mf_lowertriangle.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}
{* 03dec2004}{...}
{cmd:help mata lowertriangle()}
{hline}
{* index lowertriangle()}{...}
{* index uppertriangle()}{...}
{* index _lowertriangle()}{...}
{* index _uppertriangle()}{...}

{title:Title}

{p 4 4 2}
{bf:[M-5] lowertriangle() -- Extract lower or upper triangle}


{title:Syntax}

{p 8 12 2}
{it:numeric matrix}
{cmd:lowertriangle(}{it:numeric matrix A} [{cmd:,}
{it:numeric scalar d}]{cmd:)}

{p 8 12 2}
{it:numeric matrix}
{cmd:uppertriangle(}{it:numeric matrix A} [{cmd:,}
{it:numeric scalar d}]{cmd:)}


{p 8 12 2}
{it:void}{bind:         }
{cmd:_lowertriangle(}{it:numeric matrix A} [{cmd:,}
{it:numeric scalar d}]{cmd:)}

{p 8 12 2}
{it:void}{bind:         }
{cmd:_uppertriangle(}{it:numeric matrix A} [{cmd:,}
{it:numeric scalar d}]{cmd:)}


{p 4 4 2}
where argument {it:d} is optional.


{title:Description}

{p 4 4 2}
{cmd:lowertriangle()} returns the lower triangle of
{it:A}.

{p 4 4 2}
{cmd:uppertriangle()} returns the upper triangle of
{it:A}.

{p 4 4 2}
{cmd:_lowertriangle()} replaces {it:A} with its lower triangle.

{p 4 4 2}
{cmd:_uppertriangle()} replaces {it:A} with its upper triangle.


{title:Remarks}

{p 4 4 2}
Remarks are presented under the headings

	{bf:Optional argument d}
	{bf:Nonsquare matrices}


{title:Optional argument d}

{p 4 4 2}
Optional argument {it:d} specifies the treatment of the diagonal.
Specifying {it:d}>={cmd:.}, or not specifying {it:d} at all, means no 
special treatment; if

                                {c TLC}{c -}       {c -}{c TRC}
		                {c |} 1  2  3 {c |}
		        {it:A}    =  {c |} 4  5  6 {c |}
		                {c |} 7  8  9 {c |}
                                {c BLC}{c -}       {c -}{c BRC}

    then

                                {c TLC}{c -}       {c -}{c TRC}
		                {c |} 1  0  0 {c |}
	{cmd:lowertriangle(}{it:A}{cmd:, .)}  =  {c |} 4  5  0 {c |}
		                {c |} 7  8  9 {c |}
                                {c BLC}{c -}       {c -}{c BRC}

{p 4 4 2}
If a nonmissing value is specified for {it:d}, however, that value is 
substituted for each element of the diagonal, for example, 

                                {c TLC}{c -}       {c -}{c TRC}
		                {c |} 1  0  0 {c |}
	{cmd:lowertriangle(}{it:A}{cmd:, 1)}  =  {c |} 4  1  0 {c |}
		                {c |} 7  8  1 {c |}
                                {c BLC}{c -}       {c -}{c BRC}


{title:Nonsquare matrices}

{p 4 4 2}
{cmd:lowertriangle()} and {cmd:uppertriangle()} may be used with nonsquare
matrices.  If

                                {c TLC}{c -}          {c -}{c TRC}
		                {c |} 1  2  3  4 {c |}
		        {it:A}    =  {c |} 5  6  7  8 {c |}
		                {c |} 9 10 11 12 {c |}
                                {c BLC}{c -}          {c -}{c BRC}

    then

                                {c TLC}{c -}       {c -}{c TRC}
		                {c |} 1  0  0 {c |}
	   {cmd:lowertriangle(}{it:A}{cmd:)}  =  {c |} 5  6  0 {c |}
		                {c |} 9 10 11 {c |}
                                {c BLC}{c -}       {c -}{c BRC}

    and

                                {c TLC}{c -}          {c -}{c TRC}
		                {c |} 1  2  3  4 {c |}
	   {cmd:uppertriangle(}{it:A}{cmd:)}  =  {c |} 0  6  7  8 {c |}
		                {c |} 0  0 11 12 {c |}
                                {c BLC}{c -}          {c -}{c BRC}

{p 4 4 2}
{cmd:_lowertriangle()} and 
{cmd:_uppertriangle()}, however, may not be used with nonsquare matrices.


{title:Conformability}

    {cmd:lowertriangle(}{it:A}{cmd:,} {it:d}{cmd:)}:
		{it:A}:  {it:r x c}
		{it:d}:  1 {it:x} 1        (optional)
	   {it:result}:  {it:r x} min({it:r},{it:c})

    {cmd:uppertriangle(}{it:A}{cmd:,} {it:d}{cmd:)}:
		{it:A}:  {it:r x c}
		{it:d}:  1 {it:x} 1        (optional)
	   {it:result}:  min({it:r},{it:c}) {it:x c}

{p 4 4 2}
    {cmd:_lowertriangle(}{it:A}{cmd:,} {it:d}{cmd:)},
    {cmd:_uppertriangle(}{it:A}{cmd:,} {it:d}{cmd:)}:
{p_end}
	{it:input:}
		{it:A}:  {it:n x n}
		{it:d}:  1 {it:x} 1        (optional)
	{it:output:}
		{it:A}:  {it:n x n}


{title:Diagnostics}

{p 4 4 2}
None.


{title:Source code}

{p 4 4 2}
{view lowertriangle.mata, adopath asis:lowertriangle.mata},
{view uppertriangle.mata, adopath asis:uppertriangle.mata},
{view _lowertriangle.mata, adopath asis:_lowertriangle.mata},
{view _uppertriangle.mata, adopath asis:_uppertriangle.mata}


{title:Also see}

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

{p 4 13 2}
Online:  help for 
{bf:{help m4_manipulation:[M-4] manipulation}}
{p_end}