feat: add Matrix.mmulByTranspose()#207
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Adds `mmulByTranspose()`, which returns the matrix product of a matrix by its own transpose (`this · thisᵀ`). The result is symmetric, so only the upper triangle is computed and mirrored, and the transpose is never materialized — about twice as fast as `this.mmul(this.transpose())`. This is the Gram-style product at the heart of the normal equations (e.g. the Gauss-Newton Hessian `J·Jᵀ` in Levenberg-Marquardt). Measured ~2.4x faster than `mmul(transpose())` on a 48x2000 matrix, bit-for-bit identical. Assisted-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>
`mmulByTranspose(scale)` now computes `this · diag(scale) · thisᵀ`, the weighted Gram matrix, with `scale` a per-column factor. Without `scale` it is unchanged (`this · thisᵀ`). This covers weighted normal equations (`J·W·Jᵀ`) in a single symmetric, transpose-free pass — ~2.4x faster than `mmul(transpose().scale(...))`. Assisted-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>
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Jun 23, 2026
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What
Adds
Matrix.prototype.mmulByTranspose(scale?):J.mmulByTranspose()→J · Jᵀ(anm×mresult from anm×nmatrix).J.mmulByTranspose(scale)→J · diag(scale) · Jᵀ, the weighted Gram matrix, withscalea per-column factor.The result is symmetric, so only the upper triangle is computed and mirrored, and the transpose is never materialized.
Why
This is the Gram-style product at the heart of the (weighted) normal equations — e.g. the Gauss-Newton Hessian
J·W·Jᵀin Levenberg–Marquardt. Computing it asJ.mmul(J.transpose().scale(...))allocates a full transpose, makes a separate scaling pass, and computes alln²entries; this method does none of that.Numbers (48×2000 matrix)
mmul(transpose())J·Jᵀ(unweighted)J·diag(w)·Jᵀ(weighted)Unweighted result is bit-for-bit identical to
mmul(transpose()); weighted matches to ~1e-13 (summation order).Notes
src/matrix.js(implementation),matrix.d.ts(types),src/__tests__/matrix/utility.test.js(tests).npm testpasses (251 tests, eslint, prettier).🤖 Generated with Claude Code