---
name: "mlpack_kernel_GaussianKernel"
section: "3"
platform: "linux"
package: "mlpack-doc"
version: "1.0.10-1"
release: "Debian 8 (Jessie)"
platforms: ["linux"]
url: "https://new.carta.tech/mlpack_kernel_GaussianKernel"
---

# mlpack\_kernel\_GaussianKernel(3)

The standard Gaussian kernel.

## NAME

mlpack::kernel::GaussianKernel -

The standard Gaussian kernel.

## SYNOPSIS

### Public Member Functions

**GaussianKernel** ()\
 *Default constructor; sets bandwidth to 1.0.*  **GaussianKernel** (const double **bandwidth**)\
 *Construct the Gaussian kernel with a custom bandwidth.*  double **Bandwidth** () const \
 *Get the bandwidth.*  void **Bandwidth** (const double **bandwidth**)\
 *Modify the bandwidth.*  template\<typename VecType \> double **ConvolutionIntegral** (const VecType &a, const VecType &b)\
 *Obtain a convolution integral of the Gaussian kernel.*  template\<typename VecType \> double **Evaluate** (const VecType &a, const VecType &b) const \
 *Evaluation of the Gaussian kernel.*  double **Evaluate** (const double t) const \
 *Evaluation of the Gaussian kernel given the distance between two points.*  double **Gamma** () const \
 *Get the precalculated constant.*  double **Normalizer** (const size\_t dimension)\
 *Obtain the normalization constant of the Gaussian kernel.*  std::string **ToString** () const \
 *Convert object to string.*

### Private Attributes

double **bandwidth**\
 *Kernel bandwidth.*  double **gamma**\
 *Precalculated constant depending on the bandwidth; $ mma = -*ac{1}{2 ^2} $.

## Detailed Description

The standard Gaussian kernel.

Given two vectors $ x $, $ y $, and a bandwidth $  $ (set in the constructor),

.PP The implementation is all in the header file because it is so simple.

Definition at line 43 of file gaussian\_kernel.hpp.

## Constructor & Destructor Documentation

### mlpack::kernel::GaussianKernel::GaussianKernel ()` [inline]`

Default constructor; sets bandwidth to 1.0.

Definition at line 49 of file gaussian\_kernel.hpp.

### mlpack::kernel::GaussianKernel::GaussianKernel (const doublebandwidth)` [inline]`

Construct the Gaussian kernel with a custom bandwidth.

**Parameters:**

*bandwidth* The bandwidth of the kernel ( $$).

Definition at line 57 of file gaussian\_kernel.hpp.

## Member Function Documentation

### double mlpack::kernel::GaussianKernel::Bandwidth () const` [inline]`

Get the bandwidth.

Definition at line 120 of file gaussian\_kernel.hpp.

References bandwidth.

### void mlpack::kernel::GaussianKernel::Bandwidth (const doublebandwidth)` [inline]`

Modify the bandwidth. This takes an argument because we must update the precalculated constant (gamma).

Definition at line 124 of file gaussian\_kernel.hpp.

References bandwidth, and gamma.

### template\<typename VecType \> double mlpack::kernel::GaussianKernel::ConvolutionIntegral (const VecType &a, const VecType &b)` [inline]`

Obtain a convolution integral of the Gaussian kernel.

**Parameters:**

*a,first* vector \
 *b,second* vector

**Returns:**

the convolution integral

Definition at line 112 of file gaussian\_kernel.hpp.

References Evaluate(), mlpack::metric::LMetric\< Power, TakeRoot \>::Evaluate(), and Normalizer().

### template\<typename VecType \> double mlpack::kernel::GaussianKernel::Evaluate (const VecType &a, const VecType &b) const` [inline]`

Evaluation of the Gaussian kernel. This could be generalized to use any distance metric, not the Euclidean distance, but for now, the Euclidean distance is used.

**Template Parameters:**

*VecType* Type of vector (likely arma::vec or arma::spvec).

**Parameters:**

*a* First vector. \
 *b* Second vector.

**Returns:**

K(a, b) using the bandwidth ( $$) specified in the constructor.

Definition at line 74 of file gaussian\_kernel.hpp.

References mlpack::metric::LMetric\< Power, TakeRoot \>::Evaluate(), and gamma.

Referenced by ConvolutionIntegral().

### double mlpack::kernel::GaussianKernel::Evaluate (const doublet) const` [inline]`

Evaluation of the Gaussian kernel given the distance between two points.

**Parameters:**

*t* The distance between the two points the kernel is evaluated on.

**Returns:**

K(t) using the bandwidth ( $$) specified in the constructor.

Definition at line 87 of file gaussian\_kernel.hpp.

References gamma.

### double mlpack::kernel::GaussianKernel::Gamma () const` [inline]`

Get the precalculated constant.

Definition at line 131 of file gaussian\_kernel.hpp.

References gamma.

### double mlpack::kernel::GaussianKernel::Normalizer (const size\_tdimension)` [inline]`

Obtain the normalization constant of the Gaussian kernel.

**Parameters:**

*dimension*

**Returns:**

the normalization constant

Definition at line 99 of file gaussian\_kernel.hpp.

References bandwidth, and M\_PI.

Referenced by ConvolutionIntegral().

### std::string mlpack::kernel::GaussianKernel::ToString () const` [inline]`

Convert object to string.

Definition at line 134 of file gaussian\_kernel.hpp.

References bandwidth.

## Member Data Documentation

### double mlpack::kernel::GaussianKernel::bandwidth` [private]`

Kernel bandwidth.

Definition at line 144 of file gaussian\_kernel.hpp.

Referenced by Bandwidth(), Normalizer(), and ToString().

### double mlpack::kernel::GaussianKernel::gamma` [private]`

Precalculated constant depending on the bandwidth; $ mma = -ac{1}{2 ^2} $.

Definition at line 148 of file gaussian\_kernel.hpp.

Referenced by Bandwidth(), Evaluate(), and Gamma().

## Author

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