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#include "qr.hpp"
#include <cmath>
#include <sstream>
#include "linalg_error.hpp"
namespace linalg {
namespace {
void require_tall(const Matrix& A, const char* name) {
if (A.rows() < A.cols()) {
std::ostringstream oss;
oss << name << " requires rows >= cols, got " << A.rows() << "x" << A.cols();
throw DimensionMismatchError(oss.str());
}
}
double col_norm(const Matrix& M, std::size_t j) {
double s = 0.0;
for (std::size_t i = 0; i < M.rows(); ++i) {
s += M(i, j) * M(i, j);
}
return std::sqrt(s);
}
double col_dot(const Matrix& M, std::size_t j, const Matrix& N, std::size_t k) {
double s = 0.0;
for (std::size_t i = 0; i < M.rows(); ++i) {
s += M(i, j) * N(i, k);
}
return s;
}
} // namespace
// --- Gram-Schmidt ---
QRResult qr_classical_gs(const Matrix& A, double zero_tolerance) {
require_tall(A, "qr_classical_gs");
const std::size_t m = A.rows();
const std::size_t n = A.cols();
Matrix Q = Matrix::zeros(m, n);
Matrix R = Matrix::zeros(n, n);
for (std::size_t j = 0; j < n; ++j) {
for (std::size_t i = 0; i < m; ++i) Q(i, j) = A(i, j);
for (std::size_t k = 0; k < j; ++k) {
R(k, j) = col_dot(A, j, Q, k); // <a_j, q_k>
for (std::size_t i = 0; i < m; ++i) {
Q(i, j) -= R(k, j) * Q(i, k);
}
}
const double norm = col_norm(Q, j);
if (norm <= zero_tolerance) {
std::ostringstream oss;
oss << "qr_classical_gs: column " << j
<< " is (nearly) linearly dependent (norm = " << norm << ")";
throw SingularMatrixError(oss.str());
}
R(j, j) = norm;
for (std::size_t i = 0; i < m; ++i) Q(i, j) /= norm;
}
return QRResult{std::move(Q), std::move(R)};
}
// --- Modified Gram-Schmidt ---
QRResult qr_modified_gs(const Matrix& A, double zero_tolerance) {
require_tall(A, "qr_modified_gs");
const std::size_t m = A.rows();
const std::size_t n = A.cols();
Matrix Q = Matrix::zeros(m, n);
Matrix R = Matrix::zeros(n, n);
for (std::size_t j = 0; j < n; ++j) {
for (std::size_t i = 0; i < m; ++i) Q(i, j) = A(i, j);
for (std::size_t k = 0; k < j; ++k) {
R(k, j) = col_dot(Q, j, Q, k); // <v_running, q_k>
for (std::size_t i = 0; i < m; ++i) {
Q(i, j) -= R(k, j) * Q(i, k);
}
}
const double norm = col_norm(Q, j);
if (norm <= zero_tolerance) {
std::ostringstream oss;
oss << "qr_modified_gs: column " << j
<< " is (nearly) linearly dependent (norm = " << norm << ")";
throw SingularMatrixError(oss.str());
}
R(j, j) = norm;
for (std::size_t i = 0; i < m; ++i) Q(i, j) /= norm;
}
return QRResult{std::move(Q), std::move(R)};
}
// --- Householder QR ---
QRResult qr_householder(const Matrix& A) {
require_tall(A, "qr_householder");
const std::size_t m = A.rows();
const std::size_t n = A.cols();
// Will become R.
Matrix work = A;
Matrix Q_full = Matrix::identity(m);
for (std::size_t k = 0; k < n; ++k) {
const std::size_t p = m - k; // length of the subvector
std::vector<double> u(p);
for (std::size_t i = 0; i < p; ++i) u[i] = work(k + i, k);
const double x_norm = [&] {
double s = 0.0;
for (double v : u) s += v * v;
return std::sqrt(s);
}();
if (x_norm == 0.0) continue;
const double sigma = (u[0] >= 0.0 ? 1.0 : -1.0) * x_norm;
u[0] += sigma;
const double utu = [&] {
double s = 0.0;
for (double v : u) s += v * v;
return s;
}();
const double tau = 2.0 / utu;
// Apply H_k to work[k:, k:n]
for (std::size_t j = k; j < n; ++j) {
double dot = 0.0;
for (std::size_t i = 0; i < p; ++i) dot += u[i] * work(k + i, j);
const double coeff = tau * dot;
for (std::size_t i = 0; i < p; ++i) work(k + i, j) -= coeff * u[i];
}
// Apply H_k to Q_full[k:, 0:m]
for (std::size_t j = 0; j < m; ++j) {
double dot = 0.0;
for (std::size_t i = 0; i < p; ++i) dot += u[i] * Q_full(k + i, j);
const double coeff = tau * dot;
for (std::size_t i = 0; i < p; ++i) Q_full(k + i, j) -= coeff * u[i];
}
}
Matrix Q(m, n);
for (std::size_t i = 0; i < m; ++i)
for (std::size_t j = 0; j < n; ++j)
Q(i, j) = Q_full(j, i);
Matrix R(n, n);
for (std::size_t i = 0; i < n; ++i)
for (std::size_t j = 0; j < n; ++j)
R(i, j) = work(i, j);
return QRResult{std::move(Q), std::move(R)};
}
} // namespace linalg
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