mmathlib/matrix.hpp

#pragma once
#include "cnumber.hpp"
#include "vector.hpp"
#include <cstdint>
#include <iostream>
#include <ostream>
#include <sstream>
#include <string>
class matrix {
private:
  uint64_t num_entries;
  uint64_t entry_dimension;
  vector *entries;
  bool err;
  bool augmented = false;
  // recursive determinant
  const cnumber rdeterminant(matrix m) const {
    if (m.get_num_entries() == 2) {
      cnumber dsum(1, 0);
      cnumber osum(1, 0);
      vector diag = m.get_diagonal();
      vector odiag = m.get_off_diagonal();
      for (uint64_t i = 0; i < diag.get_dimention(); i++) {
        dsum = dsum * diag[i];
        osum = osum * odiag[i];
      }
      return dsum - osum;
    } else {
      cnumber sum = 0;
      cnumber sign(1);
      for (uint64_t i = 0; i < m.entry_dimension; i++) {
        matrix n = m.remove_first_row_and_column(i);
	if(i % 2 == 0)
		sum = sum + (m[0][i] * rdeterminant(n));
	else
		sum = sum - (m[0][i] * rdeterminant(n));
      }
      return sum;
    }
  }

public:
  // Constructors/destructor
  matrix(const uint64_t num_entries, const uint64_t entry_dimension) {
    this->num_entries = entry_dimension;
    this->entry_dimension = num_entries;
    this->err = false;
    this->entries = (vector *)malloc(sizeof(vector) * this->num_entries);
    for (uint64_t i = 0; i < entry_dimension; i++) {
      this->entries[i] = vector(this->entry_dimension);
    }
  }
  matrix(const matrix &m) {
    this->num_entries = m.num_entries;
    this->entry_dimension = m.entry_dimension;
    this->err = m.err;
    this->entries = (vector *)malloc(sizeof(vector) * m.num_entries);
    for (uint64_t i = 0; i < m.num_entries; i++) {
      this->entries[i] = m[i];
    }
  }
  ~matrix() {
    this->num_entries = 0;
    this->entry_dimension = 0;
    free(this->entries);
    this->entries = NULL;
    this->err = true;
  }
  // member functions
  const matrix add_row(uint64_t i, uint64_t j, cnumber multiplier = 1) {
    // add row i to row j
    matrix m = *this;
    m[j] = m[j] + (m.multiply_row(i, multiplier)[i]);
    return m;
  }
  const matrix augment(vector v) const {
    matrix m = *this;
    if (v.get_dimention() != this->get_num_entries()) {
      m.err = true;
      return m;
    }
    for (uint64_t i = 0; i < m.get_num_entries(); i++) {
      vector old = m[i];
      vector n(old.get_dimention() + 1);
      for (uint64_t j = 0; j < old.get_dimention(); j++)
        n[j] = old[j];
      n[old.get_dimention()] = v[i];
      m[i] = n;
    }
    m.entry_dimension = m.entry_dimension + 1;
    m.augmented = true;
    return m;
  }
  const matrix conjugate() const {
    matrix n = matrix(this->num_entries, this->entry_dimension);
    for (uint64_t i = 0; i < this->num_entries; i++) {
      for (uint64_t j = 0; j < this->entry_dimension; j++) {
        n[i][j] = this->entries[i][j].conjugate();
      }
    }

    return n;
  }
  const cnumber determinant() const {
    if (this->num_entries != this->entry_dimension)
      return 0;
    return rdeterminant(*this);
  }
  // switch row i with row j
  const matrix exchange_row(uint64_t i, uint64_t j) {
    matrix m = *this;
    vector v = m.get_entry(i);
    m[i] = m[j];
    m[j] = v;
    return m;
  }
  const vector get_column(uint64_t index) const {
    vector v(this->entry_dimension);
    for (uint64_t j = 0; j < this->entry_dimension; j++) {
      v[j] = this->entries[j][index];
    }
    return v;
  }

  const vector get_diagonal() const {
    uint64_t diag_len = this->entry_dimension;
    if (this->num_entries < diag_len) {
      diag_len = this->num_entries;
    }
    vector v(diag_len);
    for (uint64_t i = 0; i < this->num_entries; i++) {
      for (uint64_t j = 0; j < this->entry_dimension; j++) {
        if (i == j) {
          v[i] = this->entries[i][j];
        }
      }
    }
    return v;
  }
  const matrix get_echelon() const {
    matrix m = *this;
    if (!m.is_invertible()) {
      m.err = true;
    } else {
      uint64_t num_entries = m.get_num_entries();
      for (uint64_t i = 0; i < num_entries - 1; i++) {
        for (uint64_t j = i; j < num_entries; j++) {
          cnumber ratio = m[j][i] / m[i][i];
          for (uint64_t k = i; k < num_entries; k++) {
            m[j][k] = m[j][k] - (ratio * m[i][k]);
          }
        }
      }
    }
    return m;
  }
  // FIXME: This is very dumb
  const vector get_eigenvalues() const {
    if (this->is_diagonal())
      return this->get_diagonal();
    return vector(0);
  }
  const vector get_entry(uint64_t index) const { return this->entries[index]; }
  const uint64_t get_entry_dimension() const { return this->entry_dimension; }
  const uint64_t get_num_entries() const { return this->num_entries; }
  const vector get_off_diagonal() const {
    return this->rotate().get_diagonal();
  }
  const matrix hermitian_conjugate() const {
    return this->transpose().conjugate();
  }
  const matrix I() const {
    matrix m = matrix(this->num_entries, this->entry_dimension);
    for (uint64_t i = 0; i < this->num_entries; i++) {
      for (uint64_t j = 0; j < this->entry_dimension; j++) {
        if (i == j) {
          m[i][j] = cnumber(1, 0);
        } else {
          m[i][j] = 0;
        }
      }
    }
    return m;
  }
  const bool is_broken() const { return this->err; }
  const bool is_diagonal() const {
    bool result = true;
    if (this->num_entries != this->entry_dimension)
      return !result;
    for (uint64_t i = 0; i < this->num_entries; i++) {
      for (uint64_t j = 0; j < this->num_entries; j++) {
        if (i != j && this->entries[i][j] != 0)
          return !result;
      }
    }
    return result;
  }
  const bool is_eigenvalue(cnumber z) const {
    return ((*this - (this->I() * z)).determinant() == 0);
  }
  const bool is_hermitian() const {
    if (this->entry_dimension != this->num_entries)
      return false;
    return *this == this->hermitian_conjugate();
  }
  const bool is_invertible() const { return this->determinant() != 0; }
  const bool is_unitary() const {
    matrix m = this->hermitian_conjugate();
    return (*this * m == this->I());
  }
  // Multiply row by z
  const matrix multiply_row(uint64_t i, cnumber z) {
    matrix m = *this;
    m[i] = m[i] * z;
    return m;
  }

  // subtract row i from row j
  const matrix subtract_row(uint64_t i, uint64_t j, cnumber multiplier = 1) {
    matrix m = *this;
    m[j] = m[j] - (m.multiply_row(i, multiplier)[i]);
    return m;
  }

  const matrix remove_first_row_and_column(uint64_t column) const {
    matrix m(this->num_entries - 1, this->entry_dimension - 1);
    uint64_t add = 0;
    for (uint64_t i = 1; i < this->num_entries; i++) {
      for (uint64_t j = 0; j < this->entry_dimension; j++) {
        if (j != column) {
          m[i - 1][j - add] = this->get_entry(i)[j];
        } else {
          add = 1;
        }
      }
      add = 0;
    }
    return m;
  }
  const matrix rotate() const {
    matrix m = this->transpose();
    matrix n = matrix(m.entry_dimension, m.num_entries);
    for (uint64_t i = 0; i < m.entry_dimension; i++) {
      int index = m.num_entries - i - 1;
      n[i] = m[index];
    }
    return n;
  }
  const matrix transpose() const {
    matrix n = matrix(this->entry_dimension, this->num_entries);
    for (uint64_t i = 0; i < this->num_entries; i++) {
      for (uint64_t j = 0; j < this->entry_dimension; j++) {
        n[j][i] = this->entries[i][j];
      }
    }

    return n;
  }
  // Operators
  friend std::ostream &operator<<(std::ostream &os, const matrix &m) {
    char last = '\0';
    int longest = 0;
    for (uint64_t i = 0; i < m.num_entries; i++) {
      for (uint64_t j = 0; j < m.entry_dimension; j++) {
        std::ostringstream oss;
        oss << m.entries[i][j];
        std::string s = oss.str();
        if (longest < s.length())
          longest = s.length();
      }
    }
    for (uint64_t i = 0; i < m.num_entries; i++) {
      for (uint64_t j = 0; j < m.entry_dimension; j++) {
        std::ostringstream iss;
        iss << m.entries[i][j];
        std::string s = iss.str();
        int padding = longest - s.length() + 1;
        std::string symbols[3];
        symbols[0] = "|";
        std::ostringstream oss;
        oss << m.entries[i][j];
        oss << std::setw(padding) << "|";
        symbols[1] = oss.str();
        symbols[2] = "|";
        bool print = true;
        for (int k = 0; k < 3; k++) {
          int len = symbols[k].length() - 1;
          char cur = symbols[k][0];
          if (cur != last ||
              (m.augmented && j == m[i].get_dimention() - 1 && print)) {
            print = false;
            os << symbols[k];
          }
          last = symbols[k][len];
        }
      }
      if (i != m.num_entries - 1)
        os << std::endl << "|";
    }
    return os;
  }
  const bool operator==(const matrix &m) const {
    bool equal = true;
    for (uint64_t i = 0; i < this->num_entries; i++) {
      for (uint64_t j = 0; j < this->entry_dimension; j++) {
        if (this->entries[i][j] != m[i][j]) {
          equal = false;
        }
      }
    }
    return equal;
  }
  vector &operator[](const uint64_t index) { return this->entries[index]; }
  const vector operator[](const uint64_t index) const {
    return this->entries[index];
  }
  const matrix operator*(const cnumber z) const {
    matrix n(this->num_entries, this->entry_dimension);
    for (uint64_t i = 0; i < this->num_entries; i++) {
      n[i] = this->entries[i] * z;
    }

    return n;
  }

  const matrix operator*(vector &v) const {
    matrix res(this->get_num_entries(), this->get_entry_dimension());
    for (uint64_t i = 0; i < this->get_num_entries(); i++) {
      for (uint64_t j = 0; j < this->get_entry_dimension(); j++) {
        res[i][j] = (this->get_entry(i)[j] * v.get_entry(i));
      }
    }

    return res;
  }
  const matrix operator*(const matrix m) const {
    matrix n(this->num_entries, m.entry_dimension);
    if (this->num_entries != m.entry_dimension &&
        m.num_entries != this->entry_dimension) {
      n.err = true;
      return n;
    }
    for (uint64_t i = 0; i < this->entry_dimension; i++) {
      for (uint64_t j = 0; j < this->entry_dimension; j++) {
        n[i][j] = this->get_entry(i) * m.get_column(j);
      }
    }

    return n;
  }

  const matrix operator+(const matrix &m) const {
    matrix n(this->num_entries, this->entry_dimension);
    for (uint64_t i = 0; i < this->num_entries; i++) {
      n[i] = this->entries[i] + m[i];
    }

    return n;
  }
  const matrix operator-(const matrix &m) const {
    matrix n(this->num_entries, this->entry_dimension);
    for (uint64_t i = 0; i < this->num_entries; i++) {
      n[i] = this->entries[i] - m[i];
    }

    return n;
  }
  void operator=(const matrix &m) {
    this->num_entries = m.num_entries;
    this->entry_dimension = m.entry_dimension;
    this->err = m.err;
    free(this->entries);
    this->entries = (vector *)malloc(sizeof(vector) * m.num_entries);
    for (uint64_t i = 0; i < m.num_entries; i++)
      this->entries[i] = m[i];
  }
};