math_funcs.cc File Reference

#include <iostream>
#include <cmath>
#include <stdexcept>
#include "array.h"
#include "math_funcs.h"
#include "logic.h"
#include "mystring.h"

Include dependency graph for math_funcs.cc:

Go to the source code of this file.

Functions
Numeric	fac (const Index n)
	fac
Index	integer_div (const Index &x, const Index &y)
	integer_div
Numeric	LagrangeInterpol4 (ConstVectorView x, ConstVectorView y, const Numeric a)
	Lagrange Interpolation (internal function).
Numeric	last (ConstVectorView x)
	last
Index	last (const ArrayOfIndex &x)
	last
void	linspace (Vector &x, const Numeric start, const Numeric stop, const Numeric step)
	linspace
void	nlinspace (Vector &x, const Numeric start, const Numeric stop, const Index n)
	nlinspace
void	nlogspace (Vector &x, const Numeric start, const Numeric stop, const Index n)
	nlogspace
Numeric	AngIntegrate_trapezoid (ConstMatrixView Integrand, ConstVectorView za_grid, ConstVectorView aa_grid)
	AngIntegrate_trapezoid.
Numeric	AngIntegrate_trapezoid_opti (ConstMatrixView Integrand, ConstVectorView za_grid, ConstVectorView aa_grid, ConstVectorView grid_stepsize)
	AngIntegrate_trapezoid_opti.
Numeric	AngIntegrate_trapezoid (ConstVectorView Integrand, ConstVectorView za_grid)
	AngIntegrate_trapezoid.
Numeric	sign (const Numeric &x)
	sign
Variables
const Numeric	DEG2RAD
const Numeric	PI

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Detailed Description

Author:

Patrick Eriksson <Patrick.Eriksson@rss.chalmers.se>

Date:

2000-09-18

Contains basic mathematical functions.

Definition in file math_funcs.cc.

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Function Documentation

Numeric AngIntegrate_trapezoid	(	ConstVectorView	Integrand,
		ConstVectorView	za_grid
	)

AngIntegrate_trapezoid.

Performs an integration of a matrix over all directions defined in angular grids using the trapezoidal integration method. The integrand is independant of the azimuth angle. The integration over the azimuth angle gives a 2*PI

Parameters:

	Integrand	Input : The vector to be integrated
	za_grid	Input : The zenith angle grid

Author:

Claas Teichmann

Date:

2003-05-13

Returns:

The resulting integral

Definition at line 438 of file math_funcs.cc.

References DEG2RAD, is_size(), ConstVectorView::nelem(), and PI.

Numeric AngIntegrate_trapezoid	(	ConstMatrixView	Integrand,
		ConstVectorView	za_grid,
		ConstVectorView	aa_grid
	)

AngIntegrate_trapezoid.

Performs an integration of a matrix over all directions defined in angular grids using the trapezoidal integration method.

Parameters:

	Integrand	The Matrix to be integrated
	za_grid	The zenith angle grid
	aa_grid	The azimuth angle grid

Returns:

The resulting integral

Definition at line 327 of file math_funcs.cc.

References DEG2RAD, is_size(), and ConstVectorView::nelem().

Referenced by AngIntegrate_trapezoid_opti(), and scat_data_rawCheck().

Numeric AngIntegrate_trapezoid_opti	(	ConstMatrixView	Integrand,
		ConstVectorView	za_grid,
		ConstVectorView	aa_grid,
		ConstVectorView	grid_stepsize
	)

AngIntegrate_trapezoid_opti.

Performs an integration of a matrix over all directions defined in angular grids using the trapezoidal integration method.

In addition to the "old fashined" integration method, it checks whether the stepsize is constant. If it is, it uses a faster method, if not, it uses the old one.

Parameters:

	Integrand	Input : The Matrix to be integrated
	za_grid	Input : The zenith angle grid
	aa_grid	Input : The azimuth angle grid
	grid_stepsize	Input : stepsize of the grid

Returns:

The resulting integral

Author:

Claas Teichmann <claas@sat.physik.uni-bremen.de>

Date:

2003/05/28

Definition at line 377 of file math_funcs.cc.

References AngIntegrate_trapezoid(), DEG2RAD, is_size(), ConstVectorView::nelem(), and temp.

Referenced by doit_scat_fieldCalc(), doit_scat_fieldCalcLimb(), and test_AngIntegrate_trapezoid_opti().

Numeric fac

(

const Index

n

)

fac

Calculates the factorial.

The function asserts that n must be >= 0

Returns:

The factorial

Parameters:

n

Nominator

Author:

Oliver Lemke

Date:

2003-08-15

Definition at line 68 of file math_funcs.cc.

Referenced by addspec_(), g_legendre_poly_norm_schmidt(), g_legendre_poly_norm_schmidt_deriv(), g_legendre_poly_norm_schmidt_deriv1(), g_legendre_poly_norm_schmidt_deriv2(), g_legendre_poly_norm_schmidt_deriv3(), g_legendre_poly_norm_schmidt_deriv4(), legendre_poly_norm_schmidt(), legendre_poly_norm_schmidt_deriv(), lineshape_CO2_lorentz(), lineshape_doppler(), lineshape_lorentz(), lineshape_voigt_drayson(), lineshape_voigt_kuntz3(), lineshape_voigt_kuntz4(), lineshape_voigt_kuntz6(), MPM93_N2_continuum(), and xsec_species().

Index integer_div	(	const Index &	x,
		const Index &	y
	)

integer_div

Performs an integer division.

The function asserts that the reminder of the division x/y is 0.

Returns:

The quotient

Parameters:

	x	Nominator
	y	Denominator

Author:

Patrick Eriksson

Date:

2002-08-11

Definition at line 95 of file math_funcs.cc.

References is_multiple().

Numeric LagrangeInterpol4	(	ConstVectorView	x,
		ConstVectorView	y,
		const Numeric	a
	)

Lagrange Interpolation (internal function).

This function calculates the Lagrange interpolation of four interpolation points as described in Lagrange Interpolating Polynomial.
The input are the four x-axis values [x0,x1,x2,x3] and their associated y-axis values [y0,y1,y2,y3]. Furthermore the x-axis point "a" at which the interpolation should be calculated must be given as input. NOTE that the relation x2 =< x < x3 MUST hold!

Parameters:

	x	x-vector with four elements [x0,x1,x2,x3]
	y	y-vector with four elements: yj = y(xj), j=0,1,2,3
	a	interpolation point on the x-axis with x1 =< a < x2

Returns:

FIXME

Author:

Thomas Kuhn

Date:

2003-11-25

Definition at line 124 of file math_funcs.cc.

References ConstVectorView::nelem().

Index last

(

const ArrayOfIndex &

x

)

last

Returns the last value of an index array.

Returns:

The last value of x.

Parameters:

x

An index array.

Author:

Patrick Eriksson

Date:

2000-06-27

Definition at line 201 of file math_funcs.cc.

References Array< base >::nelem().

Numeric last

(

ConstVectorView

x

)

last

Returns the last value of a vector.

Returns:

The last value of x.

Parameters:

x

A vector.

Author:

Patrick Eriksson

Date:

2000-06-27

Definition at line 183 of file math_funcs.cc.

References ConstVectorView::nelem().

Referenced by chk_single_scattering_data(), interp_gfield3(), mixer_matrix(), sensor_posAddRgeoid(), sensor_responseAntenna(), sensor_responseBackend(), sensor_responseMixer(), and sensor_summation_vector().

void linspace	(	Vector &	x,
		const Numeric	start,
		const Numeric	stop,
		const Numeric	step
	)

linspace

Linearly spaced vector with specified spacing.

The first element of x is always start. The next value is start+step etc. Note that the last value can deviate from stop. The step can be both positive and negative. (in Matlab notation: start:step:stop)

Size of result is adjusted within this function!

Parameters:

	x	Output: linearly spaced vector
	start	first value in x
	stop	last value of x <= stop
	step	distance between values in x

Author:

Patrick Eriksson

Date:

2000-06-27

Definition at line 228 of file math_funcs.cc.

References Vector::resize().

Referenced by VectorLinSpace(), VectorLogSpace(), and ZaSatOccultation().

void nlinspace	(	Vector &	x,
		const Numeric	start,
		const Numeric	stop,
		const Index	n
	)

nlinspace

Linearly spaced vector with specified length.

Returns a vector equally and linearly spaced between start and stop of length n. (equals the Matlab function linspace)

The length must be > 1.

Parameters:

	x	Output: linearly spaced vector
	start	first value in x
	stop	last value of x <= stop
	n	length of x

Author:

Patrick Eriksson

Date:

2000-06-27

Definition at line 261 of file math_funcs.cc.

References Vector::resize().

Referenced by cloudboxSetEmpty(), doit_scat_fieldCalcLimb(), DoitAngularGridsSet(), DoitScatteringDataPrepare(), interpolate_raytracing_points(), pha_mat_sptFromDataDOITOpt(), pha_mat_sptFromMonoData(), and VectorNLinSpace().

void nlogspace	(	Vector &	x,
		const Numeric	start,
		const Numeric	stop,
		const Index	n
	)

nlogspace

Logarithmically spaced vector with specified length.

Returns a vector logarithmically spaced vector between start and stop of length n (equals the Matlab function logspace)

The length must be > 1.

Parameters:

	x	Output: logarithmically spaced vector
	start	first value in x
	stop	last value of x <= stop
	n	length of x

Author:

Patrick Eriksson

Date:

2000-06-27

Definition at line 294 of file math_funcs.cc.

References Vector::resize().

Referenced by VectorNLogSpace().

Numeric sign

(

const Numeric &

x

)

sign

Returns the sign of a numeric value.

The function returns 1 if the value is greater than zero, 0 if it equals zero and -1 if it is less than zero.

Returns:

The sign of x (see above).

Parameters:

x

A vector.

Author:

Patrick Eriksson

Date:

2000-06-27

Definition at line 473 of file math_funcs.cc.

Referenced by do_gridcell_2d(), binostream::float2ieee_double(), binostream::float2ieee_single(), binistream::ieee_double2float(), binistream::ieee_single2float(), poslos2cart(), raytrace_2d_linear_euler(), and surface_specular_los().

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Variable Documentation

const Numeric DEG2RAD

const Numeric PI