4.3. Reduction Functions

4.3. Reduction Functions
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4.3.1. `alltrue`

Syntax:

    template <typename                      T,
              template <typename, typename> class ViewT,
              typename                      BlockT>
    T
    alltrue(ViewT<T, BlockT> v);

Template parameters

T: is the type of the elements in the view and of the return value.
ViewT: is the type of the parameter v. It must be const_Vector, const_Matrix or const_Tensor.

Description: When T is bool, the function returns true if all elements are true, otherwise false. When T is another type, alltrue returns the application of accumulation operator band with base value ˜(T()) applied to v.

Requirements: The template parameter ViewT must be const_Vector, const_Matrix or const_Tensor.

Result: alltrue returns a scalar value of type T.

Example:

Vector<bool> bvec(4, true);

std::cout << alltrue(bvec) << std::endl; // prints 1

Vector<int> vec(3); 

vec(0) = 0x00ff; 
vec(1) = 0x119f; 
vec(2) = 0x92f7; 

std::cout << alltrue(vec) == 0x0097 << std::endl; // prints 1

See Also: band (section 4.2.8)

4.3.2. `anytrue`

Syntax:

    template <typename                      T,
              template <typename, typename> class ViewT,
              typename                      BlockT>
    T
    anytrue(ViewT<T, BlockT> v);

Template parameters

T: is the type of the elements in the view and of the return value.
ViewT: is the type of the parameter v.

Description: When T is bool, the function returns true if at least one element is true, otherwise false. When T is another type, anytrue returns the application of accumulation operator bor with base value T() applied to v.

Requirements: The template parameter ViewT must be const_Vector, const_Matrix or const_Tensor.

Result: anytrue returns a scalar value of type T.

Example:

Vector<bool> bvec(4, true);

std::cout << anytrue(bvec) << std::endl; // prints 1

Vector<int> vec(3); 

vec(0) = 0x00ff; 
vec(1) = 0x119f; 
vec(2) = 0x92f7; 

std::cout << anytrue(vec) == 0x93ff << std::endl; // prints 1

See Also: bor (section 4.2.9)

4.3.3. `maxmgsqval`

Syntax:

    template <typename                      T,
              template <typename, typename> class ViewT,
              typename                      BlockT>
    T
    maxmgsqval(
        ViewT<complex<T>, BlockT>         v,
        Index<ViewT<complex<T>, BlockT>::dim>& idx);

Template parameters

T: is the type of the elements in the view and of the return value.
ViewT: is the type of the parameter v. It must be const_Vector, const_Matrix or const_Tensor.

Description: maxmgsqval computes the maximum squared magnitude of all the elements of the view and returns that value. It also returns, through the parameter idx, the indices to locate that value in the view.

Requirements: The template parameter ViewT must be const_Vector, const_Matrix or const_Tensor. The function parameters v and idx are defined in terms of complex<T>.

Result: maxmgsqval returns a scalar value of type T.

Example:

   length_type         size = 13; 
   typedef float T;
   Vector<complex<T> > vec(size, complex<T>(3, 4));
   Index<1>            idx;
   T                   val;

   vec(1) = complex<T>(6, 8); 
   vec(2) = complex<T>(0.3, 0.4);

   val = maxmgsqval(vec, idx);
   cout << val << endl;  // prints 100
   cout << idx << endl;  // prints 1

4.3.4. `maxmgval`

Syntax:

    template <typename                      T,
              template <typename, typename> class ViewT,
              typename                      BlockT>
    T
    maxmgval(
        ViewT<T, BlockT>         v,
        Index<ViewT<T, BlockT>::dim>& idx);

Template parameters

T: is the type of the elements in the view and of the return value.
ViewT: is the type of the parameter v. It must be const_Vector, const_Matrix or const_Tensor.

Description: maxmgval computes the maximum magnitude of all the elements of the view and returns that value. It also returns, through the parameter idx, the indices to locate that value in the view.

Requirements: The template parameter ViewT must be const_Vector, const_Matrix or const_Tensor.

Result: When T is complex<W>, maxmgval returns a scalar value of type W; otherwise it returns a value of type T.

Example:

   length_type         size = 13; 
   typedef float T;
   Vector<complex<T> > vec(size, complex<T>(3, 4));
   Index<1>            idx;
   T                   val;

   vec(1) = complex<T>(6, 8); 
   vec(2) = complex<T>(0.3, 0.4);

   val = maxmgval(vec, idx);
   cout << val << endl;  // prints 10
   cout << idx << endl;  // prints 1

4.3.5. `maxval`

Syntax:

    template <typename                      T,
              template <typename, typename> class ViewT,
              typename                      BlockT>
    T
    maxval(
        ViewT<T, BlockT>         v,
        Index<ViewT<T, BlockT>::dim>& idx);

Template parameters

T: is the type of the elements in the view and of the return value.
ViewT: is the type of the parameter v. It must be const_Vector, const_Matrix or const_Tensor.

Description: maxval computes the maximum of all the elements of the view and returns that value. It also returns, through the parameter idx, the indices to locate that value in the view.

Requirements: The template parameter ViewT must be const_Vector, const_Matrix or const_Tensor.

Result: maxval returns a scalar value of type T.

Example:

Vector<float> vec(4); 

vec(0) = 0.;
vec(1) = 1.;
vec(2) = 3.;
vec(3) = 2.;

Index<1>  idx;
float val = maxval(vec,idx);
std::cout << val << std::endl;  // prints 3.0
std::cout << idx << std::endl;  // prints 2

4.3.6. `meansqval`

Syntax:

    template <typename                      T,
              template <typename, typename> class ViewT,
              typename                      BlockT>
    T
    meansqval(ViewT<T, BlockT> v);

Template parameters

T: is the type of the elements in the view and of the return value.
ViewT: is the type of the parameter v. It must be const_Vector, const_Matrix or const_Tensor.

Description: meansqval sums the squares of all the elements of the view and returns that value divided by the number of elements.

Requirements: The template parameter ViewT must be const_Vector, const_Matrix or const_Tensor.

Result: meansqval returns a scalar value of type T.

Example:

Vector<float> vec(4); 

vec(0) = 0.;
vec(1) = 1.;
vec(2) = 2.;
vec(3) = 3.;

std::cout << meansqval(vec) << std::endl;  // prints 3.5

See Also: add (section 4.2.2)

4.3.7. `meanval`

Syntax:

    template <typename                      T,
              template <typename, typename> class ViewT,
              typename                      BlockT>
    T
    meanval(ViewT<T, BlockT> v);

Template parameters

T: is the type of the elements in the view and of the return value.
ViewT: is the type of the parameter v. It must be const_Vector, const_Matrix or const_Tensor.

Description: meanval sums all the elements of the view and returns that value divided by the number of elements.

Requirements: The template parameter ViewT must be const_Vector, const_Matrix or const_Tensor.

Result: meanval returns a scalar value of type T.

Example:

Vector<float> vec(4); 

vec(0) = 0.;
vec(1) = 1.;
vec(2) = 2.;
vec(3) = 3.;

std::cout << meanval(vec) << std::endl;  // prints 1.5

See Also: add (section 4.2.2)

4.3.8. `minmgsqval`

Syntax:

    template <typename                      T,
              template <typename, typename> class ViewT,
              typename                      BlockT>
    T
    minmgsqval(
        ViewT<complex<T>, BlockT>         v,
        Index<ViewT<complex<T>, BlockT>::dim>& idx);

Template parameters

T: is the type of the elements in the view and of the return value.
ViewT: is the type of the parameter v. It must be const_Vector, const_Matrix or const_Tensor.

Description: minmgsqval computes the minimum squared magnitude of all the elements of the view and returns that value. It also returns, through the parameter idx, the indices to locate that value in the view.

Requirements: The template parameter ViewT must be const_Vector, const_Matrix or const_Tensor. The function parameters v and idx are defined in terms of complex<T>.

Result: minmgsqval returns a scalar value of type T.

Example:

   length_type         size = 13; 
   typedef float T;
   Vector<complex<T> > vec(size, complex<T>(3, 4));
   Index<1>            idx;
   T                   val;

   vec(1) = complex<T>(6, 8); 
   vec(2) = complex<T>(0.3, 0.4);

   val = minmgsqval(vec, idx);
   cout << val << endl;  // prints 0.25
   cout << idx << endl;  // prints 2

4.3.9. `minmgval`

Syntax:

    template <typename                      T,
              template <typename, typename> class ViewT,
              typename                      BlockT>
    T
    minmgval(
        ViewT<T, BlockT>         v,
        Index<ViewT<T, BlockT>::dim>& idx);

Template parameters

T: is the type of the elements in the view and of the return value.
ViewT: is the type of the parameter v. It must be const_Vector, const_Matrix or const_Tensor.

Description: minmgval computes the minimum magnitude of all the elements of the view and returns that value. It also returns, through the parameter idx, the indices to locate that value in the view.

Requirements: The template parameter ViewT must be const_Vector, const_Matrix or const_Tensor.

Result: When T is complex<W>, minmgval returns a scalar value of type W; otherwise it returns a value of type T.

Example:

   length_type         size = 13; 
   typedef float T;
   Vector<complex<T> > vec(size, complex<T>(3, 4));
   Index<1>            idx;
   T                   val;

   vec(1) = complex<T>(6, 8); 
   vec(2) = complex<T>(0.3, 0.4);

   val = minmgval(vec, idx);
   cout << val << endl;  // prints 0.5
   cout << idx << endl;  // prints 2

4.3.10. `minval`

Syntax:

    template <typename                      T,
              template <typename, typename> class ViewT,
              typename                      BlockT>
    T
    minval(
        ViewT<T, BlockT>         v,
        Index<ViewT<T, BlockT>::dim>& idx);

Template parameters

T: is the type of the elements in the view and of the return value.
ViewT: is the type of the parameter v. It must be const_Vector, const_Matrix or const_Tensor.

Description: minval computes the minimum of all the elements of the view and returns that value. It also returns, through the parameter idx, the indices to locate that value in the view.

Requirements: The template parameter ViewT must be const_Vector, const_Matrix or const_Tensor.

Result: minval returns a scalar value of type T.

Example:

Vector<float> vec(4); 

vec(0) = 3.;
vec(1) = 1.;
vec(2) = 0.;
vec(3) = 2.;

Index<1>  idx;
float val = minval(vec,idx);
std::cout << val << std::endl;  // prints 0.0
std::cout << idx << std::endl;  // prints 2

4.3.11. `sumsqval`

Syntax:

    template <typename                      T,
              template <typename, typename> class ViewT,
              typename                      BlockT>
    T
    sumsqval(ViewT<T, BlockT> v);

Template parameters

T: is the type of the elements in the view and of the return value.
ViewT: is the type of the parameter v. It must be const_Vector, const_Matrix or const_Tensor.

Description: sumsqval sums the squares of all the elements of the view and returns that value.

Requirements: The template parameter ViewT must be const_Vector, const_Matrix or const_Tensor.

Result: sumsqval returns a scalar value of type T.

Example:

Vector<float> vec(4); 

vec(0) = 0.;
vec(1) = 1.;
vec(2) = 2.;
vec(3) = 3.;

std::cout << sumsqval(vec) << std::endl;  // prints 14.0

See Also: add (section 4.2.2)

4.3.12. `sumval`

Syntax:

    template <typename                      T,
              template <typename, typename> class ViewT,
              typename                      BlockT>
    T
    sumval(ViewT<T, BlockT> v);

Template parameters

T: is the type of the elements in the view and of the return value.
ViewT: is the type of the parameter v. It must be const_Vector, const_Matrix or const_Tensor.

Description: sumval sums all the elements of the view and returns that value.

Requirements: The template parameter ViewT must be const_Vector, const_Matrix or const_Tensor.

Result: sumval returns a scalar value of type T.

Example:

Vector<float> vec(4); 

vec(0) = 0.;
vec(1) = 1.;
vec(2) = 2.;
vec(3) = 3.;

std::cout << sumval(vec) << std::endl;  // prints 6.0

See Also: add (section 4.2.2)

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