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| Syntax |
testhess(function fval, x0, h) |
| See Also | testgrad , testder |
f(x),
testhess compares these calculations
with a central difference approximation.
(The Hessian if the second derivative.)
The column vector x0 specifies the value of
x at which to check the calculations.
The column vector h has the same type and dimension as
x0. It specifies the step size to use for each component
when computing the central difference approximations.
(x1, fout)
fval(x1, fout, gout)
fval(x1, fout, gout, Hout)
The column vector x1
has the same type and dimension as x0 and specifies
the point at which to calculate the value of f(x).
The input value of fout does not matter.
Its output value is a scalar and equal to the value
f(x1).
If gout is present, its input value does not matter.
Its output value is a column vector with the same type and
dimension as x1 and
d f(x) |
gout = ------- |
i d x | x = x1
i
d d f(x) |
Hout = ----- ------ |
i,j d x d x | x = x1
i j
x by printing
the values returned by fval, the central difference
approximation, and the corresponding relative error in the command window.
(Note that in the output that checks the Hessian, gradient refers to
the gradient of the derivative which is the Hessian.)
f(x) where
/ x \ / 0 1 \
__ | 2 | __2 | |
f(x) = x * x , \/ f(x) = | | , \/ f(x) = | |
1 2 | x | | |
\ 1 / \ 1 0 /
clear
function fval(x1, fout, gout, Hout) begin
fout = x1(1) * x1(2)
if arg(0) >= 3 then ...
gout = {x1(2), x1(1)}
if arg(0) >= 4 then ...
Hout = {[0., 1.], [1., 0.]}
end
x0 = {1., 1.}
h = {.001, .001}
testhess(function fval, x0, h)