如何解决使用 f2py 和 intel 编译器将 MKL 与 fortran 链接
我有一些 Fortran 代码，其中包含对 Lapack 和 Blas 函数的调用，我正在尝试使用 f2py 编译这些函数：
- Windows 10
- Numpy 1.19 版
- 蟒蛇 Python 3.8.5
我正在尝试编译的代码的干净版本可以在链接中找到：https://software.intel.com/content/dam/develop/external/us/en/documents/mkl-cookbook -samples-120115.zip 位于 /BlockTDS_SPD/source/ 下。
可以在此链接中找到此函数的说明：https://software.intel.com/content/www/us/en/develop/documentation/mkl-cookbook/top/factoring-block-tridiagonal-symmetric-positive-definite-matrices.html。
!***********************************************************************
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! intellectual property rights must be express and approved by Intel in
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!
! Unless otherwise agreed by Intel in writing,you may not remove or alter
! this notice or any other notice embedded in Materials by Intel or Intel's
! suppliers or licensors in any way.
!
!***********************************************************************
! Content:
! Subroutine DPBLTRF for Cholesky factorization of symmetric
! positive definite block tridiagonal matrix.
!***********************************************************************
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
! DeFinition:
! ===========
! SUbroUTINE DPBLTRF(N,NB,D,LDD,B,LDB,INFO)
!
! ..Scalar arguments..
! INTEGER N,INFO
! ..
! ..Array arguments..
! REAL*8 D(LDD,*),B(LDB,*)
! ..
! Purpose:
! ========
! DPBLTRF computes Cholesky L*L^t-factorization of symmetric positive
! definite block tridiagonal matrix A
! D_1 B_1^t
! B_1 D_2 B_2^t
! B_2 D_3 B_3^t
! . . .
! . . .
! B_N-2 D_N-1 B_N-1^t
! B_N-1 D_N
! The factorization has the form A = L*L**t,where L is a lower
! bidiagonal block matrix
! L_1
! C_1 L_2
! C_2 L_3
! . . .
! . . .
! C_N-2 L_N-1
! C_N-1 L_N
! This is a block version of LAPACK DPTTRF subroutine.
!
! Arguments:
! ==========
! N (input) INTEGER
! The number of block rows of the matrix A. N >= 0.
!
! NB (input) INTEGER
! The size of blocks. NB >= 0.
!
! D (input/output) REAL*8 array,dimension (LDD,N*NB)
! On entry,the array stores N diagonal blocks (each of size NB by
! NB) of the matrix to be factored. The blocks are stored
! sequentially: first NB columns of D store block D_1,second NB
! columns store block D_2,...,last NB columns store block D_N.
! Note: As the diagonal blocks are symmetric only lower or upper
! ====
! triangle is needed to store blocks' elements. In this code
! lower storage is used!!!
! On exit,the array stores diagonal blocks of triangular factor L.
! Diagonal blocks of lower triangular factor L replace
! respective lower triangles of blocks D_j (1 <= j <= N).
! Caution: upper triangles of diagonal blocks are not zeroed on
! =======
! exit!!!
!
! LDD (input) INTEGER
! The leading dimension of array D. LDD >= NB.
!
! B (input/output) REAL*8 array,dimension (LDB,(N-1)*NB)
! On entry,the array stores sub-diagonal blocks (each of size NB
! by NB) of the matrix to be factored. The blocks are stored
! sequentially: first NB columns of B store block B_1,second
! NB columns store block B_2,last NB columns store block
! B_N-1.
! On exit,the array stores sub-diagonal blocks of triangular factor
! L.
!
! LDB (input) INTEGER
! The leading dimension of array B. LDB >= NB.
!
! INFO (output) INTEGER
! = 0: successful exit
! < 0: if INFO = -i,the i-th argument had an illegal value
! > 0: if INFO = i,the leading minor of order i (and
! therefore the matrix A itself) is not
! positive-definite,and the factorization Could not be
! completed. This may indicate an error in forming the
! matrix A.
! =====================================================================
SUbroUTINE DPBLTRF(N,INFO)
IMPLICIT NONE
! ..Scalar arguments..
INTEGER N,INFO
! ..Array arguments..
REAL*8 D(LDD,*)
! =====================================================================
! .. Local Scalars ..
INTEGER K
Cf2py integer,intent(in) N,LDB
Cf2py intent(in,out,copy) :: D,B
Cf2py integer,intent(out) :: INFO
! ..
! .. Executable Statements ..
! ..
! Test the input arguments.
INFO = 0
IF(N .LT. 0) THEN
INFO = -1
ELSE IF(NB .LT. 0) THEN
INFO = -2
ELSE IF(LDD .LT. NB) THEN
INFO = -4
ELSE IF(LDB .LT. NB) THEN
INFO = -6
END IF
IF(INFO .NE. 0) THEN
RETURN
END IF
! ..
! Compute Cholesky factorization of the first diagonal block
CALL DPOTRF('L',INFO)
IF(INFO .NE. 0) THEN
RETURN
END IF
!
! Main loop
DO K = 1,N-1
CALL DTRSM('R','L','T','N',1D0,& D(1,(K-1)*NB+1),B(1,LDB)
CALL DSYRK('L',-1D0,& B(1,D(1,K*NB+1),LDD)
CALL DPOTRF('L',INFO)
IF(INFO .NE. 0) THEN
INFO = INFO + K*NB
! INFO is equal to not local but global number of the row
RETURN
END IF
END DO
RETURN
END
我使用以下命令将代码链接到 MKL 并使用 Intel Visual Fortran 64 位编译器进行编译：
python -m numpy.f2py -c --fcompiler=intelvem -L"C:\Program Files (x86)\Intel\oneAPI\compiler\2021.2.0\windows\compiler\lib\intel64_win" -lifconsol -L"C:\Program Files (x86)\Intel\oneAPI\mkl\2021.2.0\lib\intel64" -lmkl_intel_ilp64 -L"C:\Program Files (x86)\Intel\oneAPI\mkl\2021.2.0\lib\intel64" -lmkl_sequential -L"C:\Program Files (x86)\Intel\oneAPI\mkl\2021.2.0\lib\intel64" -lmkl_core -I"C:\Program Files (x86)\Intel\oneAPI\mkl\2021.2.0\include" dpbltrf.f -m SBTCF
结果函数的签名看起来没问题：
d,b,info = dpbltrf(n,nb,d,[ldd,ldb,overwrite_d,overwrite_b])
Wrapper for ``dpbltrf``.
Parameters
----------
n : input int
nb : input int
d : input rank-2 array('d') with bounds (ldd,*)
b : input rank-2 array('d') with bounds (ldb,*)
Other Parameters
----------------
overwrite_d : input int,optional
Default: 0
ldd : input int,optional
Default: shape(d,0)
overwrite_b : input int,optional
Default: 0
ldb : input int,optional
Default: shape(b,0)
Returns
-------
d : rank-2 array('d') with bounds (ldd,*)
b : rank-2 array('d') with bounds (ldb,*)
info : int
然后我可以在 Python 中导入创建的模块并调用它。这是一个最小的例子：
import numpy as np
import matplotlib.pyplot as plt
from SBTCF import dpbltrf
print(dpbltrf.__doc__)
def mx(x,a):
x = np.ravel(x)
npts = len(x)
distances = np.abs(x[:,None] - x[None,:])
mat = np.exp(-distances / a)
return mat
# Assemble arrays
Nx = 5
Nt = 10
t = np.linspace(0,1,Nt)
mat_t = mx(t,1.0)
# Stack the arrays horizontally into the shape required by dpbltrf. D is diagonal
# and B is off-diagonal
D = mat_t
for i in range(Nx-1):
D = np.hstack([D,mat_t])
B = mat_t
for i in range(Nx-2):
B = np.hstack([B,mat_t])
#plt.imshow(D)
#plt.show()
#plt.imshow(B)
#plt.show()
d,info = dpbltrf(Nx,Nt,B)
当我尝试运行脚本时出现错误：
英特尔 MKL 错误：进入 DPOTRF 时参数 4 不正确
我确信我的参数是正确的，我怀疑问题是由错误的编译选项引起的。有人能告诉我编译命令中是否有可能导致这种情况的错误吗？或者会不会有其他问题导致了这个错误？
解决方法
您正在尝试在 Python 模块中包含 Fortran 模块。如果你想要，名字必须不同，参考这个问题
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