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mo_spatialsimilarity.f90
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!> \file mo_spatialsimilarity.f90
!> \brief Routines for bias insensitive comparison of spatial patterns.
!> \details These routines are based on the idea that spatial similarity can be assessed by comparing
!> the magnitude of neighboring pixels (e.g. is the neighboring pixel larger or smaller).
!> \author Matthias Zink, Juliane Mai
!> \date Mar 2013
MODULE mo_spatialsimilarity
! This module contains routines for the masked calculation of
! spatial similarity measures like NDV
! Written Nov 2012, Matthias Zink and Juliane Mai
! License
! -------
! This file is part of the JAMS Fortran package, distributed under the MIT License.
!
! Copyright (c) 2012-2015 Matthias Zink, Juliane Mai
!
! Permission is hereby granted, free of charge, to any person obtaining a copy
! of this software and associated documentation files (the "Software"), to deal
! in the Software without restriction, including without limitation the rights
! to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
! copies of the Software, and to permit persons to whom the Software is
! furnished to do so, subject to the following conditions:
!
! The above copyright notice and this permission notice shall be included in all
! copies or substantial portions of the Software.
!
! THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
! IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
! FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
! AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
! LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
! OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
! SOFTWARE.
USE mo_kind, ONLY: i4, sp, dp
IMPLICIT NONE
PUBLIC :: NNDV ! number of neighboring dominating values
PUBLIC :: PD ! patter dissimilarity measure
! ------------------------------------------------------------------
! NAME
! NNDV - number of neighboring dominating values
! PURPOSE
!> \brief Calculates the number of neighboring dominating values, a measure for spatial dissimilarity.
!> \details
!> NNDV = 1 - sum(abs(dominating_neighbors(mat1) - dominating_neighbors(mat2))) / count(mask)
!> dominating_neighbors(mat1) = comparison if pixel is larger than its neighbouring values
!>
!> An array element value is compared with its 8 neighbouring cells to check if these cells are larger
!> than the array element value. The result is a 3x3 matrix in which larger cells are indicated by a
!> true value. For comparison this is done with both input arrays. The resulting array is the sum of
!> substraction of the 3x3 matrices for each of the both arrays. The resulting matrix is afterwards
!> normalized to its available neighbors.
!> Furthermore an average over the entire field is calculated. The valid interval of
!> the values for NNDV is [0..1]. In which 1 indicates full agreement and 0 full dismatching.
!> <pre>
!> EXAMPLE:\n
!> mat1 = | 12 17 1 | , mat2 = | 7 9 12 |
!> | 4 10 11 | | 12 11 11 |
!> | 15 2 20 | | 5 13 7 |
!> booleans determined for every grid cell following fortran array scrolling
!> i.e. (/col1_row1, col1_row2, col1_row3, col2_row1, .. ,col3_row3/),(/3,3/)
!>
!> comp1 = | FFF FFF FTF, FFF FFF FFF, FTT FFT FFF |
!> | FFF TFT TTF, TFT TFF FTT, TFF FFT FFF |
!> | FFF FFF FFF, TTF TFF TTF, FFF FFF FFF |
!>
!> comp2 = | FFF FFT FTT, FFT FFT FTT, FFF FFF FFF |
!> | FFF FFF FFT, FTF FFT TFF, FFT TFF FFF |
!> | FFF TFF TTF, FFF FFF FFF, TTF TFF FFF |
!>
!> NNDVMatrix =
!> abs( count(comp1) - count(comp2) ) = | 1-3, 0-4, 3-0 | = | 2, 4, 3 |
!> | 4-1, 5-3, 2-2 | | 3, 2, 0 |
!> | 0-3, 5-0, 0-3 | | 3, 5, 3 |
!>
!> DISSIMILAR / VALID NEIGH CELLS
!> NNDVMatrix / VALID NEIGH CELLS = | 2, 4, 3 | / | 3, 5, 3 |
!> | 3, 2, 0 | | 5, 8, 5 |
!> | 3, 5, 3 | | 3, 5, 3 |
!>
!> = | 0.66, 0.80, 1.00 |
!> | 0.60, 0.25, 0.00 |
!> | 1.0, 1.00, 1.00 |
!>
!> NNDV = 1 - sum(NNDVMatrix) / count(mask) = 1 - (6.31666666 / 9) = 0.2981
!> </pre>
!>
!> If an optinal mask is given, the calculations are over those locations that correspond to true values in the mask.
!> mat1 and mat2 can be single or double precision. The result will have the same numerical precision.
! CALLING SEQUENCE
! out = NNDV(mat1, mat2, mask=mask, valid=valid)
! INDENT(IN)
!> \param[in] "real(sp/dp), dimension(:,:) :: mat1" 2D-array with input numbers
!> \param[in] "real(sp/dp), dimension(:,:) :: mat2" 2D-array with input numbers
! INDENT(INOUT)
! None
! INDENT(OUT)
! None
! INDENT(IN), OPTIONAL
!> \param[in] "logical,dimension(:,:),optinal :: mask" 2D-array of logical values with size(mat1/mat2).
!> If present, only those locations in mat1/mat2 having true values in mask are evaluated.
! INDENT(INOUT), OPTIONAL
! None
! INDENT(OUT), OPTIONAL
!> \param[out] "logical :: valid" indicates if the function could determine a valid value
!> result can be unvalid if entire mask is .false. for ex.
!> in this case PatternDissim is set to 0 (worst case)
! RETURN
!> \return real(sp/dp) :: NNDV — Number of neighboring dominating values
! RESTRICTIONS
! Input values must be floating points.
! EXAMPLE
! mat1 = reshape(/ 1., 2, 3., -999., 5., 6. /, (/3,3/))
! mat2 = reshape(/ 1., 2, 3., -999., 5., 6. /, (/3,3/))
! out = NNDV(mat1, mat2, mask=(mat1 >= 0. .and. mat2 >= 0.))
! -> see also example in test directory
! LITERATURE
!> \note routine based on algorithm by Luis Samaniego 2009
! HISTORY
!> \author Matthias Zink
!> \date Nov 2012
! update May 2015 created documentation
INTERFACE NNDV
MODULE PROCEDURE NNDV_sp, NNDV_dp
END INTERFACE NNDV
! ------------------------------------------------------------------
! NAME
! PD
! PURPOSE
!> \brief Calculates pattern dissimilarity (PD) measure
!> \details
!> PD = 1 - sum(dissimilarity(mat1, mat2)) / count(mask)
!> dissimilarity(mat1, mat2) = comparison if pixel is larger than its neighbouring values
!>
!> An array element value is compared with its 8 neighbouring cells to check if these cells are larger
!> than the array element value. The result is a 3x3 matrix in which larger cells are indicated by a
!> true value. For comparison this is done with both input arrays. The resulting array is the sum of
!> xor values of the 3x3 matrices for each of the both arrays. This means only neighbourhood comparisons
!> which are different in the 2 matrices are counted. This resulting matrix is afterwards normalized to its
!> available neighbors. Furthermore an average over the entire field is calculated. The valid interval of
!> the values for PD is [0..1]. In which 1 indicates full agreement and 0 full dismatching.
!>
!> <pre>
!> EXAMPLE:\n
!> mat1 = | 12 17 1 | , mat2 = | 7 9 12 |
!> | 4 10 11 | | 12 11 11 |
!> | 15 2 20 | | 5 13 7 |
!>
!> booleans determined for every grid cell following fortran array scrolling
!> i.e. (/col1_row1, col1_row2, col1_row3, col2_row1, .. ,col3_row3/),(/3,3/)
!>
!> comp1 = | FFF FFF FTF, FFF FFF FFF, FTT FFT FFF |
!> | FFF TFT TTF, TFT TFF FTT, TFF FFT FFF |
!> | FFF FFF FFF, TTF TFF TTF, FFF FFF FFF |
!>
!> comp2 = | FFF FFT FTT, FFT FFT FTT, FFF FFF FFF |
!> | FFF FFF FFT, FTF FFT TFF, FFT TFF FFF |
!> | FFF TFF TTF, FFF FFF FFF, TTF TFF FFF |
!>
!>
!> xor=neq = | FFF FFT FFT, FFT FFT FTT, FTT FFT FFF |
!> | FFF TFT TTT, TTT TFT TTT, TFT TFT FFF |
!> | FFF TFF TTF, TTF TFF TTF, TTF TFF FFF |
!>
!> DISSIMILAR / VALID NEIGH CELLS
!> PDMatrix = | 2, 4, 3 | / | 3, 5, 3 | = | 0.66, 0.80, 1.00 |
!> | 5, 8, 4 | | 5, 8, 5 | | 1.00, 1.00, 0.80 |
!> | 3, 5, 3 | | 3, 5, 3 | | 1.00, 1.00, 1.00 |
!>
!> PD = 1 - sum(PDMatrix) / count(mask) = 1 - (8.2666666 / 9) = 0.08148
!> </pre>
!>
!> If an optinal mask is given, the calculations are over those locations that correspond to true values in the mask.
!> mat1 and mat2 can be single or double precision. The result will have the same numerical precision.
! CALLING SEQUENCE
! out = PD(mat1, mat2, mask=mask, valid=valid)
! INDENT(IN)
!> \param[in] "real(sp/dp), dimension(:,:) :: mat1" 2D-array with input numbers
!> \param[in] "real(sp/dp), dimension(:,:) :: mat2" 2D-array with input numbers
! INDENT(INOUT)
! None
! INDENT(OUT)
! None
! INDENT(IN), OPTIONAL
!> \param[in] "logical,dimension(:,:),optinal :: mask" 2D-array of logical values with size(mat1/mat2)
!> If present, only those locations in mat1/mat2 having true values in mask are evaluated.
! INDENT(INOUT), OPTIONAL
! None
! INDENT(OUT), OPTIONAL
!> \param[out] "logical,optinal :: valid" indicates if the function could determine a valid value
!> result can be unvalid if entire mask is .false. for ex.
!> in this case PD is set to 0 (worst case)
! RETURN
!> \return real(sp/dp) :: PD — pattern dissimilarity measure
! RESTRICTIONS
! Input values must be floating points.
! EXAMPLE
! mat1 = reshape(/ 1., 2, 3., -999., 5., 6. /, (/3,3/))
! mat2 = reshape(/ 1., 2, 3., -999., 5., 6. /, (/3,3/))
! out = PD(mat1, mat2, mask=(mat1 >= 0. .and. mat2 >= 0.))
! -> see also example in test directory
! LITERATURE
! None
! HISTORY
!> \author Matthias Zink and Juliane Mai
!> \date Jan 2013
INTERFACE PD
MODULE PROCEDURE PD_sp, PD_dp
END INTERFACE PD
! ------------------------------------------------------------------
CONTAINS
FUNCTION NNDV_sp(mat1, mat2, mask, valid)
IMPLICIT NONE
REAL(sp), DIMENSION(:,:), INTENT(IN) :: mat1, mat2
LOGICAL, DIMENSION(:,:), OPTIONAL, INTENT(IN) :: mask
LOGICAL, OPTIONAL, INTENT(OUT) :: valid
REAL(sp) :: NNDV_sp
INTEGER(i4) :: iCo, iRo
INTEGER(i4) :: noValidPixels
INTEGER(i4), DIMENSION(size(shape(mat1)) ) :: shapemask
INTEGER(i4), DIMENSION(size(mat1, dim=1), size(mat1, dim=2)) :: validcount
REAL(sp), DIMENSION(size(mat1, dim=1)+2_i4, size(mat1, dim=2)+2_i4) :: bufferedMat1, bufferedMat2
REAL(sp) , DIMENSION(size(mat1, dim=1), size(mat1, dim=2)) :: NNDVMatrix
LOGICAL, DIMENSION(size(mat1, dim=1)+2_i4, size(mat1, dim=2)+2_i4) :: maske
LOGICAL, DIMENSION(size(mat1, dim=1), size(mat1, dim=2)) :: validmaske
! check if input has all the same dimensions
if (present(mask)) then
shapemask = shape(mask)
else
shapemask = shape(mat1)
end if
!
if (any(shape(mat1) .NE. shape(mat2))) &
stop 'NNDV_sp: shapes of input matrix 1 and input matrix 2 are not matching'
if (any(shape(mat1) .NE. shapemask)) &
stop 'NNDV_sp: shapes of input matrices and mask are not matching'
!
! additional 2 rows and 2 cols added for checking the border cells without crashing the search agorithm
! so the search windows can always cover 9 cells even if it is checking a border cell
! buffer rows are initialized as false values within mask, i.e. they are not considered for the calculation
! of the criteria
!
! initialize mask with default=.false.
maske = .false.
if (present(mask)) then
maske(2:(size(maske,dim=1)-1_i4), 2:(size(maske,dim=2)-1_i4)) = mask
else
maske(2:(size(maske,dim=1)-1_i4), 2:(size(maske,dim=2)-1_i4)) = .true.
end if
!
! initialize bufferedMat1 & bufferedMat2
bufferedMat1 = 0.0_sp
bufferedMat2 = 0.0_sp
bufferedMat1(2:(size(maske,dim=1)-1), 2:(size(maske,dim=2)-1)) = mat1
bufferedMat2(2:(size(maske,dim=1)-1), 2:(size(maske,dim=2)-1)) = mat2
!
! initialize NNDV
NNDVMatrix = 0.0_sp
!
NNDV_sp = 0.0_sp
do iCo = 2_i4, size(bufferedMat1, dim=2) - 1
do iRo = 2_i4, size(bufferedMat1, dim=1) - 1
if (.NOT. maske(iRo,iCo)) cycle
NNDVMatrix(iRo-1_i4,iCo-1_i4) = &
real( &
abs( &
count((bufferedMat1(iRo-1:iRo+1 , iCo-1:iCo+1) - bufferedMat1(iRo,iCo) > epsilon(0.0_sp)) .AND. &
(maske(iRo-1:iRo+1 , iCo-1:iCo+1))) - &
count((bufferedMat2(iRo-1:iRo+1 , iCo-1:iCo+1) - bufferedMat2(iRo,iCo) > epsilon(0.0_sp)) .AND. &
(maske(iRo-1:iRo+1 , iCo-1:iCo+1))) &
), &
sp)
! count - 1 to exclude referendce cell (iRo, iCo)
validcount(iRo-1_i4,iCo-1_i4) = count(maske(iRo-1_i4:iRo+1_i4 , iCo-1_i4:iCo+1_i4)) - 1_i4
end do
end do
!
! normalize every pixel to number of valid neighbouring cells (defined by maske) [0..8] --> [0..1]
validmaske = (maske(2:size(maske, dim=1) - 1_i4, 2:size(maske, dim=2) - 1_i4) .and. (validcount > 0_i4))
noValidPixels = count(validmaske)
if (noValidPixels .GT. 0_i4) then
NNDVMatrix = merge(NNDVMatrix/real(validcount, sp),NNDVMatrix, validmaske)
! average over all pixels
NNDV_sp = 1.0_sp - sum(NNDVMatrix, mask=validmaske) / noValidPixels
if (present(valid)) valid = .TRUE.
! case if maske is full of .false. or no valid neighbouring cells available for every pixel (validcount(:,:)=0)
else
NNDV_sp = 0.0_sp
if (present(valid)) valid = .FALSE.
end if
!
END FUNCTION NNDV_sp
FUNCTION NNDV_dp(mat1, mat2, mask, valid)
IMPLICIT NONE
REAL(dp), DIMENSION(:,:), INTENT(IN) :: mat1, mat2
LOGICAL, DIMENSION(:,:), OPTIONAL, INTENT(IN) :: mask
LOGICAL, OPTIONAL, INTENT(OUT) :: valid
REAL(dp) :: NNDV_dp
INTEGER(i4) :: iCo, iRo
INTEGER(i4) :: noValidPixels
INTEGER(i4), DIMENSION(size(shape(mat1)) ) :: shapemask
INTEGER(i4), DIMENSION(size(mat1, dim=1), size(mat1, dim=2)) :: validcount
REAL(dp), DIMENSION(size(mat1, dim=1)+2_i4, size(mat1, dim=2)+2_i4) :: bufferedMat1, bufferedMat2
REAL(dp) , DIMENSION(size(mat1, dim=1), size(mat1, dim=2)) :: NNDVMatrix
LOGICAL, DIMENSION(size(mat1, dim=1)+2_i4, size(mat1, dim=2)+2_i4) :: maske
LOGICAL, DIMENSION(size(mat1, dim=1), size(mat1, dim=2)) :: validmaske
! check if input has all the same dimensions
if (present(mask)) then
shapemask = shape(mask)
else
shapemask = shape(mat1)
end if
!
if (any(shape(mat1) .NE. shape(mat2))) &
stop 'NNDV_dp: shapes of input matrix 1 and input matrix 2 are not matching'
if (any(shape(mat1) .NE. shapemask)) &
stop 'NNDV_dp: shapes of input matrices and mask are not matching'
!
! additional 2 rows and 2 cols added for checking the border cells without crashing the search agorithm
! so the search windows can always cover 9 cells even if it is checking a border cell
! buffer rows are initialized as false values within mask, i.e. they are not considered for the calculation
! of the criteria
!
! initialize mask with default=.false.
maske = .false.
if (present(mask)) then
maske(2:(size(maske,dim=1)-1_i4), 2:(size(maske,dim=2)-1_i4)) = mask
else
maske(2:(size(maske,dim=1)-1_i4), 2:(size(maske,dim=2)-1_i4)) = .true.
end if
!
! initialize bufferedMat1 & bufferedMat2
bufferedMat1 = 0.0_dp
bufferedMat2 = 0.0_dp
bufferedMat1(2:(size(maske,dim=1)-1), 2:(size(maske,dim=2)-1)) = mat1
bufferedMat2(2:(size(maske,dim=1)-1), 2:(size(maske,dim=2)-1)) = mat2
!
! initialize NNDV
NNDVMatrix = 0.0_dp
!
NNDV_dp = 0.0_dp
do iCo = 2_i4, size(bufferedMat1, dim=2) - 1
do iRo = 2_i4, size(bufferedMat1, dim=1) - 1
if (.NOT. maske(iRo,iCo)) cycle
NNDVMatrix(iRo-1_i4,iCo-1_i4) = &
real( &
abs( &
count((bufferedMat1(iRo-1:iRo+1 , iCo-1:iCo+1) - bufferedMat1(iRo,iCo) > epsilon(0.0_dp)) .AND. &
(maske(iRo-1:iRo+1 , iCo-1:iCo+1))) - &
count((bufferedMat2(iRo-1:iRo+1 , iCo-1:iCo+1) - bufferedMat2(iRo,iCo) > epsilon(0.0_dp)) .AND. &
(maske(iRo-1:iRo+1 , iCo-1:iCo+1))) &
), &
dp)
! count - 1 to exclude referendce cell (iRo, iCo)
validcount(iRo-1_i4,iCo-1_i4) = count(maske(iRo-1_i4:iRo+1_i4 , iCo-1_i4:iCo+1_i4)) - 1_i4
end do
end do
!
! normalize every pixel to number of valid neighbouring cells (defined by maske) [0..8] --> [0..1]
validmaske = (maske(2:size(maske, dim=1) - 1_i4, 2:size(maske, dim=2) - 1_i4) .and. (validcount > 0_i4))
noValidPixels = count(validmaske)
if (noValidPixels .GT. 0_i4) then
NNDVMatrix = merge(NNDVMatrix/real(validcount, dp),NNDVMatrix, validmaske)
! average over all pixels
NNDV_dp = 1.0_dp - sum(NNDVMatrix, mask=validmaske) / noValidPixels
if (present(valid)) valid = .TRUE.
! case if maske is full of .false. or no valid neighbouring cells available for every pixel (validcount(:,:)=0)
else
NNDV_dp = 0.0_dp
if (present(valid)) valid = .FALSE.
end if
!
END FUNCTION NNDV_dp
! ----------------------------------------------------------------------------------------------------------------
FUNCTION PD_sp(mat1, mat2, mask, valid)
IMPLICIT NONE
REAL(sp), DIMENSION(:,:), INTENT(IN) :: mat1, mat2
LOGICAL, DIMENSION(:,:) , OPTIONAL, INTENT(IN) :: mask
LOGICAL, OPTIONAL, INTENT(OUT) :: valid
REAL(sp) :: PD_sp
INTEGER(i4) :: iCo, iRo
INTEGER(i4) :: noValidPixels
INTEGER(i4), DIMENSION(size(shape(mat1)) ) :: shapemask
INTEGER(i4), DIMENSION(size(mat1, dim=1), size(mat1, dim=2)) :: validcount
REAL(sp), DIMENSION(size(mat1, dim=1)+2_i4, size(mat1, dim=2)+2_i4) :: bufferedMat1, bufferedMat2
REAL(sp), DIMENSION(size(mat1, dim=1), size(mat1, dim=2)) :: PDMatrix
LOGICAL, DIMENSION(size(mat1, dim=1)+2_i4, size(mat1, dim=2)+2_i4) :: maske
LOGICAL, DIMENSION(size(mat1, dim=1), size(mat1, dim=2)) :: validmaske
! check if input has all the same dimensions
if (present(mask)) then
shapemask = shape(mask)
else
shapemask = shape(mat1)
end if
!
if (any(shape(mat1) .NE. shape(mat2))) &
stop 'PD_sp: shapes of input matrix 1 and input matrix 2 are not matching'
if (any(shape(mat1) .NE. shapemask)) &
stop 'PD_sp: shapes of input matrices and mask are not matching'
!
! additional 2 rows and 2 cols added for checking the border cells without crashing the search agorithm
! so the search windows can always cover 9 cells even if it is checking a border cell
! buffer rows are initialized as false values within mask, i.e. they are not considered for the calculation
! of the criteria
!
! initialize mask with default=.false.
maske = .false.
if (present(mask)) then
maske(2:(size(maske,dim=1)-1_i4), 2:(size(maske,dim=2)-1_i4)) = mask
else
maske(2:(size(maske,dim=1)-1_i4), 2:(size(maske,dim=2)-1_i4)) = .true.
end if
!
! initialize bufferedMat1 & bufferedMat2
bufferedMat1 = 0.0_sp
bufferedMat2 = 0.0_sp
bufferedMat1(2:(size(maske,dim=1)-1), 2:(size(maske,dim=2)-1)) = mat1
bufferedMat2(2:(size(maske,dim=1)-1), 2:(size(maske,dim=2)-1)) = mat2
!
! initialize PD
PDMatrix = 0.0_sp
do iCo = 2_i4, size(bufferedMat1, dim=2)-1_i4
do iRo = 2_i4, size(bufferedMat1, dim=1)-1_i4
! no calculation at unmasked values
if (.NOT. maske(iRo,iCo)) cycle
! .NEQV. is the fortran standard for .XOR.
! result is written to -1 column and row because of buffer
PDMatrix(iRo-1_i4,iCo-1_i4) = &
real( &
count( &
( &
! determine higher neighbouring values in mat1
(bufferedMat1(iRo-1_i4:iRo+1_i4, iCo-1_i4:iCo+1_i4) - &
bufferedMat1(iRo,iCo) > epsilon(0.0_sp)) .NEQV. &
! determine higher neighbouring values in mat2 &
(bufferedMat2(iRo-1_i4:iRo+1_i4, iCo-1_i4:iCo+1_i4) - &
bufferedMat2(iRo,iCo) > epsilon(0.0_sp)) &
) &
! exclude unmasked values
.and. (maske(iRo-1_i4:iRo+1_i4 , iCo-1_i4:iCo+1_i4)) &
), &
sp )
! count - 1 to exclude reference cell / center pixel (iRo, iCo)
validcount(iRo-1_i4,iCo-1_i4) = count(maske(iRo-1_i4:iRo+1_i4 , iCo-1_i4:iCo+1_i4)) - 1_i4
!
end do
end do
!
! normalize every pixel to number of valid neighbouring cells (defined by maske) [0..8] --> [0..1]
validmaske = (maske(2:size(maske, dim=1) - 1_i4, 2:size(maske, dim=2) - 1_i4) .and. (validcount > 0_i4))
noValidPixels = count(validmaske)
if (noValidPixels .GT. 0_i4) then
PDMatrix = merge(PDMatrix/real(validcount, sp),PDMatrix, validmaske)
! average over all pixels
PD_sp = 1.0_sp - sum(PDMatrix, mask=validmaske) / noValidPixels
if (present(valid)) valid = .TRUE.
! case if maske is full of .false. or no valid neighbouring cells available for every pixel (validcount(:,:)=0)
else
PD_sp = 0.0_sp
if (present(valid)) valid = .FALSE.
end if
!
END FUNCTION PD_sp
FUNCTION PD_dp(mat1, mat2, mask, valid)
IMPLICIT NONE
REAL(dp), DIMENSION(:,:), INTENT(IN) :: mat1, mat2
LOGICAL, DIMENSION(:,:) , OPTIONAL, INTENT(IN) :: mask
LOGICAL, OPTIONAL, INTENT(OUT) :: valid
REAL(dp) :: PD_dp
INTEGER(i4) :: iCo, iRo
INTEGER(i4) :: noValidPixels
INTEGER(i4), DIMENSION(size(shape(mat1)) ) :: shapemask
INTEGER(i4), DIMENSION(size(mat1, dim=1), size(mat1, dim=2)) :: validcount
REAL(dp), DIMENSION(size(mat1, dim=1)+2_i4, size(mat1, dim=2)+2_i4) :: bufferedMat1, bufferedMat2
REAL(dp), DIMENSION(size(mat1, dim=1), size(mat1, dim=2)) :: PDMatrix
LOGICAL, DIMENSION(size(mat1, dim=1)+2_i4, size(mat1, dim=2)+2_i4) :: maske
LOGICAL, DIMENSION(size(mat1, dim=1), size(mat1, dim=2)) :: validmaske
! check if input has all the same dimensions
if (present(mask)) then
shapemask = shape(mask)
else
shapemask = shape(mat1)
end if
!
if (any(shape(mat1) .NE. shape(mat2))) &
stop 'PD_dp: shapes of input matrix 1 and input matrix 2 are not matching'
if (any(shape(mat1) .NE. shapemask)) &
stop 'PD_dp: shapes of input matrices and mask are not matching'
!
! additional 2 rows and 2 cols added for checking the border cells without crashing the search agorithm
! so the search windows can always cover 9 cells even if it is checking a border cell
! buffer rows are initialized as false values within mask, i.e. they are not considered for the calculation
! of the criteria
!
! initialize mask with default=.false.
maske = .false.
if (present(mask)) then
maske(2:(size(maske,dim=1)-1_i4), 2:(size(maske,dim=2)-1_i4)) = mask
else
maske(2:(size(maske,dim=1)-1_i4), 2:(size(maske,dim=2)-1_i4)) = .true.
end if
!
! initialize bufferedMat1 & bufferedMat2
bufferedMat1 = 0.0_dp
bufferedMat2 = 0.0_dp
bufferedMat1(2:(size(maske,dim=1)-1), 2:(size(maske,dim=2)-1)) = mat1
bufferedMat2(2:(size(maske,dim=1)-1), 2:(size(maske,dim=2)-1)) = mat2
!
! initialize PD
PDMatrix = 0.0_dp
do iCo = 2_i4, size(bufferedMat1, dim=2)-1_i4
do iRo = 2_i4, size(bufferedMat1, dim=1)-1_i4
! no calculation at unmasked values
if (.NOT. maske(iRo,iCo)) cycle
! .NEQV. is the fortran standard for .XOR.
! result is written to -1 column and row because of buffer
PDMatrix(iRo-1_i4,iCo-1_i4) = &
real( &
count( &
( &
! determine higher neighbouring values in mat1
(bufferedMat1(iRo-1_i4:iRo+1_i4, iCo-1_i4:iCo+1_i4) - &
bufferedMat1(iRo,iCo) > epsilon(0.0_dp)) .NEQV. &
! determine higher neighbouring values in mat2 &
(bufferedMat2(iRo-1_i4:iRo+1_i4, iCo-1_i4:iCo+1_i4) - &
bufferedMat2(iRo,iCo) > epsilon(0.0_dp)) &
) &
! exclude unmasked values
.and. (maske(iRo-1_i4:iRo+1_i4 , iCo-1_i4:iCo+1_i4)) &
), &
dp )
! count - 1 to exclude referendce cell (iRo, iCo)
validcount(iRo-1_i4,iCo-1_i4) = count(maske(iRo-1_i4:iRo+1_i4 , iCo-1_i4:iCo+1_i4)) - 1_i4
!
end do
end do
!
! normalize every pixel to number of valid neighbouring cells (defined by maske) [0..8] --> [0..1]
validmaske = (maske(2:size(maske, dim=1) - 1_i4, 2:size(maske, dim=2) - 1_i4) .and. (validcount > 0_i4))
noValidPixels = count(validmaske)
if (noValidPixels .GT. 0_i4) then
PDMatrix = merge(PDMatrix/real(validcount, dp),PDMatrix, validmaske)
! average over all pixels
PD_dp = 1.0_dp - sum(PDMatrix, mask=validmaske) / noValidPixels
if (present(valid)) valid = .TRUE.
! case if maske is full of .false. or no valid neighbouring cells available for every pixel (validcount(:,:)=0)
else
PD_dp = 0.0_dp
if (present(valid)) valid = .FALSE.
end if
!
END FUNCTION PD_dp
!
END MODULE mo_spatialsimilarity