From 9ce54e11d855cced45308405e212d2955c62c013 Mon Sep 17 00:00:00 2001 From: jac2130 Date: Thu, 3 Oct 2013 13:06:35 -0400 Subject: [PATCH 1/6] adding BayesNet --- price1.eps | 1669 +++++++++++++++++++++++++++++++++ price1.pdf | Bin 0 -> 14020 bytes price1.png | Bin 0 -> 171097 bytes price2.eps | 2430 ++++++++++++++++++++++++++++++++++++++++++++++++ price2.pdf | Bin 0 -> 18254 bytes price2.png | Bin 0 -> 116138 bytes price3.eps | 1753 ++++++++++++++++++++++++++++++++++ price3.pdf | Bin 0 -> 13133 bytes price3.png | Bin 0 -> 164005 bytes price4.eps | 1661 +++++++++++++++++++++++++++++++++ price4.pdf | Bin 0 -> 13287 bytes price4.png | Bin 0 -> 162975 bytes price5.eps | 1669 +++++++++++++++++++++++++++++++++ price5.pdf | Bin 0 -> 14306 bytes price5.png | Bin 0 -> 168932 bytes price6.eps | 1782 +++++++++++++++++++++++++++++++++++ price6.pdf | Bin 0 -> 12244 bytes price6.png | Bin 0 -> 233135 bytes thinkbayes.py | 116 ++- thinkbayes.pyc | Bin 0 -> 58948 bytes thinkplot.pyc | Bin 0 -> 13675 bytes 21 files changed, 11063 insertions(+), 17 deletions(-) create mode 100644 price1.eps create mode 100644 price1.pdf create mode 100644 price1.png create mode 100644 price2.eps create mode 100644 price2.pdf create mode 100644 price2.png create mode 100644 price3.eps create mode 100644 price3.pdf create mode 100644 price3.png create mode 100644 price4.eps create mode 100644 price4.pdf create mode 100644 price4.png create mode 100644 price5.eps create mode 100644 price5.pdf create mode 100644 price5.png create mode 100644 price6.eps create mode 100644 price6.pdf create mode 100644 price6.png create mode 100644 thinkbayes.pyc create mode 100644 thinkplot.pyc diff --git a/price1.eps b/price1.eps new file mode 100644 index 0000000..5fbe198 --- /dev/null +++ b/price1.eps @@ -0,0 +1,1669 @@ +%!PS-Adobe-3.0 EPSF-3.0 +%%Title: price1.eps +%%Creator: matplotlib version 1.3.x, http://matplotlib.org/ +%%CreationDate: Wed Oct 2 10:36:34 2013 +%%Orientation: portrait +%%BoundingBox: 18 180 594 612 +%%EndComments +%%BeginProlog +/mpldict 8 dict def +mpldict begin +/m { moveto } bind def +/l { lineto } bind def +/r { rlineto } bind def +/c { curveto } bind def +/cl { closepath } bind def +/box { +m +1 index 0 r +0 exch r +neg 0 r +cl +} bind def +/clipbox { +box +clip +newpath +} bind def +%!PS-Adobe-3.0 Resource-Font +%%Title: Bitstream Vera Sans +%%Copyright: Copyright (c) 2003 by Bitstream, Inc. All Rights Reserved. +%%Creator: Converted from TrueType to type 3 by PPR +25 dict begin +/_d{bind def}bind def +/_m{moveto}_d +/_l{lineto}_d +/_cl{closepath eofill}_d +/_c{curveto}_d +/_sc{7 -1 roll{setcachedevice}{pop pop pop pop pop pop}ifelse}_d +/_e{exec}_d +/FontName /BitstreamVeraSans-Roman def +/PaintType 0 def +/FontMatrix[.001 0 0 .001 0 0]def +/FontBBox[-183 -236 1287 928]def +/FontType 3 def +/Encoding [ /space /dollar /parenleft /parenright /period /zero /one /two /three /four /five /six /seven /eight /D /F /P /a /c /e /h /i /o /p /r /s /w ] def +/FontInfo 10 dict dup begin +/FamilyName (Bitstream Vera Sans) def +/FullName (Bitstream Vera Sans) def +/Notice (Copyright (c) 2003 by Bitstream, Inc. All Rights Reserved. Bitstream Vera is a trademark of Bitstream, Inc.) def +/Weight (Roman) def +/Version (Release 1.10) def +/ItalicAngle 0.0 def +/isFixedPitch false def +/UnderlinePosition -213 def +/UnderlineThickness 143 def +end readonly def +/CharStrings 27 dict dup begin +/space{318 0 0 0 0 0 _sc +}_d +/dollar{{636 0 83 -146 553 760 _sc +338 -146 _m +289 -146 _l +289 0 _l +254 0 220 4 186 12 _c +152 19 117 30 83 45 _c +83 133 _l +116 112 150 96 184 86 _c +218 75 253 69 289 69 _c +289 292 _l +217 304 164 324 132 352 _c +99 380 83 418 83 467 _c +83 519 100 561 136 592 _c +171 622 222 640 289 645 _c +289 760 _l +338 760 _l +338 646 _l +368 645 397 642 425 637 _c +}_e{453 631 481 624 509 616 _c +509 531 _l +481 544 453 554 425 562 _c +397 570 368 574 338 576 _c +338 367 _l +412 355 466 335 501 306 _c +535 276 553 236 553 186 _c +553 131 534 88 497 56 _c +460 24 407 5 338 1 _c +338 -146 _l +289 376 _m +289 576 _l +251 572 222 561 202 544 _c +182 526 173 503 173 475 _c +173 447 182 425 200 409 _c +218 393 248 382 289 376 _c +338 282 _m +}_e{338 71 _l +379 76 410 88 431 106 _c +452 124 463 147 463 177 _c +463 205 453 228 433 245 _c +413 262 381 274 338 282 _c +_cl}_e}_d +/parenleft{390 0 86 -131 310 759 _sc +310 759 _m +266 683 234 609 213 536 _c +191 463 181 389 181 314 _c +181 238 191 164 213 91 _c +234 17 266 -56 310 -131 _c +232 -131 _l +183 -54 146 20 122 94 _c +98 168 86 241 86 314 _c +86 386 98 459 122 533 _c +146 607 182 682 232 759 _c +310 759 _l +_cl}_d +/parenright{390 0 80 -131 304 759 _sc +80 759 _m +158 759 _l +206 682 243 607 267 533 _c +291 459 304 386 304 314 _c +304 241 291 168 267 94 _c +243 20 206 -54 158 -131 _c +80 -131 _l +123 -56 155 17 177 91 _c +198 164 209 238 209 314 _c +209 389 198 463 177 536 _c +155 609 123 683 80 759 _c +_cl}_d +/period{318 0 107 0 210 124 _sc +107 124 _m +210 124 _l +210 0 _l +107 0 _l +107 124 _l +_cl}_d +/zero{636 0 66 -13 570 742 _sc +318 664 _m +267 664 229 639 203 589 _c +177 539 165 464 165 364 _c +165 264 177 189 203 139 _c 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_c +504 422 484 390 454 354 _c +446 344 420 317 376 272 _c +332 227 271 164 192 83 _c +_cl}_e}_d +/three{{636 0 76 -13 556 742 _sc +406 393 _m +453 383 490 362 516 330 _c +542 298 556 258 556 212 _c +556 140 531 84 482 45 _c +432 6 362 -13 271 -13 _c +240 -13 208 -10 176 -4 _c +144 1 110 10 76 22 _c +76 117 _l +103 101 133 89 166 81 _c +198 73 232 69 268 69 _c +330 69 377 81 409 105 _c +441 129 458 165 458 212 _c +458 254 443 288 413 312 _c +383 336 341 349 287 349 _c +}_e{202 349 _l +202 430 _l +291 430 _l +339 430 376 439 402 459 _c +428 478 441 506 441 543 _c +441 580 427 609 401 629 _c +374 649 336 659 287 659 _c +260 659 231 656 200 650 _c +169 644 135 635 98 623 _c +98 711 _l +135 721 170 729 203 734 _c +235 739 266 742 296 742 _c +370 742 429 725 473 691 _c +517 657 539 611 539 553 _c +539 513 527 479 504 451 _c +481 423 448 403 406 393 _c +_cl}_e}_d +/four{636 0 49 0 580 729 _sc +378 643 _m +129 254 _l +378 254 _l +378 643 _l +352 729 _m +476 729 _l +476 254 _l +580 254 _l +580 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bind def +/l { lineto } bind def +/r { rlineto } bind def +/c { curveto } bind def +/cl { closepath } bind def +/box { +m +1 index 0 r +0 exch r +neg 0 r +cl +} bind def +/clipbox { +box +clip +newpath +} bind def +%!PS-Adobe-3.0 Resource-Font +%%Title: Bitstream Vera Sans +%%Copyright: Copyright (c) 2003 by Bitstream, Inc. All Rights Reserved. +%%Creator: Converted from TrueType to type 3 by PPR +25 dict begin +/_d{bind def}bind def +/_m{moveto}_d +/_l{lineto}_d +/_cl{closepath eofill}_d +/_c{curveto}_d +/_sc{7 -1 roll{setcachedevice}{pop pop pop pop pop pop}ifelse}_d +/_e{exec}_d +/FontName /BitstreamVeraSans-Roman def +/PaintType 0 def +/FontMatrix[.001 0 0 .001 0 0]def +/FontBBox[-183 -236 1287 928]def +/FontType 3 def +/Encoding [ /space /dollar /parenleft /parenright /zero /one /two /three /four /five /six /seven /eight /P /a /b /c /d /e /g /i /l /n /p /r /t /x /y ] def +/FontInfo 10 dict dup begin +/FamilyName (Bitstream Vera Sans) def +/FullName (Bitstream Vera Sans) def +/Notice (Copyright (c) 2003 by Bitstream, Inc. All Rights Reserved. Bitstream Vera is a trademark of Bitstream, Inc.) def +/Weight (Roman) def +/Version (Release 1.10) def +/ItalicAngle 0.0 def +/isFixedPitch false def +/UnderlinePosition -213 def +/UnderlineThickness 143 def +end readonly def +/CharStrings 28 dict dup begin +/space{318 0 0 0 0 0 _sc +}_d +/dollar{{636 0 83 -146 553 760 _sc +338 -146 _m +289 -146 _l +289 0 _l +254 0 220 4 186 12 _c +152 19 117 30 83 45 _c +83 133 _l +116 112 150 96 184 86 _c +218 75 253 69 289 69 _c +289 292 _l +217 304 164 324 132 352 _c +99 380 83 418 83 467 _c +83 519 100 561 136 592 _c +171 622 222 640 289 645 _c +289 760 _l +338 760 _l +338 646 _l +368 645 397 642 425 637 _c +}_e{453 631 481 624 509 616 _c +509 531 _l +481 544 453 554 425 562 _c +397 570 368 574 338 576 _c +338 367 _l +412 355 466 335 501 306 _c +535 276 553 236 553 186 _c +553 131 534 88 497 56 _c +460 24 407 5 338 1 _c +338 -146 _l +289 376 _m +289 576 _l +251 572 222 561 202 544 _c +182 526 173 503 173 475 _c +173 447 182 425 200 409 _c +218 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zG3E#I_VW!AeWcr{!he6T_Xni<^9S4J{n(p7e{gHikG22#ga5sZpDQ8$_kUO8KUO2H arG47>Ai0rGE^QY-*PgdzZq)2mfBqkmN{rV4 literal 0 HcmV?d00001 diff --git a/thinkbayes.py b/thinkbayes.py index 7298400..92f7d38 100644 --- a/thinkbayes.py +++ b/thinkbayes.py @@ -28,7 +28,7 @@ import scipy.stats from scipy.special import erf, erfinv - +from networkx import DiGraph def Odds(p): """Computes odds for a given probability. @@ -64,7 +64,7 @@ def Probability2(yes, no): """Computes the probability corresponding to given odds. Example: yes=2, no=1 means 2:1 odds in favor, or 2/3 probability. - + yes, no: int or float odds in favor """ return float(yes) / (yes + no) @@ -206,7 +206,7 @@ def Scale(self, factor): def Log(self, m=None): """Log transforms the probabilities. - + Removes values with probability 0. Normalizes so that the largest logprob is 0. @@ -359,7 +359,7 @@ def Subtract(self, other): class Pmf(_DictWrapper): """Represents a probability mass function. - + Values can be any hashable type; probabilities are floating-point. Pmfs are not necessarily normalized. """ @@ -893,7 +893,7 @@ def Random(self): def Sample(self, n): """Generates a random sample from this distribution. - + Args: n: int length of the sample """ @@ -1134,6 +1134,17 @@ def LogLikelihood(self, data, hypo): data: some representation of the data """ raise UnimplementedMethodException() + """ + computes the Likelihood ratio of two hypotheses, given some data: + If Log==True, it calculates the log of the Likelihood Ratio, which is the default. + """ + def LikelihoodRatio(self, data, hyp1, hyp2, Log=True): + like1 = self.Likelihood(data, hyp1) + like2 = self.Likelihood(data, hyp2) + if not Log: + return float(like1)/like2 + else: + return math.log(float(like1)/like2) def Print(self): """Prints the hypotheses and their probabilities.""" @@ -1410,7 +1421,7 @@ def EvalGaussianPdf(x, mu, sigma): x: value mu: mean sigma: standard deviation - + returns: float probability density """ return scipy.stats.norm.pdf(x, mu, sigma) @@ -1418,7 +1429,7 @@ def EvalGaussianPdf(x, mu, sigma): def MakeGaussianPmf(mu, sigma, num_sigmas, n=201): """Makes a PMF discrete approx to a Gaussian distribution. - + mu: float mean sigma: float standard deviation num_sigmas: how many sigmas to extend in each direction @@ -1443,7 +1454,7 @@ def EvalBinomialPmf(k, n, p): Returns the probabily of k successes in n trials with probability p. """ return scipy.stats.binom.pmf(k, n, p) - + def EvalPoissonPmf(k, lam): """Computes the Poisson PMF. @@ -1511,13 +1522,13 @@ def MakeExponentialPmf(lam, high, n=200): def StandardGaussianCdf(x, root2=math.sqrt(2)): """Evaluates the CDF of the standard Gaussian distribution. - + See http://en.wikipedia.org/wiki/Normal_distribution #Cumulative_distribution_function Args: x: float - + Returns: float """ @@ -1526,14 +1537,14 @@ def StandardGaussianCdf(x, root2=math.sqrt(2)): def GaussianCdf(x, mu=0, sigma=1): """Evaluates the CDF of the gaussian distribution. - + Args: x: float mu: mean parameter - + sigma: standard deviation parameter - + Returns: float """ @@ -1543,15 +1554,15 @@ def GaussianCdf(x, mu=0, sigma=1): def GaussianCdfInverse(p, mu=0, sigma=1): """Evaluates the inverse CDF of the gaussian distribution. - See http://en.wikipedia.org/wiki/Normal_distribution#Quantile_function + See http://en.wikipedia.org/wiki/Normal_distribution#Quantile_function Args: p: float mu: mean parameter - + sigma: standard deviation parameter - + Returns: float """ @@ -1728,7 +1739,7 @@ def BinomialCoef(n, k): def LogBinomialCoef(n, k): """Computes the log of the binomial coefficient. - +v http://math.stackexchange.com/questions/64716/ approximating-the-logarithm-of-the-binomial-coefficient @@ -1739,4 +1750,75 @@ def LogBinomialCoef(n, k): """ return n * log(n) - k * log(k) - (n - k) * log(n - k) +class BayesNet(DiGraph, Joint): + """ + A BayesNet is both, a graph and a joint distribution. For now, it only + allows for binary variables and positive causal effects (in fact, all causal effects are assumed to be the same). + The joint probability is encoded, using the Noisy-OR encoding (Pearl 1988). + """ + def __init__(self, data=None, name='', p=0.5, causal_effect=0.5): + + DiGraph.__init__(self, data=data, name=name) + Joint.__init__(self) + self.p=p + self.causal_effect=causal_effect + self.n=len(self.nodes()) + self.support=[] + + def add_edges_from(self, ebunch): + #first, we rename the nodes to be indices. This is practical + #for manipulating the joint distribution (maybe not ideal). + bunchset=set([v for v, b in ebunch] + [b for v, b in ebunch]) + for i, n in enumerate(bunchset): + for l, k in ebunch: + index=ebunch.index((l, k)) + if l==n: + l=i + elif k==n: + k=i + ebunch[index]=l, k + + DiGraph.add_edges_from(self, ebunch=ebunch) + + fro, to = zip(*self.edges()) + self.indep_vars=list(set(f for f in fro if f not in set(to))) + self.dep_vars =list(set(to)) + for var in self.indep_vars: + self.node[var]['pmf']=Pmf() + self.node[var]['pmf'].Set(1,self.p) + self.node[var]['pmf'].Set(0, 1-self.p) + #for var in self.dep_vars: + # self.node[var]['pmf']=Pmf() + # self.node[var]['pmf'].Set(1,0) #first set it all to 0 + # self.node[var]['pmf'].Set(0, 1) + + + for w in self.dep_vars: + self.node[w]['weight']={} + + for i in self.nodes(): + for j in self.edge[i]: + self.node[j]['weight'][i]=(1-self.causal_effect) + + self.support=[] + n=len(self.nodes()) + for outcome in range(2**n): + self.support.append(tuple([(outcome>>i)&1 for i in xrange(n-1,-1,-1)])) + + + for outcome in self.support: + pr=[0]*len(outcome) + p_out=1 + for i in range(len(outcome)): + if i in self.indep_vars: + pr[i]=self.node[i]['pmf'].d[outcome[i]] + p_out *=pr[i] + else: + tot=1 + for node in self.node[i]['weight']: + tot *=(self.node[i]['weight'][node]**outcome[node]) + pr[i]=1-tot if outcome[i]==1 else 1-(1-tot) + p_out *=pr[i] + + self.Set(outcome, p_out) diff --git a/thinkbayes.pyc b/thinkbayes.pyc new file mode 100644 index 0000000000000000000000000000000000000000..40d7494f68dabb4f0763ef9b16c9589759149389 GIT binary patch literal 58948 zcmeHwd2n3GdEXn{00DvrcK_@)0|UY;6=JK2mnc{>OG4$(DSi9J?ahaeS6bj>~dVl~N){abhRV z@Av!q^?L&hxFiNtx#D1Vn*HwX@BY62y1V`B1ARaHi>ISP;Qre2?{oOY1=NZ`Z~<@~astg3hE>$)M#qOXq7);^wJv?(g2;OmFOHk}h&i47UTZ7`J zptM!@_WQHjg5p4OcC$abJtz(arR}DL1Z_<2a8P_GC_SQ{J?!83Xi$74>F=Zd?6962)^q#xzJ01crt^=f z{sx_YgX;T(;{K$y2mD(O1jUh{bUC?4j)g@Zxy@u2udz4lO0 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from scipy.special import erf, erfinv from networkx import DiGraph +from numpy import zeros, array +from math import sqrt, log def Odds(p): """Computes odds for a given probability. @@ -1769,18 +1771,36 @@ def __init__(self, data=None, name='', p=0.5, causal_effect=0.5): def add_edges_from(self, ebunch): #first, we rename the nodes to be indices. This is practical #for manipulating the joint distribution (maybe not ideal). - bunchset=set([v for v, b in ebunch] + [b for v, b in ebunch]) + #newbunch=[e for e in ebunch if len(e)==3] + #singletons=[v for v in e for e in ebunch if len(e)==1] + self.bunchset=bunchset=set([v for e in ebunch for v in e[:2]]) + + self.names=zeros(len(bunchset)) for i, n in enumerate(bunchset): - for l, k in ebunch: - index=ebunch.index((l, k)) + for e in ebunch: + index=ebunch.index(e) + if len(e)==3: + l, k, dd=e + dd=dd if type(dd)==dict else {'weight': dd} + if len(e)==2: + l, k = e + dd={} if l==n: + self.names[i]=n l=i elif k==n: + self.names[i]=n k=i - ebunch[index]=l, k - DiGraph.add_edges_from(self, ebunch=ebunch) + ebunch[index]=l, k, dd + + DiGraph.add_edges_from(self, ebunch=ebunch) + self.n=len(self.nodes()) + #attach the names: + for node in self.nodes(): + self.node[node]['name']=self.names[node] + #number of nodes fro, to = zip(*self.edges()) self.indep_vars=list(set(f for f in fro if f not in set(to))) self.dep_vars =list(set(to)) @@ -1799,7 +1819,12 @@ def add_edges_from(self, ebunch): for i in self.nodes(): for j in self.edge[i]: - self.node[j]['weight'][i]=(1-self.causal_effect) + if self.edge[i][j]=={} or 'weight' in self.edge[i][j] and self.edge[i][j]['weight'] in set(['+', '-']): + self.node[j]['weight'][i]=(1-self.causal_effect) + elif type(self.edge[i][j]['weight'])==float and self.edge[i][j]['weight'] >=0: + self.node[j]['weight'][i]=(1-self.edge[i][j]['weight']) + elif type(self.edge[i][j]['weight'])==float and self.edge[i][j]['weight'] <=0: + self.node[j]['weight'][i]=(1-abs(self.edge[i][j]['weight'])) self.support=[] n=len(self.nodes()) @@ -1817,8 +1842,32 @@ def add_edges_from(self, ebunch): else: tot=1 for node in self.node[i]['weight']: - tot *=(self.node[i]['weight'][node]**outcome[node]) + if self.edge[node][i]=={} or 'weight' in self.edge[node][i] and (self.edge[node][i]['weight'] =='+' or type(self.edge[node][i]['weight'])==float and self.edge[node][i]['weight'] >=0): + tot *=((1.0-self.node[i]['weight'][node])**outcome[node]) + else: + tot *=((1.0-abs(self.node[i]['weight'][node]))**(1-outcome[node])) + pr[i]=1-tot if outcome[i]==1 else 1-(1-tot) p_out *=pr[i] self.Set(outcome, p_out) + + def MakeMixture(self, other, lamb=0.5): + mixed = Joint() #mixing the two probability distributions + for x, p in self.Items(): + mixed.Set(x,lamb * p + (1 - lamb) * other.d[x]) + return mixed + + def KL_divergence(self, other): + """ Compute KL divergence of two BayesNets.""" + try: + return sum(p * log((p /other.d[x])) for x, p in self.Items() if p != 0.0 or p != 0) + except ZeroDivisionError: + return float("inf") + + def JensenShannonDivergence(self, other): + JSD = 0.0 + lamb=0.5 + mix=self.MakeMixture(other=other, lamb=0.5) + JSD=lamb * self.KL_divergence(mix) + lamb * other.KL_divergence(mix) + return JSD From 20b57dc995c4013af67d3e773d1548408118d926 Mon Sep 17 00:00:00 2001 From: jac2130 Date: Fri, 4 Oct 2013 17:02:46 -0400 Subject: [PATCH 3/6] included the possibility to add independent variables that are not causes of other variables. However, right now, those independent variables have to be added, using add_nodes, before edges are added, using add_edges_from. This is not very elegant, but it works for now. --- thinkbayes.py | 13 +++++++++---- 1 file changed, 9 insertions(+), 4 deletions(-) diff --git a/thinkbayes.py b/thinkbayes.py index aede0bb..8cbfac7 100644 --- a/thinkbayes.py +++ b/thinkbayes.py @@ -1773,9 +1773,9 @@ def add_edges_from(self, ebunch): #for manipulating the joint distribution (maybe not ideal). #newbunch=[e for e in ebunch if len(e)==3] #singletons=[v for v in e for e in ebunch if len(e)==1] - self.bunchset=bunchset=set([v for e in ebunch for v in e[:2]]) + self.bunchset=bunchset=set([v for e in ebunch for v in e[:2]] + self.nodes()) - self.names=zeros(len(bunchset)) + self.names=list(zeros(len(bunchset))) for i, n in enumerate(bunchset): for e in ebunch: index=ebunch.index(e) @@ -1793,7 +1793,12 @@ def add_edges_from(self, ebunch): k=i ebunch[index]=l, k, dd - + #taking care of the single node case: + for node in self.nodes(): + if node==n: + self.names[i]=n + self.remove_node(node) + self.add_node(i) DiGraph.add_edges_from(self, ebunch=ebunch) self.n=len(self.nodes()) @@ -1802,7 +1807,7 @@ def add_edges_from(self, ebunch): self.node[node]['name']=self.names[node] #number of nodes fro, to = zip(*self.edges()) - self.indep_vars=list(set(f for f in fro if f not in set(to))) + self.indep_vars=list(set(f for f in self.nodes() if f not in set(to))) self.dep_vars =list(set(to)) for var in self.indep_vars: self.node[var]['pmf']=Pmf() From f2dec652c029e675c17fdd379b8c8656a7db5f8f Mon Sep 17 00:00:00 2001 From: jac2130 Date: Sat, 5 Oct 2013 18:49:22 -0400 Subject: [PATCH 4/6] fixed some bugs and cleaned up code. --- thinkbayes.py | 73 ++++++++++++++++++++++++++++++++++++++++++--------- 1 file changed, 60 insertions(+), 13 deletions(-) diff --git a/thinkbayes.py b/thinkbayes.py index 8cbfac7..e72e444 100644 --- a/thinkbayes.py +++ b/thinkbayes.py @@ -1767,16 +1767,28 @@ def __init__(self, data=None, name='', p=0.5, causal_effect=0.5): self.causal_effect=causal_effect self.n=len(self.nodes()) self.support=[] + self.names=[] + self.indep_vars=[] + self.dep_vars=[] def add_edges_from(self, ebunch): #first, we rename the nodes to be indices. This is practical #for manipulating the joint distribution (maybe not ideal). #newbunch=[e for e in ebunch if len(e)==3] #singletons=[v for v in e for e in ebunch if len(e)==1] - self.bunchset=bunchset=set([v for e in ebunch for v in e[:2]] + self.nodes()) + if self.names: + self.names=sorted(set([v for e in ebunch for v in e[:2]] + self.names)) + + #if we don't sort, we get in trouble with comparing joint distributions (the same nodes can be ordered differently) + check_bunch=[(self.names[i], self.names[j]) for i, j in self.edges()] + if [e[:2] for e in ebunch] in check_bunch: + return + else: + self.names=sorted(set([v for e in ebunch for v in e[:2]])) + + + for i, n in enumerate(self.names): - self.names=list(zeros(len(bunchset))) - for i, n in enumerate(bunchset): for e in ebunch: index=ebunch.index(e) if len(e)==3: @@ -1785,30 +1797,27 @@ def add_edges_from(self, ebunch): if len(e)==2: l, k = e dd={} + if l==n: - self.names[i]=n l=i elif k==n: - self.names[i]=n k=i ebunch[index]=l, k, dd - #taking care of the single node case: for node in self.nodes(): - if node==n: - self.names[i]=n - self.remove_node(node) - self.add_node(i) - + if n ==self.node[node]['name']: + self.node[i]={'name': n} + self.edge[i]={} DiGraph.add_edges_from(self, ebunch=ebunch) + self.n=len(self.nodes()) #attach the names: for node in self.nodes(): self.node[node]['name']=self.names[node] #number of nodes fro, to = zip(*self.edges()) - self.indep_vars=list(set(f for f in self.nodes() if f not in set(to))) - self.dep_vars =list(set(to)) + self.indep_vars=sorted(set(f for f in self.nodes() if f not in set(to))) + self.dep_vars =sorted(set(to)) for var in self.indep_vars: self.node[var]['pmf']=Pmf() self.node[var]['pmf'].Set(1,self.p) @@ -1831,6 +1840,10 @@ def add_edges_from(self, ebunch): elif type(self.edge[i][j]['weight'])==float and self.edge[i][j]['weight'] <=0: self.node[j]['weight'][i]=(1-abs(self.edge[i][j]['weight'])) + self.SetProbs() + + def SetProbs(self): + self.d={} self.support=[] n=len(self.nodes()) for outcome in range(2**n): @@ -1857,6 +1870,40 @@ def add_edges_from(self, ebunch): self.Set(outcome, p_out) + def add_nodes_from(self, nodes, **attr): + H=copy.deepcopy(self) + self.clear() + if not H.nodes(): + DiGraph.add_nodes_from(self, nodes, **attr) + + self.names=names=sorted(nodes) + for i, n in enumerate(self.names): + self.node[i]={'name': n, 'pmf': Pmf()} + self.node[i]['pmf'].Set(1,self.p) + self.node[i]['pmf'].Set(0, 1-self.p) + self.remove_node(n) + self.edge[i]={} + self.indep_vars+=[i] + self.SetProbs() + return + + DiGraph.add_nodes_from(self, nodes, **attr) + #ind_vars=[var for var in H.indep_vars] + #DiGraph.add_nodes_from(self, ind_vars) + self.names=names=sorted(set(H.names + nodes)) + for i, n in enumerate(names): + try: + self.node[i], self.edge[i]=H.node[i], H.edge[i] + except: + self.node[i]={'name': n, 'pmf': Pmf()} + self.node[i]['pmf'].Set(1,self.p) + self.node[i]['pmf'].Set(0, 1-self.p) + self.remove_node(n) + self.edge[i]={} + self.indep_vars+=[i] + + self.SetProbs() + def MakeMixture(self, other, lamb=0.5): mixed = Joint() #mixing the two probability distributions for x, p in self.Items(): From 4f6a05a90ae42e900c645461367f655fbbc27fb7 Mon Sep 17 00:00:00 2001 From: jac2130 Date: Sat, 5 Oct 2013 19:06:17 -0400 Subject: [PATCH 5/6] some minor fixes. --- thinkbayes.py | 4 +++- 1 file changed, 3 insertions(+), 1 deletion(-) diff --git a/thinkbayes.py b/thinkbayes.py index e72e444..d415fd6 100644 --- a/thinkbayes.py +++ b/thinkbayes.py @@ -1755,7 +1755,9 @@ def LogBinomialCoef(n, k): class BayesNet(DiGraph, Joint): """ A BayesNet is both, a graph and a joint distribution. For now, it only - allows for binary variables and positive causal effects (in fact, all causal effects are assumed to be the same). + allows for binary variables. All methods that start with capital letters + relate more to joint distributions and those that are more graphical start + with small letters. The joint probability is encoded, using the Noisy-OR encoding (Pearl 1988). """ From 08c542d0286c603c0e7f5434c727fee070b4850c Mon Sep 17 00:00:00 2001 From: jac2130 Date: Tue, 8 Oct 2013 18:22:26 -0400 Subject: [PATCH 6/6] Now it integrates over effect parameters, based on a pmf that is fed into the BayesNet object. The default is a beta distribution with alpha=beta=2. --- #last_session.py# | 13669 ++++++++++++++++++++++++++++++++++++++++++++ .#last_session.py | 1 + last_session.py | 736 +++ thinkbayes.py | 26 +- 4 files changed, 14427 insertions(+), 5 deletions(-) create mode 100644 #last_session.py# create mode 120000 .#last_session.py create mode 100644 last_session.py diff --git a/#last_session.py# b/#last_session.py# new file mode 100644 index 0000000..729559e --- /dev/null +++ b/#last_session.py# @@ -0,0 +1,13669 @@ +>>> G=BayesNet() +Traceback (most recent call last): + File "", line 1, in +NameError: name 'BayesNet' is not defined +>>> G=BayesNet() +>>> ebunch=[('a', 'b', '+'), ('a', 'c', '+'), ('b', 'c', '-')] +>>> add_edges_from(G, ebunch) +Traceback (most recent call last): + File "", line 1, in +NameError: name 'add_edges_from' is not defined +>>> G.add_edges_from(ebunch) +>>> G.Items() +[((0, 1, 1), 0.0), ((1, 1, 0), 0.125), ((1, 0, 0), 0.0625), ((0, 0, 1), 0.25), ((1, 0, 1), 0.1875), ((0, 0, 0), 0.25), ((0, 1, 0), 0.0), ((1, 1, 1), 0.125)] +>>> 0.5**3 +0.125 +>>> f=lambda x, a, b: 1.0/(b-a) +>>> f(0.5, 0, 1) +Traceback (most recent call last): + File "", line 1, in +TypeError: () takes exactly 1 argument (3 given) +>>> f=lambda x, a, b: 1.0/(b-a) +>>> f(0.5, 0, 1) +1.0 +>>> pmf=Pmf() +>>> [pmf.Set(x, f(x, 0, 1)) for x in numpy.linspace(0, 1, 100)] +Traceback (most recent call last): + File "", line 1, in +NameError: name 'linespace' is not defined +>>> [pmf.Set(x, f(x, 0, 1)) for x in numpy.linspace(0, 1, 100)] +[None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None] +>>> pmf.Items()[:10] +sorted(pmf.Items()[:10]) +[(0.0, 1.0), (1.0, 1.0), (0.29292929292929293, 1.0), (0.6262626262626263, 1.0), (0.23232323232323235, 1.0), (0.58585858585858586, 1.0), (0.80808080808080818, 1.0), (0.17171717171717174, 1.0), (0.8787878787878789, 1.0), (0.27272727272727276, 1.0)] +>>> sorted(pmf.Items()) +[(0.0, 1.0), (0.17171717171717174, 1.0), (0.23232323232323235, 1.0), (0.27272727272727276, 1.0), (0.29292929292929293, 1.0), (0.58585858585858586, 1.0), (0.6262626262626263, 1.0), (0.80808080808080818, 1.0), (0.8787878787878789, 1.0), (1.0, 1.0)] +>>> sorted(pmf.Items()) +[(0.0, 1.0), (0.010101010101010102, 1.0), (0.020202020202020204, 1.0), (0.030303030303030304, 1.0), (0.040404040404040407, 1.0), (0.050505050505050511, 1.0), (0.060606060606060608, 1.0), (0.070707070707070718, 1.0), (0.080808080808080815, 1.0), (0.090909090909090912, 1.0), (0.10101010101010102, 1.0), (0.11111111111111112, 1.0), (0.12121212121212122, 1.0), (0.13131313131313133, 1.0), (0.14141414141414144, 1.0), (0.15151515151515152, 1.0), (0.16161616161616163, 1.0), (0.17171717171717174, 1.0), (0.18181818181818182, 1.0), (0.19191919191919193, 1.0), (0.20202020202020204, 1.0), (0.21212121212121213, 1.0), (0.22222222222222224, 1.0), (0.23232323232323235, 1.0), (0.24242424242424243, 1.0), (0.25252525252525254, 1.0), (0.26262626262626265, 1.0), (0.27272727272727276, 1.0), (0.28282828282828287, 1.0), (0.29292929292929293, 1.0), (0.30303030303030304, 1.0), (0.31313131313131315, 1.0), (0.32323232323232326, 1.0), (0.33333333333333337, 1.0), (0.34343434343434348, 1.0), (0.35353535353535359, 1.0), (0.36363636363636365, 1.0), (0.37373737373737376, 1.0), (0.38383838383838387, 1.0), (0.39393939393939398, 1.0), (0.40404040404040409, 1.0), (0.4141414141414142, 1.0), (0.42424242424242425, 1.0), (0.43434343434343436, 1.0), (0.44444444444444448, 1.0), (0.45454545454545459, 1.0), (0.4646464646464647, 1.0), (0.47474747474747481, 1.0), (0.48484848484848486, 1.0), (0.49494949494949497, 1.0), (0.50505050505050508, 1.0), (0.51515151515151525, 1.0), (0.5252525252525253, 1.0), (0.53535353535353536, 1.0), (0.54545454545454553, 1.0), (0.55555555555555558, 1.0), (0.56565656565656575, 1.0), (0.5757575757575758, 1.0), (0.58585858585858586, 1.0), (0.59595959595959602, 1.0), (0.60606060606060608, 1.0), (0.61616161616161624, 1.0), (0.6262626262626263, 1.0), (0.63636363636363646, 1.0), (0.64646464646464652, 1.0), (0.65656565656565657, 1.0), (0.66666666666666674, 1.0), (0.6767676767676768, 1.0), (0.68686868686868696, 1.0), (0.69696969696969702, 1.0), (0.70707070707070718, 1.0), (0.71717171717171724, 1.0), (0.72727272727272729, 1.0), (0.73737373737373746, 1.0), (0.74747474747474751, 1.0), (0.75757575757575768, 1.0), (0.76767676767676774, 1.0), (0.77777777777777779, 1.0), (0.78787878787878796, 1.0), (0.79797979797979801, 1.0), (0.80808080808080818, 1.0), (0.81818181818181823, 1.0), (0.8282828282828284, 1.0), (0.83838383838383845, 1.0), (0.84848484848484851, 1.0), (0.85858585858585867, 1.0), (0.86868686868686873, 1.0), (0.8787878787878789, 1.0), (0.88888888888888895, 1.0), (0.89898989898989912, 1.0), (0.90909090909090917, 1.0), (0.91919191919191923, 1.0), (0.92929292929292939, 1.0), (0.93939393939393945, 1.0), (0.94949494949494961, 1.0), (0.95959595959595967, 1.0), (0.96969696969696972, 1.0), (0.97979797979797989, 1.0), (0.98989898989898994, 1.0), (1.0, 1.0)] +>>> G.nodes() +[0, 1, 2] +>>> G.Conditional(2, 0, 1) +Traceback (most recent call last): + File "", line 1, in +TypeError: Conditional() takes at least 4 arguments (3 given) +>>> G.Conditional(2, 0, 1).Items() +<__main__.Pmf object at 0x2e090d0> +>>> G.Conditional(2, 0, 0).Items() +[(0, 0.375), (1, 0.625)] +>>> G.Conditional(2, 1, 0).Items() +[(0, 0.5), (1, 0.5)] +>>> G.Conditional(2, 1, 1).Items() +[(0, 0.41666666666666663), (1, 0.5833333333333333)] +>>> G.Conditional(2, 1, 1).Items() +[(0, 0.5), (1, 0.5)] +>>> Percentile(G, 6) +(1, 1, 0) +>>> Percentile(G, 7) +(1, 1, 0) +>>> Percentile(G, 8) +(1, 1, 0) +>>> Percentile(G, 9) +(1, 1, 0) +>>> Percentile(G, 10) +(1, 1, 0) +>>> Percentile(G, 11) +(1, 1, 0) +>>> Percentile(G, 12) +(1, 1, 0) +>>> Percentile(G, 13) +(1, 1, 0) +>>> Percentile(G, 13) +(1, 0, 0) +>>> G.P((1, 1, 0)) +Traceback (most recent call last): + File "", line 1, in +AttributeError: 'BayesNet' object has no attribute 'Probability' +>>> G.Prob((1, 1, 0)) +Traceback (most recent call last): + File "", line 1, in +AttributeError: 'BayesNet' object has no attribute 'P' +>>> G.Prob((1, 0, 0)) +0.125 +>>> G.Prob((0, 0, 0)) +0.0625 +>>> G.Prob((0, 1, 0)) +0.25 +>>> G.Prob((1, 1, 0)) +0.0 +>>> G.Prob((1, 1, 1)) +0.125 +>>> G.Prob((1, 0, 1)) +0.125 +>>> G.Prob((1, 0, 1)) +0.1875 +>>> gaus=lambda x: EvalGaussianPdf(x, 0, 1) +Traceback (most recent call last): + File "", line 1, in +NameError: name 'GausianPdf' is not defined +>>> gaus=lambda x: EvalGaussianPdf(x, 0, 1) +>>> gaus(1) +0.00013383022576488537 +>>> gaus(1.96) +0.24197072451914337 +>>> gaus(-1.96) +0.058440944333451476 +>>> gaus(-1.96) +0.058440944333451476 +>>> type(gaus) + +>>> xs=numpy.linspace(-2, 2, 0.5) +Traceback (most recent call last): + File "", line 1, in +TypeError: integer argument expected, got float +>>> xs=numpy.linspace(-2, 2, 20) +>>> xs +array([], dtype=float64) +>>> xs=numpy.linspace(-2, 2, 20) +>>> zip(*list(xs), [gaus(x) for x in xs]) +array([-2. , -1.78947368, -1.57894737, -1.36842105, -1.15789474, + -0.94736842, -0.73684211, -0.52631579, -0.31578947, -0.10526316, + 0.10526316, 0.31578947, 0.52631579, 0.73684211, 0.94736842, + 1.15789474, 1.36842105, 1.57894737, 1.78947368, 2. ]) +>>> zip(*xs, gauss) + File "", line 1 +SyntaxError: only named arguments may follow *expression +>>> xs=list(xs) +>>> gauss=[gaus(x) for x in xs] +>>> zip(*xs, gauss) + File "", line 1 +SyntaxError: only named arguments may follow *expression +>>> from pylab import * +>>> plot(xs, gauss) +[] +>>> pylab.show() +Traceback (most recent call last): + File "", line 1, in +NameError: name 'pylab' is not defined +>>> show() +>>> show() +>>> plot(xs, gauss) +[] +>>> show() +>>> gaus(5) +0.00013383022576488537 +>>> gaus(0) +1.4867195147342979e-06 +>>> gaus(1) +0.3989422804014327 +>>> gaus(1) +0.24197072451914337 +>>> pmf=MakeUniformPmf(0, 1, 100) +Traceback (most recent call last): + File "", line 1, in + File "/tmp/py28474dFK", line 775, in MakeUniformPmf + File "/tmp/py28474dFK", line 414, in Normalize +TypeError: unsupported operand type(s) for /: 'float' and 'dictionary-valueiterator' +>>> pmf=MakeUniformPmf(0, 1, 100) +Traceback (most recent call last): + File "", line 1, in + File "/tmp/py28474dFK", line 775, in MakeUniformPmf + File "/tmp/py28474dFK", line 414, in Normalize +TypeError: unsupported operand type(s) for /: 'float' and 'dictionary-valueiterator' +>>> pmf.d[0] +1.0 +>>> pmf.Normalize() +Traceback (most recent call last): + File "", line 1, in + File "/tmp/py28474dFK", line 414, in Normalize +TypeError: unsupported operand type(s) for /: 'float' and 'dictionary-valueiterator' +>>> pmf.Total() + +>>> sum(x for x in pmf.d.itervalues()) + +>>> sum(x for x in pmf.d.itervalues()) +100.0 +>>> pmf=MakeUniformPmf(0, 1, 100) +>>> pmf.d[1] +0.01 +>>> pmf.d[0.1] +0.01 +>>> pmf.d +Traceback (most recent call last): + File "", line 1, in +KeyError: 0.1 +>>> pmf.Items() +{0.0: 0.01, 1.0: 0.01, 0.29292929292929293: 0.01, 0.6262626262626263: 0.01, 0.23232323232323235: 0.01, 0.58585858585858586: 0.01, 0.80808080808080818: 0.01, 0.17171717171717174: 0.01, 0.8787878787878789: 0.01, 0.27272727272727276: 0.01, 0.96969696969696972: 0.01, 0.85858585858585867: 0.01, 0.28282828282828287: 0.01, 0.50505050505050508: 0.01, 0.61616161616161624: 0.01, 0.78787878787878796: 0.01, 0.95959595959595967: 0.01, 0.75757575757575768: 0.01, 0.54545454545454553: 0.01, 0.68686868686868696: 0.01, 0.71717171717171724: 0.01, 0.090909090909090912: 0.01, 0.44444444444444448: 0.01, 0.010101010101010102: 0.01, 0.060606060606060608: 0.01, 0.81818181818181823: 0.01, 0.40404040404040409: 0.01, 0.49494949494949497: 0.01, 0.4646464646464647: 0.01, 0.5757575757575758: 0.01, 0.37373737373737376: 0.01, 0.11111111111111112: 0.01, 0.91919191919191923: 0.01, 0.92929292929292939: 0.01, 0.25252525252525254: 0.01, 0.42424242424242425: 0.01, 0.51515151515151525: 0.01, 0.6767676767676768: 0.01, 0.56565656565656575: 0.01, 0.050505050505050511: 0.01, 0.84848484848484851: 0.01, 0.76767676767676774: 0.01, 0.30303030303030304: 0.01, 0.32323232323232326: 0.01, 0.77777777777777779: 0.01, 0.72727272727272729: 0.01, 0.15151515151515152: 0.01, 0.47474747474747481: 0.01, 0.53535353535353536: 0.01, 0.34343434343434348: 0.01, 0.70707070707070718: 0.01, 0.16161616161616163: 0.01, 0.18181818181818182: 0.01, 0.63636363636363646: 0.01, 0.60606060606060608: 0.01, 0.10101010101010102: 0.01, 0.070707070707070718: 0.01, 0.88888888888888895: 0.01, 0.97979797979797989: 0.01, 0.020202020202020204: 0.01, 0.14141414141414144: 0.01, 0.5252525252525253: 0.01, 0.19191919191919193: 0.01, 0.21212121212121213: 0.01, 0.73737373737373746: 0.01, 0.45454545454545459: 0.01, 0.66666666666666674: 0.01, 0.83838383838383845: 0.01, 0.12121212121212122: 0.01, 0.080808080808080815: 0.01, 0.59595959595959602: 0.01, 0.38383838383838387: 0.01, 0.98989898989898994: 0.01, 0.26262626262626265: 0.01, 0.93939393939393945: 0.01, 0.13131313131313133: 0.01, 0.94949494949494961: 0.01, 0.030303030303030304: 0.01, 0.69696969696969702: 0.01, 0.43434343434343436: 0.01, 0.90909090909090917: 0.01, 0.040404040404040407: 0.01, 0.31313131313131315: 0.01, 0.86868686868686873: 0.01, 0.79797979797979801: 0.01, 0.4141414141414142: 0.01, 0.48484848484848486: 0.01, 0.55555555555555558: 0.01, 0.64646464646464652: 0.01, 0.39393939393939398: 0.01, 0.36363636363636365: 0.01, 0.89898989898989912: 0.01, 0.74747474747474751: 0.01, 0.20202020202020204: 0.01, 0.65656565656565657: 0.01, 0.35353535353535359: 0.01, 0.24242424242424243: 0.01, 0.8282828282828284: 0.01, 0.22222222222222224: 0.01, 0.33333333333333337: 0.01} +>>> pmf.Items() +[(0.0, 0.01), (1.0, 0.01), (0.29292929292929293, 0.01), (0.6262626262626263, 0.01), (0.23232323232323235, 0.01), (0.58585858585858586, 0.01), (0.80808080808080818, 0.01), (0.17171717171717174, 0.01), (0.8787878787878789, 0.01), (0.27272727272727276, 0.01), (0.96969696969696972, 0.01), (0.85858585858585867, 0.01), (0.28282828282828287, 0.01), (0.50505050505050508, 0.01), (0.61616161616161624, 0.01), (0.78787878787878796, 0.01), (0.95959595959595967, 0.01), (0.75757575757575768, 0.01), (0.54545454545454553, 0.01), (0.68686868686868696, 0.01), (0.71717171717171724, 0.01), (0.090909090909090912, 0.01), (0.44444444444444448, 0.01), (0.010101010101010102, 0.01), (0.060606060606060608, 0.01), (0.81818181818181823, 0.01), (0.40404040404040409, 0.01), (0.49494949494949497, 0.01), (0.4646464646464647, 0.01), (0.5757575757575758, 0.01), (0.37373737373737376, 0.01), (0.11111111111111112, 0.01), (0.91919191919191923, 0.01), (0.92929292929292939, 0.01), (0.25252525252525254, 0.01), (0.42424242424242425, 0.01), (0.51515151515151525, 0.01), (0.6767676767676768, 0.01), (0.56565656565656575, 0.01), (0.050505050505050511, 0.01), (0.84848484848484851, 0.01), (0.76767676767676774, 0.01), (0.30303030303030304, 0.01), (0.32323232323232326, 0.01), (0.77777777777777779, 0.01), (0.72727272727272729, 0.01), (0.15151515151515152, 0.01), (0.47474747474747481, 0.01), (0.53535353535353536, 0.01), (0.34343434343434348, 0.01), (0.70707070707070718, 0.01), (0.16161616161616163, 0.01), (0.18181818181818182, 0.01), (0.63636363636363646, 0.01), (0.60606060606060608, 0.01), (0.10101010101010102, 0.01), (0.070707070707070718, 0.01), (0.88888888888888895, 0.01), (0.97979797979797989, 0.01), (0.020202020202020204, 0.01), (0.14141414141414144, 0.01), (0.5252525252525253, 0.01), (0.19191919191919193, 0.01), (0.21212121212121213, 0.01), (0.73737373737373746, 0.01), (0.45454545454545459, 0.01), (0.66666666666666674, 0.01), (0.83838383838383845, 0.01), (0.12121212121212122, 0.01), (0.080808080808080815, 0.01), (0.59595959595959602, 0.01), (0.38383838383838387, 0.01), (0.98989898989898994, 0.01), (0.26262626262626265, 0.01), (0.93939393939393945, 0.01), (0.13131313131313133, 0.01), (0.94949494949494961, 0.01), (0.030303030303030304, 0.01), (0.69696969696969702, 0.01), (0.43434343434343436, 0.01), (0.90909090909090917, 0.01), (0.040404040404040407, 0.01), (0.31313131313131315, 0.01), (0.86868686868686873, 0.01), (0.79797979797979801, 0.01), (0.4141414141414142, 0.01), (0.48484848484848486, 0.01), (0.55555555555555558, 0.01), (0.64646464646464652, 0.01), (0.39393939393939398, 0.01), (0.36363636363636365, 0.01), (0.89898989898989912, 0.01), (0.74747474747474751, 0.01), (0.20202020202020204, 0.01), (0.65656565656565657, 0.01), (0.35353535353535359, 0.01), (0.24242424242424243, 0.01), (0.8282828282828284, 0.01), (0.22222222222222224, 0.01), (0.33333333333333337, 0.01)] +>>> integrant=lambda x : x*(1/1) if abs(1-x) <=1 else 0 +>>> integrant(0) +Traceback (most recent call last): + File "", line 1, in +NameError: name 'integrat' is not defined +>>> integrant(1) +0 +>>> integrant(0.5) +1 +>>> integrant(0.3) +0.5 +>>> integrant(0.3) +0.3 +>>> from scipy.integrate import quad +>>> quad(integrand, 0, 1, x) +Traceback (most recent call last): + File "", line 1, in +NameError: name 'integrand' is not defined +>>> quad(integrand, 0, 1) +Traceback (most recent call last): + File "", line 1, in +NameError: name 'integrand' is not defined +>>> quad(integrant, 0, 1) +Traceback (most recent call last): + File "", line 1, in +NameError: name 'integrand' is not defined +>>> quad(integrant, 0, 1) +(0.5, 5.551115123125783e-15) +>>> EvalPoissonPmf(5, 3) +0.03608940886309672 +>>> EvalPoissonPmf(5, 5) +0.10081881344492448 +>>> EvalPoissonPmf(5, 7) +0.1754673697678507 +>>> EvalPoissonPmf(5, 10) +0.12771666829228961 +>>> EvalPoissonPmf(20, 10) +0.03783327480207071 +>>> EvalPoissonPmf(20, 10) +0.0018660813139987594 +>>> math.log(math.exp(2)) +7.38905609893065 +>>> math.log(math.exp(2)) +2.0 +>>> 1.5%1 +0.5 +>>> 1.5%1 +0.5 +>>> effect_pdf=lambda p: 1 if p>=0 and p<=1 else 0 +>>> effect_pdf(1.5) +1 +>>> effect_pdf(.6) +0 +>>> effect_pdf(.6) +1 +>>> gamma(5) +4.492160846229 +>>> from scipy.stats import beta +>>> beta(5, 6, 3) + +>>> numargs = beta.numargs +>>> numargs +2 +>>> rv=beta(2, 2) + +>>> rv=beta(2, 4) +>>> x = np.linspace(0, np.minimum(rv.dist.b, 3)) +>>> type(np) +Traceback (most recent call last): + File "", line 1, in +NameError: name 'typ' is not defined +>>> type(np) + +>>> rv.dist.b + +>>> rv.dist.b +1.0 +>>> h = plt.plot(x, rv.pdf(x)) +>>> plt.show() +>>> rv=beta(4, 2) +>>> h = plt.plot(x, rv.pdf(x)) +>>> plt.show() +>>> rv=beta(2, 2) +>>> h = plt.plot(x, rv.pdf(x)) +>>> plt.show() +>>> rv=beta(4, 2) +>>> h = plt.plot(x, rv.pdf(x)) +>>> plt.show() +>>> rv=beta(2, 2) +>>> h = plt.plot(x, rv.pdf(x)) +>>> plt.show() +>>> beta(4, 2)(0.5) +Traceback (most recent call last): + File "", line 1, in +TypeError: 'rv_frozen' object has no attribute '__getitem__' +>>> beta(4, 2).pdf(0.5) +Traceback (most recent call last): + File "", line 1, in +TypeError: 'rv_frozen' object is not callable +>>> beta(4, 2).pdf(0.6) +1.25 +>>> beta(4, 2).pdf(0.02) +1.7279999999999998 +>>> beta(2, 2).pdf(0.02) +0.00015680000000000002 +>>> beta(2, 2).pdf(0.5) +0.1176 +>>> beta(2, 2).pdf(0.6) +1.5 +>>> beta(2, 2).pdf(0.7) +1.4399999999999999 +>>> beta(2, 2).pdf(0.3) +1.2600000000000002 +>>> beta(2, 2).pdf(0.3) +1.26 +>>> f =beta(2, 2).pdf +>>> type(f) + +>>> f(0.5) +1.5 +>>> f=lambda x: beta(2, 2).pdf(x) +>>> type(f) + +>>> f(0.7) +1.5 +>>> f(0.1) +1.2600000000000002 +>>> f(0.5) +0.54000000000000015 +>>> f(0.5) +1.5 +>>> max(f(x) for x in linspace(0, 1, 1000)) +1.4998469543924089 +>>> max(f(x) for x in linspace(0, 1, 1000000)) +1.4999984969954943 +>>> max(f(x) for x in linspace(0, 1, 100000)) + + C-c C-z C-c C-cTraceback (most recent call last): + File "", line 1, in + File "", line 1, in + File "", line 1, in + File "/usr/lib/python2.7/dist-packages/scipy/stats/distributions.py", line 447, in pdf + return self.dist.pdf(x, *self.args, **self.kwds) + File "/usr/lib/python2.7/dist-packages/scipy/stats/distributions.py", line 1295, in pdf + goodargs = argsreduce(cond, *((x,)+args+(scale,))) + File "/usr/lib/python2.7/dist-packages/scipy/stats/distributions.py", line 635, in argsreduce + expand_arr = (cond==cond) +KeyboardInterrupt +>>> max(f(x) for x in linspace(0, 1, 1000)) + C-c C-cTraceback (most recent call last): + File "", line 1, in + File "", line 1, in + File "", line 1, in + File "/usr/lib/python2.7/dist-packages/scipy/stats/distributions.py", line 447, in pdf + return self.dist.pdf(x, *self.args, **self.kwds) + File "/usr/lib/python2.7/dist-packages/scipy/stats/distributions.py", line 1295, in pdf + goodargs = argsreduce(cond, *((x,)+args+(scale,))) + File "/usr/lib/python2.7/dist-packages/scipy/stats/distributions.py", line 636, in argsreduce + return [extract(cond, arr1 * expand_arr) for arr1 in newargs] +KeyboardInterrupt +>>> min(f(x) for x in linspace(0, 1, 1000)) +1.4999984969954943 +>>> min(f(x) for x in linspace(0, 1, 1000)) +0.0 +>>> rv=beta(2, 2) +>>> h = plt.plot(x, rv.pdf(x)) +>>> plt.show() +>>> def integrand(x): +... return f(x)*x +... +>>> integrant(0.7) +0.5 +>>> integrant(0.7) +0.7 +>>> f(0.7)*(0.7) +1.2600000000000002 +>>> f(0.7)*(0.7) +0.88200000000000012 +>>> integrand = lambda x: beta(2, 2).pdf(x)*x +... integrand = lambda x: beta(2, 2).pdf(x)*x +>>> integrant(0.7) +0.7 +>>> integrand = lambda x: beta(2, 2).pdf(x)*x +>>> integrant(0.7) +0.7 +>>> beta(2, 2).pdf(0.7)*0.7 +1.2600000000000002 +>>> f=lambda x: beta(2, 2).pdf(0.7)*0.7 +0.88200000000000012 +>>> f=lambda x: beta(2, 2).pdf(x)*x +>>> f(0.6) +0.88200000000000012 +>>> quad(f, 0, 1) +(0.8820000000000001, 9.792167077193883e-15) +>>> f(0.6) +0.88200000000000012 +>>> f=lambda x, a, b: beta(a, b).pdf(x)*x +>>> f(0.5) +0.86399999999999999 +>>> f(0.7) +0.88200000000000012 +>>> f(0.5) +0.75 +>>> quad(f, 0, 1) +(0.5, 5.551115123125783e-15) +>>> f=lambda x, a, b: beta(a, b).pdf(x)*x +>>> f(2, 2, 0.6) +0.0 +>>> f(0.6, 2, 2) +0.0 +>>> f(0.5, 2, 2) +0.86399999999999999 +>>> f(0.5, 2, 2) +0.75 +>>> def f(x): +... alpha=2 +... beta=2 +... return beta(alpha, beta).pdf(x)*x +... +>>> f(0.6) + at 0x3dd86e0> +>>> def f(x): +... alpha=2 +... beta=2 +... return beta(alpha, beta).pdf(x)*x +... +>>> beta(2, 2).pdf(0.6) + +>>> f=lambda x : beta(2, 2).pdf(x) +1.4399999999999999 +>>> f=lambda x : beta(a, b).pdf(x) +>>> f(0.6) +1.4399999999999999 +>>> f=lambda x, a, b : beta(a, b).pdf(x) +>>> f(0.5) +Traceback (most recent call last): + File "", line 1, in + File "", line 1, in +NameError: global name 'a' is not defined +>>> f=lambda x, a, b : beta(a, b).pdf(x) +>>> f(0.6, 2, 2) +1.4399999999999999 +>>> g = lambda x : f(x, 2, 2) +>>> g(0.6) +1.4399999999999999 +>>> H=BayesNet() +1.5 +>>> H=BayesNet() +1.44 +>>> H=BayesNet() +1.26 +>>> H=BayesNet() +1.26 +>>> H=BayesNet() +1.26 +>>> H=BayesNet() +1.44 +>>> H=BayesNet() +1.5 +>>> G.dep_vars +[0] +>>> G.dep_vars +[1, 2] +>>> G.nodes() +[0, 1, 2] +>>> g(0.6) +Traceback (most recent call last): + File "", line 1, in +TypeError: () takes exactly 3 arguments (1 given) +>>> g(0.6) +1.4399999999999999 +>>> pr= lambda x : 0.6*0.6*0.5*(1.0-x)*g(x) +>>> 0.6*0.6*0.5*quad(lambda x: (1.0-x)*g(x), 0, 1) +(0.09, 9.992007221626409e-16) +>>> 0.6*0.6*0.5*quad(lambda x: (1.0-x)*g(x), 0, 1) +Traceback (most recent call last): + File "", line 1, in +TypeError: can't multiply sequence by non-int of type 'float' +>>> 0.6*0.6*0.5*quad(lambda x: (1.0-x)*g(x), 0, 1)[0] +(0.5, 5.551115123125783e-15) +>>> 0.6*0.6*0.5*quad(lambda x, y: (1.0-x)*g(x)*(1.0-y)*g(y), 0, 1)[0] +0.09 +>>> 0.6*0.6*0.5*quad(lambda x, y: ((1.0-x)*g(x)*(1.0-y)*g(y)), 0, 1, 0, 1)[0] +Traceback (most recent call last): + File "", line 1, in + File "/usr/lib/python2.7/dist-packages/scipy/integrate/quadpack.py", line 247, in quad + retval = _quad(func,a,b,args,full_output,epsabs,epsrel,limit,points) + File "/usr/lib/python2.7/dist-packages/scipy/integrate/quadpack.py", line 312, in _quad + return _quadpack._qagse(func,a,b,args,full_output,epsabs,epsrel,limit) +TypeError: () takes exactly 2 arguments (1 given) +>>> 0.6*0.6*0.5*quad(lambda x, y: ((1.0-x)*g(x)*(1.0-y)*g(y)), 0, 0, 1, 1)[0] +0.0 +>>> quad(lambda x, y: ((1.0-x)*g(x)*(1.0-y)*g(y)), 0, 0, 1, 1)[0] +0.0 +>>> quad(lambda x, y: ((1.0-x)*g(x)*(1.0-y)*g(y)), 0, 0, 1, 1) +0.0 +>>> quad(lambda x, y: ((1.0-x)*g(x)*(1.0-y)*g(y)), 0, 1) +(0.0, 0.0, {'rlist': array([ 0.00000000e+000, 3.41409005e-316, 0.00000000e+000, + 0.00000000e+000, 0.00000000e+000, 0.00000000e+000, + 0.00000000e+000, 0.00000000e+000, 0.00000000e+000, + 0.00000000e+000, 0.00000000e+000, 0.00000000e+000, + 0.00000000e+000, 0.00000000e+000, 0.00000000e+000, + 0.00000000e+000, 0.00000000e+000, 0.00000000e+000, + 0.00000000e+000, 0.00000000e+000, 0.00000000e+000, + 0.00000000e+000, 0.00000000e+000, 0.00000000e+000, + 0.00000000e+000, 0.00000000e+000, 0.00000000e+000, + 0.00000000e+000, 0.00000000e+000, 0.00000000e+000, + 0.00000000e+000, 0.00000000e+000, 0.00000000e+000, + 0.00000000e+000, 0.00000000e+000, 0.00000000e+000, + 0.00000000e+000, 0.00000000e+000, 0.00000000e+000, + 0.00000000e+000, 0.00000000e+000, 0.00000000e+000, + 0.00000000e+000, 0.00000000e+000, 0.00000000e+000, + 0.00000000e+000, 0.00000000e+000, 0.00000000e+000, + 4.74303020e-322, 7.90505033e-323]), 'last': 1, 'elist': array([ 0.00000000e+000, 3.25981904e-316, 9.30819677e-321, + 2.97079545e-313, 0.00000000e+000, 0.00000000e+000, + 4.24400727e-314, 0.00000000e+000, 0.00000000e+000, + 1.06099946e-313, 0.00000000e+000, 0.00000000e+000, + 4.24400815e-314, 0.00000000e+000, 0.00000000e+000, + 1.26480805e-321, 0.00000000e+000, 0.00000000e+000, + 2.92835433e-312, 3.07441795e-316, 0.00000000e+000, + 0.00000000e+000, 0.00000000e+000, 0.00000000e+000, + 0.00000000e+000, 0.00000000e+000, 0.00000000e+000, + 0.00000000e+000, 0.00000000e+000, 0.00000000e+000, + 0.00000000e+000, 0.00000000e+000, 0.00000000e+000, + 0.00000000e+000, 0.00000000e+000, 0.00000000e+000, + 0.00000000e+000, 0.00000000e+000, 0.00000000e+000, + 0.00000000e+000, 0.00000000e+000, 0.00000000e+000, + 0.00000000e+000, 0.00000000e+000, 0.00000000e+000, + 0.00000000e+000, 0.00000000e+000, 0.00000000e+000, + 3.45845952e-323, 2.10077583e-312]), 'iord': array([ 1, 32634, 68611280, 0, 63285808, 0, + 6, 0, 809, 9, 1, 0, + 12, 13, 808, 15, 16, 0, + 18, 19, 811, 21, 22, 0, + 24, 25, 811, 27, 28, 0, + 30, 31, 51739168, 33, 34, 0, + 36, 37, 0, 39, 40, 41, + 42, 733389503, 44, 45, 8696288, 0, + 208, 0], dtype=int32), 'alist': array([ 0.00000000e+000, 3.16768964e-316, 0.00000000e+000, + 1.30294992e-319, 0.00000000e+000, 8.87835966e-321, + 2.12201148e-314, 0.00000000e+000, 0.00000000e+000, + 8.60069476e-320, 0.00000000e+000, 0.00000000e+000, + 0.00000000e+000, 0.00000000e+000, 0.00000000e+000, + 0.00000000e+000, 0.00000000e+000, 0.00000000e+000, + 0.00000000e+000, 0.00000000e+000, 0.00000000e+000, + 0.00000000e+000, 0.00000000e+000, 0.00000000e+000, + 0.00000000e+000, 0.00000000e+000, 0.00000000e+000, + 0.00000000e+000, 0.00000000e+000, 0.00000000e+000, + 0.00000000e+000, 0.00000000e+000, 0.00000000e+000, + 0.00000000e+000, 0.00000000e+000, 0.00000000e+000, + 0.00000000e+000, 0.00000000e+000, 0.00000000e+000, + 0.00000000e+000, 0.00000000e+000, 0.00000000e+000, + 0.00000000e+000, 0.00000000e+000, 0.00000000e+000, + 0.00000000e+000, 0.00000000e+000, 0.00000000e+000, + 8.48798317e-314, 8.48798317e-314]), 'blist': array([ 0.00000000e+000, 3.16918843e-316, 0.00000000e+000, + 0.00000000e+000, 0.00000000e+000, 0.00000000e+000, + 0.00000000e+000, 0.00000000e+000, 0.00000000e+000, + 0.00000000e+000, 0.00000000e+000, 0.00000000e+000, + 0.00000000e+000, 0.00000000e+000, 0.00000000e+000, + 0.00000000e+000, 0.00000000e+000, 0.00000000e+000, + 0.00000000e+000, 0.00000000e+000, 0.00000000e+000, + 0.00000000e+000, 0.00000000e+000, 0.00000000e+000, + 0.00000000e+000, 0.00000000e+000, 0.00000000e+000, + 0.00000000e+000, 0.00000000e+000, 0.00000000e+000, + 0.00000000e+000, 0.00000000e+000, 0.00000000e+000, + 0.00000000e+000, 0.00000000e+000, 0.00000000e+000, + 0.00000000e+000, 0.00000000e+000, 0.00000000e+000, + 0.00000000e+000, 0.00000000e+000, 0.00000000e+000, + 0.00000000e+000, 0.00000000e+000, 0.00000000e+000, + 0.00000000e+000, 0.00000000e+000, 0.00000000e+000, + 8.48798317e-314, 8.48798317e-314]), 'neval': 21}) +>>> quad(quad(lambda x, y: ((1.0-x)*g(x)*(1.0-y)*g(y)), 0, 1), 0, 1) +Traceback (most recent call last): + File "", line 1, in + File "/usr/lib/python2.7/dist-packages/scipy/integrate/quadpack.py", line 247, in quad + retval = _quad(func,a,b,args,full_output,epsabs,epsrel,limit,points) + File "/usr/lib/python2.7/dist-packages/scipy/integrate/quadpack.py", line 312, in _quad + return _quadpack._qagse(func,a,b,args,full_output,epsabs,epsrel,limit) +TypeError: () takes exactly 2 arguments (1 given) +>>> quad(lambda x, y: ((1.0-x)*g(x)*(1.0-y)*g(y)), 0, 1, args(x, y)) +Traceback (most recent call last): + File "", line 1, in + File "/usr/lib/python2.7/dist-packages/scipy/integrate/quadpack.py", line 247, in quad + retval = _quad(func,a,b,args,full_output,epsabs,epsrel,limit,points) + File "/usr/lib/python2.7/dist-packages/scipy/integrate/quadpack.py", line 312, in _quad + return _quadpack._qagse(func,a,b,args,full_output,epsabs,epsrel,limit) +TypeError: () takes exactly 2 arguments (1 given) +>>> quad(lambda x, y: ((1.0-x)*g(x)*(1.0-y)*g(y)), 0, 1, args=(x, y)) +Traceback (most recent call last): + File "", line 1, in +NameError: name 'args' is not defined +>>> f=lambda x, y: ((1.0-x)*g(x)*(1.0-y)*g(y)) +Traceback (most recent call last): + File "", line 1, in +NameError: name 'y' is not defined +>>> f=lambda x y: ((1.0-x)*g(x)*(1.0-y)*g(y)) +>>> f(0.6, 0.6) +Traceback (most recent call last): + File "", line 1, in + File "", line 1, in + File "", line 1, in +TypeError: () takes exactly 2 arguments (3 given) +>>> f=lambda (x,y): ((1.0-x)*g(x)*(1.0-y)*g(y)) + File "", line 1 + f=lambda x y: ((1.0-x)*g(x)*(1.0-y)*g(y)) + ^ +SyntaxError: invalid syntax +>>> f=lambda (x, y): ((1.0-x)*g(x)*(1.0-y)*g(y)) +>>> f((0.6, 0.6)) +Traceback (most recent call last): + File "", line 1, in +TypeError: () takes exactly 1 argument (2 given) +>>> f((0.6, 0.6)) +Traceback (most recent call last): + File "", line 1, in + File "", line 1, in + File "", line 1, in +TypeError: () takes exactly 1 argument (3 given) +>>> h=lambda (x, y): ((1.0-x)*g(x)*(1.0-y)*g(y)) +>>> g(0.6)*g(0.7) +Traceback (most recent call last): + File "", line 1, in + File "", line 1, in +TypeError: () takes exactly 1 argument (3 given) +>>> g(0.6) +Traceback (most recent call last): + File "", line 1, in + File "", line 1, in +TypeError: () takes exactly 1 argument (3 given) +>>> g = lambda x : f(x, 2, 2) +>>> g(0.6) +Traceback (most recent call last): + File "", line 1, in + File "", line 1, in +TypeError: () takes exactly 1 argument (3 given) +>>> f(0.6, 2, 2) +Traceback (most recent call last): + File "", line 1, in +TypeError: () takes exactly 1 argument (3 given) +>>> f=lambda x, a, b : beta(a, b).pdf(x) +>>> g = lambda x : f(x, 2, 2) +>>> g(0.6) +Traceback (most recent call last): + File "", line 1, in + File "", line 1, in +TypeError: () takes exactly 1 argument (3 given) +>>> f=lambda x, a, b : beta(a, b).pdf(x) +>>> g = lambda x : f(x, 2, 2) +>>> g(0.6) +1.4399999999999999 +>>> h=lambda (x, y): ((1.0-x)*g(x)*(1.0-y)*g(y)) +>>> h((0.6, 0.2)) +0.33177599999999996 +>>> h((0.6, 0.2)) +0.44236800000000009 +>>> quad(lambda x, y: ((1.0-x)*g(x)*(1.0-y)*g(y)), 0, 1, args=(x, y)) +Traceback (most recent call last): + File "", line 1, in +NameError: name 'y' is not defined +>>> quad(lambda y: y*g(y), 0, 1) +Traceback (most recent call last): + File "", line 1, in +NameError: name 'y' is not defined +>>> quad(lambda x, y: x*g(y), 0, 1) +(0.5, 5.551115123125783e-15) +>>> quad(lambda x, y: x*g(y), 0, 1) +Traceback (most recent call last): + File "", line 1, in + File "/usr/lib/python2.7/dist-packages/scipy/integrate/quadpack.py", line 247, in quad + retval = _quad(func,a,b,args,full_output,epsabs,epsrel,limit,points) + File "/usr/lib/python2.7/dist-packages/scipy/integrate/quadpack.py", line 312, in _quad + return _quadpack._qagse(func,a,b,args,full_output,epsabs,epsrel,limit) +TypeError: () takes exactly 2 arguments (1 given) +>>> quad(lambda x, y: x*g(y), 0, 1, args=(x, y)) + at 0x433b7d0> +>>> quad(lambda x, y: x*g(y), 0, 1, args=(y, x)) +Traceback (most recent call last): + File "", line 1, in +NameError: name 'y' is not defined +>>> tplquad(lambda x, y: x*g(y), 0, 1, args=(y, x)) +Traceback (most recent call last): + File "", line 1, in +NameError: name 'y' is not defined +>>> tplquad(lambda x, y: x*g(y), 0, 1, args=(y, x)) +Traceback (most recent call last): + File "", line 1, in +NameError: name 'tplquad' is not defined +>>> from scipy.integrate import tplquad +Traceback (most recent call last): + File "", line 1, in +ImportError: cannot import name tplquad +>>> from scipy.integrate import tplquad +>>> tplquad(lambda x, y: x*g(y), 0, 1, args=(x, y)) +Traceback (most recent call last): + File "", line 1, in +NameError: name 'y' is not defined +>>> tplquad(lambda x, y: x*g(y), 0, 1, 0, 1, args=(x, y)) +Traceback (most recent call last): + File "", line 1, in +NameError: name 'y' is not defined +>>> tplquad(lambda x, y: x*g(y), 0, 1, 0, 1, args=(x, y)) +Traceback (most recent call last): + File "", line 1, in +NameError: name 'y' is not defined +>>> 6 +>>> tplquad(g(y)*x**2, 0,1,0, 1 args=(x, y)) +Traceback (most recent call last): + File "", line 1, in +NameError: name 'y' is not defined +>>> tplquad(g(y)*x**2, 0,1,0, 1, args=(x, y)) + File "", line 1 + tplquad(g(y)*x**2, 0,1,0, 1 args=(x, y)) + ^ +SyntaxError: invalid syntax +>>> tplquad(x**2+y**2, 0,1,0, 1, args=(x, y)) +Traceback (most recent call last): + File "", line 1, in +NameError: name 'y' is not defined +>>> tplquad(lambda x, y: x**2+y**2, 0,1,0, 1, args=(x, y)) +Traceback (most recent call last): + File "", line 1, in +NameError: name 'y' is not defined +>>> tplquad(lambda x, y: d(x, y), 0,1,0, 1, args=(x, y)) +Traceback (most recent call last): + File "", line 1, in +NameError: name 'y' is not defined +>>> d=labda x, y: x**2+y**2 + File "", line 1 + labda x, y: x**2+y**2 + ^ +SyntaxError: invalid syntax +>>> d=lambda x, y: x**2+y**2 + File "", line 1 + d=labda x, y: x**2+y**2 + ^ +SyntaxError: invalid syntax +>>> d=lambda x, y: x**2+y**2 +>>> tplquad(d(x, y), 0,1,0, 1, args=(x, y)) +Traceback (most recent call last): + File "", line 1, in +NameError: name 'y' is not defined +>>> tplquad(d(x, y), 0,1,0, 1, args=(x, y)) +Traceback (most recent call last): + File "", line 1, in +NameError: name 'y' is not defined +>>> d(2, 3) +13 +>>> 2**2 + 3**2 +13 +>>> def integrand(t,n,x): +... return exp(-x*t) / t**n +... +>>> scipy.integrate.quad(integrand, 1, Inf, args=(n, x))[0] +Traceback (most recent call last): + File "", line 1, in +NameError: name 'n' is not defined +>>> import scipy.integrate +>>> integrate.quad(integrand, 1, Inf, args=(n, x))[0] +Traceback (most recent call last): + File "", line 1, in +NameError: name 'n' is not defined +>>> from scipy import integrate +>>> integrate.quad(integrand, 1, Inf, args=(n, x))[0] +Traceback (most recent call last): + File "", line 1, in +NameError: name 'n' is not defined +>>> scipy.integrate.quad_explain +Traceback (most recent call last): + File "", line 1, in +NameError: name 'quad_explain' is not defined +>>> scipy.integrate.quad_explain() + +>>> scipy.integrate.quad_explain() + +Extra information for quad() inputs and outputs: + + If full_output is non-zero, then the third output argument (infodict) + is a dictionary with entries as tabulated below. For infinite limits, the + range is transformed to (0,1) and the optional outputs are given with + respect to this transformed range. Let M be the input argument limit and + let K be infodict['last']. The entries are: + + 'neval' : The number of function evaluations. + 'last' : The number, K, of subintervals produced in the subdivision process. + 'alist' : A rank-1 array of length M, the first K elements of which are the + left end points of the subintervals in the partition of the + integration range. + 'blist' : A rank-1 array of length M, the first K elements of which are the + right end points of the subintervals. + 'rlist' : A rank-1 array of length M, the first K elements of which are the + integral approximations on the subintervals. + 'elist' : A rank-1 array of length M, the first K elements of which are the + moduli of the absolute error estimates on the subintervals. + 'iord' : A rank-1 integer array of length M, the first L elements of + which are pointers to the error estimates over the subintervals + with L=K if K<=M/2+2 or L=M+1-K otherwise. Let I be the sequence + infodict['iord'] and let E be the sequence infodict['elist']. + Then E[I[1]], ..., E[I[L]] forms a decreasing sequence. + + If the input argument points is provided (i.e. it is not None), the + following additional outputs are placed in the output dictionary. Assume the + points sequence is of length P. + + 'pts' : A rank-1 array of length P+2 containing the integration limits + and the break points of the intervals in ascending order. + This is an array giving the subintervals over which integration + will occur. + 'level' : A rank-1 integer array of length M (=limit), containing the + subdivision levels of the subintervals, i.e., if (aa,bb) is a + subinterval of (pts[1], pts[2]) where pts[0] and pts[2] are + adjacent elements of infodict['pts'], then (aa,bb) has level l if + |bb-aa|=|pts[2]-pts[1]| * 2**(-l). + 'ndin' : A rank-1 integer array of length P+2. After the first integration + over the intervals (pts[1], pts[2]), the error estimates over some + of the intervals may have been increased artificially in order to + put their subdivision forward. This array has ones in slots + corresponding to the subintervals for which this happens. + +Weighting the integrand: + + The input variables, weight and wvar, are used to weight the integrand by + a select list of functions. Different integration methods are used + to compute the integral with these weighting functions. The possible values + of weight and the corresponding weighting functions are. + + 'cos' : cos(w*x) : wvar = w + 'sin' : sin(w*x) : wvar = w + 'alg' : g(x) = ((x-a)**alpha)*((b-x)**beta) : wvar = (alpha, beta) + 'alg-loga': g(x)*log(x-a) : wvar = (alpha, beta) + 'alg-logb': g(x)*log(b-x) : wvar = (alpha, beta) + 'alg-log' : g(x)*log(x-a)*log(b-x) : wvar = (alpha, beta) + 'cauchy' : 1/(x-c) : wvar = c + + wvar holds the parameter w, (alpha, beta), or c depending on the weight + selected. In these expressions, a and b are the integration limits. + + For the 'cos' and 'sin' weighting, additional inputs and outputs are + available. + + For finite integration limits, the integration is performed using a + Clenshaw-Curtis method which uses Chebyshev moments. For repeated + calculations, these moments are saved in the output dictionary: + + 'momcom' : The maximum level of Chebyshev moments that have been computed, + i.e., if M_c is infodict['momcom'] then the moments have been + computed for intervals of length |b-a|* 2**(-l), l=0,1,...,M_c. + 'nnlog' : A rank-1 integer array of length M(=limit), containing the + subdivision levels of the subintervals, i.e., an element of this + array is equal to l if the corresponding subinterval is + |b-a|* 2**(-l). + 'chebmo' : A rank-2 array of shape (25, maxp1) containing the computed + Chebyshev moments. These can be passed on to an integration + over the same interval by passing this array as the second + element of the sequence wopts and passing infodict['momcom'] as + the first element. + + If one of the integration limits is infinite, then a Fourier integral is + computed (assuming w neq 0). If full_output is 1 and a numerical error + is encountered, besides the error message attached to the output tuple, + a dictionary is also appended to the output tuple which translates the + error codes in the array info['ierlst'] to English messages. The output + information dictionary contains the following entries instead of 'last', + 'alist', 'blist', 'rlist', and 'elist': + + 'lst' : The number of subintervals needed for the integration (call it K_f). + 'rslst' : A rank-1 array of length M_f=limlst, whose first K_f elements + contain the integral contribution over the interval (a+(k-1)c, + a+kc) where c = (2*floor(|w|) + 1) * pi / |w| and k=1,2,...,K_f. + 'erlst' : A rank-1 array of length M_f containing the error estimate + corresponding to the interval in the same position in + infodict['rslist']. + 'ierlst' : A rank-1 integer array of length M_f containing an error flag + corresponding to the interval in the same position in + infodict['rslist']. See the explanation dictionary (last entry + in the output tuple) for the meaning of the codes. +>>> quad(x**2, -inf, inf) +Traceback (most recent call last): + File "", line 1, in +NameError: name 'quand' is not defined +>>> quad(lambda x: x**2, -inf, inf) +Traceback (most recent call last): + File "", line 1, in + File "/usr/lib/python2.7/dist-packages/scipy/integrate/quadpack.py", line 247, in quad + retval = _quad(func,a,b,args,full_output,epsabs,epsrel,limit,points) + File "/usr/lib/python2.7/dist-packages/scipy/integrate/quadpack.py", line 314, in _quad + return _quadpack._qagie(func,bound,infbounds,args,full_output,epsabs,epsrel,limit) +quadpack.error: quad: first argument is not callable +>>> quad(lambda x: 1/x, -inf, inf) +/usr/lib/python2.7/dist-packages/scipy/integrate/quadpack.py:288: UserWarning: The integral is probably divergent, or slowly convergent. + warnings.warn(msg) +(-0.6631277205452187, 0.0028429183615096276) +>>> quad(lambda x: 1/x**2, -inf, inf) +(0.0, 0.0) +>>> quad(lambda x: log(x), -inf, inf) +(-1.999999997915367, 6.233105143138573e-09) +>>> quad(log, -inf, inf) +Traceback (most recent call last): + File "", line 1, in + File "/usr/lib/python2.7/dist-packages/scipy/integrate/quadpack.py", line 247, in quad + retval = _quad(func,a,b,args,full_output,epsabs,epsrel,limit,points) + File "/usr/lib/python2.7/dist-packages/scipy/integrate/quadpack.py", line 314, in _quad + return _quadpack._qagie(func,bound,infbounds,args,full_output,epsabs,epsrel,limit) + File "", line 1, in +ValueError: math domain error +>>> quad(lambda x: 3-x, -inf, inf) +Traceback (most recent call last): + File "", line 1, in + File "/usr/lib/python2.7/dist-packages/scipy/integrate/quadpack.py", line 247, in quad + retval = _quad(func,a,b,args,full_output,epsabs,epsrel,limit,points) + File "/usr/lib/python2.7/dist-packages/scipy/integrate/quadpack.py", line 314, in _quad + return _quadpack._qagie(func,bound,infbounds,args,full_output,epsabs,epsrel,limit) +ValueError: math domain error +>>> quad(lambda x: 3*(x-x**2), -inf, inf) +(-6.0, 6.661338147750939e-15) +>>> quad(lambda x: 3-1/float(x), -inf, inf) +(1.999682186528256, 0.0009627967613594635) +>>> quad(lambda x: 3-1/float(x), -inf, inf) +(-6.0, 6.661338147750939e-15) +>>> quad(beta(x, 2,2), 0, 1) +Traceback (most recent call last): + File "", line 1, in + File "/usr/lib/python2.7/dist-packages/scipy/integrate/quadpack.py", line 247, in quad + retval = _quad(func,a,b,args,full_output,epsabs,epsrel,limit,points) + File "/usr/lib/python2.7/dist-packages/scipy/integrate/quadpack.py", line 312, in _quad + return _quadpack._qagse(func,a,b,args,full_output,epsabs,epsrel,limit) +quadpack.error: quad: first argument is not callable +>>> g(0.6) +1.4399999999999999 +>>> beta(2, 2) + +>>> beta(2, 2).pdf(x) + +>>> beta(2, 2).pdf(0.6) +array([ 0. , 0.11995002, 0.23490212, 0.34485631, 0.44981258, + 0.54977093, 0.64473136, 0.73469388, 0.81965848, 0.89962516, + 0.97459392, 1.04456476, 1.10953769, 1.1695127 , 1.2244898 , + 1.27446897, 1.31945023, 1.35943357, 1.39441899, 1.4244065 , + 1.44939608, 1.46938776, 1.48438151, 1.49437734, 1.49937526, + 1.49937526, 1.49437734, 1.48438151, 1.46938776, 1.44939608, + 1.4244065 , 1.39441899, 1.35943357, 1.31945023, 1.27446897, + 1.2244898 , 1.1695127 , 1.10953769, 1.04456476, 0.97459392, + 0.89962516, 0.81965848, 0.73469388, 0.64473136, 0.54977093, + 0.44981258, 0.34485631, 0.23490212, 0.11995002, 0. ]) +>>> beta(2, 2).pdf(0.6) +1.4399999999999999 +>>> g = lambda x : f(x, 2, 2) +>>> g(0.6) +1.4399999999999999 +>>> beta(2, 2).pdf(0.6) +1.4399999999999999 +>>> quad(g*x, 0, 1) +(1.0, 1.1102230246251565e-14) +>>> quad(h, 0, 1) +Traceback (most recent call last): + File "", line 1, in +TypeError: unsupported operand type(s) for *: 'function' and 'float' +>>> h=lambda x: g(x)*x +>>> quad(h, 0, 1) +(0.5, 5.551115123125783e-15) +>>> sum(g(x)*x for x in linspace(0, 1, 1000)) +49.494949494949481 +>>> sum(g(x)*x/1000 for x in linspace(0, 1, 1000)) +499.49949949949917 +>>> sum(g(x)*x/10000 for x in linspace(0, 1, 10000)) +0.49949949949949962 +>>> sum(g(x)*x/10000 for x in linspace(0, 1, 10000)) +0.49994999499950143 +>>> plt.plot(xs, [g(x) for x in xs]) +[] +>>> plt.show() +>>> plt.plot(xs, [g(x) for x in xs]) +[] +>>> plot(xs, [g(x) for x in xs]) +[] +>>> plt.show() +>>> plot(xs, [g(x) for x in xs]) +[] +>>> show() +>>> sum(g(x)/len(xs) for x in xs) +4.8199445983379521 +>>> sum(g(x) for x in xs) +0.24099722991689759 +>>> xs +[-2.0, -1.7894736842105263, -1.5789473684210527, -1.368421052631579, -1.1578947368421053, -0.94736842105263164, -0.73684210526315796, -0.52631578947368429, -0.31578947368421062, -0.10526315789473695, 0.10526315789473673, 0.31578947368421062, 0.52631578947368407, 0.73684210526315752, 0.94736842105263142, 1.1578947368421053, 1.3684210526315788, 1.5789473684210522, 1.7894736842105261, 2.0] +>>> xs=linspace(0, 1, 100) +>>> plot(xs, [g(x) for x in xs]) +[] +>>> show() +>>> sum(g(x)*x for x in xs) +98.989898989898947 +>>> quad(g, 0, 1) +Traceback (most recent call last): + File "", line 1, in + File "/usr/lib/python2.7/dist-packages/scipy/integrate/quadpack.py", line 247, in quad + retval = _quad(func,a,b,args,full_output,epsabs,epsrel,limit,points) + File "/usr/lib/python2.7/dist-packages/scipy/integrate/quadpack.py", line 312, in _quad + return _quadpack._qagse(func,a,b,args,full_output,epsabs,epsrel,limit) +quadpack.error: quad: first argument is not callable +>>> quad(g*x, 0, 1) +(1.0, 1.1102230246251565e-14) +>>> sum(g(x)*x/float(len(x)) for x in xs) +49.494949494949481 +>>> quad(h, 0, 1) +Traceback (most recent call last): + File "", line 1, in +TypeError: unsupported operand type(s) for *: 'function' and 'float' +>>> h=lambda x: g(x)*(1-x) +>>> quad(h, 0, 1) +(0.5, 5.551115123125783e-15) +>>> sum(g(x)*x/float(len(xs)) for x in xs) +Traceback (most recent call last): + File "", line 1, in + File "/usr/lib/python2.7/dist-packages/numpy/core/fromnumeric.py", line 1500, in sum + res = _sum_(a) + File "", line 1, in +TypeError: object of type 'numpy.float64' has no len() +>>> sum(g(x)*x/float(len(xs)) for x in xs) +0.49494949494949486 +>>> h=lambda x: g(x)*(1-x) +>>> quad(h, 0, 1) +(0.5, 5.551115123125783e-15) +>>> plot(xs, [beta(4,2).pdf(x) for x in xs]) +Traceback (most recent call last): + File "", line 1, in + File "/usr/local/lib/python2.7/dist-packages/matplotlib/pyplot.py", line 2846, in plot + ret = ax.plot(*args, **kwargs) + File "/usr/local/lib/python2.7/dist-packages/matplotlib/axes.py", line 3950, in plot + self.add_line(line) + File "/usr/local/lib/python2.7/dist-packages/matplotlib/axes.py", line 1502, in add_line + self._update_line_limits(line) + File "/usr/local/lib/python2.7/dist-packages/matplotlib/axes.py", line 1513, in _update_line_limits + path = line.get_path() + File "/usr/local/lib/python2.7/dist-packages/matplotlib/lines.py", line 717, in get_path + self.recache() + File "/usr/local/lib/python2.7/dist-packages/matplotlib/lines.py", line 429, in recache + y = np.asarray(yconv, np.float_) + File "/usr/lib/python2.7/dist-packages/numpy/core/numeric.py", line 320, in asarray + return array(a, dtype, copy=False, order=order) +TypeError: float() argument must be a string or a number +>>> beta(2, 2).pdf(0.5) +1.5 +>>> sum([beta(4,2).pdf(x)*x/float(len(xs)) for x in xs]) +[] +>>> show() +>>> tot=outer([(1-x)*beta(4,2).pdf(x)/float(len(xs)) for x in xs], tot) +0.98983165670238404 +>>> quad(h, 0, 1) +(1.0, 1.1102230246251565e-14) +>>> h=lambda x: beta(4,2).pdf(x)*x +>>> h(0.5) +0.625 +>>> quad(h, 0, 1) +(0.6666666666666665, 7.401486830834376e-15) +>>> sum([beta(4,2).pdf(x)*x/float(len(xs)) for x in xs]) +0.65983166013775141 +>>> [x for x in range(1, 10) if x%2==0] +[1, 0, 1, 0, 1, 0, 1, 0, 1] +>>> less_ten_even={x for x in range(1, 10) if x%2==0} +[2, 4, 6, 8] +>>> less_ten_even={x for x in range(1, 10) if x%2==0} +>>> less_ten_even=={2, 4, 6, 8} +set([8, 2, 4, 6]) +>>> less_ten_even=={2, 4, 6, 8} +True +>>> {4, 2, 8, 6}=={2, 4, 6, 8} +True +>>> from numpy.linalg import * +Traceback (most recent call last): + File "", line 1, in +ImportError: cannot import name outer +>>> from numpy.linalg import * +>>> outer([5, 6, 7], [3, 2, 1]) +array([[15, 10, 5], + [18, 12, 6], + [21, 14, 7]]) +>>> sum(outer([5, 6, 7], [3, 2, 1])) +108 +>>> 15+10+5+18+12+6+21+14+7 +108 +>>> out=array([1]) +>>> out outer=[5, 6, 7], [3, 2, 1] + File "", line 1 + out outer=[5, 6, 7], [3, 2, 1] + ^ +SyntaxError: invalid syntax +>>> out=outer(out, outer([5, 6, 7], [3, 2, 1])) +>>> out +array([[0, 0, 0, 0, 0, 0, 0, 0, 0]]) +>>> out=array([1]) +>>> out=outer(out, out) +>>> out +array([[15, 10, 5, 18, 12, 6, 21, 14, 7]]) +>>> out=outer(out, out) +>>> out +array([[225, 150, 75, 270, 180, 90, 315, 210, 105], + [150, 100, 50, 180, 120, 60, 210, 140, 70], + [ 75, 50, 25, 90, 60, 30, 105, 70, 35], + [270, 180, 90, 324, 216, 108, 378, 252, 126], + [180, 120, 60, 216, 144, 72, 252, 168, 84], + [ 90, 60, 30, 108, 72, 36, 126, 84, 42], + [315, 210, 105, 378, 252, 126, 441, 294, 147], + [210, 140, 70, 252, 168, 84, 294, 196, 98], + [105, 70, 35, 126, 84, 42, 147, 98, 49]]) +>>> sum(out) +11664 +>>> tot=outer([(1-x)*beta(4,2).pdf(x)/float(len(xs)) for x in xs], tot) +Traceback (most recent call last): + File "", line 1, in +NameError: name 'tot' is not defined +>>> tot=array([1]) +Traceback (most recent call last): + File "", line 1, in +TypeError: 'builtin_function_or_method' object has no attribute '__getitem__' +>>> tot=array([1]) +>>> tot=outer([(1-x)*beta(4,2).pdf(x)/float(len(xs)) for x in xs], tot) +>>> tot +array([[ 0.00000000e+00], + [ 2.01978980e-07], + [ 1.58302392e-06], + [ 5.23311469e-06], + [ 1.21473406e-05], + [ 2.32284239e-05], + [ 3.92892439e-05], + [ 6.10553602e-05], + [ 8.91675365e-05], + [ 1.24184265e-04], + [ 1.66584288e-04], + [ 2.16769124e-04], + [ 2.75065591e-04], + [ 3.41728328e-04], + [ 4.16942322e-04], + [ 5.00825429e-04], + [ 5.93430899e-04], + [ 6.94749898e-04], + [ 8.04714035e-04], + [ 9.23197882e-04], + [ 1.05002150e-03], + [ 1.18495297e-03], + [ 1.32771088e-03], + [ 1.47796693e-03], + [ 1.63534834e-03], + [ 1.79944049e-03], + [ 1.96978936e-03], + [ 2.14590409e-03], + [ 2.32725951e-03], + [ 2.51329864e-03], + [ 2.70343523e-03], + [ 2.89705626e-03], + [ 3.09352452e-03], + [ 3.29218107e-03], + [ 3.49234779e-03], + [ 3.69332991e-03], + [ 3.89441854e-03], + [ 4.09489315e-03], + [ 4.29402415e-03], + [ 4.49107538e-03], + [ 4.68530664e-03], + [ 4.87597623e-03], + [ 5.06234344e-03], + [ 5.24367110e-03], + [ 5.41922810e-03], + [ 5.58829191e-03], + [ 5.75015110e-03], + [ 5.90410787e-03], + [ 6.04948058e-03], + [ 6.18560625e-03], + [ 6.31184312e-03], + [ 6.42757312e-03], + [ 6.53220445e-03], + [ 6.62517409e-03], + [ 6.70595029e-03], + [ 6.77403512e-03], + [ 6.82896701e-03], + [ 6.87032324e-03], + [ 6.89772247e-03], + [ 6.91082730e-03], + [ 6.90934674e-03], + [ 6.89303877e-03], + [ 6.86171284e-03], + [ 6.81523244e-03], + [ 6.75351756e-03], + [ 6.67654725e-03], + [ 6.58436214e-03], + [ 6.47706697e-03], + [ 6.35483309e-03], + [ 6.21790102e-03], + [ 6.06658293e-03], + [ 5.90126519e-03], + [ 5.72241091e-03], + [ 5.53056243e-03], + [ 5.32634385e-03], + [ 5.11046356e-03], + [ 4.88371680e-03], + [ 4.64698809e-03], + [ 4.40125387e-03], + [ 4.14758493e-03], + [ 3.88714898e-03], + [ 3.62121316e-03], + [ 3.35114657e-03], + [ 3.07842279e-03], + [ 2.80462240e-03], + [ 2.53143553e-03], + [ 2.26066433e-03], + [ 1.99422553e-03], + [ 1.73415299e-03], + [ 1.48260016e-03], + [ 1.24184265e-03], + [ 1.01428073e-03], + [ 8.02441876e-04], + [ 6.08983280e-04], + [ 4.36694369e-04], + [ 2.88499338e-04], + [ 1.67459670e-04], + [ 7.67766603e-05], + [ 1.97939400e-05], + [ 0.00000000e+00]]) +>>> tot=outer(tot, tot) +>>> tot +array([[ 0.00000000e+00, 0.00000000e+00, 0.00000000e+00, ..., + 0.00000000e+00, 0.00000000e+00, 0.00000000e+00], + [ 0.00000000e+00, 4.07955082e-14, 3.19737557e-13, ..., + 1.55072715e-11, 3.99795981e-12, 0.00000000e+00], + [ 0.00000000e+00, 3.19737557e-13, 2.50596474e-12, ..., + 1.21539290e-10, 3.13342806e-11, 0.00000000e+00], + ..., + [ 0.00000000e+00, 1.55072715e-11, 1.21539290e-10, ..., + 5.89465557e-09, 1.51971261e-09, 0.00000000e+00], + [ 0.00000000e+00, 3.99795981e-12, 3.13342806e-11, ..., + 1.51971261e-09, 3.91800061e-10, 0.00000000e+00], + [ 0.00000000e+00, 0.00000000e+00, 0.00000000e+00, ..., + 0.00000000e+00, 0.00000000e+00, 0.00000000e+00]]) +>>> sum(tot) +0.10889999773265797 +>>> sum(outer(tot, 0.5)) +array([[ 0.], + [ 0.], + [ 0.], + ..., + [ 0.], + [ 0.], + [ 0.]]) +>>> sum(outer(tot, 0.5)) +0.054449998866328987 +>>> (1-tot)[0] +array([[ 1. , 1. , 1. , ..., 1. , + 1. , 1. ], + [ 1. , 1. , 1. , ..., 1. , + 1. , 1. ], + [ 1. , 1. , 1. , ..., 1. , + 1. , 1. ], + ..., + [ 1. , 1. , 1. , ..., 0.99999999, + 1. , 1. ], + [ 1. , 1. , 1. , ..., 1. , + 1. , 1. ], + [ 1. , 1. , 1. , ..., 1. , + 1. , 1. ]]) +>>> (1-tot)[1][0] +array([ 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., + 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., + 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., + 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., + 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., + 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., + 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., + 1., 1., 1., 1., 1., 1., 1., 1., 1.]) +>>> sum((1-tot)) +9999.8911000022836 +>>> (1-tot)[0][0] +1.0 +>>> 0.9*0.9 +0.81 +>>> (1-tot)[2][0] +1.0 +>>> (1-tot)[2][4] +1.0 +>>> (1-tot)[2][40] +0.99999999998077049 +>>> (1-tot)[2][400] +0.9999999925830475 +>>> (1-tot)[2][-1] +Traceback (most recent call last): + File "", line 1, in +IndexError: index 400 is out of bounds for axis 0 with size 100 +>>> (1-tot)[2][60] +1.0 +>>> (1-tot)[7][60] +0.99999998906233878 +>>> (1-tot)[70][60] +0.99999957814734641 +>>> (1-tot)[-1][60] +0.99995808387504048 +>>> (1-tot)[-1][-1] +1.0 +>>> (1-tot)[-1] +1.0 +>>> (1-tot)[-1] +array([ 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., + 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., + 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., + 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., + 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., + 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., + 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., + 1., 1., 1., 1., 1., 1., 1., 1., 1.]) +>>> xs +array([ 0. , 0.01010101, 0.02020202, 0.03030303, 0.04040404, + 0.05050505, 0.06060606, 0.07070707, 0.08080808, 0.09090909, + 0.1010101 , 0.11111111, 0.12121212, 0.13131313, 0.14141414, + 0.15151515, 0.16161616, 0.17171717, 0.18181818, 0.19191919, + 0.2020202 , 0.21212121, 0.22222222, 0.23232323, 0.24242424, + 0.25252525, 0.26262626, 0.27272727, 0.28282828, 0.29292929, + 0.3030303 , 0.31313131, 0.32323232, 0.33333333, 0.34343434, + 0.35353535, 0.36363636, 0.37373737, 0.38383838, 0.39393939, + 0.4040404 , 0.41414141, 0.42424242, 0.43434343, 0.44444444, + 0.45454545, 0.46464646, 0.47474747, 0.48484848, 0.49494949, + 0.50505051, 0.51515152, 0.52525253, 0.53535354, 0.54545455, + 0.55555556, 0.56565657, 0.57575758, 0.58585859, 0.5959596 , + 0.60606061, 0.61616162, 0.62626263, 0.63636364, 0.64646465, + 0.65656566, 0.66666667, 0.67676768, 0.68686869, 0.6969697 , + 0.70707071, 0.71717172, 0.72727273, 0.73737374, 0.74747475, + 0.75757576, 0.76767677, 0.77777778, 0.78787879, 0.7979798 , + 0.80808081, 0.81818182, 0.82828283, 0.83838384, 0.84848485, + 0.85858586, 0.86868687, 0.87878788, 0.88888889, 0.8989899 , + 0.90909091, 0.91919192, 0.92929293, 0.93939394, 0.94949495, + 0.95959596, 0.96969697, 0.97979798, 0.98989899, 1. ]) +>>> outer(1-xs, 1-xs) +array([ 1. , 0.98989899, 0.97979798, 0.96969697, 0.95959596, + 0.94949495, 0.93939394, 0.92929293, 0.91919192, 0.90909091, + 0.8989899 , 0.88888889, 0.87878788, 0.86868687, 0.85858586, + 0.84848485, 0.83838384, 0.82828283, 0.81818182, 0.80808081, + 0.7979798 , 0.78787879, 0.77777778, 0.76767677, 0.75757576, + 0.74747475, 0.73737374, 0.72727273, 0.71717172, 0.70707071, + 0.6969697 , 0.68686869, 0.67676768, 0.66666667, 0.65656566, + 0.64646465, 0.63636364, 0.62626263, 0.61616162, 0.60606061, + 0.5959596 , 0.58585859, 0.57575758, 0.56565657, 0.55555556, + 0.54545455, 0.53535354, 0.52525253, 0.51515152, 0.50505051, + 0.49494949, 0.48484848, 0.47474747, 0.46464646, 0.45454545, + 0.44444444, 0.43434343, 0.42424242, 0.41414141, 0.4040404 , + 0.39393939, 0.38383838, 0.37373737, 0.36363636, 0.35353535, + 0.34343434, 0.33333333, 0.32323232, 0.31313131, 0.3030303 , + 0.29292929, 0.28282828, 0.27272727, 0.26262626, 0.25252525, + 0.24242424, 0.23232323, 0.22222222, 0.21212121, 0.2020202 , + 0.19191919, 0.18181818, 0.17171717, 0.16161616, 0.15151515, + 0.14141414, 0.13131313, 0.12121212, 0.11111111, 0.1010101 , + 0.09090909, 0.08080808, 0.07070707, 0.06060606, 0.05050505, + 0.04040404, 0.03030303, 0.02020202, 0.01010101, 0. ]) +>>> max(outer(1-xs, 1-xs)) +array([[ 1.00000000e+00, 9.89898990e-01, 9.79797980e-01, ..., + 2.02020202e-02, 1.01010101e-02, 0.00000000e+00], + [ 9.89898990e-01, 9.79900010e-01, 9.69901031e-01, ..., + 1.99979594e-02, 9.99897970e-03, 0.00000000e+00], + [ 9.79797980e-01, 9.69901031e-01, 9.60004081e-01, ..., + 1.97938986e-02, 9.89694929e-03, 0.00000000e+00], + ..., + [ 2.02020202e-02, 1.99979594e-02, 1.97938986e-02, ..., + 4.08121620e-04, 2.04060810e-04, 0.00000000e+00], + [ 1.01010101e-02, 9.99897970e-03, 9.89694929e-03, ..., + 2.04060810e-04, 1.02030405e-04, 0.00000000e+00], + [ 0.00000000e+00, 0.00000000e+00, 0.00000000e+00, ..., + 0.00000000e+00, 0.00000000e+00, 0.00000000e+00]]) +>>> max(outer(1-xs, 1-xs).all) +Traceback (most recent call last): + File "", line 1, in +ValueError: The truth value of an array with more than one element is ambiguous. Use a.any() or a.all() +>>> max(outer(1-xs, 1-xs).all()) +Traceback (most recent call last): + File "", line 1, in +TypeError: 'builtin_function_or_method' object is not iterable +>>> max(outer(1-xs, 1-xs).all()) +Traceback (most recent call last): + File "", line 1, in +TypeError: 'numpy.bool_' object is not iterable +>>> outer(1-xs, 1-xs).any() +False +>>> outer(1-xs, 1-xs)[0] +True +>>> outer(1-xs, 1-xs)[1] +array([ 1. , 0.98989899, 0.97979798, 0.96969697, 0.95959596, + 0.94949495, 0.93939394, 0.92929293, 0.91919192, 0.90909091, + 0.8989899 , 0.88888889, 0.87878788, 0.86868687, 0.85858586, + 0.84848485, 0.83838384, 0.82828283, 0.81818182, 0.80808081, + 0.7979798 , 0.78787879, 0.77777778, 0.76767677, 0.75757576, + 0.74747475, 0.73737374, 0.72727273, 0.71717172, 0.70707071, + 0.6969697 , 0.68686869, 0.67676768, 0.66666667, 0.65656566, + 0.64646465, 0.63636364, 0.62626263, 0.61616162, 0.60606061, + 0.5959596 , 0.58585859, 0.57575758, 0.56565657, 0.55555556, + 0.54545455, 0.53535354, 0.52525253, 0.51515152, 0.50505051, + 0.49494949, 0.48484848, 0.47474747, 0.46464646, 0.45454545, + 0.44444444, 0.43434343, 0.42424242, 0.41414141, 0.4040404 , + 0.39393939, 0.38383838, 0.37373737, 0.36363636, 0.35353535, + 0.34343434, 0.33333333, 0.32323232, 0.31313131, 0.3030303 , + 0.29292929, 0.28282828, 0.27272727, 0.26262626, 0.25252525, + 0.24242424, 0.23232323, 0.22222222, 0.21212121, 0.2020202 , + 0.19191919, 0.18181818, 0.17171717, 0.16161616, 0.15151515, + 0.14141414, 0.13131313, 0.12121212, 0.11111111, 0.1010101 , + 0.09090909, 0.08080808, 0.07070707, 0.06060606, 0.05050505, + 0.04040404, 0.03030303, 0.02020202, 0.01010101, 0. ]) +>>> outer(1-xs, 1-xs)[2] +array([ 0.98989899, 0.97990001, 0.96990103, 0.95990205, 0.94990307, + 0.93990409, 0.92990511, 0.91990613, 0.90990715, 0.89990817, + 0.88990919, 0.87991021, 0.86991123, 0.85991225, 0.84991327, + 0.83991429, 0.82991531, 0.81991634, 0.80991736, 0.79991838, + 0.7899194 , 0.77992042, 0.76992144, 0.75992246, 0.74992348, + 0.7399245 , 0.72992552, 0.71992654, 0.70992756, 0.69992858, + 0.6899296 , 0.67993062, 0.66993164, 0.65993266, 0.64993368, + 0.6399347 , 0.62993572, 0.61993674, 0.60993776, 0.59993878, + 0.5899398 , 0.57994082, 0.56994184, 0.55994286, 0.54994388, + 0.5399449 , 0.52994592, 0.51994694, 0.50994796, 0.49994898, + 0.48995001, 0.47995103, 0.46995205, 0.45995307, 0.44995409, + 0.43995511, 0.42995613, 0.41995715, 0.40995817, 0.39995919, + 0.38996021, 0.37996123, 0.36996225, 0.35996327, 0.34996429, + 0.33996531, 0.32996633, 0.31996735, 0.30996837, 0.29996939, + 0.28997041, 0.27997143, 0.26997245, 0.25997347, 0.24997449, + 0.23997551, 0.22997653, 0.21997755, 0.20997857, 0.19997959, + 0.18998061, 0.17998163, 0.16998265, 0.15998368, 0.1499847 , + 0.13998572, 0.12998674, 0.11998776, 0.10998878, 0.0999898 , + 0.08999082, 0.07999184, 0.06999286, 0.05999388, 0.0499949 , + 0.03999592, 0.02999694, 0.01999796, 0.00999898, 0. ]) +>>> outer(1-xs, 1-xs)[70] +array([ 0.97979798, 0.96990103, 0.96000408, 0.95010713, 0.94021018, + 0.93031323, 0.92041628, 0.91051933, 0.90062239, 0.89072544, + 0.88082849, 0.87093154, 0.86103459, 0.85113764, 0.84124069, + 0.83134374, 0.82144679, 0.81154984, 0.80165289, 0.79175594, + 0.78185899, 0.77196204, 0.7620651 , 0.75216815, 0.7422712 , + 0.73237425, 0.7224773 , 0.71258035, 0.7026834 , 0.69278645, + 0.6828895 , 0.67299255, 0.6630956 , 0.65319865, 0.6433017 , + 0.63340475, 0.62350781, 0.61361086, 0.60371391, 0.59381696, + 0.58392001, 0.57402306, 0.56412611, 0.55422916, 0.54433221, + 0.53443526, 0.52453831, 0.51464136, 0.50474441, 0.49484746, + 0.48495052, 0.47505357, 0.46515662, 0.45525967, 0.44536272, + 0.43546577, 0.42556882, 0.41567187, 0.40577492, 0.39587797, + 0.38598102, 0.37608407, 0.36618712, 0.35629017, 0.34639323, + 0.33649628, 0.32659933, 0.31670238, 0.30680543, 0.29690848, + 0.28701153, 0.27711458, 0.26721763, 0.25732068, 0.24742373, + 0.23752678, 0.22762983, 0.21773288, 0.20783594, 0.19793899, + 0.18804204, 0.17814509, 0.16824814, 0.15835119, 0.14845424, + 0.13855729, 0.12866034, 0.11876339, 0.10886644, 0.09896949, + 0.08907254, 0.07917559, 0.06927865, 0.0593817 , 0.04948475, + 0.0395878 , 0.02969085, 0.0197939 , 0.00989695, 0. ]) +>>> outer(1-xs, 1-xs)[100] +array([ 0.29292929, 0.28997041, 0.28701153, 0.28405265, 0.28109377, + 0.27813488, 0.275176 , 0.27221712, 0.26925824, 0.26629936, + 0.26334048, 0.26038159, 0.25742271, 0.25446383, 0.25150495, + 0.24854607, 0.24558718, 0.2426283 , 0.23966942, 0.23671054, + 0.23375166, 0.23079278, 0.22783389, 0.22487501, 0.22191613, + 0.21895725, 0.21599837, 0.21303949, 0.2100806 , 0.20712172, + 0.20416284, 0.20120396, 0.19824508, 0.1952862 , 0.19232731, + 0.18936843, 0.18640955, 0.18345067, 0.18049179, 0.1775329 , + 0.17457402, 0.17161514, 0.16865626, 0.16569738, 0.1627385 , + 0.15977961, 0.15682073, 0.15386185, 0.15090297, 0.14794409, + 0.14498521, 0.14202632, 0.13906744, 0.13610856, 0.13314968, + 0.1301908 , 0.12723192, 0.12427303, 0.12131415, 0.11835527, + 0.11539639, 0.11243751, 0.10947862, 0.10651974, 0.10356086, + 0.10060198, 0.0976431 , 0.09468422, 0.09172533, 0.08876645, + 0.08580757, 0.08284869, 0.07988981, 0.07693093, 0.07397204, + 0.07101316, 0.06805428, 0.0650954 , 0.06213652, 0.05917763, + 0.05621875, 0.05325987, 0.05030099, 0.04734211, 0.04438323, + 0.04142434, 0.03846546, 0.03550658, 0.0325477 , 0.02958882, + 0.02662994, 0.02367105, 0.02071217, 0.01775329, 0.01479441, + 0.01183553, 0.00887665, 0.00591776, 0.00295888, 0. ]) +>>> len(outer(1-xs, 1-xs)) +Traceback (most recent call last): + File "", line 1, in +IndexError: index 100 is out of bounds for axis 0 with size 100 +>>> outer(1-xs, 1-xs)[99] +100 +>>> outer(1-xs, 1-xs)[98] +array([ 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., + 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., + 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., + 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., + 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., + 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., + 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., + 0., 0., 0., 0., 0., 0., 0., 0., 0.]) +>>> outer(1-xs, 1-xs)[98] +array([ 0.01010101, 0.00999898, 0.00989695, 0.00979492, 0.00969289, + 0.00959086, 0.00948883, 0.0093868 , 0.00928477, 0.00918274, + 0.00908071, 0.00897868, 0.00887665, 0.00877461, 0.00867258, + 0.00857055, 0.00846852, 0.00836649, 0.00826446, 0.00816243, + 0.0080604 , 0.00795837, 0.00785634, 0.00775431, 0.00765228, + 0.00755025, 0.00744822, 0.00734619, 0.00724416, 0.00714213, + 0.0070401 , 0.00693807, 0.00683604, 0.00673401, 0.00663198, + 0.00652995, 0.00642792, 0.00632589, 0.00622385, 0.00612182, + 0.00601979, 0.00591776, 0.00581573, 0.0057137 , 0.00561167, + 0.00550964, 0.00540761, 0.00530558, 0.00520355, 0.00510152, + 0.00499949, 0.00489746, 0.00479543, 0.0046934 , 0.00459137, + 0.00448934, 0.00438731, 0.00428528, 0.00418325, 0.00408122, + 0.00397919, 0.00387716, 0.00377512, 0.00367309, 0.00357106, + 0.00346903, 0.003367 , 0.00326497, 0.00316294, 0.00306091, + 0.00295888, 0.00285685, 0.00275482, 0.00265279, 0.00255076, + 0.00244873, 0.0023467 , 0.00224467, 0.00214264, 0.00204061, + 0.00193858, 0.00183655, 0.00173452, 0.00163249, 0.00153046, + 0.00142843, 0.0013264 , 0.00122436, 0.00112233, 0.0010203 , + 0.00091827, 0.00081624, 0.00071421, 0.00061218, 0.00051015, + 0.00040812, 0.00030609, 0.00020406, 0.00010203, 0. ]) +>>> new=outer([1, 1], [1, 1]) +array([[1, 1], + [1, 1]]) +>>> new=outer(new, new) +>>> new=outer(new, new) +>>> new +array([[1, 1, 1, 1], + [1, 1, 1, 1], + [1, 1, 1, 1], + [1, 1, 1, 1]]) +>>> new=outer(new, new) +>>> new +array([[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], + [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], + [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], + [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], + [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], + [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], + [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], + [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], + [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], + [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], + [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], + [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], + [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], + [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], + [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], + [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]]) +>>> 16*16==sum(new) +True +>>> v=linspace(0, 1, 5) +>>> v +array([ 0. , 0.25, 0.5 , 0.75, 1. ]) +>>> w=linspace(0,1, 5) +>>> beta(2, 2, 0.6) +array([ 0. , 0.25, 0.5 , 0.75, 1. ]) +>>> beta(2, 2).pdf(0.5) + +>>> beta(2, 2).pdf(0.5) +1.5 +>>> outer([(1-x)*beta(4, 2).pdf(x) for x in v],[(1-y)*beta(4, 2).pdf(y) for y in w]) +array([[ 0. , 0. , 0. , 0. , 0. ], + [ 0. , 2.50282288, 0.98876953, 0.09269714, 0. ], + [ 0. , 0.98876953, 0.390625 , 0.03662109, 0. ], + [ 0. , 0.09269714, 0.03662109, 0.00343323, 0. ], + [ 0. , 0. , 0. , 0. , 0. ]]) +>>> v +array([ 0. , 0.25, 0.5 , 0.75, 1. ]) +>>> (1-0.25)**2*beta(2, 4).pdf(0.25)**2 +2.5028228759765625 +>>> plot([beta(2, 4).pdf(x) for x in linspace(0, 1, 100)], linspace(0, 1, 100)) +Traceback (most recent call last): + File "", line 1, in +NameError: name 'linespace' is not defined +>>> plot([linspace(0, 1, 100), beta(2, 4).pdf(x) for x in linspace(0, 1, 100)]) +[] +>>> show() +>>> plot([linspace(0, 1, 100), [beta(2, 4).pdf(x) for x in linspace(0, 1, 100)]) + File "", line 1 + plot([linspace(0, 1, 100), beta(2, 4).pdf(x) for x in linspace(0, 1, 100)]) + ^ +SyntaxError: invalid syntax +>>> plot(linspace(0, 1, 100), [beta(2, 4).pdf(x) for x in linspace(0, 1, 100)]) + File "", line 1 + plot([linspace(0, 1, 100), [beta(2, 4).pdf(x) for x in linspace(0, 1, 100)]) + ^ +SyntaxError: invalid syntax +>>> plot(linspace(0, 1, 100), [beta(2, 4).pdf(x) for x in linspace(0, 1, 100)]) +[] +>>> show() +>>> 1-outer([(1-x)*beta(4, 2).pdf(x) for x in v],[(1-y)*beta(4, 2).pdf(y) for y in w]) +array([[ 0. , 0. , 0. , 0. , 0. ], + [ 0. , 0.03089905, 0.10986328, 0.09269714, 0. ], + [ 0. , 0.10986328, 0.390625 , 0.32958984, 0. ], + [ 0. , 0.09269714, 0.32958984, 0.27809143, 0. ], + [ 0. , 0. , 0. , 0. , 0. ]]) +>>> 1-outer([(1-x)*beta(4, 2).pdf(x) for x in v],[(1-y)*beta(4, 2).pdf(y) for y in w]) +array([[ 1. , 1. , 1. , 1. , 1. ], + [ 1. , 0.96910095, 0.89013672, 0.90730286, 1. ], + [ 1. , 0.89013672, 0.609375 , 0.67041016, 1. ], + [ 1. , 0.90730286, 0.67041016, 0.72190857, 1. ], + [ 1. , 1. , 1. , 1. , 1. ]]) +>>> 1-(1-0.25)*(1-0.25) +0.4375 +>>> 1-0.9-0.9+0.9**2 +0.5625 +>>> 1-0.5625*beta(4, 2).pdf(0.25)**2 +0.4375 +>>> [(1-x)*beta(4, 2).pdf(x) for x in v] +[0.0, 0.17578125, 0.625, 0.52734375, 0.0] +>>> (1-0.5625)*beta(4, 2).pdf(0.25)**2 +0.9691009521484375 +>>> beta(4, 2).pdf(0.25)**2 +0.234375 +>>> beta(4, 2).pdf(0.25)**2 +0.054931640625 +>>> (1-0.5625)*beta(4, 2).pdf(0.25)**2 +0.0240325927734375 +>>> 1-(1-0.9-0.9+0.9**2)*beta(4, 2).pdf(0.9)**2 +0.010000000000000009 +>>> 1-(1-0.8-0.8+0.8**2)*beta(4, 2).pdf(0.8)**2 +0.97874236000000003 +>>> 1-(1-0.85-0.85+0.85**2)*beta(4, 2).pdf(0.85)**2 +0.83222783999999983 +>>> 1-(1-0.999-0.999+0.999**2)*beta(4, 2).pdf(0.999)**2 +0.92362722308593759 +>>> 1-(1-0.9-0.9+0.9**2)*beta(4, 2).pdf(0.9)**2 +0.99999999960239405 +>>> beta(4, 2).pdf(0.999) +0.00039760599200599816 +>>> beta(4, 2).pdf(0.8) +0.019940059980000015 +>>> beta(4, 2).pdf(0.9) +2.048 +>>> beta(4, 2).pdf(0.999) +1.4579999999999997 +>>> beta(4, 2).pdf(0.9999) +0.019940059980000015 +>>> beta(4, 2).pdf(0.9999) +0.0019994000599977794 +>>> 1-(1-0.9-0.9+0.9**2)*beta(4, 2).pdf(0.8)**2 +0.97874236000000003 +>>> 1-(1-0.9-0.9+0.9**2)*beta(4, 2).pdf(0.8)**2 +0.95805695999999996 +>>> beta(4, 2).pdf(0.8) +1.4579999999999997 +>>> beta(4, 2).pdf(0.8) +2.048 +>>> 1-(1-0.9-0.9+0.9**2)*beta(4, 2).pdf(0.9)**2 +0.95805695999999996 +>>> 1-(1-0.9-0.9+0.9**2)*(beta(4, 2).pdf(0.8)**2) +0.97874236000000003 +>>> beta(4, 2).pdf(0.9) +2.048 +>>> beta(4, 2).pdf(0.9)**2 +1.4579999999999997 +>>> beta(4, 2).pdf(0.8)**2 +2.1257639999999993 +>>> beta(4, 2).pdf(0.8)**2 +4.1943039999999998 +>>> 1-(1-0.9-0.9+0.9**2)*(beta(4, 2).pdf(0.9)**2) +0.95805695999999996 +>>> 1-(1-0.9-0.9+0.9**2)*(beta(4, 2).pdf(0.9))**2 +0.97874236000000003 +>>> 1-(1-0.9-0.9+0.9**2)*(beta(4, 2).pdf(0.8))**2 +0.97874236000000003 +>>> (1-(1-0.9-0.9+0.9**2))*(beta(4, 2).pdf(0.8))**2 +0.95805695999999996 +>>> 1-(1-0.9-0.9+0.9**2) +0.99 +>>> .99*beta(4, 2).pdf(0.9)**2 +4.1523609600000002 +>>> .99*beta(4, 2).pdf(0.9)**2 +2.1045063599999994 +>>> (1-(1-0.9-0.9+0.9**2))*(beta(4, 2).pdf(0.9))**2 +4.1523609600000002 +>>> [(1-(1-2*x+x**2))*(beta(4, 2).pdf(x))**2 for x in linspace(0, 1, 100)] +2.1045063599999994 +>>> plot(linspace(0, 1, 100), [(1-(1-2*x+x**2))*(beta(4, 2).pdf(x))**2 for x in linspace(0, 1, 100)]) +[0.0, 8.3680915501629346e-12, 1.0440410022399093e-09, 1.7383367267475884e-08, 1.268752541329204e-07, 5.892656043573313e-07, 2.0560511931131526e-06, 5.8884819397555613e-06, 1.4593999931933103e-05, 3.2385636312080679e-05, 6.5863667188914755e-05, 0.00012481414103928702, 0.000223114716568795, 0.00037973457565303555, 0.0006198119847354818, 0.00097579035386278362, 0.0014885913693440311, 0.0022088019377772411, 0.003197850259844307, 0.004529145335784906, 0.0062891535747705207, 0.0085783859214622563, 0.011512269008800131, 0.01522187428048747, 0.019854479783652498, 0.025573940395739094, 0.03256084360375152, 0.041012429582503292, 0.051142256205447587, 0.063179591750948103, 0.077368520422431877, 0.093966748366702255, 0.1132441006347313, 0.13548070246744234, 0.1609648413892914, 0.18999050983880603, 0.22285463144159448, 0.25985397752164696, 0.30128178403496109, 0.34742408277959236, 0.39855576447210228, 0.45493639506599498, 0.51680581050707675, 0.58437951895764528, 0.65784394336000751, 0.73735154103397993, 0.82301584079666601, 0.91490644183990943, 1.0130440222853423, 1.11739540894281, 1.2278687633091239, 1.3443089422445298, 1.466493095037902, 1.5941265617024947, 1.7268391403159269, 1.8641817940150873, 2.0056238708625829, 2.1505509122002548, 2.2982631272811505, 2.4479746139079883, 2.5988134064876491, 2.7498224343215116, 2.899961474074316, 3.0481101811839841, 3.1930722854748903, 3.3335810364020091, 3.4683059831665237, 3.5958611743893019, 3.7148148610907983, 3.8237007853883727, 3.9210311355689762, 4.005311246010085, 4.0750561177891553, 4.1288088327252987, 4.1651609300203862, 4.1827748105944851, 4.1804082296260798, 4.1569409326951954, 4.1114034852709489, 4.0430083390685025, 3.9511831720074833, 3.8356065311189127, 3.696245799754287, 3.5333975018328014, 3.3477299466045465, 3.140328207493055, 2.9127414179934967, 2.6670323563272844, 2.4058292785737381, 2.1323799472985869, 1.8506077892617503, 1.5651701015964539, 1.2815182108929182, 1.0059594738758921, 0.74572099182060558, 0.50901489349014006, 0.30510502318240834, 0.1443748514314134, 0.03839640599857138, 0.0] +>>> plot(linspace(0, 1, 100), [(1-(1-2*x+x**2))*(beta(4, 2).pdf(x))**2 for x in linspace(0, 1, 100)]) +[] +>>> show() +>>> sum([(1-(1-2*x+x**2))*(beta(4, 2).pdf(x))**2/len(linspace(0, 1, 100)) for x in linspace(0, 1, 100)]) +139.99997939013403 +>>> sum([(1-(1-2*x+x**2))*(beta(4, 2).pdf(x))**2/len(linspace(0, 1, 100))**2 for x in linspace(0, 1, 100)]) +1.3999997939013396 +>>> sum([(1-(1-2*x+x**2))*(beta(4, 2).pdf(x))**2/len(linspace(0, 1, 100))**2 for x in linspace(0, 1, 100)]) +0.013999997939013395 +>>> sum([(beta(4, 2).pdf(x))**2/len(linspace(0, 1, 100)) for x in linspace(0, 1, 100)]) +0.015714283653399212 +>>> sum([(beta(4, 2).pdf(x))/len(linspace(0, 1, 100)) for x in linspace(0, 1, 100)]) +1.5714283653399217 +>>> sum([x**2*(beta(4, 2).pdf(x))**2/len(linspace(0, 1, 100)) for x in linspace(0, 1, 100)]) +0.98983165670238404 +>>> sum([(1-(1-x)**2)*(beta(4, 2).pdf(x))**2/len(linspace(0, 1, 100)) for x in linspace(0, 1, 100)]) +0.7999997252640858 +>>> sum([(1-(1-x)**2)*(beta(4, 2).pdf(x))**2/len(linspace(0, 1, 100))**2 for x in linspace(0, 1, 100)]) +1.3999997939013396 +>>> sum([(1-(1-x)**2)*(beta(4, 2).pdf(x))**2 for x in linspace(0, 1, 100)]) +0.013999997939013395 +>>> sum([(1-(1-x)**2)*(beta(4, 2).pdf(x))**2 for x in linspace(0, 1, 100)])/100 +139.99997939013403 +>>> sum([(1-(1-x)**2)*(beta(4, 2).pdf(x))**2 for x in linspace(0, 1, 100)])/100 +1.3999997939013402 +>>> intermediate=(1-outer([(1-x) for x in linspace(0, 1, 100)], [(1-x) for x in linspace(0, 1, 100)]))/100*100 +>>> sum(intermediate) +array([[ 0. , 0.01010101, 0.02020202, ..., 0.97979798, + 0.98989899, 1. ], + [ 0.01010101, 0.02009999, 0.03009897, ..., 0.98000204, + 0.99000102, 1. ], + [ 0.02020202, 0.03009897, 0.03999592, ..., 0.9802061 , + 0.99010305, 1. ], + ..., + [ 0.97979798, 0.98000204, 0.9802061 , ..., 0.99959188, + 0.99979594, 1. ], + [ 0.98989899, 0.99000102, 0.99010305, ..., 0.99979594, + 0.99989797, 1. ], + [ 1. , 1. , 1. , ..., 1. , + 1. , 1. ]]) +>>> sum(intermediate) +7499.9999999999991 +>>> intermediate=(1-outer([(1-x)/100 for x in linspace(0, 1, 100)], [(1-x)/100 for x in linspace(0, 1, 100)])) +>>> sum(intermediate) +7499.9999999999991 +>>> intermediate[0] +array([[ 0. , 0.01010101, 0.02020202, ..., 0.97979798, + 0.98989899, 1. ], + [ 0.01010101, 0.02009999, 0.03009897, ..., 0.98000204, + 0.99000102, 1. ], + [ 0.02020202, 0.03009897, 0.03999592, ..., 0.9802061 , + 0.99010305, 1. ], + ..., + [ 0.97979798, 0.98000204, 0.9802061 , ..., 0.99959188, + 0.99979594, 1. ], + [ 0.98989899, 0.99000102, 0.99010305, ..., 0.99979594, + 0.99989797, 1. ], + [ 1. , 1. , 1. , ..., 1. , + 1. , 1. ]]) +>>> sum(intermediate[0]) +array([ 0. , 0.01010101, 0.02020202, 0.03030303, 0.04040404, + 0.05050505, 0.06060606, 0.07070707, 0.08080808, 0.09090909, + 0.1010101 , 0.11111111, 0.12121212, 0.13131313, 0.14141414, + 0.15151515, 0.16161616, 0.17171717, 0.18181818, 0.19191919, + 0.2020202 , 0.21212121, 0.22222222, 0.23232323, 0.24242424, + 0.25252525, 0.26262626, 0.27272727, 0.28282828, 0.29292929, + 0.3030303 , 0.31313131, 0.32323232, 0.33333333, 0.34343434, + 0.35353535, 0.36363636, 0.37373737, 0.38383838, 0.39393939, + 0.4040404 , 0.41414141, 0.42424242, 0.43434343, 0.44444444, + 0.45454545, 0.46464646, 0.47474747, 0.48484848, 0.49494949, + 0.50505051, 0.51515152, 0.52525253, 0.53535354, 0.54545455, + 0.55555556, 0.56565657, 0.57575758, 0.58585859, 0.5959596 , + 0.60606061, 0.61616162, 0.62626263, 0.63636364, 0.64646465, + 0.65656566, 0.66666667, 0.67676768, 0.68686869, 0.6969697 , + 0.70707071, 0.71717172, 0.72727273, 0.73737374, 0.74747475, + 0.75757576, 0.76767677, 0.77777778, 0.78787879, 0.7979798 , + 0.80808081, 0.81818182, 0.82828283, 0.83838384, 0.84848485, + 0.85858586, 0.86868687, 0.87878788, 0.88888889, 0.8989899 , + 0.90909091, 0.91919192, 0.92929293, 0.93939394, 0.94949495, + 0.95959596, 0.96969697, 0.97979798, 0.98989899, 1. ]) +>>> sum(intermediate[0]) +50.0 +>>> intermediate=(1/100-outer([(1-x)/100 for x in linspace(0, 1, 100)], [(1-x)/100 for x in linspace(0, 1, 100)])) +>>> sum(intermediate[0]) +99.995000000000019 +>>> intermediate=(1-outer([(1-x) for x in linspace(0, 1, 100)], [(1-x) for x in linspace(0, 1, 100)])) +>>> sum(intermediate[0]) +-0.0050000000000000001 +>>> intermediate=(1-outer([(1-x) for x in linspace(0, 1, 100)], [(1-x) for x in linspace(0, 1, 100)])) +>>> sum(intermediate[1]) +50.0 +>>> sum(intermediate[8]) +50.505050505050505 +>>> sum(intermediate[80]) +54.040404040404027 +>>> sum(intermediate[99]) +90.404040404040401 +>>> sum(intermediate[99]) +100.0 +>>> max(list(intermediate)) +Traceback (most recent call last): + File "", line 1, in +ValueError: The truth value of an array with more than one element is ambiguous. Use a.any() or a.all() +>>> max(list(intermediate)) +Traceback (most recent call last): + File "", line 1, in +ValueError: The truth value of an array with more than one element is ambiguous. Use a.any() or a.all() +>>> list(intermediate) +[array([ 0. , 0.01010101, 0.02020202, 0.03030303, 0.04040404, + 0.05050505, 0.06060606, 0.07070707, 0.08080808, 0.09090909, + 0.1010101 , 0.11111111, 0.12121212, 0.13131313, 0.14141414, + 0.15151515, 0.16161616, 0.17171717, 0.18181818, 0.19191919, + 0.2020202 , 0.21212121, 0.22222222, 0.23232323, 0.24242424, + 0.25252525, 0.26262626, 0.27272727, 0.28282828, 0.29292929, + 0.3030303 , 0.31313131, 0.32323232, 0.33333333, 0.34343434, + 0.35353535, 0.36363636, 0.37373737, 0.38383838, 0.39393939, + 0.4040404 , 0.41414141, 0.42424242, 0.43434343, 0.44444444, + 0.45454545, 0.46464646, 0.47474747, 0.48484848, 0.49494949, + 0.50505051, 0.51515152, 0.52525253, 0.53535354, 0.54545455, + 0.55555556, 0.56565657, 0.57575758, 0.58585859, 0.5959596 , + 0.60606061, 0.61616162, 0.62626263, 0.63636364, 0.64646465, + 0.65656566, 0.66666667, 0.67676768, 0.68686869, 0.6969697 , + 0.70707071, 0.71717172, 0.72727273, 0.73737374, 0.74747475, + 0.75757576, 0.76767677, 0.77777778, 0.78787879, 0.7979798 , + 0.80808081, 0.81818182, 0.82828283, 0.83838384, 0.84848485, + 0.85858586, 0.86868687, 0.87878788, 0.88888889, 0.8989899 , + 0.90909091, 0.91919192, 0.92929293, 0.93939394, 0.94949495, + 0.95959596, 0.96969697, 0.97979798, 0.98989899, 1. ]), array([ 0.01010101, 0.02009999, 0.03009897, 0.04009795, 0.05009693, + 0.06009591, 0.07009489, 0.08009387, 0.09009285, 0.10009183, + 0.11009081, 0.12008979, 0.13008877, 0.14008775, 0.15008673, + 0.16008571, 0.17008469, 0.18008366, 0.19008264, 0.20008162, + 0.2100806 , 0.22007958, 0.23007856, 0.24007754, 0.25007652, + 0.2600755 , 0.27007448, 0.28007346, 0.29007244, 0.30007142, + 0.3100704 , 0.32006938, 0.33006836, 0.34006734, 0.35006632, + 0.3600653 , 0.37006428, 0.38006326, 0.39006224, 0.40006122, + 0.4100602 , 0.42005918, 0.43005816, 0.44005714, 0.45005612, + 0.4600551 , 0.47005408, 0.48005306, 0.49005204, 0.50005102, + 0.51004999, 0.52004897, 0.53004795, 0.54004693, 0.55004591, + 0.56004489, 0.57004387, 0.58004285, 0.59004183, 0.60004081, + 0.61003979, 0.62003877, 0.63003775, 0.64003673, 0.65003571, + 0.66003469, 0.67003367, 0.68003265, 0.69003163, 0.70003061, + 0.71002959, 0.72002857, 0.73002755, 0.74002653, 0.75002551, + 0.76002449, 0.77002347, 0.78002245, 0.79002143, 0.80002041, + 0.81001939, 0.82001837, 0.83001735, 0.84001632, 0.8500153 , + 0.86001428, 0.87001326, 0.88001224, 0.89001122, 0.9000102 , + 0.91000918, 0.92000816, 0.93000714, 0.94000612, 0.9500051 , + 0.96000408, 0.97000306, 0.98000204, 0.99000102, 1. ]), array([ 0.02020202, 0.03009897, 0.03999592, 0.04989287, 0.05978982, + 0.06968677, 0.07958372, 0.08948067, 0.09937761, 0.10927456, + 0.11917151, 0.12906846, 0.13896541, 0.14886236, 0.15875931, + 0.16865626, 0.17855321, 0.18845016, 0.19834711, 0.20824406, + 0.21814101, 0.22803796, 0.2379349 , 0.24783185, 0.2577288 , + 0.26762575, 0.2775227 , 0.28741965, 0.2973166 , 0.30721355, + 0.3171105 , 0.32700745, 0.3369044 , 0.34680135, 0.3566983 , + 0.36659525, 0.37649219, 0.38638914, 0.39628609, 0.40618304, + 0.41607999, 0.42597694, 0.43587389, 0.44577084, 0.45566779, + 0.46556474, 0.47546169, 0.48535864, 0.49525559, 0.50515254, + 0.51504948, 0.52494643, 0.53484338, 0.54474033, 0.55463728, + 0.56453423, 0.57443118, 0.58432813, 0.59422508, 0.60412203, + 0.61401898, 0.62391593, 0.63381288, 0.64370983, 0.65360677, + 0.66350372, 0.67340067, 0.68329762, 0.69319457, 0.70309152, + 0.71298847, 0.72288542, 0.73278237, 0.74267932, 0.75257627, + 0.76247322, 0.77237017, 0.78226712, 0.79216406, 0.80206101, + 0.81195796, 0.82185491, 0.83175186, 0.84164881, 0.85154576, + 0.86144271, 0.87133966, 0.88123661, 0.89113356, 0.90103051, + 0.91092746, 0.92082441, 0.93072135, 0.9406183 , 0.95051525, + 0.9604122 , 0.97030915, 0.9802061 , 0.99010305, 1. ]), array([ 0.03030303, 0.04009795, 0.04989287, 0.05968779, 0.06948271, + 0.07927762, 0.08907254, 0.09886746, 0.10866238, 0.1184573 , + 0.12825222, 0.13804714, 0.14784206, 0.15763698, 0.16743189, + 0.17722681, 0.18702173, 0.19681665, 0.20661157, 0.21640649, + 0.22620141, 0.23599633, 0.24579125, 0.25558616, 0.26538108, + 0.275176 , 0.28497092, 0.29476584, 0.30456076, 0.31435568, + 0.3241506 , 0.33394552, 0.34374043, 0.35353535, 0.36333027, + 0.37312519, 0.38292011, 0.39271503, 0.40250995, 0.41230487, + 0.42209979, 0.4318947 , 0.44168962, 0.45148454, 0.46127946, + 0.47107438, 0.4808693 , 0.49066422, 0.50045914, 0.51025406, + 0.52004897, 0.52984389, 0.53963881, 0.54943373, 0.55922865, + 0.56902357, 0.57881849, 0.58861341, 0.59840833, 0.60820324, + 0.61799816, 0.62779308, 0.637588 , 0.64738292, 0.65717784, + 0.66697276, 0.67676768, 0.6865626 , 0.69635751, 0.70615243, + 0.71594735, 0.72574227, 0.73553719, 0.74533211, 0.75512703, + 0.76492195, 0.77471687, 0.78451178, 0.7943067 , 0.80410162, + 0.81389654, 0.82369146, 0.83348638, 0.8432813 , 0.85307622, + 0.86287114, 0.87266605, 0.88246097, 0.89225589, 0.90205081, + 0.91184573, 0.92164065, 0.93143557, 0.94123049, 0.95102541, + 0.96082032, 0.97061524, 0.98041016, 0.99020508, 1. ]), array([ 0.04040404, 0.05009693, 0.05978982, 0.06948271, 0.07917559, + 0.08886848, 0.09856137, 0.10825426, 0.11794715, 0.12764004, + 0.13733293, 0.14702581, 0.1567187 , 0.16641159, 0.17610448, + 0.18579737, 0.19549026, 0.20518314, 0.21487603, 0.22456892, + 0.23426181, 0.2439547 , 0.25364759, 0.26334048, 0.27303336, + 0.28272625, 0.29241914, 0.30211203, 0.31180492, 0.32149781, + 0.33119069, 0.34088358, 0.35057647, 0.36026936, 0.36996225, + 0.37965514, 0.38934803, 0.39904091, 0.4087338 , 0.41842669, + 0.42811958, 0.43781247, 0.44750536, 0.45719825, 0.46689113, + 0.47658402, 0.48627691, 0.4959698 , 0.50566269, 0.51535558, + 0.52504846, 0.53474135, 0.54443424, 0.55412713, 0.56382002, + 0.57351291, 0.5832058 , 0.59289868, 0.60259157, 0.61228446, + 0.62197735, 0.63167024, 0.64136313, 0.65105601, 0.6607489 , + 0.67044179, 0.68013468, 0.68982757, 0.69952046, 0.70921335, + 0.71890623, 0.72859912, 0.73829201, 0.7479849 , 0.75767779, + 0.76737068, 0.77706356, 0.78675645, 0.79644934, 0.80614223, + 0.81583512, 0.82552801, 0.8352209 , 0.84491378, 0.85460667, + 0.86429956, 0.87399245, 0.88368534, 0.89337823, 0.90307112, + 0.912764 , 0.92245689, 0.93214978, 0.94184267, 0.95153556, + 0.96122845, 0.97092133, 0.98061422, 0.99030711, 1. ]), array([ 0.05050505, 0.06009591, 0.06968677, 0.07927762, 0.08886848, + 0.09845934, 0.1080502 , 0.11764106, 0.12723192, 0.13682277, + 0.14641363, 0.15600449, 0.16559535, 0.17518621, 0.18477706, + 0.19436792, 0.20395878, 0.21354964, 0.2231405 , 0.23273135, + 0.24232221, 0.25191307, 0.26150393, 0.27109479, 0.28068564, + 0.2902765 , 0.29986736, 0.30945822, 0.31904908, 0.32863993, + 0.33823079, 0.34782165, 0.35741251, 0.36700337, 0.37659423, + 0.38618508, 0.39577594, 0.4053668 , 0.41495766, 0.42454852, + 0.43413937, 0.44373023, 0.45332109, 0.46291195, 0.47250281, + 0.48209366, 0.49168452, 0.50127538, 0.51086624, 0.5204571 , + 0.53004795, 0.53963881, 0.54922967, 0.55882053, 0.56841139, + 0.57800224, 0.5875931 , 0.59718396, 0.60677482, 0.61636568, + 0.62595654, 0.63554739, 0.64513825, 0.65472911, 0.66431997, + 0.67391083, 0.68350168, 0.69309254, 0.7026834 , 0.71227426, + 0.72186512, 0.73145597, 0.74104683, 0.75063769, 0.76022855, + 0.76981941, 0.77941026, 0.78900112, 0.79859198, 0.80818284, + 0.8177737 , 0.82736455, 0.83695541, 0.84654627, 0.85613713, + 0.86572799, 0.87531885, 0.8849097 , 0.89450056, 0.90409142, + 0.91368228, 0.92327314, 0.93286399, 0.94245485, 0.95204571, + 0.96163657, 0.97122743, 0.98081828, 0.99040914, 1. ]), array([ 0.06060606, 0.07009489, 0.07958372, 0.08907254, 0.09856137, + 0.1080502 , 0.11753903, 0.12702785, 0.13651668, 0.14600551, + 0.15549434, 0.16498316, 0.17447199, 0.18396082, 0.19344965, + 0.20293848, 0.2124273 , 0.22191613, 0.23140496, 0.24089379, + 0.25038261, 0.25987144, 0.26936027, 0.2788491 , 0.28833792, + 0.29782675, 0.30731558, 0.31680441, 0.32629324, 0.33578206, + 0.34527089, 0.35475972, 0.36424855, 0.37373737, 0.3832262 , + 0.39271503, 0.40220386, 0.41169268, 0.42118151, 0.43067034, + 0.44015917, 0.449648 , 0.45913682, 0.46862565, 0.47811448, + 0.48760331, 0.49709213, 0.50658096, 0.51606979, 0.52555862, + 0.53504744, 0.54453627, 0.5540251 , 0.56351393, 0.57300275, + 0.58249158, 0.59198041, 0.60146924, 0.61095807, 0.62044689, + 0.62993572, 0.63942455, 0.64891338, 0.6584022 , 0.66789103, + 0.67737986, 0.68686869, 0.69635751, 0.70584634, 0.71533517, + 0.724824 , 0.73431283, 0.74380165, 0.75329048, 0.76277931, + 0.77226814, 0.78175696, 0.79124579, 0.80073462, 0.81022345, + 0.81971227, 0.8292011 , 0.83868993, 0.84817876, 0.85766758, + 0.86715641, 0.87664524, 0.88613407, 0.8956229 , 0.90511172, + 0.91460055, 0.92408938, 0.93357821, 0.94306703, 0.95255586, + 0.96204469, 0.97153352, 0.98102234, 0.99051117, 1. ]), array([ 0.07070707, 0.08009387, 0.08948067, 0.09886746, 0.10825426, + 0.11764106, 0.12702785, 0.13641465, 0.14580145, 0.15518825, + 0.16457504, 0.17396184, 0.18334864, 0.19273544, 0.20212223, + 0.21150903, 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1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., + 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., + 1., 1., 1., 1., 1., 1., 1., 1., 1.])] +>>> list(intermediate)[0] +array([ 0. , 0.01010101, 0.02020202, 0.03030303, 0.04040404, + 0.05050505, 0.06060606, 0.07070707, 0.08080808, 0.09090909, + 0.1010101 , 0.11111111, 0.12121212, 0.13131313, 0.14141414, + 0.15151515, 0.16161616, 0.17171717, 0.18181818, 0.19191919, + 0.2020202 , 0.21212121, 0.22222222, 0.23232323, 0.24242424, + 0.25252525, 0.26262626, 0.27272727, 0.28282828, 0.29292929, + 0.3030303 , 0.31313131, 0.32323232, 0.33333333, 0.34343434, + 0.35353535, 0.36363636, 0.37373737, 0.38383838, 0.39393939, + 0.4040404 , 0.41414141, 0.42424242, 0.43434343, 0.44444444, + 0.45454545, 0.46464646, 0.47474747, 0.48484848, 0.49494949, + 0.50505051, 0.51515152, 0.52525253, 0.53535354, 0.54545455, + 0.55555556, 0.56565657, 0.57575758, 0.58585859, 0.5959596 , + 0.60606061, 0.61616162, 0.62626263, 0.63636364, 0.64646465, + 0.65656566, 0.66666667, 0.67676768, 0.68686869, 0.6969697 , + 0.70707071, 0.71717172, 0.72727273, 0.73737374, 0.74747475, + 0.75757576, 0.76767677, 0.77777778, 0.78787879, 0.7979798 , + 0.80808081, 0.81818182, 0.82828283, 0.83838384, 0.84848485, + 0.85858586, 0.86868687, 0.87878788, 0.88888889, 0.8989899 , + 0.90909091, 0.91919192, 0.92929293, 0.93939394, 0.94949495, + 0.95959596, 0.96969697, 0.97979798, 0.98989899, 1. ]) +>>> for i in flatten(intermediate): +Traceback (most recent call last): + File "", line 1, in +TypeError: 'generator' object has no attribute '__getitem__' +>>> for i in flatten(intermediate): +... print i +... +0.0 +0.010101010101 +0.020202020202 +0.030303030303 +0.040404040404 +0.0505050505051 +0.0606060606061 +0.0707070707071 +0.0808080808081 +0.0909090909091 +0.10101010101 +0.111111111111 +0.121212121212 +0.131313131313 +0.141414141414 +0.151515151515 +0.161616161616 +0.171717171717 +0.181818181818 +0.191919191919 +0.20202020202 +0.212121212121 +0.222222222222 +0.232323232323 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a/last_session.py b/last_session.py new file mode 100644 index 0000000..add2bdd --- /dev/null +++ b/last_session.py @@ -0,0 +1,736 @@ +>>> G=BayesNet() +Traceback (most recent call last): + File "", line 1, in +NameError: name 'BayesNet' is not defined +>>> G=BayesNet() +>>> ebunch=[('a', 'b', '+'), ('a', 'c', '+'), ('b', 'c', '-')] +>>> add_edges_from(G, ebunch) +Traceback (most recent call last): + File "", line 1, in +NameError: name 'add_edges_from' is not defined +>>> G.add_edges_from(ebunch) +>>> G.Items() +[((0, 1, 1), 0.0), ((1, 1, 0), 0.125), ((1, 0, 0), 0.0625), ((0, 0, 1), 0.25), ((1, 0, 1), 0.1875), ((0, 0, 0), 0.25), ((0, 1, 0), 0.0), ((1, 1, 1), 0.125)] +>>> 0.5**3 +0.125 +>>> f=lambda x, a, b: 1.0/(b-a) +>>> f(0.5, 0, 1) +Traceback (most recent call last): + File "", line 1, in +TypeError: () takes exactly 1 argument (3 given) +>>> f=lambda x, a, b: 1.0/(b-a) +>>> f(0.5, 0, 1) +1.0 +>>> pmf=Pmf() +>>> [pmf.Set(x, f(x, 0, 1)) for x in numpy.linspace(0, 1, 100)] +Traceback (most recent call last): + File "", line 1, in +NameError: name 'linespace' is not defined +>>> [pmf.Set(x, f(x, 0, 1)) for x in numpy.linspace(0, 1, 100)] +[None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None] +>>> pmf.Items()[:10] +sorted(pmf.Items()[:10]) +[(0.0, 1.0), (1.0, 1.0), (0.29292929292929293, 1.0), (0.6262626262626263, 1.0), (0.23232323232323235, 1.0), (0.58585858585858586, 1.0), (0.80808080808080818, 1.0), (0.17171717171717174, 1.0), (0.8787878787878789, 1.0), (0.27272727272727276, 1.0)] +>>> sorted(pmf.Items()) +[(0.0, 1.0), (0.17171717171717174, 1.0), (0.23232323232323235, 1.0), (0.27272727272727276, 1.0), (0.29292929292929293, 1.0), (0.58585858585858586, 1.0), (0.6262626262626263, 1.0), (0.80808080808080818, 1.0), (0.8787878787878789, 1.0), (1.0, 1.0)] +>>> sorted(pmf.Items()) +[(0.0, 1.0), (0.010101010101010102, 1.0), (0.020202020202020204, 1.0), (0.030303030303030304, 1.0), (0.040404040404040407, 1.0), (0.050505050505050511, 1.0), (0.060606060606060608, 1.0), (0.070707070707070718, 1.0), (0.080808080808080815, 1.0), (0.090909090909090912, 1.0), (0.10101010101010102, 1.0), (0.11111111111111112, 1.0), (0.12121212121212122, 1.0), (0.13131313131313133, 1.0), (0.14141414141414144, 1.0), (0.15151515151515152, 1.0), (0.16161616161616163, 1.0), (0.17171717171717174, 1.0), (0.18181818181818182, 1.0), (0.19191919191919193, 1.0), (0.20202020202020204, 1.0), (0.21212121212121213, 1.0), (0.22222222222222224, 1.0), (0.23232323232323235, 1.0), (0.24242424242424243, 1.0), (0.25252525252525254, 1.0), (0.26262626262626265, 1.0), (0.27272727272727276, 1.0), (0.28282828282828287, 1.0), (0.29292929292929293, 1.0), (0.30303030303030304, 1.0), (0.31313131313131315, 1.0), (0.32323232323232326, 1.0), (0.33333333333333337, 1.0), (0.34343434343434348, 1.0), (0.35353535353535359, 1.0), (0.36363636363636365, 1.0), (0.37373737373737376, 1.0), (0.38383838383838387, 1.0), (0.39393939393939398, 1.0), (0.40404040404040409, 1.0), (0.4141414141414142, 1.0), (0.42424242424242425, 1.0), (0.43434343434343436, 1.0), (0.44444444444444448, 1.0), (0.45454545454545459, 1.0), (0.4646464646464647, 1.0), (0.47474747474747481, 1.0), (0.48484848484848486, 1.0), (0.49494949494949497, 1.0), (0.50505050505050508, 1.0), (0.51515151515151525, 1.0), (0.5252525252525253, 1.0), (0.53535353535353536, 1.0), (0.54545454545454553, 1.0), (0.55555555555555558, 1.0), (0.56565656565656575, 1.0), (0.5757575757575758, 1.0), (0.58585858585858586, 1.0), (0.59595959595959602, 1.0), (0.60606060606060608, 1.0), (0.61616161616161624, 1.0), (0.6262626262626263, 1.0), (0.63636363636363646, 1.0), (0.64646464646464652, 1.0), (0.65656565656565657, 1.0), (0.66666666666666674, 1.0), (0.6767676767676768, 1.0), (0.68686868686868696, 1.0), (0.69696969696969702, 1.0), (0.70707070707070718, 1.0), (0.71717171717171724, 1.0), (0.72727272727272729, 1.0), (0.73737373737373746, 1.0), (0.74747474747474751, 1.0), (0.75757575757575768, 1.0), (0.76767676767676774, 1.0), (0.77777777777777779, 1.0), (0.78787878787878796, 1.0), (0.79797979797979801, 1.0), (0.80808080808080818, 1.0), (0.81818181818181823, 1.0), (0.8282828282828284, 1.0), (0.83838383838383845, 1.0), (0.84848484848484851, 1.0), (0.85858585858585867, 1.0), (0.86868686868686873, 1.0), (0.8787878787878789, 1.0), (0.88888888888888895, 1.0), (0.89898989898989912, 1.0), (0.90909090909090917, 1.0), (0.91919191919191923, 1.0), (0.92929292929292939, 1.0), (0.93939393939393945, 1.0), (0.94949494949494961, 1.0), (0.95959595959595967, 1.0), (0.96969696969696972, 1.0), (0.97979797979797989, 1.0), (0.98989898989898994, 1.0), (1.0, 1.0)] +>>> G.nodes() +[0, 1, 2] +>>> G.Conditional(2, 0, 1) +Traceback (most recent call last): + File "", line 1, in +TypeError: Conditional() takes at least 4 arguments (3 given) +>>> G.Conditional(2, 0, 1).Items() +<__main__.Pmf object at 0x2e090d0> +>>> G.Conditional(2, 0, 0).Items() +[(0, 0.375), (1, 0.625)] +>>> G.Conditional(2, 1, 0).Items() +[(0, 0.5), (1, 0.5)] +>>> G.Conditional(2, 1, 1).Items() +[(0, 0.41666666666666663), (1, 0.5833333333333333)] +>>> G.Conditional(2, 1, 1).Items() +[(0, 0.5), (1, 0.5)] +>>> Percentile(G, 6) +(1, 1, 0) +>>> Percentile(G, 7) +(1, 1, 0) +>>> Percentile(G, 8) +(1, 1, 0) +>>> Percentile(G, 9) +(1, 1, 0) +>>> Percentile(G, 10) +(1, 1, 0) +>>> Percentile(G, 11) +(1, 1, 0) +>>> Percentile(G, 12) +(1, 1, 0) +>>> Percentile(G, 13) +(1, 1, 0) +>>> Percentile(G, 13) +(1, 0, 0) +>>> G.P((1, 1, 0)) +Traceback (most recent call last): + File "", line 1, in +AttributeError: 'BayesNet' object has no attribute 'Probability' +>>> G.Prob((1, 1, 0)) +Traceback (most recent call last): + File "", line 1, in +AttributeError: 'BayesNet' object has no attribute 'P' +>>> G.Prob((1, 0, 0)) +0.125 +>>> G.Prob((0, 0, 0)) +0.0625 +>>> G.Prob((0, 1, 0)) +0.25 +>>> G.Prob((1, 1, 0)) +0.0 +>>> G.Prob((1, 1, 1)) +0.125 +>>> G.Prob((1, 0, 1)) +0.125 +>>> G.Prob((1, 0, 1)) +0.1875 +>>> gaus=lambda x: EvalGaussianPdf(x, 0, 1) +Traceback (most recent call last): + File "", line 1, in +NameError: name 'GausianPdf' is not defined +>>> gaus=lambda x: EvalGaussianPdf(x, 0, 1) +>>> gaus(1) +0.00013383022576488537 +>>> gaus(1.96) +0.24197072451914337 +>>> gaus(-1.96) +0.058440944333451476 +>>> gaus(-1.96) +0.058440944333451476 +>>> type(gaus) + +>>> xs=numpy.linspace(-2, 2, 0.5) +Traceback (most recent call last): + File "", line 1, in +TypeError: integer argument expected, got float +>>> xs=numpy.linspace(-2, 2, 20) +>>> xs +array([], dtype=float64) +>>> xs=numpy.linspace(-2, 2, 20) +>>> zip(*list(xs), [gaus(x) for x in xs]) +array([-2. , -1.78947368, -1.57894737, -1.36842105, -1.15789474, + -0.94736842, -0.73684211, -0.52631579, -0.31578947, -0.10526316, + 0.10526316, 0.31578947, 0.52631579, 0.73684211, 0.94736842, + 1.15789474, 1.36842105, 1.57894737, 1.78947368, 2. ]) +>>> zip(*xs, gauss) + File "", line 1 +SyntaxError: only named arguments may follow *expression +>>> xs=list(xs) +>>> gauss=[gaus(x) for x in xs] +>>> zip(*xs, gauss) + File "", line 1 +SyntaxError: only named arguments may follow *expression +>>> from pylab import * +>>> plot(xs, gauss) +[] +>>> pylab.show() +Traceback (most recent call last): + File "", line 1, in +NameError: name 'pylab' is not defined +>>> show() +>>> show() +>>> plot(xs, gauss) +[] +>>> show() +>>> gaus(5) +0.00013383022576488537 +>>> gaus(0) +1.4867195147342979e-06 +>>> gaus(1) +0.3989422804014327 +>>> gaus(1) +0.24197072451914337 +>>> pmf=MakeUniformPmf(0, 1, 100) +Traceback (most recent call last): + File "", line 1, in + File "/tmp/py28474dFK", line 775, in MakeUniformPmf + File "/tmp/py28474dFK", line 414, in Normalize +TypeError: unsupported operand type(s) for /: 'float' and 'dictionary-valueiterator' +>>> pmf=MakeUniformPmf(0, 1, 100) +Traceback (most recent call last): + File "", line 1, in + File "/tmp/py28474dFK", line 775, in MakeUniformPmf + File "/tmp/py28474dFK", line 414, in Normalize +TypeError: unsupported operand type(s) for /: 'float' and 'dictionary-valueiterator' +>>> pmf.d[0] +1.0 +>>> pmf.Normalize() +Traceback (most recent call last): + File "", line 1, in + File "/tmp/py28474dFK", line 414, in Normalize +TypeError: unsupported operand type(s) for /: 'float' and 'dictionary-valueiterator' +>>> pmf.Total() + +>>> sum(x for x in pmf.d.itervalues()) + +>>> sum(x for x in pmf.d.itervalues()) +100.0 +>>> pmf=MakeUniformPmf(0, 1, 100) +>>> pmf.d[1] +0.01 +>>> pmf.d[0.1] +0.01 +>>> pmf.d +Traceback (most recent call last): + File "", line 1, in +KeyError: 0.1 +>>> pmf.Items() +{0.0: 0.01, 1.0: 0.01, 0.29292929292929293: 0.01, 0.6262626262626263: 0.01, 0.23232323232323235: 0.01, 0.58585858585858586: 0.01, 0.80808080808080818: 0.01, 0.17171717171717174: 0.01, 0.8787878787878789: 0.01, 0.27272727272727276: 0.01, 0.96969696969696972: 0.01, 0.85858585858585867: 0.01, 0.28282828282828287: 0.01, 0.50505050505050508: 0.01, 0.61616161616161624: 0.01, 0.78787878787878796: 0.01, 0.95959595959595967: 0.01, 0.75757575757575768: 0.01, 0.54545454545454553: 0.01, 0.68686868686868696: 0.01, 0.71717171717171724: 0.01, 0.090909090909090912: 0.01, 0.44444444444444448: 0.01, 0.010101010101010102: 0.01, 0.060606060606060608: 0.01, 0.81818181818181823: 0.01, 0.40404040404040409: 0.01, 0.49494949494949497: 0.01, 0.4646464646464647: 0.01, 0.5757575757575758: 0.01, 0.37373737373737376: 0.01, 0.11111111111111112: 0.01, 0.91919191919191923: 0.01, 0.92929292929292939: 0.01, 0.25252525252525254: 0.01, 0.42424242424242425: 0.01, 0.51515151515151525: 0.01, 0.6767676767676768: 0.01, 0.56565656565656575: 0.01, 0.050505050505050511: 0.01, 0.84848484848484851: 0.01, 0.76767676767676774: 0.01, 0.30303030303030304: 0.01, 0.32323232323232326: 0.01, 0.77777777777777779: 0.01, 0.72727272727272729: 0.01, 0.15151515151515152: 0.01, 0.47474747474747481: 0.01, 0.53535353535353536: 0.01, 0.34343434343434348: 0.01, 0.70707070707070718: 0.01, 0.16161616161616163: 0.01, 0.18181818181818182: 0.01, 0.63636363636363646: 0.01, 0.60606060606060608: 0.01, 0.10101010101010102: 0.01, 0.070707070707070718: 0.01, 0.88888888888888895: 0.01, 0.97979797979797989: 0.01, 0.020202020202020204: 0.01, 0.14141414141414144: 0.01, 0.5252525252525253: 0.01, 0.19191919191919193: 0.01, 0.21212121212121213: 0.01, 0.73737373737373746: 0.01, 0.45454545454545459: 0.01, 0.66666666666666674: 0.01, 0.83838383838383845: 0.01, 0.12121212121212122: 0.01, 0.080808080808080815: 0.01, 0.59595959595959602: 0.01, 0.38383838383838387: 0.01, 0.98989898989898994: 0.01, 0.26262626262626265: 0.01, 0.93939393939393945: 0.01, 0.13131313131313133: 0.01, 0.94949494949494961: 0.01, 0.030303030303030304: 0.01, 0.69696969696969702: 0.01, 0.43434343434343436: 0.01, 0.90909090909090917: 0.01, 0.040404040404040407: 0.01, 0.31313131313131315: 0.01, 0.86868686868686873: 0.01, 0.79797979797979801: 0.01, 0.4141414141414142: 0.01, 0.48484848484848486: 0.01, 0.55555555555555558: 0.01, 0.64646464646464652: 0.01, 0.39393939393939398: 0.01, 0.36363636363636365: 0.01, 0.89898989898989912: 0.01, 0.74747474747474751: 0.01, 0.20202020202020204: 0.01, 0.65656565656565657: 0.01, 0.35353535353535359: 0.01, 0.24242424242424243: 0.01, 0.8282828282828284: 0.01, 0.22222222222222224: 0.01, 0.33333333333333337: 0.01} +>>> pmf.Items() +[(0.0, 0.01), (1.0, 0.01), (0.29292929292929293, 0.01), (0.6262626262626263, 0.01), (0.23232323232323235, 0.01), (0.58585858585858586, 0.01), (0.80808080808080818, 0.01), (0.17171717171717174, 0.01), (0.8787878787878789, 0.01), (0.27272727272727276, 0.01), (0.96969696969696972, 0.01), (0.85858585858585867, 0.01), (0.28282828282828287, 0.01), (0.50505050505050508, 0.01), (0.61616161616161624, 0.01), (0.78787878787878796, 0.01), (0.95959595959595967, 0.01), (0.75757575757575768, 0.01), (0.54545454545454553, 0.01), (0.68686868686868696, 0.01), (0.71717171717171724, 0.01), (0.090909090909090912, 0.01), (0.44444444444444448, 0.01), (0.010101010101010102, 0.01), (0.060606060606060608, 0.01), (0.81818181818181823, 0.01), (0.40404040404040409, 0.01), (0.49494949494949497, 0.01), (0.4646464646464647, 0.01), (0.5757575757575758, 0.01), (0.37373737373737376, 0.01), (0.11111111111111112, 0.01), (0.91919191919191923, 0.01), (0.92929292929292939, 0.01), (0.25252525252525254, 0.01), (0.42424242424242425, 0.01), (0.51515151515151525, 0.01), (0.6767676767676768, 0.01), (0.56565656565656575, 0.01), (0.050505050505050511, 0.01), (0.84848484848484851, 0.01), (0.76767676767676774, 0.01), (0.30303030303030304, 0.01), (0.32323232323232326, 0.01), (0.77777777777777779, 0.01), (0.72727272727272729, 0.01), (0.15151515151515152, 0.01), (0.47474747474747481, 0.01), (0.53535353535353536, 0.01), (0.34343434343434348, 0.01), (0.70707070707070718, 0.01), (0.16161616161616163, 0.01), (0.18181818181818182, 0.01), (0.63636363636363646, 0.01), (0.60606060606060608, 0.01), (0.10101010101010102, 0.01), (0.070707070707070718, 0.01), (0.88888888888888895, 0.01), (0.97979797979797989, 0.01), (0.020202020202020204, 0.01), (0.14141414141414144, 0.01), (0.5252525252525253, 0.01), (0.19191919191919193, 0.01), (0.21212121212121213, 0.01), (0.73737373737373746, 0.01), (0.45454545454545459, 0.01), (0.66666666666666674, 0.01), (0.83838383838383845, 0.01), (0.12121212121212122, 0.01), (0.080808080808080815, 0.01), (0.59595959595959602, 0.01), (0.38383838383838387, 0.01), (0.98989898989898994, 0.01), (0.26262626262626265, 0.01), (0.93939393939393945, 0.01), (0.13131313131313133, 0.01), (0.94949494949494961, 0.01), (0.030303030303030304, 0.01), (0.69696969696969702, 0.01), (0.43434343434343436, 0.01), (0.90909090909090917, 0.01), (0.040404040404040407, 0.01), (0.31313131313131315, 0.01), (0.86868686868686873, 0.01), (0.79797979797979801, 0.01), (0.4141414141414142, 0.01), (0.48484848484848486, 0.01), (0.55555555555555558, 0.01), (0.64646464646464652, 0.01), (0.39393939393939398, 0.01), (0.36363636363636365, 0.01), (0.89898989898989912, 0.01), (0.74747474747474751, 0.01), (0.20202020202020204, 0.01), (0.65656565656565657, 0.01), (0.35353535353535359, 0.01), (0.24242424242424243, 0.01), (0.8282828282828284, 0.01), (0.22222222222222224, 0.01), (0.33333333333333337, 0.01)] +>>> integrant=lambda x : x*(1/1) if abs(1-x) <=1 else 0 +>>> integrant(0) +Traceback (most recent call last): + File "", line 1, in +NameError: name 'integrat' is not defined +>>> integrant(1) +0 +>>> integrant(0.5) +1 +>>> integrant(0.3) +0.5 +>>> integrant(0.3) +0.3 +>>> from scipy.integrate import quad +>>> quad(integrand, 0, 1, x) +Traceback (most recent call last): + File "", line 1, in +NameError: name 'integrand' is not defined +>>> quad(integrand, 0, 1) +Traceback (most recent call last): + File "", line 1, in +NameError: name 'integrand' is not defined +>>> quad(integrant, 0, 1) +Traceback (most recent call last): + File "", line 1, in +NameError: name 'integrand' is not defined +>>> quad(integrant, 0, 1) +(0.5, 5.551115123125783e-15) +>>> EvalPoissonPmf(5, 3) +0.03608940886309672 +>>> EvalPoissonPmf(5, 5) +0.10081881344492448 +>>> EvalPoissonPmf(5, 7) +0.1754673697678507 +>>> EvalPoissonPmf(5, 10) +0.12771666829228961 +>>> EvalPoissonPmf(20, 10) +0.03783327480207071 +>>> EvalPoissonPmf(20, 10) +0.0018660813139987594 +>>> math.log(math.exp(2)) +7.38905609893065 +>>> math.log(math.exp(2)) +2.0 +>>> 1.5%1 +0.5 +>>> 1.5%1 +0.5 +>>> effect_pdf=lambda p: 1 if p>=0 and p<=1 else 0 +>>> effect_pdf(1.5) +1 +>>> effect_pdf(.6) +0 +>>> effect_pdf(.6) +1 +>>> gamma(5) +4.492160846229 +>>> from scipy.stats import beta +>>> beta(5, 6, 3) + +>>> numargs = beta.numargs +>>> numargs +2 +>>> rv=beta(2, 2) + +>>> rv=beta(2, 4) +>>> x = np.linspace(0, np.minimum(rv.dist.b, 3)) +>>> type(np) +Traceback (most recent call last): + File "", line 1, in +NameError: name 'typ' is not defined +>>> type(np) + +>>> rv.dist.b + +>>> rv.dist.b +1.0 +>>> h = plt.plot(x, rv.pdf(x)) +>>> plt.show() +>>> rv=beta(4, 2) +>>> h = plt.plot(x, rv.pdf(x)) +>>> plt.show() +>>> rv=beta(2, 2) +>>> h = plt.plot(x, rv.pdf(x)) +>>> plt.show() +>>> rv=beta(4, 2) +>>> h = plt.plot(x, rv.pdf(x)) +>>> plt.show() +>>> rv=beta(2, 2) +>>> h = plt.plot(x, rv.pdf(x)) +>>> plt.show() +>>> beta(4, 2)(0.5) +Traceback (most recent call last): + File "", line 1, in +TypeError: 'rv_frozen' object has no attribute '__getitem__' +>>> beta(4, 2).pdf(0.5) +Traceback (most recent call last): + File "", line 1, in +TypeError: 'rv_frozen' object is not callable +>>> beta(4, 2).pdf(0.6) +1.25 +>>> beta(4, 2).pdf(0.02) +1.7279999999999998 +>>> beta(2, 2).pdf(0.02) +0.00015680000000000002 +>>> beta(2, 2).pdf(0.5) +0.1176 +>>> beta(2, 2).pdf(0.6) +1.5 +>>> beta(2, 2).pdf(0.7) +1.4399999999999999 +>>> beta(2, 2).pdf(0.3) +1.2600000000000002 +>>> beta(2, 2).pdf(0.3) +1.26 +>>> f =beta(2, 2).pdf +>>> type(f) + +>>> f(0.5) +1.5 +>>> f=lambda x: beta(2, 2).pdf(x) +>>> type(f) + +>>> f(0.7) +1.5 +>>> f(0.1) +1.2600000000000002 +>>> f(0.5) +0.54000000000000015 +>>> f(0.5) +1.5 +>>> max(f(x) for x in linspace(0, 1, 1000)) +1.4998469543924089 +>>> max(f(x) for x in linspace(0, 1, 1000000)) +1.4999984969954943 +>>> max(f(x) for x in linspace(0, 1, 100000)) + + C-c C-z C-c C-cTraceback (most recent call last): + File "", line 1, in + File "", line 1, in + File "", line 1, in + File "/usr/lib/python2.7/dist-packages/scipy/stats/distributions.py", line 447, in pdf + return self.dist.pdf(x, *self.args, **self.kwds) + File "/usr/lib/python2.7/dist-packages/scipy/stats/distributions.py", line 1295, in pdf + goodargs = argsreduce(cond, *((x,)+args+(scale,))) + File "/usr/lib/python2.7/dist-packages/scipy/stats/distributions.py", line 635, in argsreduce + expand_arr = (cond==cond) +KeyboardInterrupt +>>> max(f(x) for x in linspace(0, 1, 1000)) + C-c C-cTraceback (most recent call last): + File "", line 1, in + File "", line 1, in + File "", line 1, in + File "/usr/lib/python2.7/dist-packages/scipy/stats/distributions.py", line 447, in pdf + return self.dist.pdf(x, *self.args, **self.kwds) + File "/usr/lib/python2.7/dist-packages/scipy/stats/distributions.py", line 1295, in pdf + goodargs = argsreduce(cond, *((x,)+args+(scale,))) + File "/usr/lib/python2.7/dist-packages/scipy/stats/distributions.py", line 636, in argsreduce + return [extract(cond, arr1 * expand_arr) for arr1 in newargs] +KeyboardInterrupt +>>> min(f(x) for x in linspace(0, 1, 1000)) +1.4999984969954943 +>>> min(f(x) for x in linspace(0, 1, 1000)) +0.0 +>>> rv=beta(2, 2) +>>> h = plt.plot(x, rv.pdf(x)) +>>> plt.show() +>>> def integrand(x): +... return f(x)*x +... +>>> integrant(0.7) +0.5 +>>> integrant(0.7) +0.7 +>>> f(0.7)*(0.7) +1.2600000000000002 +>>> f(0.7)*(0.7) +0.88200000000000012 +>>> integrand = lambda x: beta(2, 2).pdf(x)*x +... integrand = lambda x: beta(2, 2).pdf(x)*x +>>> integrant(0.7) +0.7 +>>> integrand = lambda x: beta(2, 2).pdf(x)*x +>>> integrant(0.7) +0.7 +>>> beta(2, 2).pdf(0.7)*0.7 +1.2600000000000002 +>>> f=lambda x: beta(2, 2).pdf(0.7)*0.7 +0.88200000000000012 +>>> f=lambda x: beta(2, 2).pdf(x)*x +>>> f(0.6) +0.88200000000000012 +>>> quad(f, 0, 1) +(0.8820000000000001, 9.792167077193883e-15) +>>> f(0.6) +0.88200000000000012 +>>> f=lambda x, a, b: beta(a, b).pdf(x)*x +>>> f(0.5) +0.86399999999999999 +>>> f(0.7) +0.88200000000000012 +>>> f(0.5) +0.75 +>>> quad(f, 0, 1) +(0.5, 5.551115123125783e-15) +>>> f=lambda x, a, b: beta(a, b).pdf(x)*x +>>> f(2, 2, 0.6) +0.0 +>>> f(0.6, 2, 2) +0.0 +>>> f(0.5, 2, 2) +0.86399999999999999 +>>> f(0.5, 2, 2) +0.75 +>>> def f(x): +... alpha=2 +... beta=2 +... return beta(alpha, beta).pdf(x)*x +... +>>> f(0.6) + at 0x3dd86e0> +>>> def f(x): +... alpha=2 +... beta=2 +... return beta(alpha, beta).pdf(x)*x +... +>>> beta(2, 2).pdf(0.6) + +>>> f=lambda x : beta(2, 2).pdf(x) +1.4399999999999999 +>>> f=lambda x : beta(a, b).pdf(x) +>>> f(0.6) +1.4399999999999999 +>>> f=lambda x, a, b : beta(a, b).pdf(x) +>>> f(0.5) +Traceback (most recent call last): + File "", line 1, in + File "", line 1, in +NameError: global name 'a' is not defined +>>> f=lambda x, a, b : beta(a, b).pdf(x) +>>> f(0.6, 2, 2) +1.4399999999999999 +>>> g = lambda x : f(x, 2, 2) +>>> g(0.6) +1.4399999999999999 +>>> H=BayesNet() +1.5 +>>> H=BayesNet() +1.44 +>>> H=BayesNet() +1.26 +>>> H=BayesNet() +1.26 +>>> H=BayesNet() +1.26 +>>> H=BayesNet() +1.44 +>>> H=BayesNet() +1.5 +>>> G.dep_vars +[0] +>>> G.dep_vars +[1, 2] +>>> G.nodes() +[0, 1, 2] +>>> g(0.6) +Traceback (most recent call last): + File "", line 1, in +TypeError: () takes exactly 3 arguments (1 given) +>>> g(0.6) +1.4399999999999999 +>>> pr= lambda x : 0.6*0.6*0.5*(1.0-x)*g(x) +>>> 0.6*0.6*0.5*quad(lambda x: (1.0-x)*g(x), 0, 1) +(0.09, 9.992007221626409e-16) +>>> 0.6*0.6*0.5*quad(lambda x: (1.0-x)*g(x), 0, 1) +Traceback (most recent call last): + File "", line 1, in +TypeError: can't multiply sequence by non-int of type 'float' +>>> 0.6*0.6*0.5*quad(lambda x: (1.0-x)*g(x), 0, 1)[0] +(0.5, 5.551115123125783e-15) +>>> 0.6*0.6*0.5*quad(lambda x, y: (1.0-x)*g(x)*(1.0-y)*g(y), 0, 1)[0] +0.09 +>>> 0.6*0.6*0.5*quad(lambda x, y: ((1.0-x)*g(x)*(1.0-y)*g(y)), 0, 1, 0, 1)[0] +Traceback (most recent call last): + File "", line 1, in + File "/usr/lib/python2.7/dist-packages/scipy/integrate/quadpack.py", line 247, in quad + retval = _quad(func,a,b,args,full_output,epsabs,epsrel,limit,points) + File "/usr/lib/python2.7/dist-packages/scipy/integrate/quadpack.py", line 312, in _quad + return _quadpack._qagse(func,a,b,args,full_output,epsabs,epsrel,limit) +TypeError: () takes exactly 2 arguments (1 given) +>>> 0.6*0.6*0.5*quad(lambda x, y: ((1.0-x)*g(x)*(1.0-y)*g(y)), 0, 0, 1, 1)[0] +0.0 +>>> quad(lambda x, y: ((1.0-x)*g(x)*(1.0-y)*g(y)), 0, 0, 1, 1)[0] +0.0 +>>> quad(lambda x, y: ((1.0-x)*g(x)*(1.0-y)*g(y)), 0, 0, 1, 1) +0.0 +>>> quad(lambda x, y: ((1.0-x)*g(x)*(1.0-y)*g(y)), 0, 1) +(0.0, 0.0, {'rlist': array([ 0.00000000e+000, 3.41409005e-316, 0.00000000e+000, + 0.00000000e+000, 0.00000000e+000, 0.00000000e+000, + 0.00000000e+000, 0.00000000e+000, 0.00000000e+000, + 0.00000000e+000, 0.00000000e+000, 0.00000000e+000, + 0.00000000e+000, 0.00000000e+000, 0.00000000e+000, + 0.00000000e+000, 0.00000000e+000, 0.00000000e+000, + 0.00000000e+000, 0.00000000e+000, 0.00000000e+000, + 0.00000000e+000, 0.00000000e+000, 0.00000000e+000, + 0.00000000e+000, 0.00000000e+000, 0.00000000e+000, + 0.00000000e+000, 0.00000000e+000, 0.00000000e+000, + 0.00000000e+000, 0.00000000e+000, 0.00000000e+000, + 0.00000000e+000, 0.00000000e+000, 0.00000000e+000, + 0.00000000e+000, 0.00000000e+000, 0.00000000e+000, + 0.00000000e+000, 0.00000000e+000, 0.00000000e+000, + 0.00000000e+000, 0.00000000e+000, 0.00000000e+000, + 0.00000000e+000, 0.00000000e+000, 0.00000000e+000, + 4.74303020e-322, 7.90505033e-323]), 'last': 1, 'elist': array([ 0.00000000e+000, 3.25981904e-316, 9.30819677e-321, + 2.97079545e-313, 0.00000000e+000, 0.00000000e+000, + 4.24400727e-314, 0.00000000e+000, 0.00000000e+000, + 1.06099946e-313, 0.00000000e+000, 0.00000000e+000, + 4.24400815e-314, 0.00000000e+000, 0.00000000e+000, + 1.26480805e-321, 0.00000000e+000, 0.00000000e+000, + 2.92835433e-312, 3.07441795e-316, 0.00000000e+000, + 0.00000000e+000, 0.00000000e+000, 0.00000000e+000, + 0.00000000e+000, 0.00000000e+000, 0.00000000e+000, + 0.00000000e+000, 0.00000000e+000, 0.00000000e+000, + 0.00000000e+000, 0.00000000e+000, 0.00000000e+000, + 0.00000000e+000, 0.00000000e+000, 0.00000000e+000, + 0.00000000e+000, 0.00000000e+000, 0.00000000e+000, + 0.00000000e+000, 0.00000000e+000, 0.00000000e+000, + 0.00000000e+000, 0.00000000e+000, 0.00000000e+000, + 0.00000000e+000, 0.00000000e+000, 0.00000000e+000, + 3.45845952e-323, 2.10077583e-312]), 'iord': array([ 1, 32634, 68611280, 0, 63285808, 0, + 6, 0, 809, 9, 1, 0, + 12, 13, 808, 15, 16, 0, + 18, 19, 811, 21, 22, 0, + 24, 25, 811, 27, 28, 0, + 30, 31, 51739168, 33, 34, 0, + 36, 37, 0, 39, 40, 41, + 42, 733389503, 44, 45, 8696288, 0, + 208, 0], dtype=int32), 'alist': array([ 0.00000000e+000, 3.16768964e-316, 0.00000000e+000, + 1.30294992e-319, 0.00000000e+000, 8.87835966e-321, + 2.12201148e-314, 0.00000000e+000, 0.00000000e+000, + 8.60069476e-320, 0.00000000e+000, 0.00000000e+000, + 0.00000000e+000, 0.00000000e+000, 0.00000000e+000, + 0.00000000e+000, 0.00000000e+000, 0.00000000e+000, + 0.00000000e+000, 0.00000000e+000, 0.00000000e+000, + 0.00000000e+000, 0.00000000e+000, 0.00000000e+000, + 0.00000000e+000, 0.00000000e+000, 0.00000000e+000, + 0.00000000e+000, 0.00000000e+000, 0.00000000e+000, + 0.00000000e+000, 0.00000000e+000, 0.00000000e+000, + 0.00000000e+000, 0.00000000e+000, 0.00000000e+000, + 0.00000000e+000, 0.00000000e+000, 0.00000000e+000, + 0.00000000e+000, 0.00000000e+000, 0.00000000e+000, + 0.00000000e+000, 0.00000000e+000, 0.00000000e+000, + 0.00000000e+000, 0.00000000e+000, 0.00000000e+000, + 8.48798317e-314, 8.48798317e-314]), 'blist': array([ 0.00000000e+000, 3.16918843e-316, 0.00000000e+000, + 0.00000000e+000, 0.00000000e+000, 0.00000000e+000, + 0.00000000e+000, 0.00000000e+000, 0.00000000e+000, + 0.00000000e+000, 0.00000000e+000, 0.00000000e+000, + 0.00000000e+000, 0.00000000e+000, 0.00000000e+000, + 0.00000000e+000, 0.00000000e+000, 0.00000000e+000, + 0.00000000e+000, 0.00000000e+000, 0.00000000e+000, + 0.00000000e+000, 0.00000000e+000, 0.00000000e+000, + 0.00000000e+000, 0.00000000e+000, 0.00000000e+000, + 0.00000000e+000, 0.00000000e+000, 0.00000000e+000, + 0.00000000e+000, 0.00000000e+000, 0.00000000e+000, + 0.00000000e+000, 0.00000000e+000, 0.00000000e+000, + 0.00000000e+000, 0.00000000e+000, 0.00000000e+000, + 0.00000000e+000, 0.00000000e+000, 0.00000000e+000, + 0.00000000e+000, 0.00000000e+000, 0.00000000e+000, + 0.00000000e+000, 0.00000000e+000, 0.00000000e+000, + 8.48798317e-314, 8.48798317e-314]), 'neval': 21}) +>>> quad(quad(lambda x, y: ((1.0-x)*g(x)*(1.0-y)*g(y)), 0, 1), 0, 1) +Traceback (most recent call last): + File "", line 1, in + File "/usr/lib/python2.7/dist-packages/scipy/integrate/quadpack.py", line 247, in quad + retval = _quad(func,a,b,args,full_output,epsabs,epsrel,limit,points) + File "/usr/lib/python2.7/dist-packages/scipy/integrate/quadpack.py", line 312, in _quad + return _quadpack._qagse(func,a,b,args,full_output,epsabs,epsrel,limit) +TypeError: () takes exactly 2 arguments (1 given) +>>> quad(lambda x, y: ((1.0-x)*g(x)*(1.0-y)*g(y)), 0, 1, args(x, y)) +Traceback (most recent call last): + File "", line 1, in + File "/usr/lib/python2.7/dist-packages/scipy/integrate/quadpack.py", line 247, in quad + retval = _quad(func,a,b,args,full_output,epsabs,epsrel,limit,points) + File "/usr/lib/python2.7/dist-packages/scipy/integrate/quadpack.py", line 312, in _quad + return _quadpack._qagse(func,a,b,args,full_output,epsabs,epsrel,limit) +TypeError: () takes exactly 2 arguments (1 given) +>>> quad(lambda x, y: ((1.0-x)*g(x)*(1.0-y)*g(y)), 0, 1, args=(x, y)) +Traceback (most recent call last): + File "", line 1, in +NameError: name 'args' is not defined +>>> f=lambda x, y: ((1.0-x)*g(x)*(1.0-y)*g(y)) +Traceback (most recent call last): + File "", line 1, in +NameError: name 'y' is not defined +>>> f=lambda x y: ((1.0-x)*g(x)*(1.0-y)*g(y)) +>>> f(0.6, 0.6) +Traceback (most recent call last): + File "", line 1, in + File "", line 1, in + File "", line 1, in +TypeError: () takes exactly 2 arguments (3 given) +>>> f=lambda (x,y): ((1.0-x)*g(x)*(1.0-y)*g(y)) + File "", line 1 + f=lambda x y: ((1.0-x)*g(x)*(1.0-y)*g(y)) + ^ +SyntaxError: invalid syntax +>>> f=lambda (x, y): ((1.0-x)*g(x)*(1.0-y)*g(y)) +>>> f((0.6, 0.6)) +Traceback (most recent call last): + File "", line 1, in +TypeError: () takes exactly 1 argument (2 given) +>>> f((0.6, 0.6)) +Traceback (most recent call last): + File "", line 1, in + File "", line 1, in + File "", line 1, in +TypeError: () takes exactly 1 argument (3 given) +>>> h=lambda (x, y): ((1.0-x)*g(x)*(1.0-y)*g(y)) +>>> g(0.6)*g(0.7) +Traceback (most recent call last): + File "", line 1, in + File "", line 1, in +TypeError: () takes exactly 1 argument (3 given) +>>> g(0.6) +Traceback (most recent call last): + File "", line 1, in + File "", line 1, in +TypeError: () takes exactly 1 argument (3 given) +>>> g = lambda x : f(x, 2, 2) +>>> g(0.6) +Traceback (most recent call last): + File "", line 1, in + File "", line 1, in +TypeError: () takes exactly 1 argument (3 given) +>>> f(0.6, 2, 2) +Traceback (most recent call last): + File "", line 1, in +TypeError: () takes exactly 1 argument (3 given) +>>> f=lambda x, a, b : beta(a, b).pdf(x) +>>> g = lambda x : f(x, 2, 2) +>>> g(0.6) +Traceback (most recent call last): + File "", line 1, in + File "", line 1, in +TypeError: () takes exactly 1 argument (3 given) +>>> f=lambda x, a, b : beta(a, b).pdf(x) +>>> g = lambda x : f(x, 2, 2) +>>> g(0.6) +1.4399999999999999 +>>> h=lambda (x, y): ((1.0-x)*g(x)*(1.0-y)*g(y)) +>>> h((0.6, 0.2)) +0.33177599999999996 +>>> h((0.6, 0.2)) +0.44236800000000009 +>>> quad(lambda x, y: ((1.0-x)*g(x)*(1.0-y)*g(y)), 0, 1, args=(x, y)) +Traceback (most recent call last): + File "", line 1, in +NameError: name 'y' is not defined +>>> quad(lambda y: y*g(y), 0, 1) +Traceback (most recent call last): + File "", line 1, in +NameError: name 'y' is not defined +>>> quad(lambda x, y: x*g(y), 0, 1) +(0.5, 5.551115123125783e-15) +>>> quad(lambda x, y: x*g(y), 0, 1) +Traceback (most recent call last): + File "", line 1, in + File "/usr/lib/python2.7/dist-packages/scipy/integrate/quadpack.py", line 247, in quad + retval = _quad(func,a,b,args,full_output,epsabs,epsrel,limit,points) + File "/usr/lib/python2.7/dist-packages/scipy/integrate/quadpack.py", line 312, in _quad + return _quadpack._qagse(func,a,b,args,full_output,epsabs,epsrel,limit) +TypeError: () takes exactly 2 arguments (1 given) +>>> quad(lambda x, y: x*g(y), 0, 1, args=(x, y)) + at 0x433b7d0> +>>> quad(lambda x, y: x*g(y), 0, 1, args=(y, x)) +Traceback (most recent call last): + File "", line 1, in +NameError: name 'y' is not defined +>>> tplquad(lambda x, y: x*g(y), 0, 1, args=(y, x)) +Traceback (most recent call last): + File "", line 1, in +NameError: name 'y' is not defined +>>> tplquad(lambda x, y: x*g(y), 0, 1, args=(y, x)) +Traceback (most recent call last): + File "", line 1, in +NameError: name 'tplquad' is not defined +>>> from scipy.integrate import tplquad +Traceback (most recent call last): + File "", line 1, in +ImportError: cannot import name tplquad +>>> from scipy.integrate import tplquad +>>> tplquad(lambda x, y: x*g(y), 0, 1, args=(x, y)) +Traceback (most recent call last): + File "", line 1, in +NameError: name 'y' is not defined +>>> tplquad(lambda x, y: x*g(y), 0, 1, 0, 1, args=(x, y)) +Traceback (most recent call last): + File "", line 1, in +NameError: name 'y' is not defined +>>> tplquad(lambda x, y: x*g(y), 0, 1, 0, 1, args=(x, y)) +Traceback (most recent call last): + File "", line 1, in +NameError: name 'y' is not defined +>>> 6 +>>> tplquad(g(y)*x**2, 0,1,0, 1 args=(x, y)) +Traceback (most recent call last): + File "", line 1, in +NameError: name 'y' is not defined +>>> tplquad(g(y)*x**2, 0,1,0, 1, args=(x, y)) + File "", line 1 + tplquad(g(y)*x**2, 0,1,0, 1 args=(x, y)) + ^ +SyntaxError: invalid syntax +>>> tplquad(x**2+y**2, 0,1,0, 1, args=(x, y)) +Traceback (most recent call last): + File "", line 1, in +NameError: name 'y' is not defined +>>> tplquad(lambda x, y: x**2+y**2, 0,1,0, 1, args=(x, y)) +Traceback (most recent call last): + File "", line 1, in +NameError: name 'y' is not defined +>>> tplquad(lambda x, y: d(x, y), 0,1,0, 1, args=(x, y)) +Traceback (most recent call last): + File "", line 1, in +NameError: name 'y' is not defined +>>> d=labda x, y: x**2+y**2 + File "", line 1 + labda x, y: x**2+y**2 + ^ +SyntaxError: invalid syntax +>>> d=lambda x, y: x**2+y**2 + File "", line 1 + d=labda x, y: x**2+y**2 + ^ +SyntaxError: invalid syntax +>>> d=lambda x, y: x**2+y**2 +>>> tplquad(d(x, y), 0,1,0, 1, args=(x, y)) +Traceback (most recent call last): + File "", line 1, in +NameError: name 'y' is not defined +>>> tplquad(d(x, y), 0,1,0, 1, args=(x, y)) +Traceback (most recent call last): + File "", line 1, in +NameError: name 'y' is not defined +>>> d(2, 3) +13 +>>> 2**2 + 3**2 +13 +>>> \ No newline at end of file diff --git a/thinkbayes.py b/thinkbayes.py index d415fd6..24b94a0 100644 --- a/thinkbayes.py +++ b/thinkbayes.py @@ -32,6 +32,10 @@ from numpy import zeros, array from math import sqrt, log +#import the beta function for priors on causal effects in BayesNet: + +from scipy.stats import beta + def Odds(p): """Computes odds for a given probability. @@ -316,7 +320,7 @@ def Remove(self, x): def Total(self): """Returns the total of the frequencies/probabilities in the map.""" - total = sum(self.d.itervalues()) + total = sum(val for val in self.d.itervalues()) return total def MaxLike(self): @@ -1761,7 +1765,12 @@ class BayesNet(DiGraph, Joint): The joint probability is encoded, using the Noisy-OR encoding (Pearl 1988). """ - def __init__(self, data=None, name='', p=0.5, causal_effect=0.5): + def __init__(self, data=None, name='', p=0.5, causal_effect=0.5, effect_pdf=lambda x, a, b : beta(a, b).pdf(x), a=2, b=2): + """ + Effect pdf is the pdf that a causal effect is assumed to be drawn from. In the absense of a "causal_effect" we integrate over this + distribution. This distribution is here assumed to be uniform between 0 and 1, but that can be easily changed (in future versions, + I) + """ DiGraph.__init__(self, data=data, name=name) Joint.__init__(self) @@ -1772,6 +1781,8 @@ def __init__(self, data=None, name='', p=0.5, causal_effect=0.5): self.names=[] self.indep_vars=[] self.dep_vars=[] + self.effect_pdf= lambda x: effect_pdf(x, a, b) + def add_edges_from(self, ebunch): #first, we rename the nodes to be indices. This is practical @@ -1862,12 +1873,17 @@ def SetProbs(self): else: tot=1 for node in self.node[i]['weight']: - if self.edge[node][i]=={} or 'weight' in self.edge[node][i] and (self.edge[node][i]['weight'] =='+' or type(self.edge[node][i]['weight'])==float and self.edge[node][i]['weight'] >=0): + if 'weight' in self.edge[node][i] and type(self.edge[node][i]['weight'])==float and self.edge[node][i]['weight'] >=0: tot *=((1.0-self.node[i]['weight'][node])**outcome[node]) - else: + elif self.edge[node][i]=={} or 'weight' in self.edge[node][i] and self.edge[node][i]['weight'] =='+': + tot=outer(tot, [self.effect_pdf(w)*(1.0-w)**outcome[node] for w in linspace(0, 1, 100)]) + + elif ('weight' in self.edge[node][i] and self.edge[node][i]['weight'] =='-'): + tot=outer(tot, [self.effect_pdf(w)*(1.0-w)**(1-outcome[node]) for w in linspace(0, 1, 100)]) + elif 'weight' in self.edge[node][i] and type(self.edge[node][i]['weight'])==float and self.edge[node][i]['weight']<=0: tot *=((1.0-abs(self.node[i]['weight'][node]))**(1-outcome[node])) - pr[i]=1-tot if outcome[i]==1 else 1-(1-tot) + pr[i]=1-mean(tot) if outcome[i]==1 else 1-(1-mean(tot)) p_out *=pr[i] self.Set(outcome, p_out)