169 jassert (n == n && n == b.rows && b.isOneColumnVector());
171 auto* x = b.getRawDataPointer();
172 const auto& A = *
this;
178 auto denominator = A (0,0);
180 if (denominator == 0)
183 b (0, 0) /= denominator;
189 auto denominator = A (0, 0) * A (1, 1) - A (0, 1) * A (1, 0);
191 if (denominator == 0)
194 auto factor = (1 / denominator);
195 auto b0 = x[0], b1 = x[1];
197 x[0] = factor * (A (1, 1) * b0 - A (0, 1) * b1);
198 x[1] = factor * (A (0, 0) * b1 - A (1, 0) * b0);
204 auto denominator = A (0, 0) * (A (1, 1) * A (2, 2) - A (1, 2) * A (2, 1))
205 + A (0, 1) * (A (1, 2) * A (2, 0) - A (1, 0) * A (2, 2))
206 + A (0, 2) * (A (1, 0) * A (2, 1) - A (1, 1) * A (2, 0));
208 if (denominator == 0)
211 auto factor = 1 / denominator;
212 auto b0 = x[0], b1 = x[1], b2 = x[2];
214 x[0] = ( ( A (0, 1) * A (1, 2) - A (0, 2) * A (1, 1)) * b2
215 + (-A (0, 1) * A (2, 2) + A (0, 2) * A (2, 1)) * b1
216 + ( A (1, 1) * A (2, 2) - A (1, 2) * A (2, 1)) * b0) * factor;
218 x[1] = -( ( A (0, 0) * A (1, 2) - A (0, 2) * A (1, 0)) * b2
219 + (-A (0, 0) * A (2, 2) + A (0, 2) * A (2, 0)) * b1
220 + ( A (1, 0) * A (2, 2) - A (1, 2) * A (2, 0)) * b0) * factor;
222 x[2] = ( ( A (0, 0) * A (1, 1) - A (0, 1) * A (1, 0)) * b2
223 + (-A (0, 0) * A (2, 1) + A (0, 1) * A (2, 0)) * b1
224 + ( A (1, 0) * A (2, 1) - A (1, 1) * A (2, 0)) * b0) * factor;
233 for (
size_t j = 0; j < n; ++j)
238 while (i < n && M (i, j) == 0)
244 for (
size_t k = 0; k < n; ++k)
245 M (j, k) += M (i, k);
250 auto t = 1 / M (j, j);
252 for (
size_t k = 0; k < n; ++k)
257 for (
size_t k = j + 1; k < n; ++k)
261 for (
size_t l = 0; l < n; ++l)
262 M (k, l) += u * M (j, l);
268 for (
int k =
static_cast<int> (n) - 2; k >= 0; --k)
269 for (
size_t i =
static_cast<size_t> (k) + 1; i < n; ++i)
270 x[k] -= M (
static_cast<size_t> (k), i) * x[i];