## crqad

Computes and plots the diagonalwise CRQA measures.

### Syntax

```
crqad(x)
crqad(x,y)
y=crqad(x,y,m,t,e,w)
y=crqad(x,y,m,t,e,w,lmin)
y=crqad(x,y,m,t,e,[],'param1','param2',...)
```

### Description

Recurrence quantification analysis of diagonals in the
cross recurrence plot of the vectors `x` and `y` as well as
`x` and `-y` for the diagonals within
the range `[-w,w]` around the main diagonal.
The output is a structure (see below).

The input vectors can be multi-column vectors, where each column will be used as a component of the phase-space vector. However, if the first column is monotonically increasing, it will be used as an time scale for plotting.

### Parameters

Dimension `m` (default 1), delay `t` (default 1), the size of
neighbourhood `e` (default 0.1) and the range size `w` (default `[]` )
are the first five numbers after
the data series; if `w=[]` then the whole plot will
be calculated. Variable `lmin`
sets the minimal length of what should be considered
to be a diagonal line. Further parameters can be used
to switch between various methods of finding the
neighbours of the phasespace trajectory, to suppress
the normalization of the data and to suppress the
GUI (useful in order to use this programme by other
programmes).

Methods of finding the neighbours. | ||

'maxnorm' | - | Maximum norm (default). |

'euclidean' | - | Euclidean norm. |

'minnorm' | - | Minimum norm. |

'nrmnorm' | - | Euclidean norm between normalized vectors (all vectors have the length one). |

'rr' | - | Maximum norm, fixed recurrence rate. |

'fan' | - | Fixed amount of nearest neighbours. |

'inter' | - | Interdependent neighbours. |

'omatrix' | - | Order matrix. |

'opattern' | - | Order patterns recurrence plot. |

Normalization of the data series. | ||

'normalize' | - | Normalization of the data (default). |

'nonormalize' | - | No normalization of the data. |

Suppressing the GUI. | ||

'gui' | - | Creates the GUI and the output plot (default). |

'nogui' | - | Suppresses the GUI and the output plot. |

'silent' | - | Suppresses all output. |

Output | ||

y.RRp | - | Recurrence rate for (x,y). |

y.RRm | - | Recurrence ratefor (x,y). |

y.DETp | - | Determinism (x,y). |

y.DETm | - | Determinism (x,-y). |

y.Lp | - | Averaged diagonal length (x,y). |

y.Lm | - | Averaged diagonal length (x,-y). |

Parameters are optional and not required.

### Limitations

For higher speed in output the whole matrix of the recurrence
plot is in the work space - this limits the application of long data
series. However, a solution for using long data series you can find
under the description for `crp`, or by using the
command `crqad_big`.

### Examples

```
a=sin(0:.1:80)+randn(1,801);
b=sin(0:.1:80)+randn(1,801);
crqad(a,b,3,15,.1,100,'fan')
```

### Remarks

A GUI for this task is under development.

### See Also

crqad,
crqa,
crp,
dl,
tt,
rpde

### References

Marwan, N., Kurths, J.: Nonlinear analysis of bivariate data with cross recurrence plots, Phys. Lett. A, 302, 2002.