AVhAvdZddlZddlmZddlmZddlmZddlmZgdZ ejdejZ ejd ejZejd ejZejd ejZdd Zd ZddZdZddZdZdZddZdZddZy)zSpecial Math Ops.N) constant_op)ops) array_ops)math_ops)erfinvndtrndtrilog_ndtrlog_cdf_laplaceiic>tj||g5tj|d}|jjt j t jfvrtd|jzt|cdddS#1swYyxYw)aGNormal distribution function. Returns the area under the Gaussian probability density function, integrated from minus infinity to x: ``` 1 / x ndtr(x) = ---------- | exp(-0.5 t**2) dt sqrt(2 pi) /-inf = 0.5 (1 + erf(x / sqrt(2))) = 0.5 erfc(x / sqrt(2)) ``` Args: x: `Tensor` of type `float32`, `float64`. name: Python string. A name for the operation (default="ndtr"). Returns: ndtr: `Tensor` with `dtype=x.dtype`. Raises: TypeError: if `x` is not floating-type. valuesxname=x.dtype=%s is not handled, see docstring for supported types.N) r name_scopeconvert_to_tensordtypeas_numpy_dtypenpfloat32float64 TypeError_ndtrrrs `/home/dcms/DCMS/lib/python3.12/site-packages/tensorflow/python/ops/distributions/special_math.pyrrks4 ~~dA3' ac*Awwbjj"**%==  I GG   8  A0BBc tjdtjdz|jd}||z}t j |}tjt j||dt j|ztjt j|ddt j|z t j|}d|zS)zImplements ndtr core logic.?@ half_sqrt_2)rr?) rconstantrsqrtrrabsrwhere_v2lesserfgreatererfc)rr$wzys rrrs$$ BGGBKqww]<++o!ll1o!mmA{#R(,,q/%9   1b !2 a(8#8(--:JLM! q.c>tj||g5tj|d}|jjt j t jfvrtd|jzt|cdddS#1swYyxYw)aThe inverse of the CDF of the Normal distribution function. Returns x such that the area under the pdf from minus infinity to x is equal to p. A piece-wise rational approximation is done for the function. This is a port of the implementation in netlib. Args: p: `Tensor` of type `float32`, `float64`. name: Python string. A name for the operation (default="ndtri"). Returns: x: `Tensor` with `dtype=p.dtype`. Raises: TypeError: if `p` is not floating-type. rprz=p.dtype=%s is not handled, see docstring for supported types.N) rrrrrrrrr_ndtri)r4rs rr r s( ~~dA3' ac*Awwbjj"**%==  I GG   !9 r c (gd}gd}gd}gd}gd}gd}fdtj|tjd kDd |z |}tj|d ktjtj |tj d |jj|}|d z } | d z} | | | z| || |z zz} | tjd tjz z} tjdtj|z} | tj| | z z } d | z |d | z |z | z }d | z |d | z |z | z }| |z }| |z }tj|tjdkD| tj| dk\||}tj|d tjdz kD|| }tjtj |j}tjtj ||}tj|d k| tj|d k\||}|S)zImplements ndtri core logic.)g~g;+@gVLgX@g-^OM) gͿgcu/@gٷaTgSi@g_6V.lgԁ 5U@g@gt ҕE?r%) glLgAcgwDglz9~@g>F^-@gN F@gBהL@gyՒm?@gێ<8@) g}yNgmENg2 3¿g < @gE؇.@gF"D@go)F@g;Z/@r%) gX0:>g4" L)L>g3?gM5iPV?gQ&^E?g T?g+@g x'1@gtՓ @) g=kv)=>gC>g)e+5?gǶ'|?g<_?gb*G?g8ҪMp @g(V@r%ctj||jj}|jst j |S|d||dd|zzS)z2Compute n_th order polynomial via Horner's method.rN)rarrayrrsizer zeros_like)varcoeffs_create_polynomials rr>z"_ndtri.._create_polynomialsW XXfcii66 7F ;;  ! !# && !9)#vabz:S@ @@r2gr%r&r"r#g @)r)rr*rexpm1fillshaper9rrr(pirlogexprr'inf)r4p0q0p1q1p2q2maybe_complement_p sanitized_mcpr/ww x_for_big_pr0 first_termsecond_term_small_psecond_term_otherwise x_for_small_p x_otherwiserinfinity_scalarinfinityx_nan_replacedr>s @rr5r5s" " "" ""A!))!rxx}n*@!R"&&+--q1"5!((qww?/ ^^IOOA. @(%%a3h &/&8&8c8Q&OQ. r2c\t|ts td|dkr td|dkDr tdt j ||g5t j |d}|jjtjk(r t}t}nL|jjtjk(r t}t}ntd |jzt!j"t%j&||t)|  t!j"t%j&||t%j*t)t%j,||t/t%j0|||cd d d S#1swYy xYw) aLog Normal distribution function. For details of the Normal distribution function see `ndtr`. This function calculates `(log o ndtr)(x)` by either calling `log(ndtr(x))` or using an asymptotic series. Specifically: - For `x > upper_segment`, use the approximation `-ndtr(-x)` based on `log(1-x) ~= -x, x << 1`. - For `lower_segment < x <= upper_segment`, use the existing `ndtr` technique and take a log. - For `x <= lower_segment`, we use the series approximation of erf to compute the log CDF directly. The `lower_segment` is set based on the precision of the input: ``` lower_segment = { -20, x.dtype=float64 { -10, x.dtype=float32 upper_segment = { 8, x.dtype=float64 { 5, x.dtype=float32 ``` When `x < lower_segment`, the `ndtr` asymptotic series approximation is: ``` ndtr(x) = scale * (1 + sum) + R_N scale = exp(-0.5 x**2) / (-x sqrt(2 pi)) sum = Sum{(-1)^n (2n-1)!! / (x**2)^n, n=1:N} R_N = O(exp(-0.5 x**2) (2N+1)!! / |x|^{2N+3}) ``` where `(2n-1)!! = (2n-1) (2n-3) (2n-5) ... (3) (1)` is a [double-factorial](https://en.wikipedia.org/wiki/Double_factorial). Args: x: `Tensor` of type `float32`, `float64`. series_order: Positive Python `integer`. Maximum depth to evaluate the asymptotic expansion. This is the `N` above. name: Python string. A name for the operation (default="log_ndtr"). Returns: log_ndtr: `Tensor` with `dtype=x.dtype`. Raises: TypeError: if `x.dtype` is not handled. TypeError: if `series_order` is a not Python `integer.` ValueError: if `series_order` is not in `[0, 30]`. z&series_order must be a Python integer.rz"series_order must be non-negative.zseries_order must be <= 30.rrrzx.dtype=%s is not supported.N) isinstanceintr ValueErrorrrrrrrrLOGNDTR_FLOAT64_LOWERLOGNDTR_FLOAT64_UPPERrLOGNDTR_FLOAT32_LOWERLOGNDTR_FLOAT32_UPPERrr*rr-rrDmaximum_log_ndtr_lowerminimum)r series_orderr lower_segment upper_segments rr r sSd L# & < ==A 9 ::B 2 33 ~~dA3' P ac*Aww++m+m   2:: -+m+m 4qww> ??   M* r    Q . LLx//=AB C H,,Q > M O P5 P P Ps EF""F+ctj|}d|ztj| z dtjdtjzzz }|tjt ||zS)zGAsymptotic expansion version of `Log[cdf(x)]`, appropriate for `x<<-1`.r"r#)rsquarerDrrC_log_ndtr_asymptotic_series)rrex_2 log_scales rrcrcrs`#Sj8<<++cBFF2:4F.FF) X\\"=a"NO OOr2c|jj}|dkrtjd|St j |}t j|}t j|}|}td|dzD]?}tjtd|zdz ||z }|dzr||z }n||z }||z}Ad|z|z S)z2Calculates the asymptotic series used in log_ndtr.rr8r?r%) rrrr9rrjrr;range_double_factorial) rrerrleven_sumodd_sumx_2nnr1s rrkrkzs '' %Q 88Au #  ! !! $(   #' $ L1$ %a "1q519-u5$9:N   a"fnn E!FFFs B B..B7)r)r )r )r)r )__doc__numpyrtensorflow.python.frameworkrrtensorflow.python.opsrr__all__r9rr^rr`r_rarrr r5r rcrkrrpr r2rrsN3++*  !bjj1 bjj1 !BJJ/ BJJ/ F :[|YPxP!&/.& -Fr2