Aggregation in `matsbyname`

In matsbyname: An Implementation of Matrix Mathematics that Respects Row and Column Names

knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>"
)
library(dplyr)
library(tibble)
library(matsbyname)
library(matsindf)

Introduction

The matsbyname package provides several functions to assist renaming and aggregating rows and columns of matrices. This vignette shows how to use those functions.

aggregate_byname()

By default (aggregation_map = NULL, margin = c(1,2), pattern_type = "exact"), aggregate_byname() sums all rows and columns with the same names, with the effect that remaining row and column names are unique.

m <- matrix(c(1, 2, 3, 4, 
              5, 6, 7, 8, 
              9, 10, 11, 12), nrow = 3, ncol = 4, byrow = TRUE,
            dimnames = list(c("duck", "duck", "goose"), 
                            c("John", "Paul", "George", "Ringo")))
m
aggregate_byname(m)

An aggregation_map can be provided, giving instructions for rows or columns to aggregate and the names of the results. aggregation_map should be a list of named strings. The entries in the list give names of rows and columns to be aggregated. The names of the list entries provide the names of the resulting aggregates.

m
aggregate_byname(m, aggregation_map = list(birds = c("duck", "goose"), 
                                           guitarists = c("John", "Paul", "George")))

The margin over which the aggregation is to be performed is given by the margin argument (1 for rows, 2 for columns).

m
aggregate_byname(m, aggregation_map = list(Beatles = c("John", "Paul", "George", "Ringo")), 
                 margin = 2)

aggregation_map can use regular expressions to identify rows and columns to aggregate. Use pattern_type = "literal" for this feature.

m
aggregate_byname(m, aggregation_map = list(guitarists = "^[JPG]"), 
                 margin = 2, pattern_type = "literal")

Note that rows and columns of aggregated matrices are always sorted alphabetically.

m
aggregate_byname(m, aggregation_map = list(birds = c("duck", "goose"), 
                                           zguitarists = c("John", "Paul", "George")))

It is an error to aggregate over a margin and leave identically named rows or columns. The following function call will fail, because it aggregates over both rows and columns (using the default margin = c(1,2)) with nothing in the aggregation_map to aggregate the two "duck" rows. The error is informative: "Row names not unique. Duplicated row names are: duck".

# Not run
aggregate_byname(m, aggregation_map = list(Beatles = c("John", "Paul", "George", "Ringo")))

Pieces

Commonly, row and column names are complex, carrying information in prefixes, suffixes, and prepositional phrases. matsbyname can aggregate by pieces of a name, using the RCLabels package internally.

We'll use the following matrix to demonstrate aggregating by pieces. The rows and columns use different notations for names (RCLabels::bracket_notation for rows and RCLabels::arrow_notation for columns). The renaming and aggregation capabilities of matsbyname still work, despite the different notations.

m_pieces <- matrix(c(1, 2, 3,
                     4, 5, 6), nrow = 2, ncol = 3, byrow = TRUE, 
                   dimnames = list(c("Electricity [from Coal]", "Electricity [from Solar]"), 
                                   c("Motors -> MD", "Cars -> MD", "LED lamps -> Light")))
m_pieces

rename_to_piece_byname()

Rows and columns can be renamed to their prefixes, suffixes, or objects of prepositions, as demonstrated below.

m_pieces
rename_to_piece_byname(m_pieces, piece = "pref", margin = 1, 
                       notation = RCLabels::bracket_notation)
rename_to_piece_byname(m_pieces, piece = "suff", margin = 1, 
                       notation = RCLabels::bracket_notation)
rename_to_piece_byname(m_pieces, piece = "from", margin = 1, 
                       notation = RCLabels::bracket_notation)
rename_to_piece_byname(m_pieces, piece = "pref", margin = 2,
                       notation = RCLabels::arrow_notation)
rename_to_piece_byname(m_pieces, piece = "suff", margin = 2,
                       notation = RCLabels::arrow_notation)

In the examples above, renaming was accomplished by specifying the notation for row or column names. But notation for row and column labels can also be inferred via RCLabels::infer_notation(). To infer notation when renaming, set inf_notation = TRUE (the default) and give a list of notations from which the notation can be inferred in the notation argument. By default, notation = list(RCLabels::notations_list), because each notation in RCLabels::notations_list is a list itself.

m_pieces
rename_to_piece_byname(m_pieces, piece = "pref", margin = 1)

When inferring notation, both margins can be renamed at the same time, despite having different notations.

rename_to_piece_byname(m_pieces, piece = "pref", margin = c(1, 2))

But margin = list(c(1, 2)) is the default, so the code can be simpler still.

rename_to_piece_byname(m_pieces, piece = "pref")
rename_to_piece_byname(m_pieces, piece = "suff")

Sometimes, a row or column label can match more than one possible notation. In the above example, the row names are inferred to conform to RCLabels::bracket_notation, the first match in RCLabels::notations_list.
To specify the most-specific notation, set choose_most_specific = TRUE. With choose_most_specific = TRUE, RCLabels::from_notation is inferred, the suffixes are different, and the renamed rows no longer contain "from ".

rename_to_piece_byname(m_pieces, piece = "suff", choose_most_specific = TRUE)

Note that "noun" is a synonym for "pref".

rename_to_piece_byname(m_pieces, piece = "noun")

The margin can be specified using row or column types from which the numerical margin is inferred.

m_pieces_with_types <- m_pieces %>% 
  setrowtype("Product") %>% setcoltype("Industry")
m_pieces_with_types
m_pieces_with_types %>% 
  rename_to_piece_byname(piece = "pref", margin = "Product")
m_pieces_with_types %>% 
  rename_to_piece_byname(piece = "suff", margin = "Product")
m_pieces_with_types %>% 
  rename_to_piece_byname(piece = "from", margin = "Product")
m_pieces_with_types %>% 
  rename_to_piece_byname(piece = "suff", margin = "Product", choose_most_specific = TRUE)
m_pieces_with_types %>% 
  rename_to_piece_byname(piece = "suff", margin = "Industry")

Such renamings can be used for aggregations in which identically named rows and columns are summed with aggregate_byname(), as demonstrated in section below.

aggregate_pieces_byname()

aggregate_pieces_byname() bundles renaming and aggregating tasks in a single function call. First, rows and/or columns are renamed to the requested piece with the rename_to_piece_byname() function. Then, aggregation is performed via aggregate_byname(), according to an aggregation_map and the pattern_type, if provided. With the default aggregation_map = NULL, identically named pieces are aggregated together.

m_pieces
# Aggregate Electricity in rows
aggregate_pieces_byname(m_pieces, piece = "pref", margin = 1, 
                        notation = RCLabels::bracket_notation)
# Aggregate useful energy types in columns
aggregate_pieces_byname(m_pieces, piece = "suff", margin = 2,
                        notation = RCLabels::arrow_notation)

When an aggregation_map is supplied, it applies to the requested piece, not to the original row and/or column names, as shown below.

m_pieces
# Aggregate by original energy type
aggregate_pieces_byname(m_pieces, piece = "from", margin = 1, 
                        notation = RCLabels::bracket_notation, 
                        aggregation_map = list(`All sources` = c("Coal", "Solar")))

aggregate_pieces_byname(m_pieces, piece = "suff", margin = 2, 
                        notation = RCLabels::arrow_notation, 
                        aggregation_map = list(`Transport` = "MD"))

Aggregations of lists and data frames of matrices

The functions for renaming and aggregating can be used on lists and data frames of matrices.

m_pieces
res <- rename_to_piece_byname(list(m_pieces, m_pieces), 
                              piece = list("pref", "suff"), 
                              margin = list(1, 2),
                              notation = list(RCLabels::bracket_notation, 
                                              RCLabels::arrow_notation))
res
df <- tibble::tibble(mats = list(m_pieces, m_pieces), 
                     pce = list("suff", "pref"), 
                     mgn = list(1, 2), 
                     am = list(list(Sources = c("Coal", "Solar")), 
                               list(Transport = c("Motors", "Cars"))), 
                     notn = list(RCLabels::from_notation, RCLabels::arrow_notation))
df
res2 <- df %>%
  dplyr::mutate(
    aggregated = aggregate_pieces_byname(mats, piece = pce, margin = mgn, 
                                         aggregation_map = am, notation = notn)
  )
res2
res2$aggregated[[1]]
res2$aggregated[[2]]

Aggregation via dplyr::summarise()

Another type of aggregation is aided by the metadata columns of a matsindf-style data frame. With single numbers, an aggregation might look like this:

df_simple <- tibble::tribble(~key, ~val, 
                             "A", 1, 
                             "A", 2, 
                             "B", 10)
df_simple
df_simple %>% 
  dplyr::group_by(key) %>% 
  dplyr::summarise(val = sum(val))

The same aggregation gives unexpected results with the default arguments to the sum_byname() function (specifically, .summarise = FALSE), because sum_byname() is ambiguous for a data frame. Should the column be returned unchanged, because each element is interpreted as the augend for a series of sums that is missing addends, in which case the length of the returned object is the same as the length of the input? Or should the list of objects be summed down the column, returning only a single item (for each group), as in the dplyr::summarise() function? (See the vignette titled "Using summarise in matsbyname" for additional detail about this ambiguity.) In the example below, the grouping has no effect on the summarise() function, because sum_byname(.summarise = FALSE) assumes that each row of val is an augend without an addend.

# 2 rows are expected. 3 are observed.
df_simple %>% 
  dplyr::group_by(key) %>% 
  dplyr::summarise(val = sum_byname(val), .groups = "drop")

To signal intention to summarise down the val column, set .summarise = TRUE in the call to sum_byname(). Note that sum_byname(.summarise = TRUE) always returns a list column, because if the summarised column were to contain matrices, it must be a list column.

res <- df_simple %>% 
  dplyr::group_by(key) %>% 
  dplyr::summarise(val = sum_byname(val, .summarise = TRUE))
# res$val is a list column.
res
res$val

The .summarise = TRUE argument works when there are matrices in a matsindf data frame, too.

m <- matrix(c(11, 12, 13,
              21, 22, 23), nrow = 2, ncol = 3, byrow = TRUE, 
            dimnames = list(c("r1", "r2"), c("c1", "c2", "c3")))
df <- tibble::tibble(key = c("A", "A", "B"), m = list(m, m, m))
unexpected <- df %>% 
  dplyr::group_by(key) %>% 
  dplyr::summarise(m = sum_byname(m), .groups = "drop")
# 2 rows are expected. 3 are observed.
unexpected
res <- df %>% 
  dplyr::group_by(key) %>% 
  dplyr::summarise(m = sum_byname(m, .summarise = TRUE))
res
res$m[[1]]
res$m[[2]]

Working with aggregation maps

An aggregation map is defined to be a named list. But the source of that named list is often a data frame in which many-to-one relationships are defined. agg_table_to_agg_map() assists converting from a two-column data frame to an aggregation map.

df <- tibble::tribble(~member, ~role, ~band, 
                      "John", "guitarists", "The Beatles", 
                      "Paul", "guitarists", "The Beatles", 
                      "George", "guitarists", "The Beatles", 
                      "Ringo", "drummers", "The Beatles", 
                      "Mick", "singers", "Rolling Stones", 
                      "Keith", "guitarists", "Rolling Stones", 
                      "Ronnie", "guitarists", "Rolling Stones", 
                      "Bill", "guitarists", "Rolling Stones", 
                      "Charlie", "drummers", "Rolling Stones")
df
bands_membs_agg_map <- agg_table_to_agg_map(df, few_colname = "band", many_colname = "member")
bands_membs_agg_map
agg_table_to_agg_map(df, few_colname = "role", many_colname = "member")

In a similar manner, an aggregation map can be converted to a data frame to assist with join operations with data frames.

agg_map_to_agg_table(bands_membs_agg_map, 
                      few_colname = "bands",
                      many_colname = "members")

Summary

The matsbyname package simplifies aggregation of matrix rows and columns based on row and column names or pieces of row and column names. In particular the functions aggregate_byname(), rename_to_piece_byname(), and aggregate_pieces_byname() provide flexibility in how renaming and aggregation can be accomplished. When working with aggregation maps, the functions agg_table_to_agg_map() and agg_map_to_agg_table() assist conversion from one data shape to another.

matsbyname documentation built on Oct. 19, 2023, 5:11 p.m.