def Compare_sorts(Sort1, Sort2, tsf):
import compare_sort
#Hacked way of making a numpy array out of uneven list; using trailing zeros
max_len = 0
for i in range(len(Sort1.units)):
if max_len< len(Sort1.units[i]): max_len=len(Sort1.units[i])
spikes1 = np.zeros((len(Sort1.units),max_len), dtype=np.int32)
for i in range(len(Sort1.units)):
spikes1[i][0:len(Sort1.units[i])]=Sort1.units[i]
spikes1=np.asfortranarray(spikes1)
max_len = 0
for i in range(len(Sort2.units)):
if max_len< len(Sort2.units[i]): max_len=len(Sort2.units[i])
spikes2 = np.zeros((len(Sort2.units),max_len), dtype=np.int32)
for i in range(len(Sort2.units)):
spikes2[i][0:len(Sort2.units[i])]=Sort2.units[i]
spikes2=np.asfortranarray(spikes2)
Siteloc = np.asfortranarray(tsf.Siteloc)
print "Into fortran..."
out_array = compare_sort.compare_sort(tsf.SampleFrequency, spikes1, spikes2, Siteloc, Sort1.maxchan, Sort2.maxchan)
print "... out of fortran"
Sort2.purity = out_array[0][0:len(Sort2.units)]
Sort2.completeness= out_array[1][0:len(Sort2.units)]
Sort2.match = out_array[2][0:len(Sort2.units)]
return
def test_reorder_vector():
nobs = 5
k_endog = 3
missing = np.zeros((k_endog, nobs))
missing[0, 0] = 1
missing[:2, 1] = 1
missing[0, 2] = 1
missing[2, 2] = 1
missing[1, 3] = 1
missing[2, 4] = 1
given = np.zeros((k_endog, nobs))
given[:, :] = np.array([1, 2, 3])[:, np.newaxis]
desired = given.copy()
given[:, 0] = [2, 3, 0]
desired[:, 0] = [0, 2, 3]
given[:, 1] = [3, 0, 0]
desired[:, 1] = [0, 0, 3]
given[:, 2] = [2, 0, 0]
desired[:, 2] = [0, 2, 0]
given[:, 3] = [1, 3, 0]
desired[:, 3] = [1, 0, 3]
given[:, 4] = [1, 2, 0]
desired[:, 4] = [1, 2, 0]
actual = np.asfortranarray(given.copy())
missing = np.asfortranarray(missing.astype(np.int32))
tools.reorder_missing_vector(actual, missing, inplace=True)
assert_equal(actual, desired)
def writeArraysToFile(stream, x, y, z):
# Check if arrays have same shape and data type
assert ( x.size == y.size == z.size ), "Different array sizes."
assert ( x.dtype.itemsize == y.dtype.itemsize == z.dtype.itemsize ), "Different item sizes."
nitems = x.size
itemsize = x.dtype.itemsize
fmt = _get_byte_order_char() + str(1) + np_to_struct[x.dtype.name] # > for big endian
if (x.flags['C_CONTIGUOUS']):
xx = np.asfortranarray(x.T).ravel()
else:
xx = x.ravel()
if (y.flags['C_CONTIGUOUS']):
yy = np.asfortranarray(y.T).ravel()
else:
yy = y.ravel()
if (z.flags['C_CONTIGUOUS']):
zz = np.asfortranarray(z.T).ravel()
else:
zz = z.ravel()
# eliminate this loop by creating a composed array.
for i in range(nitems):
bx = struct.pack(fmt, xx[i])
by = struct.pack(fmt, yy[i])
bz = struct.pack(fmt, zz[i])
stream.write(bx)
stream.write(by)
stream.write(bz)
def adjoint(self, inputs, outputs):
"""The adjoint operator.
Reads from inputs and writes to outputs.
"""
if self.implementation == Impl['halide'] :
#Halide implementation
if len(self.H.shape) == 2:
tmpin = np.asfortranarray( inputs[0][..., np.newaxis].astype(np.float32) )
else:
tmpin = np.asfortranarray( inputs[0].astype(np.float32) )
Halide('At_warp.cpp').At_warp( tmpin, self.Hf, self.tmpadj ) #Call
np.copyto(outputs[0], self.tmpadj )
else:
#CV2 version
inimg = inputs[0]
if len(self.H.shape) == 2:
# + cv2.WARP_INVERSE_MAP
warpedInput = cv2.warpPerspective(np.asfortranarray(inimg), self.Hinv.T, inimg.shape[1::-1], flags=cv2.INTER_LINEAR,
borderMode=cv2.BORDER_CONSTANT, borderValue=0.)
np.copyto( outputs[0], warpedInput )
else:
outputs[0][:] = 0.0
for j in range(self.H.shape[2]):
warpedInput = cv2.warpPerspective(np.asfortranarray(inimg[:,:,:,j]), self.Hinv[:,:,j].T, inimg.shape[1::-1], flags=cv2.INTER_LINEAR,
borderMode=cv2.BORDER_CONSTANT, borderValue=0.) #Necessary due to array layout in opencv
outputs[0] += warpedInput
def test_mem_layout():
# Test with different memory layouts of X and y
X_ = np.asfortranarray(X)
clf = GradientBoostingClassifier(n_estimators=100, random_state=1)
clf.fit(X_, y)
assert_array_equal(clf.predict(T), true_result)
assert_equal(100, len(clf.estimators_))
X_ = np.ascontiguousarray(X)
clf = GradientBoostingClassifier(n_estimators=100, random_state=1)
clf.fit(X_, y)
assert_array_equal(clf.predict(T), true_result)
assert_equal(100, len(clf.estimators_))
y_ = np.asarray(y, dtype=np.int32)
y_ = np.ascontiguousarray(y_)
clf = GradientBoostingClassifier(n_estimators=100, random_state=1)
clf.fit(X, y_)
assert_array_equal(clf.predict(T), true_result)
assert_equal(100, len(clf.estimators_))
y_ = np.asarray(y, dtype=np.int32)
y_ = np.asfortranarray(y_)
clf = GradientBoostingClassifier(n_estimators=100, random_state=1)
clf.fit(X, y_)
assert_array_equal(clf.predict(T), true_result)
assert_equal(100, len(clf.estimators_))
def consLinear( self, A, lb=None, ub=None ):
"""
sets linear constraints.
Arguments:
A: linear constraint matrix, array of size (Nconslin,N).
lb: lower bounds, array of size (Nconslin,). (default: -inf).
ub: upper bounds, array of size (Nconslin,). (default: zeros).
"""
self.conslinA = np.asfortranarray( A )
if( self.conslinA.shape != ( self.Nconslin, self.N ) ):
raise ValueError( "Argument 'A' must have size (" + str(self.Nconslin)
+ "," + str(self.N) + ")." )
if( lb is None ):
lb = -np.inf * np.ones( (self.Nconslin,) )
if( ub is None ):
ub = np.zeros( (self.Nconslin,) )
self.conslinlb = np.asfortranarray( lb )
self.conslinub = np.asfortranarray( ub )
if( self.conslinlb.shape != ( self.Nconslin, ) or
self.conslinub.shape != ( self.Nconslin, ) ):
raise ValueError( "Bounds must have size (" + str(self.Nconslin) + ",)." )
def test_bind():
mod = Representation(1, k_states=2)
# Test invalid endogenous array (it must be ndarray)
assert_raises(ValueError, lambda: mod.bind([1,2,3,4]))
# Test valid (nobs x 1) endogenous array
mod.bind(np.arange(10)*1.)
assert_equal(mod.nobs, 10)
# Test valid (k_endog x 0) endogenous array
mod.bind(np.zeros(0,dtype=np.float64))
# Test invalid (3-dim) endogenous array
assert_raises(ValueError, lambda: mod.bind(np.arange(12).reshape(2,2,3)*1.))
# Test valid F-contiguous
mod.bind(np.asfortranarray(np.arange(10).reshape(1,10)))
assert_equal(mod.nobs, 10)
# Test valid C-contiguous
mod.bind(np.arange(10).reshape(10,1))
assert_equal(mod.nobs, 10)
# Test invalid F-contiguous
assert_raises(ValueError, lambda: mod.bind(np.asfortranarray(np.arange(10).reshape(10,1))))
# Test invalid C-contiguous
assert_raises(ValueError, lambda: mod.bind(np.arange(10).reshape(1,10)))
def pixel(xp, yp, channel_is_used, min_equ_ref, mean_equ_ref, eof, max_usable_eof, ss, ms, r):
from constant import R17600, COMPONENT_PARTICLE
channel_is_used_p = np.transpose(channel_is_used[xp, yp, :, :]).astype(bool)
min_equ_ref_p = np.transpose(min_equ_ref[xp, yp, :, :])
mean_equ_ref_p = np.transpose(mean_equ_ref[xp, yp, :, :])
reg_scale = R17600 / r
if r > 1100:
eof_p = eof[xp, yp, :, :, :]
max_usable_eof_p = max_usable_eof[xp, yp, :]
else:
eof_p = eof[xp, yp, :, :]
max_usable_eof_p = max_usable_eof[xp, yp]
tau_cam_ss = np.asfortranarray(np.transpose(ss[:, math.ceil(xp/reg_scale), math.ceil(yp/reg_scale), COMPONENT_PARTICLE, :, :], [0, 3, 1, 2]))
tau_cam_ms = np.asfortranarray(np.transpose(ms[:, math.ceil(xp/reg_scale), math.ceil(yp/reg_scale), COMPONENT_PARTICLE, :, :], [0, 3, 1, 2]))
reg = collections.namedtuple('reg', 'channel_is_used min_equ_ref mean_equ_ref eof max_usable_eof')
smart = collections.namedtuple('smart', 'ss ms')
reg_p = reg(channel_is_used_p, min_equ_ref_p, mean_equ_ref_p, eof_p, max_usable_eof_p)
smart_p = smart(tau_cam_ss, tau_cam_ms)
return reg_p, smart_p
def test_nmf():
img_file = 'boat.png'
try:
img = Image.open(img_file)
except:
print("Cannot load image %s : skipping test" %img_file)
return None
I = np.array(img) / 255.
if I.ndim == 3:
A = np.asfortranarray(I.reshape((I.shape[0],I.shape[1] * I.shape[2])),dtype = myfloat)
rgb = True
else:
A = np.asfortranarray(I,dtype = myfloat)
rgb = False
m = 16;n = 16;
X = spams.im2col_sliding(A,m,n,rgb)
X = X[:,::10]
X = np.asfortranarray(X / np.tile(np.sqrt((X * X).sum(axis=0)),(X.shape[0],1)),dtype = myfloat)
########## FIRST EXPERIMENT ###########
tic = time.time()
(U,V) = spams.nmf(X,return_lasso= True,K = 49,numThreads=4,iter = -5)
tac = time.time()
t = tac - tic
print('time of computation for Dictionary Learning: %f' %t)
print('Evaluating cost function...')
Y = X - U * V
R = np.mean(0.5 * (Y * Y).sum(axis=0))
print('objective function: %f' %R)
return None
def MakeGrid(shape, step=None, start=None):
if step==None:
step = np.ones(2)
# if start not specified, we'll arrange it as assumed in fftshift
if start==None:
start = np.zeros(2)
if shape[0] % 2:
start[0] = -0.5 * (shape[0]-1) * step[0]
else:
start[0] = -0.5 * (shape[0]) * step[0]
if shape[1] % 2:
start[1] = -0.5 * (shape[1]-1) * step[1]
else:
start[1] = -0.5 * shape[1] * step[1]
x = np.arange(0, shape[0]) * step[0] + start[0]
y = np.arange(0, shape[1]) * step[1] + start[1]
xGrid, yGrid = np.meshgrid(x, y)
xGrid = np.asfortranarray(xGrid.T)
yGrid = np.asfortranarray(yGrid.T)
return xGrid, yGrid
def psiDerivativecomputations(self, dL_dpsi0, dL_dpsi1, dL_dpsi2, variance, lengthscale, Z, variational_posterior):
ARD = (len(lengthscale)!=1)
N,M,Q = self.get_dimensions(Z, variational_posterior)
psi1_gpu = self.gpuCache['psi1_gpu']
psi2n_gpu = self.gpuCache['psi2n_gpu']
l_gpu = self.gpuCache['l_gpu']
Z_gpu = self.gpuCache['Z_gpu']
mu_gpu = self.gpuCache['mu_gpu']
S_gpu = self.gpuCache['S_gpu']
gamma_gpu = self.gpuCache['gamma_gpu']
dvar_gpu = self.gpuCache['dvar_gpu']
dl_gpu = self.gpuCache['dl_gpu']
dZ_gpu = self.gpuCache['dZ_gpu']
dmu_gpu = self.gpuCache['dmu_gpu']
dS_gpu = self.gpuCache['dS_gpu']
dgamma_gpu = self.gpuCache['dgamma_gpu']
grad_l_gpu = self.gpuCache['grad_l_gpu']
grad_mu_gpu = self.gpuCache['grad_mu_gpu']
grad_S_gpu = self.gpuCache['grad_S_gpu']
grad_gamma_gpu = self.gpuCache['grad_gamma_gpu']
log_denom1_gpu = self.gpuCache['log_denom1_gpu']
log_denom2_gpu = self.gpuCache['log_denom2_gpu']
log_gamma_gpu = self.gpuCache['log_gamma_gpu']
log_gamma1_gpu = self.gpuCache['log_gamma1_gpu']
if self.GPU_direct:
dL_dpsi1_gpu = dL_dpsi1
dL_dpsi2_gpu = dL_dpsi2
dL_dpsi0_sum = gpuarray.sum(dL_dpsi0).get()
else:
dL_dpsi1_gpu = self.gpuCache['dL_dpsi1_gpu']
dL_dpsi2_gpu = self.gpuCache['dL_dpsi2_gpu']
dL_dpsi1_gpu.set(np.asfortranarray(dL_dpsi1))
dL_dpsi2_gpu.set(np.asfortranarray(dL_dpsi2))
dL_dpsi0_sum = dL_dpsi0.sum()
self.reset_derivative()
# t=self.g_psi1compDer(dvar_gpu,dl_gpu,dZ_gpu,dmu_gpu,dS_gpu,dL_dpsi1_gpu,psi1_gpu, np.float64(variance),l_gpu,Z_gpu,mu_gpu,S_gpu, np.int32(N), np.int32(M), np.int32(Q), block=(self.threadnum,1,1), grid=(self.blocknum,1),time_kernel=True)
# print 'g_psi1compDer '+str(t)
# t=self.g_psi2compDer(dvar_gpu,dl_gpu,dZ_gpu,dmu_gpu,dS_gpu,dL_dpsi2_gpu,psi2n_gpu, np.float64(variance),l_gpu,Z_gpu,mu_gpu,S_gpu, np.int32(N), np.int32(M), np.int32(Q), block=(self.threadnum,1,1), grid=(self.blocknum,1),time_kernel=True)
# print 'g_psi2compDer '+str(t)
self.g_psi1compDer.prepared_call((self.blocknum,1),(self.threadnum,1,1),dvar_gpu.gpudata,dl_gpu.gpudata,dZ_gpu.gpudata,dmu_gpu.gpudata,dS_gpu.gpudata,dgamma_gpu.gpudata,dL_dpsi1_gpu.gpudata,psi1_gpu.gpudata, log_denom1_gpu.gpudata, log_gamma_gpu.gpudata, log_gamma1_gpu.gpudata, np.float64(variance),l_gpu.gpudata,Z_gpu.gpudata,mu_gpu.gpudata,S_gpu.gpudata,gamma_gpu.gpudata,np.int32(N), np.int32(M), np.int32(Q))
self.g_psi2compDer.prepared_call((self.blocknum,1),(self.threadnum,1,1),dvar_gpu.gpudata,dl_gpu.gpudata,dZ_gpu.gpudata,dmu_gpu.gpudata,dS_gpu.gpudata,dgamma_gpu.gpudata,dL_dpsi2_gpu.gpudata,psi2n_gpu.gpudata, log_denom2_gpu.gpudata, log_gamma_gpu.gpudata, log_gamma1_gpu.gpudata, np.float64(variance),l_gpu.gpudata,Z_gpu.gpudata,mu_gpu.gpudata,S_gpu.gpudata,gamma_gpu.gpudata,np.int32(N), np.int32(M), np.int32(Q))
dL_dvar = dL_dpsi0_sum + gpuarray.sum(dvar_gpu).get()
sum_axis(grad_mu_gpu,dmu_gpu,N*Q,self.blocknum)
dL_dmu = grad_mu_gpu.get()
sum_axis(grad_S_gpu,dS_gpu,N*Q,self.blocknum)
dL_dS = grad_S_gpu.get()
sum_axis(grad_gamma_gpu,dgamma_gpu,N*Q,self.blocknum)
dL_dgamma = grad_gamma_gpu.get()
dL_dZ = dZ_gpu.get()
if ARD:
sum_axis(grad_l_gpu,dl_gpu,Q,self.blocknum)
dL_dlengscale = grad_l_gpu.get()
else:
dL_dlengscale = gpuarray.sum(dl_gpu).get()
return dL_dvar, dL_dlengscale, dL_dZ, dL_dmu, dL_dS, dL_dgamma
def actionAngleStaeckel_calcu0(E,Lz,pot,delta):
"""
NAME:
actionAngleStaeckel_calcu0
PURPOSE:
Use C to calculate u0 in the Staeckel approximation
INPUT:
E, Lz - energy and angular momentum
pot - Potential or list of such instances
delta - focal length of prolate spheroidal coordinates
OUTPUT:
(u0,err)
u0 : array, shape (len(E))
err - non-zero if error occured
HISTORY:
2012-12-03 - Written - Bovy (IAS)
"""
#Parse the potential
npot, pot_type, pot_args= _parse_pot(pot,potforactions=True)
#Set up result arrays
u0= numpy.empty(len(E))
err= ctypes.c_int(0)
#Set up the C code
ndarrayFlags= ('C_CONTIGUOUS','WRITEABLE')
actionAngleStaeckel_actionsFunc= _lib.calcu0
actionAngleStaeckel_actionsFunc.argtypes= [ctypes.c_int,
ndpointer(dtype=numpy.float64,flags=ndarrayFlags),
ndpointer(dtype=numpy.float64,flags=ndarrayFlags),
ctypes.c_int,
ndpointer(dtype=numpy.int32,flags=ndarrayFlags),
ndpointer(dtype=numpy.float64,flags=ndarrayFlags),
ctypes.c_double,
ndpointer(dtype=numpy.float64,flags=ndarrayFlags),
ctypes.POINTER(ctypes.c_int)]
#Array requirements, first store old order
f_cont= [E.flags['F_CONTIGUOUS'],
Lz.flags['F_CONTIGUOUS']]
E= numpy.require(E,dtype=numpy.float64,requirements=['C','W'])
Lz= numpy.require(Lz,dtype=numpy.float64,requirements=['C','W'])
u0= numpy.require(u0,dtype=numpy.float64,requirements=['C','W'])
#Run the C code
actionAngleStaeckel_actionsFunc(len(E),
E,
Lz,
ctypes.c_int(npot),
pot_type,
pot_args,
ctypes.c_double(delta),
u0,
ctypes.byref(err))
#Reset input arrays
if f_cont[0]: E= numpy.asfortranarray(E)
if f_cont[1]: Lz= numpy.asfortranarray(Lz)
return (u0,err.value)
def subset_selection_xtx(X, Y):
""" Subsets selection using EvalSubsetsUsingXtx in the Earth package.
"""
X = numpy.asfortranarray(X, dtype=ctypes.c_double)
Y = numpy.asfortranarray(Y, dtype=ctypes.c_double)
if Y.ndim == 1:
Y = Y.reshape((-1, 1), order="F")
if X.shape[0] != Y.shape[0]:
raise ValueError("First dimensions of bx and y must be the same")
var_count = X.shape[1]
resp_count = Y.shape[1]
cases = X.shape[0]
subsets = numpy.zeros((var_count, var_count), dtype=ctypes.c_bool,
order="F")
rss_vec = numpy.zeros((var_count,), dtype=ctypes.c_double, order="F")
weights = numpy.ones((cases,), dtype=ctypes.c_double, order="F")
rval = _c_eval_subsets_xtx(subsets, rss_vec, cases, resp_count, var_count,
X, Y, weights)
if rval == 1:
raise numpy.linalg.LinAlgError("Lin. dep. terms in X")
elif rval == 2:
raise Exception("Trying to prune the intercept.")
elif rval != 0:
raise Exception("Error %i" % rval)
subsets_ind = numpy.zeros((var_count, var_count), dtype=int)
for i, used in enumerate(subsets.T):
subsets_ind[i, :i + 1] = numpy.where(used)[0]
return subsets_ind, rss_vec
def _computations(self,do_Kmm=True, do_Kmm_grad=True):
"""
All of the computations needed. Some are optional, see kwargs.
"""
if do_Kmm:
self.Lm = jitchol(self.Kmm)
# The rather complex computations of self.A
if self.has_uncertain_inputs:
if self.likelihood.is_heteroscedastic:
psi2_beta = (self.psi2 * (self.likelihood.precision.flatten().reshape(self.batchsize, 1, 1))).sum(0)
else:
psi2_beta = self.psi2.sum(0) * self.likelihood.precision
evals, evecs = np.linalg.eigh(psi2_beta)
clipped_evals = np.clip(evals, 0., 1e6) # TODO: make clipping configurable
tmp = evecs * np.sqrt(clipped_evals)
else:
if self.likelihood.is_heteroscedastic:
tmp = self.psi1.T * (np.sqrt(self.likelihood.precision.flatten().reshape(1, self.batchsize)))
else:
tmp = self.psi1.T * (np.sqrt(self.likelihood.precision))
tmp, _ = dtrtrs(self.Lm, np.asfortranarray(tmp), lower=1)
self.A = tdot(tmp)
self.V = self.likelihood.precision*self.likelihood.Y
self.VmT = np.dot(self.V,self.q_u_expectation[0].T)
self.psi1V = np.dot(self.psi1.T, self.V)
self.B = np.eye(self.num_inducing)*self.data_prop + self.A
self.Lambda = backsub_both_sides(self.Lm, self.B.T)
self.LQL = backsub_both_sides(self.Lm,self.q_u_expectation[1].T,transpose='right')
self.trace_K = self.psi0.sum() - np.trace(self.A)/self.likelihood.precision
self.Kmmi_m, _ = dpotrs(self.Lm, self.q_u_expectation[0], lower=1)
self.projected_mean = np.dot(self.psi1,self.Kmmi_m)
# Compute dL_dpsi
self.dL_dpsi0 = - 0.5 * self.output_dim * self.likelihood.precision * np.ones(self.batchsize)
self.dL_dpsi1, _ = dpotrs(self.Lm,np.asfortranarray(self.VmT.T),lower=1)
self.dL_dpsi1 = self.dL_dpsi1.T
dL_dpsi2 = -0.5 * self.likelihood.precision * backsub_both_sides(self.Lm, self.LQL - self.output_dim * np.eye(self.num_inducing))
if self.has_uncertain_inputs:
self.dL_dpsi2 = np.repeat(dL_dpsi2[None,:,:],self.batchsize,axis=0)
else:
self.dL_dpsi1 += 2.*np.dot(dL_dpsi2,self.psi1.T).T
self.dL_dpsi2 = None
# Compute dL_dKmm
if do_Kmm_grad:
tmp = np.dot(self.LQL,self.A) - backsub_both_sides(self.Lm,np.dot(self.q_u_expectation[0],self.psi1V.T),transpose='right')
tmp += tmp.T
tmp += -self.output_dim*self.B
tmp += self.data_prop*self.LQL
self.dL_dKmm = 0.5*backsub_both_sides(self.Lm,tmp)
#Compute the gradient of the log likelihood wrt noise variance
self.partial_for_likelihood = -0.5*(self.batchsize*self.output_dim - np.sum(self.A*self.LQL))*self.likelihood.precision
self.partial_for_likelihood += (0.5*self.output_dim*self.trace_K + 0.5 * self.likelihood.trYYT - np.sum(self.likelihood.Y*self.projected_mean))*self.likelihood.precision**2
def test_mul():
## Test multiply method of a distributed matrix
ms, ns = 5, 14
gA = np.random.standard_normal((ms, ns)).astype(np.float64)
gA = np.asfortranarray(gA)
dA = core.DistributedMatrix.from_global_array(gA, rank=0)
gB = np.random.standard_normal((ms, ns)).astype(np.float64)
gB = np.asfortranarray(gB)
dB = core.DistributedMatrix.from_global_array(gB, rank=0)
dC = dA * dB
gC = dC.to_global_array(rank=0)
a = np.random.standard_normal(ns).astype(np.float64)
comm.Bcast(a, root=0) # ensure all process have the same data
dD = dA * a
gD = dD.to_global_array(rank=0)
alpha = 2.345
dE = dA * alpha
gE = dE.to_global_array(rank=0)
if rank == 0:
assert allclose(gA * gB, gC)
assert allclose(gA * a, gD)
assert allclose(gA * alpha, gE)
def test_lassoMask():
np.random.seed(0)
print("test lassoMask")
##############################################
# Decomposition of a large number of signals
##############################################
# data generation
X = np.asfortranarray(np.random.normal(size=(300,300)))
# X=X./repmat(sqrt(sum(X.^2)),[size(X,1) 1]);
X = np.asfortranarray(X / np.tile(np.sqrt((X*X).sum(axis=0)),(X.shape[0],1)),dtype= myfloat)
D = np.asfortranarray(np.random.normal(size=(300,50)))
D = np.asfortranarray(D / np.tile(np.sqrt((D*D).sum(axis=0)),(D.shape[0],1)),dtype= myfloat)
mask = np.asfortranarray((X > 0)) # generating a binary mask
param = {
'lambda1' : 0.15, # not more than 20 non-zeros coefficients
'numThreads' : -1, # number of processors/cores to use; the default choice is -1
# and uses all the cores of the machine
'mode' : spams.PENALTY} # penalized formulation
tic = time.time()
alpha = spams.lassoMask(X,D,mask,**param)
tac = time.time()
t = tac - tic
print("%f signals processed per second\n" %(float(X.shape[1]) / t))
return None
def test_cd():
np.random.seed(0)
X = np.asfortranarray(np.random.normal(size = (64,100)))
X = np.asfortranarray(X / np.tile(np.sqrt((X*X).sum(axis=0)),(X.shape[0],1)),dtype=myfloat)
D = np.asfortranarray(np.random.normal(size = (64,100)))
D = np.asfortranarray(D / np.tile(np.sqrt((D*D).sum(axis=0)),(D.shape[0],1)),dtype=myfloat)
# parameter of the optimization procedure are chosen
lambda1 = 0.015
mode = spams.PENALTY
tic = time.time()
alpha = spams.lasso(X,D,lambda1 = lambda1,mode = mode,numThreads = 4)
tac = time.time()
t = tac - tic
xd = X - D * alpha
E = np.mean(0.5 * (xd * xd).sum(axis=0) + lambda1 * np.abs(alpha).sum(axis=0))
print("%f signals processed per second for LARS" %(X.shape[1] / t))
print('Objective function for LARS: %g' %E)
tol = 0.001
itermax = 1000
tic = time.time()
# A0 = ssp.csc_matrix(np.empty((alpha.shape[0],alpha.shape[1])))
A0 = ssp.csc_matrix((alpha.shape[0],alpha.shape[1]),dtype=myfloat)
alpha2 = spams.cd(X,D,A0,lambda1 = lambda1,mode = mode,tol = tol, itermax = itermax,numThreads = 4)
tac = time.time()
t = tac - tic
print("%f signals processed per second for CD" %(X.shape[1] / t))
xd = X - D * alpha2
E = np.mean(0.5 * (xd * xd).sum(axis=0) + lambda1 * np.abs(alpha).sum(axis=0))
print('Objective function for CD: %g' %E)
print('With Random Design, CD can be much faster than LARS')
return None
def generate_itp_pn(lut):
ndim=lut.ndim-1
if ndim == 1: interpolator = interpolators.interpol_1pn
elif ndim == 2: interpolator = interpolators.interpol_2pn
elif ndim == 3: interpolator = interpolators.interpol_3pn
elif ndim == 4: interpolator = interpolators.interpol_4pn
elif ndim == 5: interpolator = interpolators.interpol_5pn
elif ndim == 6: interpolator = interpolators.interpol_6pn
elif ndim >= 7: interpolator = interpolators.interpol_npn
else:
print 'Not implemented'
return
if ndim <= 6:
if np.isfortran(lut): my_lut=lut
else: my_lut=np.asfortranarray(lut)
def function(wo):
return interpolator(wo,my_lut)
else:
if np.isfortran(lut):
flat_lut=np.asfortranarray(lut.reshape((-1,lut.shape[-1]) ,order='C'))
else:
flat_lut=np.asfortranarray(lut.reshape((-1,lut.shape[-1]), order='C'))
shape=np.array(lut.shape)
size=shape[:-1].prod()
def function(wo):
return interpolator(wo,flat_lut,shape[0:-1],shape[-1])
return function
def run():
print_complex = get_print_complex()
convolutionCPU = get_convolution_cpu()
check_results = get_check_results()
#data = np.ones((3,3)).astype('complex64')
data = np.asfortranarray(np.random.randn(3,3).astype('complex64'))
#kernel = np.ones((3,3)).astype('complex64')
kernel = np.asfortranarray(np.random.randn(3,3).astype('complex64'))
result = np.asfortranarray(np.zeros_like(data).astype('complex64'))
convolutionCPU(_get_float2_ptr(result), _get_float2_ptr(data), _get_float2_ptr(kernel), data.shape[1], data.shape[0], kernel.shape[1], kernel.shape[0], 1, 6)
print
print kernel
print
print data
print
s1 = np.array(data.shape)
s2 = np.array(kernel.shape)
print result
print
print fftconvolve(data.real, kernel.real, mode='full').astype('complex64')
def test_singular_a(self):
for b in [self.b_1dim, self.b_2dim]:
for dtype in self.dtypes:
a = np.asfortranarray(self.a_singular, dtype=dtype)
b = np.asfortranarray(b, dtype=dtype)
r = _numba_linalg_solve(a, b)
ok_(r != 0)
def test_poisson_halide(self):
"""Halide Poisson norm test
"""
if halide_installed():
# Load image
testimg_filename = os.path.join(os.path.dirname(os.path.realpath(__file__)),
'data', 'angela.jpg')
img = Image.open(testimg_filename)
np_img = np.asfortranarray(im2nparray(img))
# Convert to gray
np_img = np.mean(np_img, axis=2)
# Test problem
v = np_img
theta = 0.5
mask = np.asfortranarray(np.random.randn(*list(np_img.shape)).astype(np.float32))
mask = np.maximum(mask, 0.)
b = np_img * np_img
# Output
output = np.zeros_like(v)
tic()
Halide('prox_Poisson.cpp').prox_Poisson(v, mask, b, theta, output) # Call
print('Running took: {0:.1f}ms'.format(toc()))
# Reference
output_ref = 0.5 * (v - theta + np.sqrt((v - theta) * (v - theta) + 4 * theta * b))
output_ref[mask <= 0.5] = v[mask <= 0.5]
self.assertItemsAlmostEqual(output, output_ref)
def forward(self, inputs, outputs):
"""The forward operator.
Reads from inputs and writes to outputs.
"""
if self.implementation == Impl['halide']:
# Halide implementation
tmpin = np.asfortranarray(inputs[0].astype(np.float32))
Halide('A_warp.cpp').A_warp(tmpin, self.Hinvf, self.tmpfwd) # Call
np.copyto(outputs[0], np.reshape(self.tmpfwd, self.shape))
else:
# CV2 version
inimg = inputs[0]
if len(self.H.shape) == 2:
warpedInput = cv2.warpPerspective(np.asfortranarray(inimg), self.H.T,
inimg.shape[1::-1], flags=cv2.INTER_LINEAR,
borderMode=cv2.BORDER_CONSTANT, borderValue=0.)
# Necessary due to array layout in opencv
np.copyto(outputs[0], warpedInput)
else:
for j in range(self.H.shape[2]):
warpedInput = cv2.warpPerspective(np.asfortranarray(inimg),
self.H[:, :, j].T, inimg.shape[1::-1],
flags=cv2.INTER_LINEAR,
borderMode=cv2.BORDER_CONSTANT,
borderValue=0.)
# Necessary due to array layout in opencv
np.copyto(outputs[0][:, :, :, j], warpedInput)
def test_mask_halide(self):
"""Test mask lin op in halide.
"""
if halide_installed():
# Load image
testimg_filename = os.path.join(os.path.dirname(os.path.realpath(__file__)),
'data', 'angela.jpg')
# opens the file using Pillow - it's not an array yet
img = Image.open(testimg_filename)
np_img = np.asfortranarray(im2nparray(img))
# Test problem
output = np.zeros_like(np_img)
mask = np.asfortranarray(np.random.randn(*list(np_img.shape)).astype(np.float32))
mask = np.maximum(mask, 0.)
Halide('A_mask.cpp').A_mask(np_img, mask, output) # Call
output_ref = mask * np_img
# Transpose
output_trans = np.zeros_like(np_img)
Halide('At_mask.cpp').At_mask(np_img, mask, output_trans) # Call
self.assertItemsAlmostEqual(output, output_ref)
self.assertItemsAlmostEqual(output_trans, output_ref)
def runRandomWalking(self, w, nAlgs, nWalks = 1, nIters=-1, nErrorsLimit=-1, allowSimilar=False, pTransition=0.8,
randomSeed=0):
RunRandomWalkingResult = collections.namedtuple('RunRandomWalkingResult', 'W isSource')
nFeatures = w.shape[0]
w0 = np.tile(w, (nWalks, 1))
sessionStats = self.getStats()
if sessionStats.nFeatures != nFeatures:
raise Exception('sessionStats.nFeatures != w0.shape[1]')
W = np.asfortranarray(np.zeros((nAlgs, nFeatures)).astype(np.float32))
isSource = np.asfortranarray(np.zeros((nAlgs, 1)).astype(np.uint8))
w0_p = w0.ctypes.data_as(self.lsPlugin.c_float_p)
W_p = W.ctypes.data_as(self.lsPlugin.c_float_p)
isSource_p = isSource.ctypes.data_as(self.lsPlugin.c_uint8_p)
pTransition_p = (ctypes.c_float * 1)()
pTransition_p[0] = pTransition;
#pTransition.ctypes.data_as(self.c_float_p)
nAlgs = self.lsPlugin.dll.runRandomWalking(self.sessionId, w0_p, nWalks, nAlgs, nIters, nErrorsLimit,
allowSimilar, pTransition_p, randomSeed, W_p, isSource_p)
self.lsPlugin.verifyCall(nAlgs)
return RunRandomWalkingResult(W, isSource)
def setup(self):
self.p = numpy.array([[27, 51],
[66, 85],
[77, 45]])
self.p3 = numpy.array([[27, 51, 37],
[66, 85, 25],
[77, 45, 73]])
self.space = numpy.array((100, 100))
self.space3 = numpy.array((100, 100, 100))
self.radii = numpy.array((5, 6, 7))
self.g = nanshe.syn.data.generate_hypersphere_masks(
self.space, self.p, self.radii
)
self.g = self.g.reshape((self.g.shape[0], -1))
self.g = self.g.transpose()
self.g = numpy.asmatrix(self.g)
self.g = numpy.asfortranarray(self.g)
self.g3 = nanshe.syn.data.generate_hypersphere_masks(
self.space3, self.p3, self.radii
)
self.g3 = self.g3.reshape((self.g3.shape[0], -1))
self.g3 = self.g3.transpose()
self.g3 = numpy.asmatrix(self.g3)
self.g3 = numpy.asfortranarray(self.g3)
def _set_params(self, p):
new_kern_params = p[:self.kern.num_params_transformed()]
new_likelihood_params = p[self.kern.num_params_transformed():]
old_likelihood_params = self.likelihood._get_params()
self.kern._set_params_transformed(new_kern_params)
self.likelihood._set_params_transformed(new_likelihood_params)
self.K = self.kern.K(self.X)
#Re fit likelihood approximation (if it is an approx), as parameters have changed
if isinstance(self.likelihood, Laplace):
self.likelihood.fit_full(self.K)
self.K += self.likelihood.covariance_matrix
self.Ki, self.L, self.Li, self.K_logdet = pdinv(self.K)
# the gradient of the likelihood wrt the covariance matrix
if self.likelihood.YYT is None:
# alpha = np.dot(self.Ki, self.likelihood.Y)
alpha, _ = dpotrs(self.L, self.likelihood.Y, lower=1)
self.dL_dK = 0.5 * (tdot(alpha) - self.output_dim * self.Ki)
else:
# tmp = mdot(self.Ki, self.likelihood.YYT, self.Ki)
tmp, _ = dpotrs(self.L, np.asfortranarray(self.likelihood.YYT), lower=1)
tmp, _ = dpotrs(self.L, np.asfortranarray(tmp.T), lower=1)
self.dL_dK = 0.5 * (tmp - self.output_dim * self.Ki)
#Adding dZ_dK (0 for a non-approximate likelihood, compensates for
#additional gradients of K when log-likelihood has non-zero Z term)
self.dL_dK += self.likelihood.dZ_dK
def endog(self, value):
self._endog = np.array(value, order='A')
# (T x M)
if (self.nobs, self.k_endog) == self._endog.shape:
self._endog = self._endog.T
# (M x T)
elif (self.k_endog, self.nobs) == self._endog.shape:
pass
else:
raise ValueError('Invalid endogenous array shape. Required'
'(%d, %d) or (%d, %d). Got %s'
% (self.nobs, self.k_endog, self.k_endog,
self.nobs, str(self._endog.shape)))
if not self._endog.flags['F_CONTIGUOUS']:
self._endog = np.asfortranarray(self._endog)
# Create a new lag matrix, shaped (k_ar, nobs) = (k_ar, T)
self._lagged = np.asfortranarray(np.hstack([
self.endog[:, self.order-i:-i].T
for i in range(1, self.order+1)
]).T)
# Set calculation flags
self._recalculate = True
def test_matrix_multiply_ff(self):
"""matrix multiply two FORTRAN layout matrices"""
a = np.asfortranarray(np.random.randn(M,N))
b = np.asfortranarray(np.random.randn(N,K))
res = gulinalg.matrix_multiply(a,b)
ref = np.dot(a,b)
assert_allclose(res, ref)
def test_conjGrad():
A = np.asfortranarray(np.random.normal(size = (5000,500)))
#* np.random.seed(0)
#* A = np.asfortranarray(np.random.normal(size = (10,5)))
A = np.asfortranarray(np.dot(A.T,A),dtype=myfloat)
b = np.ones((A.shape[1],),dtype=myfloat,order="FORTRAN")
x0 = b
tol = 1e-4
itermax = int(0.5 * len(b))
tic = time.time()
for i in xrange(0,20):
y1 = np.linalg.solve(A,b)
tac = time.time()
print " Time (numpy): ", tac - tic
x1 = np.abs(b - np.dot(A,y1))
print "Mean error on b : %f" %(x1.sum() / b.shape[0])
tic = time.time()
for i in xrange(0,20):
y2 = spams.conjGrad(A,b,x0,tol,itermax)
#* y2 = spams.conjGrad(A,b)
tac = time.time()
print " Time (spams): ", tac - tic
x1 = np.dot(A,y2)
x2 = np.abs(b - x1)
print "Mean error on b : %f" %(x2.sum() / b.shape[0])
err = abs(y1 - y2)
return err.max()
def dictEval( X, D, param, lam=None, dsfactor=None, patchSize=None, patchFnGrp=None, kind='avg'):
if dsfactor is not None:
X_useme,dsz = downsamplePatchList( X, patchSize, dsfactor, kind=kind )
D_useme,Ddsz = downsamplePatchList( D, patchSize, dsfactor, kind=kind )
if patchFnGrp:
patchFnGrp.create_dataset('patchesDown', data=X_useme)
else:
X_useme = X
D_useme = D
if lam is None:
lam = param['lambda1']
alpha = spams.lasso( np.asfortranarray(X_useme), D = np.asfortranarray(D_useme), **param )
Xre = ( D * alpha )
if patchFnGrp:
patchFnGrp.create_dataset('patchesRecon', data=Xre)
xd = X - Xre
R = np.mean( (xd * xd).sum(axis=0))
if lam > 0:
print " dictEval - lambda: ", lam
R = R + lam * np.mean( np.abs(alpha).sum(axis=0))
return R
import pytest
from copy import deepcopy
import numpy as np
import tinybrain
image1x1x1 = np.array([[[[0]]]])
image1x1x1f = np.asfortranarray(image1x1x1)
image2x2x2 = np.array([[
[[1], [1]],
[[2], [2]],
], [
[[1], [0]],
[[0], [30]],
]])
image2x2x2f = np.asfortranarray(image2x2x2)
image3x3x3 = np.array([
[ #z 0 1 2
[[1], [1], [1]], # y=0
[[1], [1], [1]], # y=1 # x=0
[[1], [1], [1]], # y=2
],
[
[[2], [2], [2]], # y=0
[[2], [2], [2]], # y=1 # x=1
[[2], [2], [2]], # y=2
],
[
def enet_path(X,
y,
rho=0.5,
eps=1e-3,
n_alphas=100,
alphas=None,
precompute='auto',
Xy=None,
fit_intercept=True,
normalize=False,
copy_X=True,
verbose=False,
**params):
"""Compute Elastic-Net path with coordinate descent
The Elastic Net optimization function is::
1 / (2 * n_samples) * ||y - Xw||^2_2 +
+ alpha * rho * ||w||_1 + 0.5 * alpha * (1 - rho) * ||w||^2_2
Parameters
----------
X : numpy array of shape [n_samples, n_features]
Training data. Pass directly as fortran contiguous data to avoid
unnecessary memory duplication
y : numpy array of shape [n_samples]
Target values
rho : float, optional
float between 0 and 1 passed to ElasticNet (scaling between
l1 and l2 penalties). rho=1 corresponds to the Lasso
eps : float
Length of the path. eps=1e-3 means that
alpha_min / alpha_max = 1e-3
n_alphas : int, optional
Number of alphas along the regularization path
alphas : numpy array, optional
List of alphas where to compute the models.
If None alphas are set automatically
precompute : True | False | 'auto' | array-like
Whether to use a precomputed Gram matrix to speed up
calculations. If set to 'auto' let us decide. The Gram
matrix can also be passed as argument.
Xy : array-like, optional
Xy = np.dot(X.T, y) that can be precomputed. It is useful
only when the Gram matrix is precomputed.
fit_intercept : bool
Fit or not an intercept
normalize : boolean, optional
If True, the regressors X are normalized
copy_X : boolean, optional, default True
If True, X will be copied; else, it may be overwritten.
verbose : bool or integer
Amount of verbosity
params : kwargs
keyword arguments passed to the Lasso objects
Returns
-------
models : a list of models along the regularization path
Notes
-----
See examples/plot_lasso_coordinate_descent_path.py for an example.
See also
--------
ElasticNet
ElasticNetCV
"""
X = as_float_array(X, copy_X)
X_init = X
X, y, X_mean, y_mean, X_std = LinearModel._center_data(X,
y,
fit_intercept,
normalize,
copy=False)
X = np.asfortranarray(X) # make data contiguous in memory
n_samples, n_features = X.shape
if X_init is not X and hasattr(precompute, '__array__'):
precompute = 'auto'
if X_init is not X and Xy is not None:
Xy = None
if 'precompute' is True or \
((precompute == 'auto') and (n_samples > n_features)):
precompute = np.dot(X.T, X)
if Xy is None:
Xy = np.dot(X.T, y)
n_samples = X.shape[0]
if alphas is None:
alpha_max = np.abs(Xy).max() / (n_samples * rho)
alphas = np.logspace(np.log10(alpha_max * eps),
np.log10(alpha_max),
num=n_alphas)[::-1]
else:
alphas = np.sort(alphas)[::-1] # make sure alphas are properly ordered
coef_ = None # init coef_
models = []
n_alphas = len(alphas)
for i, alpha in enumerate(alphas):
model = ElasticNet(alpha=alpha,
rho=rho,
fit_intercept=False,
precompute=precompute)
model.set_params(**params)
model.fit(X, y, coef_init=coef_, Xy=Xy)
if fit_intercept:
model.fit_intercept = True
model._set_intercept(X_mean, y_mean, X_std)
if verbose:
if verbose > 2:
print model
elif verbose > 1:
print 'Path: %03i out of %03i' % (i, n_alphas)
else:
sys.stderr.write('.')
coef_ = model.coef_.copy()
models.append(model)
return models
def fit(self, X, y, Xy=None, coef_init=None):
"""Fit Elastic Net model with coordinate descent
Parameters
-----------
X: ndarray, (n_samples, n_features)
Data
y: ndarray, (n_samples)
Target
Xy : array-like, optional
Xy = np.dot(X.T, y) that can be precomputed. It is useful
only when the Gram matrix is precomputed.
coef_init: ndarray of shape n_features
The initial coeffients to warm-start the optimization
Notes
-----
Coordinate descent is an algorithm that considers each column of
data at a time hence it will automatically convert the X input
as a fortran contiguous numpy array if necessary.
To avoid memory re-allocation it is advised to allocate the
initial data in memory directly using that format.
"""
# X and y must be of type float64
X = np.asanyarray(X, dtype=np.float64)
y = np.asarray(y, dtype=np.float64)
n_samples, n_features = X.shape
X_init = X
X, y, X_mean, y_mean, X_std = self._center_data(X,
y,
self.fit_intercept,
self.normalize,
copy=self.copy_X)
precompute = self.precompute
if X_init is not X and hasattr(precompute, '__array__'):
# recompute Gram
# FIXME: it could be updated from precompute and X_mean
# instead of recomputed
precompute = 'auto'
if X_init is not X and Xy is not None:
Xy = None # recompute Xy
if coef_init is None:
self.coef_ = np.zeros(n_features, dtype=np.float64)
else:
self.coef_ = coef_init
alpha = self.alpha * self.rho * n_samples
beta = self.alpha * (1.0 - self.rho) * n_samples
X = np.asfortranarray(X) # make data contiguous in memory
# precompute if n_samples > n_features
if hasattr(precompute, '__array__'):
Gram = precompute
elif precompute == True or \
(precompute == 'auto' and n_samples > n_features):
Gram = np.dot(X.T, X)
else:
Gram = None
if Gram is None:
self.coef_, self.dual_gap_, self.eps_ = \
cd_fast.enet_coordinate_descent(self.coef_, alpha, beta,
X, y, self.max_iter,
self.tol)
else:
if Xy is None:
Xy = np.dot(X.T, y)
self.coef_, self.dual_gap_, self.eps_ = \
cd_fast.enet_coordinate_descent_gram(self.coef_, alpha,
beta, Gram, Xy, y, self.max_iter, self.tol)
self._set_intercept(X_mean, y_mean, X_std)
if self.dual_gap_ > self.eps_:
warnings.warn('Objective did not converge, you might want'
' to increase the number of iterations')
# return self for chaining fit and predict calls
return self
def compute_bench(samples_range, features_range):
it = 0
results = dict()
lars = np.empty((len(features_range), len(samples_range)))
lars_gram = lars.copy()
omp = lars.copy()
omp_gram = lars.copy()
max_it = len(samples_range) * len(features_range)
for i_s, n_samples in enumerate(samples_range):
for i_f, n_features in enumerate(features_range):
it += 1
n_informative = n_features / 10
print '===================='
print 'Iteration %03d of %03d' % (it, max_it)
print '===================='
# dataset_kwargs = {
# 'n_train_samples': n_samples,
# 'n_test_samples': 2,
# 'n_features': n_features,
# 'n_informative': n_informative,
# 'effective_rank': min(n_samples, n_features) / 10,
# #'effective_rank': None,
# 'bias': 0.0,
# }
dataset_kwargs = {
'n_samples': 1,
'n_components': n_features,
'n_features': n_samples,
'n_nonzero_coefs': n_informative,
'random_state': 0
}
print "n_samples: %d" % n_samples
print "n_features: %d" % n_features
y, X, _ = make_sparse_coded_signal(**dataset_kwargs)
X = np.asfortranarray(X)
gc.collect()
print "benching lars_path (with Gram):",
sys.stdout.flush()
tstart = time()
G = np.dot(X.T, X) # precomputed Gram matrix
Xy = np.dot(X.T, y)
lars_path(X, y, Xy=Xy, Gram=G, max_iter=n_informative)
delta = time() - tstart
print "%0.3fs" % delta
lars_gram[i_f, i_s] = delta
gc.collect()
print "benching lars_path (without Gram):",
sys.stdout.flush()
tstart = time()
lars_path(X, y, Gram=None, max_iter=n_informative)
delta = time() - tstart
print "%0.3fs" % delta
lars[i_f, i_s] = delta
gc.collect()
print "benching orthogonal_mp (with Gram):",
sys.stdout.flush()
tstart = time()
orthogonal_mp(X, y, precompute_gram=True,
n_nonzero_coefs=n_informative)
delta = time() - tstart
print "%0.3fs" % delta
omp_gram[i_f, i_s] = delta
gc.collect()
print "benching orthogonal_mp (without Gram):",
sys.stdout.flush()
tstart = time()
orthogonal_mp(X, y, precompute_gram=False,
n_nonzero_coefs=n_informative)
delta = time() - tstart
print "%0.3fs" % delta
omp[i_f, i_s] = delta
results['time(LARS) / time(OMP)\n (w/ Gram)'] = (lars_gram / omp_gram)
results['time(LARS) / time(OMP)\n (w/o Gram)'] = (lars / omp)
return results
def np_asfortranarray(arr):
return np.asfortranarray(arr)
def Forder(var):
return np.asfortranarray(var.T, dtype=np.float64)
from proximal.prox_fns import *
from proximal.algorithms import *
import cvxpy as cvx
import numpy as np
from scipy import ndimage
import argparse
import matplotlib.pyplot as plt
from PIL import Image
import cv2
# Load image
img = Image.open(
'./data/angela.jpg') # opens the file using Pillow - it's not an array yet
x = np.asfortranarray(im2nparray(img))
x = np.mean(x, axis=2)
x = np.maximum(x, 0.0)
# Kernel
K = Image.open('./data/kernel_snake.png'
) # opens the file using Pillow - it's not an array yet
K = np.mean(np.asfortranarray(im2nparray(K)), axis=2)
K = np.maximum(cv2.resize(K, (15, 15), interpolation=cv2.INTER_LINEAR), 0)
K /= np.sum(K)
# Generate observation
sigma_noise = 0.01
b = ndimage.convolve(x, K,
mode='wrap') + sigma_noise * np.random.randn(*x.shape)
def arma_innovations(endog,
ar_params=None,
ma_params=None,
sigma2=1,
normalize=False,
prefix=None):
"""
Compute innovations using a given ARMA process.
Parameters
----------
endog : ndarray
The observed time-series process, may be univariate or multivariate.
ar_params : ndarray, optional
Autoregressive parameters.
ma_params : ndarray, optional
Moving average parameters.
sigma2 : ndarray, optional
The ARMA innovation variance. Default is 1.
normalize : bool, optional
Whether or not to normalize the returned innovations. Default is False.
prefix : str, optional
The BLAS prefix associated with the datatype. Default is to find the
best datatype based on given input. This argument is typically only
used internally.
Returns
-------
innovations : ndarray
Innovations (one-step-ahead prediction errors) for the given `endog`
series with predictions based on the given ARMA process. If
`normalize=True`, then the returned innovations have been "whitened" by
dividing through by the square root of the mean square error.
innovations_mse : ndarray
Mean square error for the innovations.
"""
# Parameters
endog = np.array(endog)
squeezed = endog.ndim == 1
if squeezed:
endog = endog[:, None]
ar_params = np.atleast_1d([] if ar_params is None else ar_params)
ma_params = np.atleast_1d([] if ma_params is None else ma_params)
nobs, k_endog = endog.shape
ar = np.r_[1, -ar_params]
ma = np.r_[1, ma_params]
# Get BLAS prefix
if prefix is None:
prefix, dtype, _ = find_best_blas_type(
[endog, ar_params, ma_params,
np.array(sigma2)])
dtype = prefix_dtype_map[prefix]
# Make arrays contiguous for BLAS calls
endog = np.asfortranarray(endog, dtype=dtype)
ar_params = np.asfortranarray(ar_params, dtype=dtype)
ma_params = np.asfortranarray(ma_params, dtype=dtype)
sigma2 = dtype(sigma2).item()
# Get the appropriate functions
arma_transformed_acovf_fast = getattr(
_arma_innovations, prefix + 'arma_transformed_acovf_fast')
arma_innovations_algo_fast = getattr(_arma_innovations,
prefix + 'arma_innovations_algo_fast')
arma_innovations_filter = getattr(_arma_innovations,
prefix + 'arma_innovations_filter')
# Run the innovations algorithm for ARMA coefficients
arma_acovf = arima_process.arma_acovf(ar, ma, sigma2=sigma2,
nobs=nobs) / sigma2
acovf, acovf2 = arma_transformed_acovf_fast(ar, ma, arma_acovf)
theta, v = arma_innovations_algo_fast(nobs, ar_params, ma_params, acovf,
acovf2)
v = np.array(v)
if (np.any(v < 0) or not np.isfinite(theta).all()
or not np.isfinite(v).all()):
# This is defensive code that is hard to hit
raise ValueError(NON_STATIONARY_ERROR)
# Run the innovations filter across each series
u = []
for i in range(k_endog):
u_i = np.array(
arma_innovations_filter(endog[:, i], ar_params, ma_params, theta))
u.append(u_i)
u = np.vstack(u).T
if normalize:
u /= v[:, None]**0.5
# Post-processing
if squeezed:
u = u.squeeze()
return u, v
def test_multiple(self):
nodes = np.asfortranarray([[0.0, 1.0, 2.0, 3.0], [4.0, 4.5, 5.0, 5.5]])
new_nodes = self._call_function_under_test(nodes)
expected = np.asfortranarray([[0.0, 3.0], [4.0, 5.5]])
self.assertEqual(expected, new_nodes)
def prep_array(array):
return np.asfortranarray(array) if is_col_major else array
def test_linear(self):
nodes = np.asfortranarray([[5.5, 5.5]])
new_nodes = self._call_function_under_test(nodes)
expected = np.asfortranarray([[5.5]])
self.assertEqual(expected, new_nodes)
def test_no_reduce(self):
nodes = np.asfortranarray([[0.0, -1.0, 1.0, -0.75],
[2.0, 0.0, 1.0, 1.625]])
new_nodes = self._call_function_under_test(nodes)
self.assertIs(new_nodes, nodes)
def test_to_quadratic(self):
nodes = np.asfortranarray([[3.0, 2.0, 1.0, 0.0], [0.0, 2.0, 2.0, 0.0]])
was_reduced, new_nodes = self._call_function_under_test(nodes)
self.assertTrue(was_reduced)
expected = np.asfortranarray([[3.0, 1.5, 0.0], [0.0, 3.0, 0.0]])
self.assertEqual(expected, new_nodes)
def test_single(self):
nodes = np.asfortranarray([[0.0, 2.0, 4.0, 6.0], [0.0, 4.0, 6.0, 6.0]])
new_nodes = self._call_function_under_test(nodes)
expected = np.asfortranarray([[0.0, 3.0, 6.0], [0.0, 6.0, 6.0]])
self.assertEqual(expected, new_nodes)
def test_to_cubic(self):
nodes = np.asfortranarray([[0.0, 0.75, 2.0, 2.75, 2.0]])
result = self._call_function_under_test(nodes)
expected = np.asfortranarray([[0.0, 1.0, 3.0, 2.0]])
self.assertEqual(result, expected)
def test_from_cubic_not_elevated(self):
nodes = np.asfortranarray([[0.0, -1.0, 1.0, -0.75],
[2.0, 0.0, 1.0, 1.625]])
was_reduced, new_nodes = self._call_function_under_test(nodes)
self.assertFalse(was_reduced)
self.assertIs(new_nodes, nodes)
def test_to_constant(self):
nodes = np.asfortranarray([[-2.0, -2.0], [1.0, 1.0]])
result = self._call_function_under_test(nodes)
expected = np.asfortranarray([[-2.0], [1.0]])
self.assertEqual(result, expected)
def test_nodes_zero(self):
nodes = np.asfortranarray([[0.0], [0.0]])
result = self._call_function_under_test(nodes, nodes)
self.assertEqual(result, 0.0)
def test_failure_on_invalid(self):
nodes = np.asfortranarray([[0.0, -1.0, 1.0, -0.75],
[2.0, 0.0, 1.0, 1.625]])
point = np.asfortranarray([[-0.25], [1.375]])
with self.assertRaises(ValueError):
self._call_function_under_test(nodes, point)
def test_to_linear(self):
nodes = np.asfortranarray([[0.0, 1.0, 2.0], [0.0, 2.0, 4.0]])
result = self._call_function_under_test(nodes)
expected = np.asfortranarray([[0.0, 2.0], [0.0, 4.0]])
self.assertEqual(result, expected)
def test_quadratic(self):
s = 0.5
nodes = np.asfortranarray([[0.0, 0.5, 1.0], [0.0, 1.0, 0.0]])
tangent_vec = self._get_tangent_vec(s, nodes)
result = self._call_function_under_test(nodes, tangent_vec, s)
self.assertEqual(result, -4.0)
def test_outside_right(self):
# Newton's method pushes the value slightly to the right of ``1.0``.
nodes = np.asfortranarray([[0.0, 1.0, 2.0], [0.0, 1.0, 0.0]])
point = np.asfortranarray([[2.0], [0.0]])
result = self._call_function_under_test(nodes, point)
self.assertEqual(result, 1.0)
def test_linear(self):
nodes = np.asfortranarray([[0.0, 3.0], [0.0, 4.0]])
length = self._call_function_under_test(nodes)
self.assertEqual(length, 5.0)
def test_no_match(self):
nodes = np.asfortranarray([[0.0, 0.5, 1.0], [0.0, 1.0, 0.0]])
point = np.asfortranarray([[0.5], [2.0]])
self.assertIsNone(self._call_function_under_test(nodes, point))
def test_quadratic(self):
nodes = np.asfortranarray([[0.0, 2.0, 1.0], [0.0, 3.0, 6.0]])
size = self._call_function_under_test(nodes, 0.5)
self.assertEqual(size, 3.25)
def test_it(self):
nodes = np.asfortranarray([[0.0, 3.0], [1.0, 5.0]])
result = self._call_function_under_test(nodes, 0.25, 0.75)
self.assertEqual(result, np.asfortranarray([[2.25], [4.0]]))
def test_binomial_roundoff(self):
s_vals = np.asfortranarray([0.5])
degree = 55
nodes = np.eye(degree + 1, order="F")
expected = np.asfortranarray([
1.0,
55.0,
1485.0,
26235.0,
341055.0,
3478761.0,
28989675.0,
202927725.0,
1217566350.0,
6358402050.0,
29248649430.0,
119653565850.0,
438729741450.0,
1451182990950.0,
4353548972850.0,
11899700525790.0,
29749251314475.0,
68248282427325.0,
144079707346575.0,
280576272201225.0,
505037289962205.0,
841728816603675.0,
1300853625660225.0,
1866442158555975.0,
2488589544741300.0,
3085851035479212.0,
3560597348629860.0 - 0.5,
3824345300380220.0 - 0.5,
3824345300380220.0 - 0.5,
3560597348629860.0 - 0.5,
3085851035479212.0 - 0.5,
2488589544741300.0 - 0.5,
1866442158555974.0 + 0.5,
1300853625660225.0 - 0.5**2,
841728816603675.0 - 0.5**3,
505037289962205.0 - 0.5**4,
280576272201225.0 - 0.5**4,
144079707346575.0 - 0.5**5,
68248282427325.0 - 0.5**6,
29749251314475.0 - 0.5**7,
11899700525790.0 - 0.5**8,
4353548972850.0 - 3 * 0.5**11,
1451182990950.0 - 0.5**11,
438729741450.0 - 3 * 0.5**14,
119653565850.0 - 3 * 0.5**16,
29248649430.0 - 3 * 0.5**18,
6358402050.0 - 3 * 0.5**20,
1217566350.0 - 0.5**21,
202927725.0 - 3 * 0.5**25,
28989675.0 - 0.5**26,
3478761.0 - 0.5**29,
341055.0 - 3 * 0.5**34,
26235.0 - 0.5**36,
1485.0 - 0.5**40,
55.0 - 5 * 0.5**47,
1.0,
], )
evaluated = self._call_function_under_test(nodes, s_vals)
binomial_coefficients = evaluated.flatten() * 2.0**degree
self.assertEqual(expected, binomial_coefficients)
def test_degree_zero(self):
nodes = np.asfortranarray([[0.0], [0.0]])
length = self._call_function_under_test(nodes)
self.assertEqual(length, 0.0)
def test_quadratic(self):
nodes = np.asfortranarray([[0.0, 4.0, 7.0], [1.0, 6.0, 3.0]])
expected_l = np.asfortranarray([[0.0, 2.0, 3.75], [1.0, 3.5, 4.0]])
expected_r = np.asfortranarray([[3.75, 5.5, 7.0], [4.0, 4.5, 3.0]])
self._helper(nodes, expected_l, expected_r)
def test_linear(self):
nodes = np.asfortranarray([[0.0, 3.0], [0.0, -4.0]])
size = self._call_function_under_test(nodes, 0.25)
self.assertEqual(size, 0.25 * 5.0)