Question

我有一个用于计算Lyapunov指数的旧Fortran代码，我尝试将其转换为现代Fortran语法。

PROGRAM ODE 
integer, PARAMETER :: N=3 
integer, PARAMETER :: NN=12 
EXTERNAL FCN 
DIMENSION Y(NN),ZNORM(N),GSC(N),CUM(N),C(24),W(NN,9) 
Y(1) = 10.0 
Y(2) = 1.0 
Y(3) = 0.0 
! INITIAL CONDITIONS FOR LINEAR SYSTEM (ORTHONORMAL FRAME) 
DO 10 I = N+1,NN 
Y(I) = 0.0 
10 CONTINUE 
DO 20 I = 1,N 
Y((N+1)*I) = 1.0 
CUM(I) = 0.0 
20 CONTINUE 
! INTEGRATION TOLERANCE, # OF INTEGRATION STEPS, 
! TIME PER STEP, AND I/O RATE 
write (*,*) "TOL, NSTEP, STPSZE, IO ?" 
read  (*,*) TOL, NSTEP, STPSZE, IO 
! INITIALIZATION FOR INTEGRATOR 
NEQ = NN 
X=0.0
IND = 1
DO 100 I = 1,NSTEP 
XEND = STPSZE*FLOAT(I) 
! CALL ANY ODE INTEGRATOR - THIS IS AN LMSL ROUTINE 
CALL DVERK (NEQ,FCN,X,Y,XEND,TOL, IND,C,NEQ,W,IER) 
! CONSTRUCT A NEW ORTHONORMAL BASIS BY GRAM-SCHMIDT METHOD 
! NORMALIZE FIRST VECTOR 
ZNORM(1) = 0.0 
DO 30 J = 1,N 
ZNORM(1) = ZNORM(1)+Y(N*J+1)**2 
30 CONTINUE 
ZNORM(1) = SQRT(ZNORM(1)) 
DO 40 J = 1,N 
Y(N*J+1) = Y(N*J+1)/ZNORM(1) 
40 CONTINUE 
! GENERATE THE NEW ORTHONORMAL SET OF VECTORS. 
DO 80 J = 2,N 
! GENERATE J-1 GSR COEFFICIENTS. 
DO 50 K = l,(J-l) 
GSC(K) = 0.0 
DO 50 L = 1,N 
GSC(K) = GSC(K)+Y(N*L+J)*Y(N*L+K) 
50 CONTINUE 
! CONSTRUCT A NEW VECTOR. 
DO 60 K = 1,N 
DO 60 L = l,(J-l) 
Y(N*K+J) = Y(N*K+J)-GSC(L)*Y(N*K+L) 
60 CONTINUE 
! CALCULATE THE VECTOR'S NORM 
ZNORM(J) = 0.0 
DO 70 K = I,N 
ZNORM(J) = ZNORM(J)+Y(N*K+J)**2 
70 CONTINUE 
ZNORM(J) = SQRT(ZNORM(J)) 
! NORMALIZE THE NEW VECTOR. 
DO 80 K = 1,N 
Y(N*K+J) = Y(N*K+J)/ZNORM(J) 
80 CONTINUE 
! UPDATE RUNNING VECTORMAGNITUDES 
DO 90 K = 1,N 
CUM(K) = CUM(K)+ALOG(ZNORM(K) )/ALOG(2. ) 
90 CONTINUE 
! NORMALIZE EXPONENT AND PRINT EVERY IO ITERATIONS 
IF (MOD(I,IO).EQ.0) write (*,*) X,(CUM(K)/X,K = I,N) 
100 CONTINUE 
CALL EXIT 
END 
SUBROUTINE FCN (N,X,Y,YPRIME) 
! USER DEFINED ROUTINE CALLED BY IMSL INTEGRATOR. 
DIMENSION Y(12),YPRIME(12) 
! LORENZ EQUATIONS OF MOTION 
YPRIME(1) = 16.*(Y(2)-Y(1)) 
YPRIME(2) = -Y(1)*Y(3)+45.92*Y(1)-Y(2) 
YPRIME(3) = Y(1)*Y(2)-4.*Y(3) 
! 3 COPIES OF LINEARIZED EQUATIONS OF MOTION. 
DO 10 I = 0,2 
YPRIME(4+I) = 16.*(Y(7+I)-Y(4+I)) 
YPRIME(7+I) = (45.92-Y(3))*Y(4+I)-Y(7+I)-Y(1)*Y(10+I) 
YPRIME(10+I) = Y(2)*Y(4+I)+Y(1)*Y(7+I)-4.*Y(10+I) 
10 CONTINUE 
RETURN 
END

我调试了大部分内容，但我仍然留下一些我无法解决的错误。错误日志显示：

main.f95:44.14:

DO 50 L = 1,N 
              1
Warning: Obsolescent feature: Shared DO termination label 50 at (1)
main.f95:49.18:

DO 60 L = l,(J-l) 
                  1
Warning: Obsolescent feature: Shared DO termination label 60 at (1)
main.f95:59.14:

DO 80 K = 1,N 
              1
Warning: Obsolescent feature: Shared DO termination label 80 at (1)
/tmp/ccfI69Sj.o: In function `MAIN__':
main.f95:(.text+0x296): undefined reference to `dverk_'
main.f95:(.text+0x844): undefined reference to `exit_'
collect2: error: ld returned 1 exit status

有人可以帮我解决错误吗？感谢。

Answer 1

这正是编译器所说的：

Shared DO termination label

嵌套循环50使用相同的终止标签：

DO 50 K = l,(J-l) 
  GSC(K) = 0.0 
  DO 50 L = 1,N 
    GSC(K) = GSC(K)+Y(N*L+J)*Y(N*L+K) 
50 CONTINUE

在现代Fortran中，您应该使用单独的enddo语句：

DO K = l,(J-l) 
  GSC(K) = 0.0 
  DO L = 1,N 
    GSC(K) = GSC(K)+Y(N*L+J)*Y(N*L+K) 
  ENDDO
ENDDO

这省略了循环标签，但在你的代码中你不需要它（我猜）。

循环60和80

需要做同样的事情

真正的错误是对dverk和exit的未定义引用。代码中缺少这些子例程，因此我假设它们包含在外部对象/库中。您需要告诉编译器在哪里找到它们，或者将它们包含在代码中（在程序结束后或模块内）。

调试旧的fortran代码

1 个答案: