Module Mathematics

Description (classes)

Prerequisite

At least high school (and preferably undergraduate level) understanding of mathematics.

Etymology

Synopsis

The Mathematics module has a variety of mathematical classes and functions. Not all numerical operations are found herein. Very complicated operations might be in their own module, such as Deconvolution. Many whole array operations are in the ArrayMath global functions (part of the Arrays module). Mathematical operations on Lattices are found in the Lattice module. A wide variety of special Mathematical functions is planned for the Functional module.

The classes presently in this module fall into the following categories:

• A wrapper around the system math.h functions called Math.h. This contains generic mathematical functions. It is required that you always include this file rather than the system math.h file as deficiencies in the system math.h file will be implemented here.
• Complex numbers. It is expected that we will, in a future release of AIPS++, replace this with the complex number classes in the standard template library.
• Mathematical & numerical constants like pi & FLT_MAX. Physical constants have units and hence are available in the QC class in the Quanta module.
• Relationships between different numerical data types.
• Multi-dimensional Fourier transforms are done in the FFTServer class. This decomposes the transforms into a one-dimensional transforms which are done using the functions in the FFTPack class. The FFTPack class also contains functions for doing one-dimensional sine, cosine, and real-symmetric transforms.
• Numerical Convolution (both linear and circular) of multi-dimensional Arrays.
• Random numbers in a wide variety of distributions.
• Prime numbers
• Interpolation in one dimension is performed by the Interpolate1D class in the Functionals module

Classes

ACG -- Additive number generator (full description)

AutoDiff IO operations -- Implements all IO operators and functions for AutoDiff. (full description)

AutoDiff mathematical operations -- Implements all mathematical operators and functions for AutoDiff. (full description)

AutoDiff -- Class that computes partial derivatives by automatic differentiation. (full description)

AutoDiffA -- Class that computes partial derivatives by automatic differentiation. (full description)

AutoDiffRep -- Representation of an automatic differential class data (full description)

AutoDiffX -- Class that computes partial derivatives by automatic differentiation. (full description)

Binomial -- Binomial distribution (full description)

Complex NaN -- Single and double precision complex numbers (full description)

Complex comparisons -- Complex comparisons (full description)

ConvolveGridder -- Does convolutional gridding (full description)

Convolver -- A class for doing multi-dimensional convolution (full description)

DComplex NaN -- Double precision complex numbers (full description)

DComplex comparisons -- DComplex comparisons (full description)

DFTError -- Error class for DFTServer class (full description)

DFTServer -- Class containing methods for doing n-D slow Fourier transforms (full description)

DiscreteUniform -- Discrete uniform distribution (full description)

Dummy_Constants_class -- Mathematical and numerical constants. (full description)

Erlang -- Erlang distribution (full description)

ExpSincConv -- Exponential times a Sinc (full description)

FFTEnums -- Lists the different types of FFT's that can be done (full description)

FFTPack -- C++ interface to the Fortran FFTPACK library (full description)

FFTServer -- A class with methods for Fast Fourier Transforms (full description)

FUNCTYPE enum -- Enum used to identify function type for MathFunc class (full description)

FuncId -- Function ID, for use by MathFunc class (full description)

GaussianConv -- Gaussian (full description)

Geometric -- Discrete geometric distribution (full description)

Gridder -- A base class for gridding (full description)

HistAcc -- Makes a histogram from input values. (full description)

HyperGeometric -- Hypergeometric distribution (full description)

IComplex -- Integer complex numbers. (full description)

Interpolate2D -- A two dimension interpolator for Matrices or Arrays (full description)

InterpolateArray1D -- Interpolate in one dimension (full description)

KB_Conv -- A Kaiser-Bessel function (full description)

LogNormal -- Logarithmic normal distribution (full description)

MLCG -- Multiplicative linear congruential generator (full description)

Math.h interface for AIPS++ -- AIPS++ interface to math.h and other scalar math functions (full description)

MathFunc -- A class to generate values of mathematical functions (full description)

MathFuncError -- Error class for MathFunc class (full description)

MedianSlider -- Class to compute sliding median (full description)

Mod_KB_Conv -- A Kaiser-Bessel function multiplied by a Gaussian (full description)

NNGridder -- A non-negative gridding class (full description)

NegativeExpntl -- Negative exponential distribution (full description)

Normal -- Normal or Gaussian distribution (full description)

NumericTraits -- Relationships between numeric data types (full description)

NumericTraits -- A specialisation for T=DComplex of the NumericTraits class (full description)

NumericTraits_C -- NumericTraits specialization for Complex (full description)

NumericTraits_D -- NumericTraits specialization for Double (full description)

NumericTraits_DC -- NumericTraits specialization for DComplex (full description)

NumericTraits_F -- NumericTraits specialization for Float (full description)

Poisson -- Poisson distribution (full description)

Primes -- Creates a reference table of prime numbers, and some functions (full description)

RNG -- Base class for random number generators (full description)

Random -- Base class for random number distributions (full description)

SCSL -- C++ Interface to the Sgi/Cray Scientific Library (SCSL) (full description)

Scalar conversion -- Templated functions to convert scalars from one type to another. (full description)

Sinc_Conv -- Sine x / x function (full description)

Sph_Conv -- Spheroidal function (full description)

StatAcc -- A statistics accumulator (full description)

Unary -- Unary (full description)

Uniform -- Uniform distribution (full description)

VanVleck -- A class of static functions to aid with vanVleck corrections of lag data. (full description)

VectorKernel -- Make a Vector smoothing kernel from a kernel specification (full description)

Weibull -- Weibull distribution (full description)

declare -- Forward declaration complex classes (full description)

erf -- Error function (full description)

fftserver -- The C++ side of the glish fftserver tool. (full description)

fmod -- fmod (full description)

interpolate1d -- The C++ side of the glish interpolate1d tool. (full description)

inverse -- Inverse trigonometry (full description)

math -- Additional complex mathematical functions (full description)

maxmin -- Max and min, floor and ceil functions (full description)

near -- The near functions (full description)

polyfitter -- The C++ side of the glish polyfitter tool. (full description)

randomnumbers -- The C++ side of the glish randomnumbers tool. (full description)

sinusoidfitter -- The C++ side of the glish sinusoidfitter tool. (full description)

spheriodal functions -- Fred Schwab function to calculate spheriodal functions (full description)