o ?eA@sdZddlZddlmZddlmZddlmZddlmZgdZ e dej Z e d ej Ze d ej Ze d ej Zd!d d ZddZd"ddZddZd#ddZddZddZd$ddZddZd%d dZdS)&zSpecial Math Ops.N) constant_op)ops) array_ops)math_ops)erfinvndtrndtrilog_ndtrlog_cdf_laplaceiircCltj||gd$tj|dd}|jjtjtjfvr!td|jt |WdS1s/wYdS)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_ndtrrrrq/home/www/facesmatcher.com/pyenv/lib/python3.10/site-packages/tensorflow/python/ops/distributions/special_math.pyrks$c Csxtjdtd|jdd}||}t|}tt ||dt |tt |ddt |t |}d|S)zImplements ndtr core logic.?@ half_sqrt_2)rr?) rconstantrsqrtrrabsrwhere_v2lesserfgreatererfc)rr"wzyrrrrs rrcCr )aThe inverse of the CDF of the Normal distribution function. Returns x such that the area under the pdf from minus infinity to x is equal to p. A piece-wise rational approximation is done for the function. This is a port of the implementation in netlib. Args: p: `Tensor` of type `float32`, `float64`. name: Python string. A name for the operation (default="ndtri"). Returns: x: `Tensor` with `dtype=p.dtype`. Raises: TypeError: if `p` is not floating-type. rprz=p.dtype=%s is not handled, see docstring for supported types.N) rrrrrrrrr_ndtri)r0rrrrrs$c sgd}gd}gd}gd}gd}gd}fddt|td  kd ||}t|d ktt|td |jj|}|d } | d } | | | | || |} | t dtj  9} t d t |} | t | | } d | |d | || }d | |d | || }| |}| |}t|t d k| t| dk||}t|d t d k|| }tjtj|jd}tt||}t|d k| t|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#cs>t||jj}|jst|S|d||dd|S)z2Compute n_th order polynomial via Horner's method.rN)rarrayrrsizer zeros_like)varZcoeffs_create_polynomialrrr8s z"_ndtri.._create_polynomialgr#r$r r!g @)r)rr(rexpm1fillshaper3rrr&pirlogexprr%inf)r0p0q0p1q1p2q2Zmaybe_complement_pZ sanitized_mcpr-ZwwZ x_for_big_pr.Z first_termZsecond_term_small_pZsecond_term_otherwiseZ x_for_small_pZ x_otherwiserZinfinity_scalarinfinityZx_nan_replacedrr7rr1s\     r1r cCst|ts td|dkrtd|dkrtdtj||gdVtj|dd}|jjt j kr5t }t }n|jjt j krAt}t}ntd |jtt||t|  tt||ttt||tt|||Wd S1szwYd S) 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+rr>maximum_log_ndtr_lowerminimum)r series_orderrZ lower_segmentZ upper_segmentrrrr s2 2   $cCsFt|}d|t| dtdtj}|tt||S)zGAsymptotic expansion version of `Log[cdf(x)]`, appropriate for `x<<-1`.r r!)rsquarer>rr=_log_ndtr_asymptotic_series)rrTx_2Z log_scalerrrrRrs (rRc Cs|jj}|dkrtd|St|}t|}t|}|}td|dD]!}tt d|d||}|dr?||7}n||7}||9}q&d||S)z2Calculates the asymptotic series used in log_ndtr.rr2r9r#) rrrr3rrVrr5range_double_factorial) rrTrrXZeven_sumZodd_sumZx_2nnr/rrrrWzs       rWrcCs~tj||gd-tj|dd}|jjtjtjfvr!td|jt |ddt dWdS1s8wYdS) aThe inverse function for erf, the error function. Args: x: `Tensor` of type `float32`, `float64`. name: Python string. A name for the operation (default="erfinv"). Returns: x: `Tensor` with `dtype=x.dtype`. Raises: TypeError: if `x` is not floating-type. rrrrr#r!r9N) rrrrrrrrrrr&rrrrrs$cCstt|ddS)z;The double factorial function for small Python integer `n`.r2)rprodZarange)r[rrrrZsrZr cCstj||gd0tj|dd}td |}tt| }td|}t |dk||WdS1s;wYdS)aLog Laplace distribution function. This function calculates `Log[L(x)]`, where `L(x)` is the cumulative distribution function of the Laplace distribution, i.e. ```L(x) := 0.5 * int_{-infty}^x e^{-|t|} dt``` For numerical accuracy, `L(x)` is computed in different ways depending on `x`, ``` x <= 0: Log[L(x)] = Log[0.5] + x, which is exact 0 < x: Log[L(x)] = Log[1 - 0.5 * e^{-x}], which is exact ``` Args: x: `Tensor` of type `float32`, `float64`. name: Python string. A name for the operation (default="log_ndtr"). Returns: `Tensor` with `dtype=x.dtype`. Raises: TypeError: if `x.dtype` is not handled. rrrr!rUr$N) rrrrr>rr?r'log1prr()rrZlower_solutionZsafe_exp_neg_xZupper_solutionrrrr s$)r)r)rHr )r)r )__doc__numpyrZtensorflow.python.frameworkrrZtensorflow.python.opsrr__all__r3rrMrrOrNrPrrrr1r rRrWrrZr rrrrs*F     #  ^\