# SavitzkyGolayMatrix

SavitzkyGolayMatrix[r,k]

gives a matrix corresponding to a smoothing kernel of radius r for performing polynomial regression of degree k.

SavitzkyGolayMatrix[{r1,r2},{k1,k2}]

gives a matrix for performing polynomial regression of degree k1 over a window of radius r1 along rows, and degree k2 over a window of radius r2 along columns.

SavitzkyGolayMatrix[r,k,n]

gives a matrix for performing the n derivative of a polynomial regression of degree k.

SavitzkyGolayMatrix[{r1,r2 },{k1,k2,},]

gives an array using the specified parameters for each direction i.

# Details and Options

• SavitzkyGolayMatrix[r,k] can be used to smooth data using a local polynomial regression.
• SavitzkyGolayMatrix[r,k,n] can be used to compute the derivatives of data using a local polynomial regression.
• The elements of SavitzkyGolayMatrix[r,k] sum to 1.
• SavitzkyGolayMatrix allows any of r, k, and n to be lists, specifying different values for different directions.
• For integer r, SavitzkyGolayMatrix[r,] yields a × matrix.
• For noninteger r, the value of r is effectively rounded to an integer.
• SavitzkyGolayMatrix accepts a WorkingPrecision option. The default setting is .
• SavitzkyGolayMatrix can be used in functions such as ListConvolve and ImageConvolve.

# Examples

open allclose all

## Basic Examples(3)

Compute a matrix kernel for quadratic interpolation over a window of radius 5:

Compute a smoothing kernel of length 11 using a cubic interpolation:

Plot the vector:

A SavitzkyGolay matrix to compute first derivatives in the horizontal dimension:

## Scope(3)

Create a 3D smoothing kernel:

A 3D derivative kernel:

A 3D derivative kernel along the first dimension:

## Options(1)

### WorkingPrecision(1)

By default, machine precision is used in internal computations:

Use exact precision:

## Applications(2)

Use a 2D SavitzkyGolayMatrix as a smoothing kernel in ImageConvolve:

Compute the horizontal derivative of an image:

## Properties & Relations(1)

The order of the polynomial does not extend beyond twice the window size:

Wolfram Research (2014), SavitzkyGolayMatrix, Wolfram Language function, https://reference.wolfram.com/language/ref/SavitzkyGolayMatrix.html.

#### Text

Wolfram Research (2014), SavitzkyGolayMatrix, Wolfram Language function, https://reference.wolfram.com/language/ref/SavitzkyGolayMatrix.html.

#### CMS

Wolfram Language. 2014. "SavitzkyGolayMatrix." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/SavitzkyGolayMatrix.html.

#### APA

Wolfram Language. (2014). SavitzkyGolayMatrix. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/SavitzkyGolayMatrix.html

#### BibTeX

@misc{reference.wolfram_2024_savitzkygolaymatrix, author="Wolfram Research", title="{SavitzkyGolayMatrix}", year="2014", howpublished="\url{https://reference.wolfram.com/language/ref/SavitzkyGolayMatrix.html}", note=[Accessed: 21-July-2024 ]}

#### BibLaTeX

@online{reference.wolfram_2024_savitzkygolaymatrix, organization={Wolfram Research}, title={SavitzkyGolayMatrix}, year={2014}, url={https://reference.wolfram.com/language/ref/SavitzkyGolayMatrix.html}, note=[Accessed: 21-July-2024 ]}