  {it:n x n}


{title:Diagnostics}

{p 4 4 2}
None.


{title:Source code}

{p 4 4 2}
{view vandermonde.mata, adopath asis:vandermonde.mata}
    

{title:Also see}

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

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