使用Matlab fft2和MKL DFTI计算得出的不同结果

我尝试计算二维数据的前向Fourie变换时得到了不同的结果

下面是3x3矩阵的简单测试示例： Matlab，清单：

fft2([25.6798, 26.0815, 29.0069; 33.5761 37.123 38.4696; 38.6358 38.0078 37.649])

DFTI_DESCRIPTOR_HANDLE descriptor1;  
double test[3][3] = {{25.6798, 26.0815, 29.0069},
                      {33.5761, 37.123, 38.4696},
                      {38.6358, 38.0078, 37.649}};  
MKL_LONG status1, l1[2]; l1[0] = 3; l1[1] = 3;  
MKL_Complex16 fftu1[3][3];

status1 = DftiCreateDescriptor(&descriptor1, DFTI_DOUBLE, DFTI_REAL, 2, l1);  
status = DftiCommitDescriptor( descriptor1);  
status = DftiComputeForward( descriptor1, test, fftu1);

Matlab结果：

ans =
   1.0e+02 *
   3.0423 + 0.0000i  -0.0528 + 0.0339i  -0.0528 - 0.0339i
  -0.3096 + 0.0444i   0.0112 + 0.0646i  -0.0144 + 0.0225i
  -0.3096 - 0.0444i  -0.0144 - 0.0225i   0.0112 - 0.0646i

MKL，清单：

fft2([25.6798, 26.0815, 29.0069; 33.5761 37.123 38.4696; 38.6358 38.0078 37.649])

DFTI_DESCRIPTOR_HANDLE descriptor1;  
double test[3][3] = {{25.6798, 26.0815, 29.0069},
                      {33.5761, 37.123, 38.4696},
                      {38.6358, 38.0078, 37.649}};  
MKL_LONG status1, l1[2]; l1[0] = 3; l1[1] = 3;  
MKL_Complex16 fftu1[3][3];

status1 = DftiCreateDescriptor(&descriptor1, DFTI_DOUBLE, DFTI_REAL, 2, l1);  
status = DftiCommitDescriptor( descriptor1);  
status = DftiComputeForward( descriptor1, test, fftu1);

MKL结果：

4.02248e-315+2.35325e-310i 6.42285e-323+6.95254e-310i 2.35325e-310+2.35325e-310i
6.95254e-310+6.95254e-310i 2.35308e-310+2.35325e-310i 0+2.35325e-310i
2.35325e-310+2.35325e-310i 2.35325e-310+2.35325e-310i 7.41098e-323+1.03754e-322i

我发现问题可能是由描述符引起的，即MKL情况下的输出存储配置。但是我找不到设置此描述符的正确方法

---

我做错了什么？请给我一些提示。

我终于明白了。也许这个解决方案对某些人有用

下面给出了正确的C++ MKL列表，并给出了澄清意见。 首先，应在包含部分使用下一个定义：

#include <complex>
#define MKL_Complex16 std::complex<double> //This definition should be done before including MKL files. You will need it to use STL functions, for example conj, with MKL_Complex16 data
#include "mkl.h"

#包括
#定义MKL_Complex16 std:：complex//在包含MKL文件之前，应先完成此定义。您将需要它来使用STL函数，例如conj，以及MKL_Complex16数据
#包括“mkl.h”

其次，除了问题中的代码外，还应为这种情况定义DFTI_NOT_in place和DFTI_STORAGE：

DFTI_DESCRIPTOR_HANDLE descriptor1;  
double test[3][3] = {{25.6798, 26.0815, 29.0069},
                      {33.5761, 37.123, 38.4696},
                      {38.6358, 38.0078, 37.649}};  
MKL_LONG status1, l1[2]; l1[0] = 3; l1[1] = 3;  
MKL_Complex16 fftu1[3][3];
status1 = DftiCreateDescriptor(&descriptor1, DFTI_DOUBLE, DFTI_REAL, 2, l1);
status = DftiSetValue(descriptor1, DFTI_PLACEMENT, DFTI_NOT_INPLACE);
status = DftiSetValue(descriptor1, DFTI_CONJUGATE_EVEN_STORAGE, DFTI_COMPLEX_COMPLEX);  
MKL_LONG rs[2]; rs[0] = 0; rs[1] = 3; rs[2] = 1; //describing 2D 3x3 matrix
status = DftiSetValue(descriptor1, DFTI_INPUT_STRIDES, rs);
MKL_LONG cs[2]; cs[0] = 0; cs[1] = 3; cs[2] = 1; /*Describing output matrix. Warning! Only N1x(N2/2)+1 half part will contain correct answer. Rest part should be restored!!! According to the manual, cs[1]=N2/2+1, so cs[1] should be 2 in our case. But if cs[1]=2, this leads to results shift in answer.. I hope, this is (making cs[1]=N2} is a correct way to deal with shift, bu i'm not sure there. Need to be checked*/
status = DftiSetValue(descriptor1, DFTI_OUTPUT_STRIDES, cs);
status = DftiCommitDescriptor( descriptor1);  
status = DftiComputeForward( descriptor1, test, fftu1); // Forward Fourie done
/*Now the complex-valued data sequences in the conjugate-even domain can be reconstructed as described in https://software.intel.com/en-us/mkl-developer-reference-c-dfti-packed-format*/
for (size_t ii=0; ii< 3; ii++){
   for (size_t jj=3/2+1; jj< 3; jj++){
     fftu1[ii][jj] = std::conj((MKL_Complex16)fftu1 [(3-ii)%3] [(3-jj)%3]);
   }
}

DFTI\u描述符\u句柄描述符1；
双重测试[3][3]={{25.6798,26.0815,29.0069}，
{33.5761, 37.123, 38.4696},
{38.6358, 38.0078, 37.649}};  
MKL_LONG状态1，l1[2]；l1[0]=3；l1[1]=3；
MKL_Complex16 fftu1[3][3]；
状态1=DftiCreateDescriptor（&Descriptor 1，DFTI_DOUBLE，DFTI_REAL，2，l1）；
状态=DftiSetValue（描述符1，DFTI位置，DFTI未就位）；
状态=DftiSetValue（描述符1，DFTI共轭偶数存储，DFTI复数）；
MKL_LONG rs[2]；rs[0]=0；rs[1]=3；rs[2]=1//描述2D 3x3矩阵
状态=DftiSetValue（描述符1，DFTI输入步长，rs）；
MKL_LONG cs[2]；cs[0]=0；cs[1]=3；cs[2]=1/*描述输出矩阵。警告只有N1x（N2/2）+1半部分包含正确答案。其余部分应该恢复！！！根据手册，cs[1]=N2/2+1，因此在我们的例子中cs[1]应该是2。但如果cs[1]=2，这将导致答案的结果发生变化。。我希望，这是（使cs[1]=N2}处理移位的正确方法，但我不确定是否存在。需要检查*/
状态=DftiSetValue（描述符1，DFTI输出步长，cs）；
状态=DftiCommitDescriptor（描述符1）；
状态=DFTICOMPUTERFORWARD（描述符1，测试，fftu1）；//转发完成
/*现在，共轭偶数域中的复值数据序列可以按照中所述进行重构https://software.intel.com/en-us/mkl-developer-reference-c-dfti-packed-format*/
对于（尺寸ii=0；ii<3；ii++）{
对于（尺寸jj=3/2+1；jj<3；jj++）{
fftu1[ii][jj]=std:：conj（（MKL_复合物16）fftu1[（3-ii）%3][（3-jj）%3]）；
}
}

现在，fftu1结果与Matlab计算结果相同，直到小数点后第四位