Inroduction

Recently I am exploring the linear algebra features provided in Armadillo through RcppArmadillo.

Here is the note for myself.

Note these functions are only my understanding of these operators and methods. I didn’t check the source code of Armadillo and RcppArmadillo.

Basic Elements and Methods

``` cpp mat arma::mat a(5, 5); // Initialize a 5 x 5 matrix.

a.fill(0); // fill it with 0 a.n_rows; //!< number of rows in the matrix (read-only) a.n_cols; //!< number of columns in the matrix (read-only) a.n_elem; //!< number of elements in the matrix (read-only) a.vec_state; //!< 0: matrix layout; 1: column vector layout; 2: row vector layout a.mem; //!< pointer to memory used by the matrix (memory is read-only)

a.min(); a.max();



# Feature

## Matrix Multiplication

``` cpp Matrix Multiplication
const arma::mat operator*(const arma::mat& x, const arma::mat& y);

Transpose

``` cpp Transpose const arma::mat arma::trans(const arma::mat& x);

// Methods of class arma::mat // x.t() = arma::trans(x) const arma::mat arma::mat::t();


## Inverse

``` cpp Inverse
const arma::mat arma::pinv(const arma::mat& x);

Sum of Square

cpp Sum of Square inline double sumOfSquare(arma::vec& x) { return std::inner_product(x.begin(), x.end(), x.begin(), 0.0); }

Diagonal Vector

cpp Diagonal Vector const arma::colvec arma::diagvec(const arma::mat& x);

Linear Regression

``` cpp Linear Regression /** * @param X the explanatory variables * @param y the response variable * @return the vector of regression coefficients */ const arma::colvec arma::solve(const arma::mat& X, const arma::vec& y);

// Residuals arma::colvec residuals = y - X * coef;

// Residual Sum of Square double s2 = sumOfSquare(residuals);

// Std of Coef. arma::colvec sderr = arma::sqrt(s2 arma::diagvec(arma::pinv(arma::trans(X)X))); ```