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;; Basis splines.
;; Liam Healy 2008-02-18 14:43:20EST basis-splines.lisp
;; Time-stamp: <2009-05-24 22:58:41EDT basis-splines.lisp>
(in-package :gsl)
Liam Healy
committed
;;; /usr/include/gsl/gsl_bspline.h
;;; Should be subclass of interpolation?
(defmobject basis-spline "gsl_bspline"
((order sizet) (number-of-breakpoints sizet))
"Allocate a workspace for computing B-splines. The number of
breakpoints is given by number-of-breakpoints. This leads to n =
nbreak + k - 2 basis functions where k = order. Cubic B-splines are
specified by k = 4. The size of the workspace is O(5k + nbreak).")
;;; Constructing the knots vector
(defmfun knots (breakpoints workspace)
"gsl_bspline_knots"
(((mpointer breakpoints) :pointer) ((mpointer workspace) :pointer))
:documentation ; FDL
"Compute the knots associated with the given breakpoints and store
them in the workspace.")
(defmfun uniform-knots (a b workspace)
"gsl_bspline_knots_uniform"
((a :double) (b :double) ((mpointer workspace) :pointer))
:return (workspace)
:documentation ; FDL
"Compute knots uniformly on the interval [a, b] and store
them in the workspace.")
;;; Evaluation of B-splines
(defmfun evaluate
((workspace basis-spline) x
&key (B (make-marray 'double-float
:dimensions (number-of-coefficients workspace))))
"gsl_bspline_eval"
((x :double) ((mpointer B) :pointer) ((mpointer workspace) :pointer))
:documentation ; FDL
"Evaluate all B-spline basis functions at the position x and store
them in the GSL vector B, so that the ith element of B is B_i(x).
B must be of length n = nbreak + k - 2. This value is
also stored in the workspace. It is far more
efficient to compute all of the basis functions at once than to
compute them individually, due to the nature of the defining
recurrence relation.")
;;; Query settings of the B-spline
;;; These are not documented but are in
;;; /usr/include/gsl/gsl_bspline.h; are they officially supported?
(defmfun number-of-coefficients (bspline)
(((mpointer bspline) :pointer))
:c-return sizet
:gsl-version (1 9))
(defmfun order ((bspline basis-spline))
(defmfun number-of-breakpoints (bspline)
:gsl-version (1 9)
:documentation "The number of breakpoints of the basis spline bspline.")
((i sizet) ((mpointer bspline) :pointer))
:gsl-version (1 9)
:documentation "The ith breakpoint of the basis spline bspline.")
;;; Examples and unit test
(defun bspline-example (&optional (ncoeffs 8))
(ndata 200)
(nbreak (+ ncoeffs 2 (- order)))
(bw (make-basis-spline order nbreak))
(mw (make-fit-workspace ndata ncoeffs))
(B (make-marray 'double-float :dimensions ncoeffs))
(c (make-marray 'double-float :dimensions ncoeffs))
(cov (make-marray 'double-float :dimensions (list ncoeffs ncoeffs)))
(w (make-marray 'double-float :dimensions ndata))
(x (make-marray 'double-float :dimensions ndata))
(y (make-marray 'double-float :dimensions ndata))
(Xmatrix (make-marray 'double-float :dimensions (list ndata ncoeffs)))
(sigma 0.1d0))
;; The data to be fitted.
(dotimes (i ndata)
(let* ((xi (coerce (* i (/ 15 (1- ndata))) 'double-float))
(yi (+ (* (cos xi) (exp (* -0.1d0 xi)))
(sample rng 'gaussian :sigma sigma))))
(setf (maref x i) xi
(maref y i) yi
(maref w i) (/ (expt sigma 2)))))
;; Uniform breakpoints [0, 15]
(uniform-knots 0.0d0 15.0d0 bw)
;; Fit matrix
(dotimes (i ndata)
;; Compute B_j
;; Fill in row i of X
(dotimes (j ncoeffs)
(setf (maref Xmatrix i j) (maref B j))))
(linear-mfit Xmatrix y c w nil cov mw)
;; Return the smoothed curve
(loop for xi from 0.0d0 to 15.0d0 by 0.1d0
(multiple-value-setq (yval yerr)
(multi-linear-estimate B c cov))
collect yval into yvals
collect yerr into yerrs
finally (return (values yvals yerrs)))))
(save-test basis-spline (bspline-example))