Add fft, ifft, hilbert and their unit test.

src/Function2D.cpp

@@ -516,3 +516,128 @@ Matrix Aurora::median(const Matrix &aMatrix) {
     }
 }
 
+Matrix Aurora::fft(const Matrix &aMatrix) {
+    double *output = nullptr;
+    output = malloc(aMatrix.getDataSize(), true);
+    if (!aMatrix.isComplex()) {
+        cblas_dcopy(aMatrix.getDataSize(), aMatrix.getData(), 1, output, 2);
+        double zero = 0.0;
+        cblas_dcopy(aMatrix.getDataSize(), &zero, 0, output+1, 2);
+    } else {
+        cblas_zcopy(aMatrix.getDataSize(), aMatrix.getData(), 1, output, 1);
+    }
+
+    DFTI_DESCRIPTOR_HANDLE my_desc_handle = NULL;
+    MKL_LONG status;
+
+    //创建 Descriptor, 精度 double , 输入类型实数, 维度1
+    status = DftiCreateDescriptor(&my_desc_handle, DFTI_DOUBLE, DFTI_COMPLEX, 1, aMatrix.getDimSize(0));
+    if (status != DFTI_NO_ERROR) goto error;
+
+    //通过 setValue 配置Descriptor
+    //使用单独的输出数据缓存
+    status = DftiSetValue(my_desc_handle, DFTI_PLACEMENT, DFTI_INPLACE);
+    if (status != DFTI_NO_ERROR) goto error;
+
+    //每个傅里叶变换的输入距离
+    status = DftiSetValue(my_desc_handle,DFTI_INPUT_DISTANCE,aMatrix.getDimSize(0));
+    if (status != DFTI_NO_ERROR) goto error;
+
+    //每个傅里叶变换的输出距离
+    status = DftiSetValue(my_desc_handle,DFTI_OUTPUT_DISTANCE,aMatrix.getDimSize(0));
+    if (status != DFTI_NO_ERROR) goto error;
+
+    //傅里叶变换的数量
+    status = DftiSetValue(my_desc_handle,DFTI_NUMBER_OF_TRANSFORMS,aMatrix.getDimSize(1));
+    if (status != DFTI_NO_ERROR) goto error;
+
+    //提交 修改配置后的Descriptor(实际上会进行FFT的计算初始化)
+    status = DftiCommitDescriptor(my_desc_handle);
+    if (status != DFTI_NO_ERROR) goto error;
+
+    //执行计算
+    status = DftiComputeForward(my_desc_handle, output, output);
+    if (status != DFTI_NO_ERROR) goto error;
+
+    //释放资源
+    status = DftiFreeDescriptor(&my_desc_handle);
+    if (status != DFTI_NO_ERROR) goto error;
+
+    return Matrix::New(output, aMatrix.getDimSize(0), aMatrix.getDimSize(1), aMatrix.getDimSize(2), Complex);
+    error:
+        std::cerr<<"FFT fail, error message:"<<DftiErrorMessage(status)<<std::endl;
+        return Matrix();
+}
+
+Matrix Aurora::ifft(const Matrix &aMatrix) {
+    if (!aMatrix.isComplex()){
+        std::cerr<<"ifft input must be complex value"<<std::endl;
+        return Matrix();
+    }
+    DFTI_DESCRIPTOR_HANDLE my_desc_handle = NULL;
+    auto output = malloc(aMatrix.getDataSize(),true);
+    MKL_LONG status;
+
+    //创建 Descriptor, 精度 double , 输入类型实数, 维度1
+    status = DftiCreateDescriptor(&my_desc_handle, DFTI_DOUBLE, DFTI_COMPLEX, 1, aMatrix.getDimSize(0));
+    if (status != DFTI_NO_ERROR) goto error;
+    //通过 setValue 配置Descriptor
+    //使用单独的输出数据缓存
+    status = DftiSetValue(my_desc_handle, DFTI_PLACEMENT, DFTI_NOT_INPLACE);
+    if (status != DFTI_NO_ERROR) goto error;
+
+    //设置DFTI_BACKWARD_SCALE ！！！很关键，不然值不对
+    status = DftiSetValue(my_desc_handle, DFTI_BACKWARD_SCALE, 1.0f / aMatrix.getDimSize(0));
+    if (status != DFTI_NO_ERROR) goto error;
+
+    status = DftiSetValue(my_desc_handle,DFTI_INPUT_DISTANCE,aMatrix.getDimSize(0));
+    if (status != DFTI_NO_ERROR) goto error;
+
+    //每个傅里叶变换的输出距离
+    status = DftiSetValue(my_desc_handle,DFTI_OUTPUT_DISTANCE,aMatrix.getDimSize(0));
+    if (status != DFTI_NO_ERROR) goto error;
+
+    //傅里叶变换的数量
+    status = DftiSetValue(my_desc_handle,DFTI_NUMBER_OF_TRANSFORMS,aMatrix.getDimSize(1));
+    if (status != DFTI_NO_ERROR) goto error;
+
+    status = DftiCommitDescriptor(my_desc_handle);
+    if (status != DFTI_NO_ERROR) goto error;
+
+    //提交 修改配置后的Descriptor(实际上会进行FFT的计算初始化)
+    status = DftiCommitDescriptor(my_desc_handle);
+    if (status != DFTI_NO_ERROR) goto error;
+
+    //执行计算
+    status = DftiComputeBackward(my_desc_handle, aMatrix.getData(), output);
+    if (status != DFTI_NO_ERROR) goto error;
+    //释放资源
+    status = DftiFreeDescriptor(&my_desc_handle);
+    if (status != DFTI_NO_ERROR) goto error;
+    {
+        return Matrix::New(output, aMatrix.getDimSize(0), aMatrix.getDimSize(1), aMatrix.getDimSize(2), Complex);
+    }
+    error:
+    std::cerr<<"FFT fail, error message:"<<DftiErrorMessage(status)<<std::endl;
+    return Matrix();
+}
+
+Matrix Aurora::hilbert(const Matrix &aMatrix) {
+    auto x = fft(aMatrix);
+    auto h = new double[aMatrix.getDimSize(0)];
+    auto two = 2.0;
+    auto zero = 0.0;
+    cblas_dcopy(aMatrix.getDimSize(0), &zero, 0, h, 1);
+    cblas_dcopy(aMatrix.getDimSize(0) / 2, &two, 0, h, 1);
+    h[aMatrix.getDimSize(0) / 2] = ((aMatrix.getDimSize(0) << 31) >> 31) ? 2.0 : 1.0;
+    h[0] = 1.0;
+    for (int i = 0; i < aMatrix.getDimSize(1); ++i) {
+        auto p = (double *)(x.getData() + aMatrix.getDimSize(0)* i*2);
+        vdMulI(aMatrix.getDimSize(0), p, 2, h, 1, p, 2);
+        vdMulI(aMatrix.getDimSize(0), p + 1, 2, h, 1, p + 1, 2);
+    }
+    auto result = ifft( x);
+    delete[] h;
+    return result;
+}
+