# Linear kernel¶

The linear kernel is the simplest kernel function for pattern analysis.

 Operation Computational methods Programming Interface dense dense compute(…) compute_input compute_result

## Mathematical formulation¶

Refer to Developer Guide: Linear kernel.

## Programming Interface¶

All types and functions in this section are declared in the oneapi::dal::linear_kernel namespace and are available via inclusion of the oneapi/dal/algo/linear_kernel.hpp header file.

### Descriptor¶

template<typename Float = float, typename Method = method::by_default, typename Task = task::by_default>
class descriptor
Template Parameters
• Float – The floating-point type that the algorithm uses for intermediate computations. Can be float or double.

• Method – Tag-type that specifies an implementation of algorithm. Can be method::dense.

• Task – Tag-type that specifies the type of the problem to solve. Can be task::compute.

Constructors

descriptor() = default

Creates a new instance of the class with the default property values.

Properties

double shift

The coefficient $$b$$ of the linear kernel. Default value: 0.0.

Getter & Setter
double get_shift() const
auto & set_shift(double value)
double scale

The coefficient $$k$$ of the linear kernel. Default value: 1.0.

Getter & Setter
double get_scale() const
auto & set_scale(double value)

#### Method tags¶

struct dense
using by_default = dense

Alias tag-type for the dense method.

struct compute

Tag-type that parameterizes entities that are used to compute statistics, distance, and so on.

using by_default = compute

Alias tag-type for the compute task.

### Training compute(...)¶

#### Input¶

class compute_input
Template Parameters

Task – Tag-type that specifies the type of the problem to solve. Can be task::compute.

Constructors

compute_input(const table &x, const table &y)

Creates a new instance of the class with the given x and y.

Properties

const table &x

An $$n \times p$$ table with the data x, where each row stores one feature vector. Default value: table{}.

Getter & Setter
const table & get_x() const
auto & set_x(const table &data)
const table &y

An $$m \times p$$ table with the data y, where each row stores one feature vector. Default value: table{}.

Getter & Setter
const table & get_y() const
auto & set_y(const table &data)

#### Result¶

class compute_result
Template Parameters

Task – Tag-type that specifies the type of the problem to solve. Can be task::compute.

Constructors

compute_result()

Creates a new instance of the class with the default property values.

Properties

const table &values

A $$n \times m$$ table with the result kernel functions. Default value: table{}.

Getter & Setter
const table & get_values() const
auto & set_values(const table &value)

#### Operation¶

template<typename Descriptor>
linear_kernel::compute_result compute(const Descriptor &desc, const linear_kernel::compute_input &input)
Parameters
• desc – Linear Kernel algorithm descriptor linear_kernel::descriptor.

• input – Input data for the computing operation

Preconditions
input.data.is_empty == false