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kernelRegression_module.f95
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kernelRegression_module.f95
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MODULE kernelRegression
USE regression
IMPLICIT NONE
INTERFACE kernreg
MODULE PROCEDURE kernreg_kD_global
MODULE PROCEDURE kernreg_1D_global
END INTERFACE
INTERFACE kernreg_sorted
MODULE PROCEDURE kernreg_kD_global_sorted
MODULE PROCEDURE kernreg_1D_global_sorted
END INTERFACE
CONTAINS
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!!! Kernel Regression !!!!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
SUBROUTINE kernreg_kD_global(y,X,Xgrid,bandwidth,y_fit)
!
! Estimating a Kernel regression with:
! a. k dimensional covariatesa
! b. global bandwidth
! E(y|X) is computed for each value of X or Xgrid (if present)
! The estimator is outputed to y_fit
! The epanechnikov kernel is hard coded into the subroutine for speed
! X and Xgrid (if exists) are not necessarily sorted
REAL(dp), INTENT(IN), DIMENSION(:) :: y
REAL(dp), INTENT(IN), DIMENSION(:,:) :: X
REAL(dp), INTENT(IN), DIMENSION(:,:), OPTIONAL :: Xgrid
REAL(dp), INTENT(IN), DIMENSION(:), OPTIONAL :: bandwidth
REAL(dp), INTENT(OUT), DIMENSION(:), ALLOCATABLE :: y_fit
! additional variables
INTEGER(regInt) :: Nobs !number of obsevations
INTEGER(regInt) :: Ncov !Number of covariates (Note: do not include a constant)
REAL(dp), DIMENSION(:), ALLOCATABLE :: bwidth !the bandwidth vector we will use
REAL(dp), DIMENSION(:), ALLOCATABLE :: point
INTEGER(regInt) :: i,j,N
REAL(dp) :: dist,denom,numer,epa
REAL(dp), PARAMETER :: tol=1.0D-06
LOGICAL :: xgridFLAG
Nobs=SIZE(y) !number of observations
IF (Nobs .NE. SIZE(X,1)) THEN !dimension mismatch
y_fit=ZERO
RETURN
END IF
Ncov=SIZE(X,2) !number of covariates
ALLOCATE(bwidth(Ncov),point(Ncov))
IF (PRESENT(bandwidth) .AND. (SIZE(bandwidth) .EQ. Ncov)) THEN
bwidth=bandwidth
ELSE !use silverman rule of thumb
DO i=1,Ncov
bwidth(i)=silverman(Nobs,X(:,i))
END DO
END IF
!if Xgrid is an input
IF (PRESENT(Xgrid)) THEN
N=SIZE(Xgrid,1)
xgridFLAG=.TRUE.
ELSE
N=Nobs
xgridFLAG=.FALSE.
END IF
ALLOCATE(y_fit(N))
!if Xgrid is present and its 2nd dimention matches that of the covariates,
DO i=1,N
denom=ZERO
numer=ZERO
IF (xgridFLAG) THEN
point=Xgrid(i,:)
ELSE
point=X(i,:)
END IF
DO j=1,Nobs
dist=LP2((point-X(j,:))/bwidth)
IF (ABS(dist).LT.ONE) THEN
epa=0.75D0*(ONE-dist**2)
denom=denom+epa
numer=numer+epa*y(j)
END IF
END DO
IF (denom.LT.tol) THEN
y_fit(i)=ZERO
ELSE
y_fit(i)=numer/denom
END IF
END DO
END SUBROUTINE kernreg_kD_global
!--------1!--------2!--------3!--------4!--------5!--------6!--------7!--------8
SUBROUTINE kernreg_1D_global(y,X,Xgrid,bandwidth,y_fit)
!
! Estimating a Kernel regression with:
! a. 1 dimensional covariatesa
! b. global bandwidth
! E(y|X) is computed for each value of X or Xgrid (if present)
! The estimator is outputed to y_fit
! The epanechnikov kernel is hard coded into the subroutine for speed
!
! (this is a specialized version of kernreg_kD_global)
REAL(dp), INTENT(IN), DIMENSION(:) :: y
REAL(dp), INTENT(IN), DIMENSION(:) :: X
REAL(dp), INTENT(IN), DIMENSION(:), OPTIONAL :: Xgrid
REAL(dp), INTENT(IN), OPTIONAL :: bandwidth
REAL(dp), INTENT(OUT), DIMENSION(:), ALLOCATABLE :: y_fit
! additional variables
INTEGER(regInt) :: Nobs !number of obsevations
REAL(dp) :: bwidth !the bandwidth vector we will use
INTEGER(regInt) :: i,j,N
REAL(dp) :: dist,denom,numer,epa,point
REAL(dp), PARAMETER :: tol=1.0D-06
LOGICAL :: xgridFLAG
Nobs=SIZE(y)
IF (Nobs .NE. SIZE(X,1)) THEN !dimension mismatch
y_fit=ZERO
RETURN
END IF
IF (PRESENT(bandwidth)) THEN
bwidth=bandwidth
ELSE
bwidth=silverman(Nobs,X)
END IF
!if Xgrid is an input
IF (PRESENT(Xgrid)) THEN
N=SIZE(Xgrid)
xgridFLAG=.TRUE.
ELSE
N=Nobs
xgridFLAG=.FALSE.
END IF
ALLOCATE(y_fit(N))
DO i=1,N
denom=ZERO
numer=ZERO
IF (xgridFLAG) THEN
point=Xgrid(i)
ELSE
point=X(i)
END IF
DO j=1,Nobs
dist=((point-X(j))/bwidth)
IF (ABS(dist).LT.ONE) THEN
epa=0.75D0*(ONE-dist**2)
denom=denom+epa
numer=numer+epa*y(j)
END IF
END DO
IF (denom.LT.tol) THEN
y_fit(i)=ZERO
ELSE
y_fit(i)=numer/denom
END IF
END DO
END SUBROUTINE kernreg_1D_global
!--------1!--------2!--------3!--------4!--------5!--------6!--------7!--------8
SUBROUTINE kernreg_1D_global_sorted(y,X,Xgrid,bandwidth,y_fit)
!
! Estimating a Kernel regression with:
! a. 1 dimensional covariate
! b. global bandwidth
! E(y|X) is computed for each value of X or Xgrid (if present)
! The estimator is outputed to y_fit
! The epanechnikov kernel is hard coded into the subroutine for speed
!
! WARNING: The procedure assumes that (y,X) is sorted by X in an ascending way!!
! If the data is not sorted, you'll get a wrong estimate!
! If Xgrid is present, Xgrid must be sorted in an ascending way as well!!
! If not, you'll get a wrong estimate!
! (this is a specialized version of kernreg_1D_global)
REAL(dp), INTENT(IN), DIMENSION(:) :: y
REAL(dp), INTENT(IN), DIMENSION(:) :: X
REAL(dp), INTENT(IN), DIMENSION(:), OPTIONAL :: Xgrid
REAL(dp), INTENT(IN), OPTIONAL :: bandwidth
REAL(dp), INTENT(OUT), DIMENSION(:), ALLOCATABLE :: y_fit
! additional variables
INTEGER(regInt) :: Nobs !number of observations
REAL(dp) :: bwidth !the bandwidth vector we will use
INTEGER(regInt) :: i,j,N
REAL(dp) :: dist,denom,numer,epa,point
REAL(dp), PARAMETER :: tol=1.0D-06
INTEGER(regInt) :: startIndex
Nobs=SIZE(y)
IF (Nobs .NE. SIZE(X,1)) THEN !dimension mismatch
y_fit=ZERO
RETURN
END IF
IF (PRESENT(bandwidth)) THEN
bwidth=bandwidth
ELSE
bwidth=silverman(Nobs,X)
END IF
!if Xgrid is an input
IF (PRESENT(Xgrid)) THEN
N=SIZE(Xgrid)
ELSE
N=Nobs
END IF
ALLOCATE(y_fit(N))
startIndex=1
outer: DO i=1,N
denom=ZERO
numer=ZERO
IF (PRESENT(Xgrid)) THEN
point=Xgrid(i)
ELSE
point=X(i)
END IF
inner: DO j=startIndex,N
dist=((X(j)-point)/bwidth)
IF (dist.LT.-ONE) THEN
startIndex=j ! didn't reach the relevant points yet
ELSE IF (dist.GT.ONE) THEN
EXIT inner
ELSE
epa=0.75D0*(ONE-dist**2)
denom=denom+epa
numer=numer+epa*y(j)
END IF
!end inner
END DO inner
IF (denom.LT.tol) THEN
y_fit(i)=ZERO
ELSE
y_fit(i)=numer/denom
END IF
!end outer
END DO outer
END SUBROUTINE kernreg_1D_global_sorted
!--------1!--------2!--------3!--------4!--------5!--------6!--------7!--------8
SUBROUTINE kernreg_kD_global_sorted(y,X,Xgrid,bandwidth,y_fit)
!
! Estimating a Kernel regression with:
! a. k dimensional covariates
! b. global bandwidth
! E(y|X) is computed for each value of X or Xgrid (if present)
! The estimator is outputed to y_fit
! The epanechnikov kernel is hard coded into the subroutine for speed
!
! WARNING: The procedure assumes that (y,X) is sorted by X's first coordinate (column)
! in an ascending way!!
! If the data is not sorted, you'll get a wrong estimate!
! If Xgrid is present, Xgrid must be sorted by its first coordinate
! in an ascending way as well!!
! If not, you'll get a wrong estimate!
! (this is a specialized version of kernreg_kD_global)
REAL(dp), INTENT(IN), DIMENSION(:) :: y
REAL(dp), INTENT(IN), DIMENSION(:,:) :: X
REAL(dp), INTENT(IN), DIMENSION(:,:), OPTIONAL :: Xgrid
REAL(dp), INTENT(IN), DIMENSION(:), OPTIONAL :: bandwidth
REAL(dp), INTENT(OUT), DIMENSION(:), ALLOCATABLE :: y_fit
! additional variables
INTEGER(regInt) :: Nobs !number of obsevations
INTEGER(regInt) :: Ncov
REAL(dp), ALLOCATABLE, DIMENSION(:) :: bwidth !the bandwidth vector we will use
REAL(dp), ALLOCATABLE, DIMENSION(:) :: point
INTEGER(regInt) :: i,j,N
REAL(dp) :: dist1, dist,denom,numer,epa
REAL(dp), PARAMETER :: tol=1.0D-06
INTEGER(regInt) :: startIndex
Nobs=SIZE(y) !number of observations
IF (Nobs .NE. SIZE(X,1)) THEN !dimension mismatch
y_fit=ZERO
RETURN
END IF
Ncov=SIZE(X,2) !number of covariates
ALLOCATE(bwidth(Ncov),point(Ncov))
IF (PRESENT(bandwidth)) THEN
bwidth=bandwidth
ELSE
bwidth=silverman(Nobs,X)
END IF
!if Xgrid is an input
IF (PRESENT(Xgrid)) THEN
N=SIZE(Xgrid,1)
ELSE
N=Nobs
END IF
ALLOCATE(y_fit(N))
startIndex=1
outer: DO i=1,N
denom=ZERO
numer=ZERO
IF (PRESENT(Xgrid)) THEN
point=Xgrid(i,:)
ELSE
point=X(i,:)
END IF
inner: DO j=startIndex,N
dist1=((X(j,1)-point(1))/bwidth(1))
IF (dist1.LT.-ONE) THEN
startIndex=j
ELSE IF (dist1.GT.ONE) THEN
EXIT inner
ELSE
dist=LP2((point-X(j,:))/bwidth)
epa=0.75D0*(ONE-dist**2)
denom=denom+epa
numer=numer+epa*y(j)
END IF
!end inner
END DO inner
IF (denom.LT.tol) THEN
y_fit(i)=ZERO
ELSE
y_fit(i)=numer/denom
END IF
!end outer
END DO outer
END SUBROUTINE kernreg_kD_global_sorted
!--------1!--------2!--------3!--------4!--------5!--------6!--------7!--------8
END MODULE kernelRegression