test_mdptoolbox.py 14.2 KB
Newer Older
Steven Cordwell's avatar
Steven Cordwell committed
1
2
3
4
5
6
7
# -*- coding: utf-8 -*-
"""
Created on Sun May 27 23:16:57 2012

@author: -
"""

Steven Cordwell's avatar
Steven Cordwell committed
8
from mdp import check, checkSquareStochastic, exampleForest, exampleRand, MDP
Steven Cordwell's avatar
Steven Cordwell committed
9
10
from mdp import PolicyIteration, QLearning, RelativeValueIteration
from mdp import ValueIteration, ValueIterationGS
11

Steven Cordwell's avatar
Steven Cordwell committed
12
13
14
15
from numpy import absolute, array, eye, matrix, zeros
from numpy.random import rand
from scipy.sparse import eye as speye
from scipy.sparse import csr_matrix as sparse
Steven Cordwell's avatar
Steven Cordwell committed
16
#from scipy.stats.distributions import poisson
Steven Cordwell's avatar
Steven Cordwell committed
17

Steven Cordwell's avatar
Steven Cordwell committed
18
19
STATES = 10
ACTIONS = 3
20
SMALLNUM = 10e-12
Steven Cordwell's avatar
Steven Cordwell committed
21

22
23
24
25
26
27
28
# Arrays
P = array([[[0.5, 0.5],[0.8, 0.2]],[[0, 1],[0.1, 0.9]]])
R = array([[5, 10], [-1, 2]])
Pf, Rf = exampleForest()
Pr, Rr = exampleRand(STATES, ACTIONS)
Prs, Rrs = exampleRand(STATES, ACTIONS, is_sparse=True)

Steven Cordwell's avatar
Steven Cordwell committed
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
# check: square, stochastic and non-negative ndarrays

def test_check_square_stochastic_nonnegative_array_1():
    P = zeros((ACTIONS, STATES, STATES))
    R = zeros((STATES, ACTIONS))
    for a in range(ACTIONS):
        P[a, :, :] = eye(STATES)
        R[:, a] = rand(STATES)
    assert (check(P, R) == None)

def test_check_square_stochastic_nonnegative_array_2():
    P = zeros((ACTIONS, STATES, STATES))
    R = rand(ACTIONS, STATES, STATES)
    for a in range(ACTIONS):
        P[a, :, :] = eye(STATES)
    assert (check(P, R) == None)

# check: P - square, stochastic and non-negative object arrays

def test_check_P_square_stochastic_nonnegative_object_array():
    P = zeros((ACTIONS, ), dtype=object)
    R = rand(STATES, ACTIONS)
    for a in range(ACTIONS):
        P[a] = eye(STATES)
    assert (check(P, R) == None)

def test_check_P_square_stochastic_nonnegative_object_matrix():
    P = zeros((ACTIONS, ), dtype=object)
    R = rand(STATES, ACTIONS)
    for a in range(ACTIONS):
        P[a] = matrix(eye(STATES))
    assert (check(P, R) == None)

def test_check_P_square_stochastic_nonnegative_object_sparse():
    P = zeros((ACTIONS, ), dtype=object)
    R = rand(STATES, ACTIONS)
    for a in range(ACTIONS):
        P[a] = speye(STATES, STATES).tocsr()
    assert (check(P, R) == None)

# check: R - square stochastic and non-negative sparse

def test_check_R_square_stochastic_nonnegative_sparse():
    P = zeros((ACTIONS, STATES, STATES))
    R = sparse(rand(STATES, ACTIONS))
    for a in range(ACTIONS):
        P[a, :, :] = eye(STATES)
    assert (check(P, R) == None)

# check: R - square, stochastic and non-negative object arrays

def test_check_R_square_stochastic_nonnegative_object_array():
    P = zeros((ACTIONS, STATES, STATES))
    R = zeros((ACTIONS, ), dtype=object)
    for a in range(ACTIONS):
        P[a, :, :] = eye(STATES)
        R[a] = rand(STATES, STATES)
    assert (check(P, R) == None)

def test_check_R_square_stochastic_nonnegative_object_matrix():
    P = zeros((ACTIONS, STATES, STATES))
    R = zeros((ACTIONS, ), dtype=object)
    for a in range(ACTIONS):
        P[a, :, :] = eye(STATES)
        R[a] = matrix(rand(STATES, STATES))
    assert (check(P, R) == None)

def test_check_R_square_stochastic_nonnegative_object_sparse():
    P = zeros((ACTIONS, STATES, STATES))
    R = zeros((ACTIONS, ), dtype=object)
    for a in range(ACTIONS):
        P[a, :, :] = eye(STATES)
        R[a] = sparse(rand(STATES, STATES))
    assert (check(P, R) == None)

# checkSquareStochastic: square, stochastic and non-negative

def test_checkSquareStochastic_square_stochastic_nonnegative_array():
    P = rand(STATES, STATES)
    for s in range(STATES):
        P[s, :] = P[s, :] / P[s, :].sum()
    assert checkSquareStochastic(P) == None

def test_checkSquareStochastic_square_stochastic_nonnegative_matrix():
    P = rand(STATES, STATES)
    for s in range(STATES):
        P[s, :] = P[s, :] / P[s, :].sum()
    P = matrix(P)
    assert checkSquareStochastic(P) == None

def test_checkSquareStochastic_square_stochastic_nonnegative_sparse():
    P = rand(STATES, STATES)
    for s in range(STATES):
        P[s, :] = P[s, :] / P[s, :].sum()
    P = sparse(P)
    assert checkSquareStochastic(P) == None

# checkSquareStochastic: eye

def test_checkSquareStochastic_eye_array():
    P = eye(STATES)
    assert checkSquareStochastic(P) == None

def test_checkSquareStochastic_eye_matrix():
    P = matrix(eye(STATES))
    assert checkSquareStochastic(P) == None

def test_checkSquareStochastic_eye_sparse():
    P = speye(STATES, STATES).tocsr()
    assert checkSquareStochastic(P) == None
Steven Cordwell's avatar
Steven Cordwell committed
139

Steven Cordwell's avatar
Steven Cordwell committed
140
141
# exampleForest

142
143
def test_exampleForest_P_shape():
    assert (Pf == array([[[0.1, 0.9, 0.0],
Steven Cordwell's avatar
Steven Cordwell committed
144
145
146
147
148
                         [0.1, 0.0, 0.9],
                         [0.1, 0.0, 0.9]],
                        [[1, 0, 0],
                         [1, 0, 0],
                         [1, 0, 0]]])).all()
149
150
151

def test_exampleForest_R_shape():
    assert (Rf == array([[0, 0],
Steven Cordwell's avatar
Steven Cordwell committed
152
153
154
                        [0, 1],
                        [4, 2]])).all()

Steven Cordwell's avatar
Steven Cordwell committed
155
156
157
def test_exampleForest_check():
    P, R = exampleForest(10, 5, 3, 0.2)
    assert check(P, R) == None
Steven Cordwell's avatar
Steven Cordwell committed
158
159

# exampleRand
Steven Cordwell's avatar
Steven Cordwell committed
160

161
def test_exampleRand_dense_P_shape():
162
    assert (Pr.shape == (ACTIONS, STATES, STATES))
163
164

def test_exampleRand_dense_R_shape():
165
    assert (Rr.shape == (ACTIONS, STATES, STATES))
Steven Cordwell's avatar
Steven Cordwell committed
166

Steven Cordwell's avatar
Steven Cordwell committed
167
def test_exampleRand_dense_check():
168
    assert check(Pr, Rr) == None
Steven Cordwell's avatar
Steven Cordwell committed
169

170
def test_exampleRand_sparse_P_shape():
171
    assert (Prs.shape == (ACTIONS, ))
172
173

def test_exampleRand_sparse_R_shape():
174
    assert (Rrs.shape == (ACTIONS, ))
Steven Cordwell's avatar
Steven Cordwell committed
175

Steven Cordwell's avatar
Steven Cordwell committed
176
def test_exampleRand_sparse_check():
177
    assert check(Prs, Rrs) == None
Steven Cordwell's avatar
Steven Cordwell committed
178
179
180
181

# MDP

def test_MDP_P_R_1():
182
183
184
185
    P1 = zeros((2, ), dtype=object)
    P1[0] = matrix('0.5 0.5; 0.8 0.2')
    P1[1] = matrix('0 1; 0.1 0.9')
    R1 = matrix('5 10; -1 2')
186
    a = MDP(P, R, 0.9, 0.01, 1)
Steven Cordwell's avatar
Steven Cordwell committed
187
188
189
190
191
192
193
194
    assert a.P.dtype == P1.dtype
    assert a.R.dtype == R1.dtype
    for kk in range(2):
        assert (a.P[kk] == P1[kk]).all()
    assert (a.R == R1).all()

def test_MDP_P_R_2():
    R = array([[[5, 10], [-1, 2]], [[1, 2], [3, 4]]])
195
196
197
198
    P1 = zeros((2, ), dtype=object)
    P1[0] = matrix('0.5 0.5; 0.8 0.2')
    P1[1] = matrix('0 1; 0.1 0.9')
    R1 = matrix('7.5 2; -0.4 3.9')
199
    a = MDP(P, R, 0.9, 0.01, 1)
200
201
    assert type(a.P) == type(P1)
    assert type(a.R) == type(R1)
Steven Cordwell's avatar
Steven Cordwell committed
202
203
204
205
    assert a.P.dtype == P1.dtype
    assert a.R.dtype == R1.dtype
    for kk in range(2):
        assert (a.P[kk] == P1[kk]).all()
206
    assert (absolute(a.R - R1) < SMALLNUM).all()
Steven Cordwell's avatar
Steven Cordwell committed
207
208
209
210

def test_MDP_P_R_3():
    P = array([[[0.6116, 0.3884],[0, 1]],[[0.6674, 0.3326],[0, 1]]])
    R = array([[[-0.2433, 0.7073],[0, 0.1871]],[[-0.0069, 0.6433],[0, 0.2898]]])
211
    PR = matrix('0.12591304 0.20935652; 0.1871 0.2898')
212
    a = MDP(P, R, 0.9, 0.01, 1)
213
    assert (absolute(a.R - PR) < SMALLNUM).all()
Steven Cordwell's avatar
Steven Cordwell committed
214

Steven Cordwell's avatar
Steven Cordwell committed
215
# PolicyIteration
Steven Cordwell's avatar
Steven Cordwell committed
216

217
218
def test_PolicyIteration_init_policy0():
    a = PolicyIteration(P, R, 0.9)
219
220
221
222
    p = matrix('1; 1')
    assert (a.policy == p).all()

def test_PolicyIteration_init_policy0_exampleForest():
223
    a = PolicyIteration(Pf, Rf, 0.9)
224
225
226
227
    p = matrix('0; 1; 0')
    assert (a.policy == p).all()

def test_PolicyIteration_computePpolicyPRpolicy_exampleForest():
228
    a = PolicyIteration(Pf, Rf, 0.9)
229
230
231
232
233
234
235
236
237
238
    P1 = matrix('0.1 0.9 0; 1 0 0; 0.1 0 0.9')
    R1 = matrix('0; 1; 4')
    Ppolicy, Rpolicy = a.computePpolicyPRpolicy()
    assert (absolute(Ppolicy - P1) < SMALLNUM).all()
    assert (absolute(Rpolicy - R1) < SMALLNUM).all()

def test_PolicyIteration_evalPolicyIterative_exampleForest():
    v0 = matrix('0; 0; 0')
    v1 = matrix('4.47504640074458; 5.02753258879703; 23.17234211944304')
    p = matrix('0; 1; 0')
239
    a = PolicyIteration(Pf, Rf, 0.9)
240
    assert (absolute(a.V - v0) < SMALLNUM).all()
241
    a.evalPolicyIterative()
242
    assert (absolute(a.V - v1) < SMALLNUM).all()
243
244
245
246
247
    assert (a.policy == p).all()

def test_PolicyIteration_evalPolicyIterative_bellmanOperator_exampleForest():
    v = matrix('4.47504640074458; 5.02753258879703; 23.17234211944304')
    p = matrix('0; 0; 0')
248
    a = PolicyIteration(Pf, Rf, 0.9)
249
250
251
    a.evalPolicyIterative()
    policy, value = a.bellmanOperator()
    assert (policy == p).all()
252
    assert (absolute(a.V - v) < SMALLNUM).all()
253
254

def test_PolicyIteration_iterative_exampleForest():
255
    a = PolicyIteration(Pf, Rf, 0.9, eval_type=1)
256
    v = matrix('26.2439058351861 29.4839058351861 33.4839058351861')
257
258
259
    p = matrix('0 0 0')
    itr = 2
    a.iterate()
260
    assert (absolute(array(a.V) - v) < SMALLNUM).all()
261
262
263
264
265
    assert (array(a.policy) == p).all()
    assert a.iter == itr

def test_PolicyIteration_evalPolicyMatrix_exampleForest():
    v_pol = matrix('4.47513812154696; 5.02762430939227; 23.17243384704857')
266
    a = PolicyIteration(Pf, Rf, 0.9)
267
    a.evalPolicyMatrix()
268
    assert (absolute(a.V - v_pol) < SMALLNUM).all()
269
270

def test_PolicyIteration_matrix_exampleForest():
271
    a = PolicyIteration(Pf, Rf, 0.9)
272
    v = matrix('26.2440000000000 29.4840000000000 33.4840000000000')
273
274
275
    p = matrix('0 0 0')
    itr = 2
    a.iterate()
276
    assert (absolute(array(a.V) - v) < SMALLNUM).all()
277
278
    assert (array(a.policy) == p).all()
    assert a.iter == itr
Steven Cordwell's avatar
Steven Cordwell committed
279

280
281
# QLearning
def test_QLearning_exampleForest():
Steven Cordwell's avatar
Steven Cordwell committed
282
283
284
285
286
287
288
289
290
291
292
293
    a = QLearning(Pf, Rf, 0.9)
    q = matrix('26.1841860892231 18.6273657021260; ' \
               '29.5880960371007 18.5901207622881; '\
               '33.3526406657418 25.2621054631519')
    v = matrix('26.1841860892231 29.5880960371007 33.3526406657418')
    p = matrix('0 0 0')
    itr = 0
    a.iterate()
    assert (absolute(a.Q - q) < SMALLNUM).all()
    assert (absolute(array(a.V) - v) < SMALLNUM).all()
    assert (array(a.policy) == p).all()
    assert a.iter == itr
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325

# RelativeValueIteration

def test_RelativeValueIteration_exampleForest():
    a = RelativeValueIteration(Pf, Rf)
    itr = 4
    p = matrix('0 0 0')
    v = matrix('-4.360000000000000 -0.760000000000000 3.240000000000000')
    a.iterate()
    assert (array(a.policy) == p).all()
    assert a.iter == itr
    assert (absolute(array(a.V) - v) < SMALLNUM).all()

# ValueIteration

def test_ValueIteration_boundIter():
    inst = ValueIteration(P, R, 0.9, 0.01)
    assert (inst.max_iter == 28)

def test_ValueIteration_iterate():
    inst = ValueIteration(P, R, 0.9, 0.01)
    inst.iterate()
    assert (inst.V == (40.048625392716822,  33.65371175967546))
    assert (inst.policy == (1, 0))
    assert (inst.iter == 26)

def test_ValueIteration_exampleForest():
    a = ValueIteration(Pf, Rf, 0.96)
    a.iterate()
    assert (a.policy == array([0, 0, 0])).all()
    assert a.iter == 4

Steven Cordwell's avatar
Steven Cordwell committed
326
327
# ValueIterationGS

328
329
330
331
332
def test_ValueIterationGS_boundIter_exampleForest():
    a = ValueIterationGS(Pf, Rf, 0.9)
    itr = 39
    assert (a.max_iter == itr)

Steven Cordwell's avatar
Steven Cordwell committed
333
334
335
def test_ValueIterationGS_exampleForest():
    a = ValueIterationGS(Pf, Rf, 0.9)
    p = matrix('0 0 0')
336
    v = matrix('25.5833879767579 28.8306546355469 32.8306546355469')
Steven Cordwell's avatar
Steven Cordwell committed
337
338
339
340
    itr = 33
    a.iterate()
    assert (array(a.policy) == p).all()
    assert a.iter == itr
341
    assert (absolute(array(a.V) - v) < SMALLNUM).all()
342

Steven Cordwell's avatar
Steven Cordwell committed
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
#def test_JacksCarRental():
#    S = 21 ** 2
#    A = 11
#    P = zeros((A, S, S))
#    R = zeros((A, S, S))
#    for a in range(A):
#        for s in range(21):
#            for s1 in range(21):
#                c1s = int(s / 21)
#                c2s = s - c1s * 21
#                c1s1 = int(s1 / 21)
#                c2s1 = s - c1s * 21
#                cs = c1s + c2s
#                cs1 = c1s1 + c2s1
#                netmove = 5 - a
#                if (s1 < s):
#                    pass
#                else:
#                    pass
#                P[a, s, s1] = 1
#                R[a, s, s1] = 10 * (cs - cs1) - 2 * abs(a)
#    
#    inst = PolicyIteration(P, R, 0.9)
#    inst.iterate()
#    #assert (inst.policy == )
#
#def test_JacksCarRental2():
#    pass
#
#def test_GamblersProblem():
#    inst = ValueIteration()
#    inst.iterate()
#    #assert (inst.policy == )
Steven Cordwell's avatar
Steven Cordwell committed
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394

# checkSquareStochastic: not square, stochastic and non-negative

#@raises(ValueError(mdperr["mat_square"]))
#def test_checkSquareStochastic_notsquare_stochastic_nonnegative_array():
#    P = eye(STATES, STATES + 1)
#    inst.checkSquareStochastic(P)
#
#@raises(ValueError(mdperr["mat_square"]))
#def test_checkSquareStochastic_notsquare_stochastic_nonnegative_matrix():
#    P = matrix(eye(STATES, STATES + 1))
#    inst.checkSquareStochastic(P)
#
#@raises(ValueError(mdperr["mat_square"]))
#def test_checkSquareStochastic_notsquare_stochastic_nonnegative_sparse():
#    P = speye(STATES, STATES + 1).tocsr()
#    inst.checkSquareStochastic(P)

# checkSquareStochastic: square, not stochastic and non-negative
Steven Cordwell's avatar
Steven Cordwell committed
395
    
Steven Cordwell's avatar
Steven Cordwell committed
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
#def test_checkSquareStochastic_square_notstochastic_nonnegative_array():
#    P = eye(STATES)
#    i = randint(STATES)
#    j = randint(STATES)
#    P[i, j] = P[i, j] + 1
#    try:
#        inst.checkSquareStochastic(P)
#    except ValueError(mdperr["mat_stoch"]):
#        pass
#
#def test_checkSquareStochastic_square_notstochastic_nonnegative_matrix():
#    P = matrix(eye(STATES))
#    i = randint(STATES)
#    j = randint(STATES)
#    P[i, j] = P[i, j] + 1
#    try:
#        inst.checkSquareStochastic(P)
#    except ValueError(mdperr["mat_stoch"]):
#        pass
#
#def test_checkSquareStochastic_square_notstochastic_nonnegative_sparse():
#    P = speye(STATES, STATES).tolil()
#    i = randint(STATES)
#    j = randint(STATES)
#    P[i, j] = P[i, j] + 1
#    P = P.tocsr()
#    try:
#        inst.checkSquareStochastic(P)
#    except ValueError(mdperr["mat_stoch"]):
#        pass

# checkSquareStochastic: square, stochastic and negative

#def test_checkSquareStochastic_square_stochastic_negative_array():
#    P = eye(STATES, STATES)
#    i = randint(STATES)
#    j = randint(STATES)
#    while j == i:
#        j = randint(STATES)
#    P[i, i] = -1
#    P[i, j] = 1
#    try:
#        inst.checkSquareStochastic(P)
#    except ValueError(mdperr["mat_nonneg"]):
#        pass
#
#def test_checkSquareStochastic_square_stochastic_negative_matrix():
#    P = matrix(eye(STATES, STATES))
#    i = randint(STATES)
#    j = randint(STATES)
#    while j == i:
#        j = randint(STATES)
#    P[i, i] = -1
#    P[i, j] = 1
#    try:
#        inst.checkSquareStochastic(P)
#    except ValueError(mdperr["mat_nonneg"]):
#        pass
#
#def test_checkSquareStochastic_square_stochastic_negative_sparse():
#    P = speye(STATES, STATES)
#    i = randint(STATES)
#    j = randint(STATES)
#    while j == i:
#        j = randint(STATES)
#    P[i, i] = -1
#    P[i, j] = 1
#    try:
#        inst.checkSquareStochastic(P)
#    except ValueError(mdperr["mat_nonneg"]):
#        pass

#def test_check_square_stochastic_array_Rtranspose():
#    P = array([eye(STATES), eye(STATES)])
#    R = array([ones(STATES), ones(STATES)])
#    assert inst.check(P, R) == (True, "R is wrong way")