AVh*dZddlZddlZddlZddlZddlZddlZddlm Z ddl m Z ddl m Z ddl mZddlmZddlmZdd lmZdd lmZdd lmZdd lmZdd lmZddlmZddlmZedddgej:ej<ddMdZedej@ej:dMdZ!edej@ej:dMdZ"edej@ej:dMdZ#edej@ej:dMdZ$edej@ej:dMdZ%eddej@ej:dMd Z&ed!d"ej@ej:dMd#Z'ed$d%ej@ej:dMd&Z(ed'd(ej@ej:dMd)Z)ed*ej@ej:dMd+Z*ed,ej@ej:dMd-Z+ed.ej@ej:dMd/Z,ed0ej@ej:dMd1Z-ed2ej@ej:dMd3Z.ed4ej@ej:dMd5Z/ed6ej@ej:dMd7Z0ed8ej@ej:dMd9Z1e jdd:d;Z3d<Z4ed=d>ej:d?Z5d@Z6dAZ7dBZ8dCZ9dDZ:dEZ;dFZdIZ?ejdJKe?Z?dLZAy)NzArithmetic Operations that don't fit into math_ops due to dependencies. To avoid circular dependencies, some math_ops should go here. N) gen_xla_ops)ops)tensor) tensor_shape) array_ops)control_flow_ops)gen_linalg_ops)gen_special_math_ops)math_ops) tf_logging) deprecation)dispatch) tf_exportz math.lbetalbeta)v1cJtj|d|g5tj|d}tjtj |dg}tj|dg}tj |}||z }|cdddS#1swYyxYw)aComputes \\(ln(|Beta(x)|)\\), reducing along the last dimension. Given one-dimensional $z = [z_1,...,z_K]$, we define $$Beta(z) = \frac{\prod_j \Gamma(z_j)}{\Gamma(\sum_j z_j)},$$ where $\Gamma$ is the gamma function. And for $n + 1$ dimensional $x$ with shape $[N_1, ..., N_n, K]$, we define $$lbeta(x)[i_1, ..., i_n] = \log{|Beta(x[i_1, ..., i_n, :])|}.$$ In other words, the last dimension is treated as the $z$ vector. Note that if $z = [u, v]$, then $$Beta(z) = \frac{\Gamma(u)\Gamma(v)}{\Gamma(u + v)} = \int_0^1 t^{u-1} (1 - t)^{v-1} \mathrm{d}t,$$ which defines the traditional bivariate beta function. If the last dimension is empty, we follow the convention that the sum over the empty set is zero, and the product is one. Args: x: A rank `n + 1` `Tensor`, `n >= 0` with type `float`, or `double`. name: A name for the operation (optional). Returns: The logarithm of \\(|Beta(x)|\\) reducing along the last dimension. rx)nameaxisN)r name_scopeconvert_to_tensorr reduce_sumlgamma)rrlog_prod_gamma_xsum_xlog_gamma_sum_xresults V/home/dcms/DCMS/lib/python3.12/site-packages/tensorflow/python/ops/special_math_ops.pyrr-sN ~~dGaS) ac*A **8??1+=RDI    -Eooe,O  /F s A6BB"zmath.special.dawsnctj|d|g5tj|cdddS#1swYyxYw)aComputes Dawson's integral of `x` element-wise. Dawson's integral is defined as `exp(-x**2)` times the integral of `exp(t**2)` from `0` to `x`, with the domain of definition all real numbers. Dawson's function is odd. >>> tf.math.special.dawsn([-1., -0.5, 0.5, 1.]).numpy() array([-0.5380795, -0.4244364, 0.4244364, 0.5380795], dtype=float32) This implementation is based off of the Cephes math library. Args: x: A `Tensor` or `SparseTensor`. Must be one of the following types: `float32`, `float64`. name: A name for the operation (optional). Returns: A `Tensor` or `SparseTensor`, respectively. Has the same type as `x`. @compatibility(scipy) Equivalent to scipy.special.dawsn @end_compatibility dawsnN)rrr r"rrs r r"r"es96 ~~dGaS))  % %a ())) 8Azmath.special.expintctj|d|g5tj|cdddS#1swYyxYw)aComputes the Exponential integral of `x` element-wise. The Exponential integral is defined as the integral of `exp(t) / t` from `-inf` to `x`, with the domain of definition all positive real numbers. >>> tf.math.special.expint([1., 1.1, 2.1, 4.1]).numpy() array([ 1.8951179, 2.1673784, 5.3332353, 21.048464], dtype=float32) This implementation is based off of the Cephes math library. Args: x: A `Tensor` or `SparseTensor`. Must be one of the following types: `float32`, `float64`. name: A name for the operation (optional). Returns: A `Tensor` or `SparseTensor`, respectively. Has the same type as `x`. @compatibility(scipy) Equivalent to scipy.special.expi @end_compatibility expintN)rrr r&r#s r r&r&94 ~~dHqc**  & &q )***r$zmath.special.fresnel_cosctj|d|g5tj|cdddS#1swYyxYw)aComputes Fresnel's cosine integral of `x` element-wise. The Fresnel cosine integral is defined as the integral of `cos(t^2)` from `0` to `x`, with the domain of definition all real numbers. The Fresnel cosine integral is odd. >>> tf.math.special.fresnel_cos([-1., -0.1, 0.1, 1.]).numpy() array([-0.7798934 , -0.09999753, 0.09999753, 0.7798934 ], dtype=float32) This implementation is based off of the Cephes math library. Args: x: A `Tensor` or `SparseTensor`. Must be one of the following types: `float32`, `float64`. name: A name for the operation (optional). Returns: A `Tensor` or `SparseTensor`, respectively. Has the same type as `x`. @compatibility(scipy) Equivalent to scipy.special.fresnel second output. @end_compatibility fresnel_cosN)rrr r)r#s r r)r)s96 ~~dMA3//  + +A .///r$zmath.special.fresnel_sinctj|d|g5tj|cdddS#1swYyxYw)aComputes Fresnel's sine integral of `x` element-wise. The Fresnel sine integral is defined as the integral of `sin(t^2)` from `0` to `x`, with the domain of definition all real numbers. >>> tf.math.special.fresnel_sin([-1., -0.1, 0.1, 1.]).numpy() array([-0.43825912, -0.00052359, 0.00052359, 0.43825912], dtype=float32) This implementation is based off of the Cephes math library. Args: x: A `Tensor` or `SparseTensor`. Must be one of the following types: `float32`, `float64`. name: A name for the operation (optional). Returns: A `Tensor` or `SparseTensor`, respectively. Has the same type as `x`. @compatibility(scipy) Equivalent to scipy.special.fresnel first output. @end_compatibility fresnel_sinN)rrr r+r#s r r+r+s94 ~~dMA3//  + +A .///r$zmath.special.spencectj|d|g5tj|cdddS#1swYyxYw)aComputes Spence's integral of `x` element-wise. Spence's integral is defined as the integral of `log(t) / (1 - t)` from `1` to `x`, with the domain of definition all non-negative real numbers. >>> tf.math.special.spence([0.5, 1., 2., 3.]).numpy() array([ 0.58224034, 0. , -0.82246685, -1.4367464], dtype=float32) This implementation is based off of the Cephes math library. Args: x: A `Tensor` or `SparseTensor`. Must be one of the following types: `float32`, `float64`. name: A name for the operation (optional). Returns: A `Tensor` or `SparseTensor`, respectively. Has the same type as `x`. @compatibility(scipy) Equivalent to scipy.special.spence @end_compatibility spenceN)rrr r-r#s r r-r-r'r$zmath.bessel_i0zmath.special.bessel_i0ctj|d|g5tj|cdddS#1swYyxYw)aComputes the Bessel i0 function of `x` element-wise. Modified Bessel function of order 0. It is preferable to use the numerically stabler function `i0e(x)` instead. >>> tf.math.special.bessel_i0([-1., -0.5, 0.5, 1.]).numpy() array([1.26606588, 1.06348337, 1.06348337, 1.26606588], dtype=float32) Args: x: A `Tensor` or `SparseTensor`. Must be one of the following types: `half`, `float32`, `float64`. name: A name for the operation (optional). Returns: A `Tensor` or `SparseTensor`, respectively. Has the same type as `x`. @compatibility(scipy) Equivalent to scipy.special.i0 @end_compatibility bessel_i0N)rrr r/r#s r r/r/92 ~~dK!--  ) )! ,---r$zmath.bessel_i0ezmath.special.bessel_i0ectj|d|g5tj|cdddS#1swYyxYw)a4Computes the Bessel i0e function of `x` element-wise. Modified Bessel function of order 0. >>> tf.math.special.bessel_i0e([-1., -0.5, 0.5, 1.]).numpy() array([0.46575961, 0.64503527, 0.64503527, 0.46575961], dtype=float32) Args: x: A `Tensor` or `SparseTensor`. Must be one of the following types: `half`, `float32`, `float64`. name: A name for the operation (optional). Returns: A `Tensor` or `SparseTensor`, respectively. Has the same type as `x`. @compatibility(scipy) Equivalent to scipy.special.i0e @end_compatibility bessel_i0eN)rrr r2r#s r r2r29. ~~dL1#..  * *1 -...r$zmath.bessel_i1zmath.special.bessel_i1ctj|d|g5tj|cdddS#1swYyxYw)aComputes the Bessel i1 function of `x` element-wise. Modified Bessel function of order 1. It is preferable to use the numerically stabler function `i1e(x)` instead. >>> tf.math.special.bessel_i1([-1., -0.5, 0.5, 1.]).numpy() array([-0.5651591 , -0.25789431, 0.25789431, 0.5651591 ], dtype=float32) Args: x: A `Tensor` or `SparseTensor`. Must be one of the following types: `half`, `float32`, `float64`. name: A name for the operation (optional). Returns: A `Tensor` or `SparseTensor`, respectively. Has the same type as `x`. @compatibility(scipy) Equivalent to scipy.special.i1 @end_compatibility bessel_i1N)rrr r5r#s r r5r55r0r$zmath.bessel_i1ezmath.special.bessel_i1ectj|d|g5tj|cdddS#1swYyxYw)a8Computes the Bessel i1e function of `x` element-wise. Modified Bessel function of order 1. >>> tf.math.special.bessel_i1e([-1., -0.5, 0.5, 1.]).numpy() array([-0.20791042, -0.15642083, 0.15642083, 0.20791042], dtype=float32) Args: x: A `Tensor` or `SparseTensor`. Must be one of the following types: `half`, `float32`, `float64`. name: A name for the operation (optional). Returns: A `Tensor` or `SparseTensor`, respectively. Has the same type as `x`. @compatibility(scipy) Equivalent to scipy.special.i1e @end_compatibility bessel_i1eN)rrr r7r#s r r7r7Rr3r$zmath.special.bessel_k0ctj|d|g5tj|cdddS#1swYyxYw)a|Computes the Bessel k0 function of `x` element-wise. Modified Bessel function of order 0. It is preferable to use the numerically stabler function `k0e(x)` instead. >>> tf.math.special.bessel_k0([0.5, 1., 2., 4.]).numpy() array([0.92441907, 0.42102444, 0.11389387, 0.01115968], dtype=float32) Args: x: A `Tensor` or `SparseTensor`. Must be one of the following types: `half`, `float32`, `float64`. name: A name for the operation (optional). Returns: A `Tensor` or `SparseTensor`, respectively. Has the same type as `x`. @compatibility(scipy) Equivalent to scipy.special.k0 @end_compatibility bessel_k0N)rrr r9r#s r r9r9mr0r$zmath.special.bessel_k0ectj|d|g5tj|cdddS#1swYyxYw)a1Computes the Bessel k0e function of `x` element-wise. Modified Bessel function of order 0. >>> tf.math.special.bessel_k0e([0.5, 1., 2., 4.]).numpy() array([1.52410939, 1.14446308, 0.84156822, 0.60929767], dtype=float32) Args: x: A `Tensor` or `SparseTensor`. Must be one of the following types: `half`, `float32`, `float64`. name: A name for the operation (optional). Returns: A `Tensor` or `SparseTensor`, respectively. Has the same type as `x`. @compatibility(scipy) Equivalent to scipy.special.k0e @end_compatibility bessel_k0eN)rrr r;r#s r r;r;r3r$zmath.special.bessel_k1ctj|d|g5tj|cdddS#1swYyxYw)a|Computes the Bessel k1 function of `x` element-wise. Modified Bessel function of order 1. It is preferable to use the numerically stabler function `k1e(x)` instead. >>> tf.math.special.bessel_k1([0.5, 1., 2., 4.]).numpy() array([1.65644112, 0.60190723, 0.13986588, 0.0124835 ], dtype=float32) Args: x: A `Tensor` or `SparseTensor`. Must be one of the following types: `half`, `float32`, `float64`. name: A name for the operation (optional). Returns: A `Tensor` or `SparseTensor`, respectively. Has the same type as `x`. @compatibility(scipy) Equivalent to scipy.special.k1 @end_compatibility bessel_k1N)rrr r=r#s r r=r=r0r$zmath.special.bessel_k1ectj|d|g5tj|cdddS#1swYyxYw)a1Computes the Bessel k1e function of `x` element-wise. Modified Bessel function of order 1. >>> tf.math.special.bessel_k1e([0.5, 1., 2., 4.]).numpy() array([2.73100971, 1.63615349, 1.03347685, 0.68157595], dtype=float32) Args: x: A `Tensor` or `SparseTensor`. Must be one of the following types: `half`, `float32`, `float64`. name: A name for the operation (optional). Returns: A `Tensor` or `SparseTensor`, respectively. Has the same type as `x`. @compatibility(scipy) Equivalent to scipy.special.k1e @end_compatibility bessel_k1eN)rrr r?r#s r r?r?r3r$zmath.special.bessel_j0ctj|d|g5tj|cdddS#1swYyxYw)a2Computes the Bessel j0 function of `x` element-wise. Modified Bessel function of order 0. >>> tf.math.special.bessel_j0([0.5, 1., 2., 4.]).numpy() array([ 0.93846981, 0.76519769, 0.22389078, -0.39714981], dtype=float32) Args: x: A `Tensor` or `SparseTensor`. Must be one of the following types: `half`, `float32`, `float64`. name: A name for the operation (optional). Returns: A `Tensor` or `SparseTensor`, respectively. Has the same type as `x`. @compatibility(scipy) Equivalent to scipy.special.j0 @end_compatibility bessel_j0N)rrr rAr#s r rArA9. ~~dK!--  ) )! ,---r$zmath.special.bessel_j1ctj|d|g5tj|cdddS#1swYyxYw)a2Computes the Bessel j1 function of `x` element-wise. Modified Bessel function of order 1. >>> tf.math.special.bessel_j1([0.5, 1., 2., 4.]).numpy() array([ 0.24226846, 0.44005059, 0.57672481, -0.06604333], dtype=float32) Args: x: A `Tensor` or `SparseTensor`. Must be one of the following types: `half`, `float32`, `float64`. name: A name for the operation (optional). Returns: A `Tensor` or `SparseTensor`, respectively. Has the same type as `x`. @compatibility(scipy) Equivalent to scipy.special.j1 @end_compatibility bessel_j1N)rrr rDr#s r rDrDrBr$zmath.special.bessel_y0ctj|d|g5tj|cdddS#1swYyxYw)a2Computes the Bessel y0 function of `x` element-wise. Modified Bessel function of order 0. >>> tf.math.special.bessel_y0([0.5, 1., 2., 4.]).numpy() array([-0.44451873, 0.08825696, 0.51037567, -0.01694074], dtype=float32) Args: x: A `Tensor` or `SparseTensor`. Must be one of the following types: `half`, `float32`, `float64`. name: A name for the operation (optional). Returns: A `Tensor` or `SparseTensor`, respectively. Has the same type as `x`. @compatibility(scipy) Equivalent to scipy.special.y0 @end_compatibility bessel_y0N)rrr rFr#s r rFrFrBr$zmath.special.bessel_y1ctj|d|g5tj|cdddS#1swYyxYw)a2Computes the Bessel y1 function of `x` element-wise. Modified Bessel function of order 1. >>> tf.math.special.bessel_y1([0.5, 1., 2., 4.]).numpy() array([-1.47147239, -0.78121282, -0.10703243, 0.39792571], dtype=float32) Args: x: A `Tensor` or `SparseTensor`. Must be one of the following types: `half`, `float32`, `float64`. name: A name for the operation (optional). Returns: A `Tensor` or `SparseTensor`, respectively. Has the same type as `x`. @compatibility(scipy) Equivalent to scipy.special.y1 @end_compatibility bessel_y1N)rrr rHr#s r rHrH.rBr$ XlaEinsumc |jd}t|tr|j}|j d\}}|j d\}}t j ||jddj|||dt j ||jddj|||dgS)Nequation->,z {},{}->{})rKrr) get_attr isinstancebytesdecodesplitr xla_einsuminputsformat)opgradrKrUoutputleftrights r _einsum_gradr\Is [[ $(%  H>>$'.&& S!+$  ))A,%%feT:    ))A,%%fdE:   ctjj}|Ct|tj s)|j }|t|tj s)|SN)rget_default_graph_get_control_flow_contextrPrXLAControlFlowContext outer_context)contexts r _enclosing_tpu_contextre`s_  ! ! # = = ?'J 55%7##G J 55%7 .r]einsumz linalg.einsumc t|g|i|S)aTensor contraction over specified indices and outer product. Einsum allows defining Tensors by defining their element-wise computation. This computation is defined by `equation`, a shorthand form based on Einstein summation. As an example, consider multiplying two matrices A and B to form a matrix C. The elements of C are given by: $$ C_{i,k} = \sum_j A_{i,j} B_{j,k} $$ or ``` C[i,k] = sum_j A[i,j] * B[j,k] ``` The corresponding einsum `equation` is: ``` ij,jk->ik ``` In general, to convert the element-wise equation into the `equation` string, use the following procedure (intermediate strings for matrix multiplication example provided in parentheses): 1. remove variable names, brackets, and commas, (`ik = sum_j ij * jk`) 2. replace "*" with ",", (`ik = sum_j ij , jk`) 3. drop summation signs, and (`ik = ij, jk`) 4. move the output to the right, while replacing "=" with "->". (`ij,jk->ik`) Note: If the output indices are not specified repeated indices are summed. So `ij,jk->ik` can be simplified to `ij,jk`. Many common operations can be expressed in this way. For example: **Matrix multiplication** >>> m0 = tf.random.normal(shape=[2, 3]) >>> m1 = tf.random.normal(shape=[3, 5]) >>> e = tf.einsum('ij,jk->ik', m0, m1) >>> # output[i,k] = sum_j m0[i,j] * m1[j, k] >>> print(e.shape) (2, 5) Repeated indices are summed if the output indices are not specified. >>> e = tf.einsum('ij,jk', m0, m1) # output[i,k] = sum_j m0[i,j] * m1[j, k] >>> print(e.shape) (2, 5) **Dot product** >>> u = tf.random.normal(shape=[5]) >>> v = tf.random.normal(shape=[5]) >>> e = tf.einsum('i,i->', u, v) # output = sum_i u[i]*v[i] >>> print(e.shape) () **Outer product** >>> u = tf.random.normal(shape=[3]) >>> v = tf.random.normal(shape=[5]) >>> e = tf.einsum('i,j->ij', u, v) # output[i,j] = u[i]*v[j] >>> print(e.shape) (3, 5) **Transpose** >>> m = tf.ones(2,3) >>> e = tf.einsum('ij->ji', m0) # output[j,i] = m0[i,j] >>> print(e.shape) (3, 2) **Diag** >>> m = tf.reshape(tf.range(9), [3,3]) >>> diag = tf.einsum('ii->i', m) >>> print(diag.shape) (3,) **Trace** >>> # Repeated indices are summed. >>> trace = tf.einsum('ii', m) # output[j,i] = trace(m) = sum_i m[i, i] >>> assert trace == sum(diag) >>> print(trace.shape) () **Batch matrix multiplication** >>> s = tf.random.normal(shape=[7,5,3]) >>> t = tf.random.normal(shape=[7,3,2]) >>> e = tf.einsum('bij,bjk->bik', s, t) >>> # output[a,i,k] = sum_j s[a,i,j] * t[a, j, k] >>> print(e.shape) (7, 5, 2) This method does not support broadcasting on named-axes. All axes with matching labels should have the same length. If you have length-1 axes, use `tf.squeeze` or `tf.reshape` to eliminate them. To write code that is agnostic to the number of indices in the input use an ellipsis. The ellipsis is a placeholder for "whatever other indices fit here". For example, to perform a NumPy-style broadcasting-batch-matrix multiplication where the matrix multiply acts on the last two axes of the input, use: >>> s = tf.random.normal(shape=[11, 7, 5, 3]) >>> t = tf.random.normal(shape=[11, 7, 3, 2]) >>> e = tf.einsum('...ij,...jk->...ik', s, t) >>> print(e.shape) (11, 7, 5, 2) Einsum **will** broadcast over axes covered by the ellipsis. >>> s = tf.random.normal(shape=[11, 1, 5, 3]) >>> t = tf.random.normal(shape=[1, 7, 3, 2]) >>> e = tf.einsum('...ij,...jk->...ik', s, t) >>> print(e.shape) (11, 7, 5, 2) Args: equation: a `str` describing the contraction, in the same format as `numpy.einsum`. *inputs: the inputs to contract (each one a `Tensor`), whose shapes should be consistent with `equation`. **kwargs: - optimize: Optimization strategy to use to find contraction path using opt_einsum. Must be 'greedy', 'optimal', 'branch-2', 'branch-all' or 'auto'. (optional, default: 'greedy'). - name: A name for the operation (optional). Returns: The contracted `Tensor`, with shape determined by `equation`. Raises: ValueError: If - the format of `equation` is incorrect, - number of inputs or their shapes are inconsistent with `equation`. ) _einsum_v2)rKrUkwargss r rfrfjsb H 0v 0 00r]c |jdd}|rUtddjtt |j Dcgc] }t |c}dtj|d||g5}t |}|Dcgc]}|j}}t||\}tdj|z}|D]|D]~} t|dk(rH| jd k(r4| | ddd k(r)d |vr%tj|d cccdddS| jdkDsnt!d d| d|D]Pt#fd|D} | d kDsvs"t%j&ddt)|g|ccdddSt+Ft|d k(r8t-j.|d |d|d dz|dzd zzcdddS|d } |d } t1t|dz D]I} t| t|| dztz z}t3| | || dz|| dz|\} } Kt| tz }|rRt5| D cgc] \} }|vr|  }} }tj6| |} djfd| D} t| tk7rt!d|d| ddDcgc]}| j9|}}t;| |cdddScc}wcc}wcc}} wcc}w#1swYyxYw)z7Legacy implementation of einsum without using EinsumOp.rNz-Invalid keyword arguments for this function: , z. Expected: name.rfrNrrLrz"Subscript not supported: the axis z appears more than once in .c3,K|] }|vsd ywrNN).0sas r z_einsum_v1..s?aQ? zKFalling back to exponential-space implementation of einsum() because index z% is summed over more than two inputs.rMrc3,K|] }|vs| ywr_rq)rrrtoutput_axis_labelss r ruz_einsum_v1..7s !B.@)@!!BrvzInvalid equation: z9. The computed and specified output labels do not match: z vs )pop TypeErrorjoinsortedlistkeysrVrrshape%_einsum_v1_parse_and_resolve_equationsetlencountr trace ValueErrorsumloggingwarn_exponential_space_einsum_v1rerrTrange_einsum_v1_reduction enumeraterindex_transpose_if_necessary)rKrUrirkeyr input_shapesinput_axis_labels axis_labels input_labels input_counttemptemp_axis_labelsi axes_to_summissing_indicesrtrpermrxs ` @r _einsum_v1rs FD !$  7 99VD4G-HIcfSkI J KL   ~~dHx&899/T &\F%+,AGG,L,-h E*)bgg/03EEFK &+&, ! "a 'L,>,>q,AQ,F L2. .4x3Gq * *9/9/   a 1 $21#6!N!%& & &&??#4??k qQ&88 S E G H,H>v>>/9/9/"?+F q0@  # # )VAY 1! 4s : A !!%!&(:!;<99/9/> !9D(+ 3v;? #A   A& '#.@*A A B 4D:J4:1q5M4Ea!e4L4? Ad  A*+c2D.EEO!"231 ( ( d D 1d!B%!BB 6*<#==  xj)""2!348J7K1 N OO0B B!  " "1 % BD B "4 .s9/9/J-T Cq9/9/sd L<MM(BM6M 3M?M&M4AMBMM)A$M M % MMMc |jdd}tjd|}|std|d|j dj d|j dr|j ddd nd }t |t k7r'td t |d |d t dd}d |vrndjfdtjD}tD]\}}d |vs |j d }t |dk7rtdt |dz d||j td||jt dj|z } | dkr tdt || kr td| dkDr|| d nd} |jd | |<t | t |kDs| }tdDrtdd|%|jd |}d|vrtd|d|tdjt|z } djt| } | Dcic]}|dc}D]} | D]}||vs|xxdz cc<|djtfd| Dz}|fScc}w)aHelper for einsum() that splits/resolves inputs & outputs. Args: equation: Equation string given as argument to einsum(). input_shapes: List of the shapes of all inputs given to einsum() Returns: input_axis_labels, output_axis_labels where: input_axis_labels: List of length len(input_shapes) of strings representing the character label for each dimension of each given input, resolving any broadcast (...) axes, output_axis_labels: A string of character labels for each axes of output tensor, filling in missing output subscripts and broadcast axes. Raises: ValueError: If equation is in the uncorrect format, incorrect number of inputs given or broadcast axes "..." or output axes could not be resolved.  rlz^([a-zA-Z,.]+)(->[a-zA-Z.]*)?$z)Indices have incorrect format. Received: rnrNrMrmNzGot z arguments for equation "z ", expecting ...c3JK|]}|djvs|yw)rlN)r{)rrcrs r ruz8_einsum_v1_parse_and_resolve_equation..hs)P1BGG.s 13"9 1sz.Period "." found outside of ellipsis in input z/Period "." found outside of ellipsis in output c34K|]}|dk(s |ywrprq)rrrcountss r ruz8_einsum_v1_parse_and_resolve_equation..s;b6":?r;s )replacerematchrgrouprSrr{string ascii_lettersrndimsanyrr|)rKrrrx ellipsis_axesunusedrrpartsn replace_axesrindicesaxes_rrs @@r rrBsH&  c2 &( ((3X >%  @ !L MMkk!n**3/-2[[^u{{1~ab)#/00  s< !!:8*E*+,A / 00- h WWP''PPF,-'2 " u:?336u:a<.HI I ? (HI I O ! !C$7 7 q5;< < v;?EG G&'!evqbc{ 03;;E.s# NQQ. 8Q.%8 8 NscN|vrd|fS|dk(r|dvs |dk(r|vrd|fSd|fS)NrrrNrq) input_indexrtrbroadcast_axespreserved_axess r sort_keyz&_einsum_v1_reduction..sort_keysIN!Wn ! ^A%6 6 ! [ 0VmVmr]c|Sr_rq)rtrrs r z&_einsum_v1_reduction..s Xa^r]rrNrrNrl)rrrallrrr|findrr expand_dimsr multiplyr{ _get_shape _total_size_reshape_if_necessarymatmul)t0rt1rrsym_listrr sorted_axesrUaxes_strrtr_product product_axest0_shapenum_broadcast_elements_t0num_summed_elements new_shapet1_shapenum_broadcast_elements_t1uncompacted_shaperrrs ` `` ` @@@r rrs4 CM)  s288}o.() , -- CM)  s288}o.() + ,,$ N+ N NN N'#n*==L..?@EkaH 6DN1E 0+#;/ !X X34+ 8&{+9ka&1!n 5HMM!  5D 5'q 48F1I9 &"b A )  R (b) A :  S%8 9b:B'Gq>KN3~3F3G$HHL BGGL) ))"~H +^$c+&6%67!9%hK0@/@/A&BC%#n%& "$78 9 r9 -B"~H +^$s;'7789!; %#n%& 78 9 r9 -Boob"%G >#n%N1,=(>>?X^A%6!7789 :$G->?G ADN+c.2C.DDEAs;q>*S1B-CCDE F BGGL) ))q 6s M7M=ct|ttt|k7rtj||S|S)z?Like transpose(), but avoids creating a new tensor if possible.)r)r}rrr transpose)rrs r rrs0 T%D " ##   vD 11 Mr]ctd|D}td|jjD}t|t|k(rt dt ||Dr|St j||S)z=Like reshape(), but avoids creating a new tensor if possible.c3(K|] }|dn| yw)Nrrqrrrs r ruz(_reshape_if_necessary..%s>q!)B*>sc34K|]}|jywr_)valuers r ruz(_reshape_if_necessary..&s7AGG7sc3tK|]0\}}t|tj xr ||k(xs|dk(2yw)rN)rP tensor_libTensor)rrd0d1s r ruz(_reshape_if_necessary..(sA 3b"Z../ / JR2X5Ir J 3s68)tuplerdimsrrziprreshape)rr cur_shapes r rr"sr>I>>)7V\\%6%677) )nI&  3Iy1 33 M   VY //r]c|jj}t|Dcgc] \}}| | }}}|r$tj|}|D] }||||< |Scc}}w)zLike get_shape().as_list(), but explicitly queries the shape of a tensor if necessary to ensure that the returned value contains no unknown value.)ras_listrr)rrrd none_indices shape_tensors r rr/sm ,,   % )% 0>1AI!>,>??6*L !aeAh! , ?s A#A#c"d}|D]}||z} |S)zGiven list of tensor shape values, returns total size. If shape_values contains tensor values (which are results of array_ops.shape), then it returns a scalar tensor. If not, it returns an integer.rNrq) shape_valuesrvals r rr=s& & c cMF -r]c t|}|Dcgc]}|j}}t||\}}tdj ||z}dj t |}t|j |}|rtd|di} |D]} | |vst| | | <|D]} t| | | <tt||D]\} \} } | jjt| k7r5td| d| dt| d| jjd t | | j }tt| t| k7rtd | dt| |k7s|D cgc]} | j| }} tj| ||| <||| <g}|Dcgc].}|jj!Dcgc]}|r|nd  c}0}}}tt || j D]\}} g}t|D]O\} }| |vr|| j#|d  || |}t%|t&s9|d kDs?|j)|Qtt|d kDr$td | dtt|d| |vs|j)|t||D cgc]\} }tj*| |}} }d }|D]} || z} t-j.||Scc}wcc} wcc}wcc}}wcc}} w)zGFallback implementation that supports summing an index over > 2 inputs.rlzUnknown output axes: rnzInput z with axes z. has incorrect number of dimensions (expected z, got z).rz9Subscript not supported: an axis appears more than once: rrNzDimension mismatch on axis: z. Found z , expected 1.)r}rrrr{r| differencerrrrrgetrrrrinsertrPintappendrr r)rKrUrridx_inidx_outidx_allr missing_idx axis_orderrrinput_r sorted_idxpermuted reduction_idxrdimshapesjridxrexpanded_inputsexpanded_outputs r rrIs <&#)*a!''*,*9 /&' ') *' GGF7O $'G ''0+ ,[M; <<* 'b :jn' %b_JrN%&c&&&9:a&% ||SZ'  1#[(5zl&););(>2J 3u:#e*$  EeWA N PP E{j +56R%**R.6h6%%fh7fQifQi"-! " ,,. 0SR  0 "& " Z^^<=ea DF#3 3q AQil c3 C!G ++c   3t9~ 5bT: #CI/}> ?? 1&=@[{0}]*)?$z$Subscripts have incorrect format: {}rNrMrmz-Got {} inputs for equation "{}", expecting {}rLz>Output subscripts contain a label appearing more than once: {}zKOutput subscripts contain the label {} not present in the input subscripts.z/Output subscripts contain multiple ellipsis: {}cy)NrNrqrqr]r rz7_einsum_v2_parse_and_resolve_equation..sr]rz!Too many ellipses in input label zQToo many named labels in {}th subscript string of equation {} for input shape {} )dtypezhNumber of named labels in input #{} of equation {} must be equal to the number of dimensions in shape {})rrrrrVrrSrr Counterr{r|r}rr defaultdictrrrrfindnpprodfilterint64maxr)rKrrrallowed_labelsrr output_labels label_countsrinput_label_setlabelnum_output_ellipses label_to_dimrlabelsrellipsis_start ellipsis_endrresolved_shapess r r r se&&sB/. hN**  /xj J LL)11%H .n$N ((+22>B$ &%  .556GH JJQ%%c*,(- A%++a.$D-#l++ DKK L8S%68 99  ""&&u{{1~6LGG$|,- 8 Q1, M --s3}-.#m2DD HOO    A'/Ae 5#? 228&- AAA '--n=Q  ; B B8 L NN ! dN 22((3,%c, &EF<a&% }4BV[[0N 6<<7 7<"NN>5AB!EF F Vs5zA~ %<rGs  7+<4+206*<.+6 <\734 !!!'*2+52j   (( ))!)8 ! (( *)"*6 %& (( /)'/8 %& (( /)'/6 ! (( *)"*6 56 (( -)7-4 78 (( .)9.0 56 (( -)7-4 78 (( .)9.0 #$ (( -)%-4 $% (( .)&.0 #$ (( -)%-4 $% (( .)&.0 #$ (( -)%-0 #$ (( -)%-0 #$ (( -)%-0 #$ (( -)%-0k"#, 8_% O1&O1dA/HU/p}*@ 0  G=T1h $!A 3 3 3C @!!#`