# Matrix Condition Number (G Dataflow)

Computes the condition number of a matrix.

## matrix

A matrix.

This input accepts a 2D array of double-precision, floating point numbers or 2D array of complex double-precision, floating point numbers.

If norm type is 2-norm, this input must be a rectangular matrix. Otherwise, this input must be a square matrix.

## norm type

Type of norm that this node uses for the computation.

Name Value Description
2-norm 0 $‖{A‖}_{2}$ is the largest singular value of the input matrix.
1-norm 1 ${‖A‖}_{1}$ is the largest absolute column sum of the input matrix.
F-norm 2 ${‖A‖}_{f}$ is equal to $\sqrt{\mathrm{\Sigma }\text{diag}\left({A}^{T}A\right)}$ where $\text{diag}\left({A}^{T}A\right)$ means the diagonal elements of matrix $\left({A}^{T}A\right)$ and ${A}^{T}$ is the transpose of $A$.
Inf-norm 3 ${‖A‖}_{\infty }$ is the largest absolute row sum of the input matrix.

Default: 2-norm

## error in

Error conditions that occur before this node runs. The node responds to this input according to standard error behavior.

Default: No error

## condition number

Condition number of the input matrix.

When norm type is 2-norm, this value is the ratio of the largest singular value of the input matrix to the smallest singular value of the input matrix.

## error out

Error information. The node produces this output according to standard error behavior.

## Algorithm for Calculating the Condition Number of a Matrix

The output condition number defines c as the following equation:

$c={‖A‖}_{p}{‖{A}^{-1}‖}_{p}$

where ${‖A‖}_{p}$ is the norm of the input matrix. Different values of p define the different types of norms. Therefore, p defines different types of computations of condition numbers.

For the 2-norm condition number, c is the ratio of the largest, singular value of A to the smallest, singular value of A.

Where This Node Can Run:

Desktop OS: Windows

FPGA: