Namespaces
namespace	detail

Data Structures
class	SVD

Functions
template<typename dtype >
NdArray< double >	cholesky (const NdArray< dtype > &inMatrix)

template<typename dtype >
auto	det (const NdArray< dtype > &inArray)

template<typename dtype , typename... Params, std::enable_if_t< std::is_arithmetic_v< dtype >, int > = 0, std::enable_if_t< all_arithmetic_v< Params... >, int > = 0, std::enable_if_t< all_same_v< dtype, Params... >, int > = 0>
std::pair< NdArray< double >, double >	gaussNewtonNlls (const uint32 numIterations, const NdArray< dtype > &coordinates, const NdArray< dtype > &measurements, const std::function< dtype(const NdArray< dtype > &, const NdArray< dtype > &)> &function, const std::array< std::function< dtype(const NdArray< dtype > &, const NdArray< dtype > &)>, sizeof...(Params)> &derivatives, Params... initialGuess)

template<typename dtype >
NdArray< dtype >	hat (const NdArray< dtype > &inVec)

NdArray< double >	hat (const Vec3 &inVec)

template<typename dtype >
NdArray< dtype >	hat (dtype inX, dtype inY, dtype inZ)

template<typename dtype >
NdArray< double >	inv (const NdArray< dtype > &inArray)

template<typename dtype >
NdArray< double >	lstsq (const NdArray< dtype > &inA, const NdArray< dtype > &inB, double inTolerance=1e-12)

template<typename dtype >
std::pair< NdArray< double >, NdArray< double > >	lu_decomposition (const NdArray< dtype > &inMatrix)

template<typename dtype >
NdArray< double >	matrix_power (const NdArray< dtype > &inArray, int16 inPower)

template<typename dtype >
NdArray< dtype >	multi_dot (const std::initializer_list< NdArray< dtype > > &inList)

template<typename dtype >
NdArray< double >	pinv (const NdArray< dtype > &inArray)

template<typename dtype >
std::tuple< NdArray< double >, NdArray< double >, NdArray< double > >	pivotLU_decomposition (const NdArray< dtype > &inMatrix)

template<typename dtype >
NdArray< double >	solve (const NdArray< dtype > &inA, const NdArray< dtype > &inB)

template<typename dtype >
void	svd (const NdArray< dtype > &inArray, NdArray< double > &outU, NdArray< double > &outS, NdArray< double > &outVt)

Function Documentation

◆ cholesky()

template<typename dtype >

NdArray< double > nc::linalg::cholesky ( const NdArray< dtype > & inMatrix )

matrix cholesky decomposition A = L * L.transpose()

NumPy Reference: https://docs.scipy.org/doc/numpy/reference/generated/numpy.linalg.cholesky.html#numpy.linalg.cholesky

Parameters

inMatrix NdArray to be decomposed

Returns: NdArray of the decomposed L matrix

◆ det()

template<typename dtype >

auto nc::linalg::det ( const NdArray< dtype > & inArray )

matrix determinant. NOTE: can get verrrrry slow for large matrices (order > 10)

SciPy Reference: https://docs.scipy.org/doc/scipy/reference/generated/scipy.linalg.det.html#scipy.linalg.det

Parameters

inArray

Returns: matrix determinant

Examples: ReadMe.cpp.

◆ gaussNewtonNlls()

template<typename dtype , typename... Params, std::enable_if_t< std::is_arithmetic_v< dtype >, int > = 0, std::enable_if_t< all_arithmetic_v< Params... >, int > = 0, std::enable_if_t< all_same_v< dtype, Params... >, int > = 0>

std::pair< NdArray< double >, double > nc::linalg::gaussNewtonNlls	(	const uint32	numIterations,
		const NdArray< dtype > &	coordinates,
		const NdArray< dtype > &	measurements,
		const std::function< dtype(const NdArray< dtype > &, const NdArray< dtype > &)> &	function,
		const std::array< std::function< dtype(const NdArray< dtype > &, const NdArray< dtype > &)>	,
		sizeof...	Params,
		&	derivatives,
		Params...	initialGuess
	)

The Gauss�Newton algorithm is used to solve non-linear least squares problems. It is a modification of Newton's method for finding a minimum of a function. https://en.wikipedia.org/wiki/Gauss%E2%80%93Newton_algorithm

Parameters

numIterations	the number of iterations to perform
coordinates	the coordinate values. The shape needs to be [n x d], where d is the number of diminsions of the fit function (f(x) is one dimensional, f(x, y) is two dimensions, etc), and n is the number of observations that are being fit to.
measurements	the measured values that are being fit
function	a std::function of the function that is being fit. The function takes as inputs an NdArray of a single set of the coordinate values, and an NdArray of the current values of the fit parameters
derivatives	array of std::functions to calculate the function derivatives. The function that is being fit. The function takes as inputs an NdArray of a single set of the coordinate values, and an NdArray of the current values of the fit parameters
initialGuess	the initial guess of the parameters to be solved for

Returns: std::pair of NdArray of solved parameter values, and rms of the residuals value

Examples: GaussNewtonNlls.cpp.

◆ hat() [1/3]

template<typename dtype >

NdArray< dtype > nc::linalg::hat ( const NdArray< dtype > & inVec )

vector hat operator

Parameters

inVec (3x1, or 1x3 cartesian vector)

Returns: 3x3 NdArray

◆ hat() [2/3]

NdArray< double > nc::linalg::hat ( const Vec3 & inVec )

inline

vector hat operator

Parameters

inVec

Returns: 3x3 NdArray

◆ hat() [3/3]

template<typename dtype >

NdArray< dtype > nc::linalg::hat	(	dtype	inX,
		dtype	inY,
		dtype	inZ
	)

vector hat operator

Parameters

inX
inY
inZ

Returns: 3x3 NdArray

◆ inv()

template<typename dtype >

NdArray< double > nc::linalg::inv ( const NdArray< dtype > & inArray )

matrix inverse

SciPy Reference: https://docs.scipy.org/doc/scipy/reference/generated/scipy.linalg.inv.html#scipy.linalg.inv

Parameters

inArray

Returns: NdArray

Examples: ReadMe.cpp.

◆ lstsq()

template<typename dtype >

NdArray< double > nc::linalg::lstsq	(	const NdArray< dtype > &	inA,
		const NdArray< dtype > &	inB,
		double	inTolerance = `1e-12`
	)

Solves the equation a x = b by computing a vector x that minimizes the Euclidean 2-norm || b - a x ||^2. The equation may be under-, well-, or over- determined (i.e., the number of linearly independent rows of a can be less than, equal to, or greater than its number of linearly independent columns). If a is square and of full rank, then x (but for round-off error) is the "exact" solution of the equation.

SciPy Reference: https://docs.scipy.org/doc/scipy/reference/generated/scipy.linalg.lstsq.html#scipy.linalg.lstsq

Parameters

inA	coefficient matrix
inB	Ordinate or "dependent variable" values
inTolerance	(default 1e-12)

Returns: NdArray

Examples: ReadMe.cpp.

◆ lu_decomposition()

template<typename dtype >

std::pair< NdArray< double >, NdArray< double > > nc::linalg::lu_decomposition ( const NdArray< dtype > & inMatrix )

matrix LU decomposition A = LU

Parameters

inMatrix NdArray to be decomposed

Returns: std::pair<NdArray, NdArray> of the decomposed L and U matrices

◆ matrix_power()

template<typename dtype >

NdArray< double > nc::linalg::matrix_power	(	const NdArray< dtype > &	inArray,
		int16	inPower
	)

Raise a square matrix to the (integer) power n.

For positive integers n, the power is computed by repeated matrix squarings and matrix multiplications. If n == 0, the identity matrix of the same shape as M is returned. If n < 0, the inverse is computed and then raised to the abs(n).

NumPy Reference: https://docs.scipy.org/doc/numpy/reference/generated/numpy.linalg.matrix_power.html#numpy.linalg.matrix_power

Parameters

inArray
inPower

Returns: NdArray

◆ multi_dot()

template<typename dtype >

NdArray< dtype > nc::linalg::multi_dot ( const std::initializer_list< NdArray< dtype > > & inList )

Compute the dot product of two or more arrays in a single function call.

NumPy Reference: https://docs.scipy.org/doc/numpy/reference/generated/numpy.linalg.multi_dot.html#numpy.linalg.multi_dot

Parameters

inList list of arrays

Returns: NdArray

◆ pinv()

template<typename dtype >

NdArray< double > nc::linalg::pinv ( const NdArray< dtype > & inArray )

matrix psuedo-inverse

NumPy Reference: https://numpy.org/doc/stable/reference/generated/numpy.linalg.pinv.html

Parameters

inArray

Returns: NdArray

◆ pivotLU_decomposition()

template<typename dtype >

std::tuple< NdArray< double >, NdArray< double >, NdArray< double > > nc::linalg::pivotLU_decomposition ( const NdArray< dtype > & inMatrix )

matrix pivot LU decomposition PA = LU

Parameters

inMatrix NdArray to be decomposed

Returns: std::tuple<NdArray, NdArray, NdArray> of the decomposed L, U, and P matrices

◆ solve()

template<typename dtype >

NdArray< double > nc::linalg::solve	(	const NdArray< dtype > &	inA,
		const NdArray< dtype > &	inB
	)

Solve a linear matrix equation, or system of linear scalar equations. Computes the “exact” solution, x, of the well-determined, i.e., full rank, linear matrix equation ax = b.

https://numpy.org/doc/stable/reference/generated/numpy.linalg.solve.html

Parameters

inA
inB

Returns: NdArray<double> Solution to the system a x = b. Returned shape is identical to b

◆ svd()

template<typename dtype >

void nc::linalg::svd	(	const NdArray< dtype > &	inArray,
		NdArray< double > &	outU,
		NdArray< double > &	outS,
		NdArray< double > &	outVt
	)

matrix svd

NumPy Reference: https://docs.scipy.org/doc/numpy/reference/generated/numpy.linalg.svd.html#numpy.linalg.svd

Parameters

inArray	NdArray to be SVDed
outU	NdArray output U
outS	NdArray output S
outVt	NdArray output V transpose

Examples: ReadMe.cpp.

Namespaces

Data Structures

Functions

Function Documentation

◆ cholesky()

◆ det()

◆ gaussNewtonNlls()

◆ hat() [1/3]

◆ hat() [2/3]

◆ hat() [3/3]

◆ inv()

◆ lstsq()

◆ lu_decomposition()

◆ matrix_power()

◆ multi_dot()

◆ pinv()

◆ pivotLU_decomposition()

◆ solve()

◆ svd()