有没有关于如何使用英特尔 MKL FFT 的简单 C++ 示例?
Is there any simple C++ example on how to use Intel MKL FFT?
我需要执行 FFT 和逆 FFT 变换。输入将是双精度向量和矩阵。理想情况下,输出应该是 std::complex 的数组,但我可以接受双 _Complex。
我还没有找到任何简单的示例,所有英特尔示例都在一次做很多事情而没有足够的注释。
我只想要一个 C++ 中的简单示例,将 double 的向量(或矩阵)作为输入并输出 FFT 转换后的结果(最好使用 std::complex)。
我最终测试了几件事,最终得到了这三个函数,它们可以执行我想要的操作并且我考虑了简单的示例。
我针对一些输入对其进行了测试,并获得了良好的结果。我还没有做过广泛的测试。
//Note after each operation status should be 0 on success
std::vector<std::complex<float>> fft_complex(std::vector<std::complex<float>>& in){
std::vector<std::complex<float>> out(in.size());
DFTI_DESCRIPTOR_HANDLE descriptor;
MKL_LONG status;
status = DftiCreateDescriptor(&descriptor, DFTI_SINGLE, DFTI_COMPLEX, 1, in.size()); //Specify size and precision
status = DftiSetValue(descriptor, DFTI_PLACEMENT, DFTI_NOT_INPLACE); //Out of place FFT
status = DftiCommitDescriptor(descriptor); //Finalize the descriptor
status = DftiComputeForward(descriptor, in.data(), out.data()); //Compute the Forward FFT
status = DftiFreeDescriptor(&descriptor); //Free the descriptor
return out;
}
std::vector<std::complex<float>> fft_real(std::vector<float>& in_real){
std::vector<std::complex<float>> in(in_real.size());
std::copy(in_real.begin(), in_real.end(), in.begin());
return fft_complex(in);
}
std::vector<float> ifft(std::vector<std::complex<float>>& in){
std::vector<std::complex<float>> out(in.size());
DFTI_DESCRIPTOR_HANDLE descriptor;
MKL_LONG status;
status = DftiCreateDescriptor(&descriptor, DFTI_SINGLE, DFTI_COMPLEX, 1, in.size()); //Specify size and precision
status = DftiSetValue(descriptor, DFTI_PLACEMENT, DFTI_NOT_INPLACE); //Out of place FFT
status = DftiSetValue(descriptor, DFTI_BACKWARD_SCALE, 1.0f / in.size()); //Scale down the output
status = DftiCommitDescriptor(descriptor); //Finalize the descriptor
status = DftiComputeBackward(descriptor, in.data(), out.data()); //Compute the Forward FFT
status = DftiFreeDescriptor(&descriptor); //Free the descriptor
std::vector<float> output(out.size());
for(std::size_t i = 0; i < out.size(); ++i){
output[i] = out[i].real();
}
return output;
}
虽然 有效,但通常人们希望在对实数值应用傅里叶变换时使用更高效的版本。
对于实数值的傅里叶变换F
,以下成立:
F(k) = conj(F(-k))
因此只需要计算大约一半的值。使用mkl的实数傅里叶变换得到如下代码:
//helper function for fft and ifft:
DFTI_DESCRIPTOR* create_descriptor(MKL_LONG length) {
DFTI_DESCRIPTOR* handle = nullptr;
// using DFTI_DOUBLE for double precision
// using DFTI_REAL for using the real version
bool valid = (DFTI_NO_ERROR == DftiCreateDescriptor(&handle, DFTI_DOUBLE, DFTI_REAL, 1, length)) &&
// the result should not be inplace:
(DFTI_NO_ERROR == DftiSetValue(handle, DFTI_PLACEMENT, DFTI_NOT_INPLACE)) &&
// make clear that the result should be a vector of complex:
(DFTI_NO_ERROR == DftiSetValue(handle, DFTI_CONJUGATE_EVEN_STORAGE, DFTI_COMPLEX_COMPLEX));
// chosen normalization is fft(constant)[0] = constant:
(DFTI_NO_ERROR == DftiSetValue(handle, DFTI_FORWARD_SCALE, 1. / length)) &&
(DFTI_NO_ERROR == DftiCommitDescriptor(handle));
if (!valid) {
DftiFreeDescriptor(&handle);
return nullptr; //nullptr means error
}
return handle;
}
std::vector<std::complex<double>> real_fft(std::vector<double>& in) {
size_t out_size = in.size() / 2 + 1; //so many complex numbers needed
std::vector<std::complex<double>> result(out_size);
DFTI_DESCRIPTOR* handle = create_descriptor(static_cast<MKL_LONG>(in.size()));
bool valid = handle &&
(DFTI_NO_ERROR == DftiComputeForward(handle, in.data(), result.data()));
if (handle) {
valid &= (DFTI_NO_ERROR == DftiFreeDescriptor(&handle));
}
if (!valid) {
result.clear(); //empty vector -> error
}
return result;
}
对于逆向版本,我们需要知道原始向量的大小——此信息无法从傅立叶变换中恢复。虽然我们知道,如果原始实向量具有偶数个元素,则傅里叶变换中的最后一个元素是实数,但我们不能从傅里叶变换的最后一个元素是实数得出原始实向量具有偶数个元素!这就是反函数签名有点奇怪的原因:
std::vector<double> real_fft(std::vector<std::complex<double>> & in, size_t original_size) {
size_t expected_size = original_size / 2 + 1;
if (expected_size != in.size()) {
return {};// empty vector -> error
}
std::vector<double> result(original_size);
DFTI_DESCRIPTOR* handle = create_descriptor(static_cast<MKL_LONG>(original_size));
bool valid = handle &&
(DFTI_NO_ERROR == DftiComputeBackward(handle, in.data(), result.data()));
if (handle) {
valid &= (DFTI_NO_ERROR == DftiFreeDescriptor(&handle));
}
if (!valid) {
result.clear(); //empty vector -> error
}
return result;
}
注意:前向和后向变换使用相同的描述符。
我需要执行 FFT 和逆 FFT 变换。输入将是双精度向量和矩阵。理想情况下,输出应该是 std::complex 的数组,但我可以接受双 _Complex。
我还没有找到任何简单的示例,所有英特尔示例都在一次做很多事情而没有足够的注释。
我只想要一个 C++ 中的简单示例,将 double 的向量(或矩阵)作为输入并输出 FFT 转换后的结果(最好使用 std::complex)。
我最终测试了几件事,最终得到了这三个函数,它们可以执行我想要的操作并且我考虑了简单的示例。
我针对一些输入对其进行了测试,并获得了良好的结果。我还没有做过广泛的测试。
//Note after each operation status should be 0 on success
std::vector<std::complex<float>> fft_complex(std::vector<std::complex<float>>& in){
std::vector<std::complex<float>> out(in.size());
DFTI_DESCRIPTOR_HANDLE descriptor;
MKL_LONG status;
status = DftiCreateDescriptor(&descriptor, DFTI_SINGLE, DFTI_COMPLEX, 1, in.size()); //Specify size and precision
status = DftiSetValue(descriptor, DFTI_PLACEMENT, DFTI_NOT_INPLACE); //Out of place FFT
status = DftiCommitDescriptor(descriptor); //Finalize the descriptor
status = DftiComputeForward(descriptor, in.data(), out.data()); //Compute the Forward FFT
status = DftiFreeDescriptor(&descriptor); //Free the descriptor
return out;
}
std::vector<std::complex<float>> fft_real(std::vector<float>& in_real){
std::vector<std::complex<float>> in(in_real.size());
std::copy(in_real.begin(), in_real.end(), in.begin());
return fft_complex(in);
}
std::vector<float> ifft(std::vector<std::complex<float>>& in){
std::vector<std::complex<float>> out(in.size());
DFTI_DESCRIPTOR_HANDLE descriptor;
MKL_LONG status;
status = DftiCreateDescriptor(&descriptor, DFTI_SINGLE, DFTI_COMPLEX, 1, in.size()); //Specify size and precision
status = DftiSetValue(descriptor, DFTI_PLACEMENT, DFTI_NOT_INPLACE); //Out of place FFT
status = DftiSetValue(descriptor, DFTI_BACKWARD_SCALE, 1.0f / in.size()); //Scale down the output
status = DftiCommitDescriptor(descriptor); //Finalize the descriptor
status = DftiComputeBackward(descriptor, in.data(), out.data()); //Compute the Forward FFT
status = DftiFreeDescriptor(&descriptor); //Free the descriptor
std::vector<float> output(out.size());
for(std::size_t i = 0; i < out.size(); ++i){
output[i] = out[i].real();
}
return output;
}
虽然
对于实数值的傅里叶变换F
,以下成立:
F(k) = conj(F(-k))
因此只需要计算大约一半的值。使用mkl的实数傅里叶变换得到如下代码:
//helper function for fft and ifft:
DFTI_DESCRIPTOR* create_descriptor(MKL_LONG length) {
DFTI_DESCRIPTOR* handle = nullptr;
// using DFTI_DOUBLE for double precision
// using DFTI_REAL for using the real version
bool valid = (DFTI_NO_ERROR == DftiCreateDescriptor(&handle, DFTI_DOUBLE, DFTI_REAL, 1, length)) &&
// the result should not be inplace:
(DFTI_NO_ERROR == DftiSetValue(handle, DFTI_PLACEMENT, DFTI_NOT_INPLACE)) &&
// make clear that the result should be a vector of complex:
(DFTI_NO_ERROR == DftiSetValue(handle, DFTI_CONJUGATE_EVEN_STORAGE, DFTI_COMPLEX_COMPLEX));
// chosen normalization is fft(constant)[0] = constant:
(DFTI_NO_ERROR == DftiSetValue(handle, DFTI_FORWARD_SCALE, 1. / length)) &&
(DFTI_NO_ERROR == DftiCommitDescriptor(handle));
if (!valid) {
DftiFreeDescriptor(&handle);
return nullptr; //nullptr means error
}
return handle;
}
std::vector<std::complex<double>> real_fft(std::vector<double>& in) {
size_t out_size = in.size() / 2 + 1; //so many complex numbers needed
std::vector<std::complex<double>> result(out_size);
DFTI_DESCRIPTOR* handle = create_descriptor(static_cast<MKL_LONG>(in.size()));
bool valid = handle &&
(DFTI_NO_ERROR == DftiComputeForward(handle, in.data(), result.data()));
if (handle) {
valid &= (DFTI_NO_ERROR == DftiFreeDescriptor(&handle));
}
if (!valid) {
result.clear(); //empty vector -> error
}
return result;
}
对于逆向版本,我们需要知道原始向量的大小——此信息无法从傅立叶变换中恢复。虽然我们知道,如果原始实向量具有偶数个元素,则傅里叶变换中的最后一个元素是实数,但我们不能从傅里叶变换的最后一个元素是实数得出原始实向量具有偶数个元素!这就是反函数签名有点奇怪的原因:
std::vector<double> real_fft(std::vector<std::complex<double>> & in, size_t original_size) {
size_t expected_size = original_size / 2 + 1;
if (expected_size != in.size()) {
return {};// empty vector -> error
}
std::vector<double> result(original_size);
DFTI_DESCRIPTOR* handle = create_descriptor(static_cast<MKL_LONG>(original_size));
bool valid = handle &&
(DFTI_NO_ERROR == DftiComputeBackward(handle, in.data(), result.data()));
if (handle) {
valid &= (DFTI_NO_ERROR == DftiFreeDescriptor(&handle));
}
if (!valid) {
result.clear(); //empty vector -> error
}
return result;
}
注意:前向和后向变换使用相同的描述符。