# General infrastructure

library(scrutiny)

The implementation of error detection techniques in scrutiny rests on a foundation of specialized helper functions. Some of these are exported because they might be helpful in error detection more broadly, or perhaps even in other contexts.

This vignette provides an overview of scrutiny’s miscellaneous infrastructure for implementing error detection techniques. For more specific articles, see vignette("rounding") or vignette("consistency-tests").

## Count decimal places

Large parts of the package ultimately rest on either of two functions that simply count decimal places. These are digits after a number’s decimal point or some other separator. Both functions also take strings.

decimal_places() is vectorized:

decimal_places("2.80")
#> [1] 2

decimal_places(c(55.1, 6.493, 8))
#> [1] 1 3 0

vec1 <- iris %>%
dplyr::slice(1:10) %>%
dplyr::pull(Sepal.Length)

vec1
#>  [1] 5.1 4.9 4.7 4.6 5.0 5.4 4.6 5.0 4.4 4.9

vec1 %>%
decimal_places()
#>  [1] 1 1 1 1 0 1 1 0 1 1

Using strings (that are coercible to numeric) is recommended in an error detection context because trailing zeros can be crucial here. Numeric values drop trailing zeros, whereas strings preserve them:

decimal_places(7.200)
#> [1] 1

decimal_places("7.200")
#> [1] 3

decimal_places_scalar() is faster than decimal_places() but only takes a single number or string. This makes it suitable as a helper within other single-case functions.

## Restore trailing zeros

When dealing with numbers that used to have trailing zeros but lost them from being registered as numeric, call restore_zeros() to format them correctly. This can be relevant within functions that create vectors where trailing zeros matter, such as the seq_*() functions presented in the next section.

Suppose all of the following numbers originally had one decimal place, but some no longer do:

vec2 <- c(4, 6.9, 5, 4.2, 4.8, 7, 4)

vec2 %>%
decimal_places()
#> [1] 0 1 0 1 1 0 0

Now, get them back with restore_zeros():

vec2 %>%
restore_zeros()
#> [1] "4.0" "6.9" "5.0" "4.2" "4.8" "7.0" "4.0"

vec2 %>%
restore_zeros() %>%
decimal_places()
#> [1] 1 1 1 1 1 1 1

This uses the default of going by the longest mantissa and padding the other strings with decimal zeros until they have that many decimal places. However, this is just a heuristic: The longest mantissa might itself have lost decimal places. Specify the width argument to explicitly state the desired mantissa length:

vec2 %>%
restore_zeros(width = 2)
#> [1] "4.00" "6.90" "5.00" "4.20" "4.80" "7.00" "4.00"

vec2 %>%
restore_zeros(width = 2) %>%
decimal_places()
#> [1] 2 2 2 2 2 2 2

## Sequence generation

### Introduction

base::seq() offers a flexible way to generate sequences, but it is not cut out for working with decimal numbers. The by argument only allows for manual specifications of the step size, i.e., the difference between two consecutive output values. In an error detection context, there is also the problem of trailing zeros in numeric values.

Use scrutiny’s seq_*() functions to automatically determine step size from the input numbers and, by default, to supply missing trailing zeros via restore_zeros(). Output will then naturally be string.

Why are there multiple such functions? The first two disentangle the two different ways in which seq() can be used. A third function adds a way of generating sequences not directly covered by seq().

• seq_endpoint() takes two main arguments, from and to. It creates a sequence between the two, inferring step size from the greater number of decimal places among them. This corresponds to a seq() call in which to was specified.

• seq_distance() takes a from argument, uses it to infer the step size, and creates a sequence of a length specified by the length_out argument (default is 10). This corresponds to a seq() call in which length.out was specified.

• Finally, seq_disperse() creates a sequence centered around from.

Each of these functions has a *_df() variant that embeds the sequence as a tibble column.

### Examples

The seq_*() functions have some more features, such as offsets and direction reversal, but I’ll focus on the basics here.

Call seq_endpoint() to bridge two numbers at the correct decimal level:

seq_endpoint(from = 4.1, to = 6)
#>  [1] "4.1" "4.2" "4.3" "4.4" "4.5" "4.6" "4.7" "4.8" "4.9" "5.0" "5.1" "5.2"
#> [13] "5.3" "5.4" "5.5" "5.6" "5.7" "5.8" "5.9" "6.0"

seq_endpoint(from = 4.1, to = 4.15)
#> [1] "4.10" "4.11" "4.12" "4.13" "4.14" "4.15"

Call seq_distance() to get a sequence of desired length:

seq_distance(from = 4.1, length_out = 3)
#> [1] "4.1" "4.2" "4.3"

# Default for length_out is 10:
seq_distance(from = 4.1)
#>  [1] "4.1" "4.2" "4.3" "4.4" "4.5" "4.6" "4.7" "4.8" "4.9" "5.0"

Finally, call seq_disperse() to construct a sequence around from:

seq_disperse(from = 4.1, dispersion = 1:3)
#> [1] "3.8" "3.9" "4.0" "4.1" "4.2" "4.3" "4.4"

# Default for dispersion if 1:5:
seq_disperse(from = 4.1)
#>  [1] "3.6" "3.7" "3.8" "3.9" "4.0" "4.1" "4.2" "4.3" "4.4" "4.5" "4.6"

seq_disperse() is a hybrid between the two seq() wrappers explained above and the disperse*() functions introduced next.

## Sequence testing

### General points

Four predicate functions test whether a vector x represents particular kinds of sequences. These testing functions can be used as helpers, but they are also analytic tools in their own right.

is_seq_linear() returns TRUE if the difference between all neighboring values is the same:

is_seq_linear(x = 8:15)
#> [1] TRUE
is_seq_linear(x = c(8:15, 16))
#> [1] TRUE
is_seq_linear(x = c(8:15, 17))
#> [1] FALSE

is_seq_ascending() tests whether that difference is always positive…

is_seq_ascending(x = 8:15)
#> [1] TRUE
is_seq_ascending(x = 15:8)
#> [1] FALSE

# Default also tests for linearity:
is_seq_ascending(x = c(8:15, 17))
#> [1] FALSE
is_seq_ascending(x = c(8:15, 17), test_linear = FALSE)
#> [1] TRUE

…whereas is_seq_descending() tests whether it is always negative:

is_seq_descending(x = 8:15)
#> [1] FALSE
is_seq_descending(x = 15:8)
#> [1] TRUE

# Default also tests for linearity:
is_seq_descending(x = c(15:8, 2))
#> [1] FALSE
is_seq_descending(x = c(15:8, 2), test_linear = FALSE)
#> [1] TRUE

is_seq_dispersed() tests whether the vector is grouped around its from argument:

is_seq_dispersed(x = 3:7, from = 2)
#> [1] FALSE

# Direction doesn't matter here:
is_seq_dispersed(x = 3:7, from = 5)
#> [1] TRUE
is_seq_dispersed(x = 7:3, from = 5)
#> [1] TRUE

# Dispersed from 50, but not linear:
x_nonlinear <- c(49, 42, 47, 44, 50, 56, 53, 58, 51)

# Default also tests for linearity:
is_seq_dispersed(x = x_nonlinear, from = 50)
#> [1] FALSE
is_seq_dispersed(x = x_nonlinear, from = 50, test_linear = FALSE)
#> [1] TRUE

### NA handling

All the is_seq_*() functions take special care with missing values. If one or more elements of x are NA, this doesn’t necessarily mean that it’s unknown whether or not x might possibly represent the kind of sequence in question.

In these examples, it is genuinely unclear whether x is linear:

is_seq_linear(x = c(1, 2, NA, 4))
#> [1] NA
is_seq_linear(x = c(1, 2, NA, NA, NA, 6))
#> [1] NA

Linearity thus depends on the unknown, missing value behind NA:

is_seq_linear(x = c(1, 2, 3, 4))
#> [1] TRUE
is_seq_linear(x = c(1, 2, 7, 4))
#> [1] FALSE

is_seq_linear(x = c(1, 2, 3, 4, 5, 6))
#> [1] TRUE
is_seq_linear(x = c(1, 2, 17, 29, 32, 6))
#> [1] FALSE

Sometimes, however, x cannot possibly represent the tested kind of sequence, independently of the hypothetical numbers substituted for NA elements. In such cases, scrutiny’s is_seq_*() functions will always return FALSE:

is_seq_linear(x = c(1, 2, NA, 10))
#> [1] FALSE
is_seq_linear(x = c(1, 2, NA, NA, NA, 10))
#> [1] FALSE

This is very much in the spirit of consistency testing. Even if certain data are unknown, it still makes sense to check whether or not any data could possibly fill in the gaps. The is_seq_*() functions effectively ask: Are the numbers left and right of the NAs consistent with each other, given their index positions?

It is worth emphasizing that this behavior is not exotic, or specific to scrutiny. It simply asserts the fundamental ideas of NA propagation in R. For example, is_seq_ascending(x = c(1, 2, NA, 1)) is FALSE for the same reason that NA & FALSE is FALSE: The outcome is the same for all possible values of NA (Wickham 2019, ch. 3.2.3).

Leading and trailing NAs are mostly ignored when determining whether x might be the kind of sequence in question:

is_seq_linear(x = c(NA, NA, 1, 2, 3, 4, NA))
#> [1] NA
is_seq_linear(x = c(NA, NA, 1, 2, NA, 4, NA))
#> [1] NA

The only exception, is_seq_dispersed(), is particularly sensitive to NA values:

# TRUE because x is symmetrically dispersed
# from 5 and contains no NA values:
is_seq_dispersed(x = c(3:7), from = 5)
#> [1] TRUE

# NA because it might be dispersed from 5,
# depending on the values hidden behind the NAs:
is_seq_dispersed(x = c(NA, 3:7, NA), from = 5)
#> [1] NA
is_seq_dispersed(x = c(NA, NA, 3:7, NA, NA), from = 5)
#> [1] NA

# FALSE because it's not symmetrically dispersed
# around 5, no matter what the NAs stand in for:
is_seq_dispersed(x = c(NA, 3:7), from = 5)
#> [1] FALSE
is_seq_dispersed(x = c(3:7, NA), from = 5)
#> [1] FALSE
is_seq_dispersed(x = c(3:7, NA, NA), from = 5)
#> [1] FALSE
is_seq_dispersed(x = c(NA, NA, 3:7), from = 5)
#> [1] FALSE

## Disperse from (around) half with disperse_total()

Briefly, disperse_total() checks if an input total is even or odd, cuts it in half, and creates “dispersed” group sizes going out from there, with each pair of group sizes adding up to the input total. This works naturally with even totals. For odd totals, it starts with the two integers closest to half.

The function internally calls either of disperse() and disperse2(), but I recommend simply using the higher-level disperse_total(). Here are two basic examples:

# With an even total...
disperse_total(n = 70)
#> # A tibble: 12 × 2
#>        n n_change
#>    <dbl>    <dbl>
#>  1    35        0
#>  2    35        0
#>  3    34       -1
#>  4    36        1
#>  5    33       -2
#>  6    37        2
#>  7    32       -3
#>  8    38        3
#>  9    31       -4
#> 10    39        4
#> 11    30       -5
#> 12    40        5

# ...and with an odd total:
disperse_total(n = 83)
#> # A tibble: 12 × 2
#>        n n_change
#>    <dbl>    <dbl>
#>  1    41        0
#>  2    42        0
#>  3    40       -1
#>  4    43        1
#>  5    39       -2
#>  6    44        2
#>  7    38       -3
#>  8    45        3
#>  9    37       -4
#> 10    46        4
#> 11    36       -5
#> 12    47        5

## Test for subsets, supersets, and equal sets

Starting with is_subset_of(), scrutiny features a distinctive family of predicate functions that test whether one vector x is a subset of another vector y, whether x is a superset of y (i.e. the reverse of a subset), or whether x and y are equal sets.

As a teaser: These functions are divided into three subgroups based on the way the second vector, y, is constituted. For example, you might test if x is a subset of multiple other vectors taken together, or a superset of a vector y that consists of multiple values entered along with x.

Functions from this family are not currently used as helpers inside other scrutiny functions, but that may well change. Use elsewhere is also conceivable.

# References

Wickham, Hadley. 2019. Advanced r. Second edition. Boca Raton: CRC Press/Taylor; Francis Group.