def SOLVER(roadnet, surplus, objectives):
network = mygraph()
capacity = {}
supply = {i: 0. for i in roadnet.nodes()}
cost = {} # functions
#
oneway_offset = {} # for one-way roads
for i, j, road, data in roadnet.edges_iter(keys=True, data=True):
supply[j] += surplus[road]
cost_data = objectives[road]
# edge construction
if data.get('oneway', False):
# if one-way road
# record minimum allowable flow on road
zmin = cost_data.max_key()
oneway_offset[road] = zmin
supply[i] -= zmin
supply[j] += zmin
# shift and record the cost function on a forward edge only
cc = roadbm.costWrapper(cost_data)
cc_offset = offsetWrapper(cc, zmin)
network.add_edge(road, i, j)
cost[road] = cc_offset
else:
# if bi-directional road... currently, instantiate two edges
cc = roadbm.costWrapper(cost_data)
ncc = negativeWrapper(
cc) # won't have to worry about the C(0) offset
network.add_edge((road, +1), i, j)
cost[(road, +1)] = cc
#
network.add_edge((road, -1), j, i)
cost[(road, -1)] = ncc
# we need to compute the size U of the first cvxcost algorithm phase
#U = sum([ len( obj_dict ) for obj_dict in objectives.values() ])
# below is almost certainly just as good a bound, but I'm a scaredy-cat
U = sum([len(obj_dict) - 2 for obj_dict in objectives.values()])
f = MinConvexCostFlow(network, {}, supply, cost, U)
flow = {}
for i, j, road in roadnet.edges_iter(keys=True):
if road in oneway_offset:
flow[road] = f[road] + oneway_offset[road]
else:
flow[road] = f[(road, +1)] - f[(road, -1)]
flow[road] = int(flow[road])
#print flow
return flow
def SOLVER(roadnet, surplus, objectives):
network = mygraph()
capacity = {}
supply = {i: 0.0 for i in roadnet.nodes()}
cost = {} # functions
#
oneway_offset = {} # for one-way roads
for i, j, road, data in roadnet.edges_iter(keys=True, data=True):
supply[j] += surplus[road]
cost_data = objectives[road]
# edge construction
if data.get("oneway", False):
# if one-way road
# record minimum allowable flow on road
zmin = cost_data.max_key()
oneway_offset[road] = zmin
supply[i] -= zmin
supply[j] += zmin
# shift and record the cost function on a forward edge only
cc = roadbm.costWrapper(cost_data)
cc_offset = offsetWrapper(cc, zmin)
network.add_edge(road, i, j)
cost[road] = cc_offset
else:
# if bi-directional road... currently, instantiate two edges
cc = roadbm.costWrapper(cost_data)
ncc = negativeWrapper(cc) # won't have to worry about the C(0) offset
network.add_edge((road, +1), i, j)
cost[(road, +1)] = cc
#
network.add_edge((road, -1), j, i)
cost[(road, -1)] = ncc
# we need to compute the size U of the first cvxcost algorithm phase
# U = sum([ len( obj_dict ) for obj_dict in objectives.values() ])
# below is almost certainly just as good a bound, but I'm a scaredy-cat
U = sum([len(obj_dict) - 2 for obj_dict in objectives.values()])
f = MinConvexCostFlow(network, {}, supply, cost, U)
flow = {}
for i, j, road in roadnet.edges_iter(keys=True):
if road in oneway_offset:
flow[road] = f[road] + oneway_offset[road]
else:
flow[road] = f[(road, +1)] - f[(road, -1)]
flow[road] = int(flow[road])
# print flow
return flow
def discreteCostTex(S, T, ymin, ymax, zmin, zmax, zplus=None):
segment = roadbm.ONESEGMENT(S, T)
meas = roadbm.MEASURE(segment, ymin, ymax)
obj = roadbm.OBJECTIVE(meas)
Cf = roadbm.costWrapper(obj)
Z = range(zmin, zmax + 1)
C = [Cf(z) for z in Z]
cmin, cmax = min(C), max(C)
# obtain the 'star'
ZMIN, ZMAX = -max(meas), -min(meas)
CC = [(Cf(z), z) for z in range(ZMIN, ZMAX + 1)]
COPT, ZOPT = min(CC)
#str = "\\begin{tikzpicture}[x=1cm,y=.1cm]\n"
str = ''
# draw the axis
# horizontal
horz_level = np.floor(cmin)
data = {'zmin': zmin, 'zmax': zmax, 'horz': horz_level}
fmt = "\\draw [->] (%(zmin)d,%(horz)d) -- (%(zmax)f,%(horz)d) node [right] {$\\coordvar$} ;\n"
str += fmt % data
# vertical
str += "\\draw [->] (0,%(cmin)f-1) -- (0,%(cmax)f) " % {
'cmin': cmin,
'cmax': cmax
}
str += "node [above] {$\\cost(\\numarcs)$} ;\n"
# horizontal ticks
for tick in np.arange(zmin, zmax + 1, 1):
data = {'tick': tick, 'horz': horz_level}
str += "\\draw (%(tick)d,%(horz)f-.1) -- (%(tick)f,%(horz)f+.1) " % data
str += "node [below=5] {$%d$} ;\n" % tick
# scatter
for z, c in zip(Z, C):
if z == ZOPT:
str += '\\draw [fill] (%f,%f) node {$\\star$} ;\n' % (
z, c) # {$\\circ$}'
else:
str += '\\draw [fill] (%f,%f) circle (.05cm) ;\n' % (
z, c) # {$\\circ$}'
if zplus is not None and zmin <= zplus and zplus <= zmax:
str += '\\draw [] (%f,%f) circle (.2cm) ;\n' % (zplus, Cf(zplus)
) # {$\\circ$}'
#str += "\\end{tikzpicture}\n"
return str
def discreteCostTex( S, T, ymin, ymax, zmin, zmax, zplus=None ) :
segment = roadbm.ONESEGMENT( S, T )
meas = roadbm.MEASURE( segment, ymin, ymax )
obj = roadbm.OBJECTIVE( meas )
Cf = roadbm.costWrapper( obj )
Z = range(zmin,zmax+1)
C = [ Cf(z) for z in Z ]
cmin, cmax = min(C), max(C)
# obtain the 'star'
ZMIN, ZMAX = -max( meas ), -min( meas )
CC = [ ( Cf(z), z ) for z in range(ZMIN,ZMAX+1) ]
COPT, ZOPT = min(CC)
#str = "\\begin{tikzpicture}[x=1cm,y=.1cm]\n"
str = ''
# draw the axis
# horizontal
horz_level = np.floor(cmin)
data = { 'zmin' : zmin, 'zmax' : zmax, 'horz' : horz_level }
fmt = "\\draw [->] (%(zmin)d,%(horz)d) -- (%(zmax)f,%(horz)d) node [right] {$\\coordvar$} ;\n"
str += fmt % data
# vertical
str += "\\draw [->] (0,%(cmin)f-1) -- (0,%(cmax)f) " % { 'cmin' : cmin, 'cmax' : cmax }
str += "node [above] {$\\cost(\\numarcs)$} ;\n"
# horizontal ticks
for tick in np.arange(zmin,zmax+1,1) :
data = { 'tick' : tick, 'horz' : horz_level }
str += "\\draw (%(tick)d,%(horz)f-.1) -- (%(tick)f,%(horz)f+.1) " % data
str += "node [below=5] {$%d$} ;\n" % tick
# scatter
for z, c in zip( Z, C ) :
if z == ZOPT :
str += '\\draw [fill] (%f,%f) node {$\\star$} ;\n' % (z,c) # {$\\circ$}'
else :
str += '\\draw [fill] (%f,%f) circle (.05cm) ;\n' % (z,c) # {$\\circ$}'
if zplus is not None and zmin <= zplus and zplus <= zmax :
str += '\\draw [] (%f,%f) circle (.2cm) ;\n' % (zplus,Cf(zplus)) # {$\\circ$}'
#str += "\\end{tikzpicture}\n"
return str
def costFunctionTex(S, T, ymin, ymax, z=None):
if z is None:
zplus = 0
else:
zplus = z
""" C to tikz """
segment = roadbm.ONESEGMENT(S, T)
meas = roadbm.MEASURE(segment, ymin, ymax)
obj = roadbm.OBJECTIVE(meas)
Cf = roadbm.costWrapper(obj)
str = "\\begin{tikzpicture}[x=2cm,y=.1cm]\n"
# draw the axis
ZMIN, ZMAX = -max(meas), -min(meas)
WIDTH = ZMAX - ZMIN
C = [(Cf(z), z) for z in range(ZMIN, ZMAX + 1)]
CMIN, ZOPT = min(C)
CMAX, _ = max(C)
COPT = Cf(ZOPT)
ZMIN = int(min(ZMIN, np.floor(zplus)))
ZMAX = int(max(ZMAX, np.ceil(zplus)))
# horizontal
horz_level = np.floor(CMIN)
data = {'zmin': ZMIN, 'zmax': ZMAX, 'horz': horz_level}
fmt = "\\draw [->] (%(zmin)d,%(horz)d) -- (%(zmax)f,%(horz)d) node [right] {$\\coordvar$} ;\n"
str += fmt % data
# vertical
str += "\\draw [->] (0,%(cmin)f-1) -- (0,%(cmax)f) " % {
'cmin': CMIN,
'cmax': CMAX
}
str += "node [above] {$\\cost(\\numarcs)$} ;\n"
# horizontal ticks
for tick in np.arange(ZMIN, ZMAX + 1, 1):
data = {'tick': tick, 'horz': horz_level}
str += "\\draw (%(tick)d,%(horz)f-.1) -- (%(tick)f,%(horz)f+.1) " % data
str += "node [below=5] {$%d$} ;\n" % tick
# draw dashed C curve
def drawpieces(ZZ, style):
str = ''
for z1, z2 in zip(ZZ[:-1], ZZ[1:]):
c1 = Cf(z1)
c2 = Cf(z2)
data = {'z1': z1, 'z2': z2, 'c1': c1, 'c2': c2, 'style': style}
str += "\\draw [%(style)s] (%(z1)f,%(c1)f) -- (%(z2)f,%(c2)f) ;\n" % data
return str
# draw dashed C, all of it
str += drawpieces(range(ZMIN, ZMAX + 1), 'dashed')
# draw C so far
lastz = int(np.floor(zplus))
str += drawpieces(range(ZMIN, lastz + 1) + [zplus], 'thick')
# add local vertical line
str += texvline(zplus, horz_level - 1, max(CMAX, Cf(zplus)) + 1, 'dashed')
# add optimal
str += "\\draw node at (%(z)f,%(C)f) {$\\star$} ;\n" % {
'z': ZOPT,
'C': COPT
}
str += "\\end{tikzpicture}\n"
return str
def costFunctionTex( S, T, ymin, ymax, z=None ) :
if z is None :
zplus = 0
else :
zplus = z
""" C to tikz """
segment = roadbm.ONESEGMENT( S, T )
meas = roadbm.MEASURE( segment, ymin, ymax )
obj = roadbm.OBJECTIVE( meas )
Cf = roadbm.costWrapper( obj )
str = "\\begin{tikzpicture}[x=2cm,y=.1cm]\n"
# draw the axis
ZMIN, ZMAX = -max( meas ), -min( meas )
WIDTH = ZMAX - ZMIN
C = [ ( Cf(z), z ) for z in range(ZMIN,ZMAX+1) ]
CMIN, ZOPT = min(C)
CMAX, _ = max(C)
COPT = Cf(ZOPT)
ZMIN = int( min( ZMIN, np.floor( zplus ) ) )
ZMAX = int( max( ZMAX, np.ceil( zplus ) ) )
# horizontal
horz_level = np.floor(CMIN)
data = { 'zmin' : ZMIN, 'zmax' : ZMAX, 'horz' : horz_level }
fmt = "\\draw [->] (%(zmin)d,%(horz)d) -- (%(zmax)f,%(horz)d) node [right] {$\\coordvar$} ;\n"
str += fmt % data
# vertical
str += "\\draw [->] (0,%(cmin)f-1) -- (0,%(cmax)f) " % { 'cmin' : CMIN, 'cmax' : CMAX }
str += "node [above] {$\\cost(\\numarcs)$} ;\n"
# horizontal ticks
for tick in np.arange(ZMIN,ZMAX+1,1) :
data = { 'tick' : tick, 'horz' : horz_level }
str += "\\draw (%(tick)d,%(horz)f-.1) -- (%(tick)f,%(horz)f+.1) " % data
str += "node [below=5] {$%d$} ;\n" % tick
# draw dashed C curve
def drawpieces( ZZ, style ) :
str = ''
for z1,z2 in zip( ZZ[:-1], ZZ[1:] ) :
c1 = Cf(z1)
c2 = Cf(z2)
data = { 'z1' : z1, 'z2' : z2, 'c1' : c1, 'c2' : c2, 'style' : style }
str += "\\draw [%(style)s] (%(z1)f,%(c1)f) -- (%(z2)f,%(c2)f) ;\n" % data
return str
# draw dashed C, all of it
str += drawpieces( range(ZMIN,ZMAX+1), 'dashed' )
# draw C so far
lastz = int( np.floor( zplus ) )
str += drawpieces( range(ZMIN,lastz+1) + [ zplus ], 'thick' )
# add local vertical line
str += texvline( zplus, horz_level-1, max( CMAX, Cf(zplus) ) + 1, 'dashed' )
# add optimal
str += "\\draw node at (%(z)f,%(C)f) {$\\star$} ;\n" % { 'z' : ZOPT, 'C' : COPT }
str += "\\end{tikzpicture}\n"
return str
