# SOME DESCRIPTIVE TITLE.
# Copyright (C) 1999-2020, The Alibaba Group Holding Ltd.
# This file is distributed under the same license as the mars package.
# FIRST AUTHOR <EMAIL@ADDRESS>, 2020.
#
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msgid ""
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"Project-Id-Version: mars 0.5.0a2\n"
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"POT-Creation-Date: 2020-06-16 16:57+0800\n"
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#: ../../source/reference/tensor/generated/mars.tensor.fft.rfft.rst:2
msgid "mars.tensor.fft.rfft"
msgstr ""

#: mars.tensor.fft.rfft:1 of
msgid "Compute the one-dimensional discrete Fourier Transform for real input."
msgstr ""

#: mars.tensor.fft.rfft:3 of
msgid ""
"This function computes the one-dimensional *n*-point discrete Fourier "
"Transform (DFT) of a real-valued array by means of an efficient algorithm"
" called the Fast Fourier Transform (FFT)."
msgstr ""

#: mars.tensor.fft.rfft of
msgid "Parameters"
msgstr ""

#: mars.tensor.fft.rfft:7 of
msgid "Input tensor"
msgstr ""

#: mars.tensor.fft.rfft:9 of
msgid ""
"Number of points along transformation axis in the input to use. If `n` is"
" smaller than the length of the input, the input is cropped. If it is "
"larger, the input is padded with zeros. If `n` is not given, the length "
"of the input along the axis specified by `axis` is used."
msgstr ""

#: mars.tensor.fft.rfft:14 of
msgid "Axis over which to compute the FFT. If not given, the last axis is used."
msgstr ""

#: mars.tensor.fft.rfft:17 of
msgid "Normalization mode (see `mt.fft`). Default is None."
msgstr ""

#: mars.tensor.fft.rfft of
msgid "Returns"
msgstr ""

#: mars.tensor.fft.rfft:20 of
msgid ""
"**out** -- The truncated or zero-padded input, transformed along the axis"
" indicated by `axis`, or the last one if `axis` is not specified. If `n` "
"is even, the length of the transformed axis is ``(n/2)+1``. If `n` is "
"odd, the length is ``(n+1)/2``."
msgstr ""

#: mars.tensor.fft.rfft of
msgid "Return type"
msgstr ""

#: mars.tensor.fft.rfft of
msgid "Raises"
msgstr ""

#: mars.tensor.fft.rfft:26 of
msgid "If `axis` is larger than the last axis of `a`."
msgstr ""

#: mars.tensor.fft.rfft:31 of
msgid ":func:`mt.fft`"
msgstr ""

#: mars.tensor.fft.rfft:31 of
msgid "For definition of the DFT and conventions used."
msgstr ""

#: mars.tensor.fft.rfft:34 of
msgid ":func:`irfft`"
msgstr ""

#: mars.tensor.fft.rfft:34 of
msgid "The inverse of `rfft`."
msgstr ""

#: mars.tensor.fft.rfft:37 of
msgid ":func:`fft`"
msgstr ""

#: mars.tensor.fft.rfft:37 of
msgid "The one-dimensional FFT of general (complex) input."
msgstr ""

#: mars.tensor.fft.rfft:40 of
msgid ":func:`fftn`"
msgstr ""

#: mars.tensor.fft.rfft:40 of
msgid "The *n*-dimensional FFT."
msgstr ""

#: mars.tensor.fft.rfft:42 of
msgid ":func:`rfftn`"
msgstr ""

#: mars.tensor.fft.rfft:43 of
msgid "The *n*-dimensional FFT of real input."
msgstr ""

#: mars.tensor.fft.rfft:46 of
msgid "Notes"
msgstr ""

#: mars.tensor.fft.rfft:47 of
msgid ""
"When the DFT is computed for purely real input, the output is Hermitian-"
"symmetric, i.e. the negative frequency terms are just the complex "
"conjugates of the corresponding positive-frequency terms, and the "
"negative-frequency terms are therefore redundant.  This function does not"
" compute the negative frequency terms, and the length of the transformed "
"axis of the output is therefore ``n//2 + 1``."
msgstr ""

#: mars.tensor.fft.rfft:54 of
msgid ""
"When ``A = rfft(a)`` and fs is the sampling frequency, ``A[0]`` contains "
"the zero-frequency term 0*fs, which is real due to Hermitian symmetry."
msgstr ""

#: mars.tensor.fft.rfft:57 of
msgid ""
"If `n` is even, ``A[-1]`` contains the term representing both positive "
"and negative Nyquist frequency (+fs/2 and -fs/2), and must also be purely"
" real. If `n` is odd, there is no term at fs/2; ``A[-1]`` contains the "
"largest positive frequency (fs/2*(n-1)/n), and is complex in the general "
"case."
msgstr ""

#: mars.tensor.fft.rfft:63 of
msgid "If the input `a` contains an imaginary part, it is silently discarded."
msgstr ""

#: mars.tensor.fft.rfft:66 of
msgid "Examples"
msgstr ""

#: mars.tensor.fft.rfft:74 of
msgid ""
"Notice how the final element of the `fft` output is the complex conjugate"
" of the second element, for real input. For `rfft`, this symmetry is "
"exploited to compute only the non-negative frequency terms."
msgstr ""

