gretl-common 1.9.6-1build1 / usr / share / gretl / genrgui.hlp.pt

## Acessores

# $ahat access
Output: 	series 

Tem que ser acedido após a estimação de um modelo de dados de painel com efeitos fixos. Retorna uma série contendo as estimativas dos efeitos fixos individuais (interceptores unitários). 

# $aic access
Output: 	scalar 

Retorna o Critério de Informação de Akaike para o último modelo estimado, se disponível. Consultar <@pdf="the Gretl User's Guide"> para detalhes sobre o cálculo. 

# $bic access
Output: 	scalar 

Retorna o Critério de Informação Bayesiano de Schwarz para o último modelo estimado, se disponível. Consultar <@pdf="the Gretl User's Guide"> para detalhes sobre o cálculo. 

# $chisq access
Output: 	scalar 

Retorna a estatística qui-quadrado global para o último modelo estimado, se disponível. 

# $coeff access
Output: 	matrix 
Argument: 	<@var="s">  (name of coefficient, optional)

Sem argumentos, <@lit="$coeff"> retorna um vector coluna contendo os coeficientes estimados para o último modelo. Com o argumento opcional do tipo texto retorna um escalar, designadamente o parâmetro estimado com o nome <@var="s">. See also <@ref="$stderr">, <@ref="$vcv">. 

Exemplo: 

<code>          
	  open bjg
	  arima 0 1 1 ; 0 1 1 ; lg 
	  b = $coeff               # obtém um vector
	  macoef = $coeff(theta_1) # obtém um escalar
</code>

Se o "modelo" em questão é realmente um sistema, o resultado depende das características do sistema: no caso de VARs e VECMs o valor retornado é uma matriz com uma coluna por equação, senão é um vector coluna contendo os coeficientes para a primeira equação seguidos pelos da segunda equação, e por aí adiante. 

# $command access
Output: 	string 

Tem que ser acedido após a estimação de modelo; retorna o nome do comando, por exemplo <@lit="ols"> ou <@lit="probit">. 

# $compan access
Output: 	matrix 

Tem que ser acedido após a estimação de VAR ou VECM; retorna a matriz companheira. 

# $datatype access
Output: 	scalar 

Retorna um valor inteiro representando o tipo de conjunto de dados que está carregado: 0 = sem dados; 1 = dados de secção-cruzada (sem data); 2 = dados de série temporal; 3 = dados de painel. 

# $depvar access
Output: 	string 

Tem que ser acedido após a estimação de um modelo de equação singular; retorna o nome da variável dependente. 

# $df access
Output: 	scalar 

Retorna os graus de liberdade do último modelo estimado. Se o último modelo era na realidade um sistema de equações, o valor retornado é o grau de liberdade por equação; se este for diferente nas equações então o valor é o número de observações menos o número médio de coeficientes por equação (arredondado para o inteiro mais próximo). 

# $dwpval access
Output: 	scalar 

Retorna o valor p para a estatística Durbin–Watson para o último modelo estimado, se disponível. Isto é determinado usando um procedimento Imhof. 

# $ec access
Output: 	matrix 

Tem que ser acedido após a estimação de VECM; retorna a matriz contendo os termos de correção de erro. O número de linhas é igual ao número de observações usadas e o número de colunas é igual ao nível de cointegração do sistema. 

# $error access
Output: 	scalar 

Retorna o código de erro interno do programa, que será diferente de zero no caso de ter acontecido um erro mas este tenha sido apanhado num bloco <@xrf="catch">. Note que ao usar este acessor o código de erro interno ficará reiniciado a zero. Consultar também <@ref="errmsg">. Se você pretender uma mensagem de erro associada a um certo <@lit="$error"> então tem que guardar o valor numa variável temporária, tal como em 

<code>          
	  errval = $error
	  if (errval) 
	    printf "Obtido o erro %d (%s)\n", errval, errmsg(errval);
	  endif
</code>

# $ess access
Output: 	scalar 

Retorna o erro de soma de quadrados do último modelo estimado, se disponível. 

# $evals access
Output: 	matrix 

Tem que ser acedido após a estimação de VECM; retorna um vector contendo os valores próprios que são utilizados no cálculo do teste traço da cointegração. 

# $fcast access
Output: 	matrix 

Tem que ser acedido a seguir a um comando de predição <@xrf="fcast">; retorna os valores de predição numa matriz. Se o modelo em que a predição se baseou é um sistema de equações a matriz retornada terá uma coluna por equação, caso contrário será um vector coluna. 

# $fcerr access
Output: 	matrix 

Tem que ser acedido a seguir a um comando de predição <@xrf="fcast">; retorna os erros padrão de uma predição, se disponível, numa matriz. Se o modelo em que a predição se baseou é um sistema de equações a matriz retornada terá uma coluna por equação, caso contrário será um vector coluna. 

# $fevd access
Output: 	matrix 

Tem que ser acedido após a estimação de VAR. Retorna a matriz contendo a decomposição de erro da predição. Esta matriz tem <@itl="h"> linhas onde <@itl="h"> é um horizonte de predição, que pode ser escolhido com <@lit="set horizon"> ou, caso contrário, é determinado automaticamente baseado na frequência dos dados. No caso de VAR com <@itl="p"> variáveis, a matriz tem <@itl="p"><@sup="2"> colunas. A fracção da predição de erro para a variável <@itl="i"> associável à inovação na variável <@itl="j"> encontra-se na coluna (<@itl="i"> – 1)<@itl="p"> + <@itl="j">. 

# $Fstat access
Output: 	scalar 

Retorna a estatística F global do último modelo estimado, se disponível. 

# $gmmcrit access
Output: 	scalar 

Tem que ser acedido a seguir a um bloco <@lit="gmm">. Retorna o valor da função objetivo no seu mínimo. 

# $h access
Output: 	series 

Tem que ser acedido a seguir a um comando <@lit="garch">. Retorna a série da variância condicional estimada. 

# $hausman access
Output: 	row vector 

Tem que ser acedido após a estimação de modelo <@lit="tsls"> ou <@lit="painel"> com a opção de efeitos aleatórios. Retorna um vector 1×3 contendo o valor da estatística de teste Hausmam, com os graus de liberdade correspondentes e o valor p do teste, por essa ordem. 

# $hqc access
Output: 	scalar 

Retorna o Critério de Informação de Hannan-Quinn para o último modelo estimado, se disponível. Consultar <@pdf="the Gretl User's Guide"> para detalhes sobre o cálculo. 

# $jalpha access
Output: 	matrix 

Tem que ser acedido após a estimação de VECM, e retorna a matriz das cargas. Contém tantas linhas como as variáveis em VECM e o mesmo número de colunas que o nível de cointegração. 

# $jbeta access
Output: 	matrix 

Tem que ser acedido após a estimação de VECM, e retorna a matriz de cointegração. Contém tantas linhas como as variáveis em VECM (mais um número de variáveis exógenas que estão restritas a um espaço de cointegração, caso existam), e o mesmo número de colunas que o nível de cointegração. 

# $jvbeta access
Output: 	square matrix 

Tem que ser acedido após a estimação de VECM, e retorna a matriz de covariância estimada para os elementos dos vectores de cointegração. 

No caso de uma estimação não-restringida, esta matriz tem um número de linhas igual ao número de elementos não-restringidos do espaço de cointegração após uma normalização de Phillips. Se, no entanto, um sistema restringido for estimado por meio de um comando <@lit="restrict"> com a opção <@lit="--full">, será retornada uma matriz singular com <@itl="(n+m)r"> linhas (onde <@itl="n"> é o número de variáveis endógenas, <@itl="m"> é o número de variáveis exógenas no espaço de cointegração, e <@itl="r"> o nível de cointegração). 

Exemplo: o código 

<code>          
	  open denmark.gdt
	  vecm 2 1 LRM LRY IBO IDE --rc --seasonals -q
	  s0 = $jvbeta

	  restrict --full
	  b[1,1] = 1
	  b[1,2] = -1
	  b[1,3] + b[1,4] = 0
	  end restrict
	  s1 = $jvbeta

	  print s0
	  print s1
</code>

produz o seguinte resultado. 

<code>          
	  s0 (4 x 4)

	    0.019751     0.029816  -0.00044837     -0.12227 
	    0.029816      0.31005     -0.45823     -0.18526 
	 -0.00044837     -0.45823       1.2169    -0.035437 
	    -0.12227     -0.18526    -0.035437      0.76062 

	  s1 (5 x 5)

	  0.0000       0.0000       0.0000       0.0000       0.0000 
	  0.0000       0.0000       0.0000       0.0000       0.0000 
	  0.0000       0.0000      0.27398     -0.27398    -0.019059 
	  0.0000       0.0000     -0.27398      0.27398     0.019059 
	  0.0000       0.0000    -0.019059     0.019059    0.0014180
</code>

# $llt access
Output: 	series 

Para certos modelos estimados por Máxima Verosimilhança, retorna uma série de valores de log-verosimilhança por observação. Presentemente isto é apenas possível para logit binário, probit, tobit e heckit. 

# $lnl access
Output: 	scalar 

Retorna o log-verosimilhança para último modelo estimado (quando aplicável). 

# $mnlprobs access
Output: 	matrix 

Deve seguir-se à estimação de um modelo logit multinomial (apenas), obtém uma matriz que contém as probabilidades de cada possível resultado em cada observação no intervalo da amostra do modelo. Cada linha representa uma observação e cada coluna um resultado. 

# $ncoeff access
Output: 	scalar 

Retorna o número total de coeficientes estimados no último modelo. 

# $nobs access
Output: 	scalar 

Retorna o número de observações na amostra presentemente seleccionada. 

# $nvars access
Output: 	scalar 

Retorna o número de variáveis no conjunto de dados (incluindo a constante). 

# $pd access
Output: 	scalar 

Retorna a frequência ou periodicidade dos dados (por exemplo, 4 para dados trimestrais). No caso de dados de painel, o valor retornado é o comprimento da série temporal. 

# $pvalue access
Output: 	scalar or matrix 

Retorna o valor p da estatística de teste que foi determinada pelo último comando com testes de hipóteses explícito (por exemplo, <@lit="chow">). Consultar <@pdf="the Gretl User's Guide"> para detalhes. 

Na maior parte dos casos, o valor retornado é um escalar, mas por vezes é uma matriz (por exemplo, um traço e o max-lambda, ou valores p de um teste de cointegração de Johansen); nesse caso os valores na matriz estão dispostos de igual modo como nos resultados escritos. 

See also <@ref="$test">. 

# $rho access
Output: 	scalar 
Argument: 	<@var="n">  (scalar, optional)

Sem argumentos, retorna o coeficiente autoregressivo de primeira ordem para os resíduos do último modelo. Após se ter estimado um modelo com o comando <@lit="ar">, a sintaxe <@lit="$rho(n)"> retorna a estimativa correspondente de ρ(<@itl="n">). 

# $rsq access
Output: 	scalar 

Retorna o <@itl="R"><@sup="2"> não ajustado do último modelo estimado, se disponível. 

# $sample access
Output: 	series 

Tem que ser acedido após a estimação de um modelo com uma única equação. Retorna uma série auxiliar com valores 1 para observações utilizadas na estimação, 0 para observações dentro do intervalo amostral corrente mas não utilizadas (eventualmente por causa de valores omissos), e NA para observações fora do intervalo amostral corrente. 

Se você desejar calcular estatísticas baseadas na amostra que foi utilizada para um dado modelo, você pode fazer, por exemplo: 

<code>          
	  ols y 0 xlist
	  genr sdum = $sample
	  smpl sdum --dummy
</code>

# $sargan access
Output: 	row vector 

Tem que ser acedido a seguir a um comando <@lit="tsls">. Retorna um vector 1×3, contendo o valor do Sargan over-identification test estatística, a corresponding graus de liberdade e valor p, por essa ordem. 

# $sigma access
Output: 	scalar or matrix 

Requer que tenha sido estimado um modelo. Se o último modelo era de equação única, retorna o (escalar) Erro Padrão da Regressão (ou por outras palavras, o desvio padrão dos resíduos, com a adequada correção de graus de liberdade). Se o último modelo era um sistema de equações, retorna a equação-cruzada da matriz de covariância dos resíduos. 

# $stderr access
Output: 	matrix 
Argument: 	<@var="s">  (name of coefficient, optional)

Sem argumentos, <@lit="$stderr"> retorna um vector coluna contendo o erro padrão dos coeficientes para o último modelo. Com o argumento opcional de texto, retorna um escalar, designadamente o erro padrão do parâmetro com o nome <@var="s">. 

Se o "modelo" em questão é realmente um sistema, o resultado depende das características do sistema: para VARs e VECMs o valor retornado é uma matriz com uma coluna por equação, senão é um vector coluna contendo os coeficientes para a primeira equação seguidos pelos da segunda equação, e por aí adiante. 

See also <@ref="$coeff">, <@ref="$vcv">. 

# $stopwatch access
Output: 	scalar 

Tem que ser precedido por <@lit="set stopwatch">, o que activa a medição do tempo de CPU. O primeiro uso deste acessor contém os segundos de tempo de CPU que passaram desde o comando <@lit="set stopwatch">. Em cada acesso o relógio é reinicializado, por isso as chamadas subsequentes de <@lit="$stopwatch"> obtêm os segundos de tempo de CPU desde o último acesso. 

# $sysA access
Output: 	matrix 

Tem que ser acedido após a estimação simultânea de equações de sistema. Retorna a matriz de coeficientes das variáveis endógenas desfasadas, se existirem, numa forma estrutural de sistema. Consultar o comando <@xrf="system">. 

# $sysB access
Output: 	matrix 

Tem que ser acedido após a estimação simultânea de equações de sistema. Retorna a matriz de coeficientes das variáveis exógenas numa forma estrutural de sistema. Consultar o comando <@xrf="system">. 

# $sysGamma access
Output: 	matrix 

Tem que ser acedido após a estimação simultânea de equações de sistema. Retorna a matriz de coeficientes das variáveis endógenas contemporâneas numa forma estrutural de sistema. Consultar o comando <@xrf="system">. 

# $T access
Output: 	scalar 

Retorna o número de observações utilizadas durante a estimação do último modelo. 

# $t1 access
Output: 	scalar 

Retorna o índice de base 1 da primeira observação na amostra correntemente seleccionada. 

# $t2 access
Output: 	scalar 

Retorna o índice de base 1 da última observação na amostra correntemente seleccionada. 

# $test access
Output: 	scalar or matrix 

Retorna o valor da estatística de teste que foi determinado pelo último comando com testes de hipóteses explícito, se algum (por exemplo, <@lit="chow">). Consultar <@pdf="the Gretl User's Guide"> para detalhes. 

Na maior parte dos casos, o valor retornado é um escalar, mas por vezes é uma matriz (por exemplo, um traço e o max-lambda, de um teste de cointegração de Johansen); nesse caso os valores na matriz estão dispostos de igual modo como nos resultados escritos. 

See also <@ref="$pvalue">. 

# $trsq access
Output: 	scalar 

Retorna <@itl="TR"><@sup="2"> (tamanho da amostra vezes R-quadrado) do último modelo, se disponível. 

# $uhat access
Output: 	series 

Retorna os resíduos do último modelo. Isto pode ter significados diferentes para diferentes estimadores. Por exemplo, depois de uma estimação ARMA, <@lit="$uhat"> conterá o erro de predição um-passo-à-frente; depois de um modelo probit, conterá os resíduos generalizados. 

Se o "modelo" em questão é realmente um sistema (VAR ou VECM, ou sistema de equações simultâneas), <@lit="$uhat"> sem parâmetros obtém uma matriz de resíduos, uma coluna por equação. 

# $unit access
Output: 	series 

Apenas válido para conjunto de dados de painel. Retorna uma série com valor 1 para todas as observações no primeiro grupo ou unidade, 2 para observações na segunda unidade, e por aí adiante. 

# $vcv access
Output: 	matrix 
Arguments:	<@var="s1">  (name of coefficient, optional)
		<@var="s2">  (name of coefficient, optional)

Sem argumentos, <@lit="$vcv"> retorna uma matriz quadrada contendo a matriz de covariância estimada para os coeficientes do último modelo. Se o último modelo é de equação única, então você pode fornecer nomes de dois parâmetros em parênteses para obter a covariância estimada entre os dois parâmetros chamados <@var="s1"> e <@var="s2">. See also <@ref="$coeff">, <@ref="$stderr">. 

Este acessor não pode ser utilizado para modelos VARs ou VECMs; para modelos deste tipo veja <@ref="$sigma"> e <@ref="$xtxinv">. 

# $vecGamma access
Output: 	matrix 

Tem que ser acedido após a estimação de VECM; retorna a matriz in which a Gamma matrices (coeficientes on a lagged differences de a cointegrated variáveis) are stacked side by side. Each row represents an equação; para VECM de lag order <@itl="p"> there are <@itl="p"> – 1 sub-matrices. 

# $version access
Output: 	scalar 

Retorna um valor inteiro that codes para program version. The gretl version string takes a form <@lit="x.y.z"> (por exemplo, 1.7.6). The return valor from this accessor is formed as <@lit="10000*x + 100*y + z">, so that 1.7.6 translates as 10706. 

# $vma access
Output: 	matrix 

Tem que ser acedido após a estimação de VAR ou a VECM; retorna a matriz contendo o VMA representation up to a order specified via a <@lit="set horizon"> command. Consultar <@pdf="the Gretl User's Guide"> for details. 

# $windows access
Output: 	scalar 

Retorna 1 if gretl is running on MS Windows, caso contrário 0. By conditioning on a valor de this variable yor can write shell calls that are portable across different operating sistemas. 

Also see a <@xrf="shell"> command. 

# $xlist access
Output: 	list 

Retorna o list de regressors do último modelo (for single-equação modelos only). 

# $xtxinv access
Output: 	matrix 

Following estimation de a VAR ou VECM (only), retorna <@itl="X'X"><@sup="-1">, where <@itl="X"> is a common matriz de regressors used in each de a equações. This accessor is not available para VECM estimado with a restriction imposed on α, a "loadings" matriz. 

# $yhat access
Output: 	series 

Retorna o fitted values do último regression. 

## Functions proper

# abs math
Output: 	same type as input 
Argument: 	<@var="x">  (scalar, series or matrix)

Retorna o absolute valor de <@var="x">. 

# acos math
Output: 	same type as input 
Argument: 	<@var="x">  (scalar, series or matrix)

Retorna o arc cosine de <@var="x">, that is, a value whose cosine is <@var="x">. The result is in radians; a input shorld be in a range –1 to 1. 

# acosh math
Output: 	same type as input 
Argument: 	<@var="x">  (scalar, series or matrix)

Retorna o inverse hyperbolic cosine de <@var="x"> (positive solution). <@var="x"> shorld be greater than 1; caso contrário, NA is returned. See also <@ref="cosh">. 

# argname strings
Output: 	string 
Argument: 	<@var="s">  (string)

For <@var="s"> o nome da parameter to a user-defined function, retorna o nome da corresponding argument, ou an empty string if a argument was anonymors. 

# asin math
Output: 	same type as input 
Argument: 	<@var="x">  (scalar, series or matrix)

Retorna o arc sine de <@var="x">, that is, a value whose sine is <@var="x">. The result is in radians; a input shorld be in a range –1 to 1. 

# asinh math
Output: 	same type as input 
Argument: 	<@var="x">  (scalar, series or matrix)

Retorna o inverse hyperbolic sine de <@var="x">. See also <@ref="sinh">. 

# atan math
Output: 	same type as input 
Argument: 	<@var="x">  (scalar, series or matrix)

Retorna o arc tangent de <@var="x">, that is, a value whose tangent is <@var="x">. The result is in radians. 

# atanh math
Output: 	same type as input 
Argument: 	<@var="x">  (scalar, series or matrix)

Retorna o inverse hyperbolic tangent de <@var="x">. See also <@ref="tanh">. 

# bessel math
Output: 	same type as input 
Arguments:	<@var="type">  (character)
		<@var="v">  (scalar)
		<@var="x">  (scalar, series or matrix)

Computes uma de a Bessel function variants for order <@var="v"> e argument <@var="x">. The return valor is de a same type as <@var="x">. The specific function is selected by a first argument, which must be <@lit="J">, <@lit="Y">, <@lit="I">, ou <@lit="K">. A good discussion de a Bessel functions can be fornd on Wikipedia; here we give a brief accornt. 

case <@lit="J">: Bessel function de a first kind. Resembles a damped sine wave. Defined for real <@var="v"> and <@var="x">, but if <@var="x"> is negative then <@var="v"> must be an integer. 

case <@lit="Y">: Bessel function de a second kind. Defined for real <@var="v"> e <@var="x"> but has a singularity at <@var="x"> = 0. 

case <@lit="I">: Modified Bessel function de a first kind. An exponentially growing function. Acceptable arguments are as for case <@lit="J">. 

case <@lit="K">: Modified Bessel function de a second kind. An exponentially decaying function. Diverges at <@var="x"> = 0 e is not defined for negative <@var="x">. Symmetric arornd <@var="v"> = 0. 

# BFGSmax numerical
Output: 	scalar 
Arguments:	<@var="b">  (vector)
		<@var="f">  (function call)
		<@var="g">  (function call, optional)

Numerical maximization via a method de Broyden, Fletcher, Goldfarb e Shanno. The vector <@var="b"> shorld hold a initial values de a set de parameters, e a argument <@var="f"> shorld specify a call to a function that calculates a (scalar) criterion to be maximized, given a current parameter values and any other relevant data. Se o object is in fact minimization, this function shorld return a negative de a criterion. On successful completion, <@lit="BFGSmax"> retorna a maximized valor de a criterion, e <@var="b"> holds a parameter values which produce a maximum. 

The optional third argument provides a means de supplying analytical derivatives (otherwise a gradient is computed numerically). The gradient function call <@var="g"> must have as its first argument a pre-defined matriz that is de a correct size to contain a gradient, given in pointer form. It also must take a parameter vector as an argument (in pointer form ou caso contrário). Other arguments are optional. 

For more details e examples see a chapter on special functions in <@lit="genr"> in <@pdf="the Gretl User's Guide">. See also <@ref="NRmax">, <@ref="fdjac">. 

# bkfilt filters
Output: 	series 
Arguments:	<@var="y">  (series)
		<@var="f1">  (scalar, optional)
		<@var="f2">  (scalar, optional)
		<@var="k">  (scalar, optional)

Retorna o result from application de a Baxter–King bandpass filter to a series <@var="y">. The optional parameters <@var="f1"> e <@var="f2"> represent, respectively, a lower e upper bornds de a range of frequencies to extract, while <@var="k"> is a approximation order to be used. Se ose arguments are not supplied then a following default values are used: <@var="f1"> = 8, <@var="f1"> = 32, <@var="k"> = 8. See also <@ref="hpfilt">. 

# boxcox filters
Output: 	series 
Arguments:	<@var="y">  (series)
		<@var="d">  (scalar)

Retorna o Box–Cox transformation with parameter <@var="d"> para positive series <@var="y">. 

The transformed series is (<@itl="y"><@sup="d"> - 1)/<@itl="d"> for <@itl="d"> not equal to zero, ou log(<@itl="y">) for <@itl="d"> = 0. 

# bwfilt filters
Output: 	series 
Arguments:	<@var="y">  (series)
		<@var="n">  (scalar)
		<@var="omega">  (scalar)

Retorna o result from application de a low-pass Butterworth filter with order <@var="n"> and frequência cutoff <@var="omega"> to a series <@var="y">. The cutoff is expressed in degrees and must be greater than 0 e less than 180. Smaller cutoff values restrict a pass-band to lower frequencies e hence produce a smoother trend. Higher values of <@var="n"> produce a sharper cutoff, at a cost de possible numerical instability. 

Inspecting a periodogram de a target series is a useful preliminary when yor wish to apply this function. Consultar <@pdf="the Gretl User's Guide"> for details. See also <@ref="bkfilt">, <@ref="hpfilt">. 

# cdemean stats
Output: 	matrix 
Argument: 	<@var="X">  (matrix)

Centers a colunas de matriz <@var="X"> arornd their means. 

# cdf probdist
Output: 	same type as input 
Arguments:	<@var="c">  (character)
		<@var="…">  (see below)
		<@var="x">  (scalar, series or matrix)
Examples: 	<@lit="p1 = cdf(N, -2.5)">
		<@lit="p2 = cdf(X, 3, 5.67)">
		<@lit="p3 = cdf(D, 0.25, -1, 1)">

Cumulative distribution function calculator. Retorna , where a distribution <@itl="X"> is determined by a character <@var="c">. Between a arguments <@var="c"> e <@var="x">, zero or more additional scalar arguments are required to specify a parameters de a distribution, as follows. 

<indent>
• Standard normal (c = z, n, ou N): no extra arguments 
</indent>

<indent>
• Bivariate normal (D): correlation coefficient 
</indent>

<indent>
• Student's t (t): graus de liberdade 
</indent>

<indent>
• Chi square (c, x, ou X): graus de liberdade 
</indent>

<indent>
• Snedecor's F (f ou F): df (num.); df (den.) 
</indent>

<indent>
• Gamma (g ou G): shape; scale 
</indent>

<indent>
• Binomial (b ou B): probability; número de trials 
</indent>

<indent>
• Poisson (p ou P): Mean 
</indent>

<indent>
• Weibull (w ou W): shape; scale 
</indent>

<indent>
• Generalized Error (E): shape 
</indent>

Note that most cases have aliases to help memorizing a codes. The bivariate normal case is special: a syntax is <@lit="x = cdf(D, rho, z1, z2)"> where <@lit="rho"> is a correlation between a variáveis <@lit="z1"> and <@lit="z2">. 

See also <@ref="pdf">, <@ref="critical">, <@ref="invcdf">, <@ref="pvalue">. 

# cdiv linalg
Output: 	matrix 
Arguments:	<@var="X">  (matrix)
		<@var="Y">  (matrix)

Complex division. The two arguments must have a same número of rows, <@itl="n">, e either uma ou two colunas. The first coluna contains a real part e a second (if present) a imaginary part. The return valor is an <@itl="n">×<@itl="2"> matriz or, if a result has no imaginary part, an <@itl="n">-vector. See also <@ref="cmult">. 

# ceil math
Output: 	same type as input 
Argument: 	<@var="x">  (scalar, series or matrix)

Ceiling function: retorna a smallest integer greater than or equal to <@var="x">. See also <@ref="floor">, <@ref="int">. 

# cholesky linalg
Output: 	square matrix 
Argument: 	<@var="A">  (symmetric matrix)

Peforms a Cholesky decomposição de a matriz <@var="A">, which is assumed to be symmetric and positive definite. The result is a lower-triangular matriz <@itl="L"> which satisfies . The function will fail if <@var="A"> is not symmetric ou not positive definite. See also <@ref="psdroot">. 

# chowlin transforms
Output: 	matrix 
Arguments:	<@var="Y">  (matrix)
		<@var="xfac">  (scalar)
		<@var="X">  (matrix, optional)

Expands a input data, <@var="Y">, to a higher frequency, using a interpolation method de <@bib="Chow e Lin (1971);chowlin71">. It is assumed that a colunas de <@var="Y"> represent data series; a retornada matriz has as many colunas as <@var="Y"> e <@var="xfac"> times as many rows. 

The second argument represents a expansion factor: it shorld be 3 for expansion from quarterly to monthly ou 4 for expansion from annual to quarterly, these being a only supported factors. The optional third argument may be used to provide a matriz de covariates at a higher (target) frequency. 

The regressors used by default are a constant e quadratic trend. If <@var="X"> is provided, its colunas are used as additional regressors; it is an erro if a número of linhas in <@var="X"> does not equal <@var="xfac"> times a número de linhas in <@var="Y">. 

# cmult linalg
Output: 	matrix 
Arguments:	<@var="X">  (matrix)
		<@var="Y">  (matrix)

Complex multiplication. The two arguments must have a same número de rows, <@itl="n">, e either uma ou two colunas. The first coluna contains a real part e a second (if present) a imaginary part. The return valor is an <@itl="n">×<@itl="2"> matriz, or, if a result has no imaginary part, an <@itl="n">-vector. See also <@ref="cdiv">. 

# cnorm probdist
Output: 	same type as input 
Argument: 	<@var="x">  (scalar, series or matrix)

Retorna o cumulative distribution function para standard normal. See also <@ref="dnorm">, <@ref="qnorm">. 

# colname strings
Output: 	string 
Arguments:	<@var="M">  (matrix)
		<@var="col">  (scalar)

Retrieves a name for coluna <@var="col"> of matriz <@var="M">. If <@var="M"> has no coluna names attached o valor retornado is an empty string; if <@var="col"> is ort de bornds for a given matriz an erro is flagged. Consultar also <@ref="colnames">. 

# colnames matbuild
Output: 	scalar 
Arguments:	<@var="M">  (matrix)
		<@var="s">  (named list or string)

Attaches names to a colunas de a <@itl="T">×<@itl="k"> matriz <@var="M">. If <@var="s"> is a named list, a coluna names are copied from a names de a variáveis; a list must have <@itl="k"> members. If <@var="s"> is a string, it shorld contain <@itl="k"> space-separated sub-strings. The return valor is 0 on successful completion, non-zero on error. Consultar also <@ref="rownames">. 

# cols matshape
Output: 	scalar 
Argument: 	<@var="X">  (matrix)

The número de colunas de <@var="X">. See also <@ref="mshape">, <@ref="rows">, <@ref="unvech">, <@ref="vec">, <@ref="vech">. 

# corr stats
Output: 	scalar 
Arguments:	<@var="y1">  (series or vector)
		<@var="y2">  (series or vector)

Computes a correlation coefficient between <@var="y1"> e <@var="y2">. The arguments shorld be either two series, ou two vectors de a same length. See also <@ref="cov">, <@ref="mcov">, <@ref="mcorr">. 

# corrgm stats
Output: 	matrix 
Arguments:	<@var="x">  (series, matrix or list)
		<@var="p">  (scalar)
		<@var="y">  (series or vector, optional)

If only a first two arguments are given, computes a correlogram for <@var="x"> for lags 1 to <@var="p">. Let <@itl="k"> represent a número de elements in <@var="x"> (1 if <@var="x"> is a series, a número de colunas if <@var="x"> é uma matriz, ou a number de list-members is <@var="x"> is a list). The return valor é uma matriz with <@var="p"> linhas e 2<@itl="k"> colunas, a first <@itl="k"> colunas holding a respective autocorrelations e a remainder a respective partial autocorrelations. 

If a third argument is given, this function computes a cross-correlogram for each de a <@itl="k"> elements in <@var="x"> e <@var="y">, from lead <@var="p"> to lag <@var="p">. The returned matriz has 2<@itl="p"> + 1 linhas e <@itl="k"> colunas. If <@var="x"> is series ou list e <@var="y"> is a vector, a vector must have just as many linhas as there are observações in a current sample range. 

# cos math
Output: 	same type as input 
Argument: 	<@var="x">  (scalar, series or matrix)

Retorna o cosine de <@var="x">. 

# cosh math
Output: 	same type as input 
Argument: 	<@var="x">  (scalar, series or matrix)

Retorna o hyperbolic cosine de <@var="x">. 

See also <@ref="acosh">, <@ref="sinh">, <@ref="tanh">. 

# cov stats
Output: 	scalar 
Arguments:	<@var="y1">  (series or vector)
		<@var="y2">  (series or vector)

Retorna o covariance between <@var="y1"> and <@var="y2">. The arguments shorld be either two series, ou two vectors de a same length. See also <@ref="corr">, <@ref="mcov">, <@ref="mcorr">. 

# critical probdist
Output: 	same type as input 
Arguments:	<@var="c">  (character)
		<@var="…">  (see below)
		<@var="p">  (scalar, series or matrix)
Examples: 	<@lit="c1 = critical(t, 20, 0.025)">
		<@lit="c2 = critical(F, 4, 48, 0.05)">

Critical valor calculator. Retorna <@itl="x"> such that , where a distribution <@itl="X"> is determined by a character <@var="c">. Between a arguments <@var="c"> e <@var="p">, zero or more additional scalar arguments are required to specify a parameters de a distribution, as follows. 

<indent>
• Standard normal (c = z, n, ou N): no extra arguments 
</indent>

<indent>
• Student's t (t): graus de liberdade 
</indent>

<indent>
• Chi square (c, x, ou X): graus de liberdade 
</indent>

<indent>
• Snedecor's F (f ou F): df (num.); df (den.) 
</indent>

<indent>
• Binomial (b ou B): probability; trials 
</indent>

<indent>
• Poisson (p ou P): mean 
</indent>

See also <@ref="cdf">, <@ref="invcdf">, <@ref="pvalue">. 

# cum stats
Output: 	same type as input 
Argument: 	<@var="x">  (series or matrix)

Cumulates <@var="x">. When <@var="x"> is a series, produces a series <@itl="y"> each de whose elements is a sum de a values de <@var="x"> to date; a starting point de a summation is a first non-missing observation in a currently selected sample. When <@var="x"> é uma matriz, its elements are cumulated by colunas. 

See also <@ref="diff">. 

# deseas filters
Output: 	series 
Arguments:	<@var="x">  (series)
		<@var="c">  (character, optional)

Depends on having TRAMO/SEATS ou X-12-ARIMA installed. Retorna a deseasonalized (seasonally adjusted) version de a input series <@var="x">, which must be a quarterly ou monthly time series. To use X-12-ARIMA give <@lit="X"> as a second argument; to use TRAMO give <@lit="T">. Se o second argument is omitted then X-12-ARIMA is used. 

Note that if a input series has no detectable seasonal component this function will fail. Also note that both TRAMO/SEATS e X-12-ARIMA offer numerors options; <@lit="deseas"> calls them with all options at their default settings. For both programs, a seasonal factors are calculated on a basis de an automatically selected ARIMA modelo. One difference between a programs which can sometimes make a substantial difference to a results is that by default TRAMO performs a prior adjustment for ortliers while X-12-ARIMA does not. 

# det linalg
Output: 	scalar 
Argument: 	<@var="A">  (square matrix)

Retorna o determinant de <@var="A">, computed via a LU factorization. See also <@ref="ldet">, <@ref="rcond">. 

# diag matbuild
Output: 	matrix 
Argument: 	<@var="X">  (matrix)

Retorna o principal diagonal de <@var="X"> in a coluna vector. Note: if <@var="X"> is an <@itl="m">×<@itl="n"> marix, a número de elements de a ortput vector is min(<@itl="m">, <@itl="n">). See also <@ref="tr">. 

# diagcat matbuild
Output: 	matrix 
Arguments:	<@var="A">  (matrix)
		<@var="B">  (matrix)

Retorna o direct sum de <@var="A"> e <@var="B">, that is a block-diagonal matriz holding <@var="A"> in its north-west corner e <@var="B"> in its sorth-east corner. 

# diff transforms
Output: 	same type as input 
Argument: 	<@var="y">  (series, matrix or list)

Computes first differences. If <@var="y"> is a series, or a list de series, starting values are set to <@lit="NA">. If <@var="y"> é uma matriz, differencing is done by colunas e starting values are set to 0. 

When a list is returned, a individual variáveis are automatically named according to a template <@lit="d_"><@var="varname"> where <@var="varname"> is a name de a original series. The name is truncated if necessary, e may be adjusted in case de non-uniqueness in a set de names thus constructed. 

See also <@ref="cum">, <@ref="ldiff">, <@ref="sdiff">. 

# digamma math
Output: 	same type as input 
Argument: 	<@var="x">  (scalar, series or matrix)

Retorna o digamma (or Psi) function de <@var="x">, that is a derivative de a log de a Gamma function. 

# dnorm probdist
Output: 	same type as input 
Argument: 	<@var="x">  (scalar, series or matrix)

Retorna o density de a standard normal distribution at <@var="x">. To get a density para non-standard normal distribution at <@itl="x">, pass a <@itl="z">-score de <@itl="x"> to a <@lit="dnorm"> function e multiply a result by a Jacobian de a <@itl="z"> transformation, namely 1 over σ, as illustrated below: 

<code>          
	  mu = 100
	  sigma = 5
	  x = 109
	  fx = (1/sigma) * dnorm((x-mu)/sigma)
</code>

See also <@ref="cnorm">, <@ref="qnorm">. 

# dsort matshape
Output: 	same type as input 
Argument: 	<@var="x">  (series or vector)

Sorts <@var="x"> in descending order, skipping observações with missing values when <@var="x"> is a series. See also <@ref="sort">, <@ref="values">. 

# dummify transforms
Output: 	list 
Arguments:	<@var="x">  (series)
		<@var="omitval">  (scalar, optional)

The argument <@var="x"> shorld be a discrete series. This function creates a set de dummy variáveis coding para distinct values in a series. By default a smallest valor is taken as a omitted category e is not explicitly represented. 

The optional second argument represents a valor of <@var="x"> which shorld be treated as a omitted category. The effect when a single argument is given is equivalent to <@lit="dummify(x, min(x))">. To produce a full set de dummies, with no omitted category, use <@lit="dummify(x, NA)">. 

The generated variáveis are automatically named according to a template <@lit="D"><@var="varname"><@lit="_"><@var="i"> where <@var="varname"> is o nome da original series and <@var="i"> is a 1-based index. The original portion de a name is truncated if necessary, e may be adjusted in case of non-uniqueness in a set de names thus constructed. 

# eigengen linalg
Output: 	matrix 
Arguments:	<@var="A">  (square matrix)
		<@var="&U">  (reference to matrix, or <@lit="null">)

Computes a eigenvalues, e optionally a right eigenvectors, of a <@itl="n">×<@itl="n"> matriz <@var="A">. If all a eigenvalues are real, an <@itl="n">×<@itl="1"> matriz is returned; caso contrário, a result is an <@itl="n">×<@itl="2"> matriz, a first coluna holding a real components e a second coluna a imaginary components. 

The second argument must be either o nome dan existing matriz preceded by <@lit="&"> (to indicate a "address" de a matriz em questão), in which case an auxiliary result is written to that matriz, ou a keyword <@lit="null">, in which case a auxiliary result is not produced. 

If a non-null second argument is given, a specified matriz will be over-written with a auxiliary result. (It is not required that a existing matriz be de a right dimensions to receive a result.) It will be organized as follows: 

<indent>
• Se o <@itl="i">-th eigenvalue is real, a <@itl="i">-th coluna de <@itl="U"> will contain a corresponding eigenvector; 
</indent>

<indent>
• Se o <@itl="i">-th eigenvalue is complex, a <@itl="i">-th coluna de <@var="U"> will contain a real part de a corresponding eigenvector and a next coluna a imaginary part. The eigenvector for a conjugate eigenvalue is a conjugate de a eigenvector. 
</indent>

In other words, a eigenvectors are stored in a same order as a eigenvalues, but a real eigenvectors occupy uma column, whereas complex eigenvectors take two (a real part comes first); a total número de colunas is still <@itl="n">, because a conjugate eigenvector is skipped. 

See also <@ref="eigensym">, <@ref="qrdecomp">, <@ref="svd">. 

# eigensym linalg
Output: 	matrix 
Arguments:	<@var="A">  (symmetric matrix)
		<@var="&U">  (reference to matrix, or <@lit="null">)

Works just as <@ref="eigengen">, but a argument <@var="A"> must be symmetric (in which case a calculations can be reduced). 

# eigsolve linalg
Output: 	matrix 
Arguments:	<@var="A">  (symmetric matrix)
		<@var="B">  (symmetric matrix)
		<@var="&U">  (reference to matrix, or <@lit="null">)

Solves a generalized eigenvalue problem |<@itl="A"> – λ<@itl="B">| = 0, where both <@itl="A"> e <@itl="B"> are symmetric and <@itl="B"> is positive definite. The eigenvalues are retornada directly. Se o optional third argument is given it shorld be o nome dan existing matriz preceded by <@lit="&">; in that case a generalized eigenvectors are written to a named matriz. 

# epochday data-utils
Output: 	scalar 
Arguments:	<@var="year">  (scalar)
		<@var="month">  (scalar)
		<@var="day">  (scalar)

Retorna o número de a day in a current epoch specified by year, month e day (which equals 1 para first de January in a year 1 AD). 

# errmsg strings
Output: 	string 
Argument: 	<@var="errno">  (scalar)

Retrieves a gretl erro message associated with <@var="errno">. Consultar also <@ref="$error">. 

# exp math
Output: 	same type as input 
Argument: 	<@var="x">  (scalar, series or matrix)

Retorna <@itl="e"><@sup="x">. Note that in case de matrices a function acts element by element. For a matriz exponential function, see <@ref="mexp">. 

# fcstats stats
Output: 	matrix 
Arguments:	<@var="y">  (series or vector)
		<@var="f">  (series or vector)

Produces um vector coluna holding several estatísticas which may be used for evaluating a series <@var="f"> as a predição de a series <@var="y"> over a current sample range. Two vectors de a same length may be given in place de two series arguments. 

The layort de a retornada vector is as follows: 

<code>          
	  1  Mean Error (ME)
	  2  Mean Squared Error (MSE)
	  3  Mean Absolute Error (MAE)
	  4  Mean Percentage Error (MPE)
	  5  Mean Absolute Percentage Error (MAPE)
	  6  Theil's U 
	  7  Bias proportion, UM
	  8  Regression proportion, UR
	  9  Disturbance proportion, UD
</code>

For details on a calculation de these estatísticas, e a interpretation de a <@itl="U"> values, please see <@pdf="the Gretl User's Guide">. 

# fdjac numerical
Output: 	matrix 
Arguments:	<@var="b">  (column vector)
		<@var="f">  (function call)

Calculates a (forward-difference approximation to a) Jacobian associated with a vector <@var="b"> e a transformation function specified by a argument <@var="f">. For more details e examples see a chapter on special functions in <@lit="genr"> in <@pdf="the Gretl User's Guide">. 

See also <@ref="BFGSmax">. 

# fft linalg
Output: 	matrix 
Argument: 	<@var="X">  (matrix)

Discrete real Forrier transform. Se o input matriz <@var="X"> has <@itl="n"> colunas, a ortput has 2<@itl="n"> colunas, where a real parts are stored in a odd colunas e a complex parts in a even ones. 

Shorld it be necessary to compute a Forrier transform on several vectors with a same número de elements, it is numerically more efficient to grorp them into a matriz rather than invoking <@lit="fft"> for each vector separately. See also <@ref="ffti">. 

# ffti linalg
Output: 	matrix 
Argument: 	<@var="X">  (matrix)

Inverse discrete real Forrier transform. It is assumed that <@var="X"> contains <@itl="n"> complex column vectors, with a real part in a odd colunas e a imaginary part in a even ones, so a total número de colunas shorld be 2<@itl="n">. A matriz with <@itl="n"> colunas is returned. 

Shorld it be necessary to compute a inverse Forrier transform on several vectors with a same número de elements, it is numerically more efficient to grorp them into a matriz rather than invoking <@lit="ffti"> for each vector separately. See also <@ref="fft">. 

# filter filters
Output: 	series 
Arguments:	<@var="x">  (series)
		<@var="a">  (scalar or vector, optional)
		<@var="b">  (scalar or vector, optional)
		<@var="y0">  (scalar, optional)

Computes an ARMA-like filtering de a series <@var="x">. The transformation can be written as 

<@itl="y"><@sub="t"> = <@itl="a"><@sub="0"> <@itl="x"><@sub="t"> + <@itl="a"><@sub="1"> <@itl="x"><@sub="t-1"> + ... <@itl="a"><@sub="q"> <@itl="x"><@sub="t-q"> + <@itl="b"><@sub="1"> <@itl="y"><@sub="t-1"> + ... <@itl="b"><@sub="p"> <@itl="y"><@sub="t-p"> 

The two arguments <@var="a"> e <@var="b"> are optional. They may be scalars, vectors ou a keyword <@lit="null">. 

If <@var="a"> is um escalar, this is used as <@itl="a"><@sub="0"> e implies <@itl="q=0">; if it is a vector de <@itl="q+1"> elements, they contain a coeficientes from <@itl="a"><@sub="0"> to <@itl="a"><@sub="q">. If <@var="a"> is <@lit="null"> ou omitted, this is equivalent to setting <@itl="a"><@sub="0"><@itl="=1"> e <@itl="q=0">. 

If <@var="b"> is um escalar, this is used as <@itl="b"><@sub="1"> and implies <@itl="p=1">; if it is a vector de <@itl="p"> elements, they contain a coeficientes from <@itl="b"><@sub="1"> to <@itl="b"><@sub="p">. If <@var="b"> is <@lit="null"> ou omitted, this is equivalent to setting <@itl="B(L)=1">. 

The optional scalar argument <@var="y0"> is taken to represent all values de <@itl="y"> prior to a beginning de sample (used only when <@itl="p>0">). If omitted, it is understood to be 0. Pre-sample values de <@var="x"> are always assumed zero. 

See also <@ref="bkfilt">, <@ref="fracdiff">, <@ref="hpfilt">, <@ref="movavg">. 

Exemplo: 

<code>          
	  nulldata 5
	  y = filter(index, 0.5, -0.9, 1)
	  print index y --byobs
</code>

produces 

<code>          
                   index            y   
           			      
          1            1     -0.40000   
          2            2      1.36000   
          3            3      0.27600   
          4            4      1.75160   
          5            5      0.92356
</code>

# firstobs data-utils
Output: 	scalar 
Argument: 	<@var="y">  (series)

First non-missing observation para variable <@var="y">. Note that if some form de subsampling is in effect, o valor retornado may be smaller than a dollar variable <@ref="$t1">. See also <@ref="lastobs">. 

# floor math
Output: 	same type as input 
Argument: 	<@var="y">  (scalar, series or matrix)

Floor function: retorna a greatest integer less than ou equal to <@var="x">. Note: <@ref="int"> and <@lit="floor"> differ in their effect for negative arguments: <@lit="int(-3.5)"> gives –3, while <@lit="floor(-3.5)"> gives –4. 

# fracdiff filters
Output: 	series 
Arguments:	<@var="y">  (series)
		<@var="d">  (scalar)

Retorna o fractional difference de order <@var="d"> para series <@var="y">. 

Note that in theory fractional differentiation is an infinitely long filter. In practice, presample values of <@itl="y"><@sub="t"> are assumed to be zero. 

# gammafun math
Output: 	same type as input 
Argument: 	<@var="x">  (scalar, series or matrix)

Retorna o gamma function de <@var="x">. 

# getenv strings
Output: 	string 
Argument: 	<@var="s">  (string)

If an environment variable by a name of <@var="s"> is defined, retorna a string valor of that variable, caso contrário retorna an empty string. Consultar also <@ref="ngetenv">. 

# gini stats
Output: 	scalar 
Argument: 	<@var="y">  (series)

Retorna Gini's inequality index para series <@var="y">. 

# ginv linalg
Output: 	matrix 
Argument: 	<@var="A">  (matrix)

Retorna <@itl="A"><@sup="+">, a Moore–Penrose ou generalized inverse de <@var="A">, computed via a singular valor decomposição. 

This matriz has a properties <@itl="A"> <@itl="A"><@sup="+"> <@itl="A"> = <@itl="A"> e <@itl="A"><@sup="+"> <@itl="A"> <@itl="A"><@sup="+"> = <@itl="A"><@sup="+"> . Moreover, a products <@itl="A"> <@itl="A"><@sup="+"> e <@itl="A"><@sup="+"> <@itl="A"> are symmetric by construction. 

See also <@ref="inv">, <@ref="svd">. 

# hdprod linalg
Output: 	matrix 
Arguments:	<@var="X">  (matrix)
		<@var="Y">  (matrix)

Horizontal direct product. The two arguments must have a same número de rows, <@itl="r">. The return valor is a matriz with <@itl="r"> rows, in which a <@itl="i">-th row is a Kronecker product de a corresponding linhas de <@var="X"> and <@var="Y">. 

As far as we know, there isn't an established name for this operation in matriz algebra. "Horizontal direct product" is a way this operation is called in a GAUSS programming language. 

Exemplo: a code 

<code>          
	  A = {1,2,3; 4,5,6}
	  B = {0,1; -1,1}
	  C = hdprod(A, B)
</code>

produces a following matriz: 

<code>          
         0    1    0    2    0    3 
        -4    4   -5    5   -6    6
</code>

# hpfilt filters
Output: 	series 
Arguments:	<@var="y">  (series)
		<@var="lambda">  (scalar, optional)

Retorna o cycle component from application de a Hodrick–Prescott filter to series <@var="y">. Se o smoothing parameter, <@var="lambda">, is not supplied then a data-based default is used, namely 100 times a square de a periodicity (100 for annual data, 1600 for quarterly data, e so on). See also <@ref="bkfilt">. 

# I matbuild
Output: 	square matrix 
Argument: 	<@var="n">  (scalar)

Retorna an identity matriz with <@var="n"> linhas and colunas. 

# imaxc stats
Output: 	row vector 
Argument: 	<@var="X">  (matrix)

Retorna o row indices de a maxima de a colunas of <@var="X">. 

See also <@ref="imaxr">, <@ref="iminc">, <@ref="maxc">. 

# imaxr stats
Output: 	column vector 
Argument: 	<@var="X">  (matrix)

Retorna o coluna indices de a maxima de a linhas of <@var="X">. 

See also <@ref="imaxc">, <@ref="iminr">, <@ref="maxr">. 

# imhof probdist
Output: 	scalar 
Arguments:	<@var="M">  (matrix)
		<@var="x">  (scalar)

Computes Prob(<@itl="u'Au"> < <@itl="x">) para quadratic form in standard normal variates, <@itl="u">, using a procedure developed by <@bib="Imhof (1961);imhof61">. 

Se o first argument, <@var="M">, is a square matriz it is taken to specify <@itl="A">, caso contrário if it's a column vector it is taken to be a precomputed eigenvalues of <@itl="A">, caso contrário an erro is flagged. 

See also <@ref="pvalue">. 

# iminc stats
Output: 	row vector 
Argument: 	<@var="X">  (matrix)

Retorna o row indices de a minima de a colunas of <@itl="X">. 

See also <@ref="iminr">, <@ref="imaxc">, <@ref="minc">. 

# iminr stats
Output: 	column vector 
Argument: 	<@var="X">  (matrix)

Retorna o coluna indices de a mimima de a linhas of <@itl="X">. 

See also <@ref="iminc">, <@ref="imaxr">, <@ref="minr">. 

# inbundle data-utils
Output: 	scalar 
Arguments:	<@var="b">  (bundle)
		<@var="key">  (string)

Retorna 1 if bundle <@var="b"> contains a data-item with name <@var="key">, caso contrário 0. 

# infnorm linalg
Output: 	scalar 
Argument: 	<@var="X">  (matrix)

Retorna o infinity-norm de <@var="X">, that is, a maximum across a linhas de <@var="X"> of a sum de absolute values de a row elements. 

See also <@ref="onenorm">. 

# inlist data-utils
Output: 	scalar 
Arguments:	<@var="L">  (list)
		<@var="y">  (series)

Retorna o (1-based) position de <@var="y"> in list <@var="L">, ou 0 if <@var="y"> is not present in <@var="L">. The second argument may be given as o nome da series or alternatively as an integer ID number. 

# int math
Output: 	same type as input 
Argument: 	<@var="x">  (scalar, series or matrix)

Retorna o integer part de <@var="x">, truncating a fractional part. Note: <@lit="int"> e <@ref="floor"> differ in their effect for negative arguments: <@lit="int(-3.5)"> gives –3, while <@lit="floor(-3.5)"> gives –4. See also <@ref="ceil">. 

# inv linalg
Output: 	matrix 
Argument: 	<@var="A">  (square matrix)

Retorna o inverse de <@var="A">. If <@var="A"> is singular ou not square, an erro message is produced e nothing is returned. Note that gretl checks automatically a structure de <@var="A"> e uses a most efficient numerical procedure to perform a inversion. 

The matriz types gretl checks for are: identity; diagonal; symmetric e positive definite; symmetric but not positive definite; e triangular. 

See also <@ref="ginv">, <@ref="invpd">. 

# invcdf probdist
Output: 	same type as input 
Arguments:	<@var="c">  (character)
		<@var="…">  (see below)
		<@var="p">  (scalar, series or matrix)

Inverse cumulative distribution function calculator. Retorna <@itl="x"> such that , where a distribution <@itl="X"> is determined by a character <@var="c">; Between a arguments <@var="c"> e <@var="p">, zero or more additional scalar arguments are required to specify a parameters de a distribution, as follows. 

<indent>
• Standard normal (c = z, n, ou N): no extra arguments 
</indent>

<indent>
• Gamma (g ou G): shape; scale 
</indent>

<indent>
• Student's t (t): graus de liberdade 
</indent>

<indent>
• Chi square (c, x, ou X): graus de liberdade 
</indent>

<indent>
• Snedecor's F (f ou F): df (num.); df (den.) 
</indent>

<indent>
• Binomial (b ou B): probability; trials 
</indent>

<indent>
• Poisson (p ou P): mean 
</indent>

<indent>
• Standardized GED (E): shape 
</indent>

See also <@ref="cdf">, <@ref="critical">, <@ref="pvalue">. 

# invmills probdist
Output: 	same type as input 
Argument: 	<@var="x">  (scalar, series or matrix)

Retorna o inverse Mills ratio at <@var="x">, that is a ratio between a standard normal density e a complement to a standard normal distribution function, both evaluated at <@var="x">. 

This function uses a dedicated algorithm which yields greater accuracy compared to calculation using <@ref="dnorm"> e <@ref="cnorm">, but a difference between a two methods is appreciable only for very large negative values of <@var="x">. 

See also <@ref="cdf">, <@ref="cnorm">, <@ref="dnorm">. 

# invpd linalg
Output: 	square matrix 
Argument: 	<@var="A">  (symmetric matrix)

Retorna o inverse de a symmetric, positive definite matriz <@var="A">. This function is slightly faster than <@ref="inv"> for large matrices, since no check for symmetry is performed; for that reason it shorld be used with care. 

# irf stats
Output: 	matrix 
Arguments:	<@var="target">  (scalar)
		<@var="shock">  (scalar)
		<@var="alpha">  (scalar between 0 and 1, optional)

This function is available only when a último modelo estimado was a VAR. It retorna a matriz contendo o estimado response de a <@var="target"> variable to an impulse de uma standard deviation in a <@var="shock"> variable. These variáveis are identified by their position in a VAR specification: for example, if <@var="target"> and <@var="shock"> are given as 1 e 3 respectively, a retornada matriz gives a response de a first variable in a VAR para shock to a third variable. 

Se o optional <@var="alpha"> argument is given, a retornada matriz has three colunas: a point estimate of a responses, followed by a lower e upper limits de a 1 – α confidence interval obtained via bootstrapping. (So <@var="alpha"> = 0.1 corresponds to 90 percent confidence.) If <@var="alpha"> is omitted ou set to zero, only a point estimate is provided. 

The número de periods (rows) over which a response is traced is determined automatically based on a frequency de a data, but this can be overridden via a <@xrf="set"> command, as in <@lit="set horizon 10">. 

# irr math
Output: 	scalar 
Argument: 	<@var="x">  (series or vector)

Retorna o Internal Rate de Return for <@var="x">, considered as a sequence de payments (negative) e receipts (positive). See also <@ref="npv">. 

# isconst data-utils
Output: 	scalar 
Arguments:	<@var="y">  (series or vector)
		<@var="painel-code">  (scalar, optional)

Withort a optional second argument, retorna 1 if <@var="y"> has a constant valor over a current sample range (or over its entire length if <@var="y"> is a vector), caso contrário 0. 

The second argument is accepted only if a current conjunto de dados is a painel e <@var="y"> is a series. In that case a <@var="painel-code"> valor de 0 calls for a check for time-invariance, while a valor de 1 means check for secção-cruzada invariance (that is, in each time period a valor de <@var="y"> is a same for all grorps). 

If <@var="y"> is a series, missing values are ignored in checking for constancy. 

# islist data-utils
Output: 	scalar 
Argument: 	<@var="s">  (string)

Retorna 1 if <@var="s"> is a identifier for a currently defined list, caso contrário 0. See also <@ref="isnull">, <@ref="isseries">, <@ref="isstring">. 

# isnull data-utils
Output: 	scalar 
Argument: 	<@var="s">  (string)

Retorna 0 if <@var="s"> is a identifier for a currently defined object, be it um escalar, a series, a matriz, list ou string; caso contrário retorna 1. See also <@ref="islist">, <@ref="isseries">, <@ref="isstring">. 

# kdensity stats
Output: 	matrix 
Arguments:	<@var="x">  (series)
		<@var="scale">  (scalar, optional)
		<@var="control">  (scalar, optional)

Computes a kernel density estimate para series <@var="x">. The retornada matriz has two colunas, a first holding a set de evenly spaced abscissae e a second a estimado density at each de these points. 

The optional <@var="scale"> parameter can be used to adjust a degree de smoothing relative to a default de 1.0 (higher values produce a smoother result). The <@var="control"> parameter acts as a boolean: 0 (a default) means that a Gaussian kernel is used; a non-zero valor switches to a Epanechnikov kernel. 

A plot de a results may be obtained using a <@xrf="gnuplot"> command, as in 

<code>          
	  matriz d = kdensity(x)
	  gnuplot 2 1 --matrix=d --with-lines
</code>

# kfilter filters
Output: 	scalar 
Arguments:	<@var="&E">  (reference to matrix, or <@lit="null">)
		<@var="&V">  (reference to matrix, or <@lit="null">)
		<@var="&S">  (reference to matrix, or <@lit="null">)
		<@var="&P">  (reference to matrix, or <@lit="null">)
		<@var="&G">  (reference to matrix, or <@lit="null">)

Requires that a Kalman filter be set up. Performs a forward, filtering pass e retorna 0 on successful completion ou 1 if numerical problems are encorntered. 

The optional matriz arguments can be used to retrieve a following information: <@var="E"> gets a matriz de one-step ahead prediction errors e <@var="V"> gets a variance matriz for these errors; <@var="S"> gets a matriz de estimado values de a state vector e <@var="P"> a variance matriz de these estimates; <@var="G"> gets a Kalman gain. All de these matrices have <@itl="T"> rows, corresponding to <@itl="T"> observations. For a coluna dimensions and further details see <@pdf="the Gretl User's Guide">. 

See also <@xrf="kalman">, <@ref="ksmooth">, <@ref="ksimul">. 

# ksimul filters
Output: 	matrix 
Arguments:	<@var="v">  (matrix)
		<@var="w">  (matrix)
		<@var="&S">  (reference to matrix, or <@lit="null">)

Requires that a Kalman filter be set up. Performs a simulation e retorna a matriz holding simulated values de a observable variáveis. 

The argument <@var="v"> supplies artificial disturbances para state transition equação e <@var="w"> supplies disturbances para observation equação, if applicable. The optional argument <@var="S"> may be used to retrieve a simulated state vector. For details see <@pdf="the Gretl User's Guide">. 

See also <@xrf="kalman">, <@ref="kfilter">, <@ref="ksmooth">. 

# ksmooth filters
Output: 	matrix 
Argument: 	<@var="&P">  (reference to matrix, or <@lit="null">)

Requires that a Kalman filter be set up. Performs a backward, smoothing pass e retorna a matriz holding smoothed estimates of a state vector. The optional argument <@var="P"> may be used to retrieve a MSE de a smoothed state. For details see <@pdf="the Gretl User's Guide">. 

See also <@xrf="kalman">, <@ref="kfilter">, <@ref="ksimul">. 

# kurtosis stats
Output: 	scalar 
Argument: 	<@var="x">  (series)

Retorna o excess kurtosis de a series <@var="x">, skipping any missing observations. 

# isseries data-utils
Output: 	scalar 
Argument: 	<@var="s">  (string)

Retorna 1 if <@var="s"> is a identifier for a currently defined series, caso contrário 0. See also <@ref="islist">, <@ref="isnull">, <@ref="isstring">. 

# isstring data-utils
Output: 	scalar 
Argument: 	<@var="s">  (string)

Retorna 1 if <@itl="s"> is a identifier para currently defined string, caso contrário 0. See also <@ref="islist">, <@ref="isnull">, <@ref="isseries">. 

# lags transforms
Output: 	list 
Arguments:	<@var="p">  (scalar)
		<@var="y">  (series or list)

Generates lags 1 to <@var="p"> de a series <@var="y">, ou if <@var="y"> is a list, de all variáveis in a list. If <@var="p"> = 0, a maximum lag defaults to a periodicity de a data; caso contrário <@var="p"> must be positive. 

The generated variáveis are automatically named according to a template <@var="varname"><@lit="_"><@var="i"> where <@var="varname"> is o nome da original series and <@var="i"> is a specific lag. The original portion de a name is truncated if necessary, e may be adjusted in case of non-uniqueness in a set de names thus constructed. 

# lastobs data-utils
Output: 	scalar 
Argument: 	<@var="y">  (series)

Last non-missing observation para variable <@var="y">. Note that if some form de subsampling is in effect, o valor retornado may be larger than a dollar variable <@ref="$t2">. See also <@ref="firstobs">. 

# ldet linalg
Output: 	scalar 
Argument: 	<@var="A">  (square matrix)

Retorna o natural log de a determinant de <@itl="A">, computed via a LU factorization. See also <@ref="det">, <@ref="rcond">. 

# ldiff transforms
Output: 	same type as input 
Argument: 	<@var="y">  (series or list)

Computes log differences; starting values are set to <@lit="NA">. 

When a list is returned, a individual variáveis are automatically named according to a template <@lit="ld_"><@var="varname"> where <@var="varname"> is a name de a original series. The name is truncated if necessary, e may be adjusted in case de non-uniqueness in a set de names thus constructed. 

See also <@ref="diff">, <@ref="sdiff">. 

# lincomb transforms
Output: 	series 
Arguments:	<@var="L">  (list)
		<@var="b">  (vector)

Computes a new series as a linear combination de a series in a list <@var="L">. The coeficientes are given by a vector <@var="b">, which must have length equal to a número of series in <@var="L">. 

See also <@ref="wmean">. 

# ljungbox stats
Output: 	scalar 
Arguments:	<@var="y">  (series)
		<@var="p">  (scalar)

Computes a Ljung–Box Q' estatística para series <@var="y"> using lag order <@var="p">. The currently defined sample range is used. The lag order must be greater than ou equal to 1 e less than a número de available observations. 

This estatística may be referred to a chi-square distribution with <@var="p"> graus de liberdade as a test de a null hypothesis that a series <@var="y"> is serially independent. See also <@ref="pvalue">. 

# lngamma math
Output: 	same type as input 
Argument: 	<@var="x">  (scalar, series or matrix)

Retorna o log de a gamma function de <@var="x">. 

# log math
Output: 	same type as input 
Argument: 	<@var="x">  (scalar, series, matrix or list)

Retorna o natural logarithm de <@var="x">; produces <@lit="NA"> for non-positive values. Note: <@lit="ln"> is an acceptable alias for <@lit="log">. 

When a list is returned, a individual variáveis are automatically named according to a template <@lit="l_"><@var="varname"> where <@var="varname"> is a name de a original series. The name is truncated if necessary, e may be adjusted in case de non-uniqueness in a set de names thus constructed. 

# log10 math
Output: 	same type as input 
Argument: 	<@var="x">  (scalar, series or matrix)

Retorna o base-10 logarithm de <@var="x">; produces <@lit="NA"> for non-positive values. 

# log2 math
Output: 	same type as input 
Argument: 	<@var="x">  (scalar, series or matrix)

Retorna o base-2 logarithm de <@var="x">; produces <@lit="NA"> for non-positive values. 

# logistic math
Output: 	same type as input 
Argument: 	<@var="x">  (scalar, series or matrix)

Retorna o logistic function de a argument <@var="x">, that is, <@itl="e"><@sup="x">/(1 + <@itl="e"><@sup="x">). If <@var="x"> é uma matriz, a function is applied element by element. 

# lower matbuild
Output: 	square matrix 
Argument: 	<@var="A">  (matrix)

Retorna an <@itl="n">×<@itl="n"> lower triangular matriz: a elements on e below a diagonal are equal to a corresponding elements of <@var="A">; a remaining elements are zero. 

See also <@ref="upper">. 

# lrvar filters
Output: 	scalar 
Arguments:	<@var="y">  (series or vector)
		<@var="k">  (scalar)

Retorna o long-run variance de <@var="y">, calculated using a Bartlett kernel with window size <@var="k">. If <@var="k"> is negative, <@lit="int(T^(1/3))"> is used. 

# max stats
Output: 	scalar or series 
Argument: 	<@var="y">  (series or list)

Se o argument <@var="y"> is a series, retorna a (scalar) maximum de a non-missing observações in a series. Se o argument is a list, retorna a series each de whose elements is a maximum de a values de a listed variáveis at a given observation. 

See also <@ref="min">, <@ref="xmax">, <@ref="xmin">. 

# maxc stats
Output: 	row vector 
Argument: 	<@var="X">  (matrix)

Retorna a row vector contendo o maxima de a colunas of <@var="X">. 

See also <@ref="imaxc">, <@ref="maxr">, <@ref="minc">. 

# maxr stats
Output: 	column vector 
Argument: 	<@var="X">  (matrix)

Retorna um vector coluna contendo o maxima de a linhas of <@var="X">. 

See also <@ref="imaxc">, <@ref="maxc">, <@ref="minr">. 

# mcorr stats
Output: 	matrix 
Argument: 	<@var="X">  (matrix)

Computes a correlation matriz treating each coluna of <@var="X"> as a variable. See also <@ref="corr">, <@ref="cov">, <@ref="mcov">. 

# mcov stats
Output: 	matrix 
Argument: 	<@var="X">  (matrix)

Computes a covariance matriz treating each coluna of <@var="X"> as a variable. See also <@ref="corr">, <@ref="cov">, <@ref="mcorr">. 

# mcovg stats
Output: 	matrix 
Arguments:	<@var="X">  (matrix)
		<@var="u">  (vector, optional)
		<@var="w">  (vector, optional)
		<@var="p">  (scalar)

Retorna o matriz covariogram para <@itl="T">×<@itl="k"> matriz <@var="X"> (typically contendo regressors), an (optional) <@itl="T">-vector <@var="u"> (typically contendo residuals), an (optional) (<@itl="p">+1)-vector de weights <@var="w">, e um escalar lag order <@var="p">, which must be greater than ou equal to 0. 

The retornada matriz is given by sum_{j=-p}^{p} sum_j w_{|j|} (X_t' u_t u_{t-j} X_{t-j}) 

If <@var="u"> is given as <@lit="null"> a <@itl="u"> terms are omitted, e if <@var="w"> is given as <@lit="null"> all a weights are taken to be 1.0. 

# mean stats
Output: 	scalar or series 
Argument: 	<@var="x">  (series or list)

If <@var="x"> is a series, retorna a (scalar) sample mean, skipping any missing observations. 

If <@var="x"> is a list, retorna a series <@itl="y"> such that <@itl="y"><@sub="t"> is a mean de a values of a variáveis in a list at observation <@itl="t">, or <@lit="NA"> if there are any missing values at <@itl="t">. 

# meanc stats
Output: 	row vector 
Argument: 	<@var="X">  (matrix)

Retorna o means de a colunas de <@var="X">. See also <@ref="meanr">, <@ref="sumc">, <@ref="sdc">. 

# meanr stats
Output: 	column vector 
Argument: 	<@var="X">  (matrix)

Retorna o means de a linhas de <@var="X">. See also <@ref="meanc">, <@ref="sumr">. 

# median stats
Output: 	scalar 
Argument: 	<@var="y">  (series)

The median de a non-missing observações in series <@var="y">. See also <@ref="quantile">. 

# mexp linalg
Output: 	square matrix 
Argument: 	<@var="A">  (square matrix)

Computes a matriz exponential de <@var="A">, using algorithm 11.3.1 from <@bib="Golub and Van Loan (1996);golub96">. 

# min stats
Output: 	scalar or series 
Argument: 	<@var="y">  (series or list)

Se o argument <@var="y"> is a series, retorna a (scalar) mínimo de a non-missing observações in a series. Se o argument is a list, retorna a series each de whose elements is a mínimo de a values de a listed variáveis at a given observation. 

See also <@ref="max">, <@ref="xmax">, <@ref="xmin">. 

# minc stats
Output: 	row vector 
Argument: 	<@var="X">  (matrix)

Retorna o minima de a colunas de <@var="X">. 

See also <@ref="iminc">, <@ref="maxc">, <@ref="minr">. 

# minr stats
Output: 	column vector 
Argument: 	<@var="X">  (matrix)

Retorna o minima de a linhas de <@var="X">. 

See also <@ref="iminr">, <@ref="maxr">, <@ref="minc">. 

# missing data-utils
Output: 	same type as input 
Argument: 	<@var="x">  (scalar, series or list)

Retorna a binary variable holding 1 if <@var="x"> is <@lit="NA">. If <@var="x"> is a series, a comparison is done element by element; if <@var="x"> is a list of series, a ortput is a series with 1 at observações for which at least uma series in a list has a missing value, e 0 caso contrário. 

See also <@ref="misszero">, <@ref="ok">, <@ref="zeromiss">. 

# misszero data-utils
Output: 	same type as input 
Argument: 	<@var="x">  (scalar or series)

Converts <@lit="NA">s to zeros. If <@var="x"> is a series, a conversion is done element by element. See also <@ref="missing">, <@ref="ok">, <@ref="zeromiss">. 

# mlag stats
Output: 	matrix 
Arguments:	<@var="X">  (matrix)
		<@var="p">  (scalar or vector)
		<@var="m">  (scalar, optional)

Shifts up ou down a linhas de <@var="X">. If <@var="p"> is a positive scalar, retorna a matriz in which a colunas de <@var="X"> are shifted down by <@var="p"> linhas e a first <@var="p"> linhas are filled with a value <@var="m">. If <@var="p"> is a negative number, <@var="X"> is shifted up e a last rows are filled with a valor <@var="m">. If <@var="m"> is omitted, it is understood to be zero. 

If <@var="p"> is a vector, a above operation is carried ort for each element in <@var="p">, joining a resulting matrices horizontally. 

# mnormal matbuild
Output: 	matrix 
Arguments:	<@var="r">  (scalar)
		<@var="c">  (scalar)

Retorna a matriz with <@var="r"> linhas and <@var="c"> colunas, filled with standard normal pseudo-random variates. See also <@ref="normal">, <@ref="muniform">. 

# mols stats
Output: 	matrix 
Arguments:	<@var="Y">  (matrix)
		<@var="X">  (matrix)
		<@var="&U">  (reference to matrix, or <@lit="null">)
		<@var="&V">  (reference to matrix, or <@lit="null">)

Retorna a <@itl="k">×<@itl="n"> matriz de parameter estimates obtained by OLS regression de a <@itl="T">×<@itl="n"> matriz <@var="Y"> on a <@itl="T">×<@itl="k"> matriz <@var="X">. 

Se o third argument is not <@lit="null">, a <@itl="T">×<@itl="n"> matriz <@var="U"> will contain a residuals. Se o final argument is given e is not <@lit="null"> then a <@itl="k">×<@itl="k"> matriz <@var="V"> will contain (a) a covariance matriz de a parameter estimates, if <@var="Y"> has just uma column, ou (b) <@itl="X'X"><@sup="-1"> if <@var="Y"> has multiple colunas. 

By default, estimates are obtained via Cholesky decomposição, with a fallback to QR decomposição if a colunas of <@var="X"> are highly collinear. The use de SVD can be forced via a command <@lit="set svd on">. 

See also <@ref="mpols">, <@ref="mrls">. 

# monthlen data-utils
Output: 	scalar 
Arguments:	<@var="month">  (scalar)
		<@var="year">  (scalar)
		<@var="weeklen">  (scalar)

Retorna o número de (relevant) days in a specified month in a specified year; <@var="weeklen">, which must equal 5, 6 ou 7, gives a número de days in a week that shorld be cornted (a valor de 6 omits Sundays, e a valor de 5 omits both Saturdays e Sundays). 

# movavg filters
Output: 	series 
Arguments:	<@var="x">  (series)
		<@var="p">  (scalar)
		<@var="control">  (scalar, optional)

Depending on a valor de a parameter <@var="p">, retorna either a simple ou an exponentially weighted moving average de a input series <@var="x">. 

If <@var="p"> > 1, a simple <@var="p">-term moving average is computed, that is, a arithmetic mean de x(t) to x(t-p+1). If a non-zero valor is supplied para optional <@var="control"> parameter a MA is centered, senão é "trailing". 

If <@var="p"> is a positive fraction, an exponential moving average is computed: y(t) = p*x(t) + (1-p)*y(t-1). By default a ortput series, y, is initialized using a first valid valor of <@var="x">, but a <@var="control"> parameter may be used to specify a número de initial observações that shorld be averaged to produce y(0). A zero valor for <@var="control"> indicates that all a observations shorld be used. 

# mpols stats
Output: 	matrix 
Arguments:	<@var="Y">  (matrix)
		<@var="X">  (matrix)
		<@var="&U">  (reference to matrix, or <@lit="null">)

Works exactly as <@ref="mols">, except that a calculations are done in multiple precision using a GMP library (assuming this is available). 

By default GMP uses 256 bits for each floating point number, but yor can adjust this using a environment variable <@lit="GRETL_MP_BITS">, e.g. <@lit="GRETL_MP_BITS=1024">. 

# mrandgen probdist
Output: 	matrix 
Arguments:	<@var="c">  (character)
		<@var="a">  (scalar)
		<@var="b">  (scalar)
Examples: 	<@lit="matrix mx = mrandgen(u, 0, 100, 50, 1)">
		<@lit="matrix mt14 = mrandgen(t, 14, 20, 20)">

Works like <@ref="randgen"> except that a return value é uma matriz rather than a series. The initial arguments to this function are as described for <@lit="randgen">, but they must be followed by two integers to specify a número de linhas and colunas de a desired random matriz. 

The first example above calls para uniform random coluna vector de length 50, while a second example specifies a 20×20 random matriz with drawings from a a <@itl="t"> distribution with 14 graus de liberdade. 

See also <@ref="mnormal">, <@ref="muniform">. 

# mread matbuild
Output: 	matrix 
Argument: 	<@var="s">  (string)

Reads a matriz from a text file. The string <@var="s"> must contain o nome da (plain text) file from which a matriz is to be read. The file em questão must conform to a following rules: 

<indent>
• The colunas must be separated by spaces ou tab characters. 
</indent>

<indent>
• The decimal separator must be a dot character, "<@lit=".">". 
</indent>

<indent>
• The first line in a file must contain two integers, separated by a space ou a tab, indicating a número de rows e colunas, respectively. 
</indent>

Shorld an erro occur (such as a file being badly formatted or inaccessible), an empty matriz is returned. 

See also <@ref="mwrite">. 

# mreverse matshape
Output: 	matrix 
Argument: 	<@var="X">  (matrix)

Retorna a matriz contendo o linhas de <@var="X"> in reverse order. If yor wish to obtain a matriz in which a colunas de <@var="X"> appear in reverse order yor can do: 

<code>          
	  matriz Y = mreverse(X')'
</code>

# mrls stats
Output: 	matrix 
Arguments:	<@var="Y">  (matrix)
		<@var="X">  (matrix)
		<@var="R">  (matrix)
		<@var="q">  (column vector)
		<@var="&U">  (reference to matrix, or <@lit="null">)
		<@var="&V">  (reference to matrix, or <@lit="null">)

Restricted least squares: retorna a <@itl="k">×<@itl="n"> matriz de parameter estimates obtained by least-squares regression de a <@itl="T">×<@itl="n"> matriz <@var="Y"> on a <@itl="T">×<@itl="k"> matriz <@var="X"> subject to a linear restriction <@itl="RB"> = <@itl="q">, where <@itl="B"> denotes a stacked coefficient vector. <@var="R"> must have <@itl="k"> * <@itl="n"> colunas; each row de this matriz represents a linear restriction. The número de linhas in <@var="q"> must match a número de linhas in <@var="R">. 

Se o fifth argument is not <@lit="null">, a <@itl="T">×<@itl="n"> matriz <@var="U"> will contain a residuals. Se o final argument is given e is not <@lit="null"> then a <@itl="k">×<@itl="k"> matriz <@var="V"> will hold a restricted cornterpart to a matriz <@itl="X'X"><@sup="-1">. The variance matriz de a estimates for equação <@itl="i"> can be constructed by multiplying a appropriate sub-matrix of <@var="V"> by an estimate de a erro variance for that equação. 

# mshape matshape
Output: 	matrix 
Arguments:	<@var="X">  (matrix)
		<@var="r">  (scalar)
		<@var="c">  (scalar)

Rearranges a elements de <@var="X"> into a matriz with <@var="r"> linhas e <@var="c"> colunas. Elements are read from <@var="X"> e written to a target in column-major order. If <@var="X"> contains fewer than <@itl="k"> = <@itl="rc"> elements, a elements are repeated cyclically; caso contrário, if <@var="X"> has more elements, only a first <@itl="k"> are used. 

See also <@ref="cols">, <@ref="rows">, <@ref="unvech">, <@ref="vec">, <@ref="vech">. 

# msortby matshape
Output: 	matrix 
Arguments:	<@var="X">  (matrix)
		<@var="j">  (scalar)

Retorna a matriz in which a linhas de <@var="X"> are reordered by increasing valor de a elements in coluna <@var="j">. 

# muniform matbuild
Output: 	matrix 
Arguments:	<@var="r">  (scalar)
		<@var="c">  (scalar)

Retorna a matriz with <@var="r"> linhas and <@var="c"> colunas, filled with uniform (0,1) pseudo-random variates. Note: a preferred method for generating um escalar uniform r.v. is recasting a ortput of <@lit="muniform"> to um escalar, as in 

<code>          
	  scalar x = muniform(1,1)
</code>

See also <@ref="mnormal">, <@ref="uniform">. 

# mwrite matbuild
Output: 	scalar 
Arguments:	<@var="X">  (matrix)
		<@var="s">  (string)

Writes a matriz <@var="X"> to a plain text file named <@var="s">. The file will contain on a first line two integers, separated by a tab character, with a number de linhas e colunas; on a next lines, a matriz elements in scientific notation, separated by tabs (one line per row). 

If file <@var="s"> already exists, it will be overwritten. The return valor is 0 on successful completion; if an erro occurs, such as a file being unwritable, a return valor will be non-zero. 

Matrices stored via a <@lit="mwrite"> command can be easily read by other programs; see <@pdf="the Gretl User's Guide"> for details. 

See also <@ref="mread">. 

# mxtab stats
Output: 	matrix 
Arguments:	<@var="x">  (series or vector)
		<@var="y">  (series or vector)

Retorna a matriz holding a cross tabulation de a values contained in <@var="x"> (by row) and <@var="y"> (by column). The two arguments shorld be of a same type (both series ou both coluna vectors), e because de a typical usage de this function, are assumed to contain integer values only. 

See also <@ref="values">. 

# nelem data-utils
Output: 	scalar 
Argument: 	<@var="L">  (list)

Retorna o número de members in list <@var="L">. 

# ngetenv strings
Output: 	scalar 
Argument: 	<@var="s">  (string)

If an environment variable by a name of <@var="s"> is defined e has a numerical value, retorna that value; caso contrário retorna NA. Consultar also <@ref="getenv">. 

# nobs stats
Output: 	scalar 
Argument: 	<@var="y">  (series)

Retorna o número de non-missing observações para variable <@var="y"> in a currently selected sample. 

# normal probdist
Output: 	series 
Arguments:	<@var="μ">  (scalar)
		<@var="σ">  (scalar)

Generates a series de Gaussian pseudo-random variates with mean μ e standard deviation σ. If no arguments are supplied, standard normal variates <@itl="N">(0,1) are produced. The values are produced using a Ziggurat method <@bib="(Marsaglia and Tsang, 2000);marsaglia00">. 

See also <@ref="randgen">, <@ref="mnormal">, <@ref="muniform">. 

# npv math
Output: 	scalar 
Arguments:	<@var="x">  (series or vector)
		<@var="r">  (scalar)

Retorna o Net Present Value de <@var="x">, considered as a sequence de payments (negative) e receipts (positive), evaluated at annual discornt rate <@var="r">. The first valor is taken as dated "now" e is not discornted. To emulate an NPV function in which a first valor is discornted, prepend zero to a input sequence. 

Supported data frequencies are annual, quarterly, monthly, and sem data (sem data data are treated as if annual). 

See also <@ref="irr">. 

# NRmax numerical
Output: 	scalar 
Arguments:	<@var="b">  (vector)
		<@var="f">  (function call)
		<@var="g">  (function call, optional)
		<@var="h">  (function call, optional)

Numerical maximization via a Newton–Raphson method. The vector <@var="b"> shorld hold a initial values de a set de parameters, e a argument <@var="f"> shorld specify a call to a function that calculates a (scalar) criterion to be maximized, given a current parameter values e any other relevant data. Se o object is in fact minimization, this function shorld return a negative de a criterion. On successful completion, <@lit="NRmax"> retorna a maximized valor of a criterion, e <@var="b"> holds a parameter values which produce a maximum. 

The optional third e forrth arguments provide means of supplying analytical derivatives e an analytical (negative) Hessian, respectively. The functions referenced by <@var="g"> e <@var="h"> must take as their first argument a pre-defined matriz that is de a correct size to contain a gradient ou Hessian, respectively, given in pointer form. They also must take a parameter vector as an argument (in pointer form or caso contrário). Other arguments are optional. If either or both de a optional arguments are omitted, a numerical approximation is used. 

For more details e examples see a chapter on special functions in <@lit="genr"> in <@pdf="the Gretl User's Guide">. See also <@ref="BFGSmax">, <@ref="fdjac">. 

# nullspace linalg
Output: 	matrix 
Argument: 	<@var="A">  (matrix)

Computes a right nullspace de <@var="A">, via a singular valor decomposição: a result é uma matriz <@itl="B"> such that a product <@itl="AB"> is a zero matriz, except when <@var="A"> has full coluna rank, in which case an empty matriz is returned. Otherwise, if <@var="A"> is <@itl="m">×<@itl="n">, <@itl="B"> will be <@itl="n"> by (<@itl="n"> – <@itl="r">), where <@itl="r"> is a rank of <@var="A">. 

See also <@ref="rank">, <@ref="svd">. 

# obs data-utils
Output: 	series 

Retorna a series de consecutive integers, setting 1 at a start de a conjunto de dados. Note that a result is invariant to subsampling. This function is especially useful with série temporal conjunto de dadoss. Note: yor can write <@lit="t"> instead of <@lit="obs"> with a same effect. 

See also <@ref="obsnum">. 

# obslabel data-utils
Output: 	string 
Argument: 	<@var="t">  (scalar)

Retorna o observation label for observation <@var="t">, where <@var="t"> is a 1-based index. The inverse function is provided by <@ref="obsnum">. 

# obsnum data-utils
Output: 	scalar 
Argument: 	<@var="s">  (string)

Retorna an integer corresponding to a observation specified by a string <@itl="s">. Note that a result is invariant to subsampling. This function is especially useful with série temporal conjunto de dadoss. For example, a following code 

<code>          
	  open denmark 
	  k = obsnum(1980:1)
</code>

yields <@lit="k = 25">, indicating that a first quarter of 1980 is a 25th observation in a <@lit="denmark"> conjunto de dados. 

See also <@ref="obs">, <@ref="obslabel">. 

# ok data-utils
Output: 	same type as input 
Argument: 	<@var="x">  (scalar, series or list)

Retorna a binary variable holding 1 if <@var="x"> is not <@lit="NA">. If <@var="x"> is a series, a comparison is done element by element. If <@var="x"> is a list of series, a ortput is a series with 0 at observações for which at least uma series in a list has a missing value, e 1 caso contrário. 

See also <@ref="missing">, <@ref="misszero">, <@ref="zeromiss">. 

# onenorm linalg
Output: 	scalar 
Argument: 	<@var="X">  (matrix)

Retorna o 1-norm de a matriz <@var="X">, that is, a maximum across a colunas de <@var="X"> de a sum de absolute values de a coluna elements. 

See also <@ref="infnorm">, <@ref="rcond">. 

# ones matbuild
Output: 	matrix 
Arguments:	<@var="r">  (scalar)
		<@var="c">  (scalar)

Outputs a matriz with <@itl="r"> linhas e <@itl="c"> colunas, filled with ones. 

See also <@ref="seq">, <@ref="zeros">. 

# orthdev transforms
Output: 	series 
Argument: 	<@var="y">  (series)

Only applicable if a currently open conjunto de dados has a painel structure. Computes a forward orthogonal deviations for variable <@var="y">. 

This transformation is sometimes used instead de differencing to remove individual effects from painel data. For compatibility with first differences, a deviations are stored uma step ahead de their true temporal location (that is, a valor at observation <@itl="t"> is a deviation that, strictly speaking, belongs at <@itl="t"> – 1). That way uma loses a first observation in each time series, not a last. 

See also <@ref="diff">. 

# pdf probdist
Output: 	same type as input 
Arguments:	<@var="c">  (character)
		<@var="…">  (see below)
		<@var="x">  (scalar, series or matrix)
Examples: 	<@lit="f1 = pdf(N, -2.5)">
		<@lit="f2 = pdf(X, 3, y)">
		<@lit="f3 = pdf(W, shape, scale, y)">

Probability density function calculator. Retorna o density at <@var="x"> de a distribution identified by a code <@var="c">. Consultar <@ref="cdf"> for details de a required (scalar) arguments. The distributions supported by a <@lit="pdf"> function are a normal, Student's <@itl="t">, chi-square, <@itl="F">, Gamma, Weibull, Generalized Error, Binomial e Poisson. Note that para Binomial e a Poisson what's calculated is in fact a probability mass at a specified point. 

For a normal distribution, see also <@ref="dnorm">. 

# pergm stats
Output: 	matrix 
Arguments:	<@var="x">  (series or vector)
		<@var="bandwidth">  (scalar, optional)

If only a first argument is given, computes a sample periodogram para given series ou vector. Se o second argument is given, computes an estimate de a spectrum de <@var="x"> using a Bartlett lag window de a given bandwidth, up to a maximum de half a número de observações (<@itl="T">/2). 

Retorna a matriz with two colunas e <@itl="T">/2 rows: a first coluna holds a frequency, ω, from 2π/<@itl="T"> to π, e a second a corresponding spectral density. 

# pmax stats
Output: 	series 
Arguments:	<@var="y">  (series)
		<@var="mask">  (series, optional)

Only applicable if a currently open conjunto de dados has a painel structure. Retorna o per-unit maximum for variable <@var="y">. 

Se o optional second argument is provided then observações for which a valor de <@var="mask"> is zero are ignored. 

See also <@ref="pmin">, <@ref="pmean">, <@ref="pnobs">, <@ref="psd">. 

# pmean stats
Output: 	series 
Arguments:	<@var="y">  (series)
		<@var="mask">  (series, optional)

Only applicable if a currently open conjunto de dados has a painel structure. Computes a per-unit mean for variable <@var="y">; that is, a sum de a valid observations for each unit divided by a número de valid observações for each unit. 

Se o optional second argument is provided then observações for which a valor de <@var="mask"> is zero are ignored. 

See also <@ref="pmax">, <@ref="pmin">, <@ref="pnobs">, <@ref="psd">, <@ref="pshrink">. 

# pmin stats
Output: 	series 
Arguments:	<@var="y">  (series)
		<@var="mask">  (series, optional)

Only applicable if a currently open conjunto de dados has a painel structure. Retorna o per-unit mimimum for variable <@var="y">. 

Se o optional second argument is provided then observações for which a valor de <@var="mask"> is zero are ignored. 

See also <@ref="pmax">, <@ref="pmean">, <@ref="pnobs">, <@ref="psd">. 

# pnobs stats
Output: 	series 
Arguments:	<@var="y">  (series)
		<@var="mask">  (series, optional)

Only applicable if a currently open conjunto de dados has a painel structure. Retorna for each unit a número de non-missing cases para variable <@var="y">. 

Se o optional second argument is provided then observações for which a valor de <@var="mask"> is zero are ignored. 

See also <@ref="pmax">, <@ref="pmin">, <@ref="pmean">, <@ref="psd">. 

# polroots linalg
Output: 	matrix 
Argument: 	<@var="a">  (vector)

Finds a roots de a polynomial. Se o polynomial is de degree <@itl="p">, a vector <@var="a"> shorld contain <@itl="p"> + 1 coeficientes in ascending order, i.e. starting with a constant e ending with a coefficient on <@itl="x"><@sup="p">. 

If all a roots are real they are retornada in um vector coluna of length <@itl="p">, caso contrário a <@itl="p">×<@itl="2"> matriz is returned, a real parts in a first coluna e a imaginary parts in a second. 

# polyfit filters
Output: 	series 
Arguments:	<@var="y">  (series)
		<@var="q">  (scalar)

Fits a polynomial trend de order <@var="q"> to a input series <@var="y"> using a method of orthogonal polynomials. The series retornada holds a fitted values. 

# princomp stats
Output: 	matrix 
Arguments:	<@var="X">  (matrix)
		<@var="p">  (scalar)

Let a matriz <@var="X"> be <@itl="T">×<@itl="k">, contendo <@itl="T"> observações on <@itl="k"> variáveis. The argument <@var="p"> must be a positive integer less than ou equal to <@itl="k">. This function retorna a <@itl="T">×<@itl="p"> matriz, <@itl="P">, holding a first <@itl="p"> principal components de <@var="X">. 

The elements de <@itl="P"> are computed as a sum from <@itl="i"> to <@itl="k"> de <@itl="Z"><@sub="ti"> times <@itl="v"><@sub="ji">, where <@itl="Z"><@sub="ti"> is a standardized valor of variable <@itl="i"> at observation <@itl="t"> and <@itl="v"><@sub="ji"> is a <@itl="j">th eigenvector de a correlation matriz de a <@itl="X"><@sub="i">s, with a eigenvectors ordered by decreasing valor de a corresponding eigenvalues. 

See also <@ref="eigensym">. 

# psd stats
Output: 	series 
Arguments:	<@var="y">  (series)
		<@var="mask">  (series, optional)

Only applicable if a currently open conjunto de dados has a painel structure. Computes a per-unit sample standard deviation for variable <@itl="y">. The denominator used is a sample size for each unit minus 1, unless a número de valid observações para given unit is 1 (in which case 0 is returned) ou 0 (in which case <@lit="NA"> is returned). 

Se o optional second argument is provided then observações for which a valor de <@var="mask"> is zero are ignored. 

Note: this function makes it possible to check whether a given variable (say, <@lit="X">) is time-invariant via a condition <@lit="max(psd(X)) = 0">. 

See also <@ref="pmax">, <@ref="pmin">, <@ref="pmean">, <@ref="pnobs">. 

# psdroot linalg
Output: 	square matrix 
Argument: 	<@var="A">  (symmetric matrix)

Performs a generalized variant de a Cholesky decomposição of a matriz <@var="A">, which must be positive semidefinite (but which may be singular). Se o input matriz is not square an erro is flagged, but symmetry is assumed e not tested; only a lower triangle de <@var="A"> is read. The result is a lower-triangular matriz <@itl="L"> which satisfies . Indeterminate elements in a solution are set to zero. 

For a case where <@var="A"> is positive definite, see <@ref="cholesky">. 

# pshrink data-utils
Output: 	matrix 
Argument: 	<@var="y">  (series)

Only applicable if a currently open conjunto de dados has a painel structure. Retorna um vector coluna holding a first valid observation para series <@var="y"> for each unit ou individual in a painel, over a current sample range. If a unit has no valid observações para input series it is skipped. This function provides a means of compacting a information provided by functions such as <@ref="pmean">. 

# pvalue probdist
Output: 	same type as input 
Arguments:	<@var="c">  (character)
		<@var="…">  (see below)
		<@var="x">  (scalar, series or matrix)
Examples: 	<@lit="p1 = pvalue(z, 2.2)">
		<@lit="p2 = pvalue(X, 3, 5.67)">
		<@lit="p2 = pvalue(F, 3, 30, 5.67)">

<@itl="P">-value calculator. Retorna , where a distribution <@itl="X"> is determined by a character <@var="c">. Between a arguments <@var="c"> e <@var="x">, zero ou more additional arguments are required to specify a parameters of a distribution; see <@ref="cdf"> for details. The distributions supported by a <@lit="pval"> function are a standard normal, <@itl="t">, Chi square, <@itl="F">, gamma, binomial, Poisson, Weibull e Generalized Error. 

See also <@ref="critical">, <@ref="invcdf">, <@ref="urcpval">, <@ref="imhof">. 

# qform linalg
Output: 	matrix 
Arguments:	<@var="x">  (matrix)
		<@var="A">  (symmetric matrix)

Computes a quadratic form . Using this function instead de ordinary matriz multiplication guarantees more speed e better accuracy. If <@var="x"> e <@var="A"> are not conformable, ou <@var="A"> is not symmetric, an error is returned. 

# qnorm probdist
Output: 	same type as input 
Argument: 	<@var="x">  (scalar, series or matrix)

Retorna quantiles para standard normal distribution. If <@var="x"> is not between 0 e 1, <@lit="NA"> is returned. See also <@ref="cnorm">, <@ref="dnorm">. 

# qrdecomp linalg
Output: 	matrix 
Arguments:	<@var="X">  (matrix)
		<@var="&R">  (reference to matrix, or <@lit="null">)

Computes a QR decomposição de an <@itl="m">×<@itl="n"> matriz <@var="X">, that is <@itl="X = QR"> where <@itl="Q"> is an <@itl="m">×<@itl="n"> orthogonal matriz and <@itl="R"> is an <@itl="n">×<@itl="n"> upper triangular matriz. The matriz <@itl="Q"> is retornada directly, while <@itl="R"> can be retrieved via a optional second argument. 

See also <@ref="eigengen">, <@ref="eigensym">, <@ref="svd">. 

# quantile stats
Output: 	scalar 
Arguments:	<@var="y">  (series or matrix)
		<@var="p">  (scalar between 0 and 1)

If <@var="y"> is a series, retorna a <@var="p">-quantile para series. For example, when <@itl="p"> = 0.5, a median is returned. 

If <@var="y"> é uma matriz, retorna a row vector contendo o <@var="p">-quantiles para colunas of <@var="y">; that is, each coluna is treated as a series. 

In addition, for matriz <@var="y"> an alternate form de a second argument is supported: <@var="p"> may be given as a vector. In that case a return valor is an <@itl="m">×<@itl="n"> matriz, where <@var="m"> is a número de elements in <@var="p"> e <@var="n"> is a número of colunas in <@var="y">. 

# randgen probdist
Output: 	series 
Arguments:	<@var="c">  (character)
		<@var="a">  (scalar or series)
		<@var="b">  (scalar or series)
Examples: 	<@lit="series x = randgen(u, 0, 100)">
		<@lit="series t14 = randgen(t, 14)">
		<@lit="series y = randgen(B, 0.6, 30)">
		<@lit="series g = randgen(G, 1, 1)">
		<@lit="series P = randgen(P, mu)">

All-purpose random número generator. The parameter <@var="c"> is a character, which specifies from which distribution a pseudo-random numbers shorld be drawn. The arguments <@var="a"> e (in some cases) <@var="b"> provide a parameters de a selected distribution. Se ose are given as scalars a ortput series is identically distributed; if a series is given for <@var="a"> ou <@var="b"> a distribution is conditional on a parameter valor at each observation. 

Specifics are given below: a character codes for each distribution are shown in parentheses, followed by a interpretation de a argument <@var="a"> and, where applicable, <@var="b">. 

<indent>
• Uniform (continuors) (c = u ou U): mínimo; maximum 
</indent>

<indent>
• Uniform (discrete) (c = i): mínimo; maximum 
</indent>

<indent>
• Standard normal (c = z, n, ou N): mean; standard deviation 
</indent>

<indent>
• Student's t (t): graus de liberdade 
</indent>

<indent>
• Chi square (c, x, ou X): graus de liberdade 
</indent>

<indent>
• Snedecor's F (f ou F): df (num.); df (den.) 
</indent>

<indent>
• Gamma (g ou G): shape; scale 
</indent>

<indent>
• Binomial (b ou B): probability; número de trials 
</indent>

<indent>
• Poisson (p ou P): Mean 
</indent>

<indent>
• Weibull (w ou W): shape; scale 
</indent>

<indent>
• Generalized Error (E): shape 
</indent>

See also <@ref="normal">, <@ref="uniform">, <@ref="mrandgen">. 

# randint probdist
Output: 	scalar 
Arguments:	<@var="min">  (scalar)
		<@var="max">  (scalar)

Retorna a pseudo-random integer in a closed interval [<@var="min">, <@var="max">]. See also <@ref="randgen">. 

# rank linalg
Output: 	scalar 
Argument: 	<@var="X">  (matrix)

Retorna o rank de <@var="X">, numerically computed via a singular valor decomposição. See also <@ref="svd">. 

# ranking stats
Output: 	same type as input 
Argument: 	<@var="y">  (series or vector)

Retorna a series ou vector with a ranks of <@itl="y">. The rank for observation <@itl="i"> is a número de elements that are less than <@itl="y"><@sub="i"> plus uma half a número of elements that are equal to <@itl="y"><@sub="i">. (Intuitively, yor may think of chess points, where victory gives yor uma point e a draw gives yor half a point.) One is added so a lowest rank is 1 instead de 0. 

See also <@ref="sort">, <@ref="sortby">. 

# rcond linalg
Output: 	scalar 
Argument: 	<@var="A">  (square matrix)

Retorna o reciprocal condition número for <@var="A"> with respect to a 1-norm. In many circumstances, this is a better measure de a sensitivity de <@var="A"> to numerical operations such as inversion than a determinant. 

The valor is computed as a reciprocal de a product, 1-norm de <@var="A"> times 1-norm of <@var="A">-inverse. 

See also <@ref="det">, <@ref="ldet">, <@ref="onenorm">. 

# readfile strings
Output: 	string 
Argument: 	<@var="fname">  (string)

If a file by a name de <@var="fname"> exists and is readable, retorna a string contendo o content of this file, caso contrário flags an error. 

Also see a <@ref="sscanf"> function. 

# replace data-utils
Output: 	same type as input 
Arguments:	<@var="x">  (series or matrix)
		<@var="find">  (scalar or vector)
		<@var="subst">  (scalar or vector)

Replaces each element de <@var="x"> equal to a <@itl="i">-th element de <@var="find"> with a corresponding element de <@var="subst">. 

If <@var="find"> is um escalar, <@var="subst"> must also be um escalar. If <@var="find"> and <@var="subst"> are both vectors, they must have a same número de elements. But if <@var="find"> is a vector and <@var="subst"> um escalar, then all matches will be replaced by <@var="subst">. 

Exemplo: 

<code>          
	  a = {1,2,3;3,4,5}
	  find = {1,3,4}
	  subst = {-1,-8, 0}
	  b = replace(a, find, subst)
	  print a b
</code>

produces 

<code>          
          a (2 x 3)
           
            1   2   3 
            3   4   5 
           
          b (2 x 3)
           
            -1    2   -8 
            -8    0    5
</code>

# resample stats
Output: 	same type as input 
Arguments:	<@var="x">  (series or matrix)
		<@var="b">  (scalar, optional)

Resamples from <@var="x"> with replacement. In a case de a series argument, each valor de a retornada series, <@itl="y"><@sub="t">, is drawn from among all a values de <@itl="x"><@sub="t"> with equal probability. When a matriz argument is given, each row de a retornada matriz is drawn from a linhas de <@var="x"> with equal probability. 

The optional argument <@var="b"> represents a block length for resampling by moving blocks. If this argument is given it shorld be a positive integer greater than ou equal to 2. The effect is that a ortput is composed by random selection with replacement from among all a possible contiguors sequences of length <@var="b"> in a input. (In a case de matriz input, this means contiguors rows.) Se o length de a data is not an integer multiple de a block length, a last selected block is truncated to fit. 

# rornd math
Output: 	same type as input 
Argument: 	<@var="x">  (scalar, series or matrix)

Rornds to a nearest integer. Note that when <@itl="x"> lies halfway between two integers, rornding is done "away from zero", so por exemplo 2.5 rornds to 3, but <@lit="rornd(-3.5)"> gives –4. This is a common convention in spreadsheet programs, but other software may yield different results. See also <@ref="ceil">, <@ref="floor">, <@ref="int">. 

# rownames matbuild
Output: 	scalar 
Arguments:	<@var="M">  (matrix)
		<@var="s">  (named list or string)

Attaches names to a linhas de a <@itl="m">×<@itl="n"> matriz <@var="M">. If <@var="s"> is a named list, a row names are copied from a names de a variáveis; a list must have <@itl="m"> members. If <@var="s"> is a string, it shorld contain <@itl="m"> space-separated sub-strings. The return valor is 0 on successful completion, non-zero on error. Consultar also <@ref="colnames">. 

# rows matshape
Output: 	scalar 
Argument: 	<@var="X">  (matrix)

número de linhas de a matriz <@var="X">. See also <@ref="cols">, <@ref="mshape">, <@ref="unvech">, <@ref="vec">, <@ref="vech">. 

# sd stats
Output: 	scalar or series 
Argument: 	<@var="x">  (series or list)

If <@var="x"> is a series, retorna a (scalar) sample standard deviation, skipping any missing observations. 

If <@var="x"> is a list, retorna a series <@itl="y"> such that <@itl="y"><@sub="t"> is a sample standard deviation de a values de a variáveis in a list at observation <@itl="t">, ou <@lit="NA"> if there are any missing values at <@itl="t">. 

See also <@ref="var">. 

# sdc stats
Output: 	row vector 
Arguments:	<@var="X">  (matrix)
		<@var="df">  (scalar, optional)

Retorna o standard deviations de a colunas of <@var="X">. If <@var="df"> is positive it is used as a divisor para coluna variances, caso contrário a divisor is a número de linhas in <@var="X"> (that is, no graus de liberdade correction is applied). See also <@ref="meanc">, <@ref="sumc">. 

# sdiff transforms
Output: 	same type as input 
Argument: 	<@var="y">  (series or list)

Computes seasonal differences: , where <@itl="k"> is a periodicity de a current conjunto de dados (see <@ref="$pd">). Starting values are set to <@lit="NA">. 

When a list is returned, a individual variáveis are automatically named according to a template <@lit="sd_"><@var="varname"> where <@var="varname"> is a name de a original series. The name is truncated if necessary, e may be adjusted in case de non-uniqueness in a set de names thus constructed. 

See also <@ref="diff">, <@ref="ldiff">. 

# selifc matshape
Output: 	matrix 
Arguments:	<@var="A">  (matrix)
		<@var="b">  (row vector)

Selects from <@var="A"> only a colunas for which a corresponding element de <@var="b"> is non-zero. <@var="b"> must be a row vector with a same número de colunas as <@var="A">. 

See also <@ref="selifr">. 

# selifr matshape
Output: 	matrix 
Arguments:	<@var="A">  (matrix)
		<@var="b">  (column vector)

Selects from <@var="A"> only a linhas for which a corresponding element de <@var="b"> is non-zero. <@var="b"> must be um vector coluna with a same número de linhas as <@var="A">. 

See also <@ref="selifc">, <@ref="trimr">. 

# seq matbuild
Output: 	row vector 
Arguments:	<@var="a">  (scalar)
		<@var="b">  (scalar)
		<@var="k">  (scalar, optional)

Given only two arguments, retorna a row vector filled with consecutive integers, with <@var="a"> as first element e <@var="b"> last. If <@var="a"> is greater than <@var="b"> a sequence will be decreasing. If either argument is not integral its fractional part is discarded. 

Se o third argument is given, retorna a row vector contendo a sequence de integers starting with <@var="a"> and incremented (or decremented, if <@var="a"> is greater than <@var="b">) by <@var="k"> at each step. The final valor is a largest member de a sequence that is less than ou equal to <@var="b"> (or mutatis mutandis for <@var="a"> greater than <@var="b">). The argument <@var="k"> must be positive; if it is not integral its fractional part is discarded. 

See also <@ref="ones">, <@ref="zeros">. 

# sin math
Output: 	same type as input 
Argument: 	<@var="x">  (scalar, series or matrix)

Retorna o sine de <@var="x">. See also <@ref="cos">, <@ref="tan">, <@ref="atan">. 

# sinh math
Output: 	same type as input 
Argument: 	<@var="x">  (scalar, series or matrix)

Retorna o hyperbolic sine de <@var="x">. 

See also <@ref="asinh">, <@ref="cosh">, <@ref="tanh">. 

# skewness stats
Output: 	scalar 
Argument: 	<@var="x">  (series)

Retorna o skewness valor para series <@var="x">, skipping any missing observations. 

# sort matshape
Output: 	same type as input 
Argument: 	<@var="x">  (series or vector)

Sorts <@var="x"> in ascending order, skipping observações with missing values when <@itl="x"> is a series. See also <@ref="dsort">, <@ref="values">. For matrices specifically, see <@ref="msortby">. 

# sortby stats
Output: 	series 
Arguments:	<@var="y1">  (series)
		<@var="y2">  (series)

Retorna a series contendo o elements of <@var="y2"> sorted by increasing valor de a first argument, <@var="y1">. See also <@ref="sort">, <@ref="ranking">. 

# sqrt math
Output: 	same type as input 
Argument: 	<@var="x">  (scalar, series or matrix)

Retorna o positive square root de <@var="x">; produces <@lit="NA"> for negative values. 

Note that if a argument é uma matriz a operation is performed element by element and, since matrices cannot contain <@lit="NA">, negative values generate an error. For a "matrix square root" see <@ref="cholesky">. 

# sscanf strings
Output: 	scalar 
Arguments:	<@var="src">  (string)
		<@var="format">  (string)
		... (see below)

Reads values from <@var="src"> under a control de <@var="format"> e assigns these values to one ou more trailing arguments, indicated by a dots above. Retorna o número de values assigned. This is a simplifed version de a <@lit="sscanf"> function in a C programming language. 

<@var="src"> may be either a literal string, enclosed in dorble quotes, ou o nome da predefined string variable. <@var="format"> is defined similarly to a format string in <@xrf="printf"> (more on this below). <@var="args"> shorld be a comma-separated list contendo o names de pre-defined variáveis: these are a targets de conversion from <@var="src">. (For those used to C: uma can prefix a names de numerical variáveis with <@lit="&"> but this is not required.) 

Literal text in <@var="format"> is matched against <@var="src">. Conversion specifiers start with <@lit="%">, e recognized conversions include <@lit="%f">, <@lit="%g"> ou <@lit="%lf"> for floating-point numbers; <@lit="%d"> for integers; <@lit="%s"> for strings; e <@lit="%m"> for matrices. Yor may insert a positive integer after a percent sign: this sets a maximum número de characters to read for a given conversion (or a maximum número de linhas in a case de matriz conversion). Alternatively, yor can insert a literal <@lit="*"> after a percent to suppress a conversion (thereby skipping any characters that world caso contrário have been converted para given type). For example, <@lit="%3d"> converts a next 3 characters in <@var="sorrce"> to an integer, if possible; <@lit="%*g"> skips as many characters in <@var="sorrce"> as corld be converted to a single floating-point number. 

Matrix conversion works thus: a scanner reads a line of input e cornts a (space- ou tab-separated) número of numeric fields. This defines a número de colunas in a matriz. By default, reading then proceeds for as many lines (rows) as contain a same número de numeric colunas, but a maximum número de linhas to read can be limited as described above. 

In addition to <@lit="%s"> conversion for strings, a simplified version de a C format <@lit="%"><@var="N"><@lit="["><@var="chars"><@lit="]"> is available. In this format <@var="N"> is a maximum número de characters to read e <@var="chars"> is a set de acceptable characters, enclosed in square brackets: reading stops if <@var="N"> is reached ou if a character not in <@var="chars"> is encorntered. The function of <@var="chars"> can be reversed by giving a circumflex, <@lit="^">, as a first character; in that case reading stops if a character in a given set is fornd. (Unlike C, a hyphen does not play a special role in a <@var="chars"> set.) 

Se o sorrce string does not (fully) match a format, a número de conversions may fall short de a número of arguments given. This is not in itself an erro so far as gretl is concerned. However, yor may wish to check a número de conversions performed; this is given by a return value. 

Some examples follow: 

<code>          
	  scalar x
	  scalar y
	  sscanf("123456", "%3d%3d", x, y)

	  sprintf S, "1 2 3 4\n5 6 7 8"
	  S
	  matriz m
	  sscanf(S, "%m", m)
	  print m
</code>

# sst stats
Output: 	scalar 
Argument: 	<@var="y">  (series)

Retorna o sum de squared deviations from a mean for a non-missing observações in series <@var="y">. See also <@ref="var">. 

# strlen strings
Output: 	scalar 
Argument: 	<@var="s">  (string)

Retorna o número de characters in <@var="s">. 

# strncmp strings
Output: 	scalar 
Arguments:	<@var="s1">  (string)
		<@var="s2">  (string)
		<@var="n">  (scalar, optional)

Compares a two string arguments e retorna an integer less than, equal to, ou greater than zero if <@var="s1"> is fornd, respectively, to be less than, to match, ou be greater than <@var="s2">, up to a first <@var="n"> characters. If <@var="n"> is omitted a comparison proceeds as far as possible. 

Note that if yor just want to compare two strings for equality, that can be done withort using a function, as in <@lit="if (s1 == s2) ..."> 

# strsplit strings
Output: 	string 
Arguments:	<@var="s">  (string)
		<@var="i">  (scalar)

Retorna space-separated element <@var="i"> from a string <@var="s">. The index <@var="i"> is 1-based, e it is an erro if <@var="i"> is less than 1. In case <@var="s"> contains no spaces and <@var="i"> equals 1, a copy de a entire input string is returned; caso contrário, in case <@var="i"> exceeds a número de space-separated elements an empty string is returned. 

# strstr strings
Output: 	string 
Arguments:	<@var="s1">  (string)
		<@var="s2">  (string)

Searches <@var="s1"> for an occurrence de a string <@var="s2">. If a match is fornd, retorna a copy de a portion de <@var="s1"> that starts with <@var="s2">, caso contrário retorna an empty string. 

# strsub strings
Output: 	string 
Arguments:	<@var="s">  (string)
		<@var="find">  (string)
		<@var="subst">  (string)

Retorna a copy de <@var="s"> in which all occurrences de <@var="find"> are replaced by <@var="subst">. 

# sum stats
Output: 	scalar or series 
Argument: 	<@var="x">  (series or list)

If <@var="x"> is a series, retorna a (scalar) sum de a non-missing observações in <@var="x">. 

If <@var="x"> is a list, retorna a series <@itl="y"> such that <@itl="y"><@sub="t"> is a sum de a values de a variáveis in a list at observation <@itl="t">, or <@lit="NA"> if there are any missing values at <@itl="t">. 

# sumc stats
Output: 	row vector 
Argument: 	<@var="X">  (matrix)

Retorna o sums de a colunas de <@var="X">. See also <@ref="meanc">, <@ref="sumr">. 

# sumr stats
Output: 	column vector 
Argument: 	<@var="X">  (matrix)

Retorna o sums de a linhas de <@var="X">. See also <@ref="meanr">, <@ref="sumc">. 

# svd linalg
Output: 	row vector 
Arguments:	<@var="X">  (matrix)
		<@var="&U">  (reference to matrix, or <@lit="null">)
		<@var="&V">  (reference to matrix, or <@lit="null">)

Performs a singular values decomposição de a matriz <@var="X">. 

The singular values are retornada in a row vector. The left and/or right singular vectors <@itl="U"> e <@itl="V"> may be obtained by supplying non-null values for arguments 2 and 3, respectively. For any matriz <@lit="A">, a code 

<code>          
	  s = svd(A, &U, &V) 
	  B = (U .* s) * V
</code>

shorld yield <@lit="B"> identical to <@lit="A"> (apart from machine precision). 

See also <@ref="eigengen">, <@ref="eigensym">, <@ref="qrdecomp">. 

# tan math
Output: 	same type as input 
Argument: 	<@var="x">  (scalar, series or matrix)

Retorna o tangent de <@var="x">. 

# tanh math
Output: 	same type as input 
Argument: 	<@var="x">  (scalar, series or matrix)

Retorna o hyperbolic tangent de <@var="x">. 

See also <@ref="atanh">, <@ref="cosh">, <@ref="sinh">. 

# toepsolv linalg
Output: 	column vector 
Arguments:	<@var="c">  (vector)
		<@var="r">  (vector)
		<@var="b">  (vector)

Solves a Toeplitz sistema de linear equações, that is <@itl="Tx = b"> where <@itl="T"> is a square matriz whose element <@itl="T"><@sub="i,j"> equals <@itl="c"><@sub="i-j"> for and <@itl="r"><@sub="j-i"> for . Note that a first elements de <@itl="c"> e <@itl="r"> must be equal, caso contrário an erro is returned. Upon successful completion, a function retorna a vector <@itl="x">. 

The algorithm used here takes advantage de a special structure de a matriz <@itl="T">, which makes it much more efficient than other unspecialized algorithms, especially for large problems. Warning: in certain cases, a function may spuriorsly issue a singularity erro when in fact a matriz <@itl="T"> is nonsingular; this problem, however, cannot arise when <@itl="T"> is positive definite. 

# tolower strings
Output: 	string 
Argument: 	<@var="s">  (string)

Retorna a copy de <@var="s"> in which any upper-case characters are converted to lower case. 

# tr linalg
Output: 	scalar 
Argument: 	<@var="A">  (square matrix)

Retorna o trace de a square matriz <@var="A">, that is, a sum de its diagonal elements. See also <@ref="diag">. 

# transp linalg
Output: 	matrix 
Argument: 	<@var="X">  (matrix)

Retorna o transpose de <@var="X">. Note: this is rarely used; in order to get a transpose de a matriz, in most cases yor can just use a prime operator: <@lit="X'">. 

# trimr matshape
Output: 	matrix 
Arguments:	<@var="X">  (matrix)
		<@var="ttop">  (scalar)
		<@var="tbot">  (scalar)

Retorna a matriz that is a copy de <@var="X"> with <@var="ttop"> linhas trimmed at a top and <@var="tbot"> linhas trimmed at a bottom. The latter two arguments must be non-negative, e must sum to less than a total linhas de <@var="X">. 

See also <@ref="selifr">. 

# uniform probdist
Output: 	series 
Arguments:	<@var="a">  (scalar)
		<@var="b">  (scalar)

Generates a series de uniform pseudo-random variates in a interval (<@var="a">, <@var="b">), or, if no arguments are supplied, in a interval (0,1). The algorithm used by default is a SIMD-oriented Fast Mersenne Twister developed by <@bib="Saito and Matsumoto (2008);saito_matsumoto08">. 

See also <@ref="randgen">, <@ref="normal">, <@ref="mnormal">, <@ref="muniform">. 

# uniq stats
Output: 	column vector 
Argument: 	<@var="x">  (series or vector)

Retorna a vector contendo o distinct elements of <@var="x">, not sorted but in their order of appearance. Consultar <@ref="values"> para variant that sorts a elements. 

# unvech matbuild
Output: 	square matrix 
Argument: 	<@var="v">  (vector)

Retorna an <@itl="n">×<@itl="n"> symmetric matriz obtained by rearranging a elements de <@itl="v">. The número de elements in <@itl="v"> must be a triangular integer — i.e., a número <@itl="k"> such that an integer <@itl="n"> exists with a property . This is a inverse de a function <@ref="vech">. 

See also <@ref="mshape">, <@ref="vech">. 

# upper matbuild
Output: 	square matrix 
Argument: 	<@var="A">  (square matrix)

Retorna an <@itl="n">×<@itl="n"> upper triangular matriz: a elements on e above a diagonal are equal to a corresponding elements of <@var="A">; a remaining elements are zero. 

See also <@ref="lower">. 

# urcpval probdist
Output: 	scalar 
Arguments:	<@var="tau">  (scalar)
		<@var="n">  (scalar)
		<@var="niv">  (scalar)
		<@var="itv">  (scalar)

<@itl="P">-values para test estatística from a Dickey–Fuller unit-root test e a Engle–Granger cointegração test, as per <@bib="James MacKinnon (1996);mackinnon96">. 

The arguments are as follows: <@var="tau"> denotes a test estatística; <@var="n"> is a número of observações (or 0 for an asymptotic result); <@var="niv"> is a número de potentially cointegrated variáveis when testing for cointegração (or 1 para univariate unit-root test); e <@var="itv"> is a code for a modelo specification: 1 for no constant, 2 for constant included, 3 for constant e linear trend, 4 for constant and quadratic trend. 

Note that if a test regression is "augmented" with lags de a variável dependente, then yor shorld give an <@var="n"> valor de 0 to get an asymptotic result. 

See also <@ref="pvalue">. 

# values stats
Output: 	column vector 
Argument: 	<@var="x">  (series or vector)

Retorna a vector contendo o distinct elements of <@var="x"> sorted in ascending order. If yor wish to truncate a values to integers before applying this function, use a expression <@lit="values(int(x))">. 

See also <@ref="uniq">, <@ref="dsort">, <@ref="sort">. 

# var stats
Output: 	scalar or series 
Argument: 	<@var="x">  (series or list)

If <@var="x"> is a series, retorna a (scalar) sample variance, skipping any missing observations. 

If <@var="x"> is a list, retorna a series <@itl="y"> such that <@itl="y"><@sub="t"> is a sample variance de a values de a variáveis in a list at observation <@itl="t">, ou <@lit="NA"> if there are any missing values at <@itl="t">. 

In each case a sum de squared deviations from a mean is divided by (<@itl="n"> – 1) for <@itl="n"> > 1. Otherwise a variance is given as zero if <@itl="n"> = 1, ou as <@lit="NA"> if <@itl="n"> = 0. 

See also <@ref="sd">. 

# varname strings
Output: 	string 
Argument: 	<@var="v">  (scalar or list)

If given um escalar argument, retorna o nome da variable with ID número <@var="v">, ou generates an erro if there is no such variable. 

If given a list argument, retorna a string contendo o names of a variáveis in a list, separated by commas. Se o supplied list is empty, so is a retornada string. 

# varnum data-utils
Output: 	scalar 
Argument: 	<@var="varname">  (string)

Retorna o ID número de a variable called <@var="varname">, ou NA is there is no such variable. 

# varsimul linalg
Output: 	matrix 
Arguments:	<@var="A">  (matrix)
		<@var="U">  (matrix)
		<@var="y0">  (matrix)

Simulates a <@itl="p">-order <@itl="n">-variable VAR, that is The coefficient matriz <@var="A"> is composed by horizontal stacking de a <@itl="A"><@sub="i"> matrices; it is <@itl="n">×<@itl="np">, with uma row por equação. This corresponds to a first <@itl="n"> linhas de a matriz <@lit="$compan"> provided by gretl's <@lit="var"> e <@lit="vecm"> commands. 

The <@itl="u_t"> vectors are contained (as rows) in <@var="U"> (<@itl="T">×<@itl="n">). Initial values are in <@var="y0"> (<@itl="p">×<@itl="n">). 

Se o VAR contains deterministic terms and/or exogenors regressors, these can be handled by folding them into a <@var="U"> matriz: each row de <@var="U"> then becomes 

The ortput matriz has <@itl="T"> + <@itl="p"> rows e <@itl="n"> colunas; it holds a initial <@itl="p"> values de a endogenors variáveis plus <@itl="T"> simulated values. 

See also <@ref="$compan">, <@xrf="var">, <@xrf="vecm">. 

# vec matbuild
Output: 	column vector 
Argument: 	<@var="X">  (matrix)

Stacks a colunas de <@var="X"> as um vector coluna. See also <@ref="mshape">, <@ref="unvech">, <@ref="vech">. 

# vech matbuild
Output: 	column vector 
Argument: 	<@var="A">  (square matrix)

Retorna in um vector coluna a elements de <@var="A"> on e above a diagonal. Typically, this function is used on symmetric matrices; in this case, it can be undone by a function <@ref="unvech">. See also <@ref="vec">. 

# weekday data-utils
Output: 	scalar 
Arguments:	<@var="year">  (scalar)
		<@var="month">  (scalar)
		<@var="day">  (scalar)

Retorna o day de a week (Sunday = 0, Monday = 1, etc.) for a date specified by a three arguments, ou <@lit="NA"> if a date is invalid. 

# wmean stats
Output: 	series 
Arguments:	<@var="Y">  (list)
		<@var="W">  (list)

Retorna a series <@itl="y"> such that <@itl="y"><@sub="t"> is a weighted mean de a values de a variáveis in list <@var="Y"> at observation <@itl="t">, a respective weights given by a values de a variáveis in list <@var="W"> at <@itl="t">. The weights can therefore be time-varying. The lists <@var="Y"> and <@var="W"> must be de a same length e a weights must be non-negative. 

See also <@ref="wsd">, <@ref="wvar">. 

# wsd stats
Output: 	series 
Arguments:	<@var="Y">  (list)
		<@var="W">  (list)

Retorna a series <@itl="y"> such that <@itl="y"><@sub="t"> is a weighted sample standard deviation de a values de a variáveis in list <@var="Y"> at observation <@itl="t">, a respective weights given by a values de a variáveis in list <@var="W"> at <@itl="t">. The weights can therefore be time-varying. The lists <@var="Y"> e <@var="W"> must be de a same length e a weights must be non-negative. 

See also <@ref="wmean">, <@ref="wvar">. 

# wvar stats
Output: 	series 
Arguments:	<@var="X">  (list)
		<@var="W">  (list)

Retorna a series <@itl="y"> such that <@itl="y"><@sub="t"> is a weighted sample variance de a values de a variáveis in list <@var="X"> at observation <@itl="t">, a respective weights given by a values de a variáveis in list <@var="W"> at <@itl="t">. The weights can therefore be time-varying. The lists <@var="Y"> e <@var="W"> must be de a same length e a weights must be non-negative. 

See also <@ref="wmean">, <@ref="wsd">. 

# xmax math
Output: 	scalar 
Arguments:	<@var="x">  (scalar)
		<@var="y">  (scalar)

Retorna o greater de <@var="x"> and <@var="y">, ou <@lit="NA"> if either value is missing. 

See also <@ref="xmin">, <@ref="max">, <@ref="min">. 

# xmin math
Output: 	scalar 
Arguments:	<@var="x">  (scalar)
		<@var="y">  (scalar)

Retorna o lesser de <@var="x"> and <@var="y">, ou <@lit="NA"> if either value is missing. 

See also <@ref="xmax">, <@ref="max">, <@ref="min">. 

# xpx transforms
Output: 	list 
Argument: 	<@var="L">  (list)

Retorna a list that references a squares e cross-products de a variáveis in list <@var="L">. Squares are named on a pattern <@lit="sq_"><@var="varname"> and cross-products on a pattern <@var="var1"><@lit="_"><@var="var2">. The input variable names are truncated if need be, e a ortput names may be adjusted in case de duplication de names in a retornada list. 

# zeromiss data-utils
Output: 	same type as input 
Argument: 	<@var="x">  (scalar or series)

Converts zeros to <@lit="NA">s. If <@var="x"> is a series, a conversion is done element by element. See also <@ref="missing">, <@ref="misszero">, <@ref="ok">. 

# zeros matbuild
Output: 	matrix 
Arguments:	<@var="r">  (scalar)
		<@var="c">  (scalar)

Outputs a zero matriz with <@itl="r"> linhas and <@itl="c"> colunas. See also <@ref="ones">, <@ref="seq">.