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Commit 4b44d69

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mdhabermdhaber
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DOC: optimize.minimize_scalar and friends: correct documentation (scipy#17705)
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‎scipy/optimize/_minimize.py

Copy file name to clipboardExpand all lines: scipy/optimize/_minimize.py
+7-5Lines changed: 7 additions & 5 deletions
Original file line numberDiff line numberDiff line change
@@ -762,11 +762,13 @@ def minimize_scalar(fun, bracket=None, bounds=None, args=(),
762762
Scalar function, must return a scalar.
763763
bracket : sequence, optional
764764
For methods 'brent' and 'golden', `bracket` defines the bracketing
765-
interval and can either have three items ``(a, b, c)`` so that
766-
``a < b < c`` and ``fun(b) < fun(a), fun(c)`` or two items ``a`` and
767-
``c`` which are assumed to be a starting interval for a downhill
768-
bracket search (see `bracket`); it doesn't always mean that the
769-
obtained solution will satisfy ``a <= x <= c``.
765+
interval and is required.
766+
Either a triple ``(xa, xb, xc)`` satisfying ``xa < xb < xc`` and
767+
``func(xb) < func(xa) and func(xb) < func(xc)``, or a pair
768+
``(xa, xb)`` to be used as initial points for a downhill bracket search
769+
(see `scipy.optimize.bracket`).
770+
The minimizer ``res.x`` will not necessarily satisfy
771+
``xa <= res.x <= xb``.
770772
bounds : sequence, optional
771773
For method 'bounded', `bounds` is mandatory and must have two finite
772774
items corresponding to the optimization bounds.

‎scipy/optimize/_optimize.py

Copy file name to clipboardExpand all lines: scipy/optimize/_optimize.py
+51-39Lines changed: 51 additions & 39 deletions
Original file line numberDiff line numberDiff line change
@@ -2177,12 +2177,12 @@ def fminbound(func, x1, x2, args=(), xtol=1e-5, maxfun=500,
21772177
Parameters (over given interval) which minimize the
21782178
objective function.
21792179
fval : number
2180-
The function value evaluated at the minimizer.
2180+
(Optional output) The function value evaluated at the minimizer.
21812181
ierr : int
2182-
An error flag (0 if converged, 1 if maximum number of
2182+
(Optional output) An error flag (0 if converged, 1 if maximum number of
21832183
function calls reached).
21842184
numfunc : int
2185-
The number of function calls made.
2185+
(Optional output) The number of function calls made.
21862186
21872187
See also
21882188
--------
@@ -2217,12 +2217,13 @@ def fminbound(func, x1, x2, args=(), xtol=1e-5, maxfun=500,
22172217
>>> minimum = f(minimizer)
22182218
>>> minimum
22192219
0.0
2220-
>>> minimizer = optimize.fminbound(f, 3, 4)
2220+
>>> res = optimize.fminbound(f, 3, 4, full_output=True)
2221+
>>> minimizer, fval, ierr, numfunc = res
22212222
>>> minimizer
22222223
3.000005960860986
22232224
>>> minimum = f(minimizer)
2224-
>>> minimum
2225-
4.000023843479476
2225+
>>> minimum, fval
2226+
(4.000023843479476, 4.000023843479476)
22262227
"""
22272228
options = {'xatol': xtol,
22282229
'maxiter': maxfun,
@@ -2564,7 +2565,7 @@ def get_result(self, full_output=False):
25642565
def brent(func, args=(), brack=None, tol=1.48e-8, full_output=0, maxiter=500):
25652566
"""
25662567
Given a function of one variable and a possible bracket, return
2567-
the local minimum of the function isolated to a fractional precision
2568+
a local minimizer of the function isolated to a fractional precision
25682569
of tol.
25692570
25702571
Parameters
@@ -2574,11 +2575,11 @@ def brent(func, args=(), brack=None, tol=1.48e-8, full_output=0, maxiter=500):
25742575
args : tuple, optional
25752576
Additional arguments (if present).
25762577
brack : tuple, optional
2577-
Either a triple (xa,xb,xc) where xa<xb<xc and func(xb) <
2578-
func(xa), func(xc) or a pair (xa,xb) which are used as a
2579-
starting interval for a downhill bracket search (see
2580-
`bracket`). Providing the pair (xa,xb) does not always mean
2581-
the obtained solution will satisfy xa<=x<=xb.
2578+
Either a triple ``(xa, xb, xc)`` satisfying ``xa < xb < xc`` and
2579+
``func(xb) < func(xa) and func(xb) < func(xc)``, or a pair
2580+
``(xa, xb)`` to be used as initial points for a downhill bracket search
2581+
(see `scipy.optimize.bracket`).
2582+
The minimizer ``x`` will not necessarily satisfy ``xa <= x <= xb``.
25822583
tol : float, optional
25832584
Relative error in solution `xopt` acceptable for convergence.
25842585
full_output : bool, optional
@@ -2592,11 +2593,11 @@ def brent(func, args=(), brack=None, tol=1.48e-8, full_output=0, maxiter=500):
25922593
xmin : ndarray
25932594
Optimum point.
25942595
fval : float
2595-
Optimum value.
2596+
(Optional output) Optimum function value.
25962597
iter : int
2597-
Number of iterations.
2598+
(Optional output) Number of iterations.
25982599
funcalls : int
2599-
Number of objective function evaluations made.
2600+
(Optional output) Number of objective function evaluations made.
26002601
26012602
See also
26022603
--------
@@ -2609,26 +2610,27 @@ def brent(func, args=(), brack=None, tol=1.48e-8, full_output=0, maxiter=500):
26092610
convergence of golden section method.
26102611
26112612
Does not ensure that the minimum lies in the range specified by
2612-
`brack`. See `fminbound`.
2613+
`brack`. See `scipy.optimize.fminbound`.
26132614
26142615
Examples
26152616
--------
26162617
We illustrate the behaviour of the function when `brack` is of
26172618
size 2 and 3 respectively. In the case where `brack` is of the
2618-
form (xa,xb), we can see for the given values, the output need
2619-
not necessarily lie in the range (xa,xb).
2619+
form ``(xa, xb)``, we can see for the given values, the output does
2620+
not necessarily lie in the range ``(xa, xb)``.
26202621
26212622
>>> def f(x):
2622-
... return x**2
2623+
... return (x-1)**2
26232624
26242625
>>> from scipy import optimize
26252626
2626-
>>> minimum = optimize.brent(f,brack=(1,2))
2627-
>>> minimum
2628-
0.0
2629-
>>> minimum = optimize.brent(f,brack=(-1,0.5,2))
2630-
>>> minimum
2631-
-2.7755575615628914e-17
2627+
>>> minimizer = optimize.brent(f, brack=(1, 2))
2628+
>>> minimizer
2629+
1
2630+
>>> res = optimize.brent(f, brack=(-1, 0.5, 2), full_output=True)
2631+
>>> xmin, fval, iter, funcalls = res
2632+
>>> f(xmin), fval
2633+
(0.0, 0.0)
26322634
26332635
"""
26342636
options = {'xtol': tol,
@@ -2695,11 +2697,11 @@ def _minimize_scalar_brent(func, brack=None, args=(), xtol=1.48e-8,
26952697
def golden(func, args=(), brack=None, tol=_epsilon,
26962698
full_output=0, maxiter=5000):
26972699
"""
2698-
Return the minimum of a function of one variable using golden section
2700+
Return the minimizer of a function of one variable using the golden section
26992701
method.
27002702
27012703
Given a function of one variable and a possible bracketing interval,
2702-
return the minimum of the function isolated to a fractional precision of
2704+
return a minimizer of the function isolated to a fractional precision of
27032705
tol.
27042706
27052707
Parameters
@@ -2709,18 +2711,27 @@ def golden(func, args=(), brack=None, tol=_epsilon,
27092711
args : tuple, optional
27102712
Additional arguments (if present), passed to func.
27112713
brack : tuple, optional
2712-
Triple (a,b,c), where (a<b<c) and func(b) <
2713-
func(a),func(c). If bracket consists of two numbers (a,
2714-
c), then they are assumed to be a starting interval for a
2715-
downhill bracket search (see `bracket`); it doesn't always
2716-
mean that obtained solution will satisfy a<=x<=c.
2714+
Either a triple ``(xa, xb, xc)`` where ``xa < xb < xc`` and
2715+
``func(xb) < func(xa) and func(xb) < func(xc)``, or a pair (xa, xb)
2716+
to be used as initial points for a downhill bracket search (see
2717+
`scipy.optimize.bracket`).
2718+
The minimizer ``x`` will not necessarily satisfy ``xa <= x <= xb``.
27172719
tol : float, optional
27182720
x tolerance stop criterion
27192721
full_output : bool, optional
27202722
If True, return optional outputs.
27212723
maxiter : int
27222724
Maximum number of iterations to perform.
27232725
2726+
Returns
2727+
-------
2728+
xmin : ndarray
2729+
Optimum point.
2730+
fval : float
2731+
(Optional output) Optimum function value.
2732+
funcalls : int
2733+
(Optional output) Number of objective function evaluations made.
2734+
27242735
See also
27252736
--------
27262737
minimize_scalar: Interface to minimization algorithms for scalar
@@ -2739,16 +2750,17 @@ def golden(func, args=(), brack=None, tol=_epsilon,
27392750
not necessarily lie in the range ``(xa, xb)``.
27402751
27412752
>>> def f(x):
2742-
... return x**2
2753+
... return (x-1)**2
27432754
27442755
>>> from scipy import optimize
27452756
2746-
>>> minimum = optimize.golden(f, brack=(1, 2))
2747-
>>> minimum
2748-
1.5717277788484873e-162
2749-
>>> minimum = optimize.golden(f, brack=(-1, 0.5, 2))
2750-
>>> minimum
2751-
-1.5717277788484873e-162
2757+
>>> minimizer = optimize.golden(f, brack=(1, 2))
2758+
>>> minimizer
2759+
1
2760+
>>> res = optimize.golden(f, brack=(-1, 0.5, 2), full_output=True)
2761+
>>> xmin, fval, funcalls = res
2762+
>>> f(xmin), fval
2763+
(9.925165290385052e-18, 9.925165290385052e-18)
27522764
27532765
"""
27542766
options = {'xtol': tol, 'maxiter': maxiter}

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