13.50 <valarray>

The <valarray> header declares types and functions for operating on arrays of numerical values. The intention is to provide types that could be optimized on certain hardware platforms for computationally-intensive programs. The consensus in the C++ user community seems to be that the standard failed to live up to the intentions. Several other numerical libraries, such as Blitz++ and MTL, provide high-performance matrix solutions. (See Appendix B for more information about Blitz++.) Most programs do not need <valarray>.

A valarray is a class template that represents a one-dimensional array of numerical values. The array can grow at runtime. All the arithmetic operators and mathematical functions are overloaded to work with two valarray arguments or with a valarray and a scalar. You can also work with parts of an array: slices, generalized slices, masks, and indirect arrays.

A slice is a set of elements of a valarray, with a starting index, a count, and a stride (an index interval). A generalized slice (gslice) lets the stride count and length vary, which can be used to implement multidimensional arrays. A mask is a valarray of flags, in which the flags indicate whether the corresponding item is part of the masked array. An indirect array is an array of indices. Each of these concepts is explained in this section.

The most important distinguishing feature of valarrays is that they do not allow aliasing, that is, an object cannot be an element of more than one valarray. This enables additional optimizations that are not possible on ordinary arrays.

Because valarray is optimized for performance, no error-checking is performed. Referring to an index out of range or operating on arrays of different size result in undefined behavior—the same as with ordinary arrays. Unlike ordinary arrays, a convenient size( ) member function helps to ensure that you do not make mistakes.

See the <cmath> header for scalar mathematical functions and <numeric> for a few numeric algorithms. See <complex> for complex numbers.

Throughout this section, examples show valarray objects and subsets printed using operator<<, which is shown in Example 13-40.

Example 13-40. Printing a valarray or subset array

// Print a valarray on one line, enclosed by curly braces. For example: 
// "{ 1 2 3 }".
template<typename T>
void print_valarray(std::ostream& out, const std::valarray<T>& a)
{
  out << '{';
  for (size_t i = 0; i < a.size(  ); ++i)
    out << ' ' << a[i];
  out << " }";
}
   
// Print a slice_array, gslice_array, etc. by converting to a valarray.
// Converting a valarray to a valarray is wasteful, but harmless for these simple
// examples.
template<template<typename T> class U, typename T>
std::ostream& operator<<(std::ostream& out, const U<T>& x)
{
  print_valarray(out, static_cast<std::valarray<T> >(x));
  return out;
}

abs function template

Computes absolute value

template<typename T> valarray<T> abs(const valarray<T>& a);

The abs function computes the absolute value of each element of a.

Example

Example 13-41. Generalized slicing of a valarray

// Construct valarray objects from a few integers.
std::valarray<std::size_t> va(std::size_t a0)
{
  std::valarray<std::size_t> result(1);
  result[0] = a0;
  return result;
}
   
std::valarray<std::size_t> va(std::size_t a0, std::size_t a1)
{
  std::valarray<std::size_t> result(2);
  result[0] = a0;
  result[1] = a1;
  return result;
}
   
int main(  )
{
  using namespace std;
  valarray<int> a(24);
  for (size_t i = 0; i < a.size(  ); ++i)
    a[i] = i;
  cout << a << '\n';
// Prints { 0 1 2 3 4 5 6 7 8 9 10 11 ... 20 21 22 23 }
   
  cout << a[slice(1, 4, 3)] << '\n';
// Prints { 1 4 7 10 }
  cout << a[gslice(1, va(4), va(3))] << '\n';
// Prints { 1 4 7 10 }
   
  const valarray<int> const_a(a);
  cout << const_a[gslice(2, va(4, 3), va(2, 3))] << '\n';
// Prints { 2 5 8 4 7 10 6 9 12 8 11 14 }
}

Notice also that the final gslice requires a const valarray. This is because it contains degenerate slices, in which an element (e.g., 8) appears more than once in the result. The aliasing rules of a valarray prohibit multiple references to the same element, so if a const valarray were not used, the results would be undefined. By using a const valarray, the result is a copy of the sliced elements, so the two occurrences of element 8 are separate objects, not aliases for the same object, and disaster is averted.

A generalized slice is most often used to represent a multidimensional array. For example, you can treat a valarray of 24 elements as a 2 x 3 x 4 matrix. To extract a plane of the matrix, you can use a gslice. Figure 13-27 depicts the matrix and the plane. Example 13-42 shows the code.

Figure 13-27. A 3-D matrix stored in a valarray

Example 13-42. Using gslice for multidimensional arrays

// See Example 13-41 for the va function.
int main(  )
{
  using namespace std;
  valarray<int> a(24);
  for (size_t i = 0; i < a.size(  ); ++i)
    a[i] = i;
  cout << a[gslice(1, va(2, 3), va(12, 4))] << '\n';
// Prints: { 1 5 9 13 17 21 }
}

To create an n-dimensional submatrix of an m-dimensional matrix, the size and stride arrays must both have length n. The size array determines the dimensions of the result.

Use the subscript operator to take a generalized slice of a valarray. You can assign a valarray to a generalized slice, in which the righthand side of the assignment must have the same size as the size of the slice. You can also convert the slice to a valarray, which copies only those elements of the slice to the new valarray.

When you take a generalized slice of a valarray, the result is a gslice_array object, but the gslice_array type is mostly transparent to the programmer. See gslice_array later in this section for details.

Example

Example 13-43. Using gslice_array

// See Example 13-41 for the va function.
int main(  )
{
  using namespace std;
  const int data[] = { 1, 2, 3, 4, 5, 6, 7, 8 };
  valarray<int> a(data, sizeof(data)/sizeof(data[0]));
  cout << a << '\n';
// Prints { 1 2 3 4 5 6 7 8 }
   
  cout << a[gslice(1, va(2, 2), va(4, 2))] << '\n'
       << a[gslice(0, va(2, 2), va(4, 2))] << '\n';
// prints:
//  { 2 4 6 8 }
//  { 1 3 5 7 }
   
  // operator+ is not defined for gslice_array, so cast to valarray to perform
  // addition.
  cout << 
    static_cast<valarray<int> >(a[gslice(1, va(2,2), va(4,2))]) +
    static_cast<valarray<int> >(a[gslice(0, va(2,2), va(4,2))])
       << '\n';
// Prints: { 3 7 11 15 }
   
  // Simple assignment does not require casting.
  a[gslice(0, va(2, 2), va(4, 2))] = 0;
  cout << a << '\n';
// Prints: { 0 2 0 4 0 6 0 8 }
   
  // Computational assignment does not require casting.
  valarray<int> ten(10, 4);
  a[gslice(1, va(2, 2), va(4, 2))] *= ten;
  cout << a << '\n';
// Prints: { 0 20 0 40 0 60 0 80 }
}

The members of gslice_array are straightforward. When using any of the assignment operators, the valarray on the righthand side must be the same size as the gslice_array on the lefthand side. You can also assign a scalar to every element of the array. Note that the default constructor, copy constructor, and copy assignment operator are all private. The purpose of this is to restrict the use of gslice_array so it can be used only as a return value from valarray's operator[].

Example

Example 13-44. Using indirect_array

int main(  )
{
  using namespace std;
  const int data[] = { 1, 2, 3, 4, 5, 6, 7, 8 };
  valarray<int> a(data, sizeof(data)/sizeof(data[0]));
  cout << a << '\n';
// Prints: { 1 2 3 4 5 6 7 8 }
   
  // Specify the indices into a.
  const size_t p[] = { 2, 3, 5, 7 };
  valarray<size_t> indices(p, sizeof(p)/sizeof(p[0]));
  cout << a[indices] << '\n';
// Prints: { 3 4 6 8 }
   
  // Add 10 to the elements at the desired indices.
  valarray<int> ten(10, 4);
  a[indices] += ten;
  cout << a << '\n';
// Prints: { 1 2 13 14 5 16 7 18 }
   
  // Must cast to perform ordinary arithmetic.
  cout << static_cast<valarray<int> >(a[indices])
          * ten << '\n';
// Prints: { 130 140 160 180 }
}

The members of indirect_array are straightforward. When using any of the assignment operators, the valarray on the righthand side must be the same size as the indirect_array on the lefthand side. You can also assign a scalar to every element of the array. Note that the default constructor, copy constructor, and copy assignment operator are all private. The purpose of this is to restrict the use of indirect_array so it can be used only as a return value from valarray's operator[].

Example

Example 13-45. Using mask_array

// Simple average
template<typename T>
T avg(const std::valarray<T>& a)
{
  return a.sum(  ) / a.size(  );
}
   
int main(  )
{
  using namespace std;
  const int data[] = { 1, -3, 10, 42, -12, 13, -7, 69 };
  valarray<int> a(data, sizeof(data)/sizeof(data[0]));
  cout << a << '\n';
// Prints: { 1 -3 10 42 -12 13 -7 69 }
   
  // Print the values that are above average.
  cout << "avg=" << avg(a) << '\n';
  cout << a[a > avg(a)] << '\n';
// Prints: { 42 69 }
   
  // Force all negative values to be 0. Notice how no cast is needed for the
  // simple assignment.
  a[a < 0] = 0;
  cout << a << '\n';
// Prints: { 1 0 10 42 0 13 0 69 }
   
  // Other operations, such as multiplication by a scalar, are defined only for
  // valarray, so a cast is needed.
  cout << static_cast<valarray<int> >(a[a > 0]) * -1 << '\n';
// Prints: { -1 -10 -42 -13 -69 }
}

The members of mask_array are straightforward. When using any of the assignment operators, the valarray on the righthand side must be the same size as the mask_array on the lefthand side. You can also assign a scalar to every element of the array. Note that the default constructor, copy constructor, and copy assignment operator are all private. The purpose of this is to restrict the use of mask_array so it can be used only as a return value from valarray's operator[].

The & operator performs bitwise and on each x & y, in which x is a scalar or an element of a, and y is a scalar or an element of b. When operating on two arrays, they must have the same size. The resulting array has the same size as the argument array(s). The type T must be one for which operator & is defined.

operator| function template

Performs bitwise or

template<typename T>
valarray<T> operator|(const valarray<T>& a, const valarray<T>& b);
template<typename T>
valarray<T> operator|(const valarray<T>& a, const T& y);
template<typename T>
valarray<T> operator|(const T& x, const valarray<T>& b);

The | operator performs bitwise inclusive or on each x | y, in which x is a scalar or an element of a, and y is a scalar or an element of b. When operating on two arrays, they must have the same size. The resulting array has the same size as the argument array(s). The type T must be one for which operator | is defined.

operator^ function template

Performs bitwise exclusive or

template<typename T>
valarray<T> operator^(const valarray<T>& a, const valarray<T>& b);
template<typename T>
valarray<T> operator^(const valarray<T>& a, const T& y);
template<typename T>
valarray<T> operator^(const T& x, const valarray<T>& b);

The ^ operator performs bitwise exclusive or on each x ^ y, in which x is a scalar or an element of a, and y is a scalar or an element of b. When operating on two arrays, they must have the same size. The resulting array has the same size as the argument array(s). The type T must be one for which operator ^ is defined.

operator>> function template

Performs right shift

template<typename T>
valarray<T> operator>>(const valarray<T>& a, const valarray<T>& b);
template<typename T>
valarray<T> operator>>(const valarray<T>& a, const T& y);
template<typename T>
valarray<T> operator>>(const T& x, const valarray<T>& b);

The >> operator performs right shift on each x >> y, in which x is a scalar or an element of a, and y is a scalar or an element of b. When operating on two arrays, they must have the same size. The resulting array has the same size as the argument array(s). The type T must be one for which operator >> is defined.

operator<< function template

Performs left shift

template<typename T>
valarray<T> operator<<(const valarray<T>& a, const valarray<T>& b);
template<typename T>
valarray<T> operator<<(const valarray<T>& a, const T& y);
template<typename T>
valarray<T> operator<<(const T& x, const valarray<T>& b);

The << operator performs left shift on each x << y, in which x is a scalar or an element of a, and y is a scalar or an element of b. When operating on two arrays, they must have the same size. The resulting array has the same size as the argument array(s). The type T must be one for which operator << is defined.

operator&& function template

Performs logical and

template<typename T>
valarray<bool> operator&&(const valarray<T>& a, const valarray<T>& b);
template<typename T>
valarray<bool> operator&&(const valarray<T>& a, const T& y);
template<typename T>
valarray<bool> operator&&(const T& x, const valarray<T>& b);

The && operator performs logical and on each x && y, in which x is a scalar or an element of a, and y is a scalar or an element of b. When operating on two arrays, they must have the same size. The resulting array has the same size as the argument array(s). The type T must be one for which operator && is defined. As with any other overloaded operator &&, short-cut evaluation is not supported.

operator|| function template

Performs logical or

template<typename T>
valarray<bool> operator||(const valarray<T>& a, const valarray<T>& b);
template<typename T>
valarray<bool> operator||(const valarray<T>& a, const T& y);
template<typename T>
valarray<bool> operator||(const T& x, const valarray<T>& b);

The || operator performs logical or on each x || y, in which x is a scalar or an element of a, and y is a scalar or an element of b. When operating on two arrays, they must have the same size. The resulting array has the same size as the argument array(s). The type T must be one for which operator || is defined and yields a bool result or a result that can be converted to bool. As with any other overloaded operator ||, short-cut evaluation is not supported.

operator== function template

Compares for equality

template<typename T>
valarray<bool> operator==(const valarray<T>& a, const valarray<T>& b);
template<typename T>
valarray<bool> operator==(const valarray<T>& a, const T& y);
template<typename T>
valarray<bool> operator==(const T& x, const valarray<T>& b);

The == operator compares each x == y, in which x is a scalar or an element of a, and y is a scalar or an element of b. When operating on two arrays, they must have the same size. The resulting array has the same size as the argument array(s). The type T must be one for which operator == is defined and yields a bool result or a result that can be converted to bool.

operator!= function template

Compares for inequality

template<typename T>
valarray<bool> operator!=(const valarray<T>& a, const valarray<T>& b);
template<typename T>
valarray<bool> operator!=(const valarray<T>& a, const T& y);
template<typename T>
valarray<bool> operator!=(const T& x, const valarray<T>& b);

The != operator compares each x != y, in which x is a scalar or an element of a, and y is a scalar or an element of b. When operating on two arrays, they must have the same size. The resulting array has the same size as the argument array(s). The type T must be one for which operator != is defined and yields a bool result or a result that can be converted to bool.

operator< function template

Compares for less-than

template<typename T>
valarray<bool> operator<(const valarray<T>& a, const valarray<T>& b);
template<typename T>
valarray<bool> operator<(const valarray<T>& a, const T& y);
template<typename T>
valarray<bool> operator<(const T& x, const valarray<T>& b);

The < operator compares each x < y, in which x is a scalar or an element of a, and y is a scalar or an element of b. When operating on two arrays, they must have the same size. The resulting array has the same size as the argument array(s). The type T must be one for which operator < is defined and yields a bool result or a result that can be converted to bool.

operator<= function template

Compares for less-than-or-equal

template<typename T>
valarray<bool> operator<=(const valarray<T>& a, const valarray<T>& b);
template<typename T>
valarray<bool> operator<=(const valarray<T>& a, const T& y);
template<typename T>
valarray<bool> operator<=(const T& x, const valarray<T>& b);

The <= operator compares each x <= y, in which x is a scalar or an element of a, and y is a scalar or an element of b. When operating on two arrays, they must have the same size. The resulting array has the same size as the argument array(s). The type T must be one for which operator <= is defined and yields a bool result or a result that can be converted to bool.

operator> function template

Compares for greater-than

template<typename T>
valarray<bool> operator>(const valarray<T>& a, const valarray<T>& b);
template<typename T>
valarray<bool> operator>(const valarray<T>& a, const T& y);
template<typename T>
valarray<bool> operator>(const T& x, const valarray<T>& b);

The > operator compares each x > y, in which x is a scalar or an element of a, and y is a scalar or an element of b. When operating on two arrays, they must have the same size. The resulting array has the same size as the argument array(s). The type T must be one for which operator > is defined and yields a bool result or a result that can be converted to bool.

operator>= function template

Compares for greater-than-or-equal

template<typename T>
valarray<bool> operator>=(const valarray<T>& a, const valarray<T>& b);
template<typename T>
valarray<bool> operator>=(const valarray<T>& a, const T& y);
template<typename T>
valarray<bool> operator>=(const T& x, const valarray<T>& b);

The >= operator compares each x >= y, in which x is a scalar or an element of a, and y is a scalar or an element of b. When operating on two arrays, they must have the same size. The resulting array has the same size as the argument array(s). The type T must be one for which operator >= is defined and yields a bool result or a result that can be converted to bool.

pow function template

Computes power

template<typename T>
valarray<T> pow(const valarray<T>& a, const valarray<T>& b);
template<typename T>
valarray<T> pow(const valarray<T>& a, const T& y);
template<typename T>
valarray<T> pow(const T& x, const valarray<T>& b);

The pow function computes the power xy, in which x is a scalar or an element of a, and y is a scalar or an element of b.

Example

Example 13-46. A simple 2-D matrix class

template<typename T>
class matrix2D {
public:
  matrix2D(std::size_t rows, std::size_t columns) :
    rows_(rows), cols_(columns), data_(rows * columns) {}
  std::size_t rows(  ) const { return rows_; }
  std::size_t cols(  ) const { return cols_; }
  std::valarray<T> row(std::size_t r) const
    { return data_[std::slice(r*cols(  ),cols(  ), 1)]; }
  std::valarray<T> col(std::size_t c) const
    { return data_[std::slice(c, rows(  ), cols(  ))]; }
  std::slice_array<T> row(std::size_t r)
    { return data_[std::slice(r*cols(  ),cols(  ), 1)]; }
  std::slice_array<T> col(std::size_t c)
    { return data_[std::slice(c, rows(  ), cols(  ))]; }
  T& operator(  )(std::size_t r, std::size_t c)
    { return data_[r*cols(  )+c]; }
  T operator(  )(std::size_t r, std::size_t c) const
    { return row(r)[c]; }
  matrix2D<T> transpose(  ) {
    matrix2D<T> result(cols(  ), rows(  ));
    for (std::size_t i = 0; i < rows(  ); ++i)
      result.col(i) = static_cast<std::valarray<T> >(row(i));
    return result;
  }
private:
  std::size_t rows_;
  std::size_t cols_;
  std::valarray<T> data_;
};

Example

Example 13-47. Slicing a valarray

int main(  )
{
  using namespace std;
  const int data[] = { 1,2,3,4,5,6,7,8,9,10,11,12,13 };
  valarray<int> v(data, sizeof(data)/sizeof(data[0]));
  const int newdata[] = { 30, 70, 110 };
  valarray<int> rpl(newdata, 3);
  v[slice(2, 3, 4)] = rpl;
  cout << v << '\n';
// Prints: { 1 2 30 4 5 6 70 8 9 10 110 12 13}
  v[slice(3, 4, 2)] = -1;
  cout << v << '\n';
// Prints: { 1 2 30 -1 5 -1 70 -1 9 -1 110 12 13}
  valarray<int> mult(3, 2);
  v[slice(8, 2, 3)] *= mult;
  cout << v << '\n';
// Prints: { 1 2 30 -1 5 -1 70 -1 27 -1 110 36 13}
  cout << static_cast<valarray<int> >(v[slice(1, 5, 2)])
       << '\n';
// Prints: { 2 -1 -1 -1 -1}
  cout << static_cast<valarray<int> >(v[slice(4, 3, 2)]) +
          static_cast<valarray<int> >(v[slice(2, 3, 2)])
       << '\n';
// Prints: { 35 75 97}
}

The members of slice_array are straightforward. When using any of the assignment operators, the valarray on the righthand side must be the same size as the slice_array on the lefthand side. You can also assign a scalar to every element of the array. Note that the default constructor, copy constructor, and copy assignment operator are all private. The purpose of this is to restrict the use of slice_array so it can be used only as a return value from valarray's operator[].

template<typename T>
class valarray {
public:
  typedef T value_type;
   
  valarray(  );
  explicit valarray(size_t);
  valarray(const T&, size_t);
  valarray(const T*, size_t);
  valarray(const valarray&);
  valarray(const slice_array<T>&);
  valarray(const gslice_array<T>&);
  valarray(const mask_array<T>&);
  valarray(const indirect_array<T>&);
  ~valarray(  );
   
  valarray<T>& operator=(const valarray<T>&);
  valarray<T>& operator=(const T&);
  valarray<T>& operator=(const slice_array<T>&);
  valarray<T>& operator=(const gslice_array<T>&);
  valarray<T>& operator=(const mask_array<T>&);
  valarray<T>& operator=(const indirect_array<T>&);
   
  T operator[](size_t) const;
  T& operator[](size_t);
   
  valarray<T> operator[](slice) const;
  slice_array<T> operator[](slice);
  valarray<T> operator[](const gslice&) const;
  gslice_array<T> operator[](const gslice&);
  valarray<T> operator[](const valarray<bool>&) const;
  mask_array<T> operator[](const valarray<bool>&);
  valarray<T> operator[](const valarray<size_t>&) const;
  indirect_array<T> operator[](const valarray<size_t>&);
   
  valarray<T> operator+(  ) const;
  valarray<T> operator-(  ) const;
  valarray<T> operator~(  ) const;
  valarray<bool> operator!(  ) const;
   
  valarray<T>& operator*= (const T&);
  valarray<T>& operator/= (const T&);
  valarray<T>& operator%= (const T&);
  valarray<T>& operator+= (const T&);
  valarray<T>& operator-= (const T&);
  valarray<T>& operator^= (const T&);
  valarray<T>& operator&= (const T&);
  valarray<T>& operator|= (const T&);
  valarray<T>& operator<<=(const T&);
  valarray<T>& operator>>=(const T&);
  valarray<T>& operator*= (const valarray<T>&);
  valarray<T>& operator/= (const valarray<T>&);
  valarray<T>& operator%= (const valarray<T>&);
  valarray<T>& operator+= (const valarray<T>&);
  valarray<T>& operator-= (const valarray<T>&);
  valarray<T>& operator^= (const valarray<T>&);
  valarray<T>& operator|= (const valarray<T>&);
  valarray<T>& operator&= (const valarray<T>&);
  valarray<T>& operator<<=(const valarray<T>&);
  valarray<T>& operator>>=(const valarray<T>&);
   
  size_t size(  ) const;
  T sum(  ) const;
  T min(  ) const;
  T max(  ) const;
  valarray<T> shift (int) const;
  valarray<T> cshift(int) const;
  valarray<T> apply(T func(T)) const;
  valarray<T> apply(T func(const T&)) const;
  void resize(size_t sz, T c = T(  ));
};

The valarray class template represents an array of numeric values, with restrictions that permit an implementation to optimize performance. In particular, an object cannot be an element of more than one array. A subset, such as a generalized slice or indirect array, cannot specify a single element more than once, or else the behavior is undefined.

You can instantiate valarray with any numerical type as its template parameter if you limit yourself to using only operations that are defined for that type. For example, you cannot use operator<< on valarray<double> because you cannot use operator<< on scalars of type double.

Examples of using valarray can be found throughout this section.

The following are the members of valarray:

valarray( )

Constructs an empty valarray.

explicit valarray(size_t n)

Constructs a valarray of length n, in which all elements are initialized to T( ).

valarray(const T& x, size_t n)

Construct a valarray that contains n copies of x.

valarray(const T* x, size_t n)

Constructs a valarray by copying n elements from the array x.

valarray(const valarray& a)

Constructs a valarray by copying a.

valarray(const slice_array<T>& a)

valarray(const gslice_array<T>& a)

valarray(const mask_array<T>& a)

valarray(const indirect_array<T>& a)

Constructs a valarray by copying the elements referenced by a.

valarray<T> apply(T func(T)) const

valarray<T> apply(T func(const T&)) const

Returns a new array whose contents are the result of calling func for each element of the original array.

valarray<T> cshift(int n) const

Performs a circular shift (rotation) by n places. The return value is a new array that has the same size as the original, but the element at new index i comes from (i + n) % size( ) in the original.

T max( ) const

Returns the largest element of the array or an undefined value if the array is empty. Elements are compared using operator<.

T min( ) const

Returns the smallest element of the array or an undefined value if the array is empty. Elements are compared using operator<.

valarray<T>& operator=(const valarray<T>& a)

Each element of this array is assigned the corresponding elements of a. If size( ) != a.size( ), the behavior is undefined.

valarray<T>& operator=(const T& x)

Each element of this array is assigned the scalar value x.

valarray<T>& operator=(const slice_array<T>& a)

valarray<T>& operator=(const gslice_array<T>& a)

valarray<T>& operator=(const mask_array<T>& a)

valarray<T>& operator=(const indirect_array<T>& a)

Each element of this array is assigned the corresponding element from the subset array a. The value being assigned to an element must not depend on any other value in this array, that is, a cannot be a subset of *this, or, if it is, the element assigned to index i must depend only on index i and not on values at any other index.

T operator[](size_t i) const

T& operator[](size_t i)

Returns the element at index i. The behavior is undefined for i >= size( ). The anti-aliasing rule means that for any two distinct valarray objects a and b, and for all valid indices i and j, you can safely assume that the following is true: &a[i] != &b[j]. All values in a single valarray object are stored contiguously, just as in an ordinary array. References become invalid after a call to resize.

valarray<T> operator[](slice) const

slice_array<T> operator[](slice)

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

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

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

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

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

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

Returns a subset of this valarray. A subset of a const valarray is a new valarray. A subset of a non-const valarray is a helper object that maintains a reference to the original valarray. (See the descriptions of the helper classes earlier in this section for details.) Briefly, the four kinds of subsets are:

A slice object specifies a simple slice, suitable for extracting a row or column of a 2-D array.
A gslice is a generalized slice, which permits multidimensional matrices.
A mask_array is created by specifying an array of bool as the argument. If an element is true, that element is part of the resulting subset.
An indirect_array is created by specifying an array of size_t indices as the argument. Each element specifies an index, and the element at that index is added to the resulting array.

valarray<T> operator+( ) const

valarray<T> operator-( ) const

valarray<T> operator~( ) const

valarray<bool> operator!( ) const

Returns a new valarray in which each new element is the result of applying the unary operator to the corresponding element in the original array.

valarray<T>& operator*= (const T& x)

valarray<T>& operator/= (const T& x)

valarray<T>& operator%= (const T& x)

valarray<T>& operator+= (const T& x)

valarray<T>& operator-= (const T& x)

valarray<T>& operator^= (const T& x)

valarray<T>& operator&= (const T& x)

valarray<T>& operator|= (const T& x)

valarray<T>& operator<<=(const T& x)

valarray<T>& operator>>=(const T& x)

Modifies this valarray by applying the assignment operator to each element of the array. The return value is *this.

valarray<T>& operator*= (const valarray<T>& a)

valarray<T>& operator/= (const valarray<T>& a)

valarray<T>& operator%= (const valarray<T>& a)

valarray<T>& operator+= (const valarray<T>& a)

valarray<T>& operator-= (const valarray<T>& a)

valarray<T>& operator^= (const valarray<T>& a)

valarray<T>& operator|= (const valarray<T>& a)

valarray<T>& operator&= (const valarray<T>& a)

valarray<T>& operator<<=(const valarray<T>& a)

valarray<T>& operator>>=(const valarray<T>& a)

Modifies this valarray by applying the assignment operator to each element of the array and to the corresponding element of a. The behavior is undefined if size( ) != a.size( ). The return value is *this.

void resize(size_t sz, T x = T( ))

Changes the size of the array to sz and reinitializes every element of the array to x.

valarray<T> shift (int n) const

Performs a shift by n places. The return value is a new array with the same size as the original array, but the element at index i in the new array comes from index i + n in the original array. If i + n < 0 or size( ), the new element is set to T( ).

size_t size( ) const

Returns the number of elements in the array.

T sum( ) const

Returns the sum of all the elements in the array using operator+=. If the array is empty, the value is undefined.

13.50 <valarray>

Example 13-40. Printing a valarray or subset array

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Example 13-41. Generalized slicing of a valarray

Figure 13-27. A 3-D matrix stored in a valarray

Example 13-42. Using gslice for multidimensional arrays

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Example 13-43. Using gslice_array

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Example 13-44. Using indirect_array

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Example 13-45. Using mask_array

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Figure 13-28. Slicing a valarray

Example

Example 13-46. A simple 2-D matrix class

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Example 13-47. Slicing a valarray

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