为什么SciPy没问题，但英特尔MKL为什么无法解决此特征问题SPARSE_STATUS_ALLOC_FAILED

如何解决为什么SciPy没问题，但英特尔MKL为什么无法解决此特征问题SPARSE_STATUS_ALLOC_FAILED

我正在尝试解决广义特征值问题（我想要特征值和特征向量）：

[A]{x} = lambda[B]{x}

或等效形式（有限元方法）：

[M]{x} = (1/w^2)[K]{x}

[M]=[A]和[K]=[B]（分别为质量和刚度矩阵）的位置。

我的纯文本文件中同时包含[M]和[K]。这些矩阵以COO格式存储，基于0的索引，未排序。

我的文件（下载：Google Drive）：

kc: where K columns are stored
kr: where K rows are stored
kv: where K values are stored
mc,mr,mv: analogous to K,but for the M matrix

使用文件中的数据，我可以使用SciPy（Python）解决问题。由于这是一个FEA问题，因此我也已经在Abaqus CAE中解决了这个问题，因此我知道在SciPy中正确计算了特征值和特征向量：

MODE    ABAQUS (w^2)    SciPy (w^2)
1       +6.07235E+06    +6.50440E+06
2       +2.28087E+08    +2.44463E+08
3       +1.67357E+09    +1.79572E+09
4       +3.36973E+09    +3.37316E+09
5       +5.88655E+09    +6.32761E+09
(value of 1/lambda = w^2)

我的Python代码：

from scipy.sparse import coo_matrix
from scipy.sparse.linalg import eigs
from numpy import real

rows = 610
cols = 610
a_nnz = 4628
b_nnz = 9266

# read a
with open('./coo/mr') as f: a_row_indx = [int(i) for i in f]
with open('./coo/mc') as f: a_col_indx = [int(i) for i in f]
with open('./coo/mv') as f: a_val_indx = [float(i) for i in f]

# read b
with open('./coo/kr') as f: b_row_indx = [int(i) for i in f]
with open('./coo/kc') as f: b_col_indx = [int(i) for i in f]
with open('./coo/kv') as f: b_val_indx = [float(i) for i in f]

a = coo_matrix((a_val_indx,(a_row_indx,a_col_indx)),shape=(rows,cols))
b = coo_matrix((b_val_indx,(b_row_indx,b_col_indx)),cols))

eigenvalues,eigenvectors = eigs(A=a,M=b,k=10)

val = real(eigenvalues) # to remove "+0j",eigenvalues are real
v = 1.0/val

我的问题是，为什么英特尔MKL无法解决此问题？我尝试修改代码，但总是收到错误或异常：

pm(3) = 1 ! -> Exception thrown at 0x00007FFCE77556EC (mkl_core.dll) in Console1.exe: 0xC0000005: Access violation accessing location 0x0000000000000000.
pm(3) = 2 ! -> STAT = 2 SPARSE_STATUS_ALLOC_FAILED

我的Fortran代码（Visual Studio）：

include 'mkl_solvers_ee'
include 'mkl_spblas'

program main

    use mkl_solvers_ee
    use mkl_spblas
    use,intrinsic :: iso_c_binding,only : c_int,c_double
    
    implicit none
    
    type(sparse_matrix_t) :: a
    type(sparse_matrix_t) :: b
    integer(c_int),parameter :: rows = 610
    integer(c_int),parameter :: cols = 610
    integer(c_int),parameter :: a_nnz = 4628
    integer(c_int),parameter :: b_nnz = 9266
    integer(c_int) :: a_row_indx(a_nnz)
    integer(c_int) :: a_col_indx(a_nnz)
    real(c_double) :: a_values(a_nnz)
    integer(c_int) :: b_row_indx(b_nnz)
    integer(c_int) :: b_col_indx(b_nnz)
    real(c_double) :: b_values(b_nnz)
    integer :: stat
    
    character,parameter :: which = 'S'
    integer(c_int) :: pm(128)
    type(matrix_descr),parameter :: descra = matrix_descr(type = sparse_matrix_type_general,mode = sparse_fill_mode_upper,diag = sparse_diag_non_unit)
    type(matrix_descr),parameter :: descrb = matrix_descr(type = sparse_matrix_type_general,diag = sparse_diag_non_unit)
    integer(c_int),parameter :: k0 = 10
    integer(c_int) :: k
    real(c_double) :: e(k0),ee(k0)
    real(c_double) :: x(k0,cols)
    real(c_double) :: res(k0)
    
    type(sparse_matrix_t) :: acsr
    type(sparse_matrix_t) :: bcsr
    
    integer :: i
    
    ! read a
    open(unit=1,file="./coo/mr")
    open(unit=2,file="./coo/mc")
    open(unit=3,file="./coo/mv")
    do i = 1,a_nnz
        read(1,*) a_row_indx(i)
        read(2,*) a_col_indx(i)
        read(3,*) a_values(i)
    end do
    close(unit=1)
    close(unit=2)
    close(unit=3)
    
    ! read b
    open(unit=1,file="./coo/kr")
    open(unit=2,file="./coo/kc")
    open(unit=3,file="./coo/kv")
    do i = 1,b_nnz
        read(1,*) b_row_indx(i)
        read(2,*) b_col_indx(i)
        read(3,*) b_values(i)
    end do
    close(unit=1)
    close(unit=2)
    close(unit=3)
    
    ! 0 to 1 based indexing
    a_row_indx(:) = a_row_indx(:) + 1
    a_col_indx(:) = a_col_indx(:) + 1
    b_row_indx(:) = b_row_indx(:) + 1
    b_col_indx(:) = b_col_indx(:) + 1
    
    stat = mkl_sparse_d_create_coo(a,sparse_index_base_one,rows,cols,a_nnz,a_row_indx,a_col_indx,a_values)
    stat = mkl_sparse_d_create_coo(b,b_nnz,b_row_indx,b_col_indx,b_values)
    stat = mkl_sparse_convert_csr(a,sparse_operation_non_transpose,acsr)
    stat = mkl_sparse_convert_csr(b,bcsr)
    stat = mkl_sparse_ee_init(pm)
    
    !pm(1) = 0
    !pm(2) = 6
    !pm(3) = 2
    !pm(4) = 512
    !pm(5) = 60 ! 10000 
    !pm(6) = 512
    !pm(7) = 0
    !pm(8) = 0
    !pm(9) = 0
    
    !pm(3) = 1 ! -> Exception thrown at 0x00007FFCE77556EC (mkl_core.dll) in Console1.exe: 0xC0000005: Access violation accessing location 0x0000000000000000.
    !pm(3) = 2 ! -> STAT = 2 SPARSE_STATUS_ALLOC_FAILED
    
    stat = mkl_sparse_d_gv(which,pm,acsr,descra,bcsr,descrb,k0,k,e,x,res)
    
    ee(:) = 1.0 / e(:)
    
end program main
    
!   0   SPARSE_STATUS_SUCCESS           The operation was successful.
!   1   SPARSE_STATUS_NOT_INITIALIZED   The routine encountered an empty handle or matrix array.
!   2   SPARSE_STATUS_ALLOC_FAILED      Internal memory allocation failed.
!   3   SPARSE_STATUS_INVALID_VALUE     The input parameters contain an invalid value.
!   4   SPARSE_STATUS_EXECUTION_FAILED  Execution failed.
!   5   SPARSE_STATUS_INTERNAL_ERROR    An error in algorithm implementation occurred.
!   6   SPARSE_STATUS_NOT_SUPPORTED     The requested operation is not supported.

我整天都在看这段代码，我无法分辨自己在做什么错。任何帮助将不胜感激。