Classes
struct	GBMat
	General Band Matrix (LAPACK GB storage format) More...

struct	GEMat
	General Dense Matrix (LAPACK GE storage format) More...

struct	PBMat
	Packed Band Matrix (LAPACK PB storage format) More...

struct	PeriodicMat
	Periodic Band Matrix. More...

struct	Spline1D
	1-dimensional B-spline More...

struct	Spline2D
	2-dimensional B-spline (tensor product) More...

struct	Spline2D1D
	2D+1D B-spline (for axisymmetric problems) More...

struct	ZGBMat
	Complex General Band Matrix. More...

struct	ZGEMat
	Complex General Dense Matrix. More...

struct	ZPBMat
	Complex Packed Band Matrix. More...

struct	ZPeriodicMat
	Complex Periodic Band Matrix. More...

Typedefs
using	spline1d = Spline1D
	Backward-compatible name for Spline1D.

using	spline2d = Spline2D
	Backward-compatible name for Spline2D.

using	spline2d1d = Spline2D1D
	Backward-compatible name for Spline2D1D.

Functions
void	basfun (Real x, const Spline1D &sp, Real *fun, int left, int nderiv=1)
	Evaluate basis functions and derivatives at a point.

void	bsolve (const GBMat &mat, Real *b, int nrhs=1)
	Solve linear system A*x = b.

void	bsolve (const GEMat &mat, Real *b, int nrhs=1)
	Solve linear system A*x = b.

void	bsolve (const PBMat &mat, Real *b, int nrhs=1)
	Solve linear system A*x = b.

void	bsolve (const PeriodicMat &mat, Real *b, int nrhs=1)
	Solve linear system A*x = b.

void	bsolve (const ZGBMat &mat, Complex *b, int nrhs=1)
	Solve linear system A*x = b.

void	bsolve (const ZGEMat &mat, Complex *b, int nrhs=1)
	Solve linear system A*x = b.

void	bsolve (const ZPBMat &mat, Complex *b, int nrhs=1)
	Solve linear system A*x = b.

void	bsolve (const ZPeriodicMat &mat, Complex *b, int nrhs=1)
	Solve linear system A*x = b.

void	bsplvb (const Real t, int jhigh, Real x, int left, Real biatx)
	Evaluate B-spline basis functions at a point.

void	bsplvd (const Real t, int k, Real x, int left, Real a, Real *dbiatx, int nderiv)
	Evaluate B-spline basis functions and derivatives at a point.

void	bspp2d (const Real t, const Real bcoef, int n, int k, Real scrtch, Real ppcoef)
	Convert B-spline coefficients to PPFORM.

void	calc_integ (const Spline1D &sp, Real *integ)
	Calculate integral of each basis function.

void	CompMassMatrix (const Spline1D &sp, GBMat &mat)
	Compute mass matrix for FEM discretization.

void	CompMassMatrix (const Spline1D &sp, PeriodicMat &mat)
	Assemble the finite-element mass matrix with periodic index wrapping.

void	def_basfun (Real x, const Spline1D &sp, Real fun, int left=nullptr, int nderiv=1)
	Define basis functions at a point (auto-locates interval)

void	destroy (GBMat &mat)
	Release numerical storage and reset a matrix descriptor.

void	destroy (GEMat &mat)
	Release numerical storage and reset a matrix descriptor.

void	destroy (PBMat &mat)
	Release numerical storage and reset a matrix descriptor.

void	destroy (PeriodicMat &mat)
	Release numerical storage and reset a matrix descriptor.

void	destroy (ZGBMat &mat)
	Release numerical storage and reset a matrix descriptor.

void	destroy (ZGEMat &mat)
	Release numerical storage and reset a matrix descriptor.

void	destroy (ZPBMat &mat)
	Release numerical storage and reset a matrix descriptor.

void	destroy (ZPeriodicMat &mat)
	Release numerical storage and reset a matrix descriptor.

void	destroy_sp (Spline1D &sp)
	Release all 1-D Views/matrices and reset scalar metadata.

void	destroy_sp (Spline2D &sp)
	Release both one-dimensional factors and all 2-D storage.

void	destroy_sp (Spline2D1D &sp)
	Release all three factors and all 3-D storage.

Real	determinant (const GBMat &mat)
	Compute determinant of factorized matrix.

Real	determinant (const GEMat &mat)
	Compute determinant of factorized matrix.

Real	determinant (const PBMat &mat)
	Compute determinant of factorized matrix.

Complex	determinant (const ZGBMat &mat)
	Compute determinant of factorized matrix.

Complex	determinant (const ZGEMat &mat)
	Compute determinant of factorized matrix.

Complex	determinant (const ZPBMat &mat)
	Compute determinant of factorized matrix.

int	factor (GBMat &mat)
	Compute LU factorization of matrix.

int	factor (GEMat &mat)
	Compute LU factorization of matrix.

int	factor (PBMat &mat)
	Compute LU factorization of matrix.

int	factor (PeriodicMat &mat)
	Compute LU factorization of matrix.

int	factor (ZGBMat &mat)
	Compute LU factorization of matrix.

int	factor (ZGEMat &mat)
	Compute LU factorization of matrix.

int	factor (ZPBMat &mat)
	Compute LU factorization of matrix.

int	factor (ZPeriodicMat &mat)
	Compute LU factorization of matrix.

void	gauleg (Real x1, Real x2, Real x, Real w, int n)
	Compute Gauss-Legendre quadrature points and weights.

void	get_dim (const Spline1D &sp, int &dim, int nx=nullptr, int nidbas=nullptr)
	Get dimension information from 1D spline.

void	get_dim (const Spline2D &sp, int dim[2], int nx[2]=nullptr, int nidbas[2]=nullptr)
	Get dimension information from both factors of a 2-D spline.

void	get_gauss (const Spline1D &sp, int &n, int i=-1, Real x=nullptr, Real w=nullptr)
	Get Gauss quadrature information from spline.

void	get_splcoef (const Spline1D &sp, const Real bcoef, Real fvals)
	Get function values from spline coefficients.

void	getcol (const GBMat &mat, int j, Real *col)
	Expand one logical matrix column into contiguous storage.

void	getcol (const PBMat &mat, int j, Real *col)
	Expand one logical matrix column into contiguous storage.

void	getcol (const PeriodicMat &mat, int j, Real *col)
	Expand one logical matrix column into contiguous storage.

Real	getele (const GBMat &mat, int i, int j)
	Get matrix element.

Real	getele (const PBMat &mat, int i, int j)
	Get matrix element.

Real	getele (const PeriodicMat &mat, int i, int j)
	Get matrix element.

Complex	getele (const ZGBMat &mat, int i, int j)
	Get matrix element.

Complex	getele (const ZPBMat &mat, int i, int j)
	Get matrix element.

Complex	getele (const ZPeriodicMat &mat, int i, int j)
	Get matrix element.

void	getrow (const GBMat &mat, int i, Real *row)
	Get row of matrix.

void	getrow (const GEMat &mat, int i, Real *row)
	Get row of matrix.

void	getrow (const PBMat &mat, int i, Real *row)
	Get row of matrix.

void	getrow (const PeriodicMat &mat, int i, Real *row)
	Get row of matrix.

void	getrow (const ZPBMat &mat, int i, Complex *row)
	Get row of matrix.

Real *	getvalp (GBMat &mat, int i, int j)
	Get pointer to matrix value for element (i,j) Used for direct access to storage for assembly.

Real *	getvalp (GEMat &mat, int i, int j)
	Get pointer to matrix value for element (i,j) Used for direct access to storage for assembly.

Real *	getvalp (PBMat &mat, int i, int j)
	Get pointer to matrix value for element (i,j) Used for direct access to storage for assembly.

Complex *	getvalp (ZGBMat &mat, int i, int j)
	Get pointer to matrix value for element (i,j) Used for direct access to storage for assembly.

Complex *	getvalp (ZGEMat &mat, int i, int j)
	Get pointer to matrix value for element (i,j) Used for direct access to storage for assembly.

Complex *	getvalp (ZPBMat &mat, int i, int j)
	Get pointer to matrix value for element (i,j) Used for direct access to storage for assembly.

void	gridval (const Spline1D &sp, const Real xgrid, int npts, const Real bcoef, Real *fvals, int jder=0)
	Evaluate spline on a grid of points.

void	gridval (const Spline2D &sp, const Real xgrid1, int npts1, const Real xgrid2, int npts2, const Real bcoef, Real fvals, int jder1=0, int jder2=0)
	Evaluate a tensor-product spline on a Cartesian product grid.

void	gridval (const Spline2D1D &sp, const Real xgrid1, int npts1, const Real xgrid2, int npts2, const Real xgrid3, int npts3, const Real bcoef, Real *fvals, int jder1=0, int jder2=0, int jder3=0)
	Evaluate 3D spline (2D+1D) on a 3D grid.

void	init (int kl, int ku, int n, int nterms, GBMat &mat, int kmat=0, int mrows=-1)
	Initialize a general band matrix.

void	init (int kl, int ku, int n, int nterms, PeriodicMat &mat, int kmat=0)
	Initialize a real periodic band matrix and Woodbury factors.

void	init (int kl, int ku, int n, int nterms, ZGBMat &mat, int kmat=0, int mrows=-1)
	Initialize a general band matrix.

void	init (int kl, int ku, int n, int nterms, ZPeriodicMat &mat, int kmat=0)
	Initialize a real periodic band matrix and Woodbury factors.

void	init (int ku, int n, int nterms, PBMat &mat, int kmat=0)
	Initialize a real symmetric positive-definite band matrix.

void	init (int ku, int n, int nterms, ZPBMat &mat, int kmat=0)
	Initialize a real symmetric positive-definite band matrix.

void	init (int n, int nterms, GEMat &mat, int kmat=0, int mrows=-1)
	Initialize a real general dense matrix.

void	init (int n, int nterms, ZGEMat &mat, int kmat=0, int mrows=-1)
	Initialize a real general dense matrix.

void	interv (const Real *xt, int lxt, Real x, int &left, int &mflag)
	Locate interval containing x in a knot sequence.

void	interv_hint (const Real *xt, int lxt, Real x, int &left, int &mflag, int &ilo)
	Thread-safe version of interv with explicit previous guess.

bool	is_equid (const Real *grid, int n)
	Check if a grid is equidistant.

void	locintv (const Spline1D &sp, Real x, int &left)
	Locate interval containing x in spline knot sequence.

void	maddto (Real alpha, const GBMat &a, GBMat &b)
	Accumulate `B = B + alpha*A` without changing storage layout.

void	maddto (Real alpha, const GEMat &a, GEMat &b)
	Accumulate `B = B + alpha*A` without changing storage layout.

void	maddto (Real alpha, const PBMat &a, PBMat &b)
	Accumulate `B = B + alpha*A` without changing storage layout.

void	maddto (Real alpha, const PeriodicMat &a, PeriodicMat &b)
	Accumulate `B = B + alpha*A` without changing storage layout.

void	mcopy (const GBMat &src, GBMat &dst)
	Deep-copy matrix metadata and numerical storage.

void	mcopy (const GEMat &src, GEMat &dst)
	Deep-copy matrix metadata and numerical storage.

void	mcopy (const PBMat &src, PBMat &dst)
	Deep-copy matrix metadata and numerical storage.

void	mcopy (const PeriodicMat &src, PeriodicMat &dst)
	Deep-copy matrix metadata and numerical storage.

Real	ppval (const Real t, const Real coef, int n, int k, Real x, int &left)
	Evaluate polynomial in piecewise polynomial form.

void	putcol (GBMat &mat, int j, const Real *col)
	Replace one zero-based logical matrix column.

void	putcol (GEMat &mat, int j, const Real *col)
	Replace one zero-based logical matrix column.

void	putcol (PBMat &mat, int j, const Real *col)
	Replace one zero-based logical matrix column.

void	putcol (PeriodicMat &mat, int j, const Real *col)
	Replace one zero-based logical matrix column.

void	putcol (ZPBMat &mat, int j, const Complex *col)
	Replace one zero-based logical matrix column.

void	putele (GBMat &mat, Real val, int i, int j)
	Assign one zero-based logical matrix element.

void	putele (PBMat &mat, Real val, int i, int j)
	Assign one zero-based logical matrix element.

void	putele (PeriodicMat &mat, Real val, int i, int j)
	Assign one zero-based logical matrix element.

void	putele (ZGBMat &mat, Complex val, int i, int j)
	Assign one zero-based logical matrix element.

void	putele (ZPBMat &mat, Complex val, int i, int j)
	Assign one zero-based logical matrix element.

void	putele (ZPeriodicMat &mat, Complex val, int i, int j)
	Assign one zero-based logical matrix element.

void	putrow (GBMat &mat, int i, const Real *row)
	Replace one zero-based logical matrix row.

void	putrow (GEMat &mat, int i, const Real *row)
	Replace one zero-based logical matrix row.

void	putrow (PBMat &mat, int i, const Real *row)
	Replace one zero-based logical matrix row.

void	putrow (PeriodicMat &mat, int i, const Real *row)
	Replace one zero-based logical matrix row.

void	putrow (ZPBMat &mat, int i, const Complex *row)
	Replace one zero-based logical matrix row.

void	set_splcoef (Spline1D &sp, const Real fvals, Real bcoef)
	Set spline coefficients from function values.

void	set_spline (const int p[2], const int ngauss[2], const Real grid1, int ngrid1, const Real grid2, int ngrid2, Spline2D &sp, const bool period[2]=nullptr, bool nlppform=true, const int nlequid[2]=nullptr)
	Initialize a 2D spline.

void	set_spline (const int p[3], const int ngauss[3], const Real grid1, int ngrid1, const Real grid2, int ngrid2, const Real *grid3, int ngrid3, Spline2D1D &sp, const bool period[3]=nullptr, bool nlppform=true, const int nlequid[3]=nullptr)
	Initialize a 2D+1D spline.

void	set_spline (int p, int ngauss, const Real *grid, int ngrid, Spline1D &sp, bool period=false, bool nlppform=true, int nlequid=-1)
	Initialize a 1D spline.

void	updtmat (GBMat &mat, Real val, int i, int j)
	Update matrix element: mat(i,j) += val.

void	updtmat (GEMat &mat, Real val, int i, int j)
	Update matrix element: mat(i,j) += val.

void	updtmat (PBMat &mat, Real val, int i, int j)
	Update matrix element: mat(i,j) += val.

void	updtmat (PeriodicMat &mat, Real val, int i, int j)
	Update matrix element: mat(i,j) += val.

void	updtmat (ZGBMat &mat, Complex val, int i, int j)
	Update matrix element: mat(i,j) += val.

void	updtmat (ZPBMat &mat, Complex val, int i, int j)
	Update matrix element: mat(i,j) += val.

void	updtmat (ZPeriodicMat &mat, Complex val, int i, int j)
	Update matrix element: mat(i,j) += val.

void	vmx (const GBMat &mat, const Real x, Real y)
	Compute y = A*x.

void	vmx (const GBMat &mat, const Real x, Real y, int nrhs)
	Compute Y = A*X for multiple vectors.

void	vmx (const GEMat &mat, const Real x, Real y)
	Compute y = A*x.

void	vmx (const GEMat &mat, const Real x, Real y, int nrhs)
	Compute Y = A*X for multiple vectors.

void	vmx (const PBMat &mat, const Real x, Real y)
	Compute y = A*x.

void	vmx (const PeriodicMat &mat, const Real x, Real y)
	Compute y = A*x.

void	vmx (const ZGBMat &mat, const Complex x, Complex y)
	Compute y = A*x.

void	vmx (const ZGEMat &mat, const Complex x, Complex y)
	Compute y = A*x.

void	vmx (const ZPBMat &mat, const Complex x, Complex y)
	Compute y = A*x.

void	vmx (const ZPeriodicMat &mat, const Complex x, Complex y)
	Compute y = A*x.

Variables
constexpr int	JMAX = 20
	Maximum spline order supported (degree + 1)

Typedef Documentation

◆ spline1d

using orb5x::spclibs::spline1d = typedef Spline1D

Backward-compatible name for Spline1D.

◆ spline2d

using orb5x::spclibs::spline2d = typedef Spline2D

Backward-compatible name for Spline2D.

◆ spline2d1d

using orb5x::spclibs::spline2d1d = typedef Spline2D1D

Backward-compatible name for Spline2D1D.

Function Documentation

◆ basfun()

void orb5x::spclibs::basfun	(	Real	x,
		const Spline1D &	sp,
		Real *	fun,
		int	left,
		int	nderiv = `1`
	)

Evaluate basis functions and derivatives at a point.

Parameters

[in]	x	Coordinate at which to evaluate, in grid units.
[in]	sp	Initialized spline.
[out]	fun	Array of at least `ordernderiv` values and derivatives: fun[i + jorder] = jth derivative of ith basis function i = 0, ..., order-1 (basis functions) j = 0, ..., nderiv-1 (derivatives)
[in]	left	One-based interval index, retained from the Fortran interface.
[in]	nderiv	Number of derivative levels including the value; one computes only values.

◆ bsolve() [1/8]

void orb5x::spclibs::bsolve	(	const GBMat &	mat,
		Real *	b,
		int	nrhs = `1`
	)

Solve linear system A*x = b.

Parameters

mat	Factorized matrix (from factor())
b	Right-hand side vector (input), solution vector (output)
nrhs	Number of right-hand sides (default 1)

The matrix must have been factorized with factor() before calling bsolve().

◆ bsolve() [2/8]

void orb5x::spclibs::bsolve	(	const GEMat &	mat,
		Real *	b,
		int	nrhs = `1`
	)

Solve linear system A*x = b.

Parameters

mat	Factorized matrix (from factor())
b	Right-hand side vector (input), solution vector (output)
nrhs	Number of right-hand sides (default 1)

The matrix must have been factorized with factor() before calling bsolve().

◆ bsolve() [3/8]

void orb5x::spclibs::bsolve	(	const PBMat &	mat,
		Real *	b,
		int	nrhs = `1`
	)

Solve linear system A*x = b.

Parameters

mat	Factorized matrix (from factor())
b	Right-hand side vector (input), solution vector (output)
nrhs	Number of right-hand sides (default 1)

The matrix must have been factorized with factor() before calling bsolve().

◆ bsolve() [4/8]

void orb5x::spclibs::bsolve	(	const PeriodicMat &	mat,
		Real *	b,
		int	nrhs = `1`
	)

Solve linear system A*x = b.

Parameters

mat	Factorized matrix (from factor())
b	Right-hand side vector (input), solution vector (output)
nrhs	Number of right-hand sides (default 1)

The matrix must have been factorized with factor() before calling bsolve().

◆ bsolve() [5/8]

void orb5x::spclibs::bsolve	(	const ZGBMat &	mat,
		Complex *	b,
		int	nrhs = `1`
	)

Solve linear system A*x = b.

Parameters

mat	Factorized matrix (from factor())
b	Right-hand side vector (input), solution vector (output)
nrhs	Number of right-hand sides (default 1)

The matrix must have been factorized with factor() before calling bsolve().

◆ bsolve() [6/8]

void orb5x::spclibs::bsolve	(	const ZGEMat &	mat,
		Complex *	b,
		int	nrhs = `1`
	)

Solve linear system A*x = b.

Parameters

mat	Factorized matrix (from factor())
b	Right-hand side vector (input), solution vector (output)
nrhs	Number of right-hand sides (default 1)

The matrix must have been factorized with factor() before calling bsolve().

◆ bsolve() [7/8]

void orb5x::spclibs::bsolve	(	const ZPBMat &	mat,
		Complex *	b,
		int	nrhs = `1`
	)

Solve linear system A*x = b.

Parameters

mat	Factorized matrix (from factor())
b	Right-hand side vector (input), solution vector (output)
nrhs	Number of right-hand sides (default 1)

The matrix must have been factorized with factor() before calling bsolve().

◆ bsolve() [8/8]

void orb5x::spclibs::bsolve	(	const ZPeriodicMat &	mat,
		Complex *	b,
		int	nrhs = `1`
	)

Solve linear system A*x = b.

Parameters

mat	Factorized matrix (from factor())
b	Right-hand side vector (input), solution vector (output)
nrhs	Number of right-hand sides (default 1)

The matrix must have been factorized with factor() before calling bsolve().

◆ bsplvb()

void orb5x::spclibs::bsplvb	(	const Real *	t,
		int	jhigh,
		Real	x,
		int	left,
		Real *	biatx
	)

Evaluate B-spline basis functions at a point.

Evaluates all possibly nonzero B-splines at X of order jhigh with knot sequence T. Uses the recurrence relation:

               X - T(I)               T(I+J+1) - X

B(I,J+1)(X) = --------— * B(I,J)(X) + ------------— * B(I+1,J)(X) T(I+J)-T(I) T(I+J+1)-T(I+1)

Parameters

t	Knot sequence (at least left+jhigh elements)
jhigh	Order of B-splines to evaluate
x	Point at which to evaluate
left	Index such that t[left] <= x < t[left+1]
biatx	Output: B-spline values (jhigh elements)

Note: Uses 0-based indexing (Fortran version uses 1-based)

◆ bsplvd()

void orb5x::spclibs::bsplvd	(	const Real *	t,
		int	k,
		Real	x,
		int	left,
		Real *	a,
		Real *	dbiatx,
		int	nderiv
	)

Evaluate B-spline basis functions and derivatives at a point.

Computes values at X of all the relevant B-splines of order k, k-1, ..., k+1-nderiv and their derivatives.

Parameters

t	Knot sequence (at least left+k elements)
k	Order of B-splines
x	Point at which to evaluate
left	Index such that t[left] <= x < t[left+1]
a	Workspace array (k x k)
dbiatx	Output: B-spline values and derivatives (k x nderiv) dbiatx[i + m*k] = (m-1)th derivative of (left-k+i+1)th B-spline
nderiv	Number of derivatives (including value) to compute

Note: Uses 0-based indexing

◆ bspp2d()

void orb5x::spclibs::bspp2d	(	const Real *	t,
		const Real *	bcoef,
		int	n,
		int	k,
		Real *	scrtch,
		Real *	ppcoef
	)

Convert B-spline coefficients to PPFORM.

Converts B-spline representation to piecewise polynomial form.

Parameters

t	Knot sequence
bcoef	B-spline coefficients (dim elements)
n	Number of intervals
k	Order
scrtch	Scratch array (k x k)
ppcoef	Output: PPFORM coefficients (k x n)

◆ calc_integ()

void orb5x::spclibs::calc_integ	(	const Spline1D &	sp,
		Real *	integ
	)

Calculate integral of each basis function.

Parameters

[in]	sp	Initialized spline, preferably with Gauss quadrature data.
[out]	integ	Array of `sp.dim` basis integrals in coordinate units.

Note: Without stored Gauss points, a uniform-width approximation is returned.

◆ CompMassMatrix() [1/2]

void orb5x::spclibs::CompMassMatrix	(	const Spline1D &	sp,
		GBMat &	mat
	)

Compute mass matrix for FEM discretization.

Parameters

[in]	sp	Initialized nonperiodic spline with Gauss quadrature data.
[out]	mat	Initialized general band matrix representing \(M_{ij}=\int B_i(x)B_j(x)\,dx\).

◆ CompMassMatrix() [2/2]

void orb5x::spclibs::CompMassMatrix	(	const Spline1D &	sp,
		PeriodicMat &	mat
	)

Assemble the finite-element mass matrix with periodic index wrapping.

Parameters

[in]	sp	Initialized periodic spline with Gauss quadrature data.
[out]	mat	Initialized periodic band matrix representing \(M_{ij}=\int B_i(x)B_j(x)\,dx\).

◆ def_basfun()

void orb5x::spclibs::def_basfun	(	Real	x,
		const Spline1D &	sp,
		Real *	fun,
		int *	left = `nullptr`,
		int	nderiv = `1`
	)

Define basis functions at a point (auto-locates interval)

Parameters

[in]	x	Coordinate at which to evaluate, in grid units.
[in]	sp	Initialized spline.
[out]	fun	Array of at least `order*nderiv` values and derivatives.
[out]	left	Optional zero-based containing interval.
[in]	nderiv	Number of derivative levels including the value.

◆ destroy() [1/8]

void orb5x::spclibs::destroy ( GBMat & mat )

Release numerical storage and reset a matrix descriptor.

Parameters

[in,out] mat Matrix to destroy; it is empty on return.

◆ destroy() [2/8]

void orb5x::spclibs::destroy ( GEMat & mat )

Release numerical storage and reset a matrix descriptor.

Parameters

[in,out] mat Matrix to destroy; it is empty on return.

◆ destroy() [3/8]

void orb5x::spclibs::destroy ( PBMat & mat )

Release numerical storage and reset a matrix descriptor.

Parameters

[in,out] mat Matrix to destroy; it is empty on return.

◆ destroy() [4/8]

void orb5x::spclibs::destroy ( PeriodicMat & mat )

Release numerical storage and reset a matrix descriptor.

Parameters

[in,out] mat Matrix to destroy; it is empty on return.

◆ destroy() [5/8]

void orb5x::spclibs::destroy ( ZGBMat & mat )

Release numerical storage and reset a matrix descriptor.

Parameters

[in,out] mat Matrix to destroy; it is empty on return.

◆ destroy() [6/8]

void orb5x::spclibs::destroy ( ZGEMat & mat )

Release numerical storage and reset a matrix descriptor.

Parameters

[in,out] mat Matrix to destroy; it is empty on return.

◆ destroy() [7/8]

void orb5x::spclibs::destroy ( ZPBMat & mat )

Release numerical storage and reset a matrix descriptor.

Parameters

[in,out] mat Matrix to destroy; it is empty on return.

◆ destroy() [8/8]

void orb5x::spclibs::destroy ( ZPeriodicMat & mat )

Release numerical storage and reset a matrix descriptor.

Parameters

[in,out] mat Matrix to destroy; it is empty on return.

◆ destroy_sp() [1/3]

void orb5x::spclibs::destroy_sp ( Spline1D & sp )

Release all 1-D Views/matrices and reset scalar metadata.

Parameters

[in,out] sp Descriptor to return to the uninitialized state.

◆ destroy_sp() [2/3]

void orb5x::spclibs::destroy_sp ( Spline2D & sp )

Release both one-dimensional factors and all 2-D storage.

Parameters

[in,out] sp Descriptor to return to the uninitialized state.

◆ destroy_sp() [3/3]

void orb5x::spclibs::destroy_sp ( Spline2D1D & sp )

Release all three factors and all 3-D storage.

Parameters

[in,out] sp Descriptor to return to the uninitialized state.

◆ determinant() [1/6]

Real orb5x::spclibs::determinant ( const GBMat & mat )

Compute determinant of factorized matrix.

Parameters

mat	Factorized matrix

Returns: Determinant value

◆ determinant() [2/6]

Real orb5x::spclibs::determinant ( const GEMat & mat )

Compute determinant of factorized matrix.

Parameters

mat	Factorized matrix

Returns: Determinant value

◆ determinant() [3/6]

Real orb5x::spclibs::determinant ( const PBMat & mat )

Compute determinant of factorized matrix.

Parameters

mat	Factorized matrix

Returns: Determinant value

◆ determinant() [4/6]

Complex orb5x::spclibs::determinant ( const ZGBMat & mat )

Compute determinant of factorized matrix.

Parameters

mat	Factorized matrix

Returns: Determinant value

◆ determinant() [5/6]

Complex orb5x::spclibs::determinant ( const ZGEMat & mat )

Compute determinant of factorized matrix.

Parameters

mat	Factorized matrix

Returns: Determinant value

◆ determinant() [6/6]

Complex orb5x::spclibs::determinant ( const ZPBMat & mat )

Compute determinant of factorized matrix.

Parameters

mat	Factorized matrix

Returns: Determinant value

◆ factor() [1/8]

int orb5x::spclibs::factor ( GBMat & mat )

Compute LU factorization of matrix.

Parameters

mat	Matrix to factorize (modified in place)

Returns: 0 on success, non-zero on failure

For GBMat: Uses LAPACK DGBTRF For GEMat: Uses LAPACK DGETRF For PBMat: Uses LAPACK DPBTRF (Cholesky) For PeriodicMat: Uses Woodbury formula with DGBTRF

◆ factor() [2/8]

int orb5x::spclibs::factor ( GEMat & mat )

Compute LU factorization of matrix.

Parameters

mat	Matrix to factorize (modified in place)

Returns: 0 on success, non-zero on failure

For GBMat: Uses LAPACK DGBTRF For GEMat: Uses LAPACK DGETRF For PBMat: Uses LAPACK DPBTRF (Cholesky) For PeriodicMat: Uses Woodbury formula with DGBTRF

◆ factor() [3/8]

int orb5x::spclibs::factor ( PBMat & mat )

Compute LU factorization of matrix.

Parameters

mat	Matrix to factorize (modified in place)

Returns: 0 on success, non-zero on failure

For GBMat: Uses LAPACK DGBTRF For GEMat: Uses LAPACK DGETRF For PBMat: Uses LAPACK DPBTRF (Cholesky) For PeriodicMat: Uses Woodbury formula with DGBTRF

◆ factor() [4/8]

int orb5x::spclibs::factor ( PeriodicMat & mat )

Compute LU factorization of matrix.

Parameters

mat	Matrix to factorize (modified in place)

Returns: 0 on success, non-zero on failure

For GBMat: Uses LAPACK DGBTRF For GEMat: Uses LAPACK DGETRF For PBMat: Uses LAPACK DPBTRF (Cholesky) For PeriodicMat: Uses Woodbury formula with DGBTRF

◆ factor() [5/8]

int orb5x::spclibs::factor ( ZGBMat & mat )

Compute LU factorization of matrix.

Parameters

mat	Matrix to factorize (modified in place)

Returns: 0 on success, non-zero on failure

For GBMat: Uses LAPACK DGBTRF For GEMat: Uses LAPACK DGETRF For PBMat: Uses LAPACK DPBTRF (Cholesky) For PeriodicMat: Uses Woodbury formula with DGBTRF

◆ factor() [6/8]

int orb5x::spclibs::factor ( ZGEMat & mat )

Compute LU factorization of matrix.

Parameters

mat	Matrix to factorize (modified in place)

Returns: 0 on success, non-zero on failure

For GBMat: Uses LAPACK DGBTRF For GEMat: Uses LAPACK DGETRF For PBMat: Uses LAPACK DPBTRF (Cholesky) For PeriodicMat: Uses Woodbury formula with DGBTRF

◆ factor() [7/8]

int orb5x::spclibs::factor ( ZPBMat & mat )

Compute LU factorization of matrix.

Parameters

mat	Matrix to factorize (modified in place)

Returns: 0 on success, non-zero on failure

For GBMat: Uses LAPACK DGBTRF For GEMat: Uses LAPACK DGETRF For PBMat: Uses LAPACK DPBTRF (Cholesky) For PeriodicMat: Uses Woodbury formula with DGBTRF

◆ factor() [8/8]

int orb5x::spclibs::factor ( ZPeriodicMat & mat )

Compute LU factorization of matrix.

Parameters

mat	Matrix to factorize (modified in place)

Returns: 0 on success, non-zero on failure

For GBMat: Uses LAPACK DGBTRF For GEMat: Uses LAPACK DGETRF For PBMat: Uses LAPACK DPBTRF (Cholesky) For PeriodicMat: Uses Woodbury formula with DGBTRF

◆ gauleg()

void orb5x::spclibs::gauleg	(	Real	x1,
		Real	x2,
		Real *	x,
		Real *	w,
		int	n
	)

Compute Gauss-Legendre quadrature points and weights.

Computes the n-point Gauss-Legendre quadrature rule on [x1, x2].

Parameters

x1	Left endpoint of interval
x2	Right endpoint of interval
x	Output: quadrature points (n elements)
w	Output: quadrature weights (n elements)
n	Number of quadrature points

◆ get_dim() [1/2]

void orb5x::spclibs::get_dim	(	const Spline1D &	sp,
		int &	dim,
		int *	nx = `nullptr`,
		int *	nidbas = `nullptr`
	)

Get dimension information from 1D spline.

Parameters

[in]	sp	Initialized spline descriptor.
[out]	dim	Number of independent spline coefficients.
[out]	nx	Optional number of knot intervals.
[out]	nidbas	Optional polynomial degree (`order-1`).

◆ get_dim() [2/2]

void orb5x::spclibs::get_dim	(	const Spline2D &	sp,
		int	dim[2],
		int	nx[2] = `nullptr`,
		int	nidbas[2] = `nullptr`
	)

Get dimension information from both factors of a 2-D spline.

Parameters

[in]	sp	Initialized tensor-product descriptor.
[out]	dim	Two coefficient-space dimensions.
[out]	nx	Optional interval counts in the two directions.
[out]	nidbas	Optional polynomial degrees in the two directions.

◆ get_gauss()

void orb5x::spclibs::get_gauss	(	const Spline1D &	sp,
		int &	n,
		int	i = `-1`,
		Real *	x = `nullptr`,
		Real *	w = `nullptr`
	)

Get Gauss quadrature information from spline.

Parameters

[in]	sp	Initialized spline with optional quadrature storage.
[out]	n	Number of Gauss points per interval, possibly zero.
[in]	i	Zero-based interval to copy, or a negative value for count only.
[out]	x	Optional array of at least `n` abscissas; written only with `w` and valid `i`.
[out]	w	Optional array of at least `n` integration weights; written only with `x` and valid `i`.

◆ get_splcoef()

void orb5x::spclibs::get_splcoef	(	const Spline1D &	sp,
		const Real *	bcoef,
		Real *	fvals
	)

Get function values from spline coefficients.

Computes fvals = M * bcoef where M is the interpolation matrix.

Parameters

[in]	sp	Spline with its appropriate interpolation matrix initialized.
[in]	bcoef	Array of `sp.dim` spline coefficients.
[out]	fvals	Array of `sp.dim` values receiving the matrix product.

◆ getcol() [1/3]

void orb5x::spclibs::getcol	(	const GBMat &	mat,
		int	j,
		Real *	col
	)

Expand one logical matrix column into contiguous storage.

Parameters

[in]	mat	Source matrix.
[in]	j	Zero-based logical column.
[out]	col	Caller storage with at least `mrows` elements.

◆ getcol() [2/3]

void orb5x::spclibs::getcol	(	const PBMat &	mat,
		int	j,
		Real *	col
	)

Expand one logical matrix column into contiguous storage.

Parameters

[in]	mat	Source matrix.
[in]	j	Zero-based logical column.
[out]	col	Caller storage with at least `mrows` elements.

◆ getcol() [3/3]

void orb5x::spclibs::getcol	(	const PeriodicMat &	mat,
		int	j,
		Real *	col
	)

Expand one logical matrix column into contiguous storage.

Parameters

[in]	mat	Source matrix.
[in]	j	Zero-based logical column.
[out]	col	Caller storage with at least `mrows` elements.

◆ getele() [1/6]

Real orb5x::spclibs::getele	(	const GBMat &	mat,
		int	i,
		int	j
	)

Get matrix element.

Parameters

mat	Matrix
i	Row index (0-based)
j	Column index (0-based)

Returns: Matrix element value

◆ getele() [2/6]

Real orb5x::spclibs::getele	(	const PBMat &	mat,
		int	i,
		int	j
	)

Get matrix element.

Parameters

mat	Matrix
i	Row index (0-based)
j	Column index (0-based)

Returns: Matrix element value

◆ getele() [3/6]

Real orb5x::spclibs::getele	(	const PeriodicMat &	mat,
		int	i,
		int	j
	)

Get matrix element.

Parameters

mat	Matrix
i	Row index (0-based)
j	Column index (0-based)

Returns: Matrix element value

◆ getele() [4/6]

Complex orb5x::spclibs::getele	(	const ZGBMat &	mat,
		int	i,
		int	j
	)

Get matrix element.

Parameters

mat	Matrix
i	Row index (0-based)
j	Column index (0-based)

Returns: Matrix element value

◆ getele() [5/6]

Complex orb5x::spclibs::getele	(	const ZPBMat &	mat,
		int	i,
		int	j
	)

Get matrix element.

Parameters

mat	Matrix
i	Row index (0-based)
j	Column index (0-based)

Returns: Matrix element value

◆ getele() [6/6]

Complex orb5x::spclibs::getele	(	const ZPeriodicMat &	mat,
		int	i,
		int	j
	)

Get matrix element.

Parameters

mat	Matrix
i	Row index (0-based)
j	Column index (0-based)

Returns: Matrix element value

◆ getrow() [1/5]

void orb5x::spclibs::getrow	(	const GBMat &	mat,
		int	i,
		Real *	row
	)

Get row of matrix.

Parameters

mat	Matrix
i	Row index (0-based)
row	Output array (must be pre-allocated with size ncols)

◆ getrow() [2/5]

void orb5x::spclibs::getrow	(	const GEMat &	mat,
		int	i,
		Real *	row
	)

Get row of matrix.

Parameters

mat	Matrix
i	Row index (0-based)
row	Output array (must be pre-allocated with size ncols)

◆ getrow() [3/5]

void orb5x::spclibs::getrow	(	const PBMat &	mat,
		int	i,
		Real *	row
	)

Get row of matrix.

Parameters

mat	Matrix
i	Row index (0-based)
row	Output array (must be pre-allocated with size ncols)

◆ getrow() [4/5]

void orb5x::spclibs::getrow	(	const PeriodicMat &	mat,
		int	i,
		Real *	row
	)

Get row of matrix.

Parameters

mat	Matrix
i	Row index (0-based)
row	Output array (must be pre-allocated with size ncols)

◆ getrow() [5/5]

void orb5x::spclibs::getrow	(	const ZPBMat &	mat,
		int	i,
		Complex *	row
	)

Get row of matrix.

Parameters

mat	Matrix
i	Row index (0-based)
row	Output array (must be pre-allocated with size ncols)

◆ getvalp() [1/6]

Real * orb5x::spclibs::getvalp	(	GBMat &	mat,
		int	i,
		int	j
	)

Get pointer to matrix value for element (i,j) Used for direct access to storage for assembly.

Parameters

[in,out]	mat	Matrix whose physical storage is requested.
[in]	i	Zero-based logical row.
[in]	j	Zero-based logical column.

Returns: Pointer to the stored scalar, or null when (i,j) is not represented.

◆ getvalp() [2/6]

Real * orb5x::spclibs::getvalp	(	GEMat &	mat,
		int	i,
		int	j
	)

Get pointer to matrix value for element (i,j) Used for direct access to storage for assembly.

Parameters

[in,out]	mat	Matrix whose physical storage is requested.
[in]	i	Zero-based logical row.
[in]	j	Zero-based logical column.

Returns: Pointer to the stored scalar, or null when (i,j) is not represented.

◆ getvalp() [3/6]

Real * orb5x::spclibs::getvalp	(	PBMat &	mat,
		int	i,
		int	j
	)

Get pointer to matrix value for element (i,j) Used for direct access to storage for assembly.

Parameters

[in,out]	mat	Matrix whose physical storage is requested.
[in]	i	Zero-based logical row.
[in]	j	Zero-based logical column.

Returns: Pointer to the stored scalar, or null when (i,j) is not represented.

◆ getvalp() [4/6]

Complex * orb5x::spclibs::getvalp	(	ZGBMat &	mat,
		int	i,
		int	j
	)

Get pointer to matrix value for element (i,j) Used for direct access to storage for assembly.

Parameters

[in,out]	mat	Matrix whose physical storage is requested.
[in]	i	Zero-based logical row.
[in]	j	Zero-based logical column.

Returns: Pointer to the stored scalar, or null when (i,j) is not represented.

◆ getvalp() [5/6]

Complex * orb5x::spclibs::getvalp	(	ZGEMat &	mat,
		int	i,
		int	j
	)

Get pointer to matrix value for element (i,j) Used for direct access to storage for assembly.

Parameters

[in,out]	mat	Matrix whose physical storage is requested.
[in]	i	Zero-based logical row.
[in]	j	Zero-based logical column.

Returns: Pointer to the stored scalar, or null when (i,j) is not represented.

◆ getvalp() [6/6]

Complex * orb5x::spclibs::getvalp	(	ZPBMat &	mat,
		int	i,
		int	j
	)

Get pointer to matrix value for element (i,j) Used for direct access to storage for assembly.

Parameters

[in,out]	mat	Matrix whose physical storage is requested.
[in]	i	Zero-based logical row.
[in]	j	Zero-based logical column.

Returns: Pointer to the stored scalar, or null when (i,j) is not represented.

◆ gridval() [1/3]

void orb5x::spclibs::gridval	(	const Spline1D &	sp,
		const Real *	xgrid,
		int	npts,
		const Real *	bcoef,
		Real *	fvals,
		int	jder = `0`
	)

Evaluate spline on a grid of points.

Given spline coefficients bcoef, compute function values on grid.

Parameters

[in]	sp	Initialized spline.
[in]	xgrid	Evaluation coordinates of length `npts`.
[in]	npts	Number of evaluation coordinates.
[in]	bcoef	Spline coefficients of length `sp.dim`.
[out]	fvals	Evaluated values or derivatives of length `npts`.
[in]	jder	Derivative order; zero evaluates the represented function.

◆ gridval() [2/3]

void orb5x::spclibs::gridval	(	const Spline2D &	sp,
		const Real *	xgrid1,
		int	npts1,
		const Real *	xgrid2,
		int	npts2,
		const Real *	bcoef,
		Real *	fvals,
		int	jder1 = `0`,
		int	jder2 = `0`
	)

Evaluate a tensor-product spline on a Cartesian product grid.

Parameters

[in]	sp	Initialized two-dimensional descriptor.
[in]	xgrid1	First-direction coordinates of length `npts1`.
[in]	npts1	First-direction point count.
[in]	xgrid2	Second-direction coordinates of length `npts2`.
[in]	npts2	Second-direction point count.
[in]	bcoef	Coefficients of length `sp1.dim*sp2.dim`, direction 1 fastest.
[out]	fvals	Results of length `npts1*npts2`, direction 1 fastest.
[in]	jder1	Derivative order in direction 1.
[in]	jder2	Derivative order in direction 2.

◆ gridval() [3/3]

void orb5x::spclibs::gridval	(	const Spline2D1D &	sp,
		const Real *	xgrid1,
		int	npts1,
		const Real *	xgrid2,
		int	npts2,
		const Real *	xgrid3,
		int	npts3,
		const Real *	bcoef,
		Real *	fvals,
		int	jder1 = `0`,
		int	jder2 = `0`,
		int	jder3 = `0`
	)

Evaluate 3D spline (2D+1D) on a 3D grid.

Given spline coefficients bcoef, compute function values on 3D grid. Based on Fortran gridval2d1d_3d (bsplines.f90 lines 2613-2753).

Parameters

[in]	sp	2-D-plus-1-D spline (`sp12` for directions 1–2 and `sp3` for direction 3).
[in]	xgrid1	Direction-1 coordinates of length `npts1`.
[in]	npts1	Direction-1 point count.
[in]	xgrid2	Direction-2 coordinates of length `npts2`.
[in]	npts2	Direction-2 point count.
[in]	xgrid3	Direction-3 coordinates of length `npts3`.
[in]	npts3	Direction-3 point count.
[in]	bcoef	`dim1dim2dim3` coefficients, direction 1 fastest.
[out]	fvals	`npts1npts2npts3` results, direction 1 fastest.
[in]	jder1	Derivative order in direction 1.
[in]	jder2	Derivative order in direction 2.
[in]	jder3	Derivative order in direction 3.

◆ init() [1/8]

void orb5x::spclibs::init	(	int	kl,
		int	ku,
		int	n,
		int	nterms,
		GBMat &	mat,
		int	kmat = `0`,
		int	mrows = `-1`
	)

Initialize a general band matrix.

Parameters

kl	Number of subdiagonals
ku	Number of superdiagonals
n	Matrix dimension (square matrix)
nterms	Number of non-zero terms (informational)
mat	Output matrix
kmat	Optional matrix identifier
mrows	Optional number of rows (defaults to n) Allocate matrix storage and initialize dimensions, bandwidths, identifiers, and pivots.

Referenced by orb5x::Zbmat::allocate_band().

◆ init() [2/8]

void orb5x::spclibs::init	(	int	kl,
		int	ku,
		int	n,
		int	nterms,
		PeriodicMat &	mat,
		int	kmat = `0`
	)

Initialize a real periodic band matrix and Woodbury factors.

Parameters

[in]	kl	Number of subdiagonals.
[in]	ku	Number of superdiagonals.
[in]	n	Square matrix dimension.
[in]	nterms	Informational assembled-term count.
[out]	mat	Allocated periodic descriptor.
[in]	kmat	Optional caller-defined identifier. Allocate matrix storage and initialize dimensions, bandwidths, identifiers, and pivots.

◆ init() [3/8]

void orb5x::spclibs::init	(	int	kl,
		int	ku,
		int	n,
		int	nterms,
		ZGBMat &	mat,
		int	kmat = `0`,
		int	mrows = `-1`
	)

Initialize a general band matrix.

Parameters

kl	Number of subdiagonals
ku	Number of superdiagonals
n	Matrix dimension (square matrix)
nterms	Number of non-zero terms (informational)
mat	Output matrix
kmat	Optional matrix identifier
mrows	Optional number of rows (defaults to n) Allocate matrix storage and initialize dimensions, bandwidths, identifiers, and pivots.

◆ init() [4/8]

void orb5x::spclibs::init	(	int	kl,
		int	ku,
		int	n,
		int	nterms,
		ZPeriodicMat &	mat,
		int	kmat = `0`
	)

Initialize a real periodic band matrix and Woodbury factors.

Parameters

[in]	kl	Number of subdiagonals.
[in]	ku	Number of superdiagonals.
[in]	n	Square matrix dimension.
[in]	nterms	Informational assembled-term count.
[out]	mat	Allocated periodic descriptor.
[in]	kmat	Optional caller-defined identifier. Allocate matrix storage and initialize dimensions, bandwidths, identifiers, and pivots.

◆ init() [5/8]

void orb5x::spclibs::init	(	int	ku,
		int	n,
		int	nterms,
		PBMat &	mat,
		int	kmat = `0`
	)

Initialize a real symmetric positive-definite band matrix.

Parameters

[in]	ku	Number of stored upper superdiagonals.
[in]	n	Square matrix dimension.
[in]	nterms	Informational assembled-term count.
[out]	mat	Allocated packed-band descriptor.
[in]	kmat	Optional caller-defined identifier. Allocate matrix storage and initialize dimensions, bandwidths, identifiers, and pivots.

◆ init() [6/8]

void orb5x::spclibs::init	(	int	ku,
		int	n,
		int	nterms,
		ZPBMat &	mat,
		int	kmat = `0`
	)

Initialize a real symmetric positive-definite band matrix.

Parameters

[in]	ku	Number of stored upper superdiagonals.
[in]	n	Square matrix dimension.
[in]	nterms	Informational assembled-term count.
[out]	mat	Allocated packed-band descriptor.
[in]	kmat	Optional caller-defined identifier. Allocate matrix storage and initialize dimensions, bandwidths, identifiers, and pivots.

◆ init() [7/8]

void orb5x::spclibs::init	(	int	n,
		int	nterms,
		GEMat &	mat,
		int	kmat = `0`,
		int	mrows = `-1`
	)

Initialize a real general dense matrix.

Parameters

[in]	n	Number of columns and default row count.
[in]	nterms	Informational assembled-term count.
[out]	mat	Allocated matrix descriptor.
[in]	kmat	Optional caller-defined identifier.
[in]	mrows	Optional row count; negative selects `n`. Allocate matrix storage and initialize dimensions, bandwidths, identifiers, and pivots.

◆ init() [8/8]

void orb5x::spclibs::init	(	int	n,
		int	nterms,
		ZGEMat &	mat,
		int	kmat = `0`,
		int	mrows = `-1`
	)

Initialize a real general dense matrix.

Parameters

[in]	n	Number of columns and default row count.
[in]	nterms	Informational assembled-term count.
[out]	mat	Allocated matrix descriptor.
[in]	kmat	Optional caller-defined identifier.
[in]	mrows	Optional row count; negative selects `n`. Allocate matrix storage and initialize dimensions, bandwidths, identifiers, and pivots.

◆ interv()

void orb5x::spclibs::interv	(	const Real *	xt,
		int	lxt,
		Real	x,
		int &	left,
		int &	mflag
	)

Locate interval containing x in a knot sequence.

Given a nondecreasing sequence xt and a value x, finds the largest index left such that xt[left] <= x.

Parameters

xt	Knot sequence (lxt elements)
lxt	Length of knot sequence
x	Point to locate
left	Output: index of bracketing value 0 if x < xt[0] i if xt[i] <= x < xt[i+1] lxt-1 if xt[lxt-1] <= x
mflag	Output: indicates position relative to knot sequence -1: x < xt[0] 0: xt[left] <= x < xt[left+1] +1: xt[lxt-1] <= x

Note: Uses 0-based indexing

◆ interv_hint()

void orb5x::spclibs::interv_hint	(	const Real *	xt,
		int	lxt,
		Real	x,
		int &	left,
		int &	mflag,
		int &	ilo
	)

Thread-safe version of interv with explicit previous guess.

Parameters

xt	Knot sequence
lxt	Length of sequence
x	Point to locate
left	Output: interval index
mflag	Output: boundary flag
ilo	Previous guess for left (updated on output)

◆ is_equid()

bool orb5x::spclibs::is_equid	(	const Real *	grid,
		int	n
	)

Check if a grid is equidistant.

Parameters

[in]	grid	Grid coordinates of length `n`.
[in]	n	Number of coordinates.

Returns: true if grid is equidistant (within tolerance)

◆ locintv()

void orb5x::spclibs::locintv	(	const Spline1D &	sp,
		Real	x,
		int &	left
	)

Locate interval containing x in spline knot sequence.

Parameters

[in]	sp	Initialized spline and knot sequence.
[in]	x	Coordinate to locate; periodic coordinates are wrapped by `lperiod`.
[out]	left	Clamped zero-based interval index in `[0,nints-1]`.

◆ maddto() [1/4]

void orb5x::spclibs::maddto	(	Real	alpha,
		const GBMat &	a,
		GBMat &	b
	)

Accumulate B = B + alpha*A without changing storage layout.

Parameters

[in]	alpha	Scalar multiplier.
[in]	a	Source matrix.
[in,out]	b	Compatible destination/accumulator matrix.

◆ maddto() [2/4]

void orb5x::spclibs::maddto	(	Real	alpha,
		const GEMat &	a,
		GEMat &	b
	)

Accumulate B = B + alpha*A without changing storage layout.

Parameters

[in]	alpha	Scalar multiplier.
[in]	a	Source matrix.
[in,out]	b	Compatible destination/accumulator matrix.

◆ maddto() [3/4]

void orb5x::spclibs::maddto	(	Real	alpha,
		const PBMat &	a,
		PBMat &	b
	)

Accumulate B = B + alpha*A without changing storage layout.

Parameters

[in]	alpha	Scalar multiplier.
[in]	a	Source matrix.
[in,out]	b	Compatible destination/accumulator matrix.

◆ maddto() [4/4]

void orb5x::spclibs::maddto	(	Real	alpha,
		const PeriodicMat &	a,
		PeriodicMat &	b
	)

Accumulate B = B + alpha*A without changing storage layout.

Parameters

[in]	alpha	Scalar multiplier.
[in]	a	Source matrix.
[in,out]	b	Compatible destination/accumulator matrix.

◆ mcopy() [1/4]

void orb5x::spclibs::mcopy	(	const GBMat &	src,
		GBMat &	dst
	)

Deep-copy matrix metadata and numerical storage.

Parameters

[in]	src	Initialized source matrix.
[out]	dst	Independently allocated destination matrix.

◆ mcopy() [2/4]

void orb5x::spclibs::mcopy	(	const GEMat &	src,
		GEMat &	dst
	)

Deep-copy matrix metadata and numerical storage.

Parameters

[in]	src	Initialized source matrix.
[out]	dst	Independently allocated destination matrix.

◆ mcopy() [3/4]

void orb5x::spclibs::mcopy	(	const PBMat &	src,
		PBMat &	dst
	)

Deep-copy matrix metadata and numerical storage.

Parameters

[in]	src	Initialized source matrix.
[out]	dst	Independently allocated destination matrix.

◆ mcopy() [4/4]

void orb5x::spclibs::mcopy	(	const PeriodicMat &	src,
		PeriodicMat &	dst
	)

Deep-copy matrix metadata and numerical storage.

Parameters

[in]	src	Initialized source matrix.
[out]	dst	Independently allocated destination matrix.

◆ ppval()

Real orb5x::spclibs::ppval	(	const Real *	t,
		const Real *	coef,
		int	n,
		int	k,
		Real	x,
		int &	left
	)

Evaluate polynomial in piecewise polynomial form.

Evaluates the piecewise polynomial at point x using the PPFORM coefficients.

Parameters

t	Breakpoints (n+1 elements)
coef	PPFORM coefficients (k x n, column-major)
n	Number of intervals
k	Order of polynomial
x	Point at which to evaluate
left	Hint for interval location

Returns: Value of polynomial at x

◆ putcol() [1/5]

void orb5x::spclibs::putcol	(	GBMat &	mat,
		int	j,
		const Real *	col
	)

Replace one zero-based logical matrix column.

Parameters

[in,out]	mat	Matrix to modify.
[in]	j	Zero-based logical column.
[in]	col	Contiguous input with at least `mrows` elements.

◆ putcol() [2/5]

void orb5x::spclibs::putcol	(	GEMat &	mat,
		int	j,
		const Real *	col
	)

Replace one zero-based logical matrix column.

Parameters

[in,out]	mat	Matrix to modify.
[in]	j	Zero-based logical column.
[in]	col	Contiguous input with at least `mrows` elements.

◆ putcol() [3/5]

void orb5x::spclibs::putcol	(	PBMat &	mat,
		int	j,
		const Real *	col
	)

Replace one zero-based logical matrix column.

Parameters

[in,out]	mat	Matrix to modify.
[in]	j	Zero-based logical column.
[in]	col	Contiguous input with at least `mrows` elements.

◆ putcol() [4/5]

void orb5x::spclibs::putcol	(	PeriodicMat &	mat,
		int	j,
		const Real *	col
	)

Replace one zero-based logical matrix column.

Parameters

[in,out]	mat	Matrix to modify.
[in]	j	Zero-based logical column.
[in]	col	Contiguous input with at least `mrows` elements.

◆ putcol() [5/5]

void orb5x::spclibs::putcol	(	ZPBMat &	mat,
		int	j,
		const Complex *	col
	)

Replace one zero-based logical matrix column.

Parameters

[in,out]	mat	Matrix to modify.
[in]	j	Zero-based logical column.
[in]	col	Contiguous input with at least `mrows` elements.

◆ putele() [1/6]

void orb5x::spclibs::putele	(	GBMat &	mat,
		Real	val,
		int	i,
		int	j
	)

Assign one zero-based logical matrix element.

Parameters

[in,out]	mat	Matrix to modify.
[in]	val	New scalar value.
[in]	i	Zero-based logical row.
[in]	j	Zero-based logical column.

◆ putele() [2/6]

void orb5x::spclibs::putele	(	PBMat &	mat,
		Real	val,
		int	i,
		int	j
	)

Assign one zero-based logical matrix element.

Parameters

[in,out]	mat	Matrix to modify.
[in]	val	New scalar value.
[in]	i	Zero-based logical row.
[in]	j	Zero-based logical column.

◆ putele() [3/6]

void orb5x::spclibs::putele	(	PeriodicMat &	mat,
		Real	val,
		int	i,
		int	j
	)

Assign one zero-based logical matrix element.

Parameters

[in,out]	mat	Matrix to modify.
[in]	val	New scalar value.
[in]	i	Zero-based logical row.
[in]	j	Zero-based logical column.

◆ putele() [4/6]

void orb5x::spclibs::putele	(	ZGBMat &	mat,
		Complex	val,
		int	i,
		int	j
	)

Assign one zero-based logical matrix element.

Parameters

[in,out]	mat	Matrix to modify.
[in]	val	New scalar value.
[in]	i	Zero-based logical row.
[in]	j	Zero-based logical column.

◆ putele() [5/6]

void orb5x::spclibs::putele	(	ZPBMat &	mat,
		Complex	val,
		int	i,
		int	j
	)

Assign one zero-based logical matrix element.

Parameters

[in,out]	mat	Matrix to modify.
[in]	val	New scalar value.
[in]	i	Zero-based logical row.
[in]	j	Zero-based logical column.

◆ putele() [6/6]

void orb5x::spclibs::putele	(	ZPeriodicMat &	mat,
		Complex	val,
		int	i,
		int	j
	)

Assign one zero-based logical matrix element.

Parameters

[in,out]	mat	Matrix to modify.
[in]	val	New scalar value.
[in]	i	Zero-based logical row.
[in]	j	Zero-based logical column.

◆ putrow() [1/5]

void orb5x::spclibs::putrow	(	GBMat &	mat,
		int	i,
		const Real *	row
	)

Replace one zero-based logical matrix row.

Parameters

[in,out]	mat	Matrix to modify.
[in]	i	Zero-based logical row.
[in]	row	Contiguous input with at least `ncols` elements.

◆ putrow() [2/5]

void orb5x::spclibs::putrow	(	GEMat &	mat,
		int	i,
		const Real *	row
	)

Replace one zero-based logical matrix row.

Parameters

[in,out]	mat	Matrix to modify.
[in]	i	Zero-based logical row.
[in]	row	Contiguous input with at least `ncols` elements.

◆ putrow() [3/5]

void orb5x::spclibs::putrow	(	PBMat &	mat,
		int	i,
		const Real *	row
	)

Replace one zero-based logical matrix row.

Parameters

[in,out]	mat	Matrix to modify.
[in]	i	Zero-based logical row.
[in]	row	Contiguous input with at least `ncols` elements.

◆ putrow() [4/5]

void orb5x::spclibs::putrow	(	PeriodicMat &	mat,
		int	i,
		const Real *	row
	)

Replace one zero-based logical matrix row.

Parameters

[in,out]	mat	Matrix to modify.
[in]	i	Zero-based logical row.
[in]	row	Contiguous input with at least `ncols` elements.

◆ putrow() [5/5]

void orb5x::spclibs::putrow	(	ZPBMat &	mat,
		int	i,
		const Complex *	row
	)

Replace one zero-based logical matrix row.

Parameters

[in,out]	mat	Matrix to modify.
[in]	i	Zero-based logical row.
[in]	row	Contiguous input with at least `ncols` elements.

◆ set_splcoef()

void orb5x::spclibs::set_splcoef	(	Spline1D &	sp,
		const Real *	fvals,
		Real *	bcoef
	)

Set spline coefficients from function values.

Computes spline coefficients by interpolation: solve M * bcoef = fvals where M is the interpolation matrix.

Parameters

[in]	sp	Spline with its appropriate periodic or nonperiodic interpolation matrix initialized.
[in]	fvals	Function values at `sp.dim` interpolation sites.
[out]	bcoef	Array of `sp.dim` coefficients; initially receives a copy of `fvals` and is overwritten by the matrix solve when the matrix exists.

◆ set_spline() [1/3]

void orb5x::spclibs::set_spline	(	const int	p[2],
		const int	ngauss[2],
		const Real *	grid1,
		int	ngrid1,
		const Real *	grid2,
		int	ngrid2,
		Spline2D &	sp,
		const bool	period[2] = `nullptr`,
		bool	nlppform = `true`,
		const int	nlequid[2] = `nullptr`
	)

Initialize a 2D spline.

Parameters

[in]	p	Polynomial degrees `[direction 1,direction 2]`.
[in]	ngauss	Gauss-point counts per interval in the two directions.
[in]	grid1	First-direction grid edges of length `ngrid1`.
[in]	ngrid1	Number of first-direction grid edges.
[in]	grid2	Second-direction grid edges of length `ngrid2`.
[in]	ngrid2	Number of second-direction grid edges.
[out]	sp	Initialized tensor-product descriptor and coefficient View.
[in]	period	Optional two-element periodicity flags; null means nonperiodic.
[in]	nlppform	Use cached piecewise-polynomial basis evaluation.
[in]	nlequid	Optional two-element equidistance overrides; null auto-detects.

Fortran reference bsplines.f90: two-dimensional set_spline interface.

◆ set_spline() [2/3]

void orb5x::spclibs::set_spline	(	const int	p[3],
		const int	ngauss[3],
		const Real *	grid1,
		int	ngrid1,
		const Real *	grid2,
		int	ngrid2,
		const Real *	grid3,
		int	ngrid3,
		Spline2D1D &	sp,
		const bool	period[3] = `nullptr`,
		bool	nlppform = `true`,
		const int	nlequid[3] = `nullptr`
	)

Initialize a 2D+1D spline.

Parameters

[in]	p	Polynomial degrees for the three directions.
[in]	ngauss	Gauss-point counts per interval for the three directions.
[in]	grid1	First-direction grid edges of length `ngrid1`.
[in]	ngrid1	Number of first-direction grid edges.
[in]	grid2	Second-direction grid edges of length `ngrid2`.
[in]	ngrid2	Number of second-direction grid edges.
[in]	grid3	Third-direction grid edges of length `ngrid3`.
[in]	ngrid3	Number of third-direction grid edges.
[out]	sp	Initialized 2-D-plus-1-D descriptor and coefficient View.
[in]	period	Optional three-element periodicity flags; null means nonperiodic.
[in]	nlppform	Use cached piecewise-polynomial basis evaluation.
[in]	nlequid	Optional three-element equidistance overrides; null auto-detects.

Fortran reference bsplines.f90: set_spline2d1d family.

◆ set_spline() [3/3]

void orb5x::spclibs::set_spline	(	int	p,
		int	ngauss,
		const Real *	grid,
		int	ngrid,
		Spline1D &	sp,
		bool	period = `false`,
		bool	nlppform = `true`,
		int	nlequid = `-1`
	)

Initialize a 1D spline.

Parameters

[in]	p	Polynomial degree; the stored order is `p+1`.
[in]	ngauss	Gauss–Legendre points per interval, or zero to omit quadrature.
[in]	grid	Strictly ordered grid edges of length `ngrid`.
[in]	ngrid	Number of grid edges; creates `ngrid-1` intervals.
[out]	sp	Initialized descriptor, cached bases, quadrature, integrals, and coefficients.
[in]	period	Wrap the knot extension and basis indices periodically.
[in]	nlppform	Use cached piecewise-polynomial basis values during evaluation.
[in]	nlequid	Equidistance override: negative detects it, zero disables it, and a positive value enables the direct uniform-grid locator.

Fortran reference bsplines.f90: set_spline1d.

◆ updtmat() [1/7]

void orb5x::spclibs::updtmat	(	GBMat &	mat,
		Real	val,
		int	i,
		int	j
	)

Update matrix element: mat(i,j) += val.

Parameters

mat	Matrix to update
val	Value to add
i	Row index (0-based)
j	Column index (0-based)

◆ updtmat() [2/7]

void orb5x::spclibs::updtmat	(	GEMat &	mat,
		Real	val,
		int	i,
		int	j
	)

Update matrix element: mat(i,j) += val.

Parameters

mat	Matrix to update
val	Value to add
i	Row index (0-based)
j	Column index (0-based)

◆ updtmat() [3/7]

void orb5x::spclibs::updtmat	(	PBMat &	mat,
		Real	val,
		int	i,
		int	j
	)

Update matrix element: mat(i,j) += val.

Parameters

mat	Matrix to update
val	Value to add
i	Row index (0-based)
j	Column index (0-based)

◆ updtmat() [4/7]

void orb5x::spclibs::updtmat	(	PeriodicMat &	mat,
		Real	val,
		int	i,
		int	j
	)

Update matrix element: mat(i,j) += val.

Parameters

mat	Matrix to update
val	Value to add
i	Row index (0-based)
j	Column index (0-based)

◆ updtmat() [5/7]

void orb5x::spclibs::updtmat	(	ZGBMat &	mat,
		Complex	val,
		int	i,
		int	j
	)

Update matrix element: mat(i,j) += val.

Parameters

mat	Matrix to update
val	Value to add
i	Row index (0-based)
j	Column index (0-based)

◆ updtmat() [6/7]

void orb5x::spclibs::updtmat	(	ZPBMat &	mat,
		Complex	val,
		int	i,
		int	j
	)

Update matrix element: mat(i,j) += val.

Parameters

mat	Matrix to update
val	Value to add
i	Row index (0-based)
j	Column index (0-based)

◆ updtmat() [7/7]

void orb5x::spclibs::updtmat	(	ZPeriodicMat &	mat,
		Complex	val,
		int	i,
		int	j
	)

Update matrix element: mat(i,j) += val.

Parameters

mat	Matrix to update
val	Value to add
i	Row index (0-based)
j	Column index (0-based)

◆ vmx() [1/10]

void orb5x::spclibs::vmx	(	const GBMat &	mat,
		const Real *	x,
		Real *	y
	)

Compute y = A*x.

Parameters

mat	Matrix A
x	Input vector
y	Output vector

◆ vmx() [2/10]

void orb5x::spclibs::vmx	(	const GBMat &	mat,
		const Real *	x,
		Real *	y,
		int	nrhs
	)

Compute Y = A*X for multiple vectors.

Parameters

mat	Matrix A
x	Input vectors (n x nrhs)
y	Output vectors (n x nrhs)
nrhs	Number of right-hand sides

◆ vmx() [3/10]

void orb5x::spclibs::vmx	(	const GEMat &	mat,
		const Real *	x,
		Real *	y
	)

Compute y = A*x.

Parameters

mat	Matrix A
x	Input vector
y	Output vector

◆ vmx() [4/10]

void orb5x::spclibs::vmx	(	const GEMat &	mat,
		const Real *	x,
		Real *	y,
		int	nrhs
	)

Compute Y = A*X for multiple vectors.

Parameters

mat	Matrix A
x	Input vectors (n x nrhs)
y	Output vectors (n x nrhs)
nrhs	Number of right-hand sides

◆ vmx() [5/10]

void orb5x::spclibs::vmx	(	const PBMat &	mat,
		const Real *	x,
		Real *	y
	)

Compute y = A*x.

Parameters

mat	Matrix A
x	Input vector
y	Output vector

◆ vmx() [6/10]

void orb5x::spclibs::vmx	(	const PeriodicMat &	mat,
		const Real *	x,
		Real *	y
	)

Compute y = A*x.

Parameters

mat	Matrix A
x	Input vector
y	Output vector

◆ vmx() [7/10]

void orb5x::spclibs::vmx	(	const ZGBMat &	mat,
		const Complex *	x,
		Complex *	y
	)

Compute y = A*x.

Parameters

mat	Matrix A
x	Input vector
y	Output vector

◆ vmx() [8/10]

void orb5x::spclibs::vmx	(	const ZGEMat &	mat,
		const Complex *	x,
		Complex *	y
	)

Compute y = A*x.

Parameters

mat	Matrix A
x	Input vector
y	Output vector

◆ vmx() [9/10]

void orb5x::spclibs::vmx	(	const ZPBMat &	mat,
		const Complex *	x,
		Complex *	y
	)

Compute y = A*x.

Parameters

mat	Matrix A
x	Input vector
y	Output vector

◆ vmx() [10/10]

void orb5x::spclibs::vmx	(	const ZPeriodicMat &	mat,
		const Complex *	x,
		Complex *	y
	)

Compute y = A*x.

Parameters

mat	Matrix A
x	Input vector
y	Output vector

Variable Documentation

◆ JMAX

constexpr int orb5x::spclibs::JMAX = 20

constexpr

Maximum spline order supported (degree + 1)

Classes

Typedefs

Functions

Variables

Typedef Documentation

◆ spline1d

◆ spline2d

◆ spline2d1d

Function Documentation

◆ basfun()

◆ bsolve() [1/8]

◆ bsolve() [2/8]

◆ bsolve() [3/8]

◆ bsolve() [4/8]

◆ bsolve() [5/8]

◆ bsolve() [6/8]

◆ bsolve() [7/8]

◆ bsolve() [8/8]

◆ bsplvb()

◆ bsplvd()

◆ bspp2d()

◆ calc_integ()

◆ CompMassMatrix() [1/2]

◆ CompMassMatrix() [2/2]

◆ def_basfun()

◆ destroy() [1/8]

◆ destroy() [2/8]

◆ destroy() [3/8]

◆ destroy() [4/8]

◆ destroy() [5/8]

◆ destroy() [6/8]

◆ destroy() [7/8]

◆ destroy() [8/8]

◆ destroy_sp() [1/3]

◆ destroy_sp() [2/3]

◆ destroy_sp() [3/3]

◆ determinant() [1/6]

◆ determinant() [2/6]

◆ determinant() [3/6]

◆ determinant() [4/6]

◆ determinant() [5/6]

◆ determinant() [6/6]

◆ factor() [1/8]

◆ factor() [2/8]

◆ factor() [3/8]

◆ factor() [4/8]

◆ factor() [5/8]

◆ factor() [6/8]

◆ factor() [7/8]

◆ factor() [8/8]

◆ gauleg()

◆ get_dim() [1/2]

◆ get_dim() [2/2]

◆ get_gauss()

◆ get_splcoef()

◆ getcol() [1/3]

◆ getcol() [2/3]

◆ getcol() [3/3]

◆ getele() [1/6]

◆ getele() [2/6]

◆ getele() [3/6]

◆ getele() [4/6]

◆ getele() [5/6]

◆ getele() [6/6]

◆ getrow() [1/5]

◆ getrow() [2/5]

◆ getrow() [3/5]

◆ getrow() [4/5]

◆ getrow() [5/5]

◆ getvalp() [1/6]

◆ getvalp() [2/6]

◆ getvalp() [3/6]

◆ getvalp() [4/6]

◆ getvalp() [5/6]

◆ getvalp() [6/6]

◆ gridval() [1/3]

◆ gridval() [2/3]

◆ gridval() [3/3]

◆ init() [1/8]

◆ init() [2/8]