def test_assign_1d(self):
b = np.random.randn(100)
sp_b = from_numpy(b)
#a[:] = b[:] copy entire array
a = np.random.randn(100)
region_a = np.s_[0:100]
region_b = np.s_[0:100]
sp_a = assign(from_numpy(a), region_a, sp_b[region_b]).glom()
a[region_a] = b[region_b]
Assert.all_eq(sp_a, a)
# a[0] = b[1] copy one value
a = np.random.randn(100)
region_a = np.s_[0]
region_b = np.s_[1]
sp_a = assign(from_numpy(a), region_a, sp_b[region_b]).glom()
a[region_a] = b[region_b]
Assert.all_eq(sp_a, a)
# a[0:10] = b[20:30] copy range of values
a = np.random.randn(100)
region_a = np.s_[0:10]
region_b = np.s_[20:30]
sp_a = assign(from_numpy(a), region_a, sp_b[region_b]).glom()
a[region_a] = b[region_b]
Assert.all_eq(sp_a, a)
# a[30:60] = b[:30] copy range of values, not starting from 0.
a = np.random.randn(100)
region_a = np.s_[0:10]
region_b = np.s_[20:30]
sp_a = assign(from_numpy(a), region_a, sp_b[region_b]).glom()
a[region_a] = b[region_b]
Assert.all_eq(sp_a, a)
def test_assign_1d(self):
b = np.random.randn(100)
sp_b = from_numpy(b)
#a[:] = b[:] copy entire array
a = np.random.randn(100)
region_a = np.s_[0:100]
region_b = np.s_[0:100]
sp_a = assign(from_numpy(a), region_a, sp_b[region_b]).glom()
a[region_a] = b[region_b]
Assert.all_eq(sp_a, a)
# a[0] = b[1] copy one value
a = np.random.randn(100)
region_a = np.s_[0]
region_b = np.s_[1]
sp_a = assign(from_numpy(a), region_a, sp_b[region_b]).glom()
a[region_a] = b[region_b]
Assert.all_eq(sp_a, a)
# a[0:10] = b[20:30] copy range of values
a = np.random.randn(100)
region_a = np.s_[0:10]
region_b = np.s_[20:30]
sp_a = assign(from_numpy(a), region_a, sp_b[region_b]).glom()
a[region_a] = b[region_b]
Assert.all_eq(sp_a, a)
# a[30:60] = b[:30] copy range of values, not starting from 0.
a = np.random.randn(100)
region_a = np.s_[0:10]
region_b = np.s_[20:30]
sp_a = assign(from_numpy(a), region_a, sp_b[region_b]).glom()
a[region_a] = b[region_b]
Assert.all_eq(sp_a, a)
def test_assign_array_like(self):
a = np.zeros((20, 10))
b = np.ones((10, ))
region = np.s_[10, ]
sp_a = assign(from_numpy(a), region, b).glom()
a[region] = b
Assert.all_eq(sp_a, a)
def test_assign_array_like(self): a = np.zeros((20, 10)) b = np.ones((10, )) region = np.s_[10, ] sp_a = assign(from_numpy(a), region, b).glom() a[region] = b Assert.all_eq(sp_a, a)
def test_assign_expr(self):
# Small matrix
a = np.random.randn(20, 10)
b = np.random.randn(10)
region_a = np.s_[10, ]
sp_a = assign(from_numpy(a), region_a, from_numpy(b)).glom()
a[region_a] = b
Assert.all_eq(sp_a, a)
# Larger matrix
a = np.random.randn(200, 100)
b = np.random.randn(100)
region_a = np.s_[50, ]
sp_a = assign(from_numpy(a), region_a, from_numpy(b)).glom()
a[region_a] = b
Assert.all_eq(sp_a, a)
# Worst case region
a = np.random.randn(200, 100)
b = np.random.randn(3, 50)
region_a = np.s_[99:102, 25:75]
sp_a = assign(from_numpy(a), region_a, from_numpy(b)).glom()
a[region_a] = b
Assert.all_eq(sp_a, a)
def test_assign_expr(self):
# Small matrix
a = np.random.randn(20, 10)
b = np.random.randn(10)
region_a = np.s_[10, ]
sp_a = assign(from_numpy(a), region_a, from_numpy(b)).glom()
a[region_a] = b
Assert.all_eq(sp_a, a)
# Larger matrix
a = np.random.randn(200, 100)
b = np.random.randn(100)
region_a = np.s_[50, ]
sp_a = assign(from_numpy(a), region_a, from_numpy(b)).glom()
a[region_a] = b
Assert.all_eq(sp_a, a)
# Worst case region
a = np.random.randn(200, 100)
b = np.random.randn(3, 50)
region_a = np.s_[99:102, 25:75]
sp_a = assign(from_numpy(a), region_a, from_numpy(b)).glom()
a[region_a] = b
Assert.all_eq(sp_a, a)
def als(A, la=0.065, alpha=40, implicit_feedback=False, num_features=20, num_iter=10, M=None):
'''
compute the factorization A = U M' using the alternating least-squares (ALS) method.
where `A` is the "ratings" matrix which maps from a user and item to a rating score,
`U` and `M` are the factor matrices, which represent user and item preferences.
Args:
A(Expr or DistArray): the rating matrix which maps from a user and item to a rating score.
la(float): the parameter of the als.
alpha(int): confidence parameter used on implicit feedback.
implicit_feedback(bool): whether using implicit_feedback method for als.
num_features(int): dimension of the feature space.
num_iter(int): max iteration to run.
'''
num_users = A.shape[0]
num_items = A.shape[1]
AT = expr.transpose(A)
avg_rating = expr.sum(A, axis=0) * 1.0 / expr.count_nonzero(A, axis=0)
M = expr.rand(num_items, num_features)
M = expr.assign(M, np.s_[:, 0], avg_rating.reshape((avg_rating.shape[0], 1)))
#A = expr.retile(A, tile_hint=util.calc_tile_hint(A, axis=0))
#AT = expr.retile(AT, tile_hint=util.calc_tile_hint(AT, axis=0))
for i in range(num_iter):
# Recomputing U
shape = (num_users, num_features)
U = expr.outer((A, M), (0, None), fn=_solve_U_or_M_mapper,
fn_kw={'la': la, 'alpha': alpha,
'implicit_feedback': implicit_feedback, 'shape': shape},
shape=shape, dtype=np.float)
# Recomputing M
shape = (num_items, num_features)
M = expr.outer((AT, U), (0, None), fn=_solve_U_or_M_mapper,
fn_kw={'la': la, 'alpha': alpha,
'implicit_feedback': implicit_feedback, 'shape': shape},
shape=shape, dtype=np.float)
return U, M
def simulate(ts_all, te_all, lamb_all, num_paths):
'''Range over a number of independent products.
:param ts_all: DistArray
Start dates for a series of swaptions.
:param te_all: DistArray
End dates for a series of swaptions.
:param lamb_all: DistArray
Parameter values for a series of swaptions.
:param num_paths: Int
Number of paths used in random walk.
:rtype: DistArray
'''
swaptions = []
i = 0
for ts_a, te, lamb in zip(ts_all, te_all, lamb_all):
for ts in ts_a:
#start = time()
print i
time_structure = arange(None, 0, ts + DELTA, DELTA)
maturity_structure = arange(None, 0, te, DELTA)
############# MODEL ###############
# Variance reduction technique - Antithetic Variates.
eps_tmp = randn(time_structure.shape[0] - 1, num_paths)
eps = concatenate(eps_tmp, -eps_tmp, 1)
# Forward LIBOR rates for the construction of the spot measure.
f_kk = zeros((time_structure.shape[0], 2*num_paths))
f_kk = assign(f_kk, np.s_[0, :], F_0)
# Plane kxN of simulated LIBOR rates.
f_kn = ones((maturity_structure.shape[0], 2*num_paths))*F_0
# Simulations of the plane f_kn for each time step.
for t in xrange(1, time_structure.shape[0]):
f_kn_new = f_kn[1:, :]*exp(lamb*mu(f_kn, lamb)*DELTA-0.5*lamb*lamb *
DELTA + lamb*eps[t - 1, :]*sqrt(DELTA))
f_kk = assign(f_kk, np.s_[t, :], f_kn_new[0])
f_kn = f_kn_new
############## PRODUCT ###############
# Value of zero coupon bonds.
zcb = ones((int((te-ts)/DELTA)+1, 2*num_paths))
f_kn_modified = 1 + DELTA*f_kn
for j in xrange(zcb.shape[0] - 1):
zcb = assign(zcb, np.s_[j + 1], zcb[j] / f_kn_modified[j])
# Swaption price at maturity.
last_row = zcb[zcb.shape[0] - 1, :].reshape((20, ))
swap_ts = maximum(1 - last_row - THETA*DELTA*expr.sum(zcb[1:], 0), 0)
# Spot measure used for discounting.
b_ts = ones((2*num_paths, ))
tmp = 1 + DELTA * f_kk
for j in xrange(int(ts/DELTA)):
b_ts *= tmp[j].reshape((20, ))
# Swaption price at time 0.
swaption = swap_ts/b_ts
# Save expected value in bps and std.
me = mean((swaption[0:num_paths] + swaption[num_paths:])/2) * 10000
st = std((swaption[0:num_paths] + swaption[num_paths:])/2)/sqrt(num_paths)*10000
swaptions.append([me.optimized().force(), st.optimized().force()])
#print time() - start
i += 1
return swaptions
def als(A,
la=0.065,
alpha=40,
implicit_feedback=False,
num_features=20,
num_iter=10,
M=None):
'''
compute the factorization A = U M' using the alternating least-squares (ALS) method.
where `A` is the "ratings" matrix which maps from a user and item to a rating score,
`U` and `M` are the factor matrices, which represent user and item preferences.
Args:
A(Expr or DistArray): the rating matrix which maps from a user and item to a rating score.
la(float): the parameter of the als.
alpha(int): confidence parameter used on implicit feedback.
implicit_feedback(bool): whether using implicit_feedback method for als.
num_features(int): dimension of the feature space.
num_iter(int): max iteration to run.
'''
num_users = A.shape[0]
num_items = A.shape[1]
AT = expr.transpose(A)
avg_rating = expr.sum(A, axis=0) * 1.0 / expr.count_nonzero(A, axis=0)
M = expr.rand(num_items, num_features)
M = expr.assign(M, np.s_[:, 0], avg_rating.reshape(
(avg_rating.shape[0], 1)))
#A = expr.retile(A, tile_hint=util.calc_tile_hint(A, axis=0))
#AT = expr.retile(AT, tile_hint=util.calc_tile_hint(AT, axis=0))
for i in range(num_iter):
# Recomputing U
shape = (num_users, num_features)
U = expr.outer(
(A, M), (0, None),
fn=_solve_U_or_M_mapper,
fn_kw={
'la': la,
'alpha': alpha,
'implicit_feedback': implicit_feedback,
'shape': shape
},
shape=shape,
dtype=np.float)
# Recomputing M
shape = (num_items, num_features)
M = expr.outer(
(AT, U), (0, None),
fn=_solve_U_or_M_mapper,
fn_kw={
'la': la,
'alpha': alpha,
'implicit_feedback': implicit_feedback,
'shape': shape
},
shape=shape,
dtype=np.float)
return U, M
def simulate(ts_all, te_all, lamb_all, num_paths):
"""Range over a number of independent products.
:param ts_all: DistArray
Start dates for a series of swaptions.
:param te_all: DistArray
End dates for a series of swaptions.
:param lamb_all: DistArray
Parameter values for a series of swaptions.
:param num_paths: Int
Number of paths used in random walk.
:rtype: DistArray
"""
swaptions = []
i = 0
for ts_a, te, lamb in zip(ts_all, te_all, lamb_all):
for ts in ts_a:
# start = time()
print i
time_structure = arange(None, 0, ts + DELTA, DELTA)
maturity_structure = arange(None, 0, te, DELTA)
############# MODEL ###############
# Variance reduction technique - Antithetic Variates.
eps_tmp = randn(time_structure.shape[0] - 1, num_paths)
eps = concatenate(eps_tmp, -eps_tmp, 1)
# Forward LIBOR rates for the construction of the spot measure.
f_kk = zeros((time_structure.shape[0], 2 * num_paths))
f_kk = assign(f_kk, np.s_[0, :], F_0)
# Plane kxN of simulated LIBOR rates.
f_kn = ones((maturity_structure.shape[0], 2 * num_paths)) * F_0
# Simulations of the plane f_kn for each time step.
for t in xrange(1, time_structure.shape[0]):
f_kn_new = f_kn[1:, :] * exp(
lamb * mu(f_kn, lamb) * DELTA - 0.5 * lamb * lamb * DELTA + lamb * eps[t - 1, :] * sqrt(DELTA)
)
f_kk = assign(f_kk, np.s_[t, :], f_kn_new[0])
f_kn = f_kn_new
############## PRODUCT ###############
# Value of zero coupon bonds.
zcb = ones((int((te - ts) / DELTA) + 1, 2 * num_paths))
f_kn_modified = 1 + DELTA * f_kn
for j in xrange(zcb.shape[0] - 1):
zcb = assign(zcb, np.s_[j + 1], zcb[j] / f_kn_modified[j])
# Swaption price at maturity.
last_row = zcb[zcb.shape[0] - 1, :].reshape((20,))
swap_ts = maximum(1 - last_row - THETA * DELTA * expr.sum(zcb[1:], 0), 0)
# Spot measure used for discounting.
b_ts = ones((2 * num_paths,))
tmp = 1 + DELTA * f_kk
for j in xrange(int(ts / DELTA)):
b_ts *= tmp[j].reshape((20,))
# Swaption price at time 0.
swaption = swap_ts / b_ts
# Save expected value in bps and std.
me = mean((swaption[0:num_paths] + swaption[num_paths:]) / 2) * 10000
st = std((swaption[0:num_paths] + swaption[num_paths:]) / 2) / sqrt(num_paths) * 10000
swaptions.append([me.optimized().force(), st.optimized().force()])
# print time() - start
i += 1
return swaptions
