Matrix

An easy-to-use header-only C++ library for matrix representation and calcualtion. This matrix library support lazy evaluation, element-wise evaluation and so on, exploiting compile-time generic coding approach. The CRTP based class/expression backbone was deeply influenced by the famous matrix library 'Eigen'.

Features

Lazy Evaluation

This matrix library employs expression template patterns, which is enabling detatch creation of expression from real evaluation as follows.

std::vector<int> vecInts = { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 };
myMatrix<int> mat(vecInts, 2, 5);
auto matExpr = mat + mat; // a proxy matrix indicating mat(lhs) and mat(rhs) to be added.
myMatrix<int> mat2 = matExpr; // evaluation of the matExpr by initialization.
auto mat3 = matExpr.concrete() // evaluation of matExpr by function.

For loop fusion

The lazy evaluation enables multiple element-wise matrix calculation using one 'for' loop as follows.

std::vector<int> vecInts = { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 };
myMatrix<int> mat(vecInts, 2, 5);
myMatrix<int> mat2(vecInts, 2, 5);
auto matExpr = mat2 - mat - mat - mat - mat; // five calculation
auto mat3 = matExpr.concrete(); // evaluation in one 'for' loop

more examples

Element-wise evaluation / Partial evaluation

It is possible to calculate one element

... continued to the above code
auto matExpr2 = (mat2 + mat1) * mat1.t() ) // formulating expression, not evaluated
std::cout << matExpr2._v(1,0) << std::endl; // evaluate 1,0 th element then show (the other elements are not evaluated)

Masking

1. Can use mask (or filter) to select data from matrix seen.

// working as data retrive
myMatrix<int> mat1 ({1,2,3,4}, 2, 2);
myMatrix<int> mat2 = mat1.select(mat1 >= 2) - mat1.select(mat1 < 2); // mat2 --> {-1,-2;3,4}

more examples.

2. Mask for filtering element position to be updated

// working as data retrive
myMatrix<int> mat1 ({1,2,3,4}, 2, 2);
mat1.select(mat1 < 2) = - mat1; // mat1 --> {-1,2;3,4}

more examples.

3. Mask arithematic

// working as data retrive
myMatrix<int> mat1 ({1,2,3,4}, 2, 2);
mat1.select(mat1 < 2 | mat1 == 4 ) = - mat1; // mat1 --> {-1,2;3,-4}

more examples.

Upcomming Features...

Getting sub-matrix or sub-vector

myMatrix<int> mat1 ({1,2,3,4}, 2, 2);
mat1.row(1) = 10; // now data --> {1,2,10,10}

Arithmetic and Assign

myMatrix<int> mat1 ({1,2,3,4}, 2, 2);
mat1 += 10; // now data --> {11,12,13,14}

Performance

to be tested.

Further Works

• Determine Class name ... not "myMatrix" ...
• Calculation optimization.
• Numerical algorithm such as pseudo-inverse, faster matrix multiplication algorithm ....
• Study on hardware acceleration.
• More test codes for showing functions and performances.
• Better interface
• Hiding non interface functions and relate friendship
• arithmetic + assignment such as +=, -=
• Detailed To Do list ...

Limit

The original work was for practicing programming skills, so some codes could not be the optimal for numerical calculations.