Public Domain Algorithms

Version 0.5

Programmer's Manual

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Starlink User Note 194.3
H. Meyerdierks, D. Berry, P. W. Draper, G. Privett, M. Currie
12th October 2005
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Particle Physics & Astronomy Research Council

- Introduction
- Packages from which the routines were obtained
- Routine naming
- I/O and error handling
- Machine dependencies
- Test programs
- Linking with the library
- Fast Fourier transform (FFT)
- Differences between NAG and FFTPACK
- Data formats for FFTPACK and NAG
- Replacing calls to C06FAF
- Replacing calls to C06FBF
- Replacing calls to C06FCF
- Replacing calls to C06FJF
- Replacing calls to C06FUF
- Replacing calls to C06GBF and C06GCF

- One-dimensional
Interpolation and Fitting, Splines
- B-splines
- Ordinary polynomials
- Replacing calls to E01BAF
- Replacing calls to E02BAF
- Replacing calls to E02BBF
- Replacing calls to E02BCF
- Replacing calls to E02BDF
- Replacing calls to E02BEF
- Replacing calls to E02ADF
- Replacing calls to E02AEF
- Replacing calls to E02AKF
- Replacing calls to GEN_CHB2NO

- Two-dimensional
Interpolation and Fitting

- Minimisation
- Overview
- Replacing calls to E04DGF and E04DKF
- Replacing calls to E04FDF and E04GBF
- Replacing calls to E04HCF
- Replacing calls to E04JAF and E04KDF
- Replacing calls to E04YCF

- Matrices
- Overview
- Replacing calls to F01AAF
- Replacing calls to F01ABF
- Replacing calls to F04AAF
- Replacing calls to F04AEF
- Replacing calls to F04ANF and F01AXF
- Replacing calls to F04ASF and F04ATF
- Replacing calls to F04QAF

- Sorting

- Normal Distribution
- Bessel Functions
- Simple Statistics

- Pseudo-Random Numbers
- Setting the seed (replacements for G05CBF and G05CCF)
- Data type of the random numbers
- Replacements for G05CAF and G05DAF
- Replacement for G05DBF
- Replacements for G05DDF, G05DRF, and G05FFF

- User-callable routines
- PDA_BISPEV - Evaluates the bivariate spline approximation found by PDA_SURFIT.
- PDA_BSPDOC - Documentation for working with piecewise polynomial functions in B-representation.
- PDA_C2NAG - Convert FFTPACK complex Fourier transform array into equivalent NAG arrays
- PDA_CFFTB - Unnormalized inverse of PDA_CFFTF.
- PDA_CFFTF - Forward transform of a complex periodic sequence.
- PDA_CFFTI - Initialize PDA_CFFTF and PDA_CFFTB.
- PDA_CHE2D - Evaluates a 2-dimensional Chebyshev polynomial
- PDA_COVMAT - Approximates the covariance matrix of normal order statistics
- PDA_CURFIT - Smooth spline approximation. Knots can be given or determined by the routine.
- PDA_D1MACH - Floating point machine dependent constants
- PDA_DB2INK - Determines the parameters of a 2-D, interpolation function for gridded data.
- PDA_DB2VAL - Evaluates the piecewise polynomial interpolating function constructed by the routine PDA_DB2INK, or one of its partial derivatives.
- PDA_DBESJ1 - Bessel function of first kind of order one.
- PDA_DBINTK - Compute B-representation of an interpolating spline. Knots must be given.
- PDA_DBOLS - Solve E * x = f (in least squares sense) with bounds on x. E is a matrix, x and f are vectors.
- PDA_DBSQAD - Integral of a B-spline using the B-representation.
- PDA_DBVALU - Evaluate a B-spline for the function value or a derivative.
- PDA_DC2NAG - Convert FFTPACK complex Fourier transform array into equivalent NAG arrays
- PDA_DCFFTB - Unnormalized inverse of PDA_DCFFTF.
- PDA_DCFFTF - Forward transform of a complex periodic sequence.
- PDA_DCFFTI - Initialize PDA_DCFFTF and PDA_DCFFTB.
- PDA_DCOV - Calculates the covariance matrix for a nonlinear data fitting problem
- PDA_DEFC - Fit piecewise polynomial curve represented as B-splines (weighted least squares sense).
- PDA_DEFLT - Set default parameters for use by PDA_SUMSL.
- PDA_DERF - Error function erf().
- PDA_DERFC - Complementary error function erfc().
- PDA_DGEDI - Determinant and inverse of a matrix using the factors from PDA_DGEFA.
- PDA_DGEFA - Factor a matrix using Gaussian elimination. This is needed before PDA_DGEDI.
- PDA_DGEFS - Solve the problem A * x = b. A is a square matrix, x and b are vectors. Factoring of A can be re-used to solve for multi-column X and B.
- PDA_DNAG2C - Convert NAG complex Fourier transform array into array usable by FFTPACK routine PDA_DCFFTB
- PDA_DNAG2R - Convert NAG Hermitian Fourier transform array into array usable by FFTPACK routine PDA_DRFFTB
- PDA_DNFFTB - Backward FFT of N-dimensional complex array
- PDA_DNFFTF - Forward FFT of N-dimensional complex array
- PDA_DNLS1 - Minimises the sum of squares of M non-linear functions
- PDA_DNLS1E - Minimises the sum of squares of M non-linear functions (easy version)
- PDA_DP1VLU - Use coefficients from PDA_DPOLFT to evaluate polynomial fit and its derivatives.
- PDA_DPCOEF - Convert the PDA_DPOLFT coefficients to Taylor series form.
- PDA_DPLINT - Produce the polynomial which interpolates a set of discrete data points.
- PDA_DPOLCF - Coefficients of the polynomial fit (including Hermite polynomial fits) produced by PDA_DPLINT.
- PDA_DPOLFT - Weighted least-squares polynomial fit.
- PDA_DPOLVL - Evaluate polynomial and its derivatives as produced by PDA_DPLINT.
- PDA_DQED - Solves bounded nonlinear least squares and nonlinear equations.
- PDA_DR2NAG - Convert FFTPACK Hermitian Fourier transform array into equivalent NAG array
- PDA_DRFFTB - Backward transform of a real coefficient array.
- PDA_DRFFTF - Forward transform of a real periodic sequence.
- PDA_DRFFTI - Initialize PDA_DRFFTF and PDA_DRFFTB.
- PDA_DSORT - Sort array and optionally make same interchanges in auxiliary array.
- PDA_I1MACH - Integer machine dependent constants
- PDA_IDBVIP - Performs 2-D bivariate interpolation when the data is irregularly scattered in the x-y plane.
- PDA_IDSFFT - Performs smooth surface fitting when the projections of the data points in the x-y plane are irregularly distributed in the plane.
- PDA_IPERM - Forms the inverse of a permutation
- PDA_LMDIF - Minimise the sum of the squares of m nonlinear functions in n variables, function only.
- PDA_LMDIF1 - Minimise the sum of the squares of m nonlinear functions in n variables, simple interface to PDA_LMDIF.
- PDA_LSQR - Solves sparse unsymmetric, linear least squares and damped least squares problems
- PDA_NAG2C - Convert NAG complex Fourier transform array into array usable by FFTPACK routine PDA_CFFTB
- PDA_NAG2R - Convert NAG Hermitian Fourier transform array into array usable by FFTPACK routine PDA_RFFTB
- PDA_NFFTB - Backward FFT of N-dimensional complex array
- PDA_NFFTF - Forward FFT of N-dimensional complex array
- PDA_NSCOR - Calculates the approximate expected values of normal order statistics.
- PDA_PPND16 - Returns the normal deviate corresponding to a given lower tail area of P
- PDA_QSAx - Sort an array into ascending order
- PDA_QSDx - Sort an array into descending order
- PDA_QSIAx - Sort an array of pointers to access an array in ascending order
- PDA_QSIDx - Sort an array of pointers to access an array in descending order
- PDA_R2NAG - Convert FFTPACK Hermitian Fourier transform array into equivalent NAG array
- PDA_RAND - Returns pseudo-random numbers in the range 0 to 1
- PDA_RFFTB - Backward transform of a real coefficient array.
- PDA_RFFTF - Forward transform of a real periodic sequence.
- PDA_RFFTI - Initialize PDA_RFFTF and PDA_RFFTB.
- PDA_RINP[x] - Reorder an array in place using a permutation index
- PDA_RNEXP - Returns pseudo-random numbers from an exponential distribution
- PDA_RNGAM - Returns pseudo-random numbers from a gamma distribution
- PDA_RNNOR - Returns pseudo-random numbers from a Gaussian distribution
- PDA_RNPOI - Returns pseudo-random numbers from a Poisson distribution
- PDA_RNSED - Sets the seed for the PDA random-number generators
- PDA_SA - Continuous simulated annealing global optimisation algorithm. Simple constraints can be specified.
- PDA_SAAC[x] - Sorts the columns of a two dimensional array into ascending order
- PDA_SAAR[x] - Sorts the rows of a two dimensional array into ascending order
- PDA_SPLDER - Evaluate derivative of spline, given in its B-spline representation from PDA_CURFIT.
- PDA_SPLEV - Evaluate spline, given in its B-spline representation from PDA_CURFIT.
- PDA_SPLINT - Calculate integral of spline, given its normalised B-spline representation from PDA_CURFIT.
- PDA_SUBPLX - Subspace-searching simplex method for unconstrained optimization
- PDA_SUMSL - Unconstrained minimisation of a smooth non-linear function of n variables, function and gradients supplied.
- PDA_SURFIT - Find a bivariate spline approximation to irregularly spaced 2-D data.
- PDA_UNCMND - Minimise smooth non-linear function of n variables, function values only.
- PDA_V11 - Calculates an approximation to the variance of the largest normal order statistic
- PDA_XERMSG - Process error messages for SLATEC and other libraries

- Adding further routines
- Changes

- About this document ...

Starlink User Note 194

H. Meyerdierks, D. Berry, P. W. Draper, G. Privett, M. Currie

12th October 2005

E-mail:starlink@jiscmail.ac.uk

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