[numarray] (original) (raw)
29 Numerics library [numerics]
29.6 Numeric arrays [numarray]
29.6.1 Header synopsis [valarray.syn]
#include <initializer_list> // see [initializer.list.syn] 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> _unspecified_1 begin(valarray<T>& v);template<class T> _unspecified_2 begin(const valarray<T>& v);template<class T> _unspecified_1 end(valarray<T>& v);template<class T> _unspecified_2 end(const valarray<T>& v);}
The header defines five class templates (valarray,slice_array,gslice_array,mask_array, andindirect_array), two classes (sliceandgslice), and a series of related function templates for representing and manipulating arrays of values.
Thevalarrayarray classes are defined to be free of certain forms of aliasing, thus allowing operations on these classes to be optimized.
Any function returning avalarray<T>is permitted to return an object of another type, provided all the const member functions ofvalarray<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.248
Implementations introducing such replacement types shall provide additional functions and operators as follows:
- for every function taking aconst valarray<T>& other thanbegin andend, identical functions taking the replacement types shall be added;
- for every function taking twoconst valarray<T>&arguments, identical functions taking every combination ofconst valarray<T>&and replacement types shall be added.
In particular, an implementation shall allow avalarray<T>to be constructed from such replacement types and shall allow assignments and compound assignments of such types tovalarray<T>,slice_array<T>,gslice_array<T>,mask_array<T>andindirect_array<T>objects.
These library functions are permitted to throw abad_alloc exception if there are not sufficient resources available to carry out the operation.
Note that the exception is not mandated.
29.6.2 Class template valarray [template.valarray]
29.6.2.1 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 templatevalarray<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.249
29.6.2.2 Constructors [valarray.cons]
Effects: Constructs a valarraythat has zero length.250
explicit valarray(size_t n);
Effects: Constructs a valarray that has length n.
valarray(const T& v, size_t n);
Effects: Constructs a valarray that has length n.
Each element of the array is initialized with v.
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 firstnvalues pointed to by the first argument.251
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.252
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.
valarray(initializer_list<T> il);
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>&);
These conversion constructors convert one of the four reference templates to avalarray.
Effects: The destructor is applied to every element of*this; an implementation may return all allocated memory.
29.6.2.3 Assignment [valarray.assign]
valarray& operator=(const valarray& v);
Effects: Each element of the*thisarray 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().
valarray& operator=(valarray&& v) noexcept;
Effects: *this obtains the value of v.
The value of v after the assignment is not specified.
valarray& operator=(initializer_list<T> il);
Effects: Equivalent to: return *this = valarray(il);
valarray& operator=(const T& v);
Effects: Assigns v to each element of *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>&);
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 avalarray.
29.6.2.4 Element access [valarray.access]
const T& operator[](size_t n) const; T& operator[](size_t n);
Hardened preconditions: n < size() is true.
Returns: A reference to the corresponding element of the array.
[Note 1:
The expression (a[i] = q, a[i]) == qevaluates to true for any non-constant valarray<T> a, any T q, and for any size_t isuch that the value of i is less than the length of a.
— _end note_]
Remarks: The expression addressof(a[i+j]) == addressof(a[i]) + jevaluates to true for all size_t i and size_t jsuch that i+j < a.size().
The expression addressof(a[i]) != addressof(b[j])evaluates to true for any two arraysa and b and for anysize_t i and size_t jsuch 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 fromoperator new, and other techniques to generate efficientvalarrays.
— _end note_]
The reference returned by the subscript operator for an array shall be valid until the member functionresize(size_t, T) is called for that array or until the lifetime of that array ends, whichever happens first.
29.6.2.5 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.
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("cfilo", 5) — _end example_]
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("abAdeBghCjkDmnEp", 16); — _end example_]
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("dfhkmo", 6) — _end example_]
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("abcAeBgCijDlEnFp", 16) — _end example_]
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(vb, 6)] returns // valarray("cdf", 3) — _end example_]
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("abABeCghijklmnop", 16) — _end example_]
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("hfcdi", 5) — _end example_]
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("abCDeBgAEjklmnop", 16) — _end example_]
29.6.2.6 Unary operators [valarray.unary]
valarray operator+() const; valarray operator-() const; valarray operator~() const; valarray<bool> operator!() const;
Mandates: The indicated operator can be applied to operands of type Tand returns a value of type T (bool foroperator!) or which may be unambiguously implicitly converted to typeT (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.
29.6.2.7 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);
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.
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);
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.
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.
29.6.2.8 Member functions [valarray.members]
void swap(valarray& v) noexcept;
Effects: *this obtains the value ofv.
v obtains the value of *this.
Returns: The number of elements in the array.
Complexity: Constant time.
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 applyingoperator+=to a copy of an element of the array and all other elements of the array in an unspecified order.
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 usingoperator<.
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 usingoperator<.
valarray shift(int n) const;
Returns: A valarray of length size(), each of whose elements_I_ is(*this)[I + n]if I + nis non-negative and less thansize(), otherwise T().
[Note 1:
If element zero is taken as the leftmost element, a positive value of n shifts the elements left nplaces, with zero fill.
— _end note_]
[Example 1:
If the argument has the value , 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 *this; etc.
— _end example_]
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 places.
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.
void resize(size_t sz, T c = T());
Effects: Changes the length of the *this array to szand then assigns to each element the value of the second argument.
Resizing invalidates all pointers and references to elements in the array.
29.6.3 valarray non-member operations [valarray.nonmembers]
29.6.3.1 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>&);
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.
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.
29.6.3.2 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.
29.6.3.3 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 Tor which can be unambiguously implicitly converted to type T.
29.6.3.4 Specialized algorithms [valarray.special]
template<class T> void swap(valarray<T>& x, valarray<T>& y) noexcept;
Effects: Equivalent to x.swap(y).
29.6.4 Class slice [class.slice]
29.6.4.1 Overview [class.slice.overview]
namespace std { class slice { public: slice(); slice(size_t, size_t, size_t); slice(const slice&); size_t start() const; size_t size() const; size_t stride() const;friend bool operator==(const slice& x, const slice& y);};}
The sliceclass represents a BLAS-like slice from an array.
Such a slice is specified by a starting index, a length, and a stride.253
29.6.4.2 Constructors [cons.slice]
slice(); slice(size_t start, size_t length, size_t stride);
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 from an array.
— _end example_]
29.6.4.3 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.
29.6.4.4 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();
29.6.5 Class template slice_array [template.slice.array]
29.6.5.1 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 theslice subscript operatorslice_array<T> valarray<T>::operator[](slice);
It has reference semantics to a subset of an array specified by asliceobject.
[Example 1:
The expressiona[slice(1, 5, 3)] = b;has the effect of assigning the elements ofbto a slice of the elements ina.
For the slice shown, the elements selected fromaare .
— _end example_]
29.6.5.2 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 thevalarray<T>object to which theslice_arrayobject refers.
29.6.5.3 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 thevalarray<T>object to which theslice_arrayobject refers.
29.6.5.4 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 thevalarray<T>object to which theslice_arrayobject refers.
29.6.6 The gslice class [class.gslice]
29.6.6.1 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.
Agsliceis 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.
Agslicerepresents 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 thevalarraytemplate, 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 .
[Example 1:
Thegslicespecificationstart = 3length = {2, 4, 3}stride = {19, 4, 1} yields the sequence of one-dimensional indices
which are ordered as shown in the following table:
(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-constversion ofoperator[](const gslice&), the behavior is undefined.
29.6.6.2 Constructors [gslice.cons]
gslice(); gslice(size_t start, const valarray<size_t>& lengths,const valarray<size_t>& strides);
The default constructor is equivalent togslice(0, valarray<size_t>(), valarray<size_t>()).
The constructor with arguments builds agslicebased on a specification of start, lengths, and strides, as explained in the previous subclause.
29.6.6.3 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.
29.6.7 Class template gslice_array [template.gslice.array]
29.6.7.1 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 thegslicesubscript operator
gslice_array<T> valarray<T>::operator[](const gslice&);
It has reference semantics to a subset of an array specified by agsliceobject.
Thus, the expressiona[gslice(1, length, stride)] = bhas the effect of assigning the elements ofbto a generalized slice of the elements ina.
29.6.7.2 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 thevalarray<T>object to which thegslice_arrayrefers.
29.6.7.3 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;
These compound assignments have reference semantics, applying the indicated operation to the elements of the argument array and selected elements of thevalarray<T>object to which thegslice_arrayobject refers.
29.6.7.4 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 thevalarray<T>object to which thegslice_arrayobject refers.
29.6.8 Class template mask_array [template.mask.array]
29.6.8.1 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 ofb to the masked elements in a(those for which the corresponding element inmask is true).
29.6.8.2 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 thevalarray<T>object to which the mask_array object refers.
29.6.8.3 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;
These compound assignments have reference semantics, applying the indicated operation to the elements of the argument array and selected elements of thevalarray<T>object to which the mask_array object refers.
29.6.8.4 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 thevalarray<T>object to which themask_arrayobject refers.
29.6.9 Class template indirect_array [template.indirect.array]
29.6.9.1 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 anindirect_array.
Thus, the expressiona[indirect] = b;has the effect of assigning the elements ofbto the elements inawhose indices appear inindirect.
29.6.9.2 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 thevalarray<T>object to which it refers.
If theindirect_arrayspecifies an element in thevalarray<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_]
29.6.9.3 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;
These compound assignments have reference semantics, applying the indicated operation to the elements of the argument array and selected elements of thevalarray<T>object to which theindirect_arrayobject refers.
If theindirect_arrayspecifies an element in thevalarray<T>object to which it refers more than once, the behavior is undefined.
29.6.9.4 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 thevalarray<T>object to which theindirect_arrayobject refers.
29.6.10 valarray range access [valarray.range]
The iterators returned by begin and end for an array are guaranteed to be valid until the member functionresize(size_t, T) is called for that array or until the lifetime of that array ends, whichever happens first.
template<class T> _unspecified_1 begin(valarray<T>& v);template<class T> _unspecified_2 begin(const valarray<T>& v);
Returns: An iterator referencing the first value in the array.
template<class T> _unspecified_1 end(valarray<T>& v);template<class T> _unspecified_2 end(const valarray<T>& v);
Returns: An iterator referencing one past the last value in the array.