The directive CALCULATE
allows arithmetic calculations on the values of any numeric data structure; logical tests can also be done on numerical and textual values. Functions and operators are available for a very wide range of calculations on matrices and tables. Another general directive is EQUATE
, which allows values to be copied from one set of data structures to another; the structures must store values of the same mode (for example, numbers or text), but need not be of the same type.
Structure values can be deleted to save space within Genstat; attributes can also be deleted so that the structure can be redefined, for example as another type. Contents of data structures can be compared, to see if they contain the same distinct items, or whether the distinct values in one structure are a subset of those in another. You can also find all the locations where a number, identifier or string occurs within a data structure.
CALCULATE 
performs arithmetic and logical calculations 

DELETE 
allows values and attributes of data structures to be deleted 
EQUATE 
copies values between sets of data structures 
SETRELATE 
compares the sets of values in two data structures 
GETLOCATIONS 
finds locations of an identifier within a pointer, or a string within a factor or text, or a number within any numerical data structure 
There are several general directives for manipulating vectors (variates, factors or texts). Units of vectors can be sorted into systematic order or into random order. Boolean arithmetic can be performed on their contents, or you can form all the ways of partitioning them into subsets. A “restriction” can be associated with a vector, so that subsequent statements operate on only a subset of its units. A default length and labelling can be defined for vectors formed later in the job. Facilities for specific types of vector allow interpolation of values for variates, monotonic regression, calculation of regression quantiles, generation of factor values, and concatenation, editing and searching of text.
SORT 
sorts units of vectors into alphabetic or numerical order of an index vector, or forms a factor from a variate or text 

SETCALCULATE 
performs Boolean set calculations on the contents of vectors and pointers 
SETALLOCATIONS 
runs through all ways of allocating a set of objects to subsets 
RESTRICT 
defines a “restriction” on the units of a vector 
UNITS 
defines default length or labelling for vectors defined subsequently in the job 
INTERPOLATE 
calculates variates of interpolated values 
FRQUANTILES 
forms regression quantiles 
MONOTONIC 
fits an increasing monotonic regression 
GROUPS 
forms a factor (or grouping variable) from a variate or text, together with the set of distinct values that occur 
CONCATENATE 
concatenates together lines of text vectors 
EDIT 
line editor for units of text vectors 
TXBREAK 
breaks a text structure into individual words 
TXCONSTRUCT 
forms a text structure by appending or concatenating values of scalars, variates, texts, factors or pointers; allows the case of letters to be changed or values to truncated and reversed 
TXFIND 
finds a subtext within a text structure 
TXINTEGERCODES 
converts textual characters to and from their corresponding integer codes 
TXPOSITION 
locates strings within the lines of a text structure 
TXREPLACE 
replaces a subtext within a text structure 
Another general directive allows you to run many algorithms from the Numerical Algorithms Group Library, for example to build mathematical models.
NAG 
calls an algorithm from the NAG Library 

Other facilities for vectors are provided by the procedures in the Genstat Procedure Library, including:
APPEND 
appends a list of vectors of the same type 

FACAMEND 
permutes the levels and labels of a factor 
FACCOMBINATIONS 
forms a factor to indicate observations with identical values of a set of variates, texts or factors 
FACDIVIDE 
represents a factor by factorial combinations of a set of factors 
FACEXCLUDEUNUSED 
redefines the levels and labels of a factor to exclude those that are unused 
FACMERGE 
merges levels of factors 
FACPRODUCT 
forms a factor with a level for every combination of other factors 
FACSORT 
sorts the levels of a factor according to an index vector 
FACLEVSTANDARDIZE 
redefines a list of factors so that they have the same levels or labels 
FACUNIQUE 
redefines a factor so that its levels and labels are unique 
FBETWEENGROUPVECTORS 
forms variates and classifying factors containing withingroup summaries to use e.g. in a betweengroup analysis 
FDISTINCTFACTORS 
checks sets of factors to remove any that define duplicate classifications 
FMFACTORS 
forms a pointer of factors representing a multipleresponse 
FFREERESPONSEFACTOR 
forms multipleresponse factors from freeresponse data 
FREGULAR 
expands vectors onto a regular twodimensional grid 
FRESTRICTEDSET 
forms vectors with the restricted subset of a list of vectors 
FROWCANONICALMATRIX 
puts a matrix into row canonical, or reduced row echelon, form 
FSTRING 
forms a single string from a list of strings in a text 
FTEXT 
forms a text structure from a variate 
FUNIQUEVALUES 
redefines a variate or text so that its values are unique 
FVSTRING 
forms a string listing the identifiers of a set of data structures 
GRANDOM 
generates pseudorandom numbers from probability distributions 
GRMNOMIAL 
generates multinomial pseudorandom numbers

GRMULTINORMAL 
generates multivariate normal pseudorandom numbers 
JOIN 
joins or merges two sets of vectors together, based on classifying keys 
MVFILL 
replaces missing values in a vector with the previous nonmissing value 
ORTHPOLYNOMIAL 
calculates orthogonal polynomials 
QUANTILE 
calculates quantiles of the values in a variate 
RANK 
produces ranks, from the values in a variate, allowing for ties 
SAMPLE 
samples from a set of units, possibly stratified by factors 
SVSAMPLE 
constructs stratified random samples 
STACK 
combines several data sets by “stacking” the corresponding vectors 
STANDARDIZE 
standardizes columns of a data matrix to have mean 0 and variance 1 
SUBSET 
forms vectors containing subsets of the values in other vectors 
TXPAD 
pads strings of a text structure with extra characters so that their lengths are equal 
TXPROGRESSION 
forms a text containing a progression of strings 
TXSPLIT 
splits a text into individual texts, at positions on each line marked by separator character(s) 
UNSTACK 
splits vectors into individual vectors according to levels of a factor 
VEQUATE 
equates values across a set of data structures 
VINTERPOLATE 
performs linear and inverse linear interpolation between variates 
There are several procedures for calculating or fitting splines, and for manipulating series of observations of a theoretical curve.
SPLINE 
calculates a set of basis functions for M, B or Isplines 

LSPLINE 
calculates design matrices to fit a natural polynomial or trignometric Lspline as a linear mixed model 
NCSPLINE 
calculates natural cubic spline basis functions (for use e.g. in REML ) 
PENSPLINE 
calculates design matrices to fit a penalized spline as a linear mixed model 
PSPLINE 
calculates design matrices to fit a Pspline as a linear mixed model 
RADIALSPLINE 
calculates design matrices to fit a radialspline surface as a linear mixed model 
TENSORSPLINE 
calculates design matrices to fit a tensorspline surface as a linear mixed model 
ALIGNCURVE 
forms an optimal warping to align an observed series of observations with a standard series 
BASELINE 
estimates a baseline for a series of numbers whose minimum value is drifting 
PEAKFINDER 
finds the locations of peaks in an observed series 
Directives are available for eigenvalue, QR and singularvalue decompositions of matrices, and to form the values of SSPM structures.
FLRV 
calculates latent roots and vectors (that is, eigenvalues and eigenvectors) 

QRD 
calculates QR decompositions of matrices 
SVD 
calculates singularvalue decompositions of matrices 
FSSPM 
calculates values for SSPM structures (sums of squares and products, means, etc.) 
Procedures in the Library for operating on matrices include:
FCORRELATION 
forms the correlation matrix for a list of variates 

PARTIALCORRELATIONS 
calculates partial correlations for a list of variates 
FHADAMARDMATRIX 
forms Hadamard matrices 
FPROJECTIONMATRIX 
forms a projection matrix for a set of model terms 
FRTPRODUCTDESIGNMATRIX 
forms summation, or relationship, matrices for model terms 
FVCOVARIANCE 
forms the variancecovariance matrix for a list of variates 
GINVERSE 
calculates the generalized inverse of a matrix 
LINDEPENDENCE 
finds the linear relations associated with matrix singularities 
MPOWER 
forms integer powers of a square matrix 
POSSEMIDEFINITE 
calculates a positive semidefinite approximation of a nonpositive semidefinite symmetric matrix 
VMATRIX 
copies values and row/column labels from a matrix to variates and texts 
Tables can be formed containing summaries of values in variates: totals, minimum and maximum values, quantiles, numbers of missing and nonmissing values, means and variances. Manipulations of multiway structures include the ability to add various types of marginal summaries to tables, and to combine “slices” of tables, of matrices or of variates.
TABULATE 
forms tables of summaries of the values of a variate 

MARGIN 
calculates or deletes margins of tables 
COMBINE 
combines or omits “slices” of tables, matrices or variates 
Procedures in the Library for operating on tables include:
BACKTRANSFORM 
calculates backtransformed means with approximate standard errors and confidence intervals 

MEDIANTETRAD 
gives robust identification of multiple outliers in 2way tables 
MTABULATE 
tabulates data classified by multipleresponse factors 
PERCENT 
expresses the body of a table as percentages of one of its margins 
SVBOOT 
bootstraps data from random surveys 
SVCALIBRATE 
performs generalized calibration of survey data 
SVGLM 
fits generalized linear models to survey data 
SVREWEIGHT 
modifies survey weights adjusting to ensure that their overall sum weights remains unchanged 
SVSAMPLE 
constructs stratified random samples 
SVSTRATIFIED 
analyses stratified random surveys by expansion or ratio raising 
SVTABULATE 
tabulates data from random surveys, including multistage surveys and surveys with unequal probabilities of selection 
SVWEIGHT 
forms survey weights 
TABINSERT 
inserts the contents of a subtable into a table 
TABMODE 
forms summary tables of modes of values 
TABSORT 
sorts tables so their margins are in ascending or descending order 
TCOMBINE 
combines several tables into a single table 
T%CONTROL 
expresses tables as percentages of control cells 
VTABLE 
forms a variate and set of classifying factors from a table 
Directives are available for adding and removing branches of trees, and to assist in the construction and use of trees.
BASSESS 
assesses potential splits for regression and classification trees 

BCUT 
cuts a tree at a defined node, discarding nodes and information below it 
BIDENTIFY 
identifies specimens using a tree 
BJOIN 
extends a tree by joining another tree to a terminal node 
BGROW 
adds new branches to a node of a tree 
There are also procedures for displaying and pruning trees. These are provide basic utilities for treebased analysis, and are used by the existing procedures for classification trees, identification keys and regression trees (BCLASSIFICATION
, BKEY
and BREGRESSION
).
BCONSTRUCT 
constructs a tree 

BGRAPH 
plots a tree 
BPRINT 
displays a tree 
BPRUNE 
prunes a tree using minimal cost complexity 
Formulae and expressions can be interpreted, revised or constructed automatically from the contents of pointers.
FARGUMENTS 
forms lists of arguments involved in an expression 

FCLASSIFICATION 
forms classification sets for the terms in a formula or breaks a formula up into separate formulae (one for each term) 
REFORMULATE 
modifies a formula or an expression to operate on a different set of data structures 
SET2FORMULA 
forms a model formula using structures supplied in a pointer 
Values can be assigned to dummies and pointers.
ASSIGN 
sets values of dummies and pointers 

Aspects of the “environment” of the current job can be modified, such as whether or not Genstat starts output from a statistical analysis at the top of a new page, or whether it should pause during interactive output. New defaults can be set for options and parameters. Details of the environmental settings can be copied into Genstat data structures. Attributes of data structures can also be accessed.
SET 
sets details of the “environment” of a Genstat job 

SETOPTION 
sets or modifies defaults of options of Genstat directives or procedures 
SETPARAMETER 
sets or modifies defaults of parameters of Genstat directives or procedures 
GET 
gets details of the “environment” of a Genstat job 
GETATTRIBUTE 
accesses attributes of data structures 
GETNAME 
forms the name of a structure according to its IPRINT attribute 
There are also various specialist mathematical facilities.
FPARETOSET 
forms the Pareto optimal set of nondominated groups 

GALOIS 
forms addition and multiplication tables for a Galois finite field 
NCONVERT 
converts integers between base 10 and other bases 
PERMUTE 
forms all possible permutations of the integers 1…n 
PRIMEPOWER 
decomposes a positive integer into its constituent prime powers 