mf_cond.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}
{* 31mar2005}{...}
{cmd:help mata cond()}
{hline}
{* index cond()}{...}
{* index condition number}{...}

{cmd:Title}

{p 4 8 2}
{bf:[M-5] cond() -- Condition number}


{title:Syntax}

{p 8 8 2}
{it:real scalar}{bind: }
{cmd:cond(}{it:numeric matrix A}{cmd:)}

{p 8 8 2}
{it:real scalar}{bind: }
{cmd:cond(}{it:numeric matrix A}, {it:real scalar p}{cmd:)}


{title:Description}

{p 4 4 2}
{cmd:cond(}{it:A}{cmd:)} returns {cmd:cond(}{it:A}, 2{cmd:)}.

{p 4 4 2}
{cmd:cond(}{it:A}, {it:p}{cmd:)} returns the
value of the condition number of {it:A} for the specified norm {it:p}, 
where {it:p} may be 0, 1, 2, or {cmd:.} (missing).


{title:Remarks}

{p 4 4 2}
The condition number of a matrix A is

{* TeX in math mode}{...}
		{it:cond}  =  norm({it:A}, {it:p}) * norm({it:A}^(-1), {it:p})

{p 4 4 2}
These functions return missing when A is singular.

{p 4 4 2}
Values near 1 indicate that the matrix is well conditioned, and large values
indicate ill conditioning.


{title:Conformability}

    {cmd:cond(}{it:A}{cmd:)}:
		{it:A}:  {it:r x c}
    	   {it:result}:  1 {it:x} 1

    {cmd:cond(}{it:A}, {it:p}{cmd:)}:
		{it:A}:  {it:r x c}
		{it:p}:  1 {it:x} 1
    	   {it:result}:  1 {it:x} 1


{title:Diagnostics}

{p 4 4 2}
   {cmd:cond(}{it:A}{cmd:,} {it:p}{cmd:)} aborts with error if 
   {it:p} is not 0, 1, 2, or {cmd:.} (missing).

{p 4 4 2}
   {cmd:cond(}{it:A}{cmd:)} and
   {cmd:cond(}{it:A}{cmd:,} {it:p}{cmd:)}
   return missing when {it:A} is singular or if {it:A} contains missing values.

{p 4 4 2}
   {cmd:cond(}{it:A}{cmd:)} and
   {cmd:cond(}{it:A}{cmd:,} {it:p}{cmd:)}
   return 1 when {it:A} is void.

{p 4 4 2}
   {cmd:cond(}{it:A}{cmd:)} and
   {cmd:cond(}{it:A}{cmd:, 2)} return missing if the SVD algorithm fails 
   to converge, which is highly unlikely; see {bf:{help mf_svd:[M-5] svd()}}.


{title:Source code}

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


{title:Also see}

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

{p 4 13 2}
Online:  help for 
{bf:{help mf_norm:[M-5] norm()}};
{bf:{help m4_matrix:[M-4] matrix}}
{p_end}