wanmyj::Matrix - The C++ Linear Algebra Library (in development)

This repo is for the interview project of the folowing requirements

Please design and implement a Matrix family. The family should include at least following matrix types:

Dense matrix, which means most of the items in that matrix are not zero.
Sparse matrix. You can find the definition for it here: http://en.wikipedia.org/wiki/Sparse_matrix
Diagonal matrix. You can find the definition for it here: http://en.wikipedia.org/wiki/Diagonal_matrix

The operations for the matrix should at least include (prioritized):

Multiply (with another Matrix or a scalar value)
Transpose

Tasks: (prioritized)

Please design the inheritance hierarchy for this Matrix family. The design should make it as easy as possible to add one more Matrix type into the family.
Please design a good data structure for each matrix so that it costs least memory and has best performance for the operations.
Please implement the classes in template (C++).
Please try your best to make the operations have the best performance.
Please write also small test program to verify the operations.

Overview

The realization provides:

Basic initializer_list initialization of matrix
Basic matrix transpose operation
Basic matrix multiplication operation
Cascaded multiplication operation
Cross-datatype multiplication operation (e.g. Matrix<int> * Matrix<float>)
Cross-matrixtype multiplication operation (e.g. DenseMatrix<int> * DiagMatrix<int>)
DenseMatrix<double> could always catch all arithmetic operations of all derived matrices class of all datatypes

To add a derived matrix class, the minimum requirement:

Data structure specification
Proper initialization method(s)
Overload the Transpose() function
Overload the GetMatrix() function

It also would be a good practice to overload operator* for the sake of optimizations

Test Environment

c++11 standard (enable_if branch: c++14)
g++ 9.3.0
Ubuntu 18.04

Compile Cmd

(master branch) g++ -std=c++11 -I. example.cpp
(enable_if branch) g++ -std=c++14 -I. example.cpp

Example program

example.cpp:

#include <iostream>
#include <Dense_Matrix.h>
#include <Diag_Matrix.h>
#include <Sparse_Matrix.h>

using namespace Matrix;
using namespace std;
int main() {
    // dense matrix initialization (vector initializer_list)
    cout << "dense matrix initialization" << endl;

    DenseMatrix<int> Da{{1}};
    cout << "print Da" << endl;
    Da.PrintMat();

    DenseMatrix<int> Db{{1, 2, 3},{3, 1}, {2, 2, 2}};
    cout << "print Db" << endl;
    Db.PrintMat();
    
    std::vector<std::vector<double>> DVc = {
        {1, 2, 3, 4},
        {2}, 
        {5, 2, 1} 
    };
    DenseMatrix<double> Dc(DVc);
    cout << "print Dc" << endl;
    Dc.PrintMat();

    // dense matrix transpose
    Db.Transpose();
    cout << "print Db transpose" << endl;
    Db.PrintMat();

    // dense matrix multiply (Tscalar * Tmatrix, Tscalar * Fmatrix, Tmatrix * Tmatrix, Tmatrix * Fmatrix)
    cout << "dense matrix multiply\n" << endl;
    DenseMatrix<int> Di = Db * 3;
    cout << "print Di = Db * 3" << endl;
    Di.PrintMat();

    Di = 3 * Di;
    cout << "print Di = 3 * Di" << endl;
    Di.PrintMat();

    DenseMatrix<double> Dj = Dc * 3;
    cout << "print Dj = Dc * 3" << endl;
    Dj.PrintMat();

    Dj = 3.1 * Da;
    cout << "print Dj = 3.1 * Da" << endl;
    Dj.PrintMat();


    // diag matrix initialization (vector initializer_list)
    cout << "diag matrix initialization" << endl;
    DiagMatrix<int> da{1, 2, 3};
    cout << "print da{1, 2, 3}" << endl;
    da.PrintMat();

    vector<float> dvb{1, 2.4, 3};
    DiagMatrix<float> db{dvb};
    cout << "print db{dvb}" << endl;
    db.PrintMat();

    // diag matrix transpose
    db.Transpose();
    cout << "print db transpose" << endl;
    db.PrintMat();

    // diag matrix multiply (Tscalar * Tmatrix, Tscalar * Fmatrix, Tmatrix * Tmatrix, Tmatrix * Fmatrix)
    cout << "diag matrix multiply\n" << endl;

    DiagMatrix<int> di = da * 5;
    cout << "print di = da * 5" << endl;
    di.PrintMat();
    
    di = 12 * di;
    cout << "print di = 12 * di" << endl;
    di.PrintMat();

    DiagMatrix<double> dj = da * 1.3;
    cout << "print di = da * 5" << endl;
    dj.PrintMat();

    dj = 3.2 * db ;
    cout << "print dj = 3.2 * db" << endl;
    dj.PrintMat();

    // sparse matrix initialization (vector initializer_list)
    cout << "sparse matrix initialization" << endl;

    SparseMatrix<int> sa{3, 4, {{1, 2, 3}, {2, 2, 4}}};
    cout << "print sa" << endl;
    sa.PrintMat();

    std::vector<unsigned> svb1{2, 2, 1, 4};
    std::vector<unsigned> svb2{1, 2, 3, 4};
    std::vector<float> sva3{1.3, 1, 4, 8};
    SparseMatrix<float> sb(5, 5, svb1, svb2, sva3);
    cout << "print sb" << endl;
    sb.PrintMat();

    // sparse matrix transpose
    cout << "sparse matrix transpose\n" << endl;
    sb.Transpose();
    cout << "print sb transpose" << endl;
    sb.PrintMat();

    // sparse matrix multiply (Tscalar * Tmatrix, Tscalar * Fmatrix, Tmatrix * Tmatrix, Tmatrix * Fmatrix)
    cout << "diag matrix multiply\n" << endl;
    SparseMatrix<int> si = sa * 3;
    cout << "print si = sa * 3" << endl;
    si.PrintMat();

    si = 4 * si;
    cout << "print si = 4 * si" << endl;
    si.PrintMat();

    SparseMatrix<double> sj = sb * 3;
    cout << "print sj = sb * 3" << endl;
    sj.PrintMat();

    sj = 2.7 * sa;
    cout << "print sj = 2.7 * sa" << endl;
    sj.PrintMat();

    // dense(T/double) = scalar * sparse * (sparse * scalar)
    DenseMatrix<double> Ds  = 3 * ( sb * 1.2);
    cout << "print Ds  = 3 * ( sb * 1.2)" << endl;
    Ds.PrintMat();

    DenseMatrix<double> Dm  = 3 * sb * ( sb * 1.2);
    cout << "print Dm  = 3 * sb * ( sb * 1.2)" << endl;
    Dm.PrintMat();

    // dense(T/double) = sparse * (diag * scalar)
    DiagMatrix<int> dn{1, 2, 3, 4, 5};
    DenseMatrix<double> Dn  = 3.2 * sb * ( dn * 2);
    cout << "print Dn  = 3.2 * sb * ( dn * 2)" << endl;
    Dn.PrintMat();

    // dense(T/double) = diag * (scalar * (diag * scalar) * sparse.transpose)
    DenseMatrix<double> Do  = dn * (3 * (dn * 2.1) * sb.Transpose());
    cout << "print Do  = dn * (3 * (dn * 2.1) * sb.Transpose())" << endl;
    Do.PrintMat();

    // exception test
    cout << "-----------------------" << endl;
    try {
        Dc = Dc * Dc.Transpose(); //this is wrong
        cout << "Dc = Dc * Dc.Transpose()" << endl;
        Dc.PrintMat();
    } catch(const std::exception& e) {
        std::cerr << e.what() << '\n';
    }
    cin.get();
    return 0;
}

output:

dense matrix initialization
print Da
Mat row: 1 col: 1
1

print Db
Mat row: 3 col: 3
1 2 3
3 1 0
2 2 2

print Dc
Mat row: 3 col: 4
1 2 3 4
2 0 0 0
5 2 1 0

print Db transpose
Mat row: 3 col: 3
1 3 2
2 1 2
3 0 2

dense matrix multiply

print Di = Db * 3
Mat row: 3 col: 3
3 9 6
6 3 6
9 0 6

print Di = 3 * Di
Mat row: 3 col: 3
9 27 18
18 9 18
27 0 18

print Dj = Dc * 3
Mat row: 3 col: 4
3 6 9 12
6 0 0 0
15 6 3 0

print Dj = 3.1 * Da
Mat row: 1 col: 1
3.1

diag matrix initialization
print da{1, 2, 3}
Mat row: 3 col: 3
1 0 0
0 2 0
0 0 3

print db{dvb}
Mat row: 3 col: 3
1 0 0
0 2.4 0
0 0 3

print db transpose
Mat row: 3 col: 3
1 0 0
0 2.4 0
0 0 3

diag matrix multiply

print di = da * 5
Mat row: 3 col: 3
5 0 0
0 10 0
0 0 15

print di = 12 * di
Mat row: 3 col: 3
60 0 0
0 120 0
0 0 180

print dj = da * 5
Mat row: 3 col: 3
1.3 0 0
0 2.6 0
0 0 3.9

print dj = 3.2 * db
Mat row: 3 col: 3
3.2 0 0
0 7.68 0
0 0 9.6

print dj = da * dj
Mat row: 3 col: 3
3.2 0 0
0 15.36 0
0 0 28.8

sparse matrix initialization
print sa
Mat row: 3 col: 4
0 0 0 0
0 0 3 0
0 0 4 0

print sb
Mat row: 5 col: 5
0 0 0 0 0
0 0 0 4 0
0 1.3 1 0 0
0 0 0 0 0
0 0 0 0 8

sparse matrix transpose

print sb transpose
Mat row: 5 col: 5
0 0 0 0 0
0 0 1.3 0 0
0 0 1 0 0
0 4 0 0 0
0 0 0 0 8

diag matrix multiply

print si = sa * 3
Mat row: 3 col: 4
0 0 0 0
0 0 9 0
0 0 12 0

print si = 4 * si
Mat row: 3 col: 4
0 0 0 0
0 0 36 0
0 0 48 0

print sj = sb * 3
Mat row: 5 col: 5
0 0 0 0 0
0 0 3.9 0 0
0 0 3 0 0
0 12 0 0 0
0 0 0 0 24

print sj = 2.7 * sa
Mat row: 3 col: 4
0 0 0 0
0 0 8.1 0
0 0 10.8 0

print Dp  = sb * sb
Mat row: 5 col: 5
0 0 0 0 0
0 0 1.3 0 0
0 0 1 0 0
0 0 5.2 0 0
0 0 0 0 64

print Ds  = 3 * ( sb * 1.2)
Mat row: 5 col: 5
0 0 0 0 0
0 0 4.68 0 0
0 0 3.6 0 0
0 14.4 0 0 0
0 0 0 0 28.8

print Dm  = 3 * sb * ( sb * 1.2)
Mat row: 5 col: 5
0 0 0 0 0
0 0 4.68 0 0
0 0 3.6 0 0
0 0 18.72 0 0
0 0 0 0 230.4

print Dn  = 3.2 * sb * ( dn * 2)
Mat row: 5 col: 5
0 0 0 0 0
0 0 24.96 0 0
0 0 19.2 0 0
0 51.2 0 0 0
0 0 0 0 256

print Do  = dn * (3 * (dn * 2.1) * sb.Transpose())
Mat row: 5 col: 5
0 0 0 0 0
0 0 0 100.8 0
0 73.71 56.7 0 0
0 0 0 0 0
0 0 0 0 1260

-----------------------
two matrices are NOT multipliable

Reference

https://www.quantstart.com/articles/Matrix-Classes-in-C-The-Header-File/

https://www.quantstart.com/articles/Matrix-Classes-in-C-The-Source-File/

https://akrzemi1.wordpress.com/2017/12/02/your-own-type-predicate/

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wanmyj::Matrix - The C++ Linear Algebra Library (in development)

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Example program

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