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Article contents:== Outdated egg! This is an egg for CHICKEN 4, the unsupported old release. You're almost certainly looking for [[/eggref/5/bvsp-spline|the CHICKEN 5 version of this egg]], if it exists. If it does not exist, there may be equivalent functionality provided by another egg; have a look at the [[https://wiki.call-cc.org/chicken-projects/egg-index-5.html|egg index]]. Otherwise, please consider porting this egg to the current version of CHICKEN. [[tags: eggs]] [[toc:]] == bvsp-spline === Description The Chicken {{bvsp-spline}} library provides bindings to the routines in the {{BVSPIS}} Fortran library. [[http://www.netlib.org/toms/|BVSPIS]] (Boundary-Valued Shape-Preserving Interpolating Splines) is a package for computing and evaluating shape-preserving interpolating splines, and is described in P. Costantini. Algorithm 770: BVSPIS -- a package for computing boundary-valued shape-preserving interpolating splines. ACM Trans. Math. Softw. 23, No.2, 252-254 (1997) === Installation notes The Chicken {{bvsp-spline}} library must be compiled along with the {{BVSPIS}} Fortran source code, however the ACM licensing terms prevent the distribution of {{BVSPIS}} via the Chicken package system. Therefore, the user must download and unpack {{BVSPIS}}, and set the {{BVSPIS_PATH}} environment variable to indicate the location where the sources can be found. {{chicken-install}} can then be invoked as usual. The following commands perform the necessary operations when invoked from bash in a typical Linux distribution: wget http://www.netlib.org/toms/770 mkdir bvspis && awk 'NR>4' 770 > bvspis/bvspis.sh && chmod u+x bvspis/bvspis.sh pushd bvspis && ./bvspis.sh && popd BVSPIS_PATH=$PWD/bvspis chicken-install bvsp-spline === Library procedures <procedure>(compute n k x y #!key (shape-constraint 'none) (boundary-condition 'none) (derivative-computation 'order2) (d0 #f) (dnp #f) (d20 #f) (d2np #f) (eps 1e-4) (constr #f) (beta #f) (betainv #f) (rho #f) (rhoinv #f) (kmax #f) (maxstp #f) (d #f) (d2 #f) ) </procedure> Computes the coefficients of a shape-preserving spline, of continuity class C(k), k=1,2 , which interpolates a set of data points and, if required, satisfies additional boundary conditions. The result of the routine is a list of the form {{(D D2 CONSTR ERRC DIAGN)}}. {{D D2 ERRC}} provide the input parameters for {{evaluate}}, which evaluates the spline and its derivatives along a set of tabulation points. {{CONSTR}} is an SRFI-4 {{s32vector}} that contains computed constraint information. The required arguments are: ; N: the degree of the spline (must be integer >= 3) ; K: the class of continuity of the spline (first or second derivative). K=1 or K=2 and N >= 3*K ; X: SRFI-4 {{f64vector}} value containing the x coordinates of the data points (must be the same length as Y) ; Y: SRFI-4 {{f64vector}} value containing the y coordinates of the data points (must be the same length as X) The optional arguments are: ; shape-constraint: one of {{'none}}, {{'monotonicity}}, {{'convexity}}, {{'monotonicity+convexity}}, {{'local}}. Default is {{'none}} ; boundary-condition: one of {{'none}}, {{'non-separable}}, {{'separable}}. Default is {{'none}} ; derivative-computation: one of {{'order1}}, {{'order2}}, {{'order3}}, {{'classic}}. Default is {{'order2}} ; d0: left separable boundary condition for the first derivative (only used when {{boundary-condition}} is {{'separable}}) ; dnp: right separable boundary condition for the first derivative (only used when {{boundary-condition}} is {{'separable}}) ; d20: left separable boundary condition for the second derivative (only used when {{boundary-condition}} is {{'separable}} and K=2) ; d2np: right separable boundary condition for the second derivative (only used when {{boundary-condition}} is {{'separable}} and K=2) ; eps: relative tolerance of the method. Default is 1e-4 ; constr: if {{shape-constraint}} is {{'local}}, this argument containts a {{s32vector}} value with the desired constraints on the shape for each subinterval. Each element can be one of 0,1,2,3 (none, monotonicity, convexity, monotonicity and convexity constraint) ; beta: user-supplied procedure of the form {{(LAMBDA X)}}, which represents non-separable boundary conditions for the first derivatives (only used when {{boundary-condition}} is {{'non-separable}}) ; betainv: user-supplied procedure of the form {{(LAMBDA X)}}, which is the inverse of {{BETA}} (only used when {{boundary-condition}} is {{'non-separable}}) ; rho: user-supplied procedure of the form {{(LAMBDA X)}}, which represents non-separable boundary conditions for the second derivatives (only used when {{boundary-condition}} is {{'non-separable}} and K=2) ; rhoinv: user-supplied procedure of the form {{(LAMBDA X)}}, which is the inverse of {{RHO}} (only used when {{boundary-condition}} is {{'non-separable}} and K=2) ; kmax: the number of iterations allowed for selecting the minimal set {{ASTAR}} (described in the paper) ; maxstp: the number of iterations allowed for finding the set {{DSTAR}} (described in the paper) ; d: SRFI-4 {{f64vector}} value containing the first derivatives at the points in X (only used when {{derivative-computation}} is {{'classic}}) ; d2: SRFI-4 {{f64vector}} value containing the second derivatives at the points in X (only used when {{derivative-computation}} is {{'classic}} and K=2) <procedure>(evaluate n k x y d d2 xtab errc #!key (search-method 'binary) (derivatives 2))</procedure> Evaluates the given spline at points given by argument {{XTAB}}, which must be an SRFI-4 {{f64vector}} value. Arguments {{N K X Y}} have the same meaning as for the {{compute}} routine. Arguments {{D D2 ERRC}} are produced by {{compute}}. === Example (use srfi-1 srfi-4 bvsp-spline) ;; Input data (let ((x (f64vector .000000000E+00 .628318500E+00 .125663700E+01 .188495600E+01 .251327400E+01 .314159300E+01 .376991100E+01 .439823000E+01 .502654800E+01 .565486700E+01 .628318500E+01)) (y (f64vector .200000000E+00 .387785300E+00 .115105700E+01 .751056500E+00 .787785200E+00 -.200000100E+00 -.387785300E+00 -.115105700E+01 -.751056500E+00 -.787784900E+00 .200000200E+00))) ;; Set the degree and the class of continuity of the spline. (let ((n 3) (k 1)) (let-values (((d d2 constr errc diagn) (compute n k x y))) (assert (zero? errc)) (let* ((xpn 100) (dxp (/ (- (f64vector-ref x (- (f64vector-length x) 1)) (f64vector-ref x 0)) xpn)) (xp (list->f64vector (list-tabulate 100 (lambda (i) (* i dxp)))))) (let-values (((y0tab y1tab y2tab erre) (evaluate n k x y d d2 xp errc))) (print "erre = " erre) (for-each (lambda (i v) (printf "y0tab(~A) = ~A~%" (f64vector-ref xp i) (f64vector-ref y0tab i)) ) '(32 65 98) '(0.746843749779158 -0.806157453777544 -0.0795180362289622)) ))) )) === Version History * 1.0 Initial release === License Copyright 2011 Ivan Raikov. All rights reserved. This program is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version. This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. A full copy of the GPL license can be found at <http://www.gnu.org/licenses/>. Description of your changes:

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