fftpack 的分段错误
Segmentation fault with fftpack
我正在尝试使用 fftpack（特别是 rffti.f、rffti1.f、rfftf.f、rfftf1.f、radf4.f、radf2.f , radf3.f, radf5.f, radfg.f) 使用此测试代码从 https://www.netlib.org/fftpack/index.html 下载：
program test
implicit none
integer,parameter:: n=100
real,dimension(n):: x,y
integer:: i
real:: pi = 3.1415923535
x= [(i, i=1,n)]
y= sin((2*pi/100)*x)
call RFFTI(100,y)
end program test
,编译和运行:
gfortran -Wall -Wextra -o program.out \
rffti.f rffti1.f rfftf.f rfftf1.f radf4.f radf2.f radf3.f radf5.f radfg.f test.f90
./program.out
，我得到这个运行时错误：
程序收到信号 SIGSEGV：分段错误 - 内存引用无效。
此错误的回溯：
do.sh：第 6 行：9069 分段错误（核心已转储）./program.out
除此错误外，我收到以下警告：
rffti1.f:8:72:
8 | IF (J-4) 102,102,103
| 1
Warning: Fortran 2018 deleted feature: Arithmetic IF statement at (1)
rffti1.f:14:72:
14 | IF (NR) 101,105,101
| 1
Warning: Fortran 2018 deleted feature: Arithmetic IF statement at (1)
rffti1.f:24:11:
24 | IFAC(3) = 2
| 1
Warning: Array reference at (1) is out of bounds (3 > 1) in dimension 1
rffti1.f:27:11:
27 | IFAC(2) = NF
| 1
Warning: Array reference at (1) is out of bounds (2 > 1) in dimension 1
rffti1.f:35:19:
34 | DO 110 K1=1,NFM1
| 2
35 | IP = IFAC(K1+2)
| 1
Warning: Array reference at (1) out of bounds (3 > 1) in loop beginning at (2)
rfftf1.f:3:16:
3 | NF = IFAC(2)
| 1
Warning: Array reference at (1) is out of bounds (2 > 1) in dimension 1
radf4.f:13:72:
13 | IF (IDO-2) 107,105,102
| 1
Warning: Fortran 2018 deleted feature: Arithmetic IF statement at (1)
radf4.f:18:43:
16 | DO 103 I=3,IDO,2
| 2
17 | IC = IDP2-I
18 | CR2 = WA1(I-2)*CC(I-1,K,2)+WA1(I-1)*CC(I,K,2)
| 1
Warning: Array reference at (1) out of bounds (2 > 1) in loop beginning at (2)
radf4.f:19:41:
16 | DO 103 I=3,IDO,2
| 2
......
19 | CI2 = WA1(I-2)*CC(I,K,2)-WA1(I-1)*CC(I-1,K,2)
| 1
Warning: Array reference at (1) out of bounds (2 > 1) in loop beginning at (2)
radf4.f:20:43:
16 | DO 103 I=3,IDO,2
| 2
......
20 | CR3 = WA2(I-2)*CC(I-1,K,3)+WA2(I-1)*CC(I,K,3)
| 1
Warning: Array reference at (1) out of bounds (2 > 1) in loop beginning at (2)
radf4.f:21:41:
16 | DO 103 I=3,IDO,2
| 2
......
21 | CI3 = WA2(I-2)*CC(I,K,3)-WA2(I-1)*CC(I-1,K,3)
| 1
Warning: Array reference at (1) out of bounds (2 > 1) in loop beginning at (2)
radf4.f:22:43:
16 | DO 103 I=3,IDO,2
| 2
......
22 | CR4 = WA3(I-2)*CC(I-1,K,4)+WA3(I-1)*CC(I,K,4)
| 1
Warning: Array reference at (1) out of bounds (2 > 1) in loop beginning at (2)
radf4.f:23:41:
16 | DO 103 I=3,IDO,2
| 2
......
23 | CI4 = WA3(I-2)*CC(I,K,4)-WA3(I-1)*CC(I-1,K,4)
| 1
Warning: Array reference at (1) out of bounds (2 > 1) in loop beginning at (2)
radf2.f:8:72:
8 | IF (IDO-2) 107,105,102
| 1
Warning: Fortran 2018 deleted feature: Arithmetic IF statement at (1)
radf2.f:13:43:
11 | DO 103 I=3,IDO,2
| 2
12 | IC = IDP2-I
13 | TR2 = WA1(I-2)*CC(I-1,K,2)+WA1(I-1)*CC(I,K,2)
| 1
Warning: Array reference at (1) out of bounds (2 > 1) in loop beginning at (2)
radf2.f:14:41:
11 | DO 103 I=3,IDO,2
| 2
......
14 | TI2 = WA1(I-2)*CC(I,K,2)-WA1(I-1)*CC(I-1,K,2)
| 1
Warning: Array reference at (1) out of bounds (2 > 1) in loop beginning at (2)
radf3.f:16:43:
14 | DO 102 I=3,IDO,2
| 2
15 | IC = IDP2-I
16 | DR2 = WA1(I-2)*CC(I-1,K,2)+WA1(I-1)*CC(I,K,2)
| 1
Warning: Array reference at (1) out of bounds (2 > 1) in loop beginning at (2)
radf3.f:17:41:
14 | DO 102 I=3,IDO,2
| 2
......
17 | DI2 = WA1(I-2)*CC(I,K,2)-WA1(I-1)*CC(I-1,K,2)
| 1
Warning: Array reference at (1) out of bounds (2 > 1) in loop beginning at (2)
radf3.f:18:43:
14 | DO 102 I=3,IDO,2
| 2
......
18 | DR3 = WA2(I-2)*CC(I-1,K,3)+WA2(I-1)*CC(I,K,3)
| 1
Warning: Array reference at (1) out of bounds (2 > 1) in loop beginning at (2)
radf3.f:19:41:
14 | DO 102 I=3,IDO,2
| 2
......
19 | DI3 = WA2(I-2)*CC(I,K,3)-WA2(I-1)*CC(I-1,K,3)
| 1
Warning: Array reference at (1) out of bounds (2 > 1) in loop beginning at (2)
radf5.f:22:43:
20 | DO 102 I=3,IDO,2
| 2
21 | IC = IDP2-I
22 | DR2 = WA1(I-2)*CC(I-1,K,2)+WA1(I-1)*CC(I,K,2)
| 1
Warning: Array reference at (1) out of bounds (2 > 1) in loop beginning at (2)
radf5.f:23:41:
20 | DO 102 I=3,IDO,2
| 2
......
23 | DI2 = WA1(I-2)*CC(I,K,2)-WA1(I-1)*CC(I-1,K,2)
| 1
Warning: Array reference at (1) out of bounds (2 > 1) in loop beginning at (2)
radf5.f:24:43:
20 | DO 102 I=3,IDO,2
| 2
......
24 | DR3 = WA2(I-2)*CC(I-1,K,3)+WA2(I-1)*CC(I,K,3)
| 1
Warning: Array reference at (1) out of bounds (2 > 1) in loop beginning at (2)
radf5.f:25:41:
20 | DO 102 I=3,IDO,2
| 2
......
25 | DI3 = WA2(I-2)*CC(I,K,3)-WA2(I-1)*CC(I-1,K,3)
| 1
Warning: Array reference at (1) out of bounds (2 > 1) in loop beginning at (2)
radf5.f:26:43:
20 | DO 102 I=3,IDO,2
| 2
......
26 | DR4 = WA3(I-2)*CC(I-1,K,4)+WA3(I-1)*CC(I,K,4)
| 1
Warning: Array reference at (1) out of bounds (2 > 1) in loop beginning at (2)
radf5.f:27:41:
20 | DO 102 I=3,IDO,2
| 2
......
27 | DI4 = WA3(I-2)*CC(I,K,4)-WA3(I-1)*CC(I-1,K,4)
| 1
Warning: Array reference at (1) out of bounds (2 > 1) in loop beginning at (2)
radf5.f:28:43:
20 | DO 102 I=3,IDO,2
| 2
......
28 | DR5 = WA4(I-2)*CC(I-1,K,5)+WA4(I-1)*CC(I,K,5)
| 1
Warning: Array reference at (1) out of bounds (2 > 1) in loop beginning at (2)
radf5.f:29:41:
20 | DO 102 I=3,IDO,2
| 2
......
29 | DI5 = WA4(I-2)*CC(I,K,5)-WA4(I-1)*CC(I-1,K,5)
| 1
Warning: Array reference at (1) out of bounds (2 > 1) in loop beginning at (2)
RFFTI是一个初始化例程，将一些工作数据准备到一个特殊的工作数组中。
SUBROUTINE RFFTI (N,WSAVE)
DIMENSION WSAVE(1)
(1) 只是一种过时且非常不幸的写法 (*)。
您必须阅读 the manual 并了解 WSAVE 数组的大小。请注意，它是用于内部数据的特殊工作数组，不适用于您要转换的数据。
来自手册：
wsave
a work array which must be dimensioned at least 2*n+15.
the same work array can be used for both rfftf and rfftb
as long as n remains unchanged. different wsave arrays
are required for different values of n. the contents of
wsave must not be changed between calls of rfftf or rfftb.
我正在尝试使用 fftpack（特别是 rffti.f、rffti1.f、rfftf.f、rfftf1.f、radf4.f、radf2.f , radf3.f, radf5.f, radfg.f) 使用此测试代码从 https://www.netlib.org/fftpack/index.html 下载：
program test
implicit none
integer,parameter:: n=100
real,dimension(n):: x,y
integer:: i
real:: pi = 3.1415923535
x= [(i, i=1,n)]
y= sin((2*pi/100)*x)
call RFFTI(100,y)
end program test
,编译和运行:
gfortran -Wall -Wextra -o program.out \
rffti.f rffti1.f rfftf.f rfftf1.f radf4.f radf2.f radf3.f radf5.f radfg.f test.f90
./program.out
，我得到这个运行时错误：
程序收到信号 SIGSEGV：分段错误 - 内存引用无效。
此错误的回溯： do.sh：第 6 行：9069 分段错误（核心已转储）./program.out
除此错误外，我收到以下警告：
rffti1.f:8:72:
8 | IF (J-4) 102,102,103
| 1
Warning: Fortran 2018 deleted feature: Arithmetic IF statement at (1)
rffti1.f:14:72:
14 | IF (NR) 101,105,101
| 1
Warning: Fortran 2018 deleted feature: Arithmetic IF statement at (1)
rffti1.f:24:11:
24 | IFAC(3) = 2
| 1
Warning: Array reference at (1) is out of bounds (3 > 1) in dimension 1
rffti1.f:27:11:
27 | IFAC(2) = NF
| 1
Warning: Array reference at (1) is out of bounds (2 > 1) in dimension 1
rffti1.f:35:19:
34 | DO 110 K1=1,NFM1
| 2
35 | IP = IFAC(K1+2)
| 1
Warning: Array reference at (1) out of bounds (3 > 1) in loop beginning at (2)
rfftf1.f:3:16:
3 | NF = IFAC(2)
| 1
Warning: Array reference at (1) is out of bounds (2 > 1) in dimension 1
radf4.f:13:72:
13 | IF (IDO-2) 107,105,102
| 1
Warning: Fortran 2018 deleted feature: Arithmetic IF statement at (1)
radf4.f:18:43:
16 | DO 103 I=3,IDO,2
| 2
17 | IC = IDP2-I
18 | CR2 = WA1(I-2)*CC(I-1,K,2)+WA1(I-1)*CC(I,K,2)
| 1
Warning: Array reference at (1) out of bounds (2 > 1) in loop beginning at (2)
radf4.f:19:41:
16 | DO 103 I=3,IDO,2
| 2
......
19 | CI2 = WA1(I-2)*CC(I,K,2)-WA1(I-1)*CC(I-1,K,2)
| 1
Warning: Array reference at (1) out of bounds (2 > 1) in loop beginning at (2)
radf4.f:20:43:
16 | DO 103 I=3,IDO,2
| 2
......
20 | CR3 = WA2(I-2)*CC(I-1,K,3)+WA2(I-1)*CC(I,K,3)
| 1
Warning: Array reference at (1) out of bounds (2 > 1) in loop beginning at (2)
radf4.f:21:41:
16 | DO 103 I=3,IDO,2
| 2
......
21 | CI3 = WA2(I-2)*CC(I,K,3)-WA2(I-1)*CC(I-1,K,3)
| 1
Warning: Array reference at (1) out of bounds (2 > 1) in loop beginning at (2)
radf4.f:22:43:
16 | DO 103 I=3,IDO,2
| 2
......
22 | CR4 = WA3(I-2)*CC(I-1,K,4)+WA3(I-1)*CC(I,K,4)
| 1
Warning: Array reference at (1) out of bounds (2 > 1) in loop beginning at (2)
radf4.f:23:41:
16 | DO 103 I=3,IDO,2
| 2
......
23 | CI4 = WA3(I-2)*CC(I,K,4)-WA3(I-1)*CC(I-1,K,4)
| 1
Warning: Array reference at (1) out of bounds (2 > 1) in loop beginning at (2)
radf2.f:8:72:
8 | IF (IDO-2) 107,105,102
| 1
Warning: Fortran 2018 deleted feature: Arithmetic IF statement at (1)
radf2.f:13:43:
11 | DO 103 I=3,IDO,2
| 2
12 | IC = IDP2-I
13 | TR2 = WA1(I-2)*CC(I-1,K,2)+WA1(I-1)*CC(I,K,2)
| 1
Warning: Array reference at (1) out of bounds (2 > 1) in loop beginning at (2)
radf2.f:14:41:
11 | DO 103 I=3,IDO,2
| 2
......
14 | TI2 = WA1(I-2)*CC(I,K,2)-WA1(I-1)*CC(I-1,K,2)
| 1
Warning: Array reference at (1) out of bounds (2 > 1) in loop beginning at (2)
radf3.f:16:43:
14 | DO 102 I=3,IDO,2
| 2
15 | IC = IDP2-I
16 | DR2 = WA1(I-2)*CC(I-1,K,2)+WA1(I-1)*CC(I,K,2)
| 1
Warning: Array reference at (1) out of bounds (2 > 1) in loop beginning at (2)
radf3.f:17:41:
14 | DO 102 I=3,IDO,2
| 2
......
17 | DI2 = WA1(I-2)*CC(I,K,2)-WA1(I-1)*CC(I-1,K,2)
| 1
Warning: Array reference at (1) out of bounds (2 > 1) in loop beginning at (2)
radf3.f:18:43:
14 | DO 102 I=3,IDO,2
| 2
......
18 | DR3 = WA2(I-2)*CC(I-1,K,3)+WA2(I-1)*CC(I,K,3)
| 1
Warning: Array reference at (1) out of bounds (2 > 1) in loop beginning at (2)
radf3.f:19:41:
14 | DO 102 I=3,IDO,2
| 2
......
19 | DI3 = WA2(I-2)*CC(I,K,3)-WA2(I-1)*CC(I-1,K,3)
| 1
Warning: Array reference at (1) out of bounds (2 > 1) in loop beginning at (2)
radf5.f:22:43:
20 | DO 102 I=3,IDO,2
| 2
21 | IC = IDP2-I
22 | DR2 = WA1(I-2)*CC(I-1,K,2)+WA1(I-1)*CC(I,K,2)
| 1
Warning: Array reference at (1) out of bounds (2 > 1) in loop beginning at (2)
radf5.f:23:41:
20 | DO 102 I=3,IDO,2
| 2
......
23 | DI2 = WA1(I-2)*CC(I,K,2)-WA1(I-1)*CC(I-1,K,2)
| 1
Warning: Array reference at (1) out of bounds (2 > 1) in loop beginning at (2)
radf5.f:24:43:
20 | DO 102 I=3,IDO,2
| 2
......
24 | DR3 = WA2(I-2)*CC(I-1,K,3)+WA2(I-1)*CC(I,K,3)
| 1
Warning: Array reference at (1) out of bounds (2 > 1) in loop beginning at (2)
radf5.f:25:41:
20 | DO 102 I=3,IDO,2
| 2
......
25 | DI3 = WA2(I-2)*CC(I,K,3)-WA2(I-1)*CC(I-1,K,3)
| 1
Warning: Array reference at (1) out of bounds (2 > 1) in loop beginning at (2)
radf5.f:26:43:
20 | DO 102 I=3,IDO,2
| 2
......
26 | DR4 = WA3(I-2)*CC(I-1,K,4)+WA3(I-1)*CC(I,K,4)
| 1
Warning: Array reference at (1) out of bounds (2 > 1) in loop beginning at (2)
radf5.f:27:41:
20 | DO 102 I=3,IDO,2
| 2
......
27 | DI4 = WA3(I-2)*CC(I,K,4)-WA3(I-1)*CC(I-1,K,4)
| 1
Warning: Array reference at (1) out of bounds (2 > 1) in loop beginning at (2)
radf5.f:28:43:
20 | DO 102 I=3,IDO,2
| 2
......
28 | DR5 = WA4(I-2)*CC(I-1,K,5)+WA4(I-1)*CC(I,K,5)
| 1
Warning: Array reference at (1) out of bounds (2 > 1) in loop beginning at (2)
radf5.f:29:41:
20 | DO 102 I=3,IDO,2
| 2
......
29 | DI5 = WA4(I-2)*CC(I,K,5)-WA4(I-1)*CC(I-1,K,5)
| 1
Warning: Array reference at (1) out of bounds (2 > 1) in loop beginning at (2)
RFFTI是一个初始化例程，将一些工作数据准备到一个特殊的工作数组中。
SUBROUTINE RFFTI (N,WSAVE)
DIMENSION WSAVE(1)
(1) 只是一种过时且非常不幸的写法 (*)。
您必须阅读 the manual 并了解 WSAVE 数组的大小。请注意，它是用于内部数据的特殊工作数组，不适用于您要转换的数据。
来自手册：
wsave
a work array which must be dimensioned at least 2*n+15. the same work array can be used for both rfftf and rfftb as long as n remains unchanged. different wsave arrays are required for different values of n. the contents of wsave must not be changed between calls of rfftf or rfftb.