166 jassert (n == n && n == b.rows && b.isOneColumnVector());
168 auto* x = b.getRawDataPointer();
169 const auto& A = *
this;
175 auto denominator = A (0,0);
177 if (approximatelyEqual (denominator, (ElementType) 0))
180 b (0, 0) /= denominator;
186 auto denominator = A (0, 0) * A (1, 1) - A (0, 1) * A (1, 0);
188 if (approximatelyEqual (denominator, (ElementType) 0))
191 auto factor = (1 / denominator);
192 auto b0 = x[0], b1 = x[1];
194 x[0] = factor * (A (1, 1) * b0 - A (0, 1) * b1);
195 x[1] = factor * (A (0, 0) * b1 - A (1, 0) * b0);
201 auto denominator = A (0, 0) * (A (1, 1) * A (2, 2) - A (1, 2) * A (2, 1))
202 + A (0, 1) * (A (1, 2) * A (2, 0) - A (1, 0) * A (2, 2))
203 + A (0, 2) * (A (1, 0) * A (2, 1) - A (1, 1) * A (2, 0));
205 if (approximatelyEqual (denominator, (ElementType) 0))
208 auto factor = 1 / denominator;
209 auto b0 = x[0], b1 = x[1], b2 = x[2];
211 x[0] = ( ( A (0, 1) * A (1, 2) - A (0, 2) * A (1, 1)) * b2
212 + (-A (0, 1) * A (2, 2) + A (0, 2) * A (2, 1)) * b1
213 + ( A (1, 1) * A (2, 2) - A (1, 2) * A (2, 1)) * b0) * factor;
215 x[1] = -( ( A (0, 0) * A (1, 2) - A (0, 2) * A (1, 0)) * b2
216 + (-A (0, 0) * A (2, 2) + A (0, 2) * A (2, 0)) * b1
217 + ( A (1, 0) * A (2, 2) - A (1, 2) * A (2, 0)) * b0) * factor;
219 x[2] = ( ( A (0, 0) * A (1, 1) - A (0, 1) * A (1, 0)) * b2
220 + (-A (0, 0) * A (2, 1) + A (0, 1) * A (2, 0)) * b1
221 + ( A (1, 0) * A (2, 1) - A (1, 1) * A (2, 0)) * b0) * factor;
230 for (
size_t j = 0; j < n; ++j)
232 if (approximatelyEqual (M (j, j), (ElementType) 0))
235 while (i < n && approximatelyEqual (M (i, j), (ElementType) 0))
241 for (
size_t k = 0; k < n; ++k)
242 M (j, k) += M (i, k);
247 auto t = 1 / M (j, j);
249 for (
size_t k = 0; k < n; ++k)
254 for (
size_t k = j + 1; k < n; ++k)
258 for (
size_t l = 0; l < n; ++l)
259 M (k, l) += u * M (j, l);
265 for (
int k =
static_cast<int> (n) - 2; k >= 0; --k)
266 for (
size_t i =
static_cast<size_t> (k) + 1; i < n; ++i)
267 x[k] -= M (
static_cast<size_t> (k), i) * x[i];