B d!@sdZddlZddlZddlmZddlZddlmZeeZ edde j Z edde j Z ddZd d Zd d Zd dZddZddZdddZddZddZdddZdS)z} Miscellaneous utilities for `astropy.units`. None of the functions in the module are meant for use outside of the package. N)Fraction)finfog?g@cCs*td|}|dk r|d}|ddS)zS Get the first sentence from a string and remove any carriage returns. z .*?\S\.\sNr  )rematchgroupreplace)sxr `/work/yifan.wang/ringdown/master-ringdown-env/lib/python3.7/site-packages/astropy/units/utils.py_get_first_sentences  rc csddlm}g}t}xZ|D]N\}}t||js6q ||jkrBq t||jrd||j j djq | |q W|j dddxz|D]r}t |j}d}t||jrd|j d dd d }d d d|jD} |||| |j|krdndfVqWdS)z Generates the ``(unit, doc, represents, aliases, prefixes)`` tuple used to format the unit summary docs in `generate_unit_summary`. )corercSs |jS)N)namelower)r r r r Az$_iter_unit_summary..)keyz:math:`latex`z, css|]}d|dVqdS)z``Nr ).0r r r r Hsz%_iter_unit_summary..ZYesZNoN)rrsetitems isinstanceZUnitBaser PrefixUnitaddZ _representsbasesappendsortr__doc__stripZUnitZ to_stringjoinaliases) namespacerZunitsZ has_prefixesrvalunitdoc representsr'r r r _iter_unit_summary$s&      r-cCs<t}|dx t|D]}|dj|qW|S)a` Generates a summary of units from a given namespace. This is used to generate the docstring for the modules that define the actual units. Parameters ---------- namespace : dict A namespace containing units. Returns ------- docstring : str A docstring containing a summary table of the units. z .. list-table:: Available Units :header-rows: 1 :widths: 10 20 20 20 1 * - Unit - Description - Represents - Aliases - SI Prefixes z7 * - ``{}`` - {} - {} - {} - {} )ioStringIOwriter-formatgetvalue)r( docstring unit_summaryr r r generate_unit_summaryMs r5cCsxddlm}i}x4|D](\}}t||r|jjd}|||j<qWt}x t |D]}| dj |qXW| S)a Generates table entries for units in a namespace that are just prefixes without the base unit. Note that this is intended to be used *after* `generate_unit_summary` and therefore does not include the table header. Parameters ---------- namespace : dict A namespace containing units that are prefixes but do *not* have the base unit in their namespace. Returns ------- docstring : str A docstring containing a summary table of the units. r)rrzO * - Prefixes for ``{}`` - {} prefixes - {} - {} - Only ) rrrrr,r!rr.r/r-r0r1r2)r(rZfaux_namespacenmr*Z base_unitr3r4r r r generate_prefixonly_unit_summaryxs   r7cCsfyt|kotkSStk r`t|jkocCst|r dS|jtkr|St|dr,|}|jrt|jt|jkrbt|j|jdr|jSn t|j|jdrtd|jS|S|jSdS)Ng?dtyperg) r> __class__floathasattritemr<absr;complex)scaler r r sanitize_scales   rGdc Cs|dks|jtkr|S|\}}||}d\}}|d}}xt||krt|||krbtkrpnn t||S||||}}||}||||}}||||}}q>W|S)aSFraction very close to x with denominator at most max_denominator. The fraction has to be such that fraction/x is unity to within 4 ulp. If such a fraction does not exist, returns the float number. The algorithm is that of `fractions.Fraction.limit_denominator`, but sped up by not creating a fraction to start with. r)rrr)r@intas_integer_ratior8r9r) pmax_denominatorndaZn0Zd0Zn1Zd1r r r maybe_simple_fractions      rPcCst|dd}|dkrhy t|}Wn*tk rJt|sDtdnYnXt|}t|trb|S|j}|dkrx|j }n||d@dkrt|}|S)aConvert a power to a floating point value, an integer, or a Fraction. If a fractional power can be represented exactly as a floating point number, convert it to a float, to make the math much faster; otherwise, retain it as a `fractions.Fraction` object to avoid losing precision. Conversely, if the value is indistinguishable from a rational number with a low-numbered denominator, convert to a Fraction object. Parameters ---------- p : float, int, Rational, Fraction Power to be converted denominatorNz9Quantities and Units may only be raised to a scalar powerrr) getattrrA Exceptionnpisscalar ValueErrorrPrrQ numerator)rKdenomr r r validate_powers"     rYcCsf|jtk o|jtk ot|t}|jtk o:|jtk o:t|t}|rN|sNt|}n|s^|r^t|}||fS)z If either input is a Fraction, convert the other to a Fraction (at least if it does not have a ridiculous denominator). This ensures that any operation involving a Fraction will use rational arithmetic and preserve precision. )r@rIrArrrP)rObZ a_is_fractionZ b_is_fractionr r r resolve_fractionss    r[csVddlmt|tjsDt|sDtfdd|DrD||dStj||dSdS)Nr)Quantityc3s|]}t|VqdS)N)r)rr )r\r r r$sz&quantity_asanyarray..)r?)Zquantityr\rrTZndarrayrUanyZ asanyarray)rOr?r )r\r quantity_asanyarray"s , r^)rH)N)r$r.r fractionsrnumpyrTrrAZ _float_finfoZepsnegr8Zepsr9rr-r5r7r>rGrPrYr[r^r r r r s$   )+'  -