math_funcs.cc File Reference

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

Go to the source code of this file.

Functions
Numeric	fac (const Index n)
	fac More...
Index	integer_div (const Index &x, const Index &y)
	integer_div More...
Numeric	LagrangeInterpol4 (ConstVectorView x, ConstVectorView y, const Numeric a)
	Lagrange Interpolation (internal function). More...
Numeric	last (ConstVectorView x)
	last More...
Index	last (const ArrayOfIndex &x)
	last More...
void	linspace (Vector &x, const Numeric start, const Numeric stop, const Numeric step)
	linspace More...
void	nlinspace (Vector &x, const Numeric start, const Numeric stop, const Index n)
	nlinspace More...
void	nlogspace (Vector &x, const Numeric start, const Numeric stop, const Index n)
	nlogspace More...
Numeric	AngIntegrate_trapezoid (ConstMatrixView Integrand, ConstVectorView za_grid, ConstVectorView aa_grid)
	AngIntegrate_trapezoid. More...
Numeric	AngIntegrate_trapezoid_opti (ConstMatrixView Integrand, ConstVectorView za_grid, ConstVectorView aa_grid, ConstVectorView grid_stepsize)
	AngIntegrate_trapezoid_opti. More...
Numeric	AngIntegrate_trapezoid (ConstVectorView Integrand, ConstVectorView za_grid)
	AngIntegrate_trapezoid. More...
Numeric	sign (const Numeric &x)
	sign More...
Numeric	gamma_func (Numeric xx)
	Gamma Function. More...
Numeric	lgamma_func (Numeric xx)
	ln Gamma Function More...
void	unitl (Vector &x)
	lunit More...

Variables
const Numeric	DEG2RAD
const Numeric	PI

Detailed Description

Author

Patrick Eriksson Patri.nosp@m.ck.E.nosp@m.rikss.nosp@m.on@c.nosp@m.halme.nosp@m.rs.s.nosp@m.e

Date

2000-09-18

Contains basic mathematical functions.

Definition in file math_funcs.cc.

Function Documentation

AngIntegrate_trapezoid() [1/2]

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(), doit_scat_fieldNormalize(), and scat_data_arrayCheck().

AngIntegrate_trapezoid() [2/2]

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.

AngIntegrate_trapezoid_opti()

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.nosp@m.@sat.nosp@m..phys.nosp@m.ik.u.nosp@m.ni-br.nosp@m.emen.nosp@m..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().

fac()

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_(), faddeeva_algorithm_916(), 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(), hui_etal_1978_lineshape(), iyCloudRadar(), legendre_poly_norm_schmidt(), legendre_poly_norm_schmidt_deriv(), lineshape_CO2_lorentz(), lineshape_doppler(), lineshape_lorentz(), lineshape_norm_linear(), lineshape_norm_no_norm(), lineshape_norm_quadratic(), lineshape_norm_VVH(), lineshape_voigt_drayson(), lineshape_voigt_kuntz3(), lineshape_voigt_kuntz4(), lineshape_voigt_kuntz6(), MPM93_N2_continuum(), pnd_fieldGM58(), pnd_fieldMP48(), pnd_fieldSS70(), specular_losCalc(), and xsec_species().

gamma_func()

Numeric gamma_func

(

Numeric

xx

)

Gamma Function.

Returns gamma function of real argument 'x'. Returns error msg if argument is a negative integer or 0, or use lgamma function if argument exceeds 32.0.

Returns

gam Gamma function of x.

Parameters

xx

Numeric

Author

Daniel Kreyling

Date

2010-12-13

Definition at line 497 of file math_funcs.cc.

References lgamma_func().

Referenced by IWCtopnd_MH97(), LWCtopnd(), and LWCtopnd2().

integer_div()

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().

LagrangeInterpol4()

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().

last() [1/2]

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().

last() [2/2]

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 antenna2d_simplified(), chk_scat_data(), find_effective_channel_boundaries(), iyFOS(), mixer_matrix(), pos2refell_r(), refr_index_airFreeElectrons(), sensor_responseAntenna(), sensor_responseBackend(), sensor_responseMixer(), sensor_summation_vector(), and ySimpleSpectrometer().

lgamma_func()

Numeric lgamma_func

(

Numeric

xx

)

ln Gamma Function

Returns ln of gamma function for real argument 'x'.

Returns

ln Gamma function of x.

Parameters

xx

Numeric

Author

Daniel Kreyling

Date

2010-12-13

Definition at line 538 of file math_funcs.cc.

Referenced by gamma_func().

linspace()

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 ySimpleSpectrometer().

nlinspace()

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 AntennaConstantGaussian1D(), calc_ssp_fixed_test(), calc_ssp_random_test(), doit_scat_fieldCalcLimb(), DoitAngularGridsSet(), DoitScatteringDataPrepare(), f_gridFromSensorAMSU(), f_gridFromSensorHIRS(), gaussian_response_autogrid(), pha_mat_sptFromDataDOITOpt(), pha_mat_sptFromMonoData(), pnd_fieldZero(), sensor_responseFillFgrid(), and VectorNLinSpace().

nlogspace()

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().

sign()

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 Numeric.

Author

Patrick Eriksson

Date

2000-06-27

Definition at line 473 of file math_funcs.cc.

Referenced by binostream::float2ieee_double(), binostream::float2ieee_single(), geompath_from_r1_to_r2(), binistream::ieee_double2float(), binistream::ieee_single2float(), lat_crossing_3d(), poslos2cart(), r_crossing_2d(), raytrace_2d_linear_basic(), and specular_losCalc().

unitl()

void unitl

(

Vector &

x

)

lunit

Normalises a vector to have unit length.

The standard Euclidean norm is used (2-norm).

param x In/Out: A vector.

Author

Patrick Eriksson

Date

2012-02-12

Definition at line 578 of file math_funcs.cc.

References ConstVectorView::nelem().

Variable Documentation

DEG2RAD

const Numeric DEG2RAD

extern

Referenced by AngIntegrate_trapezoid(), and AngIntegrate_trapezoid_opti().

PI

const Numeric PI

extern

Referenced by AngIntegrate_trapezoid().