Generate Lists, Vectors, Data Frames and Matrices with List Comprehension

Description

Functions to transform a base expression containing free variables into a list, a vector, a data frame, or a matrix based on variable ranges and additional conditions.

Usage

gen.list(.expr, ...)

gen.vector(.expr, ...)

gen.data.frame(.expr, ..., byrow = FALSE)

gen.matrix(.expr, ..., byrow = FALSE)

Arguments

Value

The result of gen.list is a list (a vector for gen.vector) containing an entry for each combination of the free variables (i.e., the Cartesian product), where all the free variables in .expr are substituted. The function gen.vector returns a vector while gen.list may contain also more complex substructures (like vectors or lists).

The output of gen.data.frame is a data frame where each substituted .expr entry is one row. The base expression .expr should contain a (named) vector or list, such that each entry of this vector becomes a column of the returned data frame. If the vector contains a single literal without a name, this is taken as column name. For instance, gen.data.frame(a, a = 1:5) returns the same as gen.data.frame(c(a = a), a = 1:5). Default names 'V1', 'V2', ... are used, if no names are given and names can't be automatically detected.

The result of gen.matrix:

• It's similar to gen.data.frame, if .expr evaluates to a vector of length > 1, or row/column names are given. Each substituted .expr entry is one row of the matrix. In contrast to gen.data.frame, column names are not auto-generated, e.g., gen.matrix(c(a_1, a_2), a_ = 1:2) is an unnamed matrix. If the .expr argument has explicit names (e.g., c(a_1 = a_1, a_2 = a_2)), these column names are assigned to the resulting matrix.

• It's a matrix where the rows and columns are induced by the two variables within ..., if .expr is a scalar, and no names or conditions are given. If byrow is FALSE, the second variable (i.e., the inner loop) refers to the columns, otherwise it refers to the rows. For instance, gen.matrix(i + j, i = 1:3, j = 1:2) is a matrix with 3 rows and 2 columns. For gen.matrix(i + j, i = 1:3, j = 1:2, byrow = TRUE) we get 2 rows and 3 columns.

All expressions and conditions are applied to each combination of the free variables separately, i.e., they are applied row-wise and not vector-wise. For instance, the term sum(x,y) (within .expr or a condition) is equivalent to x+y.

Indices for variables

A range for a variable ending with an underscore (like x_) defines a set of ranges affecting all variables named {varname}_{index}, e.g. x_1. For instance, in gen.vector(x_1 + x_2 + x_3, x_ = 1:5) the variables x_1, x_2, x_3 are all ranging in 1:5. This can be overwritten for each single x_i, e.g., an additional argument x_3 = 1:3 assigns the range 1:3 to x_3 while x_1 and x_2 keep the range 1:5. A group of indexed variables is kept always sorted according to the position of the main variable {varname}_. For instance, the two following statements produce the same results:

• gen.vector(x_1 + x_2 + a, x_ = 1:5, a = 1:2, x_1 = 1:2)

• gen.vector(x_1 + x_2 + a, x_1 = 1:2, x_2 = 1:5, a = 1:2)

Folded expressions

Expressions and conditions support a ...-notation which works as follows:

• A vector like c(x_1, ..., x_4) is a shortcut for c(x_1, x_2, x_3, x_4).

• A named vector like c(a_1 = x_1, ..., a_3 = x_3) is a shortcut for c(a_1 = x_1, a_2 = x_2, a_3 = x_3).

• A n-ary function argument like sum(x_1, ..., x_4) is a shortcut for sum(x_1, x_2, x_3, x_4).

• Repeated expressions of binary operators can be abbreviated with the ... expressions as follows: x_1 + ... + x_4 is a shortcut for x_1 + x_2 + x_3 + x_4. Note that, due to operator precedence, 1 + x_1 + ... + x_4 will not work, but 1 + (x_1 + ... + x_4) works as expected.

• For non-commutative operators, x_1 - ... - x_4 is a shortcut for x_1 - x_2 - x_3 - x_4 which is evaluated as ((x_1 - x_2) - x_3) - x_4.

The conditions may contain itself list comprehension expressions, e.g., gen.logical.and to compose and-connected logical expressions.

Character patterns

In expression there may occur characters with {}-placeholders. The content of these placeholders is evaluated like any other part of an expression and converted to a character. For example, "a{x}" is transformed into "a1" for x = 1. Double brackets are transformed into a single bracket without evaluating the inner expression. For instance, "var{x + 1}_{{a}}" is transformed into "var2_{a}" for x = 1.

See Also

gen.named.list to generate named structures, gen.list.expr to generate expressions to be evaluated later, gen.logical.and to generate logical and/or conditions, and listcompr for an overview of all list comprehension functions.

Examples

# Sum of 1:x
gen.vector(sum(1:x), x = 1:10)

# Same as above, but return as text
gen.list("sum of 1 to {x} is {sum(1:x)}", x = 1:5)

# A list containing vectors [1], [1, 2], [1, 2, 3], ...
gen.list(gen.vector(i, i = 1:n), n = 1:10)

# A data frame of tuples (x_1, x_2, x_3) summing up to 10
gen.data.frame(c(x_1, ..., x_3), x_ = 1:10, x_1 + ... + x_3 == 10)

# Same as above, but restrict to ascending tuples with x_i <= x_(i+1)
gen.data.frame(c(x_1, ..., x_3), x_1 = 1:10, x_2 = x_1:10, x_3 = x_2:10,
               x_1 + ... + x_3 == 10)

# A data frame containing the numbers in 2:20, the sum of their divisors
# and a flag if they are "perfect" (sum of divisors equals the number)
gen.data.frame(list(n, sumdiv, perfect = (n == sumdiv)), n = 2:20, 
               sumdiv = sum(gen.vector(x, x = 1:(n-1), n %% x == 0)))
               
# A diagonal matrix with (1, ..., 5) on the diagonal
gen.matrix(if (i == j) i else 0, i = 1:5, j = 1:5)

Generate List and Vector Expressions with List Comprehension

Description

Functions to transform a base expression containing free variables into a list or a vector of expressions, based on variable ranges and additional conditions.

Usage

gen.list.expr(.expr, ...)

gen.vector.expr(.expr, ...)

gen.named.list.expr(.str, .expr, ...)

gen.named.vector.expr(.str, .expr, ...)

Arguments

Details

See gen.list for more details on the .expr and ... parameters.

See gen.named.list for more details on the .str parameter.

For variables with underscores additionally the evaluation of indices in ()-brackets is supported. For example, an expression x_(i+1) is evaluated as x_3 for i = 2.

Value

Returns an expression containing a list or a vector which might be evaluated later. The argument .expr is partially evaluated, where all free variables are substituted for which a range is given. The other variables remain untouched.

See Also

gen.list to generate lists, gen.named.list to generate named lists, and listcompr for an overview of all list comprehension functions.

Examples

# An expression which is partially evaluated
gen.list.expr(a_i + 2 * i, i = 1:4)

# Generate an expression with placeholders a_i,
# generate data for a_1, ..., a_4 and finally evaluate it
expr <- gen.vector.expr(a_i + a_(j+1), i = 1:3, j = 1:3, i != j)
data <- gen.data.frame(c(a_1 = a_1, ..., a_4 = a_4), a_ = 1:2)
eval(expr, data)

Generate Logical Conditions with List Comprehension

Description

Functions to compose and-/or-connected logical conditions, based on variable ranges and additional conditions.

Usage

gen.logical.and(.expr, ...)

gen.logical.or(.expr, ...)

Arguments

Details

See gen.list for more details on the .expr and ... parameters.

For variables with underscores additionally the evaluation of indices in ()-brackets is supported. For example, an expression x_(i+1) is evaluated as x_3 for i = 2.

Value

Returns an expression expr_1 & ... & expr_n or expr_1 | ... | expr_n where expr_i is generated from .expr, where all free variables are substituted for which a range is given. The other variables remain untouched.

The generated condition may be used within the the conditions of gen.list and similar functions from this package.

See Also

gen.list to generate lists and thereby make use of the generated logical conditions, and listcompr for an overview of all list comprehension functions.

Examples

# Returns a_1 == 1 & a_2 == 2 & a_3 == 3
gen.logical.and(a_i == i, i = 1:3)

# A data frame of tuples (x_1, x_2, x_3, x_4) summing up to 10 with x_i <= x_(i+1)
gen.data.frame(c(x_1, ..., x_4), x_ = 1:10, x_1 + ... + x_4 == 10, 
               gen.logical.and(x_i <= x_(i+1), i = 1:3))

# Get all permutations of 1:4
gen.data.frame(c(a_1, ..., a_4), a_ = 1:4, 
               gen.logical.and(a_i != a_j, i = 1:4, j = (i+1):4))
               
# Get again the permutations of 1:4, using filter from dplyr 
df <- gen.data.frame(c(a_1, ..., a_4), a_ = 1:4)
dplyr::filter(df, !!gen.logical.and(a_i != a_j, i = 1:3, j = (i+1):4))

Generate Named Lists, Vectors, Data Frames, and Matrices with List Comprehension

Description

Functions to transform patterns with placeholders into characters or into names of lists, vectors, data frames or matrices, based on variable ranges and additional conditions.

Usage

gen.named.list(.str, .expr, ...)

gen.named.vector(.str, .expr, ...)

gen.named.data.frame(.str, .expr, ..., byrow = FALSE)

gen.named.matrix(.str, .expr, ..., byrow = FALSE)

Arguments

Details

The free variables in the inner expressions (i.e., the content of the {}-brackets) of .expr are evaluated in the same way as expressions in gen.list.

See gen.list for more details on the .expr and ... parameters.

Value

These functions return lists, vectors, data frames, and matrices. They work very similar to their counterparts without ".named". Additionally the vector of characters, induced by .str, serves as a vector of names for the generated structures. In case of lists or vectors, the result is a named list or a named vector. For data frames and matrices, the names are taken as row names.

See Also

gen.list for explanations on list and vector comprehension, and listcompr for an overview of all list comprehension functions.

Examples

# sum up 1:i for i in 1:5
gen.named.list("sum_to_{x}", sum(1:x), x = 1:5)

# matrix with named columns and rows
gen.named.matrix("row{i}", gen.named.vector("col{j}", i+j, j = 1:3), i = 1:3)

# a matrix where the expression refers to the rows and not the columns
gen.named.matrix("col{i}", c(row1 = i, row2 = 10 * i, row3 = 100 * i), i = 1:10,
                 byrow = TRUE)

Summary of the listcompr Package

Description

The listcompr package offers some syntactic shortcuts to create lists, vectors and data frames containing values within a given range with given conditions. It is a light-weight package written in base R without any compiled code or dependencies to other packages.

Functions

• The main functionality of listcompr: generate lists, vectors, and data frames: gen.list

• Generate named lists, vectors, and data frames: gen.named.list

• Generate expressions containing lists and vectors: gen.list.expr

• Generate conditions to be used in other functions of listcompr: gen.logical.and

Vignettes

To learn the basics of listcompr, start with the vignette:

vignette("introduction", package = "listcompr")

Contact

To submit bugs, feature requests or other comments, feel free to write a mail to me.

Author(s)

Patrick Roocks, mail@p-roocks.de