matlab - fminbnd doesn't give the minimum value -

i'm trying built-in functions in matlab. declared function this:

function y = myfunction(x)     y = cos(4*x) .* sin(10*x) .* exp(-abs(x)); end 

then use fminbnd find minimum value:

fminbnd(@myfunction,-pi,pi) 

this gives me result:

ans =  0.7768 

however, when plot 'myfunction' in [-pi,pi], got following figure code used:

>> x = -pi:0.01:pi; >> y = myfunction(x); >> plot(x,y) 

it can seen min value -0.77, not result given fminbnd. what's wrong here? i'm new matlab , don't know i'm wrong.

first things first, fminbnd returns x-coordinate of minimum location of function. such, actual minimum located @ myfunction(0.7768). x=0.7768 location of minimum is.

now, tried running code more verbose information. specifically, wanted see how minimum changes @ each iteration. overrode default settings of fminbnd can see what's happening @ each iteration.

this get:

>> y = @(x) cos(4*x).*sin(10*x).*exp(-abs(x)); %// no need function declaration >> options = optimset('display', 'iter'); >> [x,fval,exitflag] = fminbnd(y, -pi, pi, options)   func-count     x          f(x)         procedure     1      -0.741629      0.42484        initial     2       0.741629     -0.42484        golden     3        1.65833    -0.137356        golden     4       0.775457    -0.457857        parabolic     5        1.09264     0.112139        parabolic     6       0.896609    -0.163049        golden     7       0.780727    -0.457493        parabolic     8         0.7768    -0.457905        parabolic     9       0.776766    -0.457905        parabolic    10       0.776833    -0.457905        parabolic  optimization terminated:  current x satisfies termination criteria using options.tolx of 1.000000e-04    x =           0.776799595407872   fval =          -0.457905463395071   exitflag =       1 

x location of minimum, fval y value of minimum , exitflag=1 means algorithm converged properly.

---

this not equal desired minimum. if can reference documentation of fminbnd, says this:

fminbnd may give local solutions. 

going that, reason why aren't getting right answer because have a lot of local minima in function. specifically, if zoom in x=0.7784 local minimum:

since algorithm managed find local minimum here, decides stop.
managed true minimum if restrict search boundaries of function around true minimum is. instead of [-pi,pi]... try [-1,1] instead:

>> [x,fval,exitflag] = fminbnd(y, -1, 1, options)    func-count     x          f(x)         procedure     1      -0.236068    -0.325949        initial     2       0.236068     0.325949        golden     3      -0.527864    -0.256217        golden     4       -0.32561    0.0218758        parabolic     5     -0.0557281    -0.487837        golden     6      0.0557281     0.487837        golden     7      -0.124612    -0.734908        golden     8      -0.134743    -0.731415        parabolic     9      -0.126213    -0.735006        parabolic    10      -0.126055    -0.735007        parabolic    11      -0.126022    -0.735007        parabolic    12      -0.126089    -0.735007        parabolic  optimization terminated:  current x satisfies termination criteria using options.tolx of 1.000000e-04    x =          -0.126055418940111   fval =          -0.735007134768142   exitflag =       1 

when did this, managed right minimum location , minimum itself.