(index ("compute" 0) ("evaluate" 4269))
(def (sig (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) ) " (id compute))) (p "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.") (p "The result of the routine is a list of the form " (tt "(D D2 CONSTR ERRC DIAGN)") ".  " (tt "D D2 ERRC") " provide the input parameters for " (tt "evaluate") ", which evaluates the spline and its derivatives along a set of tabulation points. " (tt "CONSTR") " is an SRFI-4 " (tt "s32vector") " that contains computed constraint information.") (p "The required arguments are:") (dl (dt "N") (dd "the degree of the spline (must be integer >= 3)") (dt "K") (dd "the class of continuity of the spline (first or second derivative). K=1 or K=2 and N >= 3*K") (dt "X") (dd "SRFI-4 " (tt "f64vector") " value containing the x coordinates of the data points (must be the same length as Y)") (dt "Y") (dd "SRFI-4 " (tt "f64vector") " value containing the y coordinates of the data points (must be the same length as X)")) (p "The optional arguments are:") (dl (dt "shape-constraint") (dd "one of " (tt "'none") ", " (tt "'monotonicity") ", " (tt "'convexity") ", " (tt "'monotonicity+convexity") ", " (tt "'local") ". Default is " (tt "'none")) (dt "boundary-condition") (dd "one of  " (tt "'none") ", " (tt "'non-separable") ", " (tt "'separable") ". Default is " (tt "'none")) (dt "derivative-computation") (dd "one of " (tt "'order1") ", " (tt "'order2") ", " (tt "'order3") ", " (tt "'classic") ". Default is " (tt "'order2")) (dt "d0") (dd "left separable boundary condition for the first derivative (only used when " (tt "boundary-condition") " is " (tt "'separable") ")") (dt "dnp") (dd "right separable boundary condition for the first derivative (only used when " (tt "boundary-condition") " is " (tt "'separable") ")") (dt "d20") (dd "left separable boundary condition for the second derivative (only used when " (tt "boundary-condition") " is " (tt "'separable") " and K=2)") (dt "d2np") (dd "right separable boundary condition for the second derivative (only used when " (tt "boundary-condition") " is " (tt "'separable") " and K=2)") (dt "eps") (dd "relative tolerance of the method. Default is 1e-4") (dt "constr") (dd "if " (tt "shape-constraint") " is " (tt "'local") ", this argument containts a " (tt "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)") (dt "beta") (dd "user-supplied procedure of the form " (tt "(LAMBDA X)") ", which represents non-separable boundary conditions for the first derivatives (only used  when " (tt "boundary-condition") " is " (tt "'non-separable") ")") (dt "betainv") (dd "user-supplied procedure of the form " (tt "(LAMBDA X)") ", which is the inverse of " (tt "BETA") " (only used  when " (tt "boundary-condition") " is " (tt "'non-separable") ")") (dt "rho") (dd "user-supplied procedure of the form " (tt "(LAMBDA X)") ", which represents non-separable boundary conditions for the second derivatives (only used  when " (tt "boundary-condition") " is " (tt "'non-separable") " and K=2)") (dt "rhoinv") (dd "user-supplied procedure of the form " (tt "(LAMBDA X)") ", which is the inverse of " (tt "RHO") " (only used  when " (tt "boundary-condition") " is " (tt "'non-separable") " and K=2)") (dt "kmax") (dd "the number of iterations allowed for selecting the minimal set " (tt "ASTAR") " (described in the paper)") (dt "maxstp") (dd "the number of iterations allowed for finding the set " (tt "DSTAR") " (described in the paper)") (dt "d") (dd "SRFI-4 " (tt "f64vector") " value containing the first derivatives at the points in X (only used when " (tt "derivative-computation") " is " (tt "'classic") ")") (dt "d2") (dd "SRFI-4 " (tt "f64vector") " value containing the second derivatives at the points in X (only used when " (tt "derivative-computation") " is " (tt "'classic") " and K=2)")))
(def (sig (procedure "(evaluate n k x y d d2 xtab errc #!key (search-method 'binary) (derivatives 2))" (id evaluate))) (p "Evaluates the given spline at points given by argument " (tt "XTAB") ", which must be an SRFI-4 " (tt "f64vector") " value.  Arguments " (tt "N K X Y") " have the same meaning as for the " (tt "compute") " routine. Arguments " (tt "D D2 ERRC") " are produced by " (tt "compute") "."))
