Mathematics_module

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Modules
	Mathematics_module_internal_classes
	Internal Mathematics_module classes and functions.

Classes
class	casacore::AutoDiff< T >
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class	casacore::AutoDiffA< T >
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struct	casacore::AutoDiffIO_global_functions_AutoDiff_IO_operations
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struct	casacore::AutoDiffMath_global_functions_AutoDiff_mathematical_operations
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class	casacore::AutoDiffX< T >
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class	casacore::Combinatorics
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class	casacore::ConvolveGridder< Domain, Range >
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class	casacore::Convolver< FType >
	Forward Declarations. More...
class	casacore::DFTError
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class	casacore::DFTServer< T >
	Class containing methods for doing n-D slow Fourier transforms. More...
class	casacore::FFTPack
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class	casacore::FFTEnums
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class	casacore::FFTServer< T, S >
	A class with methods for Fast Fourier Transforms. More...
class	casacore::FFTW
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class	casacore::GaussianBeam
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class	casacore::Geometry
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class	casacore::Gridder< Domain, Range >
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class	casacore::HistAcc< T >
	Makes a histogram from input values. More...
class	casacore::Interpolate2D
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class	casacore::InterpolateArray1D< Domain, Range >
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class	casacore::MathFuncError
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struct	casacore::MathFunc_global_functions_spheriodal_functions
	Fred Schwab function to calculate spheriodal functions. More...
struct	casacore::MathFunc_global_functions_FUNCTYPE_enum
	Enum used to identify function type for MathFunc class. More...
struct	casacore::FuncId
	Function ID, for use by MathFunc class. More...
class	casacore::MathFunc< T >
	A class to generate values of mathematical functions. More...
class	casacore::Unary< T >
	Unary. More...
class	casacore::GaussianConv< T >
	Gaussian. More...
class	casacore::KB_Conv< T >
	A Kaiser-Bessel function. More...
class	casacore::Mod_KB_Conv< T >
	A Kaiser-Bessel function multiplied by a Gaussian. More...
class	casacore::Sinc_Conv< T >
	Sine x / x function. More...
class	casacore::Sph_Conv< T >
	Spheroidal function. More...
class	casacore::ExpSincConv< T >
	Exponential times a Sinc. More...
struct	casacore::MatrixMathLA_global_functions_Linear_Algebra
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class	casacore::MedianSlider
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class	casacore::NNGridder< Domain, Range >
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class	casacore::NumericTraits< T >
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class	casacore::NumericTraits_F< Float >
	NumericTraits specialization for Float. More...
class	casacore::NumericTraits_D< Double >
	NumericTraits specialization for Double. More...
class	casacore::NumericTraits_C< Complex >
	NumericTraits specialization for Complex. More...
class	casacore::NumericTraits_DC< DComplex >
	NumericTraits specialization for DComplex. More...
class	casacore::NumericTraits< Float >
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class	casacore::NumericTraits< Double >
	A specialisation for T=Double of the NumericTraits class. More...
class	casacore::NumericTraits< Complex >
	A specialisation for T=Complex of the NumericTraits class. More...
class	casacore::RigidVector< T, n >
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struct	casacore::RigidVector_global_functions_math
	Mathematical operations involving RigidVectors More...
class	casacore::SCSL
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class	casacore::Smooth< T >
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class	casacore::SparseDiff< T >
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class	casacore::SparseDiffA< T >
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struct	casacore::SparseDiffIO_global_functions_SparseDiff_IO_operations
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struct	casacore::SparseDiffMath_global_functions_SparseDiff_mathematical_operations
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class	casacore::SparseDiffX< T >
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class	casacore::SquareMatrix< T, n >
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struct	casacore::SquareMatrix_global_functions_SqM_global_functions
	Various global math and IO functions. More...
class	casacore::StatAcc< T >
	A statistics accumulator More...
class	casacore::VanVleck
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class	casacore::VectorKernel
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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 Casacore 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.
• 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