lass::num::impl Namespace Reference

Data Structures
struct	IntPow
struct	IntDiv
struct	IntMod
struct	RangePolicy< rtClosed >
struct	RangePolicy< rtLeftOpen >
struct	RangePolicy< rtRightOpen >
struct	RangePolicy< rtOpen >
struct	Revertor
struct	Revertor< 0 >
struct	Revertor< 1 >
struct	Revertor< 2 >
struct	Revertor< 4 >
struct	EndianCaster
struct	EndianCaster< numOfBytes, endian, endian >
class	MStorage
class	MScalar
struct	MatrixExpressionTraits
struct	MatrixExpressionTraits< MScalar< T > >
class	MProd
class	MTrans
class	MFun
class	MVColumn
class	MVDiag
class	MVRightProd
class	VStorage
class	VScalar
struct	VectorExpressionTraits
struct	VectorExpressionTraits< VScalar< T > >
class	VFun
struct	Dummy
Functions
	LASS_META_ASSERT (lass::bitsPerByte==8, one_byte_is_not_8_bits)
	LASS_META_ASSERT (sizeof(lass::num::Tint8)*lass::bitsPerByte==8, Tint8_must_be_8_bits_)
	LASS_META_ASSERT (sizeof(lass::num::Tuint8)*lass::bitsPerByte==8, Tuint8_must_be_8_bits)
	LASS_META_ASSERT (sizeof(lass::num::Tint16)*lass::bitsPerByte==16, Tint16_must_be_16_bits)
	LASS_META_ASSERT (sizeof(lass::num::Tuint16)*lass::bitsPerByte==16, Tuint16_must_be_16_bits)
	LASS_META_ASSERT (sizeof(lass::num::Tint32)*lass::bitsPerByte==32, Tint32_must_be_32_bits)
	LASS_META_ASSERT (sizeof(lass::num::Tuint32)*lass::bitsPerByte==32, Tuint32_must_be_32_bits)
	LASS_META_ASSERT (sizeof(lass::num::Tint64)*lass::bitsPerByte==64, Tint64_must_be_64_bits)
	LASS_META_ASSERT (sizeof(lass::num::Tuint64)*lass::bitsPerByte==64, Tuint64_must_be_64_bits)
	LASS_META_ASSERT (sizeof(lass::num::Tfloat32)*lass::bitsPerByte==32, Tfloat32_must_be_32_bits)
	LASS_META_ASSERT (sizeof(lass::num::Tfloat64)*lass::bitsPerByte==64, Tfloat64_must_be_64_bits)
	LASS_META_ASSERT (sizeof(lass::num::TintPtr)==sizeof(void *), TintPtr_must_be_size_of_pointer)
	LASS_META_ASSERT (sizeof(lass::num::TuintPtr)==sizeof(void *), TuintPtr_must_be_size_of_pointer)
template<typename T , typename ForwardIterator >
num::Polynomial< T >	laplaceToZHelper (ForwardIterator first, ForwardIterator last, const T &samplingFrequency)
template<typename T , typename ForwardIterator1 , typename ForwardIterator2 >
std::pair< std::vector< T > , std::vector< T > >	laplaceToZ (ForwardIterator1 numeratorFirst, ForwardIterator1 numeratorLast, ForwardIterator2 denominatorFirst, ForwardIterator2 denominatorLast, const T &samplingFrequency)
template<typename T >
std::pair< std::vector< T > , std::vector< T > >	laplaceButterworthLowPass (unsigned n, const T &cutoff, const T &gain)
template<typename T >
std::pair< std::vector< T > , std::vector< T > >	laplaceButterworthHighPass (unsigned n, const T &cutoff, const T &gain)
	LASS_NUM_MATRIX_BINARY_EXPRESSION (Add,+)
	LASS_NUM_MATRIX_BINARY_EXPRESSION (Sub,-)
	LASS_NUM_MATRIX_BINARY_EXPRESSION (Mul,*)
	LASS_NUM_MATRIX_UNARY_EXPRESSION (Neg,-)
	LASS_NUM_MATRIX_UNARY_EXPRESSION (Rec,::lass::num::NumTraits< T >::one/)
template<typename T , typename RandomIterator1 , typename RandomIterator2 >
bool	ludecomp (RandomIterator1 ioMatrix, RandomIterator2 oIndex, size_t iSize, int &iD)
	Given a complex matrix iA, this routine replaces it by the LU decomposition of a rowwise permutation of itself.
template<typename T , typename RandomIterator1 , typename RandomIterator2 , typename RandomIterator3 >
void	lusolve (RandomIterator1 iMatrix, RandomIterator2 iIndex, RandomIterator3 ioColumn, size_t iSize)
	Solves the set of linear eqautions A X = B.
template<typename T , typename RandomIterator1 , typename RandomIterator2 , typename RandomIterator3 , typename RandomIterator4 , typename RandomIterator5 >
void	lumprove (RandomIterator1 iMatrix, RandomIterator2 iMatrixLU, RandomIterator3 iIndex, RandomIterator4 iColumn, RandomIterator5 ioX, size_t iSize)
	Improves a solution vector X of the linear set of equations A X = B.
template<typename T , typename RandomIterator1 , typename RandomIterator2 >
bool	cramer2 (RandomIterator1 iMatrixRowMajor, RandomIterator2 ioColumnFirst, RandomIterator2 ioColumnLast)
	Solve A X = B for 2x2 matrices with Cramer's rule.
template<typename T , typename RandomIterator1 , typename RandomIterator2 >
bool	cramer3 (RandomIterator1 iMatrixRowMajor, RandomIterator2 ioColumnFirst, RandomIterator2 ioColumnLast)
	Solve A X = B for 3x3 matrices with Cramer's rule.
template<typename T , typename RandomIterator1 , typename RandomIterator2 , typename RandomIterator3 >
bool	solveTridiagonal (RandomIterator1 iA, RandomIterator1 iB, RandomIterator1 iC, RandomIterator2 ioSolution, RandomIterator3 ioTemp, std::size_t iSize)
	Solve system of linear equations with a tridiagonal matrix.
	LASS_NUM_VECTOR_BINARY_EXPRESSION (Add,+)
	LASS_NUM_VECTOR_BINARY_EXPRESSION (Sub,-)
	LASS_NUM_VECTOR_BINARY_EXPRESSION (Mul,*)
	LASS_NUM_VECTOR_BINARY_EXPRESSION (Div,/)
	LASS_NUM_VECTOR_UNARY_EXPRESSION (Neg,-)
	LASS_NUM_VECTOR_UNARY_EXPRESSION (Rec,::lass::num::NumTraits< T >::one/)
template<typename C >
C	numMin4 (const C &k1, const C &k2, const C &k3, const C &k4)
template<typename C >
C	numMax4 (const C &k1, const C &k2, const C &k3, const C &k4)
template<typename C >
__inline void	numMinMax (const C &k1, const C &k2, C &amin, C &amax)
template<typename C >
__inline void	numMin (const C &k1, const C &k2, C &amin)
template<typename C >
void	numMax (const C &k1, const C &k2, C &amax)

---

Function Documentation

lass::num::impl::LASS_META_ASSERT	(	lass::bitsPerByte	= =8,
		one_byte_is_not_8_bits
	)

lass::num::impl::LASS_META_ASSERT	(	sizeof(lass::num::Tint8)*lass::bitsPerByte	= =8,
		Tint8_must_be_8_bits_
	)

lass::num::impl::LASS_META_ASSERT	(	sizeof(lass::num::Tuint8)*lass::bitsPerByte	= =8,
		Tuint8_must_be_8_bits
	)

lass::num::impl::LASS_META_ASSERT	(	sizeof(lass::num::Tint16)*lass::bitsPerByte	= =16,
		Tint16_must_be_16_bits
	)

lass::num::impl::LASS_META_ASSERT	(	sizeof(lass::num::Tuint16)*lass::bitsPerByte	= =16,
		Tuint16_must_be_16_bits
	)

lass::num::impl::LASS_META_ASSERT	(	sizeof(lass::num::Tint32)*lass::bitsPerByte	= =32,
		Tint32_must_be_32_bits
	)

lass::num::impl::LASS_META_ASSERT	(	sizeof(lass::num::Tuint32)*lass::bitsPerByte	= =32,
		Tuint32_must_be_32_bits
	)

lass::num::impl::LASS_META_ASSERT	(	sizeof(lass::num::Tint64)*lass::bitsPerByte	= =64,
		Tint64_must_be_64_bits
	)

lass::num::impl::LASS_META_ASSERT	(	sizeof(lass::num::Tuint64)*lass::bitsPerByte	= =64,
		Tuint64_must_be_64_bits
	)

lass::num::impl::LASS_META_ASSERT	(	sizeof(lass::num::Tfloat32)*lass::bitsPerByte	= =32,
		Tfloat32_must_be_32_bits
	)

lass::num::impl::LASS_META_ASSERT	(	sizeof(lass::num::Tfloat64)*lass::bitsPerByte	= =64,
		Tfloat64_must_be_64_bits
	)

lass::num::impl::LASS_META_ASSERT	(	sizeof(lass::num::TintPtr)	= =sizeof(void *),
		TintPtr_must_be_size_of_pointer
	)

lass::num::impl::LASS_META_ASSERT	(	sizeof(lass::num::TuintPtr)	= =sizeof(void *),
		TuintPtr_must_be_size_of_pointer
	)

template<typename T , typename ForwardIterator >

num::Polynomial<T> lass::num::impl::laplaceToZHelper	(	ForwardIterator	first,
		ForwardIterator	last,
		const T &	samplingFrequency
	)			[inline]

Definition at line 41 of file filters.inl.

References lass::prim::distance(), and lass::stde::T.

Referenced by laplaceToZ().

template<typename T , typename ForwardIterator1 , typename ForwardIterator2 >

std::pair< std::vector<T>, std::vector<T> > lass::num::impl::laplaceToZ	(	ForwardIterator1	numeratorFirst,
		ForwardIterator1	numeratorLast,
		ForwardIterator2	denominatorFirst,
		ForwardIterator2	denominatorLast,
		const T &	samplingFrequency
	)			[inline]

Definition at line 64 of file filters.inl.

References laplaceToZHelper().

Referenced by lass::num::IirFilter< T, InputIterator, OutputIterator >::doMakeLaplace().

template<typename T >

std::pair< std::vector<T>, std::vector<T> > lass::num::impl::laplaceButterworthLowPass	(	unsigned	n,
		const T &	cutoff,
		const T &	gain
	)			[inline]

Definition at line 89 of file filters.inl.

References lass::num::cos(), and lass::stde::T.

Referenced by lass::num::IirFilter< T, InputIterator, OutputIterator >::makeButterworthLowPass().

template<typename T >

std::pair< std::vector<T>, std::vector<T> > lass::num::impl::laplaceButterworthHighPass	(	unsigned	n,
		const T &	cutoff,
		const T &	gain
	)			[inline]

Definition at line 111 of file filters.inl.

References lass::num::pow(), and lass::stde::T.

Referenced by lass::num::IirFilter< T, InputIterator, OutputIterator >::makeButterworthHighPass().

lass::num::impl::LASS_NUM_MATRIX_BINARY_EXPRESSION	(	Add	,
		+
	)

lass::num::impl::LASS_NUM_MATRIX_BINARY_EXPRESSION	(	Sub	,
		-
	)

lass::num::impl::LASS_NUM_MATRIX_BINARY_EXPRESSION	(	Mul	,
		*
	)

lass::num::impl::LASS_NUM_MATRIX_UNARY_EXPRESSION	(	Neg	,
		-
	)

lass::num::impl::LASS_NUM_MATRIX_UNARY_EXPRESSION	(	Rec	,
		::lass::num::NumTraits< T >::one/
	)

template<typename T , typename RandomIterator1 , typename RandomIterator2 >

bool lass::num::impl::ludecomp	(	RandomIterator1	ioMatrix,
		RandomIterator2	oIndex,
		size_t	iSize,
		int &	iD
	)			[inline]

Given a complex matrix iA, this routine replaces it by the LU decomposition of a rowwise permutation of itself.

Parameters:

	ioMatrix	[in,out] Random iterator to first element of of a square matrix in row major order. ioMatrix is replaced by its LU decomposition. [ioMatrix, ioMatrix + iSize * iSize) must be a valid range
	oIndex	[out] records the row permutations effected by the partial pivoting. [oIndex, oIndex + iSize) must be a valid range.
	iSize	[in] size of matrix
	oD	[out] indicates the number of row interchanges was even (+1) or odd (-1).

Returns:

- true: LU decomposition completed

• false: matrix ioMatrix is singular

This routine is used in combination with lusolve() to solve linear equations and lumprove() to improve the solution.

Method: Crout's algorithm with partial pivoting.

Definition at line 85 of file matrix_solve.inl.

References lass::num::conj(), LASS_ASSERT, lass::num::norm(), std::swap(), and lass::stde::T.

Referenced by lass::num::Matrix< T, S >::invert().

template<typename T , typename RandomIterator1 , typename RandomIterator2 , typename RandomIterator3 >

void lass::num::impl::lusolve	(	RandomIterator1	iMatrix,
		RandomIterator2	iIndex,
		RandomIterator3	ioColumn,
		size_t	iSize
	)			[inline]

Solves the set of linear eqautions A X = B.

Definition at line 222 of file matrix_solve.inl.

References lass::stde::T.

Referenced by lass::num::Matrix< T, S >::invert(), and lumprove().

template<typename T , typename RandomIterator1 , typename RandomIterator2 , typename RandomIterator3 , typename RandomIterator4 , typename RandomIterator5 >

void lass::num::impl::lumprove	(	RandomIterator1	iMatrix,
		RandomIterator2	iMatrixLU,
		RandomIterator3	iIndex,
		RandomIterator4	iColumn,
		RandomIterator5	ioX,
		size_t	iSize
	)			[inline]

Improves a solution vector X of the linear set of equations A X = B.

Definition at line 297 of file matrix_solve.inl.

References lusolve().

template<typename T , typename RandomIterator1 , typename RandomIterator2 >

bool lass::num::impl::cramer2	(	RandomIterator1	iMatrixRowMajor,
		RandomIterator2	ioColumnFirst,
		RandomIterator2	ioColumnLast
	)			[inline]

Solve A X = B for 2x2 matrices with Cramer's rule.

Parameters:

	iMatrix	[in] Random iterator to first element of matrix A in row major order. A must be of size 2x2. [iMatrix, iMatrix + 4) must be a valid range
	ioColumn	[in,out] Random iterator to first element of B as input Random iterator to first element of X as output [iColumn, iColumn + 2) must be a valid range

Definition at line 344 of file matrix_solve.inl.

References lass::num::inv(), LASS_ASSERT, and lass::stde::T.

template<typename T , typename RandomIterator1 , typename RandomIterator2 >

bool lass::num::impl::cramer3	(	RandomIterator1	iMatrixRowMajor,
		RandomIterator2	ioColumnFirst,
		RandomIterator2	ioColumnLast
	)			[inline]

Solve A X = B for 3x3 matrices with Cramer's rule.

Definition at line 390 of file matrix_solve.inl.

References lass::num::inv(), LASS_ASSERT, and lass::stde::T.

template<typename T , typename RandomIterator1 , typename RandomIterator2 , typename RandomIterator3 >

bool lass::num::impl::solveTridiagonal	(	RandomIterator1	iA_1,
		RandomIterator1	iB_0,
		RandomIterator1	iC_0,
		RandomIterator2	ioSolution,
		RandomIterator3	ioTemp,
		std::size_t	iSize
	)			[inline]

Solve system of linear equations with a tridiagonal matrix.

Definition at line 460 of file matrix_solve.inl.

References lass::stde::T.

lass::num::impl::LASS_NUM_VECTOR_BINARY_EXPRESSION	(	Add	,
		+
	)

lass::num::impl::LASS_NUM_VECTOR_BINARY_EXPRESSION	(	Sub	,
		-
	)

lass::num::impl::LASS_NUM_VECTOR_BINARY_EXPRESSION	(	Mul	,
		*
	)

lass::num::impl::LASS_NUM_VECTOR_BINARY_EXPRESSION	(	Div	,
		/
	)

lass::num::impl::LASS_NUM_VECTOR_UNARY_EXPRESSION	(	Neg	,
		-
	)

lass::num::impl::LASS_NUM_VECTOR_UNARY_EXPRESSION	(	Rec	,
		::lass::num::NumTraits< T >::one/
	)

template<typename C >

C lass::num::impl::numMin4	(	const C &	k1,
		const C &	k2,
		const C &	k3,
		const C &	k4
	)			[inline]

Definition at line 498 of file interval.h.

template<typename C >

C lass::num::impl::numMax4	(	const C &	k1,
		const C &	k2,
		const C &	k3,
		const C &	k4
	)			[inline]

Definition at line 512 of file interval.h.

template<typename C >

__inline void lass::num::impl::numMinMax	(	const C &	k1,
		const C &	k2,
		C &	amin,
		C &	amax
	)			[inline]

Definition at line 526 of file interval.h.

template<typename C >

__inline void lass::num::impl::numMin	(	const C &	k1,
		const C &	k2,
		C &	amin
	)			[inline]

Definition at line 540 of file interval.h.

template<typename C >

void lass::num::impl::numMax	(	const C &	k1,
		const C &	k2,
		C &	amax
	)			[inline]

Definition at line 548 of file interval.h.