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LRV directive

Declares one or more LRV data structures.

Options

ROWS = scalar, vector or pointer Number of rows, or row labels, for the matrix; default *
COLUMNS = scalar, vector or pointer Number of columns, or column labels, for matrix and diagonal matrix; default *

Parameters

IDENTIFIER = identifiers Identifiers of the LRVs
VECTORS = matrices Matrix to contain the latent vectors for each LRV
ROOTS = diagonal matrices Diagonal matrix to contain the latent roots for each LRV
TRACE = scalars Trace of the matrix

Description

The LRV is a compound data structure. These are similar to pointers in that they point to other structures, but they have a fixed number of elements which must be of the correct types and must form a consistent set (in terms of their sizes and so on). You can refer to elements of compound structures in exactly the same way as the elements of pointers, but the suffixes and their labels are fixed for each type of structure. Unlike pointers, the labels are also not case sensitive; Genstat will recognize the label in either upper case or lower case, or in any mixture of the two.

The LRV structure is used to store latent roots and vectors resulting from the decomposition of a matrix (by the FLRV directive), or produced in multivariate analysis. It points to three structures (identified by their suffixes):

    [1] or ['Vectors'] is a matrix whose columns are the latent vectors (the word "Vector" is used here in its mathematical sense rather than in the more specific Genstat sense; in fact, latent vectors are most conveniently stored in matrices rather than in Genstat vectors);
    [2] or ['Roots'] is a diagonal matrix whose elements are the latent roots;
    [3] or ['Trace'] is a scalar holding the trace of the matrix, which is the sum of all its latent roots.

The length of each latent vector is specified by the ROWS option; this then defines the number of rows in the 'VECTORS' matrix. The COLUMNS option defines the number of latent roots to be stored; this is also the number of latent vectors, and so indicates the number of columns in the 'VECTORS' matrix and the number of elements in the 'ROOTS' matrix. If you do not specify the number of columns Genstat will set it to be the same as the number of rows. The value of COLUMNS can be less than the value of ROWS; however, it must not exceed than that of ROWS, otherwise Genstat gives an error diagnostic. Row and column labels can be defined, as in the MATRIX directive.

You can specify identifiers for the three individual elements of the LRV by using the VECTORS, ROOTS and TRACE parameters. If you have declared them already they must be of the correct type (and you can also have given them values). If you have given these identifiers row or column settings, then these will be used for the LRV declaration and must match any of the corresponding options of LRV that you choose to set.

Options: ROWS, COLUMNS.

Parameters: IDENTIFIER, VECTORS, ROOTS, TRACE.

See also

Directives: FLRV, DIAGONALMATRIX, MATRIX, POINTER, QRD, SVD, SYMMETRICMATRIX.

Commands for: Data structures, Multivariate and cluster analysis.

Example

" Example LRV-1: Latent roots and vectors"

POINTER [VALUES=stem,leaf,root,petal,pollen] Vars 
SYMMETRICMATRIX [ROWS=Vars] Symm
READ Symm
 1.000
-0.655  1.000
-0.945  0.866  1.000
-0.756  0.000  0.500  1.000
 0.500 -0.982 -0.756  0.189  1.000:
PRINT Symm

" Declare a latent roots and vectors structure"
LRV [ROWS=Vars; COLUMNS=2] Latent; VECTORS=Lvecs

" Form the values of the structure"
FLRV Symm; Latent
PRINT Latent['Vectors','Roots']
Updated on March 7, 2019

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