Declares one or more diagonal matrix data structures.
Options
ROWS = scalar, vector, pointer or text |
Number of rows, or labels for rows (and columns); default * |
|---|---|
VALUES = numbers |
Values for all the diagonal matrices; default * |
MODIFY = string token |
Whether to modify (instead of redefining) existing structures (yes, no); default no |
IPRINT = string tokens |
Information to be used by default to identify the diagonal matrices in output (identifier, extra); if this is not set, they will be identified in the standard way for each type of output |
Parameters
IDENTIFIER = identifiers |
Identifiers of the diagonal matrices |
|---|---|
VALUES = identifiers |
Values for each diagonal matrix |
DECIMALS = scalars |
Number of decimal places for printing |
EXTRA = texts |
Extra text associated with each identifier |
MINIMUM = scalars |
Minimum value for the contents of each structure |
MAXIMUM = scalars |
Maximum value for the contents of each structure |
DREPRESENTATION = scalars or texts |
Default format to use when the contents represent dates and times |
Description
Diagonal matrices are square matrices that have zero entries except on their leading diagonals: for example,
2 0 0
0 1 0
0 0 3
Another example is the identity matrix, which has a diagonal of values equal to 1. To save space, Genstat has a special structure for diagonal matrices, and these can be declared using the DIAGONALMATRIX directive.
Because a diagonal matrix is square, Genstat requires you to specify only the number of rows. This is done using the ROWS option. The simplest method is to use a scalar to define the number of rows explicitly. Alternatively, you can set ROWS to a variate, text or pointer, whose length then defines the number of rows and whose values will then be used as labels, for example when the matrix is printed. Finally, if you specify a factor, the number of levels defines the number of rows and the labels if available, or otherwise the levels, are used for labelling.
When you give the values of a diagonal matrix, either in a declaration or when its values are read, you should specify only the diagonal elements. (Genstat does not store the off-diagonal elements, but assumes them to be zero.) Similarly, when a diagonal matrix is printed it appears as a column of numbers; Genstat omits the off-diagonal zeros. For example:
DIAGONALMATRIX [ROWS=3; VALUES=2,1,3] D
declares the diagonal matrix D and gives it the values shown above.
Values can be assigned to the diagonal matrices by either the VALUES option or the VALUES parameter. The option defines a common value for all the matrices in the declaration, while the parameter allows them each to be given a different value. If both the option and the parameter are specified, the parameter takes precedence.
If the MODIFY option is set to yes any existing attributes and values of the diagonal matrices are retained (if still appropriate); otherwise these are lost.
The DECIMALS parameter allows you to define a number of decimal places to be used by default when each diagonal matrix is printed. You can associate a text of extra annotation with each diagonal matrix using the EXTRA parameter. The MINIMUM and MAXIMUM parameters allow you to define lower and upper limits on the values in each diagonal matrix. Genstat then prints warnings if any values outside that range are allocated to the matrix. The DREPRESENTATION parameter allows a scalar or a single-valued text to be specified for each diagonal matrix to indicate that the matrix stores dates and times, and to define a format to be used for these, by default, when they are printed; details are given in the description of the PRINT directive.
The IPRINT option can be set to specify how the diagonal matrices will be identified in output. If IPRINT is not set, they will be identified in whatever way is usual for the section of output concerned. For example, the PRINT directive generally uses their identifiers (although this can be changed using the IPRINT option of PRINT itself).
Options: ROWS, VALUES, MODIFY, IPRINT.
Parameters: IDENTIFIER, VALUES, DECIMALS, EXTRA, MINIMUM, MAXIMUM, DREPRESENTATION.
See also
Directives: LRV, MATRIX, SYMMETRICMATRIX, SSPM.
Commands for: Data structures.
Example
" Example DIAG-1: declaring a diagonal matrix" DIAGONALMATRIX [ROWS=3; VALUES=2,1,3] D PRINT D