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§ šýT,�í[ ãóL—dZddlZddlZgZd„Zeddd¦«eddd¦«edd d ¦«edd d ¦«edd d¦«eddd¦«eddd¦«eddd¦«eddd¦«eddd¦«eddd¦«eddd¦«eddd¦«eddd¦«eddd¦«e�rLgZe ¦«eD�]\ZZej e¦«  d d!¦«Z e   d ¦«Z gZe D]‘Zejd"e¦«Zergereej e ¦«¦«Ze e d#¦«›d$e›�¦«e d%¦«Œ|e e¦«Œ’d  e¦«Z e d&e›d!e ›�¦«�Œd  e¦«Zeee¬'¦«zZ[[[[[ [[[ [[[dS)(zo ========= Constants ========= .. currentmodule:: numpy NumPy includes several constants: %(constant_list)s éNcó>—t ||f¦«dS)N)Ú constantsÚappend)ÚmoduleÚnameÚdocs úg/builddir/build/BUILD/cloudlinux-venv-1.0.12/venv/lib64/python3.11/site-packages/numpy/doc/constants.pyÚ add_newdocr s €Ý ×Ò�d˜C�[Ñ!Ô!Ð!Ð!Ð!óÚnumpyÚpizv ``pi = 3.1415926535897932384626433...`` References ---------- https://en.wikipedia.org/wiki/Pi ÚeaE Euler's constant, base of natural logarithms, Napier's constant. ``e = 2.71828182845904523536028747135266249775724709369995...`` See Also -------- exp : Exponential function log : Natural logarithm References ---------- https://en.wikipedia.org/wiki/E_%28mathematical_constant%29 Ú euler_gammauœ ``γ = 0.5772156649015328606065120900824024310421...`` References ---------- https://en.wikipedia.org/wiki/Euler-Mascheroni_constant Úinfaõ IEEE 754 floating point representation of (positive) infinity. Returns ------- y : float A floating point representation of positive infinity. See Also -------- isinf : Shows which elements are positive or negative infinity isposinf : Shows which elements are positive infinity isneginf : Shows which elements are negative infinity isnan : Shows which elements are Not a Number isfinite : Shows which elements are finite (not one of Not a Number, positive infinity and negative infinity) Notes ----- NumPy uses the IEEE Standard for Binary Floating-Point for Arithmetic (IEEE 754). This means that Not a Number is not equivalent to infinity. Also that positive infinity is not equivalent to negative infinity. But infinity is equivalent to positive infinity. `Inf`, `Infinity`, `PINF` and `infty` are aliases for `inf`. Examples -------- >>> np.inf inf >>> np.array([1]) / 0. array([ Inf]) ÚnanaÐ IEEE 754 floating point representation of Not a Number (NaN). Returns ------- y : A floating point representation of Not a Number. See Also -------- isnan : Shows which elements are Not a Number. isfinite : Shows which elements are finite (not one of Not a Number, positive infinity and negative infinity) Notes ----- NumPy uses the IEEE Standard for Binary Floating-Point for Arithmetic (IEEE 754). This means that Not a Number is not equivalent to infinity. `NaN` and `NAN` are aliases of `nan`. Examples -------- >>> np.nan nan >>> np.log(-1) nan >>> np.log([-1, 1, 2]) array([ NaN, 0. , 0.69314718]) Únewaxisa A convenient alias for None, useful for indexing arrays. Examples -------- >>> newaxis is None True >>> x = np.arange(3) >>> x array([0, 1, 2]) >>> x[:, newaxis] array([[0], [1], [2]]) >>> x[:, newaxis, newaxis] array([[[0]], [[1]], [[2]]]) >>> x[:, newaxis] * x array([[0, 0, 0], [0, 1, 2], [0, 2, 4]]) Outer product, same as ``outer(x, y)``: >>> y = np.arange(3, 6) >>> x[:, newaxis] * y array([[ 0, 0, 0], [ 3, 4, 5], [ 6, 8, 10]]) ``x[newaxis, :]`` is equivalent to ``x[newaxis]`` and ``x[None]``: >>> x[newaxis, :].shape (1, 3) >>> x[newaxis].shape (1, 3) >>> x[None].shape (1, 3) >>> x[:, newaxis].shape (3, 1) ÚNZEROaÚ IEEE 754 floating point representation of negative zero. Returns ------- y : float A floating point representation of negative zero. See Also -------- PZERO : Defines positive zero. isinf : Shows which elements are positive or negative infinity. isposinf : Shows which elements are positive infinity. isneginf : Shows which elements are negative infinity. isnan : Shows which elements are Not a Number. isfinite : Shows which elements are finite - not one of Not a Number, positive infinity and negative infinity. Notes ----- NumPy uses the IEEE Standard for Binary Floating-Point for Arithmetic (IEEE 754). Negative zero is considered to be a finite number. Examples -------- >>> np.NZERO -0.0 >>> np.PZERO 0.0 >>> np.isfinite([np.NZERO]) array([ True]) >>> np.isnan([np.NZERO]) array([False]) >>> np.isinf([np.NZERO]) array([False]) ÚPZEROaÚ IEEE 754 floating point representation of positive zero. Returns ------- y : float A floating point representation of positive zero. See Also -------- NZERO : Defines negative zero. isinf : Shows which elements are positive or negative infinity. isposinf : Shows which elements are positive infinity. isneginf : Shows which elements are negative infinity. isnan : Shows which elements are Not a Number. isfinite : Shows which elements are finite - not one of Not a Number, positive infinity and negative infinity. Notes ----- NumPy uses the IEEE Standard for Binary Floating-Point for Arithmetic (IEEE 754). Positive zero is considered to be a finite number. Examples -------- >>> np.PZERO 0.0 >>> np.NZERO -0.0 >>> np.isfinite([np.PZERO]) array([ True]) >>> np.isnan([np.PZERO]) array([False]) >>> np.isinf([np.PZERO]) array([False]) ÚNANzÌ IEEE 754 floating point representation of Not a Number (NaN). `NaN` and `NAN` are equivalent definitions of `nan`. Please use `nan` instead of `NAN`. See Also -------- nan ÚNaNzÌ IEEE 754 floating point representation of Not a Number (NaN). `NaN` and `NAN` are equivalent definitions of `nan`. Please use `nan` instead of `NaN`. See Also -------- nan ÚNINFa¡ IEEE 754 floating point representation of negative infinity. Returns ------- y : float A floating point representation of negative infinity. See Also -------- isinf : Shows which elements are positive or negative infinity isposinf : Shows which elements are positive infinity isneginf : Shows which elements are negative infinity isnan : Shows which elements are Not a Number isfinite : Shows which elements are finite (not one of Not a Number, positive infinity and negative infinity) Notes ----- NumPy uses the IEEE Standard for Binary Floating-Point for Arithmetic (IEEE 754). This means that Not a Number is not equivalent to infinity. Also that positive infinity is not equivalent to negative infinity. But infinity is equivalent to positive infinity. Examples -------- >>> np.NINF -inf >>> np.log(0) -inf ÚPINFzá IEEE 754 floating point representation of (positive) infinity. Use `inf` because `Inf`, `Infinity`, `PINF` and `infty` are aliases for `inf`. For more details, see `inf`. See Also -------- inf ÚinftyÚInfÚInfinityú z z^(\s+)[-=]+\s*$éz .. rubric:: Úz .. data:: )Ú constant_list)Ú__doc__ÚreÚtextwraprr Ú constants_strÚsortrrÚdedentÚreplaceÚsÚsplitÚlinesÚ new_linesÚlineÚmatchÚmÚpopÚprevrÚgroupÚjoinÚdict©r r úr4sšðð ð ð € € € Ø€€€ð € ð"ð"ð"ð € ˆ7�Dðñ ô ð ð € ˆ7�Cðñ ô ð ð" € ˆ7�Mðñ ô ð ð € ˆ7�Eð%ñ& ô& ð& ðP € ˆ7�Eðñ ô ð ðB € ˆ7�Ið*ñ+ ô+ ð+ ðZ € ˆ7�Gð*ñ+ ô+ ð+ ðZ € ˆ7�Gð*ñ+ ô+ ð+ ðZ € ˆ7�Eð ñ  ô  ð  ð € ˆ7�Eð ñ  ô  ð  ð € ˆ7�Fð#ñ$ ô$ ð$ ðL € ˆ7�Fð ñ  ô  ð  ð € ˆ7�Gð ñ  ô  ð  ð € ˆ7�Eð ñ  ô  ð  ð € ˆ7�Jð ñ  ô  ð  ð ñ+Ø€MØ ‡N‚NÑÔÐØðEñE‰ ˆˆcØ ˆHŒO˜CÑ Ô × (Ò (¨¨xÑ 8Ô 8ˆð—’˜‘ ” ˆØˆ Øð 'ð 'ˆDØ�”Ð+¨TÑ2Ô2ˆAØð '�Yð 'Ø&�x” y§}¢}¡¤Ñ7Ô7�Ø× Ò °q·w²w¸q±z´z°z°zÀ4À4Ð!HÑIÔIÐIØ× Ò  Ñ$Ô$Ð$Ð$à× Ò  Ñ&Ô&Ð&Ð&Ø �IŠI�iÑ Ô ˆð ×Òи4¸4¸4ÀÀÐCÑDÔDÐDÑDØ—I’I˜mÑ,Ô,€Mà˜˜¨=Ð9Ñ9Ô9Ñ9€GØ�t˜SØ ˆe�Y  1 dà ˆzˆzˆzr