# embedding

##### Construction of embedding vectors using the method of delays

This function generates both the uniform and non-uniform embedding vectors set from an univariate time serie considering the argument set selected by the user.

##### Usage

`embedding(x, m = 3, lag = 1, timelapse = c("FIXED", "VARIABLE"))`

##### Arguments

- x
a numeric vector, time serie, data frame or matrix depending on the method selected in

`timelapse`

.- m
a non-negative integer denoting the embedding dimension (Default 3).

- lag
a non-negative integer denoting the reconstruction delay (Default 1).

- timelapse
a character denoting if you consider that the observations are sampled at uniform time intervals

`FIXED`

or with a variable time-lapse between each observation`VARIABLE`

(Default`FIXED`

).

##### Details

If `FIXED`

has been selected `x`

must be a numeric vector or time serie. Otherwise `VARIABLE`

has to be specified. In this case `x`

must be a data frame or matrix with two columns. First, the date with the following format `YMD H:M:OS3`

considering milliseconds e.g., 20190407 00:00:03.347. If you don't consider milliseconds you must put .000 after the seconds. It should be an object of class `Factor`

. Second, the univariate time serie as a sequence of numerical values.

##### Value

A data frame with the uniform or non-uniform embedding vectors by columns from an univariate time serie considering the parameter set selected by the user.

##### References

Ruelle, D., Takens, F. 1971 On the nature of turbulence. Communications in Mathematical Physics 20(3):167-192.

Packard, N.H., Crutchfield, J.P., Farmer, J.D., Shaw, R.S. 1980 Geometry from a time serie. Physical Review Letters 45:712-716.

Takens, F. 1981 Detecting strange attractors in turbulence. Springer Berlin Heidelberg.

Sauer, T., Yorke, J.A., Casdagli, M. 1991 Embedology. Journal of Statistical Physics 65(3):579-616.

Huke, J.P., Broomhead, D.S. 2007 Embedding theorems for non-uniformly sampled dynamical systems. Nonlinearity 20(9):205-244.

##### See Also

##### Examples

```
# NOT RUN {
## The first ten values corresponding to the uniform embedding
## vectors set for m=5 and lag=1 are showed by simulating
## time series from the logistic equation.
data<-logistic.ts(u.min=4,u.max=4,B=100,doplot=FALSE)
ts<-data$`Logistic 100`$time.serie
embed<-embedding(ts,m=5,lag=1,timelapse="FIXED")
show(head(embed, 10))
# }
```

*Documentation reproduced from package DChaos, version 0.1-1, License: GPL (>= 2)*