mf_reldif.hlp

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{smcl}
{* 08feb2005}{...}
{cmd:help mata reldif()}
{hline}
{* index reldif()}{...}
{* index mreldif()}{...}
{* index mreldifsym()}{...}
{* index mreldifre()}{...}

{title:Title}

{p 4 8 2}
{bf:[M-5] reldif() -- Relative/absolute difference}


{title:Syntax}

{p 8 8 2}
{it:real matrix}{bind:    }
{cmd:reldif(}{it:numeric matrix X}{cmd:,}
{it:numeric matrix Y}{cmd:)}

{p 8 8 2}
{it:real scalar}{bind:   }
{cmd:mreldif(}{it:numeric matrix X}{cmd:,}
{it:numeric matrix Y}{cmd:)}

{p 8 8 2}
{it:real scalar}
{cmd:mreldifsym(}{it:numeric matrix X}{cmd:)}

{p 8 8 2}
{it:real scalar}{bind: }
{cmd:mreldifre(}{it:numeric matrix X}{cmd:)}


{title:Description}

{p 4 4 2}
{cmd:reldif(}{it:X}, {it:Y}{cmd:)} returns the "relative" difference 
defined by 

		      |X - Y|
		r =  ---------
		      |Y| + 1

{p 4 4 2}
calculated element-by-element.

{p 4 4 2}
{cmd:mreldif(}{it:X}, {it:Y}{cmd:)} returns the maximum relative difference
and is equivalent to {cmd:max(reldif(}{it:X}, {it:Y}{cmd:))}.

{p 4 4 2}
{cmd:mreldifsym(}{it:X}{cmd:)} is equivalent to 
{cmd:mreldif(}{it:X}{cmd:',} {it:X}{cmd:)}, and so is a measure of 
how far the matrix is from being symmetric (Hermitian).

{p 4 4 2}
{cmd:mreldifre(}{it:X}{cmd:)} is equivalent to 
{cmd:mreldif(Re(}{it:X}{cmd:),} {it:X}{cmd:)}, and so is a measure of 
how far the matrix is from being real.


{title:Conformability}

    {cmd:reldif(}{it:X}, {it:Y}{cmd:)}:
		{it:X}:  {it:r x c}
		{it:y}:  {it:r x c}
	   {it:result}:  {it:r x c}

    {cmd:mreldif(}{it:X}, {it:Y}{cmd:)}:
		{it:X}:  {it:r x c}
		{it:y}:  {it:r x c}
	   {it:result}:  1 {it:x} 1

    {cmd:mreldifsym(}{it:X}{cmd:)}:
		{it:X}:  {it:n x n}
	   {it:result}:  1 {it:x} 1

    {cmd:mreldifre(}{it:X}{cmd:)}:
		{it:X}:  {it:r x c}
	   {it:result}:  1 {it:x} 1

{title:Diagnostics}

{p 4 4 2}
The relative difference function treats equal missing values as having a 
difference of 0 and different missing values as having a difference of 
missing ({cmd:.}):

{p 8 8 2}
{cmd:reldif(., .)} == {cmd:reldif(.a, .a)} == ... == {cmd:reldif(.z, .z)} == 0

{p 8 8 2}
{cmd:reldif(., .a)} == {cmd:reldif(., .z)} == ... == {cmd:reldif(.y, .z)} == .


{title:Source code}

{p 4 4 2}
Functions are built-in.


{title:Also see}

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

{p 4 13 2}
Online:  help for 
{bf:{help m4_utility:[M-4] utility}}
{p_end}