Matrix Condition Number (G Dataflow)

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Last Modified: March 15, 2017

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 $\sqrt{Σ diag (A^{T} A)}$ where $diag (A^{T} A)$ means the diagonal elements of matrix $(A^{T} A)$ 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.

Standard Error Behavior

Many nodes provide an error in input and an error out output so that the node can respond to and communicate errors that occur while code is running. The value of error in specifies whether an error occurred before the node runs. Most nodes respond to values of error in in a standard, predictable way.

error in does not contain an error	error in contains an error

If no error occurred before the node runs, the node begins execution normally. If no error occurs while the node runs, it returns no error. If an error does occur while the node runs, it returns that error information as error out.	If an error occurred before the node runs, the node does not execute. Instead, it returns the error in value as error out.

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.

Standard Error Behavior

error in does not contain an error	error in contains an error

If no error occurred before the node runs, the node begins execution normally. If no error occurs while the node runs, it returns no error. If an error does occur while the node runs, it returns that error information as error out.	If an error occurred before the node runs, the node does not execute. Instead, it returns the error in value as error out.

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:

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