29 Numerics library [numerics]

29.7 Numeric arrays [numarray]

29.7.1 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 T&);
  template<class T> valarray<T> operator* (const 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 T&);
  template<class T> valarray<T> operator/ (const 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 T&);
  template<class T> valarray<T> operator% (const 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 T&);
  template<class T> valarray<T> operator+ (const 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 T&);
  template<class T> valarray<T> operator- (const 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 T&);
  template<class T> valarray<T> operator^ (const 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 T&);
  template<class T> valarray<T> operator& (const 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 T&);
  template<class T> valarray<T> operator| (const 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 T&);
  template<class T> valarray<T> operator<<(const 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 T&);
  template<class T> valarray<T> operator>>(const 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 T&);
  template<class T> valarray<bool> operator&&(const 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 T&);
  template<class T> valarray<bool> operator||(const 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 T&);
  template<class T> valarray<bool> operator==(const 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 T&);
  template<class T> valarray<bool> operator!=(const 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 T&);
  template<class T> valarray<bool> operator< (const 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 T&);
  template<class T> valarray<bool> operator> (const 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 T&);
  template<class T> valarray<bool> operator<=(const 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 T&);
  template<class T> valarray<bool> operator>=(const T&, 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 T&);
  template<class T> valarray<T> atan2(const T&, 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 T&);
  template<class T> valarray<T> pow(const T&, 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);
}
1
#
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.
2
#
The valarray array classes are defined to be free of certain forms of aliasing, thus allowing operations on these classes to be optimized.
3
#
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.275
4
#
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 ([valarray.range]), 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.
5
#
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.
6
#
These library functions are permitted to throw a bad_­alloc ([bad.alloc]) exception if there are not sufficient resources available to carry out the operation.
Note that the exception is not mandated.
275)
Annex [implimits] recommends a minimum number of recursively nested template instantiations.
This requirement thus indirectly suggests a minimum allowable complexity for valarray expressions.

29.7.2 Class template valarray [template.valarray]

29.7.2.1 Class template valarray 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>;
}
1
#
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.276
2
#
An implementation is permitted to qualify any of the functions declared in <valarray> as inline.
276)
The intent is to specify an array template that has the minimum functionality necessary to address aliasing ambiguities and the proliferation of temporaries.
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.

29.7.2.2 valarray constructors [valarray.cons]

valarray();
1
#
Effects: Constructs a valarray that has zero length.277
explicit valarray(size_t n);
2
#
Effects: Constructs a valarray that has length n.
Each element of the array is value-initialized ([dcl.init]).
valarray(const T& v, size_t n);
3
#
Effects: Constructs a valarray that has length n.
Each element of the array is initialized with v.
valarray(const T* p, size_t n);
4
#
Requires: p points to an array ([dcl.array]) of at least n elements.
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.278
valarray(const valarray& v);
5
#
Effects: Constructs a valarray that has the same length as v.
The elements are initialized with the values of the corresponding elements of v.279
valarray(valarray&& v) noexcept;
6
#
Effects: Constructs a valarray that has the same length as v.
The elements are initialized with the values of the corresponding elements of v.
7
#
Complexity: Constant.
valarray(initializer_list<T> il);
8
#
Effects: Equivalent to valarray(il.begin(), il.size()).
valarray(const slice_array<T>&); valarray(const gslice_array<T>&); valarray(const mask_array<T>&); valarray(const indirect_array<T>&);
9
#
These conversion constructors convert one of the four reference templates to a valarray.
~valarray();
10
#
Effects: The destructor is applied to every element of *this; an implementation may return all allocated memory.
277)
This default constructor is essential, since arrays of valarray may be useful.
After initialization, the length of an empty array can be increased with the resize member function.
278)
This constructor is the preferred method for converting a C array to a valarray object.
279)
This copy constructor creates a distinct array rather than an alias.
Implementations in which arrays share storage are permitted, but they shall implement a copy-on-reference mechanism to ensure that arrays are conceptually distinct.

29.7.2.3 valarray assignment [valarray.assign]

valarray& operator=(const valarray& v);
1
#
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.
2
#
Postconditions: size() == v.size().
3
#
Returns: *this.
valarray& operator=(valarray&& v) noexcept;
4
#
Effects: *this obtains the value of v.
The value of v after the assignment is not specified.
5
#
Returns: *this.
6
#
Complexity: Linear.
valarray& operator=(initializer_list<T> il);
7
#
Effects: Equivalent to: return *this = valarray(il);
valarray& operator=(const T& v);
8
#
Effects: Assigns v to each element of *this.
9
#
Returns: *this.
valarray& operator=(const slice_array<T>&); valarray& operator=(const gslice_array<T>&); valarray& operator=(const mask_array<T>&); valarray& operator=(const indirect_array<T>&);
10
#
Requires: 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.
11
#
These operators allow the results of a generalized subscripting operation to be assigned directly to a valarray.

29.7.2.4 valarray element access [valarray.access]

const T& operator[](size_t n) const; T& operator[](size_t n);
1
#
Requires: n < size().
2
#
Returns: A reference to the corresponding element of the array.
[ Note
:
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
 ]
3
#
Remarks: The expression &a[i+j] == &a[i] + j evaluates to true for all size_­t i and size_­t j such that i+j < a.size().
4
#
The expression &a[i] != &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
:
This property indicates an absence of aliasing and may be used to advantage by optimizing compilers.
Compilers may take advantage of inlining, constant propagation, loop fusion, tracking of pointers obtained from operator new, and other techniques to generate efficient valarrays.
— end note
 ]
5
#
The reference returned by the subscript operator for an array shall be valid until the member function resize(size_­t, T) ([valarray.members]) is called for that array or until the lifetime of that array ends, whichever happens first.

29.7.2.5 valarray subset operations [valarray.sub]

1
#
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) must exist.
valarray operator[](slice slicearr) const;
2
#
Returns: A valarray containing those elements of the controlled sequence designated by slicearr.
[ Example
: 
const valarray<char> v0("abcdefghijklmnop", 16);
// v0[slice(2, 5, 3)] returns valarray<char>("cfilo", 5)
— end example
 ]
slice_array<T> operator[](slice slicearr);
3
#
Returns: An object that holds references to elements of the controlled sequence selected by slicearr.
[ Example
: 
valarray<char> v0("abcdefghijklmnop", 16);
valarray<char> v1("ABCDE", 5);
v0[slice(2, 5, 3)] = v1;
// v0 == valarray<char>("abAdeBghCjkDmnEp", 16);
— end example
 ]
valarray operator[](const gslice& gslicearr) const;
4
#
Returns: A valarray containing those elements of the controlled sequence designated by gslicearr.
[ Example
: 
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
 ]
gslice_array<T> operator[](const gslice& gslicearr);
5
#
Returns: An object that holds references to elements of the controlled sequence selected by gslicearr.
[ Example
: 
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
 ]
valarray operator[](const valarray<bool>& boolarr) const;
6
#
Returns: A valarray containing those elements of the controlled sequence designated by boolarr.
[ Example
: 
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
 ]
mask_array<T> operator[](const valarray<bool>& boolarr);
7
#
Returns: An object that holds references to elements of the controlled sequence selected by boolarr.
[ Example
: 
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
 ]
valarray operator[](const valarray<size_t>& indarr) const;
8
#
Returns: A valarray containing those elements of the controlled sequence designated by indarr.
[ Example
: 
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
 ]
indirect_array<T> operator[](const valarray<size_t>& indarr);
9
#
Returns: An object that holds references to elements of the controlled sequence selected by indarr.
[ Example
: 
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
 ]

29.7.2.6 valarray unary operators [valarray.unary]

valarray operator+() const; valarray operator-() const; valarray operator~() const; valarray<bool> operator!() const;
1
#
Requires: Each of these operators may only be instantiated for a type T to which the indicated operator can be applied and for which the indicated operator returns a value which is of type T (bool for operator!) or which may be unambiguously implicitly converted to type T (bool for operator!).
2
#
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.

29.7.2.7 valarray compound assignment [valarray.cassign]

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);
1
#
Requires: size() == v.size().
Each of these operators may only be instantiated for a type T if the indicated operator can be applied to two operands of type T.
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.
2
#
Effects: Each of these operators performs the indicated operation on each of the elements of *this and the corresponding element of v.
3
#
Returns: *this.
4
#
Remarks: The appearance of an array on the left-hand side of a compound assignment does not invalidate references or pointers.
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);
5
#
Requires: Each of these operators may only be instantiated for a type T if the indicated operator can be applied to two operands of type T.
6
#
Effects: Each of these operators applies the indicated operation to each element of *this and v.
7
#
Returns: *this
8
#
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.

29.7.2.8 valarray member functions [valarray.members]

void swap(valarray& v) noexcept;
1
#
Effects: *this obtains the value of v.
v obtains the value of *this.
2
#
Complexity: Constant.
size_t size() const;
3
#
Returns: The number of elements in the array.
4
#
Complexity: Constant time.
T sum() const;
5
#
Requires: size() > 0.
This function may only be instantiated for a type T to which operator+= can be applied.
6
#
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.
T min() const;
7
#
Requires: size() > 0
8
#
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<.
T max() const;
9
#
Requires: size() > 0.
10
#
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<.
valarray shift(int n) const;
11
#
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
:
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
 ]
12
#
[ Example
:
If the argument has the value -2, the first two elements of the result will be value-initialized ([dcl.init]); the third element of the result will be assigned the value of the first element of the argument; etc.
— end example
 ]
valarray cshift(int n) const;
13
#
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 places.
valarray apply(T func(T)) const; valarray apply(T func(const T&)) const;
14
#
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.
void resize(size_t sz, T c = T());
15
#
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.

29.7.3 valarray non-member operations [valarray.nonmembers]

29.7.3.1 valarray binary operators [valarray.binary]

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>&);
1
#
Requires: Each of these operators may only be instantiated for a type T to which the indicated operator can be applied and for which the indicated operator returns a value which is of type T or which can be unambiguously implicitly converted to type T.
The argument arrays have the same length.
2
#
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.
template<class T> valarray<T> operator* (const valarray<T>&, const T&); template<class T> valarray<T> operator* (const T&, const valarray<T>&); template<class T> valarray<T> operator/ (const valarray<T>&, const T&); template<class T> valarray<T> operator/ (const T&, const valarray<T>&); template<class T> valarray<T> operator% (const valarray<T>&, const T&); template<class T> valarray<T> operator% (const T&, const valarray<T>&); template<class T> valarray<T> operator+ (const valarray<T>&, const T&); template<class T> valarray<T> operator+ (const T&, const valarray<T>&); template<class T> valarray<T> operator- (const valarray<T>&, const T&); template<class T> valarray<T> operator- (const T&, const valarray<T>&); template<class T> valarray<T> operator^ (const valarray<T>&, const T&); template<class T> valarray<T> operator^ (const T&, const valarray<T>&); template<class T> valarray<T> operator& (const valarray<T>&, const T&); template<class T> valarray<T> operator& (const T&, const valarray<T>&); template<class T> valarray<T> operator| (const valarray<T>&, const T&); template<class T> valarray<T> operator| (const T&, const valarray<T>&); template<class T> valarray<T> operator<<(const valarray<T>&, const T&); template<class T> valarray<T> operator<<(const T&, const valarray<T>&); template<class T> valarray<T> operator>>(const valarray<T>&, const T&); template<class T> valarray<T> operator>>(const T&, const valarray<T>&);
3
#
Requires: Each of these operators may only be instantiated for a type T to which the indicated operator can be applied and for which the indicated operator returns a value which is of type T or which can be unambiguously implicitly converted to type T.
4
#
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.

29.7.3.2 valarray 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>&);
1
#
Requires: Each of these operators may only be instantiated for a type T to which the indicated operator can be applied and for which the indicated operator returns a value which is of type bool or which can be unambiguously implicitly converted to type bool.
The two array arguments have the same length.
2
#
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 T&); template<class T> valarray<bool> operator==(const T&, const valarray<T>&); template<class T> valarray<bool> operator!=(const valarray<T>&, const T&); template<class T> valarray<bool> operator!=(const T&, const valarray<T>&); template<class T> valarray<bool> operator< (const valarray<T>&, const T&); template<class T> valarray<bool> operator< (const T&, const valarray<T>&); template<class T> valarray<bool> operator> (const valarray<T>&, const T&); template<class T> valarray<bool> operator> (const T&, const valarray<T>&); template<class T> valarray<bool> operator<=(const valarray<T>&, const T&); template<class T> valarray<bool> operator<=(const T&, const valarray<T>&); template<class T> valarray<bool> operator>=(const valarray<T>&, const T&); template<class T> valarray<bool> operator>=(const T&, const valarray<T>&); template<class T> valarray<bool> operator&&(const valarray<T>&, const T&); template<class T> valarray<bool> operator&&(const T&, const valarray<T>&); template<class T> valarray<bool> operator||(const valarray<T>&, const T&); template<class T> valarray<bool> operator||(const T&, const valarray<T>&);
3
#
Requires: Each of these operators may only be instantiated for a type T to which the indicated operator can be applied and for which the indicated operator returns a value which is of type bool or which can be unambiguously implicitly converted to type bool.
4
#
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.

29.7.3.3 valarray 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 T&); template<class T> valarray<T> atan2(const T&, 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 T&); template<class T> valarray<T> pow (const T&, 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>&);
1
#
Requires: Each of these functions may only be instantiated for a type T to which a unique function with the indicated name can be applied (unqualified).
This function shall return a value which is of type T or which can be unambiguously implicitly converted to type T.

29.7.3.4 valarray specialized algorithms [valarray.special]

template <class T> void swap(valarray<T>& x, valarray<T>& y) noexcept;
1
#
Effects: Equivalent to x.swap(y).

29.7.4 Class slice [class.slice]

29.7.4.1 Class slice 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;
  };
}
1
#
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.280
280)
BLAS stands for Basic Linear Algebra Subprograms. C++ programs may 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.

29.7.4.2 slice constructors [cons.slice]

slice(); slice(size_t start, size_t length, size_t stride); slice(const slice&);
1
#
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.
2
#
[ Example
:
slice(3, 8, 2) constructs a slice which selects elements 3, 5, 7, .
17 from an array.
— end example
 ]

29.7.4.3 slice access functions [slice.access]

size_t start() const; size_t size() const; size_t stride() const;
1
#
Returns: The start, length, or stride specified by a slice object.
2
#
Complexity: Constant time.

29.7.5 Class template slice_­array [template.slice.array]

29.7.5.1 Class template slice_­array 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
  };
}
1
#
The slice_­array 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.
2
#
[ Example
:
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, .
, 13.
— end example
 ]

29.7.5.2 slice_­array assignment [slice.arr.assign]

void operator=(const valarray<T>&) const; const slice_array& operator=(const slice_array&) const;
1
#
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.

29.7.5.3 slice_­array 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;
1
#
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.

29.7.5.4 slice_­array fill function [slice.arr.fill]

void operator=(const T&) const;
1
#
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.

29.7.6 The gslice class [class.gslice]

29.7.6.1 The gslice class 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;
  };
}
1
#
This class represents a generalized slice out of an array.
A gslice is defined by a starting offset (s), a set of lengths (), and a set of strides ().
The number of lengths shall equal the number of strides.
2
#
A gslice represents a mapping from a set of indices (), 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

where the multidimensional indices range in value from 0 to .

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

which are ordered as shown in the following table:

	
		,    
		,    
		,    
		,    
		,    
		,    
		, 
		, 
		, 
		, 
		, 
		, 
		, 
		, 
		…
That is, the highest-ordered index turns fastest.
— end example
 ]
4
#
It is possible to have degenerate generalized slices in which an address is repeated.
5
#
[ Example
:
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
	,  
	,  
	,  
	,  
	,  
	,  
	…
— end example
 ]
6
#
If a degenerate slice is used as the argument to the non-const version of operator[](const gslice&), the behavior is undefined.

29.7.6.2 gslice constructors [gslice.cons]

gslice(); gslice(size_t start, const valarray<size_t>& lengths, const valarray<size_t>& strides); gslice(const gslice&);
1
#
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 section.

29.7.6.3 gslice access functions [gslice.access]

size_t start() const; valarray<size_t> size() const; valarray<size_t> stride() const;
1
#
Returns: The representation of the start, lengths, or strides specified for the gslice.
2
#
Complexity: start() is constant time.
size() and stride() are linear in the number of strides.

29.7.7 Class template gslice_­array [template.gslice.array]

29.7.7.1 Class template gslice_­array 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
  };
}
1
#
This template is a helper template used by the slice subscript operator
gslice_array<T> valarray<T>::operator[](const gslice&);
2
#
It has reference semantics to a subset of an array specified by a gslice object.
3
#
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.

29.7.7.2 gslice_­array assignment [gslice.array.assign]

void operator=(const valarray<T>&) const; const gslice_array& operator=(const gslice_array&) const;
1
#
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.

29.7.7.3 gslice_­array 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;
1
#
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 gslice_­array object refers.

29.7.7.4 gslice_­array fill function [gslice.array.fill]

void operator=(const T&) const;
1
#
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.

29.7.8 Class template mask_­array [template.mask.array]

29.7.8.1 Class template mask_­array 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
  };
}
1
#
This template is a helper template used by the mask subscript operator:
mask_array<T> valarray<T>::operator[](const valarray<bool>&).
2
#
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.)

29.7.8.2 mask_­array assignment [mask.array.assign]

void operator=(const valarray<T>&) const; const mask_array& operator=(const mask_array&) const;
1
#
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.

29.7.8.3 mask_­array 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;
1
#
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 mask object refers.

29.7.8.4 mask_­array fill function [mask.array.fill]

void operator=(const T&) const;
1
#
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.

29.7.9 Class template indirect_­array [template.indirect.array]

29.7.9.1 Class template indirect_­array 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
  };
}
1
#
This template is a helper template used by the indirect subscript operator
indirect_array<T> valarray<T>::operator[](const valarray<size_t>&).
2
#
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.

29.7.9.2 indirect_­array assignment [indirect.array.assign]

void operator=(const valarray<T>&) const; const indirect_array& operator=(const indirect_array&) const;
1
#
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.
2
#
If the indirect_­array specifies an element in the valarray<T> object to which it refers more than once, the behavior is undefined.
3
#
[ Example
: 
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
 ]

29.7.9.3 indirect_­array 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;
1
#
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 indirect_­array object refers.
2
#
If the indirect_­array specifies an element in the valarray<T> object to which it refers more than once, the behavior is undefined.

29.7.9.4 indirect_­array fill function [indirect.array.fill]

void operator=(const T&) const;
1
#
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.

29.7.10 valarray range access [valarray.range]

1
#
In the begin and end function templates that follow, unspecified1 is a type that meets the requirements of a mutable random access iterator ([random.access.iterators]) and of a contiguous iterator ([iterator.requirements.general]) 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 random access iterator ([random.access.iterators]) and of a contiguous iterator ([iterator.requirements.general]) whose value_­type is the template parameter T and whose reference type is const T&.
2
#
The iterators returned by begin and end for an array are guaranteed to be valid until the member function resize(size_­t, T) ([valarray.members]) 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);
3
#
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);
4
#
Returns: An iterator referencing one past the last value in the array.