def redraw_fn(f, axes):
img = imread(img_files[f])
x1, y1, w1, h1 = track_gt[f]
x2, y2, w2, h2 = tuple(sample[f].tolist())
x1 = int(x1 - w1 / 2)
x2 = int(x2 - w2 / 2)
y1 = int(y1 - h1 / 2)
y2 = int(y2 - h2 / 2)
if not redraw_fn.initialized:
im = axes.imshow(img, animated=True)
bb1 = Rectangle(
(x1, y1),
w1,
h1,
fill=False, # remove background
edgecolor="red",
gid='gt')
bb2 = Rectangle(
(x2, y2),
w2,
h2,
fill=False, # remove background
edgecolor="blue",
gid='sample')
t1 = axes.text(0,
0,
'[{} {}]'.format(x1, y1),
bbox=dict(facecolor='red', alpha=0.5))
t2 = axes.text(300,
0,
'[{} {}]'.format(x2, y2),
bbox=dict(facecolor='blue', alpha=0.5))
axes.add_patch(bb1)
axes.add_patch(bb2)
redraw_fn.im = im
redraw_fn.bb1 = bb1
redraw_fn.bb2 = bb2
redraw_fn.t1 = t1
redraw_fn.t2 = t2
redraw_fn.initialized = True
else:
redraw_fn.im.set_array(img)
redraw_fn.bb1.set_xy((x1, y1))
redraw_fn.bb1.set_width(w1)
redraw_fn.bb1.set_height(h1)
redraw_fn.t1.set_text('[{} {}]'.format(x1, y1))
redraw_fn.bb2.set_xy((x2, y2))
redraw_fn.bb2.set_width(w2)
redraw_fn.bb2.set_height(h2)
redraw_fn.t2.set_text('[{} {}]'.format(x2, y2))
def redraw_fn(f, axes):
img = imread(img_files[f])
x, y, w, h = tuple(bbox[f, :])
w = w - x
h = h - y
frame = frames[f]
vis = viss[f]
if not redraw_fn.initialized:
im = axes.imshow(img, animated=True)
bb = Rectangle(
(x, y),
w,
h,
fill=False, # remove background
edgecolor="red")
t1 = axes.text(0,
0,
'[f:{} vis:{:1.2f}]'.format(frame, vis),
bbox=dict(facecolor='red', alpha=0.5))
axes.add_patch(bb)
redraw_fn.im = im
redraw_fn.bb1 = bb
redraw_fn.t1 = t1
redraw_fn.initialized = True
else:
redraw_fn.im.set_array(img)
redraw_fn.bb1.set_xy((x, y))
redraw_fn.bb1.set_width(w)
redraw_fn.bb1.set_height(h)
redraw_fn.t1.set_text('[f:{} vis:{:1.2f}]'.format(frame, vis))
def create_bbox(bbox, color):
return Rectangle(
(bbox[0], bbox[1]),
bbox[2],
bbox[3],
fill=False, # remove background\n",
edgecolor=color)
def redraw_fn(f, ax):
img = imgs[f]
box = boxs[f]
x, y, w, h = box
if not redraw_fn.initialized:
redraw_fn.img_handle = ax.imshow(img)
box_artist = Rectangle((x, y), w, h,
fill=False, # remove background
lw=2,
edgecolor="red")
ax.add_patch(box_artist)
redraw_fn.box_handle = box_artist
redraw_fn.last_time = time.time()
redraw_fn.text_handle = ax.text(0., 1 - 0.05,
'Resolution {}x{}, FPS: {:.2f}'.format(img.shape[1], img.shape[0], 0),
transform=ax.transAxes,
color='yellow', size=12)
redraw_fn.initialized = True
else:
redraw_fn.img_handle.set_array(img)
redraw_fn.box_handle.set_xy((x, y))
redraw_fn.box_handle.set_width(w)
redraw_fn.box_handle.set_height(h)
current_time = time.time()
redraw_fn.text_handle.set_text('Resolution {}x{}, FPS: {:.2f}'.format(img.shape[1], img.shape[0],
1 / (current_time - redraw_fn.last_time)))
redraw_fn.last_time = current_time
def make_placement_plot(nodes, pl, scl, dest):
# Read bookshelf files
parse_bookshelf_scl(scl)
node_dict = dict()
parse_bookshelf_nodes(nodes, node_dict)
parse_bookshelf_pl(pl, node_dict)
fig = plt.figure() # Figure
ax = fig.add_subplot(1, 1, 1) # AxesSubplot
patches = set()
for k, v in node_dict.items():
llx, lly = v.llx, v.lly
w, h = v.width, v.height
patches.add(Rectangle((llx, lly), w, h))
print("Adding collection.")
ax.add_collection(PatchCollection(patches, alpha=0.4))
print("Done.")
fig.show()
ax.set_xlim([0, 1000])
ax.set_ylim([0, 1000])
fig.savefig('test.png')
def plotobs(self, ax, scale=1):
'''plot all obstacles'''
obstacles = scale * np.array(self.obstacles)
if self.dim == 2:
for box in obstacles:
l = box[2] - box[0]
w = box[3] - box[1]
box_plt = Rectangle((box[0], box[1]),
l,
w,
color='k',
zorder=1)
ax.add_patch(box_plt)
elif self.dim == 3:
for box in obstacles:
X, Y, Z = cuboid_data(box)
ax.plot_surface(X,
Y,
Z,
rstride=1,
cstride=1,
color=(0.1, 0.15, 0.3, 0.2),
zorder=1)
else:
print('can not plot for given dimensions')
def square(r, c, size=1, facecolor='k', edgecolor='0.7', linewidth=None):
from matplotlib.pyplot import Rectangle
# r and c must be swapped: row -> y axis, col -> x axis
return Rectangle((c, r),
size,
size,
facecolor=facecolor,
edgecolor=edgecolor,
linewidth=linewidth)
def bound_words(fig, bounds, hold=True):
ax = fig.gca()
for bound in bounds:
_, x, y, width, height = bound
ax.add_artist(
Rectangle((x, y), width, height, fill=False, edgecolor='k'))
if hold:
show()
def redraw_fn(idx, axes):
idx += 1
img = imread(img_files[idx])
x_gt, y_gt, w_gt, h_gt = vot_rect(bboxes_gt[idx])
b_seq = bbox_seq[idx - 1].split(',')
b_seq = map(float, b_seq)
overlap = float(overlap_seq[idx - 1])
objectness = float(objectness_seq[idx - 1])
if not redraw_fn.initialized:
# import pdb; pdb.set_trace()
axes, axes_p = axes
redraw_fn.im_p = axes_p.imshow(imread(plot_png))
redraw_fn.im = axes.imshow(img)
redraw_fn.bb1 = Rectangle((x_gt, y_gt), w_gt, h_gt, fill=False, edgecolor='red', linewidth=5)
redraw_fn.bb2 = Rectangle((b_seq[0], b_seq[1]), b_seq[2], b_seq[3], fill=False, edgecolor='blue', linewidth=5)
axes.add_patch(redraw_fn.bb2)
axes.add_patch(redraw_fn.bb1)
redraw_fn.text1 = axes.text(0.03, 0.97, '{}: {}'.format(seq, idx+1), fontdict={'size':10,},
ha='left', va='top', bbox={'facecolor':'yellow', 'alpha':0.7}, transform=axes.transAxes)
redraw_fn.text2 = axes.text(0.03, 0.92, 'olap: {:.2f}'.format(overlap), fontdict={'size':10,},
ha='left', va='top', bbox={'facecolor':'blue', 'alpha':0.7}, transform=axes.transAxes)
redraw_fn.text3 = axes.text(0.03, 0.87, 'obj: {:.2f}'.format(objectness), fontdict={'size':10,},
ha='left', va='top', bbox={'facecolor':'red', 'alpha':0.7}, transform=axes.transAxes)
redraw_fn.text1_p = axes_p.text(0.03, 0.97, '{}: {}'.format(seq, idx+1), fontdict={'size':10,},
ha='left', va='top', bbox={'facecolor':'yellow', 'alpha':0.7}, transform=axes_p.transAxes)
redraw_fn.text2_p = axes_p.text(0.03, 0.92, 'olap: {:.2f}'.format(overlap), fontdict={'size':10,},
ha='left', va='top', bbox={'facecolor':'blue', 'alpha':0.7}, transform=axes_p.transAxes)
redraw_fn.text3_p = axes_p.text(0.03, 0.87, 'obj: {:.2f}'.format(objectness), fontdict={'size':10,},
ha='left', va='top', bbox={'facecolor':'red', 'alpha':0.7}, transform=axes_p.transAxes)
redraw_fn.initialized = True
else:
# import pdb; pdb.set_trace()
redraw_fn.im.set_array(img)
# redraw_fn.im_p.set_array(imread(plot_png))
set_bbox(redraw_fn.bb1, vot_rect(bboxes_gt[idx]))
set_bbox(redraw_fn.bb2, b_seq)
redraw_fn.text1.set_text('{}: {}'.format(seq, idx+1))
redraw_fn.text2.set_text('olap: {:.2f}'.format(overlap))
redraw_fn.text3.set_text('obj: {:.2f}'.format(objectness))
redraw_fn.text1_p.set_text('{}: {}'.format(seq, idx+1))
redraw_fn.text2_p.set_text('olap: {:.2f}'.format(overlap))
redraw_fn.text3_p.set_text('obj: {:.2f}'.format(objectness))
def make_plot(language, xs, ys):
settings = dict(xmin=0,
xmax=5,
ymin=0,
ymax=0.6,
magmin=0.05,
magmax=0.5,
coercivitymin=1.5,
coercivitymax=4)
colour_main = "#ffffff"
colour_highlight = "#ffffff"
pyplot.gcf().set_size_inches(80 / 25.4, 58 / 25.4)
pyplot.xlabel(r"$B_{\mathrm{cr}} / B_\mathrm{c}$")
pyplot.ylabel(r"$M_{\mathrm{rs}} / M_{\mathrm{s}}$")
pyplot.xlim(settings["xmin"], settings["xmax"])
pyplot.ylim(settings["ymin"], settings["ymax"])
pyplot.gca().add_patch(
Rectangle((0, 0), settings["xmax"], settings["ymax"], fc=colour_main))
pyplot.gca().add_patch(
Rectangle((settings["coercivitymin"], settings["magmin"]),
settings["coercivitymax"] - settings["coercivitymin"],
settings["magmax"] - settings["magmin"],
fc=colour_highlight))
pyplot.annotate("SD", (0.05, 0.53))
pyplot.annotate("PSD", (1.60, 0.42))
pyplot.annotate({"it": "PD", "en": "MD"}[language], (4.1, 0.01))
pyplot.hlines([settings["magmin"], settings["magmax"]], 0., 5.)
pyplot.vlines([settings["coercivitymin"], settings["coercivitymax"]], 0.0,
0.6)
pyplot.subplots_adjust(left=0.15, bottom=0.18, right=0.97, top=0.96)
pyplot.plot(xs,
ys,
"o",
color="none",
mew=0.6,
ms=4.0,
mec="black",
mfc="none",
alpha=0.6)
pyplot.savefig(os.path.join("..", "script-output", "fig-day-plot.pdf"),
transparent=True)
def draw_mesh_boundary(mesh: Mesh, ax):
width = mesh.x_range[1] - mesh.x_range[0]
height = mesh.y_range[1] - mesh.y_range[0]
r = Rectangle((-width / 2, -height / 2),
width,
height,
fill=False,
linewidth=0.5,
edgecolor='black',
linestyle='--',
zorder=20)
ax.add_artist(r)
def generate_plot(circuit):
x_coords = [c.x for c in circuit.terminals]
y_coords = [c.y for c in circuit.terminals]
x_min, y_min = min(x_coords), min(y_coords)
x_max, y_max = max(x_coords), max(y_coords)
#---------------------------------------
# Make placement plot
#---------------------------------------
from matplotlib.pyplot import Rectangle
from matplotlib.collections import PatchCollection
fig = plt.figure()
fig.set_size_inches(10, 10)
ax = fig.add_subplot(1, 1, 1)
# Plot the placement
patches = set()
for comb in circuit.combs:
patches.add(Rectangle((comb.x, comb.y), comb.w, comb.h))
ax.add_collection(
PatchCollection(patches,
facecolor='#147DFF',
edgecolor='dimgrey',
lw=0.25))
patches = set()
for latch in circuit.latches:
patches.add(Rectangle((latch.x, latch.y), latch.w, latch.h))
ax.add_collection(
PatchCollection(patches,
facecolor='#969696',
edgecolor='dimgrey',
lw=0.25))
# ax.set_xlim([0, x_max])
# ax.set_ylim([0, y_max])
ax.autoscale()
fig.savefig('foo2.png', dpi=200)
def draw_cell_boundary(ax,
width,
height,
x_offset=0,
y_offset=0,
color=(0.8, 0.8, 0.8)):
r = Rectangle((-width / 2 + x_offset, -height / 2 + y_offset),
width,
height,
fill=False,
linewidth=1,
edgecolor=color,
linestyle='--')
ax.plot(x_offset, y_offset, 'b+', color=color)
ax.add_artist(r)
return r
def extended_hinton(ax,
V,
C,
vmax=None,
cmin=None,
cmax=None,
cmap=None,
matrix_style=False,
alpha=1,
enforce_box=False):
if cmap is None:
cmap = cm.jet
if vmax is None: vmax = np.amax(np.abs(V))
if cmax is None: cmax = np.amax(C)
if cmin is None: cmin = np.amin(C)
cnorm = Normalize(vmin=cmin, vmax=cmax, clip=True)
cmapable = ScalarMappable(norm=cnorm, cmap=cmap)
if matrix_style:
V, C = V.T, C.T
ax.patch.set_facecolor([0, 0, 0, 0])
for (x, y), w in np.ndenumerate(V):
s = C[x, y]
color = cmap(cnorm(s)) # cmap(s / cmax)
size = np.abs(w / vmax)
rect = Rectangle([x - size / 2, y - size / 2],
size,
size,
facecolor=color,
edgecolor=color,
alpha=alpha)
ret = ax.add_patch(rect)
if enforce_box:
ax.axis('tight')
try:
ax.set_aspect('equal', 'box')
except:
pass
#ax.autoscale_view()
#ax.invert_yaxis()
return cnorm
def drawPlot(self):
ion()
self.fig = plt.figure()
# draw cart
self.axes = self.fig.add_subplot(111, aspect='equal')
self.box = Rectangle(xy=(self.cart_location - self.cartwidth / 2.0, -self.cartheight),
width=self.cartwidth, height=self.cartheight)
self.axes.add_artist(self.box)
self.box.set_clip_box(self.axes.bbox)
# draw pole
self.pole = Line2D([self.cart_location, self.cart_location + np.sin(self.pole_angle)],
[0, np.cos(self.pole_angle)], linewidth=3, color='black')
self.axes.add_artist(self.pole)
self.pole.set_clip_box(self.axes.bbox)
# set axes limits
self.axes.set_xlim(-10, 10)
self.axes.set_ylim(-0.5, 2)
def render_batch_sample_predictions(positives,
batch_sample,
color=("g", "b", "purple")):
images = batch_sample.to("cpu").detach(
) if batch_sample.device.type == "cuda" else batch_sample.detach()
# config artist assign
n_row, n_col, figsize = [2, 4,
(15,
7.5)] if len(images) == 8 else [2, 2, (8, 8)]
fig, axis = figure_preproduction(n_row, n_col, figsize)
for i, (mods, positive) in enumerate(zip(images, positives)):
ax = axis[divmod(i, n_col)]
ax.imshow(mods[1], cmap="gray")
for x, y, w, h, lbl in positive:
ax.add_patch(
Rectangle((x - w / 2, y - h / 2),
w,
h,
fill=False,
color=color[int(lbl)]))
plt.show()
def make_color_legend_rects(colors, labels=None):
"""
Make list of rectangles and labels for making legends.
Parameters
----------
colors : pandas.Series or list
Pandas series whose values are colors and index is labels.
Alternatively, you can provide a list with colors and provide the labels
as a list.
labels : list
If colors is a list, this should be the list of corresponding labels.
Returns
-------
out : pd.Series
Pandas series whose values are matplotlib rectangles and whose index are
the legend labels for those rectangles. You can add each of these
rectangles to your axis using ax.add_patch(r) for r in out then create a
legend whose labels are out.values and whose labels are
legend_rects.index:
for r in legend_rects:
ax.add_patch(r)
lgd = ax.legend(legend_rects.values, labels=legend_rects.index)
"""
from matplotlib.pyplot import Rectangle
if labels:
d = dict(zip(labels, colors))
se = pd.Series(d)
else:
se = colors
rects = []
for i in se.index:
r = Rectangle((0, 0), 0, 0, fc=se[i])
rects.append(r)
out = pd.Series(rects, index=se.index)
return out
def redraw_fn(idx, axes):
idx += 1
img = imread(img_files[idx])
if not redraw_fn.initialized:
redraw_fn.im = axes.imshow(img)
if args.r is not None:
x, y, w, h = bbox_seq_dict[args.r][idx]
redraw_fn.bb1 = Rectangle((x, y),
w,
h,
fill=False,
edgecolor='red',
alpha=0.7,
linewidth=3)
axes.add_patch(redraw_fn.bb1)
if args.g is not None:
x, y, w, h = bbox_seq_dict[args.g][idx]
redraw_fn.bb2 = Rectangle((x, y),
w,
h,
fill=False,
edgecolor='green',
alpha=0.7,
linewidth=3)
axes.add_patch(redraw_fn.bb2)
if args.b is not None:
x, y, w, h = bbox_seq_dict[args.b][idx]
redraw_fn.bb3 = Rectangle((x, y),
w,
h,
fill=False,
edgecolor='blue',
alpha=0.7,
linewidth=3)
axes.add_patch(redraw_fn.bb3)
if args.y is not None:
x, y, w, h = bbox_seq_dict[args.y][idx]
redraw_fn.bb4 = Rectangle((x, y),
w,
h,
fill=False,
edgecolor='yellow',
alpha=0.7,
linewidth=3)
axes.add_patch(redraw_fn.bb4)
redraw_fn.text1 = axes.text(0.03,
0.97,
'{}: {}'.format(seq, idx + 1),
fontdict={
'size': 10,
},
ha='left',
va='top',
bbox={
'facecolor': 'yellow',
'alpha': 0.7
},
transform=axes.transAxes)
redraw_fn.initialized = True
else:
redraw_fn.im.set_array(img)
if args.r is not None:
set_bbox(redraw_fn.bb1, bbox_seq_dict[args.r][idx])
if args.g is not None:
set_bbox(redraw_fn.bb2, bbox_seq_dict[args.g][idx])
if args.b is not None:
set_bbox(redraw_fn.bb3, bbox_seq_dict[args.b][idx])
if args.y is not None:
set_bbox(redraw_fn.bb4, bbox_seq_dict[args.y][idx])
redraw_fn.text1.set_text('{}: {}'.format(seq, idx + 1))
def show_locomotion(motor_diameter, wheel_diameter, motor_shift, pcb_thick,
module, pinion_z, gear_z):
pinion_reference_diameter = module * pinion_z
gear_reference_diameter = module * gear_z
gear_external_diameter = module * (gear_z + 2)
ax = plt.gca()
ax.cla()
# Motor and pinion
motor_height = wheel_diameter / 2. + motor_shift
motor = Circle(
(0, motor_height),
radius=motor_diameter / 2.,
color='black',
linewidth=0,
)
pinion = Circle(
(0, motor_height),
radius=pinion_reference_diameter / 2.,
color='yellow',
linewidth=0,
)
ax.add_artist(motor)
ax.add_artist(pinion)
# PCB
height = motor_height - motor_diameter / 2. - pcb_thick
width = motor_diameter + 2 * wheel_diameter
pcb = Rectangle(
(-width / 2., height),
width=width,
height=pcb_thick,
color='green',
linewidth=0,
)
ax.add_artist(pcb)
# Gears and wheels
wheel_shift = (pinion_reference_diameter + gear_reference_diameter) / 2.
alpha = asin(motor_shift / wheel_shift)
wheel_shift = wheel_shift * cos(alpha)
height = wheel_diameter / 2.
gear0 = Circle(
(-wheel_shift, height),
radius=gear_reference_diameter / 2.,
color='gray',
linewidth=0,
)
gear1 = Circle(
(wheel_shift, height),
radius=gear_reference_diameter / 2.,
color='gray',
linewidth=0,
)
wheel0 = Circle((-wheel_shift, height),
radius=wheel_diameter / 2.,
color='blue',
linewidth=0,
alpha=0.5)
wheel1 = Circle((wheel_shift, height),
radius=wheel_diameter / 2.,
color='blue',
linewidth=0,
alpha=0.5)
ax.add_artist(gear0)
ax.add_artist(gear1)
ax.add_artist(wheel0)
ax.add_artist(wheel1)
# Change plot limits to fit everything
x_limit = pinion_reference_diameter + wheel_diameter
y_limit = max(wheel_diameter, motor_height + motor_diameter / 2.)
ax.set_xlim((-x_limit, x_limit))
ax.set_ylim((0, y_limit))
ax.set_aspect('equal')
# Calculate free space between the PCB and the floor
pcb_floor_space = min(motor_height - motor_diameter / 2. - pcb_thick,
motor_height - motor_diameter / 2.)
wheel_wheel_space = 2 * wheel_shift - wheel_diameter
gear_wheel_space = (wheel_diameter - gear_external_diameter) / 2.
ax.set_title('''PCB to floor: %.2f mm
Between wheels: %.2f mm
Gear (external diameter) to wheel: %.2f mm''' %
(pcb_floor_space, wheel_wheel_space, gear_wheel_space))
plt.show()
cds=so2_cds_uncorr,
velo=PLUME_VELO,
pix_dists=pix_dists_line,
cds_err=calib.err(),
pix_dists_err=pix_dist_err)
# IMPORTANT STUFF FINISHED (below follow some plots)
ax2 = plot_retrieval_points_into_image(so2_img_corr)
pcs_line.plot_line_on_grid(ax=ax2, ls="-", color="g")
ax2.legend(loc="best", framealpha=0.5, fancybox=True, fontsize=20)
ax2.set_title("Dilution corrected AA image", fontsize=12)
ax2.get_xaxis().set_ticks([])
ax2.get_yaxis().set_ticks([])
x0, y0, w, h = pyplis.helpers.roi2rect(AMBIENT_ROI)
ax2.add_patch(Rectangle((x0, y0), w, h, fc="none", ec="c"))
fig, ax3 = subplots(1, 1)
ax3.plot(so2_cds_uncorr, ls="-", color="#ff33e3",
label=r"Uncorr: $\Phi_{SO2}=$%.2f (+/- %.2f) kg/s"
% (phi_uncorr / 1000.0, phi_uncorr_err / 1000.0))
ax3.plot(so2_cds_corr, "-g", lw=3,
label=r"Corr: $\Phi_{SO2}=$%.2f (+/- %.2f) kg/s"
% (phi_corr / 1000.0, phi_corr_err / 1000.0))
ax3.set_title("Cross section profile", fontsize=12)
ax3.legend(loc="best", framealpha=0.5, fancybox=True, fontsize=12)
ax3.set_xlim([0, len(pix_dists_line)])
ax3.set_ylim([0, 5e18])
ax3.set_ylabel(r"$S_{SO2}$ [cm$^{-2}$]", fontsize=14)
ax3.set_xlabel("PCS", fontsize=14)
def runpar(f, g, H, Lg, Lh, l, u, bound, circle, A=None, b=None, E=None, d=None, Tol=1e-2, Heur=0, TolType='r', Vis=0, nsize=12, SD=1, qpsolver='cvxopt'):
# Optional Inputs
# Tolerance
# Heuristic lattice (0 - off, 1 - on)
# Tolerance type (r - relative, a - absolute)
# Visualisation (0 - off, 1 - on)
# Step Debugging (0 - off, 1 - on)
# Node Size
# QP Solver (cvxopt, quadprog, nag)
# MPI
from mpi4py import MPI
# MPI comm
comm = MPI.COMM_WORLD
rank = comm.Get_rank()
# Number of processors
numprocs = comm.Get_size()
# Print node names for each processors
print('Processor %i is on node %s') % (rank,str(MPI.Get_processor_name()))
# Create local groups for load balacing on each node
from numpy import ceil
nodes = [[0]]
bins = int(ceil(numprocs/nsize))
for i in range(bins):
nodes.append([])
for p in range(1,numprocs):
nodes[(p % bins)+1].append(p)
print nodes
# Get D
D = len(l)
if(D > 25):
raise RuntimeError('Hashing for greater than 25D not yet implemented.')
# Balance Test
def balance_test(lst):
for p1 in reversed(range(0,len(lst))):
for p2 in range(0,p1):
if( abs(lst[p1]-lst[p2])/(max(min(lst[p1],lst[p2]),1)) > 0.1):
return True
return False
if(Heur == 0):
ksp = 3**D
kspi = ksp
else:
# Load relevant normalised lattice
from numpy import loadtxt, array, sqrt
if(D == 2):
lat = array([[0., 0.], [1., 0.], [-1., 0.],
[0.5, sqrt(3.)/2.], [-0.5, sqrt(3.)/2.],
[0.5, -sqrt(3.)/2.], [-0.5, -sqrt(3.)/2.]])
elif(D == 3):
lat = loadtxt('d3')
elif(D == 4):
lat = loadtxt('d4')
elif(D == 5):
lat = loadtxt('d5')
elif(D == 6):
lat = loadtxt('e6')
elif(D == 7):
lat = loadtxt('e7')
elif(D == 8):
lat = loadtxt('e8')
else:
raise RuntimeError('A lattice for '+str(D)+' Dimensions has yet to be provided.')
# Get kissing number + 1
ksp = lat.shape[0]
kspi = 2**D
# Master Process
if(rank == 0):
# Necessary functions
from itertools import product
from numpy import array, sqrt, empty, zeros, inf, hstack, isinf, argmin, argmax, all,ones, identity, vstack, dot
from numpy.linalg import norm
from math import floor
from time import time
# Import cvxopt solver
from cvxopt import matrix
from cvxopt.solvers import qp, options
# Set tolerance options
options['show_progress'] = False
options['abstol'] = 1e-9
options['reltol'] = 1e-8
options['feastol'] = 1e-9
# Initialise empty arrays
if A is None:
A = empty((0,D))
b = empty(0)
if E is None:
E = empty((0,D))
d = empty(0)
# Check if circle has feasible point
def mfeasible(c, lfather=None, ufather=None):
#box containing the ball
c.lReduced = c.xc - c.r * ones(D)
c.uReduced = c.xc + c.r * ones(D)
# check if the sub-ball is in the domain reduced of the father
def checkAndUpdateBound():
# intersection between the box of the ball and the box reduced of the father
for i in range(0,D):
if c.lReduced[i]<lfather[i]:
c.lReduced[i]=lfather[i]
if c.uReduced[i]>ufather[i]:
c.uReduced[i]=ufather[i]
checkAndUpdateBound()
# Solve QP to check feasibility
sol = qp(matrix(2*identity(D)),matrix(-2*c.xc),matrix(vstack([-1*identity(D),identity(D),A])),matrix(hstack([-l,u,b])),matrix(E),matrix(d))
mxopt = array(sol['x']).flatten()
mr = sol['primal objective']
mr = mr + dot(c.xc,c.xc)
# Check if point lies inside domain
if(mr <= (c.r**2)):
mf = 1
else:
mf = 0
mxopt = None
return mf, mxopt
# Timer
timer = time()
r = norm(u-l)/2 # Radius
xc = (u+l)/2 # Centre
cn = circle(xc,r)
mfeas, cxopt = mfeasible(cn,l,u)
# Upper bound
ubound = f(cxopt)
#lower bound and reduced domain
_, l, u = bound(cn,Lg,Lh,f,g,H,D,A,b,E,d,ubound,True)
#%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
# 0.c
# Split ball
if(Heur == 0):
# Split circle into more circles
inc = r/sqrt(D) # Increment
rn = r/2 # New radius
# Create square spoke configuration
spk = array([p for p in product([-inc,0,inc], repeat=D)])
else:
# Split circle into more circles
inc = r # Increment
rn = r/2 # New radius
# Scale configuration
spk = inc*lat
# Array to distribute amongst processes
darray = empty((kspi,D+1))
boundarray = empty(2*D)
boundarray = hstack([l,u])
reqidsend = []
reqboundsend = []
# Create surrounding circles
for i in range(0,kspi):
# Create centre
xcn = xc + spk[i,:]
# Add to distribution list
darray[i,:] = hstack([array([rn]),xcn])
# 0.c
# Distribute data evenly amongst processes
ihi = 0
trem = kspi
prem = numprocs-1
for p in range(0,numprocs-1):
tproc = int(round(trem/prem))
ilo = ihi + 1
ihi = ihi + tproc
print('Master sending data elements [%i:%i] to processor %i') % (ilo-1,ihi,p+1)
comm.Ssend(array([ihi-ilo+1],dtype='i'), dest=p+1, tag=9) # send array size
reqidsend.append(comm.Issend(darray[ilo-1:ihi,:], dest=p+1, tag=10)) # send data array (Isend?)
reqboundsend.append(comm.Issend(boundarray, dest=p+1, tag=6))
prem = prem - 1
trem = trem - tproc
# Initial communication setup
lclists = [1 for i in range(1,numprocs)]
zerolist = [0 for i in range(1,numprocs)]
confd = empty(1,dtype='i')
reqbrecv = []
reqbsend = []
rarr = empty((numprocs-1,2))
reqdreq = [MPI.REQUEST_NULL for i in range(1,numprocs)]
reqconf = [MPI.REQUEST_NULL for i in range(1,numprocs)]
reqdreqn = [MPI.REQUEST_NULL for i in range(1,numprocs)]
reqconfn = [MPI.REQUEST_NULL for i in range(1,numprocs)]
# Initial local upper bound
U = inf
# 0.d-e
# Initial rlist, xclist and comm setup
rlist = []
xclist = []
rxcndat = empty((numprocs-1,2),dtype='i')
dwait = 0
reqxcndat = []
reqxcnrecv = [MPI.REQUEST_NULL for i in range(1,numprocs)]
reqxcnsend = [MPI.REQUEST_NULL for i in range(1,numprocs)]
# Loop counter
#itr = 0
# Asynchronously receive U and len(clist)
for p in range(0,numprocs-1):
# New Receive
reqbrecv.append(comm.Irecv(rarr[p], source=p+1, tag=2))
# Send U
reqbsend.append(comm.Issend(array([U]), dest=p+1, tag=3))
# Make sure data has been sent
print('Master waiting for initial data sends to complete...')
for p in range(0,numprocs-1):
reqidsend[p].Wait()
reqboundsend[p].Wait()
print('done.')
# Asynchronously receive xcn from all workers
for p in range(0,numprocs-1):
reqxcndat.append(comm.Irecv(rxcndat[p], source=p+1, tag=12))
#%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
# 1.
#and(rad > 1e-15)
#and((time()-timer) < 3000)
while((lclists != zerolist)and(not(all(rxcndat == 0)))):
# Update iteration count
#itr = itr + 1
# 1.a
# Asynchronously receive U and len(clist)
for p in range(0,numprocs-1):
if(reqbrecv[p].Test()):
# Update U and len(clist)
if(rarr[p,0] < U):
U = rarr[p,0]
lclists[p] = rarr[p,1]
# New Receive
reqbrecv[p] = comm.Irecv(rarr[p], source=p+1, tag=2)
# 1.b
# Asynchronously send U = min(p in {1,...,P}) Up
# where Up = rarr[p]
for p in range(0,numprocs-1):
# If previous communication has finished start new
if(reqbsend[p].Test()):
# Send U
reqbsend[p] = comm.Issend(array([U]), dest=p+1, tag=3)
# 1.c
# If data check requested, process accordingly
# If all data sizes received and previous sends have completed
if(MPI.Request.Testall(reqxcndat))and(MPI.Request.Testall(reqxcnsend)):
# If not waiting to receive data
if(dwait == 0):
print('Data check from all processors received.')
# If any of the processors has ran out of work, ensure it is skipped
plist = []
for p in range(0,numprocs-1):
if(rxcndat[p,1] == 0):
reqxcnrecv[p] = MPI.REQUEST_NULL
else:
plist.append(p)
# Set up arrays to store data
rxcn = [None for p in range(0,numprocs-1)]
for p in plist:
rxcn[p] = empty(rxcndat[p,0],dtype='i')
# Receive data from all workers
for p in plist:
reqxcnrecv[p] = comm.Irecv(rxcn[p], source=p+1, tag=14)
# Waiting for data
dwait = 1
# If data from all workers received
if(MPI.Request.Testall(reqxcnrecv)):
# Arrays to send
nc = [None for p in range(0,numprocs-1)]
# Perform data check for all workers
for p in plist:
# If radius already in list
if rxcndat[p,1] in rlist:
# Check if xcns already exist
ridx = rlist.index(rxcndat[p,1])
nc[p] = array(map(int,[a in xclist[ridx] for a in rxcn[p]]),dtype='i')
# Add any new xcns to xclist
xclist[ridx]+=[rxcn[p][i] for i in range(0,len(nc[p])) if nc[p][i]==0]
# Else add radius and xcns to respective lists
else:
rlist.append(rxcndat[p,1])
xclist.append(list(rxcn[p]))
nc[p] = zeros(rxcndat[p,0],dtype='i')
# Send result of check back (Isend?)
reqxcnsend[p] = comm.Issend(nc[p], dest=p+1, tag=14)
print('Data check returned to processor %i.') % (p+1)
# Post new receives for all processors
for p in range(0,numprocs-1):
# Ansynchronously receive xcn
reqxcndat[p] = comm.Irecv(rxcndat[p], source=p+1, tag=12)
# Not waiting for data
dwait = 0
#%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
# 1.d
# Load Balancing spread across nodes
# Take snapshot of load
slist = lclists[:]
# Get load on each node
lnode = []
for node in nodes:
# Master proc, skip
if(len(node)==1):
pass
# Actual Node with workers
else:
# Create list
blist = []
for n in node:
blist.append(slist[n-1])
# Get load per node
lnode.append(blist)
# Get total load per node
tload = [sum(lnode[i]) for i in range(len(lnode))]
# Iteration counter
it = 0
while((balance_test(tload))and(it < numprocs)):
# Subtract smallest load
ml = min(tload)
tload = map(lambda x: x-ml, tload)
# Find amount to redistribute
load = int(floor(sum(tload)/len(lnode)))
# Find nodes with smallest & largest load
minn = argmin(tload)
maxn = argmax(tload)
# Calculate node load to send
nload = min(tload[maxn],max(load-tload[minn],0))
# Find procs with smallest & largest load on max/min nodes
lminp = argmin(lnode[minn])
lmaxp = argmax(lnode[maxn])
# Get proc number
gminp = nodes[minn+1][lminp]
gmaxp = nodes[maxn+1][lmaxp]
# Calculate actual load to send
lfrac = 3
aload = min(int(lnode[maxn][lmaxp]/lfrac),max(nload-lnode[minn][lminp],0))
# Fraction of processors on node
dfrac = len(nodes[minn+1])
# Send load from largest to smallest if previous send has completed and aload/dfrac > 0
if((reqdreqn[gmaxp-1].Test())and(reqconfn[gmaxp-1].Test())and(int(aload/dfrac) > 0)):
# Send load from largest to smallest
print('Intercomm: Master allocating %i subproblems from processor %i to node %i processors ') % (aload,gmaxp,minn+1),
print nodes[minn+1][0:]
# Send data allocation request
reqdreqn[gmaxp-1] = comm.Issend(array([minn+1,aload],dtype='i'), dest=gmaxp, tag=24)
print('Intercomm: Data allocation request sent asynchronously.')
# Wait for confirmation of data send
reqconfn[gmaxp-1] = comm.Irecv(confd, source=gmaxp, tag=26)
# Update load per node
for i in range(len(nodes[minn+1])):
lnode[minn][i]+= min(int(aload/dfrac),lnode[maxn][lmaxp])
lnode[maxn][lmaxp] -= min(aload,lnode[maxn][lmaxp])
# Update tload
tload = [sum(lnode[i]) for i in range(len(lnode))]
# Iteration counter
it += 1
# 1.e
# Load Balancing on each node
# For each node (excl master)
for node in nodes:
# Master proc, skip
if(len(node)==1):
pass
# Actual Node with workers
else:
# Copy list
blist = []
for n in node:
blist.append(lclists[n-1])
# Subtract smallest load
ml = min(blist)
blist = map(lambda x: x-ml, blist)
# Find load amount to redistribute
load = int(floor(sum(blist)/len(blist)))
# Iteration counter
biter = 0
while((balance_test(blist))and(biter < len(blist))):
# Find procs with smallest & largest load
minp = argmin(blist)
maxp = argmax(blist)
# Convert to global proc numbers
gminp = node[minp]
gmaxp = node[maxp]
# Calculate actual load to send
aload = max(load-int(blist[minp]),0)
# If previous send has completed and aload > 0
if((reqdreq[gmaxp-1].Test())and(reqconf[gmaxp-1].Test())and(aload > 0)):
# Send load from largest to smallest
print('Master allocating %i subproblems from processor %i to processor %i') % (aload,gmaxp,gminp)
# Send data allocation request
reqdreq[gmaxp-1] = comm.Issend(array([gminp,aload],dtype='i'), dest=gmaxp, tag=0)
print('Data allocation request sent asynchronously.')
# Wait for confirmation of data send
reqconf[gmaxp-1] = comm.Irecv(confd, source=gmaxp, tag=22)
# Update blist
blist[minp] += min(aload,blist[maxp])
blist[maxp] -= min(aload,blist[maxp])
# Update iteration counter
biter += 1
#%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
# 2
# If all finished, send kill signals
print('Master sending kill signals...')
for p in range(0,numprocs-1):
comm.Ssend(array([1],dtype='i'), dest=p+1, tag=4)
# Kill any pending data checks (Isend?)
for p in range(0,numprocs-1):
reqxcnsend[p] = comm.Issend(array([0],dtype='i'), dest=p+1, tag=14)
# Clean up redundant messages
for p in range(0,numprocs-1):
#reqbsend[p].Cancel()
reqbrecv[p].Cancel()
#reqdreq[p].Cancel()
#reqbsend[p].Free()
reqbrecv[p].Free()
#reqdreq[p].Free()
# 3
# Receive xopt from all processors
reqe = []
earr = empty((numprocs-1,D))
U = inf
for p in range(0,numprocs-1):
# New Receive
#print('Master posting asynchronous receive of final data from processor %i') % (p+1)
reqe.append(comm.Irecv(earr[p], source=p+1, tag=5))
#print('posted.')
for p in range(0,numprocs-1):
print('Master waiting to receive final data from processor %i') % (p+1)
reqe[p].Wait()
print('Final data from processor %i received') % (p+1)
# Find xopt with smallest U
if(not(any(isinf(earr[p])))):
if(f(earr[p]) < U):
xopt = earr[p]
U = f(xopt)
#xopt = empty(D)
# How do you count iterations?
itr = None
# Output end result
print('Minimum value of %f at (') % U, #f(xopt),
for i in range(0,D-1):
print('%f,') % xopt[i],
print('%f)') % xopt[D-1]
print('found with'),
if(TolType == 'a'):
print('absolute'),
else:
print('relative'),
print('tolerance %f.') % Tol
tol = Tol
xs = xopt
fxs = U #f(xopt)
print('Elapsed time %f seconds.') % (time()-timer)
return xs, fxs, tol, itr
# Worker processes
else:
# import necessary functions
from heapq import heappush, heappop
from numpy import array, sqrt, dot, identity, hstack, vstack, inf, empty, ones, zeros, tile, roll, all
from numpy.linalg import norm
from itertools import product
from sys import float_info
from math import floor, ceil
from time import time
# Vector Hash function: http://stackoverflow.com/questions/5928725/hashing-2d-3d-and-nd-vectors
#htsize = 499 # Hash Table size
res = 1e-5 # Resolution
# Twenty five arbitrarily chosen 8-digit primes
primes = [73856093, 19349663, 83492791, 15485863, 86028121, 32452843, 67867967, 49979687,
86028157, 13769629, 95189161, 29223841, 83972821, 39271703, 79186817, 47286739,
98767549, 14139199, 64244023, 18551173, 55621541, 10920859, 53615137, 24405817,
43176253]
# Pick up scattered list
rsize = array([0],dtype='i')
comm.Recv(rsize, source=0, tag=9)
rarray = empty((rsize[0],D+1))
boundarray = empty(2*D)
comm.Recv(rarray, source=0, tag=10)
comm.Recv(boundarray, source=0, tag=6)
print('Processor %i received initial data') % rank
lr = boundarray[0:D]
ur = boundarray[D:2*D]
# Hash function
def hashnd(x):
result = 0
for i in range(0,D):
result = result ^ (int(floor(x[i]/res))*primes[i])
return result
# Hash radius
def hashrn(r):
return int(r*1e8)
# Initialise empty arrays
if A is None:
A = empty((0,D))
b = empty(0)
if E is None:
E = empty((0,D))
d = empty(0)
# QuadProg++ solver (fast!)
if(qpsolver == 'quadprog'):
# Import QuadProg++ solver
from PyQuadProg import PyQuadProg
# Check if circle has feasible point
def mfeasible(c):
# Solve QP to check feasibility
sol = PyQuadProg(2*identity(D),-2*c.xc,E.transpose(),-1*d,vstack([identity(D),-1*identity(D),-1*A]).transpose(),hstack([-l,u,b]))
mxopt = sol.x.getArray()
mr = dot(mxopt,mxopt) + dot(mxopt,-2*c.xc) + dot(c.xc,c.xc)
# Check if point lies inside domain
if(mr < (c.r**2)):
mf = 1
else:
mf = 0
mxopt = None
return mf, mxopt
# CVXOPT QP solver (slow)
elif(qpsolver == 'cvxopt'):
# Import cvxopt solver
from cvxopt import matrix
from cvxopt.solvers import qp, options
# Set tolerance options
options['show_progress'] = False
options['abstol'] = 1e-9
options['reltol'] = 1e-8
options['feastol'] = 1e-9
# Check if circle has feasible point
def mfeasible(c, lfather=None, ufather=None):
#box containing the ball
c.lReduced = c.xc - c.r * ones(D)
c.uReduced = c.xc + c.r * ones(D)
# check if the sub-ball is in the domain reduced of the father
def checkAndUpdateBound():
check=1
for i in range(0,D):
# check the intersection between the subball and the reduction of the father's ball
# if there isn't intersection, then discard the subball (check = 0)
if c.lReduced[i]>ufather[i] or c.uReduced[i]<lfather[i]:
check=0
break
# intersection of the subball with the orginal domain (reduced at first step)
if c.lReduced[i]<lr[i]:
c.lReduced[i]=lr[i]
if c.uReduced[i]>ur[i]:
c.uReduced[i]=ur[i]
return check
check=1
if lfather is not None and ufather is not None:
check = checkAndUpdateBound()
if check==1:
# Solve QP to check feasibility
sol = qp(matrix(2*identity(D)),matrix(-2*c.xc),matrix(vstack([-1*identity(D),identity(D),A])),matrix(hstack([-lr,ur,b])),matrix(E),matrix(d))
mxopt = array(sol['x']).flatten()
mr = sol['primal objective']
mr = mr + dot(c.xc,c.xc)
# Check if point lies inside domain
if(mr <= (c.r**2)):
mf = 1
else:
mf = 0
mxopt = None
else:
mf = 0
mxopt = None
return mf, mxopt
# NAG QP solver (fast!)
elif(qpsolver == 'nag'):
# Import QP Solver
from qpsolver_lincon import qpsolver_lincon
# Check if circle has feasible point
def mfeasible(c):
# Solve QP to check feasibility
mxopt = c.xc.copy()
mr = qpsolver_lincon(2*identity(D),-2*c.xc,hstack([l,-inf,d]),hstack([u,b,d]),mxopt,vstack([A,E]),D,A.shape[0]+E.shape[0])
mr = mr + dot(c.xc,c.xc)
# Check if point lies inside domain
if(mr < (c.r**2)):
mf = 1
else:
mf = 0
mxopt = None
return mf, mxopt
# Visualisation
if(Vis == 1):
from matplotlib.pyplot import figure, Rectangle, Circle, gca, show, title, axis, draw
from colorsys import hsv_to_rgb
from random import random
# Draw bound constraints [l,u]
fig = figure('Processor '+str(rank))
gca().add_patch(Rectangle((l[0],l[1]), u[0]-l[0], u[1]-l[1], fill=False))
axis([l[0]-1,u[0]+1,l[1]-1,u[1]+1])
title('Processor '+str(rank))
show(block=False)
# Circle drawing procedure
def drawc(c):
# Draw circle colured according to partition
gca().add_patch(Circle((c.xc[0],c.xc[1]), radius=c.r , color=hsv_to_rgb(random(),1,1), fill=False))
axis('equal')
draw()
# Priority queue
clist = [] # list of entries arranged in a heap
# Add a new task
def add_task(task):
heappush(clist, (task.lbound, task))
# Remove and return the lowest priority task. Raise KeyError if empty.
def pop_task():
while clist:
return heappop(clist)
raise KeyError('Pop from an empty priority queue!')
# Remove and return (in an mpi transfer array) the n lowest priority tasks
def npop_task(n):
carray = empty((n,(3*D)+2))
for i in range(0,n):
celm = pop_task()
carray[i,0:D+2] = hstack([array([celm[0],celm[1].r]),celm[1].xc])
carray[i,D+2:2*D+2] = celm[1].lReduced
carray[i,2*D+2:3*D+2] = celm[1].uReduced
return carray
# Initial local upper bound
U = inf
# Bound communication setup
rarr = empty(1)
karr = empty(1,dtype='i')
kill = 0
dwait = 0
dwaits = 0
reqdsend = MPI.REQUEST_NULL
reqdsizesend = MPI.REQUEST_NULL
reqconf = MPI.REQUEST_NULL
reqnsend = MPI.REQUEST_NULL
dwaitn = 0
dwaitsn = 0
reqdsendn = [MPI.REQUEST_NULL for i in range(1,numprocs)]
reqdsizesendn = [MPI.REQUEST_NULL for i in range(1,numprocs)]
reqconfn = MPI.REQUEST_NULL
# 1.b-c
# Bound intial list and convert to priority queue
for k in range(0,rsize):
# Create circle
cn = circle(rarray[k,1:D+1],rarray[k,0])
# Check if circle is feasible
mfeas, cxopt = mfeasible(cn,lr,ur)
# If circle has a feasible point (i.e. it's feasible)
if(mfeas != 0):
# Upper bound
ubound = f(cxopt)
# Update U and xopt
if(ubound < U):
U = ubound
xopt = cxopt
# Bound circle
cn.lbound, cn.lReduced, cn.uReduced = bound(cn,Lg,Lh,f,g,H,D,A,b,E,d,U,True,cn.r*2)
# Add to priority queue
add_task(cn)
# Visualise
if(Vis ==1):
drawc(cn)
initialRadius = cn.r*2
# 1.d
# Asynchronously send U and len(clist)
reqbsend = comm.Issend(array([U,len(clist)]), dest=0, tag=2)
# 1.e
# Asynchronously receive U
reqbrecv = comm.Irecv(rarr, source=0, tag=3)
# Debug Output
if (SD == 1):
#if(rank == 0):
print('Time: %f') % (time()),
print('Processor %i Number of elements: %i') % (rank,len(clist))
print('U: %f') % U
#print('L: %f') % L
#print('Circle radius: %e') % rad
print('----------------------------')
# Intial data request
rq_proc_load = empty(2,dtype='i')
rq_proc_loadn = empty(2,dtype='i')
reqd = comm.Irecv(rq_proc_load, source=0, tag=0)
reqdn = comm.Irecv(rq_proc_loadn, source=0, tag=24)
# Initial kill signal request
reqk = comm.Irecv(karr, source=0, tag=4)
#%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
# 2
optimality = False
while(kill == 0):
# Set tolerance
if((TolType == 'r')and(abs(U) > float_info.epsilon)):
cutoff = U - Tol*abs(U)
else:
cutoff = U - Tol
# Prune list
i = 0
while(i < len(clist)):
if(clist[i][0] > cutoff):
del clist[i]
i=i-1
i = i+1
# If there is work left to do
if(len(clist) != 0):
# Get circle with smallest lbound
L, cslb = pop_task()
if(Heur == 0):
# Split circle into more circles
inc = cslb.r/sqrt(D) # Increment
rn = cslb.r/2 # New radius
xc = cslb.xc # Centre
# Create square spoke configuration
spk = array([p for p in product([-inc,0,inc], repeat=D)])
# Move centre to start of spoke array
spk = roll(spk,int(ceil(ksp/2)),axis=0)
else:
# Split circle into more circles
inc = cslb.r # Increment
rn = cslb.r/2 # New radius
xc = cslb.xc # Centre
# Scale configuration
spk = inc*lat
# Create surrounding circles
# Create centre
nc = zeros(ksp)
xcn = tile(xc,(ksp,1)) + spk
# Check if circles exists locally
for k in range(0,len(clist)):
for i in range(0,ksp):
if(all(xcn[i,:] == clist[k][1].xc)):
nc[i] = 1
# Check if circles exists globally
# Remove local duplicates
dxcn = []
hdxcn = []
for i in range(0,ksp):
if(nc[i] == 0):
dxcn.append(xcn[i,:])
hdxcn.append(hashnd(xcn[i,:]))
xcn = array(dxcn)
hxcn = array(hdxcn,dtype='i')
del dxcn[:]
del hdxcn[:]
# Send data asynchronously
#print('Processor %i sending data check to master processor.') % rank
comm.Send(array([len(hxcn),hashrn(rn)],dtype='i'), dest=0, tag=12) # send array size
_ = comm.Issend(hxcn, dest=0, tag=14) # send data array (Isend?)
#print('Data check sent. Awaiting response.')
# Receive data asynchronously
nc = empty(len(hxcn),dtype='i')
reqdcheck = comm.Irecv(nc, source=0, tag=14)
#print('Data check completed successfully.')
# Start bounding balls
lcn = []
lmfeas = []
lcxopt = []
lubound = []
for i in range(0,len(xcn)):
# Create circle
lcn.append(circle(xcn[i,:],rn))
mfeas, cxopt = mfeasible(lcn[i],cslb.lReduced,cslb.uReduced)
lmfeas.append(mfeas)
lcxopt.append(cxopt)
# Bound if feasible
if(mfeas != 0):
# Lower bound
lcn[i].lbound, lcn[i].lReduced, lcn[i].uReduced = bound(lcn[i],Lg,Lh,f,g,H,D,A,b,E,d,U,optimality,initialRadius)
# Upper bound
lubound.append(f(cxopt))
else:
# Don't need upper bound
lubound.append(None)
if(reqdcheck.Test()): # Test if data check received
break
else:
print('Processor %i started waiting for data check.') % rank
wtimer = time() # Time wait time
reqdcheck.Wait() # Wait for data check
print('Processor %i spent %f seconds waiting for data check from master.') % (rank,time()-wtimer)
# Finish bounding
for j in range(0,len(xcn)):
# If circle doesn't already exist somewhere
if(nc[j] == 0):
# If circle already bounded
if(j <= i):
# And circle feasible
if(lmfeas[j] != 0):
# Update U and xopt
if(lubound[j] < U):
U = lubound[j]
xopt = lcxopt[j]
# Add to priority queue
add_task(lcn[j])
# Visualise
if(Vis ==1):
drawc(lcn[j])
else:
# Create circle
cn = circle(xcn[j,:],rn)
mfeas, cxopt = mfeasible(cn,cslb.lReduced,cslb.uReduced)
# If circle has a feasible point (i.e. it's feasible)
if(mfeas != 0):
# Upper bound
ubound = f(cxopt)
# Update U and xopt
if(ubound < U):
U = ubound
xopt = cxopt
# Lower bound
cn.lbound, cn.lReduced, cn.uReduced = bound(cn,Lg,Lh,f,g,H,D,A,b,E,d,U,optimality,initialRadius)
# Add to priority queue
add_task(cn)
# Visualise
if(Vis ==1):
drawc(cn)
# Intercomm: Send data if requested and previous data send has completed
if((reqdn.Test())and(MPI.Request.Testall(reqdsendn))and(MPI.Request.Testall(reqdsizesendn))and(reqconfn.Test())):
print('Intercomm: Node %i needs data from processor %i') % (rq_proc_loadn[0],rank)
# Workload to send
nit = min(int(rq_proc_loadn[1]/len(nodes[rq_proc_loadn[0]])),len(clist)/len(nodes[rq_proc_loadn[0]]))
if(nit > 0):
print('Intercomm: Sending %i subproblems from processor %i to node %i each of processors') % (nit,rank,rq_proc_loadn[0]),
print nodes[rq_proc_loadn[0]][0:]
# Send data asynchronously
for p in nodes[rq_proc_loadn[0]]:
reqdsizesendn[p-1] = comm.Issend(array([nit,rank],dtype='i'), dest=p, tag=30) # send array size
reqdsendn[p-1] = comm.Issend(npop_task(nit), dest=p, tag=28) # send data array
print('Intercomm: Data sent asynchronously.')
# Send confirmation to master
reqconfn = comm.Issend(array([1],dtype='i'), dest=0, tag=26)
else:
print('Intercomm: Not enough data to send.')
# Send confirmation to master
reqconfn = comm.Issend(array([1],dtype='i'), dest=0, tag=26)
# Wait for other data requests
reqdn = comm.Irecv(rq_proc_loadn, source=0, tag=24)
# Send data if requested and previous data send has completed
if((reqd.Test())and(reqdsend.Test())and(reqdsizesend.Test())and(reqconf.Test())):
print('Processor %i needs data from processor %i') % (rq_proc_load[0],rank)
# Workload to send
nit = min(rq_proc_load[1],len(clist))
print('Sending %i subproblems from processor %i to processor %i') % (nit,rank,rq_proc_load[0])
# Send data asynchronously (Isend?)
reqdsizesend = comm.Issend(array([nit,rank],dtype='i'), dest=rq_proc_load[0], tag=11) # send array size
reqdsend = comm.Issend(npop_task(nit), dest=rq_proc_load[0], tag=1) # send data array (Isend?)
print('Data sent asynchronously.')
# Send confirmation to master (Isend?)
reqconf = comm.Issend(array([1],dtype='i'), dest=0, tag=22)
# Wait for other data requests
reqd = comm.Irecv(rq_proc_load, source=0, tag=0)
# Debug Output
if (SD == 1):
#if(rank == 0):
print('Time: %f') % (time()),
print('Processor %i Number of elements: %i') % (rank,len(clist))
print('U: %f') % U
print('LL: %f') % L
#print('Circle radius: %e') % rad
print('----------------------------')
# Run out of work
else:
# Notify master that ran out of work if previous send completed
if(reqnsend.Test()):
print('Time: %f') % (time()),
print('Processor %i ran out of work!') % rank
reqnsend = comm.Issend(array([0,0],dtype='i'), dest=0, tag=12)
# If not waiting to receive data size
if(dwaits == 0):
# Receive data
print('Processor %i asynchronously waiting to receive data.') % rank
darrsize = array([0,0],dtype='i')
reqdsize = comm.Irecv(darrsize, source=MPI.ANY_SOURCE, tag=11)
# Waiting for data size
dwaits = 1
# If data size received
if(reqdsize.Test()):
# If not waiting to receive data
if(dwait == 0):
darr = empty((darrsize[0],(3*D)+2))
reqds = comm.Irecv(darr,source=darrsize[1], tag=1)
# Waiting for data
dwait = 1
# If data received
if(reqds.Test()):
for i in range(0,darrsize[0]):
ctemp = circle(darr[i,2:2+D],darr[i,1])
ctemp.lbound = darr[i,0]
ctemp.lReduced = darr[i,2+D:2+2*D]
ctemp.uReduced = darr[i,2+2*D:2+3*D]
add_task(ctemp)
print('Data received succesfully.')
# Not waiting for data size or data
dwaits = 0
dwait = 0
# Intercomm: If not waiting to receive data size
if(dwaitsn == 0):
# Receive data
print('Intercomm: Processor %i asynchronously waiting to receive data.') % rank
darrsizen = array([0,0],dtype='i')
reqdsizen = comm.Irecv(darrsizen, source=MPI.ANY_SOURCE, tag=30)
# Waiting for data size
dwaitsn = 1
# Intercomm: If data size received
if(reqdsizen.Test()):
# If not waiting to receive data
if(dwaitn == 0):
darrn = empty((darrsizen[0],(3*D)+2))
reqdsn = comm.Irecv(darrn,source=darrsizen[1], tag=28)
# Waiting for data
dwaitn = 1
# If data received
if(reqdsn.Test()):
for i in range(0,darrsizen[0]):
ctemp = circle(darrn[i,2:2+D],darrn[i,1])
ctemp.lbound = darrn[i,0]
ctemp.lReduced = darrn[i,2+D:2+2*D]
ctemp.uReduced = darrn[i,2+2*D:2+3*D]
add_task(ctemp)
print('Intercomm: Data received succesfully.')
# Not waiting for data size or data
dwaitsn = 0
dwaitn = 0
# Asynchronously send UL and len(clist)
# If previous communication has finished start new
if(reqbsend.Test()):
# Send UL and len(clist)
reqbsend = comm.Issend(array([U,len(clist)]), dest=0, tag=2)
if(reqbrecv.Test()):
# Update U
if(rarr[0] < U):
U = rarr[0]
# New Receive
reqbrecv = comm.Irecv(rarr, source=0, tag=3)
# Asynchronously receive kill signal
if(reqk.Test()):
kill = 1
# Say if finished!
print('Processor %i has finished!') % rank
# Clean up redundant messages
#reqbsend.Cancel()
reqbrecv.Cancel()
#reqd.Cancel()
#reqbsend.Free()
reqbrecv.Free()
#reqd.Free()
# Send xopt to master
print('Processor %i sending final data to master') % rank
if('xopt' not in locals()): # No xopt
xopt = inf*ones(D)
comm.Ssend(xopt, dest=0, tag=5)
# Display figures and wait
if(Vis == 1):
show()
return None, None, None, None
def animate(i):
pass
N = 10
width = 10
tab = permutation(N)
fig = figure(figsize=(len(tab), 3))
axis('off')
axis('equal')
axis([0, len(tab) * width, 0, width])
rectangles = [
gca().add_patch(
Rectangle(array([i * width, 0]), width - 1, width - 1, fc='b'))
for i in range(N)
]
annotations = [
gca().annotate(tab[i],
array([i * width, 0]) + array([(width - 1) * .5,
(width - 1) * .5]),
color='w',
weight='bold',
fontsize=20,
ha='center',
va='center') for i in range(N)
]
indices = [n for n in range(N)]
ani = FuncAnimation(fig,
def runpar(f,
g,
H,
Lg,
Lh,
l,
u,
bound,
circle,
A=None,
b=None,
E=None,
d=None,
Tol=1e-2,
Heur=0,
TolType='r',
Vis=0,
SD=1,
Rtol=1e-15,
TimeQP=0,
TimeWidle=0,
qpsolver='cvxopt'):
# Optional Inputs
# Tolerance
# Heuristic lattice (0 - off, 1 - on)
# Tolerance type (r - relative, a - absolute)
# Visualisation (0 - off, 1 - on)
# Step Debugging (0 - off, 1 - on)
# Radius Tolerance
# Time Worker Idling (0 - off, 1 - on)
# Time QP solves (0 - off, 1 - on)
# QP Solver (quadprog, cvxopt, nag)
# MPI
from mpi4py import MPI
# MPI comm
comm = MPI.COMM_WORLD
rank = comm.Get_rank()
# Get D
D = len(l)
# Master Process
if (rank == 0):
# Number of processors
numprocs = comm.Get_size()
# Import necessary functions
from numpy import array, pi, sqrt, dot, identity, hstack, vstack, empty, inf
from numpy.linalg import norm
from time import time
from itertools import product
from sys import float_info
# Initialise empty arrays
if (A is None):
A = empty((0, D))
b = empty(0)
if (E is None):
E = empty((0, D))
d = empty(0)
# QuadProg++ solver (fast!)
if (qpsolver == 'quadprog'):
# Import QuadProg++ solver
from PyQuadProg import PyQuadProg
# Check if circle has feasible point
def mfeasible(c):
# Solve QP to check feasibility
sol = PyQuadProg(
2 * identity(D), -2 * c.xc, E.transpose(), -1 * d,
vstack([identity(D), -1 * identity(D),
-1 * A]).transpose(), hstack([-l, u, b]))
mxopt = sol.x.getArray()
mr = dot(mxopt, mxopt) + dot(mxopt, -2 * c.xc) + dot(
c.xc, c.xc)
# Check if point lies inside domain
if (mr < (c.r**2)):
mf = 1
else:
mf = 0
mxopt = None
return mf, mxopt
# CVXOPT QP solver (slow)
elif (qpsolver == 'cvxopt'):
# Import cvxopt solver
from cvxopt import matrix
from cvxopt.solvers import qp, options
# Set tolerance options
options['show_progress'] = False
options['abstol'] = 1e-9
options['reltol'] = 1e-8
options['feastol'] = 1e-9
# Check if circle has feasible point
def mfeasible(c):
# Solve QP to check feasibility
sol = qp(matrix(2 * identity(D)), matrix(-2 * c.xc),
matrix(vstack([-1 * identity(D),
identity(D), A])),
matrix(hstack([-l, u, b])), matrix(E), matrix(d))
mxopt = array(sol['x']).flatten()
mr = sol['primal objective']
mr = mr + dot(c.xc, c.xc)
# Check if point lies inside domain
if (mr < (c.r**2)):
mf = 1
else:
mf = 0
mxopt = None
return mf, mxopt
# NAG QP solver (fast!)
elif (qpsolver == 'nag'):
# Import QP Solver
from qpsolver_lincon import qpsolver_lincon
# Check if circle has feasible point
def mfeasible(c):
# Solve QP to check feasibility
mxopt = c.xc.copy()
mr = qpsolver_lincon(2 * identity(D), -2 * c.xc,
hstack([l, -inf, d]), hstack([u, b,
d]), mxopt,
vstack([A, E]), D,
A.shape[0] + E.shape[0])
mr = mr + dot(c.xc, c.xc)
# Check if point lies inside domain
if (mr < (c.r**2)):
mf = 1
else:
mf = 0
mxopt = None
return mf, mxopt
# Visualisation
if (Vis == 1):
from matplotlib.pyplot import figure, Rectangle, Circle, gca, show, title, axis, draw
# Draw bound constraints [l,u]
fig = figure('Processor ' + str(rank))
gca().add_patch(
Rectangle((l[0], l[1]), u[0] - l[0], u[1] - l[1], fill=False))
axis([l[0] - 1, u[0] + 1, l[1] - 1, u[1] + 1])
title('Master Processor')
show(block=False)
# Circle drawing procedure
def drawc(c, col):
# Draw circle
gca().add_patch(
Circle((c.xc[0], c.xc[1]),
radius=c.r,
color=col,
fill=False))
axis('equal')
draw()
if (Heur == 0):
ksp = 3**D
else:
# Load relevant normalised lattice
from numpy import loadtxt
from pkg_resources import resource_stream
if (D == 2):
lat = array([[0., 0.], [1., 0.], [-1., 0.],
[0.5, sqrt(3.) / 2.], [-0.5, sqrt(3.) / 2.],
[0.5, -sqrt(3.) / 2.], [-0.5, -sqrt(3.) / 2.]])
elif (D == 3):
lat = loadtxt(resource_stream('obb', 'lattices/d3'))
elif (D == 4):
lat = loadtxt(resource_stream('obb', 'lattices/d4'))
elif (D == 5):
lat = loadtxt(resource_stream('obb', 'lattices/d5'))
elif (D == 6):
lat = loadtxt(resource_stream('obb', 'lattices/e6'))
elif (D == 7):
lat = loadtxt(resource_stream('obb', 'lattices/e7'))
elif (D == 8):
lat = loadtxt(resource_stream('obb', 'lattices/e8'))
else:
raise RuntimeError('A lattice for ' + str(D) +
' Dimensions has yet to be provided.')
# Get kissing number + 1
ksp = lat.shape[0]
# Set up initial circle
c0 = circle((u + l) / 2, norm(u - l) / 2)
c0.xopt = c0.xc
# Bound circle
c0.lbound = bound(c0, Lg, Lh, f, g, H, D)
# Upper bound
c0.ubound = f(c0.xopt)
# Set up circle list
clist = [c0]
cslb = clist[0]
# Update global bounds
U = cslb.ubound
L = cslb.lbound
xopt = cslb.xopt
rad = cslb.r
# Loop counter
itr = 0
timer = time()
if (TimeQP == 1):
qptime = 0
# Debug Output
if (SD == 1):
print('----------------------------')
print('Number of elements: %i') % len(clist)
print('U: %f') % U
print('L: %f') % L
print('Circle radius: %e') % rad
print('----------------------------')
# Set tolerance
if ((TolType == 'r') and (abs(U) > float_info.epsilon)):
cutoff = (U - L) / abs(U)
else:
cutoff = U - L
#and((time()-timer) < 3000)
while ((cutoff > Tol) and (rad > Rtol)):
# Update iteration count
itr = itr + 1
# Prune list
i = 0
while (i < len(clist)):
if (clist[i].lbound > U):
# Visualise
if (Vis == 1):
drawc(clist[i], 'k')
del clist[i]
i = i - 1
i = i + 1
if (Heur == 0):
# Split circle into more circles
inc = (cslb.r) / sqrt(D) # Increment
rn = (cslb.r) / 2 # New radius
xc = cslb.xc # Centre
# Visualise
if (Vis == 1):
drawc(cslb, 'k')
clist.remove(cslb) # Remove split circle from list
# Create square spoke configuration
spk = array([p for p in product([-inc, 0, inc], repeat=D)])
else:
# Split circle into more circles
inc = cslb.r # Increment
rn = (cslb.r) / 2 # New radius
xc = cslb.xc # Centre
# Visualise
if (Vis == 1):
drawc(cslb, 'k')
clist.remove(cslb) # Remove split circle from list
# Scale configuration
spk = inc * lat
# List to distribute amongst processes
dlist = []
# Create surrounding circles
for i in range(0, ksp):
# Create centre
xcn = xc + spk[i, :]
# Check if circle exists
nc = 0
for k in range(0, len(clist)):
if (all(xcn == clist[k].xc)):
nc = 1
# If circle doesn't exist
if (nc == 0):
# Create circle
cn = circle(xcn, rn)
# Time QP Solve
if (TimeQP == 1):
eltime = MPI.Wtime()
mfeas, cn.xopt = mfeasible(cn)
if (TimeQP == 1):
qptime += MPI.Wtime() - eltime
# If circle has a feasible point (i.e. it's feasible)
if (mfeas != 0):
# Add to distribution list
dlist.append(cn)
# Visualise
if (Vis == 1):
drawc(cn, 'b')
# Distribute data evenly amongst processes
ihi = 0
trem = len(dlist)
prem = numprocs
req = []
for p in range(0, numprocs - 1):
tproc = int(round(trem / prem))
ilo = ihi + 1
ihi = ihi + tproc
req.append(
comm.isend(dlist[ilo - 1:ihi],
dest=numprocs - 1 - p,
tag=0))
prem = prem - 1
trem = trem - tproc
# Distribute remaining data to self
tproc = int(round(trem / prem))
# Bound each item allocated to self
for k in range(ihi, ihi + tproc):
# Bound circle
dlist[k].ubound = f(dlist[k].xopt)
dlist[k].lbound = bound(dlist[k], Lg, Lh, f, g, H, D)
# Add to circle list
clist.append(dlist[k])
# Gather data back up
for p in range(0, numprocs - 1):
# Make sure data has been sent
req[p].Wait()
# Get list of bounded circles from other processes
dlist = comm.recv(source=numprocs - 1 - p, tag=1)
# Add to clist
clist += dlist
# Find circle c with smallest ubound
cslb = min(clist, key=lambda x: x.ubound)
# Update global feasible upper bound
U = cslb.ubound
xopt = cslb.xopt
rad = cslb.r
# Find circle with smallest lbound
cslb = min(clist, key=lambda x: x.lbound)
L = cslb.lbound
# Set tolerance
if ((TolType == 'r') and (abs(U) > float_info.epsilon)):
cutoff = (U - L) / abs(U)
else:
cutoff = U - L
# Debug Output
if (SD == 1):
print('Number of elements: %i') % len(clist)
print('U: %f') % U
print('L: %f') % L
print('Circle radius: %e') % rad
print('----------------------------')
# Output end result
print('Minimum value of %f at (') % f(xopt),
for i in range(0, D - 1):
print('%f,') % xopt[i],
print('%f)') % xopt[D - 1]
print('found with'),
if ((TolType == 'r') and (abs(U) > float_info.epsilon)):
print('relative'),
else:
print('absolute'),
print('tolerance %f in %i iterations.') % (cutoff, itr)
tol = cutoff
xs = xopt
fxs = f(xopt)
print('Elapsed time %f seconds.') % (time() - timer)
if (TimeQP == 1):
print('Time taken for QP solves is %f seconds') % qptime
# Kill worker processes
for p in range(0, numprocs - 1):
comm.send(None, dest=numprocs - 1 - p, tag=0)
# Display figures and wait
if (Vis == 1):
show()
return xs, fxs, tol, itr
# Worker processes
else:
# Idle time
if (TimeWidle == 1):
eltime = MPI.Wtime()
itime = 0
# Pick up scattered list
rlist = comm.recv(source=0, tag=0)
# Idle time
if (TimeWidle == 1):
itime += MPI.Wtime() - eltime
while (rlist != None):
# Bound each item in the list
for k in range(0, len(rlist)):
# Bound circle
rlist[k].ubound = f(rlist[k].xopt)
rlist[k].lbound = bound(rlist[k], Lg, Lh, f, g, H, D)
# Send bounded list
comm.send(rlist, dest=0, tag=1)
# Idle time
if (TimeWidle == 1):
eltime = MPI.Wtime()
# Pick up next scattered list
rlist = comm.recv(source=0, tag=0)
# Idle time
if (TimeWidle == 1):
itime += MPI.Wtime() - eltime
# Output idle time
if (TimeWidle == 1):
print('Processor %i has been idle for %f seconds') % (rank, itime)
return None, None, None, None