Author: Matthew Kuperus Heun
Date: 2025-01-13

# RCLabels

#### Matthew Kuperus Heun

#### 2025-01-13

## Introduction

Working with matrices often requires manipulating row and column labels to achieve desired outcomes for matrix mathematics. The `RCLabels` package (Row and Column Labels) provides convenient tools for manipulating those labels.

## Use cases

Two applications of matrix mathematics are input-output analysis in economics and physical supply-use table (PSUT) matrices for energy conversion chain (ECC) analysis. In those contexts, row and column labels describe processing stages or flows of goods or services between processing stages. Row and column labels can benefit those applications, ensuring that like quantities are added, subtracted, multiplied, or divided, etc., provided that row and column labels are respected during matrix operations.

One package that respects row and column labels is `matsbyname`, thereby making economic and ECC input-output analyses easier. Easy manipulation of row and column labels is, therefore, an enabling capability for using the `matsbyname` package. This package (`RCLabels`) provides easy manipulation of row and column labels. In fact, the `matsbyname` package uses `RCLabels` functions internally.

## Label structure

Row and column labels are always character strings, often with a prefix–suffix structure, where the prefix and suffix are denoted by a separator or delimited in other ways. Example row and column labels include

- “pref -> suff” (separator “->”)
- “pref [suff]” (suffix delimited by “ [” and “]”)
- “(pref) (suff)” (prefix and suffix both surrounded by “(” and “)”)
- “pref.suff” (separator “.”)

Prefixes are usually the “thing” of interest, e.g. an energy carrier (“Coal”) or a processing stage in an energy conversion chain (“Main activity producer electricity plants”). Suffixes are usually modifiers or metadata about the thing (the prefix). Suffixes can describe the destination of an energy carrier (“Light [-> Industry in USA]”). Suffixes can describe the output of a processing stage (“Production [of Coal in ZAR]”).

## Working with row and column labels

The `RCLabels` package streamlines working with row and column labels.

### Notation

`RCLabels` enables creation of notation objects that describe the structure of a row or column label via the `notation_vec()` function.

    # Create a notation object.
    my_notation <- notation_vec(pref_start = "(", pref_end = ") ",
                                suff_start = "[", suff_end = "]")

    # Notation objects are character vectors.
    my_notation
    #> pref_start   pref_end suff_start   suff_end
    #>        "("       ") "        "["        "]"

Several notation objects are provided for convenience within RCLabels.

    arrow_notation
    #> pref_start   pref_end suff_start   suff_end
    #>         ""     " -> "     " -> "         ""
    paren_notation
    #> pref_start   pref_end suff_start   suff_end
    #>         ""       " ("       " ("        ")"
    bracket_notation
    #> pref_start   pref_end suff_start   suff_end
    #>         ""       " ["       " ["        "]"
    first_dot_notation
    #> pref_start   pref_end suff_start   suff_end
    #>         ""        "."        "."         ""
    from_notation
    #> pref_start   pref_end suff_start   suff_end
    #>         ""  " [from "  " [from "        "]"
    of_notation
    #> pref_start   pref_end suff_start   suff_end
    #>         ""    " [of "    " [of "        "]"
    to_notation
    #> pref_start   pref_end suff_start   suff_end
    #>         ""    " [to "    " [to "        "]"
    bracket_arrow_notation
    #> pref_start   pref_end suff_start   suff_end
    #>         ""    " [-> "    " [-> "        "]"

Note that identical `pref_end` and `suff_start` values (as shown in all notations above) are interpreted as a single delimiter throughout the `RCLables` package. Empty strings (`""`) mean that no indication is given for the start or end of a prefix or suffix.

### Creating row and column labels

Row and column labels can be created with the `paste_pref_suff()` function

    my_label <- paste_pref_suff(pref = "Coal", suff = "from Coal mines in USA",
                                notation = my_notation)
    my_label
    #> [1] "(Coal) [from Coal mines in USA]"

### Manipulating row and column labels (prefixes and suffixes)

Row and column labels can be manipulated using several helpful functions.

    # Split the prefix from the suffix to obtain a named list of strings.
    split_pref_suff(my_label, notation = my_notation)
    #> $pref
    #> [1] "Coal"
    #>
    #> $suff
    #> [1] "from Coal mines in USA"

    # Flip the prefix and suffix, maintaining the same notation.
    flip_pref_suff(my_label, notation = my_notation)
    #> [1] "(from Coal mines in USA) [Coal]"

    # Change the notation.
    switch_notation(my_label, from = my_notation, to = paren_notation)
    #> [1] "Coal (from Coal mines in USA)"

    # Change the notation and flip the prefix and suffix.
    switch_notation(my_label, from = my_notation, to = paren_notation, flip = TRUE)
    #> [1] "from Coal mines in USA (Coal)"

The prefix or suffix can be extracted from a row or column label.

    get_pref_suff(my_label, which = "pref", notation = my_notation)
    #>   pref
    #> "Coal"
    get_pref_suff(my_label, which = "suff", notation = my_notation)
    #>                     suff
    #> "from Coal mines in USA"

### Vectors and lists of row and column labels

The functions in `RCLabels` work with vectors and lists of row and column labels.

    labels <- c("a [of b in c]", "d [of e in f]", "g [of h in i]")
    labels
    #> [1] "a [of b in c]" "d [of e in f]" "g [of h in i]"

    split_pref_suff(labels, notation = bracket_notation)
    #> $pref
    #> [1] "a" "d" "g"
    #>
    #> $suff
    #> [1] "of b in c" "of e in f" "of h in i"

This feature means that the functions in `RCLabels` can be used on data frames. Note that `transpose = TRUE` ensures that a single list column is created.

    labels
    #> [1] "a [of b in c]" "d [of e in f]" "g [of h in i]"

    df <- tibble::tibble(labels = labels)
    result <- df %>%
      dplyr::mutate(
        split = split_pref_suff(labels, notation = bracket_notation, transpose = TRUE)
      )
    result$split[[1]]
    #> $pref
    #> [1] "a"
    #>
    #> $suff
    #> [1] "of b in c"
    result$split[[2]]
    #> $pref
    #> [1] "d"
    #>
    #> $suff
    #> [1] "of e in f"
    result$split[[3]]
    #> $pref
    #> [1] "g"
    #>
    #> $suff
    #> [1] "of h in i"

## Nouns and prepositions

As discussed above, the prefix is often the “thing” of interest, and the remainder of the label (the suffix) modifies the prefix. This use case is so common that we introduce additional terms that enable additional functionality. The prefix is usually a noun (one or more words), and the suffix usually consists of prepositional phrases (each consisting of a preposition and an object). `RCLabels` includes a list of common prepositions.

    prepositions_list
    #> [1] "in"   "into" "from" "of"   "->"   "to"

## Working with row and column labels (nouns and prepositions)

`RCLabels` supports the “nouns and prepositions” view of row and column labels with several functions. `get_nouns()` extracts the nouns from a row or column label.

    labels
    #> [1] "a [of b in c]" "d [of e in f]" "g [of h in i]"

    # Extract the nouns.
    get_nouns(labels, notation = bracket_notation)
    #> noun noun noun
    #>  "a"  "d"  "g"

    # Extract the prepositional phrases.
    get_pps(labels, notation = bracket_notation)
    #>         pps         pps         pps
    #> "of b in c" "of e in f" "of h in i"

    # Extract the prepositions themselves.
    get_prepositions(labels, notation = bracket_notation)
    #> $prepositions
    #> [1] "of" "in"
    #>
    #> $prepositions
    #> [1] "of" "in"
    #>
    #> $prepositions
    #> [1] "of" "in"

    # Extract the objects of the prepositions.
    # Objects are named by the preposition of their phrase.
    get_objects(labels, notation = bracket_notation)
    #> $objects
    #>  of  in
    #> "b" "c"
    #>
    #> $objects
    #>  of  in
    #> "e" "f"
    #>
    #> $objects
    #>  of  in
    #> "h" "i"

    # The get_piece() function is a convenience function
    # that extracts just what you want.
    get_piece(labels, piece = "noun", notation = bracket_notation)
    #> noun noun noun
    #>  "a"  "d"  "g"
    get_piece(labels, piece = "pref")
    #> pref pref pref
    #>  "a"  "d"  "g"
    get_piece(labels, piece = "suff")
    #>        suff        suff        suff
    #> "of b in c" "of e in f" "of h in i"
    get_piece(labels, piece = "of")
    #> [[1]]
    #>  of
    #> "b"
    #>
    #> [[2]]
    #>  of
    #> "e"
    #>
    #> [[3]]
    #>  of
    #> "h"
    get_piece(labels, piece = "in")
    #> [[1]]
    #>  in
    #> "c"
    #>
    #> [[2]]
    #>  in
    #> "f"
    #>
    #> [[3]]
    #>  in
    #> "i"
    # An empty string is returned when the preposition is missing.
    get_piece(labels, piece = "bogus")
    #> [[1]]
    #> bogus
    #>    ""
    #>
    #> [[2]]
    #> bogus
    #>    ""
    #>
    #> [[3]]
    #> bogus
    #>    ""

Labels can be split into their component pieces.

    labels
    #> [1] "a [of b in c]" "d [of e in f]" "g [of h in i]"
    # Split the labels into pieces, named by "noun" and prepositions.
    split_labels <- split_noun_pp(labels,
                                 prepositions = prepositions_list,
                                 notation = bracket_notation)
    split_labels
    #> [[1]]
    #> noun   of   in
    #>  "a"  "b"  "c"
    #>
    #> [[2]]
    #> noun   of   in
    #>  "d"  "e"  "f"
    #>
    #> [[3]]
    #> noun   of   in
    #>  "g"  "h"  "i"

    # Recombine split labels.
    paste_noun_pp(split_labels, notation = bracket_notation)
    #> [1] "a [of b in c]" "d [of e in f]" "g [of h in i]"

    # Recombine with a new notation.
    paste_noun_pp(split_labels, notation = paren_notation)
    #> [1] "a (of b in c)" "d (of e in f)" "g (of h in i)"

## Modifying row and column labels

To modify row and column labels, use one of the `modify_*` functions.

    labels
    #> [1] "a [of b in c]" "d [of e in f]" "g [of h in i]"

    # Set new values for nouns.
    modify_nouns(labels,
                 new_nouns = c("Coal", "Oil", "Natural gas"),
                 notation = bracket_notation)
    #> [1] "Coal [of b in c]"        "Oil [of e in f]"
    #> [3] "Natural gas [of h in i]"

To modify other pieces of labels, use the `modify_label_pieces()` function. `modify_label_pieces()` enables assigning new values using a “one-to-many” approach that enables aggregation.

    labels
    #> [1] "a [of b in c]" "d [of e in f]" "g [of h in i]"

    # Change nouns in several labels to "Production" and "Manufacture",
    # as indicated by the modification map.
    modify_label_pieces(labels,
                        piece = "noun",
                        mod_map = list(Production = c("a", "b", "c", "d"),
                                       Manufacture = c("g", "h", "i", "j")),
                        notation = bracket_notation)
    #> [1] "Production [of b in c]"  "Production [of e in f]"
    #> [3] "Manufacture [of h in i]"

    # Change the objects of the "in" preposition,
    # according to the modification map.
    modify_label_pieces(labels,
                        piece = "in",
                        mod_map = list(GHA = "c", ZAF = c("f", "i")),
                        notation = bracket_notation)
    #> [1] "a [of b in GHA]" "d [of e in ZAF]" "g [of h in ZAF]"

    # Change the objects of "of" prepositions,
    # according to the modification map.
    modify_label_pieces(labels,
                        piece = "of",
                        mod_map = list(Coal = "b", `Crude oil` = c("e", "h")),
                        notation = bracket_notation)
    #> [1] "a [of Coal in c]"      "d [of Crude oil in f]" "g [of Crude oil in i]"

To eliminate a piece of a label altogether, use the `remove_label_pieces()` function.

    labels
    #> [1] "a [of b in c]" "d [of e in f]" "g [of h in i]"

    # Eliminate all of the prepositional phrases that begin with "in".
    remove_label_pieces(labels,
                        piece = "in",
                        notation = bracket_notation)
    #> [1] "a [of b]" "d [of e]" "g [of h]"

    # Eliminate all of the prepositional phrases that begin with "of" and "in".
    # Note that some spaces remain.
    remove_label_pieces(labels,
                        piece = c("of", "in"),
                        notation = bracket_notation)
    #> [1] "a [ ]" "d [ ]" "g [ ]"

With much power comes much responsibility!

## Detecting strings in labels

There are times when it is helpful to know if a string is in a label. `match_by_pattern()` searches for matches in row and column labels by regular expression. Internally, `match_by_pattern()` uses `grepl()` for regular expression matching.

    labels <- c("Production [of b in c]", "d [of Coal in f]", "g [of h in USA]")

    # With default `pieces` argument, matching is done for whole labels.
    match_by_pattern(labels, regex_pattern = "Production")
    #> [1]  TRUE FALSE FALSE
    match_by_pattern(labels, regex_pattern = "Coal")
    #> [1] FALSE  TRUE FALSE
    match_by_pattern(labels, regex_pattern = "USA")
    #> [1] FALSE FALSE  TRUE

    # Check beginnings of labels: match!
    match_by_pattern(labels, regex_pattern = "^Production")
    #> [1]  TRUE FALSE FALSE
    # Check at ends of labels: no match!
    match_by_pattern(labels, regex_pattern = "Production$")
    #> [1] FALSE FALSE FALSE

    # Search by prefix or suffix.
    match_by_pattern(labels, regex_pattern = "Production", pieces = "pref")
    #> [1]  TRUE FALSE FALSE
    match_by_pattern(labels, regex_pattern = "Production", pieces = "suff")
    #> [1] FALSE FALSE FALSE
    # When pieces is "pref" or "suff", only one can be specified.
    # The following function call gives an error.
    # match_by_pattern(labels, regex_pattern = "Production", pieces = c("pref", "to"))

    # Search by noun or preposition.
    match_by_pattern(labels, regex_pattern = "Production", pieces = "noun")
    #> [1]  TRUE FALSE FALSE
    match_by_pattern(labels, regex_pattern = "Production", pieces = "in")
    #> [1] FALSE FALSE FALSE
    # Searching can be done with complicated regex patterns.
    match_by_pattern(labels,
                     regex_pattern = make_or_pattern(c("c", "f")),
                     pieces = "in")
    #> [1]  TRUE  TRUE FALSE
    match_by_pattern(labels,
                     regex_pattern = make_or_pattern(c("b", "Coal", "USA")),
                     pieces = "in")
    #> [1] FALSE FALSE  TRUE
    match_by_pattern(labels,
                     regex_pattern = make_or_pattern(c("b", "Coal", "USA")),
                     pieces = c("of", "in"))
    #> [1] TRUE TRUE TRUE
    # Works with custom lists of prepositions.
    match_by_pattern(labels,
                     regex_pattern = make_or_pattern(c("b", "Coal", "GBR", "USA")),
                     pieces = c("noun", "of", "in", "to"),
                     prepositions = c("of", "to", "in"))
    #> [1] TRUE TRUE TRUE

## Replacing strings in labels

There are times when it is helpful to replace strings in labels. The `replace_by_pattern()` function will replace strings in row and column labels by regular expression pattern. Note that `replace_by_pattern()` is similar to `match_by_pattern()`, except `replace_by_pattern()` has an additional argument, `replacement`. Internally, `replace_by_pattern()` uses `gsub()` to perform regular expression matching.

    labels <- c("Production [of b in c]", "d [of Coal in f]", "g [of h in USA]")
    labels
    #> [1] "Production [of b in c]" "d [of Coal in f]"       "g [of h in USA]"

    # If `pieces = "all"` (the default), the entire label is available for replacements.
    replace_by_pattern(labels,
                       regex_pattern = "Production",
                       replacement = "Manufacture")
    #> [1] "Manufacture [of b in c]" "d [of Coal in f]"
    #> [3] "g [of h in USA]"
    replace_by_pattern(labels,
                       regex_pattern = "Coal",
                       replacement = "Oil")
    #> [1] "Production [of b in c]" "d [of Oil in f]"        "g [of h in USA]"
    replace_by_pattern(labels,
                       regex_pattern = "USA",
                       replacement = "GHA")
    #> [1] "Production [of b in c]" "d [of Coal in f]"       "g [of h in GHA]"

    # Replace by prefix and suffix.
    replace_by_pattern(labels,
                       regex_pattern = "Production",
                       replacement = "Manufacture",
                       pieces = "pref")
    #> [1] "Manufacture [of b in c]" "d [of Coal in f]"
    #> [3] "g [of h in USA]"
    replace_by_pattern(labels,
                       regex_pattern = "Coa",
                       replacement = "Bow",
                       pieces = "suff")
    #> [1] "Production [of b in c]" "d [of Bowl in f]"       "g [of h in USA]"
    # Nothing should change, because USA is in the suffix.
    replace_by_pattern(labels,
                       regex_pattern = "SA",
                       replacement = "SSR",
                       pieces = "pref")
    #> [1] "Production [of b in c]" "d [of Coal in f]"       "g [of h in USA]"
    # Now USA --> USSR, because USA is in the suffix.
    replace_by_pattern(labels,
                       regex_pattern = "SA",
                       replacement = "SSR",
                       pieces = "suff")
    #> [1] "Production [of b in c]" "d [of Coal in f]"       "g [of h in USSR]"
    # This will throw an error, because only "pref" or "suff" can be specified.
    # replace_by_pattern(labels,
    #                    regex_pattern = "SA",
    #                    replacement = "SSR",
    #                    pieces = c("pref", "suff")

    # Replace by noun or preposition.
    replace_by_pattern(labels,
                       regex_pattern = "Production",
                       replacement = "Manufacture",
                       pieces = "noun")
    #> [1] "Manufacture [of b in c]" "d [of Coal in f]"
    #> [3] "g [of h in USA]"
    replace_by_pattern(labels,
                       regex_pattern = "^Pro",
                       replacement = "Con",
                       pieces = "noun")
    #> [1] "Conduction [of b in c]" "d [of Coal in f]"       "g [of h in USA]"
    # Won't match: wrong side of string.
    replace_by_pattern(labels,
                       regex_pattern = "Pro$",
                       replacement = "Con",
                       pieces = "noun")
    #> [1] "Production [of b in c]" "d [of Coal in f]"       "g [of h in USA]"
    # No change, because "Production" is a noun.
    replace_by_pattern(labels,
                       regex_pattern = "Production",
                       replacement = "Manufacture",
                       pieces = "of")
    #> [1] "Production [of b in c]" "d [of Coal in f]"       "g [of h in USA]"
    # Now try with "of".
    replace_by_pattern(labels,
                       regex_pattern = "Coal",
                       replacement = "Oil",
                       pieces = "of")
    #> [1] "Production [of b in c]" "d [of Oil in f]"        "g [of h in USA]"
    # No change, because "Coal" is not "in" anything.
    replace_by_pattern(labels,
                       regex_pattern = "Coal",
                       replacement = "Oil",
                       pieces = "in")
    #> [1] "Production [of b in c]" "d [of Coal in f]"       "g [of h in USA]"
    # Now try in "in".
    replace_by_pattern(labels,
                       regex_pattern = "USA",
                       replacement = "GBR",
                       pieces = "in")
    #> [1] "Production [of b in c]" "d [of Coal in f]"       "g [of h in GBR]"
    replace_by_pattern(labels,
                       regex_pattern = "A$",
                       replacement = "upercalifragilisticexpialidocious",
                       pieces = "in")
    #> [1] "Production [of b in c]"
    #> [2] "d [of Coal in f]"
    #> [3] "g [of h in USupercalifragilisticexpialidocious]"

## Conclusion

The `RCLabels` package streamlines the manipulation of row and column labels for matrices. Applications include input-output analysis in economics and energy conversion chain analysis or anywhere row and column labels are important for matrix mathematics.