R语言如何使用RcppEigen进行矩阵运算

这篇文章主要介绍了R语言如何使用RcppEigen进行矩阵运算，具有一定借鉴价值，感兴趣的朋友可以参考下，希望大家阅读完这篇文章之后大有收获，下面让小编带着大家一起了解一下。

创建cpp文件

其创建方式可以参考上篇博客：让你的R代码更快--Rcpp入门

代码示例

然后我们定义一个

来做矩阵乘法并求其迹（trace）的函数。

// [[Rcpp::depends(RcppEigen)]]#include using namespace Eigen;using namespace std;//[[Rcpp::export]]double myfun (MatrixXd X, MatrixXd Y) {  double Z;    Z = (X.adjoint() * Y).trace();  cout << Z << endl;   return Z;}

前三行表示载入Eigen库

// [[Rcpp::depends(RcppEigen)]]#include using namespace Eigen;

里面的转置函数adjoint()，求迹函数trace()，都需要用到这个库，如果不使用命名空间Eigen后面库里面就要这样用Eigen::adjoint()，Eigen::trace()。

后面我们使用using namespace std;则是因为cout需要用到，这个可以在运行函数的时候展现我们的中间变量，也是一个比较有用的操作，当然如果不需要的话，就可以不用命名变量空间：std。

下面就是我们的函数：

//[[Rcpp::export]]double myfun (MatrixXd X, MatrixXd Y) {  double Z;    Z = (X.adjoint() * Y).trace();  cout << Z << endl;   return Z;}

//[[Rcpp::export]]为我们需要导出到R中的时候需要添加，double型的矩阵在Eigen中命名为MatrixXd，整型矩阵为MatrixXi；类似，对应的向量命名方式为：VectorXd与VectorXi。

里面的内容就是我们按照公式敲的函数。

下面我们介绍一些Eigen库中的其它一些矩阵操作。

其他矩阵操作

这部分原文：A simple quickref for Eigen

命名

Matrix A;               // Fixed rows and cols. Same as Matrix3d.Matrix B;         // Fixed rows, dynamic cols.Matrix C;   // Full dynamic. Same as MatrixXd.Matrix E;     // Row major; default is column-major.Matrix3f P, Q, R;                     // 3x3 float matrix.Vector3f x, y, z;                     // 3x1 float matrix.RowVector3f a, b, c;                  // 1x3 float matrix.VectorXd v;                           // Dynamic column vector of doublesdouble s;

基础用法

// Basic usage// Eigen          // Matlab           // commentsx.size()          // length(x)        // vector sizeC.rows()          // size(C,1)        // number of rowsC.cols()          // size(C,2)        // number of columnsx(i)              // x(i+1)           // Matlab is 1-basedC(i,j)            // C(i+1,j+1)       //A.resize(4, 4);   // Runtime error if assertions are on.B.resize(4, 9);   // Runtime error if assertions are on.A.resize(3, 3);   // Ok; size didn't change.B.resize(3, 9);   // Ok; only dynamic cols changed.                  A << 1, 2, 3,     // Initialize A. The elements can also be     4, 5, 6,     // matrices, which are stacked along cols     7, 8, 9;     // and then the rows are stacked.B << A, A, A;     // B is three horizontally stacked A's.A.fill(10);       // Fill A with all 10's.

定义矩阵

// Eigen                                    // MatlabMatrixXd::Identity(rows,cols)               // eye(rows,cols)C.setIdentity(rows,cols)                    // C = eye(rows,cols)MatrixXd::Zero(rows,cols)                   // zeros(rows,cols)C.setZero(rows,cols)                        // C = zeros(rows,cols)MatrixXd::Ones(rows,cols)                   // ones(rows,cols)C.setOnes(rows,cols)                        // C = ones(rows,cols)MatrixXd::Random(rows,cols)                 // rand(rows,cols)*2-1            // MatrixXd::Random returns uniform random numbers in (-1, 1).C.setRandom(rows,cols)                      // C = rand(rows,cols)*2-1VectorXd::LinSpaced(size,low,high)          // linspace(low,high,size)'v.setLinSpaced(size,low,high)               // v = linspace(low,high,size)'VectorXi::LinSpaced(((hi-low)/step)+1,      // low:step:hi                    low,low+step*(size-1))  //

对矩阵的一些基础操作1

// Matrix slicing and blocks. All expressions listed here are read/write.// Templated size versions are faster. Note that Matlab is 1-based (a size N// vector is x(1)...x(N)).// Eigen                           // Matlabx.head(n)                          // x(1:n)x.head()                        // x(1:n)x.tail(n)                          // x(end - n + 1: end)x.tail()                        // x(end - n + 1: end)x.segment(i, n)                    // x(i+1 : i+n)x.segment(i)                    // x(i+1 : i+n)P.block(i, j, rows, cols)          // P(i+1 : i+rows, j+1 : j+cols)P.block(i, j)          // P(i+1 : i+rows, j+1 : j+cols)P.row(i)                           // P(i+1, :)P.col(j)                           // P(:, j+1)P.leftCols()                 // P(:, 1:cols)P.leftCols(cols)                   // P(:, 1:cols)P.middleCols(j)              // P(:, j+1:j+cols)P.middleCols(j, cols)              // P(:, j+1:j+cols)P.rightCols()                // P(:, end-cols+1:end)P.rightCols(cols)                  // P(:, end-cols+1:end)P.topRows()                  // P(1:rows, :)P.topRows(rows)                    // P(1:rows, :)P.middleRows(i)              // P(i+1:i+rows, :)P.middleRows(i, rows)              // P(i+1:i+rows, :)P.bottomRows()               // P(end-rows+1:end, :)P.bottomRows(rows)                 // P(end-rows+1:end, :)P.topLeftCorner(rows, cols)        // P(1:rows, 1:cols)P.topRightCorner(rows, cols)       // P(1:rows, end-cols+1:end)P.bottomLeftCorner(rows, cols)     // P(end-rows+1:end, 1:cols)P.bottomRightCorner(rows, cols)    // P(end-rows+1:end, end-cols+1:end)P.topLeftCorner()       // P(1:rows, 1:cols)P.topRightCorner()      // P(1:rows, end-cols+1:end)P.bottomLeftCorner()    // P(end-rows+1:end, 1:cols)P.bottomRightCorner()   // P(end-rows+1:end, end-cols+1:end)

基础操作2

// Of particular note is Eigen's swap function which is highly optimized.// Eigen                           // MatlabR.row(i) = P.col(j);               // R(i, :) = P(:, j)R.col(j1).swap(mat1.col(j2));      // R(:, [j1 j2]) = R(:, [j2, j1])

// Views, transpose, etc;// Eigen                           // MatlabR.adjoint()                        // R'R.transpose()                      // R.' or conj(R')       // Read-writeR.diagonal()                       // diag(R)               // Read-writex.asDiagonal()                     // diag(x)R.transpose().colwise().reverse()  // rot90(R)              // Read-writeR.rowwise().reverse()              // fliplr(R)R.colwise().reverse()              // flipud(R)R.replicate(i,j)                   // repmat(P,i,j)

矩阵基础运算1

// All the same as Matlab, but matlab doesn't have *= style operators.// Matrix-vector.  Matrix-matrix.   Matrix-scalar.y  = M*x;          R  = P*Q;        R  = P*s;a  = b*M;          R  = P - Q;      R  = s*P;a *= M;            R  = P + Q;      R  = P/s;                   R *= Q;          R  = s*P;                   R += Q;          R *= s;                   R -= Q;          R /= s;

矩阵基础运算2

// Vectorized operations on each element independently// Eigen                       // MatlabR = P.cwiseProduct(Q);         // R = P .* QR = P.array() * s.array();     // R = P .* sR = P.cwiseQuotient(Q);        // R = P ./ QR = P.array() / Q.array();     // R = P ./ QR = P.array() + s.array();     // R = P + sR = P.array() - s.array();     // R = P - sR.array() += s;                // R = R + sR.array() -= s;                // R = R - sR.array() < Q.array();         // R < QR.array() <= Q.array();        // R <= QR.cwiseInverse();              // 1 ./ RR.array().inverse();           // 1 ./ RR.array().sin()                // sin(R)R.array().cos()                // cos(R)R.array().pow(s)               // R .^ sR.array().square()             // R .^ 2R.array().cube()               // R .^ 3R.cwiseSqrt()                  // sqrt(R)R.array().sqrt()               // sqrt(R)R.array().exp()                // exp(R)R.array().log()                // log(R)R.cwiseMax(P)                  // max(R, P)R.array().max(P.array())       // max(R, P)R.cwiseMin(P)                  // min(R, P)R.array().min(P.array())       // min(R, P)R.cwiseAbs()                   // abs(R)R.array().abs()                // abs(R)R.cwiseAbs2()                  // abs(R.^2)R.array().abs2()               // abs(R.^2)(R.array() < s).select(P,Q );  // (R < s ? P : Q)R = (Q.array()==0).select(P,R) // R(Q==0) = P(Q==0)R = P.unaryExpr(ptr_fun(func)) // R = arrayfun(func, P)   // with: scalar func(const scalar &x);

求最小最大值、迹等

// Reductions.int r, c;// Eigen                  // MatlabR.minCoeff()              // min(R(:))R.maxCoeff()              // max(R(:))s = R.minCoeff(&r, &c)    // [s, i] = min(R(:)); [r, c] = ind2sub(size(R), i);s = R.maxCoeff(&r, &c)    // [s, i] = max(R(:)); [r, c] = ind2sub(size(R), i);R.sum()                   // sum(R(:))R.colwise().sum()         // sum(R)R.rowwise().sum()         // sum(R, 2) or sum(R')'R.prod()                  // prod(R(:))R.colwise().prod()        // prod(R)R.rowwise().prod()        // prod(R, 2) or prod(R')'R.trace()                 // trace(R)R.all()                   // all(R(:))R.colwise().all()         // all(R)R.rowwise().all()         // all(R, 2)R.any()                   // any(R(:))R.colwise().any()         // any(R)R.rowwise().any()         // any(R, 2)

点乘等

// Dot products, norms, etc.// Eigen                  // Matlabx.norm()                  // norm(x).    Note that norm(R) doesn't work in Eigen.x.squaredNorm()           // dot(x, x)   Note the equivalence is not true for complexx.dot(y)                  // dot(x, y)x.cross(y)                // cross(x, y) Requires #include 

特征值与特征向量

// Eigenvalue problems// Eigen                          // MatlabA.eigenvalues();                  // eig(A);EigenSolver eig(A);     // [vec val] = eig(A)eig.eigenvalues();                // diag(val)eig.eigenvectors();               // vec// For self-adjoint matrices use SelfAdjointEigenSolver<>

形式转换

 Type conversion// Eigen                  // MatlabA.cast();         // double(A)A.cast();          // single(A)A.cast();            // int32(A)A.real();                 // real(A)A.imag();                 // imag(A)// if the original type equals destination type, no work is done

矩阵初始化0

// Note that for most operations Eigen requires all operands to have the same type:MatrixXf F = MatrixXf::Zero(3,3);A += F;                // illegal in Eigen. In Matlab A = A+F is allowedA += F.cast(); // F converted to double and then added (generally, conversion happens on-the-fly)

Map等操作

// Eigen can map existing memory into Eigen matrices.float array[3];Vector3f::Map(array).fill(10);            // create a temporary Map over array and sets entries to 10int data[4] = {1, 2, 3, 4};Matrix2i mat2x2(data);                    // copies data into mat2x2Matrix2i::Map(data) = 2*mat2x2;           // overwrite elements of data with 2*mat2x2MatrixXi::Map(data, 2, 2) += mat2x2;      // adds mat2x2 to elements of data (alternative syntax if size is not know at compile time)

求解Ax = b

// Solve Ax = b. Result stored in x. Matlab: x = A \ b.x = A.ldlt().solve(b));  // A sym. p.s.d.    #include x = A.llt() .solve(b));  // A sym. p.d.      #include x = A.lu()  .solve(b));  // Stable and fast. #include x = A.qr()  .solve(b));  // No pivoting.     #include x = A.svd() .solve(b));  // Stable, slowest. #include // .ldlt() -> .matrixL() and .matrixD()// .llt()  -> .matrixL()// .lu()   -> .matrixL() and .matrixU()// .qr()   -> .matrixQ() and .matrixR()// .svd()  -> .matrixU(), .singularValues(), and .matrixV()

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