Symbolic Hessian matrix of symbolic scalar expression.
The Hessian of a scalar expression f is the matrix consisting of second derivatives:
syms f(x, y, z)
hessian(f)
⇒ (sym 3×3 matrix)
⎡ 2 2 2 ⎤
⎢ ∂ ∂ ∂ ⎥
⎢ ───(f(x, y, z)) ─────(f(x, y, z)) ─────(f(x, y, z))⎥
⎢ 2 ∂y ∂x ∂z ∂x ⎥
⎢ ∂x ⎥
⎢ ⎥
⎢ 2 2 2 ⎥
⎢ ∂ ∂ ∂ ⎥
⎢─────(f(x, y, z)) ───(f(x, y, z)) ─────(f(x, y, z))⎥
⎢∂y ∂x 2 ∂z ∂y ⎥
⎢ ∂y ⎥
⎢ ⎥
⎢ 2 2 2 ⎥
⎢ ∂ ∂ ∂ ⎥
⎢─────(f(x, y, z)) ─────(f(x, y, z)) ───(f(x, y, z)) ⎥
⎢∂z ∂x ∂z ∂y 2 ⎥
⎣ ∂z ⎦
x can be a scalar, vector or cell list. If omitted,
it is determined using symvar.
Example:
f = x*y;
hessian(f)
⇒ (sym 2×2 matrix)
⎡0 1⎤
⎢ ⎥
⎣1 0⎦
See also: @sym/jacobian, @sym/divergence, @sym/gradient, @sym/curl, @sym/laplacian.
Package: symbolic