gretl-common 2016a-1 / usr / share / gretl / genrcli.hlp.pt

## Acessores
# $ahat
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
Output:     scalar

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

# $bic
Output:     scalar

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

# $chisq
Output:     scalar

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

# $coeff
Output:     matrix or scalar
Argument:   s (name of coefficient, optional)

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

Exemplo:

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

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
Output:     string

Tem que ser acedido após a estimação de modelo; retorna o nome do
comando, por exemplo ols ou probit.

# $compan
Output:     matrix

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

# $datatype
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
Output:     string

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

# $df
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
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
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
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
"catch". Note que ao usar este acessor o código de erro interno ficará
reiniciado a zero. Consultar também "errmsg". Se você pretender uma
mensagem de erro associada a um certo $error então tem que guardar o valor
numa variável temporária, tal como em

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

See also "catch", "errmsg".

# $ess
Output:     scalar

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

# $evals
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
Output:     matrix

Tem que ser acedido a seguir a um comando de predição "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
Output:     matrix

Tem que ser acedido a seguir a um comando de predição "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
Output:     matrix

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

# $Fstat
Output:     scalar

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

# $gmmcrit
Output:     scalar

Tem que ser acedido a seguir a um bloco gmm. Retorna o valor da função
objetivo no seu mínimo.

# $h
Output:     series

Tem que ser acedido a seguir a um comando garch. Retorna a série da
variância condicional estimada.

# $hausman
Output:     row vector

Tem que ser acedido após a estimação de modelo tsls ou painel com a
opção de efeitos aleatórios. Retorna um vector 1 x 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
Output:     scalar

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

# $huge
Output:     scalar

Retorna um enorme número positivo. Por omissão isto é 1,0E100, mas o
valor pode ser moficado usando o comando "set".

# $jalpha
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
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
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 restrict com a
opção --full, será retornada uma matriz singular com (n+m)r linhas (onde
n é o número de variáveis endógenas, m é o número de variáveis
exógenas no espaço de cointegração, e r o nível de cointegração).

Exemplo: o código

	  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

produz o seguinte resultado.

	  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 

# $llt
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
Output:     scalar

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

# $macheps
Output:     scalar

Retorna o valor do "épsilon de máquina", que dá um limite superior para o
erro relativo devido aos arredondamentos da aritmética de vírgula
flutuante de dupla-precisão.

# $mnlprobs
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
Output:     integer

Retorna o número total de coeficientes estimados no último modelo.

# $nobs
Output:     integer

Retorna o número de observações na amostra presentemente selecionada.

# $nvars
Output:     integer

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

# $obsdate
Output:     series

Applicable when the current dataset is time-series with annual, quarterly,
monthly or decennial frequency, or is dated daily or weekly, or when the
dataset is a panel with time-series information set appropriately (see the
"setobs" command). The returned series holds 8-digit numbers on the pattern
YYYYMMDD (ISO 8601 "basic" date format), which correspond to the day of the
observation, or the first day of the observation period in case of a
time-series frequency less than daily.

Such a series can be helpful when using the "join" command.

# $obsmajor
Output:     series

Applicable when the observations in the current dataset have a major:minor
structure, as in quarterly time series (year:quarter), monthly time series
(year:month), hourly data (day:hour) and panel data (individual:period).
Returns a series holding the major or low-frequency component of each
observation (for example, the year).

See also "$obsminor", "$obsmicro".

# $obsmicro
Output:     series

Applicable when the observations in the current dataset have a
major:minor:micro structure, as in dated daily time series (year:month:day).
Returns a series holding the micro or highest-frequency component of each
observation (for example, the day).

See also "$obsmajor", "$obsminor".

# $obsminor
Output:     series

Applicable when the observations in the current dataset have a major:minor
structure, as in quarterly time series (year:quarter), monthly time series
(year:month), hourly data (day:hour) and panel data (individual:period).
Returns a series holding the minor or high-frequency component of each
observation (for example, the month).

See also "$obsmajor", "$obsmicro".

# $pd
Output:     integer

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.

# $pi
Output:     scalar

Retorna o valor de pi com precisão dupla.

# $pvalue
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, chow). Consultar
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 "$test".

# $rho
Output:     scalar
Argument:   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 ar, a sintaxe $rho(n) retorna a estimativa correspondente de rho(n).

# $rsq
Output:     scalar

Retorna o R^2 não ajustado do último modelo estimado, se disponível.

# $sample
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:

	  ols y 0 xlist
	  genr sdum = $sample
	  smpl sdum --dummy

# $sargan
Output:     row vector

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

# $sigma
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
Output:     matrix or scalar
Argument:   s (name of coefficient, optional)

Sem argumentos, $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
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 "$coeff", "$vcv".

# $stopwatch
Output:     scalar

Tem que ser precedido por 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 set stopwatch. Em cada acesso o relógio é
reinicializado, por isso as chamadas subsequentes de $stopwatch obtêm os
segundos de tempo de CPU desde o último acesso.

# $sysA
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 "system".

# $sysB
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 "system".

# $sysGamma
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
"system".

# $sysinfo
Output:     bundle

Returns a bundle containing information on the capabilities of the gretl
build and the system on which gretl is running. The members of the bundle
are as follows:

  mpi: integer, equals 1 if the system supports MPI (Message Passing
  Interface), otherwise 0.

  omp: integer, equals 1 if gretl is built with support for Open MP,
  otherwise 0.

  nproc: integer, the number of processors available.

  mpimax: integer, the maximum number of MPI processes that can be run in
  parallel. This is zero if MPI is not supported, otherwise it equals the
  local nproc value unless an MPI hosts file has been specified, in which
  case it is the sum of the number of processors or "slots" across all the
  machines referenced in that file.

  wordlen: integer, either 32 or 64 for 32- and 64-bit systems respectively.

  os: string representing the operating system, either linux, osx, windows
  or other.

  hostname: the name of the host machine on which the current gretl process
  is running (with a fallback of localhost in case the name cannot be
  determined).

Note that individual elements in the bundle can be accessed using "dot"
notation without any need to copy the whole bundle under a user-specified
name. For example,

	  if $sysinfo.os == "linux"
	    # do something linux-specific
	  endif

# $T
Output:     integer

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

# $t1
Output:     integer

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

# $t2
Output:     integer

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

# $test
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, chow).
Consultar 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 "dpvalue".

# $trsq
Output:     scalar

Retorna TR^2 (tamanho da amostra vezes R-quadrado) do último modelo, se
disponível.

# $uhat
Output:     series

Retorna os resíduos do último modelo. Isto pode ter significados
diferentes para diferentes estimadores. Por exemplo, depois de uma
estimação ARMA, $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), $uhat sem parâmetros obtém uma matriz de
resíduos, uma coluna por equação.

# $unit
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
Output:     matrix or scalar
Arguments:  s1 (name of coefficient, optional)
            s2 (name of coefficient, optional)

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

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

# $vecGamma
Output:     matrix

Tem que ser acedido após a estimação de VECM; retorna uma matriz onde as
matrizes Gama (coeficientes das diferenças desfasadas das variáveis
cointegradas) estão lado-a-lado. Cada linha representa uma equação; para
VECM com grau de desfasamento p existem p - 1 sub-matrizes.

# $version
Output:     scalar

Retorna um valor inteiro que representa a versão do programa. A versão de
gretl em texto tem a forma x.y.z (por exemplo, 1.7.6). O valor de retorno
deste acessor é formado por 10000*x + 100*y + z, sendo que 1.7.6 resulta em
10706.

# $vma
Output:     matrix

Tem que ser acedido após a estimação de VAR ou VECM; retorna a matriz
contendo a representação VMA até um grau definido com o comando set
horizon. Consultar the Gretl User's Guide para detalhes.

# $windows
Output:     integer

Retorna 1 se gretl estiver a correr em MS Windows, 0 caso contrário.
Condicionando pelo valor desta variável você pode escrever chamadas a
comandos de sistema que são portáveis entre diferentes sistemas
operativos.

Ver também o comando "shell".

# $xlist
Output:     list

Retorna a lista de regressores do último modelo (apenas para modelos com
uma única equação).

# $xtxinv
Output:     matrix

Seguindo a estimação de VAR ou VECM (apenas), retorna X'X^-1, onde X é a
matriz conjunta de regressores utilizados em cada uma das equações. Este
acessor não está disponível para VECM estimado com uma restrição
imposta sobre α, a matriz "cargas" .

# $yhat
Output:     series

Retorna os valores ajustados da última regressão.

# $ylist
Output:     list

Se o modelo anteriormente estimado foi um VAR, VECM ou sistema de equações
simultâneas, retorna a lista associada de variáveis endógenas. Se o
último modelo tem apenas uma equação, este acessor retorna uma lista com
um único elemento, a variável dependente. No caso especial do modelo
biprobit a lista contém dois elementos.

## Funções
# abs
Output:     same type as input
Argument:   x (scalar, series or matrix)

Retorna o valor absoluto de x.

# acos
Output:     same type as input
Argument:   x (scalar, series or matrix)

Retorna o arcoseno de x, ou seja, um valor de cujo cosseno é x. O resultado
é em radianos; o argumento deve variar de -1 a 1.

# acosh
Output:     same type as input
Argument:   x (scalar, series or matrix)

Returns the inverse hyperbolic cosine of x (positive solution). x should be
greater than 1; otherwise, NA is returned. See also "cosh".

# aggregate
Output:     matrix
Arguments:  x (series or list)
            byvar (series or list)
            funcname (string)

In the simplest version, both x and byvar are individual series. In that
case this function returns a matrix with three columns: the first holds the
distinct values of byvar, sorted in ascending order; the second holds the
count of observations at which byvar takes on each of these values; and the
third holds the values of the statistic specified by funcname calculated on
series x, using only those observations at which byvar takes on the value
given in the first column.

More generally, if byvar is a list with n members then the left-hand n
columns hold the combinations of the distinct values of each of the n series
and the count column holds the number of observations at which each
combination is realized. If x is a list with m members then the rightmost m
columns hold the values of the specified statistic for each of the x
variables, again calculated on the sub-sample indicated in the first
column(s).

The following values of funcname are supported "natively": "sum", "sumall",
"mean", "sd", "var", "sst", "skewness", "kurtosis", "min", "max", "median",
"nobs" and "gini". Each of these functions takes a series argument and
returns a scalar value, and in that sense can be said to "aggregate" the
series in some way. You may give the name of a user-defined function as the
aggregator; like the built-ins, such a function must take a single series
argument and return a scalar value.

Note that although a count of cases is provided automatically the nobs
function is not redundant as an aggregator, since it gives the number of
valid (non-missing) observations on x at each byvar combination.

For a simple example, suppose that region represents a coding of
geographical region using integer values 1 to n, and income represents
household income. Then the following would produce an n x 3 matrix holding
the region codes, the count of observations in each region, and mean
household income for each of the regions:

	  matrix m = aggregate(income, region, mean)

For an example using lists, let gender be a male/female dummy variable, let
race be a categorical variable with three values, and consider the
following:

	  list BY = gender race
	  list X = income age
	  matrix m = aggregate(X, BY, sd)

The aggregate call here will produce a 6 x 5 matrix. The first two columns
hold the 6 distinct combinations of gender and race values; the middle
column holds the count for each of these combinations; and the rightmost two
columns contain the sample standard deviations of income and age.

Note that if byvar is a list, some combinations of the byvar values may not
be present in the data (giving a count of zero). In that case the value of
the statistics for x are recorded as NaN (not a number). If you want to
ignore such cases you can use the "selifr" function to select only those
rows that have a non-zero count. The column to test is one place to the
right of the number of byvar variables, so we can do:

	  matrix m = aggregate(X, BY, sd)
	  scalar c = nelem(BY)
	  m = selifr(m, m[,c+1])

# argname
Output:     string
Argument:   s (string)

For s the name of a parameter to a user-defined function, returns the name
of the corresponding argument, or an empty string if the argument was
anonymous.

# asin
Output:     same type as input
Argument:   x (scalar, series or matrix)

Returns the arc sine of x, that is, the value whose sine is x. The result is
in radians; the input should be in the range -1 to 1.

# asinh
Output:     same type as input
Argument:   x (scalar, series or matrix)

Returns the inverse hyperbolic sine of x. See also "sinh".

# atan
Output:     same type as input
Argument:   x (scalar, series or matrix)

Returns the arc tangent of x, that is, the value whose tangent is x. The
result is in radians.

# atanh
Output:     same type as input
Argument:   x (scalar, series or matrix)

Returns the inverse hyperbolic tangent of x. See also "tanh".

# atof
Output:     scalar
Argument:   s (string)

Closely related to the C library function of the same name. Returns the
result of converting the string s (or the leading portion thereof, after
discarding any initial white space) to a floating-point number. Unlike C's
atof, however, the decimal character is always assumed (for reasons of
portability) to be ".". Any characters that follow the portion of s that
converts to a floating-point number under this assumption are ignored.

If none of s (following any discarded white space) is convertible under the
stated assumption, NA is returned.

	  # examples
	  x = atof("1.234") # gives x = 1.234 
	  x = atof("1,234") # gives x = 1
	  x = atof("1.2y")  # gives x = 1.2
	  x = atof("y")     # gives x = NA
	  x = atof(",234")  # gives x = NA

See also "sscanf" for more flexible string to numeric conversion.

# bessel
Output:     same type as input
Arguments:  type (character)
            v (scalar)
            x (scalar, series or matrix)

Computes one of the Bessel function variants for order v and argument x. The
return value is of the same type as x. The specific function is selected by
the first argument, which must be J, Y, I, or K. A good discussion of the
Bessel functions can be found on Wikipedia; here we give a brief account.

case J: Bessel function of the first kind. Resembles a damped sine wave.
Defined for real v and x, but if x is negative then v must be an integer.

case Y: Bessel function of the second kind. Defined for real v and x but has
a singularity at x = 0.

case I: Modified Bessel function of the first kind. An exponentially growing
function. Acceptable arguments are as for case J.

case K: Modified Bessel function of the second kind. An exponentially
decaying function. Diverges at x = 0 and is not defined for negative x.
Symmetric around v = 0.

# BFGSmax
Output:     scalar
Arguments:  b (vector)
            f (function call)
            g (function call, optional)

Numerical maximization via the method of Broyden, Fletcher, Goldfarb and
Shanno. The vector b should hold the initial values of a set of parameters,
and the argument f should specify a call to a function that calculates the
(scalar) criterion to be maximized, given the current parameter values and
any other relevant data. If the object is in fact minimization, this
function should return the negative of the criterion. On successful
completion, BFGSmax returns the maximized value of the criterion, and b
holds the parameter values which produce the maximum.

The optional third argument provides a means of supplying analytical
derivatives (otherwise the gradient is computed numerically). The gradient
function call g must have as its first argument a pre-defined matrix that is
of the correct size to contain the gradient, given in pointer form. It also
must take the parameter vector as an argument (in pointer form or
otherwise). Other arguments are optional.

For more details and examples see the chapter on numerical methods in the
Gretl User's Guide. See also "NRmax", "fdjac", "simann".

# bkfilt
Output:     series
Arguments:  y (series)
            f1 (integer, optional)
            f2 (integer, optional)
            k (integer, optional)

Returns the result from application of the Baxter-King bandpass filter to
the series y. The optional parameters f1 and f2 represent, respectively, the
lower and upper bounds of the range of frequencies to extract, while k is
the approximation order to be used. If these arguments are not supplied then
the following default values are used: f1 = 8, f1 = 32, k = 8. See also
"bwfilt", "hpfilt".

# boxcox
Output:     series
Arguments:  y (series)
            d (scalar)

Returns the Box-Cox transformation with parameter d for the positive series
y.

The transformed series is (y^d - 1)/d for d not equal to zero, or log(y) for
d = 0.

# bwfilt
Output:     series
Arguments:  y (series)
            n (integer)
            omega (scalar)

Returns the result from application of a low-pass Butterworth filter with
order n and frequency cutoff omega to the series y. The cutoff is expressed
in degrees and must be greater than 0 and less than 180. Smaller cutoff
values restrict the pass-band to lower frequencies and hence produce a
smoother trend. Higher values of n produce a sharper cutoff, at the cost of
possible numerical instability.

Inspecting the periodogram of the target series is a useful preliminary when
you wish to apply this function. See the Gretl User's Guide for details. See
also "bkfilt", "hpfilt".

# cdemean
Output:     matrix
Argument:   X (matrix)

Centers the columns of matrix X around their means.

# cdf
Output:     same type as input
Arguments:  c (character)
            ... (see below)
            x (scalar, series or matrix)
Examples:   p1 = cdf(N, -2.5)
            p2 = cdf(X, 3, 5.67)
            p3 = cdf(D, 0.25, -1, 1)

Cumulative distribution function calculator. Returns P(X <= x), where the
distribution X is determined by the character c. Between the arguments c and
x, zero or more additional scalar arguments are required to specify the
parameters of the distribution, as follows.

  Standard normal (c = z, n, or N): no extra arguments

  Bivariate normal (D): correlation coefficient

  Student's t (t): degrees of freedom

  Chi square (c, x, or X): degrees of freedom

  Snedecor's F (f or F): df (num.); df (den.)

  Gamma (g or G): shape; scale

  Binomial (b or B): probability; number of trials

  Poisson (p or P): Mean

  Weibull (w or W): shape; scale

  Generalized Error (E): shape

Note that most cases have aliases to help memorizing the codes. The
bivariate normal case is special: the syntax is x = cdf(D, rho, z1, z2)
where rho is the correlation between the variables z1 and z2.

See also "pdf", "critical", "invcdf", "pvalue".

# cdiv
Output:     matrix
Arguments:  X (matrix)
            Y (matrix)

Complex division. The two arguments must have the same number of rows, n,
and either one or two columns. The first column contains the real part and
the second (if present) the imaginary part. The return value is an n x 2
matrix or, if the result has no imaginary part, an n-vector. See also
"cmult".

# ceil
Output:     same type as input
Argument:   x (scalar, series or matrix)

Ceiling function: returns the smallest integer greater than or equal to x.
See also "floor", "int".

# cholesky
Output:     square matrix
Argument:   A (positive definite matrix)

Peforms a Cholesky decomposition of the matrix A, which is assumed to be
symmetric and positive definite. The result is a lower-triangular matrix L
which satisfies A = LL'. The function will fail if A is not symmetric or not
positive definite. See also "psdroot".

# chowlin
Output:     matrix
Arguments:  Y (matrix)
            xfac (integer)
            X (matrix, optional)

Expands the input data, Y, to a higher frequency, using the interpolation
method of Chow and Lin (1971). It is assumed that the columns of Y represent
data series; the returned matrix has as many columns as Y and xfac times as
many rows.

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

The regressors used by default are a constant and quadratic trend. If X is
provided, its columns are used as additional regressors; it is an error if
the number of rows in X does not equal xfac times the number of rows in Y.

# cmult
Output:     matrix
Arguments:  X (matrix)
            Y (matrix)

Complex multiplication. The two arguments must have the same number of rows,
n, and either one or two columns. The first column contains the real part
and the second (if present) the imaginary part. The return value is an n x 2
matrix, or, if the result has no imaginary part, an n-vector. See also
"cdiv".

# cnorm
Output:     same type as input
Argument:   x (scalar, series or matrix)

Returns the cumulative distribution function for a standard normal. See also
"dnorm", "qnorm".

# colname
Output:     string
Arguments:  M (matrix)
            col (integer)

Retrieves the name for column col of matrix M. If M has no column names
attached the value returned is an empty string; if col is out of bounds for
the given matrix an error is flagged. See also "colnames".

# colnames
Output:     scalar
Arguments:  M (matrix)
            s (named list or string)

Attaches names to the columns of the T x k matrix M. If s is a named list,
the column names are copied from the names of the variables; the list must
have k members. If s is a string, it should contain k space-separated
sub-strings. The return value is 0 on successful completion, non-zero on
error. See also "rownames".

Example:

	  matrix M = {1, 2; 2, 1; 4, 1}
	  colnames(M, "Col1 Col2")
	  print M

# cols
Output:     integer
Argument:   X (matrix)

Returns the number of columns of X. See also "mshape", "rows", "unvech",
"vec", "vech".

# corr
Output:     scalar
Arguments:  y1 (series or vector)
            y2 (series or vector)

Computes the correlation coefficient between y1 and y2. The arguments should
be either two series, or two vectors of the same length. See also "cov",
"mcov", "mcorr".

# corrgm
Output:     matrix
Arguments:  x (series, matrix or list)
            p (integer)
            y (series or vector, optional)

If only the first two arguments are given, computes the correlogram for x
for lags 1 to p. Let k represent the number of elements in x (1 if x is a
series, the number of columns if x is a matrix, or the number of
list-members is x is a list). The return value is a matrix with p rows and
2k columns, the first k columns holding the respective autocorrelations and
the remainder the respective partial autocorrelations.

If a third argument is given, this function computes the cross-correlogram
for each of the k elements in x and y, from lead p to lag p. The returned
matrix has 2p + 1 rows and k columns. If x is series or list and y is a
vector, the vector must have just as many rows as there are observations in
the current sample range.

# cos
Output:     same type as input
Argument:   x (scalar, series or matrix)

Returns the cosine of x.

# cosh
Output:     same type as input
Argument:   x (scalar, series or matrix)

Returns the hyperbolic cosine of x.

See also "acosh", "sinh", "tanh".

# cov
Output:     scalar
Arguments:  y1 (series or vector)
            y2 (series or vector)

Returns the covariance between y1 and y2. The arguments should be either two
series, or two vectors of the same length. See also "corr", "mcov", "mcorr".

# critical
Output:     same type as input
Arguments:  c (character)
            ... (see below)
            p (scalar, series or matrix)
Examples:   c1 = critical(t, 20, 0.025)
            c2 = critical(F, 4, 48, 0.05)

Critical value calculator. Returns x such that P(X > x) = p, where the
distribution X is determined by the character c. Between the arguments c and
p, zero or more additional scalar arguments are required to specify the
parameters of the distribution, as follows.

  Standard normal (c = z, n, or N): no extra arguments

  Student's t (t): degrees of freedom

  Chi square (c, x, or X): degrees of freedom

  Snedecor's F (f or F): df (num.); df (den.)

  Binomial (b or B): probability; trials

  Poisson (p or P): mean

See also "cdf", "invcdf", "pvalue".

# cum
Output:     same type as input
Argument:   x (series or matrix)

Cumulates x (that is, creates a running sum). When x is a series, produces a
series y each of whose elements is the sum of the values of x to date; the
starting point of the summation is the first non-missing observation in the
currently selected sample. When x is a matrix, its elements are cumulated by
columns.

See also "diff".

# deseas
Output:     series
Arguments:  x (series)
            c (character, optional)

Depends on having TRAMO/SEATS or X-12-ARIMA installed. Returns a
deseasonalized (seasonally adjusted) version of the input series x, which
must be a quarterly or monthly time series. To use X-12-ARIMA give X as the
second argument; to use TRAMO give T. If the second argument is omitted then
X-12-ARIMA is used.

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

# det
Output:     scalar
Argument:   A (square matrix)

Returns the determinant of A, computed via the LU factorization. See also
"ldet", "rcond".

# diag
Output:     matrix
Argument:   X (matrix)

Returns the principal diagonal of X in a column vector. Note: if X is an m x
n matrix, the number of elements of the output vector is min(m, n). See also
"tr".

# diagcat
Output:     matrix
Arguments:  A (matrix)
            B (matrix)

Returns the direct sum of A and B, that is a matrix holding A in its
north-west corner and B in its south-east corner. If both A and B are
square, the resulting matrix is block-diagonal.

# diff
Output:     same type as input
Argument:   y (series, matrix or list)

Computes first differences. If y is a series, or a list of series, starting
values are set to NA. If y is a matrix, differencing is done by columns and
starting values are set to 0.

When a list is returned, the individual variables are automatically named
according to the template d_varname where varname is the name of the
original series. The name is truncated if necessary, and may be adjusted in
case of non-uniqueness in the set of names thus constructed.

See also "cum", "ldiff", "sdiff".

# digamma
Output:     same type as input
Argument:   x (scalar, series or matrix)

Returns the digamma (or Psi) function of x, that is the derivative of the
log of the Gamma function.

# dnorm
Output:     same type as input
Argument:   x (scalar, series or matrix)

Returns the density of the standard normal distribution at x. To get the
density for a non-standard normal distribution at x, pass the z-score of x
to the dnorm function and multiply the result by the Jacobian of the z
transformation, namely 1 over sigma, as illustrated below:

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

See also "cnorm", "qnorm".

# dsort
Output:     same type as input
Argument:   x (series or vector)

Sorts x in descending order, skipping observations with missing values when
x is a series. See also "sort", "values".

# dummify
Output:     list
Arguments:  x (series)
            omitval (scalar, optional)

The argument x should be a discrete series. This function creates a set of
dummy variables coding for the distinct values in the series. By default the
smallest value is taken as the omitted category and is not explicitly
represented.

The optional second argument represents the value of x which should be
treated as the omitted category. The effect when a single argument is given
is equivalent to dummify(x, min(x)). To produce a full set of dummies, with
no omitted category, use dummify(x, NA).

The generated variables are automatically named according to the template
Dvarname_i where varname is the name of the original series and i is a
1-based index. The original portion of the name is truncated if necessary,
and may be adjusted in case of non-uniqueness in the set of names thus
constructed.

# easterday
Output:     same type as input
Argument:   x (scalar, series or matrix)

Given the year in argument x, returns the date of Easter in the Gregorian
calendar as month + day/100. Note that April the 10th, is, under this
convention, 4.1; hence, 4.2 is April the 20th, not April the 2nd (which
would be 4.02).

	  scalar e = easterday(2014)
	  scalar m = floor(e)
	  scalar d = 100*(e-m)

# eigengen
Output:     matrix
Arguments:  A (square matrix)
            &U (reference to matrix, or null)

Computes the eigenvalues, and optionally the right eigenvectors, of the n x
n matrix A. If all the eigenvalues are real an n x 1 matrix is returned;
otherwise the result is an n x 2 matrix, the first column holding the real
components and the second column the imaginary components.

The second argument must be either the name of an existing matrix preceded
by & (to indicate the "address" of the matrix in question), in which case an
auxiliary result is written to that matrix, or the keyword null, in which
case the auxiliary result is not produced.

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

  If the i-th eigenvalue is real, the i-th column of U will contain the
  corresponding eigenvector;

  If the i-th eigenvalue is complex, the i-th column of U will contain the
  real part of the corresponding eigenvector and the next column the
  imaginary part. The eigenvector for the conjugate eigenvalue is the
  conjugate of the eigenvector.

In other words, the eigenvectors are stored in the same order as the
eigenvalues, but the real eigenvectors occupy one column, whereas complex
eigenvectors take two (the real part comes first); the total number of
columns is still n, because the conjugate eigenvector is skipped.

See also "eigensym", "eigsolve", "qrdecomp", "svd".

# eigensym
Output:     matrix
Arguments:  A (symmetric matrix)
            &U (reference to matrix, or null)

Works just as "eigengen", but the argument A must be symmetric (in which
case the calculations can be reduced). The eigenvalues are returned in
ascending order.

# eigsolve
Output:     matrix
Arguments:  A (symmetric matrix)
            B (symmetric matrix)
            &U (reference to matrix, or null)

Solves the generalized eigenvalue problem |A - lambdaB| = 0, where both A
and B are symmetric and B is positive definite. The eigenvalues are returned
directly, arranged in ascending order. If the optional third argument is
given it should be the name of an existing matrix preceded by &; in that
case the generalized eigenvectors are written to the named matrix.

# epochday
Output:     scalar or series
Arguments:  year (scalar or series)
            month (scalar or series)
            day (scalar or series)

Returns the number of the day in the current epoch specified by year, month
and day. The epoch day equals 1 for the first of January in the year 1 AD;
it stood at 733786 on 2010-01-01. If any of the arguments are given as
series the value returned is a series, otherwise it is a scalar.

For the inverse function, see "isodate".

# errmsg
Output:     string
Argument:   errno (integer)

Retrieves the gretl error message associated with errno. See also "$error".

# exp
Output:     same type as input
Argument:   x (scalar, series or matrix)

Returns e^x. Note that in case of matrices the function acts element by
element. For the matrix exponential function, see "mexp".

# fcstats
Output:     matrix
Arguments:  y (series or vector)
            f (series or vector)

Produces a column vector holding several statistics which may be used for
evaluating the series f as a forecast of the series y over the current
sample range. Two vectors of the same length may be given in place of two
series arguments.

The layout of the returned vector is as follows:

	  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

For details on the calculation of these statistics, and the interpretation
of the U values, please see the Gretl User's Guide.

# fdjac
Output:     matrix
Arguments:  b (column vector)
            fcall (function call)

Calculates a numerical approximation to the Jacobian associated with the
n-vector b and the transformation function specified by the argument fcall.
The function call should take b as its first argument (either straight or in
pointer form), followed by any additional arguments that may be needed, and
it should return an m x 1 matrix. On successful completion fdjac returns an
m x n matrix holding the Jacobian. Example:

	  matrix J = fdjac(theta, myfunc(&theta, X))

The function can use three different methods: simple forward-difference,
bilateral difference or 4-nodes Richardson extrapolation. Respectively:

J_0 = (f(x+h) - f(x))/h

J_1 = (f(x+h) - f(x-h))/2h

J_2 = [8 (f(x+h) - f(x-h)) - (f(x+2h) - f(x-2h))] /12h

The three alternatives above provide, generally, a trade-off between
accuracy and speed. You can choose among methods by using the "set" command
and specify the value 0, 1 or 2 for the fdjac_quality variable.

For more details and examples see the chapter on numerical methods in the
Gretl User's Guide.

See also "BFGSmax", "set".

# fft
Output:     matrix
Argument:   X (matrix)

Discrete real Fourier transform. If the input matrix X has n columns, the
output has 2n columns, where the real parts are stored in the odd columns
and the complex parts in the even ones.

Should it be necessary to compute the Fourier transform on several vectors
with the same number of elements, it is numerically more efficient to group
them into a matrix rather than invoking fft for each vector separately. See
also "ffti".

# ffti
Output:     matrix
Argument:   X (matrix)

Inverse discrete real Fourier transform. It is assumed that X contains n
complex column vectors, with the real part in the odd columns and the
imaginary part in the even ones, so the total number of columns should be
2n. A matrix with n columns is returned.

Should it be necessary to compute the inverse Fourier transform on several
vectors with the same number of elements, it is numerically more efficient
to group them into a matrix rather than invoking ffti for each vector
separately. See also "fft".

# filter
Output:     series
Arguments:  x (series or matrix)
            a (scalar or vector, optional)
            b (scalar or vector, optional)
            y0 (scalar, optional)

Computes an ARMA-like filtering of the argument x. The transformation can be
written as

y_t = a_0 x_t + a_1 x_t-1 + ... a_q x_t-q + b_1 y_t-1 + ... b_p y_t-p

If argument x is a series, the result will be itself a series. Otherwise, if
x is a matrix with T rows and k columns, the result will be a matrix of the
same size, in which the filtering is performed column by column.

The two arguments a and b are optional. They may be scalars, vectors or the
keyword null.

If a is a scalar, this is used as a_0 and implies q=0; if it is a vector of
q+1 elements, they contain the coefficients from a_0 to a_q. If a is null or
omitted, this is equivalent to setting a_0=1 and q=0.

If b is a scalar, this is used as b_1 and implies p=1; if it is a vector of
p elements, they contain the coefficients from b_1 to b_p. If b is null or
omitted, this is equivalent to setting B(L)=1.

The optional scalar argument y0 is taken to represent all values of y prior
to the beginning of sample (used only when p>0). If omitted, it is
understood to be 0. Pre-sample values of x are always assumed zero.

See also "bkfilt", "bwfilt", "fracdiff", "hpfilt", "movavg", "varsimul".

Example:

	  nulldata 5
	  y = filter(index, 0.5, -0.9, 1)
	  print index y --byobs
	  x = seq(1,5)' ~ (1 | zeros(4,1))
	  w = filter(x, 0.5, -0.9, 1)
	  print x w

produces

                   index            y   

          1            1     -0.40000   
          2            2      1.36000   
          3            3      0.27600   
          4            4      1.75160   
          5            5      0.92356   

          x (5 x 2)

            1   1 
            2   0 
            3   0 
            4   0 
            5   0 

          w (5 x 2)

              -0.40000     -0.40000 
                1.3600      0.36000 
               0.27600     -0.32400 
                1.7516      0.29160 
               0.92356     -0.26244 

# firstobs
Output:     integer
Argument:   y (series)

Returns the 1-based index of the first non-missing observation for the
series y. Note that if some form of subsampling is in effect, the value
returned may be smaller than the dollar variable "$t1". See also "lastobs".

# fixname
Output:     string
Argument:   rawname (string)

Intended for use in connection with the "join" command. Returns the result
of converting rawname to a valid gretl identifier, which must start with a
letter, contain nothing but (ASCII) letters, digits and the underscore
character, and must not exceed 31 characters. The rules used in conversion
are:

1. Skip any leading non-letters.

2. Until the 31-character limit is reached or the input is exhausted:
transcribe "legal" characters; skip "illegal" characters apart from spaces;
and replace one or more consecutive spaces with an underscore, unless the
previous character transcribed is an underscore in which case space is
skipped.

# floor
Output:     same type as input
Argument:   y (scalar, series or matrix)

Floor function: returns the greatest integer less than or equal to x. Note:
"int" and floor differ in their effect for negative arguments: int(-3.5)
gives -3, while floor(-3.5) gives -4.

# fracdiff
Output:     series
Arguments:  y (series)
            d (scalar)

Returns the fractional difference of order d for the series y.

Note that in theory fractional differentiation is an infinitely long filter.
In practice, presample values of y_t are assumed to be zero.

# gammafun
Output:     same type as input
Argument:   x (scalar, series or matrix)

Returns the gamma function of x.

# getenv
Output:     string
Argument:   s (string)

If an environment variable by the name of s is defined, returns the string
value of that variable, otherwise returns an empty string. See also
"ngetenv".

# getline
Output:     scalar
Arguments:  source (string)
            target (string)

This function is used to read successive lines from source, which should be
a named string variable. On each call a line from the source is written to
target (which must also be a named string variable), with the newline
character stripped off. The valued returned is 1 if there was anything to be
read (including blank lines), 0 if the source has been exhausted.

Here is an example in which the content of a text file is broken into lines:

	  string s = readfile("data.txt")
	  string line
	  scalar i = 1
	  loop while getline(s, line)
	    printf "line %d = '%s'\n", i++, line
	  endloop

In this example we can be sure that the source is exhausted when the loop
terminates. If the source might not be exhausted you should follow your
regular call(s) to getline with a "clean up" call, in which target is
replaced by null (or omitted altogether) as in

	  getline(s, line)
	  getline(s, null)

Note that although the reading position advances at each call to getline,
source is not modified by this function, only target.

# ghk
Output:     matrix
Arguments:  C (matrix)
            A (matrix)
            B (matrix)
            U (matrix)

Computes the GHK (Geweke, Hajivassiliou, Keane) approximation to the
multivariate normal distribution function; see for example Geweke (1991).
The value returned is an n x 1 vector of probabilities.

The argument C (m x m) should give the Cholesky factor (lower triangular) of
the covariance matrix of the m normal variates. The arguments A and B should
both be n x m, giving respectively the lower and upper bounds applying to
the variates at each of n observations. Where variates are unbounded, this
should be indicated using the built-in constant "$huge" or its negative.

The matrix U should be m x r, with r the number of pseudo-random draws from
the uniform distribution; suitable functions for creating U are "muniform"
and "halton".

In the following example, the series P and Q should be numerically very
similar to one another, P being the "true" probability and Q its GHK
approximation:

	  nulldata 20
	  series inf1 = -2*uniform()
	  series sup1 = 2*uniform()
	  series inf2 = -2*uniform()
	  series sup2 = 2*uniform()

	  scalar rho = 0.25
	  matrix V = {1, rho; rho, 1}

	  series P = cdf(D, rho, inf1, inf2) - cdf(D, rho, sup1, inf2) \
	  - cdf(D, rho, inf1, sup2) + cdf(D, rho, sup1, sup2)

	  C = cholesky(V)
	  U = muniform(2, 100)

	  series Q = ghk(C, {inf1, inf2}, {sup1, sup2}, U)

# gini
Output:     scalar
Argument:   y (series)

Returns Gini's inequality index for the series y.

# ginv
Output:     matrix
Argument:   A (matrix)

Returns A^+, the Moore-Penrose or generalized inverse of A, computed via the
singular value decomposition.

This matrix has the properties A A^+ A = A and A^+ A A^+ = A^+ . Moreover,
the products A A^+ and A^+ A are symmetric by construction.

See also "inv", "svd".

# halton
Output:     matrix
Arguments:  m (integer)
            r (integer)
            offset (integer, optional)

Returns an m x r matrix containing m Halton sequences of length r; m is
limited to a maximum of 40. The sequences are contructed using the first m
primes. By default the first 10 elements of each sequence are discarded, but
this figure can be adjusted via the optional offset argument, which should
be a non-negative integer. See Halton and Smith (1964).

# hdprod
Output:     matrix
Arguments:  X (matrix)
            Y (matrix)

Horizontal direct product. The two arguments must have the same number of
rows, r. The return value is a matrix with r rows, in which the i-th row is
the Kronecker product of the corresponding rows of X and Y.

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

Example: the code

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

produces the following matrix:

         0    1    0    2    0    3 
        -4    4   -5    5   -6    6 

# hpfilt
Output:     series
Arguments:  y (series)
            lambda (scalar, optional)

Returns the cycle component from application of the Hodrick-Prescott filter
to series y. If the smoothing parameter, lambda, is not supplied then a
data-based default is used, namely 100 times the square of the periodicity
(100 for annual data, 1600 for quarterly data, and so on). See also
"bkfilt", "bwfilt".

# I
Output:     square matrix
Argument:   n (integer)

Returns an identity matrix with n rows and columns.

# imaxc
Output:     row vector
Argument:   X (matrix)

Returns the row indices of the maxima of the columns of X.

See also "imaxr", "iminc", "maxc".

# imaxr
Output:     column vector
Argument:   X (matrix)

Returns the column indices of the maxima of the rows of X.

See also "imaxc", "iminr", "maxr".

# imhof
Output:     scalar
Arguments:  M (matrix)
            x (scalar)

Computes Prob(u'Au < x) for a quadratic form in standard normal variates, u,
using the procedure developed by Imhof (1961).

If the first argument, M, is a square matrix it is taken to specify A,
otherwise if it's a column vector it is taken to be the precomputed
eigenvalues of A, otherwise an error is flagged.

See also "pvalue".

# iminc
Output:     row vector
Argument:   X (matrix)

Returns the row indices of the minima of the columns of X.

See also "iminr", "imaxc", "minc".

# iminr
Output:     column vector
Argument:   X (matrix)

Returns the column indices of the mimima of the rows of X.

See also "iminc", "imaxr", "minr".

# inbundle
Output:     integer
Arguments:  b (bundle)
            key (string)

Checks whether bundle b contains a data-item with name key. The value
returned is an integer code for the type of the item: 0 for no match, 1 for
scalar, 2 for series, 3 for matrix, 4 for string and 5 for bundle. The
function "typestr" may be used to get the string corresponding to this code.

# infnorm
Output:     scalar
Argument:   X (matrix)

Returns the infinity-norm of X, that is, the maximum across the rows of X of
the sum of absolute values of the row elements.

See also "onenorm".

# inlist
Output:     integer
Arguments:  L (list)
            y (series)

Returns the (1-based) position of y in list L, or 0 if y is not present in
L. The second argument may be given as the name of a series or alternatively
as an integer ID number.

# int
Output:     same type as input
Argument:   x (scalar, series or matrix)

Returns the integer part of x, truncating the fractional part. Note: int and
"floor" differ in their effect for negative arguments: int(-3.5) gives -3,
while floor(-3.5) gives -4. See also "ceil".

# inv
Output:     matrix
Argument:   A (square matrix)

Returns the inverse of A. If A is singular or not square, an error message
is produced and nothing is returned. Note that gretl checks automatically
the structure of A and uses the most efficient numerical procedure to
perform the inversion.

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

See also "ginv", "invpd".

# invcdf
Output:     same type as input
Arguments:  c (character)
            ... (see below)
            p (scalar, series or matrix)

Inverse cumulative distribution function calculator. Returns x such that P(X
<= x) = p, where the distribution X is determined by the character c;
Between the arguments c and p, zero or more additional scalar arguments are
required to specify the parameters of the distribution, as follows.

  Standard normal (c = z, n, or N): no extra arguments

  Gamma (g or G): shape; scale

  Student's t (t): degrees of freedom

  Chi square (c, x, or X): degrees of freedom

  Snedecor's F (f or F): df (num.); df (den.)

  Binomial (b or B): probability; trials

  Poisson (p or P): mean

  Standardized GED (E): shape

See also "cdf", "critical", "pvalue".

# invmills
Output:     same type as input
Argument:   x (scalar, series or matrix)

Returns the inverse Mills ratio at x, that is the ratio between the standard
normal density and the complement to the standard normal distribution
function, both evaluated at x.

This function uses a dedicated algorithm which yields greater accuracy
compared to calculation using "dnorm" and "cnorm", but the difference
between the two methods is appreciable only for very large negative values
of x.

See also "cdf", "cnorm", "dnorm".

# invpd
Output:     square matrix
Argument:   A (positive definite matrix)

Returns the inverse of the symmetric, positive definite matrix A. This
function is slightly faster than "inv" for large matrices, since no check
for symmetry is performed; for that reason it should be used with care.

# irf
Output:     matrix
Arguments:  target (integer)
            shock (integer)
            alpha (scalar between 0 and 1, optional)

This function is available only when the last model estimated was a VAR or
VECM. It returns a matrix containing the estimated response of the target
variable to an impulse of one standard deviation in the shock variable.
These variables are identified by their position in the VAR specification:
for example, if target and shock are given as 1 and 3 respectively, the
returned matrix gives the response of the first variable in the VAR for a
shock to the third variable.

If the optional alpha argument is given, the returned matrix has three
columns: the point estimate of the responses, followed by the lower and
upper limits of a 1 - α confidence interval obtained via bootstrapping. (So
alpha = 0.1 corresponds to 90 percent confidence.) If alpha is omitted or
set to zero, only the point estimate is provided.

The number of periods (rows) over which the response is traced is determined
automatically based on the frequency of the data, but this can be overridden
via the "set" command, as in set horizon 10.

# irr
Output:     scalar
Argument:   x (series or vector)

Returns the Internal Rate of Return for x, considered as a sequence of
payments (negative) and receipts (positive). See also "npv".

# isconst
Output:     integer
Arguments:  y (series or vector)
            panel-code (integer, optional)

Without the optional second argument, returns 1 if y has a constant value
over the current sample range (or over its entire length if y is a vector),
otherwise 0.

The second argument is accepted only if the current dataset is a panel and y
is a series. In that case a panel-code value of 0 calls for a check for
time-invariance, while a value of 1 means check for cross-sectional
invariance (that is, in each time period the value of y is the same for all
groups).

If y is a series, missing values are ignored in checking for constancy.

# isnan
Output:     same type as input
Argument:   x (scalar or matrix)

Given a scalar argument, returns 1 if x is "Not a Number" (NaN), otherwise
0. Given a matrix argument, returns a matrix of the same dimensions with 1s
in positions where the corresponding element of the input is NaN and 0s
elsewhere.

# isnull
Output:     integer
Argument:   name (string)

Returns 0 if name is the identifier for a currently defined object, be it a
scalar, a series, a matrix, list, string or bundle; otherwise returns 1.

# isoconv
Output:     scalar
Arguments:  date (series)
            &year (reference to series)
            &month (reference to series)
            &day (reference to series, optional)

Given a series date holding dates in ISO 8601 "basic" format (YYYYMMDD),
this function writes the year, month and (optionally) day components into
the series named by the second and subsequent arguments. An example call,
assuming the series dates contains suitable 8-digit values:

	  series y, m, d
	  isoconv(dates, &y, &m, &d)

The return value from this function is 0 on successful completion, non-zero
on error.

# isodate
Output:     see below
Arguments:  ed (scalar or series)
            as-string (boolean, optional)

The argument ed is interpreted as an epoch day (which equals 1 for the first
of January in the year 1 AD). The default return value -- of the same type
as ed -- is an 8-digit number, or a series of such numbers, on the pattern
YYYYMMDD (ISO 8601 "basic" format), giving the calendar date corresponding
to the epoch day.

If ed is a scalar (only) and the optional second argument as-string is
non-zero, the return value is not numeric but rather a string on the pattern
YYYY-MM-DD (ISO 8601 "extended" format).

For the inverse function, see "epochday".

# iwishart
Output:     matrix
Arguments:  S (symmetric matrix)
            v (integer)

Given S (a positive definite p x p scale matrix), returns a drawing from the
Inverse Wishart distribution with v degrees of freedom. The returned matrix
is also p x p. The algorithm of Odell and Feiveson (1966) is used.

# kdensity
Output:     matrix
Arguments:  x (series)
            scale (scalar, optional)
            control (boolean, optional)

Computes a kernel density estimate for the series x. The returned matrix has
two columns, the first holding a set of evenly spaced abscissae and the
second the estimated density at each of these points.

The optional scale parameter can be used to adjust the degree of smoothing
relative to the default of 1.0 (higher values produce a smoother result).
The control parameter acts as a boolean: 0 (the default) means that the
Gaussian kernel is used; a non-zero value switches to the Epanechnikov
kernel.

A plot of the results may be obtained using the "gnuplot" command, as in

	  matrix d = kdensity(x)
	  gnuplot 2 1 --matrix=d --with-lines --suppress-fitted

# kfilter
Output:     scalar
Arguments:  &E (reference to matrix, or null)
            &V (reference to matrix, or null)
            &S (reference to matrix, or null)
            &P (reference to matrix, or null)
            &G (reference to matrix, or null)

Requires that a Kalman filter be set up. Performs a forward, filtering pass
and returns 0 on successful completion or 1 if numerical problems are
encountered.

The optional matrix arguments can be used to retrieve the following
information: E gets the matrix of one-step ahead prediction errors and V
gets the variance matrix for these errors; S gets the matrix of estimated
values of the state vector and P the variance matrix of these estimates; G
gets the Kalman gain. All of these matrices have T rows, corresponding to T
observations. For the column dimensions and further details see the Gretl
User's Guide.

See also "kalman", "ksmooth", "ksimul".

# ksimul
Output:     matrix
Arguments:  v (matrix)
            w (matrix)
            &S (reference to matrix, or null)

Requires that a Kalman filter be set up. Performs a simulation and returns a
matrix holding simulated values of the observable variables.

The argument v supplies artificial disturbances for the state transition
equation and w supplies disturbances for the observation equation, if
applicable. The optional argument S may be used to retrieve the simulated
state vector. For details see the Gretl User's Guide.

See also "kalman", "kfilter", "ksmooth".

# ksmooth
Output:     matrix
Argument:   &P (reference to matrix, or null)

Requires that a Kalman filter be set up. Performs a backward, smoothing pass
and returns a matrix holding smoothed estimates of the state vector. The
optional argument P may be used to retrieve the MSE of the smoothed state.
For details see the Gretl User's Guide.

See also "kalman", "kfilter", "ksimul".

# kurtosis
Output:     scalar
Argument:   x (series)

Returns the excess kurtosis of the series x, skipping any missing
observations.

# lags
Output:     list
Arguments:  p (integer)
            y (series or list)
            bylag (boolean, optional)

Generates lags 1 to p of the series y, or if y is a list, of all series in
the list. If p = 0, the maximum lag defaults to the periodicity of the data;
otherwise p must be positive.

The generated variables are automatically named according to the template
varname_i where varname is the name of the original series and i is the
specific lag. The original portion of the name is truncated if necessary,
and may be adjusted in case of non-uniqueness in the set of names thus
constructed.

When y is a list and the lag order is greater than 1, the default ordering
of the terms in the returned list is by variable: all lags of the first
series in the input list followed by all lags of the second series, and so
on. The optional third argument can be used to change this: if bylag is
non-zero then the terms are ordered by lag: lag 1 of all the input series,
then lag 2 of all the series, and so on.

# lastobs
Output:     integer
Argument:   y (series)

Returns the 1-based index of the last non-missing observation for the series
y. Note that if some form of subsampling is in effect, the value returned
may be larger than the dollar variable "$t2". See also "firstobs".

# ldet
Output:     scalar
Argument:   A (square matrix)

Returns the natural log of the determinant of A, computed via the LU
factorization. See also "det", "rcond".

# ldiff
Output:     same type as input
Argument:   y (series or list)

Computes log differences; starting values are set to NA.

When a list is returned, the individual variables are automatically named
according to the template ld_varname where varname is the name of the
original series. The name is truncated if necessary, and may be adjusted in
case of non-uniqueness in the set of names thus constructed.

See also "diff", "sdiff".

# lincomb
Output:     series
Arguments:  L (list)
            b (vector)

Computes a new series as a linear combination of the series in the list L.
The coefficients are given by the vector b, which must have length equal to
the number of series in L.

See also "wmean".

# ljungbox
Output:     scalar
Arguments:  y (series)
            p (integer)

Computes the Ljung-Box Q' statistic for the series y using lag order p, over
the currently defined sample range. The lag order must be greater than or
equal to 1 and less than the number of available observations.

This statistic may be referred to the chi-square distribution with p degrees
of freedom as a test of the null hypothesis that the series y is not
serially correlated. See also "pvalue".

# lngamma
Output:     same type as input
Argument:   x (scalar, series or matrix)

Returns the log of the gamma function of x.

# log
Output:     same type as input
Argument:   x (scalar, series, matrix or list)

Returns the natural logarithm of x; produces NA for non-positive values.
Note: ln is an acceptable alias for log.

When a list is returned, the individual variables are automatically named
according to the template l_varname where varname is the name of the
original series. The name is truncated if necessary, and may be adjusted in
case of non-uniqueness in the set of names thus constructed.

# log10
Output:     same type as input
Argument:   x (scalar, series or matrix)

Returns the base-10 logarithm of x; produces NA for non-positive values.

# log2
Output:     same type as input
Argument:   x (scalar, series or matrix)

Returns the base-2 logarithm of x; produces NA for non-positive values.

# loess
Output:     series
Arguments:  y (series)
            x (series)
            d (integer, optional)
            q (scalar, optional)
            robust (boolean, optional)

Performs locally-weighted polynomial regression and returns a series holding
predicted values of y for each non-missing value of x. The method is as
described by William Cleveland (1979).

The optional arguments d and q specify the order of the polynomial in x and
the proportion of the data points to be used in local estimation,
respectively. The default values are d = 1 and q = 0.5. The other acceptable
values for d are 0 and 2. Setting d = 0 reduces the local regression to a
form of moving average. The value of q must be greater than 0 and cannot
exceed 1; larger values produce a smoother outcome.

If a non-zero value is given for the robust argument the local regressions
are iterated twice, with the weights being modified based on the residuals
from the previous iteration so as to give less influence to outliers.

See also "nadarwat", and in addition see the Gretl User's Guide for details
on nonparametric methods.

# logistic
Output:     same type as input
Argument:   x (scalar, series or matrix)

Returns the logistic function of the argument x, that is, e^x/(1 + e^x). If
x is a matrix, the function is applied element by element.

# lower
Output:     square matrix
Argument:   A (matrix)

Returns an n x n lower triangular matrix: the elements on and below the
diagonal are equal to the corresponding elements of A; the remaining
elements are zero.

See also "upper".

# lrvar
Output:     scalar
Arguments:  y (series or vector)
            k (integer)

Returns the long-run variance of y, calculated using a Bartlett kernel with
window size k. If k is negative, int(T^(1/3)) is used.

# max
Output:     scalar or series
Argument:   y (series or list)

If the argument y is a series, returns the (scalar) maximum of the
non-missing observations in the series. If the argument is a list, returns a
series each of whose elements is the maximum of the values of the listed
variables at the given observation.

See also "min", "xmax", "xmin".

# maxc
Output:     row vector
Argument:   X (matrix)

Returns a row vector containing the maxima of the columns of X.

See also "imaxc", "maxr", "minc".

# maxr
Output:     column vector
Argument:   X (matrix)

Returns a column vector containing the maxima of the rows of X.

See also "imaxc", "maxc", "minr".

# mcorr
Output:     matrix
Argument:   X (matrix)

Computes a correlation matrix treating each column of X as a variable. See
also "corr", "cov", "mcov".

# mcov
Output:     matrix
Argument:   X (matrix)

Computes a covariance matrix treating each column of X as a variable. See
also "corr", "cov", "mcorr".

# mcovg
Output:     matrix
Arguments:  X (matrix)
            u (vector, optional)
            w (vector, optional)
            p (integer)

Returns the matrix covariogram for a T x k matrix X (typically containing
regressors), an (optional) T-vector u (typically containing residuals), an
(optional) (p+1)-vector of weights w, and a lag order p, which must be
greater than or equal to 0.

The returned matrix is given by

sum_{j=-p}^p sum_j w_{|j|} (X_t' u_t u_{t-j} X_{t-j})

If u is given as null the u terms are omitted, and if w is given as null all
the weights are taken to be 1.0.

# mean
Output:     scalar or series
Argument:   x (series or list)

If x is a series, returns the (scalar) sample mean, skipping any missing
observations.

If x is a list, returns a series y such that y_t is the mean of the values
of the variables in the list at observation t, or NA if there are any
missing values at t.

# meanc
Output:     row vector
Argument:   X (matrix)

Returns the means of the columns of X. See also "meanr", "sumc", "sdc".

# meanr
Output:     column vector
Argument:   X (matrix)

Returns the means of the rows of X. See also "meanc", "sumr".

# median
Output:     scalar
Argument:   y (series)

The median of the non-missing observations in series y. See also "quantile".

# mexp
Output:     square matrix
Argument:   A (square matrix)

Computes the matrix exponential of A, using algorithm 11.3.1 from Golub and
Van Loan (1996).

# min
Output:     scalar or series
Argument:   y (series or list)

If the argument y is a series, returns the (scalar) minimum of the
non-missing observations in the series. If the argument is a list, returns a
series each of whose elements is the minimum of the values of the listed
variables at the given observation.

See also "max", "xmax", "xmin".

# minc
Output:     row vector
Argument:   X (matrix)

Returns the minima of the columns of X.

See also "iminc", "maxc", "minr".

# minr
Output:     column vector
Argument:   X (matrix)

Returns the minima of the rows of X.

See also "iminr", "maxr", "minc".

# missing
Output:     same type as input
Argument:   x (scalar, series or list)

Returns a binary variable holding 1 if x is NA. If x is a series, the
comparison is done element by element; if x is a list of series, the output
is a series with 1 at observations for which at least one series in the list
has a missing value, and 0 otherwise.

See also "misszero", "ok", "zeromiss".

# misszero
Output:     same type as input
Argument:   x (scalar or series)

Converts NAs to zeros. If x is a series, the conversion is done element by
element. See also "missing", "ok", "zeromiss".

# mlag
Output:     matrix
Arguments:  X (matrix)
            p (scalar or vector)
            m (scalar, optional)

Shifts up or down the rows of X. If p is a positive scalar, returns a matrix
in which the columns of X are shifted down by p rows and the first p rows
are filled with the value m. If p is a negative number, X is shifted up and
the last rows are filled with the value m. If m is omitted, it is understood
to be zero.

If p is a vector, the above operation is carried out for each element in p,
joining the resulting matrices horizontally.

# mnormal
Output:     matrix
Arguments:  r (integer)
            c (integer)

Returns a matrix with r rows and c columns, filled with standard normal
pseudo-random variates. See also "normal", "muniform".

# mols
Output:     matrix
Arguments:  Y (matrix)
            X (matrix)
            &U (reference to matrix, or null)
            &V (reference to matrix, or null)

Returns a k x n matrix of parameter estimates obtained by OLS regression of
the T x n matrix Y on the T x k matrix X.

If the third argument is not null, the T x n matrix U will contain the
residuals. If the final argument is given and is not null then the k x k
matrix V will contain (a) the covariance matrix of the parameter estimates,
if Y has just one column, or (b) X'X^-1 if Y has multiple columns.

By default, estimates are obtained via Cholesky decomposition, with a
fallback to QR decomposition if the columns of X are highly collinear. The
use of SVD can be forced via the command set svd on.

See also "mpols", "mrls".

# monthlen
Output:     integer
Arguments:  month (integer)
            year (integer)
            weeklen (integer)

Returns the number of (relevant) days in the specified month in the
specified year; weeklen, which must equal 5, 6 or 7, gives the number of
days in the week that should be counted (a value of 6 omits Sundays, and a
value of 5 omits both Saturdays and Sundays).

# movavg
Output:     series
Arguments:  x (series)
            p (scalar)
            control (integer, optional)

Depending on the value of the parameter p, returns either a simple or an
exponentially weighted moving average of the input series x.

If p > 1, a simple p-term moving average is computed, that is, the
arithmetic mean of x(t) to x(t-p+1). If a non-zero value is supplied for the
optional control parameter the MA is centered, otherwise it is "trailing".

If p is a positive fraction, an exponential moving average is computed: y(t)
= p*x(t) + (1-p)*y(t-1). By default the output series, y, is initialized
using the first valid value of x, but the control parameter may be used to
specify the number of initial observations that should be averaged to
produce y(0). A zero value for control indicates that all the observations
should be used.

# mpols
Output:     matrix
Arguments:  Y (matrix)
            X (matrix)
            &U (reference to matrix, or null)

Works exactly as "mols", except that the calculations are done in multiple
precision using the GMP library.

By default GMP uses 256 bits for each floating point number, but you can
adjust this using the environment variable GRETL_MP_BITS, e.g.
GRETL_MP_BITS=1024.

# mrandgen
Output:     matrix
Arguments:  d (string)
            p1 (scalar)
            p2 (scalar, conditional)
            p3 (scalar, conditional)
            rows (integer)
            cols (integer)
Examples:   matrix mx = mrandgen(u, 0, 100, 50, 1)
            matrix mt14 = mrandgen(t, 14, 20, 20)

Works like "randgen" except that the return value is a matrix rather than a
series. The initial arguments to this function (the number of which depends
on the selected distribution) are as described for randgen, but they must be
followed by two integers to specify the number of rows and columns of the
desired random matrix.

The first example above calls for a uniform random column vector of length
50, while the second example specifies a 20 x 20 random matrix with drawings
from the t distribution with 14 degrees of freedom.

See also "mnormal", "muniform".

# mread
Output:     matrix
Arguments:  fname (string)
            import (boolean, optional)

Reads a matrix from a text file. The string fname must contain the name of
the file from which the matrix is to be read. If this name has the suffix
".gz" it is assumed that gzip compression has been applied in writing the
file.

The file in question may start with any number of comment lines, defined as
lines that start with the hash mark, #; such lines are ignored. Beyond that,
the content must conform to the following rules:

  The first non-comment line must contain two integers, separated by a space
  or a tab, indicating the number of rows and columns, respectively.

  The columns must be separated by spaces or tab characters.

  The decimal separator must be the dot character, ".".

If a non-zero value is given for the optional import argument, the input
file is looked for in the user's "dot" directory. This is intended for use
with the matrix-exporting functions offered in the context of the "foreign"
command. In this case the fname argument should be a plain filename, without
any path component.

Should an error occur (such as the file being badly formatted or
inaccessible), an empty matrix is returned.

See also "mwrite".

# mreverse
Output:     matrix
Argument:   X (matrix)

Returns a matrix containing the rows of X in reverse order. If you wish to
obtain a matrix in which the columns of X appear in reverse order you can
do:

	  matrix Y = mreverse(X')'

# mrls
Output:     matrix
Arguments:  Y (matrix)
            X (matrix)
            R (matrix)
            q (column vector)
            &U (reference to matrix, or null)
            &V (reference to matrix, or null)

Restricted least squares: returns a k x n matrix of parameter estimates
obtained by least-squares regression of the T x n matrix Y on the T x k
matrix X subject to the linear restriction RB = q, where B denotes the
stacked coefficient vector. R must have k * n columns; each row of this
matrix represents a linear restriction. The number of rows in q must match
the number of rows in R.

If the fifth argument is not null, the T x n matrix U will contain the
residuals. If the final argument is given and is not null then the k x k
matrix V will hold the restricted counterpart to the matrix X'X^-1. The
variance matrix of the estimates for equation i can be constructed by
multiplying the appropriate sub-matrix of V by an estimate of the error
variance for that equation.

# mshape
Output:     matrix
Arguments:  X (matrix)
            r (integer)
            c (integer)

Rearranges the elements of X into a matrix with r rows and c columns.
Elements are read from X and written to the target in column-major order. If
X contains fewer than k = rc elements, the elements are repeated cyclically;
otherwise, if X has more elements, only the first k are used.

See also "cols", "rows", "unvech", "vec", "vech".

# msortby
Output:     matrix
Arguments:  X (matrix)
            j (integer)

Returns a matrix in which the rows of X are reordered by increasing value of
the elements in column j. This is a stable sort: rows that share the same
value in column j will not be interchanged.

# muniform
Output:     matrix
Arguments:  r (integer)
            c (integer)

Returns a matrix with r rows and c columns, filled with uniform (0,1)
pseudo-random variates. Note: the preferred method for generating a scalar
uniform r.v. is to use the "randgen1" function.

See also "mnormal", "uniform".

# mwrite
Output:     integer
Arguments:  X (matrix)
            fname (string)
            export (boolean, optional)

Writes the matrix X to a plain text file named fname. The file will contain
on the first line two integers, separated by a tab character, with the
number of rows and columns; on the next lines, the matrix elements in
scientific notation, separated by tabs (one line per row).

If file fname already exists, it will be overwritten. The return value is 0
on successful completion; if an error occurs, such as the file being
unwritable, the return value will be non-zero.

If a non-zero value is given for the export argument, the output file will
be written into the user's "dot" directory, where it is accessible by
default via the matrix-loading functions offered in the context of the
"foreign" command. In this case a plain filename, without any path
component, should be given for the second argument.

Matrices stored via the mwrite command can be easily read by other programs;
see the Gretl User's Guide for details.

An extension to the basic behavior of this function is available: if fname
has the suffix ".gz" then the file is written with gzip compression.

See also "mread".

# mxtab
Output:     matrix
Arguments:  x (series or vector)
            y (series or vector)

Returns a matrix holding the cross tabulation of the values contained in x
(by row) and y (by column). The two arguments should be of the same type
(both series or both column vectors), and because of the typical usage of
this function, are assumed to contain integer values only.

See also "values".

# nadarwat
Output:     series
Arguments:  y (series)
            x (series)
            h (scalar)

Returns the Nadaraya-Watson nonparametric estimator of the conditional mean
of y given x. It returns a series holding the nonparametric estimate of
E(y_i|x_i) for each nonmissing element of the series x.

The kernel function K is given by K = exp(-x^2 / 2h) for |x| < T and zero
otherwise.

The argument h, known as the bandwidth, is a parameter (a positive real
number) given by the user. This is usually a small number: larger values of
h make m(x) smoother; a popular choice is n^-0.2. More details are given in
the Gretl User's Guide.

The scalar T is used to prevent numerical problems when the kernel function
is evaluated too far away from zero and is called the trim parameter.

The trim parameter can be adjusted via the nadarwat_trim setting, as a
multiple of h. The default value is 4.

The user may provide a negative value for the bandwidth: this is interpreted
as conventional syntax to obtain the leave-one-out estimator, that is a
variant of the estimator that does not use the i-th observation for
evaluating m(x_i). This makes the Nadaraya-Watson estimator more robust
numerically and its usage is normally advised when the estimator is computed
for inference purposes. Of course, the bandwidth actually used is the
absolute value of h.

# nelem
Output:     integer
Argument:   L (list)

Returns the number of members in the list L.

# ngetenv
Output:     scalar
Argument:   s (string)

If an environment variable by the name of s is defined and has a numerical
value, returns that value; otherwise returns NA. See also "getenv".

# nobs
Output:     integer
Argument:   y (series)

Returns the number of non-missing observations for the variable y in the
currently selected sample.

# normal
Output:     series
Arguments:  mu (scalar)
            sigma (scalar)

Generates a series of Gaussian pseudo-random variates with mean mu and
standard deviation sigma. If no arguments are supplied, standard normal
variates N(0,1) are produced. The values are produced using the Ziggurat
method (Marsaglia and Tsang, 2000).

See also "randgen", "mnormal", "muniform".

# npv
Output:     scalar
Arguments:  x (series or vector)
            r (scalar)

Returns the Net Present Value of x, considered as a sequence of payments
(negative) and receipts (positive), evaluated at annual discount rate r; r
must be expressed as a number, not a percentage (5% = 0.05). The first value
is taken as dated "now" and is not discounted. To emulate an NPV function in
which the first value is discounted, prepend zero to the input sequence.

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

See also "irr".

# NRmax
Output:     scalar
Arguments:  b (vector)
            f (function call)
            g (function call, optional)
            h (function call, optional)

Numerical maximization via the Newton-Raphson method. The vector b should
hold the initial values of a set of parameters, and the argument f should
specify a call to a function that calculates the (scalar) criterion to be
maximized, given the current parameter values and any other relevant data.
If the object is in fact minimization, this function should return the
negative of the criterion. On successful completion, NRmax returns the
maximized value of the criterion, and b holds the parameter values which
produce the maximum.

The optional third and fourth arguments provide means of supplying
analytical derivatives and an analytical (negative) Hessian, respectively.
The functions referenced by g and h must take as their first argument a
pre-defined matrix that is of the correct size to contain the gradient or
Hessian, respectively, given in pointer form. They also must take the
parameter vector as an argument (in pointer form or otherwise). Other
arguments are optional. If either or both of the optional arguments are
omitted, a numerical approximation is used.

For more details and examples see the chapter on numerical methods in the
Gretl User's Guide. See also "BFGSmax", "fdjac".

# nullspace
Output:     matrix
Argument:   A (matrix)

Computes the right nullspace of A, via the singular value decomposition: the
result is a matrix B such that the product AB is a zero matrix, except when
A has full column rank, in which case an empty matrix is returned.
Otherwise, if A is m x n, B will be n by (n - r), where r is the rank of A.

See also "rank", "svd".

# obs
Output:     series

Returns a series of consecutive integers, setting 1 at the start of the
dataset. Note that the result is invariant to subsampling. This function is
especially useful with time-series datasets. Note: you can write t instead
of obs with the same effect.

See also "obsnum".

# obslabel
Output:     string
Argument:   t (integer)

Returns the observation label for observation t, where t is a 1-based index.
The inverse function is provided by "obsnum".

# obsnum
Output:     integer
Argument:   s (string)

Returns an integer corresponding to the observation specified by the string
s. Note that the result is invariant to subsampling. This function is
especially useful with time-series datasets. For example, the following code

	  open denmark 
	  k = obsnum(1980:1)

yields k = 25, indicating that the first quarter of 1980 is the 25th
observation in the denmark dataset.

See also "obs", "obslabel".

# ok
Output:     see below
Argument:   x (scalar, series, matrix or list)

If x is a scalar, returns 1 if x is not NA, otherwise 0. If x is a series,
returns a series with value 1 at observations with non-missing values and
zeros elsewhere. If x is a list, the output is a series with 0 at
observations for which at least one series in the list has a missing value,
and 1 otherwise.

If x is a matrix the behavior is a little different, since matrices cannot
contain NAs: the function returns a matrix of the same dimensions as x, with
1s in positions corresponding to finite elements of x and 0s in positions
where the elements are non-finite (either infinities or not-a-number, as per
the IEEE 754 standard).

See also "missing", "misszero", "zeromiss". But note that these functions
are not applicable to matrices.

# onenorm
Output:     scalar
Argument:   X (matrix)

Returns the 1-norm of the matrix X, that is, the maximum across the columns
of X of the sum of absolute values of the column elements.

See also "infnorm", "rcond".

# ones
Output:     matrix
Arguments:  r (integer)
            c (integer)

Outputs a matrix with r rows and c columns, filled with ones.

See also "seq", "zeros".

# orthdev
Output:     series
Argument:   y (series)

Only applicable if the currently open dataset has a panel structure.
Computes the forward orthogonal deviations for variable y.

This transformation is sometimes used instead of differencing to remove
individual effects from panel data. For compatibility with first
differences, the deviations are stored one step ahead of their true temporal
location (that is, the value at observation t is the deviation that,
strictly speaking, belongs at t - 1). That way one loses the first
observation in each time series, not the last.

See also "diff".

# pdf
Output:     same type as input
Arguments:  c (character)
            ... (see below)
            x (scalar, series or matrix)
Examples:   f1 = pdf(N, -2.5)
            f2 = pdf(X, 3, y)
            f3 = pdf(W, shape, scale, y)

Probability density function calculator. Returns the density at x of the
distribution identified by the code c. See "cdf" for details of the required
(scalar) arguments. The distributions supported by the pdf function are the
normal, Student's t, chi-square, F, Gamma, Weibull, Generalized Error,
Binomial and Poisson. Note that for the Binomial and the Poisson what's
calculated is in fact the probability mass at the specified point.

For the normal distribution, see also "dnorm".

# pergm
Output:     matrix
Arguments:  x (series or vector)
            bandwidth (scalar, optional)

If only the first argument is given, computes the sample periodogram for the
given series or vector. If the second argument is given, computes an
estimate of the spectrum of x using a Bartlett lag window of the given
bandwidth, up to a maximum of half the number of observations (T/2).

Returns a matrix with two columns and T/2 rows: the first column holds the
frequency, omega, from 2pi/T to pi, and the second the corresponding
spectral density.

# pmax
Output:     series
Arguments:  y (series)
            mask (series, optional)

Only applicable if the currently open dataset has a panel structure. Returns
a series holding the maxima of variable y for each cross-sectional unit
(repeated for each time period).

If the optional second argument is provided then observations for which the
value of mask is zero are ignored.

See also "pmin", "pmean", "pnobs", "psd", "pxsum", "pshrink", "psum".

# pmean
Output:     series
Arguments:  y (series)
            mask (series, optional)

Only applicable if the currently open dataset has a panel structure. Returns
a series holding the time-mean of variable y for each cross-sectional unit,
the values being repeated for each period. Missing observations are skipped
in calculating the means.

If the optional second argument is provided then observations for which the
value of mask is zero are ignored.

See also "pmax", "pmin", "pnobs", "psd", "pxsum", "pshrink", "psum".

# pmin
Output:     series
Arguments:  y (series)
            mask (series, optional)

Only applicable if the currently open dataset has a panel structure. Returns
a series holding the minima of variable y for each cross-sectional unit
(repeated for each time period).

If the optional second argument is provided then observations for which the
value of mask is zero are ignored.

See also "pmax", "pmean", "pnobs", "psd", "pshrink", "psum".

# pnobs
Output:     series
Arguments:  y (series)
            mask (series, optional)

Only applicable if the currently open dataset has a panel structure. Returns
a series holding the number of valid observations of variable y for each
cross-sectional unit (repeated for each time period).

If the optional second argument is provided then observations for which the
value of mask is zero are ignored.

See also "pmax", "pmin", "pmean", "psd", "pshrink", "psum".

# polroots
Output:     matrix
Argument:   a (vector)

Finds the roots of a polynomial. If the polynomial is of degree p, the
vector a should contain p + 1 coefficients in ascending order, i.e. starting
with the constant and ending with the coefficient on x^p.

If all the roots are real they are returned in a column vector of length p,
otherwise a p x 2 matrix is returned, the real parts in the first column and
the imaginary parts in the second.

# polyfit
Output:     series
Arguments:  y (series)
            q (integer)

Fits a polynomial trend of order q to the input series y using the method of
orthogonal polynomials. The series returned holds the fitted values.

# princomp
Output:     matrix
Arguments:  X (matrix)
            p (integer)
            covmat (boolean, optional)

Let the matrix X be T x k, containing T observations on k variables. The
argument p must be a positive integer less than or equal to k. This function
returns a T x p matrix, P, holding the first p principal components of X.

The optional third argument acts as a boolean switch: if it is non-zero the
principal components are computed on the basis of the covariance matrix of
the columns of X (the default is to use the correlation matrix).

The elements of P are computed as the sum from i to k of Z_ti times v_ji,
where Z_ti is the standardized value of variable i at observation t and v_ji
is the jth eigenvector of the correlation (or covariance) matrix of the
X_is, with the eigenvectors ordered by decreasing value of the corresponding
eigenvalues.

See also "eigensym".

# prodc
Output:     row vector
Argument:   X (matrix)

Returns the product of the elements of X, by column. See also "prodr",
"meanc", "sdc", "sumc".

# prodr
Output:     column vector
Argument:   X (matrix)

Returns the product of the elements of X, by row. See also "prodc", "meanr",
"sumr".

# psd
Output:     series
Arguments:  y (series)
            mask (series, optional)

Only applicable if the currently open dataset has a panel structure. Returns
a series holding the sample standard deviation of variable y for each
cross-sectional unit (with the values repeated for each time period). The
denominator used is the sample size for each unit minus 1, unless the number
of valid observations for the given unit is 1 (in which case 0 is returned)
or 0 (in which case NA is returned).

If the optional second argument is provided then observations for which the
value of mask is zero are ignored.

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

See also "pmax", "pmin", "pmean", "pnobs", "pshrink", "psum".

# psdroot
Output:     square matrix
Argument:   A (symmetric matrix)

Performs a generalized variant of the Cholesky decomposition of the matrix
A, which must be positive semidefinite (but which may be singular). If the
input matrix is not square an error is flagged, but symmetry is assumed and
not tested; only the lower triangle of A is read. The result is a
lower-triangular matrix L which satisfies A = LL'. Indeterminate elements in
the solution are set to zero.

For the case where A is positive definite, see "cholesky".

# pshrink
Output:     matrix
Argument:   y (series)

Only applicable if the currently open dataset has a panel structure. Returns
a column vector holding the first valid observation for the series y for
each cross-sectional unit in the panel, over the current sample range. If a
unit has no valid observations for the input series it is skipped.

This function provides a means of compacting the series returned by
functions such as "pmax" and "pmean", in which a value pertaining to each
cross-sectional unit is repeated for each time period.

# psum
Output:     series
Arguments:  y (series)
            mask (series, optional)

Only applicable if the currently open dataset has a panel structure. Returns
a series holding the sum over time of variable y for each cross-sectional
unit, the values being repeated for each period. Missing observations are
skipped in calculating the sums.

If the optional second argument is provided then observations for which the
value of mask is zero are ignored.

See also "pmax", "pmean", "pmin", "pnobs", "psd", "pxsum", "pshrink".

# pvalue
Output:     same type as input
Arguments:  c (character)
            ... (see below)
            x (scalar, series or matrix)
Examples:   p1 = pvalue(z, 2.2)
            p2 = pvalue(X, 3, 5.67)
            p2 = pvalue(F, 3, 30, 5.67)

P-value calculator. Returns P(X > x), where the distribution X is determined
by the character c. Between the arguments c and x, zero or more additional
arguments are required to specify the parameters of the distribution; see
"cdf" for details. The distributions supported by the pval function are the
standard normal, t, Chi square, F, gamma, binomial, Poisson, Weibull and
Generalized Error.

See also "critical", "invcdf", "urcpval", "imhof".

# pxsum
Output:     series
Arguments:  y (series)
            mask (series, optional)

Only applicable if the currently open dataset has a panel structure. Returns
a series holding the sum of the values of y for each cross-sectional unit in
each period (the values being repeated for each unit).

If the optional second argument is provided then observations for which the
value of mask is zero are ignored.

Note that this function works in a different dimension from the "pmean"
function.

# qform
Output:     matrix
Arguments:  x (matrix)
            A (symmetric matrix)

Computes the quadratic form Y = xAx'. Using this function instead of
ordinary matrix multiplication guarantees more speed and better accuracy. If
x and A are not conformable, or A is not symmetric, an error is returned.

# qnorm
Output:     same type as input
Argument:   x (scalar, series or matrix)

Returns quantiles for the standard normal distribution. If x is not between
0 and 1, NA is returned. See also "cnorm", "dnorm".

# qrdecomp
Output:     matrix
Arguments:  X (matrix)
            &R (reference to matrix, or null)

Computes the QR decomposition of an m x n matrix X, that is X = QR where Q
is an m x n orthogonal matrix and R is an n x n upper triangular matrix. The
matrix Q is returned directly, while R can be retrieved via the optional
second argument.

See also "eigengen", "eigensym", "svd".

# quadtable
Output:     matrix
Arguments:  n (integer)
            type (integer, optional)
            a (scalar, optional)
            b (scalar, optional)

Returns an n x 2 matrix for use with Gaussian quadrature (numerical
integration). The first column holds the nodes or abscissae, the second the
weights.

The first argument specifies the number of points (rows) to compute. The
second argument codes for the type of quadrature: use 1 for Gauss-Hermite
(the default); 2 for Gauss-Legendre; or 3 for Gauss-Laguerre. The
significance of the optional parameters a and b depends on the selected
type, as explained below.

Gaussian quadrature is a method of approximating numerically the definite
integral of some function of interest. Let the function be represented as
the product f(x)W(x). The types of quadrature differ in the specification of
the component W(x): in the Hermite case this is exp(-x^2); in the Laguerre
case, exp(-x); and in the Legendre case simply W(x) = 1.

For each specification of W, one can compute a set of nodes, x_i, and
weights, w_i, such that the sum from i=1 to n of w_if(x_i) approximates the
desired integral. The method of Golub and Welsch (1969) is used.

When the Gauss-Legendre type is selected, the optional arguments a and b can
be used to control the lower and upper limits of integration, the default
values being -1 and 1. (In Hermite quadrature the limits are fixed at minus
and plus infinity, while in the Laguerre case they are fixed at 0 and
infinity.)

In the Hermite case a and b play a different role: they can be used to
replace the default form of W(x) with the (closely related) normal
distribution with mean a and standard deviation b. Supplying values of 0 and
1 for these parameters, for example, has the effect of making W(x) into the
standard normal pdf, which is equivalent to multiplying the default nodes by
the square root of two and dividing the weights by the square root of pi.

# quantile
Output:     scalar or matrix
Arguments:  y (series or matrix)
            p (scalar between 0 and 1)

If y is a series, returns the p-quantile for the series. For example, when p
= 0.5, the median is returned.

If y is a matrix, returns a row vector containing the p-quantiles for the
columns of y; that is, each column is treated as a series.

In addition, for matrix y an alternate form of the second argument is
supported: p may be given as a vector. In that case the return value is an m
x n matrix, where m is the number of elements in p and n is the number of
columns in y.

# randgen
Output:     series
Arguments:  d (string)
            p1 (scalar or series)
            p2 (scalar or series, conditional)
            p3 (scalar, conditional)
Examples:   series x = randgen(u, 0, 100)
            series t14 = randgen(t, 14)
            series y = randgen(B, 0.6, 30)
            series g = randgen(G, 1, 1)
            series P = randgen(P, mu)

All-purpose random number generator. The argument d is a string (in most
cases just a single character) which specifies the distribution from which
the pseudo-random numbers should be drawn. The arguments p1 to p3 specify
the parameters of the selected distribution; the number of such parameters
depends on the distribution. For distributions other than the beta-binomial,
the parameters p1 and (if applicable) p2 may be given as either scalars or
series: if they are given as scalars the output series is identically
distributed, while if a series is given for p1 or p2 the distribution is
conditional on the parameter value at each observation. In the case of the
beta-binomial all the parameters must be scalars.

Specifics are given below: the string code for each distribution is shown in
parentheses, followed by the interpretation of the argument p1 and, where
applicable, p2 and p3.

  Uniform (continuous) (u or U): minimum, maximum

  Uniform (discrete) (i): minimum, maximum

  Normal (z, n, or N): mean, standard deviation

  Student's t (t): degrees of freedom

  Chi square (c, x, or X): degrees of freedom

  Snedecor's F (f or F): df (num.), df (den.)

  Gamma (g or G): shape, scale

  Binomial (b or B): probability, number of trials

  Poisson (p or P): mean

  Weibull (w or W): shape, scale

  Generalized Error (E): shape

  Beta (beta): shape1, shape2

  Beta-Binomial (bb): trials, shape1, shape2

See also "normal", "uniform", "mrandgen", "randgen1".

# randgen1
Output:     scalar
Arguments:  d (character)
            p1 (scalar)
            p2 (scalar, conditional)
Examples:   scalar x = randgen1(z, 0, 1)
            scalar g = randgen1(g, 3, 2.5)

Works like "randgen" except that the return value is a scalar rather than a
series.

The first example above calls for a value from the standard normal
distribution, while the second specifies a drawing from the Gamma
distribution with shape 3 and scale 2.5.

See also "mrandgen".

# randint
Output:     integer
Arguments:  min (integer)
            max (integer)

Returns a pseudo-random integer in the closed interval [min, max]. See also
"randgen".

# rank
Output:     integer
Argument:   X (matrix)

Returns the rank of X, numerically computed via the singular value
decomposition. See also "svd".

# ranking
Output:     same type as input
Argument:   y (series or vector)

Returns a series or vector with the ranks of y. The rank for observation i
is the number of elements that are less than y_i plus one half the number of
elements that are equal to y_i. (Intuitively, you may think of chess points,
where victory gives you one point and a draw gives you half a point.) One is
added so the lowest rank is 1 instead of 0.

See also "sort", "sortby".

# rcond
Output:     scalar
Argument:   A (square matrix)

Returns the reciprocal condition number for A with respect to the 1-norm. In
many circumstances, this is a better measure of the sensitivity of A to
numerical operations such as inversion than the determinant.

The value is computed as the reciprocal of the product, 1-norm of A times
1-norm of A-inverse.

See also "det", "ldet", "onenorm".

# readfile
Output:     string
Arguments:  fname (string)
            codeset (string, optional)

If a file by the name of fname exists and is readable, returns a string
containing the content of this file, otherwise flags an error.

In the case where fname starts with the indentifier of a supported internet
protocol (http://, ftp://, https://), libcurl is invoked to download the
resource.

If the text to be read is not encoded in UTF-8, gretl will try recoding it
from the current locale codeset if that is not UTF-8, or from ISO-8859-15
otherwise. If this simple default does not meet your needs you can use the
optional second argument to specify a codeset. For example, if you want to
read text in Microsoft codepage 1251 and that is not your locale codeset,
you should give a second argument of "cp1251".

Also see the "sscanf" and "getline" functions.

# regsub
Output:     string
Arguments:  s (string)
            match (string)
            repl (string)

Returns a copy of s in which all occurrences of the pattern match are
replaced using repl. The arguments match and repl are interpreted as
Perl-style regular expressions.

See also "strsub" for simple substitution of literal strings.

# remove
Output:     integer
Argument:   fname (string)

If a file by the name of fname exists and is writable by the user, removes
(deletes) the named file. Returns 0 on successful completion, non-zero if
there is no such file or the file cannot be removed.

# replace
Output:     same type as input
Arguments:  x (series or matrix)
            find (scalar or vector)
            subst (scalar or vector)

Replaces each element of x equal to the i-th element of find with the
corresponding element of subst.

If find is a scalar, subst must also be a scalar. If find and subst are both
vectors, they must have the same number of elements. But if find is a vector
and subst a scalar, then all matches will be replaced by subst.

Example:

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

produces

          a (2 x 3)

            1   2   3 
            3   4   5 

          b (2 x 3)

            -1    2   -8 
            -8    0    5 

# resample
Output:     same type as input
Arguments:  x (series or matrix)
            b (integer, optional)

Resamples from x with replacement. In the case of a series argument, each
value of the returned series, y_t, is drawn from among all the values of x_t
with equal probability. When a matrix argument is given, each row of the
returned matrix is drawn from the rows of x with equal probability.

The optional argument b represents the block length for resampling by moving
blocks. If this argument is given it should be a positive integer greater
than or equal to 2. The effect is that the output is composed by random
selection with replacement from among all the possible contiguous sequences
of length b in the input. (In the case of matrix input, this means
contiguous rows.) If the length of the data is not an integer multiple of
the block length, the last selected block is truncated to fit.

# round
Output:     same type as input
Argument:   x (scalar, series or matrix)

Rounds to the nearest integer. Note that when x lies halfway between two
integers, rounding is done "away from zero", so for example 2.5 rounds to 3,
but round(-3.5) gives -4. This is a common convention in spreadsheet
programs, but other software may yield different results. See also "ceil",
"floor", "int".

# rownames
Output:     integer
Arguments:  M (matrix)
            s (named list or string)

Attaches names to the rows of the m x n matrix M. If s is a named list, the
row names are copied from the names of the variables; the list must have m
members. If s is a string, it should contain m space-separated sub-strings.
The return value is 0 on successful completion, non-zero on error. See also
"colnames".

Example:

      matrix M = {1,2;2,1;4,1} 
      rownames(M, "Row1 Row2 Row3")
      print M      

# rows
Output:     integer
Argument:   X (matrix)

Returns the number of rows of the matrix X. See also "cols", "mshape",
"unvech", "vec", "vech".

# sd
Output:     scalar or series
Argument:   x (series or list)

If x is a series, returns the (scalar) sample standard deviation, skipping
any missing observations.

If x is a list, returns a series y such that y_t is the sample standard
deviation of the values of the variables in the list at observation t, or NA
if there are any missing values at t.

See also "var".

# sdc
Output:     row vector
Arguments:  X (matrix)
            df (scalar, optional)

Returns the standard deviations of the columns of X. If df is positive it is
used as the divisor for the column variances, otherwise the divisor is the
number of rows in X (that is, no degrees of freedom correction is applied).
See also "meanc", "sumc".

# sdiff
Output:     same type as input
Argument:   y (series or list)

Computes seasonal differences: y(t) - y(t-k), where k is the periodicity of
the current dataset (see "$pd"). Starting values are set to NA.

When a list is returned, the individual variables are automatically named
according to the template sd_varname where varname is the name of the
original series. The name is truncated if necessary, and may be adjusted in
case of non-uniqueness in the set of names thus constructed.

See also "diff", "ldiff".

# selifc
Output:     matrix
Arguments:  A (matrix)
            b (row vector)

Selects from A only the columns for which the corresponding element of b is
non-zero. b must be a row vector with the same number of columns as A.

See also "selifr".

# selifr
Output:     matrix
Arguments:  A (matrix)
            b (column vector)

Selects from A only the rows for which the corresponding element of b is
non-zero. b must be a column vector with the same number of rows as A.

See also "selifc", "trimr".

# seq
Output:     row vector
Arguments:  a (integer)
            b (integer)
            k (integer, optional)

Given only two arguments, returns a row vector filled with consecutive
integers, with a as first element and b last. If a is greater than b the
sequence will be decreasing. If either argument is not integral its
fractional part is discarded.

If the third argument is given, returns a row vector containing a sequence
of integers starting with a and incremented (or decremented, if a is greater
than b) by k at each step. The final value is the largest member of the
sequence that is less than or equal to b (or mutatis mutandis for a greater
than b). The argument k must be positive; if it is not integral its
fractional part is discarded.

See also "ones", "zeros".

# setnote
Output:     integer
Arguments:  b (bundle)
            key (string)
            note (string)

Sets a descriptive note for the object identified by key in the bundle b.
This note will be shown when the print command is used on the bundle. This
function returns 0 on success or non-zero on failure (for example, if there
is no object in b under the given key).

# simann
Output:     scalar
Arguments:  b (vector)
            f (function call)
            maxit (integer, optional)

Implements simulated annealing, which may be helpful in improving the
initialization for a numerical optimization problem.

The first argument holds the intial value of a parameter vector and the
second argument specifies a function call which returns the (scalar) value
of the maximand. The optional third argument specifies the maximum number of
iterations (which defaults to 1024). On successful completion, simann
returns the final value of the maximand.

For more details and an example see the chapter on numerical methods in the
Gretl User's Guide. See also "BFGSmax", "NRmax".

# sin
Output:     same type as input
Argument:   x (scalar, series or matrix)

Returns the sine of x. See also "cos", "tan", "atan".

# sinh
Output:     same type as input
Argument:   x (scalar, series or matrix)

Returns the hyperbolic sine of x.

See also "asinh", "cosh", "tanh".

# skewness
Output:     scalar
Argument:   x (series)

Returns the skewness value for the series x, skipping any missing
observations.

# sort
Output:     same type as input
Argument:   x (series or vector)

Sorts x in ascending order, skipping observations with missing values when x
is a series. See also "dsort", "values". For matrices specifically, see
"msortby".

# sortby
Output:     series
Arguments:  y1 (series)
            y2 (series)

Returns a series containing the elements of y2 sorted by increasing value of
the first argument, y1. See also "sort", "ranking".

# sqrt
Output:     same type as input
Argument:   x (scalar, series or matrix)

Returns the positive square root of x; produces NA for negative values.

Note that if the argument is a matrix the operation is performed element by
element and, since matrices cannot contain NA, negative values generate an
error. For the "matrix square root" see "cholesky".

# sscanf
Output:     integer
Arguments:  src (string)
            format (string)
            ... (see below)

Reads values from src under the control of format and assigns these values
to one or more trailing arguments, indicated by the dots above. Returns the
number of values assigned. This is a simplifed version of the sscanf
function in the C programming language.

src may be either a literal string, enclosed in double quotes, or the name
of a predefined string variable. format is defined similarly to the format
string in "printf" (more on this below). args should be a comma-separated
list containing the names of pre-defined variables: these are the targets of
conversion from src. (For those used to C: one can prefix the names of
numerical variables with & but this is not required.)

Literal text in format is matched against src. Conversion specifiers start
with %, and recognized conversions include %f, %g or %lf for floating-point
numbers; %d for integers; %s for strings; and %m for matrices. You may
insert a positive integer after the percent sign: this sets the maximum
number of characters to read for the given conversion (or the maximum number
of rows in the case of matrix conversion). Alternatively, you can insert a
literal * after the percent to suppress the conversion (thereby skipping any
characters that would otherwise have been converted for the given type). For
example, %3d converts the next 3 characters in source to an integer, if
possible; %*g skips as many characters in source as could be converted to a
single floating-point number.

Matrix conversion works thus: the scanner reads a line of input and counts
the (space- or tab-separated) number of numeric fields. This defines the
number of columns in the matrix. By default, reading then proceeds for as
many lines (rows) as contain the same number of numeric columns, but the
maximum number of rows to read can be limited as described above.

In addition to %s conversion for strings, a simplified version of the C
format %N[chars] is available. In this format N is the maximum number of
characters to read and chars is a set of acceptable characters, enclosed in
square brackets: reading stops if N is reached or if a character not in
chars is encountered. The function of chars can be reversed by giving a
circumflex, ^, as the first character; in that case reading stops if a
character in the given set is found. (Unlike C, the hyphen does not play a
special role in the chars set.)

If the source string does not (fully) match the format, the number of
conversions may fall short of the number of arguments given. This is not in
itself an error so far as gretl is concerned. However, you may wish to check
the number of conversions performed; this is given by the return value.

Some examples follow:

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

	  sprintf S, "1 2 3 4\n5 6 7 8"
	  S
	  matrix m
	  sscanf(S, "%m", m)
	  print m

# sst
Output:     scalar
Argument:   y (series)

Returns the sum of squared deviations from the mean for the non-missing
observations in series y. See also "var".

# strlen
Output:     integer
Argument:   s (string)

Returns the number of characters in the string s. Note that this does not
necessarily equal the number of bytes if some characters are outside of the
printable-ASCII range.

# strncmp
Output:     integer
Arguments:  s1 (string)
            s2 (string)
            n (integer, optional)

Compares the two string arguments and returns an integer less than, equal
to, or greater than zero if s1 is found, respectively, to be less than, to
match, or be greater than s2, up to the first n characters. If n is omitted
the comparison proceeds as far as possible.

Note that if you just want to compare two strings for equality, that can be
done without using a function, as in if (s1 == s2) ...

# strsplit
Output:     string
Arguments:  s (string)
            i (integer)

Returns space-separated element i from the string s. The index i is 1-based,
and it is an error if i is less than 1. In case s contains no spaces and i
equals 1, a copy of the entire input string is returned; otherwise, in case
i exceeds the number of space-separated elements an empty string is
returned.

# strstr
Output:     string
Arguments:  s1 (string)
            s2 (string)

Searches s1 for an occurrence of the string s2. If a match is found, returns
a copy of the portion of s1 that starts with s2, otherwise returns an empty
string.

# strstrip
Output:     string
Argument:   s (string)

Returns a copy of the argument s from which leading and trailing white space
have been removed.

# strsub
Output:     string
Arguments:  s (string)
            find (string)
            subst (string)

Returns a copy of s in which all occurrences of find are replaced by subst.
See also "regsub" for more complex string replacement via regular
expressions.

# substr
Output:     string
Arguments:  s (string)
            start (integer)
            end (integer)

Returns a substring of s, from the character with (1-based) index start to
that with index end, inclusive.

# sum
Output:     scalar or series
Argument:   x (series, matrix or list)

If x is a series, returns the (scalar) sum of the non-missing observations
in x. See also "sumall".

If x is a matrix, returns the sum of the elements of the matrix.

If x is a list, returns a series y such that y_t is the sum of the values of
the variables in the list at observation t, or NA if there are any missing
values at t.

# sumall
Output:     scalar
Argument:   x (series)

Returns the sum of the observations of x over the current sample range, or
NA if there are any missing values.

# sumc
Output:     row vector
Argument:   X (matrix)

Returns the sums of the columns of X. See also "meanc", "sumr".

# sumr
Output:     column vector
Argument:   X (matrix)

Returns the sums of the rows of X. See also "meanr", "sumc".

# svd
Output:     row vector
Arguments:  X (matrix)
            &U (reference to matrix, or null)
            &V (reference to matrix, or null)

Performs the singular values decomposition of the matrix X.

The singular values are returned in a row vector. The left and/or right
singular vectors U and V may be obtained by supplying non-null values for
arguments 2 and 3, respectively. For any matrix A, the code

	  s = svd(A, &U, &V) 
	  B = (U .* s) * V

should yield B identical to A (apart from machine precision).

See also "eigengen", "eigensym", "qrdecomp".

# tan
Output:     same type as input
Argument:   x (scalar, series or matrix)

Returns the tangent of x.

# tanh
Output:     same type as input
Argument:   x (scalar, series or matrix)

Returns the hyperbolic tangent of x.

See also "atanh", "cosh", "sinh".

# toepsolv
Output:     column vector
Arguments:  c (vector)
            r (vector)
            b (vector)

Solves a Toeplitz system of linear equations, that is Tx = b where T is a
square matrix whose element T_i,j equals c_i-j for i>=j and r_j-i for i<=j.
Note that the first elements of c and r must be equal, otherwise an error is
returned. Upon successful completion, the function returns the vector x.

The algorithm used here takes advantage of the special structure of the
matrix T, which makes it much more efficient than other unspecialized
algorithms, especially for large problems. Warning: in certain cases, the
function may spuriously issue a singularity error when in fact the matrix T
is nonsingular; this problem, however, cannot arise when T is positive
definite.

# tolower
Output:     string
Argument:   s (string)

Returns a copy of s in which any upper-case characters are converted to
lower case.

# toupper
Output:     string
Argument:   s (string)

Returns a copy of s in which any lower-case characters are converted to
upper case.

# tr
Output:     scalar
Argument:   A (square matrix)

Returns the trace of the square matrix A, that is, the sum of its diagonal
elements. See also "diag".

# transp
Output:     matrix
Argument:   X (matrix)

Returns the transpose of X. Note: this is rarely used; in order to get the
transpose of a matrix, in most cases you can just use the prime operator:
X'.

# trimr
Output:     matrix
Arguments:  X (matrix)
            ttop (integer)
            tbot (integer)

Returns a matrix that is a copy of X with ttop rows trimmed at the top and
tbot rows trimmed at the bottom. The latter two arguments must be
non-negative, and must sum to less than the total rows of X.

See also "selifr".

# typestr
Output:     string
Argument:   typecode (integer)

Returns the name of the gretl data-type corresponding to typecode. This is
intended for use in conjunction with the function "inbundle". The value
returned is one of "scalar", "series", "matrix", "string", "bundle" or
"null".

# uniform
Output:     series
Arguments:  a (scalar)
            b (scalar)

Generates a series of uniform pseudo-random variates in the interval (a, b),
or, if no arguments are supplied, in the interval (0,1). The algorithm used
by default is the SIMD-oriented Fast Mersenne Twister developed by Saito and
Matsumoto (2008).

See also "randgen", "normal", "mnormal", "muniform".

# uniq
Output:     column vector
Argument:   x (series or vector)

Returns a vector containing the distinct elements of x, not sorted but in
their order of appearance. See "values" for a variant that sorts the
elements.

# unvech
Output:     square matrix
Argument:   v (vector)

Returns an n x n symmetric matrix obtained by rearranging the elements of v.
The number of elements in v must be a triangular integer -- i.e., a number k
such that an integer n exists with the property k = n(n+1)/2. This is the
inverse of the function "vech".

See also "mshape", "vech".

# upper
Output:     square matrix
Argument:   A (square matrix)

Returns an n x n upper triangular matrix: the elements on and above the
diagonal are equal to the corresponding elements of A; the remaining
elements are zero.

See also "lower".

# urcpval
Output:     scalar
Arguments:  tau (scalar)
            n (integer)
            niv (integer)
            itv (integer)

P-values for the test statistic from the Dickey-Fuller unit-root test and
the Engle-Granger cointegration test, as per James MacKinnon (1996).

The arguments are as follows: tau denotes the test statistic; n is the
number of observations (or 0 for an asymptotic result); niv is the number of
potentially cointegrated variables when testing for cointegration (or 1 for
a univariate unit-root test); and itv is a code for the model specification:
1 for no constant, 2 for constant included, 3 for constant and linear trend,
4 for constant and quadratic trend.

Note that if the test regression is "augmented" with lags of the dependent
variable, then you should give an n value of 0 to get an asymptotic result.

See also "pvalue".

# values
Output:     column vector
Argument:   x (series or vector)

Returns a vector containing the distinct elements of x sorted in ascending
order. If you wish to truncate the values to integers before applying this
function, use the expression values(int(x)).

See also "uniq", "dsort", "sort".

# var
Output:     scalar or series
Argument:   x (series or list)

If x is a series, returns the (scalar) sample variance, skipping any missing
observations.

If x is a list, returns a series y such that y_t is the sample variance of
the values of the variables in the list at observation t, or NA if there are
any missing values at t.

In each case the sum of squared deviations from the mean is divided by (n -
1) for n > 1. Otherwise the variance is given as zero if n = 1, or as NA if
n = 0.

See also "sd".

# varname
Output:     string
Argument:   v (integer or list)

If given an integer argument, returns the name of the variable with ID
number v, or generates an error if there is no such variable.

If given a list argument, returns a string containing the names of the
variables in the list, separated by commas. If the supplied list is empty,
so is the returned string.

# varnum
Output:     integer
Argument:   varname (string)

Returns the ID number of the variable called varname, or NA is there is no
such variable.

# varsimul
Output:     matrix
Arguments:  A (matrix)
            U (matrix)
            y0 (matrix)

Simulates a p-order n-variable VAR, that is y(t) = A1 y(t-1) + ... + Ap
y(t-p) + u(t). The coefficient matrix A is composed by horizontal stacking
of the A_i matrices; it is n x np, with one row per equation. This
corresponds to the first n rows of the matrix $compan provided by gretl's
var and vecm commands.

The u_t vectors are contained (as rows) in U (T x n). Initial values are in
y0 (p x n).

If the VAR contains deterministic terms and/or exogenous regressors, these
can be handled by folding them into the U matrix: each row of U then becomes
u(t) = B' x(t) + e(t).

The output matrix has T + p rows and n columns; it holds the initial p
values of the endogenous variables plus T simulated values.

See also "$compan", "var", "vecm".

# vec
Output:     column vector
Argument:   X (matrix)

Stacks the columns of X as a column vector. See also "mshape", "unvech",
"vech".

# vech
Output:     column vector
Argument:   A (square matrix)

Returns in a column vector the elements of A on and above the diagonal.
Typically, this function is used on symmetric matrices; in this case, it can
be undone by the function "unvech". See also "vec".

# weekday
Output:     integer
Arguments:  year (integer)
            month (integer)
            day (integer)

Returns the day of the week (Sunday = 0, Monday = 1, etc.) for the date
specified by the three arguments, or NA if the date is invalid.

# wmean
Output:     series
Arguments:  Y (list)
            W (list)

Returns a series y such that y_t is the weighted mean of the values of the
variables in list Y at observation t, the respective weights given by the
values of the variables in list W at t. The weights can therefore be
time-varying. The lists Y and W must be of the same length and the weights
must be non-negative.

See also "wsd", "wvar".

# wsd
Output:     series
Arguments:  Y (list)
            W (list)

Returns a series y such that y_t is the weighted sample standard deviation
of the values of the variables in list Y at observation t, the respective
weights given by the values of the variables in list W at t. The weights can
therefore be time-varying. The lists Y and W must be of the same length and
the weights must be non-negative.

See also "wmean", "wvar".

# wvar
Output:     series
Arguments:  X (list)
            W (list)

Returns a series y such that y_t is the weighted sample variance of the
values of the variables in list X at observation t, the respective weights
given by the values of the variables in list W at t. The weights can
therefore be time-varying. The lists Y and W must be of the same length and
the weights must be non-negative.

See also "wmean", "wsd".

# xmax
Output:     scalar
Arguments:  x (scalar)
            y (scalar)

Returns the greater of x and y, or NA if either value is missing.

See also "xmin", "max", "min".

# xmin
Output:     scalar
Arguments:  x (scalar)
            y (scalar)

Returns the lesser of x and y, or NA if either value is missing.

See also "xmax", "max", "min".

# xpx
Output:     list
Argument:   L (list)

Returns a list that references the squares and cross-products of the
variables in list L. Squares are named on the pattern sq_varname and
cross-products on the pattern var1_var2. The input variable names are
truncated if need be, and the output names may be adjusted in case of
duplication of names in the returned list.

# zeromiss
Output:     same type as input
Argument:   x (scalar or series)

Converts zeros to NAs. If x is a series, the conversion is done element by
element. See also "missing", "misszero", "ok".

# zeros
Output:     matrix
Arguments:  r (integer)
            c (integer)

Outputs a zero matrix with r rows and c columns. See also "ones", "seq".