hessp, hesscplx#
Purpose#
Computes the matrix of second partial derivatives (Hessian matrix) of a function defined as a procedure. hesscplx()
allows for
complex arguments.
Format#
- h = hessp(&f, x0)#
- Parameters:
&f (function pointer) – pointer to a single-valued function
, defined as a procedure, taking a single Kx1 vector argument (f: ); may be defined in terms of global arguments in addition to x.x0 (Kx1 vector) – the point at which the Hessian of
is to be computed
- Returns:
h (KxK matrix) – Second derivatives of f with respect to x at x0; this matrix will be symmetric.
Examples#
// X matrix
x = { 1, 2, 3 };
proc g(b);
retp( exp(x'b));
endp;
// Parameter startvalues
b0 = { 3, 2, 1 };
// Compute Hessian
h = hessp(&g, b0);
The resulting matrix of second partial derivatives of
22026.865 44053.686 66080.596
h = 44053.686 88107.753 132161.059
66080.596 132161.059 198240.695
Remarks#
This procedure requires
No more than 3-4 digit accuracy should be expected from this function, though it is possible for greater accuracy to be achieved with some functions.
It is important that the function be properly scaled, in order to obtain greatest possible accuracy. Specifically, scale it so that the first derivatives are approximately the same size. If these derivatives differ by more than a factor of 100 or so, the results can be meaningless.
Source#
hessp.src
See also
Functions gradp()
, gradcplx()