def get_angle_potential_value(atoms, angle):
i = angle.atomi
j = angle.atomj
k = angle.atomk
rij = rel_pos_pbc(atoms, i, j)
dij = linalg.norm(rij)
eij = rij / dij
rkj = rel_pos_pbc(atoms, k, j)
dkj = linalg.norm(rkj)
ekj = rkj / dkj
eijekj = np.dot(eij, ekj)
if np.abs(eijekj) > 1.0:
eijekj = np.sign(eijekj)
a = np.arccos(eijekj)
if angle.cos:
da = np.cos(a) - np.cos(angle.a0)
else:
da = a - angle.a0
da = da - np.around(da / np.pi) * np.pi
v = 0.5 * angle.k * da ** 2
angle.a = a
return i, j, k, v
def checkNumericalGradient():
# This code can be used to check your numerical gradient implementation
# in computeNumericalGradient()
# It analytically evaluates the gradient of a very simple function called
# simpleQuadraticFunction (see below) and compares the result with your numerical
# solution. Your numerical gradient implementation is incorrect if
# your numerical solution deviates too much from the analytical solution.
# Evaluate the function and gradient at x = [4; 10]; (Here, x is a 2d vector.)
x = np.array([4,10])
value,grad = simpleQuadraticFunction(x)
# Use your code to numerically compute the gradient of simpleQuadraticFunction at x.
# (The notation "lambda x: simpleQuadraticFunction(x)[0]" creates a function
# that only returns the cost and not the grad of simpleQuadraticFunction.)
numgrad = computeNumericalGradient(lambda x: simpleQuadraticFunction(x)[0],x)
# Visually examine the two gradient computations. The two columns
# you get should be very similar.
print(np.array([numgrad,grad]).T)
print("The above two columns you get should be very similar.")
print("(Left-Your Numerical Gradient, Right-Analytical Gradient)\n\n")
# Evaluate the norm of the difference between two solutions.
# If you have a correct implementation, and assuming you used EPSILON = 0.0001
# in computeNumericalGradient.m, then diff below should be 2.1452e-12
diff = norm(numgrad-grad)/norm(numgrad+grad)
print(diff)
print("Norm of the difference between numerical and analytical gradient (should be < 1e-9)\n\n")
def plot(self, string):
walls = decode_string_to_tuplearray(string)
""" publish walls with cubes """
for i, (p1, p2) in enumerate(walls):
marker = get_marker('wall_%d' % i, Marker.CUBE)
# set scale
marker.scale.x = norm(p1-p2)
marker.scale.y = 20
marker.scale.z = 1e3
# set color
marker.color.r = 1.0
marker.color.a = 1.0
# set position
p = marker.pose.position
p.x, p.y = .5 * (p1 + p2)
p.z = .5e3
# set orientation
dp = p2 - p1
psi = acos(dp[0]/norm(dp))
o = marker.pose.orientation
o.x, o.y, o.z, o.w = quaternion_from_euler(0, 0, psi)
# publish
publisher.publish(marker)
for i in range(len(walls), self.prev_num_plotted_walls):
marker = get_marker('wall_%d' % i, Marker.CUBE)
p = marker.pose.position
p.x = -1e20
publisher.publish(marker)
self.prev_num_plotted_walls = len(walls)
def _rank1(X, profunc1, args1, profunc2, args2, niter=500, eps=1e-6): u = X.sum(axis=1); u /= norm(u) v = X.sum(axis=0); v /= norm(v) rho_old = dot(dot(u,X),v) for i in xrange(niter): alpha = dot(X,v) if profunc1 == None: u = alpha else: u = profunc1(alpha, **args1) u /= norm(u) beta = dot(X.T,u) if profunc2 == None: v = beta else: v = profunc2(beta, **args2) rho = norm(v) v /= rho if abs(rho-rho_old) <= eps: break else: rho_old = rho return u, rho, v
def test3():
import spacy.en
from spacy.parts_of_speech import ADV
nlp = spacy.en.English()
# Find log probability of Nth most frequent word
probs = [lex.prob for lex in nlp.vocab]
probs.sort()
is_adverb = lambda tok: tok.pos == ADV and tok.prob < probs[-1000]
tokens = nlp(u"‘Give it back,’ he pleaded abjectly, ‘it’s mine.’")
o = u''.join(tok.string.upper() if is_adverb(tok) else tok.string for tok in tokens)
assert o == u'‘Give it back,’ he pleaded ABJECTLY, ‘it’s mine.’'
pleaded = tokens[7]
assert pleaded.repvec.shape == (300,)
o = pleaded.repvec[:5]
assert sum(o) != 0
from numpy import dot
from numpy.linalg import norm
cosine = lambda v1, v2: dot(v1, v2) / (norm(v1) * norm(v2))
words = [w for w in nlp.vocab if w.check(IS_LOWER) and w.has_repvec]
words.sort(key=lambda w: cosine(w.repvec, pleaded.repvec))
words.reverse()
o = [w.orth_ for w in words[0:20]]
assert o == [u'pleaded', u'pled', u'plead', u'confessed', u'interceded',
u'pleads', u'testified', u'conspired', u'motioned', u'demurred',
u'countersued', u'remonstrated', u'begged', u'apologised',
u'consented', u'acquiesced', u'petitioned', u'quarreled',
u'appealed', u'pleading']
o = [w.orth_ for w in words[50:60]]
assert o == [u'counselled', u'bragged', u'backtracked', u'caucused', u'refiled',
u'dueled', u'mused', u'dissented', u'yearned', u'confesses']
o = [w.orth_ for w in words[100:110]]
assert o == [u'cabled', u'ducked', u'sentenced', u'perjured', u'absconded',
u'bargained', u'overstayed', u'clerked', u'confided', u'sympathizes']
def __init__(self, v1, v2):
self.v1 = v1
self.v2 = v2
self.a = la.norm(v1)
self.b = la.norm(v2)
self.alpha = np.arcsin(np.dot(v1,v2)/(self.a*self.b))
self.area = self.v1.dot(self.v2)
def isparallel(O1,O2):
'''
Judge whether two array-like vectors are parallel to each other.
Parameters
----------
O1,O2 : 1d array-like
The input vectors.
Returns
-------
int
* 0: not parallel
* 1: parallel
* -1: anti-parallel
'''
norm1=nl.norm(O1)
norm2=nl.norm(O2)
if norm1<RZERO or norm2<RZERO:
return 1
elif O1.shape[0]==O2.shape[0]:
buff=np.inner(O1,O2)/(norm1*norm2)
if np.abs(buff-1)<RZERO:
return 1
elif np.abs(buff+1)<RZERO:
return -1
else:
return 0
else:
raise ValueError("isparallel error: the shape of the array-like vectors does not match.")
def project_aln(alignment, weighted_3d_algn, weight):
'''computes projected weighted alignment based on the
alignment in ascii format, the weighted 3D alginment
tensor (weighted_3d_algn) & the weight matrix (weight)
it does so by computing the frequencies first call (aa_freq)
'''
algn_shape = get_algn_shape(alignment)
no_seq = algn_shape.no_seq
no_pos = algn_shape.no_pos
no_aa = algn_shape.no_aa
algn_aa_freq = aa_freq(alignment)
proj_vect = zeros((no_pos, no_aa))
wt_mat = zeros((no_aa, no_pos))
for i in range(0, no_pos):
for aa in range(0, no_aa):
wt_mat[aa, i] = weight[i, aa]*algn_aa_freq[aa, i]
if LA.norm(wt_mat[:, i]) > 0:
proj_vect[i, :] = wt_mat[:, i] / LA.norm(wt_mat[:, i])
prj_wt_aln = zeros((no_seq, no_pos))
for i in range(0, no_pos):
for aa in range(0, no_aa):
prj_wt_aln[:, i]\
= prj_wt_aln[:, i]\
+ proj_vect[i, aa] * weighted_3d_algn[:, i, aa]
return ProjectionMatrices(prj_wt_aln, proj_vect)
def test_retrieve_data(self):
ptree = PropertyTree()
ptree.put_string('type', 'SeriesRC')
ptree.put_double('series_resistance', 100e-3)
ptree.put_double('capacitance', 2.5)
device = EnergyStorageDevice(ptree)
ptree = PropertyTree()
ptree.put_string('type', 'ElectrochemicalImpedanceSpectroscopy')
ptree.put_double('frequency_upper_limit', 1e+2)
ptree.put_double('frequency_lower_limit', 1e-1)
ptree.put_int('steps_per_decade', 1)
ptree.put_int('steps_per_cycle', 64)
ptree.put_int('cycles', 2)
ptree.put_int('ignore_cycles', 1)
ptree.put_double('dc_voltage', 0)
ptree.put_string('harmonics', '3')
ptree.put_string('amplitudes', '5e-3')
ptree.put_string('phases', '0')
eis = Experiment(ptree)
with File('trash.hdf5', 'w') as fout:
eis.run(device, fout)
spectrum_data = eis._data
with File('trash.hdf5', 'r') as fin:
retrieved_data = retrieve_impedance_spectrum(fin)
print(spectrum_data['impedance'] - retrieved_data['impedance'])
print(retrieved_data)
self.assertEqual(linalg.norm(spectrum_data['frequency'] -
retrieved_data['frequency'], inf), 0.0)
# not sure why we don't get equality for the impedance
self.assertLess(linalg.norm(spectrum_data['impedance'] -
retrieved_data['impedance'], inf), 1e-10)
def problem8():
"problem set 2.1, problem 8, page 56"
import LUdecomp
A = np.array([[-3,6,-4],[9,-8,24],[-12,24,-26]],dtype=float)
A_orig = A.copy()
LU = LUdecomp.LUdecomp(A)
b = np.array([-3,65,-42],dtype=float)
b_orig = b.copy()
x = LUdecomp.LUsolve(LU,b)
# extract L and U for verification
U = np.triu(LU) #
L = np.tril(LU)
L[ np.diag_indices_from(L) ] = 1.0
print("""
Problem 8:
A =
{}
LU decomposition A = LU, LU (in one matrix) =
{}
Solving Ax=b, with b = {}
Solution x = {}
Verifying solution:
residual ||Ax-b||_2 = {}
||A - dot(L,U)||_inf = {}
""".format(A_orig,LU,b_orig,x,
la.norm(np.dot(A_orig,x)-b_orig,2),
la.norm(A_orig - np.dot(L,U),np.inf))
)
def sparse_calculate_error(mat, sketch, normalized=True):
cov = (mat.transpose()).dot(mat).todense()
cov_sketch = np.dot(sketch.T, sketch)
if normalized:
return (ln.norm(cov - cov_sketch, ord=2) / sparse_squared_frobenius_norm(mat))
else:
return ln.norm(cov - cov_sketch, ord=2)
def genGraph(S_actual, S_est, S_previous, empCov_set, nodeID, e1, e2, e3, e4, display = False):
D = np.where(S_est != 0)[0].shape[0]
T = np.where(S_actual != 0)[0].shape[0]
TandD = float(np.where(np.logical_and(S_actual,S_est) == True)[0].shape[0])
P = TandD/D
R = TandD/T
offDiagDiff = S_actual - S_est
offDiagDiff = offDiagDiff - np.diag(np.diag(offDiagDiff))
S_diff = (S_est - S_previous)
S_diff = S_diff - np.diag(np.diag(S_diff))
ind = (S_diff < 1e-2) & (S_diff > - 1e-2)
S_diff[ind] = 0
K = np.count_nonzero(S_diff)
e1.append( alg.norm(offDiagDiff, 'fro'))
e2.append(2* P*R/(P+R))
K = float(np.where(np.logical_and((S_est>0) != (S_previous>0), S_est>0) == True)[0].shape[0])
e3.append(-np.log(alg.det(S_est)) + np.trace(np.dot(S_est, empCov_set[nodeID])) + K)
e4.append(alg.norm(S_est - S_previous, 'fro'))
display = False
if display == True:
if (nodeID >timeShift -10) and (nodeID < timeShift + 10):
print 'nodeID = ', nodeID
print 'S_true = ', S_actual,'\nS_est', S_est
# print 'S_error = ',S_actual - S_est, '\n its Fro error = ', alg.norm(S_actual - S_est, 'fro')
print 'D = ',D,'T = ', T,'TandD = ', TandD,'K = ', K,'P = ', P,'R = ', R,'Score = ', 2* P*R/(P+R)
return e1, e2, e3, e4
def compute_TPS_K(ctrl_pts, landmarks = None, _lambda = 0):
"""
Compute the kernel matrix for thin-plate splines.
Reference:
Landmark-based Image Analysis, Karl Rohr, p195
"""
#kernel_func = [lambda r,_lambda=0: 0 if r==0 else r*r*log(r), lambda r,_lambda=0: -r]
#the above definition is not used because the if else syntax is not supported in Python2.4
def kernel_func_2d(r, _lambda=0):
#_lambda reserved for regularization
if r == 0:
return 0
else:
return r*r*log(r)
def kernel_func_3d(r, _lambda=0):
#_lambda reserved for regularization
return -r
kernel_func = (kernel_func_2d, kernel_func_3d)
[n,d] = ctrl_pts.shape
K = [kernel_func[d-2](norm(ctrl_pts[i]-ctrl_pts[j]), _lambda) for i in arange(n) for j in arange(n)]
K = array(K).reshape(n,n)
if landmarks is not None:
[m,d] = landmarks.shape # assert (d,d) equal
U = [kernel_func[d-2](norm(landmarks[i]-ctrl_pts[j]), _lambda) for i in arange(m) for j in arange(n)]
U = array(U).reshape(m,n)
else:
U = None
return K,U
def Normal(a, b):
"""finds the unit normal vector of 2 vectors"""
vector = cross(a, b)
length = norm(vector)
normal = vector / length
assert allclose(norm(normal), 1.)
return normal
def evaluate(self, locations):
total = 0
for i, layer in enumerate(self._all_edges):
s = layer.shape
for j1 in range(s[0]):
if j1 == self.nodes[i].shape[1]:
break
for j2 in range(s[1]):
#firstpoint = (i*hscale + hoff, j1*vscale + voff)
#secondpoint = ((i+1)*hscale + hoff, j2*vscale + voff)
one = locations[(i, j1)]
two = locations[(i + 1, j2)]
distance = linalg.norm(one - two)
f = distance * distance
influence = abs(layer[j1, j2])
# quality is decreased when connected things are far apart
total -= f * influence
for _, v in locations:
for _, v2 in locations:
if v != v2:
d = linalg.norm(v - v2)
total += 1000 / d # this is like electric potential
return total
def sphere_project(v,r):
"""
sphere_project - project point X,Y,Z to the surface of sphere radius r
V = sphere_project(v,r,c)
Cartesian inputs:
v is the vertex matrix, Nx3 (XYZ)
r is the sphere radius, 1x1 (default 1)
c is the sphere centroid, 1x3 (default 0,0,0)
XYZ are converted to spherical coordinates and their radius is
adjusted according to r, from c toward XYZ (defined with theta,phi)
V is returned as Cartesian 3D coordinates
"""
from numpy.linalg import norm
for i in xrange(v.shape[0]):
c0 = 0.207
c1 = 2.000
c2 = -1.123
R = r
X = v[0]
Y = v[1]
a = ((X**2) +(Y**2))/(R**2)
Z = (0.5*R*(1.0-a)**(0.5))*(c0 + c1*a + c2*(a**2))
magn = norm(v[i])
vecnorm = v[i]/norm(v[i])
v[i] = vecnorm*r
def AreaNormal(nodes):
"""
Returns area,unitNormal
n = Normal = a x b
Area = 1/2 * |a x b|
V = <v1,v2,v3>
|V| = sqrt(v1^0.5+v2^0.5+v3^0.5) = norm(V)
Area = 0.5 * |n|
unitNormal = n/|n|
"""
(n0, n1, n2) = nodes
a = n0 - n1
b = n0 - n2
vector = cross(a, b)
length = norm(vector)
normal = vector / length
area = 0.5 * length
if not allclose(norm(normal), 1.):
print("a = ", a)
print("b = ", b)
print("normal = ", normal)
print("length = ", length)
sys.exit('check...')
return area, normal
def decompose(m):
'''
Factor 3x4 camera matrix into 3x3 internal and 3x4 external.
This is an RQ decomposition,
enforcing a --+ signature for the internal matrix and
positive determinant for the rotation matrix.
The internal matrix is also normalised.
NumPy only provides QR,
and the index gymnastics required to convert QR to RQ
make it faster to use a custom routine.
'''
r = np.zeros_like(m[:, :-1])
q = np.empty_like(m)
r[2, 2] = la.norm(m[2, :-1])
q[2, :] = m[2, :] / r[2, 2]
r[1, 2] = inner(m[1, :-1], q[2, :-1])
w = m[1, :] - r[1, 2] * q[2, :]
r[1, 1] = -la.norm(w[:-1])
q[1, :] = w / r[1, 1]
r[0, 1:] = inner(m[0, :-1], q[1:, :-1])
w = m[0, :] - dot(r[0, 1:], q[1:, :])
r[0, 0] = -la.norm(w[:-1])
q[0, :] = w / r[0, 0]
q *= np.sign(la.det(q[:, :-1]))
return r / r[2, 2], q
def getjvq():
from np.linalg import norm
unit = io.read("POSCAR_unit")
atoms = io.read("POSCAR")
supercell = map(
int,
norm(
atoms.cell,
axis=1) /
norm(
unit.cell,
axis=1) +
[.5] *
3)
c = supercell
q = []
u = [int(x / 2) * 2 + 1 for x in c]
for i in range(u[0]):
for j in range(u[1]):
for k in range(u[2]):
b = np.array([float(i - c[0] / 2) / c[0],
float(j - c[1] / 2) / c[1],
float(k - c[2] / 2) / c[2]])
q.append(b)
allpos = np.load('allpos.npy')
v = np.gradient(allpos)[0]
def subgradientPolyakCFM(f, sgf, x0, lowerBounder, gamma=1, maxIters=100, report=None):
''' Use the Polyak step size and CFM direction update rule. '''
xk = x0
gk = sgf(x0)
sk = gk
lb = lowerBounder(xk)
fb = f(xk)
# Using optimal step size for fixed number of iterations
for k in arange(maxIters) + 1:
if report:
report(xk, k)
sko = sk
gko = gk
gk = sgf(xk)
#betak = 0.25
'''betak = (- gamma * gk.dot(sko)/(norm(sko)**2)
if sko.dot(gk) < 0 else 0 )'''
betak = (- gamma * gk.dot(gko) / (norm(gko) ** 2)
if gko.dot(gk) < 0 else 0 )
#sk = gk + betak*sko
sk = gk + betak * gko
nfb = f(xk)
fb = fb if fb < nfb else nfb
if nfb < fb:
nlb = lowerBounder(xk)
lb = lb if lb > nlb else nlb
alphak = 0.5 * (fb - lb) / (norm(sk)) #**2 ) #* (k ** -0.66)
xk = xk - alphak * sk
return xk
def fastica_defl(X, nIC=None, guess=None,
nonlinfn = pow3nonlin,
termtol = 5e-7, maxiters = 2e3):
nPC, siglen = X.shape
nIC = nIC or nPC-1
guess = guess or randn(nPC,nIC)
if _orth_loaded:
guess = orth(guess)
B = zeros(guess.shape, np.float64)
errvec = []
icc = 0
while icc < nIC:
w = randn(nPC,1) - 0.5
w -= dot(dot(B, transp(B)), w)
w /= norm(w)
wprev = zeros(w.shape)
for i in xrange(long(maxiters) +1):
w -= dot(dot(B, transp(B)), w)
w /= norm(w)
#wprev = w.copy()
if (norm(w-wprev) < termtol) or (norm(w + wprev) < termtol):
B[:,icc] = transp(w)
icc += 1
break
wprev = w.copy()
return B.real, errvec
def hexagon_bz(reciprocals=None,nk=100,vh='H'):
'''
The whole hexagonal BZ.
'''
if reciprocals is not None:
b1=reciprocals[0]
b2=reciprocals[1]
temp=np.inner(b1,b2)/nl.norm(b1)/nl.norm(b2)
assert np.abs(np.abs(temp)-0.5)<RZERO
if np.abs(temp+0.5)<RZERO: b2=-b2
else:
if vh in ('H','h'):
b1=np.array([np.sqrt(3.0)/2,0.5])*4*np.pi/np.sqrt(3.0)
b2=np.array([np.sqrt(3.0)/2,-0.5])*4*np.pi/np.sqrt(3.0)
else:
b1=np.array([1.0,0.0])*4*np.pi/np.sqrt(3.0)
b2=np.array([0.5,np.sqrt(3.0)/2])*4*np.pi/np.sqrt(3.0)
p0,p1,p2,p3,p4=-(b1+b2)/3,(b1+b2)/3,(b1+b2)*2/3,(b1*2-b2)/3,(b2*2-b1)/3
mesh=np.zeros((nk**2,b1.shape[0]))
for i in range(nk):
for j in range(nk):
coords=b1*i/nk+b2*j/nk+p0
if isintratriangle(coords,p1,p2,p3,vertexes=(False,True,False),edges=(True,True,False)): coords=coords-b1
if isintratriangle(coords,p1,p2,p4,vertexes=(False,True,False),edges=(True,True,False)): coords=coords-b2
mesh[i*nk+j,:]=coords
volume=np.abs(np.cross(b1,b2))
return BaseSpace(('k',mesh,volume))
def distance(self, other, method='euclidean'):
"""
Distance between the center of this source and another.
Parameters
----------
other : Source, or array-like
Either another source, or the center coordinates of another source
method : str
Specify a distance measure to used for spatial distance between source
centers. Current options include Euclidean distance ('euclidean') and
L1-norm ('l1').
"""
from numpy.linalg import norm
checkParams(method, ['euclidean', 'l1'])
if method == 'l1':
order = 1
else:
order = 2
if isinstance(other, Source):
return norm(self.center - other.center, ord=order)
elif isinstance(other, list) or isinstance(other, ndarray):
return norm(self.center - asarray(other), ord=order)
def reset(self, direction, speed):
# initial location
p = [random.uniform(-1, 1) for i in range(3)]
p /= norm(p)
# orienting point
o = [0, 0, 0]
mini = min(range(len(p)), key=lambda i: abs(p[i]))
o[mini] = 1 if p[mini] < 0 else -1
# velocity vector
v = cross(p, o)
v /= norm(v)
v *= speed*pi/180
r = 1.145
shape = SphericalPolygon([rotate(rotate(p, o, r*random.uniform(0.9,1.1)), p, th)
for th in [i*pi/8 for i in range(16)]])
for t in self.tiles.values():
t.bottom = 0
t.layers = [Layer('T', 1)] if shape.contains(t.vector) else []
t.limit()
self._indexedtiles = []
for t in self.tiles.values():
self._indexedtiles.append(t)
self._index = PointTree(dict([[self._indexedtiles[i].vector, i]
for i in range(len(self._indexedtiles))]))
self._direction = direction
self._velocity = v
def test_ordinary(self):
N=4
np.random.seed()
state,target=np.zeros((2,)*N),SQN(0.0)
for index in QuantumNumbers.decomposition([SQNS(0.5)]*N,signs=[1]*N,target=target):
state[index]=np.random.random()
state=state.reshape((-1,))
sites=[Label('S%s'%i,qns=SQNS(0.5),flow=1) for i in range(N)]
bonds=[Label('B%s'%i,qns=None,flow=None) for i in range(N+1)]
bonds[+0]=bonds[+0].replace(qns=SQNS(0.0),flow=+1)
bonds[-1]=bonds[-1].replace(qns=QuantumNumbers.mono(target),flow=-1)
for cut in range(N+1):
mps=MPS.fromstate(state,sites,bonds,cut=cut,ttype='D')
self.assertTrue(all(mps.iscanonical()))
self.assertAlmostEqual(norm(state-mps.state),0.0)
for cut in range(N+1):
mps.canonicalize(cut)
self.assertTrue(all(mps.iscanonical()))
for cut in range(N+1):
mps=MPS.fromstate(state,sites,bonds,cut=cut,ttype='S')
self.assertTrue(all(mps.iscanonical()))
self.assertAlmostEqual(norm(state-mps.state),0.0)
for cut in range(N+1):
mps.canonicalize(cut)
self.assertTrue(all(mps.iscanonical()))
def summarize_evaluation(query=None, url=None, summary=None):
j=[]
if url:
b = URL(url)
a = Document(b.download(cached=True))
for b in a.get_elements_by_tagname("p"):
j.append(plaintext(b.content).encode("utf-8"))
j = [word for sentence in j for word in sentence.split() if re.match("^[a-zA-Z_-]*$", word) or '.' in word or "'" in word or '"' in word]
j = ' '.join(j)
lsa = LSA(stopwords, ignore_characters)
sentences = j.split('.')
sentences = [sentence for sentence in sentences if len(sentence)>1 and sentence != '']
for sentence in sentences:
lsa.parse(sentence)
else:
lsa = LSA(stopwords, ignore_characters)
for sentence in query:
lsa.parse(sentence)
lsa.build()
lsa.calc()
lsa2 = LSA(stopwords, ignore_characters)
for sentence in summary:
lsa2.parse(sentence)
lsa2.build()
lsa2.calc()
vectors =[(dot(lsa.S,lsa.U[0,:]),dot(lsa.S,lsa.U[i,:])) for i in range(len(lsa.U))]
vectors2 =[(dot(lsa2.S,lsa2.U[0,:]),dot(lsa2.S,lsa2.U[i,:])) for i in range(len(lsa2.U))]
angles = [arccos(dot(a,b)/(norm(a,2)*norm(b,2))) for a in vectors for b in vectors2]
return str(abs(1 - float(angles[1])/float(pi/2)))
def cosine_similarity(a, b):
tn = np.inner(a, b)
td = la.norm(a) * la.norm(b)
if td != 0.0:
return tn / td
else:
return 0.0
def fista(objfunc, dfunc, p, Profunc, regu, args={'lam':100.0}, theta=None, eta=2, L0=1.0, maxiter=500, eps=1e-6):
if theta == None:
theta = uniform(-0.1, 0.1, size=p)
x_old, y = theta, theta
tk_old, L, i = 1.0, L0, 0
while i < maxiter:
fy, dfy = objfunc(y), dfunc(y)
# step one
while True:
xk = Profunc(y, dfy, L, regu, args)
if objfunc(xk) <= fy + dot(xk-y, dfy) + (L/2.0) * norm(xk-y)**2:
break
else:
L *= eta
# step two
tk = (1.0 + sqrt(1.0+4.0*tk_old**2))/2.0
dx = xk - x_old
y = xk + (tk_old-1.0)/tk * dx
tk_old = tk
x_old = xk
i += 1
if norm(dx) <= eps:
return xk
return xk
def check_cost_function(lambda_coef=0):
X_t = np.random.rand(4, 3)
Theta_t = np.random.rand(5, 3)
Y = X_t.dot(Theta_t.T)
Y[np.random.rand(*Y.shape) > 0.5] = 0
R = np.zeros_like(Y)
R[Y != 0] = 1
X = np.random.randn(*X_t.shape);
Theta = np.random.randn(*Theta_t.shape);
num_movies, num_users = Y.shape
num_features = Theta_t.shape[1]
J = lambda t: cofi_cost_func(t, Y, R, num_users, num_movies, num_features, lambda_coef)[0]
numgrad = compute_numerical_gradient(J, np.hstack((X.ravel(), Theta.ravel())))
cost, grad = cofi_cost_func(np.hstack((X.ravel(), Theta.ravel())), Y, R, num_users, num_movies, num_features, lambda_coef)
for i, j in zip(numgrad, grad):
print i, j
print('The above two columns you get should be very similar.\n'
'(Left-Your Numerical Gradient, Right-Analytical Gradient)\n')
diff = norm(numgrad-grad)/norm(numgrad+grad)
print('If your backpropagation implementation is correct, then \n'
'the relative difference will be small (less than 1e-9). \n'
'Relative Difference: %s' % diff)
def __init__(self,reciprocals,path):
'''
Constructor.
Parameters
----------
reciprocals : iterable of 1d ndarray
The translation vectors of the reciprocal lattice.
path : str
The str-formed path.
'''
path=path.replace(' ', '')
assert path[0] in KMap.database and path[1]==':'
space,path,database,reciprocals=path[0],path[2:].split(','),KMap.database[path[0]],np.asarray(reciprocals)
if space=='L':
assert len(reciprocals)==1
elif space=='S':
assert len(reciprocals)==2
inner=np.inner(reciprocals[0],reciprocals[1])/nl.norm(reciprocals[0])/nl.norm(reciprocals[1])
assert np.abs(inner)<RZERO
elif space=='H':
assert len(reciprocals)==2
inner=np.inner(reciprocals[0],reciprocals[1])/nl.norm(reciprocals[0])/nl.norm(reciprocals[1])
assert np.abs(np.abs(inner)-0.5)<RZERO
if np.abs(inner+0.5)<RZERO: reciprocals[1]=-reciprocals[1]
for segment in path:
segment=segment.split('-')
assert len(segment)==2
self.append([reciprocals.T.dot(database[segment[0]]),reciprocals.T.dot(database[segment[1]])])
def reward_function(self, debug=0):
"""""
Reward Function: Working with PPO great results.
Shaping with some ideas based on Continuous Lunar Lander v.2 gym environment:
https://gym.openai.com/envs/LunarLanderContinuous-v2/
"""""
self.reward = 0
velocity = self.state[1:6:2]
euler_angles = self.ang
psi = self.ang[2]
body_ang_vel = self.state[-3:]
action = self.action
shaping = -SHAPING_WEIGHT/np.sum(SHAPING_INTERNAL_WEIGHTS)*(SHAPING_INTERNAL_WEIGHTS[0]*norm(velocity/BB_VEL)+
SHAPING_INTERNAL_WEIGHTS[1]*norm(psi/4)+
SHAPING_INTERNAL_WEIGHTS[2]*norm(euler_angles[0:2]/BB_ANG))
#CASCADING REWARDS
r_state = np.concatenate((velocity, [psi]))
for TR_i, TR_Pi in zip(TR, TR_P):
if norm(r_state) < norm(np.ones(len(r_state))*TR_i):
shaping += TR_Pi
if norm(euler_angles[0:2]) < norm(np.ones(2)*TR_i*4):
shaping += TR_Pi
break
if self.prev_shaping is not None:
self.reward = shaping - self.prev_shaping
self.prev_shaping = shaping
#ABSOLUTE CONTROL PENALTY
## TOTAL REWARD SHAPING ##
abs_control = -np.sum(np.square(action - self.zero_control)) * P_C
self.reward += + abs_control
#SOLUTION ACHIEVED?
self.target_state = 9*(TR[0]**2)
self.current_state = np.sum(np.square(np.concatenate((velocity, euler_angles, body_ang_vel))))
if self.current_state < self.target_state:
self.reward += SOLVED_REWARD
self.solved = 1
if self.ppo_training:
self.done = True
elif self.i >= self.n:
self.reward = self.reward
self.solved = 0
self.done=True
elif self.done:
self.reward += BROKEN_REWARD
self.solved = 0
def gaussian_kernel(x, y, sigma=5.0):
return np.exp(-linalg.norm(x-y)**2 / (2 * (sigma ** 2)))
# Compute four eigenmodes:
index = [0,2,5,8]
Lam, V = eig(-L)
ii = argsort(Lam)
Lam = Lam[ii]
#V = V[:,ii]
ii = ii[index]
V = real(V[:,ii])
Lam = sqrt(Lam[index]/Lam[0])
# Plot eigenmodes with nodal lines underneath:
[rr,tt] = meshgrid(r[0:N2+1],hstack([0,t]))
xx = rr*cos(tt)
yy = rr*sin(tt)
z = exp(1j*pi*arange(-100,101)/100)
fig = plt.figure()
for i in range(0,4):
u = reshape(V[:,i], (N2,M)).T
u = hstack([zeros((M+1,1)),vstack([u[M-1,:],u[0:M,:]])])
u = u/norm(u)
ax = fig.add_subplot(2,2,i+1, projection='3d')
plt.hold('on')
ax.plot_surface(xx, yy, u, rstride=1, cstride=1, cmap="coolwarm", alpha=0.3)
ax.set_xlim(-1.05, 1.05)
ax.set_ylim(-1.05, 1.05)
ax.set_zlim(-1.05, 1.05)
ax.set_axis_off()
#plt.contour(xx, yy, u-1)
#plt.plot()
plt.show()
def Classo_R2(pb, lam, compute=True):
pb_type = pb.type # can be 'Path-Alg', 'P-PDS' , 'PF-PDS' or 'DR'
(m, d, k), (A, C, y) = pb.dim, pb.matrix
lamb, rho = lam * pb.lambdamax, pb.rho
if lam < 1e-5:
pb_type = "DR"
compute = "True"
# here we simply refer to Classo_R1 that is called line 42.
# Path-Alg
# here we compute the path algo until our lambda, and just take the last beta
if pb_type == "Path-Alg":
if pb.intercept:
AA, CC = A[:, 1:], C[:, 1:]
else:
AA, CC = A[:, :], C[:, :]
out = solve_path((AA, CC, y),
lam,
False,
rho,
"R2",
intercept=pb.intercept)
if pb.intercept:
beta0, beta = out[0][-1], out[1][-1]
beta = np.array([beta0] + list(beta))
else:
beta = out[0][-1]
return beta
# DR :
regpath = pb.regpath
r = lamb / (2 * rho)
if pb_type == "DR":
if compute:
pb.init_R1(r=r)
x = Classo_R1(pb.prob_R1, lamb / pb.prob_R1.lambdamax)
beta = x[:-m]
if pb.intercept:
betaO = pb.prob_R1.ybar - np.vdot(pb.prob_R1.Abar, x)
beta = np.array([betaO] + list(beta))
return beta
else:
pb.add_r(r=r)
if len(pb.init) == 3:
pb.prob_R1.init = pb.init
x, warm_start = Classo_R1(pb.prob_R1, lamb / pb.prob_R1.lambdamax)
beta = x[:-m]
if pb.intercept:
betaO = pb.prob_R1.ybar - np.vdot(pb.prob_R1.Abar, x)
beta = np.array([betaO] + list(beta))
return (beta, warm_start)
tol = pb.tol * LA.norm(y) / LA.norm(A, "fro") # tolerance rescaled
if compute:
pb.compute_param()
tau, Proj, AtA, Aty = pb.tauN, proj_c(C, d), pb.AtA, pb.Aty
gamma = pb.gam / (2 * (pb.AtAnorm + r**2))
t = lamb * gamma
w, tm, zerom, zerod = (
t * pb.weights,
t * np.ones(m),
np.zeros(m),
np.zeros(d),
)
o, xbar, x, v = pb.init
# vectors usefull to compute the prox of f(b)= sum(wi |bi|)
# FORWARD BACKWARD
if pb_type == "P-PDS":
for i in range(pb.N):
grad = AtA.dot(x) - Aty
v = v + tau * C.dot(xbar)
S = x - 2 * gamma * grad - 2 * gamma * r * (A.T).dot(o) - (
C.T).dot(v)
o = prox(
o * (1 - 2 * gamma * r**2) + 2 * gamma * r * (y - A.dot(x)),
tm,
zerom,
)
p = prox(S, w, zerod)
nw_x = Proj.dot(p)
eps = nw_x - x
xbar = p + eps
if i % 10 == 2 and LA.norm(eps) < tol: # 0.6
if regpath:
return (x, (o, xbar, x, v))
else:
return x
x = nw_x
if LA.norm(x) > 1e10:
raise ValueError("The algorithm of P-PDS diverges")
raise ValueError(
"The algorithm of P-PDS did not converge after %i iterations " %
pb.N)
else: # "PF-PDS"
for i in range(pb.N):
grad = AtA.dot(x) - Aty
S1 = x - 2 * gamma * grad - 2 * gamma * r * (A.T).dot(o) - (
C.T).dot(v)
S2 = o * (1 - 2 * gamma * r**2) + 2 * gamma * r * (y - A.dot(x))
p1 = prox(S1, w, zerod)
p2 = prox(S2, tm, zerom)
v = v + tau * C.dot(p1)
v2 = v + tau * C.dot(x)
eps1 = (p1 + 2 * gamma * (Aty - AtA.dot(p1) - r * A.T.dot(o)) -
C.T.dot(v2) - S1)
eps2 = p2 + 2 * r * gamma * (y - r * p2 - A.dot(x)) - S2
x = x + eps1
o = o + eps2
if i % 10 == 2 and LA.norm(eps1) + LA.norm(eps2) < tol:
if regpath:
return (x, (o, xbar, x, v))
else:
return x
if LA.norm(x) + LA.norm(o) + LA.norm(v) > 1e6:
raise ValueError("The algorithm of PF-PDS diverges")
raise ValueError(
"The algorithm of PF-PDS did not converge after %i iterations " %
pb.N)
def euclidean(p, Q):
return numpy.apply_along_axis(lambda q: linalg.norm(p - q), 0, Q)
def hellinger(p, Q):
factor = 1 / math.sqrt(2)
sqrt_p = numpy.sqrt(p)
return factor * numpy.apply_along_axis(
lambda q: linalg.norm(sqrt_p - numpy.sqrt(q)), 0, Q)
def main():
dimension_number, exp_number = 2, 20
x_min_dist, x_max_dist, y_min_dist, y_max_dist, x0, dot_num, points_seq_style, way_style, exact_solution_style, \
figsize, uniform_distr_low, uniform_distr_high, calc_epsilon, min_dist_between_points, level_max_diff = \
-10.0, 10.0, -10.0, 10.0, [0, 0], 500, 'ko', 'k-', 'ro', (15, 7.5), -5, 5, 1e-4, 1, 1000
a, b, c = \
rand(dimension_number, dimension_number) * (uniform_distr_high - uniform_distr_low) + uniform_distr_low, \
rand(dimension_number) * (uniform_distr_high - uniform_distr_low) + uniform_distr_low, 0
for j in range(exp_number):
b = rand(dimension_number) * (uniform_distr_high -
uniform_distr_low) + uniform_distr_low
while True:
a = rand(dimension_number, dimension_number) * (
uniform_distr_high - uniform_distr_low) + uniform_distr_low
hessian_of_f = (a + a.T) / 2
flag = False
for i in range(dimension_number):
if linalg.det(hessian_of_f[:i + 1, :i + 1]) < 1e-15:
flag = True
break
if not flag:
break
exact_solution = linalg.solve(hessian_of_f, b)
x0 = rand(dimension_number)
x0[0] = x0[0] * (x_max_dist -
x_min_dist) + exact_solution[0] + x_min_dist
x0[1] = x0[1] * (y_max_dist -
y_min_dist) + exact_solution[1] + y_min_dist
points_seq, _ = r_algorithm(f,
x0,
args=(a, b, c),
form='B',
calc_epsilon=calc_epsilon,
iter_lim=100,
step_method='adaptive',
default_step=10,
step_red_mult=0.75,
step_incr_mult=1.25,
lim_num=3,
reduction_epsilon=1e-15)
argmin = points_seq[points_seq.shape[0] - 1]
count = 0
while count < points_seq.shape[0] - 1:
if linalg.norm(points_seq[count] -
points_seq[count + 1]) < min_dist_between_points:
points_seq = np.delete(points_seq, count + 1, 0)
count -= 1
count += 1
points_seq = np.append(points_seq,
argmin).reshape(points_seq.shape[0] + 1, 2)
levels = np.sort(
f(np.array([points_seq[:, 0], points_seq[:, 1]]), (a, b, c)))
count = 0
while count < levels.size - 1:
if levels[count + 1] - levels[count] > level_max_diff:
levels = np.insert(levels, count + 1,
(levels[count + 1] + levels[count]) / 2.0)
count -= 1
count += 1
levels = np.array(list(set(levels)))
levels.sort()
x, y = \
np.linspace(exact_solution[0] + x_min_dist, exact_solution[0] + x_max_dist, dot_num), \
np.linspace(exact_solution[1] + y_min_dist, exact_solution[1] + y_max_dist, dot_num)
xx, yy = np.meshgrid(x, y)
z = f(np.array([xx, yy]), (a, b, c))
plt.figure(figsize=figsize)
plt.grid(True)
numerical_contour = plt.contour(x, y, z, levels=levels)
plt.clabel(numerical_contour, inline=1, fontsize=10)
plt.plot(points_seq[:, 0],
points_seq[:, 1],
points_seq_style,
label=u"Наближення")
for i in range(points_seq.shape[0] - 1):
plt.plot([points_seq[i][0], points_seq[i + 1][0]],
[points_seq[i][1], points_seq[i + 1][1]], way_style)
plt.plot(exact_solution[0], exact_solution[1], exact_solution_style)
plt.show()
plt.close()
def _tracemin_fiedler(L, X, normalized, tol, method):
"""Compute the Fiedler vector of L using the TraceMIN-Fiedler algorithm.
"""
n = X.shape[0]
if normalized:
# Form the normalized Laplacian matrix and determine the eigenvector of
# its nullspace.
e = sqrt(L.diagonal())
D = spdiags(1. / e, [0], n, n, format='csr')
L = D * L * D
e *= 1. / norm(e, 2)
if not normalized:
def project(X):
"""Make X orthogonal to the nullspace of L.
"""
X = asarray(X)
for j in range(X.shape[1]):
X[:, j] -= X[:, j].sum() / n
else:
def project(X):
"""Make X orthogonal to the nullspace of L.
"""
X = asarray(X)
for j in range(X.shape[1]):
X[:, j] -= dot(X[:, j], e) * e
if method is None:
method = 'pcg'
if method == 'pcg':
# See comments below for the semantics of P and D.
def P(x):
x -= asarray(x * X * X.T)[0, :]
if not normalized:
x -= x.sum() / n
else:
x = daxpy(e, x, a=-ddot(x, e))
return x
solver = _PCGSolver(lambda x: P(L * P(x)), lambda x: D * x)
elif method == 'chol' or method == 'lu':
# Convert A to CSC to suppress SparseEfficiencyWarning.
A = csc_matrix(L, dtype=float, copy=True)
# Force A to be nonsingular. Since A is the Laplacian matrix of a
# connected graph, its rank deficiency is one, and thus one diagonal
# element needs to modified. Changing to infinity forces a zero in the
# corresponding element in the solution.
i = (A.indptr[1:] - A.indptr[:-1]).argmax()
A[i, i] = float('inf')
solver = (_CholeskySolver if method == 'chol' else _LUSolver)(A)
else:
raise nx.NetworkXError('unknown linear system solver.')
# Initialize.
Lnorm = abs(L).sum(axis=1).flatten().max()
project(X)
W = asmatrix(ndarray(X.shape, order='F'))
while True:
# Orthonormalize X.
X = qr(X)[0]
# Compute interation matrix H.
W[:, :] = L * X
H = X.T * W
sigma, Y = eigh(H, overwrite_a=True)
# Compute the Ritz vectors.
X *= Y
# Test for convergence exploiting the fact that L * X == W * Y.
res = dasum(W * asmatrix(Y)[:, 0] - sigma[0] * X[:, 0]) / Lnorm
if res < tol:
break
# Depending on the linear solver to be used, two mathematically
# equivalent formulations are used.
if method == 'pcg':
# Compute X = X - (P * L * P) \ (P * L * X) where
# P = I - [e X] * [e X]' is a projection onto the orthogonal
# complement of [e X].
W *= Y # L * X == W * Y
W -= (W.T * X * X.T).T
project(W)
# Compute the diagonal of P * L * P as a Jacobi preconditioner.
D = L.diagonal()
D += 2. * (asarray(X) * asarray(W)).sum(axis=1)
D += (asarray(X) * asarray(X * (W.T * X))).sum(axis=1)
D[D < tol * Lnorm] = 1.
D = 1. / D
# Since TraceMIN is globally convergent, the relative residual can
# be loose.
X -= solver.solve(W, 0.1)
else:
# Compute X = L \ X / (X' * (L \ X)). L \ X can have an arbitrary
# projection on the nullspace of L, which will be eliminated.
W[:, :] = solver.solve(X)
project(W)
X = (inv(W.T * X) * W.T).T # Preserves Fortran storage order.
return sigma, asarray(X)
def gaussian(sigma):
return lambda x,y:\
np.exp(-np.sqrt(la.norm(x-y)**2/(2*sigma**2)))
def main():
# Training settings
parser = argparse.ArgumentParser(description='PyTorch Cifar Example')
use_cuda = True
kwargs = {'num_workers': 1, 'pin_memory': True} if use_cuda else {}
transform_test = transforms.Compose([
transforms.ToTensor()
])
testset = torchvision.datasets.CIFAR10(root='./data', train=False, download=True, transform=transform_test)
testloader = torch.utils.data.DataLoader(testset, batch_size=100, shuffle=False, num_workers=16)
#classes = ('plane', 'car', 'bird', 'cat', 'deer', 'dog', 'frog', 'horse', 'ship', 'truck')
# test_loader = torch.utils.data.DataLoader(
# datasets.MNIST('../data', train=False, transform=transforms.Compose([
# transforms.ToTensor()
# #transforms.Normalize((0.1307,), (0.3081,))
# ])),
# batch_size=1000, shuffle=True, **kwargs)
args = parser.parse_args()
gpu = 0
torch.manual_seed(1)
device = torch.device("cuda" if use_cuda else "cpu")
#device = "cpu"
model = ResNet18_adv(w=1).to(device)
model = AttackPGD(model)
model = torch.nn.DataParallel(model)
torch.cuda.set_device(gpu)
model.cuda(gpu)
criterion = CrossEntropyLossMaybeSmooth(smooth_eps=0.0).cuda(gpu)
load_model = 'resnet18_adv_w1.pt'
# unlike resume, load model does not care optimizer status or start_epoch
print('==> Loading from {}'.format(load_model))
model.load_state_dict(torch.load(load_model,map_location = {'cuda:0':'cuda:{}'.format(gpu)}))
print(model)
validate(model, testloader,criterion, device)
for name,W in model.named_parameters():
W = W.cpu().detach().numpy()
shape = W.shape
W2d = W.reshape(shape[0],-1)
column_l2_norm = LA.norm(W2d,2,axis=0)
zero_column = np.sum(column_l2_norm == 0)
nonzero_column = np.sum(column_l2_norm !=0)
print ("column sparsity of layer {} is {}".format(name,zero_column/(zero_column+nonzero_column)))
for name,W in model.named_parameters():
W = W.cpu().detach().numpy()
shape = W.shape
W2d = W.reshape(shape[0],-1)
row_l2_norm = LA.norm(W2d,2,axis=1)
zero_row = np.sum(row_l2_norm == 0)
nonzero_row = np.sum(row_l2_norm !=0)
print ('filter sparsity of layer {} is {}'.format(name,zero_row/(zero_row+nonzero_row)))
def normalize(vec):
return vec / npl.norm(vec)
def radial_basis(gamma=10):
return lambda x, y: np.exp(-gamma * la.norm(np.subtract(x, y)))
vessel_d['specific_impulse'] = vessel.specific_impulse
#print(game_delta_time)
if nav_mode == 'gfold': #跟随gfold路径
(tf, x, u, m, s, z) = gfold_path
#n_i = max(n_i + game_delta_time * 0.2 * N/tf, find_nearest_index(x, error, vel))
n_i = max(n_i - game_delta_time * 0.2 * N / tf,
find_nearest_index(x, error, vel))
print(n_i)
# x_i = (x[0:3, n_i] + x[0:3, min(n_i+1 ,N-1)]) / 2
# v_i = (x[3:6, n_i] + x[3:6, min(n_i+1 ,N-1)]) / 2
# u_i = (u[:, n_i] + u[:, min(n_i+1 ,N-1)]) / 2
(x_i, v_i, u_i) = sample_index(n_i)
(x_i_, v_i_,
u_i_) = sample_index(n_i + min(1.5 * N / tf,
npl.norm(vel) / 50 * N / tf))
#v_i_dir = v_i / npl.norm(v_i)
# target_a = u_i_
# target_v = v_i_
# target_x = x_i # + np.dot((error - x_i), v_i_dir) * v_i_dir
# #print(n_i, target_a, target_v, target_x)
# target_a += (target_v - vel) * k_v + (target_x - error) * k_x
target_a = u_i + (v_i - vel) * k_v + (x_i - error) * k_x
target_a_ = u_i_ + (v_i_ - vel) * k_v + (x_i - error) * k_x
if debug_lines:
target_line.start = error
target_line.end = (x_i[0], x_i[1], x_i[2])
target2_line.start = error
def test_empty(self):
assert_equal(norm([]), 0.0)
assert_equal(norm(array([], dtype=self.dt)), 0.0)
assert_equal(norm(atleast_2d(array([], dtype=self.dt))), 0.0)
def almost_equal_norm(self, other, tol, relative=True):
"""
Compare whether two array types are almost equal, normwise.
If the 'relative' parameter is 'True' (the default) then the
'tol' parameter (which must be positive) is interpreted as a
relative tolerance, and the comparison returns 'True' only if
abs(norm(self-other)) <= tol*abs(norm(self)).
If 'relative' is 'False', then 'tol' is an absolute tolerance,
and the comparison is true only if
abs(norm(self-other)) <= tol
Other meta-data (type, dtype, and length) must be exactly equal.
If either object's memory lives on the GPU it will be copied to
the CPU for the comparison, which may be slow. But the original
object itself will not have its memory relocated nor scheme
changed.
Parameters
----------
other
another Python object, that should be tested for
almost-equality with 'self', based on their norms.
tol
a non-negative number, the tolerance, which is interpreted
as either a relative tolerance (the default) or an absolute
tolerance.
relative
A boolean, indicating whether 'tol' should be interpreted
as a relative tolerance (if True, the default if this argument
is omitted) or as an absolute tolerance (if tol is False).
Returns
-------
boolean
'True' if the data agree within the tolerance, as
interpreted by the 'relative' keyword, and if the types,
lengths, and dtypes are exactly the same.
"""
# Check that the tolerance is non-negative and raise an
# exception otherwise.
if (tol < 0):
raise ValueError("Tolerance cannot be negative")
# Check that the meta-data agree; the type check is written in
# this way so that this method may be safely called from
# subclasses as well.
if type(other) != type(self):
return False
if self.dtype != other.dtype:
return False
if len(self) != len(other):
return False
# The numpy() method will move any GPU memory onto the CPU.
# Slow, but the user was warned.
diff = self.numpy() - other.numpy()
dnorm = norm(diff)
if relative:
return (dnorm <= tol * norm(self))
else:
return (dnorm <= tol)
def clamp_mag(vec, maxmag):
mag = npl.norm(vec)
if mag > maxmag:
return vec / mag * maxmag
return vec
def compute_z_phi(samples, alpha):
return np.array([(math.exp((-1) * alpha * math.pow(LA.norm(sample), 2)))
for sample in samples]).sum()
def stupidNormals(S, hardCodedJac, dim):
'''
Hard Coded normal calculator for the different members
for dim 1 there are no normals, for dim = 2 the normals are to the lines
for dim = 3 the normals are to the faces only
OUTPUT:
normal- is the normal vector to a member that has been normalized
it is an np.array of the form [x,y,z]
'''
if dim == 1:
normal = []
print('error: no normals for dim=1')
elif dim == 2:
if S == 0:
normal = []
print('error: no normals for S = 0')
elif S == 1:
temp = np.cross(hardCodedJac[:, 0], np.array([0, 0, 1]))
normal = 1 / LA.norm(temp) * temp
elif S == 2:
temp = np.cross(np.array([0, 0, 1]), hardCodedJac[:, 0])
normal = 1 / LA.norm(temp) * temp
elif S == 3:
temp = np.cross(np.array([0, 0, 1]), hardCodedJac[:, 1])
normal = 1 / LA.norm(temp) * temp
elif S == 4:
temp = np.cross(hardCodedJac[:, 1], np.array([0, 0, 1]))
normal = 1 / LA.norm(temp) * temp
else:
normal = []
print('error: S outside of range')
elif dim == 3:
if S == 0:
normal = []
print('error: no normals for S = 0')
elif S == 6:
temp = np.cross(hardCodedJac[:, 2], hardCodedJac[:, 1])
normal = 1 / LA.norm(temp) * temp
elif S == 5:
temp = np.cross(hardCodedJac[:, 1], hardCodedJac[:, 2])
normal = 1 / LA.norm(temp) * temp
elif S == 4:
temp = np.cross(hardCodedJac[:, 0], hardCodedJac[:, 2])
normal = 1 / LA.norm(temp) * temp
elif S == 3:
temp = np.cross(hardCodedJac[:, 2], hardCodedJac[:, 0])
normal = 1 / LA.norm(temp) * temp
elif S == 2:
temp = np.cross(hardCodedJac[:, 1], hardCodedJac[:, 0])
normal = 1 / LA.norm(temp) * temp
elif S == 1:
temp = np.cross(hardCodedJac[:, 0], hardCodedJac[:, 1])
normal = 1 / LA.norm(temp) * temp
else:
normal = []
print('error: S outside of range')
return (normal)
def displacement_stress(self, model, positions, q, dofs):
n = self.n
o1 = zeros(n, 'float64')
e1 = zeros(n, 'float64')
f1 = zeros(n, 'float64')
o4 = zeros(n, 'float64')
e4 = zeros(n, 'float64')
f4 = zeros(n, 'float64')
As = self.get_area_by_element_id(self.property_id)
Es = self.get_E_by_element_id(self.property_id)
Gs = self.get_G_by_element_id(self.property_id)
Js = self.get_J_by_element_id(self.property_id)
Cs = self.get_c_by_element_id(self.property_id)
for i in range(n):
A = As[i]
E = Es[i]
G = Gs[i]
E = Es[i]
J = Js[i]
C = Cs[i]
n1, n2 = self.node_ids[i, :]
p1 = positions[n1]
p2 = positions[n2]
v1 = p1 - p2
L = norm(p1 - p2)
if L == 0.0:
msg = 'invalid CTUBE length=0.0\n%s' % (self.__repr__())
raise ZeroDivisionError(msg)
#========================
#mat = self.get_material_from_index(i)
#jmat = searchsorted(mat.material_id, self.material_id[i])
#E = mat.E[jmat]
#G = mat.G[jmat]
#G = self.G()
#print("A=%g E=%g G=%g J=%g L=%g" % (A, E, G, J, L))
k_axial = A * E / L
k_torsion = G * J / L
#k_axial = 1.0
#k_torsion = 2.0
#k = array([[1., -1.], [-1., 1.]]) # 1D rod
Lambda = _Lambda(v1, debug=False)
#print("**dofs =", dofs)
n11 = dofs[(n1, 1)]
n21 = dofs[(n2, 1)]
n12 = dofs[(n1, 2)]
n22 = dofs[(n2, 2)]
n13 = dofs[(n1, 3)]
n23 = dofs[(n2, 3)]
# moments
n14 = dofs[(n1, 4)]
n24 = dofs[(n2, 4)]
n15 = dofs[(n1, 5)]
n25 = dofs[(n2, 5)]
n16 = dofs[(n1, 6)]
n26 = dofs[(n2, 6)]
q_axial = array([
q[n11], q[n12], q[n13],
q[n21], q[n22], q[n23]
])
q_torsion = array([
q[n14], q[n15], q[n16],
q[n24], q[n25], q[n26]
])
#print("type=%s n1=%s n2=%s" % (self.type, n1, n2))
#print("n11=%s n12=%s n21=%s n22=%s" %(n11,n12,n21,n22))
#print("q2[%s] = %s" % (self.eid, q2))
#print("Lambda = \n"+str(Lambda))
#print("Lsize = ", Lambda.shape)
#print("qsize = ", q.shape)
u_axial = dot(array(Lambda), q_axial)
du_axial = -u_axial[0] + u_axial[1]
u_torsion = dot(array(Lambda), q_torsion)
du_torsion = -u_torsion[0] + u_torsion[1]
#L = self.Length()
#E = self.E()
#A = self.area()
#C = self.C()
#J = self.J()
#G = self.G()
axial_strain = du_axial / L
torsional_strain = du_torsion * C / L
axial_stress = E * axial_strain
torsional_stress = G * torsional_strain
axial_force = axial_stress * A
torsional_moment = du_torsion * G * J / L
#print("axial_strain = %s [psi]" % axial_strain)
#print("axial_stress = %s [psi]" % axial_stress)
#print("axial_force = %s [lb]\n" % axial_force)
o1[i] = axial_stress
o4[i] = torsional_stress
e1[i] = axial_strain
e4[i] = torsional_strain
f1[i] = axial_force
f4[i] = torsional_moment
return (e1, e4,
o1, o4,
f1, f4)
def is_unit_vector(vector):
return math.isclose(LA.norm(vector), 1.0, rel_tol=1e-2)
def main(ctx_factory, dim=2, order=4, visualize=False):
cl_ctx = ctx_factory()
queue = cl.CommandQueue(cl_ctx)
actx = PyOpenCLArrayContext(
queue,
allocator=cl_tools.MemoryPool(cl_tools.ImmediateAllocator(queue)),
force_device_scalars=True,
)
# {{{ parameters
# domain [-d/2, d/2]^dim
d = 1.0
# number of points in each dimension
npoints = 20
# final time
final_time = 1.0
# velocity field
c = np.array([0.5] * dim)
norm_c = la.norm(c)
# flux
flux_type = "central"
# }}}
# {{{ discretization
from meshmode.mesh.generation import generate_box_mesh
mesh = generate_box_mesh(
[np.linspace(-d / 2, d / 2, npoints) for _ in range(dim)], order=order)
from grudge import DiscretizationCollection
dcoll = DiscretizationCollection(actx, mesh, order=order)
# }}}
# {{{ weak advection operator
def f(x):
return actx.np.sin(3 * x)
def u_analytic(x, t=0):
return f(-np.dot(c, x) / norm_c + t * norm_c)
from grudge.models.advection import WeakAdvectionOperator
adv_operator = WeakAdvectionOperator(
dcoll,
c,
inflow_u=lambda t: u_analytic(thaw(dcoll.nodes(dd=BTAG_ALL), actx),
t=t),
flux_type=flux_type)
nodes = thaw(dcoll.nodes(), actx)
u = u_analytic(nodes, t=0)
def rhs(t, u):
return adv_operator.operator(t, u)
dt = adv_operator.estimate_rk4_timestep(actx, dcoll, fields=u)
logger.info("Timestep size: %g", dt)
# }}}
# {{{ time stepping
from grudge.shortcuts import set_up_rk4
dt_stepper = set_up_rk4("u", dt, u, rhs)
plot = Plotter(actx, dcoll, order, visualize=visualize, ylim=[-1.1, 1.1])
step = 0
norm_u = 0.0
for event in dt_stepper.run(t_end=final_time):
if not isinstance(event, dt_stepper.StateComputed):
continue
if step % 10 == 0:
norm_u = actx.to_numpy(op.norm(dcoll, event.state_component, 2))
plot(event, "fld-weak-%04d" % step)
step += 1
logger.info("[%04d] t = %.5f |u| = %.5e", step, event.t, norm_u)
# NOTE: These are here to ensure the solution is bounded for the
# time interval specified
assert norm_u < 1
def norm(self):
""" Quaternion norm.
"""
n = norm(self.__quat);
return n
def side_contact(poly1, poly2):
'''
Returns (length,normal) giving length of "face-to-face" contact, and if so
left and right endpoints, and a unit vector facing poly1 normal to the
contact.
'''
# first check if the polygons can possibly be in contact
# note: we don't need to factor in collision tol, since the radius is a
# maximum reached at a corner point, never at a side point, so this is
# always a conservative check
com_dist = norm(poly1.pos - poly2.pos)
if com_dist > max(poly1.radius, poly2.radius):
return 0, None, None, None
best_side = None
best_score = .01
for i1,(p1p1,p1p2,s1) in enumerate(poly1.side_pos_iter()):
for i2,(p2p1,p2p2,s2) in enumerate(poly2.side_pos_iter()):
anglediff = abs(np.dot(s1,s2))/(norm(s1)*norm(s2))
if 1-anglediff < ANGLE_TOL:
# I believe this always has to be minimized with p1p2
# assuming coords entered consistently cw or ccw
# Lines should be in reverse orientation to each other
z = p1p1-p2p2
score = norm(np.cross(z/norm(z),s2/norm(s2)))
if score < best_score:
best_side = (i1,i2)
best_score = score
crosslen1 = norm(p1p1-p2p1)
crosslen2 = norm(p2p2-p1p2)
minlen = min(norm(s1),norm(s2))
contact_length = min(minlen, crosslen1, crosslen2)
# Again, with CW assumption, this turns toward object 1
normal = np.array([p2p2[1] - p2p1[1], p2p1[0] - p2p2[0]])
a,b,c,d = p1p1,p1p2,p2p1,p2p2
if a[0] > b[0]:
a,b = b,a
if c[0] > d[0]:
c,d = d,c
if a[0] < c[0] and c[0] < b[0]:
left = c
else:
left = a
if a[0] < d[0] and d[0] < b[0]:
right = d
else:
right = b
#assert(abs(contact_length - norm(right - left)) / abs(contact_length) < EPSILON)
if not best_side:
return 0,None, None, None
unit_normal = -normal/norm(normal)
return contact_length, left, right, unit_normal
def get_stiffness_matrix(self, i, model, positions, index0s, knorm=1.0):
#print("----------------")
pid = self.property_id[i]
assert isinstance(pid, int), pid
A = self.get_area_by_element_id(pid)
E = self.get_E_by_element_id(pid)
G = self.get_G_by_element_id(pid)
J = self.get_J_by_element_id(pid)
#print('A=%s E=%s G=%s J=%s' % (A, E, G, J))
#========================
#(n1, n2) = self.node_ids()
n1 = self.node_ids[i, 0]
n2 = self.node_ids[i, 1]
i1 = index0s[n1]
i2 = index0s[n2]
#print("n0", n0)
#print("n1", n1)
n1 = positions[n1]
n2 = positions[n2]
#p1 = model.Node(n1).xyz
v1 = n1 - n2
L = norm(v1)
if L == 0.0:
msg = 'invalid CROD length=0.0\n%s' % (self.__repr__())
raise ZeroDivisionError(msg)
#========================
#print("A=%g E=%g G=%g J=%g L=%g" % (A, E, G, J, L))
k_axial = A * E / L
k_torsion = G * J / L
#k_axial = 1.0
#k_torsion = 2.0
k = array([[1., -1.],
[-1., 1.]]) # 1D rod
Lambda = _Lambda(v1, debug=True)
K = dot(dot(transpose(Lambda), k), Lambda)
Ki, Kj = K.shape
# for testing
#K = ones((Ki, Ki), 'float64')
K2 = zeros((Ki*2, Kj*2), 'float64')
if k_axial == 0.0 and k_torsion == 0.0:
dofs = []
n_ijv = []
K2 = []
elif k_torsion == 0.0: # axial; 2D or 3D
K2 = K * k_axial
dofs = array([
i1, i1+1, i1+2,
i2, i2+1, i2+2,
], 'int32')
n_ijv = [
# axial
(n1, 1), (n1, 2), (n1, 3),
(n2, 1), (n2, 2), (n2, 3),
]
elif k_axial == 0.0: # torsion; assume 3D
K2 = K * k_torsion
dofs = array([
i1+3, i1+4, i1+5,
i2+3, i2+4, i2+5,
], 'int32')
n_ijv = [
# torsion
(n1, 4), (n1, 5), (n2, 6),
(n2, 4), (n2, 5), (n1, 6),
]
else: # axial + torsion; assume 3D
# u1fx, u1fy, u1fz, u2fx, u2fy, u2fz
K2[:Ki, :Ki] = K * k_axial
# u1mx, u1my, u1mz, u2mx, u2my, u2mz
K2[Ki:, Ki:] = K * k_torsion
dofs = array([
i1, i1+1, i1+2,
i2, i2+1, i2+2,
i1+3, i1+4, i1+5,
i2+3, i2+4, i2+5,
], 'int32')
n_ijv = [
# axial
(n1, 1), (n1, 2), (n1, 3),
(n2, 1), (n2, 2), (n2, 3),
# torsion
(n1, 4), (n1, 5), (n1, 6),
(n2, 4), (n2, 5), (n2, 6),
]
#Fg = dot(dot(transpose(Lambda), grav), Lambda)
#print("K=\n", K / knorm)
#print("K2=\n", K2 / knorm)
#========================
#print(K / knorm)
#print("K[%s] = \n%s\n" % (self.eid, list_print(K/knorm)))
self.model.log.info('dofs = %s' % dofs)
self.model.log.info('K =\n%s' % list_print(K / knorm))
return(K2, dofs, n_ijv)
def update(self):
'''
This function is called once each time step. All position and velocity
updates, and all collisions are handled within.
'''
if energylog:
self.log.write(','.join([str(x) for x in self.energy()]) + '\n')
# Apply linear damping force if exists
if len(self.global_damping_force) == 0:
gdf = []
else:
gdf = [self.global_damping_force]
dt = self.time_disc
max_collision_overlap = COLLISION_TOL + 1
first_iter = True
# Check there is at least one 'true' collision, AND time is stable
if verbosity>2:
print('in:',self.objs[0].com.pos[1])
if verbosity:
hashes = [hash(obj) for obj in self.objs]
k = 0
while max_collision_overlap > COLLISION_TOL and dt > TIME_TOL:
k+=1
if k == 2:print('starting collision: ', self.state // self.time_disc)
if k > 1:print(k,end=', ')
if first_iter:
first_iter = False
else:
dt /= 2
for i,obj in enumerate(self.objs):
obj.reverse_update()
if verbosity:
if hash(obj) != hashes[i]:
print('WRONG, dt = ',dt)
print(obj)
# Do first pass of position, velocity and acceleration updates for
# each object in the world
for obj in self.objs:
#obj.forces = []
obj.pre_update(gdf, dt)
# check_collisions() compiles a list of collisions with information:
# (1,2) the two objects contained in the collision
# (3) the (signed) unit vector normal to the surface of collision
# (4) (unsigned) magnitude of normal vector
collisions = self.check_collisions()
magnitudes = [abs(magnitude) for _,__,___,magnitude in collisions]
if collisions:
max_collision_overlap = max(magnitudes)
else:
max_collision_overlap = 0
if max_collision_overlap > 0:# and dt < TIME_TOL:
if verbosity == 1:
print(dt,max_collision_overlap, self.objs[0].com.pos[1])
if dt < TIME_TOL:
print("Warning: time became too small while still in collision. ({0},{1})".format(dt,max_collision_overlap))
for obj in self.objs:
obj.reverse_update()
collisions = self.check_collisions()
while collisions:
for obj1, obj2, unit_normal_vec, normal_vec_mag in collisions:
# Makes things easier if the first object is never fixed
if obj1.is_fixed:
obj1,obj2 = obj2,obj1
[side_length, left, right, normal] = side_contact(obj1,obj2)
if side_length:
# Check if torque is induced
# (TODO: this is not gravity-direction neutral)
if obj1.com.pos[0] < left[0] or obj1.com.pos[0] > right[0]:
pass # induce torque
# Reassemble normal vector with some added spacing so two
# objects are definitely non-overlapping after collision
# resolution
normal_vec = unit_normal_vec * (normal_vec_mag + EPSILON)
if verbosity>1:
print("normal vec: ", normal_vec)
# obj1 is NEVER fixed, so this branch is for a collision with a
# free object and a fixed object
#
# 1. The free object updates its position by the normal vector
# 2. The free object updates its velocity by twice the (negated)
# component of its velocity normal to the surface
#
#print(obj1.is_fixed, obj2.is_fixed)
if obj2.is_fixed:
for i in range(len(obj1.points)):
obj1.points[i].pos += normal_vec
vdotN = np.dot(obj1.points[i].vel, unit_normal_vec)
obj1.points[i].vel -= (1+ELASTICITY)*vdotN*unit_normal_vec
# TODO: why is this here?
if norm(normal_vec) > VIBRATE_TOL:
obj1.com.pos += normal_vec
vdotN = np.dot(obj1.com.vel, unit_normal_vec)
#if norm(vdotN) > VIBRATE_TOL:
##obj1.com.vel -= (1+ELASTICITY)*vdotN * unit_normal_vec
#J = obj1.mass*
K0 = .5*obj1.mass*norm(obj1.com.vel)**2
obj1.com.vel -= (1+ELASTICITY)*vdotN * unit_normal_vec
# Update heat energy, dispersed equally to each object
H = .5*obj1.mass*(1-ELASTICITY**2)*(vdotN**2)
K1 = .5*obj1.mass*norm(obj1.com.vel)**2
obj1.heat += H/2
obj2.heat += H/2
self.heat += H
obj1.finish_update()
obj2.finish_update()
# Only other possible case is that both objects are free
else:
v1 = obj1.com.vel
mtotal = obj1.mass + obj2.mass
mprop1 = obj1.mass / mtotal
mprop2 = 1-mprop1
obj1.com.pos += mprop1 * (normal_vec)
vn1 = np.dot(obj1.com.vel,unit_normal_vec)
vn2 = np.dot(obj2.com.vel,unit_normal_vec)
v1_update = (mprop1 - mprop2)*vn1 + 2*mprop2*vn2
obj1.com.vel += (v1_update - np.dot(obj1.com.vel,unit_normal_vec))*unit_normal_vec
for point in obj1.points:
point.pos += mprop1 * (normal_vec)
point.vel += (v1_update - np.dot(point.vel,unit_normal_vec))*unit_normal_vec
obj1.finish_update()
obj2.com.pos -= mprop2 * normal_vec
v2_update = 2*mprop1*vn1 + (mprop2 - mprop1)*vn2
obj2.com.vel += (v2_update - np.dot(obj2.com.vel,unit_normal_vec))*unit_normal_vec
for point in obj2.points:
point.pos -= mprop2 * (normal_vec)
point.vel += (v2_update - np.dot(point.vel,unit_normal_vec))*unit_normal_vec
obj2.finish_update()
if verbosity>1:
print("inits", v0a,v0b)
print("a_update=",vn2, v1_update)
print("b_update=",vn1, v2_update)
print("va1 =", obj1.com.vel, v0a+vn1)
print("vb1 =", obj2.com.vel, v0b+vn2)
print('K1a=',K0a + .5*obj1.mass*(vn1**2 - vn2**2), .5*obj1.mass*norm(obj1.com.vel)**2)
print('K1b=',K0b + .5*obj2.mass*(vn2**2 - vn1**2), .5*obj2.mass*norm(obj2.com.vel)**2)
#print('mafter:',obj1.momentum(normal_vec) , obj2.momentum(normal_vec))
collisions = self.check_collisions()
# Do second (final) pass for each object in the world
for obj in self.objs:
# Obj.com x,v,a attrs are given to Obj itself
obj.finish_update()
# Update the remainder of the time step
# ensures each frame transition is consistent time width
collisions = self.check_collisions()
if collisions:
print('time eval: ', self.state // self.time_disc)
magnitudes = [abs(magnitude) for _,__,___,magnitude in collisions]
print('1/2still {0} collisions (dt = {1}),{2},{3},{4}'.format(len(collisions),dt,magnitudes,collisions[0][0],collisions[0][1]))
if dt != self.time_disc:
for obj in self.objs:
obj.pre_update(gdf, self.time_disc - dt)
obj.finish_update()
collisions = self.check_collisions()
if collisions:
magnitudes = [abs(magnitude) for _,__,___,magnitude in collisions]
print('2/2still {0} collisions (dt = {1}),{2}'.format(len(collisions),dt,magnitudes))
# Advance time
self.state += self.time_disc
def __init__(self, subcase_id, location,
titles, headers, dxyz, linked_scale_factor, #xyz, scalar,
scales, data_formats=None,
nlabels=None, labelsize=None, ncolors=None, colormap='jet',
set_max_min=False, uname='NastranGeometry'):
"""
Defines a Displacement/Eigenvector result
Parameters
----------
subcase_id : int
the flag that points to self.subcases for a message
headers : List[str]
the sidebar word
titles : List[str]
the legend title
#xyz : (nnodes, 3)
#the nominal xyz locations
#scalars : (nnodes,n) float ndarray
##the data to make a contour plot with
#does nothing
dxyz : (nnodes, 3)
the delta xyz values
linked_scale_factor : bool
is the displacement scale factor linked
displacements/loads steps should be
force/eigenvectors should not be
scales : List[float]
the table (e.g., deflection, SPC Forces) scale factors
nominally, this starts as an empty list and is filled later
data_formats : List[str]
the type of data result (e.g. '%i', '%.2f', '%.3f')
ncolors : int; default=None
sets the default for reverting the legend ncolors
set_max_min : bool; default=False
set default_mins and default_maxs
Unused
------
#deflects : bool; default=True
#seems to be an unused parameter...
uname : str
some unique name for ...
"""
GuiResultCommon.__init__(self)
self.subcase_id = subcase_id
self.location = location
assert location in ['node', 'centroid'], 'location=%r' % location
self.linked_scale_factor = linked_scale_factor
#assert self.subcase_id > 0, self.subcase_id
self.dxyz = dxyz
self.dim = len(self.dxyz.shape)
self.uname = uname
#self.dxyz_norm = norm(dxyz, axis=1)
#self.deflects = deflects
self.titles = titles
self.headers = headers
self.scales = scales
self.subcase_id = subcase_id
self.data_type = self.dxyz.dtype.str # '<c8', '<f4'
self.is_real = True if self.data_type in ['<f4', '<f8'] else False
#print('self.data_type = %r' % self.data_type)
self.is_complex = not self.is_real
self.nlabels = nlabels
self.labelsize = labelsize
self.ncolors = ncolors
self.colormap = colormap
self.data_formats = data_formats
self.titles_default = deepcopy(self.titles)
self.headers_default = deepcopy(self.headers)
self.scales_default = deepcopy(self.scales)
self.data_formats_default = deepcopy(self.data_formats)
if self.dim == 2:
ntimes = 1
self.default_mins = zeros(1, dtype=self.dxyz.dtype)
self.default_maxs = zeros(1, dtype=self.dxyz.dtype)
normi = norm(self.dxyz, axis=1)
self.default_mins[0] = normi.min().real
self.default_maxs[0] = normi.max().real
elif self.dim == 3:
ntimes = self.dxyz.shape[0]
self.default_mins = zeros(ntimes)
self.default_maxs = zeros(ntimes)
for itime in range(ntimes):
normi = norm(self.dxyz[itime, :, :], axis=1)
self.default_mins[itime] = normi.min().real
self.default_maxs[itime] = normi.max().real
if not self.is_real:
#: stored in degrees
self.phases = np.zeros(ntimes)
else:
raise NotImplementedError('dim=%s' % self.dim)
if set_max_min:
self.min_values = deepcopy(self.default_mins)
self.max_values = deepcopy(self.default_maxs)
else:
self.max_values = None
self.min_values = None
def momentum(self, direction):
return self.mass * np.dot(self.com.vel, direction)/norm(direction)
def polypoly_collision(poly1, poly2):
'''
Determine whether two polygons are currently intersecting each other
'''
# array of edges in the form
# poly1_edges = [(Point1, Point2), (Point2, Point3), ..., (Point[n], Point1)]
poly1_edges = zip(poly1.points, poly1.points[1:] + [poly1.points[0]])
# array of outward-facing normals for each of the previous edges
poly1_normals = [np.array([p2.pos[1] - p1.pos[1], p1.pos[0] - p2.pos[0]]) for p1,p2 in poly1_edges]
poly2_edges = zip(poly2.points, poly2.points[1:] + [poly2.points[0]])
poly2_normals = [np.array([p2.pos[1] - p1.pos[1], p1.pos[0] - p2.pos[0]]) for p1,p2 in poly2_edges]
if verbosity >= 2:
print('IN COLLISION')
if verbosity >= 3:
print([p.pos for p in poly1.points[:-1]])
print([p.pos for p in poly2.points[:-1]])
overlap = np.inf
for axis,flag in list(zip(poly1_normals,[1]*len(poly1_normals))) + list(zip(poly2_normals, [2]*len(poly2_normals))):
# Normalize
normal_axis = axis / norm(axis)
# Determine projection bounds onto separating axis (perpindicular to separating line
# initialize bounds with current edge
poly1_bounds = [np.dot(normal_axis, poly1.points[0].pos)]*2
poly2_bounds = [np.dot(normal_axis, poly2.points[0].pos)]*2
# increase bounds as necessary if other edges increase projection line length
for point in poly1.points:
curr = np.dot(normal_axis, point.pos)
if curr < poly1_bounds[0]:
poly1_bounds[0] = curr
if curr > poly1_bounds[1]:
poly1_bounds[1] = curr
for point in poly2.points:
curr = np.dot(normal_axis, point.pos)
if curr < poly2_bounds[0]:
poly2_bounds[0] = curr
if curr > poly2_bounds[1]:
poly2_bounds[1] = curr
mag_flag = 1
if poly1_bounds[0] > poly2_bounds[0]:
mag_flag = 2
poly1_bounds,poly2_bounds = poly2_bounds, poly1_bounds
#If a single check fails, then there is no collision
if poly1_bounds[1] < poly2_bounds[0]:
return [],None
# Save axis and overlap magnitude if this is the smallest gap
current_overlap = poly1_bounds[1] - poly2_bounds[0]
if verbosity>1:
print('co:',current_overlap,poly1_bounds,poly2_bounds)
if current_overlap < overlap:
fix_axis = normal_axis
fix_mag_flag = mag_flag
overlap = current_overlap
'''
Sanity Check: This whole fix_axis direction makes physical sense. It
is resolving the collision in a direction which *must* be orthogonal to one
of the two objects' sides, which should be the only way a collision could
happen, aside from some point-point intersection which is a.s. not the case.
'''
if fix_mag_flag:
fix_axis *= -1
return fix_axis, overlap
# Debug
import sys
sys.path.append("../")
from nn.sdnn import DNN
from nn.iris import IrisDF
from numpy.linalg import norm
# http://ufldl.stanford.edu/wiki/index.php/Gradient_checking_and_advanced_optimization
if __name__ == "__main__":
df = IrisDF()
Xs = df.X_train # np.array([[0.68619022, 0.31670318, 0.61229281, 0.232249 ]])
ys = df.y_train # np.array([[1, 0, 0]])
nn = DNN(shape=[4, 6, 3])
calc_grad = nn.objective(nn.get_params(), Xs, ys)[1]
num_grad = nn.compute_num_grads(Xs, ys)
print(calc_grad, end="\n\n")
print(num_grad, end="\n\n")
print(norm(calc_grad - num_grad) /
(norm(calc_grad + num_grad))) # e-9 or less !
def k_energy(self):
return .5*self.mass * norm(self.vel)**2
