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Slice semantics potentially differ per object; new semantics can be introduced when operator overloading the indexing operator. With Python standard lists (which are dynamic arrays), every slice is a copy. Slices of NumPy arrays, by contrast, are views onto the same underlying buffer.
first – the index of the first element in the slice; last – the index of the last element in the slice; end – one more than the index of last element in the slice; len – the length of the slice (= end - first) step – the number of array elements in each (default 1)
The possible slicings depend on the implementation details: for example, Fortran allows slicing off one column of a matrix variable, but not a row, and treat it as a vector; whereas C allow slicing off a row from a matrix, but not a column. On the other hand, other slicing operations are possible when array types are implemented in other ways.
Python sets are very much like mathematical sets, and support operations like set intersection and union. Python also features a frozenset class for immutable sets, see Collection types. Dictionaries (class dict) are mutable mappings tying keys and corresponding values. Python has special syntax to create dictionaries ({key: value})
Based on the original definition of Weiser, [3] informally, a static program slice S consists of all statements in program P that may affect the value of variable v in a statement x. The slice is defined for a slicing criterion C=(x,v) where x is a statement in program P and v is variable in x.
In Python, the ellipsis is a nullary expression that represents the Ellipsis singleton. It's used particularly in NumPy, where an ellipsis is used for slicing an arbitrary number of dimensions for a high-dimensional array: [10]
The fundamental idea behind array programming is that operations apply at once to an entire set of values. This makes it a high-level programming model as it allows the programmer to think and operate on whole aggregates of data, without having to resort to explicit loops of individual scalar operations.
Note how the use of A[i][j] with multi-step indexing as in C, as opposed to a neutral notation like A(i,j) as in Fortran, almost inevitably implies row-major order for syntactic reasons, so to speak, because it can be rewritten as (A[i])[j], and the A[i] row part can even be assigned to an intermediate variable that is then indexed in a separate expression.