KTH Toolbox: math

Files
file	math_tools.f
	Set of math related tools for KTH modules.

Functions/Subroutines
real function	math_stepf (x)
	Step function. More...
real function	math_ran_dst (ix, iy, iz, ieg, xl, fcoeff)
	Give random distribution depending on position. More...
real function	math_ran_rng (lower, upper)
	Give random number in the defined range. More...
real function	math_zbqlu01 ()
	Marsaglia-Zaman random number generator. More...
subroutine	math_zbqlini (seed)
	Initialise Marsaglia-Zaman random number generator. More...
subroutine	math_edgind (istart, istop, iskip, iedg, nx, ny, nz)
	Give bounds for loops to extract edge. More...
subroutine	math_etovec (vec, edg, vfld, nx, ny, nz)
	Extract element edge. More...
subroutine	math_rot3da (vo, vi, va, an)
	3D rotation of a vector along given axis More...

Detailed Description

Function/Subroutine Documentation

math_edgind()

subroutine math_edgind	(	integer	istart,
		integer	istop,
		integer	iskip,
		integer	iedg,
		integer	nx,
		integer	ny,
		integer	nz
	)

Give bounds for loops to extract edge.

Note

All edge related routines used IXCN and ESKIP, but this caused some problems as these arrays have to be continuosly updated for different levels in pressure solver, so I add this routine.

Parameters

[out]	istart	lower loop bound
[out]	istop	upper loop bound
[out]	iskip	stride
[in]	iedg	edge number
[in]	nx,ny,nz	element size

math_etovec()

subroutine math_etovec	(	real, dimension(nx)	vec,
		integer	edg,
		real, dimension(nx*ny*nz)	vfld,
		integer	nx,
		integer	ny,
		integer	nz
	)

Extract element edge.

Note

This routine works on singe element not whole field.

Parameters

[out]	vec	vector containg edge values
[in]	edg	edge number
[in]	vfld	pointer to singe element in the field
[in]	nx,ny,nz	element size

math_ran_dst()

real function math_ran_dst	(	integer	ix,
		integer	iy,
		integer	iz,
		integer	ieg,
		real, dimension(ldim)	xl,
		real, dimension(3)	fcoeff
	)

Give random distribution depending on position.

The original Nek5000 rundom number generator is implementted in ran1. This totally ad-hoc random number generator below could be preferable to the origina one for the simple reason that it gives the same initial cindition independent of the number of processors, which is important for code verification.

Parameters

[in]	ix,iy,iz	GLL point index
[in]	ieg	global element number
[in]	xl	physical point coordinates
[in]	fcoeff	function coefficients

Returns

random distribution

math_ran_rng()

real function math_ran_rng	(	real	lower,
		real	upper
	)

Give random number in the defined range.

Parameters

[in]

lower,upper

range for random numer

Returns

random number in the defined range

math_rot3da()

subroutine math_rot3da	(	real, dimension(ldim)	vo,
		real, dimension(ldim)	vi,
		real, dimension(ldim)	va,
		real	an
	)

3D rotation of a vector along given axis

Parameters

[in]	vo	output vector
[in]	vi	input vector
[in]	va	rotation axis
[in]	an	rotation angle

math_stepf()

real function math_stepf

(

real

x

)

Step function.

Continuous step function:

\begin{eqnarray*} stepf(x) = \left\{ \begin{array}{ll} 0 &\mbox{ if $x \leq x_{min}$} \\ \left(1+e^{\left((x-1)^{-1} + x^{-1}\right)}\right)^{-1} &\mbox{ if $x \leq x_{max}$} \\ 1 &\mbox{ if $x > x_{max}$} \end{array} \right. \end{eqnarray*}

with \( x_{min} = 0.02\) and \( x_{max}=0.98\)

Parameters

[in]

x

function argument

Returns

math_stepf

math_zbqlini()

subroutine math_zbqlini

(

integer

seed

)

Initialise Marsaglia-Zaman random number generator.

To initialise the random number generator - either repeatably or nonrepeatably.

Parameters

[in]

seed

number which generates elements of the array ZBQLIX

math_zbqlu01()

real function math_zbqlu01

Marsaglia-Zaman random number generator.

Returns a uniform random number between 0 & 1, using a Marsaglia-Zaman type subtract-with-borrow generator.

Remarks

Uses double precision, rather than integer, arithmetic throughout because MZ's INTEGER constants overflow 32-bit INTEGER storage (which goes from -2^31 to 2^31). Ideally, we would explicitly truncate all INTEGER quantities at each stage to ensure that the DOUBLE PRECISION representations DO not accumulate approximation error; however, on some machines the USE of DNINT to accomplish this is seriously slow (run-time increased by a factor of about 3). This DOUBLE PRECISION version has been tested against an INTEGER implementation that uses long integers (non-standard and, again, slow) - the output was identical up to the 16th decimal place after 10^10 calls, so we're probably OK ... In current implementation we follow Nek5000 compilation rulles prolonging all reals to doulbe with compiler flaggs.

Author

Richard Chandler (richa.nosp@m.rd@s.nosp@m.tats..nosp@m.ucl..nosp@m.ac.uk)

Paul Northrop (north.nosp@m.rop@.nosp@m.stats.nosp@m..ox..nosp@m.ac.uk)

Returns

random number