random_routines Module Reference

Data Types
type	randxy_data

Functions/Subroutines
real function	rgauss ()
subroutine	resample_randxy_data (randxy)
subroutine	init_randxy_data (randxy, np, xp, yp, lscale, gridsize, index_corr)
subroutine	deallocate_randxy_data (randxy)
subroutine	adjust_nxl4fft (nxl)
subroutine	random_field (nxl, nyl, kmax, lmax, spec_dens_2D, pert_field, ifaxx, ifaxy, trigsx, trigsy)
subroutine	corr_to_spec (index_corr, lscale, nxl, nyl, gridsize, kmax, lmax, corr, spec_dens_2D, ifaxx, ifaxy, trigsx, trigsy)
subroutine	gen_corr (index_corr, gridsize, lscale, nxl, nyl, corr)
subroutine	interpol_grid2point (np, xp, yp, zp, NX, NY, X, Y, Z)
subroutine	fft2d (inv, nxl, nyl, a, kmax, lmax, ahat, ifaxx, ifaxy, trigsx, trigsy)
subroutine	fft99a (A, WORK, TRIGS, INC, JUMP, N, LOT)
subroutine	fft99b (WORK, A, TRIGS, INC, JUMP, N, LOT)
subroutine	fft991 (A, WORK, TRIGS, IFAX, INC, JUMP, N, LOT, ISIGN)
subroutine	set99 (TRIGS, IFAX, N)
subroutine	fax (IFAX, N, MODE)
subroutine	fftrig (TRIGS, N, MODE)
subroutine	vpassm (A, B, C, D, TRIGS, INC1, INC2, INC3, INC4, LOT, N, IFAC, LA)

Detailed Description

Routines for random number generation, including routines for spatially correlated random fields.

Function/Subroutine Documentation

adjust_nxl4fft()

subroutine random_routines::adjust_nxl4fft

(

integer, intent(inout)

nxl

)

Adjust the size of random field to fulfill requirement of subroutine fft991.

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corr_to_spec()

subroutine random_routines::corr_to_spec	(	integer	index_corr,
		real	lscale,
		integer	nxl,
		integer	nyl,
		real	gridsize,
		integer	kmax,
		integer	lmax,
		real, dimension(nxl,nyl)	corr,
		real, dimension(0:kmax,-lmax:lmax)	spec_dens_2D,
		integer, dimension(13)	ifaxx,
		integer, dimension(13)	ifaxy,
		real, dimension(3*nxl/2+1)	trigsx,
		real, dimension(3*nyl/2+1)	trigsy
	)

Generate correlation in physical space and transform to spectral density in spectral space.

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deallocate_randxy_data()

subroutine random_routines::deallocate_randxy_data

(

type(randxy_data), intent(inout)

randxy

)

Subroutine that deallocates any allocated memory in a randxy_data variable.

fax()

subroutine random_routines::fax	(	integer, dimension(10)	IFAX,
		integer	N,
		integer	MODE
	)

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fft2d()

subroutine random_routines::fft2d	(	logical	inv,
		integer	nxl,
		integer	nyl,
		real, dimension(nxl,nyl)	a,
		integer	kmax,
		integer	lmax,
		complex, dimension(0:kmax,-lmax:lmax)	ahat,
		integer, dimension(13)	ifaxx,
		integer, dimension(13)	ifaxy,
		real, dimension(3*nxl/2+1)	trigsx,
		real, dimension(3*nyl/2+1)	trigsy
	)

2D Fourier transform to spectal space

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fft991()

subroutine random_routines::fft991	(	real, dimension(*)	A,
		real, dimension(*)	WORK,
		real, dimension(*)	TRIGS,
		integer, dimension(13)	IFAX,
		integer	INC,
		integer	JUMP,
		integer	N,
		integer	LOT,
		integer	ISIGN
	)

Multiple real/half-complex periodic Fast Fourier Transform.

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fft99a()

subroutine random_routines::fft99a	(	real, dimension(*)	A,
		real, dimension(*)	WORK,
		real, dimension(*)	TRIGS,
		integer	INC,
		integer	JUMP,
		integer	N,
		integer	LOT
	)

Preprocessing for fft99 routine (spectral to grid point transform)

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fft99b()

subroutine random_routines::fft99b	(	real, dimension(*)	WORK,
		real, dimension(*)	A,
		real, dimension(*)	TRIGS,
		integer	INC,
		integer	JUMP,
		integer	N,
		integer	LOT
	)

Postprocessing for fft99 routine (grid point to spectral transform)

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fftrig()

subroutine random_routines::fftrig	(	real, dimension(*)	TRIGS,
		integer	N,
		integer	MODE
	)

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gen_corr()

subroutine random_routines::gen_corr	(	integer	index_corr,
		real	gridsize,
		real	lscale,
		integer	nxl,
		integer	nyl,
		real, dimension(nxl,nyl)	corr
	)

Generate correlation function in physical space.

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init_randxy_data()

subroutine random_routines::init_randxy_data	(	type(randxy_data), intent(inout)	randxy,
		integer, intent(in)	np,
		real, dimension(np), intent(in)	xp,
		real, dimension(np), intent(in)	yp,
		real, intent(in)	lscale,
		real, intent(in)	gridsize,
		integer, intent(in)	index_corr
	)

Initialisation of data used for generation of spatially correlated random numbers with the subroutine resample_randxy_data.

Parameters

[in,out]	randxy	data structure
[in]	np	n:o spatial points (model units, sub-basins)
[in]	xp	easting(x) coordinates
[in]	yp	northing(y) coordinates
[in]	lscale	correlation length scale
[in]	gridsize	gridsize for the 2D field where the random numbers are generated
[in]	index_corr	correlation type: 1 Gaussian, 2 Compact 5th degree polynomial, 3 Power law

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interpol_grid2point()

subroutine random_routines::interpol_grid2point	(	integer, intent(in)	np,
		real, dimension(np), intent(in)	xp,
		real, dimension(np), intent(in)	yp,
		real, dimension(np), intent(out)	zp,
		integer, intent(in)	NX,
		integer, intent(in)	NY,
		real, dimension(nx), intent(in)	X,
		real, dimension(ny), intent(in)	Y,
		real, dimension(nx,ny), intent(in)	Z
	)

Interpolation from regular grid Z(X,Y) to points zp(xp,yp) using bilinear interpolation.

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random_field()

subroutine random_routines::random_field	(	integer	nxl,
		integer	nyl,
		integer	kmax,
		integer	lmax,
		real, dimension(0:kmax,-lmax:lmax)	spec_dens_2D,
		real, dimension(nxl,nyl)	pert_field,
		integer, dimension(13)	ifaxx,
		integer, dimension(13)	ifaxy,
		real, dimension(3*nxl/2+1)	trigsx,
		real, dimension(3*nyl/2+1)	trigsy
	)

Generates a sample of a 2D spatially correlated random field with mean 0 and stdev 1.

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resample_randxy_data()

subroutine random_routines::resample_randxy_data

(

type(randxy_data), intent(inout)

randxy

)

Subroutine for creating pseudo-random number (gaussian) with spatial correlation for point coordinates (x,y)

Algorithm

Generate a new 2D random field

Interpolate to the requested x,y coordinates

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rgauss()

real function random_routines::rgauss

Function for generation pseudo-random number from normal distribution N(0,1).

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set99()

subroutine random_routines::set99	(	real, dimension(*)	TRIGS,
		integer, dimension(13)	IFAX,
		integer	N
	)

An initialisation routine that must be called once before a sequence of calls to the FFT routines (provided that N is not changed).

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vpassm()

subroutine random_routines::vpassm	(	real, dimension(*)	A,
		real, dimension(*)	B,
		real, dimension(*)	C,
		real, dimension(*)	D,
		real, dimension(*)	TRIGS,
		integer	INC1,
		integer	INC2,
		integer	INC3,
		integer	INC4,
		integer	LOT,
		integer	N,
		integer	IFAC,
		integer	LA
	)

Performs one pass through data as part of the multiple complex FFT routine,.

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