Next: Introduction
PDA
Public Domain Algorithms
Version 0.5
Programmer's Manual
Starlink User Note 194.3
H. Meyerdierks, D. Berry, P. W. Draper, G. Privett, M. Currie
12th October 2005
Retrieve hardcopy
Contents
- 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)
- One-dimensional
Interpolation and Fitting, Splines
- Two-dimensional
Interpolation and Fitting
- Minimisation
- Matrices
- Sorting
- Normal Distribution
- Bessel Functions
- Simple Statistics
- Pseudo-Random Numbers
- 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 ...
Next: Introduction
PDA [1ex
Starlink User Note 194
H. Meyerdierks, D. Berry, P. W. Draper, G. Privett, M. Currie
12th October 2005
E-mail:starlink@jiscmail.ac.uk
Copyright © 2013 Science and Technology Facilities Council
![\includegraphics[width=2.0in]{sun194_1.eps}](img1.png)