o 8Va9@sdZddlmZddlmZddlmZddZddZd d Z d d Z d dZ ddZ ddZ ddZddZddZddZddZddZdd Zd!d"Zd#d$Zd%d&Zd'd(Zd)d*Zd+d,Zd-d.Zd/d0Zd1d2Zd3S)4zC The module contains implemented functions for interval arithmetic.reduce)interval) import_modulecCstt|ttfr tt|St|tr8|jdkr-|jdkr-tdtt|jt|j|jdStt|jt|jSt )Nris_valid) isinstanceintfloatrabsstartendmaxrNotImplementedErrorxrJ/usr/lib/python3/dist-packages/sympy/plotting/intervalmath/lib_interval.pyAbss  "rcCZtd}t|ttfrt||||St|tr+t||j||j|jdSt )z(evaluates the exponential of an intervalnumpyr) rrr r rexpr r rrrnprrrr   rcCtd}t|ttfr |dkrt|j |jddSt||St|tr^|js3t|j |j|jdS|jdkrBt|j |jddS|j dkrQt|j |jddSt||j ||jSt )z.evaluates the natural logarithm of an intervalrrFrN) rrr r rinflogrr r rrrrrr"s   rcCr)z5evaluates the logarithm to the base 10 of an intervalrrFrN) rrr r rrlog10rr r rrrrrr8s   rcCsZtd}t|ttfrt||St|tr+||j}||j}t|||jdSt )z(evaluates the tan inverse of an intervalrr) rrr r rZarctanr r rrrrr r rrratanM   r cCstd}t|ttfrt||St|tr|js"tdd|jdSt|j|j d\}}t|j |j d\}}t ||j||j }t ||j||j }||dkr`tdd|jdS||krlt|||jdS|dd|ddkrzd}|dd|ddkrd}t||St )z!evaluates the sine of an intervalrr@)rrr r rsinrdivmodr pir minrrrrZna__nbr r rrrr'[s(   r'cCs.td}t|ttfrt||St|tr||jr#||js+tdd|j dSt |j|j d\}}t |j|j d\}}t | |j| |j}t| |j| |j}||dkritdd|j dS||krut|||j dS|d|dkrd}|dd|ddkrd}t|||j dSt)z Evaluates the cos of an intervalrr"r#rr$r%)rrr r rr'Zisfiniter r rr(r)r*cosrrr+rrrr/xs(  r/cCst|t|S)z Evaluates the tan of an interval)r'r/rrrrtansr0cCstd}t|ttfr |dkrt||St|j |jddSt|trS|jdkr4t|j |jddS|jdkrCt|j |jddSt||j||j|j dSt )z(Evaluates the square root of an intervalrrFrN) rrr r rsqrtrr r rrrrrrr1s   r1cGtd}tdd|DstSdd|D}t|dkr9tdd|Dr/t|j |jdd St|j |jd d Sd d|D}d d|D}tt|t|S) z,Evaluates the minimum of a list of intervalsrcs |] }t|tttfVqdSNrr r r.0argrrr zimin..cS$g|]}t|ttfs|jr|qSrrr r rr7arrr  zimin..rcs|]}|jduVqdSFNrr=rrrr9FrNcS$g|]}t|ttfr |n|jqSrrr r r r=rrrr?cSrDrrr r r r=rrrr?rF)rallrlenrrr*argsrnew_argsZ start_arrayZ end_arrayrrrimins rMcGr2) z,Evaluates the maximum of a list of intervalsrcsr3r4r5r6rrrr9r:zimax..cSr;rr<r=rrrr?r@zimax..rcsrArBrr=rrrr9rCFrNcSrDrrEr=rrrr?rFcSrDrrGr=rrrr?rF)rrHrrIrrrrJrrrimaxs rNcCr)z,Evaluates the hyperbolic sine of an intervalrr) rrr r rsinhr r rrrrrrrOrrOcCstd}t|ttfrt||||St|trN|jdkr:|jdkr:t||j||j}td||j dS||j}||j}t|||j dSt )z+Evaluates the hyperbolic cos of an intervalrrr#r) rrr r rcoshr r rrr)rrr r rrrrPs   rPcCr)z+Evaluates the hyperbolic tan of an intervalrr) rrr r rtanhr r rrrrrrrQrrQcCtd}t|ttfr&t|dkrt|j |jddSt||||St|trl|jdus:|j dks:|j dkrDt|j |jddS|j dksN|j dkrXt|j |jddS||j }||j }t|||jdSdS)z)Evaluates the inverse sine of an intervalrr#Frr"N) rrr r r rrZarcsinrr r rrrrasins    rScCrR)z(Evaluates the inverse cos of an intervalrr#Frr"N) rrr r r rrZarccosrr r rrrracoss    rTcCtd}t|ttfrt||St|trE|jdur&t|j |jddS||j}||j }||kr>t|||jdSt||ddSt S)z$Evaluates the ceiling of an intervalrFrN) rrr r rceilrrr r rrrrrrV4    rVcCrU)z"Evaluates the floor of an intervalrFrN) rrr r rfloorrrr r rrrrrrXIrWrXcCstd}t|ttfr |dkrt|j |jddSt||St|trW|jdkr4t|j |jddS|jdkrCt|j |jddS||j}||j}t|||j dSt S)z6Evaluates the inverse hyperbolic cosine of an intervalrr#FrN) rrr r rrZarccoshr r rrrrrracosh^s     rYcCsZtd}t|ttfrt||St|tr+||j}||j}t|||jdSt S)z4Evaluates the inverse hyperbolic sine of an intervalrr) rrr r rZarcsinhr r rrrrrrasinhwr!rZcCstd}t|ttfr"t|dkrt|j |jddSt||St|trh|jdus6|j dks6|j dkr@t|j |jddS|j dksJ|j dkrTt|j |jddS||j }||j }t|||jdSt S)z7Evaluates the inverse hyperbolic tangent of an intervalrr#Frr"N) rrr r r rrZarctanhrr r rrrrratanhs    r[cGdd}t||S)zZDefines the three valued ``And`` behaviour for a 2-tuple of three valued logic valuescS|ddus |ddurd}n|ddus|ddurd}nd}|ddus,|ddur2d}||fS|ddus>|ddurDd}||fSd}||fS)NrFTr#rZ cmp_intervalaZ cmp_intervalbfirstsecondrrr reduce_andszAnd..reduce_andr)rKrarrrAnds rbcGr\)zYDefines the three valued ``Or`` behaviour for a 2-tuple of three valued logic valuescSr])NrTFr#rr^rrr reduce_orszOr..reduce_orr)rKrcrrrOrs rdN)__doc__ functoolsrZsympy.plotting.intervalmathrZsympy.externalrrrrrr r'r/r0r1rMrNrOrPrQrSrTrVrXrYrZr[rbrdrrrrs6