is.NSD {CEGO} | R Documentation |

## Check for Negative Semi-Definiteness

### Description

This function checks whether a symmetric matrix is Negative Semi-Definite (NSD). That means, it is determined whether all eigenvalues of the matrix are non-positive. Note that this function does not check whether the matrix is actually symmetric.

### Usage

```
is.NSD(X, tol = 1e-08)
```

### Arguments

`X` |
a symmetric matrix |

`tol` |
torelance value. Eigenvalues between Symmetric, NSD matrices are, e.g., correlation or kernel matrices. Such matrices are used in models like Kriging or Support Vector regression. |

### Value

boolean, which is TRUE if X is NSD

### See Also

### Examples

```
# The following permutations will produce
# a non-PSD kernel matrix with Insert distance
# and a PSD distance matrix with Hamming distance
# (for the given theta value of 0.01)-
# The respective negative should be (non-) NSD
x <- list(c(2,1,4,3),c(2,4,3,1),c(4,2,1,3),c(4,3,2,1),c(1,4,3,2))
K <- exp(-0.01*distanceMatrix(x,distancePermutationInsert))
is.NSD(-K)
K <- exp(-0.01*distanceMatrix(x,distancePermutationHamming))
is.NSD(-K)
```

[Package

*CEGO*version 2.4.3 Index]