View source: R/create.polygonal.basis.R

create.polygonal.basis | R Documentation |

A basis is set up for constructing polygonal lines, consisting of straight line segments that join together.

```
create.polygonal.basis(rangeval=NULL, argvals=NULL, dropind=NULL,
quadvals=NULL, values=NULL, basisvalues=NULL, names='polygon',
axes=NULL)
```

`rangeval` |
a numeric vector of length 2 defining the interval over which the
functional data object can be evaluated; default value is
If If length(rangeval)>2 and |

`argvals` |
a strictly increasing vector of argument values at which line segments join to form a polygonal line. |

`dropind` |
a vector of integers specifiying the basis functions to be dropped, if any. For example, if it is required that a function be zero at the left boundary, this is achieved by dropping the first basis function, the only one that is nonzero at that point. |

`quadvals` |
a matrix with two columns and a number of rows equal to the number
of quadrature points for numerical evaluation of the penalty
integral. The first column of |

`values` |
a list containing the basis functions and their derivatives
evaluated at the quadrature points contained in the first
column of |

`basisvalues` |
A list of lists, allocated by code such as vector("list",1). This
is designed to avoid evaluation of a basis system repeatedly
at a set of argument values. Each sublist corresponds to a specific
set of argument values, and must have at least two components, which
may be named as you wish. The first component of a sublist contains
the argument values. The second component contains a matrix of
values of the basis functions evaluated at the arguments in the
first component. The third and subsequent components, if present,
contain matrices of values their derivatives up to a maximum
derivative order. Whenever function basisobj$basisvalues <- vector("list",1) basisobj$basisvalues[[1]] <- list(args=evalargs, values=basismat) |

`names` |
either a character vector of the same length as the number of basis
functions or a single character string to which |

`axes` |
an optional list used by selected |

The actual basis functions consist of triangles, each with its apex over an argument value. Note that in effect the polygonal basis is identical to a B-spline basis of order 2 and a knot or break value at each argument value. The range of the polygonal basis is set to the interval defined by the smallest and largest argument values.

a basis object with the type `polyg`

.

Ramsay, James O., Hooker, Giles, and Graves, Spencer (2009),
*Functional data analysis with R and Matlab*, Springer, New York.

Ramsay, James O., and Silverman, Bernard W. (2005),
*Functional Data Analysis, 2nd ed.*, Springer, New York.

Ramsay, James O., and Silverman, Bernard W. (2002),
*Applied Functional Data Analysis*, Springer, New York.

`basisfd`

,
`create.bspline.basis`

,
`create.constant.basis`

,
`create.exponential.basis`

,
`create.fourier.basis`

,
`create.monomial.basis`

,
`create.power.basis`

```
# Create a polygonal basis over the interval [0,1]
# with break points at 0, 0.1, ..., 0.95, 1
(basisobj <- create.polygonal.basis(seq(0,1,0.1)))
# plot the basis
oldpar <- par(no.readonly=TRUE)
plot(basisobj)
par(oldpar)
```

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