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@TYEclipse TYEclipse released this 02 Oct 21:52
· 1 commit to main since this release
v0.2.0
86cb3f7

dsh-linalg v0.2.0

Two user-visible additions on top of v0.1.3 — no breaking changes.

New tool: matrix_eigen

Eigen-decomposition of a real symmetric matrix (cyclic Jacobi method, full double precision):

  • all eigenvalues in descending order + a matching unit eigenvector per eigenvalue
  • deterministic sign convention: the leading non-zero component of each eigenvector is positive
  • maxResidual — the largest |A·v − λ·v| entry actually measured, reported so accuracy is visible instead of assumed
  • traceSum — sum of the eigenvalues, equal to the trace (self-check in every reply)
  • non-square / non-symmetric input and non-convergence are errors, never a guessed spectrum

matrix_compute gains two operations

  • rank — rank via reduced row echelon form (rectangular input allowed)
  • power — integer matrix power by binary exponentiation; exponent takes −64…64, negative exponents invert first (clean failure on singular input), 0 gives the identity

Quality

  • every numeric expectation in the tests is produced by the independent oracle test/oracle/anchors.py (exact fractions arithmetic for det/inverse/rref/rank/power, closed-form spectra — 2 − 2·cos(kπ/5), 1 ± 2√2, and an integer matrix with the exact spectrum 8, 4, 0, −8 — cross-checked against an independent pure-Python Jacobi implementation). python3 test/oracle/anchors.py --check self-verifies.
  • tests 97 → 128, coverage 92.91% → 94.48% (baseline ratcheted up)

安装（两者等价）：dsh plugin --profile <profile> add github:TYEclipse/dsh-linalg

dsh-linalg v0.2.0（中文）

在 v0.1.3 基础上新增两项用户可见能力，无破坏性变更。

新工具 matrix_eigen：实对称矩阵特征分解（循环 Jacobi 旋转，全双精度）——特征值降序 + 每个特征值对应的单位特征向量；符号约定为首个非零分量为正；回复里带 maxResidual（实测的 max|A·v − λ·v|，精度可见而非假设）与 traceSum（特征值之和 = 迹，自检）。非方阵 / 非对称 / 不收敛一律报错，不给猜测的谱。

matrix_compute 新增两个操作：rank（行最简形求秩，允许长方形输入）、power（二进制快速幂，exponent 取 −64…64，负指数先求逆、奇异矩阵明确报错，0 得单位阵）。

质量：测试里的每一个数值断言都由独立 oracle test/oracle/anchors.py 产出（det/inverse/rref/rank/power 走 fractions 精确算术；特征值走闭式解 2 − 2·cos(kπ/5)、1 ± 2√2，以及一个谱恰为 8, 4, 0, −8 的整数矩阵，并与独立的纯 Python Jacobi 实现交叉核对）。测试 97 → 128 条，覆盖率 92.91% → 94.48%（基线棘轮上调）。

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