(ph6SSKrSSKrSSKJr SSKJrJrJrJ r J r J r SSK J r /SQrS SjrSSjrSSjrS rS rSS jrSS jrg)N)_asarray_validated)array_namespacexp_sizexp_broadcast_promotexp_copyxp_float_to_complex is_complex)array_api_extra) logsumexpsoftmax log_softmaxc `[X5n[XSSUS9up[R"USUS9nUb[R"USUS9OUnUc[ [ UR 55OUn[U5S:wa,[R"SSS9 [XXUS 9upgSSS5 Od[R"UR5nSX'UR[ U5UR*URS 9nUR!U5nUR#WRS 5(aU(a=UR%W5n ['[)UR+U5U55n XS --nO>> import numpy as np >>> from scipy.special import logsumexp >>> a = np.arange(10) >>> logsumexp(a) 9.4586297444267107 >>> np.log(np.sum(np.exp(a))) 9.4586297444267107 With weights >>> a = np.arange(10) >>> b = np.arange(10, 0, -1) >>> logsumexp(a, b=b) 9.9170178533034665 >>> np.log(np.sum(b*np.exp(a))) 9.9170178533034647 Returning a sign flag >>> logsumexp([1,2],b=[1,-1],return_sign=True) (1.5413248546129181, -1.0) Notice that `logsumexp` does not directly support masked arrays. To use it on a masked array, convert the mask into zero weights: >>> a = np.ma.array([np.log(2), 2, np.log(3)], ... mask=[False, True, False]) >>> b = (~a.mask).astype(int) >>> logsumexp(a.data, b=b), np.log(5) 1.6094379124341005, 1.6094379124341005 T)ensure_writeableforce_floatingxp)ndimrNrignore)divideinvalid)axis return_signrdtypecomplex floating?)r)rrxpx atleast_ndtuplerangerrnperrstate _logsumexpasarrayshapefullinfrsignisdtyperealr _wrap_radiansimagsqueeze) arbkeepdimsrroutsgnr&r+r-s K/var/www/html/venv/lib/python3.13/site-packages/scipy/special/_logsumexp.pyr r sz  B tDUW XDA qqR(A,-MqqR(qA#'<5qvv TDqzQ [[( ;!!TrRHC< ; 177# ggeElRVVG177g;ggcl zz#))/00 773A aaC A A" a /C zz!''?++ HHQVaR!VQ ' FF1IFF2775>BJJt5;;J,OOPP ((1+q !E )C c  ''#,C 8O CII / /vv!G 8Or<c[USS9n[R"XSS9n[R"X- 5nU[R"X1SS9- $)a Compute the softmax function. The softmax function transforms each element of a collection by computing the exponential of each element divided by the sum of the exponentials of all the elements. That is, if `x` is a one-dimensional numpy array:: softmax(x) = np.exp(x)/sum(np.exp(x)) Parameters ---------- x : array_like Input array. axis : int or tuple of ints, optional Axis to compute values along. Default is None and softmax will be computed over the entire array `x`. Returns ------- s : ndarray An array the same shape as `x`. The result will sum to 1 along the specified axis. Notes ----- The formula for the softmax function :math:`\sigma(x)` for a vector :math:`x = \{x_0, x_1, ..., x_{n-1}\}` is .. math:: \sigma(x)_j = \frac{e^{x_j}}{\sum_k e^{x_k}} The `softmax` function is the gradient of `logsumexp`. The implementation uses shifting to avoid overflow. See [1]_ for more details. .. versionadded:: 1.2.0 References ---------- .. [1] P. Blanchard, D.J. Higham, N.J. Higham, "Accurately computing the log-sum-exp and softmax functions", IMA Journal of Numerical Analysis, Vol.41(4), :doi:`10.1093/imanum/draa038`. Examples -------- >>> import numpy as np >>> from scipy.special import softmax >>> np.set_printoptions(precision=5) >>> x = np.array([[1, 0.5, 0.2, 3], ... [1, -1, 7, 3], ... [2, 12, 13, 3]]) ... Compute the softmax transformation over the entire array. >>> m = softmax(x) >>> m array([[ 4.48309e-06, 2.71913e-06, 2.01438e-06, 3.31258e-05], [ 4.48309e-06, 6.06720e-07, 1.80861e-03, 3.31258e-05], [ 1.21863e-05, 2.68421e-01, 7.29644e-01, 3.31258e-05]]) >>> m.sum() 1.0 Compute the softmax transformation along the first axis (i.e., the columns). >>> m = softmax(x, axis=0) >>> m array([[ 2.11942e-01, 1.01300e-05, 2.75394e-06, 3.33333e-01], [ 2.11942e-01, 2.26030e-06, 2.47262e-03, 3.33333e-01], [ 5.76117e-01, 9.99988e-01, 9.97525e-01, 3.33333e-01]]) >>> m.sum(axis=0) array([ 1., 1., 1., 1.]) Compute the softmax transformation along the second axis (i.e., the rows). >>> m = softmax(x, axis=1) >>> m array([[ 1.05877e-01, 6.42177e-02, 4.75736e-02, 7.82332e-01], [ 2.42746e-03, 3.28521e-04, 9.79307e-01, 1.79366e-02], [ 1.22094e-05, 2.68929e-01, 7.31025e-01, 3.31885e-05]]) >>> m.sum(axis=1) array([ 1., 1., 1.]) F check_finiteTr>)rr"amaxrOrC)r:rx_max exp_x_shifteds r4r r sGv 151A GGA4 0EFF19%M 266-TJ JJr<c[USS9n[R"XSS9nURS:aSU[R"U5)'O[R"U5(dSnX- n[R "U5n[R "SS9 [R"XASS9n[R"U5nSSS5 UW- nU$!,(df  N=f) aCompute the logarithm of the softmax function. In principle:: log_softmax(x) = log(softmax(x)) but using a more accurate implementation. Parameters ---------- x : array_like Input array. axis : int or tuple of ints, optional Axis to compute values along. Default is None and softmax will be computed over the entire array `x`. Returns ------- s : ndarray or scalar An array with the same shape as `x`. Exponential of the result will sum to 1 along the specified axis. If `x` is a scalar, a scalar is returned. Notes ----- `log_softmax` is more accurate than ``np.log(softmax(x))`` with inputs that make `softmax` saturate (see examples below). .. versionadded:: 1.5.0 Examples -------- >>> import numpy as np >>> from scipy.special import log_softmax >>> from scipy.special import softmax >>> np.set_printoptions(precision=5) >>> x = np.array([1000.0, 1.0]) >>> y = log_softmax(x) >>> y array([ 0., -999.]) >>> with np.errstate(divide='ignore'): ... y = np.log(softmax(x)) ... >>> y array([ 0., -inf]) FrZTr>rr)rN) rr"r\rrNrOr#rCrQ)r:rr]tmpexp_tmprXr2s r4r r [sh 151A GGA4 0E zzA~%&r{{5!!" [[   )CffSkG H % FF7 5ffQi & )C J & %s ,C C)NNFF)N)r?N)r7numpyr"scipy._lib._utilrscipy._lib._array_apirrrrrr scipy._libr r__all__r r,rHrKr$r r rr<r4rgsN /. 1|.~-DI7t^KBFr<