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

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)

ConvolveGridder -- Does convolutional gridding (full description)

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

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

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

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

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

Linear Algebra -- Linear algebra functions on Vectors and Matrices. (full description)

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

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

MatrixSolver -- MatrixSolver.h: the base class for solvers of linear equations AX=B (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)

NNLSMatrixSolver -- NNLSMatrixSolver.h: the base class for NNLS solvers of linear equations AX=B (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)

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

RigidVector -- Fast Vector classes with fixed (templated) length (full description)

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

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

Sph_Conv -- Spheroidal function (full description)

SqM_global_functions -- Various global math and IO functions. (full description)

SquareMatrix -- Fast Square Matrix class with fixed (templated) size (full description)

StatAcc -- A statistics accumulator (full description)

Unary -- Unary (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)

math -- Mathematical operations involving RigidVectors (full description)

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