Ńň )čJc @s%ddkZddkZddkZddkZddklZlZlZddkl Z d„Z e d„Z d„Z d„Zd„Zd „Zd „Zd „Zd „Zd „Zdfd„ƒYZd„Zd„Zedjo6eeiƒdjoeeidƒneƒndS(i˙˙˙˙N(tarangetlogtlogn(t rv_discretecCst|ƒdt|ƒS(Ngđ?(tsumtlen(tL((s sailing.pytmean#scCs]|djot|ƒ}ntitg}|D]}|||dq1~ƒt|ƒƒS(sWThe standard deviation of a set of values. Pass in the mean if you already know it.iN(tNoneRtmathtsqrtRR(tvaluestmeanvalt_[1]tx((s sailing.pytstddev%s cCs…t|ƒ}t|ƒ}|ddjo ||dS||dd|dd!}yt|ƒSWntj oti|ƒSXdS(sReturn the middle value, when the values are sorted. If there are an odd number of elements, try to average the middle two. If they can't be averaged (e.g. they are strings), choose one at random. >>> median([10, 100, 11]) 11 >>> median([1, 2, 3, 4]) 2.5 iiN(RtsortedRt TypeErrortrandomtchoice(R tntmiddle2((s sailing.pytmedian-s   cCstid|dƒS(s. Return a random integer from [0, n). ii(Rtrandint(R((s sailing.pyt my_randintBscCs||d||dfS(s˘ Returns (x + v[0], y + v[1]). EXAMPLES:: >>> add_vector(0, 0, (0, 1)) (0, 1) >>> add_vector(0, 0, (-2, 1)) (-2, 1) ii((Rtytv((s sailing.pyt add_vectorIs cCsPxI|D]A}t|ƒdjotSx |D]}|djotSq,WqWtS(są Rows must sum to 1 and no entry can be negative. EXAMPLE:: >>> wind_array = [ [0.4, 0.3, 0.0, 0.0, 0.0, 0.0, 0.0, 0.3], [0.4, 0.3, 0.3, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.4, 0.3, 0.3, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.4, 0.3, 0.3, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.4, 0.2, 0.4, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.3, 0.3, 0.4, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.3, 0.3, 0.4], [0.4, 0.0, 0.0, 0.0, 0.0, 0.0, 0.3, 0.3] ] >>> check_probability_matrix(wind_array) True ii(RtFalsetTrue(tPRR((s sailing.pytcheck_probability_matrixVs cCs‚|djpt‚|djpt‚|djpt‚|djpt‚t||ƒ}|d|jo|Sd|SdS(s Absolute difference in directions. EXAMPLES:: >>> abs_direction_difference(0, 1) 1 >>> abs_direction_difference(3, 2) 1 >>> abs_direction_difference(3, 5) 2 >>> abs_direction_difference(3, 7) 4 iiN(tAssertionErrortabs(td1td2R((s sailing.pytabs_direction_differencepscCsĂ|djpt‚|djpt‚|djpt‚|djpt‚t||ƒ}|djodS|djodS|djodS|djod S|d jod St‚d S( s9 The tack of the boat depends on the relative difference of the boat's direction and the wind. EXAMPLES:: >>> tack(0, 0) 'away' >>> tack(0, 7) 'down' >>> tack(0, 2) 'cross' >>> tack(0, 3) 'up' >>> tack(0, 4) 'into' iitawayitdownitcrossitupitintoN(R R$t ValueError(tboat_directiontwind_directiontd((s sailing.pyttack‹s      cCs3||}x|djo|d7}q W|djS(sL Relative to the boat, is the wind blowing to the left of the boat? iiiii(iii((t boat_dirnt wind_dirntw((s sailing.pyt wind_on_leftŽs   cCsź|djpt‚|djpt‚|djod S|djod S|djodS|djodS|djodS|djodS|d jodS|d jodSd S(sÔ The direction 0 is north so we move by (0, 1) in cartesian coordinates. EXAMPLES:: >>> direction_vector(0) # north (0, 1) >>> direction_vector(6) # west (-1, 0) iiiiii˙˙˙˙iiiiN(ii(ii(ii(ii˙˙˙˙(ii˙˙˙˙(i˙˙˙˙i˙˙˙˙(i˙˙˙˙i(i˙˙˙˙i(R (R-((s sailing.pytdirection_vectorźs$         tSailingcBseZd„Zd„Zd„Zd„Zd„Zd„Zd„Zd„Z d„Z d „Z d „Z d „Z d „Zd „Zd„ZRS(cCs¤d|_||_ddddddddgddddddddgddddddddgddddddddgddddddddgddddddddgddddddddgddddddddgg|_|d|_|d|_hdd6d d 6d d 6dd 6|_g|_xbtt|iƒƒD]K}t t|i|ƒƒ|i|g}|ii t ddd|ƒƒqQWdS(NgÍĚĚĚĚĚě?gš™™™™™Ů?g333333Ó?ggš™™™™™É?iiR(iR'iR&R%tnametcustmR ( tgammat lake_sizet wind_arraytend_xtend_ytcoststwind_distributiontrangeRRtappendR(tselfR8titvals((s sailing.pyt__init__Ös&  $  % &c cs‘xŠt|iƒD]y}xpt|iƒD]_}xVtdƒD]H}x?tdƒD]1}x(tdƒD]}|||||fVq_WqLWq9Wq&WqWdS(sk Instead of storing the states in a large list/dictionary, we provide an iterator. iN(R>R8(R@RRR-tw1tw2((s sailing.pytstatesňs   cCs$|d|df|i|ifjS(Nii(R:R;(R@tstate((s sailing.pyt is_terminal˙scCs/y|i||ƒWntj otSXtS(N(tcosttKeyErrorRR(R@RGtaction((s sailing.pytis_intos cCs tdƒ}x3to+tdƒ}t||ƒdjoPqqW|i|ƒ}xHto@t|iƒt|iƒ|||f}|i|ƒpPqTqTW|S(NiR)(RRR.tnew_windR8RH(R@RDR-RERG((s sailing.pyt random_state s   ' cCsh|\}}}}}t||t|ƒƒ\}}|t|iƒjo|t|iƒjotStS(N(RR3R>R8RR(R@RGRKRRt_tx2ty2((s sailing.pyt stays_in_lakes ,c Cs×|\}}}}}t||t|ƒƒ\}} |i||ƒpdSd} y| |i||ƒ7} Wntj odSXxNtdƒD]@} || ||| f} | |i|i|| ƒ|| 7} qW| S(Nii( RR3RRRRIRJR>R7ttransition_probability( R@tVtstnew_dRRRORERPRQt this_costtw3ts_new((s sailing.pytaverage_cost_of_transition!s )cCs‰|\}}}}}|\}} } } } t| ƒ\} }||| jodS| ||jodS|| jodS|i|| S(sĹ What is the probability of moving from state s1 to s2? s1 = (x1, y1, _, w1, w2) s2 = (x2, y2, d2, w2_2, w3) The boat was at (x1, y1) and travelled to (x2, y2). Then it must be the case that (x2, y2) = (x1, y1) + direction_vector(d2). If this does not hold then the probability is 0. If the previous wind direction of s2 does not match the new wind direction of s1 then the probability is 0 (so we need w2_2 == w2). Finally, the probability of moving from s1 to s2 is just the probability of the wind changing from w2=w2_2 to w3, which is stored in the global variable wind_array. >>> x1, y1 = 1, 1 >>> x2, y2 = 2, 1 >>> d1 = 0 >>> d2 = 2 # the direction that we just travelled >>> w1 = 3 >>> w2 = 2 >>> w2_2 = w2 >>> lake_size = 5 >>> S = Sailing(lake_size) >>> S.transition_probability((x1, y1, d1, w1, w2), (x2, y2, d2, w2_2, 1)) 0.40000000000000002 >>> S.transition_probability((x1, y1, d1, w1, w2), (x2, y2, d2, w2_2, 0)) 0.0 i(R3R9(R@ts1ts2tx1ty1RORDRERPRQR#tw2_2RXtd_vec1td_vec2((s sailing.pyRS8s' cCs|i|iƒS(s´ The wind is currently blowing in direction w and it changes to a new direction according to the matrix wind_array, which is encoded by general probability distribution in wind_probability_space. EXAMPLES:: >>> lake_size = 5 >>> S = Sailing(lake_size) >>> S.new_wind(0) in range(8) True >>> S.new_wind(4) in range(8) True (R=trvs(R@R1((s sailing.pyRMrscCs|d}|it||ƒS(s+ If we are in state s and we decide to travel in direction d, how much will this cost? Note that the wind for this new leg is in the last element of s. EXAMPLES:: >>> x1, y1 = 1, 1 >>> x2, y2 = 2, 1 >>> d1 = 0 >>> d2 = 2 >>> w1 = 3 >>> w2 = 2 >>> s = (x1, y1, d1, w1, w2) >>> lake_size = 5 >>> S = Sailing(lake_size) >>> S.cost(s, 0) 3 >>> S.cost(s, 1) 2 i˙˙˙˙(R<R.(R@RUR-RM((s sailing.pyRI‡s c Csş|\}}}}}|i|ƒodSd}d} xwtdƒD]i} |i||| ƒ} | djoqCn|djo| }| } qC| | jo| }| } qCqCW|| fS(sŠ If we are in state s, use the value vector V to work out the best direction to travel in and its estimated cost. i˙˙˙˙ii(i˙˙˙˙iN(RHRR>RZ( R@RURTRRR-RDREtmin_dt min_d_costRVt new_d_cost((s sailing.pyt best_action˘s"     c CsŽh}h}h}x^|iƒD]P}d||R?RuRRR(R@Rntnr_simstsimsRAtsims_avgt sims_stddev((s sailing.pytrun_simulations˙scCsƒ|i|ƒodS|i||ƒ}t|d|dt|ƒƒ\}}|i|dƒ}||||d|f}||fS(s Use the generative model of S to find the next state given that we are in state and take action action. iii˙˙˙˙N(RHRRIRR3RM(R@RGRKRIRPRQRXt new_state((s sailing.pytsample_next_state s&(t__name__t __module__RCRFRHRLRNRRRZRSRMRIRfRrRuRzR|(((s sailing.pyR4Ős      :    "  c CsAd}td|ƒ}|iddƒ\}}}}dGHd}dGH|i||ƒ\}}} Hd||fGHHd GHd |GHd t|iƒƒGHd |GHHd |GHd |GHd t|ƒGHd | GHHd} d} xK|iƒD]=} | d| dfdjo| d7} | || 7} qŕqŕWd|i|i| | fGHdS(NiR8Rkgš™™™™™š?sDone with value iterationičsRunning simulations...sLake size: %d x %dsValue iteration:s Mean cost: %.1fs Median cost: %.1fs Standard dev: %.1fsSimulations (run %d times):giis;Mean cost to sail across lake from (1, 1) to (%d, %d): %.1f(ii(R4RrRzRR tkeysR:R;( R8tSRTRnRpRqRvRwRxRytv_11t v_11_countRU((s sailing.pytvalue_iteration_examples:       cCs˜t|ƒ}|idƒ\}}}}dt|ƒd}t|dƒ}ti||ƒti||ƒti||ƒti||ƒ|iƒdS(Ng{ŽGáz„?tlake_s.pkltwb(R4Rrtstrtopentpickletdumptclose(R8R€RTRnRpRqt lake_filenametoutput((s sailing.pytsave_optimal_solution>s t__main__ii(R RˆRRhtscipyRRRt scipy.statsRRRRRRRRR$R.R2R3R4RƒRR}Rtargvteval(((s sailing.pyts.           #  ˙E %