iknots

Normalized total variation of n-th finite differences is calculated for each column in
<code>y</code> then averaged. These averaged values are fitted by a linear spline to
find knot positions that equalize the jumps of n-th derivative. 
NB. This function is used internally in <code>(fit)smbsp()</code> and a priori
has no interest to be called directly by user.

Build and use B-splines for interpolation and regression.
In case of regression, equality constraints as well as monotonicity
and/or positivity of B-spline weights can be imposed. Moreover,
knot positions (not only spline weights) can be part of
optimized parameters too. For this end, 'bspline' is able to calculate
Jacobian of basis vectors as function of knot positions. User is provided with
functions calculating spline values at arbitrary points. These
functions can be differentiated and integrated to obtain B-splines calculating
derivatives/integrals at any point. B-splines of this package can
simultaneously operate on a series of curves sharing the same set of
knots. 'bspline' is written with concern about computing
performance that's why the basis and Jacobian calculation is implemented in C++.
The rest is implemented in R but without notable impact on computing speed.

Serguei Sokol

bspline

B-Spline Interpolation and Regression

iknots function

<dl><dt>x</dt>
<dd>Numeric vector</dd>
<dt>y</dt>
<dd>Numeric vector or matrix</dd>
<dt>nki</dt>
<dd>Integer scalar, number of internal knots to estimate (1 by default)</dd>
<dt>n</dt>
<dd>Integer scalar, polynomial order of B-spline (3 by default)</dd>
<dt>lenfit</dt>
<dd>Integer scalar, length of knots for linear spline to fit the total variation)</dd></dl>

Arguments

Normalized total variation of n-th finite differences is calculated for each column in
<code>y</code> then averaged. These averaged values are fitted by a linear spline to
find knot positions that equalize the jumps of n-th derivative. 
NB. This function is used internally in <code>(fit)smbsp()</code> and a priori
has no interest to be called directly by user.

Estimate internal knot positions equalizing jumps in n-th derivative — iknots

<dl>

<dt>x</dt>
<dd>Numeric vector</dd>


<dt>y</dt>
<dd>Numeric vector or matrix</dd>


<dt>nki</dt>
<dd>Integer scalar, number of internal knots to estimate (1 by default)</dd>


<dt>n</dt>
<dd>Integer scalar, polynomial order of B-spline (3 by default)</dd>


<dt>lenfit</dt>
<dd>Integer scalar, length of knots for linear spline to fit the total variation)</dd>

</dl>

iknots: Estimate internal knot positions equalizing jumps in n-th derivative

Description

Usage

Value

Arguments