360 lines
8.8 KiB
Cython
360 lines
8.8 KiB
Cython
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#!/usr/bin/env cython
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# coding: utf-8
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# cython: embedsignature=True
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from __future__ import division
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cimport cython
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import numpy as np
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cimport numpy as np
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ctypedef cython.floating DTYPE_t
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from libc.math cimport log, exp, fabs
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from cython.parallel import prange
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def mean_absolute_difference(a, b):
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"""Mean absolute difference between two arrays, using :func:`~gensim._matutils._mean_absolute_difference`.
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Parameters
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----------
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a : numpy.ndarray
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Input 1d array, supports float16, float32 and float64.
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b : numpy.ndarray
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Input 1d array, supports float16, float32 and float64.
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Returns
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-------
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float
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mean(abs(a - b)).
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"""
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if a.shape != b.shape:
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raise ValueError("a and b must have same shape")
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if a.dtype == np.float64:
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return _mean_absolute_difference[double](a, b)
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elif a.dtype == np.float32:
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return _mean_absolute_difference[float](a, b)
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elif a.dtype == np.float16:
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return _mean_absolute_difference[float](a.astype(np.float32), b.astype(np.float32))
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@cython.boundscheck(False)
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@cython.wraparound(False)
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@cython.cdivision(True)
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cdef DTYPE_t _mean_absolute_difference(DTYPE_t[:] a, DTYPE_t[:] b) nogil:
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"""Mean absolute difference between two arrays.
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Parameters
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----------
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a : numpy.ndarray
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Input 1d array.
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b : numpy.ndarray
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Input 1d array.
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Returns
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-------
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DTYPE_t
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mean(abs(a - b))
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"""
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cdef DTYPE_t result = 0.0
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cdef size_t i
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cdef size_t j
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cdef size_t I = a.shape[0]
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cdef size_t N = I
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for i in range(I):
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result += fabs(a[i] - b[i])
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result /= N
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return result
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def logsumexp(x):
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"""Log of sum of exponentials, using :func:`~gensim._matutils._logsumexp_2d`.
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Parameters
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----------
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x : numpy.ndarray
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Input 2d matrix, supports float16, float32 and float64.
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Returns
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-------
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float
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log of sum of exponentials of elements in `x`.
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Warnings
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--------
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By performance reasons, doesn't support NaNs or 1d, 3d, etc arrays like :func:`scipy.special.logsumexp`.
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"""
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if x.dtype == np.float64:
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return _logsumexp_2d[double](x)
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elif x.dtype == np.float32:
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return _logsumexp_2d[float](x)
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elif x.dtype == np.float16:
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return _logsumexp_2d[float](x.astype(np.float32))
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@cython.boundscheck(False)
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@cython.wraparound(False)
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@cython.cdivision(True)
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cdef DTYPE_t _logsumexp_2d(DTYPE_t[:, :] data) nogil:
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"""Log of sum of exponentials.
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Parameters
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----------
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x : numpy.ndarray
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Input 2d matrix.
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Returns
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-------
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DTYPE_t
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log of sum of exponentials of elements in `data`.
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"""
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cdef DTYPE_t max_val = data[0, 0]
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cdef DTYPE_t result = 0.0
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cdef size_t i
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cdef size_t j
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cdef size_t I = data.shape[0]
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cdef size_t J = data.shape[1]
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for i in range(I):
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for j in range(J):
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if data[i, j] > max_val:
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max_val = data[i, j]
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for i in range(I):
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for j in range(J):
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result += exp(data[i, j] - max_val)
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result = log(result) + max_val
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return result
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def dirichlet_expectation(alpha):
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"""Expected value of log(theta) where theta is drawn from a Dirichlet distribution.
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Using :func:`~gensim._matutils.dirichlet_expectation_1d` or :func:`~gensim._matutils.dirichlet_expectation_2d`.
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Parameters
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----------
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alpha : numpy.ndarray
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Dirichlet parameter 2d matrix or 1d vector, if 2d - each row is treated as a separate parameter vector,
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supports float16, float32 and float64.
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Returns
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-------
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numpy.ndarray
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Log of expected values, dimension same as `alpha.ndim`.
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"""
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if alpha.ndim == 2:
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return dirichlet_expectation_2d(alpha)
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else:
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return dirichlet_expectation_1d(alpha)
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def dirichlet_expectation_2d(alpha):
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"""Expected value of log(theta) where theta is drawn from a Dirichlet distribution.
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Using :func:`~gensim._matutils._dirichlet_expectation_2d`.
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Parameters
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----------
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alpha : numpy.ndarray
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Dirichlet parameter 2d matrix, each row is treated as a separate parameter vector,
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supports float16, float32 and float64.
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Returns
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-------
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numpy.ndarray
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Log of expected values, 2d matrix.
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"""
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if alpha.dtype == np.float64:
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out = np.zeros(alpha.shape, dtype=alpha.dtype)
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_dirichlet_expectation_2d[double](alpha, out)
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elif alpha.dtype == np.float32:
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out = np.zeros(alpha.shape, dtype=alpha.dtype)
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_dirichlet_expectation_2d[float](alpha, out)
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elif alpha.dtype == np.float16:
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out = np.zeros(alpha.shape, dtype=np.float32)
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_dirichlet_expectation_2d[float](alpha.astype(np.float32), out)
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out = out.astype(np.float16)
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return out
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def dirichlet_expectation_1d(alpha):
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"""Expected value of log(theta) where theta is drawn from a Dirichlet distribution.
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Using :func:`~gensim._matutils._dirichlet_expectation_1d`.
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Parameters
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----------
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alpha : numpy.ndarray
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Dirichlet parameter 1d vector, supports float16, float32 and float64.
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Returns
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-------
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numpy.ndarray
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Log of expected values, 1d vector.
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"""
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if alpha.dtype == np.float64:
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out = np.zeros(alpha.shape, dtype=alpha.dtype)
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_dirichlet_expectation_1d[double](alpha, out)
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elif alpha.dtype == np.float32:
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out = np.zeros(alpha.shape, dtype=alpha.dtype)
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_dirichlet_expectation_1d[float](alpha, out)
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elif alpha.dtype == np.float16:
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out = np.zeros(alpha.shape, dtype=np.float32)
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_dirichlet_expectation_1d[float](alpha.astype(np.float32), out)
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out = out.astype(np.float16)
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return out
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@cython.boundscheck(False)
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@cython.wraparound(False)
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cdef void _dirichlet_expectation_1d(DTYPE_t[:] alpha, DTYPE_t[:] out) nogil:
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"""Expected value of log(theta) where theta is drawn from a Dirichlet distribution.
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Parameters
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----------
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alpha : numpy.ndarray
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Dirichlet parameter 1d vector.
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out : numpy.ndarray
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Output array, contains log of expected values.
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"""
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cdef DTYPE_t sum_alpha = 0.0
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cdef DTYPE_t psi_sum_alpha = 0.0
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cdef size_t i
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cdef size_t I = alpha.shape[0]
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for i in range(I):
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sum_alpha += alpha[i]
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psi_sum_alpha = _digamma(sum_alpha)
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for i in range(I):
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out[i] = _digamma(alpha[i]) - psi_sum_alpha
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@cython.boundscheck(False)
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@cython.wraparound(False)
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cdef void _dirichlet_expectation_2d(DTYPE_t[:, :] alpha, DTYPE_t[:, :] out) nogil:
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"""Expected value of log(theta) where theta is drawn from a Dirichlet distribution.
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Parameters
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----------
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alpha : numpy.ndarray
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Dirichlet parameter matrix, each row is treated as a parameter vector for its own Dirichlet.
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out : numpy.ndarray
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Log of expected values, 2d matrix.
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"""
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cdef DTYPE_t sum_alpha = 0.0
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cdef DTYPE_t psi_sum_alpha = 0.0
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cdef size_t i, j
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cdef size_t I = alpha.shape[0]
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cdef size_t J = alpha.shape[1]
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for i in range(I):
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sum_alpha = 0.0
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for j in range(J):
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sum_alpha += alpha[i, j]
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psi_sum_alpha = _digamma(sum_alpha)
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for j in range(J):
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out[i, j] = _digamma(alpha[i, j]) - psi_sum_alpha
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def digamma(DTYPE_t x):
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"""Digamma function for positive floats, using :func:`~gensim._matutils._digamma`.
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Parameters
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----------
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x : float
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Positive value.
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Returns
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-------
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float
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Digamma(x).
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"""
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return _digamma(x)
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@cython.cdivision(True)
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cdef inline DTYPE_t _digamma(DTYPE_t x,) nogil:
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"""Digamma function for positive floats.
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Parameters
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----------
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x : float
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Positive value.
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Notes
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-----
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Adapted from:
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* Authors:
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* Original FORTRAN77 version by Jose Bernardo.
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* C version by John Burkardt.
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* Reference: Jose Bernardo, Algorithm AS 103: Psi (Digamma) Function,
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Applied Statistics, Volume 25, Number 3, 1976, pages 315-317.
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* Licensing: This code is distributed under the GNU LGPL license.
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Returns
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-------
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float
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Digamma(x).
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"""
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cdef DTYPE_t c = 8.5;
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cdef DTYPE_t euler_mascheroni = 0.57721566490153286060;
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cdef DTYPE_t r;
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cdef DTYPE_t value;
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cdef DTYPE_t x2;
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if ( x <= 0.000001 ):
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value = - euler_mascheroni - 1.0 / x + 1.6449340668482264365 * x;
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return value;
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# Reduce to DIGAMA(X + N).
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value = 0.0;
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x2 = x;
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while ( x2 < c ):
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value = value - 1.0 / x2;
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x2 = x2 + 1.0;
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# Use Stirling's (actually de Moivre's) expansion.
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r = 1.0 / x2;
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value = value + log ( x2 ) - 0.5 * r;
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r = r * r;
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value = value \
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- r * ( 1.0 / 12.0 \
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- r * ( 1.0 / 120.0 \
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- r * ( 1.0 / 252.0 \
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- r * ( 1.0 / 240.0 \
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- r * ( 1.0 / 132.0 ) ) ) ) )
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return value;
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