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Matrix Condition Number (G Dataflow)

Last Modified: December 4, 2016

Computes the condition number of a matrix.

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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.

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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 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 is the largest absolute row sum of the input matrix.

Default: 2-norm

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error in

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

Default: No error

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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.

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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:


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