Quadratic Form

# Summary

• Plugin name : Quadratic Form
• Version : 0.1
• Author : Fabien Lotte
• Company : IRISA-INSA Rennes
• Short description : Perform a quadratic matrix operation on the input signals m (result = m^T * A * m)
• Documentation template generation date : Dec 30 2016

# Description

a square matrix A (which can be seen as a spatial filter) is applied to the input signals m (a vector). Then the transpose m^T of the input signals is multiplied to the resulting vector. In other words the output o is such as: o = m^T * A * m.

a square matrix A (which can be seen as a spatial filter) is applied to the input signals m (a vector). Then the transpose m^T of the input signals is multiplied to the resulting vector. In other words the output o is such as: o = m^T * A * m.

# Inputs

## 1. input signal

The input signal to be used in the computation of the quadratic form

• Type identifier : Signal (0x5ba36127, 0x195feae1)

# Outputs

## 1. output signal

the results of the computation of the quadratic form, perform with the input signals and the matrix defined in the settings

• Type identifier : Signal (0x5ba36127, 0x195feae1)

# Settings

## 1. Matrix values

The values of the matrix coefficients. These values are entered as a single line of values, which line should correspond to the concatenation of each matrix row. For instance the setting "1 2 3 4" corresponds to the matrix:

[1 2] [3 4]

• Type identifier : String (0x79a9edeb, 0x245d83fc)
• Default value : [ 1 0 0 1 ]

## 2. Number of rows/columns (square matrix)

The number of rows/columns of the matrix (the number of rows is equal to the number of columns as the matrix is square. For the matrix given as example above, this setting should be equal to "2".

• Type identifier : Integer (0x007deef9, 0x2f3e95c6)
• Default value : [ 2 ]

# Miscellaneous

this box could typically be used to compute the current density in a given brain region, for instance using the inverse solution sLORETA. In such a case the matrix using as parameter should be a matrix obtained thanks to this sLORETA inverse solution. see the following paper for details:

Congedo M. (2006), Subspace Projection Filters for Real-Time Brain Electromagnetic Imaging, IEEE Transactions on Biomedical Engineering, 53(8), 1624-34