Compile-time linear algebra in C++
This library provides the class template ctla::matrix
and its associated operations for compile-time (constexpr) linear algebra.
Key features
• Header-only library
• All functions constexpr, all computation done at compile time
• Intuitive syntax for initialisation, indexing, augmenting
• Matrix arithmetic including inverses and linear systems supported
• Block matrices supported
• Runtime printing in MATLAB-compatible syntax if required
• Documentation…not written. Available matrix operations can be found in matrix.h, and see the examples start_here.cpp, arithmetic.cpp, regression.cpp, blocks.cpp.
Installation
Nothing to install. Just #include "matrix.h" and off you go.
Requires
C++17 conforming compiler. Tested on Clang 5.0 and GCC 7.2.
Example
// ********************************
// Simple linear regression example
// ********************************
#include "matrix.h"
using namespace ctla;
template<auto Val>
struct Print{
// force a compile error, hopefully with a message that outputs Val
char dummy[0*Val-1];
};
void regression() {
// The input values
constexpr auto x = seq<1,10>().T();
// The response values
constexpr matrix<double, 10, 1> y(
{3.8180, 5.0613, 5.2806, 4.0659, 4.1211, 2.2983, 0.2743, -0.9785, -6.8954, -10.4222}
);
// Try a linear model y = c0 + c1*x
constexpr auto A_linear = augc(ones<double,10,1>(), x);
constexpr auto c_linear = A_linear % y; // c = A % y means solve the linear system A*c = y
// (in the least squares sense if necessary)
constexpr auto y_linear = A_linear * c_linear;
// Compute the R^2 value
constexpr auto SStot = normsq(y - mean(y));
constexpr auto SSres_linear = normsq(y - y_linear);
constexpr auto Rsquared_linear = 1 - SSres_linear / SStot;
Print<int(Rsquared_linear*100)>();
// compiler prints error about Print<76> i.e. R^2 == 76%
// Try a quadratic model y = c0 + c1*x + c2*x^2
constexpr auto A_quadratic = augc(A_linear, mul(x,x));
constexpr auto c_quadratic = A_quadratic % y;
constexpr auto y_quadratic = A_quadratic * c_quadratic;
// See if we get a better R^2 value
constexpr auto SSres_quadratic = normsq(y - y_quadratic);
constexpr auto Rsquared_quadratic = 1 - SSres_quadratic / SStot;
Print<int(Rsquared_quadratic*100)>();
// compiler prints error about Print<98> i.e. R^2 == 98%
}