orb5x::spclibs Namespace Reference

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
using	spline2d = Spline2D
using	spline2d1d = 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)
void	bsolve (const PBMat &mat, Real *b, int nrhs=1)
void	bsolve (const PeriodicMat &mat, Real *b, int nrhs=1)
void	bsolve (const ZGBMat &mat, Complex *b, int nrhs=1)
void	bsolve (const ZGEMat &mat, Complex *b, int nrhs=1)
void	bsolve (const ZPBMat &mat, Complex *b, int nrhs=1)
void	bsolve (const ZPeriodicMat &mat, Complex *b, int nrhs=1)
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)
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)
void	destroy (GEMat &mat)
void	destroy (PBMat &mat)
void	destroy (PeriodicMat &mat)
void	destroy (ZGBMat &mat)
void	destroy (ZGEMat &mat)
void	destroy (ZPBMat &mat)
void	destroy (ZPeriodicMat &mat)
void	destroy_sp (Spline1D &sp)
void	destroy_sp (Spline2D &sp)
void	destroy_sp (Spline2D1D &sp)
Real	determinant (const GBMat &mat)
	Compute determinant of factorized matrix.
Real	determinant (const GEMat &mat)
Real	determinant (const PBMat &mat)
Complex	determinant (const ZGBMat &mat)
Complex	determinant (const ZGEMat &mat)
Complex	determinant (const ZPBMat &mat)
int	factor (GBMat &mat)
	Compute LU factorization of matrix.
int	factor (GEMat &mat)
int	factor (PBMat &mat)
int	factor (PeriodicMat &mat)
int	factor (ZGBMat &mat)
int	factor (ZGEMat &mat)
int	factor (ZPBMat &mat)
int	factor (ZPeriodicMat &mat)
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 2D 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)
	Get column of matrix.
void	getcol (const PBMat &mat, int j, Real *col)
void	getcol (const PeriodicMat &mat, int j, Real *col)
Real	getele (const GBMat &mat, int i, int j)
	Get matrix element.
Real	getele (const PBMat &mat, int i, int j)
Real	getele (const PeriodicMat &mat, int i, int j)
Complex	getele (const ZGBMat &mat, int i, int j)
Complex	getele (const ZPBMat &mat, int i, int j)
Complex	getele (const ZPeriodicMat &mat, int i, int j)
void	getrow (const GBMat &mat, int i, Real *row)
	Get row of matrix.
void	getrow (const GEMat &mat, int i, Real *row)
void	getrow (const PBMat &mat, int i, Real *row)
void	getrow (const PeriodicMat &mat, int i, Real *row)
void	getrow (const ZPBMat &mat, int i, Complex *row)
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)
Real *	getvalp (PBMat &mat, int i, int j)
Complex *	getvalp (ZGBMat &mat, int i, int j)
Complex *	getvalp (ZGEMat &mat, int i, int j)
Complex *	getvalp (ZPBMat &mat, int i, int j)
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 2D spline on a 2D 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 periodic band matrix.
void	init (int kl, int ku, int n, int nterms, ZGBMat &mat, int kmat=0, int mrows=-1)
void	init (int kl, int ku, int n, int nterms, ZPeriodicMat &mat, int kmat=0)
void	init (int ku, int n, int nterms, PBMat &mat, int kmat=0)
	Initialize a packed band matrix.
void	init (int ku, int n, int nterms, ZPBMat &mat, int kmat=0)
void	init (int n, int nterms, GEMat &mat, int kmat=0, int mrows=-1)
	Initialize a general dense matrix.
void	init (int n, int nterms, ZGEMat &mat, int kmat=0, int mrows=-1)
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)
	Add matrices: B = B + alpha*A.
void	maddto (Real alpha, const GEMat &a, GEMat &b)
void	maddto (Real alpha, const PBMat &a, PBMat &b)
void	maddto (Real alpha, const PeriodicMat &a, PeriodicMat &b)
void	mcopy (const GBMat &src, GBMat &dst)
void	mcopy (const GEMat &src, GEMat &dst)
void	mcopy (const PBMat &src, PBMat &dst)
void	mcopy (const PeriodicMat &src, PeriodicMat &dst)
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)
	Set column of matrix.
void	putcol (GEMat &mat, int j, const Real *col)
void	putcol (PBMat &mat, int j, const Real *col)
void	putcol (PeriodicMat &mat, int j, const Real *col)
void	putcol (ZPBMat &mat, int j, const Complex *col)
void	putele (GBMat &mat, Real val, int i, int j)
	Set matrix element.
void	putele (PBMat &mat, Real val, int i, int j)
void	putele (PeriodicMat &mat, Real val, int i, int j)
void	putele (ZGBMat &mat, Complex val, int i, int j)
void	putele (ZPBMat &mat, Complex val, int i, int j)
void	putele (ZPeriodicMat &mat, Complex val, int i, int j)
void	putrow (GBMat &mat, int i, const Real *row)
	Set row of matrix.
void	putrow (GEMat &mat, int i, const Real *row)
void	putrow (PBMat &mat, int i, const Real *row)
void	putrow (PeriodicMat &mat, int i, const Real *row)
void	putrow (ZPBMat &mat, int i, const Complex *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)
void	updtmat (PBMat &mat, Real val, int i, int j)
void	updtmat (PeriodicMat &mat, Real val, int i, int j)
void	updtmat (ZGBMat &mat, Complex val, int i, int j)
void	updtmat (ZPBMat &mat, Complex val, int i, int j)
void	updtmat (ZPeriodicMat &mat, Complex val, int i, int j)
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)
void	vmx (const GEMat &mat, const Real *x, Real *y, int nrhs)
void	vmx (const PBMat &mat, const Real *x, Real *y)
void	vmx (const PeriodicMat &mat, const Real *x, Real *y)
void	vmx (const ZGBMat &mat, const Complex *x, Complex *y)
void	vmx (const ZGEMat &mat, const Complex *x, Complex *y)
void	vmx (const ZPBMat &mat, const Complex *x, Complex *y)
void	vmx (const ZPeriodicMat &mat, const Complex *x, Complex *y)

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

Typedef Documentation

spline1d

using orb5x::spclibs::spline1d = Spline1D

spline2d

using orb5x::spclibs::spline2d = Spline2D

spline2d1d

using orb5x::spclibs::spline2d1d = 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

x	Point at which to evaluate
sp	Spline
fun	Output: basis function values and derivatives fun[i + j*order] = jth derivative of ith basis function i = 0, ..., order-1 (basis functions) j = 0, ..., nderiv-1 (derivatives)
left	Interval index (1-based as in Fortran)
nderiv	Number of derivatives to compute (including function value)

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 )

bsolve() [3/8]

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

bsolve() [4/8]

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

bsolve() [5/8]

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

bsolve() [6/8]

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

bsolve() [7/8]

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

bsolve() [8/8]

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

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

sp	Spline
integ	Output: integrals (sp.dim elements)

CompMassMatrix() [1/2]

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

Compute mass matrix for FEM discretization.

Parameters

sp	Spline
mat	Output: mass matrix

CompMassMatrix() [2/2]

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

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

x	Point at which to evaluate
sp	Spline
fun	Output: basis function values and derivatives
left	Output (optional): interval index (0-based)
nderiv	Number of derivatives

destroy() [1/8]

void orb5x::spclibs::destroy

(

GBMat &

mat

)

destroy() [2/8]

void orb5x::spclibs::destroy

(

GEMat &

mat

)

destroy() [3/8]

void orb5x::spclibs::destroy

(

PBMat &

mat

)

destroy() [4/8]

void orb5x::spclibs::destroy

(

PeriodicMat &

mat

)

destroy() [5/8]

void orb5x::spclibs::destroy

(

ZGBMat &

mat

)

destroy() [6/8]

void orb5x::spclibs::destroy

(

ZGEMat &

mat

)

destroy() [7/8]

void orb5x::spclibs::destroy

(

ZPBMat &

mat

)

destroy() [8/8]

void orb5x::spclibs::destroy

(

ZPeriodicMat &

mat

)

destroy_sp() [1/3]

void orb5x::spclibs::destroy_sp

(

Spline1D &

sp

)

destroy_sp() [2/3]

void orb5x::spclibs::destroy_sp

(

Spline2D &

sp

)

destroy_sp() [3/3]

void orb5x::spclibs::destroy_sp

(

Spline2D1D &

sp

)

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

)

determinant() [3/6]

Real orb5x::spclibs::determinant

(

const PBMat &

mat

)

determinant() [4/6]

Complex orb5x::spclibs::determinant

(

const ZGBMat &

mat

)

determinant() [5/6]

Complex orb5x::spclibs::determinant

(

const ZGEMat &

mat

)

determinant() [6/6]

Complex orb5x::spclibs::determinant

(

const ZPBMat &

mat

)

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

)

factor() [3/8]

int orb5x::spclibs::factor

(

PBMat &

mat

)

factor() [4/8]

int orb5x::spclibs::factor

(

PeriodicMat &

mat

)

factor() [5/8]

int orb5x::spclibs::factor

(

ZGBMat &

mat

)

factor() [6/8]

int orb5x::spclibs::factor

(

ZGEMat &

mat

)

factor() [7/8]

int orb5x::spclibs::factor

(

ZPBMat &

mat

)

factor() [8/8]

int orb5x::spclibs::factor

(

ZPeriodicMat &

mat

)

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

sp	Input spline
dim	Output: dimension of spline space
nx	Output (optional): number of intervals
nidbas	Output (optional): spline degree

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 2D spline.

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

sp	Input spline
n	Output: number of Gauss points per interval
i	Optional: interval index (0-based)
x	Output (if i provided): Gauss points for interval i
w	Output (if i provided): Gauss weights for interval 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

sp	Spline
bcoef	Spline coefficients
fvals	Output: function values

getcol() [1/3]

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

Get column of matrix.

getcol() [2/3]

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

getcol() [3/3]

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

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 )

getele() [3/6]

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

getele() [4/6]

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

getele() [5/6]

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

getele() [6/6]

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

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 )

getrow() [3/5]

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

getrow() [4/5]

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

getrow() [5/5]

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

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.

getvalp() [2/6]

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

getvalp() [3/6]

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

getvalp() [4/6]

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

getvalp() [5/6]

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

getvalp() [6/6]

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

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

sp	Spline
xgrid	Grid of points (npts points)
npts	Number of grid points
bcoef	Spline coefficients (sp.dim elements)
fvals	Output: function values at grid points
jder	Derivative order to compute (default 0 = function value)

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 2D spline on a 2D grid.

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

sp	2D+1D spline (sp12 for first two dimensions, sp3 for third)
xgrid1	Grid points in direction 1 (npts1 points)
npts1	Number of grid points in direction 1
xgrid2	Grid points in direction 2 (npts2 points)
npts2	Number of grid points in direction 2
xgrid3	Grid points in direction 3 (npts3 points)
npts3	Number of grid points in direction 3
bcoef	Spline coefficients (dim1 * dim2 * dim3 elements, row-major)
fvals	Output: function values at grid points (npts1 * npts2 * npts3, row-major)
jder1	Derivative order in direction 1 (default 0)
jder2	Derivative order in direction 2 (default 0)
jder3	Derivative order in direction 3 (default 0)

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)

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 periodic band matrix.

init() [3/8]

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

init() [4/8]

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

init() [5/8]

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

Initialize a packed band matrix.

init() [6/8]

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

init() [7/8]

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

Initialize a general dense matrix.

init() [8/8]

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

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

grid	Grid points
n	Number of grid points

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

sp	Spline
x	Point to locate
left	Output: interval index (0-based, 0 to nints-1)

maddto() [1/4]

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

Add matrices: B = B + alpha*A.

maddto() [2/4]

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

maddto() [3/4]

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

maddto() [4/4]

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

mcopy() [1/4]

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

mcopy() [2/4]

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

mcopy() [3/4]

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

mcopy() [4/4]

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

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 )

Set column of matrix.

putcol() [2/5]

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

putcol() [3/5]

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

putcol() [4/5]

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

putcol() [5/5]

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

putele() [1/6]

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

Set matrix element.

putele() [2/6]

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

putele() [3/6]

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

putele() [4/6]

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

putele() [5/6]

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

putele() [6/6]

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

putrow() [1/5]

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

Set row of matrix.

putrow() [2/5]

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

putrow() [3/5]

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

putrow() [4/5]

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

putrow() [5/5]

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

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

sp	Spline (must have interpolation matrix set up)
fvals	Function values at interpolation sites
bcoef	Output: spline coefficients

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

p	Degrees in each direction (p[0], p[1])
ngauss	Number of Gauss points in each direction
grid1	Grid points in direction 1
ngrid1	Number of grid points in direction 1
grid2	Grid points in direction 2
ngrid2	Number of grid points in direction 2
sp	Output: initialized 2D spline
period	Periodicity flags for each direction
nlppform	Use PPFORM for evaluation
nlequid	Equidistant flags (-1 for auto-detect)

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

p	Degrees in each direction (p[0], p[1], p[2])
ngauss	Number of Gauss points in each direction
grid1,grid2,grid3	Grid points in each direction
ngrid1,ngrid2,ngrid3	Number of grid points
sp	Output: initialized 2D+1D spline
period	Periodicity flags
nlppform	Use PPFORM
nlequid	Equidistant flags

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

p	Spline degree (order = p + 1)
ngauss	Number of Gauss quadrature points per interval (0 to skip)
grid	Grid points (nints+1 points defining nints intervals)
ngrid	Number of grid points
sp	Output: initialized spline
period	Whether the spline is periodic
nlppform	Whether to use PPFORM for evaluation (default true)
nlequid	Whether the grid is equidistant (auto-detected if not specified)

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 )

updtmat() [3/7]

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

updtmat() [4/7]

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

updtmat() [5/7]

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

updtmat() [6/7]

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

updtmat() [7/7]

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

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 )

vmx() [4/10]

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

vmx() [5/10]

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

vmx() [6/10]

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

vmx() [7/10]

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

vmx() [8/10]

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

vmx() [9/10]

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

vmx() [10/10]

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

Variable Documentation

JMAX

int orb5x::spclibs::JMAX = 20

constexpr

Maximum spline order supported (degree + 1).