def test_sparse_rand():
A = sps.rand(10000, 30000, 0.001)
Ad = A.todense()
start_time = time.time()
rand_svd(A, 200)
print "Sparse time: ", time.time() - start_time
start_time = time.time()
rand_svd(Ad, 200)
print "Dense time: ", time.time() - start_time
def test_sparse_rand():
A = sps.rand(10000, 30000, 0.001)
Ad = A.todense()
start_time = time.time()
rand_svd(A, 200)
print "Sparse time: ", time.time() - start_time
start_time = time.time()
rand_svd(Ad, 200)
print "Dense time: ", time.time() - start_time
def time_batches():
A = np.ones((10000, 10000))
start_time = time.time()
rand_svd(A, k=200)
print "Large: ", time.time() - start_time
B = np.ones((1000, 10000))
start_time =time.time()
rand_svd(B, k=200)
print "Small: ", time.time() - start_time
start_time = time.time()
np.linalg.svd(B)
print "Exact: ", time.time() - start_time
def time_batches():
A = np.ones((10000, 10000))
start_time = time.time()
rand_svd(A, k=200)
print "Large: ", time.time() - start_time
B = np.ones((1000, 10000))
start_time = time.time()
rand_svd(B, k=200)
print "Small: ", time.time() - start_time
start_time = time.time()
np.linalg.svd(B)
print "Exact: ", time.time() - start_time
def _sparse_rand_sketch(self, mat_b):
print "In sparse rand sketch"
mat_u, vec_sigma, mat_vt = rand_svd(mat_b, self.l, raw=True)
squared_sv_center = vec_sigma[self.del_ind] ** 2
sigma_tilde = list(vec_sigma[:self.alpha_ind]) + [(0.0 if d < 0.0 else math.sqrt(d)) for d in (vec_sigma ** 2 - squared_sv_center)[self.alpha_ind:]]
# saves us from having to construct a diagonal matrix
new_mat_b = (mat_vt.T * np.array(sigma_tilde)).T
return sps.vstack((sps.lil_matrix(new_mat_b), sps.lil_matrix((self.b_size, self.m))), format='lil')
def _rand_svd_sketch(self, mat_b):
# does computation in place
# works for dense mat_b
mat_u, vec_sigma, mat_vt = rand_svd(mat_b, self.l, raw=True)
squared_sv_center = vec_sigma[self.del_ind] ** 2
# below can be done in numpy for sure
#trunc_vec = vec_sigma[self.alpha_ind:]
#trunc_vec = trunc_vec **2 - squared_sv_center
#trunc_vec[trunc_vec < 0] = 0
#np.sqrt(trunc_vec, out=trunc_vec)
sigma_tilde = list(vec_sigma[:self.alpha_ind]) + [(0.0 if d < 0.0 else math.sqrt(d)) for d in (vec_sigma ** 2 - squared_sv_center)[self.alpha_ind:]]
mat_b[:self.l, :] = (mat_vt.T * np.array(sigma_tilde)).T
mat_b[self.l:, :] = np.zeros((self.b_size, self.m))
def _rand_svd_sketch(self, mat_b):
# use fbpca rand_svd (PCA) function to approximate PCA
# only want first l values,
# do we care about block size for power iteration method?
mat_u, vec_sigma, mat_vt = rand_svd(mat_b, self.l, raw=True)
# need to return an (l + b) X ncols matrix, so add b rows of zero to result
extra_rows = self.b_size
vec_sigma = np.hstack((vec_sigma, np.zeros(extra_rows)))
mat_vt = np.vstack((mat_vt, np.zeros((extra_rows, self.m))))
squared_sv_center = vec_sigma[self.l-1] ** 2
if self.track_del:
self.delta = self.delta + squared_sv_center
sigma_tilda = [(0.0 if d < 0.0 else math.sqrt(d)) for d in (vec_sigma ** 2 - squared_sv_center)]
return np.dot(np.diagflat(sigma_tilda), mat_vt)
def _old_rand_svd_sketch(self, mat_b):
def old_svd():
if (self.l + self.b_size > self.m):
# then vec_sigma, mat_vt will be m, m X m respectively, we need to make them larger
extra_rows = self.l + self.b_size - self.m
vec_sigma = np.hstack((vec_sigma, np.zeros(extra_rows)))
mat_vt = np.vstack((mat_vt, np.zeros((extra_rows, self.m))))
# obtain squared singular value for threshold
squared_sv_center = vec_sigma[self.del_ind] ** 2
# update sigma to shrink the row norms, only subtract from alpha_ind to end of vector
sigma_tilde = list(vec_sigma[:self.alpha_ind]) + [(0.0 if d < 0.0 else math.sqrt(d)) for d in (vec_sigma ** 2 - squared_sv_center)[self.alpha_ind:]]
# update matrix B where at least half rows are all zero
mat_b[:] = np.dot(np.diagflat(sigma_tilde), mat_vt)
# use fbpca rand_svd (PCA) function to approximate PCA
# do we care about block size for power iteration method?
mat_u, vec_sigma, mat_vt = rand_svd(mat_b, self.l, raw=True)
# need to return an (l + b) X ncols matrix, so add b rows of zero to result
extra_rows = self.b_size
vec_sigma = np.hstack((vec_sigma, np.zeros(extra_rows)))
mat_vt = np.vstack((mat_vt, np.zeros((extra_rows, self.m))))
squared_sv_center = vec_sigma[self.del_ind] ** 2
sigma_tilde = list(vec_sigma[:self.alpha_ind]) + [(0.0 if d < 0.0 else math.sqrt(d)) for d in (vec_sigma ** 2 - squared_sv_center)[self.alpha_ind:]]
return np.dot(np.diagflat(sigma_tilde), mat_vt)
