a RG5d9@sdZddlmZddlmZddlmZddZddZd d Z d d Z d dZ ddZ ddZ ddZddZddZddZddZddZdd Zd!d"Zd#d$Zd%d&Zd'd(Zd)d*Zd+d,Zd-d.Zd/d0Zd1d2Zd3S)4zC The module contains implemented functions for interval arithmetic.reduce)interval) import_modulecCszt|ttfrtt|St|trr|jdkrZ|jdkrZtdtt|jt|j|jdStt|jt|jSnt dS)Nris_valid) isinstanceintfloatrabsstartendmaxrNotImplementedErrorxrd/var/www/html/django/DPS/env/lib/python3.9/site-packages/sympy/plotting/intervalmath/lib_interval.pyAbss  "rcCs^td}t|ttfr,t||||St|trVt||j||j|jdSt dS)z(evaluates the exponential of an intervalnumpyrN) rrr r rexpr r rrrnprrrrs   rcCstd}t|ttfrB|dkr2t|j |jddSt||Snt|tr|jsht|j |j|jdS|jdkrt|j |jddS|j dkrt|j |jddSt||j ||jSt dS)z.evaluates the natural logarithm of an intervalrrFrN) rrr r rinflogrr r rrrrrr"s   rcCstd}t|ttfrB|dkr2t|j |jddSt||Snt|tr|jsht|j |j|jdS|jdkrt|j |jddS|j dkrt|j |jddSt||j ||jSt dS)z5evaluates the logarithm to the base 10 of an intervalrrFrN) rrr r rrlog10rr r rrrrrr8s   rcCs^td}t|ttfr$t||St|trV||j}||j}t|||jdSt dS)z(evaluates the tan inverse of an intervalrrN) rrr r rarctanr r rrrrr r rrratanMs   rcCs(td}t|ttfr$t||St|tr |jsFtdd|jdSt|j|j d\}}t|j |j d\}}t ||j||j }t ||j||j }||dkrtdd|jdS||krt|||jdS|dd|ddkrd}|dd|ddkrd}t||Snt dS) z!evaluates the sine of an intervalrr@N)rrr r rsinrdivmodr pir minrrrrna__nbr r rrrr$[s(   r$cCs:td}t|ttfr$t||St|tr2||jrH||jsXtdd|j dSt |j|j d\}}t |j|j d\}}t | |j| |j}t| |j| |j}||dkrtdd|j dS||krt|||j dS|d|dkrd}|dd|ddkr d}t|||j dSntdS) z Evaluates the cos of an intervalrrr rr!r"N)rrr r rr$isfiniter r rr%r&r'cosrrr(rrrr.xs(  r.cCst|t|S)z Evaluates the tan of an interval)r$r.rrrrtansr/cCstd}t|ttfrB|dkr,t||St|j |jddSnlt|tr|jdkrjt|j |jddS|jdkrt|j |jddSt||j||j|j dSnt dS)z(Evaluates the square root of an intervalrrFrN) rrr r rsqrtrr r rrrrrrr0s   r0cGstd}tdd|DstSdd|D}t|dkrrtdd|Dr^t|j |jdd St|j |jd d Sd d|D}d d|D}tt|t|Sd S) z,Evaluates the minimum of a list of intervalsrcss|]}t|tttfVqdSNrr r r.0argrrr zimin..cSs$g|]}t|ttfs|jr|qSrrr r rr4arrr szimin..rcss|]}|jduVqdSFNrr9rrrr6r7FrNcSs$g|]}t|ttfr|n|jqSrrr r r r9rrrr;scSs$g|]}t|ttfr|n|jqSrrr r r r9rrrr;s)rallrlenrrr'argsrnew_argsZ start_array end_arrayrrrimins rEcGstd}tdd|DstSdd|D}t|dkrrtdd|Dr^t|j |jdd St|j |jd d Sd d|D}d d|D}tt|t|Sd S) z,Evaluates the maximum of a list of intervalsrcss|]}t|tttfVqdSr1r2r3rrrr6r7zimax..cSs$g|]}t|ttfs|jr|qSrr8r9rrrr;szimax..rcss|]}|jduVqdSr<rr9rrrr6r7FrNcSs$g|]}t|ttfr|n|jqSrr=r9rrrr;scSs$g|]}t|ttfr|n|jqSrr>r9rrrr;s)rr?rr@rrrrArrrimaxs rFcCs^td}t|ttfr,t||||St|trVt||j||j|jdSt dS)z,Evaluates the hyperbolic sine of an intervalrrN) rrr r rsinhr r rrrrrrrGs   rGcCstd}t|ttfr,t||||St|tr|jdkrt|jdkrtt||j||j}td||j dS||j}||j}t|||j dSnt dS)z+Evaluates the hyperbolic cos of an intervalrrr rN) rrr r rcoshr r rrr)rrr r rrrrHs   rHcCs^td}t|ttfr,t||||St|trVt||j||j|jdSt dS)z+Evaluates the hyperbolic tan of an intervalrrN) rrr r rtanhr r rrrrrrrIs   rIcCstd}t|ttfrNt|dkr6t|j |jddSt||||Snt|tr|jdusv|j dksv|j dkrt|j |jddS|j dks|j dkrt|j |jddS||j }||j }t|||jdSdS)z)Evaluates the inverse sine of an intervalrr FrrN) rrr r r rrarcsinrr r rrrrasins    rKcCstd}t|ttfrNt|dkr6t|j |jddSt||||Snt|tr|jdusv|j dksv|j dkrt|j |jddS|j dks|j dkrt|j |jddS||j }||j }t|||jdSdS)z(Evaluates the inverse cos of an intervalrr FrrN) rrr r r rrarccosrr r rrrracoss    rMcCstd}t|ttfr$t||St|tr|jdurLt|j |jddS||j}||j }||kr|t|||jdSt||ddSnt SdS)z$Evaluates the ceiling of an intervalrFrN) rrr r rceilrrr r rrrrrrN4s    rNcCstd}t|ttfr$t||St|tr|jdurLt|j |jddS||j}||j }||kr|t|||jdSt||ddSnt SdS)z"Evaluates the floor of an intervalrFrN) rrr r rfloorrrr r rrrrrrOIs    rOcCstd}t|ttfrB|dkr2t|j |jddSt||Sntt|tr|jdkrjt|j |jddS|jdkrt|j |jddS||j}||j}t|||j dSnt SdS)z6Evaluates the inverse hyperbolic cosine of an intervalrr FrN) rrr r rrarccoshr r rrrrrracosh^s     rQcCs^td}t|ttfr$t||St|trV||j}||j}t|||jdSt SdS)z4Evaluates the inverse hyperbolic sine of an intervalrrN) rrr r rarcsinhr r rrrrrrasinhws   rScCstd}t|ttfrFt|dkr6t|j |jddSt||Snt|tr|jdusn|j dksn|j dkrt|j |jddS|j dks|j dkrt|j |jddS||j }||j }t|||jdSnt SdS)z7Evaluates the inverse hyperbolic tangent of an intervalrr FrrN) rrr r r rrarctanhrr r rrrrratanhs    rUcGsdd}t||S)zZDefines the three valued ``And`` behaviour for a 2-tuple of three valued logic valuescSs|ddus|ddurd}n"|ddus6|ddur.reduce_andr)rBrYrrrAndsrZcGsdd}t||S)zYDefines the three valued ``Or`` behaviour for a 2-tuple of three valued logic valuescSs|ddus|ddurd}n"|ddus6|ddur.reduce_orr)rBr[rrrOrsr\N)__doc__ functoolsrZsympy.plotting.intervalmathrsympy.externalrrrrrrr$r.r/r0rErFrGrHrIrKrMrNrOrQrSrUrZr\rrrrs4