This is a proposal for the WG2 multidimensional arrays package. These arrays are general: that is, the components may be any Scheme object. However, future proposals may add support for numeric-only arrays.
The axes of an array are its dimensions: a vector has one axis, a matrix has two, and so on. The rank of a vector is the number of axes it has. Note that in this proposal, the objects called "vectors" in Scheme are referred to as "Scheme vectors".
Every array has a shape, which is a Scheme vector of non-negative exact integers that specify the number of distinct values on each of its axes. Thus an array with shape #(4) is a vector whose axis contains 4 elements, by default labeled from 0 to 3, and an array with shape #(2 7) is a 2 x 7 matrix whose rows range by default from 0 to 1 and whose columns range by default from 0 to 6 respectively. A component of the shape MAY be 0, in which case the vector has no components. A rank-0 vector's shape is #(), and it has exactly one component.
It is possible to create arrays whose indexes have a lower bound other than 0, in which case the upper bound is not the same as the shape. In addition, the valid index values of a specific axis may be restricted to exact multiples of an integer known as the step.
Each array has associated with it a storage object, which for the purposes of this proposal is a Scheme vector. It is possible for many arrays to be associated with a single storage object. The locations associated with a storage object are known as storage elements. The values put into storage elements are eqv? to the values fetched from them.
An array's size is the total number of storage objects associated with it. This is the product of the components of the array's shape, or 1 if the shape has no components.
(make-array shape [initial-value])
(make-array lower-bounds upper-bounds [ steps [ initial-value ] ])
The first form of this procedure returns a newly allocated array whose shape is shape. The second form specifies the lower bounds (inclusive) and the upper bounds (exclusive) of the dimensions, along with the step values, if any (which default to 1 in each axis). All of these arguments are Scheme vectors. It is an error if they do not have the same length.
All the components of the new array are set to initial value if it is specified; otherwise their values are undefined.
(array shape obj ...)
Returns a newly allocatedn array whose shape is shape. Each obj is used to initialize the contents of the array in row-major order. This procedure cannot specify lower bounds or steps.
(vector->array shape vector)
(vector->array lower-bounds upper-bounds [ steps ] vector)
(list->array shape list)
(list->array lower-bounds upper-bounds [ steps ] list)
Returns a newly allocated array with shape shape, or with the specified lower-bounds, upper-bounds, and steps, containing the components of vector or list in storage order. If shape is omitted, the result has the same shape as vector.
(array? obj)
Returns #t if obj is an array and #f otherwise.
(array-shape array)
(array-lower-bounds array)
(array-upper-bounds array)
(array-steps array)
(array-strides array)
Returns the shape, lower bounds, upper bounds, steps, or strides of array as Scheme vectors. It is an error to m may be the same (in the sense of eqv?) as other arrays of the same shape. It is an error to mutate the results of these procedures.
(array-rank array)
Returns the rank of array.
(array-size array)
Returns the size of array.
(array-in-bounds? array subscript ...)
Returns #t if subscripts, which MUST be exact integers, are valid subscripts for array, and #f otherwise. A subscript is valid if it is non-negative and less than the corresponding component of the shape.
(array-storage array)
Returns the storage associated with an array.
(array-copy array)
Returns a new array with the same shape, bounds, steps, and strides as array. However, the storage object is a copy of the storage object of array.
(array-ref array subscript ...)
Returns the component of array specified by subscripts, which MUST be exact integers. It is an error to specify an invalid subscript.
(array-set! array subscript ... value)
Sets the component of array specified by subscripts, which MUST be exact integers, to value. Returns undefined values. It is an error to specify an invalid subscript.
(array-map proc array ...)
Applies proc to each corresponding component of the arrays in row-major order. It returns a newly allocated array with the same shape as array and containing components which are the results of the appropriate applications. It is an error unless all the arrays have the same shape. It is also an error unless proc accepts at least as many arguments as there are arrays.
(array-map! proc array ...)
Applies proc to each corresponding component of the arrays in row-major order and places the results into array. It is an error unless all the arrays have the same shape. It is also an error unless proc accepts at least as many arguments as there are arrays.
(array-for-each proc array ...)
Applies proc to each corresponding component of the arrays in storage order, discarding the results. Returns undefined values. It is an error unless all the arrays have the same shape. It is also an error unless proc accepts at least as many arguments as there are arrays.
(array-fold proc nil array ...)
Invokes proc on each component of arrays in storage order. Each invocation is passed as arguments a Scheme vector containing the array indices of the current component, and the result of the previous invocation, in that order. The Scheme vector may be reused by successive calls on proc. For the first invocation, nil is used as the final argument. Returns the result of the last invocation. It is an error unless all the arrays have the same shape. It is also an error unless proc accepts at least as many arguments as there are arrays.
(array->vector array)
Returns a newly allocated Scheme vector containing the components of array in row-major order.
(array->list array)
Returns a newly allocated list containing the components of array in row-major order.
(array->nested-vector array)
Returns a newly allocated Scheme vector whose components are also newly constructed Scheme vectors, and so on as far down as necessary to cover every axis of the vector. Bottom-level vectors contain the components of array. Thus, if array has rank 1, the result is a vector; if the array has rank 2, the result is a vector of vectors, and so on. It is an error if array has rank 0.
(array->nested-list array)
Returns a newly allocated list whose components are also newly constructed lists, and so on as far down as necessary to cover every axis of array. Bottom-level lists contain the components of array. Thus, if array has rank 1, the result is a list; if the array has rank 2, the result is a list of lists, and so on. It is an error if array has rank 0.
(nested-vector->array rank nested-vector)
Returns a newly allocated array with rank rank whose components are initialized from nested-vector. It is an error if nested-vector is not rectangular. As a special case, if rank is 0, the sole component is nested-vector, which need not be a vector.
(nested-list->array rank nested-list)
Returns an array with rank rank whose components are initialized from nested-list. It is an error if nested-list is not rectangular. As a special case, if rank is 0, the sole component is nested-list, which need not be a list.
See AdvancedArraysCowan.