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""" 

This module provides the routine to adjust subplot layouts so that there are 

no overlapping axes or axes decorations. All axes decorations are dealt with 

(labels, ticks, titles, ticklabels) and some dependent artists are also dealt 

with (colorbar, suptitle, legend). 

 

Layout is done via :meth:`~matplotlib.gridspec`, with one constraint per 

gridspec, so it is possible to have overlapping axes if the gridspecs 

overlap (i.e. using :meth:`~matplotlib.gridspec.GridSpecFromSubplotSpec`). 

Axes placed using ``figure.subplots()`` or ``figure.add_subplots()`` will 

participate in the layout. Axes manually placed via ``figure.add_axes()`` 

will not. 

 

See Tutorial: :doc:`/tutorials/intermediate/constrainedlayout_guide` 

 

""" 

 

# Development Notes: 

 

# What gets a layoutbox: 

# - figure 

# - gridspec 

# - subplotspec 

# EITHER: 

# - axes + pos for the axes (i.e. the total area taken by axis and 

# the actual "position" argument that needs to be sent to 

# ax.set_position.) 

# - The axes layout box will also encomapss the legend, and that is 

# how legends get included (axes legeneds, not figure legends) 

# - colorbars are sibblings of the axes if they are single-axes 

# colorbars 

# OR: 

# - a gridspec can be inside a subplotspec. 

# - subplotspec 

# EITHER: 

# - axes... 

# OR: 

# - gridspec... with arbitrary nesting... 

# - colorbars are siblings of the subplotspecs if they are multi-axes 

# colorbars. 

# - suptitle: 

# - right now suptitles are just stacked atop everything else in figure. 

# Could imagine suptitles being gridspec suptitles, but not implimented 

# 

# Todo: AnchoredOffsetbox connected to gridspecs or axes. This would 

# be more general way to add extra-axes annotations. 

 

from __future__ import (absolute_import, division, print_function, 

unicode_literals) 

 

import numpy as np 

import logging 

import warnings 

 

from matplotlib.legend import Legend 

import matplotlib.transforms as transforms 

import matplotlib._layoutbox as layoutbox 

 

_log = logging.getLogger(__name__) 

 

 

def get_axall_tightbbox(ax, renderer): 

''' 

Get the tight_bbox of the axis ax, and any dependent decorations, like 

a `Legend` instance. 

''' 

 

# main bbox of the axis.... 

bbox = ax.get_tightbbox(renderer=renderer) 

# now add the possibility of the legend... 

for child in ax.get_children(): 

if isinstance(child, Legend): 

bboxn = child._legend_box.get_window_extent(renderer) 

bbox = transforms.Bbox.union([bbox, bboxn]) 

# add other children here.... 

return bbox 

 

 

def in_same_column(colnum0min, colnum0max, colnumCmin, colnumCmax): 

if colnum0min >= colnumCmin and colnum0min <= colnumCmax: 

return True 

if colnum0max >= colnumCmin and colnum0max <= colnumCmax: 

return True 

return False 

 

 

def in_same_row(rownum0min, rownum0max, rownumCmin, rownumCmax): 

if rownum0min >= rownumCmin and rownum0min <= rownumCmax: 

return True 

if rownum0max >= rownumCmin and rownum0max <= rownumCmax: 

return True 

return False 

 

 

###################################################### 

def do_constrained_layout(fig, renderer, h_pad, w_pad, 

hspace=None, wspace=None): 

 

""" 

Do the constrained_layout. Called at draw time in 

``figure.constrained_layout()`` 

 

Parameters 

---------- 

 

 

fig: Figure 

is the ``figure`` instance to do the layout in. 

 

renderer: Renderer 

the renderer to use. 

 

h_pad, w_pad : float 

are in figure-normalized units, and are a padding around the axes 

elements. 

 

hspace, wspace : float 

are in fractions of the subplot sizes. 

 

""" 

 

''' Steps: 

 

1. get a list of unique gridspecs in this figure. Each gridspec will be 

constrained separately. 

2. Check for gaps in the gridspecs. i.e. if not every axes slot in the 

gridspec has been filled. If empty, add a ghost axis that is made so 

that it cannot be seen (though visible=True). This is needed to make 

a blank spot in the layout. 

3. Compare the tight_bbox of each axes to its `position`, and assume that 

the difference is the space needed by the elements around the edge of 

the axes (decorations) like the title, ticklabels, x-labels, etc. This 

can include legends who overspill the axes boundaries. 

4. Constrain gridspec elements to line up: 

a) if colnum0 neq colnumC, the two subplotspecs are stacked next to 

each other, with the appropriate order. 

b) if colnum0 == columnC line up the left or right side of the 

_poslayoutbox (depending if it is the min or max num that is equal). 

c) do the same for rows... 

5. The above doesn't constrain relative sizes of the _poslayoutboxes at 

all, and indeed zero-size is a solution that the solver often finds more 

convenient than expanding the sizes. Right now the solution is to compare 

subplotspec sizes (i.e. drowsC and drows0) and constrain the larger 

_poslayoutbox to be larger than the ratio of the sizes. i.e. if drows0 > 

drowsC, then ax._poslayoutbox > axc._poslayoutbox * drowsC / drows0. This 

works fine *if* the decorations are similar between the axes. If the 

larger subplotspec has much larger axes decorations, then the constraint 

above is incorrect. 

 

We need the greater than in the above, in general, rather than an equals 

sign. Consider the case of the left column having 2 rows, and the right 

column having 1 row. We want the top and bottom of the _poslayoutboxes to 

line up. So that means if there are decorations on the left column axes 

they will be smaller than half as large as the right hand axis. 

 

This can break down if the decoration size for the right hand axis (the 

margins) is very large. There must be a math way to check for this case. 

 

''' 

 

invTransFig = fig.transFigure.inverted().transform_bbox 

 

# list of unique gridspecs that contain child axes: 

gss = set([]) 

for ax in fig.axes: 

if hasattr(ax, 'get_subplotspec'): 

gs = ax.get_subplotspec().get_gridspec() 

if gs._layoutbox is not None: 

gss.add(gs) 

if len(gss) == 0: 

warnings.warn('There are no gridspecs with layoutboxes. ' 

'Possibly did not call parent GridSpec with the figure= ' 

'keyword') 

 

# check for unoccupied gridspec slots and make ghost axes for these 

# slots... Do for each gs separately. This is a pretty big kludge 

# but shoudn't have too much ill effect. The worst is that 

# someone querrying the figure will wonder why there are more 

# axes than they thought. 

if fig._layoutbox.constrained_layout_called < 1: 

for gs in gss: 

nrows, ncols = gs.get_geometry() 

hassubplotspec = np.zeros(nrows * ncols, dtype=bool) 

axs = [] 

for ax in fig.axes: 

if (hasattr(ax, 'get_subplotspec') 

and ax._layoutbox is not None 

and ax.get_subplotspec().get_gridspec() == gs): 

axs += [ax] 

for ax in axs: 

ss0 = ax.get_subplotspec() 

if ss0.num2 is None: 

ss0.num2 = ss0.num1 

hassubplotspec[ss0.num1:(ss0.num2 + 1)] = True 

for nn, hss in enumerate(hassubplotspec): 

if not hss: 

# this gridspec slot doesn't have an axis so we 

# make a "ghost". 

ax = fig.add_subplot(gs[nn]) 

ax.set_frame_on(False) 

ax.set_xticks([]) 

ax.set_yticks([]) 

ax.set_facecolor((1, 0, 0, 0)) 

 

# for each axes, make a margin between the *pos* layoutbox and the 

# *axes* layoutbox be a minimum size that can accomodate the 

# decorations on the axis. 

for ax in fig.axes: 

_log.debug(ax._layoutbox) 

if ax._layoutbox is not None: 

pos = ax.get_position(original=True) 

tightbbox = get_axall_tightbbox(ax, renderer) 

bbox = invTransFig(tightbbox) 

# use stored h_pad if it exists 

h_padt = ax._poslayoutbox.h_pad 

if h_padt is None: 

h_padt = h_pad 

w_padt = ax._poslayoutbox.w_pad 

if w_padt is None: 

w_padt = w_pad 

ax._poslayoutbox.edit_left_margin_min(-bbox.x0 + 

pos.x0 + w_padt) 

ax._poslayoutbox.edit_right_margin_min(bbox.x1 - 

pos.x1 + w_padt) 

ax._poslayoutbox.edit_bottom_margin_min( 

-bbox.y0 + pos.y0 + h_padt) 

ax._poslayoutbox.edit_top_margin_min(bbox.y1-pos.y1+h_padt) 

_log.debug('left %f', (-bbox.x0 + pos.x0 + w_pad)) 

_log.debug('right %f', (bbox.x1 - pos.x1 + w_pad)) 

_log.debug('bottom %f', (-bbox.y0 + pos.y0 + h_padt)) 

# Sometimes its possible for the solver to collapse 

# rather than expand axes, so they all have zero height 

# or width. This stops that... It *should* have been 

# taken into account w/ pref_width... 

if fig._layoutbox.constrained_layout_called < 1: 

ax._poslayoutbox.constrain_height_min(20, strength='weak') 

ax._poslayoutbox.constrain_width_min(20, strength='weak') 

ax._layoutbox.constrain_height_min(20, strength='weak') 

ax._layoutbox.constrain_width_min(20, strength='weak') 

ax._poslayoutbox.constrain_top_margin(0, strength='weak') 

ax._poslayoutbox.constrain_bottom_margin(0, 

strength='weak') 

ax._poslayoutbox.constrain_right_margin(0, strength='weak') 

ax._poslayoutbox.constrain_left_margin(0, strength='weak') 

 

# do layout for suptitle. 

if fig._suptitle is not None: 

sup = fig._suptitle 

bbox = invTransFig(sup.get_window_extent(renderer=renderer)) 

height = bbox.y1 - bbox.y0 

sup._layoutbox.edit_height(height+h_pad) 

 

# OK, the above lines up ax._poslayoutbox with ax._layoutbox 

# now we need to 

# 1) arrange the subplotspecs. We do it at this level because 

# the subplotspecs are meant to contain other dependent axes 

# like colorbars or legends. 

# 2) line up the right and left side of the ax._poslayoutbox 

# that have the same subplotspec maxes. 

 

if fig._layoutbox.constrained_layout_called < 1: 

 

# arrange the subplotspecs... This is all done relative to each 

# other. Some subplotspecs conatain axes, and others contain gridspecs 

# the ones that contain gridspecs are a set proportion of their 

# parent gridspec. The ones that contain axes are not so constrained. 

figlb = fig._layoutbox 

for child in figlb.children: 

if child._is_gridspec_layoutbox(): 

# farm the gridspec layout out. 

# 

# This routine makes all the subplot spec containers 

# have the correct arrangement. It just stacks the 

# subplot layoutboxes in the correct order... 

arange_subplotspecs(child, hspace=hspace, wspace=wspace) 

 

# - Align right/left and bottom/top spines of appropriate subplots. 

# - Compare size of subplotspec including height and width ratios 

# and make sure that the axes spines are at least as large 

# as they should be. 

for gs in gss: 

# for each gridspec... 

nrows, ncols = gs.get_geometry() 

width_ratios = gs.get_width_ratios() 

height_ratios = gs.get_height_ratios() 

if width_ratios is None: 

width_ratios = np.ones(ncols) 

if height_ratios is None: 

height_ratios = np.ones(nrows) 

 

# get axes in this gridspec.... 

axs = [] 

for ax in fig.axes: 

if (hasattr(ax, 'get_subplotspec') 

and ax._layoutbox is not None): 

if ax.get_subplotspec().get_gridspec() == gs: 

axs += [ax] 

rownummin = np.zeros(len(axs), dtype=np.int8) 

rownummax = np.zeros(len(axs), dtype=np.int8) 

colnummin = np.zeros(len(axs), dtype=np.int8) 

colnummax = np.zeros(len(axs), dtype=np.int8) 

width = np.zeros(len(axs)) 

height = np.zeros(len(axs)) 

 

for n, ax in enumerate(axs): 

ss0 = ax.get_subplotspec() 

if ss0.num2 is None: 

ss0.num2 = ss0.num1 

rownummin[n], colnummin[n] = divmod(ss0.num1, ncols) 

rownummax[n], colnummax[n] = divmod(ss0.num2, ncols) 

width[n] = np.sum( 

width_ratios[colnummin[n]:(colnummax[n] + 1)]) 

height[n] = np.sum( 

height_ratios[rownummin[n]:(rownummax[n] + 1)]) 

 

for nn, ax in enumerate(axs[:-1]): 

ss0 = ax.get_subplotspec() 

 

# now compare ax to all the axs: 

# 

# If the subplotspecs have the same colnumXmax, then line 

# up their right sides. If they have the same min, then 

# line up their left sides (and vertical equivalents). 

rownum0min, colnum0min = rownummin[nn], colnummin[nn] 

rownum0max, colnum0max = rownummax[nn], colnummax[nn] 

width0, height0 = width[nn], height[nn] 

alignleft = False 

alignright = False 

alignbot = False 

aligntop = False 

alignheight = False 

alignwidth = False 

for mm in range(nn+1, len(axs)): 

axc = axs[mm] 

rownumCmin, colnumCmin = rownummin[mm], colnummin[mm] 

rownumCmax, colnumCmax = rownummax[mm], colnummax[mm] 

widthC, heightC = width[mm], height[mm] 

# Horizontally align axes spines if they have the 

# same min or max: 

if not alignleft and colnum0min == colnumCmin: 

# we want the _poslayoutboxes to line up on left 

# side of the axes spines... 

layoutbox.align([ax._poslayoutbox, 

axc._poslayoutbox], 

'left') 

alignleft = True 

 

if not alignright and colnum0max == colnumCmax: 

# line up right sides of _poslayoutbox 

layoutbox.align([ax._poslayoutbox, 

axc._poslayoutbox], 

'right') 

alignright = True 

# Vertically align axes spines if they have the 

# same min or max: 

if not aligntop and rownum0min == rownumCmin: 

# line up top of _poslayoutbox 

_log.debug('rownum0min == rownumCmin') 

layoutbox.align([ax._poslayoutbox, axc._poslayoutbox], 

'top') 

aligntop = True 

 

if not alignbot and rownum0max == rownumCmax: 

# line up bottom of _poslayoutbox 

_log.debug('rownum0max == rownumCmax') 

layoutbox.align([ax._poslayoutbox, axc._poslayoutbox], 

'bottom') 

alignbot = True 

########### 

# Now we make the widths and heights of position boxes 

# similar. (i.e the spine locations) 

# This allows vertically stacked subplots to have 

# different sizes if they occupy different amounts 

# of the gridspec: i.e. 

# gs = gridspec.GridSpec(3,1) 

# ax1 = gs[0,:] 

# ax2 = gs[1:,:] 

# then drows0 = 1, and drowsC = 2, and ax2 

# should be at least twice as large as ax1. 

# But it can be more than twice as large because 

# it needs less room for the labeling. 

# 

# For height, this only needs to be done if the 

# subplots share a column. For width if they 

# share a row. 

 

drowsC = (rownumCmax - rownumCmin + 1) 

drows0 = (rownum0max - rownum0min + 1) 

dcolsC = (colnumCmax - colnumCmin + 1) 

dcols0 = (colnum0max - colnum0min + 1) 

 

if not alignheight and drows0 == drowsC: 

ax._poslayoutbox.constrain_height( 

axc._poslayoutbox.height * height0 / heightC) 

alignheight = True 

elif in_same_column(colnum0min, colnum0max, 

colnumCmin, colnumCmax): 

if height0 > heightC: 

ax._poslayoutbox.constrain_height_min( 

axc._poslayoutbox.height * height0 / heightC) 

# these constraints stop the smaller axes from 

# being allowed to go to zero height... 

axc._poslayoutbox.constrain_height_min( 

ax._poslayoutbox.height * heightC / 

(height0*1.8)) 

elif height0 < heightC: 

axc._poslayoutbox.constrain_height_min( 

ax._poslayoutbox.height * heightC / height0) 

ax._poslayoutbox.constrain_height_min( 

ax._poslayoutbox.height * height0 / 

(heightC*1.8)) 

# widths... 

if not alignwidth and dcols0 == dcolsC: 

ax._poslayoutbox.constrain_width( 

axc._poslayoutbox.width * width0 / widthC) 

alignwidth = True 

elif in_same_row(rownum0min, rownum0max, 

rownumCmin, rownumCmax): 

if width0 > widthC: 

ax._poslayoutbox.constrain_width_min( 

axc._poslayoutbox.width * width0 / widthC) 

axc._poslayoutbox.constrain_width_min( 

ax._poslayoutbox.width * widthC / 

(width0*1.8)) 

elif width0 < widthC: 

axc._poslayoutbox.constrain_width_min( 

ax._poslayoutbox.width * widthC / width0) 

ax._poslayoutbox.constrain_width_min( 

axc._poslayoutbox.width * width0 / 

(widthC*1.8)) 

 

fig._layoutbox.constrained_layout_called += 1 

fig._layoutbox.update_variables() 

# Now set the position of the axes... 

for ax in fig.axes: 

if ax._layoutbox is not None: 

newpos = ax._poslayoutbox.get_rect() 

_log.debug('newpos %r', newpos) 

# Now set the new position. 

# ax.set_position will zero out the layout for 

# this axis, allowing users to hard-code the position, 

# so this does the same w/o zeroing layout. 

ax._set_position(newpos, which='original') 

 

 

def arange_subplotspecs(gs, hspace=0, wspace=0): 

""" 

arange the subplotspec children of this gridspec, and then recursively 

do the same of any gridspec children of those gridspecs... 

""" 

sschildren = [] 

for child in gs.children: 

if child._is_subplotspec_layoutbox(): 

for child2 in child.children: 

# check for gridspec children... 

name = (child2.name).split('.')[-1][:-3] 

if name == 'gridspec': 

arange_subplotspecs(child2, hspace=hspace, wspace=wspace) 

sschildren += [child] 

# now arrange the subplots... 

for child0 in sschildren: 

ss0 = child0.artist 

nrows, ncols = ss0.get_gridspec().get_geometry() 

if ss0.num2 is None: 

ss0.num2 = ss0.num1 

rowNum0min, colNum0min = divmod(ss0.num1, ncols) 

rowNum0max, colNum0max = divmod(ss0.num2, ncols) 

sschildren = sschildren[1:] 

for childc in sschildren: 

ssc = childc.artist 

rowNumCmin, colNumCmin = divmod(ssc.num1, ncols) 

if ssc.num2 is None: 

ssc.num2 = ssc.num1 

rowNumCmax, colNumCmax = divmod(ssc.num2, ncols) 

# OK, this tells us the relative layout of ax 

# with axc 

thepad = wspace / ncols 

if colNum0max < colNumCmin: 

layoutbox.hstack([ss0._layoutbox, ssc._layoutbox], 

padding=thepad) 

if colNumCmax < colNum0min: 

layoutbox.hstack([ssc._layoutbox, ss0._layoutbox], 

padding=thepad) 

 

#### 

# vertical alignment 

thepad = hspace / nrows 

if rowNum0max < rowNumCmin: 

layoutbox.vstack([ss0._layoutbox, 

ssc._layoutbox], 

padding=thepad) 

if rowNumCmax < rowNum0min: 

layoutbox.vstack([ssc._layoutbox, 

ss0._layoutbox], 

padding=thepad) 

 

 

def layoutcolorbarsingle(ax, cax, shrink, aspect, location, pad=0.05): 

""" 

Do the layout for a colorbar, to not oeverly pollute colorbar.py 

 

`pad` is in fraction of the original axis size. 

""" 

axlb = ax._layoutbox 

axpos = ax._poslayoutbox 

axsslb = ax.get_subplotspec()._layoutbox 

lb = layoutbox.LayoutBox( 

parent=axsslb, 

name=axsslb.name + '.cbar', 

artist=cax) 

 

if location in ('left', 'right'): 

lbpos = layoutbox.LayoutBox( 

parent=lb, 

name=lb.name + '.pos', 

tightwidth=False, 

pos=True, 

subplot=False, 

artist=cax) 

 

if location == 'right': 

# arrange to right of parent axis 

layoutbox.hstack([axlb, lb], padding=pad * axlb.width, 

strength='strong') 

else: 

layoutbox.hstack([lb, axlb], padding=pad * axlb.width) 

# constrain the height and center... 

layoutbox.match_heights([axpos, lbpos], [1, shrink]) 

layoutbox.align([axpos, lbpos], 'v_center') 

# set the width of the pos box 

lbpos.constrain_width(shrink * axpos.height * (1/aspect), 

strength='strong') 

elif location in ('bottom', 'top'): 

lbpos = layoutbox.LayoutBox( 

parent=lb, 

name=lb.name + '.pos', 

tightheight=True, 

pos=True, 

subplot=False, 

artist=cax) 

 

if location == 'bottom': 

layoutbox.vstack([axlb, lb], padding=pad * axlb.height) 

else: 

layoutbox.vstack([lb, axlb], padding=pad * axlb.height) 

# constrain the height and center... 

layoutbox.match_widths([axpos, lbpos], 

[1, shrink], strength='strong') 

layoutbox.align([axpos, lbpos], 'h_center') 

# set the height of the pos box 

lbpos.constrain_height(axpos.width * aspect * shrink, 

strength='medium') 

 

return lb, lbpos 

 

 

def layoutcolorbargridspec(parents, cax, shrink, aspect, location, pad=0.05): 

""" 

Do the layout for a colorbar, to not oeverly pollute colorbar.py 

 

`pad` is in fraction of the original axis size. 

""" 

 

gs = parents[0].get_subplotspec().get_gridspec() 

# parent layout box.... 

gslb = gs._layoutbox 

 

lb = layoutbox.LayoutBox(parent=gslb.parent, 

name=gslb.parent.name + '.cbar', 

artist=cax) 

if location in ('left', 'right'): 

lbpos = layoutbox.LayoutBox( 

parent=lb, 

name=lb.name + '.pos', 

tightwidth=False, 

pos=True, 

subplot=False, 

artist=cax) 

 

if location == 'right': 

# arrange to right of the gridpec sibbling 

layoutbox.hstack([gslb, lb], padding=pad * gslb.width, 

strength='strong') 

else: 

layoutbox.hstack([lb, gslb], padding=pad * gslb.width) 

# constrain the height and center... 

# This isn't quite right. We'd like the colorbar 

# pos to line up w/ the axes poss, not the size of the 

# gs. 

maxrow = -100000 

minrow = 1000000 

maxax = None 

minax = None 

 

for ax in parents: 

subspec = ax.get_subplotspec() 

nrows, ncols = subspec.get_gridspec().get_geometry() 

for num in [subspec.num1, subspec.num2]: 

rownum1, colnum1 = divmod(subspec.num1, ncols) 

if rownum1 > maxrow: 

maxrow = rownum1 

maxax = ax 

if rownum1 < minrow: 

minrow = rownum1 

minax = ax 

# invert the order so these are bottom to top: 

maxposlb = minax._poslayoutbox 

minposlb = maxax._poslayoutbox 

# now we want the height of the colorbar pos to be 

# set by the top and bottom of these poss 

# bottom top 

# b t 

# h = (top-bottom)*shrink 

# b = bottom + (top-bottom - h) / 2. 

lbpos.constrain_height( 

(maxposlb.top - minposlb.bottom) * 

shrink, strength='strong') 

lbpos.constrain_bottom( 

(maxposlb.top - minposlb.bottom) * 

(1 - shrink)/2 + minposlb.bottom, 

strength='strong') 

 

# set the width of the pos box 

lbpos.constrain_width(lbpos.height * (shrink / aspect), 

strength='strong') 

elif location in ('bottom', 'top'): 

lbpos = layoutbox.LayoutBox( 

parent=lb, 

name=lb.name + '.pos', 

tightheight=True, 

pos=True, 

subplot=False, 

artist=cax) 

 

if location == 'bottom': 

layoutbox.vstack([gslb, lb], padding=pad * gslb.width) 

else: 

layoutbox.vstack([lb, gslb], padding=pad * gslb.width) 

 

maxcol = -100000 

mincol = 1000000 

maxax = None 

minax = None 

 

for ax in parents: 

subspec = ax.get_subplotspec() 

nrows, ncols = subspec.get_gridspec().get_geometry() 

for num in [subspec.num1, subspec.num2]: 

rownum1, colnum1 = divmod(subspec.num1, ncols) 

if colnum1 > maxcol: 

maxcol = colnum1 

maxax = ax 

if rownum1 < mincol: 

mincol = colnum1 

minax = ax 

maxposlb = maxax._poslayoutbox 

minposlb = minax._poslayoutbox 

lbpos.constrain_width((maxposlb.right - minposlb.left) * 

shrink) 

lbpos.constrain_left( 

(maxposlb.right - minposlb.left) * 

(1-shrink)/2 + minposlb.left) 

# set the height of the pos box 

lbpos.constrain_height(lbpos.width * shrink * aspect, 

strength='medium') 

 

return lb, lbpos