gretl-common 1.9.6-1build1 / usr / share / gretl / genrcli.hlp

## Accessors
# $ahat
Output:     series

Must follow the estimation of a fixed-effect panel data model. Returns a
series containing the estimates of the individual fixed effects (per-unit
intercepts).

# $aic
Output:     scalar

Returns the Akaike Information Criterion for the last estimated model, if
available. See the Gretl User's Guide for details of the calculation.

# $bic
Output:     scalar

Returns Schwarz's Bayesian Information Criterion for the last estimated
model, if available. See the Gretl User's Guide for details of the
calculation.

# $chisq
Output:     scalar

Returns the overall chi-square statistic from the last estimated model, if
available.

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

With no arguments, $coeff returns a column vector containing the estimated
coefficients for the last model. With the optional string argument it
returns a scalar, namely the estimated parameter named s. See also
"$stderr", "$vcv".

Example:

	  open bjg
	  arima 0 1 1 ; 0 1 1 ; lg 
	  b = $coeff               # gets a vector
	  macoef = $coeff(theta_1) # gets a scalar

If the "model" in question is actually a system, the result depends on the
characteristics of the system: for VARs and VECMs the value returned is a
matrix with one column per equation, otherwise it is a column vector
containing the coefficients from the first equation followed by those from
the second equation, and so on.

# $command
Output:     string

Must follow the estimation of a model; returns the command word, for example
ols or probit.

# $compan
Output:     matrix

Must follow the estimation of a VAR or a VECM; returns the companion matrix.

# $datatype
Output:     scalar

Returns an integer value representing the sort of dataset that is currently
loaded: 0 = no data; 1 = cross-sectional (undated) data; 2 = time-series
data; 3 = panel data.

# $depvar
Output:     string

Must follow the estimation of a single-equation model; returns the name of
the dependent variable.

# $df
Output:     scalar

Returns the degrees of freedom of the last estimated model. If the last
model was in fact a system of equations, the value returned is the degrees
of freedom per equation; if this differs across the equations then the value
given is the number of observations minus the mean number of coefficients
per equation (rounded up to the nearest integer).

# $dwpval
Output:     scalar

Returns the p-value for the Durbin-Watson statistic for the model last
estimated, if available. This is computed using the Imhof procedure.

# $ec
Output:     matrix

Must follow the estimation of a VECM; returns a matrix containing the error
correction terms. The number of rows equals the number of observations used
and the number of columns equals the cointegration rank of the system.

# $error
Output:     scalar

Returns the program's internal error code, which will be non-zero in case an
error has occurred but has been trapped using "catch". Note that using this
accessor causes the internal error code to be reset to zero. See also
"errmsg". If you want to get the error message associated with a given
$error you need to store the value in a temporary variable, as in

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

# $ess
Output:     scalar

Returns the error sum of squares of the last estimated model, if available.

# $evals
Output:     matrix

Must follow the estimation of a VECM; returns a vector containing the
eigenvalues that are used in computing the trace test for cointegration.

# $fcast
Output:     matrix

Must follow the "fcast" forecasting command; returns the forecast values as
a matrix. If the model on which the forecast was based is a system of
equations the returned matrix will have one column per equation, otherwise
it is a column vector.

# $fcerr
Output:     matrix

Must follow the "fcast" forecasting command; returns the standard errors of
the forecasts, if available, as a matrix. If the model on which the forecast
was based is a system of equations the returned matrix will have one column
per equation, otherwise it is a column vector.

# $fevd
Output:     matrix

Must follow estimation of a VAR. Returns a matrix containing the forecast
error decomposition. This matrix has h rows where h is the forecast horizon,
which can be chosen using set horizon or otherwise is set automatically
based on the frequency of the data. For a VAR with p variables, the matrix
has p^2 columns. The fraction of the forecast error for variable i
attributable to innovation in variable j is found in column (i - 1)p + j.

# $Fstat
Output:     scalar

Returns the overall F-statistic from the last estimated model, if available.

# $gmmcrit
Output:     scalar

Must follow a gmm block. Returns the value of the objective function at its
minimum.

# $h
Output:     series

Must follow a garch command. Returns the estimated conditional variance
series.

# $hausman
Output:     row vector

Must follow estimation of a model via either tsls or panel with the random
effects option. Returns a 1 x 3 vector containing the value of the Hausman
test statistic, the corresponding degrees of freedom and the p-value for the
test, in that order.

# $hqc
Output:     scalar

Returns the Hannan-Quinn Information Criterion for the last estimated model,
if available. See the Gretl User's Guide for details of the calculation.

# $jalpha
Output:     matrix

Must follow the estimation of a VECM, and returns the loadings matrix. It
has as many rows as variables in the VECM and as many columns as the
cointegration rank.

# $jbeta
Output:     matrix

Must follow the estimation of a VECM, and returns the cointegration matrix.
It has as many rows as variables in the VECM (plus the number of exogenous
variables that are restricted to the cointegration space, if any), and as
many columns as the cointegration rank.

# $jvbeta
Output:     square matrix

Must follow the estimation of a VECM, and returns the estimated covariance
matrix for the elements of the cointegration vectors.

In the case of unrestricted estimation, this matrix has a number of rows
equal to the unrestricted elements of the cointegration space after the
Phillips normalization. If, however, a restricted system is estimated via
the restrict command with the --full option, a singular matrix with (n+m)r
rows will be returned (n being the number of endogenous variables, m the
number of exogenous variables that are restricted to the cointegration
space, and r the cointegration rank).

Example: the code

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

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

	  print s0
	  print s1

produces the following output.

	  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

For selected models estimated via Maximum Likelihood, returns the series of
per-observation log-likelihood values. At present this is supported only for
binary logit and probit, tobit and heckit.

# $lnl
Output:     scalar

Returns the log-likelihood for the last estimated model (where applicable).

# $mnlprobs
Output:     matrix

Following estimation of a multinomial logit model (only), retrieves a matrix
holding the estimated probabilities of each possible outcome at each
observation in the model's sample range. Each row represents an observation
and each column an outcome.

# $ncoeff
Output:     scalar

Returns the total number of coefficients estimated in the last model.

# $nobs
Output:     scalar

Returns the number of observations in the currently selected sample.

# $nvars
Output:     scalar

Returns the number of variables in the dataset (including the constant).

# $pd
Output:     scalar

Returns the frequency or periodicity of the data (e.g. 4 for quarterly
data). In the case of panel data the value returned is the time-series
length.

# $pvalue
Output:     scalar or matrix

Returns the p-value of the test statistic that was generated by the last
explicit hypothesis-testing command, if any (e.g. chow). See the Gretl
User's Guide for details.

In most cases the return value is a scalar but sometimes it is a matrix (for
example, the trace and lambda-max p-values from the Johansen cointegration
test); in that case the values in the matrix are laid out in the same
pattern as the printed results.

See also "$test".

# $rho
Output:     scalar
Argument:   n (scalar, optional)

Without arguments, returns the first-order autoregressive coefficient for
the residuals of the last model. After estimating a model via the ar
command, the syntax $rho(n) returns the corresponding estimate of rho(n).

# $rsq
Output:     scalar

Returns the unadjusted R^2 from the last estimated model, if available.

# $sample
Output:     series

Must follow estimation of a single-equation model. Returns a dummy series
with value 1 for observations used in estimation, 0 for observations within
the currently defined sample range but not used (presumably because of
missing values), and NA for observations outside of the current range.

If you wish to compute statistics based on the sample that was used for a
given model, you can do, for example:

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

# $sargan
Output:     row vector

Must follow a tsls command. Returns a 1 x 3 vector, containing the value of
the Sargan over-identification test statistic, the corresponding degrees of
freedom and p-value, in that order.

# $sigma
Output:     scalar or matrix

Requires that a model has been estimated. If the last model was a single
equation, returns the (scalar) Standard Error of the Regression (or in other
words, the standard deviation of the residuals, with an appropriate degrees
of freedom correction). If the last model was a system of equations, returns
the cross-equation covariance matrix of the residuals.

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

With no arguments, $stderr returns a column vector containing the standard
error of the coefficients for the last model. With the optional string
argument it returns a scalar, namely the standard error of the parameter
named s.

If the "model" in question is actually a system, the result depends on the
characteristics of the system: for VARs and VECMs the value returned is a
matrix with one column per equation, otherwise it is a column vector
containing the coefficients from the first equation followed by those from
the second equation, and so on.

See also "$coeff", "$vcv".

# $stopwatch
Output:     scalar

Must be preceded by set stopwatch, which activates the measurement of CPU
time. The first use of this accessor yields the seconds of CPU time that
have elapsed since the set stopwatch command. At each access the clock is
reset, so subsequent uses of $stopwatch yield the seconds of CPU time since
the previous access.

# $sysA
Output:     matrix

Must follow estimation of a simultaneous equations system. Returns the
matrix of coefficients on the lagged endogenous variables, if any, in the
structural form of the system. See the "system" command.

# $sysB
Output:     matrix

Must follow estimation of a simultaneous equations system. Returns the
matrix of coefficients on the exogenous variables in the structural form of
the system. See the "system" command.

# $sysGamma
Output:     matrix

Must follow estimation of a simultaneous equations system. Returns the
matrix of coefficients on the contemporaneous endogenous variables in the
structural form of the system. See the "system" command.

# $T
Output:     scalar

Returns the number of observations used in estimating the last model.

# $t1
Output:     scalar

Returns the 1-based index of the first observation in the currently selected
sample.

# $t2
Output:     scalar

Returns the 1-based index of the last observation in the currently selected
sample.

# $test
Output:     scalar or matrix

Returns the value of the test statistic that was generated by the last
explicit hypothesis-testing command, if any (e.g. chow). See the Gretl
User's Guide for details.

In most cases the return value is a scalar but sometimes it is a matrix (for
example, the trace and lambda-max statistics from the Johansen cointegration
test); in that case the values in the matrix are laid out in the same
pattern as the printed results.

See also "dpvalue".

# $trsq
Output:     scalar

Returns TR^2 (sample size times R-squared) from the last model, if
available.

# $uhat
Output:     series

Returns the residuals from the last model. This may have different meanings
for different estimators. For example, after an ARMA estimation $uhat will
contain the one-step-ahead forecast error; after a probit model, it will
contain the generalized residuals.

If the "model" in question is actually a system (a VAR or VECM, or system of
simultaneous equations), $uhat with no parameters retrieves the matrix of
residuals, one column per equation.

# $unit
Output:     series

Valid for panel datasets only. Returns a series with value 1 for all
observations on the first unit or group, 2 for observations on the second
unit, and so on.

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

With no arguments, $vcv returns a square matrix containing the estimated
covariance matrix for the coefficients of the last model. If the last model
was a single equation, then you may supply the names of two parameters in
parentheses to retrieve the estimated covariance between the parameters
named s1 and s2. See also "$coeff", "$stderr".

This accessor is not available for VARs or VECMs; for models of that sort
see "$sigma" and "$xtxinv".

# $vecGamma
Output:     matrix

Must follow the estimation of a VECM; returns a matrix in which the Gamma
matrices (coefficients on the lagged differences of the cointegrated
variables) are stacked side by side. Each row represents an equation; for a
VECM of lag order p there are p - 1 sub-matrices.

# $version
Output:     scalar

Returns an integer value that codes for the program version. The gretl
version string takes the form x.y.z (for example, 1.7.6). The return value
from this accessor is formed as 10000*x + 100*y + z, so that 1.7.6
translates as 10706.

# $vma
Output:     matrix

Must follow the estimation of a VAR or a VECM; returns a matrix containing
the VMA representation up to the order specified via the set horizon
command. See the Gretl User's Guide for details.

# $windows
Output:     scalar

Returns 1 if gretl is running on MS Windows, otherwise 0. By conditioning on
the value of this variable you can write shell calls that are portable
across different operating systems.

Also see the "shell" command.

# $xlist
Output:     list

Returns the list of regressors from the last model (for single-equation
models only).

# $xtxinv
Output:     matrix

Following estimation of a VAR or VECM (only), returns X'X^-1, where X is the
common matrix of regressors used in each of the equations. This accessor is
not available for a VECM estimated with a restriction imposed on α, the
"loadings" matrix.

# $yhat
Output:     series

Returns the fitted values from the last regression.

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

Returns the absolute value of x.

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

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

# 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".

# 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 special functions in genr
in the Gretl User's Guide. See also "NRmax", "fdjac".

# bkfilt
Output:     series
Arguments:  y (series)
            f1 (scalar, optional)
            f2 (scalar, optional)
            k (scalar, 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
"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 (scalar)
            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 (symmetric 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 (scalar)
            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 (scalar)

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".

# cols
Output:     scalar
Argument:   X (matrix)

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 (scalar)
            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. 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 marix, 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 block-diagonal matrix holding A
in its north-west corner and B in its south-east corner.

# 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.

# 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", "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).

# 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. 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
Arguments:  year (scalar)
            month (scalar)
            day (scalar)

Returns the number of the day in the current epoch specified by year, month
and day (which equals 1 for the first of January in the year 1 AD).

# errmsg
Output:     string
Argument:   errno (scalar)

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)
            f (function call)

Calculates the (forward-difference approximation to the) Jacobian associated
with the vector b and the transformation function specified by the argument
f. For more details and examples see the chapter on special functions in
genr in the Gretl User's Guide.

See also "BFGSmax".

# 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)
            a (scalar or vector, optional)
            b (scalar or vector, optional)
            y0 (scalar, optional)

Computes an ARMA-like filtering of the series 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

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", "fracdiff", "hpfilt", "movavg".

Example:

	  nulldata 5
	  y = filter(index, 0.5, -0.9, 1)
	  print index y --byobs

produces

                   index            y   

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

# firstobs
Output:     scalar
Argument:   y (series)

First non-missing observation for the variable 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".

# 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".

# 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".

# 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".

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

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:     scalar
Arguments:  b (bundle)
            key (string)

Returns 1 if bundle b contains a data-item with name key, otherwise 0.

# 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:     scalar
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 (symmetric 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 (scalar)
            shock (scalar)
            alpha (scalar between 0 and 1, optional)

This function is available only when the last model estimated was a VAR. 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:     scalar
Arguments:  y (series or vector)
            panel-code (scalar, 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.

# islist
Output:     scalar
Argument:   s (string)

Returns 1 if s is the identifier for a currently defined list, otherwise 0.
See also "isnull", "isseries", "isstring".

# isnull
Output:     scalar
Argument:   s (string)

Returns 0 if s is the identifier for a currently defined object, be it a
scalar, a series, a matrix, list or string; otherwise returns 1. See also
"islist", "isseries", "isstring".

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

# 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.

# isseries
Output:     scalar
Argument:   s (string)

Returns 1 if s is the identifier for a currently defined series, otherwise
0. See also "islist", "isnull", "isstring".

# isstring
Output:     scalar
Argument:   s (string)

Returns 1 if s is the identifier for a currently defined string, otherwise
0. See also "islist", "isnull", "isseries".

# lags
Output:     list
Arguments:  p (scalar)
            y (series or list)

Generates lags 1 to p of the series y, or if y is a list, of all variables
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.

# lastobs
Output:     scalar
Argument:   y (series)

Last non-missing observation for the variable 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 (scalar)

Computes the Ljung-Box Q' statistic for the series y using lag order p. The
currently defined sample range is used. 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 serially
independent. 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.

# 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 (scalar)

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 (scalar)

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 scalar 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 (scalar)
            c (scalar)

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:     scalar
Arguments:  month (scalar)
            year (scalar)
            weeklen (scalar)

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 (scalar, 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 (assuming this is available).

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:  c (character)
            a (scalar)
            b (scalar)
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 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 the t distribution with 14 degrees of freedom.

See also "mnormal", "muniform".

# mread
Output:     matrix
Argument:   s (string)

Reads a matrix from a text file. The string s must contain the name of the
(plain text) file from which the matrix is to be read. The file in question
must conform to the following rules:

  The columns must be separated by spaces or tab characters.

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

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

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 (scalar)
            c (scalar)

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 (scalar)

Returns a matrix in which the rows of X are reordered by increasing value of
the elements in column j.

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

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 recasting the output of muniform to a scalar, as in

	  scalar x = muniform(1,1)

See also "mnormal", "uniform".

# mwrite
Output:     scalar
Arguments:  X (matrix)
            s (string)

Writes the matrix X to a plain text file named s. 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 s 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.

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

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".

# nelem
Output:     scalar
Argument:   L (list)

Returns the number of members in 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:     scalar
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. 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 special functions in genr
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 (scalar)

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

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

Returns a binary variable holding 1 if x is not 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 0 at observations for which at least one series in the list
has a missing value, and 1 otherwise.

See also "missing", "misszero", "zeromiss".

# 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 (scalar)
            c (scalar)

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
the per-unit maximum for variable y.

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".

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

Only applicable if the currently open dataset has a panel structure.
Computes the per-unit mean for variable y; that is, the sum of the valid
observations for each unit divided by the number of valid observations for
each unit.

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", "pshrink".

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

Only applicable if the currently open dataset has a panel structure. Returns
the per-unit mimimum for variable y.

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".

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

Only applicable if the currently open dataset has a panel structure. Returns
for each unit the number of non-missing cases for the variable y.

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".

# 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 (scalar)

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 (scalar)

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 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 matrix of the X_is, with the
eigenvectors ordered by decreasing value of the corresponding eigenvalues.

See also "eigensym".

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

Only applicable if the currently open dataset has a panel structure.
Computes the per-unit sample standard deviation for variable y. 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".

# 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 unit or individual 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 information provided by
functions such as "pmean".

# 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".

# 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".

# 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:  c (character)
            a (scalar or series)
            b (scalar or series)
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 parameter c is a character, which
specifies from which distribution the pseudo-random numbers should be drawn.
The arguments a and (in some cases) b provide the parameters of the selected
distribution. If these are given as scalars the output series is identically
distributed; if a series is given for a or b the distribution is conditional
on the parameter value at each observation.

Specifics are given below: the character codes for each distribution are
shown in parentheses, followed by the interpretation of the argument a and,
where applicable, b.

  Uniform (continuous) (c = u or U): minimum; maximum

  Uniform (discrete) (c = i): minimum; maximum

  Standard normal (c = 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

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

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

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

# rank
Output:     scalar
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
Argument:   fname (string)

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.

Also see the "sscanf" function.

# 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 (scalar, 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:     scalar
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".

# rows
Output:     scalar
Argument:   X (matrix)

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 (scalar)
            b (scalar)
            k (scalar, 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".

# 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:     scalar
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:     scalar
Argument:   s (string)

Returns the number of characters in s.

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

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.

# 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.

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

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

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.

# 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.

# 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 (scalar)
            tbot (scalar)

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".

# 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 (scalar)
            niv (scalar)
            itv (scalar)

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 (scalar or list)

If given a scalar 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:     scalar
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:     scalar
Arguments:  year (scalar)
            month (scalar)
            day (scalar)

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 (scalar)
            c (scalar)

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