我正在尝试编写一个程序来计算ising系统的哈密顿函数。程序的第一部分工作，我获得了我想要的矩阵，但是当我试图通过使用子程序zheev来获得这个复数* 16矩阵的特征值时会出现问题。当我读到我必须调用它2次，以便为整数lwork分配最好的值。但对于给定的矩阵，而不是像matlab那样得到特征值（-2.236，-1,1,2.236），我得到（132,0,1,0）。有人能帮助我吗？
非常感谢
module matrices
implicit none
type matrix
complex*16, dimension(:,:), allocatable :: el
integer :: row, col
end type
contains
type(matrix) function assign0(row, col)
integer :: ii, jj, row, col
assign0%row = row
assign0%col = col
allocate(assign0%el(assign0%row, assign0%col))
do ii = 1, assign0%row
do jj = 1, assign0%col
assign0%el(ii, jj) = cmplx(0d0, 0d0)
enddo
enddo
end function assign0
type(matrix) function assignid(row, col)
integer :: ii, jj, row, col
assignid%row = row
assignid%col = col
allocate(assignid%el(assignid%row, assignid%col))
do ii = 1, assignid%row
jj = ii
assignid%el(ii, jj) = cmplx(1d0, 0d0)
enddo
end function assignid
type(matrix) function assignsigx()
allocate(assignsigx%el(assignsigx%row, assignsigx%col))
assignsigx = assign0(2, 2)
assignsigx%el(1, 2) = (1d0, 0d0)
assignsigx%el(2, 1) = (1d0, 0d0)
end function
type(matrix) function assignsigz()
allocate(assignsigz%el(assignsigz%row, assignsigz%col))
assignsigz = assign0(2, 2)
assignsigz%el(1, 1) = (1d0, 0d0)
assignsigz%el(2, 2) = (-1d0, 0d0)
end function
type(matrix) function prodscal(lambda, ma1)
type(matrix) :: ma1
real :: lambda
integer :: ii, jj
prodscal%row = ma1%row
prodscal%col = ma1%col
allocate(prodscal%el(prodscal%row, prodscal%col))
do ii = 1, ma1%row
do jj = 1, ma1%col
prodscal%el(ii, jj) = lambda*ma1%el(ii, jj)
enddo
enddo
end function prodscal
type(matrix) function matsum(ma1, ma2, sign)
type(matrix) :: ma1, ma2
integer :: ii, jj, sign
matsum%row = ma1%row
matsum%col = ma1%col
allocate(matsum%el(matsum%row, matsum%col))
do ii = 1, ma1%row
do jj = 1, ma1%col
if (sign .gt. 0) then
matsum%el(ii, jj) = ma1%el(ii, jj) + ma2%el(ii, jj)
else
matsum%el(ii, jj) = ma1%el(ii, jj) - ma2%el(ii, jj)
endif
enddo
enddo
end function matsum
type(matrix) function tensprod(ma1, ma2)
type(matrix) :: ma1, ma2
integer :: ii, jj, kk, ll
tensprod%row = ma1%row*ma2%row
tensprod%col = ma1%col*ma2%col
allocate(tensprod%el(tensprod%row, tensprod%col))
tensprod = assign0(tensprod%row, tensprod%col)
do ii = 1, ma1%row
do jj = 1, ma1%col
do kk = 1, ma2%row
do ll = 1, ma2%col
tensprod%el((ii - 1)*ma2%row + kk, (jj - 1)*ma2%col + ll) = ma1%el(ii, jj)*ma2%el(kk, ll)
enddo
enddo
enddo
enddo
end function tensprod
end module matrices
program test
use matrices
implicit none
interface
function getdim()
integer :: getdim
end function getdim
end interface
integer :: row, col, ii, jj, N, ind, info, lwork, aus
type(matrix), dimension(2, 2) :: arrmat1, arrmat2
type(matrix), dimension(2) :: element1, element2, element3
type(matrix) :: elementtot, elementtot1, elementtot2
real :: lambda
double precision, dimension(:), allocatable :: w, rwork
complex*16, dimension(:), allocatable :: work
N = 2
allocate(w(15))
allocate(rwork(15))
allocate(work(15))
lwork = -1
aus = 2
lambda = 1d0
do ii = 1, N
ind = ii
do jj = 1, N
if(jj .eq. ind) then
arrmat1(ii, jj) = assignsigz()
else
arrmat1(ii, jj) = assignid(2, 2)
endif
enddo
enddo
do ii = 1, N
ind = ii
do jj = 1, N
if(jj .eq. ind) then
arrmat2(ii, jj) = assignsigx()
else
arrmat2(ii, jj) = assignid(2, 2)
endif
enddo
enddo
do ii = 1, N
element1(ii) = tensprod(arrmat1(ii, 1), arrmat1(ii, 2))
if (N .gt. 2) then
do jj = 3, N
element1(ii) = tensprod(element1(ii), arrmat1(ii, jj))
enddo
endif
enddo
do ii = 1, N
element2(ii) = tensprod(arrmat2(ii, 1), arrmat2(ii, 2))
if (N .gt. 2) then
do jj = 3, N
element2(ii) = tensprod(element2(ii), arrmat2(ii, jj))
enddo
endif
enddo
do ii = 1, N - 1
element3(ii) = assign0(2**N, 2**N)
element3(ii)%el = matmul(element2(ii + 1)%el, element2(ii)%el)
enddo
elementtot = assign0(2**N, 2**N)
elementtot1 = assign0(2**N, 2**N)
elementtot2 = assign0(2**N, 2**N)
do ii = 1, N
elementtot1 = matsum(elementtot1, element1(ii), 1)
enddo
do ii = 1, N - 1
elementtot2 = matsum(elementtot2, element3(ii), 1)
enddo
elementtot2 = prodscal(lambda, elementtot2)
elementtot = matsum(elementtot1, elementtot2, 1)
do ii = 1, 2**N
write(*,'(20G12.4)') elementtot%el(ii, 1:2**N)
enddo
call zheev('N', 'U', 2**N, elementtot%el, 2**N, w, work, lwork, rwork, info)
lwork = int(work(1))
call zheev('N', 'U', 2**N, elementtot%el, 2**N, w, work, lwork, rwork, info)
print*, '***', info
do ii = 1, 2**N
write(*,'(20G12.4)') work(ii)
enddo
stop
end program test
答案 0 :(得分：1)
您的assignsigx和assignsigz函数正在根据相应返回值的row和col组件的未定义值为其返回值分配空间。您可能希望传递要使用的row和col尺寸，就像在assign0和assignid函数中一样。要么只是取出引用未定义组件的分配行，让后续分配使用assign0来处理它？</ p>
如果我取出第33和39行，使用NAG Fortran编译器进行编译和运行并打开完整检查告诉我
Extension: test.f90, line 4: Byte count on numeric data type
detected at *@16
Extension: test.f90, line 112: Byte count on numeric data type
detected at *@16
Questionable: test.f90, line 199: Variable AUS set but never referenced
Warning: test.f90, line 199: Unused local variable COL
Warning: test.f90, line 199: Unused interface for procedure GETDIM
Warning: test.f90, line 199: Unused local variable ROW
Questionable: test.f90, line 17: Intrinsic function CMPLX with double precision argument and no KIND= argument returns single precision result
Questionable: test.f90, line 29: Intrinsic function CMPLX with double precision argument and no KIND= argument returns single precision result
[NAG Fortran Compiler normal termination, 8 warnings]
Runtime Error: test.f90, line 87: Reference to undefined variable MA2%EL(KK,LL)
Program terminated by fatal error
Abort (core dumped)
当tensprod为ii时，崩溃是在第145行第一次调用1。 kk中的ll和ma2%el(kk,ll)分别为1和2。这似乎是因为你没有将assignid中的非对角元素归零。如果我也这样做，那么我看到了
Extension: test.f90, line 4: Byte count on numeric data type
detected at *@16
Extension: test.f90, line 113: Byte count on numeric data type
detected at *@16
Questionable: test.f90, line 200: Variable AUS set but never referenced
Warning: test.f90, line 200: Unused local variable COL
Warning: test.f90, line 200: Unused interface for procedure GETDIM
Warning: test.f90, line 200: Unused local variable ROW
Questionable: test.f90, line 17: Intrinsic function CMPLX with double precision argument and no KIND= argument returns single precision result
Questionable: test.f90, line 30: Intrinsic function CMPLX with double precision argument and no KIND= argument returns single precision result
[NAG Fortran Compiler normal termination, 8 warnings]
2.000 0.000 0.000 0.000 0.000 0.000 1.000 0.000
0.000 0.000 0.000 0.000 1.000 0.000 0.000 0.000
0.000 0.000 1.000 0.000 0.000 0.000 0.000 0.000
1.000 0.000 0.000 0.000 0.000 0.000 -2.000 0.000
Runtime Error: zheev.f90, line 1: Invalid reference to procedure ZHEEV - Dummy array WORK (number 7) has 36 elements but actual argument only has 15 elements
Program terminated by fatal error
Abort (core dumped)
所以我认为，正如francescalus指出的那样，你遗漏调整大小work的问题肯定是个问题。
如果我根据新work重新调整lwork（通过解除分配并重新分配），我会得到结果
2.000 0.000 0.000 0.000 0.000 0.000 1.000 0.000
0.000 0.000 0.000 0.000 1.000 0.000 0.000 0.000
0.000 0.000 1.000 0.000 0.000 0.000 0.000 0.000
1.000 0.000 0.000 0.000 0.000 0.000 -2.000 0.000
*** 0
36.00 0.000
0.000 0.000
1.000 0.000
顺便说一下，为什么以打印work结束？在进行工作空间查询时，唯一感兴趣的是work(1)。