mo_kernel.f90 File Reference

Module for kernel regression and kernel density estimation. More...

Go to the source code of this file.

Data Types
interface	mo_kernel::kernel_cumdensity
	Approximates the cumulative density function (CDF). More...
interface	mo_kernel::kernel_density
	Approximates the probability density function (PDF). More...
interface	mo_kernel::kernel_density_h
	Approximates the bandwith h of the kernel. More...
interface	mo_kernel::kernel_regression
	Multi-dimensional non-parametric kernel regression. More...
interface	mo_kernel::kernel_regression_h
	Approximates the bandwith h of the kernel for regression. More...
interface	mo_kernel::nadaraya_watson
interface	mo_kernel::allocate_globals
interface	mo_kernel::cross_valid_density
interface	mo_kernel::cross_valid_regression
interface	mo_kernel::mesh
interface	mo_kernel::golden
interface	mo_kernel::trapzd
interface	mo_kernel::polint

Modules
module	mo_kernel
	Module for kernel regression and kernel density estimation.

Functions/Subroutines
real(dp) function, dimension(:), allocatable	mo_kernel::kernel_cumdensity_1d_dp (ix, h, silverman, xout, romberg, nintegrate, epsint, mask, nodata)
real(sp) function, dimension(:), allocatable	mo_kernel::kernel_cumdensity_1d_sp (ix, h, silverman, xout, romberg, nintegrate, epsint, mask, nodata)
real(dp) function, dimension(:), allocatable	mo_kernel::kernel_density_1d_dp (ix, h, silverman, xout, mask, nodata)
real(sp) function, dimension(:), allocatable	mo_kernel::kernel_density_1d_sp (ix, h, silverman, xout, mask, nodata)
real(dp) function	mo_kernel::kernel_density_h_1d_dp (ix, silverman, mask)
real(sp) function	mo_kernel::kernel_density_h_1d_sp (ix, silverman, mask)
real(dp) function, dimension(:), allocatable	mo_kernel::kernel_regression_1d_dp (ix, iy, h, silverman, xout, mask, nodata)
real(sp) function, dimension(:), allocatable	mo_kernel::kernel_regression_1d_sp (ix, iy, h, silverman, xout, mask, nodata)
real(dp) function, dimension(:), allocatable	mo_kernel::kernel_regression_2d_dp (ix, iy, h, silverman, xout, mask, nodata)
real(sp) function, dimension(:), allocatable	mo_kernel::kernel_regression_2d_sp (ix, iy, h, silverman, xout, mask, nodata)
real(dp) function	mo_kernel::kernel_regression_h_1d_dp (ix, iy, silverman, mask)
real(sp) function	mo_kernel::kernel_regression_h_1d_sp (ix, iy, silverman, mask)
real(dp) function, dimension(size(ix, 2))	mo_kernel::kernel_regression_h_2d_dp (ix, iy, silverman, mask)
real(sp) function, dimension(size(ix, 2))	mo_kernel::kernel_regression_h_2d_sp (ix, iy, silverman, mask)
real(dp) function	mo_kernel::nadaraya_watson_1d_dp (z, y, mask, valid)
real(sp) function	mo_kernel::nadaraya_watson_1d_sp (z, y, mask, valid)
real(dp) function	mo_kernel::nadaraya_watson_2d_dp (z, y, mask, valid)
real(sp) function	mo_kernel::nadaraya_watson_2d_sp (z, y, mask, valid)
real(dp) function	mo_kernel::cross_valid_regression_dp (h)
real(sp) function	mo_kernel::cross_valid_regression_sp (h)
real(dp) function	mo_kernel::cross_valid_density_1d_dp (h)
real(sp) function	mo_kernel::cross_valid_density_1d_sp (h)
subroutine	mo_kernel::allocate_globals_1d_dp (x, y, xout)
subroutine	mo_kernel::allocate_globals_1d_sp (x, y, xout)
subroutine	mo_kernel::allocate_globals_2d_dp (x, y, xout)
subroutine	mo_kernel::allocate_globals_2d_sp (x, y, xout)
subroutine	mo_kernel::deallocate_globals ()
real(sp) function	mo_kernel::golden_sp (ax, bx, cx, func, tol, xmin)
subroutine	shft2 (a, b, c)
subroutine	shft3 (a, b, c, d)
real(dp) function	mo_kernel::golden_dp (ax, bx, cx, func, tol, xmin)
subroutine	shft2 (a, b, c)
subroutine	shft3 (a, b, c, d)
real(dp) function, dimension(n)	mo_kernel::mesh_dp (start, end, n, delta)
real(sp) function, dimension(n)	mo_kernel::mesh_sp (start, end, n, delta)
subroutine	mo_kernel::trapzd_dp (kernel, x, h, a, b, res, n)
subroutine	mo_kernel::trapzd_sp (kernel, x, h, a, b, res, n)
subroutine	mo_kernel::polint_dp (xa, ya, x, y, dy)
subroutine	mo_kernel::polint_sp (xa, ya, x, y, dy)

Variables
real(sp), dimension(:,:), allocatable	mo_kernel::global_x_sp
real(sp), dimension(:,:), allocatable	mo_kernel::global_xout_sp
real(sp), dimension(:), allocatable	mo_kernel::global_y_sp
real(dp), dimension(:,:), allocatable	mo_kernel::global_x_dp
real(dp), dimension(:,:), allocatable	mo_kernel::global_xout_dp
real(dp), dimension(:), allocatable	mo_kernel::global_y_dp

Detailed Description

Module for kernel regression and kernel density estimation.

This module provides routines for kernel regression of data as well as kernel density estimation of both probability density functions (PDF) and cumulative density functions (CDF).
So far only a Gaussian kernel is implemented (Nadaraya-Watson) which can be used for one- and multidimensional data.
Furthermore, the estimation of the bandwith needed for kernel methods is provided by either Silverman''s rule of thumb or a Cross-Vaildation approach.
The Cross-Validation method is actually an optimization of the bandwith and might be the most costly part of the kernel smoother. Therefore, the bandwith estimation is not necessarily part of the kernel smoothing but can be determined first and given as an optional argument to the smoother.

Changelog

• Juliane Mai, Mar 2013
• Stephan Thober, Mar 2013
• Matthias Cuntz, Mar 2013
• Matthias Cuntz, May 2013
  • sort -> qsort
  • module procedure golden
• Stephan Thober, Jul 2015
  • using sort_index in favor of qsort_index
• Matthias Cuntz, Mar 2016
  • Romberg integration in cumdensity
• Juliane Mai

Date

Mar 2013

Copyright

Copyright 2005-2024, the CHS Developers, Sabine Attinger: All rights reserved. FORCES is released under the LGPLv3+ license

The UFZ (CHS) FORCES code is free software. You can redistribute it and/or modify it under the terms of the GNU General Public License as published by the free Software Foundation either version 3 of the License, or (at your option) any later version.

This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.

You received a copy of the GNU Lesser General Public License along with the UFZ CHS FORCES code. It can be found in the files COPYING and COPYING.LESSER provided with this software. The complete GNU license text can also be found at http://www.gnu.org/licenses/.

Definition in file mo_kernel.f90.

Function/Subroutine Documentation

shft2() [1/2]

subroutine golden_sp::shft2 ( real(sp), intent(out)  a, real(sp), intent(inout)  b, real(sp), intent(in)  c  )

private

Definition at line 2430 of file mo_kernel.f90.

shft2() [2/2]

subroutine golden_dp::shft2 ( real(dp), intent(out)  a, real(dp), intent(inout)  b, real(dp), intent(in)  c  )

private

Definition at line 2500 of file mo_kernel.f90.

shft3() [1/2]

subroutine golden_sp::shft3 ( real(sp), intent(out)  a, real(sp), intent(inout)  b, real(sp), intent(inout)  c, real(sp), intent(in)  d  )

private

Definition at line 2438 of file mo_kernel.f90.

shft3() [2/2]

subroutine golden_dp::shft3 ( real(dp), intent(out)  a, real(dp), intent(inout)  b, real(dp), intent(inout)  c, real(dp), intent(in)  d  )

private

Definition at line 2508 of file mo_kernel.f90.