# HG changeset patch # User Francois Bissey # Date 1303875601 -43200 # Node ID 8be9360958bf6e982b9ce4578023af3430aa018a # Parent c3fd103cb942608643f5b9a69b65bf08ea1cfd20 #9958 fixing numerical noise part 1 diff --git a/sage/ext/fast_callable.pyx b/sage/ext/fast_callable.pyx --- a/sage/ext/fast_callable.pyx +++ b/sage/ext/fast_callable.pyx @@ -382,7 +382,7 @@ sin(add(ipow(v_0, 2), v_1)) sage: fc = fast_callable(expr, domain=float) sage: fc(5, 7) - 0.55142668124169059 + 0.5514266812416906 """ cdef Expression et if isinstance(x, Expression): diff --git a/sage/finance/fractal.pyx b/sage/finance/fractal.pyx --- a/sage/finance/fractal.pyx +++ b/sage/finance/fractal.pyx @@ -65,7 +65,7 @@ sage: N = 2^15 sage: s = [1/math.sqrt(k+1) for k in [0..N]] sage: s[:5] - [1.0, 0.70710678118654746, 0.57735026918962584, 0.5, 0.44721359549995793] + [1.0, 0.7071067811865475, 0.5773502691896258, 0.5, 0.4472135954999579] We run the simulation:: diff --git a/sage/finance/markov_multifractal.py b/sage/finance/markov_multifractal.py --- a/sage/finance/markov_multifractal.py +++ b/sage/finance/markov_multifractal.py @@ -97,7 +97,7 @@ sage: msm = finance.MarkovSwitchingMultifractal(8,1.4,1,0.95,3) sage: msm.m0() - 1.3999999999999999 + 1.4 """ return self.__m0 @@ -133,7 +133,7 @@ sage: msm = finance.MarkovSwitchingMultifractal(8,1.4,0.01,0.95,3) sage: msm.gamma_kbar() - 0.94999999999999996 + 0.95 """ return self.__gamma_kbar @@ -161,7 +161,7 @@ sage: msm = finance.MarkovSwitchingMultifractal(8,1.4,1.0,0.95,3) sage: msm.gamma() - (0.001368852970712986, 0.0041009402016725094, 0.012252436441829..., 0.03630878209190..., 0.10501923017634..., 0.28312883556311..., 0.6315968501359..., 0.95000000000000...) + (0.001368852970712986, 0.004100940201672509, 0.012252436441829..., 0.03630878209190..., 0.10501923017634..., 0.28312883556311..., 0.6315968501359..., 0.95000000000000...) """ try: return self.__gamma diff --git a/sage/finance/time_series.pyx b/sage/finance/time_series.pyx --- a/sage/finance/time_series.pyx +++ b/sage/finance/time_series.pyx @@ -27,7 +27,7 @@ sage: t.standard_deviation() 0.33729638212891383 sage: t.mean() - -0.089334255069294391 + -0.08933425506929439 sage: t.variance() 0.1137688493972542... @@ -1269,7 +1269,7 @@ sage: v = finance.TimeSeries([1,1,1,2,3]); v [1.0000, 1.0000, 1.0000, 2.0000, 3.0000] sage: v.mean() - 1.6000000000000001 + 1.6 """ return self.sum() / self._length @@ -1317,9 +1317,9 @@ sage: v = finance.TimeSeries([1,1,1,2,3]); v [1.0000, 1.0000, 1.0000, 2.0000, 3.0000] sage: v.moment(1) - 1.6000000000000001 + 1.6 sage: v.moment(2) - 3.2000000000000002 + 3.2 """ if k <= 0: raise ValueError, "k must be positive" @@ -1349,7 +1349,7 @@ sage: v = finance.TimeSeries([1,2,3]) sage: v.central_moment(2) - 0.66666666666666663 + 0.6666666666666666 Note that the central moment is different from the moment here, since the mean is not `0`:: @@ -1362,7 +1362,7 @@ sage: mu = v.mean(); mu 2.0 sage: ((1-mu)^2 + (2-mu)^2 + (3-mu)^2) / 3 - 0.66666666666666663 + 0.6666666666666666 """ if k == 1: return float(0) @@ -1431,11 +1431,11 @@ sage: mu = v.mean(); sum([(a-mu)^2 for a in v])/len(v) 14.4 sage: v.autocovariance(1) - -2.70000000... + -2.7 sage: mu = v.mean(); sum([(v[i]-mu)*(v[i+1]-mu) for i in range(len(v)-1)])/len(v) - -2.70000000... + -2.7 sage: v.autocovariance(1) - -2.70000000... + -2.7 We illustrate with a random sample that an independently and identically distributed distribution with zero mean and @@ -1548,9 +1548,9 @@ sage: v = finance.TimeSeries([1,1,1,2,3]); v [1.0000, 1.0000, 1.0000, 2.0000, 3.0000] sage: v.variance() - 0.80000000000000004 + 0.8 sage: v.variance(bias=True) - 0.64000000000000001 + 0.64 TESTS:: @@ -1594,7 +1594,7 @@ sage: v.standard_deviation() 0.8944271909... sage: v.standard_deviation(bias=True) - 0.8000000000... + 0.8 TESTS:: @@ -2182,13 +2182,13 @@ sage: s = a.standard_deviation() sage: len(a.clip_remove(-s,s))/float(len(a)) - 0.68309399999999998 + 0.683094 sage: len(a.clip_remove(-2*s,2*s))/float(len(a)) - 0.95455900000000005 + 0.954559 sage: len(a.clip_remove(-3*s,3*s))/float(len(a)) 0.997228 sage: len(a.clip_remove(-5*s,5*s))/float(len(a)) - 0.99999800000000005 + 0.999998 There were no "six sigma events":: diff --git a/sage/functions/hyperbolic.py b/sage/functions/hyperbolic.py --- a/sage/functions/hyperbolic.py +++ b/sage/functions/hyperbolic.py @@ -150,7 +150,7 @@ sage: tanh(3.1415) 0.996271386633702 sage: float(tanh(pi)) - 0.996272076220749... + 0.99627207622075 sage: tan(3.1415/4) 0.999953674278156 sage: tanh(pi/4) @@ -541,7 +541,7 @@ sage: arccoth(2).n(200) 0.54930614433405484569762261846126285232374527891137472586735 sage: float(arccoth(2)) - 0.54930614433405489 + 0.5493061443340549 sage: latex(arccoth(x)) {\rm arccoth}\left(x\right) @@ -639,7 +639,7 @@ sage: arccsch(1).n(200) 0.88137358701954302523260932497979230902816032826163541075330 sage: float(arccsch(1)) - 0.88137358701954305 + 0.881373587019543 sage: latex(arccsch(x)) {\rm arccsch}\left(x\right) diff --git a/sage/functions/log.py b/sage/functions/log.py --- a/sage/functions/log.py +++ b/sage/functions/log.py @@ -155,9 +155,9 @@ sage: ln(2.0) 0.693147180559945 sage: ln(float(-1)) - 3.1415926535897931j + 3.141592653589793j sage: ln(complex(-1)) - 3.1415926535897931j + 3.141592653589793j We do not currently support a ``hold`` parameter in functional notation:: @@ -207,9 +207,9 @@ sage: log(float(0)) -inf sage: log(float(-1)) - 3.1415926535897931j + 3.141592653589793j sage: log(x).subs(x=float(-1)) - 3.1415926535897931j + 3.141592653589793j """ GinacFunction.__init__(self, 'log', latex_name=r'\log', conversions=dict(maxima='log')) @@ -337,7 +337,7 @@ sage: complex(polylog(4,2)) (2.4278628067547032-0.17437130002545306j) sage: float(polylog(4,0.5)) - 0.51747906167389934 + 0.5174790616738993 sage: z = var('z') sage: polylog(2,z).series(z==0, 5) diff --git a/sage/functions/min_max.py b/sage/functions/min_max.py --- a/sage/functions/min_max.py +++ b/sage/functions/min_max.py @@ -214,7 +214,7 @@ sage: f = max_symbolic(sin(x), cos(x)) sage: r = integral(f, x, 0, 1) sage: r.n() - 0.87391244115672628 + 0.8739124411567263 """ return max_symbolic(args) diff --git a/sage/functions/special.py b/sage/functions/special.py --- a/sage/functions/special.py +++ b/sage/functions/special.py @@ -1441,9 +1441,9 @@ sage: float(jacobi("sn",1/2,1/2)) 0.4707504736556572 sage: float(inverse_jacobi("sn",0.47,1/2)) - 0.49909823132221959 + 0.4990982313222196 sage: float(inverse_jacobi("sn",0.4707504,0.5)) - 0.49999991146655481 + 0.4999999114665548 sage: P = plot(inverse_jacobi('sn', x, 0.5), 0, 1, plot_points=20) Now to view this, just type show(P). diff --git a/sage/functions/spike_function.py b/sage/functions/spike_function.py --- a/sage/functions/spike_function.py +++ b/sage/functions/spike_function.py @@ -38,9 +38,9 @@ sage: from sage.functions.spike_function import SpikeFunction sage: S = SpikeFunction([(0,1),(1,2),(pi,-5)]) sage: S - A spike function with spikes at [0.0, 1.0, 3.1415926535897931] + A spike function with spikes at [0.0, 1.0, 3.141592653589793] sage: S.support - [0.0, 1.0, 3.1415926535897931] + [0.0, 1.0, 3.141592653589793] """ def __init__(self, v, eps=0.0000001): """ @@ -141,7 +141,7 @@ A spike function with spikes at [-3.0, -1.0, 2.0] sage: P = S.plot_fft_abs(8) sage: p = P[0]; p.ydata - [5.0, 5.0, 3.3679586919241769, 3.3679586919241769, 4.1231056256176606, 4.1231056256176606, 4.7599216642180551, 4.7599216642180551] + [5.0, 5.0, 3.367958691924177, 3.367958691924177, 4.123105625617661, 4.123105625617661, 4.759921664218055, 4.759921664218055] """ w = self.vector(samples = samples, xmin=xmin, xmax=xmax) xmin, xmax = self._ranges(xmin, xmax) diff --git a/sage/functions/trig.py b/sage/functions/trig.py --- a/sage/functions/trig.py +++ b/sage/functions/trig.py @@ -790,7 +790,7 @@ sage: maxima.atan2(1,-1) 3*%pi/4 sage: math.atan2(1,-1) - 2.3561944901923448 + 2.356194490192345 More examples:: diff --git a/sage/geometry/polyhedra.py b/sage/geometry/polyhedra.py --- a/sage/geometry/polyhedra.py +++ b/sage/geometry/polyhedra.py @@ -5612,7 +5612,7 @@ sage: proj = p.projection() sage: filled_poly = proj.render_fill_2d() sage: filled_poly.axes_width() - 0.8000... + 0.8 """ poly = [polygon2d(self.coordinates_of(p), **kwds) for p in self.polygons] diff --git a/sage/geometry/toric_plotter.py b/sage/geometry/toric_plotter.py --- a/sage/geometry/toric_plotter.py +++ b/sage/geometry/toric_plotter.py @@ -773,8 +773,7 @@ sage: from sage.geometry.toric_plotter import color_list sage: color_list("grey", 1) - [RGB color (0.50196078431372548, - 0.50196078431372548, 0.50196078431372548)] + [RGB color (0.5019607843137255, 0.5019607843137255, 0.5019607843137255)] sage: len(color_list("grey", 3)) 3 sage: color_list("rainbow", 3) diff --git a/sage/gsl/integration.pyx b/sage/gsl/integration.pyx --- a/sage/gsl/integration.pyx +++ b/sage/gsl/integration.pyx @@ -73,15 +73,15 @@ EXAMPLES: To integrate the function $x^2$ from 0 to 1, we do sage: numerical_integral(x^2, 0, 1, max_points=100) - (0.33333333333333331, 3.7007434154171879e-15) + (0.3333333333333333, 3.700743415417188e-15) To integrate the function $\sin(x)^3 + \sin(x)$ we do sage: numerical_integral(sin(x)^3 + sin(x), 0, pi) - (3.333333333333333, 3.7007434154171883e-14) + (3.333333333333333, 3.700743415417188e-14) The input can be any callable: sage: numerical_integral(lambda x: sin(x)^3 + sin(x), 0, pi) - (3.333333333333333, 3.7007434154171883e-14) + (3.333333333333333, 3.700743415417188e-14) We check this with a symbolic integration: sage: (sin(x)^3+sin(x)).integral(x,0,pi) @@ -122,7 +122,7 @@ If we want to change the error tolerances and gauss rule used sage: f = x^2 sage: numerical_integral(f, 0, 1, max_points=200, eps_abs=1e-7, eps_rel=1e-7, rule=4) - (0.33333333333333331, 3.7007434154171879e-15) + (0.3333333333333333, 3.700743415417188e-15) For a Python function with parameters: sage: f(x,a) = 1/(a+x^2) @@ -159,7 +159,7 @@ We can also numerically integrate symbolic expressions using either this function (which uses GSL) or the native integration (which uses Maxima): sage: exp(-1/x).nintegral(x, 1, 2) # via maxima - (0.50479221787318396, 5.6043194293440752e-15, 21, 0) + (0.504792217873184, 5.604319429344075e-15, 21, 0) sage: numerical_integral(exp(-1/x), 1, 2) (0.50479221787318..., 5.60431942934407...e-15) diff --git a/sage/gsl/probability_distribution.pyx b/sage/gsl/probability_distribution.pyx --- a/sage/gsl/probability_distribution.pyx +++ b/sage/gsl/probability_distribution.pyx @@ -887,7 +887,7 @@ sage: for _ in range(10000): ... counts[X.get_random_element()] += 1 sage: float(counts[1]/counts[0]) - 3.0420371867421179 + 3.042037186742118 """ diff --git a/sage/interfaces/maxima.py b/sage/interfaces/maxima.py --- a/sage/interfaces/maxima.py +++ b/sage/interfaces/maxima.py @@ -128,7 +128,7 @@ sage: a = maxima('(1 + sqrt(2))^5') sage: float(a) - 82.012193308819747 + 82.01219330881975 sage: a.numer() 82.01219330881975 diff --git a/sage/interfaces/maxima_abstract.py b/sage/interfaces/maxima_abstract.py --- a/sage/interfaces/maxima_abstract.py +++ b/sage/interfaces/maxima_abstract.py @@ -627,7 +627,7 @@ sage: t(2) sin(2) sage: float(t(2)) - 0.90929742682568171 + 0.9092974268256817 sage: loads(t.dumps()) gamma(x)*sin(x) """ @@ -1592,11 +1592,11 @@ EXAMPLES:: sage: float(maxima("3.14")) - 3.1400000000000001 + 3.14 sage: float(maxima("1.7e+17")) 1.7e+17 sage: float(maxima("1.7e-17")) - 1.6999999999999999e-17 + 1.7e-17 """ try: return float(repr(self.numer())) diff --git a/sage/interfaces/r.py b/sage/interfaces/r.py --- a/sage/interfaces/r.py +++ b/sage/interfaces/r.py @@ -167,7 +167,7 @@ sage: rr = r.dnorm(r.seq(-3,3,0.1)) sage: sum(rr._sage_()) - 9.9772125168981081 + 9.977212516898108 Or you get a dictionary to be able to access all the information. diff --git a/sage/lfunctions/dokchitser.py b/sage/lfunctions/dokchitser.py --- a/sage/lfunctions/dokchitser.py +++ b/sage/lfunctions/dokchitser.py @@ -315,7 +315,7 @@ 0.998583063162746 sage: a = delta_qexp(1000) sage: sum(a[n]/float(n)^14 for n in range(1,1000)) - 0.99858306316274592 + 0.9985830631627459 Illustrate that one can give a list of complex numbers for v (see trac 10937):: diff --git a/sage/misc/explain_pickle.py b/sage/misc/explain_pickle.py --- a/sage/misc/explain_pickle.py +++ b/sage/misc/explain_pickle.py @@ -848,12 +848,12 @@ sage: from sage.misc.explain_pickle import * sage: test_pickle(float(pi)) 0: \x80 PROTO 2 - 2: G BINFLOAT 3.1415926535897931 + 2: G BINFLOAT 3.141592653589793 11: . STOP highest protocol among opcodes = 2 explain_pickle in_current_sage=True/False: float(RR(3.1415926535897931)) - result: 3.1415926535897931 + result: 3.141592653589793 """ self.push(self.sib(f)) diff --git a/sage/misc/prandom.py b/sage/misc/prandom.py --- a/sage/misc/prandom.py +++ b/sage/misc/prandom.py @@ -167,7 +167,7 @@ EXAMPLES: sage: [random() for i in [1 .. 4]] - [0.111439293741037, 0.51434751341916773, 0.044689685248156419, 0.33249060644241302] + [0.111439293741037, 0.5143475134191677, 0.04468968524815642, 0.332490606442413] """ return _pyrand().random() @@ -180,7 +180,7 @@ sage: uniform(0, 1) 0.111439293741037 sage: uniform(e, pi) - 0.51434751341916773*pi + 0.48565248658083227*e + 0.5143475134191677*pi + 0.48565248658083227*e sage: RR(_) 2.93601069876846 """ @@ -213,7 +213,7 @@ sage: [expovariate(1.0) for i in range(3)] [1.10114367058632, 0.652772818610748, 1.69983589896220] sage: [expovariate(1000) for i in range(3)] - [0.00035543583938093908, 0.0025254102812587195, 0.0001175899408167489] + [0.0003554358393809391, 0.0025254102812587195, 0.0001175899408167489] """ return _pyrand().expovariate(lambd) @@ -239,11 +239,11 @@ EXAMPLES: sage: [gauss(0, 1) for i in range(3)] - [0.91910117576579153, 0.77445267562464837, 0.86389968668008765] + [0.9191011757657915, 0.7744526756246484, 0.8638996866800877] sage: [gauss(0, 100) for i in range(3)] - [24.916051749154448, -62.992720615792727, -8.1993122536718...] + [24.916051749154448, -62.99272061579273, -8.1993122536718...] sage: [gauss(1000, 10) for i in range(3)] - [998.75907000456607, 996.10873385116918, 1010.1256817458031] + [998.7590700045661, 996.1087338511692, 1010.1256817458031] """ return _pyrand().gauss(mu, sigma) @@ -256,7 +256,7 @@ EXAMPLES: sage: [lognormvariate(100, 10) for i in range(3)] - [2.9410355688290246e+37, 2.2257548162070125e+38, 4.1422994517174461e+43] + [2.9410355688290246e+37, 2.2257548162070125e+38, 4.142299451717446e+43] """ return _pyrand().lognormvariate(mu, sigma) @@ -267,11 +267,11 @@ EXAMPLES: sage: [normalvariate(0, 1) for i in range(3)] - [-1.3725589805594069, -1.1701670364898928, 0.043241005551101427] + [-1.372558980559407, -1.1701670364898928, 0.04324100555110143] sage: [normalvariate(0, 100) for i in range(3)] - [37.456958750417691, 159.63477432332979, 124.10293211240089] + [37.45695875041769, 159.6347743233298, 124.1029321124009] sage: [normalvariate(1000, 10) for i in range(3)] - [1008.5303090383741, 989.86248926448945, 985.77289211502421] + [1008.5303090383741, 989.8624892644895, 985.7728921150242] """ return _pyrand().normalvariate(mu, sigma) @@ -285,7 +285,7 @@ EXAMPLES: sage: [vonmisesvariate(1.0r, 3.0r) for i in range(1, 5)] - [0.89832863935542584, 0.67180300070412846, 2.0308777524813397, 1.714325253725145...] + [0.8983286393554258, 0.6718030007041285, 2.0308777524813397, 1.714325253725145...] """ return _pyrand().vonmisesvariate(mu, kappa) @@ -305,7 +305,7 @@ EXAMPLES: sage: [weibullvariate(1, 3) for i in range(1, 5)] - [0.49069775546342537, 0.89721855646112125, 0.35757384653194202, 0.73937725551684697] + [0.49069775546342537, 0.8972185564611213, 0.357573846531942, 0.739377255516847] """ return _pyrand().weibullvariate(alpha, beta) diff --git a/sage/misc/preparser.py b/sage/misc/preparser.py --- a/sage/misc/preparser.py +++ b/sage/misc/preparser.py @@ -173,7 +173,7 @@ sage: z = 3.1415R sage: z - 3.1415000000000002 + 3.1415 sage: type(z) diff --git a/sage/misc/randstate.pyx b/sage/misc/randstate.pyx --- a/sage/misc/randstate.pyx +++ b/sage/misc/randstate.pyx @@ -55,24 +55,24 @@ sage: set_random_seed(0) sage: rtest() - (303, -0.187141682737491, 1/2*x^2 - 1/95*x - 1/2, (1,2,3)(4,5), [ 0, 0, 0, 0, 1 ], 963229057, 8045, 0.96619117347084138) # 32-bit - (303, -0.187141682737491, 1/2*x^2 - 1/95*x - 1/2, (1,2,3)(4,5), [ 0, 0, 0, 0, 1 ], 265625921, 8045, 0.96619117347084138) # 64-bit + (303, -0.187141682737491, 1/2*x^2 - 1/95*x - 1/2, (1,2,3)(4,5), [ 0, 0, 0, 0, 1 ], 963229057, 8045, 0.9661911734708414) # 32-bit + (303, -0.187141682737491, 1/2*x^2 - 1/95*x - 1/2, (1,2,3)(4,5), [ 0, 0, 0, 0, 1 ], 265625921, 8045, 0.9661911734708414) # 64-bit sage: set_random_seed(1) sage: rtest() (978, 0.184109262667515, -3*x^2 - 1/12, (4,5), [ 0, 1, 1, 0, 0 ], 1161603091, 60359, 0.83350776541997362) # 32-bit - (978, 0.184109262667515, -3*x^2 - 1/12, (4,5), [ 0, 1, 1, 0, 0 ], 807447831, 60359, 0.83350776541997362) # 64-bit + (978, 0.184109262667515, -3*x^2 - 1/12, (4,5), [ 0, 1, 1, 0, 0 ], 807447831, 60359, 0.8335077654199736) # 64-bit sage: set_random_seed(2) sage: rtest() (207, 0.505364206568040, 4*x^2 + 1/2, (1,2)(4,5), [ 0, 0, 1, 0, 1 ], 637693405, 27695, 0.19982565117278328) # 32-bit (207, 0.505364206568040, 4*x^2 + 1/2, (1,2)(4,5), [ 0, 0, 1, 0, 1 ], 1642898426, 27695, 0.19982565117278328) # 64-bit sage: set_random_seed(0) sage: rtest() - (303, -0.187141682737491, 1/2*x^2 - 1/95*x - 1/2, (1,2,3)(4,5), [ 0, 0, 0, 0, 1 ], 963229057, 8045, 0.96619117347084138) # 32-bit - (303, -0.187141682737491, 1/2*x^2 - 1/95*x - 1/2, (1,2,3)(4,5), [ 0, 0, 0, 0, 1 ], 265625921, 8045, 0.96619117347084138) # 64-bit + (303, -0.187141682737491, 1/2*x^2 - 1/95*x - 1/2, (1,2,3)(4,5), [ 0, 0, 0, 0, 1 ], 963229057, 8045, 0.9661911734708414) # 32-bit + (303, -0.187141682737491, 1/2*x^2 - 1/95*x - 1/2, (1,2,3)(4,5), [ 0, 0, 0, 0, 1 ], 265625921, 8045, 0.9661911734708414) # 64-bit sage: set_random_seed(1) sage: rtest() - (978, 0.184109262667515, -3*x^2 - 1/12, (4,5), [ 0, 1, 1, 0, 0 ], 1161603091, 60359, 0.83350776541997362) # 32-bit - (978, 0.184109262667515, -3*x^2 - 1/12, (4,5), [ 0, 1, 1, 0, 0 ], 807447831, 60359, 0.83350776541997362) # 64-bit + (978, 0.184109262667515, -3*x^2 - 1/12, (4,5), [ 0, 1, 1, 0, 0 ], 1161603091, 60359, 0.8335077654199736) # 32-bit + (978, 0.184109262667515, -3*x^2 - 1/12, (4,5), [ 0, 1, 1, 0, 0 ], 807447831, 60359, 0.8335077654199736) # 64-bit sage: set_random_seed(2) sage: rtest() (207, 0.505364206568040, 4*x^2 + 1/2, (1,2)(4,5), [ 0, 0, 1, 0, 1 ], 637693405, 27695, 0.19982565117278328) # 32-bit @@ -86,8 +86,8 @@ sage: initial_seed() 12345L sage: rtest() - (720, 0.0216737401150802, x^2 - x, (), [ 1, 0, 0, 0, 0 ], 912534076, 14005, 0.92053315995181839) # 32-bit - (720, 0.0216737401150802, x^2 - x, (), [ 1, 0, 0, 0, 0 ], 1911581957, 14005, 0.92053315995181839) # 64-bit + (720, 0.0216737401150802, x^2 - x, (), [ 1, 0, 0, 0, 0 ], 912534076, 14005, 0.9205331599518184) # 32-bit + (720, 0.0216737401150802, x^2 - x, (), [ 1, 0, 0, 0, 0 ], 1911581957, 14005, 0.9205331599518184) # 64-bit sage: initial_seed() 12345L @@ -151,7 +151,7 @@ (0.111439293741037, 539332L, 8.26785106378383, 1.3893337539828183) sage: set_random_seed(1) sage: random(), getrandbits(20), uniform(5.0, 10.0), normalvariate(0, 1) - (0.82940228518742587, 624859L, 5.77894484361117, -0.42013668263087578) + (0.8294022851874259, 624859L, 5.77894484361117, -0.4201366826308758) sage: set_random_seed(0) sage: random(), getrandbits(20), uniform(5.0, 10.0), normalvariate(0, 1) (0.111439293741037, 539332L, 8.26785106378383, 1.3893337539828183) @@ -222,8 +222,8 @@ sage: set_random_seed(0) sage: r1 = rtest(); r1 - (303, -0.187141682737491, 1/2*x^2 - 1/95*x - 1/2, (1,2,3)(4,5), [ 0, 0, 0, 0, 1 ], 963229057, 8045, 0.96619117347084138) # 32-bit - (303, -0.187141682737491, 1/2*x^2 - 1/95*x - 1/2, (1,2,3)(4,5), [ 0, 0, 0, 0, 1 ], 265625921, 8045, 0.96619117347084138) # 64-bit + (303, -0.187141682737491, 1/2*x^2 - 1/95*x - 1/2, (1,2,3)(4,5), [ 0, 0, 0, 0, 1 ], 963229057, 8045, 0.9661911734708414) # 32-bit + (303, -0.187141682737491, 1/2*x^2 - 1/95*x - 1/2, (1,2,3)(4,5), [ 0, 0, 0, 0, 1 ], 265625921, 8045, 0.9661911734708414) # 64-bit sage: r2 = rtest(); r2 (105, -0.581229341007821, -x^2 - x - 6, (1,3), [ 1, 0, 0, 1, 1 ], 14082860, 1271, 0.001767155077382232) # 32-bit (105, -0.581229341007821, -x^2 - x - 6, (1,3), [ 1, 0, 0, 1, 1 ], 53231108, 1271, 0.001767155077382232) # 64-bit @@ -234,8 +234,8 @@ sage: r1 == rtest() True sage: with seed(1): rtest() - (978, 0.184109262667515, -3*x^2 - 1/12, (4,5), [ 0, 1, 1, 0, 0 ], 1161603091, 60359, 0.83350776541997362) # 32-bit - (978, 0.184109262667515, -3*x^2 - 1/12, (4,5), [ 0, 1, 1, 0, 0 ], 807447831, 60359, 0.83350776541997362) # 64-bit + (978, 0.184109262667515, -3*x^2 - 1/12, (4,5), [ 0, 1, 1, 0, 0 ], 1161603091, 60359, 0.8335077654199736) # 32-bit + (978, 0.184109262667515, -3*x^2 - 1/12, (4,5), [ 0, 1, 1, 0, 0 ], 807447831, 60359, 0.8335077654199736) # 64-bit sage: r2m = rtest(); r2m (105, -0.581229341007821, -x^2 - x - 6, (1,3), [ 1, 0, 0, 1, 1 ], 14082860, 19769, 0.001767155077382232) # 32-bit (105, -0.581229341007821, -x^2 - x - 6, (1,3), [ 1, 0, 0, 1, 1 ], 53231108, 19769, 0.001767155077382232) # 64-bit @@ -277,8 +277,8 @@ ... finally: ... ctx.__exit__(None, None, None) - (978, 0.184109262667515, -3*x^2 - 1/12, (4,5), [ 0, 1, 1, 0, 0 ], 1161603091, 60359, 0.83350776541997362) # 32-bit - (978, 0.184109262667515, -3*x^2 - 1/12, (4,5), [ 0, 1, 1, 0, 0 ], 807447831, 60359, 0.83350776541997362) # 64-bit + (978, 0.184109262667515, -3*x^2 - 1/12, (4,5), [ 0, 1, 1, 0, 0 ], 1161603091, 60359, 0.8335077654199736) # 32-bit + (978, 0.184109262667515, -3*x^2 - 1/12, (4,5), [ 0, 1, 1, 0, 0 ], 807447831, 60359, 0.8335077654199736) # 64-bit False sage: r2m == rtest() True diff --git a/sage/modular/modform/eis_series.py b/sage/modular/modform/eis_series.py --- a/sage/modular/modform/eis_series.py +++ b/sage/modular/modform/eis_series.py @@ -343,7 +343,7 @@ -0.291657724743873 sage: L = eisenstein_series_lseries(20) sage: L(2) - -5.02355351645987 + -5.02355351645989 """ f = eisenstein_series_qexp(weight,prec) from sage.lfunctions.all import Dokchitser diff --git a/sage/modules/free_module_element.pyx b/sage/modules/free_module_element.pyx --- a/sage/modules/free_module_element.pyx +++ b/sage/modules/free_module_element.pyx @@ -3123,11 +3123,11 @@ sage: type(vec) sage: answers - [(0.5, 5.5511151231257843e-15, 21, 0), (0.3333333333333..., 3.7007434154171903e-15, 21, 0), (0.45969769413186..., 5.1036696439228408e-15, 21, 0)] + [(0.5, 5.551115123125784e-15, 21, 0), (0.3333333333333..., 3.70074341541719e-15, 21, 0), (0.45969769413186..., 5.103669643922841e-15, 21, 0)] sage: r=vector([t,0,1], sparse=True) sage: r.nintegral(t,0,1) - ((0.5, 0.0, 1.0), {0: (0.5, 5.5511151231257843e-15, 21, 0), 2: (1.0, 1.11022302462515...e-14, 21, 0)}) + ((0.5, 0.0, 1.0), {0: (0.5, 5.551115123125784e-15, 21, 0), 2: (1.0, 1.11022302462515...e-14, 21, 0)}) """ # If Cython supported lambda functions, we would just do diff --git a/sage/stats/basic_stats.py b/sage/stats/basic_stats.py --- a/sage/stats/basic_stats.py +++ b/sage/stats/basic_stats.py @@ -239,7 +239,7 @@ 2.5 sage: x = finance.TimeSeries([1..100]) sage: variance(x) - 841.66666666666663 + 841.6666666666666 sage: variance(x, bias=True) 833.25 sage: class MyClass: diff --git a/sage/stats/hmm/chmm.pyx b/sage/stats/hmm/chmm.pyx --- a/sage/stats/hmm/chmm.pyx +++ b/sage/stats/hmm/chmm.pyx @@ -124,7 +124,7 @@ of states produced obs:: sage: m.viterbi(obs) - ([1, 0, 1, 0, 1, 1, 0, 1, 0, 1], -16.677382701707881) + ([1, 0, 1, 0, 1, 1, 0, 1, 0, 1], -16.67738270170788) We use the Baum-Welch iterative algorithm to find another model for which our observation sequence is more likely:: @@ -258,9 +258,9 @@ sage: m[0] (1.0, 0.5) sage: m[1] - (-2.0, 0.29999999999999999) + (-2.0, 0.3) sage: m[-1] - (-2.0, 0.29999999999999999) + (-2.0, 0.3) sage: m[3] Traceback (most recent call last): ... @@ -476,7 +476,7 @@ sage: m = hmm.GaussianHiddenMarkovModel([[.1,.9],[.5,.5]], [(1,.5), (-1,3)], [.1,.9]) sage: m.log_likelihood([1,1,1]) - -4.2978807660724856 + -4.297880766072486 sage: set_random_seed(0); s = m.sample(20) sage: m.log_likelihood(s) -40.115714129484... @@ -577,7 +577,7 @@ sage: m.viterbi([-2,-1,.1,0.1]) ([1, 1, 0, 1], -9.61823698847639...) sage: m.viterbi([-2,-1,.1,0.3]) - ([1, 1, 1, 0], -9.5660236533785135) + ([1, 1, 1, 0], -9.566023653378513) """ cdef TimeSeries _obs if not isinstance(obs, TimeSeries): @@ -812,7 +812,7 @@ sage: m = hmm.GaussianHiddenMarkovModel([[.1,.9],[.5,.5]], [(1,.5), (-1,3)], [.1,.9]) sage: m.log_likelihood([-2,-1,.1,0.1]) - -8.8582822159862751 + -8.858282215986275 sage: m.baum_welch([-2,-1,.1,0.1]) (22.164539478647512, 8) sage: m.log_likelihood([-2,-1,.1,0.1]) diff --git a/sage/stats/hmm/distributions.pyx b/sage/stats/hmm/distributions.pyx --- a/sage/stats/hmm/distributions.pyx +++ b/sage/stats/hmm/distributions.pyx @@ -146,7 +146,7 @@ sage: P = hmm.GaussianMixtureDistribution([(.3,1,2),(.7,-1,1)]); P 0.3*N(1.0,2.0) + 0.7*N(-1.0,1.0) sage: P[0] - (0.29999999999999999, 1.0, 2.0) + (0.3, 1.0, 2.0) sage: P.is_fixed() False sage: P.fix(1) @@ -213,13 +213,13 @@ sage: P = hmm.GaussianMixtureDistribution([(.2,-10,.5),(.6,1,1),(.2,20,.5)]) sage: P[0] - (0.20000000000000001, -10.0, 0.5) + (0.2, -10.0, 0.5) sage: P[2] - (0.20000000000000001, 20.0, 0.5) + (0.2, 20.0, 0.5) sage: [-1] [-1] sage: P[-1] - (0.20000000000000001, 20.0, 0.5) + (0.2, 20.0, 0.5) sage: P[3] Traceback (most recent call last): ... @@ -393,7 +393,7 @@ sage: P = hmm.GaussianMixtureDistribution([(.2,-10,.5),(.6,1,1),(.2,20,.5)]) sage: P.sample() - 19.658243610875129 + 19.65824361087513 sage: P.sample(1) [-10.4683] sage: P.sample(5) @@ -497,7 +497,7 @@ sage: P = hmm.GaussianMixtureDistribution([(.2,-10,.5),(.6,1,1),(.2,20,.5)]) sage: P.prob_m(.5, 0) - 2.760811768050888...e-97 + 2.7608117680508...e-97 sage: P.prob_m(.5, 1) 0.21123919605857971 sage: P.prob_m(.5, 2) diff --git a/sage/stats/hmm/hmm.pyx b/sage/stats/hmm/hmm.pyx --- a/sage/stats/hmm/hmm.pyx +++ b/sage/stats/hmm/hmm.pyx @@ -266,7 +266,7 @@ sage: m.log_likelihood([0,1,0,1,0,1]) -4.66693474691329... sage: m.viterbi([0,1,0,1,0,1]) - ([1, 1, 1, 1, 1, 1], -5.3788328422087481) + ([1, 1, 1, 1, 1, 1], -5.378832842208748) sage: m.baum_welch([0,1,0,1,0,1]) (0.0, 22) sage: m @@ -479,7 +479,7 @@ sage: m.log_likelihood([0, 1, 0, 1, 1, 0, 1, 0, 0, 0]) -7.3301308009370825 sage: m.log_likelihood([0, 1, 0, 1, 1, 0, 1, 0, 0, 0], scale=False) - -7.3301308009370816 + -7.330130800937082 sage: m.log_likelihood([]) 0.0 @@ -493,7 +493,7 @@ sage: m = hmm.DiscreteHiddenMarkovModel([[0.4,0.6],[0.1,0.9]], [[0.1,0.9],[0.5,0.5]], [.2,.8]) sage: m.log_likelihood([0,1]*1000, scale=True) - -1433.8206666527281 + -1433.820666652728 sage: m.log_likelihood([0,1]*1000, scale=False) -inf """ @@ -591,7 +591,7 @@ non-scaled algorithm:: sage: m._forward_scale(stats.IntList([0,1]*1000)) - -1433.8206666527281 + -1433.820666652728 sage: m._forward(stats.IntList([0,1]*1000)) -inf @@ -599,7 +599,7 @@ sage: set_random_seed(0); v = m.sample(1000) sage: m._forward_scale(v) - -686.87531893650555 + -686.8753189365056 """ # This is just like self._forward(obs) above, except at every step of the # algorithm, we rescale the vector alpha so that the sum of @@ -855,7 +855,7 @@ sage: m = hmm.DiscreteHiddenMarkovModel([[0.1,0.9],[0.9,0.1]], [[1,0],[0,1]], [.2,.8]) sage: m._viterbi(stats.IntList([1]*5)) - ([1, 1, 1, 1, 1], -9.4334839232903924) + ([1, 1, 1, 1, 1], -9.433483923290392) sage: m._viterbi(stats.IntList([0]*5)) ([0, 0, 0, 0, 0], -10.819778284410283) @@ -934,7 +934,7 @@ sage: m = hmm.DiscreteHiddenMarkovModel([[0.1,0.9],[0.9,0.1]], [[.5,.5],[0,1]], [.2,.8]) sage: m._viterbi_scale(stats.IntList([1]*10)) - ([1, 0, 1, 0, 1, 0, 1, 0, 1, 0], -4.6371240950343733) + ([1, 0, 1, 0, 1, 0, 1, 0, 1, 0], -4.637124095034373) Long sequences should not overflow:: @@ -1202,7 +1202,7 @@ sage: m = hmm.DiscreteHiddenMarkovModel([[0.1,0.9],[0.9,0.1]], [[.5,.5],[.2,.8]], [.2,.8]) sage: set_random_seed(0); v = m.sample(100) sage: m.baum_welch(v,fix_emissions=True) - (-66.986308569187742, 100) + (-66.98630856918774, 100) sage: m.emission_matrix() [0.5 0.5] [0.2 0.8]