;ò …Rã?c@sµd„Zd„Zd„Zd„Zddd„ZedjoqdklZlZd GHeed d fd d ƒZ eed d fdƒZ dZ d GHdGe GHde GHd GHndS(cCsx|\}}t||ƒ|}d||ƒ||ƒ}x/td|ƒD]}|||||ƒ}qJW||SdS(s­Returns the integral of |function| (a function of one variable) over |interval| (a sequence of length two containing the lower and upper limit of the integration interval), calculated using the trapezoidal rule using |numtraps| trapezoids. Example: >>>from Scientific.Functions.Romberg import romberg >>>from Numeric import pi >>>romberg(tan, (0.0, pi/3.0)) yields '0.693147180562' f0.5iN( sintervalsloxshixsfloatsnumtrapsshsfunctionssumsrangesi(sfunctionsintervalsnumtrapsshixshssumsislox((sG/mit/python/lib/python2.3/site-packages/Scientific/Functions/Romberg.pys trapezoid s  cCsÃ|djo dGHdSn¦|djo$d||dƒ||dƒSnu|d}t|d|dƒ|}|dd|}d}x/td|ƒD]}|||||ƒ}q™W|SdS(Nis#numtraps must be > 0 in difftrap().if0.5if0.0( snumtrapssfunctionsintervalsnumtosumsfloatshsloxssumsrangesi(sfunctionsintervalsnumtrapssishssumsnumtosumslox((sG/mit/python/lib/python2.3/site-packages/Scientific/Functions/Romberg.pysdifftraps  $ cCs"d|}||||dSdS(Nf4.0f1.0(skstmpscsb(sbscskstmp((sG/mit/python/lib/python2.3/site-packages/Scientific/Functions/Romberg.pys romberg_diff8s cCsÞd}}dG| GdG|GHdGHddddfGHxptt|ƒƒD]\}d d ||d |d|d fGx(t|d ƒD]}d |||GqƒWdGHqFWdGHdG|||GdGd t|ƒd d GdGHdS(NisRomberg integration ofsfromss %6s %9s %9ssStepssStepSizesResultss%6d %9fiif1.0s%9fsThe final result issaftersfunction evaluations.(sisjsfunctionsintervalsrangeslensresmat(sfunctionsintervalsresmatsjsi((sG/mit/python/lib/python2.3/site-packages/Scientific/Functions/Romberg.pys printresmat>s   & f9.9999999999999995e-08ic CsTd}}|d|d}t|||ƒ} || }|gg} ||d} xÜt || ƒ|joÄ|d}| t|||ƒ} | i gƒ| |i || |ƒxIt |ƒD];}| |i t| |d|| |||dƒƒq¿W| ||}| |d|d} |d}qUW|ot||| ƒn|SdS(sSReturns the integral of |function| (a function of one variable) over |interval| (a sequence of length two containing the lower and upper limit of the integration interval), calculated using Romberg integration up to the specified |accuracy|. If |show| is 1, the triangular array of the intermediate results will be printed.iif2.0iN(sisnsintervalsintrangesdifftrapsfunctionsordsumsresultsresmatsaccuracys lastresultsabssappendsrangesks romberg_diffsshows printresmat( sfunctionsintervalsaccuracysshowsisksnsintrangesresults lastresultsresmatsordsum((sG/mit/python/lib/python2.3/site-packages/Scientific/Functions/Romberg.pysrombergNs.      s__main__(stanspisf0.5f1.0sshowiièf0.48504222994229101s2Trapezoidal rule with 1000 function evaluations =s:Theoretical result (correct to all shown digits) = %15.14fN( s trapezoidsdifftraps romberg_diffs printresmatsrombergs__name__smathstanspisrststheo( stheos printresmatsrombergsdifftraps romberg_diffsrsts trapezoidstanspi((sG/mit/python/lib/python2.3/site-packages/Scientific/Functions/Romberg.pys? s