Category E. Interpolation

E1. Univariate data (curve fitting) E3. Service routines BSPDOC-A Documentation for BSPLINE, a package of subprograms for working with piecewise polynomial functions in B-representation. E1. Univariate data (curve fitting) E1A. Polynomial splines (piecewise polynomials) BINT4-S Compute the B-representation of a cubic spline DBINT4-D which interpolates given data. BINTK-S Compute the B-representation of a spline which interpolates DBINTK-D given data. BSPDOC-A Documentation for BSPLINE, a package of subprograms for working with piecewise polynomial functions in B-representation. PCHDOC-A Documentation for PCHIP, a Fortran package for piecewise cubic Hermite interpolation of data. PCHIC-S Set derivatives needed to determine a piecewise monotone DPCHIC-D piecewise cubic Hermite interpolant to given data. User control is available over boundary conditions and/or treatment of points where monotonicity switches direction. PCHIM-S Set derivatives needed to determine a monotone piecewise DPCHIM-D cubic Hermite interpolant to given data. Boundary values are provided which are compatible with monotonicity. The interpolant will have an extremum at each point where mono- tonicity switches direction. (See PCHIC if user control is desired over boundary or switch conditions.) PCHSP-S Set derivatives needed to determine the Hermite represen- DPCHSP-D tation of the cubic spline interpolant to given data, with specified boundary conditions. E1B. Polynomials POLCOF-S Compute the coefficients of the polynomial fit (including DPOLCF-D Hermite polynomial fits) produced by a previous call to POLINT. POLINT-S Produce the polynomial which interpolates a set of discrete DPLINT-D data points. E3. Service routines (e.g., grid generation, evaluation of fitted functions) (search also class N5) BFQAD-S Compute the integral of a product of a function and a DBFQAD-D derivative of a B-spline. BSPDR-S Use the B-representation to construct a divided difference DBSPDR-D table preparatory to a (right) derivative calculation. BSPEV-S Calculate the value of the spline and its derivatives from DBSPEV-D the B-representation. BSPPP-S Convert the B-representation of a B-spline to the piecewise DBSPPP-D polynomial (PP) form. BSPVD-S Calculate the value and all derivatives of order less than DBSPVD-D NDERIV of all basis functions which do not vanish at X. BSPVN-S Calculate the value of all (possibly) nonzero basis DBSPVN-D functions at X. BSQAD-S Compute the integral of a K-th order B-spline using the DBSQAD-D B-representation. BVALU-S Evaluate the B-representation of a B-spline at X for the DBVALU-D function value or any of its derivatives. CHFDV-S Evaluate a cubic polynomial given in Hermite form and its DCHFDV-D first derivative at an array of points. While designed for use by PCHFD, it may be useful directly as an evaluator for a piecewise cubic Hermite function in applications, such as graphing, where the interval is known in advance. If only function values are required, use CHFEV instead. CHFEV-S Evaluate a cubic polynomial given in Hermite form at an DCHFEV-D array of points. While designed for use by PCHFE, it may be useful directly as an evaluator for a piecewise cubic Hermite function in applications, such as graphing, where the interval is known in advance. INTRV-S Compute the largest integer ILEFT in 1 .LE. ILEFT .LE. LXT DINTRV-D such that XT(ILEFT) .LE. X where XT(*) is a subdivision of the X interval. PCHBS-S Piecewise Cubic Hermite to B-Spline converter. DPCHBS-D PCHCM-S Check a cubic Hermite function for monotonicity. DPCHCM-D PCHFD-S Evaluate a piecewise cubic Hermite function and its first DPCHFD-D derivative at an array of points. May be used by itself for Hermite interpolation, or as an evaluator for PCHIM or PCHIC. If only function values are required, use PCHFE instead. PCHFE-S Evaluate a piecewise cubic Hermite function at an array of DPCHFE-D points. May be used by itself for Hermite interpolation, or as an evaluator for PCHIM or PCHIC. PCHIA-S Evaluate the definite integral of a piecewise cubic DPCHIA-D Hermite function over an arbitrary interval. PCHID-S Evaluate the definite integral of a piecewise cubic DPCHID-D Hermite function over an interval whose endpoints are data points. PFQAD-S Compute the integral on (X1,X2) of a product of a function DPFQAD-D F and the ID-th derivative of a B-spline, (PP-representation). POLYVL-S Calculate the value of a polynomial and its first NDER DPOLVL-D derivatives where the polynomial was produced by a previous call to POLINT. PPQAD-S Compute the integral on (X1,X2) of a K-th order B-spline DPPQAD-D using the piecewise polynomial (PP) representation. PPVAL-S Calculate the value of the IDERIV-th derivative of the DPPVAL-D B-spline from the PP-representation.