Basic Operators and Functions for Vectors

Basically, operators and functions for vectors operate element-wise.

Basic operators for vectors

The basic operators +, -, *, and / work for vectors of variables and expressions. The following example demonstrates how these operators work for a vector of size 3:

#include "qbpp.hpp"

int main() {
  auto x = qbpp::var("x", 3);
  auto y = qbpp::var("y", 3);
  auto f = 6 * -(x + 1) * (y - 1);
  auto g = f / 3;
  std::cout << "f = " << f << std::endl;
  for (size_t i = 0; i < x.size(); ++i) {
    std::cout << "f[" << i << "] = " << f[i] << std::endl;
  }
  std::cout << "g = " << g << std::endl;
  for (size_t i = 0; i < x.size(); ++i) {
    std::cout << "g[" << i << "] = " << g[i] << std::endl;
  }
}

This program produces the following output:

Variable Limit: 1000/1000 (CPU/GPU)
f = {6 -6*x[0]*y[0] +6*x[0] -6*y[0],6 -6*x[1]*y[1] +6*x[1] -6*y[1],6 -6*x[2]*y[2] +6*x[2] -6*y[2]}
f[0] = 6 -6*x[0]*y[0] +6*x[0] -6*y[0]
f[1] = 6 -6*x[1]*y[1] +6*x[1] -6*y[1]
f[2] = 6 -6*x[2]*y[2] +6*x[2] -6*y[2]
g = {2 -2*x[0]*y[0] +2*x[0] -2*y[0],2 -2*x[1]*y[1] +2*x[1] -2*y[1],2 -2*x[2]*y[2] +2*x[2] -2*y[2]}
g[0] = 2 -2*x[0]*y[0] +2*x[0] -2*y[0]
g[1] = 2 -2*x[1]*y[1] +2*x[1] -2*y[1]
g[2] = 2 -2*x[2]*y[2] +2*x[2] -2*y[2]

Compound opertors for vectors

Similarly, the compound operators +=, -=, *=, and /= work for vectors of variables and expressions. The following example demonstrates how these operators work for a vector of size 3:

#include "qbpp.hpp"

int main() {
  auto x = qbpp::var("x", 3);
  auto y = qbpp::var("y", 3);
  auto f = 6 * x + 4;
  f += 3 * y;
  std::cout << "f = " << f << std::endl;
  f -= 12;
  std::cout << "f = " << f << std::endl;
  f *= 2 * y;
  std::cout << "f = " << f << std::endl;
  f /= 2;
  std::cout << "f = " << f << std::endl;
}

This program produces the following output:

f = {4 +6*x[0] +3*y[0],4 +6*x[1] +3*y[1],4 +6*x[2] +3*y[2]}
f = {-8 +6*x[0] +3*y[0],-8 +6*x[1] +3*y[1],-8 +6*x[2] +3*y[2]}
f = {12*x[0]*y[0] +6*y[0]*y[0] -16*y[0],12*x[1]*y[1] +6*y[1]*y[1] -16*y[1],12*x[2]*y[2] +6*y[2]*y[2] -16*y[2]}
f = {6*x[0]*y[0] +3*y[0]*y[0] -8*y[0],6*x[1]*y[1] +3*y[1]*y[1] -8*y[1],6*x[2]*y[2] +3*y[2]*y[2] -8*y[2]}

Square functions for vectors

Square functions also work for vectors, as demonstrated below:

#include "qbpp.hpp"

int main() {
  auto x = qbpp::var("x", 3);
  auto f = x + 1;
  std::cout << "f = " << qbpp::sqr(f) << std::endl;
  std::cout << "f = " << f << std::endl;
  f.sqr();
  std::cout << "f = " << f << std::endl;
}

This program produces the following output:

f = {1 +x[0]*x[0] +x[0] +x[0],1 +x[1]*x[1] +x[1] +x[1],1 +x[2]*x[2] +x[2] +x[2]}
f = {1 +x[0],1 +x[1],1 +x[2]}
f = {1 +x[0]*x[0] +x[0] +x[0],1 +x[1]*x[1] +x[1] +x[1],1 +x[2]*x[2] +x[2] +x[2]}

Simplfy functions for vectors

Simplify functions also work for vectors, as demonstrated below:

#include "qbpp.hpp"

int main() {
  auto x = qbpp::var("x", 3);
  auto f = qbpp::sqr(x - 1);
  std::cout << "f = " << f << std::endl;
  std::cout << "simplified(f) = " << qbpp::simplify(f) << std::endl;
  std::cout << "simplified_as_binary(f) = " << qbpp::simplify_as_binary(f)
            << std::endl;
  std::cout << "simplified_as_spin(f) = " << qbpp::simplify_as_spin(f)
            << std::endl;
}

This program produces the following output:

f = {1 +x[0]*x[0] -x[0] -x[0],1 +x[1]*x[1] -x[1] -x[1],1 +x[2]*x[2] -x[2] -x[2]}
simplified(f) = {1 -2*x[0] +x[0]*x[0],1 -2*x[1] +x[1]*x[1],1 -2*x[2] +x[2]*x[2]}
simplified_as_binary(f) = {1 -x[0],1 -x[1],1 -x[2]}
simplified_as_spin(f) = {2 -2*x[0],2 -2*x[1],2 -2*x[2]}

NOTE These operators and functions also work for multi-dimensional arrays.