Basic-matrix-operations-no-iostream.ino

Arduino sketch that demonstrates some of the basic features.

Boards:

Nano 33 IoT, Teensy 3.x

---

Aimed at Arduino boards without STL ostream support. Tested on Teensy 3.2, compiles for Teensy 3.0, 3.5, 3.6 as well.

Expected output

Solve system Ax = v
-------------------
 
A = 
   1.000000e+00   6.000000e+00   2.000000e+00
   3.000000e+00   2.000000e+00   1.000000e+00
   5.000000e+00   1.000000e+00   3.000000e+00
 
v =
   9.000000e+00
   6.000000e+00
   9.000000e+00
 
QR factorization of A:
Q =
  -1.690309e-01   9.636759e-01  -2.067787e-01
  -5.070926e-01   9.486964e-02   8.566545e-01
  -8.451543e-01  -2.496570e-01  -4.726370e-01
R =
  -5.916080e+00  -2.873524e+00  -3.380617e+00
   0.000000e+00   5.722137e+00   1.273250e+00
   0.000000e+00   0.000000e+00  -9.748137e-01
 
solution x =
   1.000000e+00
   1.000000e+00
   1.000000e+00
 
Basic matrix operations
-----------------------
 
C×B + D =
   3.200000e+01   3.900000e+01
   6.100000e+01   7.700000e+01
 
Basic vector operations
-----------------------
 
a   =         1.000000e+00   2.000000e+00   3.000000e+00
b   =         4.000000e+00   6.000000e+00   5.000000e+00
a×b =        -8.000000e+00   7.000000e+00  -2.000000e+00
a·b =      31.00
 
Element access
--------------
 
A[2,0] = 5.00
A[2,0] ← 100
   1.000000e+00   6.000000e+00   2.000000e+00
   3.000000e+00   2.000000e+00   1.000000e+00
   1.000000e+02   1.000000e+00   3.000000e+00

 
#include <Linear_Algebra.h> // Include the library first
 
#include <Linear_Algebra.h> // Include the library first
 
// Then include the necessary headers:
#include <include/linalg/HouseholderQR.hpp> 
#include <include/linalg/Matrix.hpp>
 
void setup() {
  Serial.begin(115200);
  while (!Serial)
    ;
 
  Serial.println("Solve system Ax = v");
  Serial.println("-------------------\n");
  SquareMatrix A = {
    {1, 6, 2},
    {3, 2, 1},
    {5, 1, 3},
  };
  Vector x = Vector::ones(3);
  Vector v = A * x;
 
  HouseholderQR qr(A); // QR factorization
  Vector x_solution = qr.solve(v);
 
  Serial.println("A = ");
  Serial.println(A);
  Serial.println("v =");
  Serial.println(v);
  Serial.println("QR factorization of A:");
  Serial.println("Q =");
  Serial.println(qr.get_Q());
  Serial.println("R =");
  Serial.println(qr.get_R());
  Serial.println("solution x =");
  Serial.println(x_solution);
 
  Serial.println("Basic matrix operations");
  Serial.println("-----------------------\n");
  Matrix B = {
    {1, 2},
    {3, 4},
    {5, 6},
  };
  Matrix C = {
    {1, 2, 3},
    {4, 5, 6},
  };
  Matrix D = {
    {10, 11},
    {12, 13},
  };
  Matrix E = C * B + D;
  Serial.println("C×B + D =");
  Serial.println(E);
 
  Serial.println("Basic vector operations");
  Serial.println("-----------------------\n");
  RowVector a = {1, 2, 3};
  RowVector b = {4, 6, 5};
  RowVector c = a.cross(b);
  double d = a.dot(b);
  Serial.print("a   =      ");
  Serial.print(a);
  Serial.print("b   =      ");
  Serial.print(b);
  Serial.print("a×b =      ");
  Serial.print(c);
  Serial.print("a·b =      ");
  Serial.println(d);
  Serial.println();
 
  Serial.println("Element access");
  Serial.println("--------------\n");
  Serial.print("A[2,0] = ");
  Serial.println(A(2, 0));
  //               │  └─ column
  //               └──── row
  Serial.println("A[2,0] ← 100");
  A(2, 0) = 100; // assign a new value to the element
  Serial.println("A =");
  Serial.println(A);
}
 
void loop() {}