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utils.py
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utils.py
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import os
import io
import numpy as np
import torch
from scipy.ndimage.filters import gaussian_filter
from scipy.interpolate import RectBivariateSpline
from scipy.spatial.distance import cdist
from skimage.transform import resize as resize_image
from skimage import measure
from skimage.color import rgb2gray
from tqdm import tqdm
import matplotlib.pyplot as plt
from mpl_toolkits.axes_grid1 import make_axes_locatable
from matplotlib import colors
from IPython.display import Image, display, clear_output
from matplotlib.collections import LineCollection
from DeepTopOpt.FEA import LinearElasticity # local library
def plot_design(ax,mesh,rho,vol_field,fixed_dofs,load):
"""Plot the given design (rho) on the provided figure axes
Args:
ax(object): figure object axes
mesh(object): finite element mesh object
rho(nelx x nely float matrix): density matrix
vol_field(nelx x nely float matrix): volume field
fixed_dofs(N x 1 int array): fixed degrees-of-freedom
load(ndof x 1 float array): load vector
"""
buffer = 2 # buffer around image to present graphical objects which extend outside the design domain
pix_offset = 0.5-buffer # pixel center offset
rho = np.pad(rho,buffer)
# get volume fraction and calculate difference
volfrac = np.sum(vol_field)/len(mesh.IX)
volume_violation = np.sum(rho)/len(mesh.IX) - volfrac
ax.set_title("Volfrac: "+str(round(volfrac,3))+" Vol. diff.: "+str(round(volume_violation,3)))
# plot design
ax.imshow(-rho,cmap='gray',interpolation='none',norm=colors.Normalize(vmin=-1,vmax=0))
# plot loads
load_nodes = np.unique(mesh.dof2nodeid(np.nonzero(load)[0]))
for node in load_nodes:
magx = load[2*node][0]
magy = -load[2*node+1][0] # reverse due to opposite y-coordinate for images and mesh
xn = mesh.XY[node,0]
yn = mesh.XY[node,1]
ax.arrow(xn-pix_offset,yn-pix_offset,magx,magy,width=0.5,color='r')
# plot boundary conditions
even_dofs = fixed_dofs%2==0
uneven_dofs = even_dofs!=True
horz_bound_nodes = mesh.dof2nodeid(fixed_dofs[even_dofs])
vert_bound_nodes = mesh.dof2nodeid(fixed_dofs[uneven_dofs])
ax.scatter(mesh.XY[horz_bound_nodes][:,0]-pix_offset,mesh.XY[horz_bound_nodes][:,1]-pix_offset,marker='>',color='b')
ax.scatter(mesh.XY[vert_bound_nodes][:,0]-pix_offset,mesh.XY[vert_bound_nodes][:,1]-pix_offset,marker='^',color='g')
ax.axis('off')
def plot_field(ax,field_data):
"""Plot 2-d field data with a fitted colorbar on the provided figure axes
Args:
ax(object): figure object axes
field_data(nelx x nely float matrix): element-wise field values
"""
im = ax.imshow(field_data, cmap='jet')
divider = make_axes_locatable(ax)
cax = divider.append_axes("right", size="2%", pad=0.5)
cbar = plt.colorbar(im,cax=cax)
cbar.ax.locator_params(nbins=8)
def train_plot(mesh,compliance,volume_violation,rho,psi,vol_field,fixed_dofs,load):
"""Plots convergence curve along with two random designs from the batch.
Mostly used for evaluation of training procedure in jupyter notebooks
Args:
mesh(object): finite element mesh object
compliance(Nx1 float array): torch array with compliance values for each train iteration
volume_violation(Nx1 float array): torch array with volume violation values for each train iteration
rho(B x 1 x nely x nelx float matrix): torch matrix with densities for each entry in the batch
fixed_dofs(B x N float matrix): numpy matrix with fixed_dofs for each entry in the batch
load(B x ndof x 1 float matrix): numpy matrix with loads for each entry in the batch
"""
# transform from tensors to numpy
rho = rho.squeeze(1).detach().cpu().numpy()
psi = psi.cpu().squeeze(1).numpy()
vol_field = vol_field.cpu().squeeze(1).numpy()
fixed_dofs = fixed_dofs.numpy()
load = load.numpy()
tmp_img = "tmp_design_out.png"
fig = plt.figure(constrained_layout=True,figsize=(12,6))
gs = fig.add_gridspec(2, 2)
ax0 = fig.add_subplot(gs[:, 0])
ax1 = fig.add_subplot(gs[0, 1])
ax2 = fig.add_subplot(gs[1, 1])
# plot convergence
ax0.set_xlabel('Iter')
ax0.set_ylabel('Compliance')
ax0.plot(np.arange(len(compliance)), compliance,color='b')
ax0.tick_params(axis='y', labelcolor='b')
ax0_twin = ax0.twinx()
ax0_twin.set_ylabel('Vol. violation')
ax0_twin.plot(np.arange(len(volume_violation)), volume_violation,color='r')
ax0_twin.tick_params(axis='y', labelcolor='r')
# plot designs
plot_design(ax1,mesh,rho[0],vol_field[0],remove_padding(fixed_dofs[0],-1),load[0])
plot_design(ax2,mesh,rho[1],vol_field[1],remove_padding(fixed_dofs[1],-1),load[1])
#ax2.imshow(psi[0],cmap="gray")
#ax2.axis("off")
plt.savefig(tmp_img)
plt.close(fig)
display(Image(filename=tmp_img))
clear_output(wait=True)
os.remove(tmp_img)
def tensorboard_plot(mesh,rho,vol_field,fixed_dofs,load):
"""Function used to create images saved by tensorboard"""
# transform inputs from tensors to numpy
rho = rho.squeeze(1).detach().cpu().numpy()
vol_field = vol_field.cpu().squeeze(1).numpy()
fixed_dofs = fixed_dofs.numpy()
load = load.numpy()
# setup plot
rows = 4
cols = 2
fig, axarr = plt.subplots(rows,cols,figsize=(12,12))
it=0
for i in range(rows):
for j in range(cols):
ax = axarr[i][j]
plot_design(ax,mesh,rho[it],vol_field[it],remove_padding(fixed_dofs[it],-1),load[it])
it+=1
fig.tight_layout()
buf = io.BytesIO()
plt.savefig(buf, format='png')
plt.close(fig)
buf.seek(0)
return buf
def plot_grad_flow(named_parameters):
"""Plots the gradient flow through each of the layers in the network"""
ave_grads = []
layers = []
for n, p in named_parameters:
if(p.requires_grad) and ("bias" not in n):
layers.append(n)
ave_grads.append(p.grad.abs().mean())
plt.plot(ave_grads, alpha=0.3, color="b")
plt.hlines(0, 0, len(ave_grads)+1, linewidth=1, color="k" )
plt.xticks(range(0,len(ave_grads), 1), layers, rotation="vertical")
plt.xlim(xmin=0, xmax=len(ave_grads))
plt.xlabel("Layers")
plt.ylabel("average gradient")
plt.title("Gradient flow")
plt.grid(True)
def remove_padding(X,pad_value):
"""Convience function used to remove padding from inputs which have been
padded during batch generation"""
return X[X!=pad_value]
def count_model_parameters(model):
"""Count trainable parameters of a given model
Args:
model(object): torch model object
Returns:
trainable_parameters(int): number of trainable parameters
"""
return sum(p.numel() for p in model.parameters() if p.requires_grad)
def normalize_data(x):
"""Normalize data to values between 0-1
Args:
x(NxN float matrix): data to be normalized
Returns:
x_norm((NxN float matrix): normalized data
"""
return (x-x.min())/(x.max()-x.min())
def standardize_data(x):
"""Standardize data by subtrating mean and dividing with standard deviation
Args:
x(NxN float matrix): data to be standardized
Returns:
x_norm((NxN float matrix): standardized data
"""
return (x-x.mean())/x.std()
class StreamlineGenerator():
"""Class used to generate streamlines
Args:
nelx(int): number of elements in x-direction of the mesh
nely(int): number of elements in y-direction of the mesh
U(nely x nelx float matrix): velocity-direction in x
V(nely x nelx float matrix): velocity-direction in y
vmag(nely x nelx float matrix): magnitude of velocity field
min_length(float): minimum length of streamlines
color(str): plotting color of streamlines
"""
def __init__(self,nelx,nely,U,V,vmag,min_length,color):
self.nelx = nelx
self.nely = nely
self.rscale = min(nelx,nely)/10
self.interpU = RectBivariateSpline(np.arange(nely), np.arange(nelx), U)
self.interpV = RectBivariateSpline(np.arange(nely), np.arange(nelx), V)
self.interpMag = RectBivariateSpline(np.arange(nely), np.arange(nelx), vmag)
self.min_length = min_length
self.color = color
def integrate_streamline(self,xpos,ypos,max_iter=100):
"""Euler integration of a streamline from starting point (xpos,ypos)"""
x_line = [xpos]
y_line = [ypos]
v_line = []
dt = self.rscale
it = 0
while (xpos>=0 and xpos<=self.nelx) and (ypos>=0 and ypos<=self.nely):
# calculate velocity-direction and magnitude in a given point
u = self.interpU(ypos,xpos)[0][0]
v = self.interpV(ypos,xpos)[0][0]
vmag = self.interpMag(ypos,xpos)[0][0]
# update positions
xpos+=dt*u
ypos+=dt*v
# save points
x_line.append(xpos)
y_line.append(ypos)
v_line.append(vmag)
# terminate if velocity is too small or maximum number of iterations is reached
it+=1
if it>=max_iter or vmag<1e-4:
break
return np.array(x_line), np.array(y_line), np.array(v_line)
def generate_streamlines(self,seed_points):
"""Generate streamlines based on a set of seed points"""
streamlines = []
# loop over all seed points
for idx,(x0,y0) in enumerate(seed_points):
x_strm,y_strm,v_strm = self.integrate_streamline(x0,y0)
dx = np.abs(x_strm[-1]-x_strm[0])
dy = np.abs(y_strm[-1]-y_strm[0])
line_length = np.sqrt(dx**2+dy**2)
# save to matplotlib line collection if streamline is longer than the
# specified minimum length threshold
if line_length>self.min_length:
lc = self.create_linecollection(x_strm,y_strm,v_strm)
streamlines.append(lc)
return streamlines
def create_linecollection(self,x,y,v):
"""Creates matplotlib linecollection based on the set of points in the streamline"""
points = np.array([x, y]).T.reshape(-1, 1, 2)
segments = np.concatenate([points[:-1], points[1:]], axis=1)
lw = v*20+2
lc = LineCollection(segments, linewidths=lw,color=self.color)
return lc
def stream2grayscale(strm1_lc,strm2_lc,nelx,nely,dpi):
"""Given two line collections of streamlines create a grayscale image
Args:
strm1_lc(matplotlib.LineCollection): streamlines corresponding to principal stress direction 1
strm2_lc(matplotlib.LineCollection): streamlines corresponding to principal stress direction 2
Returns:
img_gray(nely*dpi/10 x nelx*dpi/10): grayscale image
"""
# plot the two line collections
fig,ax = plt.subplots(1,1,figsize=(12,6),dpi=dpi)
plt.gca().set_axis_off()
plt.subplots_adjust(top = 1, bottom = 0, right = 1, left = 0,
hspace = 0, wspace = 0)
for lc in strm1_lc:
ax.add_collection(lc)
for lc in strm2_lc:
ax.add_collection(lc)
ax.set_xlim([0,nelx])
ax.set_ylim([0,nely])
ax.invert_yaxis()
plt.margins(0,0)
# save the image as a buffer
io_buf = io.BytesIO()
fig.savefig(io_buf, format='raw', dpi=dpi)
io_buf.seek(0)
# create numpy array from buffer
img_arr = np.reshape(np.frombuffer(io_buf.getvalue(), dtype=np.uint8),
newshape=(int(fig.bbox.bounds[3]), int(fig.bbox.bounds[2]), -1))
io_buf.close()
# save numpy array as grayscale image
img_gray = rgb2gray(img_arr)
plt.close()
return img_gray
def density_sort_threshold(rho,volfrac,Emin=1e-9):
"""Sort densities and threshold based on volume constraint"""
_,nely,nelx = rho.shape
rho_flat = rho.flatten()
vol_idx = int(np.floor(volfrac*nelx*nely))
ind = np.argsort(rho_flat)[::-1]
rho_flat[ind[:vol_idx]] = 1
rho_flat[ind[vol_idx:]] = 1e-9
rho_thres = rho_flat.reshape((nely,nelx))
return rho_thres
def remove_disconnects(rho):
"""Use connected components analysis to identify disconnected regions and remove them"""
# connected components analysis
label_img, nr_labels = measure.label(rho,background=0,return_num=True)
# only keep the two largest labels (background + largest component)
max_labels = np.argsort([np.sum(label_img==i) for i in range(nr_labels+1)])[-2:]
# mask on all labels not part of the largest components
small_label_mask = np.logical_and(label_img!=max_labels[0],label_img!=max_labels[1])
# set all small labels to background
label_img[small_label_mask] = 0
# convert to zero-one
label_img[label_img>0] = 1
return label_img
def postprocess_designs(rho,vol_field):
"""Post process a batch of designs by first using a threshold based
on density sorting, and then a connected component analysis"""
batch_size = rho.shape[0]
device = rho.device
# convert input tensors to cpu numpy arrays
rho = rho.cpu().numpy()
vol_field = vol_field.cpu().numpy()
for i in range(batch_size):
volfrac = vol_field[i,0,0,0]
rho[i] = density_sort_threshold(rho[i],volfrac)
rho[i] = remove_disconnects(rho[i])
# move rho to gpu
rho = torch.tensor(rho,dtype=torch.float32).to(device)
return rho
class DataGen:
"""Class for generating training and test data
Args:
mesh(object): finite element mesh object
volfrac_range(2x1 float array): array with lowest and highest volume fraction
load_range(2x2 float array): array indicating domain where a load may be applied
n_bc_samples(int): number of samples per boundary condition
"""
def __init__(self,mesh,volfrac_range,load_range,n_bc_samples):
self.mesh = mesh
self.volfrac_range = volfrac_range
self.load_x_range = load_range[0]
self.load_y_range = load_range[1]
self.n_bc_samples = n_bc_samples
def gen_volfracs(self,n_samples):
"""Generate a specified number of volume fractions within the allowed range"""
return np.random.uniform(self.volfrac_range[0],self.volfrac_range[1],n_samples)
def gen_rand_unit_vec(self,ndim):
"""Generate a unit vector with a given dimension"""
x = np.random.standard_normal(ndim)
return x / np.linalg.norm(x)
def gen_rand_unit_vectors(self,ndim,n_samples):
"""Generate a specified number of unit vectors"""
return [self.gen_rand_unit_vec(ndim) for _ in range(n_samples)]
def gen_rand_pos(self,x_range,y_range):
"""Generate a random position within the allowed domain"""
return np.array([np.random.randint(x_range[0],x_range[1]+1),np.random.randint(y_range[0],y_range[1]+1)])
def gen_rand_positions(self,x_range,y_range,n_samples):
"""Generate a specified number of random positions"""
return [self.gen_rand_pos(x_range,y_range) for _ in range(n_samples)]
def gen_load_positions(self,fixed,n_samples):
"""Generate random load positions within the specified load domain
a new position is generated if the load is too close to the boundary condition """
bound_rad = max(self.mesh.nelx,self.mesh.nely)//10
fixed_pos = self.mesh.XY[self.mesh.dof2nodeid(fixed)]
n_pos = 0
load_pos_arr = np.empty((0,2))
while n_pos < n_samples:
load_pos = np.array(self.gen_rand_positions(self.load_x_range,self.load_y_range,n_samples-n_pos))
dist_mat = cdist(fixed_pos,load_pos) # get distance between all load positions and boundary positions
rem_idx = np.unique(np.nonzero(dist_mat<bound_rad)[1]) # remove all indices which violates the boundary radius
load_pos = np.delete(load_pos,rem_idx,axis=0)
load_pos_arr = np.append(load_pos_arr, load_pos, axis=0)
n_pos = len(load_pos_arr)
return load_pos_arr
def check_system_conditioning(self,BCs):
"""Check system conditioning by trying to solve the problem with the specified load
and boundary conditions on a fully solid domain"""
# insert boundary conditions
fea = LinearElasticity(self.mesh)
for bc in BCs:
if bc[0]=='wall':
fea.insert_wall_boundary(wall_pos=bc[1],wall_ax=bc[2],bound_dir=bc[3])
elif bc[0]=='point':
fea.insert_point_boundary(bound_pos=bc[1],bound_dir=bc[2])
# insert 45 deg point load in the middle of domain
fea.insert_point_load(load_pos=[self.mesh.nelx//2,self.mesh.nely//2],load_mag=[1,1])
# check conditioning of system
try:
rho = np.ones((self.mesh.nelx,self.mesh.nely))
U = fea.solve_system(rho,sparse=True)
except:
print("BC:",bc)
print("Unconditioned system matrix")
def generate_dataset_dicts(self,bc_cmbs,testset_indices,trainset=True,cond_check=True):
"""Generate a dictionary containing the volume fraction, load and boundary conditions
for each sample in the dataset
Args:
bc_cmbs(list): A list of boundary condition combinations, an example would be
[["wall",0,"y","xy"],"point",(30,10),"xy"],[...]]
testset_indices(integer list): indices in the bc_cmbs list which belong to the testset
trainset(bool): boolean specifying whether to generate train or testset
Returns:
dataset_dicts(list): list of dictionaries containing information about each sample
in the dataset
"""
# run initial test to check system conditioning
if cond_check==True:
print("Running system conditioning test")
for cmb in bc_cmbs:
self.check_system_conditioning(cmb)
print("System conditioning test parsed")
# loop over all bc combinations and generate data samples
dataset_dicts = []
for idx,cmb in enumerate(bc_cmbs):
fea = LinearElasticity(self.mesh)
# skip combinations based on whether training or test set is being generated
if trainset==True:
if idx in testset_indices:
continue
else:
if idx not in testset_indices:
continue
# insert boundary conditions(s) in physics class
wall_bc_list = []
point_bc_list = []
for bc in cmb:
if bc[0]=='wall':
fea.insert_wall_boundary(wall_pos=bc[1],wall_ax=bc[2],bound_dir=bc[3])
wall_bc_list.append(bc)
elif bc[0]=='point':
fea.insert_point_boundary(bound_pos=bc[1],bound_dir=bc[2])
point_bc_list.append(bc)
# generate volume fractions and load positioning and magnitude
volfracs = self.gen_volfracs(self.n_bc_samples)
load_magnitudes = self.gen_rand_unit_vectors(2,self.n_bc_samples)
load_positions = self.gen_load_positions(fea.fixed_dofs,self.n_bc_samples)
# save sample parameters in list of dictionaries
for (load_pos,load_mag,vol) in zip(load_positions,load_magnitudes,volfracs):
dataset_dicts.append({"wall_BC":wall_bc_list,"point_BC":point_bc_list,
"load_pos":load_pos,"load_mag":load_mag,"volfrac":vol})
return dataset_dicts