Mathematics_module [scimath package (libcasa_scimath)]

Mathematical types, constants, operations. More...

Classes
class	casa::AutoDiff< T >
	Class that computes partial derivatives by automatic differentiation. More...
class	casa::AutoDiffA< T >
	Class that computes partial derivatives by automatic differentiation. More...
struct	casa::AutoDiffIO_global_functions_AutoDiff_IO_operations
	Implements all IO operators and functions for AutoDiff. More...
struct	casa::AutoDiffMath_global_functions_AutoDiff_mathematical_operations
	Implements all mathematical operators and functions for AutoDiff. More...
class	casa::AutoDiffX< T >
	Class that computes partial derivatives by automatic differentiation. More...
class	casa::ConvolveGridder< Domain, Range >
	Does convolutional gridding. More...
class	casa::Convolver< FType >
	A class for doing multi-dimensional convolution. More...
class	casa::DFTError
	Error class for DFTServer class. More...
class	casa::DFTServer< T >
	Class containing methods for doing n-D slow Fourier transforms. More...
class	casa::FFTPack
	C++ interface to the Fortran FFTPACK library. More...
class	casa::FFTEnums
	Lists the different types of FFT's that can be done. More...
class	casa::FFTServer< T, S >
	A class with methods for Fast Fourier Transforms. More...
class	casa::FFTW
	C++ interface to the FFTWw library. More...
class	casa::Gridder< Domain, Range >
	A base class for gridding. More...
class	casa::HistAcc< T >
	Makes a histogram from input values. More...
class	casa::Interpolate2D
	A two dimension interpolator for Matrices or Arrays. More...
class	casa::InterpolateArray1D< Domain, Range >
	Interpolate in one dimension. More...
class	casa::MathFuncError
	Error class for MathFunc class. More...
struct	casa::MathFunc_global_functions_spheriodal_functions
	Fred Schwab function to calculate spheriodal functions. More...
struct	casa::MathFunc_global_functions_FUNCTYPE_enum
	Enum used to identify function type for MathFunc class. More...
struct	casa::FuncId
	Function ID, for use by MathFunc class. More...
class	casa::MathFunc< T >
	A class to generate values of mathematical functions. More...
class	casa::Unary< T >
	Unary. More...
class	casa::GaussianConv< T >
	Gaussian. More...
class	casa::KB_Conv< T >
	A Kaiser-Bessel function. More...
class	casa::Mod_KB_Conv< T >
	A Kaiser-Bessel function multiplied by a Gaussian. More...
class	casa::Sinc_Conv< T >
	Sine x / x function. More...
class	casa::Sph_Conv< T >
	Spheroidal function. More...
class	casa::ExpSincConv< T >
	Exponential times a Sinc. More...
struct	casa::MatrixMathLA_global_functions_Linear_Algebra
	Linear algebra functions on Vectors and Matrices. More...
class	casa::MedianSlider
	Class to compute sliding median. More...
class	casa::NNGridder< Domain, Range >
	A non-negative gridding class. More...
class	casa::NumericTraits< T >
	Relationships between numeric data types. More...
class	casa::NumericTraits_F< Float >
	NumericTraits specialization for Float. More...
class	casa::NumericTraits_D< Double >
	NumericTraits specialization for Double. More...
class	casa::NumericTraits_C< Complex >
	NumericTraits specialization for Complex. More...
class	casa::NumericTraits_DC< DComplex >
	NumericTraits specialization for DComplex. More...
class	casa::NumericTraits< Float >
	A specialisation for T=Float of the NumericTraits class. More...
class	casa::NumericTraits< Double >
	A specialisation for T=Double of the NumericTraits class. More...
class	casa::NumericTraits< Complex >
	A specialisation for T=Complex of the NumericTraits class. More...
class	casa::RigidVector< T, n >
	Fast Vector classes with fixed (templated) length. More...
struct	casa::RigidVector_global_functions_math
	Mathematical operations involving RigidVectors. More...
class	casa::SCSL
	C++ Interface to the Sgi/Cray Scientific Library (SCSL). More...
class	casa::SparseDiff< T >
	Class that computes partial derivatives by automatic differentiation. More...
class	casa::SparseDiffA< T >
	Class that computes partial derivatives by automatic differentiation. More...
struct	casa::SparseDiffIO_global_functions_SparseDiff_IO_operations
	Implements all IO operators and functions for SparseDiff. More...
struct	casa::SparseDiffMath_global_functions_SparseDiff_mathematical_operations
	Implements all mathematical operators and functions for SparseDiff. More...
class	casa::SparseDiffX< T >
	Class that computes partial derivatives by automatic differentiation. More...
class	casa::SquareMatrix< T, n >
	Fast Square Matrix class with fixed (templated) size. More...
struct	casa::SquareMatrix_global_functions_SqM_global_functions
	Various global math and IO functions. More...
class	casa::StatAcc< T >
	A statistics accumulator. More...
class	casa::VanVleck
	A class of static functions to aid with vanVleck corrections of lag data. More...
class	casa::VectorKernel
	Make a Vector smoothing kernel from a kernel specification. More...
Modules
	Mathematics_module_internal_classes
	Internal Mathematics_module classes and functions.

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Detailed Description

Mathematical types, constants, operations.

See below for an overview of the classes in this module.

Prerequisite

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

Review Status

Reviewed By:

UNKNOWN

Date Reviewed:

before2004/08/25

Etymology

Mathematicians may argue that everything is mathematics, and hence all of AIPS++ should be in this module. However this module will only contain core mathematical operations that are independent of astronomical applications.

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 (see (file="ArrayMath.h"))ArrayMath global functions (part of the Arrays module). Mathematical operations on Lattices are found in the Lattices module. A wide variety of special Mathematical functions is planned for the Functionals module.

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

• A wrapper around the system math.h functions called (see (file="Math.h"))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.
• (see (file=NumericTraits.h))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.
• (see (file="Random.h"))Random numbers in a wide variety of distributions.
• Interpolation in one dimension is performed by the Interpolate1D class in the Functionals module