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186 | 186 | This uses u-substitution: since `1/x = d/dx(ln(x))`, the integral becomes |
187 | 187 | `∫ h'(x)/h(x) dx = ln|h(x)|`. |
188 | 188 |
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| 189 | +- **Matrix Decompositions**: Added four matrix decomposition functions for |
| 190 | + numerical linear algebra: |
| 191 | + - `LUDecomposition(A)` → `[P, L, U]` - LU factorization with partial pivoting |
| 192 | + - `QRDecomposition(A)` → `[Q, R]` - QR factorization using Householder reflections |
| 193 | + - `CholeskyDecomposition(A)` → `L` - Cholesky factorization for positive definite matrices |
| 194 | + - `SVD(A)` → `[U, Σ, V]` - Singular Value Decomposition |
| 195 | + |
| 196 | + ```javascript |
| 197 | + ce.box(['LUDecomposition', [[4, 3], [6, 3]]]).evaluate(); |
| 198 | + // → [P, L, U] where PA = LU |
| 199 | + |
| 200 | + ce.box(['QRDecomposition', [[1, 2], [3, 4]]]).evaluate(); |
| 201 | + // → [Q, R] where A = QR, Q orthogonal, R upper triangular |
| 202 | + |
| 203 | + ce.box(['CholeskyDecomposition', [[4, 2], [2, 2]]]).evaluate(); |
| 204 | + // → L where A = LL^T |
| 205 | + |
| 206 | + ce.box(['SVD', [[1, 2], [3, 4]]]).evaluate(); |
| 207 | + // → [U, Σ, V] where A = UΣV^T |
| 208 | + ``` |
| 209 | + This uses u-substitution: since `1/x = d/dx(ln(x))`, the integral becomes |
| 210 | + `∫ h'(x)/h(x) dx = ln|h(x)|`. |
| 211 | + |
189 | 212 | - **Multi-Argument Function Derivatives**: Added derivative support for: |
190 | 213 |
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191 | 214 | - **Log(x, base)** - Logarithm with custom base: |
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