def timing_op2_complex(self, ufunc, dtype=np.float64):
n_vec = 40000
max_bin_exp = 200
rg = np.random.default_rng(1)
op1 = rg.random([n_vec],
dtype=dtype) + 1j * rg.random([n_vec], dtype=dtype)
exp1 = rg.integers(-max_bin_exp, max_bin_exp)
e_op1 = Xrange_array(op1, exp1)
op1 = op1 * 2.**exp1
op2 = rg.random([n_vec],
dtype=dtype) + 1j * rg.random([n_vec], dtype=dtype)
exp2 = rg.integers(-max_bin_exp, max_bin_exp)
e_op2 = Xrange_array(op2, exp2)
op2 = op2 * 2.**exp2
t0 = -time.time()
e_res = ufunc(e_op1, e_op2)
t0 += time.time()
t1 = -time.time()
expected = ufunc(op1, op2)
t1 += time.time()
np.testing.assert_array_equal(e_res.to_standard(), expected)
print("\ntiming", ufunc, dtype, t0, t1, t0 / t1)
return t0 / t1
def test_cumprod(self):
almost = True
cmp_op = False
for dtype in [np.float32, np.float64]:
# We need to prevent overflow of 'standard numbers' for the test
# to be meaningful...
if dtype == np.float32:
n_vec = 100
max_bin_exp = 3
resh = (4, 5, 5)
else:
n_vec = 200
max_bin_exp = 10
resh = (4, 10, 5)
rg = np.random.default_rng(1)
op1 = (rg.random([n_vec], dtype=dtype) +
1j * rg.random([n_vec], dtype=dtype))
op1 *= 2.**rg.integers(low=-max_bin_exp,
high=max_bin_exp,
size=[n_vec])
op2 = (rg.random([n_vec], dtype=dtype))
exp_shift_array = rg.integers(low=-max_bin_exp,
high=max_bin_exp,
size=[n_vec])
expected = np.cumprod(op1)
res = np.cumprod(Xrange_array(op1))
_matching(res, expected, almost, dtype, cmp_op)
expected = np.cumprod(op2 * 2.**exp_shift_array)
res = np.cumprod(Xrange_array(op2, exp_shift_array))
_matching(res, expected, almost, dtype, cmp_op, ktol=2.)
_op3 = Xrange_array(op2, exp_shift_array).reshape(*resh)
op3 = (op2 * 2.**exp_shift_array).reshape(resh)
for axis in range(3):
res = np.cumprod(_op3, axis=axis)
expected = np.cumprod(op3, axis=axis)
_matching(res, expected, almost, dtype, cmp_op)
expected = np.cumprod(op1 * 2.**exp_shift_array)
res = np.cumprod(Xrange_array(op1, exp_shift_array))
_matching(res, expected, almost, dtype, cmp_op, ktol=8)
_op4 = Xrange_array(op1, exp_shift_array).reshape(*resh)
op4 = (op1 * 2.**exp_shift_array).reshape(*resh)
for axis in range(3):
res = np.cumprod(_op4, axis=axis)
expected = np.cumprod(op4, axis=axis)
_matching(res, expected, almost, dtype, cmp_op)
def test_sub(self):
for (dtypea, dtypeb
) in crossed_dtypes: #, np.complex128]: # np.complex64 np.float32
with self.subTest(dtypea=dtypea, dtypeb=dtypeb):
nvec = 10000
xa, stda = generate_random_xr(dtypea,
nvec=nvec) # , max_bin_exp=250)
xb, stdb = generate_random_xr(dtypeb, nvec=nvec, seed=800)
res = Xrange_array.empty(xa.shape,
dtype=np.result_type(dtypea, dtypeb))
expected = stda - stdb
numba_test_sub(xa, xb, res)
# Numba timing without compilation
t_numba = -time.time()
numba_test_sub(xa, xb, res)
t_numba += time.time()
# numpy timing
t_np = -time.time()
res_np = xa - xb
t_np += time.time()
_matching(res, expected)
_matching(res_np, expected)
print("t_numba", t_numba)
print("t_numpy", t_np, t_numba / t_np)
expr = (t_numba < t_np)
self.assertTrue(expr, msg="Numba speed below numpy")
# Test substract a scalar
numba_test_sub(xa, stdb, res)
_matching(res, expected)
numba_test_sub(stda, xb, res)
_matching(res, expected)
def test_abs2(self):
for dtype in (np.float64, np.complex128): # np.complex64 np.float32
with self.subTest(dtype=dtype):
nvec = 10000
xa, stda = generate_random_xr(dtype, nvec=nvec, max_bin_exp=75)
# Adjust the mantissa to be sure to trigger a renorm for some
# (around 30 %) cases
xa = np.asarray(xa)
exp = np.copy(xa["exp"])
xa["mantissa"] *= 2.**(2 * exp)
xa["exp"] = -exp
xa = xa.view(Xrange_array)
res = Xrange_array.empty(xa.shape, dtype=dtype)
expected = np.abs(stda)**2
numba_test_abs(xa, res)
# Numba timing without compilation
t_numba = -time.time()
numba_test_abs2(xa, res)
t_numba += time.time()
_matching(res,
expected,
almost=True,
dtype=np.float64,
ktol=2.)
def test_div(self):
for (dtypea, dtypeb
) in crossed_dtypes: #, np.complex128]: # np.complex64 np.float32
with self.subTest(dtypea=dtypea, dtypeb=dtypeb):
nvec = 100000
xa, stda = generate_random_xr(dtypea,
nvec=nvec,
max_bin_exp=75)
# Adjust the mantissa to be sure to trigger a renorm for some
# (around 30 %) cases
xa = np.asarray(xa)
exp = np.copy(xa["exp"])
xa["mantissa"] *= 2.**(2 * exp)
xa["exp"] = -exp
xa = xa.view(Xrange_array)
xb, stdb = generate_random_xr(dtypeb, nvec=nvec, seed=7800)
res = Xrange_array.empty(xa.shape,
dtype=np.result_type(dtypea, dtypeb))
expected = stda / stdb
numba_test_div(xa, xb, res)
# Numba timing without compilation
t_numba = -time.time()
numba_test_div(xa, xb, res)
t_numba += time.time()
# numpy timing
t_np = -time.time()
res_np = xa / xb
t_np += time.time()
_matching(res,
expected,
almost=True,
dtype=np.float64,
ktol=2.)
_matching(res_np,
expected,
almost=True,
dtype=np.float64,
ktol=2.)
print("t_numba", t_numba)
print("t_numpy", t_np, t_numba / t_np)
expr = (t_numba < t_np)
self.assertTrue(expr, msg="Numba speed below numpy")
# Test divide by a scalar
numba_test_div(xa, stdb, res)
_matching(res,
expected,
almost=True,
dtype=np.float64,
ktol=2.)
numba_test_div(stda, xb, res)
_matching(res,
expected,
almost=True,
dtype=np.float64,
ktol=2.)
def test_sum(self):
almost = True
cmp_op = False
for dtype in [np.float32, np.float64]:
n_vec = 1000
max_bin_exp = 20
rg = np.random.default_rng(1)
op1 = (rg.random([n_vec], dtype=dtype) +
1j * rg.random([n_vec], dtype=dtype))
op1 *= 2.**rg.integers(low=-max_bin_exp,
high=max_bin_exp,
size=[n_vec])
op2 = (rg.random([n_vec], dtype=dtype))
exp_shift_array = rg.integers(low=-max_bin_exp,
high=max_bin_exp,
size=[n_vec])
expected = np.sum(op1)
res = np.sum(Xrange_array(op1))
_matching(res, expected, almost, dtype, cmp_op)
expected = np.sum(op2 * 2.**exp_shift_array)
res = np.sum(Xrange_array(op2, exp_shift_array))
_matching(res, expected, almost, dtype, cmp_op)
_op3 = Xrange_array(op2, exp_shift_array).reshape(10, 10, 10)
op3 = (op2 * 2.**exp_shift_array).reshape(10, 10, 10)
for axis in range(3):
res = np.sum(_op3, axis=axis)
expected = np.sum(op3, axis=axis)
_matching(res, expected, almost, dtype, cmp_op)
expected = np.sum(op1 * 2.**exp_shift_array)
res = np.sum(Xrange_array(op1, exp_shift_array))
_matching(res, expected, almost, dtype, cmp_op)
_op4 = Xrange_array(op1, exp_shift_array).reshape(10, 10, 10)
op4 = (op1 * 2.**exp_shift_array).reshape(10, 10, 10)
for axis in range(3):
res = np.sum(_op4, axis=axis)
expected = np.sum(op4, axis=axis)
_matching(res, expected, almost, dtype, cmp_op)
def test_setitem(self):
for dtype in [np.float64, np.complex128]:
with self.subTest(dtype=dtype):
nvec = 500
xr, std = generate_random_xr(dtype, nvec=nvec)
xr2 = Xrange_array.zeros(xr.shape, dtype)
for i in range(nvec):
val_tuple = (xr._mantissa[i], xr._exp[i])
numba_test_setitem(xr2, i, val_tuple)
_matching(xr2, std)
def timing_abs2_complex(self, dtype=np.float64):
import time
n_vec = 40000
max_bin_exp = 20
rg = np.random.default_rng(1)
op = rg.random([n_vec],
dtype=dtype) + 1j * rg.random([n_vec], dtype=dtype)
exp = rg.integers(-max_bin_exp, max_bin_exp)
e_op = Xrange_array(op, exp)
op = op * 2.**exp
t0 = -time.time()
e_res = e_op.abs2()
t0 += time.time()
t1 = -time.time()
expected = op * np.conj(op)
t1 += time.time()
np.testing.assert_array_equal(e_res.to_standard(), expected)
return t0 / t1
def test_angle(self):
for dtype in [np.float32, np.float64]:
n_vec = 1000
max_bin_exp = 20
rg = np.random.default_rng(1)
op1 = (rg.random([n_vec], dtype=dtype) +
1j * rg.random([n_vec], dtype=dtype))
exp_shift_array = rg.integers(low=-max_bin_exp,
high=max_bin_exp,
size=[n_vec])
_op1 = Xrange_array(op1, exp_shift_array)
op1 *= 2.**exp_shift_array
np.testing.assert_array_equal(np.angle(op1), np.angle(_op1))
def test_item_assignment(self):
Xa = Xrange_array(["1.0e1002", "2.0e1000"])
with np.printoptions(precision=10, linewidth=100) as _:
assert Xa[0].__str__() == " 1.0000000000e+1002"
assert type(Xa[0]) is Xrange_array
assert Xa[0] == Xrange_array("1.0e1002")
Xa[1] = Xrange_array("9.876543e-999")
assert Xa[1] == Xrange_array("9.876543e-999")
Xb = Xa + 1.j * Xa
assert Xb[0] == Xa[0] + 1.j * Xa[0]
Xb[0] = Xa[0] + 3.14j * Xa[0]
assert Xb[0] == Xa[0] + 3.14j * Xa[0]
Xb[0] = Xa[0]
assert Xb[0] == Xa[0]
Xb = Xa + 2.j * Xa
assert np.all(Xb.real == Xa)
assert np.all(Xb.imag == 2 * Xa)
Xb.real = -Xa
assert np.all(Xb.real == -Xa)
assert np.all(Xb.imag == 2 * Xa)
Xb.imag = -2 * Xa
assert np.all(Xb.real == -Xa)
assert np.all(Xb.imag == -2. * Xa)
def test_sqrt(self):
for dtype in (np.float64, np.complex128): # np.complex64 np.float32
with self.subTest(dtype=dtype):
nvec = 10000
xa, stda = generate_random_xr(dtype, nvec=nvec, max_bin_exp=75)
# sqrt not defined for negative reals
if dtype == np.float64:
xa = np.abs(xa)
stda = np.abs(stda)
# Adjust the mantissa to be sure to trigger a renorm for some
# (around 30 %) cases
xa = np.asarray(xa)
exp = np.copy(xa["exp"])
xa["mantissa"] *= 2.**(2 * exp)
xa["exp"] = -exp
xa = xa.view(Xrange_array)
res = Xrange_array.empty(xa.shape, dtype=dtype)
expected = np.sqrt(stda)
numba_test_sqrt(xa, res)
# Numba timing without compilation
t_numba = -time.time()
numba_test_sqrt(xa, res)
t_numba += time.time()
# numpy timing
t_np = -time.time()
res_np = np.sqrt(xa)
t_np += time.time()
_matching(res,
expected,
almost=True,
dtype=np.float64,
ktol=2.)
_matching(res_np,
expected,
almost=True,
dtype=np.float64,
ktol=2.)
print("t_numba", t_numba)
print("t_numpy", t_np, t_numba / t_np)
expr = (t_numba < t_np)
self.assertTrue(expr, msg="Numba speed below numpy")
def generate_random_xr(dtype, nvec=500, max_bin_exp=200, seed=100):
"""
Generates a random Xrange array
dtype: mantissa dtype
nvec: number of pts
max_bin_exp max of base 2 exponent abs
seed : random seed
Return
Xrange array, standard array
"""
rg = np.random.default_rng(seed)
if dtype in from_complex.keys():
r_dtype = from_complex[dtype]
mantissa = ((rg.random([nvec], dtype=r_dtype) * 2. - 1.) + 1j *
(2. * rg.random([nvec], dtype=r_dtype) - 1.))
else:
mantissa = rg.random([nvec], dtype=dtype) * 2. - 1.
exp = rg.integers(low=-max_bin_exp, high=max_bin_exp, size=[nvec])
xr = Xrange_array(mantissa, exp=exp)
std = mantissa.copy() * (2.**exp)
return xr, std
def test_print(self):
""" Testing basic Xrange array prints """
Xrange_array.MAX_COUNTER = 5
a = np.array([1., 1., np.pi, np.pi], dtype=np.float64)
Xa = Xrange_array(a)
for exp10 in range(1001):
Xa = Xa * [-10., 0.1, 10., -0.1]
str8 = ("[-1.00000000e+1001 1.00000000e-1001"
" 3.14159265e+1001 -3.14159265e-1001]")
str8_m = ("[ 1.00000000e+1001 -1.00000000e-1001"
" -3.14159265e+1001 3.14159265e-1001]")
str2 = ("[-1.00e+1001 1.00e-1001 3.14e+1001 -3.14e-1001]")
with np.printoptions(precision=2, linewidth=100) as _:
assert Xa.__str__() == str2
with np.printoptions(precision=8, linewidth=100) as _:
assert Xa.__str__() == str8
with np.printoptions(precision=8, linewidth=100) as _:
assert (-Xa).__str__() == str8_m
a = np.array([0.999999, 1.00000, 0.9999996, 0.9999994],
dtype=np.float64)
str5 = "[ 9.99999e-01 1.00000e+00 1.00000e+00 9.99999e-01]"
for k in range(10):
Xa = Xrange_array(a * 0.5**k, k * np.ones([4], dtype=np.int32))
with np.printoptions(precision=5) as _:
assert Xa.__str__() == str5
a = 1.j * np.array([1., 1., np.pi, np.pi], dtype=np.float64)
Xa = Xrange_array(a)
for exp10 in range(1000):
Xa = [-10., 0.1, 10., -0.1] * Xa
str2 = ("[ 0.00e+00➕1.00e+1000j 0.00e+00➕1.00e-1000j"
" 0.00e+00➕3.14e+1000j 0.00e+00➕3.14e-1000j]")
with np.printoptions(precision=2, linewidth=100) as _:
assert Xa.__str__() == str2
a = np.array([[0.1, 10.], [np.pi, 1. / np.pi]], dtype=np.float64)
Xa = Xrange_array(a)
Ya = np.copy(Xa).view(Xrange_array)
for exp10 in range(21):
Xa = np.sqrt(Xa * Xa * Xa * Xa)
for exp10 in range(21):
Ya = Ya * Ya
str6 = ("[[ 1.000000e-2097152 1.000000e+2097152]\n"
" [ 7.076528e+1042598 1.413122e-1042599]]")
with np.printoptions(precision=6, linewidth=100) as _:
assert Xa.__str__() == str6
assert Ya.__str__() == str6
Xa = Xrange_array([["123.456e-1789", "-.3e-7"], ["1.e700", "1.0"]])
str6 = ("[[ 1.234560e-1787 -3.000000e-08]\n"
" [ 1.000000e+700 1.000000e+00]]")
str6_sq = ("[[ 1.524138e-3574 9.000000e-16]\n"
" [ 1.000000e+1400 1.000000e+00]]")
Xb = Xa - 1.j * Xa**2
with np.printoptions(precision=6, linewidth=100) as _:
assert Xa.__str__() == str6
assert (Xa**2).__str__() == str6_sq
# Testing accuracy of mantissa for highest exponents
Xa = Xrange_array([["1.0e+646456992", "1.23456789012345e+646456992"],
["1.0e+646456991", "1.23456789012345e+646456991"],
["1.0e+646456990", "1.23456789012345e+646456990"],
["-1.0e-646456991", "1.23456789012345e-646456991"],
["1.0e-646456992", "1.23456789012345e-646456992"]])
str_14 = (
"[[ 1.00000000000000e+646456992 1.23456789012345e+646456992]\n"
" [ 1.00000000000000e+646456991 1.23456789012345e+646456991]\n"
" [ 1.00000000000000e+646456990 1.23456789012345e+646456990]\n"
" [-1.00000000000000e-646456991 1.23456789012345e-646456991]\n"
" [ 1.00000000000000e-646456992 1.23456789012345e-646456992]]")
with np.printoptions(precision=14, linewidth=100) as _:
assert Xa.__str__() == str_14
Xb = np.array([1., -1.j]) * np.pi * Xrange_array(
["1.e+646456991", "1.e-646456991"])
str_14 = ("[ 3.14159265358979e+646456991➕0.00000000000000e+00j\n"
" 0.00000000000000e+00➖3.14159265358979e-646456991j]")
with np.printoptions(precision=14, linewidth=100) as _:
assert Xb.__str__() == str_14
def test_template_view(self):
"""
Testing basic array capabilities
Array creation via __new__, template of view
real and imag are views
"""
a = np.linspace(0., 5., 12, dtype=np.complex128)
b = Xrange_array(a)
# test shape of b and its mantissa / exponenent fields
assert b.shape == a.shape
assert b._mantissa.shape == a.shape
assert b._exp.shape == a.shape
# b is a full copy not a view
b11_val = b[11]
assert b[11] == b11_val #(5.0 + 0.j, 0, 0)
m = b._mantissa
assert m[11] == 5.
assert a[11] != 10.
a[11] = 10.
assert b[11] == b11_val
# you have to make a new instance to see the modification
b = Xrange_array(a)
assert b[11] != b11_val
m = b._mantissa
assert m[11] == 10.
# Testing Xrange_array from template
c = b[10:]
# test shape Xrange_array subarray and its mantissa / exponenent
assert c.shape == a[10:].shape
assert c._mantissa.shape == a[10:].shape
assert c._exp.shape == a[10:].shape
# modifying subarray modifies array
new_val = (12345. + 0.j, 6)
c[1] = Xrange_array(*new_val)
assert b[11] == c[1]
# modifying array modifies subarray
new_val = (98765. + 0.j, 4)
b[10] = Xrange_array(*new_val)
assert b[10] == c[0]
# Testing Xrange_array from view
d = a.view(Xrange_array)
assert d.shape == a.shape
assert d._mantissa.shape == a[:].shape
# modifying array modifies view
val = a[5]
assert d._mantissa[5] == val
val = 8888888.
a[5] = val
# Check that imag and real are views of the original array
e = Xrange_array(a + 2.j * a)
assert e.to_standard()[4] == (20. + 40.j) / 11.
re = (e.real).copy()
re[4] = Xrange_array(np.pi, 0)
e.real = re
im = (e.imag).copy()
im[4] = Xrange_array(-np.pi, 0)
e.imag = im
assert e.to_standard()[4] == (1. - 1.j) * np.pi
bb = Xrange_array(np.linspace(0., 5., 12, dtype=np.float64))
np.testing.assert_array_equal(bb.real, bb)
bb.real[0] = Xrange_array(1.875, 6) # 120...
assert bb.to_standard()[0] == 120.
np.testing.assert_array_equal(bb.imag.to_standard(), 0.)
def test_edge_cases(self):
_dtype = np.complex128
base = np.linspace(0., 1500., 11, dtype=_dtype)
base2 = np.linspace(-500., 500., 11, dtype=np.float64)
# mul
b = (Xrange_array((2. - 1.j) * base) * Xrange_array(
(-1. + 1.j) * base2))
expected = ((2. - 1j) * base) * ((-1. + 1.j) * base2)
_matching(b, expected)
# add
b = (Xrange_array((2. - 1.j) * base) + Xrange_array(
(-1. + 1.j) * base2))
expected = ((2. - 1.j) * base) + ((-1. + 1j) * base2)
_matching(b, expected)
# <=
b = (Xrange_array((2. - 1j) * base).real <= Xrange_array(
(-1. + 1j) * base2).real)
expected = ((2. - 1j) * base).real <= ((-1. + 1j) * base2).real
np.testing.assert_array_equal(b, expected)
# Testing equality with "almost close" floats
base = -np.ones([40], dtype=np.float64)
base = np.linspace(0., 1., 40, dtype=np.float64)
base2 = base + np.linspace(-1., 1., 40) * np.finfo(np.float64).eps
exp = np.zeros(40, dtype=np.int32)
_base = Xrange_array(base, exp)
_base2 = Xrange_array(base2 * 2., exp - 1)
# print("######################1")
# print("_base", _base)
# print("_base2", _base2)
# print("== ref: ", base == base2)
np.testing.assert_array_equal(_base == _base2, base == base2)
np.testing.assert_array_equal(_base == base2, base == base2)
# print("######################1.1")
np.testing.assert_array_equal(_base[:2] == _base2[:2],
base[:2] == base2[:2])
# print("!=", _base != _base2)
# print("ref: ", base != base2)
np.testing.assert_array_equal(_base != _base2, base != base2)
np.testing.assert_array_equal(_base <= _base2, base <= base2)
np.testing.assert_array_equal(_base >= _base2, base >= base2)
np.testing.assert_array_equal(_base < _base2, base < base2)
np.testing.assert_array_equal(_base > _base2, base > base2)
shift = np.arange(40)
_base2 = Xrange_array(base2 / 2**shift, exp + shift)
np.testing.assert_array_equal(_base != _base2, base != base2)
# print("######################2")
np.testing.assert_array_equal(_base == _base2, base == base2)
np.testing.assert_array_equal(_base > _base2, base > base2)
# print("######################exit")
_base = _base * (1. + 1.j)
_base2 = _base2 * (1. + 1.j)
base = base * (1. + 1.j)
base2 = base2 * (1. + 1.j)
np.testing.assert_array_equal(_base == _base2, base == base2)
np.testing.assert_array_equal(_base != _base2, base != base2)
np.testing.assert_array_equal(_base[2] != _base2[2],
base[2] != base2[2])
np.testing.assert_array_equal(_base[20] != _base2[20],
base[20] != base2[20])
np.testing.assert_array_equal(_base[20] == _base2[20],
base[20] == base2[20])
np.testing.assert_array_equal(_base.real == _base2.real,
base.real == base2.real)
np.testing.assert_array_equal(_base.real != _base2.real,
base.real != base2.real)
np.testing.assert_array_equal(_base[20].real == _base2[20].real,
base[20].real == base2[20].real)
np.testing.assert_array_equal(_base.real[20] == _base2.real[20],
base.real[20] == base2.real[20])
np.testing.assert_array_equal(_base.real <= _base2.real,
base.real <= base2.real)
np.testing.assert_array_equal(_base[20].real <= _base2[20].real,
base[20].real <= base2[20].real)
np.testing.assert_array_equal(_base[2].real <= _base2[2].real,
base[2].real <= base2[2].real)
# Testing complex equality logic
a = np.array([1., 1., 1., 1.]) + 1.j * np.array([1., 1., 1., 1.])
b = np.array([1., 1., -1., -1.]) + 1.j * np.array([1., -1., 1., -1.])
a_ = Xrange_array(a)
b_ = Xrange_array(b)
np.testing.assert_array_equal(a_ == b_, a == b)
np.testing.assert_array_equal(a_ == b, a == b)
np.testing.assert_array_equal(a == b_, a == b)
np.testing.assert_array_equal(a_ != b_, a != b)
np.testing.assert_array_equal(a_ != b, a != b)
np.testing.assert_array_equal(a != b_, a != b)
def test_Xrange_SA(self):
arr = [1., 2., 5.]
_P = Xrange_SA(arr, 10)
P = np.polynomial.Polynomial(arr)
_matching(_P.coeffs, P.coef)
_matching((_P * _P).coeffs, (P * P).coef)
_matching((_P * 2.).coeffs, (P * 2.).coef)
_matching((2. * _P).coeffs, (2. * P).coef)
_matching((_P + _P).coeffs, (P + P).coef)
_matching((_P + 2.).coeffs, (P + 2.).coef)
_matching((2. + _P).coeffs, (2. + P).coef)
_matching((_P - (2. * _P)).coeffs, (P - (2. * P)).coef)
_matching((_P - 2.).coeffs, (P - 2.).coef)
two = Xrange_array([2.])
_matching((_P * two).coeffs, (P * 2.).coef)
_matching((two * _P).coeffs, (2. * P).coef)
_matching((_P + two).coeffs, (P + 2.).coef)
_matching((two + _P).coeffs, (2. + P).coef)
_matching((_P - (two * _P)).coeffs, (P - (2. * P)).coef)
_matching((_P - two).coeffs, (P - 2.).coef)
arrP = [1., 2., 3., 4.]
arrQ = [4., 3., 2.]
_P = Xrange_SA(arrP, 3)
_Q = Xrange_SA(arrQ, 3)
P = np.polynomial.Polynomial(arrP)
Q = np.polynomial.Polynomial(arrQ)
_prod = _P * _Q
prod = P * Q
res = prod - prod.cutdeg(3)
_matching(_prod.err, np.sqrt(np.sum(np.abs(res.coef)**2)))
arrP = [1. - 1.j, 2. + 4.j, 3. + 1.j, 4. - 3.j]
arrQ = [4. - 7.j, 3. - 1.j, 2. + 2.j]
_P = Xrange_SA(arrP, 3)
_Q = Xrange_SA(arrQ, 3)
P = np.polynomial.Polynomial(arrP)
Q = np.polynomial.Polynomial(arrQ)
_prod = _P * _Q
prod = P * Q
res = prod - prod.cutdeg(3)
_matching(_prod.err, np.sqrt(np.sum(np.abs(res.coef)**2)), almost=True)
arr = [1. + 1.j, 1 - 1.j]
_P = Xrange_SA(arr, 10)
P = np.polynomial.Polynomial(arr)
_matching((_P * _P).coeffs, (P * P).coef)
for dtype in [np.float32, np.float64, np.complex64, np.complex128]:
with self.subTest(dtype=dtype):
n_vec = 100
rg = np.random.default_rng(101)
if dtype in [np.float32, np.float64]:
arr = rg.random([n_vec], dtype=dtype)
else:
real_dtype = (np.float32
if dtype is np.complex64 else np.float64)
arr = rg.random([n_vec], dtype=real_dtype) + 1.j * (
rg.random([n_vec], dtype=real_dtype))
_P = Xrange_SA(arr, 1000)
P = np.polynomial.Polynomial(arr)
_matching((_P * _P).coeffs, (P * P).coef,
almost=True,
ktol=3.,
dtype=dtype)
n_vec2 = 83
if dtype in [np.float32, np.float64]:
arr2 = rg.random([n_vec2], dtype=dtype)
else:
real_dtype = (np.float32
if dtype is np.complex64 else np.float64)
arr2 = rg.random([n_vec2], dtype=real_dtype) + 1.j * (
rg.random([n_vec2], dtype=real_dtype))
_Q = Xrange_polynomial(arr2, 1000)
Q = np.polynomial.Polynomial(arr2)
# checking with cutdeg - op_errT
for cutdeg in range(120, 470,
10): # not testing below cutdeg...
_P = Xrange_SA(arr, cutdeg)
_Q = Xrange_SA(arr2, cutdeg)
_prod = _Q * _P
prod = Q * P
_matching(_prod.coeffs,
prod.cutdeg(cutdeg).coef,
almost=True,
ktol=3.,
dtype=dtype)
res = prod - prod.cutdeg(cutdeg)
_matching(_prod.err,
np.sqrt(np.sum(np.abs(res.coef)**2)),
almost=True,
ktol=10.,
dtype=dtype)
def std_SA_loop(P0, n_iter, ref_path, kcX):
xr_2 = Xrange_array(2.) #(1j, numba.int32(1))
P0 = P0 * (P0 + xr_2 * ref_path[0]) + kcX
return P0
def test_expr(self):
for (dtypea, dtypeb
) in crossed_dtypes: #, np.complex128]: # np.complex64 np.float32
dtype_res = np.result_type(dtypea, dtypeb)
nvec = 10000
xa, stda = generate_random_xr(dtypea,
nvec=nvec) # , max_bin_exp=250)
xb, stdb = generate_random_xr(dtypeb, nvec=nvec, seed=800)
res = Xrange_array.empty(xa.shape, dtype=dtype_res)
def get_numba_expr(case):
if case == 0:
def numba_expr(xa, xb, out):
n, = xa.shape
for i in range(n):
out[i] = xa[i] * xb[i] * xa[i]
elif case == 1:
def numba_expr(xa, xb, out):
n, = xa.shape
for i in range(n):
out[i] = xa[i] * xb[i] + xa[i] - 7.8
elif case == 2:
def numba_expr(xa, xb, out):
n, = xa.shape
for i in range(n):
out[i] = (xb[i] * 2.) * (xa[i] + xa[i] * xb[i]) + (
xa[i] * xb[i] - 7.8 + xb[i])
elif case == 3:
def numba_expr(xa, xb, out):
n, = xa.shape
for i in range(n):
out[i] = (
(xb[i] * 2.) *
(xa[i] + np.abs(xa[i] * xb[i]) + 1.) +
(xa[i] * np.sqrt(np.abs(xb[i]) + 7.8) + xb[i]))
else:
raise ValueError(case)
return numba.njit(numba_expr)
def get_std_expr(case):
if case == 0:
def std_expr(xa, xb):
return xa * xb * xa
elif case == 1:
def std_expr(xa, xb):
return xa * xb + xa - 7.8
elif case == 2:
def std_expr(xa, xb):
return (xb * 2.) * (xa + xa * xb) + (xa * xb - 7.8 +
xb)
elif case == 3:
def std_expr(xa, xb):
return ((xb * 2.) * (xa + np.abs(xa * xb) + 1.) +
(xa * np.sqrt(np.abs(xb) + 7.8) + xb))
else:
raise ValueError(case)
return std_expr
n_case = 4
for case in range(n_case):
with self.subTest(dtypea=dtypea, dtypeb=dtypeb, expr=case):
expected = get_std_expr(case)(stda, stdb)
# numpy timing
t_np = -time.time()
res_np = get_std_expr(case)(xa, xb)
t_np += time.time()
numba_expr = get_numba_expr(case)
numba_expr(xa, xb, res)
# Numba timing without compilation
t_numba = -time.time()
numba_expr(xa, xb, res)
t_numba += time.time()
_matching(res,
expected,
almost=True,
dtype=np.float64,
ktol=2.)
_matching(res_np,
expected,
almost=True,
dtype=np.float64,
ktol=2.)
print("t_numba", t_numba)
print("t_numpy", t_np, t_numba / t_np)
expr = (t_numba < t_np)
self.assertTrue(expr, msg="Numba speed below numpy")
def test_Xrange_polynomial(self):
arr = [1., 2., 5.]
_P = Xrange_polynomial(arr, 10)
P = np.polynomial.Polynomial(arr)
_matching(_P.coeffs, P.coef)
_matching((_P * _P).coeffs, (P * P).coef)
_matching((_P * 2).coeffs, (P * 2).coef)
_matching((2 * _P).coeffs, (2 * P).coef)
_matching((_P + _P).coeffs, (P + P).coef)
_matching((_P + 2).coeffs, (P + 2).coef)
_matching((2 + _P).coeffs, (2 + P).coef)
two = Xrange_array([2.])
_matching((_P * two).coeffs, (P * 2).coef)
_matching((two * _P).coeffs, (2 * P).coef)
_matching((_P + two).coeffs, (P + 2).coef)
_matching((two + _P).coeffs, (2 + P).coef)
_matching((_P - (2 * _P)).coeffs, (P - (2 * P)).coef)
_matching((_P - 2).coeffs, (P - 2).coef)
arr = [1. + 1.j, 1 - 1.j]
_P = Xrange_polynomial(arr, 2)
P = np.polynomial.Polynomial(arr)
_matching((_P * _P).coeffs, (P * P).coef)
for dtype in [np.float32, np.float64, np.complex64, np.complex128]:
n_vec = 100
rg = np.random.default_rng(101)
if dtype in [np.float32, np.float64]:
arr = rg.random([n_vec], dtype=dtype)
else:
real_dtype = np.float32 if dtype is np.complex64 else np.float64
arr = rg.random([n_vec], dtype=real_dtype) + 1.j * (rg.random(
[n_vec], dtype=real_dtype))
_P = Xrange_polynomial(arr, 1000)
P = np.polynomial.Polynomial(arr)
_matching((_P * _P).coeffs, (P * P).coef,
almost=True,
ktol=3.,
dtype=dtype)
n_vec2 = 83
if dtype in [np.float32, np.float64]:
arr2 = rg.random([n_vec2], dtype=dtype)
else:
real_dtype = np.float32 if dtype is np.complex64 else np.float64
arr2 = rg.random([n_vec2], dtype=real_dtype) + 1.j * (
rg.random([n_vec2], dtype=real_dtype))
_Q = Xrange_polynomial(arr2, 1000)
Q = np.polynomial.Polynomial(arr2)
_matching((_Q * _P).coeffs, (Q * P).coef,
almost=True,
ktol=3.,
dtype=dtype)
_matching((_P * _Q).coeffs, (P * Q).coef,
almost=True,
ktol=3.,
dtype=dtype)
_matching(_P([1.]),
P(np.asarray([1.])),
almost=True,
ktol=3.,
dtype=dtype)
_matching(_P([1.j]),
P(np.asarray([1.j])),
almost=True,
ktol=3.,
dtype=dtype)
_matching(_P([arr]),
P(np.asarray([arr])),
almost=True,
ktol=3.,
dtype=dtype)
# checking with cutdeg
for cutdeg in range(1, 400, 10):
_P = Xrange_polynomial(arr, cutdeg)
_Q = Xrange_polynomial(arr2, cutdeg)
_matching((_Q * _P).coeffs, (Q * P).cutdeg(cutdeg).coef,
almost=True,
ktol=3.,
dtype=dtype)
_P = Xrange_polynomial(arr, cutdeg=1000)
coeff = Xrange_array("1.e-1000")
arr = [1., 2., 5.]
_P = Xrange_polynomial(arr, 10)
P = np.polynomial.Polynomial(arr)
_matching((2. * _P).coeffs, (2. * P).coef)
_matching((_P * 2.).coeffs, (P * 2.).coef)
_matching((2. + _P).coeffs, (2. + P).coef)
_matching((_P + 2.).coeffs, (P + 2.).coef)
_matching((coeff + _P).coeffs, (_P + coeff).coeffs)
coeff * _P
_P * coeff
def _test_op1(ufunc, almost=False, cmp_op=False, ktol=1.0):
"""
General framework for testing unary operators on Xrange arrays
"""
# print("testing function", ufunc)
rg = np.random.default_rng(100)
n_vec = 500
max_bin_exp = 20
# testing binary operation of reals extended arrays
for dtype in [np.float64, np.float32]:
# print("dtype", dtype)
op1 = rg.random([n_vec], dtype=dtype)
op1 *= 2.**rg.integers(low=-max_bin_exp,
high=max_bin_exp,
size=[n_vec])
expected = ufunc(op1)
res = ufunc(Xrange_array(op1))
_matching(res, expected, almost, dtype, cmp_op, ktol)
# Checking datatype
assert res._mantissa.dtype == dtype
# with non null shift array # culprit
exp_shift_array = rg.integers(low=-max_bin_exp,
high=max_bin_exp,
size=[n_vec])
expected = ufunc(op1 * (2.**exp_shift_array).astype(dtype))
_matching(ufunc(Xrange_array(op1, exp_shift_array)), expected, almost,
dtype, cmp_op, ktol)
# test "scalar"
_matching(ufunc(Xrange_array(op1, exp_shift_array)[0]), expected[0],
almost, dtype, cmp_op, ktol)
# print("c2")
# testing binary operation of reals extended arrays
for dtype in [np.float32, np.float64]:
op1 = (rg.random([n_vec], dtype=dtype) +
1j * rg.random([n_vec], dtype=dtype))
op1 *= 2.**rg.integers(low=-max_bin_exp,
high=max_bin_exp,
size=[n_vec])
expected = ufunc(op1)
res = ufunc(Xrange_array(op1))
_matching(res, expected, almost, dtype, cmp_op, ktol)
# Checking datatype
to_complex = {np.float32: np.complex64, np.float64: np.complex128}
if ufunc in [np.abs]:
assert res._mantissa.dtype == dtype
else:
assert res._mantissa.dtype == to_complex[dtype]
# with non null shift array
exp_shift_array = rg.integers(low=-max_bin_exp,
high=max_bin_exp,
size=[n_vec])
expected = ufunc(op1 * (2.**exp_shift_array))
_matching(ufunc(Xrange_array(op1, exp_shift_array)), expected, almost,
dtype, cmp_op, ktol)
def _test_op2(ufunc, almost=False, cmp_op=False):
"""
General framework for testing operations between 2 Xrange arrays.
"""
# print("testing operation", ufunc)
rg = np.random.default_rng(100)
# ea_type = (Xrange_array._FLOAT_DTYPES +
# Xrange_array._COMPLEX_DTYPES)
n_vec = 500
max_bin_exp = 20
exp_shift = 2
# testing binary operation of reals extended arrays
for dtype in [np.float32, np.float64]:
op1 = rg.random([n_vec], dtype=dtype)
op2 = rg.random([n_vec], dtype=dtype)
op1 *= 2.**rg.integers(low=-max_bin_exp,
high=max_bin_exp,
size=[n_vec])
op2 *= 2.**rg.integers(low=-max_bin_exp,
high=max_bin_exp,
size=[n_vec])
# testing operation between 2 Xrange_arrays OR between ER_A and
# a standard np.array
expected = ufunc(op1, op2)
res = ufunc(Xrange_array(op1), Xrange_array(op2))
_matching(res, expected, almost, dtype, cmp_op)
# # testing operation between 2 Xrange_arrays OR between ER_A and
# # a standard np.array xith dim 2
expected_2d = ufunc(op1.reshape(50, 10), op2.reshape(50, 10))
res_2d = ufunc(Xrange_array(op1.reshape(50, 10)),
Xrange_array(op2.reshape(50, 10)))
_matching(res_2d, expected_2d, almost, dtype, cmp_op)
# Checking datatype
if ufunc in [np.add, np.multiply, np.subtract, np.divide]:
assert res._mantissa.dtype == dtype
if ufunc not in [np.equal, np.not_equal]:
_matching(ufunc(op1, Xrange_array(op2)), expected, almost, dtype,
cmp_op)
_matching(ufunc(Xrange_array(op1), op2), expected, almost, dtype,
cmp_op)
# Testing with non-null exponent
exp_shift_array = rg.integers(low=-exp_shift,
high=exp_shift,
size=[n_vec])
expected = ufunc(op1 * 2.**exp_shift_array, op2 * 2.**-exp_shift_array)
_matching(
ufunc(Xrange_array(op1, exp_shift_array),
Xrange_array(op2, -exp_shift_array)), expected, almost,
dtype, cmp_op)
# testing operation of an Xrange_array with a scalar
if ufunc not in [np.equal, np.not_equal]:
expected = ufunc(op1[0], op2)
_matching(ufunc(op1[0], Xrange_array(op2)), expected, almost,
dtype, cmp_op)
expected = ufunc(op2, op1[0])
_matching(ufunc(Xrange_array(op2), op1[0]), expected, almost,
dtype, cmp_op)
# testing operation of an Xrange_array with a "Xrange" scalar
if ufunc not in [np.equal, np.not_equal]:
expected = ufunc(op1[0], op2)
_matching(ufunc(Xrange_array(op1)[0], Xrange_array(op2)), expected,
almost, dtype, cmp_op)
expected = ufunc(op2, op1[0])
_matching(ufunc(Xrange_array(op2),
Xrange_array(op1)[0]), expected, almost, dtype,
cmp_op)
if cmp_op and (ufunc not in [np.equal, np.not_equal]):
return
if ufunc in [np.maximum]:
return
# testing binary operation of complex extended arrays
for dtype in [np.float32, np.float64]:
n_vec = 20
max_bin_exp = 20
rg = np.random.default_rng(1)
op1 = (rg.random([n_vec], dtype=dtype) +
1j * rg.random([n_vec], dtype=dtype))
op2 = (rg.random([n_vec], dtype=dtype) +
1j * rg.random([n_vec], dtype=dtype))
op1 *= 2.**rg.integers(low=-max_bin_exp,
high=max_bin_exp,
size=[n_vec])
op2 *= 2.**rg.integers(low=-max_bin_exp,
high=max_bin_exp,
size=[n_vec])
# testing operation between 2 Xrange_arrays OR between ER_A and
# a standard np.array
expected = ufunc(op1, op2)
res = ufunc(Xrange_array(op1), Xrange_array(op2))
_matching(res, expected, almost, dtype, cmp_op)
# Checking datatype
if ufunc in [np.add, np.multiply, np.subtract, np.divide]:
to_complex = {np.float32: np.complex64, np.float64: np.complex128}
assert res._mantissa.dtype == to_complex[dtype]
_matching(ufunc(op1, Xrange_array(op2)), expected, almost, dtype,
cmp_op)
_matching(ufunc(Xrange_array(op1), op2), expected, almost, dtype,
cmp_op)
# Testing with non-null exponent (real and imag)
expected = ufunc(op1 * 2.**exp_shift, op2 * 2.**-exp_shift)
exp_shift_array = exp_shift * np.ones([n_vec], dtype=np.int32)
_matching(
ufunc(Xrange_array(op1, exp_shift_array),
Xrange_array(op2, -exp_shift_array)), expected, almost,
dtype, cmp_op)
# Testing cross product of real with complex
expected = ufunc(op1 * 2.**exp_shift, (op2 * 2.**-exp_shift).real)
exp_shift_array = exp_shift * np.ones([n_vec], dtype=np.int32)
_matching(
ufunc(Xrange_array(op1, exp_shift_array),
Xrange_array(op2, -exp_shift_array).real), expected, almost,
dtype, cmp_op)
expected = ufunc((op1 * 2.**exp_shift).imag, op2 * 2.**-exp_shift)
_matching(
ufunc(
Xrange_array(op1, exp_shift_array).imag,
Xrange_array(op2, -exp_shift_array)), expected, almost, dtype,
cmp_op)
# testing operation of an Xrange_array with a scalar
expected = ufunc(op1[0], op2)
_matching(ufunc(op1[0], Xrange_array(op2)), expected, almost, dtype,
cmp_op)
expected = ufunc(op2, op1[0])
_matching(ufunc(Xrange_array(op2), op1[0]), expected, almost, dtype,
cmp_op)
@numba.njit
def numba_test_sa_mul(sa0, sa1):
return sa0 * sa1
@numba.njit
def numba_test_sa_mul_0(sa0, sa1):
return sa0 * sa1[0]
@numba.njit
def numba_test_sa_mul0(sa0, sa1):
return sa0[0] * sa1
two = Xrange_array([2.])
@numba.njit
def numba_SA_loop(P0, n_iter, ref_path, kcX):
xr_2 = numba_xr.Xrange_scalar(complex(2.), numba.int32(0))
print("xr_2", xr_2.mantissa, xr_2.exp)
print("two[0]", two[0].mantissa, two[0].exp)
P0 = P0 * (P0 + xr_2 * ref_path[0]) + kcX
#P0 = (P0 + xr_2 * ref_path[0]) + kcX
# print()
# P0 = P0 + kcX
return P0
def std_SA_loop(P0, n_iter, ref_path, kcX):
