26 Numerics library [numerics]

26.7 Numeric arrays [numarray]

26.7.1 Header <valarray> synopsis [valarray.syn]

#include <initializer_list> namespace std { template<class T> class valarray; // An array of type T class slice; // a BLAS-like slice out of an array template<class T> class slice_array; class gslice; // a generalized slice out of an array template<class T> class gslice_array; template<class T> class mask_array; // a masked array template<class T> class indirect_array; // an indirected array template<class T> void swap(valarray<T>&, valarray<T>&) noexcept; template<class T> valarray<T> operator* (const valarray<T>&, const valarray<T>&); template<class T> valarray<T> operator* (const valarray<T>&, const typename valarray<T>::value_type&); template<class T> valarray<T> operator* (const typename valarray<T>::value_type&, const valarray<T>&); template<class T> valarray<T> operator/ (const valarray<T>&, const valarray<T>&); template<class T> valarray<T> operator/ (const valarray<T>&, const typename valarray<T>::value_type&); template<class T> valarray<T> operator/ (const typename valarray<T>::value_type&, const valarray<T>&); template<class T> valarray<T> operator% (const valarray<T>&, const valarray<T>&); template<class T> valarray<T> operator% (const valarray<T>&, const typename valarray<T>::value_type&); template<class T> valarray<T> operator% (const typename valarray<T>::value_type&, const valarray<T>&); template<class T> valarray<T> operator+ (const valarray<T>&, const valarray<T>&); template<class T> valarray<T> operator+ (const valarray<T>&, const typename valarray<T>::value_type&); template<class T> valarray<T> operator+ (const typename valarray<T>::value_type&, const valarray<T>&); template<class T> valarray<T> operator- (const valarray<T>&, const valarray<T>&); template<class T> valarray<T> operator- (const valarray<T>&, const typename valarray<T>::value_type&); template<class T> valarray<T> operator- (const typename valarray<T>::value_type&, const valarray<T>&); template<class T> valarray<T> operator^ (const valarray<T>&, const valarray<T>&); template<class T> valarray<T> operator^ (const valarray<T>&, const typename valarray<T>::value_type&); template<class T> valarray<T> operator^ (const typename valarray<T>::value_type&, const valarray<T>&); template<class T> valarray<T> operator& (const valarray<T>&, const valarray<T>&); template<class T> valarray<T> operator& (const valarray<T>&, const typename valarray<T>::value_type&); template<class T> valarray<T> operator& (const typename valarray<T>::value_type&, const valarray<T>&); template<class T> valarray<T> operator| (const valarray<T>&, const valarray<T>&); template<class T> valarray<T> operator| (const valarray<T>&, const typename valarray<T>::value_type&); template<class T> valarray<T> operator| (const typename valarray<T>::value_type&, const valarray<T>&); template<class T> valarray<T> operator<<(const valarray<T>&, const valarray<T>&); template<class T> valarray<T> operator<<(const valarray<T>&, const typename valarray<T>::value_type&); template<class T> valarray<T> operator<<(const typename valarray<T>::value_type&, const valarray<T>&); template<class T> valarray<T> operator>>(const valarray<T>&, const valarray<T>&); template<class T> valarray<T> operator>>(const valarray<T>&, const typename valarray<T>::value_type&); template<class T> valarray<T> operator>>(const typename valarray<T>::value_type&, const valarray<T>&); template<class T> valarray<bool> operator&&(const valarray<T>&, const valarray<T>&); template<class T> valarray<bool> operator&&(const valarray<T>&, const typename valarray<T>::value_type&); template<class T> valarray<bool> operator&&(const typename valarray<T>::value_type&, const valarray<T>&); template<class T> valarray<bool> operator||(const valarray<T>&, const valarray<T>&); template<class T> valarray<bool> operator||(const valarray<T>&, const typename valarray<T>::value_type&); template<class T> valarray<bool> operator||(const typename valarray<T>::value_type&, const valarray<T>&); template<class T> valarray<bool> operator==(const valarray<T>&, const valarray<T>&); template<class T> valarray<bool> operator==(const valarray<T>&, const typename valarray<T>::value_type&); template<class T> valarray<bool> operator==(const typename valarray<T>::value_type&, const valarray<T>&); template<class T> valarray<bool> operator!=(const valarray<T>&, const valarray<T>&); template<class T> valarray<bool> operator!=(const valarray<T>&, const typename valarray<T>::value_type&); template<class T> valarray<bool> operator!=(const typename valarray<T>::value_type&, const valarray<T>&); template<class T> valarray<bool> operator< (const valarray<T>&, const valarray<T>&); template<class T> valarray<bool> operator< (const valarray<T>&, const typename valarray<T>::value_type&); template<class T> valarray<bool> operator< (const typename valarray<T>::value_type&, const valarray<T>&); template<class T> valarray<bool> operator> (const valarray<T>&, const valarray<T>&); template<class T> valarray<bool> operator> (const valarray<T>&, const typename valarray<T>::value_type&); template<class T> valarray<bool> operator> (const typename valarray<T>::value_type&, const valarray<T>&); template<class T> valarray<bool> operator<=(const valarray<T>&, const valarray<T>&); template<class T> valarray<bool> operator<=(const valarray<T>&, const typename valarray<T>::value_type&); template<class T> valarray<bool> operator<=(const typename valarray<T>::value_type&, const valarray<T>&); template<class T> valarray<bool> operator>=(const valarray<T>&, const valarray<T>&); template<class T> valarray<bool> operator>=(const valarray<T>&, const typename valarray<T>::value_type&); template<class T> valarray<bool> operator>=(const typename valarray<T>::value_type&, const valarray<T>&); template<class T> valarray<T> abs (const valarray<T>&); template<class T> valarray<T> acos (const valarray<T>&); template<class T> valarray<T> asin (const valarray<T>&); template<class T> valarray<T> atan (const valarray<T>&); template<class T> valarray<T> atan2(const valarray<T>&, const valarray<T>&); template<class T> valarray<T> atan2(const valarray<T>&, const typename valarray<T>::value_type&); template<class T> valarray<T> atan2(const typename valarray<T>::value_type&, const valarray<T>&); template<class T> valarray<T> cos (const valarray<T>&); template<class T> valarray<T> cosh (const valarray<T>&); template<class T> valarray<T> exp (const valarray<T>&); template<class T> valarray<T> log (const valarray<T>&); template<class T> valarray<T> log10(const valarray<T>&); template<class T> valarray<T> pow(const valarray<T>&, const valarray<T>&); template<class T> valarray<T> pow(const valarray<T>&, const typename valarray<T>::value_type&); template<class T> valarray<T> pow(const typename valarray<T>::value_type&, const valarray<T>&); template<class T> valarray<T> sin (const valarray<T>&); template<class T> valarray<T> sinh (const valarray<T>&); template<class T> valarray<T> sqrt (const valarray<T>&); template<class T> valarray<T> tan (const valarray<T>&); template<class T> valarray<T> tanh (const valarray<T>&); template<class T> unspecified1 begin(valarray<T>& v); template<class T> unspecified2 begin(const valarray<T>& v); template<class T> unspecified1 end(valarray<T>& v); template<class T> unspecified2 end(const valarray<T>& v); }

The header <valarray> defines five class templates (valarray, slice_array, gslice_array, mask_array, and indirect_array), two classes (slice and gslice), and a series of related function templates for representing and manipulating arrays of values.

The valarray array classes are defined to be free of certain forms of aliasing, thus allowing operations on these classes to be optimized.

Any function returning a valarray<T> is permitted to return an object of another type, provided all the const member functions of valarray<T> are also applicable to this type.

This return type shall not add more than two levels of template nesting over the most deeply nested argument type.254

Implementations introducing such replacement types shall provide additional functions and operators as follows:

(4.1)
for every function taking a const valarray<T>& other than begin and end, identical functions taking the replacement types shall be added;
(4.2)
for every function taking two const valarray<T>& arguments, identical functions taking every combination of const valarray<T>& and replacement types shall be added.

In particular, an implementation shall allow a valarray<T> to be constructed from such replacement types and shall allow assignments and compound assignments of such types to valarray<T>, slice_array<T>, gslice_array<T>, mask_array<T> and indirect_array<T> objects.

These library functions are permitted to throw a bad_alloc exception if there are not sufficient resources available to carry out the operation.

Note that the exception is not mandated.

254)

[implimits] recommends a minimum number of recursively nested template instantiations.

This requirement thus indirectly suggests a minimum allowable complexity for valarray expressions.

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26.7.2 Class template valarray [template.valarray]

26.7.2.1 Overview [template.valarray.overview]

namespace std { template<class T> class valarray { public: using value_type = T; // [valarray.cons], construct/destroy valarray(); explicit valarray(size_t); valarray(const T&, size_t); valarray(const T*, size_t); valarray(const valarray&); valarray(valarray&&) noexcept; valarray(const slice_array<T>&); valarray(const gslice_array<T>&); valarray(const mask_array<T>&); valarray(const indirect_array<T>&); valarray(initializer_list<T>); ~valarray(); // [valarray.assign], assignment valarray& operator=(const valarray&); valarray& operator=(valarray&&) noexcept; valarray& operator=(initializer_list<T>); valarray& operator=(const T&); valarray& operator=(const slice_array<T>&); valarray& operator=(const gslice_array<T>&); valarray& operator=(const mask_array<T>&); valarray& operator=(const indirect_array<T>&); // [valarray.access], element access const T& operator[](size_t) const; T& operator[](size_t); // [valarray.sub], subset operations valarray operator[](slice) const; slice_array<T> operator[](slice); valarray operator[](const gslice&) const; gslice_array<T> operator[](const gslice&); valarray operator[](const valarray<bool>&) const; mask_array<T> operator[](const valarray<bool>&); valarray operator[](const valarray<size_t>&) const; indirect_array<T> operator[](const valarray<size_t>&); // [valarray.unary], unary operators valarray operator+() const; valarray operator-() const; valarray operator~() const; valarray<bool> operator!() const; // [valarray.cassign], compound assignment valarray& operator*= (const T&); valarray& operator/= (const T&); valarray& operator%= (const T&); valarray& operator+= (const T&); valarray& operator-= (const T&); valarray& operator^= (const T&); valarray& operator&= (const T&); valarray& operator|= (const T&); valarray& operator<<=(const T&); valarray& operator>>=(const T&); valarray& operator*= (const valarray&); valarray& operator/= (const valarray&); valarray& operator%= (const valarray&); valarray& operator+= (const valarray&); valarray& operator-= (const valarray&); valarray& operator^= (const valarray&); valarray& operator|= (const valarray&); valarray& operator&= (const valarray&); valarray& operator<<=(const valarray&); valarray& operator>>=(const valarray&); // [valarray.members], member functions void swap(valarray&) noexcept; size_t size() const; T sum() const; T min() const; T max() const; valarray shift (int) const; valarray cshift(int) const; valarray apply(T func(T)) const; valarray apply(T func(const T&)) const; void resize(size_t sz, T c = T()); }; template<class T, size_t cnt> valarray(const T(&)[cnt], size_t) -> valarray<T>; }

The class template valarray<T> is a one-dimensional smart array, with elements numbered sequentially from zero.

It is a representation of the mathematical concept of an ordered set of values.

For convenience, an object of type valarray<T> is referred to as an “array” throughout the remainder of [numarray].

The illusion of higher dimensionality may be produced by the familiar idiom of computed indices, together with the powerful subsetting capabilities provided by the generalized subscript operators.255

255)

The intent is to specify an array template that has the minimum functionality necessary to address aliasing ambiguities and the proliferation of temporary objects.

Thus, the valarray template is neither a matrix class nor a field class.

However, it is a very useful building block for designing such classes.

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26.7.2.2 Constructors [valarray.cons]

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valarray();

Effects: Constructs a valarray that has zero length.256

🔗

explicit valarray(size_t n);

Effects: Constructs a valarray that has length n.

Each element of the array is value-initialized .

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valarray(const T& v, size_t n);

Effects: Constructs a valarray that has length n.

Each element of the array is initialized with v.

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valarray(const T* p, size_t n);

Preconditions: [p, p + n) is a valid range.

Effects: Constructs a valarray that has length n.

The values of the elements of the array are initialized with the first n values pointed to by the first argument.257

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valarray(const valarray& v);

Effects: Constructs a valarray that has the same length as v.

The elements are initialized with the values of the corresponding elements of v.258

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valarray(valarray&& v) noexcept;

Effects: Constructs a valarray that has the same length as v.

The elements are initialized with the values of the corresponding elements of v.

Complexity: Constant.

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valarray(initializer_list<T> il);

Effects: Equivalent to valarray(il.begin(), il.size()).

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valarray(const slice_array<T>&);
valarray(const gslice_array<T>&);
valarray(const mask_array<T>&);
valarray(const indirect_array<T>&);

These conversion constructors convert one of the four reference templates to a valarray.

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~valarray();

Effects: The destructor is applied to every element of *this; an implementation may return all allocated memory.

256)

This default constructor is essential, since arrays of valarray can be useful.

After initialization, the length of an empty array can be increased with the resize member function.

⮥

257)

This constructor is the preferred method for converting a C array to a valarray object.

⮥

258)

This copy constructor creates a distinct array rather than an alias.

Implementations in which arrays share storage are permitted, but they would need to implement a copy-on-reference mechanism to ensure that arrays are conceptually distinct.

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26.7.2.3 Assignment [valarray.assign]

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valarray& operator=(const valarray& v);

Effects: Each element of the *this array is assigned the value of the corresponding element of v.

If the length of v is not equal to the length of *this, resizes *this to make the two arrays the same length, as if by calling resize(v.size()), before performing the assignment.

Postconditions: size() == v.size().

Returns: *this.

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valarray& operator=(valarray&& v) noexcept;

Effects: *this obtains the value of v.

The value of v after the assignment is not specified.

Returns: *this.

Complexity: Linear.

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valarray& operator=(initializer_list<T> il);

Effects: Equivalent to: return *this = valarray(il);

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valarray& operator=(const T& v);

Effects: Assigns v to each element of *this.

Returns: *this.

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valarray& operator=(const slice_array<T>&);
valarray& operator=(const gslice_array<T>&);
valarray& operator=(const mask_array<T>&);
valarray& operator=(const indirect_array<T>&);

Preconditions: The length of the array to which the argument refers equals size().

The value of an element in the left-hand side of a valarray assignment operator does not depend on the value of another element in that left-hand side.

These operators allow the results of a generalized subscripting operation to be assigned directly to a valarray.

26.7.2.4 Element access [valarray.access]

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const T&  operator[](size_t n) const;
T& operator[](size_t n);

Preconditions: n < size() is true.

Returns: A reference to the corresponding element of the array.

[Note 1:

The expression (a[i] = q, a[i]) == q evaluates to true for any non-constant valarray<T> a, any T q, and for any size_t i such that the value of i is less than the length of a.

— end note]

Remarks: The expression addressof(a[i+j]) == addressof(a[i]) + j evaluates to true for all size_t i and size_t j such that i+j < a.size().

The expression addressof(a[i]) != addressof(b[j]) evaluates to true for any two arrays a and b and for any size_t i and size_t j such that i < a.size() and j < b.size().

[Note 2:

This property indicates an absence of aliasing and can be used to advantage by optimizing compilers.

Compilers can take advantage of inlining, constant propagation, loop fusion, tracking of pointers obtained from operator new, and other techniques to generate efficient valarrays.

— end note]

The reference returned by the subscript operator for an array shall be valid until the member function resize(size_t, T) is called for that array or until the lifetime of that array ends, whichever happens first.

26.7.2.5 Subset operations [valarray.sub]

The member operator[] is overloaded to provide several ways to select sequences of elements from among those controlled by *this.

Each of these operations returns a subset of the array.

The const-qualified versions return this subset as a new valarray object.

The non-const versions return a class template object which has reference semantics to the original array, working in conjunction with various overloads of operator= and other assigning operators to allow selective replacement (slicing) of the controlled sequence.

In each case the selected element(s) shall exist.

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valarray operator[](slice slicearr) const;

Returns: A valarray containing those elements of the controlled sequence designated by slicearr.

[Example 1: const valarray<char> v0("abcdefghijklmnop", 16); // v0[slice(2, 5, 3)] returns valarray<char>("cfilo", 5) — end example]

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slice_array<T> operator[](slice slicearr);

Returns: An object that holds references to elements of the controlled sequence selected by slicearr.

[Example 2: valarray<char> v0("abcdefghijklmnop", 16); valarray<char> v1("ABCDE", 5); v0[slice(2, 5, 3)] = v1; // v0 == valarray<char>("abAdeBghCjkDmnEp", 16); — end example]

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valarray operator[](const gslice& gslicearr) const;

Returns: A valarray containing those elements of the controlled sequence designated by gslicearr.

[Example 3: const valarray<char> v0("abcdefghijklmnop", 16); const size_t lv[] = { 2, 3 }; const size_t dv[] = { 7, 2 }; const valarray<size_t> len(lv, 2), str(dv, 2); // v0[gslice(3, len, str)] returns // valarray<char>("dfhkmo", 6) — end example]

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gslice_array<T> operator[](const gslice& gslicearr);

Returns: An object that holds references to elements of the controlled sequence selected by gslicearr.

[Example 4: valarray<char> v0("abcdefghijklmnop", 16); valarray<char> v1("ABCDEF", 6); const size_t lv[] = { 2, 3 }; const size_t dv[] = { 7, 2 }; const valarray<size_t> len(lv, 2), str(dv, 2); v0[gslice(3, len, str)] = v1; // v0 == valarray<char>("abcAeBgCijDlEnFp", 16) — end example]

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valarray operator[](const valarray<bool>& boolarr) const;

Returns: A valarray containing those elements of the controlled sequence designated by boolarr.

[Example 5: const valarray<char> v0("abcdefghijklmnop", 16); const bool vb[] = { false, false, true, true, false, true }; // v0[valarray<bool>(vb, 6)] returns // valarray<char>("cdf", 3) — end example]

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mask_array<T> operator[](const valarray<bool>& boolarr);

Returns: An object that holds references to elements of the controlled sequence selected by boolarr.

[Example 6: valarray<char> v0("abcdefghijklmnop", 16); valarray<char> v1("ABC", 3); const bool vb[] = { false, false, true, true, false, true }; v0[valarray<bool>(vb, 6)] = v1; // v0 == valarray<char>("abABeCghijklmnop", 16) — end example]

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valarray operator[](const valarray<size_t>& indarr) const;

Returns: A valarray containing those elements of the controlled sequence designated by indarr.

[Example 7: const valarray<char> v0("abcdefghijklmnop", 16); const size_t vi[] = { 7, 5, 2, 3, 8 }; // v0[valarray<size_t>(vi, 5)] returns // valarray<char>("hfcdi", 5) — end example]

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indirect_array<T> operator[](const valarray<size_t>& indarr);

Returns: An object that holds references to elements of the controlled sequence selected by indarr.

[Example 8: valarray<char> v0("abcdefghijklmnop", 16); valarray<char> v1("ABCDE", 5); const size_t vi[] = { 7, 5, 2, 3, 8 }; v0[valarray<size_t>(vi, 5)] = v1; // v0 == valarray<char>("abCDeBgAEjklmnop", 16) — end example]

26.7.2.6 Unary operators [valarray.unary]

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valarray operator+() const;
valarray operator-() const;
valarray operator~() const;
valarray<bool> operator!() const;

Mandates: The indicated operator can be applied to operands of type T and returns a value of type T (bool for operator!) or which may be unambiguously implicitly converted to type T (bool for operator!).

Returns: A valarray whose length is size().

Each element of the returned array is initialized with the result of applying the indicated operator to the corresponding element of the array.

26.7.2.7 Compound assignment [valarray.cassign]

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valarray& operator*= (const valarray& v);
valarray& operator/= (const valarray& v);
valarray& operator%= (const valarray& v);
valarray& operator+= (const valarray& v);
valarray& operator-= (const valarray& v);
valarray& operator^= (const valarray& v);
valarray& operator&= (const valarray& v);
valarray& operator|= (const valarray& v);
valarray& operator<<=(const valarray& v);
valarray& operator>>=(const valarray& v);

Mandates: The indicated operator can be applied to two operands of type T.

Preconditions: size() == v.size() is true.

The value of an element in the left-hand side of a valarray compound assignment operator does not depend on the value of another element in that left hand side.

Effects: Each of these operators performs the indicated operation on each of the elements of *this and the corresponding element of v.

Returns: *this.

Remarks: The appearance of an array on the left-hand side of a compound assignment does not invalidate references or pointers.

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valarray& operator*= (const T& v);
valarray& operator/= (const T& v);
valarray& operator%= (const T& v);
valarray& operator+= (const T& v);
valarray& operator-= (const T& v);
valarray& operator^= (const T& v);
valarray& operator&= (const T& v);
valarray& operator|= (const T& v);
valarray& operator<<=(const T& v);
valarray& operator>>=(const T& v);

Mandates: The indicated operator can be applied to two operands of type T.

Effects: Each of these operators applies the indicated operation to each element of *this and v.

Returns: *this

Remarks: The appearance of an array on the left-hand side of a compound assignment does not invalidate references or pointers to the elements of the array.

26.7.2.8 Member functions [valarray.members]

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void swap(valarray& v) noexcept;

Effects: *this obtains the value of v.

v obtains the value of *this.

Complexity: Constant.

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size_t size() const;

Returns: The number of elements in the array.

Complexity: Constant time.

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T sum() const;

Mandates: operator+= can be applied to operands of type T.

Preconditions: size() > 0 is true.

Returns: The sum of all the elements of the array.

If the array has length 1, returns the value of element 0.

Otherwise, the returned value is calculated by applying operator+= to a copy of an element of the array and all other elements of the array in an unspecified order.

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T min() const;

Preconditions: size() > 0 is true.

Returns: The minimum value contained in *this.

For an array of length 1, the value of element 0 is returned.

For all other array lengths, the determination is made using operator<.

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T max() const;

Preconditions: size() > 0 is true.

Returns: The maximum value contained in *this.

For an array of length 1, the value of element 0 is returned.

For all other array lengths, the determination is made using operator<.

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valarray shift(int n) const;

Returns: A valarray of length size(), each of whose elements I is (*this)[I + n] if I + n is non-negative and less than size(), otherwise T().

[Note 1:

If element zero is taken as the leftmost element, a positive value of n shifts the elements left n places, with zero fill.

— end note]

[Example 1:

If the argument has the value -2, the first two elements of the result will be value-initialized; the third element of the result will be assigned the value of the first element of the argument; etc.

— end example]

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valarray cshift(int n) const;

Returns: A valarray of length size() that is a circular shift of *this.

If element zero is taken as the leftmost element, a non-negative value of n shifts the elements circularly left n places and a negative value of n shifts the elements circularly right

- n

places.

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valarray apply(T func(T)) const;
valarray apply(T func(const T&)) const;

Returns: A valarray whose length is size().

Each element of the returned array is assigned the value returned by applying the argument function to the corresponding element of *this.

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void resize(size_t sz, T c = T());

Effects: Changes the length of the *this array to sz and then assigns to each element the value of the second argument.

Resizing invalidates all pointers and references to elements in the array.

26.7.3 valarray non-member operations [valarray.nonmembers]

26.7.3.1 Binary operators [valarray.binary]

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template<class T> valarray<T> operator* (const valarray<T>&, const valarray<T>&);
template<class T> valarray<T> operator/ (const valarray<T>&, const valarray<T>&);
template<class T> valarray<T> operator% (const valarray<T>&, const valarray<T>&);
template<class T> valarray<T> operator+ (const valarray<T>&, const valarray<T>&);
template<class T> valarray<T> operator- (const valarray<T>&, const valarray<T>&);
template<class T> valarray<T> operator^ (const valarray<T>&, const valarray<T>&);
template<class T> valarray<T> operator& (const valarray<T>&, const valarray<T>&);
template<class T> valarray<T> operator| (const valarray<T>&, const valarray<T>&);
template<class T> valarray<T> operator<<(const valarray<T>&, const valarray<T>&);
template<class T> valarray<T> operator>>(const valarray<T>&, const valarray<T>&);

Mandates: The indicated operator can be applied to operands of type T and returns a value of type T or which can be unambiguously implicitly converted to T.

Preconditions: The argument arrays have the same length.

Returns: A valarray whose length is equal to the lengths of the argument arrays.

Each element of the returned array is initialized with the result of applying the indicated operator to the corresponding elements of the argument arrays.

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template<class T> valarray<T> operator* (const valarray<T>&,
                                         const typename valarray<T>::value_type&);
template<class T> valarray<T> operator* (const typename valarray<T>::value_type&,
                                         const valarray<T>&);
template<class T> valarray<T> operator/ (const valarray<T>&,
                                         const typename valarray<T>::value_type&);
template<class T> valarray<T> operator/ (const typename valarray<T>::value_type&,
                                         const valarray<T>&);
template<class T> valarray<T> operator% (const valarray<T>&,
                                         const typename valarray<T>::value_type&);
template<class T> valarray<T> operator% (const typename valarray<T>::value_type&,
                                         const valarray<T>&);
template<class T> valarray<T> operator+ (const valarray<T>&,
                                         const typename valarray<T>::value_type&);
template<class T> valarray<T> operator+ (const typename valarray<T>::value_type&,
                                         const valarray<T>&);
template<class T> valarray<T> operator- (const valarray<T>&,
                                         const typename valarray<T>::value_type&);
template<class T> valarray<T> operator- (const typename valarray<T>::value_type&,
                                         const valarray<T>&);
template<class T> valarray<T> operator^ (const valarray<T>&,
                                         const typename valarray<T>::value_type&);
template<class T> valarray<T> operator^ (const typename valarray<T>::value_type&,
                                         const valarray<T>&);
template<class T> valarray<T> operator& (const valarray<T>&,
                                         const typename valarray<T>::value_type&);
template<class T> valarray<T> operator& (const typename valarray<T>::value_type&,
                                         const valarray<T>&);
template<class T> valarray<T> operator| (const valarray<T>&,
                                         const typename valarray<T>::value_type&);
template<class T> valarray<T> operator| (const typename valarray<T>::value_type&,
                                         const valarray<T>&);
template<class T> valarray<T> operator<<(const valarray<T>&,
                                         const typename valarray<T>::value_type&);
template<class T> valarray<T> operator<<(const typename valarray<T>::value_type&,
                                         const valarray<T>&);
template<class T> valarray<T> operator>>(const valarray<T>&,
                                         const typename valarray<T>::value_type&);
template<class T> valarray<T> operator>>(const typename valarray<T>::value_type&,
                                         const valarray<T>&);

Mandates: The indicated operator can be applied to operands of type T and returns a value of type T or which can be unambiguously implicitly converted to T.

Returns: A valarray whose length is equal to the length of the array argument.

Each element of the returned array is initialized with the result of applying the indicated operator to the corresponding element of the array argument and the non-array argument.

26.7.3.2 Logical operators [valarray.comparison]

🔗

template<class T> valarray<bool> operator==(const valarray<T>&, const valarray<T>&);
template<class T> valarray<bool> operator!=(const valarray<T>&, const valarray<T>&);
template<class T> valarray<bool> operator< (const valarray<T>&, const valarray<T>&);
template<class T> valarray<bool> operator> (const valarray<T>&, const valarray<T>&);
template<class T> valarray<bool> operator<=(const valarray<T>&, const valarray<T>&);
template<class T> valarray<bool> operator>=(const valarray<T>&, const valarray<T>&);
template<class T> valarray<bool> operator&&(const valarray<T>&, const valarray<T>&);
template<class T> valarray<bool> operator||(const valarray<T>&, const valarray<T>&);

Mandates: The indicated operator can be applied to operands of type T and returns a value of type bool or which can be unambiguously implicitly converted to bool.

Preconditions: The two array arguments have the same length.

Returns: A valarray<bool> whose length is equal to the length of the array arguments.

Each element of the returned array is initialized with the result of applying the indicated operator to the corresponding elements of the argument arrays.

🔗

template<class T> valarray<bool> operator==(const valarray<T>&,
                                            const typename valarray<T>::value_type&);
template<class T> valarray<bool> operator==(const typename valarray<T>::value_type&,
                                            const valarray<T>&);
template<class T> valarray<bool> operator!=(const valarray<T>&,
                                            const typename valarray<T>::value_type&);
template<class T> valarray<bool> operator!=(const typename valarray<T>::value_type&,
                                            const valarray<T>&);
template<class T> valarray<bool> operator< (const valarray<T>&,
                                            const typename valarray<T>::value_type&);
template<class T> valarray<bool> operator< (const typename valarray<T>::value_type&,
                                            const valarray<T>&);
template<class T> valarray<bool> operator> (const valarray<T>&,
                                            const typename valarray<T>::value_type&);
template<class T> valarray<bool> operator> (const typename valarray<T>::value_type&,
                                            const valarray<T>&);
template<class T> valarray<bool> operator<=(const valarray<T>&,
                                            const typename valarray<T>::value_type&);
template<class T> valarray<bool> operator<=(const typename valarray<T>::value_type&,
                                            const valarray<T>&);
template<class T> valarray<bool> operator>=(const valarray<T>&,
                                            const typename valarray<T>::value_type&);
template<class T> valarray<bool> operator>=(const typename valarray<T>::value_type&,
                                            const valarray<T>&);
template<class T> valarray<bool> operator&&(const valarray<T>&,
                                            const typename valarray<T>::value_type&);
template<class T> valarray<bool> operator&&(const typename valarray<T>::value_type&,
                                            const valarray<T>&);
template<class T> valarray<bool> operator||(const valarray<T>&,
                                            const typename valarray<T>::value_type&);
template<class T> valarray<bool> operator||(const typename valarray<T>::value_type&,
                                            const valarray<T>&);

Mandates: The indicated operator can be applied to operands of type T and returns a value of type bool or which can be unambiguously implicitly converted to bool.

Returns: A valarray<bool> whose length is equal to the length of the array argument.

Each element of the returned array is initialized with the result of applying the indicated operator to the corresponding element of the array and the non-array argument.

26.7.3.3 Transcendentals [valarray.transcend]

🔗

template<class T> valarray<T> abs  (const valarray<T>&);
template<class T> valarray<T> acos (const valarray<T>&);
template<class T> valarray<T> asin (const valarray<T>&);
template<class T> valarray<T> atan (const valarray<T>&);
template<class T> valarray<T> atan2(const valarray<T>&, const valarray<T>&);
template<class T> valarray<T> atan2(const valarray<T>&, const typename valarray<T>::value_type&);
template<class T> valarray<T> atan2(const typename valarray<T>::value_type&, const valarray<T>&);
template<class T> valarray<T> cos  (const valarray<T>&);
template<class T> valarray<T> cosh (const valarray<T>&);
template<class T> valarray<T> exp  (const valarray<T>&);
template<class T> valarray<T> log  (const valarray<T>&);
template<class T> valarray<T> log10(const valarray<T>&);
template<class T> valarray<T> pow  (const valarray<T>&, const valarray<T>&);
template<class T> valarray<T> pow  (const valarray<T>&, const typename valarray<T>::value_type&);
template<class T> valarray<T> pow  (const typename valarray<T>::value_type&, const valarray<T>&);
template<class T> valarray<T> sin  (const valarray<T>&);
template<class T> valarray<T> sinh (const valarray<T>&);
template<class T> valarray<T> sqrt (const valarray<T>&);
template<class T> valarray<T> tan  (const valarray<T>&);
template<class T> valarray<T> tanh (const valarray<T>&);

Mandates: A unique function with the indicated name can be applied (unqualified) to an operand of type T.

This function returns a value of type T or which can be unambiguously implicitly converted to type T.

26.7.3.4 Specialized algorithms [valarray.special]

🔗

template<class T> void swap(valarray<T>& x, valarray<T>& y) noexcept;

Effects: Equivalent to x.swap(y).

26.7.4 Class slice [class.slice]

26.7.4.1 Overview [class.slice.overview]

namespace std { class slice { public: slice(); slice(size_t, size_t, size_t); size_t start() const; size_t size() const; size_t stride() const; friend bool operator==(const slice& x, const slice& y); }; }

The slice class represents a BLAS-like slice from an array.

Such a slice is specified by a starting index, a length, and a stride.259

259)

BLAS stands for Basic Linear Algebra Subprograms.

C++ programs can instantiate this class.

See, for example, Dongarra, Du Croz, Duff, and Hammerling: A set of Level 3 Basic Linear Algebra Subprograms; Technical Report MCS-P1-0888, Argonne National Laboratory (USA), Mathematics and Computer Science Division, August, 1988.

⮥

26.7.4.2 Constructors [cons.slice]

🔗

slice();
slice(size_t start, size_t length, size_t stride);
slice(const slice&);

The default constructor is equivalent to slice(0, 0, 0).

A default constructor is provided only to permit the declaration of arrays of slices.

The constructor with arguments for a slice takes a start, length, and stride parameter.

[Example 1:

slice(3, 8, 2) constructs a slice which selects elements

3, 5, 7, \dots, 17

from an array.

— end example]

26.7.4.3 Access functions [slice.access]

🔗

size_t start() const;
size_t size() const;
size_t stride() const;

Returns: The start, length, or stride specified by a slice object.

Complexity: Constant time.

26.7.4.4 Operators [slice.ops]

🔗

friend bool operator==(const slice& x, const slice& y);

Effects: Equivalent to: return x.start() == y.start() && x.size() == y.size() && x.stride() == y.stride();

26.7.5 Class template slice_array [template.slice.array]

26.7.5.1 Overview [template.slice.array.overview]

namespace std { template<class T> class slice_array { public: using value_type = T; void operator= (const valarray<T>&) const; void operator*= (const valarray<T>&) const; void operator/= (const valarray<T>&) const; void operator%= (const valarray<T>&) const; void operator+= (const valarray<T>&) const; void operator-= (const valarray<T>&) const; void operator^= (const valarray<T>&) const; void operator&= (const valarray<T>&) const; void operator|= (const valarray<T>&) const; void operator<<=(const valarray<T>&) const; void operator>>=(const valarray<T>&) const; slice_array(const slice_array&); ~slice_array(); const slice_array& operator=(const slice_array&) const; void operator=(const T&) const; slice_array() = delete; // as implied by declaring copy constructor above }; }

This template is a helper template used by the slice subscript operator slice_array<T> valarray<T>::operator[](slice);

It has reference semantics to a subset of an array specified by a slice object.

[Example 1:

The expression a[slice(1, 5, 3)] = b; has the effect of assigning the elements of b to a slice of the elements in a.

For the slice shown, the elements selected from a are

1, 4, \dots, 13

— end example]

26.7.5.2 Assignment [slice.arr.assign]

🔗

void operator=(const valarray<T>&) const;
const slice_array& operator=(const slice_array&) const;

These assignment operators have reference semantics, assigning the values of the argument array elements to selected elements of the valarray<T> object to which the slice_array object refers.

26.7.5.3 Compound assignment [slice.arr.comp.assign]

🔗

void operator*= (const valarray<T>&) const;
void operator/= (const valarray<T>&) const;
void operator%= (const valarray<T>&) const;
void operator+= (const valarray<T>&) const;
void operator-= (const valarray<T>&) const;
void operator^= (const valarray<T>&) const;
void operator&= (const valarray<T>&) const;
void operator|= (const valarray<T>&) const;
void operator<<=(const valarray<T>&) const;
void operator>>=(const valarray<T>&) const;

These compound assignments have reference semantics, applying the indicated operation to the elements of the argument array and selected elements of the valarray<T> object to which the slice_array object refers.

26.7.5.4 Fill function [slice.arr.fill]

🔗

void operator=(const T&) const;

This function has reference semantics, assigning the value of its argument to the elements of the valarray<T> object to which the slice_array object refers.

26.7.6 The gslice class [class.gslice]

26.7.6.1 Overview [class.gslice.overview]

namespace std { class gslice { public: gslice(); gslice(size_t s, const valarray<size_t>& l, const valarray<size_t>& d); size_t start() const; valarray<size_t> size() const; valarray<size_t> stride() const; }; }

This class represents a generalized slice out of an array.

A gslice is defined by a starting offset (s), a set of lengths (

l_{j}

), and a set of strides (

d_{j}

The number of lengths shall equal the number of strides.

A gslice represents a mapping from a set of indices (

i_{j}

), equal in number to the number of strides, to a single index k.

It is useful for building multidimensional array classes using the valarray template, which is one-dimensional.

The set of one-dimensional index values specified by a gslice are

k = s + \sum j i_{j} d_{j}

where the multidimensional indices

i_{j}

range in value from 0 to

l_{i j} - 1

[Example 1:

The gslice specification start = 3 length = {2, 4, 3} stride = {19, 4, 1} yields the sequence of one-dimensional indices

k = 3 + (0, 1) \times 19 + (0, 1, 2, 3) \times 4 + (0, 1, 2) \times 1

which are ordered as shown in the following table:

	 $(i_{0}, i_{1}, i_{2}, k) =$ 
		 $(0, 0, 0, 3)$ ,    
		 $(0, 0, 1, 4)$ ,    
		 $(0, 0, 2, 5)$ ,    
		 $(0, 1, 0, 7)$ ,    
		 $(0, 1, 1, 8)$ ,    
		 $(0, 1, 2, 9)$ ,    
		 $(0, 2, 0, 11)$ , 
		 $(0, 2, 1, 12)$ , 
		 $(0, 2, 2, 13)$ , 
		 $(0, 3, 0, 15)$ , 
		 $(0, 3, 1, 16)$ , 
		 $(0, 3, 2, 17)$ , 
		 $(1, 0, 0, 22)$ , 
		 $(1, 0, 1, 23)$ , 
		…      
		 $(1, 3, 2, 36)$

That is, the highest-ordered index turns fastest.

— end example]

It is possible to have degenerate generalized slices in which an address is repeated.

[Example 2:

If the stride parameters in the previous example are changed to {1, 1, 1}, the first few elements of the resulting sequence of indices will be

	 $(0, 0, 0, 3)$ ,  
	 $(0, 0, 1, 4)$ ,  
	 $(0, 0, 2, 5)$ ,  
	 $(0, 1, 0, 4)$ ,  
	 $(0, 1, 1, 5)$ ,  
	 $(0, 1, 2, 6)$ ,  
	…

— end example]

If a degenerate slice is used as the argument to the non-const version of operator[](const gslice&), the behavior is undefined.

26.7.6.2 Constructors [gslice.cons]

🔗

gslice();
gslice(size_t start, const valarray<size_t>& lengths,
       const valarray<size_t>& strides);
gslice(const gslice&);

The default constructor is equivalent to gslice(0, valarray<size_t>(), valarray<size_t>()).

The constructor with arguments builds a gslice based on a specification of start, lengths, and strides, as explained in the previous subclause.

26.7.6.3 Access functions [gslice.access]

🔗

size_t           start()  const;
valarray<size_t> size() const;
valarray<size_t> stride() const;

Returns: The representation of the start, lengths, or strides specified for the gslice.

Complexity: start() is constant time.

size() and stride() are linear in the number of strides.

26.7.7 Class template gslice_array [template.gslice.array]

26.7.7.1 Overview [template.gslice.array.overview]

namespace std { template<class T> class gslice_array { public: using value_type = T; void operator= (const valarray<T>&) const; void operator*= (const valarray<T>&) const; void operator/= (const valarray<T>&) const; void operator%= (const valarray<T>&) const; void operator+= (const valarray<T>&) const; void operator-= (const valarray<T>&) const; void operator^= (const valarray<T>&) const; void operator&= (const valarray<T>&) const; void operator|= (const valarray<T>&) const; void operator<<=(const valarray<T>&) const; void operator>>=(const valarray<T>&) const; gslice_array(const gslice_array&); ~gslice_array(); const gslice_array& operator=(const gslice_array&) const; void operator=(const T&) const; gslice_array() = delete; // as implied by declaring copy constructor above }; }

This template is a helper template used by the gslice subscript operator

🔗

gslice_array<T> valarray<T>::operator[](const gslice&);

It has reference semantics to a subset of an array specified by a gslice object.

Thus, the expression a[gslice(1, length, stride)] = b has the effect of assigning the elements of b to a generalized slice of the elements in a.

26.7.7.2 Assignment [gslice.array.assign]

🔗

void operator=(const valarray<T>&) const;
const gslice_array& operator=(const gslice_array&) const;

These assignment operators have reference semantics, assigning the values of the argument array elements to selected elements of the valarray<T> object to which the gslice_array refers.

26.7.7.3 Compound assignment [gslice.array.comp.assign]

🔗

void operator*= (const valarray<T>&) const;
void operator/= (const valarray<T>&) const;
void operator%= (const valarray<T>&) const;
void operator+= (const valarray<T>&) const;
void operator-= (const valarray<T>&) const;
void operator^= (const valarray<T>&) const;
void operator&= (const valarray<T>&) const;
void operator|= (const valarray<T>&) const;
void operator<<=(const valarray<T>&) const;
void operator>>=(const valarray<T>&) const;

26.7.7.4 Fill function [gslice.array.fill]

🔗

void operator=(const T&) const;

This function has reference semantics, assigning the value of its argument to the elements of the valarray<T> object to which the gslice_array object refers.

26.7.8 Class template mask_array [template.mask.array]

26.7.8.1 Overview [template.mask.array.overview]

namespace std { template<class T> class mask_array { public: using value_type = T; void operator= (const valarray<T>&) const; void operator*= (const valarray<T>&) const; void operator/= (const valarray<T>&) const; void operator%= (const valarray<T>&) const; void operator+= (const valarray<T>&) const; void operator-= (const valarray<T>&) const; void operator^= (const valarray<T>&) const; void operator&= (const valarray<T>&) const; void operator|= (const valarray<T>&) const; void operator<<=(const valarray<T>&) const; void operator>>=(const valarray<T>&) const; mask_array(const mask_array&); ~mask_array(); const mask_array& operator=(const mask_array&) const; void operator=(const T&) const; mask_array() = delete; // as implied by declaring copy constructor above }; }

This template is a helper template used by the mask subscript operator:

🔗

mask_array<T> valarray<T>::operator[](const valarray<bool>&).

It has reference semantics to a subset of an array specified by a boolean mask.

Thus, the expression a[mask] = b; has the effect of assigning the elements of b to the masked elements in a (those for which the corresponding element in mask is true).

26.7.8.2 Assignment [mask.array.assign]

🔗

void operator=(const valarray<T>&) const;
const mask_array& operator=(const mask_array&) const;

These assignment operators have reference semantics, assigning the values of the argument array elements to selected elements of the valarray<T> object to which the mask_array object refers.

26.7.8.3 Compound assignment [mask.array.comp.assign]

🔗

void operator*= (const valarray<T>&) const;
void operator/= (const valarray<T>&) const;
void operator%= (const valarray<T>&) const;
void operator+= (const valarray<T>&) const;
void operator-= (const valarray<T>&) const;
void operator^= (const valarray<T>&) const;
void operator&= (const valarray<T>&) const;
void operator|= (const valarray<T>&) const;
void operator<<=(const valarray<T>&) const;
void operator>>=(const valarray<T>&) const;

26.7.8.4 Fill function [mask.array.fill]

🔗

void operator=(const T&) const;

This function has reference semantics, assigning the value of its argument to the elements of the valarray<T> object to which the mask_array object refers.

26.7.9 Class template indirect_array [template.indirect.array]

26.7.9.1 Overview [template.indirect.array.overview]

namespace std { template<class T> class indirect_array { public: using value_type = T; void operator= (const valarray<T>&) const; void operator*= (const valarray<T>&) const; void operator/= (const valarray<T>&) const; void operator%= (const valarray<T>&) const; void operator+= (const valarray<T>&) const; void operator-= (const valarray<T>&) const; void operator^= (const valarray<T>&) const; void operator&= (const valarray<T>&) const; void operator|= (const valarray<T>&) const; void operator<<=(const valarray<T>&) const; void operator>>=(const valarray<T>&) const; indirect_array(const indirect_array&); ~indirect_array(); const indirect_array& operator=(const indirect_array&) const; void operator=(const T&) const; indirect_array() = delete; // as implied by declaring copy constructor above }; }

This template is a helper template used by the indirect subscript operator

🔗

indirect_array<T> valarray<T>::operator[](const valarray<size_t>&).

It has reference semantics to a subset of an array specified by an indirect_array.

Thus, the expression a[indirect] = b; has the effect of assigning the elements of b to the elements in a whose indices appear in indirect.

26.7.9.2 Assignment [indirect.array.assign]

🔗

void operator=(const valarray<T>&) const;
const indirect_array& operator=(const indirect_array&) const;

These assignment operators have reference semantics, assigning the values of the argument array elements to selected elements of the valarray<T> object to which it refers.

If the indirect_array specifies an element in the valarray<T> object to which it refers more than once, the behavior is undefined.

[Example 1:

int addr[] = {2, 3, 1, 4, 4}; valarray<size_t> indirect(addr, 5); valarray<double> a(0., 10), b(1., 5); a[indirect] = b; results in undefined behavior since element 4 is specified twice in the indirection.

— end example]

26.7.9.3 Compound assignment [indirect.array.comp.assign]

🔗

void operator*= (const valarray<T>&) const;
void operator/= (const valarray<T>&) const;
void operator%= (const valarray<T>&) const;
void operator+= (const valarray<T>&) const;
void operator-= (const valarray<T>&) const;
void operator^= (const valarray<T>&) const;
void operator&= (const valarray<T>&) const;
void operator|= (const valarray<T>&) const;
void operator<<=(const valarray<T>&) const;
void operator>>=(const valarray<T>&) const;

If the indirect_array specifies an element in the valarray<T> object to which it refers more than once, the behavior is undefined.

26.7.9.4 Fill function [indirect.array.fill]

🔗

void operator=(const T&) const;

This function has reference semantics, assigning the value of its argument to the elements of the valarray<T> object to which the indirect_array object refers.

26.7.10 valarray range access [valarray.range]

In the begin and end function templates that follow, unspecified1 is a type that meets the requirements of a mutable Cpp17RandomAccessIterator ([random.access.iterators]) and models contiguous_iterator ([iterator.concept.contiguous]), whose value_type is the template parameter T and whose reference type is T&.

unspecified2 is a type that meets the requirements of a constant Cpp17RandomAccessIterator and models contiguous_iterator, whose value_type is the template parameter T and whose reference type is const T&.

The iterators returned by begin and end for an array are guaranteed to be valid until the member function resize(size_t, T) is called for that array or until the lifetime of that array ends, whichever happens first.

🔗

template<class T> unspecified1 begin(valarray<T>& v);
template<class T> unspecified2 begin(const valarray<T>& v);

Returns: An iterator referencing the first value in the array.

🔗

template<class T> unspecified1 end(valarray<T>& v);
template<class T> unspecified2 end(const valarray<T>& v);

Returns: An iterator referencing one past the last value in the array.

26 Numerics library [numerics]

26.7 Numeric arrays [numarray]

26.7.1 Header <valarray> synopsis [valarray.syn]

26.7.2 Class template valarray [template.valarray]

26.7.2.1 Overview [template.valarray.overview]

26.7.2.2 Constructors [valarray.cons]

26.7.2.3 Assignment [valarray.assign]

26.7.2.4 Element access [valarray.access]

26.7.2.5 Subset operations [valarray.sub]

26.7.2.6 Unary operators [valarray.unary]

26.7.2.7 Compound assignment [valarray.cassign]

26.7.2.8 Member functions [valarray.members]

26.7.3 valarray non-member operations [valarray.nonmembers]

26.7.3.1 Binary operators [valarray.binary]

26.7.3.2 Logical operators [valarray.comparison]

26.7.3.3 Transcendentals [valarray.transcend]

26.7.3.4 Specialized algorithms [valarray.special]

26.7.4 Class slice [class.slice]

26.7.4.1 Overview [class.slice.overview]

26.7.4.2 Constructors [cons.slice]

26.7.4.3 Access functions [slice.access]

26.7.4.4 Operators [slice.ops]

26.7.5 Class template slice_­array [template.slice.array]

26.7.5.1 Overview [template.slice.array.overview]

26.7.5.2 Assignment [slice.arr.assign]

26.7.5.3 Compound assignment [slice.arr.comp.assign]

26.7.5.4 Fill function [slice.arr.fill]

26.7.6 The gslice class [class.gslice]

26.7.6.1 Overview [class.gslice.overview]

26.7.6.2 Constructors [gslice.cons]

26.7.6.3 Access functions [gslice.access]

26.7.7 Class template gslice_­array [template.gslice.array]

26.7.7.1 Overview [template.gslice.array.overview]

26.7.7.2 Assignment [gslice.array.assign]

26.7.7.3 Compound assignment [gslice.array.comp.assign]

26.7.7.4 Fill function [gslice.array.fill]

26.7.8 Class template mask_­array [template.mask.array]

26.7.8.1 Overview [template.mask.array.overview]

26.7.8.2 Assignment [mask.array.assign]

26.7.8.3 Compound assignment [mask.array.comp.assign]

26.7.8.4 Fill function [mask.array.fill]

26.7.9 Class template indirect_­array [template.indirect.array]

26.7.9.1 Overview [template.indirect.array.overview]

26.7.9.2 Assignment [indirect.array.assign]

26.7.9.3 Compound assignment [indirect.array.comp.assign]

26.7.9.4 Fill function [indirect.array.fill]

26.7.10 valarray range access [valarray.range]

26.7.5 Class template slice_array [template.slice.array]

26.7.7 Class template gslice_array [template.gslice.array]

26.7.8 Class template mask_array [template.mask.array]

26.7.9 Class template indirect_array [template.indirect.array]