396 lines
7.4 KiB
C++
396 lines
7.4 KiB
C++
/*
|
|
* g++ -O3 -Wall --std=c++11 qr_standalone.cpp -o qr_standalone
|
|
*/
|
|
#include <cstdio>
|
|
#include <cstdlib>
|
|
#include <cstring> // for memset
|
|
#include <limits>
|
|
#include <iostream>
|
|
#include <vector>
|
|
|
|
#include <math.h>
|
|
|
|
class Vector;
|
|
|
|
class Matrix {
|
|
|
|
public:
|
|
// default constructor (don't allocate)
|
|
Matrix() : m(0), n(0), data(nullptr) {}
|
|
|
|
// constructor with memory allocation, initialized to zero
|
|
Matrix(int m_, int n_) : Matrix() {
|
|
m = m_;
|
|
n = n_;
|
|
allocate(m_,n_);
|
|
}
|
|
|
|
// copy constructor
|
|
Matrix(const Matrix& mat) : Matrix(mat.m,mat.n) {
|
|
|
|
for (int i = 0; i < m; i++)
|
|
for (int j = 0; j < n; j++)
|
|
(*this)(i,j) = mat(i,j);
|
|
}
|
|
|
|
// constructor from array
|
|
template<int rows, int cols>
|
|
Matrix(double (&a)[rows][cols]) : Matrix(rows,cols) {
|
|
|
|
for (int i = 0; i < m; i++)
|
|
for (int j = 0; j < n; j++)
|
|
(*this)(i,j) = a[i][j];
|
|
}
|
|
|
|
// destructor
|
|
~Matrix() {
|
|
deallocate();
|
|
}
|
|
|
|
|
|
// access data operators
|
|
double& operator() (int i, int j) {
|
|
return data[i+m*j]; }
|
|
double operator() (int i, int j) const {
|
|
return data[i+m*j]; }
|
|
|
|
// operator assignment
|
|
Matrix& operator=(const Matrix& source) {
|
|
|
|
// self-assignment check
|
|
if (this != &source) {
|
|
if ( (m*n) != (source.m * source.n) ) { // storage cannot be reused
|
|
allocate(source.m,source.n); // re-allocate storage
|
|
}
|
|
// storage can be used, copy data
|
|
std::copy(source.data, source.data + source.m*source.n, data);
|
|
}
|
|
return *this;
|
|
}
|
|
|
|
// compute minor
|
|
void compute_minor(const Matrix& mat, int d) {
|
|
|
|
allocate(mat.m, mat.n);
|
|
|
|
for (int i = 0; i < d; i++)
|
|
(*this)(i,i) = 1.0;
|
|
for (int i = d; i < mat.m; i++)
|
|
for (int j = d; j < mat.n; j++)
|
|
(*this)(i,j) = mat(i,j);
|
|
|
|
}
|
|
|
|
// Matrix multiplication
|
|
// c = a * b
|
|
// c will be re-allocated here
|
|
void mult(const Matrix& a, const Matrix& b) {
|
|
|
|
if (a.n != b.m) {
|
|
std::cerr << "Matrix multiplication not possible, sizes don't match !\n";
|
|
return;
|
|
}
|
|
|
|
// reallocate ourself if necessary i.e. current Matrix has not valid sizes
|
|
if (a.m != m or b.n != n)
|
|
allocate(a.m, b.n);
|
|
|
|
memset(data,0,m*n*sizeof(double));
|
|
|
|
for (int i = 0; i < a.m; i++)
|
|
for (int j = 0; j < b.n; j++)
|
|
for (int k = 0; k < a.n; k++)
|
|
(*this)(i,j) += a(i,k) * b(k,j);
|
|
|
|
}
|
|
|
|
void transpose() {
|
|
for (int i = 0; i < m; i++) {
|
|
for (int j = 0; j < i; j++) {
|
|
double t = (*this)(i,j);
|
|
(*this)(i,j) = (*this)(j,i);
|
|
(*this)(j,i) = t;
|
|
}
|
|
}
|
|
}
|
|
|
|
// take c-th column of m, put in v
|
|
void extract_column(Vector& v, int c);
|
|
|
|
// memory allocation
|
|
void allocate(int m_, int n_) {
|
|
|
|
// if already allocated, memory is freed
|
|
deallocate();
|
|
|
|
// new sizes
|
|
m = m_;
|
|
n = n_;
|
|
|
|
data = new double[m_*n_];
|
|
memset(data,0,m_*n_*sizeof(double));
|
|
|
|
} // allocate
|
|
|
|
// memory free
|
|
void deallocate() {
|
|
|
|
if (data)
|
|
delete[] data;
|
|
|
|
data = nullptr;
|
|
|
|
}
|
|
|
|
int m, n;
|
|
|
|
private:
|
|
double* data;
|
|
|
|
}; // struct Matrix
|
|
|
|
// column vector
|
|
class Vector {
|
|
|
|
public:
|
|
// default constructor (don't allocate)
|
|
Vector() : size(0), data(nullptr) {}
|
|
|
|
// constructor with memory allocation, initialized to zero
|
|
Vector(int size_) : Vector() {
|
|
size = size_;
|
|
allocate(size_);
|
|
}
|
|
|
|
// destructor
|
|
~Vector() {
|
|
deallocate();
|
|
}
|
|
|
|
// access data operators
|
|
double& operator() (int i) {
|
|
return data[i]; }
|
|
double operator() (int i) const {
|
|
return data[i]; }
|
|
|
|
// operator assignment
|
|
Vector& operator=(const Vector& source) {
|
|
|
|
// self-assignment check
|
|
if (this != &source) {
|
|
if ( size != (source.size) ) { // storage cannot be reused
|
|
allocate(source.size); // re-allocate storage
|
|
}
|
|
// storage can be used, copy data
|
|
std::copy(source.data, source.data + source.size, data);
|
|
}
|
|
return *this;
|
|
}
|
|
|
|
// memory allocation
|
|
void allocate(int size_) {
|
|
|
|
deallocate();
|
|
|
|
// new sizes
|
|
size = size_;
|
|
|
|
data = new double[size_];
|
|
memset(data,0,size_*sizeof(double));
|
|
|
|
} // allocate
|
|
|
|
// memory free
|
|
void deallocate() {
|
|
|
|
if (data)
|
|
delete[] data;
|
|
|
|
data = nullptr;
|
|
|
|
}
|
|
|
|
// ||x||
|
|
double norm() {
|
|
double sum = 0;
|
|
for (int i = 0; i < size; i++) sum += (*this)(i) * (*this)(i);
|
|
return sqrt(sum);
|
|
}
|
|
|
|
// divide data by factor
|
|
void rescale(double factor) {
|
|
for (int i = 0; i < size; i++) (*this)(i) /= factor;
|
|
}
|
|
|
|
void rescale_unit() {
|
|
double factor = norm();
|
|
rescale(factor);
|
|
}
|
|
|
|
int size;
|
|
|
|
private:
|
|
double* data;
|
|
|
|
}; // class Vector
|
|
|
|
// c = a + b * s
|
|
void vmadd(const Vector& a, const Vector& b, double s, Vector& c)
|
|
{
|
|
if (c.size != a.size or c.size != b.size) {
|
|
std::cerr << "[vmadd]: vector sizes don't match\n";
|
|
return;
|
|
}
|
|
|
|
for (int i = 0; i < c.size; i++)
|
|
c(i) = a(i) + s * b(i);
|
|
}
|
|
|
|
// mat = I - 2*v*v^T
|
|
// !!! m is allocated here !!!
|
|
void compute_householder_factor(Matrix& mat, const Vector& v)
|
|
{
|
|
|
|
int n = v.size;
|
|
mat.allocate(n,n);
|
|
for (int i = 0; i < n; i++)
|
|
for (int j = 0; j < n; j++)
|
|
mat(i,j) = -2 * v(i) * v(j);
|
|
for (int i = 0; i < n; i++)
|
|
mat(i,i) += 1;
|
|
}
|
|
|
|
// take c-th column of a matrix, put results in Vector v
|
|
void Matrix::extract_column(Vector& v, int c) {
|
|
if (m != v.size) {
|
|
std::cerr << "[Matrix::extract_column]: Matrix and Vector sizes don't match\n";
|
|
return;
|
|
}
|
|
|
|
for (int i = 0; i < m; i++)
|
|
v(i) = (*this)(i,c);
|
|
}
|
|
|
|
void matrix_show(const Matrix& m, const std::string& str="")
|
|
{
|
|
std::cout << str << "\n";
|
|
for(int i = 0; i < m.m; i++) {
|
|
for (int j = 0; j < m.n; j++) {
|
|
printf(" %8.3f", m(i,j));
|
|
}
|
|
printf("\n");
|
|
}
|
|
printf("\n");
|
|
}
|
|
|
|
// L2-norm ||A-B||^2
|
|
double matrix_compare(const Matrix& A, const Matrix& B) {
|
|
// matrices must have same size
|
|
if (A.m != B.m or A.n != B.n)
|
|
return std::numeric_limits<double>::max();
|
|
|
|
double res=0;
|
|
for(int i = 0; i < A.m; i++) {
|
|
for (int j = 0; j < A.n; j++) {
|
|
res += (A(i,j)-B(i,j)) * (A(i,j)-B(i,j));
|
|
}
|
|
}
|
|
|
|
res /= A.m*A.n;
|
|
return res;
|
|
}
|
|
|
|
void householder(Matrix& mat,
|
|
Matrix& R,
|
|
Matrix& Q)
|
|
{
|
|
|
|
int m = mat.m;
|
|
int n = mat.n;
|
|
|
|
// array of factor Q1, Q2, ... Qm
|
|
std::vector<Matrix> qv(m);
|
|
|
|
// temp array
|
|
Matrix z(mat);
|
|
Matrix z1;
|
|
|
|
for (int k = 0; k < n && k < m - 1; k++) {
|
|
|
|
Vector e(m), x(m);
|
|
double a;
|
|
|
|
// compute minor
|
|
z1.compute_minor(z, k);
|
|
|
|
// extract k-th column into x
|
|
z1.extract_column(x, k);
|
|
|
|
a = x.norm();
|
|
if (mat(k,k) > 0) a = -a;
|
|
|
|
for (int i = 0; i < e.size; i++)
|
|
e(i) = (i == k) ? 1 : 0;
|
|
|
|
// e = x + a*e
|
|
vmadd(x, e, a, e);
|
|
|
|
// e = e / ||e||
|
|
e.rescale_unit();
|
|
|
|
// qv[k] = I - 2 *e*e^T
|
|
compute_householder_factor(qv[k], e);
|
|
|
|
// z = qv[k] * z1
|
|
z.mult(qv[k], z1);
|
|
|
|
}
|
|
|
|
Q = qv[0];
|
|
|
|
// after this loop, we will obtain Q (up to a transpose operation)
|
|
for (int i = 1; i < n && i < m - 1; i++) {
|
|
|
|
z1.mult(qv[i], Q);
|
|
Q = z1;
|
|
|
|
}
|
|
|
|
R.mult(Q, mat);
|
|
Q.transpose();
|
|
}
|
|
|
|
double in[][3] = {
|
|
{ 12, -51, 4},
|
|
{ 6, 167, -68},
|
|
{ -4, 24, -41},
|
|
{ -1, 1, 0},
|
|
{ 2, 0, 3},
|
|
};
|
|
|
|
int main()
|
|
{
|
|
Matrix A(in);
|
|
Matrix Q, R;
|
|
|
|
matrix_show(A,"A");
|
|
|
|
// compute QR decompostion
|
|
householder(A, R, Q);
|
|
|
|
matrix_show(Q,"Q");
|
|
matrix_show(R,"R");
|
|
|
|
// compare Q*R to the original matrix A
|
|
Matrix A_check;
|
|
A_check.mult(Q, R);
|
|
|
|
// compute L2 norm ||A-A_check||^2
|
|
double l2 = matrix_compare(A,A_check);
|
|
|
|
// display Q*R
|
|
matrix_show(A_check, l2 < 1e-12 ? "A == Q * R ? yes" : "A == Q * R ? no");
|
|
|
|
return EXIT_SUCCESS;
|
|
}
|