def checkConstantInit(val, st, signed, wl, fpf):
"""Check the constant init, by comparing the three methods"""
methods = ('', 'log','Benoit','threshold')
c = [Constant(val, wl=wl, signed=signed, method=method, fpf=fpf, name=st) for method in methods]
# check the mantissa range
for cst in c:
if signed:
assert((-2 ** (wl - 1) <= cst.mantissa < -2 ** (wl - 2)) or (2 ** (wl-2) <= cst.mantissa < 2 ** (wl-1)))
else:
assert(2 ** (wl-1) <= cst.mantissa < 2 ** wl)
# check str and value method
str(c)
repr(c)
assert(cst.value == val)
# compare the three constants (compare their FPF, mantissa and approx)
cst = c[0]
for i in range(1,len(c)):
assert(cst.FPF == c[i].FPF)
assert(cst.mantissa == c[i].mantissa)
assert(cst.approx == c[i].approx)
# check if |c - c_FxP| < 2 ^(l-1)
for cst in c:
if cst.mantissa == -2**(cst.FPF.wl-1):
assert(almosteq(cst.approx, val, abs_eps=ldexp(1, cst.FPF.lsb)))
else:
assert (almosteq(cst.approx, val, abs_eps=ldexp(1, cst.FPF.lsb - 1)))
# check relative and absolute error
cst = c[0]
def system02_minimizer(p, l, i, kdpl, kdpi):
kdpl = mpf(kdpl)
kdpi = mpf(kdpi)
if almosteq(kdpl, mpf_zero, mpf_tol):
kdpl += mpf_tol
if almosteq(kdpi, mpf_zero, mpf_tol):
kdpi += mpf_tol
p = mpf(p)
l = mpf(l)
i = mpf(i)
def f(p_f, l_f, i_f):
pl = p_f * l_f / kdpl
pi = p_f * i_f / kdpi
return p - (p_f + pl + pi), l - (l_f + pl), i - (i_f + pi)
p_f, l_f, i_f = findroot(f, [mpf_zero, mpf_zero, mpf_zero],
tol=mpf_tol,
maxsteps=1e6)
return {
"pf": p_f,
"lf": l_f,
"if": i_f,
"pl": (p_f * l_f) / kdpl,
"pi": (p_f * i_f) / kdpi,
}
def test_radial_sc_equatorial_medium_ecc():
aa = 0
slr = 6
ecc = 0.5
x = 1
r1_ch, r2_ch, r3_ch, r4_ch = radial_roots(aa, slr, ecc, x, digits)
r1 = mpf(
"12.0000000000000000000000000000000000000000000000000000000000"
+ "0000000000000000000000000000000000000000000000000000000000000"
+ "000000000"
)
r2 = mpf(
"4.00000000000000000000000000000000000000000000000000000000000"
+ "0000000000000000000000000000000000000000000000000000000000000"
"000000000"
)
r3 = mpf(
"6.00000000000000000000000000000000000000000000000000000000000"
+ "0000000000000000000000000000000000000000000000000000000000000"
+ "0000000"
)
r4 = mpf("0")
assert almosteq(r1_ch, r1, eps)
assert almosteq(r2_ch, r2, eps)
assert almosteq(r3_ch, r3, eps)
assert almosteq(r4_ch, r4, eps)
def test_radial_kerr_polar_high_ecc():
aa = 0.9
slr = 6
ecc = 0.9999
x = 0
r1_ch, r2_ch, r3_ch, r4_ch = radial_roots(aa, slr, ecc, x, digits)
r1 = mpf(
"60000.0000000000000000000000000000000000000000000000000000000"
+ "0000000000000000000000000000000000000000000000000000000000000"
+ "00000"
)
r2 = mpf(
"3.00015000750037501875093754687734386719335966798339916995849"
+ "7924896244812240612030601530076503825191259562978148907445372"
+ "268613431"
)
r3 = mpf(
"4.23160150405948518323888791308221551987498093592515288030115"
+ "945354089115861330121257783337210134827499637485386611824933"
)
r4 = mpf(
"0.49286586348019811079088367661175558062941254382055084863641"
+ "0998598718916996297039941129876200032081561790988663968206728"
)
assert almosteq(r1_ch, r1, eps)
assert almosteq(r2_ch, r2, eps)
assert almosteq(r3_ch, r3, eps)
assert almosteq(r4_ch, r4, eps)
def mini(r):
nonlocal txi, tv
xi = [r]
y = f(r)
v = r*f(r) + mpmath.quad(f, [r, mpmath.inf])
if verbose:
print('Trying r={0} (v={1})'.format(r, v), file=sys.stderr)
for i in itertools.count():
xm1 = xi[i]
h = v / xm1
y += h
if y >= maximum or mpmath.almosteq(y, maximum, abs_eps=mpmath.mp.eps * 2**10):
break
# We solve for x via secant method instead of using f's inverse.
x = mpmath.findroot(lambda x: f(x) - y, xm1)
xi.append(x)
xi.append(mpmath.mpf())
if len(xi) == nseg:
if mpmath.almosteq(y, maximum, abs_eps=mpmath.mp.eps * 2**10):
txi, tv = xi[::-1], v
return 0
# If y > maximum, then v is too large, which means r is too far
# left, so we want to return a negative value. The opposite holds
# true when y < maximum.
return maximum - y
return len(xi) - nseg + h*mpmath.sign(len(xi) - nseg)
def test_radial_kerr_high_ecc():
aa = 0.9
slr = 6
ecc = 0.9999
x = 0.5
r1_ch, r2_ch, r3_ch, r4_ch = radial_roots(aa, slr, ecc, x, digits)
r1 = mpf(
"60000.0000000000000000000000000000000000000000000000000000000"
+ "0000000000000000000000000000000000000000000000000000000000000"
+ "00000"
)
r2 = mpf(
"3.00015000750037501875093754687734386719335966798339916995849"
+ "7924896244812240612030601530076503825191259562978148907445372"
+ "268613431"
)
r3 = mpf(
"2.09909631071719289113848288619813896273182343075993333860146"
+ "83275256205764755741564757727720651989485563951626108414"
)
r4 = mpf(
"0.54443257307207486035051683847000616594344254063022881916146"
+ "92087614587124232498346668603991435731832877296511569358"
)
assert almosteq(r1_ch, r1, eps)
assert almosteq(r2_ch, r2, eps)
assert almosteq(r3_ch, r3, eps)
assert almosteq(r4_ch, r4, eps)
def test_radial_sc_equatorial_low_ecc():
aa = 0
slr = 6
ecc = 0.1
x = 1
r1_ch, r2_ch, r3_ch, r4_ch = radial_roots(aa, slr, ecc, x, digits)
r1 = mpf(
"6.66666666666666666666666666666666666666666666666666666666666"
+ "6666666666666666666666666666666666666666666666666666666666666"
+ "666666667"
)
r2 = mpf(
"5.45454545454545454545454545454545454545454545454545454545454"
+ "5454545454545454545454545454545454545454545454545454545454545"
+ "454545455"
)
r3 = mpf(
"6.00000000000000000000000000000000000000000000000000000000000"
+ "0000000000000000000000000000000000000000000000000000000000000"
+ "0000000"
)
r4 = mpf("0")
assert almosteq(r1_ch, r1, eps)
assert almosteq(r2_ch, r2, eps)
assert almosteq(r3_ch, r3, eps)
assert almosteq(r4_ch, r4, eps)
def test_radial_kerr_even_higher_ecc():
aa = 0.9
slr = 6
ecc = 0.999999
x = 0.5
r1_ch, r2_ch, r3_ch, r4_ch = radial_roots(aa, slr, ecc, x, digits)
r1 = mpf(
"6000000.00000000000000000000000000000000000000000000000000000"
+ "0000000000000000000000000000000000000000000000000000000000000"
+ "00000"
)
r2 = mpf(
"3.00000150000075000037500018750009375004687502343751171875585"
+ "9377929688964844482422241211120605560302780151390075695037847"
+ "518923759"
)
r3 = mpf(
"2.09909500849781985664788052724951917390754315839076840288258"
+ "30079641104679477801203514429959540281638544173538"
)
r4 = mpf(
"0.54443186482151970276714708796651839555550722672128921192288"
+ "90618833999920935428791168827444874586729766166531"
)
assert almosteq(r1_ch, r1, eps)
assert almosteq(r2_ch, r2, eps)
assert almosteq(r3_ch, r3, eps)
assert almosteq(r4_ch, r4, eps)
def test_radial_sc_equatorial_high_ecc():
aa = 0
slr = 6
ecc = 0.9999
x = 1
r1_ch, r2_ch, r3_ch, r4_ch = radial_roots(aa, slr, ecc, x, digits)
r1 = mpf(
"60000.0000000000000000000000000000000000000000000000000000000"
+ "0000000000000000000000000000000000000000000000000000000000000"
+ "00000"
)
r2 = mpf(
"3.00015000750037501875093754687734386719335966798339916995849"
+ "7924896244812240612030601530076503825191259562978148907445372"
+ "268613431"
)
r3 = mpf(
"6.00000000000000000000000000000000000000000000000000000000000"
+ "0000000000000000000000000000000000000000000000000000000000000"
+ "0000000"
)
r4 = mpf("0")
assert almosteq(r1_ch, r1, eps)
assert almosteq(r2_ch, r2, eps)
assert almosteq(r3_ch, r3, eps)
assert almosteq(r4_ch, r4, eps)
def test_radial_kerr_polar_circular():
aa = 0.9
slr = 6
ecc = 0
x = 0
r1_ch, r2_ch, r3_ch, r4_ch = radial_roots(aa, slr, ecc, x, digits)
r1 = mpf(
"6.000000000000000000000000000000000000000000000000000000000"
+ "0000000000000000000000000000000000000000000000000000"
)
r2 = mpf(
"6.000000000000000000000000000000000000000000000000000000000"
+ "0000000000000000000000000000000000000000000000000000"
)
r3 = mpf(
"4.561339049348941915090005888955490497757108282190278250268"
+ "4625285077077054441036020702100329684574966701226"
)
r4 = mpf(
"0.483045392174790095490549865184069452309707597442151923012"
+ "88456761367172626346831436319680699788709729280148"
)
assert almosteq(r1_ch, r1, eps)
assert almosteq(r2_ch, r2, eps)
assert almosteq(r3_ch, r3, eps)
assert almosteq(r4_ch, r4, eps)
def my_assert_allclose_mp(A, AA, abs_tol):
if AA.cols != A.cols or A.rows != AA.rows:
raise ValueError('Trying to assert_close two matrices of different size! ')
#if matrices are complex, then we need to check real and imaginary parts separately
#we hope that if A[0,0] is complex, then all the elements are complex
#this is to avoid the chek inside for for loops
if abs_tol:
if isinstance(A[0, 0], mpmath.mpc):
for i in range(0, A.rows):
for j in range(0, A.cols):
if not mpmath.almosteq(A[i,j].real, AA[i,j].real, abs_eps=abs_tol) or not mpmath.almosteq(A[i,j].imag, AA[i,j.imag], abs_eps=abs_tol):
assert False
else:
for i in range(0, A.rows):
for j in range(0, A.cols):
if not mpmath.almosteq(A[i, j], AA[i, j], abs_eps=abs_tol) :
assert False
else:
assert False
assert True
def test_basic():
with mpmath.workdps(50):
ntotal = 20
ngood = 14
nsample = 5
# Precomputed results using Wolfram
# PMF{HypergeometricDistribution[5, 14, 20], k}
# CDF{HypergeometricDistribution[5, 14, 20], k}
expected_pmf = [
mpmath.mpf('1/2584'),
mpmath.mpf('35/2584'),
mpmath.mpf('455/3876'),
mpmath.mpf('455/1292'),
mpmath.mpf('1001/2584'),
mpmath.mpf('1001/7752'),
]
expected_cdf = [
mpmath.mpf('1/2584'),
mpmath.mpf('9/646'),
mpmath.mpf('509/3876'),
mpmath.mpf('937/1938'),
mpmath.mpf('6751/7752'),
mpmath.mpf('1'),
]
for k in range(len(expected_pmf)):
p = hypergeometric.pmf(k, ntotal, ngood, nsample)
assert mpmath.almosteq(p, expected_pmf[k])
c = hypergeometric.cdf(k, ntotal, ngood, nsample)
assert mpmath.almosteq(c, expected_cdf[k])
s = hypergeometric.sf(k, ntotal, ngood, nsample)
assert mpmath.almosteq(s, 1 - expected_cdf[k])
def system12_minimizer(p, l, kdpl1, kdpl2):
p = mpf(p)
l = mpf(l)
kdpl1 = mpf(kdpl1)
kdpl2 = mpf(kdpl2)
if almosteq(kdpl1, mpf_zero, mpf_tol):
kdpl1 += mpf_tol
if almosteq(kdpl2, mpf_zero, mpf_tol):
kdpl2 += mpf_tol
def f(p_f, l_f):
pl1 = p_f * l_f / kdpl1
pl2 = p_f * l_f / kdpl2
pl12 = (pl1 * l_f + pl2 * l_f) / (kdpl1 + kdpl2)
return p - (p_f + pl1 + pl2 + pl12), l - (l_f + pl1 + pl2 + 2 * pl12)
p_f, l_f = findroot(f, [mpf_zero, mpf_zero], tol=mpf_tol, maxsteps=1e6)
pl1 = (p_f * l_f) / kdpl1
pl2 = (p_f * l_f) / kdpl2
return {
"pf": p_f,
"lf": l_f,
"pl1": pl1,
"pl2": pl2,
"pl12": (pl1 * l_f + pl2 * l_f) / (kdpl1 + kdpl2),
}
def test_radial_kerr_circular():
aa = 0.9
slr = 6
ecc = 0
x = 0.5
r1_ch, r2_ch, r3_ch, r4_ch = radial_roots(aa, slr, ecc, x, digits)
r1 = mpf(
"6.000000000000000000000000000000000000000000000000000000000"
+ "0000000000000000000000000000000000000000000000000000"
)
r2 = mpf(
"6.000000000000000000000000000000000000000000000000000000000"
+ "0000000000000000000000000000000000000000000000000000"
)
r3 = mpf(
"2.107201636766182477809036698351808785794321226845138552595"
+ "5383217548393926383743377377252142128804042090704"
)
r4 = mpf(
"0.547821639683837105742296185097970225527479832053292059782"
+ "11748376227722039540247078504892434983412451743782"
)
assert almosteq(r1_ch, r1, eps)
assert almosteq(r2_ch, r2, eps)
assert almosteq(r3_ch, r3, eps)
assert almosteq(r4_ch, r4, eps)
def __eq__(self, another):
if (isinstance(another, Opinion)):
return (mpmath.almosteq(self.getBelief(), another.getBelief(),epsilon) and \
mpmath.almosteq(self.getDisbelief(), another.getDisbelief(),epsilon) and \
mpmath.almosteq(self.getUncertainty(), another.getUncertainty(),epsilon) and\
mpmath.almosteq(self.getBase(), another.getBase(),epsilon)
)
return NotImplemented
def _sf_sympy(self, t, output='float'):
if output == 'float':
return np.float64(self._sf_sympy(t, output='mpf'))
if t < min(self.a) or mp.almosteq(t, min(self.a), 1e-8):
return mp.mpf(1)
elif t > max(self.a) or mp.almosteq(t, max(self.a), 1e-8):
return mp.mpf(0)
else:
return self._symbolic_sf.subs(self._t, t)
def test_specific_values_from_wolfram():
# The function is MarcumQ[m, a, b] in Wolfram.
with mpmath.workdps(50):
values = [
[(1, 1, 2),
mpmath.mpf(
'0.269012060035909996678516959220271087421337500744873384155')
],
[(4, 2, 2),
mpmath.mpf(
'0.961002639616864002974959310625974743642314730388958932865')
],
[(10, 2, 7),
mpmath.mpf(
'0.003419880268711142942584170929968429599523954396941827739')
],
[(10, 2, 20),
mpmath.mpf(
'1.1463968305097683198312254572377449552982286967700350e-63')
],
[(25, 3, 1),
mpmath.mpf(
'0.999999999999999999999999999999999985610186498600062604510')
],
[(100, 5, 25),
mpmath.mpf(
'6.3182094741234192918553754494227940871375208133861094e-36')
],
]
for (m, a, b), expected in values:
q = marcumq(m, a, b)
assert mpmath.almosteq(q, expected)
values = [
[(0.5, 1, 2),
mpmath.mpf(
'0.839994848036912854058580730864442945100083598568223741623')
],
[(0.5, 5, 13),
mpmath.mpf(
'0.99999999999999937790394257282158764840048274118115775113')
],
[(0.5, 5, mpmath.mpf('1/13')),
mpmath.mpf(
'2.3417168332795098320214996797055274037932802604709459e-7')],
[(0.75, 5, mpmath.mpf('0.001')),
mpmath.mpf(
'7.6243509472783061143887290663443105556790864676878435e-11')
],
[(51 / 2, 5, mpmath.mpf('0.1')),
mpmath.mpf(
'9.9527768099307883918427141035705197017192239618506806e-91')]
]
for (m, a, b), expected in values:
c = cmarcumq(m, a, b)
assert mpmath.almosteq(c, expected)
def test_polar_kerr_polar_circular():
aa = 0.9
slr = 6
ecc = 0
x = 0
zp_ch, zm_ch = polar_roots(aa, slr, ecc, x, digits)
zm = mpf("1")
zp = mpf("0")
assert almosteq(zm_ch, zm, eps)
assert almosteq(zp_ch, zp, eps)
def test_polar_sc_polar_high_ecc():
aa = 0
slr = 6
ecc = 0.9999
x = 0
zp_ch, zm_ch = polar_roots(aa, slr, ecc, x, digits)
zm = mpf("1")
zp = mpf("0")
assert almosteq(zm_ch, zm, eps)
assert almosteq(zp_ch, zp, eps)
def test_sf_invsf():
with mpmath.workdps(50):
x = mpmath.mpf('1.5')
p = benktander1.sf(x, 2, 3)
# Expected value computed with Wolfram Alpha:
# SurvivalFunction[BenktanderGibratDistribution[2, 3], 3/2]
valstr = '0.40103000157608789634710325190011195010750064239976147223'
expected = mpmath.mpf(valstr)
assert mpmath.almosteq(p, expected)
x1 = benktander1.invsf(expected, 2, 3)
assert mpmath.almosteq(x1, x)
def compareValues( result1, result2 ):
if isinstance( result1, RPNMeasurement ):
if isinstance( result2, RPNMeasurement ):
return result1.__eq__( result2 )
else:
return almosteq( result1.getValue( ), result2 )
else:
if isinstance( result2, RPNMeasurement ):
return almosteq( result1, result2.getValue( ) )
else:
return almosteq( result1, result2 )
def test_cdf_invcdf():
with mpmath.workdps(50):
x = mpmath.mpf('1.5')
p = benktander1.cdf(x, 2, 3)
# Expected value computed with Wolfram Alpha:
# CDF[BenktanderGibratDistribution[2, 3], 3/2]
valstr = '0.59896999842391210365289674809988804989249935760023852777'
expected = mpmath.mpf(valstr)
assert mpmath.almosteq(p, expected)
x1 = benktander1.invcdf(expected, 2, 3)
assert mpmath.almosteq(x1, x)
def _pdf_mpmath(self, t, output='float'):
if output == 'float':
return np.float64(self._pdf_mpmath(t, output='mpf'))
if t<min(self.a) or t>max(self.a) or\
mp.almosteq(t, min(self.a), 1e-8) or\
mp.almosteq(t, max(self.a), 1e-8):
return mp.mpf(0)
y = [(self.N - 1) * mp.power(x, self.N - 2)
for x in np.maximum(self.a - t, 0)]
y = [y1 / y2 for y1, y2 in zip(y, self._proda_jni_mpmath)]
return mp.fsum(y)
def _sf_mpmath(self, t, output='float'):
if output == 'float':
return np.float64(self._sf_mpmath(t, output='mpf'))
if t < min(self.a) or mp.almosteq(t, min(self.a), 1e-8):
return mp.mpf(1)
elif t > max(self.a) or mp.almosteq(t, max(self.a), 1e-8):
return mp.mpf(0)
else:
y = [mp.power(max(yy, 0), self.N - 1) for yy in self.a - t]
y = [y1 / y2 for y1, y2 in zip(y, self._proda_jni_mpmath)]
return mp.fsum(y)
def test_polar_sc_equatorial_medium_ecc():
aa = 0
slr = 6
ecc = 0.5
x = 1
zp_ch, zm_ch = polar_roots(aa, slr, ecc, x, digits)
zm = mpf("0")
zp = mpf(
"3.61813613493316347176174480364074910973864204973384028770038052303616\
506466441146913692007177631707371674097219948449810066411613")
assert almosteq(zm_ch, zm, eps)
assert almosteq(zp_ch, zp, eps)
def test_polar_sc_equatorial_high_ecc():
aa = 0
slr = 6
ecc = 0.9999
x = 1
zp_ch, zm_ch = polar_roots(aa, slr, ecc, x, digits)
zm = mpf("0")
zp = mpf(
"4.24242858159851701578554748323491974415361125635078536064052378598976\
876818690433867661492273770095319175758399527157325757304661")
assert almosteq(zm_ch, zm, eps)
assert almosteq(zp_ch, zp, eps)
def test_polar_sc_equatorial_low_ecc():
aa = 0
slr = 6
ecc = 0.1
x = 1
zp_ch, zm_ch = polar_roots(aa, slr, ecc, x, digits)
zm = mpf("0")
zp = mpf(
"3.46988959179744133351400773640924026761245476148250978303554387894263\
507063490349890758982948765400825359194934322782659963821907")
assert almosteq(zm_ch, zm, eps)
assert almosteq(zp_ch, zp, eps)
def test_polar_kerr_circular_equatorial():
aa = 0.9
slr = 6
ecc = 0
x = 1
zp_ch, zm_ch = polar_roots(aa, slr, ecc, x, digits)
zm = mpf("0")
zp = mpf(
"2.81576412442877462061915538563996125884423339096478120511885059807601\
627376072301848960531274422940925849602470358318845423602414")
assert almosteq(zm_ch, zm, eps)
assert almosteq(zp_ch, zp, eps)
def test_Q1_identities():
with mpmath.workdps(50):
for a in [mpmath.mp.mpf(1), mpmath.mp.mpf(13)]:
q1 = marcumq(1, a, a)
expected = 0.5 * (1 + mpmath.exp(-a**2) * mpmath.besseli(0, a**2))
assert mpmath.almosteq(q1, expected)
for a, b in [(1, 2), (10, 3.5)]:
total = marcumq(1, a, b) + marcumq(1, b, a)
expected = 1 + mpmath.exp(-(a**2 + b**2) / 2) * mpmath.besseli(
0, a * b)
assert mpmath.almosteq(total, expected)
def test_polar_sc_circular_equatorial():
aa = 0
slr = 6
ecc = 0
x = 1
zp_ch, zm_ch = polar_roots(aa, slr, ecc, x, digits)
zm = mpf("0")
zp = mpf(
"3.46410161513775458705489268301174473388561050762076125611161395890386\
603381760007416229237351449715135125228283081340605993989019")
assert almosteq(zm_ch, zm, eps)
assert almosteq(zp_ch, zp, eps)
def test_constants_sc_polar_circular():
aa = 0
slr = 6
ecc = 0
x = 0
En_ch, Lz_ch, Q_ch = calc_constants(aa, slr, ecc, x, digits)
En = mpf("0.94280904158206336586779248280646538571311458358463204878" +
"4453158660488318974738025900258356218427715156676")
Lz = mpf("0")
Q = mpf("12")
assert almosteq(En_ch, En, eps)
assert almosteq(Lz_ch, Lz, eps)
assert almosteq(Q_ch, Q, eps)
def test_basic_pdf():
with mpmath.workdps(50):
# Precomputed results using Wolfram
# PDF[NoncentralChiSquareDistribution[k, lam], x}
expected = mpmath.mpf(
'0.12876542477554595251711369063259389422017597538321')
assert mpmath.almosteq(ncx2.pdf(1, 2, 3), expected)
expected = mpmath.mpf(
'6.91617141220678829079562729724319046638618761057660e-17')
assert mpmath.almosteq(ncx2.pdf(100, 2, 3), expected)
def mpIntDigits(num):
if not mpmath.almosteq(num,0):
a = mpmath.log(abs(num), b=10)
b = mpmath.nint(a)
if mpmath.almosteq(a,b):
return int(b)+1
else:
c = mpmath.ceil(a)
try:
return int(c)
except:
pass
else:
return 0
def _findLeaving(self, enteringPos):
increase = mp.fsub(mp.inf,'1')
idx = mp.inf
pos = -1
# find the variable with the smaller upper bound to the increase in the entering variable
# if there are multiple choices, set the one with the smaller index on the list of basic indexes
for i in range(self.m):
upperBound = self._getUpperBound(self.b[i], self.A[i, enteringPos])
# if this variable impose more constraint on the increase of the entering variable
# than the current leaving variable, then this is the new leaving variable
if upperBound <= mp.fsub(increase, self.tolerance):
idx = self.basicIdx[i]
pos = i
increase = upperBound
# if this variable impose the same constraint on the increase of the entering variable
# than the current leaving variable (considering the tolerance) but has a lower index,
# then this is the new leaving variable
elif mp.almosteq(upperBound, increase, self.tolerance) and self.basicIdx[i] < idx:
idx = self.basicIdx[i]
pos = i
if pos >= 0:
return idx, pos
else:
return Dictionary.UNBOUNDEDCODE, Dictionary.UNBOUNDED
def testAllConversions( unitTypeTable, unitConversionMatrix ):
print( 'Testing all conversions for consistency...' )
print( )
validated = 0
for unitType, unitList in unitTypeTable.items( ):
for unit1, unit2, unit3 in itertools.permutations( unitList, 3 ):
try:
factor1 = unitConversionMatrix[ unit1, unit2 ]
factor2 = unitConversionMatrix[ unit2, unit3 ]
factor3 = unitConversionMatrix[ unit1, unit3 ]
except:
continue
epsilon = power( 10, fneg( validationPrecision ) )
if not almosteq( fmul( factor1, factor2 ), factor3, rel_eps=epsilon ):
print( 'conversion inconsistency found for ' + unit1 + ', ' + unit2 + ', and', unit3, file=sys.stderr )
print( unit1 + ' --> ' + unit2, factor1, file=sys.stderr )
print( unit2 + ' --> ' + unit3, factor2, file=sys.stderr )
print( unit3 + ' --> ' + unit1, factor3, file=sys.stderr )
print( )
validated += 1
if validated % 1000 == 0:
print( '\r' + '{:,} conversion permutations validated...'.format( validated ), end='' )
print( '\r' + '{:,} conversion permutations were validated to {:,} digits precision.'. \
format( validated, validationPrecision ) )
print( 'No consistency problems detected.' )
def are_perp(m1,m2):
"""
slopes are perpendicular
m1,m2 in (-inf,inf)
"""
if m2 == 0:
return m1 == float('inf') or m1 == -float('inf')
else:
return mp.almosteq(m1,-1./m2) # THE CHANGE TO
def compareValues( result1, result2 ):
if isinstance( result1, RPNMeasurement ) != isinstance( result2, RPNMeasurement ):
return False
if isinstance( result1, RPNMeasurement ):
return result1.__eq__( result2 )
else:
if isinf( result1 ):
if isinf( result2 ):
return True
else:
raise ValueError( 'unit test failed' )
print( '**** error in results comparison' )
print( type( result1 ), type( result2 ) )
print( result1, result2, 'are not equal' )
return almosteq( result1, result2 )
def emit(name, iname, cdf, args, no_small=False):
V = []
for arg in sorted(args):
y = cdf(*arg)
if isinstance(y, mpf):
e = sp.nsimplify(y, rational=True)
if e.is_Rational and e.q <= 1000 and \
mp.almosteq(mp.mpf(e), y, 1e-25):
y = e
else:
y = N(y)
V.append(arg + (y,))
for v in V:
if name:
test(name, *v)
for v in V:
if iname and (not no_small or 1/1000 <= v[-1] <= 999/1000):
test(iname, *(v[:-2] + v[:-3:-1]))
def _isInteger(num, tolerance = mp.power(10,-6)): return mp.almosteq(num, mp.nint(num), tolerance)
db3 scaling coefficients
Wavelet Analysis: The Scalable Structure of Information (2002)
Howard L. Resnikoff, Raymond O.Jr. Wells
Table 10.3 page 263
'''
db3 = [( _1 + sqrt10 + mp.sqrt(_5 + _2*sqrt10))/_16,
( _5 + sqrt10 + _3*mp.sqrt(_5 + _2*sqrt10))/_16,
(_10 - _2*sqrt10 + _2*mp.sqrt(_5 + _2*sqrt10))/_16,
(_10 - _2*sqrt10 - _2*mp.sqrt(_5 + _2*sqrt10))/_16,
( _5 + sqrt10 - _3*mp.sqrt(_5 + _2*sqrt10))/_16,
( _1 + sqrt10 - mp.sqrt(_5 + _2*sqrt10))/_16]
db3 = np.array(db3)
D6 = db3
for a in [D2, D4, D6]:
norm = mpmath.norm(a)
assert mpmath.almosteq(norm, mp.sqrt(_2))
def wavelet_coefficients(a):
# TODO: is this just true for Daubechies wavelets?
N = len(a)
return np.array([(-1)**k*a[N-1-k] for k in range(N)])
# maps from genus (i.e. vanishing moments) to the scaling coefficients
daubechies_wavelets = {
1: D2,
2: D4,
3: D6,
}