chebyshev_m – chebpak

Uses

- f95_precision
- utils_math_m
- blas95
- constants_m

Functions

public function cheb_eval(n, x) result(res)

Evaluates a Chebyshev polynomial of degree n at x (-1 <= x <= 1).

Arguments

Type	Intent	Optional	Attributes		Name
integer,	intent(in)			::	n
real(kind=rp),	intent(in)			::	x

Return Value real(kind=rp)

public function cheb_ser_eval(n, c, x) result(res)

f(x), x E [-1,1] is given by the following appproximation formula in terms of Chebyshev polynomials:

Arguments

Type	Intent	Attributes		Name
integer,	intent(in)		::	n	Highest degree of T_n (x).
real(kind=rp),	intent(in),	dimension(0:n)	::	c	Chebyshev coefficients
real(kind=rp),	intent(in)		::	x	x E [-1,1] the point where the sum is to be evaluated.

Return Value real(kind=rp)

public function cheb_ser_eval2(nx, ny, c, x, y, rwrk) result(res)

f(x,y), (x,y) E [-1,1]x[-1,1] is given by the following appproximation formula in terms of Chebyshev polynomials:

Arguments

Type	Intent	Attributes		Name
integer,	intent(in)		::	nx	Highest degree of polynomial along x and y.
integer,	intent(in)		::	ny	Highest degree of polynomial along x and y.
real(kind=rp),	intent(in),	dimension(:)	::	c	Chebyshev coefficients
real(kind=rp),	intent(in)		::	x	(x,y) E [-1,1]x[-1,1] the point where the series is to be evaluated.
real(kind=rp),	intent(in)		::	y	(x,y) E [-1,1]x[-1,1] the point where the series is to be evaluated.
real(kind=rp),	intent(inout),	dimension(:)	::	rwrk	Work array of size at least ny+1

Return Value real(kind=rp)

public function cheb_ser_eval3(nx, ny, nz, c, x, y, z, rwrk) result(res)

f(x,y), (x,y) E [-1,1]x[-1,1] is given by the following appproximation formula in terms of Chebyshev polynomials:

Arguments

Type	Intent	Attributes		Name
integer,	intent(in)		::	nx	Highest degree of polynomial along x and y.
integer,	intent(in)		::	ny	Highest degree of polynomial along x and y.
integer,	intent(in)		::	nz	Highest degree of polynomial along x and y.
real(kind=rp),	intent(in),	dimension(:)	::	c	Chebyshev coefficients
real(kind=rp),	intent(in)		::	x	(x,y) E [-1,1]x[-1,1]x[-1,1] the point where the series is to be evaluated.
real(kind=rp),	intent(in)		::	y	(x,y) E [-1,1]x[-1,1]x[-1,1] the point where the series is to be evaluated.
real(kind=rp),	intent(in)		::	z	(x,y) E [-1,1]x[-1,1]x[-1,1] the point where the series is to be evaluated.
real(kind=rp),	intent(inout),	dimension(:)	::	rwrk	Work array of size at least nz + 1 + (max(ny,nz)+1)

Return Value real(kind=rp)

public function cheb_quad(tag, a, b, n, x, f) result(valint)

This subroutine evaluates an integral using Gauss-Chebyshev (CGL/CGR/CG) quadrature for a single variable.

Arguments

Type	Intent	Attributes		Name
character(len=*),	intent(in)		::	tag	{`'CGL'`, `'CG'`, `'CGR'`} Type of nodes, where `'CGL'`: Chebyshev-Gauss-Lobatto, `'CG'`: Chebyshev-Gauss, and `'CGR'`: Chebyshev-Gauss-Radau.
real(kind=rp),	intent(in)		::	a	Domain bounds [a, b]
real(kind=rp),	intent(in)		::	b	Domain bounds [a, b]
integer,	intent(in)		::	n	Number of nodes is n+1
real(kind=rp),	intent(in),	dimension(0:n)	::	x	Nodal coordinates in [-1, 1]
real(kind=rp),	intent(in),	dimension(0:n)	::	f	Value of the function at the nodes

Return Value real(kind=rp)

public function cheb_quad2(tag, x0, x1, y0, y1, nx, ny, x, y, f, rwrk) result(valint)

This subroutine evaluates an integral using Gauss-Chebyshev (CGL/CGR/CG) quadrature for two variables.

Arguments

Type	Intent	Attributes		Name
character(len=*),	intent(in)		::	tag	{`'CGL'`, `'CG'`, `'CGR'`} Type of nodes, where `'CGL'`: Chebyshev-Gauss-Lobatto, `'CG'`: Chebyshev-Gauss, and `'CGR'`: Chebyshev-Gauss-Radau.
real(kind=rp),	intent(in)		::	x0	Domain bounds [x0, x1]x[y0, y1] along x and y directions.
real(kind=rp),	intent(in)		::	x1	Domain bounds [x0, x1]x[y0, y1] along x and y directions.
real(kind=rp),	intent(in)		::	y0	Domain bounds [x0, x1]x[y0, y1] along x and y directions.
real(kind=rp),	intent(in)		::	y1	Domain bounds [x0, x1]x[y0, y1] along x and y directions.
integer,	intent(in)		::	nx	Number of nodes along x and y directions are (nx+1) and (ny+1)
integer,	intent(in)		::	ny	Number of nodes along x and y directions are (nx+1) and (ny+1)
real(kind=rp),	intent(in),	dimension(:)	::	x	(nx+1,). Nodal coordinates along x direction in [-1, 1]
real(kind=rp),	intent(in),	dimension(:)	::	y	(ny+1,). Nodal coordinates along y direction in [-1, 1]
real(kind=rp),	intent(in),	dimension(:)	::	f	((nx+1)*(ny+1),). Value of the function at the nodes
real(kind=rp),	intent(inout),	dimension(:)	::	rwrk	Workspace array of size at least (ny+1)

Return Value real(kind=rp)

public function cheb_quad3(tag, x0, x1, y0, y1, z0, z1, nx, ny, nz, x, y, z, f, rwrk) result(valint)

This subroutine evaluates an integral using Gauss-Chebyshev (CGL/CGR/CG) quadrature for three variables.

Arguments

Type	Intent	Attributes		Name
character(len=*),	intent(in)		::	tag	{`'CGL'`, `'CG'`, `'CGR'`} Type of nodes, where `'CGL'`: Chebyshev-Gauss-Lobatto, `'CG'`: Chebyshev-Gauss, and `'CGR'`: Chebyshev-Gauss-Radau.
real(kind=rp),	intent(in)		::	x0	Domain bounds [x0, x1]x[y0, y1]x[z0, z1] along x, y, and z directions.
real(kind=rp),	intent(in)		::	x1	Domain bounds [x0, x1]x[y0, y1]x[z0, z1] along x, y, and z directions.
real(kind=rp),	intent(in)		::	y0	Domain bounds [x0, x1]x[y0, y1]x[z0, z1] along x, y, and z directions.
real(kind=rp),	intent(in)		::	y1	Domain bounds [x0, x1]x[y0, y1]x[z0, z1] along x, y, and z directions.
real(kind=rp),	intent(in)		::	z0	Domain bounds [x0, x1]x[y0, y1]x[z0, z1] along x, y, and z directions.
real(kind=rp),	intent(in)		::	z1	Domain bounds [x0, x1]x[y0, y1]x[z0, z1] along x, y, and z directions.
integer,	intent(in)		::	nx	Number of nodes along x, y, and z directions are (nx+1), (ny+1), and (nz+1).
integer,	intent(in)		::	ny	Number of nodes along x, y, and z directions are (nx+1), (ny+1), and (nz+1).
integer,	intent(in)		::	nz	Number of nodes along x, y, and z directions are (nx+1), (ny+1), and (nz+1).
real(kind=rp),	intent(in),	dimension(:)	::	x	(nx+1,). Nodal coordinates along x direction in [-1,1]
real(kind=rp),	intent(in),	dimension(:)	::	y	(ny+1,). Nodal coordinates along y direction in [-1,1]
real(kind=rp),	intent(in),	dimension(:)	::	z	(nz+1,). Nodal coordinates along z direction in [-1,1]
real(kind=rp),	intent(in),	dimension(:)	::	f	((nx+1)(ny+1)(nz+1),). Value of the function at the nodes
real(kind=rp),	intent(inout),	dimension(:)	::	rwrk	Workspace array of size at least nz + 1 + (max(ny,nz)+1)

Return Value real(kind=rp)

public function lag_intrp(n, x, w, f, p) result(res)

Evaluates the Lagrange interpolant (barycentric) at a given point p from nodal coordinates and nodal function values in 1D.

Arguments

Type	Intent	Attributes		Name
integer,	intent(in)		::	n	Number of interpolant nodes = n+1.
real(kind=rp),	intent(in),	dimension(:)	::	x	(n,). Nodal coordinates in strictly ascending order
real(kind=rp),	intent(in),	dimension(:)	::	w	(n,). Barycentric weights
real(kind=rp),	intent(in),	dimension(:)	::	f	(n,). Value of the function at the nodes
real(kind=rp),	intent(in)		::	p	Coordinate of the interpolation point.

Return Value real(kind=rp)

Subroutines

public subroutine cheb_node(tag, a, b, n, xcol, is_descending)

This subroutine returns coordinates of the Chebyshev nodes in [a,b].

Arguments

Type	Intent	Optional	Attributes		Name
character(len=*),	intent(in)			::	tag	{`'CGL'`, `'CG'`, `'CGR'`} Type of nodes, where `'CGL'`: Chebyshev-Gauss-Lobatto, `'CG'`: Chebyshev-Gauss, and `'CGR'`: Chebyshev-Gauss-Radau.
real(kind=rp),	intent(in)			::	a	Domain bounds [a, b]
real(kind=rp),	intent(in)			::	b	Domain bounds [a, b]
integer,	intent(in)			::	n	Degree of polynomial.
real(kind=rp),	intent(out),		dimension(0:n)	::	xcol	(n+1,). Vector of nodal coordinates.
logical,	intent(in),	optional		::	is_descending	{T,F} Coordinates in ascending (default) or descending order.

public subroutine cheb_n1dmat(x0, x1, n, rwrk, dm)

Calculates the nodal first derivative matrix for CGL nodes in [x0,x1] Assumes the nodal coordinates to be in ascending order in the domain [-1,1].

Arguments

Type	Intent	Attributes		Name
real(kind=rp),	intent(in)		::	x0	Domain bounds [x0, x1]
real(kind=rp),	intent(in)		::	x1	Domain bounds [x0, x1]
integer,	intent(in)		::	n	Degree of the polynomial
real(kind=rp),	intent(inout),	dimension(:), target	::	rwrk	Workspace array of minimum size 2*(n+1)
real(kind=rp),	intent(out),	dimension(:,:)	::	dm	(n+1,n+1). Nodal first derivative matrix

public subroutine cheb_n2dmat(n, dm1, dm2)

Calculates the nodal second derivative matrix for CGL/CG/CGR nodes.

Arguments

Type	Intent	Attributes		Name
integer,	intent(in)		::	n	Degree of the polynomial
real(kind=rp),	intent(in),	dimension(:,:)	::	dm1	(n+1,n+1). Nodal first derivative matrix
real(kind=rp),	intent(out),	dimension(:,:)	::	dm2	(n+1,n+1). Nodal second derivative matrix

public subroutine cheb_tensorize_ndm2(var, nx, ny, dmat, tdm)

Tensorize the nodal derivative matrix for two variables in the domain [-1,1]x[-1,1].

Arguments

Type	Intent	Attributes		Name
character(len=1),	intent(in)		::	var	Independent variable {'x', 'y'}
integer,	intent(in)		::	nx	Degree of the polynomial along x and y directions
integer,	intent(in)		::	ny	Degree of the polynomial along x and y directions
real(kind=rp),	intent(in),	dimension(:,:)	::	dmat	(nx+1, nx+1) or (ny+1, ny+1) Nodal derivative matrix in the domain [-1,1].
real(kind=rp),	intent(out),	dimension(:,:)	::	tdm	Tensorized derivative matrix with nrows = ncols = (nx+1)*(ny+1)

public subroutine cheb_tensorize_ndm3(var, nx, ny, nz, dmat, tdm)

Tensorize the nodal derivative matrix for three variables in the domain [-1,1]x[-1,1]X[-1,1].

Arguments

Type	Intent	Attributes		Name
character(len=1),	intent(in)		::	var	Independent variable {'x', 'y', 'z'}
integer,	intent(in)		::	nx	Degree of the polynomial along x, y, and z directions
integer,	intent(in)		::	ny	Degree of the polynomial along x, y, and z directions
integer,	intent(in)		::	nz	Degree of the polynomial along x, y, and z directions
real(kind=rp),	intent(in),	dimension(:,:)	::	dmat	(nx+1, nx+1) or (ny+1, ny+1) or (nz+1, nz+1). Nodal derivative matrix in the domain [-1,1].
real(kind=rp),	intent(out),	dimension(:,:)	::	tdm	Tensorized derivative matrix with nrows = ncols = (nx+1)(ny+1)(nz+1)

public subroutine cheb_nod_deriv(dm, f, fp)

Calculates the derivative of a 1D function at the nodes.

Arguments

Type	Intent	Attributes		Name
real(kind=rp),	intent(in),	dimension(:,:)	::	dm	((n+1),(n+1)) Differentiation matrix, where the number of nodes = n+1
real(kind=rp),	intent(in),	dimension(:)	::	f	(n+1,). Value of the function at the nodes.
real(kind=rp),	intent(out),	dimension(:)	::	fp	(n+1,). Value of the derivative at the nodes.

public subroutine cheb_nod_deriv2(nx, ny, dmx, dmy, f, fpx, fpy)

Calculates the derivative of a 2D function at the nodes.

Arguments

Type	Intent	Attributes		Name
integer,	intent(in)		::	nx	Number of nodes along x = nx+1 and along y = ny+1
integer,	intent(in)		::	ny	Number of nodes along x = nx+1 and along y = ny+1
real(kind=rp),	intent(in),	dimension(:,:)	::	dmx	((nx+1),(nx+1)) Differentiation matrix along x
real(kind=rp),	intent(in),	dimension(:,:)	::	dmy	((ny+1),(ny+1)) Differentiation matrix along y
real(kind=rp),	intent(in),	dimension(:)	::	f	(m,), where m = (nx+1)*(ny+1). Value of the function at the nodes.
real(kind=rp),	intent(out),	dimension(:)	::	fpx	(m,), where m = (nx+1)*(ny+1). Value of the derivatives at the nodes.
real(kind=rp),	intent(out),	dimension(:)	::	fpy	(m,), where m = (nx+1)*(ny+1). Value of the derivatives at the nodes.

public subroutine cheb_nod_deriv3(nx, ny, nz, dmx, dmy, dmz, f, fpx, fpy, fpz)

Calculates the derivative of a 3D function at the nodes.

Arguments

Type	Intent	Attributes		Name
integer,	intent(in)		::	nx	Number of nodes along x = nx+1, along y = ny+1, and along z = nz+1
integer,	intent(in)		::	ny	Number of nodes along x = nx+1, along y = ny+1, and along z = nz+1
integer,	intent(in)		::	nz	Number of nodes along x = nx+1, along y = ny+1, and along z = nz+1
real(kind=rp),	intent(in),	dimension(:,:)	::	dmx	((nx+1),(nx+1)) Differentiation matrix along x
real(kind=rp),	intent(in),	dimension(:,:)	::	dmy	((ny+1),(ny+1)) Differentiation matrix along y
real(kind=rp),	intent(in),	dimension(:,:)	::	dmz	((nz+1),(nz+1)) Differentiation matrix along z
real(kind=rp),	intent(in),	dimension(:)	::	f	(m,), where m = (nx+1)(ny+1)(nz+1). Value of the function at the nodes.
real(kind=rp),	intent(out),	dimension(:)	::	fpx	(m,), where m = (nx+1)(ny+1)(nz+1). Value of the derivatives at the nodes.
real(kind=rp),	intent(out),	dimension(:)	::	fpy	(m,), where m = (nx+1)(ny+1)(nz+1). Value of the derivatives at the nodes.
real(kind=rp),	intent(out),	dimension(:)	::	fpz	(m,), where m = (nx+1)(ny+1)(nz+1). Value of the derivatives at the nodes.

public subroutine cheb_dctmat(n, mat, rwrk)

Calculates the discrete Chebyshev transform matrix for a single variable. The matrix is not symmetric and assumes the nodal coordinates to be in ascending order.

Arguments

Type	Intent	Attributes		Name
integer,	intent(in)		::	n	Degree of polynomial
real(kind=rp),	intent(out),	dimension(:,:)	::	mat	((n+1),(n+1)) Transform matrix.
real(kind=rp),	intent(inout),	dimension(:)	::	rwrk	Workspace array of minimum size (n+1)

public subroutine cheb_dctmat2(nx, ny, mat, rwrk)

This subroutine transforms the function values at the CGL points to the coefficients of the Chebyshev series for two variables. The matrix is not symmetric and assumes the nodal coordinates to be in ascending order.

Arguments

Type	Intent	Attributes		Name
integer,	intent(in)		::	nx	Degree of polynomial along x direction
integer,	intent(in)		::	ny	Degree of polynomial along y direction
real(kind=rp),	intent(out),	dimension(:,:)	::	mat	((nx+1)(ny+1),(nx+1)(ny+1)) matrix. Transform matrix.
real(kind=rp),	intent(inout),	dimension(:), target	::	rwrk	Workspace array of minimum size (nx+1) + (ny+1)

public subroutine cheb_dictmat(n, mat)

Calculates the discrete inverse Chebyshev transform matrix. The matrix is not symmetric and yields the nodal function values assuming the nodal coordinates are in ascending order.

Arguments

Type	Intent	Optional	Attributes		Name
integer,	intent(in)			::	n	Degree of polynomial
real(kind=rp),	intent(out),		dimension(:,:)	::	mat	(n+1,n+1). Inverse transform matrix.

public subroutine bary_weights(n, w)

Calculates the barycentric weights for a given set of nodes. As of now, assumues CGL nodes. TODO: extend stably for the general case (CGL, CGR, CG)

Arguments

Type	Intent	Optional	Attributes		Name
integer,	intent(in)			::	n	Number of interpolation nodes = n+1.
real(kind=rp),	intent(out),		dimension(:)	::	w	(n+1,). Barycentric weights

public subroutine lag_intrp_mat(n, m, x, w, z, mat)

Computes the Lagrange interpolation (barycentric) matrix.

Arguments

Type	Intent	Attributes		Name
integer,	intent(in)		::	n	Number of nodes = n+1
integer,	intent(in)		::	m	Number of interpolation points = m+1
real(kind=rp),	intent(in),	dimension(:)	::	x	(n+1,). Nodal coordinates in strictly ascending order
real(kind=rp),	intent(in),	dimension(:)	::	w	(n+1,). Barycentric weights
real(kind=rp),	intent(in),	dimension(:)	::	z	(m+1,). Coordinates at which the function is to be interpolated
real(kind=rp),	intent(out),	dimension(:,:)	::	mat	(m+1,n+1). Interpolation matrix

public subroutine lag_intrp_grd(mat, f, fintrp)

Interpolates nodal function values to a grid using barycentric lagrange interpolation.

Arguments

Type	Intent	Attributes		Name
real(kind=rp),	intent(in),	dimension(:,:)	::	mat	(np,n). Interpolation matrix
real(kind=rp),	intent(in),	dimension(:)	::	f	(n,). Value of the function at the nodes
real(kind=rp),	intent(out),	dimension(:)	::	fintrp	(np,). Value of the function at the nodes

public subroutine lag_intrp_grd2(nx, ny, npx, npy, matx, maty, f, fintrp, rwrk)

Interpolates nodal function values to a grid using barycentric lagrange interpolation in two variables.

Arguments

Type	Intent	Attributes		Name
integer,	intent(in)		::	nx	Number of nodes along x = nx+1 and along y = ny+1
integer,	intent(in)		::	ny	Number of nodes along x = nx+1 and along y = ny+1
integer,	intent(in)		::	npx	Number of interpolating points along x = npx+1 and along y = npy+1
integer,	intent(in)		::	npy	Number of interpolating points along x = npx+1 and along y = npy+1
real(kind=rp),	intent(in),	dimension(:,:)	::	matx	(npx+1,nx+1). Interpolation matrix along x
real(kind=rp),	intent(in),	dimension(:,:)	::	maty	(npy+1,npy+1). Interpolation matrix along y
real(kind=rp),	intent(in),	dimension(:)	::	f	((nx+1)*(ny+1),). Value of the function at the nodes
real(kind=rp),	intent(out),	dimension(:)	::	fintrp	((npx+1)*(npy+1),). Value of the function at the nodes
real(kind=rp),	intent(inout),	dimension(:)	::	rwrk	Workspace array of minimum size (npx+1)*(ny+1).

public subroutine lag_intrp_grd3(nx, ny, nz, npx, npy, npz, matx, maty, matz, f, fintrp, rwrk)

Interpolates nodal function values to a grid using barycentric lagrange interpolation in three variables.

Arguments

Type	Intent	Attributes		Name
integer,	intent(in)		::	nx	Number of nodes along x = nx+1, along y = ny+1, and along z = nz+1
integer,	intent(in)		::	ny	Number of nodes along x = nx+1, along y = ny+1, and along z = nz+1
integer,	intent(in)		::	nz	Number of nodes along x = nx+1, along y = ny+1, and along z = nz+1
integer,	intent(in)		::	npx	Number of interpolating points along x = npx+1, along y = npy+1, and along z = npz+1
integer,	intent(in)		::	npy	Number of interpolating points along x = npx+1, along y = npy+1, and along z = npz+1
integer,	intent(in)		::	npz	Number of interpolating points along x = npx+1, along y = npy+1, and along z = npz+1
real(kind=rp),	intent(in),	dimension(:,:)	::	matx	(npx+1,nx+1). Interpolation matrix along x
real(kind=rp),	intent(in),	dimension(:,:)	::	maty	(npy+1,ny+1). Interpolation matrix along y
real(kind=rp),	intent(in),	dimension(:,:)	::	matz	(npz+1,nz+1). Interpolation matrix along z
real(kind=rp),	intent(in),	dimension(:)	::	f	(nx+1)(ny+1)(nz+1), ). Value of the function at the nodes
real(kind=rp),	intent(out),	dimension(:)	::	fintrp	(npx+1)(npy+1)(npz+1), ). Value of the function at the interpolation points.
real(kind=rp),	intent(inout),	dimension(:)	::	rwrk	Workspace array, minimum size (npx+1)(npy+1)(nz+1)+(npx+1)*(ny+1)

chebyshev_m Module

Contents

Functions

Subroutines

Uses

Functions

public function cheb_eval(n, x) result(res)

Arguments

Return Value real(kind=rp)

public function cheb_ser_eval(n, c, x) result(res)

Arguments

Return Value real(kind=rp)

public function cheb_ser_eval2(nx, ny, c, x, y, rwrk) result(res)

Arguments

Return Value real(kind=rp)

public function cheb_ser_eval3(nx, ny, nz, c, x, y, z, rwrk) result(res)

Arguments

Return Value real(kind=rp)

public function cheb_quad(tag, a, b, n, x, f) result(valint)

Arguments

Return Value real(kind=rp)

public function cheb_quad2(tag, x0, x1, y0, y1, nx, ny, x, y, f, rwrk) result(valint)

Arguments

Return Value real(kind=rp)

public function cheb_quad3(tag, x0, x1, y0, y1, z0, z1, nx, ny, nz, x, y, z, f, rwrk) result(valint)

Arguments

Return Value real(kind=rp)

public function lag_intrp(n, x, w, f, p) result(res)

Arguments

Return Value real(kind=rp)

Subroutines

public subroutine cheb_node(tag, a, b, n, xcol, is_descending)

Arguments

public subroutine cheb_n1dmat(x0, x1, n, rwrk, dm)

Arguments

public subroutine cheb_n2dmat(n, dm1, dm2)

Arguments

public subroutine cheb_tensorize_ndm2(var, nx, ny, dmat, tdm)

Arguments

public subroutine cheb_tensorize_ndm3(var, nx, ny, nz, dmat, tdm)

Arguments

public subroutine cheb_nod_deriv(dm, f, fp)

Arguments

public subroutine cheb_nod_deriv2(nx, ny, dmx, dmy, f, fpx, fpy)

Arguments

public subroutine cheb_nod_deriv3(nx, ny, nz, dmx, dmy, dmz, f, fpx, fpy, fpz)

Arguments

public subroutine cheb_dctmat(n, mat, rwrk)

Arguments

public subroutine cheb_dctmat2(nx, ny, mat, rwrk)

Arguments

public subroutine cheb_dictmat(n, mat)

Arguments

public subroutine bary_weights(n, w)

Arguments

public subroutine lag_intrp_mat(n, m, x, w, z, mat)

Arguments

public subroutine lag_intrp_grd(mat, f, fintrp)

Arguments

public subroutine lag_intrp_grd2(nx, ny, npx, npy, matx, maty, f, fintrp, rwrk)

Arguments

public subroutine lag_intrp_grd3(nx, ny, nz, npx, npy, npz, matx, maty, matz, f, fintrp, rwrk)

Arguments