Method on @sym: jacobian (f) ¶

Method on @sym: jacobian (f, x) ¶

Symbolic Jacobian of symbolic expression.

The Jacobian of a scalar expression is:

syms f(x, y, z)
jacobian(f)
  ⇒ (sym 1×3 matrix)
      ⎡∂               ∂               ∂             ⎤
      ⎢──(f(x, y, z))  ──(f(x, y, z))  ──(f(x, y, z))⎥
      ⎣∂x              ∂y              ∂z            ⎦

x can be a scalar, vector or cell list. If omitted, it is determined using symvar.

Example:

f = sin(x*y);
jacobian(f)
  ⇒ (sym) [y⋅cos(x⋅y)  x⋅cos(x⋅y)]  (1×2 matrix)

jacobian(f, [x y z])
  ⇒ (sym) [y⋅cos(x⋅y)  x⋅cos(x⋅y)  0]  (1×3 matrix)

For vector input, the output is a matrix:

syms f(x,y,z) g(x,y,z)
jacobian([f; g])
  ⇒ (sym 2×3 matrix)
      ⎡∂               ∂               ∂             ⎤
      ⎢──(f(x, y, z))  ──(f(x, y, z))  ──(f(x, y, z))⎥
      ⎢∂x              ∂y              ∂z            ⎥
      ⎢                                              ⎥
      ⎢∂               ∂               ∂             ⎥
      ⎢──(g(x, y, z))  ──(g(x, y, z))  ──(g(x, y, z))⎥
      ⎣∂x              ∂y              ∂z            ⎦

Example:

jacobian([2*x + 3*z; 3*y^2 - cos(x)])
  ⇒ (sym 2×3 matrix)
      ⎡  2      0   3⎤
      ⎢              ⎥
      ⎣sin(x)  6⋅y  0⎦

See also: @sym/divergence, @sym/gradient, @sym/curl, @sym/laplacian, @sym/hessian.

Package: symbolic