imat

Calculate matrix for obtaining coefficients of indefinite integral of B-spline.
They can be calculated as <code>iqw=Mi %*% qw</code>. Here, iqw are coefficients
of the indefinite integral of B-spline,
Mi is the matrix returned by this function, and qw are the coefficients
of integrated B-spline. 
As per the nature of the indefinite integral, this coefficients are defined up to
arbitrary additive constant.

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

imat function

<dl><dt>nqw</dt>
<dd>Integer scalar, row number of qw matrix (i.e. degree of freedom of a B-spline)</dd>
<dt>xk</dt>
<dd>Numeric vector, knot positions</dd>
<dt>n</dt>
<dd>Integer scalar, B-spline polynomial order</dd>
<dt>f</dt>
<dd>Function from which previous parameters can be retrieved.
If both f and any of previous parameters are given then explicitly
set parameters take precedence over those retrieved from f.</dd></dl>

Arguments

Calculate matrix for obtaining coefficients of indefinite integral of B-spline.
They can be calculated as <code>iqw=Mi %*% qw</code>. Here, iqw are coefficients
of the indefinite integral of B-spline,
Mi is the matrix returned by this function, and qw are the coefficients
of integrated B-spline. 
As per the nature of the indefinite integral, this coefficients are defined up to
arbitrary additive constant.

Integration matrix of B-spline — imat

<dl>

<dt>nqw</dt>
<dd>Integer scalar, row number of qw matrix (i.e. degree of freedom of a B-spline)</dd>


<dt>xk</dt>
<dd>Numeric vector, knot positions</dd>


<dt>n</dt>
<dd>Integer scalar, B-spline polynomial order</dd>


<dt>f</dt>
<dd>Function from which previous parameters can be retrieved.
If both f and any of previous parameters are given then explicitly
set parameters take precedence over those retrieved from f.</dd>

</dl>

imat: Integration matrix of B-spline

Description

Usage

Value

Arguments