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std.experimental.ndslice.slice

This is a submodule of std.experimental.ndslice.
Authors:
Ilya Yaroshenko
auto sliced(Flag!"replaceArrayWithPointer" ra = Yes.replaceArrayWithPointer, Flag!"allowDownsize" ad = No.allowDownsize, Range, size_t N)(Range range, size_t[N] lengths...)
if (!isStaticArray!Range && !isNarrowString!Range && N);

auto sliced(Flag!"replaceArrayWithPointer" ra = Yes.replaceArrayWithPointer, Flag!"allowDownsize" ad = No.allowDownsize, size_t N, Range)(Range range, size_t[N] lengths, size_t shift = 0)
if (!isStaticArray!Range && !isNarrowString!Range && N);

template sliced(Names...) if (Names.length && !anySatisfy!(isType, Names) && allSatisfy!(isStringValue, Names))

auto sliced(Flag!"replaceArrayWithPointer" ra = Yes.replaceArrayWithPointer, Flag!"allowDownsize" ad = No.allowDownsize, Range)(Range range)
if (!isStaticArray!Range && !isNarrowString!Range && hasLength!Range);
Creates an n-dimensional slice-shell over a range.
Parameters:
Range range a random access range or an array; only index operator auto opIndex(size_t index) is required for ranges. The length of the range should be equal to the sum of shift and the product of lengths. If ad, the length of the range should be greater than or equal to the sum of shift and the product of lengths.
size_t[N] lengths list of lengths for each dimension
size_t shift index of the first element of a range. The first shift elements of range are ignored.
Names names of elements in a slice tuple. Slice tuple is a slice, which holds single set of lengths and strides for a number of ranges.
ra If yes, the array will be replaced with its pointer to improve performance. Use no for compile time function evaluation.
ad If yes, no assert error will be thrown for range, which has a length and its length is greater then the sum of shift and the product of lengths.
Returns:
n-dimensional slice
Examples:
Creates a slice from an array.
auto slice = slice!int(5, 6, 7);
writeln(slice.length); // 5
writeln(slice.elementsCount); // 5 * 6 * 7
static assert(is(typeof(slice) == Slice!(3, int*)));
Examples:
Creates a slice using shift parameter.
import std.range : iota;
auto slice = (5 * 6 * 7 + 9).iota.sliced([5, 6, 7], 9);
writeln(slice.length); // 5
writeln(slice.elementsCount); // 5 * 6 * 7
writeln(slice[0, 0, 0]); // 9
Examples:
Creates an 1-dimensional slice over a range.
import std.range : iota;
auto slice = 10.iota.sliced;
writeln(slice.length); // 10
Examples:
Vandermonde matrix
auto vandermondeMatrix(Slice!(1, double*) x)
{
    auto ret = slice!double(x.length, x.length);
    foreach (i; 0 .. x.length)
    foreach (j; 0 .. x.length)
        ret[i, j] = x[i] ^^ j;
    return ret;
}

auto x = [1.0, 2, 3, 4, 5].sliced(5);
auto v = vandermondeMatrix(x);
assert(v ==
    [[  1.0,   1,   1,   1,   1],
     [  1.0,   2,   4,   8,  16],
     [  1.0,   3,   9,  27,  81],
     [  1.0,   4,  16,  64, 256],
     [  1.0,   5,  25, 125, 625]]);
Examples:
Creates a slice composed of named elements, each one of which corresponds to a given argument. See also assumeSameStructure.
import std.algorithm.comparison : equal;
import std.experimental.ndslice.selection : byElement;
import std.range : iota;

auto alpha = 12.iota;
auto beta = new int[12];

auto m = sliced!("a", "b")(alpha, beta, 4, 3);
foreach (r; m)
    foreach (e; r)
        e.b = e.a;
assert(equal(alpha, beta));

beta[] = 0;
foreach (e; m.byElement)
    e.b = e.a;
assert(equal(alpha, beta));
Examples:
Random access range primitives for slices over user defined types
struct MyIota
{
    //`[index]` operator overloading
    auto opIndex(size_t index)
    {
        return index;
    }
}

alias S = Slice!(3, MyIota);
import std.range.primitives;
static assert(hasLength!S);
static assert(hasSlicing!S);
static assert(isRandomAccessRange!S);

auto slice = MyIota().sliced(20, 10);
writeln(slice[1, 2]); // 12
auto sCopy = slice.save;
writeln(slice[1, 2]); // 12
Examples:
Slice tuple and flags
import std.typecons : Yes, No;
static immutable a = [1, 2, 3, 4, 5, 6];
static immutable b = [1.0, 2, 3, 4, 5, 6];
alias namedSliced = sliced!("a", "b");
auto slice = namedSliced!(No.replaceArrayWithPointer, Yes.allowDownsize)
    (a, b, 2, 3);
writeln(slice[1, 2].a); // slice[1, 2].b
template assumeSameStructure(Names...) if (Names.length && !anySatisfy!(isType, Names) && allSatisfy!(isStringValue, Names))
Groups slices into a slice tuple. The slices must have identical structure. Slice tuple is a slice, which holds single set of lengths and strides for a number of ranges.
Parameters:
Names names of elements in a slice tuple
Returns:
n-dimensional slice
See Also:
Examples:
import std.algorithm.comparison : equal;
import std.experimental.ndslice.selection : byElement, iotaSlice;

auto alpha = iotaSlice(4, 3);
auto beta = slice!int(4, 3);

auto m = assumeSameStructure!("a", "b")(alpha, beta);
foreach (r; m)
    foreach (e; r)
        e.b = cast(int)e.a;
writeln(alpha); // beta

beta[] = 0;
foreach (e; m.byElement)
    e.b = cast(int)e.a;
writeln(alpha); // beta
Examples:
import std.algorithm.iteration : map, sum, reduce;
import std.algorithm.comparison : max;
import std.experimental.ndslice.iteration : transposed;
import std.typecons : No;

/// Returns maximal column average.
auto maxAvg(S)(S matrix) {
    return matrix.transposed.map!sum.reduce!max
         / matrix.length;
}
enum matrix = [1, 2,
               3, 4].sliced!(No.replaceArrayWithPointer)(2, 2);
///Сompile time function evaluation
static assert(maxAvg(matrix) == 3);
Examples:
import std.algorithm.iteration : map, sum, reduce;
import std.algorithm.comparison : max;
import std.experimental.ndslice.iteration : transposed;
import std.typecons : No;

/// Returns maximal column average.
auto maxAvg(S)(S matrix) {
    return matrix.transposed.map!sum.reduce!max
         / matrix.length;
}
enum matrix = [1, 2,
               3, 4].sliced!(No.replaceArrayWithPointer)(2, 2);
///Сompile time function evaluation
static assert(maxAvg(matrix) == 3);
Slice!(N, Select!(ra, T*, T[])) slice(T, Flag!"replaceArrayWithPointer" ra = Yes.replaceArrayWithPointer, size_t N)(size_t[N] lengths...);

auto slice(T, Flag!"replaceArrayWithPointer" ra = Yes.replaceArrayWithPointer, size_t N)(size_t[N] lengths, T init);

auto slice(Flag!"replaceArrayWithPointer" ra = Yes.replaceArrayWithPointer, size_t N, Range)(Slice!(N, Range) slice);
Creates an array and an n-dimensional slice over it.
Parameters:
size_t[N] lengths list of lengths for each dimension
Slice!(N, Range) slice slice to copy shape and data from
Returns:
n-dimensional slice
Examples:
auto tensor = slice!int(5, 6, 7);
writeln(tensor.length); // 5
writeln(tensor.elementsCount); // 5 * 6 * 7
static assert(is(typeof(tensor) == Slice!(3, int*)));

// creates duplicate using `slice`
auto dup = tensor.slice;
writeln(dup); // tensor
Examples:
auto tensor = slice([2, 3], 5);
writeln(tensor.elementsCount); // 2 * 3
writeln(tensor[1, 1]); // 5
auto uninitializedSlice(T, Flag!"replaceArrayWithPointer" ra = Yes.replaceArrayWithPointer, size_t N)(size_t[N] lengths...);
Creates an uninitialized array and an n-dimensional slice over it.
Parameters:
size_t[N] lengths list of lengths for each dimension
slice slice to copy shape and data from
Returns:
uninitialized n-dimensional slice
Examples:
auto tensor = uninitializedSlice!int(5, 6, 7);
writeln(tensor.length); // 5
writeln(tensor.elementsCount); // 5 * 6 * 7
static assert(is(typeof(tensor) == Slice!(3, int*)));
auto makeSlice(Flag!"replaceArrayWithPointer" ra = Yes.replaceArrayWithPointer, Allocator, size_t N, Range)(auto ref Allocator alloc, Slice!(N, Range) slice);

SliceAllocationResult!(N, T, ra) makeSlice(T, Flag!"replaceArrayWithPointer" ra = Yes.replaceArrayWithPointer, Allocator, size_t N)(auto ref Allocator alloc, size_t[N] lengths...);

SliceAllocationResult!(N, T, ra) makeSlice(T, Flag!"replaceArrayWithPointer" ra = Yes.replaceArrayWithPointer, Allocator, size_t N)(auto ref Allocator alloc, size_t[N] lengths, T init);

SliceAllocationResult!(N, T, ra) makeSlice(T, Flag!"replaceArrayWithPointer" ra = Yes.replaceArrayWithPointer, Allocator, size_t N, Range)(auto ref Allocator alloc, Slice!(N, Range) slice);
Allocates an array through a specified allocator and creates an n-dimensional slice over it. See also std.experimental.allocator.
Parameters:
Allocator alloc allocator
size_t[N] lengths list of lengths for each dimension
T init default value for array initialization
Slice!(N, Range) slice slice to copy shape and data from
Returns:
a structure with fields array and slice

Note: makeSlice always returns slice with mutable elements

Examples:
import std.experimental.allocator;
import std.experimental.allocator.mallocator;

auto tup = makeSlice!int(Mallocator.instance, 2, 3, 4);

writeln(tup.array.length); // 24
writeln(tup.slice.elementsCount); // 24
writeln(tup.array.ptr); // &tup.slice[0, 0, 0]

// makes duplicate using `makeSlice`
tup.slice[0, 0, 0] = 3;
auto dup = makeSlice(Mallocator.instance, tup.slice);
writeln(dup.slice); // tup.slice

Mallocator.instance.dispose(tup.array);
Mallocator.instance.dispose(dup.array);
Examples:
Initialization with default value
import std.experimental.allocator;
import std.experimental.allocator.mallocator;

auto tup = makeSlice(Mallocator.instance, [2, 3, 4], 10);
auto slice = tup.slice;
writeln(slice[1, 1, 1]); // 10
Mallocator.instance.dispose(tup.array);
SliceAllocationResult!(N, T, ra) makeUninitializedSlice(T, Flag!"replaceArrayWithPointer" ra = Yes.replaceArrayWithPointer, Allocator, size_t N)(auto ref Allocator alloc, size_t[N] lengths...);
Allocates an uninitialized array through a specified allocator and creates an n-dimensional slice over it. See also std.experimental.allocator.
Parameters:
Allocator alloc allocator
size_t[N] lengths list of lengths for each dimension
init default value for array initialization
slice slice to copy shape and data from
Returns:
a structure with fields array and slice
Examples:
import std.experimental.allocator;
import std.experimental.allocator.mallocator;

auto tup = makeUninitializedSlice!int(Mallocator.instance, 2, 3, 4);

writeln(tup.array.length); // 24
writeln(tup.slice.elementsCount); // 24
writeln(tup.array.ptr); // &tup.slice[0, 0, 0]

Mallocator.instance.dispose(tup.array);
struct SliceAllocationResult(size_t N, T, Flag!"replaceArrayWithPointer" ra);
Structure used by makeSlice and makeUninitializedSlice.
T[] array;
Slice!(N, Select!(ra, T*, T[])) slice;
auto ndarray(size_t N, Range)(Slice!(N, Range) slice);
Creates a common n-dimensional array from a slice.
Parameters:
Slice!(N, Range) slice slice
Returns:
multidimensional D array
Examples:
import std.experimental.ndslice.selection : iotaSlice;
auto slice = iotaSlice(3, 4);
auto m = slice.ndarray;
static assert(is(typeof(m) == size_t[][]));
writeln(m); // [[0, 1, 2, 3], [4, 5, 6, 7], [8, 9, 10, 11]]
auto makeNdarray(T, Allocator, size_t N, Range)(auto ref Allocator alloc, Slice!(N, Range) slice);
Allocates a common n-dimensional array using data from a slice.
Parameters:
Allocator alloc allocator (optional)
Slice!(N, Range) slice slice
Returns:
multidimensional D array
Examples:
import std.experimental.allocator;
import std.experimental.allocator.mallocator;
import std.experimental.ndslice.selection : iotaSlice;

auto slice = iotaSlice(3, 4);
auto m = Mallocator.instance.makeNdarray!long(slice);

static assert(is(typeof(m) == long[][]));

static immutable ar = [[0L, 1, 2, 3], [4L, 5, 6, 7], [8L, 9, 10, 11]];
writeln(m); // ar

foreach (ref row; m)
    Mallocator.instance.dispose(row);
Mallocator.instance.dispose(m);
@property auto shape(T)(T[] array, ref int err);
Shape of a common n-dimensional array.
Parameters:
T[] array common n-dimensional array
int err error flag
Returns:
static array of dimensions type of size_t[n]
Examples:
int err;
size_t[2] shape = [[1, 2, 3], [4, 5, 6]].shape(err);
writeln(shape); // [2, 3]
writeln(err); // 0

[[1, 2], [4, 5, 6]].shape(err);
assert(err != 0);
Examples:
Slice from ndarray
int err;
auto array = [[1, 2, 3], [4, 5, 6]];
auto slice = array.shape(err).slice!int;
writeln(err); // 0
slice[] = [[1, 2, 3], [4, 5, 6]];
writeln(slice); // array
template as(T)
Convenience function that creates a lazy view, where each element of the original slice is converted to the type T. It uses mapSlice  and to  composition under the hood.
Parameters:
Slice!(N, Range) slice a slice to create a view on.
Returns:
A lazy slice with elements converted to the type T.
Examples:
import std.experimental.ndslice.slice : as;
import std.experimental.ndslice.selection : diagonal;

auto matrix = slice!double([2, 2], 0);
auto stringMatrixView = matrix.as!string;
assert(stringMatrixView ==
        [["0", "0"],
         ["0", "0"]]);

matrix.diagonal[] = 1;
assert(stringMatrixView ==
        [["1", "0"],
         ["0", "1"]]);

/// allocate new slice composed of strings
Slice!(2, string*) stringMatrix = stringMatrixView.slice;
auto as(size_t N, Range)(Slice!(N, Range) slice);
class SliceException: object.Exception;
Base Exception class for std.experimental.ndslice.
pure nothrow @nogc @safe this(string msg, string file = __FILE__, uint line = cast(uint)1041, Throwable next = null);
template DeepElementType(S : Slice!(N, Range), size_t N, Range)
Returns the element type of the Slice type.
Examples:
import std.range : iota;
static assert(is(DeepElementType!(Slice!(4, const(int)[]))     == const(int)));
static assert(is(DeepElementType!(Slice!(4, immutable(int)*))  == immutable(int)));
static assert(is(DeepElementType!(Slice!(4, typeof(100.iota))) == int));
//packed slice
static assert(is(DeepElementType!(Slice!(2, Slice!(5, int*)))  == Slice!(4, int*)));
struct Structure(size_t N);
size_t[N] lengths;
sizediff_t[N] strides;
struct Slice(size_t _N, _Range) if (_N && _N < 256LU && (!is(Unqual!_Range : Slice!(N0, Range0), size_t N0, Range0) && (isPointer!_Range || is(typeof(_Range.init[size_t.init]))) || is(_Range == Slice!(N1, Range1), size_t N1, Range1)));
Presents an n-dimensional view over a range.

Definitions

In order to change data in a slice using overloaded operators such as =, +=, ++, a syntactic structure of type <slice to change>[<index and interval sequence...>] must be used. It is worth noting that just like for regular arrays, operations a = b and a[] = b have different meanings. In the first case, after the operation is carried out, a simply points at the same data as b does, and the data which a previously pointed at remains unmodified. Here, а and b must be of the same type. In the second case, a points at the same data as before, but the data itself will be changed. In this instance, the number of dimensions of b may be less than the number of dimensions of а; and b can be a Slice, a regular multidimensional array, or simply a value (e.g. a number).
In the following table you will find the definitions you might come across in comments on operator overloading.
@@@DEPRECATED_2017-04@@@ @@@DEPRECATED_2017-04@@@ @@@DEPRECATED_2017-04@@@ @@@DEPRECATED_2017-04@@@ @@@DEPRECATED_2017-04@@@
Definition Examples at N == 3
An interval is a part of a sequence of type i .. j. 2..$-3, 0..4
An index is a part of a sequence of type i. 3, $-1
A partially defined slice is a sequence composed of intervals and indexes with an overall length strictly less than N. [3], [0..$], [3, 3], [0..$,0..3], [0..$,2]
A fully defined index is a sequence composed only of indexes with an overall length equal to N. [2,3,1]
A fully defined slice is an empty sequence or a sequence composed of indexes and at least one interval with an overall length equal to N. [], [3..$,0..3,0..$-1], [2,0..$,1]

Internal Binary Representation

Multidimensional Slice is a structure that consists of lengths, strides, and a pointer. For ranges, a shell is used instead of a pointer. This shell contains a shift of the current initial element of a multidimensional slice and the range itself. With the exception of overloaded operators, no functions in this package change or copy data. The operations are only carried out on lengths, strides, and pointers. If a slice is defined over a range, only the shift of the initial element changes instead of the pointer.

Internal Representation for Pointers

Type definition
Slice!(N, T*)
Schema
Slice!(N, T*)
    size_t[N]     lengths
    sizediff_t[N] strides
    T*            ptr

Example: Definitions

import std.experimental.ndslice;
auto a = new double[24];
Slice!(3, double*) s = a.sliced(2, 3, 4);
Slice!(3, double*) t = s.transposed!(1, 2, 0);
Slice!(3, double*) r = t.reversed!1;
Representation
s________________________
    lengths[0] ::=  2
    lengths[1] ::=  3
    lengths[2] ::=  4

    strides[0] ::= 12
    strides[1] ::=  4
    strides[2] ::=  1

    ptr        ::= &a[0]

t____transposed!(1, 2, 0)
    lengths[0] ::=  3
    lengths[1] ::=  4
    lengths[2] ::=  2

    strides[0] ::=  4
    strides[1] ::=  1
    strides[2] ::= 12

    ptr        ::= &a[0]

r______________reversed!1
    lengths[0] ::=  2
    lengths[1] ::=  3
    lengths[2] ::=  4

    strides[0] ::= 12
    strides[1] ::= -4
    strides[2] ::=  1

    ptr        ::= &a[8] // (old_strides[1] * (lengths[1] - 1)) = 8

Internal Representation for Ranges

Type definition
Slice!(N, Range)
Representation
Slice!(N, Range)
    size_t[N]     lengths
    sizediff_t[N] strides
    PtrShell!T    ptr
        sizediff_t shift
        Range      range

Example: Definitions

import std.experimental.ndslice;
import std.range : iota;
auto a = iota(24);
alias A = typeof(a);
Slice!(3, A) s = a.sliced(2, 3, 4);
Slice!(3, A) t = s.transposed!(1, 2, 0);
Slice!(3, A) r = t.reversed!1;
Representation
s________________________
    lengths[0] ::=  2
    lengths[1] ::=  3
    lengths[2] ::=  4

    strides[0] ::= 12
    strides[1] ::=  4
    strides[2] ::=  1

        shift  ::=  0
        range  ::=  a

t____transposed!(1, 2, 0)
    lengths[0] ::=  3
    lengths[1] ::=  4
    lengths[2] ::=  2

    strides[0] ::=  4
    strides[1] ::=  1
    strides[2] ::= 12

        shift  ::=  0
        range  ::=  a

r______________reversed!1
    lengths[0] ::=  2
    lengths[1] ::=  3
    lengths[2] ::=  4

    strides[0] ::= 12
    strides[1] ::= -4
    strides[2] ::=  1

        shift  ::=  8 // (old_strides[1] * (lengths[1] - 1)) = 8
        range  ::=  a

Examples:
Slicing, indexing, and arithmetic operations.
import std.experimental.ndslice.iteration : transposed;
import std.experimental.ndslice.selection : iotaSlice;
auto tensor = iotaSlice(3, 4, 5).slice;

writeln(tensor[1, 2]); // tensor[1][2]
writeln(tensor[1, 2, 3]); // tensor[1][2][3]

writeln(tensor[0 .. $, 0 .. $, 4]); // tensor.transposed!2[4]
assert(&tensor[0..$, 0..$, 4][1, 2] is &tensor[1, 2, 4]);

tensor[1, 2, 3]++; //`opIndex` returns value by reference.
--tensor[1, 2, 3]; //`opUnary`

++tensor[];
tensor[] -= 1;

// `opIndexAssing` accepts only fully defined indexes and slices.
// Use an additional empty slice `[]`.
static assert(!__traits(compiles, tensor[0 .. 2] *= 2));

tensor[0 .. 2][] *= 2;          //OK, empty slice
tensor[0 .. 2, 3, 0..$] /= 2; //OK, 3 index or slice positions are defined.

//fully defined index may be replaced by a static array
size_t[3] index = [1, 2, 3];
writeln(tensor[index]); // tensor[1, 2, 3]
Examples:
Operations with rvalue slices.
import std.experimental.ndslice.iteration : transposed, everted;

auto tensor = slice!int(3, 4, 5);
auto matrix = slice!int(3, 4);
auto vector = slice!int(3);

foreach (i; 0..3)
    vector[i] = i;

// fills matrix columns
matrix.transposed[] = vector;

// fills tensor with vector
// transposed tensor shape is (4, 5, 3)
//            vector shape is (      3)
tensor.transposed!(1, 2)[] = vector;


// transposed tensor shape is (5, 3, 4)
//            matrix shape is (   3, 4)
tensor.transposed!2[] += matrix;

// transposed tensor shape is (5, 4, 3)
// transposed matrix shape is (   4, 3)
tensor.everted[] ^= matrix.transposed; // XOR
Examples:
Creating a slice from text. See also std.format.
import std.algorithm,  std.conv, std.exception, std.format,
    std.functional, std.string, std.range;

Slice!(2, int*) toMatrix(string str)
{
    string[][] data = str.lineSplitter.filter!(not!empty).map!split.array;

    size_t rows    = data   .length.enforce("empty input");
    size_t columns = data[0].length.enforce("empty first row");

    data.each!(a => enforce(a.length == columns, "rows have different lengths"));

    auto slice = slice!int(rows, columns);
    foreach (i, line; data)
        foreach (j, num; line)
            slice[i, j] = num.to!int;
    return slice;
}

auto input = "\r1 2  3\r\n 4 5 6\n";

auto matrix = toMatrix(input);
writeln(matrix); // [[1, 2, 3], [4, 5, 6]]

// back to text
auto text2 = format("%(%(%s %)\n%)\n", matrix);
writeln(text2); // "1 2 3\n4 5 6\n"
size_t[PureN] _lengths;
Direct access to the lengths. Use for ndslice plugins only.
sizediff_t[PureN] _strides;
Direct access to the strides. Use for ndslice plugins only.
SlicePtr!PureRange _ptr;
Direct access to the pointer. Use for ndslice plugins only.
this(in size_t[PureN] lengths, in sizediff_t[PureN] strides, PureRange range);
This constructor should be used only for integration with other languages or libraries such as Julia and numpy.
Parameters:
size_t[PureN] lengths lengths
sizediff_t[PureN] strides strides
PureRange range range or pointer to iterate on
Examples:
Creates a 2-dimentional slice with custom strides.
import std.experimental.ndslice.selection : byElement;
import std.algorithm.comparison : equal;
import std.range : only;

uint[8] array = [1, 2, 3, 4, 5, 6, 7, 8];
auto slice = Slice!(2, uint*)([2, 2], [4, 1], array.ptr);

writeln(&slice[0, 0]); // &array[0]
writeln(&slice[0, 1]); // &array[1]
writeln(&slice[1, 0]); // &array[4]
writeln(&slice[1, 1]); // &array[5]
assert(slice.byElement.equal(only(1, 2, 5, 6)));

array[2] = 42;
assert(slice.byElement.equal(only(1, 2, 5, 6)));

array[1] = 99;
assert(slice.byElement.equal(only(1, 99, 5, 6)));
const pure nothrow @nogc ref @trusted ConstThis toConst();
Implicit cast to const slices in case of underlaying range is a pointer.
@property auto ptr();
Returns:
Pointer to the first element of a slice if slice is defined as Slice!(N, T*) or plain structure with two fields shift and range otherwise. In second case the expression range[shift] refers to the first element. For slices with named elements the type of a return value has the same behavior like a pointer.

Note: ptr is defined only for non-packed slices.

Attention: ptr refers to the first element in the memory representation if and only if all strides are positive.

const @property size_t[N] shape();
Returns:
static array of lengths
Examples:
Regular slice
import std.experimental.ndslice.selection : iotaSlice;
assert(iotaSlice(3, 4, 5)
    .shape == cast(size_t[3])[3, 4, 5]);
Examples:
Packed slice
import std.experimental.ndslice.selection : pack, iotaSlice;
assert(iotaSlice(3, 4, 5, 6, 7)
    .pack!2
    .shape == cast(size_t[3])[3, 4, 5]);
const @property Structure!N structure();
Returns:
static array of lengths and static array of strides
See Also:
Examples:
Regular slice
import std.experimental.ndslice.selection : iotaSlice;
assert(iotaSlice(3, 4, 5)
    .structure == Structure!3([3, 4, 5], [20, 5, 1]));
Examples:
Modified regular slice
import std.experimental.ndslice.selection : pack, iotaSlice;
import std.experimental.ndslice.iteration : reversed, strided, transposed;
assert(iotaSlice(3, 4, 50)
    .reversed!2      //makes stride negative
    .strided!2(6)    //multiplies stride by 6 and changes corresponding length
    .transposed!2    //brings dimension `2` to the first position
    .structure == Structure!3([9, 3, 4], [-6, 200, 50]));
Examples:
Packed slice
import std.experimental.ndslice.selection : pack, iotaSlice;
assert(iotaSlice(3, 4, 5, 6, 7)
    .pack!2
    .structure == Structure!3([3, 4, 5], [20 * 42, 5 * 42, 1 * 42]));
@property auto save();
Forward range primitive.
Examples:
Forward range
import std.experimental.ndslice.selection : iotaSlice;
auto slice = iotaSlice(2, 3).save;
Examples:
Pointer type.
//slice type is `Slice!(2, int*)`
auto slice = slice!int(2, 3).save;
const @property size_t length(size_t dimension = 0)()
if (dimension < N);
Multidimensional length property.
Returns:
length of the corresponding dimension
Examples:
import std.experimental.ndslice.selection : iotaSlice;
auto slice = iotaSlice(3, 4, 5);
writeln(slice.length); // 3
writeln(slice.length!0); // 3
writeln(slice.length!1); // 4
writeln(slice.length!2); // 5
const @property sizediff_t stride(size_t dimension = 0)()
if (dimension < N);
Multidimensional stride property.
Returns:
stride of the corresponding dimension
Examples:
Regular slice
import std.experimental.ndslice.selection : iotaSlice;
auto slice = iotaSlice(3, 4, 5);
writeln(slice.stride); // 20
writeln(slice.stride!0); // 20
writeln(slice.stride!1); // 5
writeln(slice.stride!2); // 1
Examples:
Modified regular slice
import std.experimental.ndslice.iteration : reversed, strided, swapped;
import std.experimental.ndslice.selection : iotaSlice;
assert(iotaSlice(3, 4, 50)
    .reversed!2      //makes stride negative
    .strided!2(6)    //multiplies stride by 6 and changes the corresponding length
    .swapped!(1, 2)  //swaps dimensions `1` and `2`
    .stride!1 == -6);
const @property bool empty(size_t dimension = 0)()
if (dimension < N);

@property ref auto front(size_t dimension = 0)()
if (dimension < N);

@property auto front(size_t dimension = 0, T)(T value)
if (dimension == 0);

@property ref auto back(size_t dimension = 0)()
if (dimension < N);

@property auto back(size_t dimension = 0, T)(T value)
if (dimension == 0);

void popFront(size_t dimension = 0)()
if (dimension < N);

void popBack(size_t dimension = 0)()
if (dimension < N);

void popFrontExactly(size_t dimension = 0)(size_t n)
if (dimension < N);

void popBackExactly(size_t dimension = 0)(size_t n)
if (dimension < N);

void popFrontN(size_t dimension = 0)(size_t n)
if (dimension < N);

void popBackN(size_t dimension = 0)(size_t n)
if (dimension < N);
Multidimensional input range primitive.
Examples:
import std.range.primitives;
import std.experimental.ndslice.selection : iotaSlice;
auto slice = iotaSlice(10, 20, 30);

static assert(isRandomAccessRange!(typeof(slice)));
static assert(hasSlicing!(typeof(slice)));
static assert(hasLength!(typeof(slice)));

writeln(slice.shape); // cast(size_t[3])[10, 20, 30]
slice.popFront;
slice.popFront!1;
slice.popBackExactly!2(4);
writeln(slice.shape); // cast(size_t[3])[9, 19, 26]

auto matrix = slice.front!1;
writeln(matrix.shape); // cast(size_t[2])[9, 26]

auto column = matrix.back!1;
writeln(column.shape); // cast(size_t[1])[9]

slice.popFrontExactly!1(slice.length!1);
writeln(slice.empty); // false
writeln(slice.empty!1); // true
writeln(slice.empty!2); // false
writeln(slice.shape); // cast(size_t[3])[9, 0, 26]

assert(slice.back.front!1.empty);

slice.popFrontN!0(40);
slice.popFrontN!2(40);
writeln(slice.shape); // cast(size_t[3])[0, 0, 0]
const bool anyEmpty();
Returns:
true if for any dimension the length equals to 0, and false otherwise.
Examples:
import std.experimental.ndslice.selection : iotaSlice;
auto s = iotaSlice(2, 3);
assert(!s.anyEmpty);
s.popFrontExactly!1(3);
assert(s.anyEmpty);
ref auto backward(size_t[N] index);
Convenience function for backward indexing.
Returns:
this[$-index[0], $-index[1], ..., $-index[N-1]]
Examples:
import std.experimental.ndslice.selection : iotaSlice;
auto s = iotaSlice(2, 3);
writeln(s[$ - 1, $ - 2]); // s.backward([1, 2])
const size_t elementsCount();
Returns:
Total number of elements in a slice
Examples:
Regular slice
import std.experimental.ndslice.selection : iotaSlice;
writeln(iotaSlice(3, 4, 5).elementsCount); // 60
Examples:
Packed slice
import std.experimental.ndslice.selection : pack, evertPack, iotaSlice;
auto slice = iotaSlice(3, 4, 5, 6, 7, 8);
auto p = slice.pack!2;
writeln(p.elementsCount); // 360
writeln(p[0, 0, 0, 0].elementsCount); // 56
writeln(p.evertPack.elementsCount); // 56
bool opEquals(size_t NR, RangeR)(Slice!(NR, RangeR) rslice)
if (Slice!(NR, RangeR).PureN == PureN);

bool opEquals(T)(T[] rarrary);
Overloading == and !=
Examples:
auto a = [1, 2, 3, 4].sliced(2, 2);

assert(a != [1, 2, 3, 4, 5, 6].sliced(2, 3));
assert(a != [[1, 2, 3], [4, 5, 6]]);

writeln(a); // [1, 2, 3, 4].sliced(2, 2)
writeln(a); // [[1, 2], [3, 4]]

assert(a != [9, 2, 3, 4].sliced(2, 2));
assert(a != [[9, 2], [3, 4]]);
const @safe size_t toHash();
Computes hash value using MurmurHash3 algorithms without the finalization step. Built-in associative arrays have the finalization step.
Returns:
Hash value type of size_t.
Examples:
import std.experimental.ndslice.selection : iotaSlice;
const sl = iotaSlice(3, 7);
size_t hash = sl.toHash;
Examples:
import std.experimental.ndslice.iteration : allReversed;
import std.experimental.ndslice.selection : iotaSlice;

// hash is the same for allocated data and for generated data
auto a = iotaSlice(3, 7);
auto b = iotaSlice(3, 7).slice;

writeln(a.toHash); // b.toHash
writeln(typeid (typeof(a)).getHash(&a)); // typeid (typeof(b)).getHash(&b)

// hash does not depend on strides
a = iotaSlice(3, 7).allReversed;
b = iotaSlice(3, 7).allReversed.slice;

writeln(a.toHash); // b.toHash
writeln(typeid (typeof(a)).getHash(&a)); // typeid (typeof(b)).getHash(&b)
const @trusted auto toMurmurHash3(uint size, uint opt = size_t.sizeof == 8 ? 64 : 32)();
Computes hash value using MurmurHash3 algorithms without the finalization step.
Returns:
Hash value type of MurmurHash3!(size, opt).get().
ref auto opIndex(size_t I)(size_t[I] _indexes...)
if (I && I <= N);

ref auto opCall()(size_t[N] _indexes...);
Examples:
auto slice = slice!int(5, 2);

auto q = &slice[3, 1];      // D & C order
auto p = &slice(1, 3);      // Math & Fortran order
assert(p is q);
*q = 4;
assert(slice[3, 1] == 4);   // D & C order
assert(slice(1, 3) == 4);   // Math & Fortran order

size_t[2] indexP = [1, 3];
size_t[2] indexQ = [3, 1];
assert(slice[indexQ] == 4);  // D & C order
assert(slice(indexP) == 4);  // Math & Fortran order
auto opIndex(Slices...)(Slices slices)
if (isPureSlice!Slices);
Examples:
auto slice = slice!int(5, 3);

/// Fully defined slice
writeln(slice[]); // slice
auto sublice = slice[0..$-2, 1..$];

/// Partially defined slice
auto row = slice[3];
auto col = slice[0..$, 1];
void opIndexAssign(size_t RN, RRange, Slices...)(Slice!(RN, RRange) value, Slices slices)
if (isFullPureSlice!Slices && RN <= ReturnType!(opIndex!Slices).N);
Assignment of a value of Slice type to a fully defined slice.

Optimization: SIMD instructions may be used if both slices have the last stride equals to 1.

Examples:
auto a = slice!int(2, 3);
auto b = [1, 2, 3, 4].sliced(2, 2);

a[0..$, 0..$-1] = b;
writeln(a); // [[1, 2, 0], [3, 4, 0]]

// fills both rows with b[0]
a[0..$, 0..$-1] = b[0];
writeln(a); // [[1, 2, 0], [1, 2, 0]]

a[1, 0..$-1] = b[1];
writeln(a[1]); // [3, 4, 0]

a[1, 0..$-1][] = b[0];
writeln(a[1]); // [1, 2, 0]
Examples:
Left slice is packed
import std.experimental.ndslice.selection : blocks, iotaSlice;
auto a = slice!size_t(4, 4);
a.blocks(2, 2)[] = iotaSlice(2, 2);

assert(a ==
        [[0, 0, 1, 1],
         [0, 0, 1, 1],
         [2, 2, 3, 3],
         [2, 2, 3, 3]]);
Examples:
Both slices are packed
import std.experimental.ndslice.selection : blocks, iotaSlice, pack;
auto a = slice!size_t(4, 4);
a.blocks(2, 2)[] = iotaSlice(2, 2, 2).pack!1;

assert(a ==
        [[0, 1, 2, 3],
         [0, 1, 2, 3],
         [4, 5, 6, 7],
         [4, 5, 6, 7]]);
void opIndexAssign(T, Slices...)(T[] value, Slices slices)
if (isFullPureSlice!Slices && !isDynamicArray!DeepElemType && DynamicArrayDimensionsCount!(T[]) <= ReturnType!(opIndex!Slices).N);
Assignment of a regular multidimensional array to a fully defined slice.

Optimization: SIMD instructions may be used if the slice has the last stride equals to 1.

Examples:
auto a = slice!int(2, 3);
auto b = [[1, 2], [3, 4]];

a[] = [[1, 2, 3], [4, 5, 6]];
writeln(a); // [[1, 2, 3], [4, 5, 6]]

a[0..$, 0..$-1] = [[1, 2], [3, 4]];
writeln(a); // [[1, 2, 3], [3, 4, 6]]

a[0..$, 0..$-1] = [1, 2];
writeln(a); // [[1, 2, 3], [1, 2, 6]]

a[1, 0..$-1] = [3, 4];
writeln(a[1]); // [3, 4, 6]

a[1, 0..$-1][] = [3, 4];
writeln(a[1]); // [3, 4, 6]
Examples:
Packed slices
import std.experimental.ndslice.selection : blocks;
auto a = slice!int(4, 4);
a.blocks(2, 2)[] = [[0, 1], [2, 3]];

assert(a ==
        [[0, 0, 1, 1],
         [0, 0, 1, 1],
         [2, 2, 3, 3],
         [2, 2, 3, 3]]);
void opIndexAssign(T, Slices...)(T value, Slices slices)
if (isFullPureSlice!Slices && (!isDynamicArray!T || isDynamicArray!DeepElemType) && !is(T : Slice!(RN, RRange), size_t RN, RRange));
Assignment of a value (e.g. a number) to a fully defined slice.

Optimization: SIMD instructions may be used if the slice has the last stride equals to 1.

Examples:
auto a = slice!int(2, 3);

a[] = 9;
writeln(a); // [[9, 9, 9], [9, 9, 9]]

a[0..$, 0..$-1] = 1;
writeln(a); // [[1, 1, 9], [1, 1, 9]]

a[0..$, 0..$-1] = 2;
writeln(a); // [[2, 2, 9], [2, 2, 9]]

a[1, 0..$-1] = 3;
writeln(a[1]); // [3, 3, 9]

a[1, 0..$-1] = 4;
writeln(a[1]); // [4, 4, 9]

a[1, 0..$-1][] = 5;
writeln(a[1]); // [5, 5, 9]
Examples:
Packed slices have the same behavior.
import std.experimental.ndslice.selection : pack;
auto a = slice!int(2, 3).pack!1;

a[] = 9;
writeln(a); // [[9, 9, 9], [9, 9, 9]]
ref auto opIndexAssign(T)(T value, size_t[N] _indexes...);
Assignment of a value (e.g. a number) to a fully defined index.
Examples:
auto a = slice!int(2, 3);

a[1, 2] = 3;
writeln(a[1, 2]); // 3
ref auto opIndexOpAssign(string op, T)(T value, size_t[N] _indexes...);
Op Assignment op= of a value (e.g. a number) to a fully defined index.
Examples:
auto a = slice!int(2, 3);

a[1, 2] += 3;
writeln(a[1, 2]); // 3
void opIndexOpAssign(string op, size_t RN, RRange, Slices...)(Slice!(RN, RRange) value, Slices slices)
if (isFullPureSlice!Slices && RN <= ReturnType!(opIndex!Slices).N);
Op Assignment op= of a value of Slice type to a fully defined slice.

Optimization: SIMD instructions may be used if both slices have the last stride equals to 1.

Examples:
auto a = slice!int(2, 3);
auto b = [1, 2, 3, 4].sliced(2, 2);

a[0..$, 0..$-1] += b;
writeln(a); // [[1, 2, 0], [3, 4, 0]]

a[0..$, 0..$-1] += b[0];
writeln(a); // [[2, 4, 0], [4, 6, 0]]

a[1, 0..$-1] += b[1];
writeln(a[1]); // [7, 10, 0]

a[1, 0..$-1][] += b[0];
writeln(a[1]); // [8, 12, 0]
Examples:
Left slice is packed
import std.experimental.ndslice.selection : blocks, iotaSlice;
auto a = slice!size_t(4, 4);
a.blocks(2, 2)[] += iotaSlice(2, 2);

assert(a ==
        [[0, 0, 1, 1],
         [0, 0, 1, 1],
         [2, 2, 3, 3],
         [2, 2, 3, 3]]);
Examples:
Both slices are packed
import std.experimental.ndslice.selection : blocks, iotaSlice, pack;
auto a = slice!size_t(4, 4);
a.blocks(2, 2)[] += iotaSlice(2, 2, 2).pack!1;

assert(a ==
        [[0, 1, 2, 3],
         [0, 1, 2, 3],
         [4, 5, 6, 7],
         [4, 5, 6, 7]]);
void opIndexOpAssign(string op, T, Slices...)(T[] value, Slices slices)
if (isFullPureSlice!Slices && !isDynamicArray!DeepElemType && DynamicArrayDimensionsCount!(T[]) <= ReturnType!(opIndex!Slices).N);
Op Assignment op= of a regular multidimensional array to a fully defined slice.

Optimization: SIMD instructions may be used if the slice has the last stride equals to 1.

Examples:
auto a = slice!int(2, 3);

a[0..$, 0..$-1] += [[1, 2], [3, 4]];
writeln(a); // [[1, 2, 0], [3, 4, 0]]

a[0..$, 0..$-1] += [1, 2];
writeln(a); // [[2, 4, 0], [4, 6, 0]]

a[1, 0..$-1] += [3, 4];
writeln(a[1]); // [7, 10, 0]

a[1, 0..$-1][] += [1, 2];
writeln(a[1]); // [8, 12, 0]
Examples:
Packed slices
import std.experimental.ndslice.selection : blocks;
auto a = slice!int(4, 4);
a.blocks(2, 2)[] += [[0, 1], [2, 3]];

assert(a ==
        [[0, 0, 1, 1],
         [0, 0, 1, 1],
         [2, 2, 3, 3],
         [2, 2, 3, 3]]);
Examples:
Packed slices have the same behavior.
import std.experimental.ndslice.selection : pack;
auto a = slice!int(2, 3).pack!1;

a[] += 9;
writeln(a); // [[9, 9, 9], [9, 9, 9]]
void opIndexOpAssign(string op, T, Slices...)(T value, Slices slices)
if (isFullPureSlice!Slices && (!isDynamicArray!T || isDynamicArray!DeepElemType) && !is(T : Slice!(RN, RRange), size_t RN, RRange));
Op Assignment op= of a value (e.g. a number) to a fully defined slice.

Optimization: SIMD instructions may be used if the slice has the last stride equals to 1.

Examples:
auto a = slice!int(2, 3);

a[] += 1;
writeln(a); // [[1, 1, 1], [1, 1, 1]]

a[0..$, 0..$-1] += 2;
writeln(a); // [[3, 3, 1], [3, 3, 1]]

a[1, 0..$-1] += 3;
writeln(a[1]); // [6, 6, 1]
ref auto opIndexUnary(string op)(size_t[N] _indexes...);
Increment ++ and Decrement -- operators for a fully defined index.
Examples:
auto a = slice!int(2, 3);

++a[1, 2];
writeln(a[1, 2]); // 1
void opIndexUnary(string op, Slices...)(Slices slices)
if (isFullPureSlice!Slices && (op == "++" || op == "--"));
Increment ++ and Decrement -- operators for a fully defined slice.
Examples:
auto a = slice!int(2, 3);

++a[];
writeln(a); // [[1, 1, 1], [1, 1, 1]]

--a[1, 0..$-1];
writeln(a[1]); // [0, 0, 1]