TBD - arrays are multidimensional objects based on top of one-dimensional storage objects
TBD: array, storage class, storage object, index, dimension, rank, upper bound, lower bound, stride, offset, start, end
A storage class is a group of storage objects with the same behavior. A storage object maps a non-negative exact integer index into a storage location. There are standard storage classes, but it is also possible for programmers to create their own storage classes. Each storage class allows creating a storage object of a given size, accessing a location by its index, and mutating a location by its index to a new value. Note that the procedures used to do this need not be the standard procedures such as make-vector, vector-ref, and vector-set!; they may be more efficient equivalents.
vector-storage-class
Used to create and manipulate a Scheme vector as storage.
bytevector-u8-storage-class
bytevector-s8-storage-class
bytevector-u16-storage-class
bytevector-u16be-storage-class
bytevector-u16le-storage-class
bytevector-s16-storage-class
bytevector-s16be-storage-class
bytevector-s16le-storage-class
bytevector-u32-storage-class
bytevector-u32be-storage-class
bytevector-u32le-storage-class
bytevector-s32-storage-class
bytevector-s32be-storage-class
bytevector-s32le-storage-class
bytevector-u64-storage-class
bytevector-u64be-storage-class
bytevector-u64le-storage-class
bytevector-s64-storage-class
bytevector-s64be-storage-class
bytevector-s64le-storage-class
bytevector-f32-storage-class
bytevector-f32be-storage-class
bytevector-f32le-storage-class
bytevector-f64-storage-class
bytevector-f64be-storage-class
bytevector-f64le-storage-class
bytevector-c64-storage-class
bytevector-c64be-storage-class
bytevector-c64le-storage-class
bytevector-c128-storage-class
bytevector-c128be-storage-class
bytevector-c128le-storage-class
Used to create and manipulate a Scheme bytevector as storage, viewed as one of the given kinds of numeric vectors: signed or unsigned 8-bit, 16-bit, 32-bit, and 64-bit integers, 32-bit and 64-bit floats, and 64-bit and 128-bit float complex numbers. All can be in native byte order, little-endian byte order, or big-endian byte order, though the u8 and s8 classes have only native byte order.
u8vector-storage-class
s8vector-storage-class
bytevector-u16-storage-class
bytevector-s16-storage-class
bytevector-u32-storage-class
bytevector-s32-storage-class
bytevector-u64-storage-class
bytevector-s64-storage-class
bytevector-f32-storage-class
bytevector-f64-storage-class
bytevector-c64-storage-class
bytevector-c128-storage-class
Used to create and manipulate native numeric vectors as as storage. Note that only native byte order is provided.
sparse-storage-class
Used to create and manipulate an object of arbitrary type (run-length-encoded vector, hash table, tree, etc.) that provides a sparse representation of the mapping between indexes and arbitrary Scheme objects.
(make-storage-class constructor accessor mutator)
Returns a storage class with the specified procedures as constructor, accessor, and mutator. The invocation protocols are (constructor size), where size is a non-negative integer; (accessor storage-object index), where storage-object is a storage object returned by a call to the constructor and index is a non-negative integer less than size, and (mutator storage-object index value), where value is a value which can be stored in storage-object. Storage classes created by this procedure do not have to have actual storage objects (they can access and mutate values algorithmicallly), in which case they can ignore the storage-object argument.
(array? obj)
Returns #t if obj is an array, and #f otherwise.
(make-array storage-class [ lower-bounds ] upper-bounds)
Returns a newly allocated array with a newly allocated storage object. The lower and upper bounds of the array's dimensions are specified as vectors: they must be of the same length. If lower-bounds is not given, it is understood to be all zeros.
(array-storage-class array)
Returns the storage class with which array was created. Note that there is no way to access the storage object, as it may not exist.
(array-rank array)
Return the rank (number of dimensions) of array. Note that "rank" is an APL term that has nothing to do with matrix ranks.
(array-lower-bounds array)
Return a vector containing the lower bounds of array. It is an error to mutate this vector.
(array-upper-bounds array)
Return a vector containing the upper bounds of array. It is an error to mutate this vector.
(array-strides array)
Return a vector containing the strides of array. It is an error to mutate this vector.
(array-lower-bound array n)
Return a vector containing the nth lower bound of array.
(array-upper-bounds array n)
Return a vector containing the nth upper bound of array.
(array-stride array n)
Return a vector containing the nth stride of array.
(array-offset array)
Returns the storage offset of array. This is the storage index of the location whose array index is specified by all zeros.
(array-ref array index)
Returns the value of the element of array specified by index, which is a vector. Note that this is different from the array-ref of most Lisp systems, which specify the index as a sequence of arguments.
(array-for-each proc array [ start [ end ] ])
Iterates over the elements of array starting at the index start and ending at the index end, and calling proc on each element. Each invocation of proc receives array, the current index, and the value of the element at that index. It is an error to mutate the index.
(array-for-each-index proc array [ start [ end ] ])
Iterates over the indexes of array starting at the index start and ending at the index end, and calling proc on each element. Each invocation of proc receives array and the current index. The value returned by proc is discarded. It is an error to mutate the index.
(array-set! array index value)
Sets the value of the element of array specified by index to value. Note that this is different from the array-set! of most Lisp systems, which specify the index as a sequence of arguments.
(array-tabulate! proc array [ start [ end ] ])
Iterates over the elements of array starting at the index start (each dimension is inclusive) and ending at the index end (each dimension is exclusive), and calling proc on each element. Each invocation of proc receives array and the current index. Whatever proc returns becomes the value of the array at the index. It is an error for proc to mutate the index.
FIXME from here down.
(array-map proc array ...)
Returns a newly allocated array with the same structure as the arrays, which must all have the same structure. For each valid index value, proc is invoked in arbitrary order, passing the index and all the arrays. The index may or may not be the same Scheme vector for each call. Whatever proc returns becomes the value of the storage element corresponding to that index in the result array.
(array-map! proc array ...)
The arrays must all have the same structure. For each valid index value, proc is invoked in arbitrary order, passing the index and all the arrays. The index may or may not be the same Scheme vector for each call. Whatever proc returns becomes the value of the storage element corresponding to that index in the first array argument. The value returned is undefined.
(array-fold proc seed array ...)
The arrays must all have the same structure. For each valid index value, proc is invoked in row-major order, passing the index, all the arrays, and the seed value. The index may or may not be the same Scheme vector for each call. The result is used as the seed for the next call to 'proc', and the final seed is returned.
(array-reduce proc array axis [ n ])
Returns a newly allocated array whose rank is one less than the rank of array, by combining all the groups of elements of length n (default 1) 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-cumulate proc array axis)
Returns a newly allocated 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)
Returns a newly allocated 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)
Returns a newly allocated 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 + * vector1 vector2) computes the usual dot product of vector1 and vector2.
(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 array. Bottom-level Scheme vectors contain the components of array. Thus, if array has rank 1, the result is a Scheme vector; if the array has rank 2, the result is a Scheme vector containing Scheme vectors, and so on. As a special case, if array has rank 0, the sole component is returned.
(nested-vector->array rank nested-vector)
Returns a newly allocated array with rank rank whose components are initialized from the Scheme vectornested-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 Scheme vector.
See AdvancedArraysCowan.