linear algebra Using the lattice basis LB and the reciprocal

linear algebra

Using the lattice basis LB and the reciprocal lattice basis RLB given for graphite, you wish to determine the location of a point of interest within the lattice given by Give the coordinates of this point both with respect to the standard basis vectors for R^3, and with respect to the lattice basis LB. Explain your steps carefully. Which basis of the three seems most natural for this point of interest?

Solution

Ans-

This is a generic function, with methods supplied for matrices, data frames and vectors (including lists). Packages and users can add further methods.

For ordinary vectors, the result is simply x[subset & !is.na(subset)].

For data frames, the subset argument works on the rows. Note that subset will be evaluated in the data frame, so columns can be referred to (by name) as variables in the expression (see the examples).

The select argument exists only for the methods for data frames and matrices. It works by first replacing column names in the selection expression with the corresponding column numbers in the data frame and then using the resulting integer vector to index the columns. This allows the use of the standard indexing conventions so that for example ranges of columns can be specified easily, or single columns can be dropped (see the examples).

The drop argument is passed on to the indexing method for matrices and data frames: note that the default for matrices is different from that for indexing.

Factors may have empty levels after subsetting; unused levels are not automatically removed. See droplevels for a way to drop all unused levels from a data frame.

Value

An object similar to x contain just the selected elements (for a vector), rows and columns (for a matrix or data frame), and so on.

Warning

This is a convenience function intended for use interactively. For programming it is better to use the standard subsetting functions like [, and in particular the non-standard evaluation of argument subset can have unanticipated consequences.

Author(s)

Peter Dalgaard and Brian Ripley

See Also

[, transform droplevels

Examples