158 lines
6.3 KiB
Fortran
158 lines
6.3 KiB
Fortran
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!=======================================================================
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MODULE TEST_INT_HUBBARD
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!
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USE ACCURACY_REAL
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!
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! This module contains the test subroutine for the Hubbard double integral
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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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SUBROUTINE CALC_TEST_HUBBARD
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!
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! This subroutine tests the Hubbard double integral occuring
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! in the calculation of the correlation energy
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!
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! Reference : J. Hubbard, Proc. Roy. Soc. A 243, 336-352 (1958)
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!
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!
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! Author : D. Sébilleau
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!
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! Last modified : 15 Dec 2020
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!
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!
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!
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USE DIMENSION_CODE, ONLY : NZ_MAX
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USE MATERIAL_PROP, ONLY : RS
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USE REAL_NUMBERS, ONLY : ZERO,ONE,TWO,HALF,FOURTH
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USE PI_ETC, ONLY : PI,PI_INV
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USE UTILITIES_1, ONLY : ALFA
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USE INTEGRATION, ONLY : INTEGR_L
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!
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IMPLICIT NONE
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!
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INTEGER :: IX,IY
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INTEGER :: LOGF
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!
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REAL (WP) :: XI,HX,HY
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REAL (WP) :: X,X3,Y
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REAL (WP) :: A(NZ_MAX,NZ_MAX)
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REAL (WP) :: SIGMA(NZ_MAX,NZ_MAX)
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REAL (WP) :: F1(NZ_MAX),F2(NZ_MAX)
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REAL (WP) :: INT_1,INT_2
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REAL (WP) :: NUM1,NUM2,DEN1,DEN2,Z1,Z2
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!
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REAL (WP), PARAMETER :: MX = 5.0E0_WP ! upper integration
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REAL (WP), PARAMETER :: MY = 5.0E0_WP ! bounds in x and y
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!
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REAL (WP), PARAMETER :: SM = 1.0E-8_WP ! starting grid value
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!
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REAL (WP) :: FLOAT,LOG,ABS
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!
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LOGF = 6 ! log file
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!
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XI = TWO * ALFA('3D') * PI_INV * RS ! ref. 1 eq. (28)
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!
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HX = MX / FLOAT(NZ_MAX - 1) ! x-step
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HY = MY / FLOAT(NZ_MAX - 1) ! y-step
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!
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WRITE(LOGF,10) !
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WRITE(LOGF,20) !
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WRITE(LOGF,30) !
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WRITE(LOGF,20) !
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!
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WRITE(LOGF,40) NZ_MAX,MX !
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WRITE(LOGF,40) NZ_MAX,MY !
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WRITE(LOGF,20) !
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!
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! Construction the functions A and Sigma
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!
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DO IX = 1, NZ_MAX !
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!
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X = SM + FLOAT(IX - 1) * HX !
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X3 = X * X * X !
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!
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DO IY = 1, NZ_MAX !
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!
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Y = SM + FLOAT(IY - 1) * HY !
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!
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! Calculation of Sigma(x,y) ! ref. 1 eq. (26)
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!
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IF(Y > X * (X + TWO)) THEN !
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SIGMA(IX,IY) = ZERO !
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ELSE IF(X > TWO .AND. Y < X * (X - TWO)) THEN !
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SIGMA(IX,IY) = ZERO !
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ELSE IF( X > TWO .AND. X * (X - TWO) < Y .AND. & !
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Y < X * (X + TWO) & !
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.OR. & !
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X < TWO .AND. X * (TWO - X) < Y .AND. & !
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Y < X * (X + TWO) & !
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) THEN !
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SIGMA(IX,IY) = - PI * XI * HALF * ( ONE - FOURTH * & !
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(Y / X - X)**2 & !
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) / X3 !
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ELSE IF(X < TWO .AND. ZERO < Y .AND. & !
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Y < X * (TWO - X)) THEN !
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SIGMA(IX,IY) = - PI * XI * Y * HALF / X3 !
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END IF !
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!
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! Calculation of A(x,y) ! ref. 1 eq. (27)
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!
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NUM1 = Y - X * (X + TWO) !
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NUM2 = Y + X * (X + TWO) !
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DEN1 = Y - X * (X - TWO) !
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DEN2 = Y + X * (X - TWO) !
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!
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Z1 = (Y / X - X)**2 !
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Z2 = (Y / X + X)**2 !
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!
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A(IX,IY) = - XI * ( X + & !
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HALF * (ONE - FOURTH * Z1) * & !
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LOG(ABS(NUM1 / DEN1)) + & !
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HALF * (ONE - FOURTH * Z2) * & !
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LOG(ABS(NUM2 / DEN2)) & !
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) / X3 !
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!
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! y-integrand
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!
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F2(IY) = ATAN( SIGMA(IX,IY) / (ONE - A(IX,IY)) ) - & !
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SIGMA(IX,IY) !
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!
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END DO !
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!
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! Computing the integral over y
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!
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CALL INTEGR_L(F2,HY,NZ_MAX,NZ_MAX,INT_2,1) !
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!
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! x-integrand
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!
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F1(IX) = X * X * INT_2 !
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!
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END DO !
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!
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! Computing the integral over x
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!
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CALL INTEGR_L(F1,HX,NZ_MAX,NZ_MAX,INT_1,1) !
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!
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WRITE(LOGF,60) INT_1 !
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!
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WRITE(LOGF,80) !
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!
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! Formats:
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!
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10 FORMAT(6X,'_________________________________________________________')
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20 FORMAT(5X,'| |')
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30 FORMAT(5X,'|',3X,'Test of the integrals contained in HUbbard eps_c |')
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40 FORMAT(5X,'|',5X,'Integr. points: ',I4,' Up. bound x: ',F8.3,9X,'|')
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50 FORMAT(5X,'|',5X,'Integr. points: ',I4,' Up. bound y: ',F8.3,9X,'|')
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60 FORMAT(5X,'|',36X,'INT = ',F8.3,7X,'|')
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80 FORMAT(5X,'|_________________________________________________________|',/)
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!
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END SUBROUTINE CALC_TEST_HUBBARD
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!
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END MODULE TEST_INT_HUBBARD
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