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| Syntax |
fordiff(function f, x, h) |
| See Also | cendiff , coldiff , testder |
f(x) returns a column vector with the same type as x,
x is a real or double-precision column vector specifying the
point at which to approximate the Jacobian of f,
and h is a column vector,
with the same type and dimension as x,
that specifies the step size for approximating partials of f.
J(x) is the Jacobian of f(x)
if the (i,j)-th element of J(x)
is the partial of the i-th element of f(x)
with respect to the j-th element of x.
The return value of fordiff has the same type as x,
the same number of rows as f(x),
and the same number of columns as x has rows.
h(j) is 0,
partials with respect to x(j) are not approximated,
and 0 is returned in the corresponding column of the return value.
fordiff and
cendiff
can be used to approximate derivatives for both
optimization and zero-finding algorithms.
The cendiff function is more accurate,
but it requires more function evaluations.
2
f(x) = x
x = 1.
This example approximates this derivative using a forward difference
with a .01 step size.
function f(x) begin
return x^2
end
x = 1.
h = .01
print fordiff(function f, x, h)
O-Matrix will respond
2.01