Version:

Last Modified: March 15, 2017

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.

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.

**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.

Error information.

The node produces this output according to standard error behavior.

Standard Error Behavior

**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.

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: