蚂蚁的问题

kerb

以下的内容根据fortran code群聊天记录，尝试写的，不知道是否能对网名“蚂蚁”的群友有所帮助

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001	!--------------------------------------------------------------------------------

002	PROGRAM SOLVE

003	IMPLICIT NONE

004	INTEGER, PARAMETER::DP=KIND(1.0_16)

005	INTEGER,PARAMETER::M=8

006	REAL(KIND=DP),PARAMETER::EPS=5.Q-34

007	REAL(KIND=DP)::A,B,ALPHA,PP,INTGVAL,C,P,D,X

008	REAL(KIND=DP),EXTERNAL::YOUR_FUNC

009	INTEGER::I

010	P=0.345_DP

011	PP=1.0_DP-P

012

A=0.0_DP

013

B=100.0

014	ALPHA=1.5Q0

015	!这一部分确定积分上限的大体范围

016	DO I=1000,1,-1

017	D=YOUR_FUNC(B,ALPHA)

018	IF(D>1.E-1)THEN

019

EXIT

020

ELSE

021

B=B-1.0

022

END IF

023

END DO

024

025	WRITE(*,FMT="(A,E41.34)")"B = ", B

026

027

X=B

028	!这一部分用牛顿法精细求解积分区间上限

029	DO I=1,200000

030	CALL PHI_GAMMA(A,X,M,ALPHA,INTGVAL)

031	C=INTGVAL-PP

032	D=YOUR_FUNC(X,ALPHA)

033

034	IF(ABS(C)>D)THEN

035	IF(C<0.0_DP)THEN

036

X=X+C

037

ELSE

038

X=X-C

039

END IF

040

ELSE

041

X=X-C/D

042

ENDIF

043

044	WRITE(*,FMT="(A,I2.2,2X,A,E41.34,2X,A,E41.34,2X,A,E41.34)")"I = ",I,"C = ",C,"X = ",X,"FUNVAL = ",D

045

046	IF(ABS(C)<EPS.OR.X<A)EXIT

047	!READ(*,*)

048

END DO

049	!The precision of X is 4--5digits

050	END PROGRAM

051	!--------------------------------------------------------------------------------

052

053	SUBROUTINE PHI_GAMMA(A,B,M,ALPHA,INTGVAL)

054	IMPLICIT NONE

055	INTEGER, PARAMETER::DP=KIND(1.0_16)

056

057	REAL(KIND=DP),INTENT(IN)::A,B

058

059	REAL(KIND=DP),INTENT(IN)::ALPHA

060	REAL(KIND=DP),INTENT(OUT)::INTGVAL

061	INTEGER,INTENT(IN)::M

062

063	REAL(KIND=DP),EXTERNAL::YOUR_FUNC

064	REAL(KIND=DP),EXTERNAL::GUALEGINTG12

065

066

067	! A1   B1/A2 B2/A3  B3/A4...BM-1/AM  BM

068	! A|-----|-----|------|.......|-----|B

069

070	REAL(KIND=DP)::AX(M)

071	REAL(KIND=DP)::BX(M)

072	REAL(KIND=DP)::DX

073

074	INTEGER::I

075

076	DX=(B-A)/REAL(M,KIND=DP)

077	INTGVAL=0.0_DP

078

DO I=1,M

079	AX(I)=A+REAL(I-1,KIND=DP)*DX

080	BX(I)=AX(I)+DX

081	INTGVAL=INTGVAL+GUALEGINTG12(YOUR_FUNC,ALPHA,AX(I),BX(I))

082

ENDDO

083

RETURN

084	END SUBROUTINE PHI_GAMMA

085	!--------------------------------------------------------------------------------

086	FUNCTION YOUR_FUNC(X,ALPHA)

087	IMPLICIT NONE

088	INTEGER, PARAMETER::DP=KIND(1.0_16)

089	REAL(KIND=DP)::YOUR_FUNC

090	REAL(KIND=DP),INTENT(IN)::X,ALPHA

091	REAL(KIND=DP)::ALF1,TEMP

092	ALF1=ALPHA-1.0_DP

093	TEMP=GAMMA(ALPHA)

094	!................

095	!FOR EXAMPLE

096	!YOUR_FUNC=SIN(X)+ALPHA !OR YOUR_FUNC=X*X+ALPHA

097	YOUR_FUNC=((X**ALF1)*EXP(-X))/TEMP

098

RETURN

099	END FUNCTION YOUR_FUNC

100	!--------------------------------------------------------------------------------

101

102	FUNCTION GUALEGINTG12(YOUR_FUNC,ALPHA,A,B)

103	IMPLICIT NONE

104	INTEGER, PARAMETER::DP=KIND(1.0_16)

105	REAL(KIND=DP)::GUALEGINTG12

106	REAL(KIND=DP),INTENT(IN)::A,B

107	REAL(KIND=DP)::YOUR_FUNC,ALPHA

108	EXTERNAL::YOUR_FUNC

109	REAL(KIND=DP)::RSLT

110	REAL(KIND=DP)::X,APB2,ASB2

111	INTEGER::I

112	!--------------------------------------------------------------------------------

113	!12-POINT GAUSS-LEGENDRE WEIGHTS AND ABSCISSAS

114	!--------------------------------------------------------------------------------

115	!GAUSS WEIGHTS

116	REAL(KIND=DP)::WEIGHTS(12)=(/&

117	0.4717533638651182719461596148501741D-01,&

118	0.1069393259953184309602547181939961D+00,&

119	0.1600783285433462263346525295433591D+00,&

120	0.2031674267230659217490644558097984D+00,&

121	0.2334925365383548087608498989248781D+00,&

122	0.2491470458134027850005624360429511D+00,&

123	0.2491470458134027850005624360429511D+00,&

124	0.2334925365383548087608498989248781D+00,&

125	0.2031674267230659217490644558097984D+00,&

126	0.1600783285433462263346525295433591D+00,&

127	0.1069393259953184309602547181939961D+00,&

128	0.4717533638651182719461596148501741D-01 &

129

/)

130	!GAUSS NODES IN INTERVAL[-1.0, 1.0]

131	REAL(KIND=DP)::NODES(12)=(/&

132	-0.9815606342467192506905490901492809D+00,&

133	-0.9041172563704748566784658661190962D+00,&

134	-0.7699026741943046870368938332128180D+00,&

135	-0.5873179542866174472967024189405343D+00,&

136	-0.3678314989981801937526915366437176D+00,&

137	-0.1252334085114689154724413694638531D+00,&

138	0.1252334085114689154724413694638531D+00,&

139	0.3678314989981801937526915366437176D+00,&

140	0.5873179542866174472967024189405343D+00,&

141	0.7699026741943046870368938332128180D+00,&

142	0.9041172563704748566784658661190962D+00,&

143	0.9815606342467192506905490901492809D+00 &

144

/)

145	!--------------------------------------------------------------------------------

146	RSLT=0.0_DP

147	ASB2=0.5Q0*(B-A)

148	APB2=0.5Q0*(B+A)

149

DO I=1,12

150	X=ASB2*NODES(I)+APB2

151	RSLT=RSLT+WEIGHTS(I)*YOUR_FUNC(X,ALPHA)

152

ENDDO

153	RSLT=RSLT*ASB2

154	GUALEGINTG12=RSLT

155

RETURN

156	END FUNCTION GUALEGINTG12

157	!--------------------------------------------------------------------------------

渡箭

帮助大大滴，非常感谢热心的kerb老师