&]\c@`sdZddlmZmZmZddlmZddlZddlm Z ddl m Z m Z ddl mZmZmZddlmZddl Zd d lmZie jd 6e jd 6e jd 6e jd6e jd6e jd6e jd6Zie jd 6e jd6e jd6e jd6ZdZd d d d d ge_ ie_!dZ"d dddddge"_ ie jd 6e jd6e"_!dZ#ddddddge#_ ie#_!dZ$d ddge$_ ie$_!dZ%ddge%_ ie jd 6e jd6e jd 6e%_!dZ&ddddge&_ ie jd6e jd 6e jd 6e&_!d Z'd!d"ge'_ ie jd6e jd 6e jd 6e'_!d#e(fd$YZ)d%e(fd&YZ*d'e(fd(YZ+d)e(fd*YZ,d+e(fd,YZ-dS(-sA Unit tests for nonlinear solvers Author: Ondrej Certik May 2007 i(tdivisiontprint_functiontabsolute_import(tassert_N(txrange(tnonlintroot(tmatrixtdiagtdot(tinvi(tpressure_networktandersont diagbroydent linearmixingtexcitingmixingtbroyden1tbroyden2tkrylovcC`satj|j}ttdddddg}d}| ||t|j||}|S(Niig?ig?g{Gz?(tnptasmatrixtTRRtfloat(txtdtctf((s?lib/python2.7/site-packages/scipy/optimize/tests/test_nonlin.pytFs !$cC`s|S(N((R((s?lib/python2.7/site-packages/scipy/optimize/tests/test_nonlin.pytF2*siiiiicC`s|S(N((R((s?lib/python2.7/site-packages/scipy/optimize/tests/test_nonlin.pytF2_lucky3scC`s2tjd}tjd}tj|||S(Ns-2 1 0; 1 -2 1; 0 1 -2s1 2 3(RtmatR (RtAtb((s?lib/python2.7/site-packages/scipy/optimize/tests/test_nonlin.pytF3;scC`sPd}||d|ddtj|d tj|d dd|gS(Ng@ii(Rtexp(RR((s?lib/python2.7/site-packages/scipy/optimize/tests/test_nonlin.pyt F4_powellEsiicC`s%t|dtjddddgS(Nig?(R Rtarray(R((s?lib/python2.7/site-packages/scipy/optimize/tests/test_nonlin.pytF5Psg@cC`s|\}}tjddgddgg}tj|d|ddd tj|tj|d g}tjj|| S( Ng/$gffffff-@g+,?grD0?iiiiii(RR$tsinR"tlinalgtsolve(Rtx1tx2tJ0tv((s?lib/python2.7/site-packages/scipy/optimize/tests/test_nonlin.pytF6Zs  &ggffffff?t TestNonlincB`sVeZdZddZddZejjdZdZ dZ dZ RS(s Check the Broyden methods for a few test problems. broyden1, broyden2, and newton_krylov must succeed for all functions. Some of the others don't -- tests in KNOWN_BAD are skipped. g{Gz?c C`sM|||jd|dddd}ttj||j|kdS(Ntf_toltmaxiteritverbosei(txinRRtabsolutetmax(tselfRtfuncR/R((s?lib/python2.7/site-packages/scipy/optimize/tests/test_nonlin.pyt_check_nonlin_funcws$c C`sYt||jd|di|d6dd6dd6}ttj|jj|kdS(NtmethodtoptionstftoliR0itdisp(RR2RRR3tfunR4(R5RR8R/tres((s?lib/python2.7/site-packages/scipy/optimize/tests/test_nonlin.pyt _check_root{scO`sdS(N((R5tatkw((s?lib/python2.7/site-packages/scipy/optimize/tests/test_nonlin.pyt_check_func_failscC`sxtttttttgD]m}xdtjD]V}||j jkru|t jkr/|j ||q/q/n|j ||q/WqWdS(N( RRRR!R#R%R-tSOLVERStvaluest KNOWN_BADt MUST_WORKRAR7(R5RR6((s?lib/python2.7/site-packages/scipy/optimize/tests/test_nonlin.pyttest_problem_nonlins"c `sTt_fd}tjttjddddddd|tjdS( Nc`st_tj|jS(N(tTruet_tol_norm_usedRR3R4(R(R5(s?lib/python2.7/site-packages/scipy/optimize/tests/test_nonlin.pytlocal_norm_funcs R/g{Gz?R0iR1ittol_norm(tFalseRHRt newton_krylovRR2R(R5RI((R5s?lib/python2.7/site-packages/scipy/optimize/tests/test_nonlin.pyttest_tol_norm_calleds  $cC`sxxtttttttgD][}xRtD]J}||jkrc|t kr)|j ||q)q)n|j ||q)WqWdS(N( RRRR!R#R%R-RBRDRERAR>(R5Rtmeth((s?lib/python2.7/site-packages/scipy/optimize/tests/test_nonlin.pyttest_problem_roots"  ( t__name__t __module__t__doc__R7R>tpytesttmarktxfailRARFRMRO(((s?lib/python2.7/site-packages/scipy/optimize/tests/test_nonlin.pyR.ns   t TestSecantc B`s^eZdZejdddddgeejdddddgeejdddddgeejdddddgeejdddddgeejdddddgeejdddddgeejdddddgegZgeD]Zedd^q Zdd Z d Z d Z d Z d Z dZRS(sDCheck that some Jacobian approximations satisfy the secant conditioniiiiii iic K`s}||}|j|jd|jddxItt|jd|jdD]$\}\}}|j||xtt||dD]m}|j||d|j||} |j||d|j||} t t j | |j | qW||krQ|j||d|j||} |j||d|j||} t t j | |j |  qQqQWdS(s| Check that the given Jacobian approximation satisfies secant conditions for last `npoints` points. iiN( tsetuptxstfstNonet enumeratetziptupdateRtminRRtallcloseR(( R5tjac_clstnpointsR@tjactjRRtktdxtdf((s?lib/python2.7/site-packages/scipy/optimize/tests/test_nonlin.pyt _check_secants !6 $$# $$cC`s|jtjdS(N(RgRt BroydenFirst(R5((s?lib/python2.7/site-packages/scipy/optimize/tests/test_nonlin.pyt test_broyden1scC`s|jtjdS(N(RgRt BroydenSecond(R5((s?lib/python2.7/site-packages/scipy/optimize/tests/test_nonlin.pyt test_broyden2sc C`s&tjdd}|j|jd|jddtjdd }xtt |jd|jdD]\}\}}||j|}||j|}||t ||dddf|dddft ||7}|j ||t tj |j|ddd d qjWdS( Ntalphag?iiiitrtolg|=tatolgvIh%<=g$(RRhRWRXRYRZRtidentityR[R\R R]RR_ttodense(R5RbtBtlast_jRRRfRe((s?lib/python2.7/site-packages/scipy/optimize/tests/test_nonlin.pyttest_broyden1_updates!6Hc C`s,tjdd}|j|jd|jddtjdd}xtt |jd|jdD]\}\}}||j|}||j|}||t ||dddf|dddft ||7}|j ||t tj |jt|ddd d qjWdS( NRlg?iigiRmg|=RngvIh%<=(RRjRWRXRYRZRRoR[R\R R]RR_RpR (R5RbtHRrRRRfRe((s?lib/python2.7/site-packages/scipy/optimize/tests/test_nonlin.pyttest_broyden2_updates!6HcC`s&|jtjdddddddS(NtMitw0iRa(RgRtAnderson(R5((s?lib/python2.7/site-packages/scipy/optimize/tests/test_nonlin.pyt test_andersons(RPRQRRRR$RRXRRYRgRiRkRsRuRy(((s?lib/python2.7/site-packages/scipy/optimize/tests/test_nonlin.pyRVs $!     t TestLinearcB`s>eZdZedZdZdZdZdZRS(s]Solve a linear equation; some methods find the exact solution in a finite number of stepsc `stjjdtjj|||rKdtjj||ntjj||rdtjj|nfd}tj|tj||d|dddddd }ttj t |d ddS( Ni{y?c`st|S(N(R (R(RR (s?lib/python2.7/site-packages/scipy/optimize/tests/test_nonlin.pyR6sR0R/gư>t line_searchR1iRn( RtrandomtseedtrandnRt nonlin_solvetzerosRZRR_R (R5RbtNR0tcomplexR@R6tsol((RR s?lib/python2.7/site-packages/scipy/optimize/tests/test_nonlin.pyt_checks !cC`sH|jtjddddt|jtjddddtdS(NRlg?ii)(RRRhRKRG(R5((s?lib/python2.7/site-packages/scipy/optimize/tests/test_nonlin.pyRis"cC`sH|jtjddddt|jtjddddtdS(NRlg?ii)(RRRjRKRG(R5((s?lib/python2.7/site-packages/scipy/optimize/tests/test_nonlin.pyRk s"cC`sT|jtjddddddt|jtjddddddtdS(NRvi2Rlg?ii(RRRxRKRG(R5((s?lib/python2.7/site-packages/scipy/optimize/tests/test_nonlin.pyRys(cC`sB|jtjddtdd|jtjddtdddS(Niitinner_mi (RRtKrylovJacobianRKRG(R5((s?lib/python2.7/site-packages/scipy/optimize/tests/test_nonlin.pyt test_krylovs( RPRQRRRKRRiRkRyR(((s?lib/python2.7/site-packages/scipy/optimize/tests/test_nonlin.pyRzs     tTestJacobianDotSolvecB`seeZdZdZeddZdZdZdZdZ dZ d Z d Z RS( sFCheck that solve/dot methods in Jacobian approximations are consistentcC`s|ddtj|j|S(Nii(RR R(R5R((s?lib/python2.7/site-packages/scipy/optimize/tests/test_nonlin.pyt_funcsgư>c `stjjdd}fd}fd}||||_tjj|}||} | j||j||jx>td|D],} ||} t| drtj | } t| dr | j | } tj j | | }|| |dnt| d rY| j | } tj j | j j| }|| |d nt| d r| j| }tj| | }|||d nt| d r| j| }tj| j j| }|||dqnt| d rCt| drC| j| }| j | j|}|||dnt| d rt| d r| j| }| j| j |}|||dn||}| j||j|qWdS(Ni{ic`s9tjj|}r5|dtjj|}n|S(Ny?(RR|trand(R?tq(R(s?lib/python2.7/site-packages/scipy/optimize/tests/test_nonlin.pyR$sc`sYt||j}t|j}||krUtd||fndS(Ns %s: err %g(tabsR4tAssertionError(R?R tmsgRR(ttol(s?lib/python2.7/site-packages/scipy/optimize/tests/test_nonlin.pyt assert_close*s it __array__R(ssolve vs arraytrsolvesrsolve vs arraytmatvecs dot vs arraytrmatvecsrmatvec vs arrays dot vs solvesrmatvec vs rsolve(RR|R}RRRWRRthasattrR$R(R'RRtconjRR RR](R5R`RRR@RRRtx0RbRdR,tJdtGvtGv2tJvtJv2R((RRs?lib/python2.7/site-packages/scipy/optimize/tests/test_nonlin.pyt _check_dotsL   cC`s0|jtjdt|jtjdtdS(NR(RRRhRKRG(R5((s?lib/python2.7/site-packages/scipy/optimize/tests/test_nonlin.pyRi[scC`s0|jtjdt|jtjdtdS(NR(RRRjRKRG(R5((s?lib/python2.7/site-packages/scipy/optimize/tests/test_nonlin.pyRk_scC`s0|jtjdt|jtjdtdS(NR(RRRxRKRG(R5((s?lib/python2.7/site-packages/scipy/optimize/tests/test_nonlin.pyRycscC`s0|jtjdt|jtjdtdS(NR(RRt DiagBroydenRKRG(R5((s?lib/python2.7/site-packages/scipy/optimize/tests/test_nonlin.pyttest_diagbroydengscC`s0|jtjdt|jtjdtdS(NR(RRt LinearMixingRKRG(R5((s?lib/python2.7/site-packages/scipy/optimize/tests/test_nonlin.pyttest_linearmixingkscC`s0|jtjdt|jtjdtdS(NR(RRtExcitingMixingRKRG(R5((s?lib/python2.7/site-packages/scipy/optimize/tests/test_nonlin.pyttest_excitingmixingoscC`s<|jtjdtdd|jtjdtdddS(NRRgMbP?(RRRRKRG(R5((s?lib/python2.7/site-packages/scipy/optimize/tests/test_nonlin.pyRss( RPRQRRRRKRRiRkRyRRRR(((s?lib/python2.7/site-packages/scipy/optimize/tests/test_nonlin.pyRs <      tTestNonlinOldTestscB`szeZdZdZdZdZdZdZdZdZ dZ d Z d Z d Z d ZRS( s Test case for a simple constrained entropy maximization problem (the machine translation example of Berger et al in Computational Linguistics, vol 22, num 1, pp 39--72, 1996.) cC`s]tjttjdddd}ttj|dkttjt|dkdS(Ntiteri Rlig& .>(RRRR2Rtnorm(R5R((s?lib/python2.7/site-packages/scipy/optimize/tests/test_nonlin.pyRi~s!cC`s]tjttjdddd}ttj|dkttjt|dkdS(NRi Rlig& .>(RRRR2RR(R5R((s?lib/python2.7/site-packages/scipy/optimize/tests/test_nonlin.pyRks!c C`sDtjttjdddddd}ttj|dkdS(NRi RlgQ?RvigQ?(RR RR2RR(R5R((s?lib/python2.7/site-packages/scipy/optimize/tests/test_nonlin.pyRys'cC`s]tjttjdddd}ttj|dkttjt|dkdS(NRi<Rlg?gHz>(RRRR2RR(R5R((s?lib/python2.7/site-packages/scipy/optimize/tests/test_nonlin.pyRs!cC`s]tjttjdddd}ttj|dkttjt|dkdS(NRiRlg?gh㈵>(RRRR2RR(R5R((s?lib/python2.7/site-packages/scipy/optimize/tests/test_nonlin.pyt test_excitings!cC`s]tjttjdddd}ttj|dkttjt|dkdS(NRi Rlig:0yE>(RR RR2RR(R5R((s?lib/python2.7/site-packages/scipy/optimize/tests/test_nonlin.pyRs!c C`sotttjdddidd6idd6d6}ttj|jd kttj|jd kdS( NR8RR9i tnitiRlt jac_optionsg& .>(RRR2RRRRR<(R5R=((s?lib/python2.7/site-packages/scipy/optimize/tests/test_nonlin.pyttest_root_broyden1sc C`sotttjdddidd6idd6d6}ttj|jd kttj|jd kdS( NR8RR9i RiRlRg& .>(RRR2RRRRR<(R5R=((s?lib/python2.7/site-packages/scipy/optimize/tests/test_nonlin.pyttest_root_broyden2sc C`sZtttjdddidd6idd6dd 6d 6}ttj|jd kdS( NR8R R9i RgQ?RliRvRgQ?(RRR2RRRR(R5R=((s?lib/python2.7/site-packages/scipy/optimize/tests/test_nonlin.pyttest_root_andersons c C`sotttjdddidd6idd6d6}ttj|jd kttj|jd kdS( NR8RR9i<Rg?RlRgHz>(RRR2RRRRR<(R5R=((s?lib/python2.7/site-packages/scipy/optimize/tests/test_nonlin.pyttest_root_linearmixings  c C`sotttjdddidd6idd6d6}ttj|jd kttj|jd kdS( NR8RR9iRg?RlRgh㈵>(RRR2RRRRR<(R5R=((s?lib/python2.7/site-packages/scipy/optimize/tests/test_nonlin.pyttest_root_excitingmixings  c C`sotttjdddidd6idd6d6}ttj|jd kttj|jd kdS( NR8R R9i RiRlRg:0yE>(RRR2RRRRR<(R5R=((s?lib/python2.7/site-packages/scipy/optimize/tests/test_nonlin.pyttest_root_diagbroydens  (RPRQRRRiRkRyRRRRRRRRR(((s?lib/python2.7/site-packages/scipy/optimize/tests/test_nonlin.pyRxs           (.RRt __future__RRRt numpy.testingRRStscipy._lib.sixRtscipy.optimizeRRtnumpyRRR t numpy.linalgR Rt test_minpackR R R RRRRRLRBRERR2RDRRR!R#R%R-tobjectR.RVRzRR(((s?lib/python2.7/site-packages/scipy/optimize/tests/test_nonlin.pyts`                    5L*_