Interpolation and Approximation

CURVE AND SURFACE FITTING WITH SPLINES

ROUTINE DESCRIPTION
SPLINE_CONSTRAINTS Returns the derived type array result.
SPLINE_VALUES Returns an array result, given an array of input.
SPLINE_FITTING Weighted least-squares fitting by B-splines to discrete One-Dimensional data is performed.
SURFACE_CONSTRAINTS Returns the derived type array result given optional input.
SURFACE_VALUES Returns a tensor product array result, given two arrays of independent variable values.
SURFACE_FITTING Weighted least-squares fitting by tensor product B-splines to discrete Two-dimensional data is performed.
 

CUBIC SPLINE INTERPOLATION

ROUTINE DESCRIPTION
CSIEZ Computes the cubic spline interpolant with the 'not-a-knot' condition and returns values of the interpolant at specified points.
CSINT Computes the cubic spline interpolant with the 'not-a-knot' condition.
CSDEC Computes the cubic spline interpolant with specified derivative endpoint conditions.
CSHER Computes the Hermite cubic spline interpolant.
CSAKM Computes the Akima cubic spline interpolant.
CSCON Computes a cubic spline interpolant that is consistent with the concavity of the data.
CSPER Computes the cubic spline interpolant with periodic boundary conditions.
 

CUBIC SPLINE EVALUATION AND INTEGRATION

ROUTINE DESCRIPTION
CSVAL Evaluates a cubic spline.
CSDER Evaluates the derivative of a cubic spline.
CS1GD Evaluates the derivative of a cubic spline on a grid.
CSITG Evaluates the integral of a cubic spline.
 

B-SPLINE INTERPOLATION

ROUTINE DESCRIPTION
ROUTINE DESCRIPTION
SPLEZ Computes the values of a spline that either interpolates or fits user-supplied data.
BSINT Computes the spline interpolant, returning the B-spline coefficients.
BSNAK Computes the “not-a-knot” spline knot sequence.
BSOPK Computes the “optimal” spline knot sequence.
BS2IN Computes a two-dimensional tensor-product spline interpolant, returning the tensor-product B-spline coefficients.
BS3IN Computes a three-dimensional tensor-product spline interpolant, returning the tensor-product B-spline coefficients.
 

SPLINE EVALUATION, INTEGRATION, AND CONVERSION TO PIECEWISE POLYNOMIAL GIVEN THE B-SPLINE REPRESENTATION

ROUTINE DESCRIPTION
BSVAL Evaluates a spline, given its B-spline representation.
BSDER Evaluates the derivative of a spline, given its B-spline representation.
BS1GD Evaluates the derivative of a spline on a grid, given its B-spline representation.
BSITG Evaluates the integral of a spline, given its B-spline representation.
BS2VL Evaluates a two-dimensional tensor-product spline, given its tensor-product B-spline representation.
BS2DR Evaluates the derivative of a two-dimensional tensor-product spline, given its tensor-product B-spline representation.
BS2GD Evaluates the derivative of a two-dimensional tensor-product spline, given its tensor-product B-spline representation on a grid.
BS2IG Evaluates the integral of a tensor-product spline on a rectangular domain,given its tensor-product B-spline representation.
BS3VL Evaluates a three-dimensional tensor-product spline, given its tensor-product B-spline representation.
BS3DR Evaluates the derivative of a three-dimensional tensor-product spline, given its tensor-product B-spline representation.
BS3GD Evaluates the derivative of a three-dimensional tensor-product spline, given its tensor-product B-spline representation on a grid.
BS3IG Evaluates the integral of a tensor-product spline in three dimensions over a three-dimensional rectangle, given its tensor-product B-spline representation.
BSCPP Converts a spline in B-spline representation to piecewise polynomial representation.
 

PIECEWISE POLYNOMIAL

ROUTINE DESCRIPTION
PPVAL Evaluates a piecewise polynomial.
PPDER Evaluates the derivative of a piecewise polynominal.
PP1GD Evaluates the derivative of a piecewise polynomial on a grid.
PPITG Evaluates the integral of a piecewise polynomial.
 

QUADRATIC POLYNOMIAL INTERPOLATION ROUTINES FOR GRIDDED DATA

ROUTINE DESCRIPTION
QDVAL Evaluates a function defined on a set of points using quadratic interpolation.
QDDER Evaluates the derivative of a function defined on a set of points using quadratic interpolation.
QD2VL Evaluates a function defined on a rectangular grid using quadratic interpolation.
QD2DR Evaluates the derivative of a function defined on a rectangular grid using quadratic interpolation.
QD3VL Evaluates a function defined on a rectangular three-dimensional grid using quadratic interpolation.
DQ3DR Evaluates the derivative of a function defined on a rectangular three-dimensional grid using quadratic interpolation.
 

MULTI-DIMENSIONAL INTERPOLATION

ROUTINE DESCRIPTION
SURF Computes a smooth bivariate interpolant to scattered data that is locally a quintic polynomial in two variables.
SURFND Performs multidimensional interpolation and differentiation for up to 7 dimensions.
 

LEAST-SQUARES APPROXIMATION

ROUTINE DESCRIPTION
RLINE Fits a line to a set of data points using least squares.
RCURV Fits a polynomial curve using least squares.
FNLSQ Computes a least-squares approximation with user-supplied basis functions.
BSLSQ Computes the least-squares spline approximation, and returns the B-spline coefficients.
BSVLS Computes the variable knot B-spline least squares approximation to given data.
CONFIT Computes the least-squares constrained spline approximation, returning the Bspline coefficients.
BSLS2 Computes a two-dimensional tensor-product spline approximant using least squares, returning the tensor-product B-spline coefficients.
BSLS3 Computes a three-dimensional tensor-product spline approximant using least squares, returning the tensor-product B-spline coefficients.
 

CUBIC SPLINE SMOOTHING

ROUTINE DESCRIPTION
CSSED Smooths one-dimensional data by error detection.
CSSMH Computes a smooth cubic spline approximation to noisy data.
CSSCV Computes a smooth cubic spline approximation to noisy data using cross-validation to estimate the smoothing parameter.
 

RATIONAL L APPROXIMATION

ROUTINE DESCRIPTION
RATCH Computes a rational weighted Chebyshev approximation to a continuous function on an interval.