forked from arvindks/TensorCUR
/
testid.py
315 lines (219 loc) · 8.15 KB
/
testid.py
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
from core import *
from lowrank import *
import numpy as np
from sktensor import dtensor, cp_als, khatrirao
from decomp import *
from numpy.linalg import norm
import matplotlib
matplotlib.rcParams['xtick.labelsize'] = 15.
matplotlib.rcParams['ytick.labelsize'] = 15.
np.random.seed(223)
def ten_id(A, r, method = 'svd'):
rank = (r,r,r)
A = dtensor(A)
Amodes = matricize(A)
if method == 'svd':
T = hosvd(A, rank, method = 'svd')
elif method == 'randsvd':
T = hosvd(A, rank, method = 'randsvd')
elif method == 'rid':
#Tensor ID
T = hoid(A, rank, method = 'rid')
elif method == 'pqr':
#Tensor ID
T = hoid(A, rank, method = 'qr')
elif method == 'id':
#Tensor ID
T = hoid(A, rank, method = 'rrqr')
elif method == 'stid':
T,_ = sthoid(A, rank, method = 'rrqr')
else:
raise NotImplementedError
#Tmodes = T.matricize()
#err = [np.linalg.norm(tm-am)/np.linalg.norm(am) for am,tm in zip(Amodes,Tmodes)]
am = A.unfold(0)
tm = T.G.ttm(T.U).unfold(0)
err = norm(tm-am)/norm(am)
return (err, T.I) if method == 'id' else err
def lowrank_to_id(A, H, rank, method = 'deim'):
Amodes = matricize(A)
T, modeerr = tensor_to_id(A, H, rank, method = method)
#Tmodes = T.matricize()
#err = [np.linalg.norm(tm-am)/np.linalg.norm(am) for am,tm in zip(Amodes,Tmodes)]
am = A.unfold(0)
tm = T.G.ttm(T.U).unfold(0)
err = norm(tm-am)/norm(am)
return err, modeerr
def leverage_accuracy(A, H, maxr, ns = 10):
#Compute right singular vectors
v = []
Amodes = matricize(A)
for d in range(A.ndim):
_, _, vh = np.linalg.svd(Amodes[d], full_matrices = False)
v.append(vh[:ns,:].T)
lev_mode_err = np.zeros((maxr,3), dtype = 'd')
err_lev = np.zeros((maxr,), dtype = 'd')
#Compute accuracy
for r in np.arange(maxr):
clst = []
for d, mode in zip(range(A.ndim), Amodes):
q, fact = leverage_sampling(v[d], r+1)
clst.append(mode[:,q])
lev_mode_err[r,d] = fact
cinv = [np.linalg.pinv(c) for c in clst]
T = Tucker(G = A.ttm(cinv), U = clst);
am = A.unfold(0)
tm = T.G.ttm(T.U).unfold(0)
err_lev[r] = norm(tm-am)/norm(am)
#Tmodes = T.matricize();
#err = [np.linalg.norm(tm-am)/np.linalg.norm(am) for am,tm in zip(Amodes,Tmodes)]
#err_lev[r] = np.max(np.array(err))
return err_lev, lev_mode_err
def test1(A, maxr = 10, fname = 'hilbert'):
err_s = np.zeros((maxr,), dtype = 'd')
err_r = np.zeros((maxr,), dtype = 'd')
err_p = np.zeros((maxr,), dtype = 'd')
err_i = np.zeros((maxr,), dtype = 'd')
err_st = np.zeros((maxr,), dtype = 'd')
for r in np.arange(maxr):
err_s[r] = ten_id(A, r = r+1, method = 'svd')
err_r[r] = ten_id(A, r = r+1, method = 'randsvd')
err_p[r] = ten_id(A, r = r+1, method = 'pqr')
err_i[r], _ = ten_id(A, r = r+1, method = 'id')
err_st[r] = ten_id(A, r = r+1, method = 'stid')
plt.figure()
plt.semilogy(np.arange(maxr)+1, err_s, 'k-', linewidth = 2.)
plt.semilogy(np.arange(maxr)+1, err_r, 'g-', linewidth = 2.)
plt.semilogy(np.arange(maxr)+1, err_i, 'r--', linewidth = 2.)
plt.semilogy(np.arange(maxr)+1, err_p, 'c.-', linewidth = 2.)
plt.semilogy(np.arange(maxr)+1, err_st, 'm-', linewidth = 2.)
plt.legend(('HOSVD', 'HORID', 'HOID - RRQR', 'HOID - PQR', 'STHOID'))
plt.xlabel('Rank [r]', fontsize = 18.)
plt.ylabel('rel. err.' , fontsize = 18.)
plt.title('Relative Error', fontsize = 24)
plt.savefig('figs/hoid_' + fname + '.png')
return
def test2(A, maxr = 10, fname = 'hilbert', ns = 10):
A = dtensor(A)
Amodes = matricize(A)
err_deim = np.zeros((maxr,), dtype = 'd')
err_dime = np.zeros((maxr,), dtype = 'd')
err_rrqr = np.zeros((maxr,), dtype = 'd')
deim_mode_err = np.zeros((maxr,3), dtype = 'd')
dime_mode_err = np.zeros((maxr,3), dtype = 'd')
rrqr_mode_err = np.zeros((maxr,3), dtype = 'd')
for r in np.arange(maxr):
#Approximate the matrix using HOSVD
rank = (r+1,r+1,r+1)
H = hosvd(A, rank, method = 'randsvd')
err_deim[r], mode = lowrank_to_id(A, H, rank, method = 'deim')
deim_mode_err[r,:] = mode
err_dime[r], mode = lowrank_to_id(A, H, rank, method = 'dime')
dime_mode_err[r,:] = mode
err_rrqr[r], mode = lowrank_to_id(A, H, rank, method = 'rrqr')
rrqr_mode_err[r,:] = mode
err_lev, lev_mode_err = leverage_accuracy(A, H, maxr, ns = ns)
plt.figure()
plt.semilogy(np.arange(maxr) + 1, np.max(deim_mode_err,axis=1) , \
'k-', linewidth = 2., label = r'DEIM')
plt.semilogy(np.arange(maxr) + 1, np.max(dime_mode_err,axis=1) , \
'c-', linewidth = 2., label = r'PQR')
plt.semilogy(np.arange(maxr) + 1, np.max(rrqr_mode_err,axis=1) , \
'r--', linewidth = 2., label = r'RRQR')
plt.xlabel('Rank [r]', fontsize = 18.)
plt.ylabel(r'max. $||(P^*V)^{-1}||_F$' , fontsize = 18.)
plt.title('Error constants', fontsize = 24)
plt.legend(loc = 4)
plt.savefig('figs/deim_err_' + fname + '.png')
plt.figure()
plt.semilogy(np.arange(maxr) + 1, lev_mode_err, linewidth = 2.)
plt.xlabel('Rank [r]', fontsize = 18.)
plt.ylabel(r'$||(P^*V)^{-1}||_F$' , fontsize = 18.)
plt.legend(('Mode 1', 'Mode 2', 'Mode 3'))
plt.title('Error constants - Leverage scores ', fontsize = 20)
plt.savefig('figs/lev_err_' + fname + '.png')
plt.figure()
plt.semilogy(np.arange(maxr)+1, err_deim, 'k-', linewidth = 3.)
plt.semilogy(np.arange(maxr)+1, err_dime, 'c.-', linewidth = 2.)
plt.semilogy(np.arange(maxr)+1, err_rrqr, 'r--', linewidth = 2.)
plt.semilogy(np.arange(maxr)+1, err_lev, 'b-', linewidth = 2.)
plt.legend(('DEIM', 'PQR', 'RRQR', 'Lev'), loc = 3)
plt.xlabel('Rank [r]', fontsize = 18.)
plt.ylabel('rel. err.' , fontsize = 18.)
plt.title('Relative Error', fontsize = 24)
plt.savefig('figs/deim_' + fname + '.png')
return
def test3(A, maxr = 10, fname = 'hilbert', ns = 10):
A = dtensor(A)
Amodes = matricize(A)
H = hosvd(A, rank = A.shape, method = 'svd')
err_lev, lev_mode_err = leverage_accuracy(A, H, maxr, ns = ns)
plt.figure()
plt.semilogy(np.arange(maxr) + 1, lev_mode_err, linewidth = 2.)
plt.xlabel('Rank [r]', fontsize = 18.)
plt.ylabel(r'$||(P^*V)^{-1}||_F$' , fontsize = 18.)
plt.legend(('Mode 1', 'Mode 2', 'Mode 3'))
plt.title('Error constants - Leverage scores ', fontsize = 20)
plt.savefig('figs/lev_err_' + fname + '.png')
return
def generate_tensor(n = 20, opt = 0):
mfact = 2. if opt == 0 else 1000.
e1 = np.arange(10) + 1; e2 = np.arange(10,n) + 1;
fact = np.concatenate((mfact/e1,1./e2))
from scipy.sparse import rand
u = rand(n, n, density = 0.1).todense()
v = rand(n, n, density = 0.1).todense()
w = rand(n, n, density = 0.1).todense()
U = [u, v, w]
G = np.zeros((n,n,n), dtype = 'd')
for k in range(n): G[k,k,k] = fact[k]
T = Tucker(G = G, U = U)
return T
def vis_ind(A, fname = 'hilbert'):
#Visualize indices
_, ind = ten_id(A, r = 10, method = 'id')
plotindlst(dtensor(A), ind)
plt.savefig('figs/indlst' + fname + '.png')
return
def example1(n = 20, visualize = False):
#Generate tensor
arr = np.arange(n)+1
x, y, z = np.meshgrid(arr, arr, arr)
A = 1./np.sqrt(x**2. + y**2. + z**2.)
import matplotlib.pyplot as plt
plt.close('all')
#Plot error using HOSVD, HORSVD, HOID
test1(A, maxr = 8, fname = 'hilbert')
#Plot Error using DEIM and DIME and leverage score
test2(A, maxr = 8, fname = 'hilbert', ns = -1)
if visualize: vis_ind(A, fname = 'hilbert')
return
def example2(n = 20, opt = 1, ns = 10, visualize = False):
#Generate Tucker factorization
T = generate_tensor(n = n, opt = 1)
modes = T.matricize(method = 'kron')
#Generate full tensor
A = dtensor(np.reshape(np.array(modes[0]),(n,n,n)))
#Plot error using HOSVD, HORSVD, HOID
test1(A, maxr = 15, fname = 'sparse')
#Plot Error using DEIM and DIME and leverage score
test2(A, maxr = 15, fname = 'sparse', ns = ns)
if visualize: vis_ind(A, fname = 'sparse')
return
def example2b(n = 20, opt = 1):
#Generate Tucker factorization
T = generate_tensor(n = n, opt = 1)
modes = T.matricize()
#Generate full tensor
A = dtensor(np.reshape(np.array(modes[0]),(n,n,n)))
#Plot Error using DEIM and DIME and leverage score
test3(A, maxr = 15, fname = 'sparse_10', ns = 15)
test3(A, maxr = 15, fname = 'sparse_all', ns = -1)
return
if __name__ == '__main__':
import matplotlib.pyplot as plt
plt.close('all')
example1(n = 50, visualize = False)
#example2(n = 50, opt = 1, ns = -1)
#example2b(n = 50, opt = 1)
plt.show()