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| !Copyright (c) 2022 Fang Ouyang and Longwei Chen All rights reserved. | ||
| ! | ||
| !Redistribution and use in source and binary forms, with or without | ||
| !modification, are permitted provided that the following conditions are met: | ||
| ! | ||
| !1. Redistributions of source code must retain the above copyright notice, this | ||
| ! list of conditions and the following disclaimer. | ||
| ! | ||
| !2. Redistributions in binary form must reproduce the above copyright notice, | ||
| ! this list of conditions and the following disclaimer in the documentation | ||
| ! and/or other materials provided with the distribution. | ||
| ! | ||
| !3. Neither the name of the copyright holder nor the names of its | ||
| ! contributors may be used to endorse or promote products derived from | ||
| ! this software without specific prior written permission. | ||
| ! | ||
| !THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" | ||
| !AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE | ||
| !IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE | ||
| !DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE | ||
| !FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL | ||
| !DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR | ||
| !SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER | ||
| !CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, | ||
| !OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE | ||
| !OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. | ||
|
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| SUBROUTINE GaussFFT_2D_Fast(NX,NY,DX,DY,NG,AP,TP,X,Y,OFST,FI,FO,SIGN) | ||
| !-------------------------------------------------------------------------------------------------- | ||
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| IMPLICIT NONE | ||
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| INTEGER(KIND=4)::NX,NY,NG,SIGN | ||
| REAL (KIND=8)::DX,DY,X(NX),Y(NY),AP(NG),TP(NG) | ||
| COMPLEX(KIND=8)::FI(NX,NY),FO(NG,NG,NX,NY),OFST(NG,NG,NX,NY) | ||
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| INTEGER(KIND=4)::I,J | ||
| REAL (KIND=8)::PI,CC | ||
| COMPLEX(KIND=8)::CP_I | ||
|
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| !-------------------------------------------------------------------------------------------------- | ||
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| PI=3.14159265358979323846 | ||
| CP_I=(0.,1.) | ||
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| IF(SIGN==1) THEN | ||
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| FO(:,:,:,:)=0. | ||
|
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| CC=DX*DY | ||
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| DO I=1,NG | ||
| DO J=1,NG | ||
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| FO(I,J,:,:)=FI*OFST(I,J,:,:)*CC | ||
|
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| CALL FFT_2D(NX,NY,FO(I,J,:,:),1) | ||
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| END DO | ||
| END DO | ||
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| END IF | ||
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| IF(SIGN==-1) THEN | ||
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| FI(:,:)=0. | ||
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| CC=NX*NY*DX*DY | ||
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| DO I=1,NG | ||
| DO J=1,NG | ||
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| CALL FFT_2D(NX,NY,FO(I,J,:,:),-1) | ||
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| FI=FI+FO(I,J,:,:)/OFST(I,J,:,:)*AP(I)*AP(J)/CC | ||
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| END DO | ||
| END DO | ||
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| END IF | ||
|
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| !-------------------------------------------------------------------------------------------------- | ||
| RETURN | ||
| END SUBROUTINE | ||
| !-------------------------------------------------------------------------------------------------- | ||
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| SUBROUTINE GaussPoint(N_Guass,AP,TP) | ||
| !-------------------------------------------------------------------------------------------------- | ||
| IMPLICIT NONE | ||
|
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| INTEGER(KIND=4)::N_Guass | ||
| REAL (KIND=8)::AP(N_Guass),TP(N_Guass) | ||
| !-------------------------------------------------------------------------------------------------- | ||
|
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| AP(:)=0.; TP(:)=0. | ||
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| IF(N_Guass==1) THEN | ||
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| TP(1) = 0. | ||
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| AP(1) = 1. | ||
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| ELSE IF(N_Guass==2) THEN | ||
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| TP(1) = (3.-sqrt(3.))/6. | ||
| TP(2) = (3.+sqrt(3.))/6. | ||
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| AP(1) = 0.5 | ||
| AP(2) = 0.5 | ||
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| ELSE IF(N_Guass==3) THEN | ||
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| TP(1) = (5.-sqrt(15.))/10. | ||
| TP(2) = 0.5 | ||
| TP(3) = (5.+sqrt(15.))/10. | ||
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| AP(1) = 5./18. | ||
| AP(2) = 4./9. | ||
| AP(3) = 5./18. | ||
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| ELSE IF(N_Guass==4) THEN | ||
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| TP(1) = 0.069431844202974 | ||
| TP(2) = 0.330009478207572 | ||
| TP(3) = 0.669990521792428 | ||
| TP(4) = 0.930568155797026 | ||
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| AP(1) = 0.173927422568727 | ||
| AP(2) = 0.326072577431273 | ||
| AP(3) = 0.326072577431273 | ||
| AP(4) = 0.173927422568727 | ||
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| END IF | ||
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| !-------------------------------------------------------------------------------------------------- | ||
| RETURN | ||
| END SUBROUTINE | ||
| !-------------------------------------------------------------------------------------------------- | ||
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| SUBROUTINE WaveNumberSequence(M,P) | ||
| !-------------------------------------------------------------------------------------------------- | ||
| IMPLICIT NONE | ||
|
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| INTEGER(KIND=4)::M,I | ||
| INTEGER(KIND=4)::P(M) | ||
| !-------------------------------------------------------------------------------------------------- | ||
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| P(:)=0. | ||
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| IF(MOD(M,2)==0) THEN | ||
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| P(1)=0 | ||
| P(M/2+1)=-M/2 | ||
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| DO I=1,M/2-1 | ||
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| P(I+1)=I | ||
| P(M-I+1)=-I | ||
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| END DO | ||
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| ELSE | ||
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| P(1)=0 | ||
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| DO I=1,(M-1)/2 | ||
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| P(I+1)=I | ||
| P(M-I+1)=-I | ||
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| END DO | ||
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| END IF | ||
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| !-------------------------------------------------------------------------------------------------- | ||
| RETURN | ||
| END SUBROUTINE | ||
| !-------------------------------------------------------------------------------------------------- | ||
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| SUBROUTINE FFT_2D(NX,NY,F,SIGN) | ||
| !-------------------------------------------------------------------------------------------------- | ||
| IMPLICIT NONE | ||
|
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| INCLUDE 'FFTW3.F' | ||
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| INTEGER(KIND=4)::SIGN,NX,NY | ||
| COMPLEX(KIND=8)::F(NX,NY) | ||
| COMPLEX(KIND=8),ALLOCATABLE::FO(:,:) | ||
| INTEGER(KIND=8)::FWD,BWD,STATUS | ||
| !-------------------------------------------------------------------------------------------------- | ||
|
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| ALLOCATE(FO(NX,NY)); FO(:,:)=0. | ||
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| IF(SIGN==1) THEN | ||
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| FWD=0; STATUS=0 | ||
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| CALL DFFTW_PLAN_DFT_2D(FWD,NX,NY,F,FO,FFTW_FORWARD,FFTW_ESTIMATE) | ||
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| CALL DFFTW_EXECUTE(FWD,F,FO) | ||
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| CALL DFFTW_DESTROY_PLAN(FWD) | ||
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| F(:,:)=FO(:,:) | ||
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| END IF | ||
|
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| IF(SIGN==-1) THEN | ||
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| BWD=0; STATUS=0 | ||
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| CALL DFFTW_PLAN_DFT_2D(BWD,NX,NY,F,FO,FFTW_BACKWARD,FFTW_ESTIMATE) | ||
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| CALL DFFTW_EXECUTE_DFT(BWD,F,FO) | ||
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| CALL DFFTW_DESTROY_PLAN(BWD) | ||
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| F(:,:)=FO(:,:) | ||
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| END IF | ||
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| DEALLOCATE(FO) | ||
| !-------------------------------------------------------------------------------------------------- | ||
| RETURN | ||
| END SUBROUTINE | ||
| !-------------------------------------------------------------------------------------------------- |