170 lines
4.3 KiB
Fortran
170 lines
4.3 KiB
Fortran
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!=======================================================================
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!
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MODULE SPH_BESSEL
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!
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! This module provides the spherical Bessel functions
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!
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! It contains the following functions:
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!
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! * FUNCTION SPH_BESSJ0(X) --> j_0(X)
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! * FUNCTION SPH_BESSJ1(X) --> j_1(X)
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! * FUNCTION SPH_BESSN0(X) --> n_0(X)
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! * FUNCTION SPH_BESSN1(X) --> n_1(X)
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! * FUNCTION SPH_BESSI0(X) --> i_0(X)
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! * FUNCTION SPH_BESSI1(X) --> i_1(X)
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! * FUNCTION SPH_BESSK0(X) --> k_0(X)
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! * FUNCTION SPH_BESSK1(X) --> k_1(X)
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!
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! Modules used: ACCURACY_REAL
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!
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USE ACCURACY_REAL
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!
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CONTAINS
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!
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!=======================================================================
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!
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FUNCTION SPH_BESSJ0(X)
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!
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! This function calculates the first kind spherical Bessel function
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! of order 0
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!
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IMPLICIT NONE
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!
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REAL (WP), INTENT(IN) :: X
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REAL (WP) :: SPH_BESSJ0
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!
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REAL (WP) :: DSIN
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!
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SPH_BESSJ0 = DSIN(X) / X !
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!
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END FUNCTION SPH_BESSJ0
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!
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!=======================================================================
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!
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FUNCTION SPH_BESSJ1(X)
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!
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! This function calculates the first kind spherical Bessel function
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! of order 1
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!
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IMPLICIT NONE
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!
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REAL (WP), INTENT(IN) :: X
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REAL (WP) :: SPH_BESSJ1
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!
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REAL (WP) :: DSIN,DCOS
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!
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SPH_BESSJ1 = DSIN(X) / (X*X) - DCOS(X) / X !
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!
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END FUNCTION SPH_BESSJ1
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!
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!=======================================================================
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!
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FUNCTION SPH_BESSN0(X)
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!
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! This function calculates the second kind spherical Bessel function
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! of order 0
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!
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IMPLICIT NONE
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!
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REAL (WP), INTENT(IN) :: X
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REAL (WP) :: SPH_BESSN0
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!
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REAL (WP) :: DCOS
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!
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SPH_BESSN0 = - DCOS(X) / X !
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!
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END FUNCTION SPH_BESSN0
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!
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!=======================================================================
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!
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FUNCTION SPH_BESSN1(X)
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!
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! This function calculates the second kind spherical Bessel function
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! of order 1
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!
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IMPLICIT NONE
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!
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REAL (WP), INTENT(IN) :: X
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REAL (WP) :: SPH_BESSN1
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!
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REAL (WP) :: DSIN,DCOS
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!
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SPH_BESSN1 = - DCOS(X) / (X*X) - DSIN(X) / X !
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!
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END FUNCTION SPH_BESSN1
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!
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!=======================================================================
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!
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FUNCTION SPH_BESSI0(X)
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!
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! This function calculates the first kind modified spherical Bessel function
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! of order 0
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!
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IMPLICIT NONE
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!
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REAL (WP), INTENT(IN) :: X
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REAL (WP) :: SPH_BESSI0
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!
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REAL (WP) :: DSINH
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!
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SPH_BESSI0 = DSINH(X) / X !
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!
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END FUNCTION SPH_BESSI0
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!
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!=======================================================================
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!
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FUNCTION SPH_BESSI1(X)
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!
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! This function calculates the first kind modified spherical Bessel function
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! of order 1
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!
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IMPLICIT NONE
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!
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REAL (WP), INTENT(IN) :: X
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REAL (WP) :: SPH_BESSI1
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!
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REAL (WP) :: DSINH,DCOSH
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!
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SPH_BESSI1 = (X*DCOSH(X) - DSINH(X)) / (X*X) !
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!
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END FUNCTION SPH_BESSI1
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!
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!=======================================================================
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!
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FUNCTION SPH_BESSK0(X)
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!
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! This function calculates the second kind modified spherical Bessel function
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! of order 0
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!
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IMPLICIT NONE
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!
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REAL (WP), INTENT(IN) :: X
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REAL (WP) :: SPH_BESSK0
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!
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REAL (WP) :: DEXP
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!
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SPH_BESSK0 = DEXP(-X) / X !
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!
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END FUNCTION SPH_BESSK0
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!
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!=======================================================================
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!
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FUNCTION SPH_BESSK1(X)
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!
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! This function calculates the second kind modified spherical Bessel function
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! of order 1
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!
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IMPLICIT NONE
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!
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REAL (WP), INTENT(IN) :: X
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REAL (WP) :: SPH_BESSK1
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!
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REAL (WP) :: DEXP
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!
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SPH_BESSK1 = (DEXP(-X)*(X + 1.0E0_WP)) / (X*X) !
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!
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END FUNCTION SPH_BESSK1
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!
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END MODULE SPH_BESSEL
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