m4_matrix.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}
{* 02apr2005}{...}
{cmd:help m4 matrix}
{hline}
{* index matrix functions}{...}
{* index mathematical functions}{...}

{title:Title}

{p 4 4 2}
{bf:[M-4] matrix -- Matrix functions}


{title:Contents}

{col 5}   {bf:[M-5]}
{col 5}{bf:Manual entry{col 22}Function{col 40}Purpose}
{col 5}{hline}

{col 5}   {c TLC}{hline 17}{c TRC}
{col 5}{hline 3}{c RT}{it: Characteristics }{c LT}{hline}
{col 5}   {c BLC}{hline 17}{c BRC}

{col 5}{bf:{help mf_trace:trace()}}{...}
{col 22}{cmd:trace()}{...}
{col 40}trace of matrix
{...}

{col 5}{bf:{help mf_det:det()}}{...}
{col 22}{cmd:det()}{...}
{col 40}determinant
{col 22}{cmd:dettriangular()}{...}
{col 40}determinant of triangular matrix

{col 5}{bf:{help mf_norm:norm()}}{...}
{col 22}{cmd:norm()}{...}
{col 40}matrix and vector norms
{...}

{col 5}{bf:{help mf_cond:cond()}}{...}
{col 22}{cmd:cond()}{...}
{col 40}matrix condition number
{...}

{col 5}{bf:{help mf_rank:rank()}}{...}
{col 22}{cmd:rank()}{...}
{col 40}rank of matrix


{col 5}   {c TLC}{hline 46}{c TRC}
{col 5}{hline 3}{c RT}{it: Cholesky decomposition, solvers, & inverters }{c LT}{hline}
{col 5}   {c BLC}{hline 46}{c BRC}

{col 5}{bf:{help mf_cholesky:cholesky()}}{...}
{col 22}{cmd:cholesky()}{...}
{col 40}Cholesky square-root decomposition {it:A}={it:GG}{bf:'}

{col 5}{bf:{help mf_cholsolve:cholsolve()}}{...}
{col 22}{cmd:cholsolve()}{...}
{col 40}solve {it:AX} = {it:B} for {it:X}

{col 5}{bf:{help mf_cholinv:cholinv()}}{...}
{col 22}{cmd:cholinv()}{...}
{col 40}inverse of pos. def. symmetric matrix

{col 5}{bf:{help mf_invsym:invsym()}}{...}
{col 22}{cmd:invsym()}{...}
{col 40}real symmetric matrix inversion

{col 5}   {c TLC}{hline 40}{c TRC}
{col 5}{hline 3}{c RT}{it: LU decomposition, solvers, & inverters }{c LT}{hline}
{col 5}   {c BLC}{hline 40}{c BRC}

{col 5}{bf:{help mf_lud:lud()}}{...}
{col 22}{cmd:lud()}{...}
{col 40}LU decomposition {it:A} = {it:PLU}

{col 5}{bf:{help mf_lusolve:lusolve()}}{...}
{col 22}{cmd:lusolve()}{...}
{col 40}solve {it:AX} = {it:B} for {it:X}

{col 5}{bf:{help mf_luinv:luinv()}}{...}
{col 22}{cmd:luinv()}{...}
{col 40}inverse of square matrix

{col 5}   {c TLC}{hline 40}{c TRC}
{col 5}{hline 3}{c RT}{it: QR decomposition, solvers, & inverters }{c LT}{hline}
{col 5}   {c BLC}{hline 40}{c BRC}

{col 5}{bf:{help mf_qrd:qrd()}}{...}
{col 22}{cmd:qrd()}{...}
{col 40}QR decomposition {it:A} = {it:QR}
{col 22}{cmd:qrdp()}{...}
{col 40}QR decomposition {it:A} = {it:QRP}{bf:'}
{col 22}{cmd:hqrd()}{...}
{col 40}QR decomposition {it:A} = {it:f}({it:H}){it:R1}
{col 22}{cmd:hqrdp()}{...}
{col 40}QR decomposition {it:A} = {it:f}({it:H},{it:tau}){it:R1}{it:P}{bf:'}
{col 22}{cmd:hqrdmultq()}{...}
{col 40}return {it:QX} or {it:Q}{bf:'}{it:X}, {it:Q} = {it:f}({it:H},{it:tau})
{col 22}{cmd:hqrdmultq1t()}{...}
{col 40}return {it:Q1}{bf:'}{it:X},     {it:Q1} = {it:f}({it:H},{it:tau})
{col 22}{cmd:hqrdq()}{...}
{col 40}return {it:Q}  = {it:f}({it:H},{it:tau})
{col 22}{cmd:hqrdq1()}{...}
{col 40}return {it:Q1} = {it:f}({it:H},{it:tau})
{col 22}{cmd:hqrdr()}{...}
{col 40}return {it:R}
{col 22}{cmd:hqrdr1()}{...}
{col 40}return {it:R1}

{col 5}{bf:{help mf_qrsolve:qrsolve()}}{...}
{col 22}{cmd:qrsolve()}{...}
{col 40}solve {it:AX} = {it:B} for {it:X}

{col 5}{bf:{help mf_qrinv:qrinv()}}{...}
{col 22}{cmd:qrinv()}{...}
{col 40}generalized inverse of matrix

{col 5}   {c TLC}{hline 52}{c TRC}
{col 5}{hline 3}{c RT}{it: Singular value decomposition, solvers, & inverters }{c LT}{hline}
{col 5}   {c BLC}{hline 52}{c BRC}

{col 5}{bf:{help mf_svd:svd()}}{...}
{col 22}{cmd:svd()}{...}
{col 40}singular value decomposition {it:A} = {it:UDV}{bf:'}
{col 22}{cmd:svdsv()}{...}
{col 40}singular values {it:s}

{col 5}{bf:{help mf_fullsvd:fullsvd()}}{...}
{col 22}{cmd:fullsvd()}{...}
{col 40}singular value decomposition {it:A} = {it:USV}{bf:'}
{col 22}{cmd:fullsdiag()}{...}
{col 40}convert {it:s} to {it:S} 

{col 5}{bf:{help mf_svsolve:svsolve()}}{...}
{col 22}{cmd:svsolve()}{...}
{col 40}solve {it:AX} = {it:B} for {it:X}

{col 5}{bf:{help mf_pinv:pinv()}}{...}
{col 22}{cmd:pinv()}{...}
{col 40}Moore-Penrose pseudoinverse

{col 5}   {c TLC}{hline 20}{c TRC}
{col 5}{hline 3}{c RT}{it: Triangular solvers }{c LT}{hline}
{col 5}   {c BLC}{hline 20}{c BRC}

{col 5}{bf:{help mf_solvelower:solvelower()}}{...}
{col 22}{cmd:solvelower()}{...}
{col 40}solve {it:AX} = {it:B} for {it:X}, {it:A} lower triangular
{col 22}{cmd:solveupper()}{...}
{col 40}solve {it:AX} = {it:B} for {it:X}, {it:A} upper triangular

{col 5}   {c TLC}{hline 42}{c TRC}
{col 5}{hline 3}{c RT}{it: Eigensystems, powers, and transcendental }{c LT}{hline}
{col 5}   {c BLC}{hline 42}{c BRC}

{col 5}{bf:{help mf_eigensystem:eigensystem()}}{...}
{col 22}{cmd:eigensystem()}{...}
{col 40}eigenvalues & eigenvectors
{col 22}{cmd:eigenvalues()}{...}
{col 40}eigenvalues
{col 22}{cmd:symeigensystem()}{...}
{col 40}eigenvalues & eigenvectors of symmetric
{col 22}{cmd:symeigenvalues()}{...}
{col 40}eigenvalues of symmetric
{col 22}{cmd:lefteigensystem()}{...}
{col 40}eigenvalues & left eigenvectors

{col 5}{bf:{help mf_matpowersym:matpowersym()}}{...}
{col 22}{cmd:matpowersym()}{...}
{col 40}powers of symmetric matrix

{col 5}{bf:{help mf_matexpsym:matexpsym()}}{...}
{col 22}{cmd:matexpsym()}{...}
{col 40}exponentiation of symmetric matrix
{col 22}{cmd:matlogsym()}{...}
{col 40}logarithm of symmetric matrix

{col 5}   {c TLC}{hline 15}{c TRC}
{col 5}{hline 3}{c RT}{it: Equilibration }{c LT}{hline}
{col 5}   {c BLC}{hline 15}{c BRC}

{col 5}{bf:{help mf__equilrc:_equilrc()}}{...}
{col 22}{cmd:_equilrc()}{...}
{col 40}row/column equilibration
{col 22}{cmd:_equilr()}{...}
{col 40}row equilibration
{col 22}{cmd:_equilc()}{...}
{col 40}column equilibration
{col 22}{cmd:_perhapsequilrc()}{...}
{col 40}row/column equilibration if necs.
{col 22}{cmd:_perhapsequilr()}{...}
{col 40}row equilibration if necs.
{col 22}{cmd:_perhapsequilc()}{...}
{col 40}column equilibration if necs.
{col 22}{cmd:rowscalefactors()}{...}
{col 40}row scale factors for equilibration
{col 22}{cmd:colscalefactors()}{...}
{col 40}column scale factors for equilibration
{col 5}{hline}


{title:Description}

{p 4 4 2}
The above functions are what most people would call mathematical matrix
functions.  


{title:Remarks}

{p 4 4 2}
For other mathematical functions, see

	{bf:{help m4_scalar:[M-4] scalar}}          Scalar mathematical functions

	{bf:{help m4_mathematical:[M-4] mathematical}}    Important mathematical functions
	

{title:Also see}

{p 4 13 2}
Manual:  {hi:[M-4] matrix}

{p 4 13 2}
Online:  help for 
{bf:{help m4_intro:[M-4] intro}},
{bf:{help mata:[M-0] intro}}
{p_end}