---
name: "mlpack_kernel_LaplacianKernel"
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_LaplacianKernel"
---

# mlpack\_kernel\_LaplacianKernel(3)

The standard Laplacian kernel.

## NAME

mlpack::kernel::LaplacianKernel -

The standard Laplacian kernel.

## SYNOPSIS

### Public Member Functions

**LaplacianKernel** ()\
 *Default constructor; sets bandwidth to 1.0.*  **LaplacianKernel** (double **bandwidth**)\
 *Construct the Laplacian kernel with a custom bandwidth.*  double **Bandwidth** () const \
 *Get the bandwidth.*  double & **Bandwidth** ()\
 *Modify the bandwidth.*  template\<typename VecType \> double **Evaluate** (const VecType &a, const VecType &b) const \
 *Evaluation of the Laplacian kernel.*  double **Evaluate** (const double t) const \
 *Evaluation of the Laplacian kernel given the distance between two points.*  std::string **ToString** () const \
 *Return a string representation of the kernel.*

### Private Attributes

double **bandwidth**\
 *Kernel bandwidth.*

## Detailed Description

The standard Laplacian 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 40 of file laplacian\_kernel.hpp.

## Constructor & Destructor Documentation

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

Default constructor; sets bandwidth to 1.0.

Definition at line 46 of file laplacian\_kernel.hpp.

### mlpack::kernel::LaplacianKernel::LaplacianKernel (doublebandwidth)` [inline]`

Construct the Laplacian kernel with a custom bandwidth.

**Parameters:**

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

Definition at line 54 of file laplacian\_kernel.hpp.

## Member Function Documentation

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

Get the bandwidth.

Definition at line 91 of file laplacian\_kernel.hpp.

References bandwidth.

### double& mlpack::kernel::LaplacianKernel::Bandwidth ()` [inline]`

Modify the bandwidth.

Definition at line 93 of file laplacian\_kernel.hpp.

References bandwidth.

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

Evaluation of the Laplacian 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 70 of file laplacian\_kernel.hpp.

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

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

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

**Parameters:**

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

**Returns:**

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

Definition at line 84 of file laplacian\_kernel.hpp.

References bandwidth.

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

Return a string representation of the kernel.

Definition at line 96 of file laplacian\_kernel.hpp.

References bandwidth.

## Member Data Documentation

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

Kernel bandwidth.

Definition at line 106 of file laplacian\_kernel.hpp.

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

## Author

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