∂ — Derivativef∂X: gradient; requires scalar output. U(f∂)X: vector–Jacobian product, with U shaped like the output. Result has X’s shape.
Currently supports real evaluators C∘Ⓟ, including factored and exponent-table forms.
f←1x 2x 3x∘Ⓟ ⋄ f∂2x ⍝ 14x
f←1x 2x 3x∘Ⓟ ⋄ f∂∂2x ⍝ 6x
f←1x 2x 3x∘Ⓟ ⋄ 10x 20x(f∂)1x 2x ⍝ 80x 280x
Multivariate gradients retain the coordinate enclosure. A shared scalar coordinate sums partials.
f←(⊂2 3⍴1x 2x 0x 1x 0x 2x)∘Ⓟ ⋄ f∂⊂3x 4x ⍝ ⊂6x 8x
f←(⊂2 3⍴1x 2x 0x 1x 0x 2x)∘Ⓟ ⋄ f∂3x ⍝ 12x
Repeated ∂ requires scalar input/output and one variable. DOMAIN: unsupported function or nonfinite/non-real data. RANK: monadic array output. LENGTH: wrong cotangent shape.