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This is a continuation of ArraysCowan, put on a separate page for convenience.

## Advanced procedures

These procedures are mostly derived in function, and sometimes in name, from ISO/IEC 8485 and ISO 17351, which standardize basic and extended APL respectively.

`(array-collapse `*array*` `*j*`)`

Let *k* be the rank of *array*. This procedure constructs and returns an array of rank *j*, which MUST be less than or equal to *k*, whose components are arrays of rank *k* - *j*. The shape of the returned array is equal to the first *j* components of the shape of *array*, and the shapes of its subarrays are equal to the remaining *k*-*j* components.

`(array-explode `*array*` `*j*`)`

Let *k* be the rank of *array*. This procedure constructs and returns an array of rank *j*, which MUST be greater than or equal to *k*. Each component of *array* MUST be an array of rank *j* - *k*, all of which MUST have the same shape. The shape of the returned array is the shape of *array* concatenated with the shape of any of its components, and each component is the corresponding component of the corresponding subarray of *array*.

`(array-reshape `*shape*` `*array*`)`

Constructs and returns a new array of shape *shape* whose components in row-major order are the same (in the sense of `eqv?`) as the components of *array* in row-major order. (APL reshape.)

`(array-reverse `*array*` `*axis*`)`

Constructs and returns an array with the same shape as *array*, but whose elements on the specified *axis* are reversed. *Axis* must be a non-negative integer less than the rank of *array*. (APL reverse.)

`(array-compress `*array*` `*booleans*` `*axis*`)`

Constructs and returns an array with the same shape as *array* except possibly along the *axis* dimension. The array is sliced along *axis* and the elements of *booleans* (a vector of boolean values) are used to decide which slices to incorporate into the result: if the corresponding boolean is `#t`, the slice is incorporated, otherwise not. (APL compress.)

`(array-expand `*array*` `*booleans*` `*nil*` `*axis*`)`

Constructs and returns an array with the same shape as *array* except possibly along the *axis* dimension. *Array* is sliced along *axis* and the elements of *booleans* (which MUST be a vector of boolean values) are used to decide where, if anywhere, *nil* (which must have the same shape as a slice) is to be interpolated: if the corresponding boolean is `#t`, *nil* is interpolated, otherwise the next slice is incorporated. The size of *booleans* MUST be equal to the value of the *axis* dimension in the result. (APL expand.)

`(array-rearrange `*array*` `*vector*` `*axis*`)`

Constructs and returns an array with the same shape as *array*. *Array* is sliced along the *axis* dimension, and the slices are reassembled in the order given by *vector*, which MUST be a vector of exact integers. The slice whose number appears in the first element of *vector* appears first in the result, and so on. (Generalized version of APL rotate.)

`(array-rearrange-axes `*array*` `*vector*`)`

Constructs and returns an array whose shape is a permutation of the shape of *array*. *Vector*, which MUST be a vector of exact integers, specifies how to permute it. The axis whose number appears in the first element of *vector* appears as the first axis of the result, and so on. (APL dyadic transpose with integer-valued vector.)

`(subarray `*array*` `*start-subscripts*` `*end-subscripts*`)`

Constructs and returns a smaller array with the same rank as *array* whose elements begin at the "lower left" corner specified by the list *start-subscripts* and end at the "upper right" corner specified by the list *end-subscripts*. (APL take and drop.)

`(array-recursive-ref `*array*` `*subscript* ...`)`

Applies `array-ref` to the *array* using the first *i* subscripts, where *i* is the rank of *array*. If there are more subscripts, the result MUST be an array. Apply `array-ref` to the result using the next *j* subscripts, where *j* is the rank of the result. Repeat until there are no more subscripts, returning the last result. (APL enlist.)

## Higher-order procedures

These procedures are mostly derived in function, and sometimes in name, from ISO/IEC 8485 and ISO 17351, which standardize basic and extended APL respectively.

`(array-reduce `*proc*` `*array*` `*axis*`)`

Constructs and returns an array whose rank is one less than the rank of *array*, by combining all the elements along *axis* using *proc*, which MUST be a two-argument procedure. The order and number of invocations of *proc* is unspecified. If there is only one such element, it is unchanged. (APL reduce.)

`(array-reduce-by-groups`*proc*` `*array*` `*axis*` `*n*`)`

Constructs and returns an array with the same rank as the rank of *array*, by combining all the groups of elements of length *n* along *axis* using *proc*, which MUST be a two-argument procedure. The order and number of invocations of *proc* is unspecified. If there is only one such group of elements, it is unchanged. (APL N-wise reduction.)

`(array-scan `*proc*` `*array*` `*axis*`)`

Constructs and returns an array whose shape is the same as the shape of *array*. Each element along *axis* is constructed by reducing (as if by `array-reduce`) successive prefixes of the elements of *array* along that axis. (APL scan.)

`(array-outer-product `*proc*` `*array1*` `*array2*`)`

Constructs and returns an array whose shape is the concatenation of the shapes of *array1* and *array2*. Each component of the new array is the result of applying *proc* to every element of *array1* and every element of *array2*. The order and number of invocations of *proc* is unspecified. (APL outer product.)

`(array-inner-product `*proc1*` `*proc2*` `*array1*` `*array2*`)`

Constructs and returns an array whose shape is equal to the shape of *array1* without its last element concatenated with the shape of *array2* without its first element; these elements MUST be numerically equal. It is an error if both arrays have rank 0.

Each element of the result array results from applying *proc2* to the corresponding elements of the last vectors of *array1* and the first vectors of *array2* and then reducing them with *proc1* to a single value. The order and number of invocations of the procedures is unspecified.

In particular, if both arrays have rank 1, the last and first vectors are the whole of the arrays, and the result has rank 0; if both arrays have rank 2, the last vectors of *array1* are the column-wise vectors, and the first vectors of *array2* are the row-wise vectors, and the result has rank 2. (APL inner product.)

Example: `(array-inner-product + * #(1 2 3) #(4 5 6))` computes the usual dot product of *vector1* and *vector2*.