NumCpp(C++版本Numpy)使用筆記

一、簡介

NumCpp：Python NumPy庫的一個Templatized Header Only C ++實現
NumCpp 是一個高性能的數學計算 C++ 庫，它提供了一個簡單的 Numpy/Matlab 類似的接口。
NumCpp中的主要數據結構是NdArray。它本質上是一個 2D 數組類，一維數組實現爲1xN數組。還有一個DataCube類作爲便利容器提供，用於存儲2D數組NdArray，但它通過簡單容器的用途有限。

地址 https://github.com/dpilger26/NumCpp
文檔地址 https://dpilger26.github.io/NumCpp/doxygen/html/index.html

二、使用

1.源碼

$ git clone https://github.com/dpilger26/NumCpp

源碼中的src文件夾下的文件能夠直接被項目使用：

# 拷貝到項目中
$ cp NumCpp/src/ /home/toson/project/pro1/

// 引用頭文件即可使用
#include"src/NumCpp.hpp"

三、程序

#include"NumCpp.hpp"
#include"boost/filesystem.hpp"
#include<iostream>

int main()
{
    // Containers
    nc::NdArray<int> a0 = { {1, 2}, {3, 4} };
    nc::NdArray<int> a1 = { {1, 2}, {3, 4}, {5, 6} };
    a1.reshape(2, 3);
    auto a2 = a1.astype<double>();

    // Initializers
    auto a3 = nc::linspace<int>(1, 10, 5);
    auto a4 = nc::arange<int>(3, 7);
    auto a5 = nc::eye<int>(4);
    auto a6 = nc::zeros<int>(3, 4);
    auto a7 = nc::NdArray<int>(3, 4) = 0;
    auto a8 = nc::ones<int>(3, 4);
    auto a9 = nc::NdArray<int>(3, 4) = 1;
    auto a10 = nc::nans(3, 4);
    auto a11 = nc::NdArray<double>(3, 4) = nc::constants::nan;
    auto a12 = nc::empty<int>(3, 4);
    auto a13 = nc::NdArray<int>(3, 4);

    // Slicing/Broadcasting
    auto a14 = nc::Random<int>::randInt({ 10, 10 }, 0, 100);
    auto value = a14(2, 3);
    auto slice = a14({ 2, 5 }, { 2, 5 });
    auto rowSlice = a14(a14.rSlice(), 7);
    auto values = a14[a14 > 50];
    a14.putMask(a14 > 50, 666);

    // Random
    nc::Random<>::seed(666);
    auto a15 = nc::Random<double>::randN({3, 4});
    auto a16 = nc::Random<int>::randInt({3, 4}, 0, 10);
    auto a17 = nc::Random<double>::rand({3, 4});
    auto a18 = nc::Random<double>::choice(a17, 3);

    // Concatenation
    auto a = nc::Random<int>::randInt({3, 4}, 0, 10);
    auto b = nc::Random<int>::randInt({3, 4}, 0, 10);
    auto c = nc::Random<int>::randInt({3, 4}, 0, 10);

    auto a19 = nc::stack({ a, b, c }, nc::Axis::ROW);
    auto a20 = nc::vstack({ a, b, c });
    auto a21 = nc::hstack({ a, b, c });
    auto a22 = nc::append(a, b, nc::Axis::COL);

    // Diagonal, Traingular, and Flip
    auto d = nc::Random<int>::randInt({5, 5}, 0, 10);
    auto a23 = nc::diagonal(d);
    auto a24 = nc::triu(a);
    auto a25 = nc::tril(a);
    auto a26 = nc::flip(d, nc::Axis::ROW);
    auto a27 = nc::flipud(d);
    auto a28 = nc::fliplr(d);

    // iteration
    for (auto it = a.begin(); it < a.end(); ++it)
    {
        std::cout << *it << " ";
    }
    std::cout << std::endl;

    for (auto& arrayValue : a)
    {
        std::cout << arrayValue << " ";
    }
    std::cout << std::endl;

    // Logical
    auto a29 = nc::where(a > 5, a, b);
    auto a30 = nc::any(a);
    auto a31 = nc::all(a);
    auto a32 = nc::logical_and(a, b);
    auto a33 = nc::logical_or(a, b);
    auto a34 = nc::isclose(a, b);
    auto a35 = nc::allclose(a, b);

    // Comparisons
    auto a36 = nc::equal(a, b);
    auto a37 = a == b;
    auto a38 = nc::not_equal(a, b);
    auto a39 = a != b;
    auto a40 = nc::nonzero(a);

    // Minimum, Maximum, Sorting
    auto value1 = nc::min(a);
    auto value2 = nc::max(a);
    auto value3 = nc::argmin(a);
    auto value4 = nc::argmax(a);
    auto a41 = nc::sort(a, nc::Axis::ROW);
    auto a42 = nc::argsort(a, nc::Axis::COL);
    auto a43 = nc::unique(a);
    auto a44 = nc::setdiff1d(a, b);
    auto a45 = nc::diff(a);

    // Reducers
    auto value5 = nc::sum<int>(a);
    auto a46 = nc::sum<int>(a, nc::Axis::ROW);
    auto value6 = nc::prod<int>(a);
    auto a47 = nc::prod<int>(a, nc::Axis::ROW);
    auto value7 = nc::mean(a);
    auto a48 = nc::mean(a, nc::Axis::ROW);
    auto value8 = nc::count_nonzero(a);
    auto a49 = nc::count_nonzero(a, nc::Axis::ROW);

    // I/O
    a.print();
    std::cout << a << std::endl;

    auto tempDir = boost::filesystem::temp_directory_path();
    auto tempTxt = (tempDir / "temp.txt").string();
    a.tofile(tempTxt, "\n");
    auto a50 = nc::fromfile<int>(tempTxt, "\n");

    auto tempBin = (tempDir / "temp.bin").string();
    nc::dump(a, tempBin);
    auto a51 = nc::load<int>(tempBin);

    // Mathematical Functions

    // Basic Functions
    auto a52 = nc::abs(a);
    auto a53 = nc::sign(a);
    auto a54 = nc::remainder(a, b);
    auto a55 = nc::clip(a, 3, 8);
    auto xp = nc::linspace<double>(0.0, 2.0 * nc::constants::pi, 100);
    auto fp = nc::sin(xp);
    auto x = nc::linspace<double>(0.0, 2.0 * nc::constants::pi, 1000);
    auto f = nc::interp(x, xp, fp);

    // Exponential Functions
    auto a56 = nc::exp(a);
    auto a57 = nc::expm1(a);
    auto a58 = nc::log(a);
    auto a59 = nc::log1p(a);

    // Power Functions
    auto a60 = nc::power<int>(a, 4);
    auto a61 = nc::sqrt(a);
    auto a62 = nc::square(a);
    auto a63 = nc::cbrt(a);

    // Trigonometric Functions
    auto a64 = nc::sin(a);
    auto a65 = nc::cos(a);
    auto a66 = nc::tan(a);

    // Hyperbolic Functions
    auto a67 = nc::sinh(a);
    auto a68 = nc::cosh(a);
    auto a69 = nc::tanh(a);

    // Classification Functions
    auto a70 = nc::isnan(a.astype<double>());
    //nc::isinf(a);

    // Linear Algebra
    auto a71 = nc::norm<int>(a);
    auto a72 = nc::dot<int>(a, b.transpose());

    auto a73 = nc::Random<int>::randInt({3, 3}, 0, 10);
    auto a74 = nc::Random<int>::randInt({4, 3}, 0, 10);
    auto a75 = nc::Random<int>::randInt({1, 4}, 0, 10);
    auto value9 = nc::linalg::det(a73);
    auto a76 = nc::linalg::inv(a73);
    auto a77 = nc::linalg::lstsq(a74, a75);
    auto a78 = nc::linalg::matrix_power<int>(a73, 3);
    auto a79 = nc::linalg::multi_dot<int>({ a, b.transpose(), c });

    nc::NdArray<double> u;
    nc::NdArray<double> s;
    nc::NdArray<double> vt;
    nc::linalg::svd(a.astype<double>(), u, s, vt);

    return 0;
}

四、如果有問題

1.遇到頭文件問題

fatal error: NumCpp/Types.hpp: No such file or directory
 #include"NumCpp/Types.hpp"

請檢查CMakeLists.txt中：include_directories()中包含路徑。

2.依賴問題

/usr/local/include/boost/math/special_functions/lanczos.hpp:104:25: note: use -std=gnu++11 or -fext-numeric-literals to enable more built-in suffixes
/usr/local/include/boost/math/special_functions/lanczos.hpp:105:25: error: unable to find numeric literal operator ‘operator""Q’
          static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 35, 32.12388941444332003446077108933558534361)),

參照依賴項：

• C ++標準： C ++ 11，C ++ 14 或 C ++ 17
• 編譯器： VS 2017/2019，GCC 7.4.0 或 Clang 6.0
• Boost版本： 1.68 或 1.70

檢查GCC版本

$ gcc -v
gcc version 5.4.0 20160609 (Ubuntu 5.4.0-6ubuntu1~16.04.11)

檢查boost版本

$ dpkg -S /usr/include/boost/version.hpp
libboost1.68-dev:amd64: /usr/include/boost/version.hpp

附：boost編譯
下載boost1.68：https://dl.bintray.com/boostorg/release/1.68.0/source/

$ tar -zxvf boost_1_68_0.tar.gz
$ cd boost_1_68_0/
# 編譯
$ ./bootstrap.sh --with-libraries=all --with-toolset=gcc
# 安裝
$ ./b2 install --prefix=/usr

3. Linux編譯問題

note: use -std=gnu++11 or -fext-numeric-literals to enable more built-in suffixes
error: unable to find numeric literal operator ‘operator""Q’
static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 35, 32.12388941444332003446077108933558534361)),

需要在項目中的CMake編譯選項中增加：

SET(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -fext-numeric-literals")

In function `boost::system::generic_category()':
undefined reference to `boost::system::detail::generic_category_ncx()'

在CMake編譯時需要依賴庫：boost_system

五、運算效率

基於：Ubuntu 16.04LTS，Core-i7 8700，Clion

1.nc::dot<double>運算太耗時

auto mel = nc::dot<double>(mel_basis, mag);     //20ms
//注：mel_basis爲shape(80,1025)，mag爲shape(1025,109)

//我後來優化爲使用opencv來實現的
cv::Mat cv_mel = cv_mel_basis * cv_mag;     //2ms

2.nc::log10(nc::maximum(...))運算還將就，不過opencv更快

// to decibel           //2ms
mel = nc::log10(nc::maximum(mel, nc::NdArray<double>(mel.shape().rows, mel.shape().cols) = 1e-5)) * 20;
mag = nc::log10(nc::maximum(mag, nc::NdArray<double>(mag.shape().rows, mag.shape().cols) = 1e-5)) * 20;
    
//嘗試使用opencv來實現      //0ms(<0.5ms)
cv::log(cv::max(cv_mel, 1e-5), cv_mel);

3.nc::pad()的實現與numpy不一樣：
numpy可以實現一維填充（一維數列），而numcpp會將每個維度都進行填充。
比如我想實現一維數列的填充，結果出來後成爲了二維數列了。
並且無法完成reflect填充。

//注：ncbuffer的shape(1,43350)
auto ncbuffer_pad = nc::pad(ncbuffer, nc::uint16(pad_lenght), 0.0);
//nc::pad()會將二維也進行填充，成爲2049*45398

我當初是自己寫循環實現的，後來使用opencv裏的copyMakeBorder來完成reflect填充：

cv::copyMakeBorder(cv_padbuffer, cv_padbuffer, 0, 0, pad_lenght, pad_lenght, cv::BORDER_REFLECT_101);//cv::BORDER_REFLECT

這裏發現opencv裏copyMakeBorder的BORDER_REFLECT填充是這樣的：
例：fedcba|abcdefgh|hgfedcb
我要實現numpy裏的reflect填充，它的效果是這樣的：
例：gfedcb|abcdefgh|gfedcba
所以應該使用BORDER_REFLECT_101。

4.其他。。。