LU::LU(int const m, int const n, double const* A)
: m_LU(A, A + m * n),
m_piv(m),
m_pivSign(1),
m_rows(m),
m_cols(n)
{
// Use a "left-looking", dot-product, Crout/Doolittle algorithm.
for (int i = 0; i < m; ++i) {
m_piv[i] = i;
}
std::vector<double> LUcolj(m);
// Outer loop.
for (int j = 0; j < n; ++j) {
// Make a copy of the j-th column to localize references.
for (int i = 0; i < m; ++i) {
LUcolj[i] = m_LU[i * n + j];
}
// Apply previous transformations.
for (int i = 0; i < m; ++i) {
double* LUrowi = &m_LU[i * n];
// Most of the time is spent in the following dot product.
int kmax = std::min(i, j);
double s = 0.0;
for (int k = 0; k < kmax; ++k) {
s += LUrowi[k]*LUcolj[k];
}
LUrowi[j] = LUcolj[i] -= s;
}
// Find pivot and exchange if necessary.
int p = j;
for (int i = j + 1; i < m; ++i) {
if (fabs(LUcolj[i]) > fabs(LUcolj[p])) {
p = i;
}
}
if (p != j) {
for (int k = 0; k < n; k++) {
std::swap(m_LU[p * n + k], m_LU[j * n + k]);
}
std::swap(m_piv[p], m_piv[j]);
m_pivSign = -m_pivSign;
}
// Compute multipliers.
if (j < m && m_LU[j * n + j] != 0.0) {
for (int i = j + 1; i < m; ++i) {
m_LU[i * n + j] /= m_LU[j * n + j];
}
}
}
}
LUDecomposition::LUDecomposition (const Matrix& A) {
// Use a "left-looking", dot-product, Crout/Doolittle algorithm.
LU = A;
m = A.size1();
n = A.size2();
piv = PivotVector(m);
for (int i = 0; i < m; i++) {
piv(i) = i;
}
pivsign = 1;
Vector LUcolj(m);
// Outer loop.
for (int j = 0; j < n; j++) {
// Make a copy of the j-th column to localize references.
for (int i = 0; i < m; i++) {
LUcolj(i) = LU(i,j);
}
// Apply previous transformations.
for (int i = 0; i < m; i++) {
matrix_row<Matrix> LUrowi(LU,i);
// Most of the time is spent in the following dot product.
int kmax = std::min(i,j);
double s = 0.0;
for (int k = 0; k < kmax; k++) {
s += LUrowi(k)*LUcolj(k);
}
LUrowi(j) = LUcolj(i) -= s;
}
// Find pivot and exchange if necessary.
int p = j;
for (int i = j+1; i < m; i++) {
if (std::abs(LUcolj(i)) > std::abs(LUcolj(p))) {
p = i;
}
}
if (p != j) {
for (int k = 0; k < n; k++) {
double t = LU(p,k); LU(p,k) = LU(j,k); LU(j,k) = t;
}
int k = piv(p); piv(p) = piv(j); piv(j) = k;
pivsign = -pivsign;
}
// Compute multipliers.
if (j < m && LU(j,j) != 0.0) {
for (int i = j+1; i < m; i++) {
LU(i,j) /= LU(j,j);
}
}
}
}
