NumCpp(C++版本Numpy)使用笔记

一、简介

NumCpp：Python NumPy库的一个Templatized Header Only C ++实现
NumCpp 是一个高性能的数学计算 C++ 库，它提供了一个简单的 Numpy/Matlab 类似的接口。
NumCpp中的主要数据结构是NdArray。它本质上是一个 2D 数组类，一维数组实现为1xN数组。还有一个DataCube类作为便利容器提供，用于存储2D数组NdArray，但它通过简单容器的用途有限。

地址 https://github.com/dpilger26/NumCpp
文档地址 https://dpilger26.github.io/NumCpp/doxygen/html/index.html

二、使用

1.源码

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

源码中的src文件夹下的文件能够直接被项目使用：

# 拷贝到项目中
$ cp NumCpp/src/ /home/toson/project/pro1/

// 引用头文件即可使用
#include"src/NumCpp.hpp"

三、程序

#include"NumCpp.hpp"
#include"boost/filesystem.hpp"
#include

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

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

    // Slicing/Broadcasting
    auto a14 = nc::Random::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::randN({3, 4});
    auto a16 = nc::Random::randInt({3, 4}, 0, 10);
    auto a17 = nc::Random::rand({3, 4});
    auto a18 = nc::Random::choice(a17, 3);

    // Concatenation
    auto a = nc::Random::randInt({3, 4}, 0, 10);
    auto b = nc::Random::randInt({3, 4}, 0, 10);
    auto c = nc::Random::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::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(a);
    auto a46 = nc::sum(a, nc::Axis::ROW);
    auto value6 = nc::prod(a);
    auto a47 = nc::prod(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(tempTxt, "\n");

    auto tempBin = (tempDir / "temp.bin").string();
    nc::dump(a, tempBin);
    auto a51 = nc::load(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(0.0, 2.0 * nc::constants::pi, 100);
    auto fp = nc::sin(xp);
    auto x = nc::linspace(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(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());
    //nc::isinf(a);

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

    auto a73 = nc::Random::randInt({3, 3}, 0, 10);
    auto a74 = nc::Random::randInt({4, 3}, 0, 10);
    auto a75 = nc::Random::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(a73, 3);
    auto a79 = nc::linalg::multi_dot({ a, b.transpose(), c });

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

    return 0;
}

四、如果有问题

1.遇到头文件问题

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

请检查CMakeLists.txt中：include_directories()中包含路径。

2.依赖问题

/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(BOOST_MATH_BIG_CONSTANT(T, 35, 32.12388941444332003446077108933558534361)),

参照依赖项：

• C ++标准： C ++ 11，C ++ 14 或 C ++ 17
• 编译器： VS 2017/2019，GCC 7.4.0 或 Clang 6.0
• Boost版本： 1.68 或 1.70

检查GCC版本

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

检查boost版本

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

附：boost编译
下载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/
# 编译
$ ./bootstrap.sh --with-libraries=all --with-toolset=gcc
# 安装
$ ./b2 install --prefix=/usr

3. Linux编译问题

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(BOOST_MATH_BIG_CONSTANT(T, 35, 32.12388941444332003446077108933558534361)),

需要在项目中的CMake编译选项中增加：

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编译时需要依赖库：boost_system

五、运算效率

基于：Ubuntu 16.04LTS，Core-i7 8700，Clion

1.nc::dot运算太耗时

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

//我后来优化为使用opencv来实现的
cv::Mat cv_mel = cv_mel_basis * cv_mag;     //2ms

2.nc::log10(nc::maximum(...))运算还将就，不过opencv更快

// to decibel           //2ms
mel = nc::log10(nc::maximum(mel, nc::NdArray(mel.shape().rows, mel.shape().cols) = 1e-5)) * 20;
mag = nc::log10(nc::maximum(mag, nc::NdArray(mag.shape().rows, mag.shape().cols) = 1e-5)) * 20;
    
//尝试使用opencv来实现      //0ms(<0.5ms)
cv::log(cv::max(cv_mel, 1e-5), cv_mel);

3.nc::pad()的实现与numpy不一样：
numpy可以实现一维填充（一维数列），而numcpp会将每个维度都进行填充。
比如我想实现一维数列的填充，结果出来后成为了二维数列了。
并且无法完成reflect填充。

//注：ncbuffer的shape(1,43350)
auto ncbuffer_pad = nc::pad(ncbuffer, nc::uint16(pad_lenght), 0.0);
//nc::pad()会将二维也进行填充，成为2049*45398

我当初是自己写循环实现的，后来使用opencv里的copyMakeBorder来完成reflect填充：

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

这里发现opencv里copyMakeBorder的BORDER_REFLECT填充是这样的：
例：fedcba|abcdefgh|hgfedcb
我要实现numpy里的reflect填充，它的效果是这样的：
例：gfedcb|abcdefgh|gfedcba
所以应该使用BORDER_REFLECT_101。

4.其他。。。