Standard ML tensor/multidimensional array library.
INDEX -Signature-
Indices are a enumerable finite set of data with an order and a map to a continous nonnegative interval of integers. In this implementation each index is a list of integers,
[i1,...,in]
and each set of indices is defined by a shape, which has the same shape of an index but with each integer incremented by one
shape = [k1,...,kn]
0 < i1 < k1
type storage = RowMajor | ColumnMajor order : storage
Identifies:
1) the underlying algorithms for this structure
2) the most significant index
3) the index that varies more slowly
4) the total order
RowMajor means that first index is most significant and varies
more slowly, while ColumnMajor means that last index is the most
significant and varies more slowly. For instance
RowMajor => [0,0]<[0,1]<[1,0]<[1,1] (C, C++, Pascal)
ColumnMajor => [0,0]>[1,0]>[0,1]>[1,1] (Fortran)
last shape first shape Returns the last/first index that belongs to the sed defined by 'shape'.
inBounds shape index Checkes whether 'index' belongs to the set defined by 'shape'.
toInt shape index As we said, indices can be sorted and mapped to a finite set of integers. 'toInt' obtaines the integer number that corresponds to a certain index.
indexer shape It is equivalent to the partial evaluation 'toInt shape' but optimized for 'shape'.
next shape index prev shape index next' shape index prev' shape index Obtain the following or previous index to the one we supply. next and prev return an object of type 'index option' so that if there is no such following/previous, the output is NONE. On the other hand, next'/prev' raise an exception when the output is not well defined and their output is always of type index. next/prev/next'/prev' raise an exception if 'index' does not belong to the set of 'shape'.
all shape f any shape f app shape f Iterates 'f' over every index of the set defined by 'shape'. 'all' stops when 'f' first returns false, 'any' stops when 'f' first returns true and 'app' does not stop and discards the output of 'f'.
compare(a,b) Returns LESS/GREATER/EQUAL according to the total order which is defined in the set of all indices. <,>,eq,<=,>=,<> Reduced comparisons which are defined in terms of 'compare'.
+,- Index addition and subtraction incr,decr Index increment and decrement by a constant
validShape t validIndex t Checks whether 't' conforms a valid shape or index.
iteri shape f
TENSOR -Signature-
Polymorphic tensors of any type. With 'tensor' we denote a (mutable) array of any rank, with as many indices as one wishes, and that may be traversed (map, fold, etc) according to any of those indices.
type 'a tensor Polymorphic tensor whose elements are all of type 'a.
val storage = RowMajor | ColumnMajor RowMajor = data is stored in consecutive cells, first index varying fastest (FORTRAN convention) ColumnMajor = data is stored in consecutive cells, last index varying fastest (C,C++,Pascal,CommonLisp convention)
new ([i1,...,in],init) Build a new tensor with n indices, each of sizes i1...in, filled with 'init'.
fromArray (shape,data) fromList (shape,data) Use 'data' to fill a tensor of that shape. An exception is raised if 'data' is too large or too small to properly fill the vector. Later use of a 'data' array is disregarded -- one must think that the tensor now owns the array.
length tensor rank tensor shape tensor Return the number of elements, the number of indices and the shape (size of each index) of the tensor.
toArray tensor Return the data of the tensor in the form of an array. Mutation of this array may lead to unexpected behavior.
sub (tensor,[i1,...,in]) update (tensor,[i1,...,in],new_value) Access the element that is indexed by the numbers [i1,..,in]
app f a appi f a The same as 'map' and 'mapi' but the function 'f' outputs nothing and no new array is produced, i.e. one only seeks the side effect that 'f' may produce.
map2 operation a b Apply function 'f' to pairs of elements of 'a' and 'b' and build a new tensor with the output. Both operands must have the same shape or an exception is raised. The procedure is sequential, as specified by 'storage'.
foldl operation a n Fold-left the elements of tensor 'a' along the n-th index.
all test a any test a Folded boolean tests on the elements of the tensor.
insert a b index Inserts b into a starting at the given index a and b must be of the same rank, with b smaller than a
cat a b int Concatenates a and b along the given axis