GFTConvolution2D.f90 File Reference

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Functions/Subroutines
subroutine	gft2dconvolution (isp, ny, mx, niy, mjx, spatdatain, kerneltransf, spatdataout)
subroutine	gft2dtransformkernel (ny, mx, niy, mjx, y_dim_kernel, x_dim_kernel, kernelin, kerneltransf)
	GFT2DTransformKernel
subroutine	setdimsforfft (ispec)
	SetDimsForFFT
subroutine	lowpassfilter (dimy_start, dimy_end, dimx_start, dimx_end, filterexpo, filter)
	LowPassFilter

Function/Subroutine Documentation

gft2dconvolution()

subroutine gft2dconvolution	(	integer, intent(in)	isp,
		integer, intent(in)	ny,
		integer, intent(in)	mx,
		integer, intent(in)	niy,
		integer, intent(in)	mjx,
		real(kind=gft_prec), dimension(0:ny-1,mx), intent(in)	spatdatain,
		complex(kind=gft_prec), dimension(0:niy/2,mjx), intent(in)	kerneltransf,
		real(kind=gft_prec), dimension(0:ny-1,mx), intent(out)	spatdataout )

GFT2DConvolution
Convolution by Fast Fourier Transform (FFT) of seed dispersal kernel and seed production area

---

done in several steps:

1. The seed production intermediate area is stored to the 0,0 corner of the large area for zero-padding !>
   
2. A forward 2D FFT (REAL to complex) is done with the seed production on the large area
3. The fourier transformed seed production is multiplied with the fourier transformed dispersal kernel, Convolution
4. the product is back-fourier-transformed (complex to REAL)
5. The resulting REAL area is cleaned from noise (negative or very low positive values) ¨
6. and stored to the intermediate area (adapted from example program rcr.f90)

USE GFT

• IN:

  • Parameters

    ny	maxlatEvenext, y-dimension of intermediate area, a bit more than maxlat
    mx	maxlonEvenext, x-dimension of intermediate area, a bit more than maxlon
    niy	maxlatExt, y-dimension of large area
    mjx	maxlonExt, x-dimension of large area
    kernelTransf	transformed kernel

  • FROM GFT
    • GFT_Prec : INTEGER : precision of the GFT calculations
    • GFT_RCR : TYPE : derived TYPE for 1D, 2D and 3D Real-Complex and Complex-Real FFT
    • GFT_set_fft : INTERFACE : contains settings for all kind of FFTs
    • GFT_do_fft : INTERFACE : contains subroutines for performing all kind of FFTs
    • GFT_end_fft : INTERFACE : contains subroutines for ending all kind of FFTs
• OUT:
  
  • spatDataOut: the seed rain on the intermediate area
• CALLED FROM:
  • GFT_Interact.f90
• CALLS:
  • GFT_set_fft.f90, GFT_do_fft.f90, GFT_end_fft.f90 from modules starting with "GFT" for the FFTs
  • PrintMatrixASXY2File (in GFT_Interact.f90)

Definition at line 37 of file GFTConvolution2D.f90.

gft2dtransformkernel()

subroutine gft2dtransformkernel	(	integer, intent(in)	ny,
		integer, intent(in)	mx,
		integer, intent(in)	niy,
		integer, intent(in)	mjx,
		integer, intent(in)	y_dim_kernel,
		integer, intent(in)	x_dim_kernel,
		real (kind=gft_prec), dimension(0:(y_dim_kernel-1),x_dim_kernel ), intent(in)	kernelin,
		complex(kind=gft_prec), dimension(0:(niy/2),mjx), intent(out)	kerneltransf )

GFT2DTransformKernel

---

Fast Fourier transforms the seed dispersal kernel to the frequency domain !> done in several steps: #- the kernel is stored to the center of the intermediate area #- it is mirrored to the corners of this intermediate area #- the intermediate area with the mirrored kernel is stored to the 0,0, corner of the large are #- the fft transformation is done

• USE: GFT
• IN:

  • Parameters

    ny	maxlatEvenext, y-dimension of intermediate area, a bit more than maxlat
    mx	maxlonEvenext, x-dimension of intermediate area, a bit more than maxlon
    niy	maxlatExt, y-dimension of large area
    mjx	maxlonExt, x-dimension of large area
    y_dim_kernel	rad* 2 +2.; y-dimension of kernel
    x_dim_kernel	rad* 2 +2.; x-dimension of kernel (normally the same as y_dim_kernel
    kernelIn	this is the kernel

  • FROM GFT
    • GFT_Prec : INTEGER : precision of the GFT calculations
    • GFT_RCR : TYPE : derived TYPE for 1D, 2D and 3D Real-Complex and Complex-Real FFT
    • GFT_set_fft : INTERFACE : contains settings for all kind of FFTs
    • GFT_do_fft : INTERFACE : contains subroutines for performing all kind of FFTs
    • GFT_end_fft : INTERFACE : contains subroutines for ending all kind of FFTs
• OUT:
  

  • Parameters

    kernelTransf

    the Fourier Transform of the kernel on the large area (complex)

• CALLED FROM:
  • CalculateKernelTransformation in GFT_Interact.f90
• CALLS:
  • ReorderKernelForGFT in ReorderKernelForGFT.f90
  • GFT_set_fft.f90, GFT_do_fft.f90, GFT_end_fft.f90 from GFT programs for the FFTs
  • PrintMatrixASXY2File in GFT_Interact.f90

Definition at line 166 of file GFTConvolution2D.f90.

lowpassfilter()

subroutine lowpassfilter	(	integer, intent(in)	dimy_start,
		integer, intent(in)	dimy_end,
		integer, intent(in)	dimx_start,
		integer, intent(in)	dimx_end,
		real, intent(in)	filterexpo,
		complex(kind=gft_prec), dimension(dimy_start:dimy_end,dimx_start:dimx_end), intent(out)	filter )

LowPassFilter

---

Attempt for filtering the noise out in frequency domain. Not used currently.
Here a distance weighted low pass filter, i.e. decreasing with distance from (0,1) cell. dimy-start is normally 0, dimx_start is normally 1

• USE: GFT
  
• IN:

  • Parameters

    dimy_start,dimy_end,dimx_start,dimx_end	: INTEGER, dimension bounds of the areas in frequency domain
    filterexpo:factor	determining the slope of decrease with distance

  • FROM GFT
    • GFT_Prec : INTEGER : precision of the GFT calculations
• OUT:
  

  • Parameters

    filter,the

    filter to be multiplied to the signal, i.e. the transformed kernel, the transformed seed production

• CALLED FROM:
  • GFT2DConvolution in GFTConvolution2D.f90

Definition at line 283 of file GFTConvolution2D.f90.

setdimsforfft()

subroutine setdimsforfft

(

integer, intent(in)

ispec

)

SetDimsForFFT

---

Sets the dimenstions of the Fast Fourier Transformations, for the next even (intermediate) area and for the large extended area

• USE: All_par
• IN:

  • Parameters

    ispec

    : species identifier

  • FROM All_par
    • maxlat, maxlon: INTEGER: y-dimension and x-dimension of simulation area
      
• OUT: :
  
  • via All_par
    
    • spec(maxspc) : TYPE(SpecProperties) : species properties, here the area dimensions for fft:
      
      • maxlatExt, maxlonExt: INTEGER, dimensions of large extended area
      • maxlatEvenExt, maxlonEvenExt: INTEGER, dimensions of intermediate area (here set to maxlatEven and maxlonEven)
        
• CALLED FROM:
  • GetSpc in GetSpc.f90

Definition at line 236 of file GFTConvolution2D.f90.