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Show optimal solution on simplex path and cosmetic changes.
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The optimal solution (filled in) and the initial solution (open) are both shown
always shown on the visualization. The add_feasible_region function takes an
argument called theme which can be light, dark, or outline. This is used to
create the LP feasible region outline and for highlighting the current node's
feasible region in the branch and bound visual.
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@henryrobbins
henryrobbins committed Oct 29, 2020
1 parent 422e9dd commit 97c3136
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Showing 2 changed files with 101 additions and 60 deletions.
4 changes: 1 addition & 3 deletions gilp/simplex.py
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Original file line number Diff line number Diff line change
Expand Up @@ -597,9 +597,7 @@ def branch_and_bound_iteration(lp: LP,
try:
sol = simplex(lp=lp, feas_tol=feas_tol)
x = sol.x
B = sol.B
value = sol.obj_val
opt = sol.optimal
except Infeasible:
return BnbIter(fathomed=True, incumbent=incumbent,
best_bound=best_bound, left_LP=None, right_LP=None)
Expand Down Expand Up @@ -639,7 +637,7 @@ def create_branch(lp, i, bound, branch):
incumbent = x
best_bound = value
return BnbIter(fathomed=True, incumbent=incumbent,
best_bound=best_bound, left_LP=None, right_LP=None)
best_bound=best_bound, left_LP=None, right_LP=None)
return True, incumbent, best_bound, None, None
return BnbIter(fathomed=False, incumbent=incumbent,best_bound=best_bound,
left_LP=left_LP, right_LP=right_LP)
Expand Down
157 changes: 100 additions & 57 deletions gilp/visualize.py
View file
Original file line number Diff line number Diff line change
Expand Up @@ -2,9 +2,8 @@
import networkx as nx
import itertools
import plotly.graph_objects as plt
from .simplex import (LP, phase_one, simplex_iteration, simplex, equality_form,
branch_and_bound_iteration, UnboundedLinearProgram,
Infeasible)
from .simplex import (LP, simplex, equality_form, branch_and_bound_iteration,
UnboundedLinearProgram, Infeasible)
from .style import (format, Figure, equation_string, linear_string, label,
table, vector, scatter, equation, polygon, plot_tree)
from .geometry import (intersection, halfspace_intersection, interior_point,
Expand All @@ -26,33 +25,25 @@
Return vector indices.
"""

# Sphinx documentation:
# BACKGROUND_COLOR = '#FCFCFC'
# FIG_WIDTH = 700

# Jupyter Notebook:
# BACKGROUND_COLOR = 'white'
# FIG_WIDTH = 950

# Color theme

PRIMARY_COLOR = '#1976d2'
PRIMARY_LIGHT_COLOR = '#63a4ff'
PRIMARY_DARK_COLOR = '#004ba0'
SECONDARY_COLOR = '#d60000'
PRIMARY_COLOR = '#1565c0'
PRIMARY_LIGHT_COLOR = '#5e92f3'
PRIMARY_DARK_COLOR = '#003c8f'
SECONDARY_COLOR = '#d50000'
SECONDARY_LIGHT_COLOR = '#ff5131'
SECONDARY_DARK_COLOR = '#9c0000'
SECONDARY_DARK_COLOR = '#9b0000'
PRIMARY_FONT_COLOR = '#ffffff'
SECONDARY_FONT_COLOR = '#ffffff'
TERTIARY_COLOR = '#DFDFDF'
TERTIARY_LIGHT_COLOR = 'white'
TERTIARY_LIGHT_COLOR = 'white' # Jupyter Notebook: white, Sphinx: #FCFCFC
TERTIARY_DARK_COLOR = '#404040'

# Figure Dimensions

FIG_HEIGHT = 500
"""Default figure height."""
FIG_WIDTH = 950
FIG_WIDTH = 950 # Jupyter Notebook: 950, Sphinx: 700
"""Default figure width."""
LEGEND_WIDTH = 200
"""Default legend width."""
Expand Down Expand Up @@ -89,15 +80,14 @@

BFS_SCATTER = dict(marker=dict(size=20, color='gray', opacity=1e-7),
hoverinfo='text',
hoverlabel=dict(bgcolor=SECONDARY_LIGHT_COLOR,
bordercolor=SECONDARY_DARK_COLOR,
hoverlabel=dict(bgcolor=TERTIARY_LIGHT_COLOR,
bordercolor=TERTIARY_DARK_COLOR,
font_family='Arial',
font_color=SECONDARY_FONT_COLOR,
font_color=TERTIARY_DARK_COLOR,
align='left'))
"""Template attributes for LP basic feasible solutions (BFS)."""

VECTOR = dict(mode='lines', line=dict(width=6,
color=SECONDARY_COLOR), visible=False)
VECTOR = dict(mode='lines', line_color=SECONDARY_COLOR, visible=False)
"""Template attributes for a 3d or 3d vector."""

CONSTRAINT_LINE = dict(mode='lines', showlegend=True,
Expand All @@ -124,11 +114,11 @@
ISOPROFIT_IN_POLYGON = dict(mode="lines+markers",
surfacecolor=SECONDARY_COLOR,
marker=dict(size=5,
color=SECONDARY_COLOR,
opacity=1),
symbol='circle',
color=SECONDARY_COLOR),
line=dict(width=5,
color=SECONDARY_COLOR),
visible=False)
visible=False)
"""Template attributes for (3d) LP isoprofit plane (interior)."""

ISOPROFIT_OUT_POLYGON = dict(surfacecolor='gray', mode="none",
Expand Down Expand Up @@ -163,7 +153,8 @@ def set_up_figure(n: int, type: str = 'table') -> Figure:
layout = dict(width=FIG_WIDTH,
height=FIG_HEIGHT,
title=dict(text="<b>Geometric Interpretation of LPs</b>",
font=dict(size=18, color=TERTIARY_DARK_COLOR),
font=dict(size=18,
color=TERTIARY_DARK_COLOR),
x=0, y=0.99, xanchor='left', yanchor='top'),
legend=dict(title=dict(text='<b>Constraint(s)</b>',
font=dict(size=14)),
Expand Down Expand Up @@ -220,9 +211,13 @@ def axis(n: int):
name='test',
hoverinfo='none',
fillcolor=PRIMARY_COLOR,
marker=dict(size=5,
color=SECONDARY_COLOR,
opacity=1))
line_color=PRIMARY_DARK_COLOR,
line=dict(width=4),
marker_line=dict(width=2,
color=SECONDARY_COLOR),
marker=dict(size=9,
color=TERTIARY_LIGHT_COLOR,
opacity=0.99))
scatter = [plt.Scatter({**default_scatter, **dict(line_color='#173D90')}),
plt.Scatter({**default_scatter, **dict(line_color='#1469FE')}),
plt.Scatter({**default_scatter, **dict(line_color='#65ADFF')}),
Expand All @@ -235,21 +230,25 @@ def axis(n: int):
visible=True,
showlegend=False,
hoverinfo='none',
surfacecolor=PRIMARY_COLOR,
surfacecolor=PRIMARY_LIGHT_COLOR,
line=dict(width=6, color=PRIMARY_COLOR),
marker_line=dict(width=1,
color=SECONDARY_COLOR),
marker=dict(size=5,
color=SECONDARY_COLOR,
opacity=1))]
symbol='circle-open',
color=SECONDARY_LIGHT_COLOR,
opacity=0.99))]

# Named annotations templates for branch and bound tree nodes
layout['annotations'] = [
dict(name='current', visible=False,
align="center", bgcolor=SECONDARY_LIGHT_COLOR,
bordercolor=SECONDARY_DARK_COLOR, borderwidth=2, borderpad=3,
font=dict(size=12, color=TERTIARY_DARK_COLOR), ax=0, ay=0),
align="center", bgcolor='#45568B',
bordercolor=TERTIARY_DARK_COLOR, borderwidth=2, borderpad=3,
font=dict(size=12, color=TERTIARY_LIGHT_COLOR), ax=0, ay=0),
dict(name='explored', visible=False,
align="center", bgcolor=PRIMARY_LIGHT_COLOR,
bordercolor=PRIMARY_DARK_COLOR, borderwidth=2, borderpad=3,
font=dict(size=12, color=PRIMARY_FONT_COLOR), ax=0, ay=0),
align="center", bgcolor='#D8E4F9',
bordercolor=TERTIARY_DARK_COLOR, borderwidth=2, borderpad=3,
font=dict(size=12, color=TERTIARY_DARK_COLOR), ax=0, ay=0),
dict(name='unexplored', visible=False,
align="center", bgcolor=TERTIARY_LIGHT_COLOR,
bordercolor=TERTIARY_DARK_COLOR, borderwidth=2, borderpad=3,
Expand Down Expand Up @@ -280,7 +279,7 @@ def add_feasible_region(fig: Figure,
set_axes: bool = True,
basic_sol: bool = True,
show_basis: bool = True,
color: str = None):
theme: str = 'light'):
"""Add the feasible region of the LP to the figure.
Add a visualization of the LP feasible region to the figure. In 2d, the
Expand All @@ -293,8 +292,7 @@ def add_feasible_region(fig: Figure,
set_axis (bool): True if the figure's axes should be set.
basic_sol (bool): True if the entire BFS is shown. Default to True.
show_basis (bool) : True if the basis is shown within the BFS label.
color (str): Color of the feasible region. Defaults to None.
theme (str): One of light, dark, or outline. Defaults to light
Raises:
ValueError: The LP must be in standard inequality form.
InfiniteFeasibleRegion: Can not visualize.
Expand Down Expand Up @@ -336,10 +334,26 @@ def add_feasible_region(fig: Figure,
unique_bfs, unique_val = np.abs(unique[:,:-1]), unique[:,-1]
pts = [np.array([bfs[:n]]).transpose() for bfs in unique_bfs]

# light theme by default
opacity = 0.2
surface_color = PRIMARY_COLOR
line_color = PRIMARY_DARK_COLOR

if theme == 'dark':
surface_color = PRIMARY_DARK_COLOR
line_color = '#002659'
opacity = 0.2 + {2: 0.25, 3: 0.1}[lp.n]
if theme == 'outline':
surface_color = TERTIARY_LIGHT_COLOR
line_color = TERTIARY_DARK_COLOR
opacity = 0.1

# Plot feasible region
if n == 2:
fig.add_trace(polygon(x_list=pts,
fillcolor=color,
fillcolor=surface_color,
line_color=line_color,
opacity=opacity,
template=REGION_2D_POLYGON), 'feasible_region')
if n == 3:
if via_hs_intersection:
Expand All @@ -355,7 +369,9 @@ def add_feasible_region(fig: Figure,
if len(face_pts) > 0:
traces.append(polygon(x_list=face_pts,
ordered=via_hs_intersection,
surfacecolor=color,
surfacecolor=surface_color,
line_color=line_color,
opacity=opacity,
template=REGION_3D_POLYGON))
fig.add_traces(traces,'feasible_region')

Expand Down Expand Up @@ -631,8 +647,7 @@ def add_simplex_path(fig: Figure,
path = simplex(lp=lp, pivot_rule=rule, initial_solution=initial_solution,
iteration_limit=iteration_limit,feas_tol=feas_tol).path

# Add initial solution and tableau
fig.add_trace(scatter(x_list=[path[0].x[:lp.n]]),'path0')
# Add initial tableau
tab_template = {'canonical': CANONICAL_TABLE,
'dictionary': DICTIONARY_TABLE}[tableau_form]
if tableaus:
Expand Down Expand Up @@ -664,6 +679,12 @@ def add_simplex_path(fig: Figure,
fig.add_trace(mid_tab,('table'+str(i*2-1)), row=1, col=2)
fig.add_trace(tab,('table'+str(i*2)), row=1, col=2)

# Add initial and optimal solution
fig.add_trace(scatter(x_list=[path[0].x[:lp.n]]),'path0')
fig.add_trace(scatter(x_list=[path[-1].x[:lp.n]],
marker_symbol='circle',
marker_color=SECONDARY_COLOR),'optimal')

# Create each step of the iteration slider
steps = []
for i in range(2*len(path)-1):
Expand All @@ -672,6 +693,7 @@ def add_simplex_path(fig: Figure,
visible[fig.get_indices('table',containing=True)] = False
visible[fig.get_indices('path',containing=True)] = False
visible[fig.get_indices('tree_edges',containing=True)] = True
visible[fig.get_indices('optimal')] = True
if tableaus:
visible[fig.get_indices('table'+str(i))] = True
for j in range(i+1):
Expand All @@ -690,18 +712,33 @@ def add_simplex_path(fig: Figure,
return plt.layout.Slider(params)


def lp_visual(lp: LP) -> plt.Figure:
"""Render a plotly figure visualizing the geometry of an LP."""
def lp_visual(lp: LP,
basic_sol: bool = True,
show_basis: bool = True,) -> plt.Figure:
"""Render a plotly figure visualizing the geometry of an LP.
Args:
lp (LP): LP on which to run simplex
basic_sol (bool): True if the entire BFS is shown. Default to True.
show_basis (bool) : True if the basis is shown within the BFS label.
Returns:
plt.Figure: A plotly figure showing the geometry of feasible region.
"""
fig = set_up_figure(lp.n)
add_feasible_region(fig, lp)
add_feasible_region(fig=fig,
lp=lp,
basic_sol=basic_sol,
show_basis=show_basis)
add_constraints(fig, lp)
slider = add_isoprofits(fig, lp)
fig.update_layout(sliders=[slider])
return fig


def simplex_visual(lp: LP,
basic_sol: bool = True,
show_basis: bool = True,
tableau_form: str = 'dictionary',
rule: str = 'bland',
initial_solution: np.ndarray = None,
Expand All @@ -711,6 +748,8 @@ def simplex_visual(lp: LP,
Args:
lp (LP): LP on which to run simplex
basic_sol (bool): True if the entire BFS is shown. Default to True.
show_basis (bool) : True if the basis is shown within the BFS label.
tableau_form (str): Displayed tableau form. Default is 'dictionary'
rule (str): Pivot rule to be used. Default is 'bland'
initial_solution (np.ndarray): An initial solution. Default is None.
Expand All @@ -728,7 +767,10 @@ def simplex_visual(lp: LP,
n,m,A,b,c = lp.get_coefficients()

fig = set_up_figure(lp.n)
add_feasible_region(fig, lp)
add_feasible_region(fig=fig,
lp=lp,
basic_sol=basic_sol,
show_basis=show_basis)
add_constraints(fig, lp)
iter_slider = add_simplex_path(fig=fig,
lp=lp,
Expand Down Expand Up @@ -792,13 +834,10 @@ def bnb_visual(lp: LP,
try:
sol = simplex(lp=current)
x = sol.x
B = sol.B
value = sol.obj_val
opt = sol.optimal
z_str = format(np.matmul(lp.c.transpose(),x[:lp.n]))
x_str = ', '.join(map(str, [format(i) for i in x[:lp.n]]))
x_str = 'x* = (%s)' % x_str
sol_str = '%s<br>%s' % (z_str,x_str)
sol_str = '%s<br>%s' % (format(value), x_str)
except Infeasible:
sol_str = 'infeasible'

Expand All @@ -812,13 +851,17 @@ def bnb_visual(lp: LP,

# draw outline of original LP and remaining feasible region
if current != lp:
add_feasible_region(fig, lp, color='white', set_axes=False,
basic_sol=False, show_basis=False)
add_feasible_region(fig=fig,
lp=lp,
theme='outline',
set_axes=False,
basic_sol=False,
show_basis=False)
for feas_reg in feasible_regions:
try:
if current == feas_reg:
add_feasible_region(fig, feas_reg,
color=PRIMARY_DARK_COLOR,
theme='dark',
set_axes=False, basic_sol=False,
show_basis=False)
else:
Expand Down

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