Category K. Approximation (search also class L8)

K1. Least squares (L-2) approximation K6. Service routines BSPDOC-A Documentation for BSPLINE, a package of subprograms for working with piecewise polynomial functions in B-representation. K1. Least squares (L-2) approximation K1A. Linear least squares (search also classes D5, D6, D9) K1A1. Unconstrained K1A1A. Univariate data (curve fitting) K1A1A1. Polynomial splines (piecewise polynomials) EFC-S Fit a piecewise polynomial curve to discrete data. DEFC-D The piecewise polynomials are represented as B-splines. The fitting is done in a weighted least squares sense. FC-S Fit a piecewise polynomial curve to discrete data. DFC-D The piecewise polynomials are represented as B-splines. The fitting is done in a weighted least squares sense. Equality and inequality constraints can be imposed on the fitted curve. K1A1A2. Polynomials PCOEF-S Convert the POLFIT coefficients to Taylor series form. DPCOEF-D POLFIT-S Fit discrete data in a least squares sense by polynomials DPOLFT-D in one variable. K1A2. Constrained K1A2A. Linear constraints EFC-S Fit a piecewise polynomial curve to discrete data. DEFC-D The piecewise polynomials are represented as B-splines. The fitting is done in a weighted least squares sense. FC-S Fit a piecewise polynomial curve to discrete data. DFC-D The piecewise polynomials are represented as B-splines. The fitting is done in a weighted least squares sense. Equality and inequality constraints can be imposed on the fitted curve. LSEI-S Solve a linearly constrained least squares problem with DLSEI-D equality and inequality constraints, and optionally compute a covariance matrix. SBOCLS-S Solve the bounded and constrained least squares DBOCLS-D problem consisting of solving the equation E*X = F (in the least squares sense) subject to the linear constraints C*X = Y. SBOLS-S Solve the problem DBOLS-D E*X = F (in the least squares sense) with bounds on selected X values. WNNLS-S Solve a linearly constrained least squares problem with DWNNLS-D equality constraints and nonnegativity constraints on selected variables. K1B. Nonlinear least squares K1B1. Unconstrained SCOV-S Calculate the covariance matrix for a nonlinear data DCOV-D fitting problem. It is intended to be used after a successful return from either SNLS1 or SNLS1E. K1B1A. Smooth functions K1B1A1. User provides no derivatives SNLS1-S Minimize the sum of the squares of M nonlinear functions DNLS1-D in N variables by a modification of the Levenberg-Marquardt algorithm. SNLS1E-S An easy-to-use code which minimizes the sum of the squares DNLS1E-D of M nonlinear functions in N variables by a modification of the Levenberg-Marquardt algorithm. K1B1A2. User provides first derivatives SNLS1-S Minimize the sum of the squares of M nonlinear functions DNLS1-D in N variables by a modification of the Levenberg-Marquardt algorithm. SNLS1E-S An easy-to-use code which minimizes the sum of the squares DNLS1E-D of M nonlinear functions in N variables by a modification of the Levenberg-Marquardt algorithm. K6. Service routines (e.g., mesh 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. DBSPDR-D Use the B-representation to construct a divided difference BSPDR-S 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. 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. 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). 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. PVALUE-S Use the coefficients generated by POLFIT to evaluate the DP1VLU-D polynomial fit of degree L, along with the first NDER of its derivatives, at a specified point.