/home/docs/checkouts/readthedocs.org/user_builds/flowsieve/checkouts/read_the_docs_testing/differentiation_tools.hpp File Reference

Collection of all differentiation-related functions. More...

#include <stdio.h>
#include <stdlib.h>
#include <vector>
#include <string>
#include "constants.hpp"

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Functions
void	differentiation_vector (std::vector< double > &diff_array, const double delta, const int index, const int order_of_deriv=1, const int diff_ord=constants::DiffOrd)
	Assign appropriate differentiation vector. More...
void	non_uniform_diff_vector (std::vector< double > &diff_array, const std::vector< double > &grid, const int Iref, const int LB, const int UB, const int diff_ord=constants::DiffOrd)
	Assign appropriate differentiation vector. More...
void	spher_derivative_at_point (const std::vector< double *> &deriv_vals, const std::vector< const std::vector< double > *> &fields, const std::vector< double > &grid, const std::string &dim, const int Itime, const int Idepth, const int Ilat, const int Ilon, const int Ntime, const int Ndepth, const int Nlat, const int Nlon, const std::vector< bool > &mask, const int order_of_deriv=1, const int diff_ord=constants::DiffOrd)
	Computes latitudinal derivative at a specific point. More...
void	Cart_derivatives_at_point (const std::vector< double *> &x_deriv_vals, const std::vector< double *> &y_deriv_vals, const std::vector< double *> &z_deriv_vals, const std::vector< const std::vector< double > *> &fields, const std::vector< double > &latitude, const std::vector< double > &longitude, const int Itime, const int Idepth, const int Ilat, const int Ilon, const int Ntime, const int Ndepth, const int Nlat, const int Nlon, const std::vector< bool > &mask, const int order_of_deriv=1, const int diff_ord=constants::DiffOrd)
	Computes all Cartesian derivative at a specific point. More...
void	get_diff_vector (std::vector< double > &diff_vector, int &LB_ret, const std::vector< double > &grid, const std::string &dim, const int Itime, const int Idepth, const int Ilat, const int Ilon, const int Ntime, const int Ndepth, const int Nlat, const int Nlon, const std::vector< bool > &mask, const int order_of_deriv, const int diff_ord=constants::DiffOrd)
	Function to return coefficients for differentiation at a target point in space. More...

Detailed Description

Collection of all differentiation-related functions.

Function Documentation

Cart_derivatives_at_point()

void Cart_derivatives_at_point	(	const std::vector< double *> &	x_deriv_vals,
		const std::vector< double *> &	y_deriv_vals,
		const std::vector< double *> &	z_deriv_vals,
		const std::vector< const std::vector< double > *> &	fields,
		const std::vector< double > &	latitude,
		const std::vector< double > &	longitude,
		const int	Itime,
		const int	Idepth,
		const int	Ilat,
		const int	Ilon,
		const int	Ntime,
		const int	Ndepth,
		const int	Nlat,
		const int	Nlon,
		const std::vector< bool > &	mask,
		const int	order_of_deriv = 1,
		const int	diff_ord = constants::DiffOrd
	)

Computes all Cartesian derivative at a specific point.

Computation is done via chain rule on spherical coordinate derivatives. Since both lat- and lon- derivatives are taken, the cost increase to compute all three Cartesian derivatives in comparison to computing a single Cartesian derivative is negligible.

Calls latitude_derivative_at_point() and longitude_derivative_at_point()

Parameters

[in,out]	x_deriv_vals	vector of pointers to return x-deriv values
[in,out]	y_deriv_vals	vector of pointers to return y-deriv values
[in,out]	z_deriv_vals	vector of pointers to return z-deriv values
[in]	fields	vector of pointers to fields to differentiate
[in]	latitude	(1D) latitude array
[in]	longitude	(1D) longitude array
[in]	Itime,Idepth,Ilat,Ilon	Indices for the target point in space
[in]	Ntime,Ndepth,Nlat,Nlon	Sizes of the dimensions
[in]	mask	array to distinguish land/water cells

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differentiation_vector()

void differentiation_vector	(	std::vector< double > &	diff_array,
		const double	delta,
		const int	index,
		const int	order_of_deriv = 1,
		const int	diff_ord = constants::DiffOrd
	)

Assign appropriate differentiation vector.

This function produces the differentiation vector necessary for computing the value of a derivative at a single point.

This function implicitly assumes a uniform grid.

For first derivatives, can use 2nd, 4th, and 6th order convergence.

For second derivatives, can use 2nd and 4th order convergence

The grid need not be centred (to account for coastlines).

Parameters

[in,out]	diff_array	vector into which to store the differentiation coefficients
[in]	delta	the (constant) grid spacing
[in]	index	index for where in the stencil you want the derivative
[in]	order_of_deriv	order of the derivative (default is first derivative)
[in]	diff_ord	convergence order (default is specified in constants.hpp)

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get_diff_vector()

void get_diff_vector	(	std::vector< double > &	diff_vector,
		int &	LB_ret,
		const std::vector< double > &	grid,
		const std::string &	dim,
		const int	Itime,
		const int	Idepth,
		const int	Ilat,
		const int	Ilon,
		const int	Ntime,
		const int	Ndepth,
		const int	Nlat,
		const int	Nlon,
		const std::vector< bool > &	mask,
		const int	order_of_deriv,
		const int	diff_ord = constants::DiffOrd
	)

Function to return coefficients for differentiation at a target point in space.

This is used for the Toroidal projection, which requires building a Laplacian matrix.

Parameters

[in,out]	diff_vector	vector into which to store the coefficients
[in,out]	LB_ret	index of the lower bound of the stencil (returned)
[in]	grid	grid on which to differentiate
[in]	dim	name of the differentiation dimension ("lon", "lat")
[in]	Itime,Idepth,Ilat,Ilon	Indices for the target point in space
[in]	Ntime,Ndepth,Nlat,Nlon	Sizes of the dimensions
[in]	mask	mask to distinguish land/water cells
[in]	order_of_deriv	order of the derivative
[in]	diff_ord	convergence order of the derivative (default from constants.hpp)

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non_uniform_diff_vector()

void non_uniform_diff_vector	(	std::vector< double > &	diff_array,
		const std::vector< double > &	grid,
		const int	Iref,
		const int	LB,
		const int	UB,
		const int	diff_ord = constants::DiffOrd
	)

Assign appropriate differentiation vector.

This function produces the differentiation vector necessary for computing the value of a derivative at a single point.

The grid need not the uniform.

For first derivatives, 2nd order convergence can be used.

Second derivatives not yet implemented.

The grid need not be centred (to account for coastlines).

Parameters

[in,out]	diff_array	vector into which to store the differentiation coefficients
[in]	grid	vector giving the grid on which the derivative is taken
[in]	Iref	integer giving the index for the point at which you want the derivative
[in]	LB	integer giving the lower bound for the differentiation stencil
[in]	UB	integer giving the upper bound for the differentiation stencil
[in]	diff_ord	convergence order (default is specified in constants.hpp)

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spher_derivative_at_point()

void spher_derivative_at_point	(	const std::vector< double *> &	deriv_vals,
		const std::vector< const std::vector< double > *> &	fields,
		const std::vector< double > &	grid,
		const std::string &	dim,
		const int	Itime,
		const int	Idepth,
		const int	Ilat,
		const int	Ilon,
		const int	Ntime,
		const int	Ndepth,
		const int	Nlat,
		const int	Nlon,
		const std::vector< bool > &	mask,
		const int	order_of_deriv = 1,
		const int	diff_ord = constants::DiffOrd
	)

Computes latitudinal derivative at a specific point.

Parameters

[in,out]	deriv_vals	vector of pointers to return values
[in]	fields	vector of pointers to fields to differentiate
[in]	grid	(1D) latitude or longitude array
[in]	dim	"lat" or "lon": dimensional along which to differentate
[in]	Itime,Idepth,Ilat,Ilon	Indices for the target point in space
[in]	Ntime,Ndepth,Nlat,Nlon	Sizes of the dimensions
[in]	mask	array to distinguish land/water cells
[in]	order_of_deriv	order of the derivative (1st deriv, 2nd deriv, etc)
[in]	diff_ord	convergence order (default is specified in constants.hpp)

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