Last Modified: December 4, 2016

Computes the condition number of a 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.

Type of norm that this node uses for the computation.

Name | Value | Description |
---|---|---|

2-norm | 0 | $\Vert {A\Vert}_{2}$ is the largest singular value of the input matrix. |

1-norm | 1 | ${\Vert A\Vert}_{1}$ is the largest absolute column sum of the input matrix. |

F-norm | 2 | ${\Vert A\Vert}_{f}$ is equal to $\sqrt{{\displaystyle \mathrm{\Sigma}}\text{diag}\left({A}^{T}A\right)}$ 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 | ${\Vert A\Vert}_{\infty}$ is the largest absolute row sum of the input matrix. |

**Default: **2-norm

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

**Default: **No error

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.

The output **condition number** defines *c* as the following equation:

$c={\Vert A\Vert}_{p}{\Vert {A}^{-1}\Vert}_{p}$

where
${\Vert A\Vert}_{p}$ 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: