bifW0ddlZddlZddlZddlZddlZddlZddlZddlZddlZddl Z ddl m Z m Z mZmZmZmZddlmcmZddlmZddlZddlmZmZmZmZmZmZm Z m!Z!m"Z"m#Z#m$Z$m%Z%m&Z&m'Z'm(Z(m)Z)m*Z*ddl+m,Z-ddl.m/cm,Z0ddl1m2Z2m3Z3m4Z4m5Z5m6Z6ddl7m8Z8m9Z9ddlm:Z:m;Z;mcm?Z@ddlAmBZBdd lCmDZDdd lEmFZFdd lmGZHdd lmIZJdd lmKZKejjZMeeGddZNeeGddZOdZPdZQdZRdZSdZTe fdZUdRdZVdde fdZWdZXGddZYeeGdd ZZd!Z[dSd"Z\ejjd#d$d%gZ^eeGd&d'Z_Gd(d)Z`dTd*Zad+Zbd,ZcGd-d.Zdd/Zeee)Gd0d1Zfd2Zgd3Zhd4ZiGd5d6Zjee(Gd7d8ZkGd9d:ZlGd;d<Zmd=Znd>Zoee:Gd?d@ZpdAZqGdBdCZrGdDdEZsee;GdFdGesZtee;GdHdIesZuee<GdJdKZvee<GdLdMZwGdNdOZxGdPdQZyy)UN)xp_assert_equalxp_assert_closexp_default_dtype concat_1dmake_xp_test_casexp_ravel)raises)BSplineBPolyPPolymake_interp_splinemake_lsq_splinesplevsplrepsplprepsplder splantidersprootsplintinsert CubicSpline NdBSplinemake_smoothing_splineRegularGridInterpolator) _not_a_knot_augknt_woodbury_algorithm_periodic_knots_make_interp_per_full_matr) Fperiodic root_rati)generate_knots make_splrep make_splprep) AxisError)_run_concurrent_barrier) make_ndbspl) _dfitpack) _bsplines)_dierckxceZdZdZdZdZdZdZdZe dd e d d e d d dZ dZ dZ dZ dZdZdZdZdZdZdZdZdZdZdZdZdZdZd Zd!Zd"Zd#Zd$Z d%Z!e"jFjId&e%d'd(d)Z&d*Z'd+Z(e"jFjId,gd-e"jFjId.e%d/d0Z)d1Z*d2Z+d3Z,e"jFjId4gd5d6Z-e"jFjId4gd5d7Z.d8Z/d9Z0d:Z1e"jFjee3jhd;k(dZ6y?)@ TestBSplinec tttftfit ddgdgdt j d5tttfit dt jgdgddddtttfit dt jgdgdtttfit ddgdgdtttfit dgdggdgdtttfit gd dgdtttfit gd ddgd tttfit gd gd dtttfit gd gd dtttfit gdgdd d\}}|j||zdz|j}|jt jj|}t|||}t||jt||j||j k(sJy#1swYxYw)N??rtckignore)invalidrr.rr.r9r9)r=r0@@@)r0r0r0cubic@)r=rr.r.r9r;)r0r.r. r;dtype) assert_raises TypeError ValueErrorr dictnperrstatenaninfarangefloat64asarrayrandomrr2r3r4)selfxpnr4r2r3bs `/home/cdr/jupyterlab/.venv/lib/python3.12/site-packages/scipy/interpolate/tests/test_bsplines.py test_ctorzTestBSpline.test_ctor4sy*-w 1!SbTQ/ 1 [[ * S *g RBFF tq1Q R Sj'NTQKB41-MNj'JTQGtq-IJj'MTaS1#J2$!-LM j'KTI!-JKj' <RH: < i O1\WM Oi K1\SI K j' B, a@ B1 IIac!e2::I . JJryy''* + Aq! 133133ACCxx; S Ss 3IIc2t}|j}t|j|dddt|j|ddd|j |dk(sJt jt5d|_dddy#1swYyxYw)NrV瞯<atolrtolr.r9foo) _make_random_splinetckrr2r3r4pytestr AttributeError)rSrVr`s rWtest_tckzTestBSpline.test_tckWs}  !eeSV%e<SV%e<ssc!f}}]]> * AE   s <B  Bct|jgd|jddgd}|jddd}|j|dk|jd|j d }t |||y) N)rr0r9r?r<rr1r9 r0rEr@)r rQlinspacewhererPr)rSrTrVxxexpecteds rWtest_call_namespacezTestBSpline.test_call_namespacecso bjj, B70Cq I [[Ar "88BGRZZ"**Z%EsK"x(ctjddd}tddgdgd}t||tj|dztgdddgd}t||tj |d kdd y) Nrr.rer?r1)rffffff?r.r;r<rmr@)rKrfr r ones_likerg)rSrhrVs rW test_degree_0zTestBSpline.test_degree_0lsu [[Ar " q!f *"r||B/#56 lq!f 2"rxxT 3<=rkc |jgd}|jgd}d}t|||}|jddd|j}t |||dt || z|dt |dz | zz|d t |d z | zzd t tj|||f\}}} t||| |f} t |||j| d y) Nr:)r0r9r;r.r0r?2rErrTr9+=r\) rQr rfrPrB_012maprKr) rSrTr2r3r4rVxx_npt_npc_np splev_results rW test_degree_1zTestBSpline.test_degree_1us JJ ' JJ{ #  Aq!  KKS"BJJK 7 aD aDqR 1Q4acb(9#9 9AaDqsrARr?r@)r7r.gr>reT extrapolatersrt)rQr reshaper rfr)rSrTr4r2r3bpbsplrhs rWtest_bernsteinzTestBSpline.test_bernsteins  JJsAaCyA3!9, - JJ' ( 2::a)2::q!f+= >q!Q [[b" %240RT2 @rkz dask.arrayz"_naive_eval is not dask-compatiblereasonz jax.numpyztoo slow; XXX a slow-if marker?torchz OOB on CIc t|}|j\}}}|j|||| dz d}||}|j|Dcgc]}t |||||c}} t || d|j|Dcgc]}t |||||c}} t || dycc}wcc}w)Nrrr.rqrsrt)r_r`rfstack _naive_evalr _naive_eval_2) rSrTrVr2r3r4rhy_brwy_ny_n2s rWtest_rndm_naive_evalz TestBSpline.test_rndm_naive_evals 2 &%%1a [[1q!Aw +ehhC1 Aq!Q26CDSu-xx2Faq!Qb9FGT. DGs B9 B>c t}|j\}}}tj|||| dz d}t ||t ||||fdy)Nr.rqrsrt)r_r`rKrfrrrSrVr2r3r4rhs rWtest_rndm_splevzTestBSpline.test_rndm_splevsV  !%%1a [[1q!Aw +"uR!Q3%@rkctjjd}tj|jd}|jd}t ||}t |}|j |j}}tj|||| dz d}t||t||dy)Nr.Prsrt) rKrR RandomStatesortrr r2r4rfrr) rSrngrwyr`rVr2r4rhs rWtest_rndm_splrepzTestBSpline.test_rndm_splrepsii##D) GGCJJrN # JJrNQl SMssACC1 [[1q!Aw +"uR~E:rkc@t|}|j|j|_|j|j|j |j|j dz d|j }t|||j|y)Nrrr.drE)r_rnr3rfr2r4rPr)rSrTrVrhs rWtest_rndm_unityzTestBSpline.test_rndm_unityso 2 &ll133 [[QSS133tAv;2::[ F"r||B/0rkctjjd}d\}}tj|j|}|j|ddf}t |j ||f\}}t |||}|||| dz } }|| |z |j |jdzz} || jdk(sJy) Nrr;sizer.r;r<)r;r<rrr)rKrRrrrvrQr shape) rSrTrrUr4r2r3rVtmtprhs rWtest_vectorizationzTestBSpline.test_vectorizationsii##D)1 GGCJJqM " JJQ1IJ &2::1v&1 Aq! 1q!AwB 27bjjI)>?? ?u{{o---rkc Xtjjd}d\}}tj|j||zdz}|j|}tj||j|dzf}t |||t |||}}|d|dz } tj |d| z |d| zd} t|| || dt|| t| |||fdt|| t| |||fdy) Nr)!r;r.r7rrqrsrt) rKrRrrr_r rfrr) rSrrUr4r2r3c_padrVb_paddtrhs rW test_len_czTestBSpline.test_len_cs ii##D)1 GGCJJqs1u% & JJqMaAaC()1a#WQq%95 rUQqT\ [[1AbEBJ 3"uRyu5"uR!Q3%@"uR!UA7eDrkc t}|j\}}}|||| dz }}dD])}t|||g|||dz|dz g|dd+y)Nr.TF绽|=& .>Hz>r[r_r`r) rSnum_parallel_threadsrVr2_r4rrextraps rWtest_endpointszTestBSpline.test_endpointsss  !%%1a1q!AwB# WF Ar2h/rEz2:6?dQU W Wrkc t}|j\}}}t|||dz| dz dz |||dz| dz dzdy)Nr.rrrtr)rSrrVr2rr4s rWtest_continuityzTestBSpline.test_continuitys\  !%%1a!AaC1+-.!AaC1+2E0F rkct|}|j\}}}|d|dz }|j|||z || dz |zd}|||k||| dz kz}t|||d|||dt t j |||f\} } } |j t| | | |fd } t||d| y) Nrrr7rr.rqTrF)ext)r_r`rfrrvrKrQr) rSrTrVr2r3r4rrhmaskxx_npryrzr{s rW test_extrapzTestBSpline.test_extraps 2 &%%1a rUQqT\ [[1AqbdGbL" 5!r b1aRT7l+ "T(5"T(6 8  RAJ7tTzz%dAA"FG "$/>rkct}|j\}}}|ddz |ddzg}||}tjtj|rJy)Nrr.r7)r_r`rKallisnan)rSrVr2rr4rhyys rWtest_default_extrapzTestBSpline.test_default_extrapsY  !%%1adQh" " rU66"((2,''''rkc ftjjd}tj|jd}|jd}t |j ||f\}}d}t |||d}|jd|dzz }|d |dz }|j|||z |||zd } ||| ||z ||||z zz} t tj | ||f\} } } t||jk(rd nd }t|| |j t| | | |f| |j gd} ||| ||z ||||z zz} t|| d|| dt||jk(rd yd y)Nrr<r;periodicrrr.r7rq-q=gH׊>rt)r7r?r.TrsgƠ>) rKrRrrrvrQr rrfrrPrr)rSrTrr2r3r4rVrUrrhxyxy_npryrzr\s rWtest_periodic_extrapz TestBSpline.test_periodic_extrapsii##D) GGCJJqM " JJqM2::1v&1  Aq! 4 GGAJ!a%  rUQqT\ [[1AaD2Ir 2 qTR!A$Y1Q4!A$;/ / RAJ7tT(, :u bE2::eED$?;<4 ZZ ( qTR!A$Y1Q4!A$;/ / bj ) bd #*2."**< CG rkct}|j\}}}tj|||f}t j |||| d}t ||||ddy)Nrrsr[)r_r`r from_splinerKrfr)rSrVr2r3r4pprhs rW test_ppolyzTestBSpline.test_ppolysa  !%%1a   1ay ) [[1q!uc *"r"vE>rkcjt}|j\}}}tj|d|dd}tj||f}t d|dzD])}t ||||f|}t||||d+t|||dztj|dy) Nrr7rqr.dernursrt) r_r`rKrfrrangerr zeros_like)rSrVr2r3r4rhryds rWtest_derivative_rndmz TestBSpline.test_derivative_rndm#s  !%%1a [[1qub ) UU2q5\AaC= ;CrAq!9#.B B" E : ; "1 r}}R'8uErkcd}gd}tjjd}tjdd|jdddf}t |||}tj gd}t |||dk7dz |||dk7dztj|d |d rJtj d d g}t ||dz d ||dzd tj d dg}tj||dz d ||dzd rJtj||dz d||dzdrJy)Nr9) r7r7rr.r.r;r<rrrrrrrr)r.r;r<rrrg2H@gη@r;r<r.r)rKrRrrr rQrallclose) rSr4r2rr3rVrwx0x1s rWtest_derivative_jumpsz!TestBSpline.test_derivative_jumps0sP  2ii##D) EE!Q 1 q!+ , Aq!  JJ| $!AF)e+,!AF)e+, .;;q{AgJ777ZZA "u*+"u*+ - ZZA ;;qe2Ab5jQ4GHHH;;qUq11QY13EFFFFrkc |jddd}tj|jgd}t t j||j |jf\}}}|jt||||jf}t|||dt||jk(rdnd}t|||jt||j |tj|jgd }|jd d d |j }t|||j|dk||zd|z d zdy)Nr7r<rrr.r9r;)r2rsrtrrErr.r.r9rr9rer.r>)rfr basis_elementrQrvrKr2r3rr4rrrPB_0123rg) rSrTrhrVrryrzr{r\s rWtest_basis_element_quadraticz(TestBSpline.test_basis_element_quadraticJs" [[Q #  ! !BJJ|$< = RaccN;tTzz%dACC/@"AB "|%8&r*bjj8Ud"rzz&*BJJzGdS  ! !BJJ|$< = [[Ar[ 4"aBB 3% Arkc t}|j\}}}tj|||| dz d}t ||t ||||dy)Nr.rrsrt)r_r`rKrfr_sum_basis_elementsrs rWtest_basis_element_rndmz#TestBSpline.test_basis_element_rndmZsU  !%%1a [[1q!Aw +"22q!Q?eLrkct}|j\}}}|dz}t|||}t||jj|}t||jj |}t j|||| dz d}t||j||dt||j ||dy)Ny?@r.rrsrt) r_r`r r3realimagrKrfr) rSrVr2r3r4ccb_reb_imrhs rW test_cmplxzTestBSpline.test_cmplx`s  !%%1a (^ Ar1 q!##((A&q!##((A& [[1q!Aw +" DH59" DH59rkctj|jgd}|j||jsJy)Nr)r rrQrrM)rSrTrVs rWtest_nanzTestBSpline.test_nanms5  ! !"**\": ;xx"&& """rkc td|}|j\}}}t|||}|j|||| dz d}t d|D].}|j }t |||||dd0y)Nr)r4rTr.rrr[)r_r`r rfr derivativer) rSrTrVr2r3r4b0rhjs rWtest_derivative_methodz"TestBSpline.test_derivative_methodrs ! +%%1a Q1  [[1q!Aw +q! FA A Br1Iqu5u E Frkct|}|j\}}}|j|||| dz d}t|j j |||dd|j |||fd}|j ||fd}t|||}t|j j |||ddy)Nrrr.rrsr[axisr9)r_r`rfrantiderivativerrr )rSrTrVr2r3r4rhs rWtest_antiderivative_methodz&TestBSpline.test_antiderivative_method{s 2 &%%1a [[1q!Aw +7((*557;"E 7 HHaAYQH ' HHaV!H $ Aq! 7((*557;"E 7rkc  tj|jgd}tj|j ddddsJtj|j ddddsJtj|j ddddsJtj|j ddddsJtj|j ddddsJtj|j ddddsJtj|j ddd dsJtj|j ddd d dsJtj|j ddd ddsJtj|j ddd ddsJtj|j ddd t jdd|jdsJd |_ |j}|j|d|dz |j}tj|j dd|sJtj|j ddd|zsJtj|j dd|sJtj|j ddd|zsJt|j dd|j|d|dz t|j dd|j|d|dz |dz|dz t|j dd|j|d|dz |dz|dz t|j dd|j|d|dz |dz|dz d|zzt|j dd|j|d|dz t|j dd|j|d|dz t|j dd|j|d|dz d|zz y)Nr8rr.rrsabs_tolr7r=TrFrr9rEiii?r;g+@rir<) r rrQmathisclose integrate_implrr`rrrPr)rSrTrVi period_ints rW test_integralzTestBSpline.test_integrals  ! !"**Y"7 8||AKK1-sEBBB||AKK1-xGGG||AKK1-tUCCC||AKK1-sEBBB||AKK1-xGGG||AKK1-tUCCC||AKKA.UCCC||AKKA4K@#uUUU||AKKA5KA3PUVVV||AKK25KA4QVWWW||AKK25KA!LLB6G GG#   ZZ!qt 2::Z> ||AKK1-z:::||AKK1-rJ???||AKKB/<<<||AKKB/Z@@@ C- 1S6AcF?3 5 C+ 1Q4!A$;1#5##>? A Hf5 1Q4!A$;1#5##>? A C0 1Q4!A$;1#5##>Z#OP R  Ar*BJJqtad{,CD B,bjj1!.EF Ar* 1Q4!A$;Z#?@ Brkcgd}t||}d|_tj|}dD]1\}}t |j |||j ||3y)Nr:r))r)rr)r )r rr rrr)rSrwrVprrs rWtest_integrate_ppolyz TestBSpline.test_integrate_ppolys`  q! $"   a 5 1FB AKKB/KKB/ 1 1rkctjgd}dD]C}|jdd|}t|tj sJ|j dk(rCJy)Nr8rrr.r)r rr isinstancerKndarrayndim)rSrVrress rWtest_integrate_0D_alwaysz$TestBSpline.test_integrate_0D_alwayssY  ! !) ,( !K++a +.BN)__name__ __module__ __qualname__rkrWBrs rkr)rr.r9r9)r r __class__rr)rSrrVs rWtest_subclassingzTestBSpline.test_subclassingsg   OOL ){{a||~''1,,,!++q000rkrrr<c d\}}|jdd||zdz}gd}|dz}|j||t|}tjj d}|j |j |} t|| ||} | jj||f|d|z||dzdzk(sJ|j d }| |j|d||jz||dzdzk(sJ| j dz | jfD]$} tttfit|| || &t|| ||jt|| ||jd t|| ||jt|| ||jd fD]} | j | j k(rJy) Nrrr.rrrr<rrrr)r2r3r4rr9)rfrtuplerKrRrrQr r3rrrGr%rJrrr) rSrrTrUr4r2shpos_axisrr3rVaxb1s rW test_axiszTestBSpline.test_axiss1 KK1a!eai ( !8 (A 2Yii##D) JJszzrz* + Aq!$ 'ssyyR\Ob(m;b!oMMMM ZZ "u{{b(mbhh6HQJKHHHHFF7Q;' :B )W : 1QR8 : : 1a.99;1a.99!<1a.==?1a.==a@B %B77aff$ $$  %rkc (d}|jgd}|jgdgdg}t|||d}t||dddf|}t||dddf|}t|d |j|d |d gy) Nr9)rr.r9r;r<rr)r7r9rr7)r9rr.r7rrr.rB)rQr rr)rSrTr4r2r3splspl0spl1s rW test_neg_axiszTestBSpline.test_neg_axiss  JJ, - JJ 6 7aAB'q!AqD'1%q!AqD'1%C"((DItCy+A"BCrkcd}d}d}dD] }||||tdddD] }|||dd}tdd D] }|||d y ) a7 Splines with different boundary conditions are built on different types of vectors of knots. As far as design matrix depends only on vector of knots, `k` and `x` it is useful to make tests for different boundary conditions (and as following different vectors of knots). cBtjjd}tj|j |dzdz }|j |dzdz }|dk(r|d|d<t ||||}tj t|j|z dz }t|j|||}tj||j|j} t| |jz|d t|| d y ) zY To avoid repetition of code the following function is provided. r(rrr7rr4bc_typer.rsrtN)rKrRrr random_sampler eyelenr2r design_matrixtoarrayrr3) rUr4r4rrwrrr3 des_matr_def des_matr_csrs rWrun_design_matrix_testszHTestBSpline.test_design_matrix_bc_types..run_design_matrix_testss))''-C))!,r1B67A!!!$r)B.A*$u!%aaADs466{Q*+A074661a03L"00151244;GI  L466115 A L,U CrkrDr;clampednaturalrr9 not-a-knotrrrN)r)rSr<rUr4bcs rWtest_design_matrix_bc_typesz'TestBSpline.test_design_matrix_bc_typess| D*  ( .B #Aq" - .q!Q 8A #Aq, 7 8 q! 6A #Aq* 5 6rkr)FTrdegreerc tjjd}|jd|dzz}tj|tj |}}|}tj tj|dz |dz |tj||d|dzztj|dz|dz|f}tjt||z dz } t|| ||} t| |tj||||jtj|dz |dz |dz|dzg}|s;tj t"5tj||||dddyt| |tj||||jy#1swYyxYw)z;Test that design_matrix(x) is equivalent to BSpline(..)(x).rrer.r9rN)rKrRrr5aminamaxrrfr6r7r rr8r9arrayrar rI) rSrrCrrwxminxmaxr4r2r3bsplines rW'test_design_matrix_same_as_BSpline_callz3TestBSpline.test_design_matrix_same_as_BSpline_call%sii##D)   bFQJ/ 0WWQZd  EE"++dQhq&9++dD!vz*:;++dQhq&9: ; FF3q6A:> "!Q;/ AJ--aA{CKKM HHdRi4#:tbyA Bz* <%%aA{; < <  %%aA{;CCE  < r?r@r@r@r>r;)g?gmਪ?gK}\UU?r=rsrt)r r8r9r)rSr2des_matrs rWtest_design_matrix_t_shapesz'TestBSpline.test_design_matrix_t_shapesRs7 ,((Q2::<;<" $rkctjjd}d}d}tj|j |dzdz }|j |dzdz }t |||}t t5tj||jddd|dddd}gd }gd }t t5tj|||dddy#1swYCxYw#1swYyxYw) Nrrer;r2rrMr7r9)r=r0r>r?r@@r~) rKrRrrr5r rGrIr r8r2)rSrrUr4rwrrr2s rWtest_design_matrix_assertsz&TestBSpline.test_design_matrix_assertsZsii##D)   GGC%%a(2-2 3   a 2 % *!!Q!,: & 6  ! !!TVVDbD\1 5 6  $  : & +  ! !!Q * + +  6 6  + +s(C, C8,C58Dr4)r?r>rr@ctjjd}tj|jd}|jd}|dk(r|d|d<t |||}t j ||}tjddd}t||||d t|||}t|j|jd y) Nrrrrr7r4r.rZrt) rKrRrrrr from_power_basisrfrr r3) rSr4rrwrcbrrhbspl_news rWtest_from_power_basisz!TestBSpline.test_from_power_basislsii##D) GGCJJrN # JJrN j aDAbE Aw /''G< [[Ar "2Ru5%aG< 7rkctjjd}tj|jd}|jd|jddzz}|dk(r|d|d<t |||}t j ||}t||j|}t||j|}t|j|jd|jzzd y) Nrrr/rrr7rXrZrt) rKrRrrrr rYr rrrr3) rSr4rrwrrZr bspl_new_real bspl_new_imags rWtest_from_power_basis_complexz)TestBSpline.test_from_power_basis_complex|sii##D) GGCJJrN # JJrNSZZ^b0 0 j aDAbE Aw /''G<*1affgF *1affgF  "}2F FUSrkctjgd}tjgd}tjt ||dd}t |j gddy) a} For x = [0, 1, 2, 3, 4] and y = [1, 1, 1, 1, 1] the coefficients of Cubic Spline in the power basis: $[[0, 0, 0, 0, 0],\$ $[0, 0, 0, 0, 0],\$ $[0, 0, 0, 0, 0],\$ $[1, 1, 1, 1, 1]]$ It could be shown explicitly that coefficients of the interpolating function in B-spline basis are c = [1, 1, 1, 1, 1, 1, 1] r:)r.r.r.r.r.r?rX)r0r.r.r.r.r.r.rZrtN)rKrGr rYrrr3)rSrwrrs rWtest_from_power_basis_exmpz&TestBSpline.test_from_power_basis_exmpsO HH_ % HH_ %'' Aq)(L09; 7eDrkcdtjddg}tjdg}|jd|jdtjddd}|jdt ||d}t ||tj |dzy)Nrr.r?Fwriterer1)rKrGsetflagsrfr rrn)rSr2r3rhrVs rWtest_read_onlyzTestBSpline.test_read_onlys HHaV  HHcUO     [[Ar " %  a1 ""r||B/#56rkcBt}fd}td||y)Nrrcp|j\}}}j|||| dz d}||y)Nr.i')r`rf)rrVr2r4rhrTs rW worker_fnz/TestBSpline.test_concurrency..worker_fns9eeGAq!QqT1aRT7E2B bErkre)r_r&)rSrTrVrjs ` rWtest_concurrencyzTestBSpline.test_concurrencys 2 &  Iq1rkcygwinz'threading.get_native_id not implemented)rr c nt}tjddd}||}tj}tj t |jd|dd|jj|jj}|j|ddtj t |jd|dd|jj|jj}|j|dd||_||_ t|||y) Nrr.rer2z.datzw+)moderFrr3) r_rKrf threading get_native_idmemmapstrjoinr2rFrr3r)rStmpdirrVrhritidt_mmc_mms rW test_memmapzTestBSpline.test_memmaps ! [[Ar "R5%%'yyV[[1SE78t ssyy ;##QyyV[[1SE78t ssyy ;##Q"x(rkN)7rrrrXrcrjror|rskip_xp_backendsrrrrrrrrrrrrrrrrrrrrr rrr!ramark parametrizerr)r/rBrKrPrSrVr\r`rbrgrkxfailsysplatformrbrxrrkrWr,r,1s!F )>D @l+OPk*KLgk2 /3MQ /A ;1 .E&W? ( 6? FG4A M :# F 7+BZ 1!1 [[VU2q\2%3%:D(6T [[],EF [[XuQx01G4C"$+$ [[Y)CD 8D 8 [[Y)CD TD TE& 7 2 [[  8 )  )rkr,c>eZdZejj dgddZejj dgddZdZejj dgd d Z ejj d d d gdZ dZ dZ y ) TestInsertxval)r=r0rBr<@@c |jd|j}|j|dz}t||d}|j|j |j f}tt||}|j|}t|j|j|jdt|j|j|jd|j dz d||dk7r|n|dd} |j| d |dd|ddzzf} t|| || d|j|dz} t|| d} t||j!|| fd d} | j|} t| j|jdt| j|j!|j|j| j|jfd d||dk7r|n|dd} |j| d |dd|ddzzf} t| | | | dy) NrrEr;rMrZrtr.r7rr)rOrPsinr _t_cr4r r insert_knotrr2rQr3concatcosr)rSrrTrwrr,r`spl_1fspl_1rhy1spl_y1spl_yyspl_yy1s rW test_insertzTestInsert.test_inserts IIarzzI * FF1IqL A+vvsvvsuu%&s+,%FHH!5EBFHHYsuufQh,?!@uM!B%-QQsV YYC123B01 2Br7VVAY\#ArQ/#ArxxBax'@AF$$T* 5777 II HHcood+--v/A/A$/G/I/IJQRH S !B%-QQsV YYC123B01 2r GBKe!DEa(FHH!5EBFHHYsuufQh,?!@uM!B%-QQsV YYC123B01 2Br7rkc6tjjd}d\}}|jtj|j ||zdz}|j|j |ddf}t |||}|j|j ||dz|| dz }|j|} |j|j ||dz|| dz d } t|| | | d y) N90rCr.rr;r9)lowhighrrrrrZrt) rKrR default_rngrQruniformr rr) rSrTrrUr4r2r3r,xvrrhs rWtest_insert_randomzTestInsert.test_insert_randomsii##E*1 JJrwws{{!A{67 8 JJs{{Aq {2 3aA ZZ !A#Qr!tW = ># ZZ !A#Qr!tW2 F GBr7rkr) r皙?r>r@@@@gffffff@rc |jd|j}|j|dz}t||d\}}}t |j ||f\}}t |||d}|j|} t||jd\} } }t| j|j | d t| jd| d z |j | d| d z d tjjd j!d dd} |j | } t| | |j t#| | | |fd y)NrrEr;rMrrTperrZrtr.rrr)r)rOrPrrrvrQr rrr`rr2r3rKrRrrr)rSrrTrwrr2r3r4r,rtfcfrrhs rWtest_insert_periodiczTestInsert.test_insert_periodics0 IIarzzI * FF1IqLA#1a2::1v&1aA:6#2swwD1 BBe<!A 2er!t9(=EJ %%d+333K ZZ b 2::eEBA;.G#HuUrkrNrc|jd|jdztjz}|j ||j |}}t ||d|zzd}||_t ||d}||_t ||d}||_d} |j| } |j| } |j| } t| j| jd t| j| jd t| j| jd| jzzd y) NrrEr9r/r;rM @rZrt) rOrPrKpirrr rrrr2r3) rSrrTrwy_rey_imr,spl_respl_imrrspl_1respl_1ims rW test_complexzTestInsert.test_complex0s IIarzzI *Q . 6VVAYq d D2d7Na8%#Atq1(#Atq1( #$$R($$R(77R \!9Frkcd}d}tjdg|dzzgdzdg|dzzz}tjt||z dz }t |||d}t t 5t||||fd dddt t 5|j|dddy#1swY3xYw#1swYyxYw) Nrr;rr.r9r;r<rrrrTr) rKrGonesr7r rGrIrr)rSrr4r2r3r,s rW+test_insert_periodic_too_few_internal_knotsz6TestInsert.test_insert_periodic_too_few_internal_knotsGs  HHaS!A#Y-QqS 9 : GGCFQJN #aA:6 : & , 21ayd + ,: & OOB    , ,  s2B6C6B?C cd}tjdg|dzzgdzdg|dzzz}tjt||z dz }t |||}t t 5|jddddt t 5|jddddt t 5|jdddddy#1swY^xYw#1swYAxYw#1swYyxYw) Nr;rr.rrr7rr)rKrGrr7r rGrIr)rSr4r2r3r,s rWtest_insert_no_extrapz TestInsert.test_insert_no_extrap[s  HHaS!A#Y-QqS 9 : GGCFQJN #aA : & OOB  : &  OOA  : & $ OOAO # $ $      $ $s$.CC)C5C&)C25C>) rrrrarzr{rrrrrrrrrkrWrrs [[V%AB!=C!=H [[C 8 8 8 [[T$8VV" [[]T:,>?G@G, ( $rkrc dd}dD]S}t|}tt|D].\}}|||td|dzD]}||||dd0Uy)Nc |j\}}}tj|}tj|ddz d|dd|ddzz|ddzf}t t ||||f||||||d|d|j y) Nrrrr.r7zder = z k = )r\r]err_msg)r`rKuniquerrrr4) rVrrr\r]r2r3r4rws rW check_splevz,test_knots_multiplicity..check_splevos%%1a IIaL EE!A$s(C122A/2s: ;a!QC0!As)se6!##.G Irkr.r9r;r<rrMr.r)rrsrs)r_ enumerate_make_multiplesr)rr4rVrr(rs rWtest_knots_multiplicityrkssI6 ! $q12 6EAr A Q!} 6B3u5 6 66rkcb|dk(r|||cxkr ||dzkrdSdS|||z||k(rd}n)|||z |||z||z z t||dz ||z}|||zdz||dzk(rd}||zS|||zdz|z |||zdz||dzz z t||dz |dz|z}||zS)zw Naive way to compute B-spline basis functions. Useful only for testing! computes B(x; t[i],..., t[i+k+1]) rr.r0r=_naive_Brwr4r r2c1c2s rWrrs  Avda(!AaC&(s1(c11v1~ !A$h1Q3!A$ '(1ac1a*@ @1Qx1QqS6  G!AhlQqs1uX!A#. /(1ac1Q32J J Grkck(rn|jdz cxkr dzksJJk\rjdz ksJtfdtddzDS)z= Naive B-spline evaluation. Useful only for testing! r.rc3RK|]}|z t|z z ywNr).0rr3r r4r2rws rW z_naive_eval..s-F1q1vAqsA..Fs$') searchsortedrsumr)rwr2r3r4rTr s```` @rWrrs AaDy  OOAq !A % Q41 !A#    6a!''!*q.(( ( Fa1 F FFrkcjddzz }|dzk\sJjd|k\sJcxkr |ksJJtfdt|DS)z'Naive B-spline evaluation, another way.rr.c3FK|]}|t|zywrrrr r3r4r2rws rWrz _naive_eval_2..s%=qqthq!Q**=!)rrr)rwr2r3r4rTrUs```` rWrrsr  acA !8O8 771:?? Q41 !    =E!H= ==rkct||dzz }||dzk\sJ|jd|k\sJd}t|D]F}tj||||zdzd|}|||t j |zz }H|S)Nr.rr=r9Fr)r7rrr rrK nan_to_num)rwr2r3r4rUsr rVs rWrrs A!A#A !8O8 771:?? A 1X% @G ! !!Aac!e*% @ C QqTBMM!$ $$% Hrkctj|}tj||dk|dkDz|dk\|dkz|dk\|dkzgdddg}|j|S)z+ A linear B-spline function B(x | 0, 1, 2).rr9r.cyNr=rrws rWzB_012..rkc|Srrrs rWrzB_012..sArkc d|z SNr>rrs rWrzB_012..s Ark)rK atleast_1d piecewiserQ)rwrTresults rWrurusr aA \\!q1uQ/!VA.!VQ/1)+~FHF ::f rkctj|}|dk|dkD|dkz|dkDg}|dk(r dddg}n|dk(r ddd g}ntd |tj|||}|S) z0A quadratic B-spline function B(x | 0, 1, 2, 3).r.r9rc||zdz Srrrs rWrzB_0123..s1Q3r6rkcd|dz dzz S)Ng?rr9rrs rWrzB_0123..s41T6A+-rkcd|z dzdz S)Nr?r9rrs rWrzB_0123..sBqD19q=rkcyNr0rrs rWrzB_0123..rrkcy)Ngrrs rWrzB_0123..rrkcyrrrs rWrzB_0123..rrkznever be here: der=)rKrrIr)rwrcondsfuncspiecess rWrrs aA UQUq1u%q1u -E ax!-(* .se455 \\!UE *F Mrk#r;c(tjjd}tj|j||zdz}|j|}|j ||j |}}t j |||S)N{r.)rKrRrrrQr construct_fast)rUr4rTrr2r3s rWr_r_sp ))   $C  1Q3q5!"A 1 A ::a="**Q-qA  ! !!Q **rkc#K|j|j}}|jj}|d|dd|d|d<t ||||jj}|d|d|dzt ||||jj}|d|| dz dt |||yw) zIncrease knot multiplicity.rrNr.r7)r3r4r2copyr )rVr3r4t1s rWrrs 33qA B2Br"I VBrF "a  B!uBt!H "a  B2Br!tuI "a sBcNeZdZdZdZdZdZdZdZdZ dZ d Z d Z d Z y ) TestInteropcltjddtjzd}tj|}t ||}|j |j |jf|_|||c|_ |_ |_ tjddtjzd|_ tj|j |j |j f}tj||f|_t!|j |j|j|_y)Nrr@rr)rKrfrrr r2r3r4r`rhrrVxnewc_dstackrr b2)rSrhrrVrs rW setup_methodzTestInterop.setup_methods [[BruuHb ) VVBZ r2 &CCacc?#%r1 $&KK2bee8R0 UU133QSS= !))RH%!##tww,rkc  |j|j|j}}}tt ||||ddtt ||j ||ddtt j|Dcgc]}t ||c}||ddttd5t ||dddttd|jjdz}|jj|}|j||j f}tt jt ||||j|ddycc}w#1swYxYw)NrZr[zCalling splev.. with BSplinematchr.r)rrVrrrr`rKrQrGrIr$rr3r transposer2r4)rSrrVrrwr%rr`s rW test_splevzTestInterop.test_splevs.iia dA$e% 9dAEE*$e% 9 #>AE!QK#>?$e% 9 :-K L  $O 5BDDII& '$ . TT^^B ttR 5s#344**2.U H$?   sE5 > E::Fc|j|j}}t||}tj||\}}}t |d|dt |d|d|d|k(sJt||d\}}}}t |d|dt |d|d|d|k(sJt ||} t || dt |} t || |dy)NrrZrtr.r9T) full_output)rhrrr rrr ) rSrwrr`r2r3r4tck_frrrVs rW test_splrepzTestInterop.test_splrepsww1Ql,,q!$1aA.A.1v{{ 1$7q!Qa!%0a!%0Qx1}}1c]2E* SM1Q4e,rkc&|j|j}}tj||f}t t 5t ||dddt t 5tj ||dddt td5t |dd|dddddt td5tj |dd|dddddy#1swYxYw#1swYxxYw#1swYXxYw#1swYyxYw)Nm > k must holdrr;) rhrrKrrGrIrr rH)rSrwry2s rWtest_splrep_errorszTestInterop.test_splrep_errors/sww1 UU1a4[ : &  1bM  : & LLB  9,= > ! 1Ra5!BQ%  ! 9,= > ' LL2A"1 & ' '     ! ! ' 's/ C#!C/C;=D#C,/C8;DDctjdtjjd}t |\}}t j|\}}t ||dt tjt|||dt tjt|||dt |dd\\}}}}}t ||dt tjt|||dy) NrrEr;rrZrtrT)rr) rKrOrPrrr rrQr) rSrwrVur`u1b_fu_frs rW test_splprepzTestInterop.test_splprep?s IIb + 3 3F ;qz1--"R 2E* 5A;/? 5C=115A&a1$? cAq!3U+ 5c?3QUCrkctjdjd}ttd5t |dddttd5t j |dddtjddd}ttd 5t |gdddttd 5t j |gdddgd }ttd 5t |gdddttd 5t j |gdddgd }gd }ttd 5t |gd|gdddy#1swY0xYw#1swYxYw#1swYxYw#1swYxYw#1swYxYw#1swYvxYw#1swYyxYw)N<rztoo many values to unpackrrr2r;)numr ) >Ir >KrzInvalid inputs)r.r;r9r<)rg333333?g?r.) rKrOrrGrIrr rfrH)rSrwrs rWtest_splprep_errorszTestInterop.test_splprep_errorsNsy IIe  $ $Y / :-H I  AJ  :-H I  MM!   KK21 % 9,= >  QCL  9,= >  MM1#   E :-= >  QCL  :-= >  MM1#     :-= > % qc4^ $ % %/                % %sS E0E=" F F< F""F. F:0E:=F FF"F+.F7:Gc|j|j}}tjgdtjz}t t ||ddt t |j|j|jf|ddttd5t |dddd|jjdd d }tjt |j||jfd}|jd k(sJt ||z tj|d y#1swYxYw)N)rrrBrrr[zCalling sproot.. with BSplinerrq)mestr.r9r)r;r9r<rrt)rVrrKrGrrrr2r3r4rGrIrrQrr)rSrVrrootsc2rrrs rW test_sprootzTestInterop.test_sprootks2-.ruu4q 5t$?QSS!##/TM:-L M 2B  ddnnQ1% ZZc2440r: ;xx9$$$U BMM"$5EB  s #EE c J|j|j}}ttdd|tdd|jddttdd||j ddddt td5tdd|ddd|jjddd}tjtdd|j||jf}|jd k(sJt|tdd|dd y#1swYxYw) Nrr.rsF)r\check_0dzCalling splint.. with BSplinerr9)r;r9)r\ check_shape)rVrrrr`rrGrIr3rrKrQr2r4r)rSrVrrintegrs rW test_splintzTestInterop.test_splint|s2q!Qq!QUU+%% Iq!Q Aq) G:-L M  1a  ddnnQ1%F1a"$$RTT):;<||v%%%q!Qe H  s DD"c |j|jfD]@}t|jt|jz }|jj }|dkDr9t j|t j|f|jddzf}dD]}t|}tj|jj ||jf}t|j|ddt|j|dd|j|dk(sJt|tsJt|t rJCyNrr.r.r9r;rZrtr9)rVrr7r2r3rrKrzerosrrr r4rrr r$rSrVctb_crUbdtck_ds rW test_splderzTestInterop.test_splders&&$''" 0AQSSCH$B##((*CAveeC2%#))AB-*?!@@A 0AY acchhj#qss%;<eAhU;eAhU;ttuQx'''!"g...!%/// 0 0rkc |j|jfD]@}t|jt|jz }|jj }|dkDr9t j|t j|f|jddzf}dD]}t|}tj|jj ||jf}t|j|ddt|j|dd|j|dk(sJt|tsJt|t rJCyr')rVrr7r2r3rrKrr)rrr r4rrr r$r*s rWtest_splantiderzTestInterop.test_splantiders&&$''" 0AQSSCH$B##((*CAveeC2%#))AB-*?!@@A 0]((!##((*c133)?@eAhU;eAhU;ttuQx'''!"g...!%/// 0 0rkc|j|j|j}}}|jjdz}d|j||j|dzzz}t ||t ||j|j |jf}}tt||t||dt|tsJt|tsJtt|j j}|j j|dddz} t ||j| |jf} t ||} tt!j"t|| jddd| |dt| tsJt| tsJy)Nr9rr.rZrtrr)rVrrhr2rrr3r4rrrr r$rrrrKrQ) rSrVrrhrtnbntck_nr%rtck_n2bn2s rWrzTestInterop.test_insertsbFFDGGTWWr2 CCHHM !##a&133qs8# $2qM6"qssACCo#>Eb" b%(u 6"g&&&%'''5# $ TT^^BqrFTM *RTT2rtt,-Rn  5V#45??1aHBe -#w'''&%(((rkN)rrrrrr r rrr r%r/r1rrrkrWrrs= -H6-0' D%:C"H(0"0")rkrceZdZejddej zZejeZdZ dZ dZ dZ e jjdgdd Ze jjdgdd Zd Zd Ze jjdgd dZdZdZdZe jjdgddZdZdZdZdZdZe jj=ddZdZ dZ!dZ"dZ#d Z$d!Z%d"Z&d#Z'e jjdgd$d%Z(d&Z)d'Z*d(Z+d)Z,d*Z-y+), TestInterpr=r>cn|j|j|j|jfSr)rQrhr)rSrTs rW_get_xyzTestInterp._get_xys'zz$''"BJJtww$777rkctt5t|j|jddddy#1swYyxYw)NrBrM)rGrHr rhrrSs rWtest_non_int_orderzTestInterp.test_non_int_orders3 9 % 8 tww3 7 8 8 8s #<Ac|j|\}}t||d}t|||ddt||dd}t|||ddy)NrrMrsr[r7r4rr;r rrSrTrhrrVs rW test_order_0zTestInterp.test_order_0Vb!B r2 +"rE: r2 4"rE:rkc|j|\}}t||d}t|||ddt||dd}t|||ddy)Nr.rMrsr[r7r@rArBs rW test_linearzTestInterp.test_linearrDrkr4rc|gd}gd}ttd5t|||dddy#1swYyxYw)Nrr.r9r;r<r)rr.r9r;r<rrrz Shapes of xrrMrGrIr rSr4rwrs rWtest_incompatible_x_yz TestInterp.test_incompatible_x_ys7  $ :] ; * q!q ) * * *s2;cgd}gd}ttd5t|||dddgd}ttd5t|||dddgd}tj|j d}ttd5t|||dddy#1swYxYw#1swYfxYw#1swYyxYw) N)rr.r.r9r;r<rHzx to not have duplicatesrrM)rr9r.r;r<rzExpect x to be a 1D strictly)r.r7)rGrIr rKrQrrJs rW test_broken_xzTestInterp.test_broken_xs   :-G H * q!q ) *  :-K L * q!q ) *  JJqM ! !' * :-K L * q!q ) * * * * * *  * *s#B.B:C.B7:CCc~|j|\}}dD]$}t|||}t|||dd&y)Nr9r;r<rrrrsr[rA)rSrTrhrr4rVs rWtest_not_a_knotzTestInterp.test_not_a_knotsCb!B# ?A"2r1-A AbE2E > ?rkc|j|\}}t||dd}t|||ddtddD]&}t||d|||d |d (t||ddd }t|||ddtddD]&}t||d|||d |d (y) Nrrr3rsr[r.rrr7dy=rtr4r4r)r;r rr)rSrTrhrrVr s rW test_periodiczTestInterp.test_periodicsb!B r2J ?"rE:q! IA AbeNAbfO% H I r2JR H"rE:q! IA AbeNAbfO% H IrkrOcVd}tjjd}tj|j |dz}|j |dz}|d|d<|j ||j |}}t |||d}t|||d y) Nrrrerr7rrr3rsrt)rKrRrrr5rQr r)rSr4rTrUrrwrrVs rWtest_periodic_randomzTestInterp.test_periodic_randoms ii##D) GGC%%a(2- .   a 3 &u!zz!}bjjm1 q!q* =!ae,rkc|jjd}tjj d}|j |dztj z}tj|}d|d<dtj z|d<tjd|f}tj||d<tj||d<|j||j|}}t||ddd }t|D] }t||||dd|fd "t||d||dd y) Nrrr9r=r7r.rrrSrsrt)rhrrKrRrr5rrr)rrrQr rr)rSrTrUrrwrrVr s rWtest_periodic_axiszTestInterp.test_periodic_axis$s GGMM! ii##D)   a 1 $ruu , GGAJ!BEE " HHaV vvay!vvay!zz!}bjjm1 q!q*1 Eq :A AadGQq!tW5 9 :!A$1R56rkc0tjjd}d}d}tj|j |}|j |}|ddz |d<t t 5t|||ddddy#1swYyxYw) Nrrrr7r.rrr3)rKrRrrr5rGrIr )rSrr4rUrwrs rWtest_periodic_points_exceptionz)TestInterp.test_periodic_points_exception5sii##D)   GGC%%a( )   a uqy! : & > q!q* = > > >s 3B  BcPtjjd}d}d}tj|j |}|j |}tj |d|zz}t t5t||||ddddy#1swYyxYw)Nrr;rr9r) rKrRrrr5r)rGrIr )rSrr4rUrwrr2s rWtest_periodic_knots_exceptionz(TestInterp.test_periodic_knots_exception@sii##D)   GGC%%a( )   a  HHQQY  : & 7 q!Q: 6 7 7 7s BB%rct|j|j|d}t|j|jd|}t |j|}t |||jdt d|D]:}t |j||}t |||j| d <y) Nrr3T)rr4rsrtr.rrr)r rhrrrrr)rSr4rVr`r,r s rWtest_periodic_splevzTestInterp.test_periodic_splevKs tww1j ITWWdgg415DGGS!QtwwZe4q! ?A!,C C477q!1 > ?rkc t|j|jdd}t|j|jd}t ||j||jdt j jd}d}t j|j|dz}|j|d z}|d |d <t||dd}t||d}t ||||dy) Nr;rr3rXrsrtrrerr7r) r rhrrrrKrRrrr5)rSrVcubrrUrwrs rWtest_periodic_cubiczTestInterp.test_periodic_cubicXs tww1j I$''477J?$'' CLu=ii##D)  GGC%%a(2- .   a 3 &u! q!q* =!Q 3!c!f51rkcTdt|j|jd}t|jt |j|jt j fd}t||j||jdy)Nr;rr3c,t|tS)Nrr)rrK)rwr3r4r2s rWrz6TestInterp.test_periodic_full_matrix..osK1ar$Brkrsrt)r rhrrrrK vectorizer)rSrVr(r3r4r2s @@@rWtest_periodic_full_matrixz$TestInterp.test_periodic_full_matrixhsu  tww1j I DGGQ ' &twwA > \\B C$'' BtwwKerlrXrsr[r=r)r;rrr rrr)rSrTr4rhrr2rVs rWtest_knots_not_data_sitesz$TestInterp.test_knots_not_data_sitess b!B b! r!u$AB"Sb'!R'! r"v%  r2q!)/6('; = "rE:||AbeQKe<<<||AbfaL#u===rkcd}|jddg}|jddg}t|||dgdgf}|jddd|j}|dz}t |||d d y) Nr;r=r0r.r=rkrXrrErsr[)rQr rfrPr)rSrTr4rwrrVrhrs rWtest_minimum_points_and_derivz(TestInterp.test_minimum_points_and_derivs{  JJBx  JJBx  q!Q'WI0F G [[R2::[ 6 U"rE:rkcgdx}}tt5t||dgdfdddtt5t||ddddtt5t||dgdddtt5t||ddddd\}}tt5t||||fdddy#1swYxYw#1swYxYw#1swYuxYw#1swY[xYw#1swYyxYw)N)r0r9r;r<rrryrX*)ryryrI)rSrwrlrs rWtest_deriv_speczTestInterp.test_deriv_specs%$A : & @ q!wi-> ? @: & 6 q!W 5 6: & 8 q!gY 7 8: & 1 q!R 0 1 "1 : & 5 q!aV 4 5 5 @ @ 6 6 8 8 1 1  5 5s:CC%C) C57DCC&)C25C>D c |jd}|dz}dgdg}}ttd5t||||fddddgdg}}ttd 5t||||fdddy#1swY:xYw#1swYyxYw) Nrr9)rrr.rzBad boundary conditions at 0.rrX)irzBad boundary conditions at 6.)rOrGrIr )rSrTrwrr}r~s rWtest_deriv_order_too_largez%TestInterp.test_deriv_order_too_larges IIaL qDx&1 :-L M 5 q!aV 4 5x'1 :-L M 5 q!aV 4 5 5  5 5  5 5sA8B8BB cd}|j|\}}|d|zz}dgdg}}t|||||f}t|||ddtj||dd |dd d sJtj||d d |dd d sJd D]%}t||| }t|||dd'y)Nr;r/)r.y@)r.y@@rXrsr[rr.rr7rr.rM)r;r rcmathr)rSrTr4rhrrmrnrVs rWrzTestInterp.test_complexs b!B #b&[!zK=u r2q5%. A"rE:}}Qr!ua[%(1+uEEE}}Qr"vq\58A;FFF ?A"2rQ/A AbE2E > ?rkc|jd|j}|jd|j}dD]}t|||}||y)NrerErrM)rOint32r )rSrTrwrr4rVs rW test_int_xyzTestInterp.test_int_xysT IIbI ) IIbI ) A"1a1-A aD rkct|jddd}|ddd}|ddd}dD]}t|||y)Nr7r.rrrrM)rfr )rSrTrhrwrr4s rWtest_sliced_inputzTestInterp.test_sliced_inputsI [[Q $ ssG ssG *A q!q ) *rkc|jd|j}|dz}|j|j|j fD]=}t j |dj |}ttt||?y)NrerEr9r7) rOrPrMrNxpxatsetrGrIr )rSrTrwrzs rWtest_check_finitezTestInterp.test_check_finite"sp IIb I + qD&&"&&266'* @Aq" !!!$A *&8!Q ? @rk)r.r9r;rcvttd}|Dcgc]}|dz }}t|||ycc}w)Nrer9rM)listrr )rSr4rwars rWtest_list_inputzTestInterp.test_list_input+s9 rO aQT  1a1% s 6c|j|\}}|j||fd}dddgfg}dddgfg}t||d||f}t|||d d t||d d|j |d d|j d d t||d d|j |d d|j d d y)Nr.rr0r>r?r@r;r3rsr[rrEr7)r;rr rrQrP)rSrTrhrrmrnrVs rWtest_multiple_rhszTestInterp.test_multiple_rhs2sb!B XXr2hQX 'b"Xb"X r2UEN C"rE: beQK JJuQx{"**J 5E   bfaL JJuQx{"**J 5E rkctjjd}d\}}tj|j|}|j|dddf}t |||}|j j |dddfk(sJd|jdfg}d|jdfg}t |||||f }|j j ||zdz dddfk(sJy) Nrr;rrrrrr.rrrrX)rKrRrrr r3r) rSrr4rUrwrrVd_ld_rs rW test_shapeszTestInterp.test_shapesCsii##D)1 GGCJJAJ& ' JJQ1aLJ ) q!Q 'ssyyQ1aL(((3::i()*3::i()* q!Qc ;ssyyQUQY1a0000rkc|j|\}}|j|}t||dd}t||ddgdgf}t|j|jdt||dd}t||ddgdgf}t|j|jdt||d d }t||d dd gf}t|j|jdt||dd }t||dd}t|j|jdt t 5t||dd ddd|j|j||j|fd}dddgfg}d ddgfg}t||d||f}t||dd}t|j|jdtjjd}d\} } tj|j| } |j| dddf} |j| |j| } } d|jdfg} d|jdfg}t| | | | |f}t| | | d}t|j|jdy#1swYyxYw)Nr;r?r3rlrZrt)r?r>rr9)Nr>ryr@typor.rr=r=rrrrrrrrXr>)r;rr rr3rGrIrrrKrRrrrQr))rSrTrhrr(rrmrnrr4rUrwrrrs rWtest_string_aliaseszTestInterp.test_string_aliasesRsb!B VVBZ B!Y ? B!vh5I Jbdd/ B!(>@ B!*0F8(<>bdd/ B!5F G B!dXJ5G Hbdd/ B!\ B B!T :bdd/: & < r2F ; <XXrvvbz266":.QX 7b"Xb"X B!eU^ D B!(>@bdd/ii##D)1 GGCJJAJ& ' JJQ1aLJ )zz!}bjjm1288I&'(288I&'( 1a#s < 1a ;bdd/1 < rCrFrarzr{rKrMrPrTrVrXrZr\r^rarerirorrr|rurwrzrrrrrrrrrrrrrrkrWr9r9s RBEE "B B88;; [[S,/*0*  [[S,/ *0 *? I  [[S"45 -6 -7" > 7 [[S,/ ?0 ?2 = ,;, T [[j) E* E>& ;5. 5?"*@ [[S,/&0&  " 130j 9?rkr9c|j|jk(sJ|j|j|zdzk(sJ|j}tj||ftj}t |D]R}||}|||k(r|}ntj ||dz }t j||||} | ||||z |dzf<Ttj||} | S)zAssemble an spline order k with knots t to interpolate y(x) using full matrices. Not-a-knot BC only. This routine is here for testing only (even though it's functional). r.rE) rrKr)rPrrr*evaluate_all_bsplslr) rwrr2r4rUArrleftbbr3s rWrrs 66QVV   66QVVaZ!^ ## # A !Qrzz*A 1X !t 1Q4<D??1d+a/D ' '1dD 9 !T!VDF]  ! AA HrkcFttj|||f\}}}|j}|j|z dz }tj||ftj }t |D]R}||}|||k(r|} ntj||dz } tj|||| } | ||| |z | dzf<Ttj|j|} tj|j|} tj| | } | || ffS)z,Make the least-square spline, full matrices.r.rE)rvrKrQrr)rPrrr*rdotTrr)rwrr2r4rrUrrrrrrYr3s rWmake_lsq_full_matrixrs "**q!Qi(GAq! A  QA !Qrzz*A 1X !t 1Q4<D??1d+a/D ' '1dD 9 !T!VDF]  ! qssAA qssAA AA q!f9rkmethodnorm-eqqrc eZdZejj dZd\ZZejej eZ ej eZ e eje de ddeZedZedZdZed Zed Zd Zed Zd ZedZedZedZedZedZej<j?de e!dddZ"dZ#y)TestLSQr)rr;rr7rc|j|j|j|jf\}}}}t ||||\}}t |||||}t |j||jj|j|z dz fk(sJ|\} } tjj| |d\} } } } t |j| y)Nrr.r7)rcond) rwrr2r4rrrr3rrrKrlstsq) rSrrwrr2r4c0AYrVaarrrs rW test_lstsqzTestLSQ.test_lstsqsVVTVVTVVTVV3 1a%aAq1B Aq!Qv 6R ssyyQVVaZ!^----Biioob!2o6 Aq!R rkcgt|j|j|j|jf|j \}}}}|j |}t|||||}t||||||} t|j| jdt|j| jd|j | j k(sJy)Nrwrrsrt) rvrQrwrr2r4rnrrr3) rSrrTrwrr2r4rrVb_ws rW test_weightszTestLSQ.test_weightssHc"**tvvtvvtvv&>?GG 1a LLO Aq!Qv 6aAqAf=SUU/SUU/sscee||rkcTgt|j|j|j|jf|j \}}}}t jjdj|jd}|j|}t|||||d}t|||||d}t||||d} t|j|jd |j|j| j|jz dkrJy) Nrrrrrrrrsrt)rvrQrwrr2r4rKrRrrrrrr3rabs) rSrTrwrr2r4rb_neb_qrb_no_ws rWtest_weights_samezTestLSQ.test_weights_samesGc"**tvvtvvtvv&>?GG 1a II ! !$ ' / /QWWQZ / @ JJqMq!QQyAq!QQt< Aq!D9U366"&&DFF!23e;<<<$$5;7a"Q%''78::qss/ $7s 0D((D-cgt|j|j|jf|j|j \}}}}d}t jj||f}|j|}t||||d}t||||d} t|j| jdy)Nr;rrrrrZrt) rvrQrwr2r4rUrKrRrrr3) rSrTrwr2r4rUrrrb_neqs rWtest_multiple_rhs_3zTestLSQ.test_multiple_rhs_3:sGc"**tvvtvv&67GGG 1a II  1d)  , JJqMq!Q$71a9=e4rkcgt|j|j|jf|j\}}}|j|j dz}t |||||}t ||j||||}t ||j||||} t||||d| |zzddy)N?@rr/rZr[) rvrQrwr2r4rrrrr) rSrrTrwr2r4rOrVrrs rWrzTestLSQ.test_complexCs=3rzzDFFDFF#34rZrt)rKrOfloat32rrrfloatr)rSrrwrr2spl_f32spl_f64x2s rW test_f32_xyzTestLSQ.test_f32_xyms IIb + IIb + AO!!QQv>! HHUOQXXe_ahhuo6 eafn # WR[u=rkctjddd}|ddd}|ddd}t|d}t|||d|y)Nr7r.rr;r)rKrfrr)rSrrhrwrr2s rWrzTestLSQ.test_sliced_inputzsK[[Q $ ssG ssG AqM1a1V4rkc tjdjt}|dz}t |d}tj tj tj fD] }||d<ttt||||"y)N r9r;r7r) rKrOrrrrMrNrGrIr)rSrrwrr2rs rWtest_checkfinitezTestLSQ.test_checkfinitesq IIbM  ' qD AqM&&"&&266'* OAAbE *oq!Qv N Orkc|j|j|j}}}|jd|jd|jdt ||||y)NFrd)rwrr2r)rwrr2rfrrs rWrgzTestLSQ.test_read_onlysU&&$&&$&&a1      !qAf5rkr4r.c|j|j}}ttj|d|dd|}t ||||d}t ||||d}|dd|ddzdz }t ||||d y) Nrr7rrrrr.r>rZrt)rwrrrKrfrr)rSr4rwrr2 spl_norm_eqspl_qrrhs rWtest_qr_vs_norm_eqzTestLSQ.test_qr_vs_norm_eqsvvtvv1 BKK!aeQ/ 3%aA9E  AqAd;eafn # B%@rkcdtj|jd}tj|jd}t |j|j|j dd}t |||j dd}|dd|ddzdz }t ||||d y) Nr9r;rrr.r7r>rZrt)rKrepeatrwrrr2r)rSrwrrspl_2rhs rWtest_duplicateszTestLSQ.test_duplicatess IIdffa  IIdffa !DI1dff$?eafn #b 5959rkN)$rrrrKrRrrrUr4rrwrrrfr2parametrize_lsq_methodsrrrrrrrrrrrrrgrarzr{rrrrrrkrWrrsz ))   %C DAq 1 A 1 A  AaD!B%+Q/A ! !   =:: 0 05 M MM,55 > >55OO66 [[S$uQ{"34A5A:rkrc,eZdZdZdZedZdZy) PackedMatrixasA simplified CSR format for when non-zeros in each row are consecutive. Assuming that each row of an `(m, nc)` matrix 1) only has `nz` non-zeros, and 2) these non-zeros are consecutive, we only store an `(m, nz)` matrix of non-zeros and a 1D array of row offsets. This way, a row `i` of the original matrix A is ``A[i, offset[i]: offset[i] + nz]``. c||_||_||_|jdk(sJ|jdk(sJ|jd|jdk(sJy)Nr9r.r)rrncrr)rSrrrs rW__init__zPackedMatrix.__init__sW vv{{{{awwqzV\\!_,,,rkcL|jjd|jfSNr)rrrr=s rWrzPackedMatrix.shapesvv||A''rkcjtj|j}|jjd}t |jdD]_}t |j |j|z |}|j|d|f|||j||j||zf<a|S)Nr.r)rKr)rrrminrr)rSoutnelemr nels rWtodensezPackedMatrix.todenseshhtzz" Qsyy|$ JAdgg A.6C:>&&DSD/C4;;q>$++a.3"666 7 J rkN)rrr__doc__rpropertyrrrrkrWrrs%-((rkrc 6ddlm}|j}|j}|j}|j \}}|j d|k(sJ|j } |j } t||D]} || } t| |D]} | t| |k\r(|| | df| | df\}}}|| | df<td|D]*}t||| | |f| | |f\| | |f<| | |dz f<,d| | df<t| j dD]'}t||| | |f| | |f\| | |f<| | |f<)tt| j d}t| tj|tj|}|| fS)zjThis is a python counterpart of the `_qr_reduce` routine, declared in interpolate/src/__fitpack.h r)dlartgr.r=r7rE)scipy.linalg.lapackr rrrrrrrfprotarrrKrGint64)a_prstartrowr rrrrnzRrr oirr3rr~r}offsR_ps rW _qr_reduce_pyrs+ A ZZF B GGEAr 771:?? A B 8Q F AYr2 FAC2JQq!tWa1g.GAq!AadG1b\ D%+Aq!AqD'1QT7%C"!Q$1ac6 DAaeH288A;' F%+Aq"QT(Bq!tH%E"1a4"QT( F FF* aggaj! "D q"((4rxx8" =C 7Nrkc8||z||zz}| |z||zz}||fS)zLGivens rotate [a, b]. [aa] = [ c s] @ [a] [bb] [-s c] [b] r)r3rrrVrrs rWr r s1 A#!)B A!B r6Mrkc|j}|j\}}|j}|jd|jdk(sJtj|d|}||dz ||dz dfz ||dz df<t |dz ddD]P}t |||z }||d|df||dz||zdfzjd} ||| z ||dfz ||df<R|S)zBacksubsitution solve upper triangular banded `R @ c = y.` `R` is in the "packed" format: `R[i, :]` is `a[i, i:i+k+1]` rNr..r9r7r)rrrrKrrrr) rrrrrrr3r rsumms rWfpbackrs A GGEAr B 771: ## # afART7Qr!tQwZ'AbdCiL 2a4R ."bdm!QsUD.!Aac!C%in$55:::BdTka1g-!S& . Hrkc0eZdZdZdZdZdZdZdZy) TestGivensQRc|d}tj|t}|dzdd|zz z}t||}||||fS)Nr;rEr.)rKrOrr)rSrUr4rwrr2s rW_get_xytzTestGivensQR._get_xytsF  IIau % qD1ac7N 1 !Qzrkc td}|j|\}}}}tj|||}tj|j \}}|j |z} |j\} } | |jd|z dz k(sJ|jdd|dz} tj| tj} |jj| |dz} t| | | }|dddf}tj | | | |t#tj$|j |z|j |z tj&|dt#tj$t)| |dddfz t)| |dddfztj&| dtj*|| }tj,|j.|j0||||tj2||\}}}t#||dddfdy) Nrerr.rErZrtgvIh%L=-a=)rr r8rrrrrindicesrKascontiguousarrayr datarrr* qr_reducerminimumrrrrrrrn)rSrUrwrr2r4a_csrqr~qTyrrrrry_c_fullc_bandedrs rW test_vs_fullzTestGivensQR.test_vs_full#s ]]1% 1a%%aA.uuU]]_%1ccAg 2QWWQZ!^a''''w!A#w'%%fBHH= JJ  q!A# & FB ' q$wZ1fb"-  199;?#$99;?457]]15EE S 3sR1X~#6#&sR1X~#689;s9KRW Y!S!!addAr1aaRTU!QAU;rkcd}|j|\}}}}tj|||}|j\}}||jd|z dz k(sJ|jdd|dz} t j | t j} |jj||dz} t| | |} |dddf} t| | \} }tj| | || t| j| jdt!| j"| j"d| j$| j$k(sJt|| dy) Nrerr.rErZrtF) check_dtype)rr r8rrrKr r r!rrrr*r"rrrrr)rSrUrwrr2r4r$rrrrrr'RRrs rWtest_py_vs_compiledz TestGivensQR.test_py_vs_compiledFs, ]]1% 1a%%aA. 2QWWQZ!^a''''w!A#w'%%fBHH= JJ  q!A# & FB ' q$wZq"%B1fb2.acc. 188?uu}}BU+rkc6d}|j|\}}}}tjd|dzt}t j ||||\}}} |j d} tj|||} | |dddfzj} | jj| |dzf} | jdd|dzjtj}t|| dt!||| |j d|z dz k(sJy)Nrer.rErrZrt)rrKrOrr* data_matrixrr r8tocsrr!rrrr rr)rSrUrwrr2r4rrrrrr$a_wA_offset_s rWtest_data_matrixzTestGivensQR.test_data_matrixas ]]1% 1a IIa1E * ,,Q1a8 62 GGAJ%%aA.qDz!((* XX  q!A#h '++g1g&--bhh72E*(QWWQZ!^a''''rkc d}|j|\}}}}tj||dzf}tj|||tj |\}}}t |||} tj||||t| |} tj||||||tj ||\} } } t| | dy)Nrer9rsrt) rrKrr*r0rnrr"rr) rSrUrwrr2r4rrrrr3rrs rW test_fpbackzTestGivensQR.test_fpbackrs ]]1% 1a EE!QT'N ,,Q1bll1oF 62 FB '1fb!, 1aL??1b!Q1bll1oqIAqAE*rkc d}|j|\}}}}tj|dzft}|D]N}t t j |||||dz|t t j ||||d|z|Py)Nrer.rEr9)rrKr)rrr*r)rSrUrwrr2r4 zero_arrayrs rWtest_evaluate_all_bsplz#TestGivensQR.test_evaluate_all_bspls ]]1% 1aXXq1uhe4  LD **1aq!a%@* N **1aq!A#>  L LrkN) rrrrr*r.r5r7r:rrkrWrrs"! ? ( !!Q ' ( (+ , , , , 6 6 . .  - - ( (sHG:G!G(G4 H8 H GG%(G14G=H  Hctjtd5}|d}|d}|d}dddt|}t |dddy#1swY,xYw) ae Data is generated in the following way: >>> np.random.seed(1234) >>> n = 100 >>> x = np.sort(np.random.random_sample(n) * 4 - 2) >>> y = np.sin(x) + np.random.normal(scale=.5, size=n) >>> np.savetxt('x.csv', x) >>> np.savetxt('y.csv', y) We obtain the result of performing the GCV smoothing splines package (by Woltring, gcvspl) on the sample data points using its version for Octave (https://github.com/srkuberski/gcvspl). In order to use this implementation, one should clone the repository and open the folder in Octave. In Octave, we load up ``x`` and ``y`` (generated from Python code above): >>> x = csvread('x.csv'); >>> y = csvread('y.csv'); Then, in order to access the implementation, we compile gcvspl files in Octave: >>> mex gcvsplmex.c gcvspl.c >>> mex spldermex.c gcvspl.c The first function computes the vector of unknowns from the dataset (x, y) while the second one evaluates the spline in certain points with known vector of coefficients. >>> c = gcvsplmex( x, y, 2 ); >>> y0 = spldermex( x, c, 2, x, 0 ); If we want to compare the results of the gcvspl code, we can save ``y0`` in csv file: >>> csvwrite('y0.csv', y0); z gcvspl.npzrwry_GCVSPLN-C6?F)r\r]r,)rKloadrBrr)rSr!rwrrKy_comprs rWtest_compare_with_GCVSPLz,TestSmoothingSpline.test_compare_with_GCVSPLsqRWWY|, - (S AS AJ'H  ( .'1-a0 4US ( (s AA#ctjjd}d}tj|j |dzdz }|dztj d|zz|dzz|j dd|z}|j||j|}}t||d}t||dd }|j|d |d d|z}t||||d y)z In case the regularization parameter is 0, the resulting spline is an interpolation spline with natural boundary conditions. rrr<r9r;r=r)lamr?rXrr7rZrtN) rKrRrrr5rrFrQrr rfr) rSrTrrUrwr spline_GCV spline_interpgrids rWtest_non_regularized_casez-TestSmoothingSpline.test_non_regularized_cases ii##D)  GGC%%a(1,q0 1 qD266!a%= 1a4 '#**Ra*@ @zz!}bjjm1*1aR8 *1aIF {{1Q42A. 4(%d+" $rkr9ctjjd}d}tj|j |dzdz }|dztj d|zz|dzz|j dd|z}t|j||f\}}t||}|jtdd D]}|j|}tj|t|j!d t|||} t#|||||z } t#| ||||z } | | kst%d | d d | d y)Nrrr<r9r;r=rrerg>@zJSpline with weights should be closer to the points than the original one: z.4z < )rKrRrrr5rrFrvrQrchoicerrrrrrrrI) rSrTrrUrwrr,indrspl_worigweighteds rWtest_weighted_smoothing_splinez2TestSmoothingSpline.test_weighted_smoothing_spline sZii##D)  GGC%%a(1,q0 1 qD266!a%= 1a4 '#**Ra*@ @2::1v&1#Aq)::eCjr:2 3C A FF1c#h  # #C ()!Q2Es1S6{QsV+,D53=1S612Hh $CCG)3$,R="233 3rkN) rrrrIrOrUrarz fail_slowr\rrkrWrDrDs6 (>6Tp$* [[133rkrDc  |\ |\tz dz }|dzk\sJtz dz dzk\sJt fdt|D}tj|S)z-A naive 2D tensort product spline evaluation.r.c 3K|]9}tD])}||ft|zt |z+;ywr)rr) rixiyr3r4nytxtyrwrs rWrzbspline2..' sU7E"I7&(Bi!Aq"b/)AaBO;7;7s?A)r7rrrKrQ) rr2r3r4nxrrbrcrdrwrs `` @@@@@rWbspline2rf s DAq FB R1qB !A#II R1qB !A#II 77b 7 7C ::c?rkcb|dk(r|||cxkr ||dzkrdSdS|||z||k(rd}n)|||z |||z||z z t||dz ||z}|||zdz||dzk(rd}||zS|||zdz|z |||zdz||dzz z t||dz |dz|z}||zS)Nrr.r0r=rrs rWrr, sAvda(!AaC&(s1(c11v1~ !A$h1Q3!A$ '!AqsAq/ 91Qx1QqS6  7N!AhlQqs1uX!A#. /!AqsAaC2C C 7Nrkctz dz }|dzk\rt|k\sJtfdt|DS)Nr.c3FK|]}|t|zywrrhrs rWrzbspline..= s$6qta1am#6r)r7rr)rwr2r3r4rUs```` rWrJrJ: sD A QA 1H3q6Q;' ' 6U1X6 66rkceZdZddZdZy) NdBSpline0ct|}|t|jksJ t|td|D|_td|D|_||_y#t$r |f|z}YGwxYw)aTensor product spline object. c[i1, i2, ..., id] * B(x1, i1) * B(x2, i2) * ... * B(xd, id) Parameters ---------- c : ndarray, shape (n1, n2, ..., nd, ...) b-spline coefficients t : tuple of 1D ndarrays knot vectors in directions 1, 2, ... d ``len(t[i]) == n[i] + k + 1`` k : int or length-d tuple of integers spline degrees. c3FK|]}tj|ywr)operatorindex)rkis rWrz&NdBSpline0.__init__..Y s6bx~~b)6s!c3RK|]}tj|t!yw)rEN)rKrQr)rtis rWrz&NdBSpline0.__init__..Z s?rrzz"E22?s%'N)r7rrHr$r4r2r3)rSr2r3r4rs rWrzNdBSpline0.__init__A sx1vs177|###  F 6A66?Q??  T A s A((A:9A:cbt|j}t||k(sJdg|z}t|D]}|j|||}}|j|}|||k(r|||<nt j ||dz ||<||||cxkr|||dzksJJ|||k\r||t||z krJt |}d}t|Dcgc]'}t|||j|z ||dz)} }tj| D]o} |j| t jt|Dcgc]0}t|||j|| ||j|2c}z} || z }qt j|Scc}wcc}w)Nnoner.r) r7r2rr4rKrr$ itertoolsproductr3prodrrQ) rSrwrr rtdxdr4ritersidxterms rW__call__zNdBSpline0.__call__] s466{1v~~JtOt 4AVVAY!Bq ARU{!r2.2!ad8r/R!QZ/ // //Q4191B! !3 33 4 !H d}gd}|Dcgc]\}}|dz|dzd|zzz}}}|j|\}}} |j||||fd} d} t|| d} | | } t||| | }| jdk(sJt | |j|gd zd | |jt j|dd | j j|dzk(sJt | ||j||j dddfdd|j| d}t||d}|| } | jdk(sJ|jd|j |z}t | |d ||jt j|dd |j j|dzk(sJt |||j||j ddddfddycc}}w)Nr9rr;rrrrrMr<r<rsrtr7rEFgvIh%,=rrrr9r9)r9r9) rrrrrrKr3rQrPrr)rSrTrrrwrrrrr4c2_4rbspl2_4r val_singlec2_22bspl2_22 target2_22s rWtest_2D_separable_2z!TestNdBSpline.test_2D_separable_2 s /467&1a!Q$!Q$1*%77%%%, BxxRR(qx1 B*)Yr2q)"- ||t###*!12 @ r{  BHHRL"$5 8N$NNNN  6 8+s C Cc tjjd}d}tjddddtj|j ddzddddf }tjddddtj|j ddzddddf }|j |j |z dz |j |z dz f}t||f|| }d }t||t|||f||d tjgd gdf}t|||Dcgc]}t|||f||c}d ycc}w)Nrr;rrrrr<r.rM)r0r0rsrtr.rr9皙?g?@) rKrRrrrrrrrrfr) rSrr4rcrdr3r,rrs rWtest_2D_randomzTestNdBSpline.test_2D_random sAii##E*  UU1aArwws{{{':;a?Aq!K L UU1aArwws{{{':;a?Aq!K L KKbggaik27719Q;7K 8R!q) B b"Xq!45 BUU;"#$B@BC""r2h15C" $Cs7E c|j\}}}}gd}|Dcgc]\}}|dz|dzd|zzz}}}t||||f} | |jt|fk(sJt | ||dycc}}w)N)ffffff?r)rBg333333@)rrr;r9rMrsrt)rrrr7r) rSrrkxkyrrwrrrs rW test_2D_mixedzTestNdBSpline.test_2D_mixed0 s++-BB 1467&1a!Q$!Q$1*%77"bRH-Ry3r7+---b U ,8sBc|j|\}}}}gd}t||||f}dddddd d |zd fd d |zd fdd d|zfdd d|zfdd|zd |zfdi}|jD]y\} } |j|D cgc]\} } | | | c} } |j} ||| }t || d|j | |}t || d{dD]M}tt5|||dddtt5|j |dddOycc} } w#1swY;xYw#1swYlxYw)NrrrrMrc*d|dzz|dzd|zzzSNr;r9rrwrs rWrz2TestNdBSpline.test_2D_derivative..@ sQTQTAaCZ!8rkr.r.c$d|dzzd|zdzzSrrrs rWrz2TestNdBSpline.test_2D_derivative..A sQTQqS1W!5rk)rrc$|dz|dzd|zzzSrrrs rWrz2TestNdBSpline.test_2D_derivative..B sAA!!4rkr9r.cyrrrs rWrz2TestNdBSpline.test_2D_derivative..C rrkrcyrrrs rWrz2TestNdBSpline.test_2D_derivative..D rrkr;cyrrrs rWrz2TestNdBSpline.test_2D_derivative..E rrkcyrrrs rWrz2TestNdBSpline.test_2D_derivative..F rrkcyrrrs rWrz2TestNdBSpline.test_2D_derivative..G rrkrErrsrt))r7rr7rr.) rritemsrQrPrrrGrI)rSrTrrrrrr test_casesr expected_fnrwr expected_valsdirect via_methodbad_nus rWtest_2D_derivativez TestNdBSpline.test_2D_derivative9 s++r+2BB 1"bRH- 8 5 4 rT1I~ rT1I~ "I~ "I~ rT1R4L.   *//1 COB JJ/12tq!Q"2"**'M 2"%F FM >.))"-b1J J E B C# )Fz* %bV$ %z* )  ( ) )  )3 % % ) )sE  E$EE E c tjjd}d\}}tjddddtj|j ddzddddf }tjddddtj|j ddzddddf }|j |j |z d z |j |z d z f}tjgd gd f}t||f|||f }t||f|||f } t|||D cgc] } | |  c} d ycc} w)Nr)r9r;rrrr;rr<r.rrrMrsrt) rKrRrrrrrrrrlr rSrrrrcrdr3rrbspl2_0rTs rWtest_2D_mixed_randomz"TestNdBSpline.test_2D_mixed_random_ s.ii##E*B UU1aArwws{{{':;a?Aq!K L UU1aArwws{{{':;a?Aq!K L KKbgglQ." q0@AK B UU;"#$2r(A"b2b"XqRH5b /122 @2s*E ctjd}tjddz}t||dzd}t||dzd|zzd}|jdddf|jdddfz}t |j |j f||j |j f}|dzdddf|dzd|zzdddfz}t||f|}tj||D cgc] \} } | | f } } } || } tj| jrJt| || dt| j|j|dycc} } w) Nrrrr;rMr9rsrt)rKrOr r3rr2r4rrvrwranyrrr) rSrwrspl_xspl_yrrvaluesrgirrVrbxis rWtest_tx_neq_tyzTestNdBSpline.test_tx_neq_tyo sM IIaL IIaL3 "1ada0"1adQqSjA6 WWQW a 0 0%''577+R%''5771CDQ$4AqD1Q3Ja#88%q!ff5!*!2!21a!8 9Aq!f 9 92h88C=$$&&&SW51 FLL16F :s<E6c|jd}|dz}t||d}|dzd|zz}t||d}|dzd|zzdz}t||d}|j|j|jf} |jddddf|jddddfz|jddddfz} | | dfS)Nrr;rMr9r.r) rSrTrwrr,rry_2rrrs rW make_3d_casezTestNdBSpline.make_3d_case s IIaL qD A+dQqSj"1cQ/dQqSj1n"1cQ/eeUWWegg &eeAtTM"ggdAtm$%ggdD!m$%2qyrkctjjd}|jddz\}}}|dz|dzd|zzz|dzd|zzdzz}|j \}}}t ||d} t |||D cgc]} | } } | | } | jd k(sJt| |d ycc} w) Nrr;rDrrr;r9r.rMrDrsrt) rKrRrrrrziprr) rSrrwrrrt3c3r4bspl3rrrs rWtest_3D_separablezTestNdBSpline.test_3D_separable sii##E*++7++a/1aAA!$1qs Q7%%' B"bA&Q1 &Aa & &r||u$$$U3's B=c ^|j|\}}}t||d}tjj d}|j ddz\}}} t ||| D cgc]} | } } |j| } dd d d d d } | jD]z\}}| Dcgc]\}}}||||}}}}|j||j}t|| ||dt|j|| |d|ycc} wcc}}}w)Nrrr;rMrrrrcHd|dzz|dzd|zzz|dzd|zzdzzS)Nr;r9r.rrwrrs rWrz2TestNdBSpline.test_3D_derivative.. s4q1a4x1a4!A#:'>!Q$1*q.'QrkcBd|z|dzd|zzz|dzd|zzdzzSNrr;r9r.rrs rWrz2TestNdBSpline.test_3D_derivative.. s0q1u1qs ';q!taczA~'NrkcBd|zd|dzzdzz|dzd|zzdzzSrrrs rWrz2TestNdBSpline.test_3D_derivative.. s0q1u!Q$ ';q!taczA~'Nrkc*d|zd|dzzdzzdzS)Nrr;r9rrs rWrz2TestNdBSpline.test_3D_derivative.. s q1u!Q$ ';a'?rkcyrrrs rWrz2TestNdBSpline.test_3D_derivative.. rrk))r.rr)r9rr)r9r.r)r9r.r;)r9r.r<rErrsrt) rrrKrRrrrrQrrPrr)rSrTrrr4rrrwrrrxi_nprrrrxi_yi_zi_rs rWtest_3D_derivativez TestNdBSpline.test_3D_derivative s2%%%, B"bA&ii##E*++7++a/1a1aL)q)) ZZ RNN?*   *//1 QOB MRSSMCc[c37SMSJJ}BJJJGM E",m% H 0E,,R04m% P  Q*Ts , D#1D( c jtjjd}d}tjddddtj|j ddzddddf }tjddddtj|j ddzddddf }tjddddtj|j ddzddddf }|j |j |z dz |j |z dz |j |z dz f}t|||f|| }t|||f|| }d } t|| || d tjgd gdgdf} t|| | D cgc] } ||  c} d ycc} w)Nrr;rrrrr<r.rM)r0r0r.rsrtrrg?rgffffff?) rKrRrrrrrrrlrr) rSrr4rcrdtzr3r,spl_0rrTs rWtest_3D_randomzTestNdBSpline.test_3D_random sii##E*  UU1aArwws{{{':;a?Aq!K L UU1aArwws{{{':;a?Aq!K L UU1aArwws{{{':;a?Aq!K L KKbggaik27719Q; ! DK ER a1-BB<a0 Br7 UU;""#$ Bb!9%)!9F!9sF0 c tjjd}d}tjddddtj|j ddzddddf }tjddddtj|j ddzddddf }tjddddtj|j ddzddddf }|j |j |z dz |j |z dz |j |z dz f|j |j |z dz |j |z dz |j |z dz fd zz}t|||f|| }t|||f|j| }t|||f|j| } tjgd gd gd f} t|| || d | | zzdy)Nrr;rrrrr<r.r/rMrrrrsrt) rKrRrrrrrrrrrr) rSrr4rcrdrr3r,rrrs rWtest_3D_random_complexz$TestNdBSpline.test_3D_random_complex sii##E*  UU1aArwws{{{':;a?Aq!K L UU1aArwws{{{':;a?Aq!K L UU1aArwws{{{':;a?Aq!K L [[rwwqy{BGGAIaK1E[ F [[rwwqy{BGGAIaK1E[ Fr IJR a1-BB<15BB<15 UU;""#$ Br Rr ]2 @rk cls_extrapNT call_extrapcR|j\}}}t||d|}gdgdgd} }}ttj||| f\}}} t ||| D cgc]} | } } |dz|dzd|zzz| dzd| zzdzz} || |} t | | d ycc} w Nr;)r4r)r7r)r+rr)r7g@r9r.rrsrtrrrvrKrQrr)rSrrrrr4rrwrrrrrrs rWtest_extrapolate_3D_separablez+TestNdBSpline.test_extrapolate_3D_separable s%%' B"bA:>a1bjj1a),1aQ1 &Aa & &AA!$1qs Q7r{3U3 's B$r)FT)TNc\|j\}}}|\}}t||d|}gdgdgd} } }ttj|| | f\}} } t || | D cgc]} | } } |dz| dzd| zzz| dzd| zzdzz} || |}t || d ycc} wrr)rSrrrr4rrrrwrrrrrrs rWtest_extrapolate_3D_separable_2z-TestNdBSpline.test_extrapolate_3D_separable_2 s%%' B"( K"bA:>a1bjj1a),1aQ1 &Aa & &AA!$1qs Q7r{3U3 's% B)c|j\}}}t||d}gdgdgd}}}ttj|||f\}}}t |||Dcgc]}|} }|dz|dzd|zzz|dzd|zzdzz} || d } tj | d sJtj | d sJt| dd | dd d ycc}w)Nr;rM)rr.r)r+rr)r7rrr9r.Frrr7rsrt)rrrvrKrQrrr) rSrrr4rrwrrrrrrs rW#test_extrapolate_false_3D_separablez1TestNdBSpline.test_extrapolate_false_3D_separable s%%' B"bA&nna1bjj1a),1aQ1 &Aa & &AA!$1qs Q7ru-xxq """xxr ###q fQrl? 's Cc |j\}}}t||d}tjddtjdddtjg}tjdddtjdd d g}tjd dddtjd d g}t |||Dcgc]}|} }|dz|dzd|zzz|dzd|zzdzz} tj |tj |ztj |z} tj| | <|| } tj | | jsJt| | d ycc}w)Nr;rMrr.r9rr+rrr7rrsrt) rrrKrQrMrrrr) rSrrr4rrwrrrrrrrs rW test_x_nan_3DzTestNdBSpline.test_x_nan_3D sD%%' B"bA& JJArvvq!Q7 8 JJCBFFAsC8 9 JJCArvvsC8 9Q1 &Aa & &AA!$1qs Q7xx{RXXa[(288A;6vvt rxxt %))+++U3's> E<c tjjd}d\}}tj|j ddd}tj |df|z||df|zf}tj|j ddd}tj |df|z||df|zf}|dddj jrJ|dddj jrJ|j |jdz|z d z |jdz|z d z f }|j}|j jrJtjgd gd f}t|ddd|dddf|||f }t|ddd|dddf|||f } t|||D cgc] } | |  c} dycc} w)Nrr;r;rr<rr7r9r.rrrrMrsrt)rKrRrrrrflags c_contiguousrrrrrlrrs rWtest_non_c_contiguousz#TestNdBSpline.test_non_c_contiguous$ sii##E*B WWS[[QQR[8 9 UUBqE8B;RVIbL0 1 WWS[[QQR[8 9 UUBqE8B;RVIbL0 1cc7==----cc7==---- KKbggqj2o1277A:?Q3FGK H CC77'''' UU;"#$2cc7BssG,aB8<b1gr#A#w/r2h?b /122 @2s:G c|j\}}}t||d}tdD]}d||j_d|j_t||d}|d|dk(sJy)Nr;rMFr()rrrr writeable)rSrrr4rr bspl3_s rW test_readonlyzTestNdBSpline.test_readonly= sy%%' B"bA&q *A$)BqEKK ! *"2rQ'Y6)#4444rkcr|j\}}}tjgdgdg}t|||j |||}tj|||||g}|j d|j dk(sJt |j|jdtt5tjgd||gdzdddttd5tjd d gg||gdzdddy#1swYBxYw#1swYyxYw) Nr()r<rrrgؗҜ ? 9  # #aVHb1#a% 8 9 9 : : 9 9sD!9D-!D*-D6c tjjd}d}tjddddtj|j ddzddddf }tjddddtj|j ddzddddf }tjddddtj|j ddzddddf }|j |j |z dz |j |z dz |j |z dz f}t|||f|| }d }td ||y) Nrr;rrrrr<r.rMcLtjgdgdgdf}||y)Nrrr)rKr)rr,rs rWrjz1TestNdBSpline.test_concurrency..worker_fnb s&{&&'(B Grkre) rKrRrrrrrrr&) rSrr4rcrdrr3r,rjs rWrkzTestNdBSpline.test_concurrencyX s+ii##E*  UU1aArwws{{{':;a?Aq!K L UU1aArwws{{{':;a?Aq!K L UU1aArwws{{{':;a?Aq!K L KKbggaik27719Q; ! DK ER a1-  Is3rk)rrrrrKrrrrrrrrrrrrrrrrarzr{rrrrrrr rkrrkrWrr} sB,!  " &*9X)$V>&$&,$)L@ G(!& 4Q0G&@& [[\D$<8 [[]T4L9 4:9 4 [[X |'DE4F4 @ 4$@2 5 94rkrc<eZdZdZdZej jdgddZdZ dZ dZ d Z ej jd e je jgd Zd Zej jd gddZdZy) TestMakeNDctjd}tjddz}|dddfdz|dzd|zzdddfz}tj||Dcgc] \}}||f }}}t ||f|d}t |||j dt||dzd}t||dzd|zzd} |jdddf| jdddfz} t | |jd d d d l m } | ||f|d } t | |||dycc}}w)Nrrr;r9r.rMrZrtrRrr[)rlinearrrs) rKrOrvrwr'rravelr r3scipy.interpolater) rSrwrrrrVrrrrrRGIrs rWtest_2D_separable_simplez#TestMakeND.test_2D_separable_simplel s1 IIaL IIaL3 1d7Q!Q$1*dAg!66!*!2!21a!8 9Aq!f 9 9Aq66Q/R&,,.u=#1ada0"1adQqSjA6 WWQW a 0 0DFFQ7 E1a&&2Bb6:s&D?ctjd}tjd}tj||Dcgc] \}}||f }}}|dddfdz|dzd|zzdddfz}tj||||f}t ||f|dt j}||} tj||||fjt} | jdk(sJt| jddd| d|jd } t ||f| dt j}||} | jd k(sJt| jdddd| jd dycc}}w) Nrr;r9r4solver)$r<r<rsrtr)rr9r9) rKrOrvrwrr'sslspsolverrrrr) rSrwrrrVrrvalues4rrrvalues22s rWtest_2D_separable_trailing_dimsz*TestMakeND.test_2D_separable_trailing_dims si IIaL IIaL!*!2!21a!8 9Aq!f 9 91d7Q!Q$1*dAg!66))VVVV<=Aq67a DbFFFF;<CCEJ||w&&&q!Q/U ,??<0Aq68qEb||z)))q!Q2|45 B':sF r4)rr)r;r.)r.r;rc~tjd}tjddz}tj||Dcgc] \}}||f }}}|dzdddf|dzd|zzdddfz}t ||f||t j }t|||jdycc}}w) Nrrrr;r9rrZrt) rKrOrvrwr'rrrr) rSr4rwrrrVrrrs rWrzTestMakeND.test_2D_mixed s IIaL IIaL3 !*!2!21a!8 9Aq!f 9 9Q$4AqD1Q3Ja#88Aq66Qs{{CR&,,.u= :sB9c*tjd}tjddz}tj|d<|dddfdz|dzd|zzdddfz}tt5t ||f|ddddy#1swYyxYw)Nrrr7r;r9r.rM)rKrOrMrGrIr')rSrwrrs rW test_2D_nanszTestMakeND.test_2D_nans s IIaL IIaL3 "1d7Q!Q$1*dAg!66 : & - A! , - - -s /B  Bc tjgd}tjgd}tjgdgdgdgdgdgdg}|||fS)N)rr>r?r@rr)r.r9r.r9r.r.)r.r9r;r9r.r.)r.r9r9r9r.r.)rKrG)rSrwrrs rW_get_sample_2d_datazTestMakeND._get_sample_2d_data sR HH. / HH. / HH""""""   !Qwrkc|j\}}}t||f|d}t||f|d}tjgdgdgj }t ||||dy) Nr.rMrrr.gffffff@g333333@rffffff @333333?r;r.r%r&r@rUr0r;rsrtr"r'rrKrGrrrSrwrrrrrs rWtest_2D_vs_RGI_linearz TestMakeND.test_2D_vs_RGI_linear sq**,1aAq61*%q!faA XX66899:  R#b'6rkc|j\}}}t||f|dtj}t ||f|d}t j gdgdgj}t||||dy) Nr;r cubic_legacyrr$r'rsrt r"r'rrrrKrGrrr)s rWtest_2D_vs_RGI_cubiczTestMakeND.test_2D_vs_RGI_cubic sw**,1aAq61#++>%q!faG XX66899:  R#b'6rkrc|j\}}}t||f|d|d}t||f|d}tjgdgdgj }t ||||dd y) Nr;ư>)r4rr]r,rr$r'rsrr[r()rSrrwrrrrrs rWtest_2D_vs_RGI_cubic_iterativez)TestMakeND.test_2D_vs_RGI_cubic_iterative sy **,1aAq61&tD%q!faG XX66899:  R#b'DArkc|j\}}}t||f|dtj}t ||f|d}t j gdgdgj}t||||dy) Nrrquintic_legacyrr$r'rsrtr-r)s rWtest_2D_vs_RGI_quinticz!TestMakeND.test_2D_vs_RGI_quintic sx**,1aAq61#++>%q!fa8HI XX66899:  R#b'6rkzk, meth))r.r)r;r,)rr3ctjjd}tj|j d}tj|j d}tj|j d}|j d}t |||f||t j}t|||f||} tjj d d d } t|| | | d y)Ni@rrrrr#rrgffffff?rrCrrsrt) rKrRrcumsumrr'rrrr) rSr4methrndmrwrrrrrrs rWtest_3D_random_vs_RGIz TestMakeND.test_3D_random_vs_RGI syy$$V, IIdlll* + IIdlll* + IIdlll* +9-Aq!9f#++F%q!QiE YY  3Sw  ?R#b'6rkc:|j\}}}ddi}ttd5t||f|fddi|dddttd5t||ft j ||ffddi|dddy#1swYJxYw#1swYyxYw)Nmaxiterr.rrr4r;)r"rGrIr'rKr)rSrwrr solver_argss rWtest_solver_err_not_convergedz(TestMakeND.test_solver_err_not_converged s**,1a !n :X 6 7 A 6Q 6+ 6 7:X 6 G A 1a& 1 FQ F+ F G G 7 7 G GsB'BBBN)rrrrrrarzr{rr r"r*r.rgmresgcrotmkr1r4r9r=rrkrWrrk s7(B4 [[S"JK>L>- 77 [[X 3;;'?@ BA B7 [[N 7 7GrkrcHeZdZdZdZdZdZdZdZdZ dZ d Z d Z y ) TestFpcheccd}tjdjdd}tjd}tjt d5t j|||dddtjt d5t j|||dddy#1swYExYw#1swYyxYw)Nr.rr9rz 1D sequencer)rKrOrrar rI_bfpcheckrSr4r2rws rW test_1D_x_tzTestFpchec.test_1D_x_t s  IIbM ! !!Q ' IIbM ]]:] ; JJq!Q  ]]:] ; JJq!Q       sB4C4B=C cd}d|dzzdz }|dz}tj|}tj|}tj|||dk(sJt j t d5tj|||dddd|dzzdz}||z dz }tj|}tj|}tj|||dk(sJt j t d5tj|||dddy#1swYxYw#1swYyxYw)Nr;r9r.rDrez Need k+1*r) rKrOdfitpackfpchecrar rIrCrD)rSr4rUrr2rws rWtest_condition_1zTestFpchec.test_condition_1 s  AY] F IIaL IIaLq!Q'2--- ]]:[ 9 JJq!Q   qsGaK EAI IIaL IIaLq!Q'2--- ]]:[ 9 JJq!Q       s4D)D5)D25D>cd}dg|dzzdgzdg|dzzz}gd}tj|||dk(sJtj|||J|j }|d|d<tj|||dk(sJt j td 5tj|||ddd|j }|d|d<tj|||dk(sJt j td 5tj|||dddy#1swYyxYw#1swYyxYw) Nr;rr.r9r)r.r9r;r<rr7rz Last k knots*rzFirst k knots*rHrIrCrDrrar rI)rSr4r2rwtts rWtest_condition_2zTestFpchec.test_condition_2( s:  C1IOqc1Q3i ' q!Q'1,,,zz!Q"*** VVXA2q"a(B... ]]:_ = ! JJq"a  !VVX21q"a(B... ]]:-= > ! JJq"a  ! !  ! !  ! !s"D2D>2D;>Ecd}dg|dzzddgzdg|dzzz}gd}tj|||dk(sJtj|||Jdg|dzzddgzdg|dzzz}tj|||dk(sJt j t d 5tj|||dddy#1swYyxYw) Nr;rr.r9rr.r9r;rr<rzInternal knots*r)rHrIrCrDrar rIrEs rWtest_condition_3zTestFpchec.test_condition_3> s  C1IA !ac * "q!Q'1,,,zz!Q"*** C1IA !ac *q!Q'2--- ]]:-> ? JJq!Q    s #CC c2d}dg|dzzdg|dzzz}gd}tj|||dk(sJtj|||J|j }|d|d<tj|||dk(sJtj|||J|j }|ddz |d<tj|||dk(sJt j td5tj|||ddd|j }|d dz|d <tj|||dk(sJt j td5tj|||dddy#1swY|xYw#1swYyxYw) Nr;rr.rrPr2zOut of bounds*rr7rL)rSr4r2rwrhs rWtest_condition_4zTestFpchec.test_condition_4K s  C1IQqS ! "q!Q'1,,,zz!Q"*** VVX!1r1a(A---zz!Q"*** VVX!q1r1a(B... ]]:-= > ! JJr1a  !VVX22r1a(B... ]]:-= > ! JJr1a  ! !  ! !  ! !s.F F F  Fcd}gd}gd}tj|||dk(sJtjtd5t j |||dddgd}tj|||dk(sJtjtd5t j |||dddy#1swYexYw#1swYyxYw)Nr.)rrr.r9r9)rrrrqSchoenberg-Whitney*r)rrrrHrIrar rIrCrDrEs rWtest_condition_5_x1xmz TestFpchec.test_condition_5_x1xmj s   q!Q'2--- ]]:-B C JJq!Q   q!Q'2--- ]]:-B C JJq!Q       sB>C >C Ccd}gd}ddg}tj|||dk(sJtj|||Jy)Nr.)rrr.r.rg333333?r)rHrIrCrDrEs rWtest_condition_5_k1zTestFpchec.test_condition_5_k1x sI   #Jq!Q'1,,,zz!Q"***rkcd}dg|dzzdgzdg|dzzz}dgdz}tj|||dk(sJtjtd5t j |||ddddg|dzzdgzdg|dzzz}dgdz}tj|||dk(sJtjtd5t j |||dddy#1swY~xYw#1swYyxYw) Nr;rr.r9rrqrVrrWrEs rWtest_condition_5_1zTestFpchec.test_condition_5_1 s   C1IOqc1Q3i ' CEq!Q'2--- ]]:-B C JJq!Q  C1IOqc1Q3i ' CEq!Q'2--- ]]:-B C JJq!Q       sC, C8,C58Dcd}dg|dzzddgzdg|dzzz}dgdzdgz}tj|||dk(sJtjtd 5t j |||ddddgdzddgz}tj|||dk(sJt j |||Jy#1swYJxYw) Nr;rr.r9rrr<rqrVrrWrEs rWtest_condition_5_2zTestFpchec.test_condition_5_2 s  C1IA !ac * E!GqcMq!Q'2--- ]]:-B C JJq!Q  E!Gq!f q!Q'1,,,zz!Q"***   s B==Ccd}gd}gd}tj|||dk(sJtjtd5t j |||dddy#1swYyxYw)Nr.) rrr9r;r<rrrr)r.r.r.@r`r`rrqrVrrWrEs rWtest_condition_5_3zTestFpchec.test_condition_5_3 s`  ' )q!Q'2--- ]]:-B C JJq!Q    s A##A,N) rrrrFrJrNrRrTrXrZr\r^rarrkrWrArA s4   *!,  !>  +   + rkrActj|||| }tt|dz Dcgc]}|||||dzj  }}||dd}tt|D]'}||dz }||xx|z cc<||dzxx|zcc<)|dxx|dz cc<t t |t |d||fScc}w)z)Split the knot interval into "runs". r.r7r9rZrt)rKrrr7rr) rwr2r4 residualsr`r fpartscarriescarrys rW_splitrg s AaG $B6;CGAI6F Gi1b1g&**, GF G1R!G 3w<  Qq U qs u   2J)B-JCKYe< 2:Hs#Cc\t||||\}}d}d}tt|D]$}||dz||z dkDs|||kDs|}||}&|dk(r td||||dzzdzdz} || } t j || } tj |d| | || df} | S)z Insert a new knot given reduals.ig}Ô%Ir.z5Internal error, please report it to SciPy developers.r9N)rgrr7rIrKrr) rwr2r4rcrdr`idx_max fpart_maxr  idx_newknotnew_knotidx_tt_news rW _add_knotro s1a+JFBGI 3v; " ac7RU?Q 6!9y#8Gq I" $PQQg;GAI.2q8K~H OOAx (E EE!FU)Xqy0 1E LrkceZdZdZej j dgddZdZdZ dZ dZ d Z d Z d Zej j d gd ej j dgddZdZdZy)TestGenerateKnotsctjdt}|dzdd|zz z}d}tjdg|dzzdg|dzzz}t ||||}|||z d z}d d lm}|j||||}t||||} t|| d t ||||} | ||z d z} |j|||| } t|||| } t| | d y)NrrEr;r0r.r=r)r4r2r9r_fitpack_reprorZrt) rKrOrrGrrrtadd_knotror)rSrwrr4r2r,rc_frnew_tnew_t_pyspl2 residuals2new_t2 new_t2_pys rWtest_split_add_knotz%TestGenerateKnots.test_split_add_knot s IIau % qD2q1u:   HHbT1Q3Z2$!*, -aa1-VaZ!O ; Q1i0Q1i0xe4q!qE21gkA% a:6a:6  6rkr4rc0|jd|j}|j||jzdz }t t |||dd}t |||dd}|j||j}t||dy)NrrErr4rr7rZrt) rOrPrrrr"rrQr)rSr4rTrwrr2rMs rWtest_s0zTestGenerateKnots.test_s0 s IIarzzI * FF1RUU719  1Q/ 0 4 AqA #A & ZZ"**Z -2E*rkcd}|j||j}|dz}tt||dd}|j t t j|d}t|d|dy) NrerEr;rrr7rZrt)rOrPrr"rQrrKrrSrTrUrwrknotsris rW test_s0_1zTestGenerateKnots.test_s0_1 sh  IIarzzI * qD^AqA34::k"**Q-;<b 8%8rkcd}|j|}|dz}tt||dd}|jt t j|d}t |d|dy)Nrr;rrr7rZrt)rOrr"rQrrKrrs rW test_s0_n20zTestGenerateKnots.test_s0_n20 s_  IIaL qD^AqA34::k"**Q-;<b 8%8rkc tjd}|dz}tt5t t ||ddddddy#1swYyxYw)Nrer;rr4rnest)rKrOrGrIrr"rSrwrs rW test_s0_nestzTestGenerateKnots.test_s0_nest sJ IIbM qD : & : 1QR8 9 : : :s A  Ac|jd|j}|j|tjzdz }d}t t |||d}gdgdgdgd gd g}|Dcgc]}|j||j!}}t|t|k(sJt||D]\}} t|| d t|||d\}} } t|d |j|d ycc}w)aY To generate the `wanted` list below apply the following diff and rerun the test. The stdout will contain successive iterations of the `t` array. $ git diff scipy/interpolate/fitpack/fpcurf.f diff --git a/scipy/interpolate/fitpack/fpcurf.f b/scipy/interpolate/fitpack/fpcurf.f index 1afb1900f1..d817e51ad8 100644 --- a/scipy/interpolate/fitpack/fpcurf.f +++ b/scipy/interpolate/fitpack/fpcurf.f @@ -216,6 +216,9 @@ c t(j+k) <= x(i) <= t(j+k+1) and store it in fpint(j),j=1,2,...nrint. do 190 l=1,nplus c add a new knot. call fpknot(x,m,t,n,fpint,nrdata,nrint,nest,1) + print*, l, nest, ': ', t + print*, "n, nmax = ", n, nmax + c if n=nmax we locate the knots as for interpolation. if(n.eq.nmax) go to 10 c test whether we cannot further increase the number of knots. rrEr;rr)r=r=r=r=rrrr) r=r=r=r=r@rrrr r=r=r=r=r>r@rrrr) r=r=r=r=r>r@rrrrr) r=r=r=r=r>r?r@rUrrrrrZrtr7N) rOrPrrKrrr"rQr7rrr) rSrTrwrr4rwantedwantr2rMrs rW test_s_switchzTestGenerateKnots.test_s_switch s. IIarzzI * FF1RUU719  ^AqA6726:>A   BHH"**T*4HH5zS[(((' /EAr Ar . /Ad+1ab 2::a=u=Is2$Dc`ttd}t||dd}t|y)Nrrr.)rr4)rrr"next)rSrwgens rWrz!TestGenerateKnots.test_list_input> s& qNQSA. S rkc |jd|j}|j||jzdz }d}t t ||d|d}t |d|jgd|jd tt5t t ||dd dddy#1swYyxYw) NrrErr;rerr7rrZrtr<)r4r) rOrPrrrr"rrQrGrI)rSrTrwrrrs rW test_nestzTestGenerateKnots.test_nestD s IIarzzI * FF1RUU719  ^AqA<= "I JJ?rzzJ R : & 4 12 3 4 4 4s B99Cc tjd}tj|tjzdz }t t 5t t||tjddddt t 5t t||tjd dddy#1swYMxYw#1swYyxYw)NrrDr) rKrOrrrGrIrr"rrs rWrzTestGenerateKnots.test_weightsU s IIaL FF1RUU719  : & 8 1 " 6 7 8: & 6 1 4 5 6 6 8 8 6 6s+C,CCCnpts)rQrqrr)r{Gz?rctjjd}dtj|j |z}tj |tj zdz tj|dz dz z}d}t||||d}tt||||d }t||d y) Nrrerrr9r;rrr7rZrt) rKrRrrrrrexprrr"r) rSrrr8rwrr4r2rMs rWtest_vs_splrepz TestGenerateKnots.test_vs_splrep_ syy$$U+ rwwt|||./ / FF1RUU72: !A# !2 2  1a1 "1 % .Aa0 1" 5AE*rkc*d}tj|}|dz}tt||dd}t j t 5}t||dd}dddtdk(sJt|ddy#1swY,xYw)Nr;Jz5rr.r7r) rKrOrr"rawarnsRuntimeWarningrr7r)rSrUrwrrr~r`s rWtest_s_too_smallz"TestGenerateKnots.test_s_too_smallr s  IIaL qD^AqA78 \\. ) -QAe,C -1v{{b 3q6* - -s B  Bctgdgdgdd}tjtd5t |dddy#1swYyxYw)N)r=r0r>r?)r@rUrr)r=r=r=r=r.)rrzweights are zeror)r"rar rIr)rSrs rWtest_zero_weightsz#TestGenerateKnots.test_zero_weights s=]M]aP ]]:-? @  I   s AAN)rrrr}rarzr{rrrrrrrrrrrrrkrWrqrq s70 [[S/2+3+99:*>X 4"6 [[V]3 [[S.1+24+" +rkrqcZ|jd}|||z dz ||z }|d|zz dz }||dz||z dz }tj|d}|dddxxdz cc<|dddxxdzcc<t|tj||z dz |||}tj |dz |jdft }td|jddD]"} || ddf|| dzddfz || dzddf<$|||z |ztj|z z}|S)zStraitforward way to compute the discontinuity matrix. For testing ONLY. This routine returns a dense matrix, while `_fitpack_repro.disc` returns a packed one. rr.r9NrrrE) rrKrr r6emptyrrr factorial) r2r4rUdeltanrintrstiirmatrr s rW disc_naiver sD  A a!eaiL1Q4 E !GaKE 1Q3qs1uB ))B C!HH1II(266!a%!)$a(3A 88U1Waggaj) 7D 1aggaj! $,!Q$!AaCF)+QT1W , U5[1 t~~a0 00D KrkceZdZdZddZdZy)F_densezm The r.h.s. of ``f(p) = s``, an analog of _fitpack_repro.F Uses full matrices, so is for tests only. Nc||_||_||_||_|t j |t n||_||_|jjdk(sJt|t j|jd|z dz |||}||jdddfz|_ ddlm} t!| j#||j%|_|jdk(sJ||jz} tj(| t j*|j&jdf|_||_y)NrEr.rrrs)rwrr2r4rKrnrrrrr r6ra_denserrtrdiscrb_denserr)rr) rSrwrr2r4rrrrrvrs rWrzF_dense.__init__ s12au-&vv{{aU'!RVVAGGAJNQ$67 TUVW40 ;#SXXa^4<<> vv{{ Z%%BHHT\\%7%7%:;;<rkctj|j|j|z f}ddlm}m}||d\}}|j|jz}|jd}||d|d|f|d|} t|j| |j|j} tj|jdz| |j |j"z dzz} | |_| |j&z S)Nr)rreconomic)rnr.rr9)rKvstackrr scipy.linalgrrrrrr r2r4rrrrwrr,r) rSrabrrr%r~qyrr3r,fps rWr~zF_dense.__call__ s YY dllQ&67 8 +":&1 SS477] WWQZ !CRC"H+r#2w 'dffaT5E5EF VVDFFAITVVtvv!5 99 :DFF{rk)NT)rrrrrr~rrkrWrr s.rkrceZdZdZefdZdZdZejjdgddZ dZ ejjdgdd Z ejjd Zejjdgd d Zd ZejjdddgejjdgddZejjdddgdZejjdddgejjdgddZejjdgdejjdgddZejjdgdejjdgddZy)_TestMakeSplrepBaseNc|jdk(r<|jddtjzd}|j |}d}|||fS|jddd}|j |dzdz dz}d}|||fS) Nrrr9regq@H&?rrDgQ @)r4rfrKrr)rSrTrwrrs rW _get_xyktz_TestMakeSplrepBase._get_xykt s <<: % Aqw+AAAa7N Aq"%A$ #Q&AAa7Nrkc tjddd}tjddd}tt5t |||j dddtt5t ddd|j dddtt5tj |jdddf}t ||d|j dddtj d}tt5t ||d z|d|j dddtj d }tt5t ||d z|d|j dddtj |jddf}tt5t ||d z|d|j dddtt5t |ddd |d zd|j dddtt5t ||d zd d|j dddtt5t ||d zd |j dddtt5t ||d zd dd|j dddtt5t ||d zdd|j dddtt5t tjdtjdd|j dddy#1swYxYw#1swYxYw#1swYxxYw#1swY;xYw#1swYxYw#1swYxYw#1swYxYw#1swY\xYw#1swY5xYw#1swY xYw#1swYxYw#1swYyxYw)NrrerDrrXr.r9rrr4r;)rrr4r7rBr4rr4)r4rrr4)rrr4r ) rKrfrGrIr#r4rrrrHrOrSrwrrs rWtest_input_errorsz%_TestMakeSplrepBase.test_input_errors s, KK2r " KK2r " : & 4 1dll 3 4: & ; 1T\\ : ;: & ;Aq)*A 1T\\ : ; GGBK : & C 1a41T\\ B CWWR[L : & C 1a41T\\ B C GGQWWQZO $ : & C 1a41T\\ B C: & D $B$Adll C D9 % E 1a43#t|| D E: & = 1a42t|| < =: & K 1a411T\\ J K: & E 1a412t|| D E: & Q  ! biilc4<< P Q Qa 4 4 ; ; ; ;  C C  C C  C C D D E E = = K K E E Q QsL8.M=MMM,,M9!#NNN N-:N:/AO8MMMM),M69NNN N*-N7:OOc xtt|||||jd}t|||||j}t||||||j}t |j |j dt |j |j d|j|jk(sJy)Nrr7)r2r4rr4rZrt)rr"r4r#rr2r3r4)rSrwrr4rr2spl_autospl_ts rW_test_with_knotsz$_TestMakeSplrepBase._test_with_knotss 1Q E Fr Jq!qAt||DAqAaF EGG%8 EGG%8zzUWW$$$rkr4r.r9r;r<rrcT|j\}}}|j||||yr)rr)rSr4rwrrs rWtest_with_knotsz#_TestMakeSplrepBase.test_with_knots!s(.."1a aAq)rkcVt||||j}t||||j}tt ||||jd}t |j |j dt |j|dt |j|dy)Nr3r7rZrt)r#r4r rr"rr3r2)rSrwrr4r,spl_ir2s rW_test_default_sz#_TestMakeSplrepBase._test_default_s's|!Q!T\\:"1a1dllC 14<<@ A" EuwwU3qu-/rkcR|j\}}}|j|||yr)rr)rSr4rwrrs rWtest_default_sz"_TestMakeSplrepBase.test_default_s0s&.."1a Q1%rkc d}|jdk(r>tjddtjzd}tj|}ntj d}|dz}t j5t jdtt||d||jdk(}dddt j5t jdtt||d||j }dddtjdttj|jdg|j d zzf|d d y#1swYxYw#1swYnxYw) NgKH9rrr9rr;r5r4rrrr.rrt)r4rKrfrrrOwarningscatch_warnings simplefilterrrr#rr2rr3r4)rSrrwrr`r,s rWrz$_TestMakeSplrepBase.test_s_too_small5sB  <<: % Aqw+Aq A " A1A  $ $ & K  ! ! Aadllj.HJC  K $ $ & D  ! ! aa1dllCC  D s1v&ceeaS#%%']23AU , K K D Ds>8E(5E4(E14E=r(c$d}|jdk(r>tjddtjz|}tj|}ntj |}|dz}t ||||j}t |||d|j}|jjd k(sJ|jjd k(sJt ||d d |zz z|d|j}|jjd k(sJy) Nrerrr9r;r3h㈵>rr.) r4rKrfrrrOr#r3r)rSr4rUrwrr,rrs rW test_shapez_TestMakeSplrepBase.test_shapeRs  <<: % Aqw*Aq A ! A1A!Q!T\\:AqAt||DuuzzQww||q   Aq1ac7{a4Nww||q   rkcd}ddtjz}}tj|||dz}tj|}t t 5t ||dddddy#1swYyxYw)Nrerr9r.:0yE>nonsenser)rKrrfrrGrIr#rSNrrVrwrs rWtest_error_on_invalid_bc_typez1_TestMakeSplrepBase.test_error_on_invalid_bc_typegsf !BEE'1 KK1a!e $ FF1I : & : 1j 9 : : :s A//A8r4rrc tjddtjzd}tj|}tjddt |}t ||||d|dk(}t |||d|| }t|j|dttj|jdg|jdzzf|dd y) Nrr9rer.rrrrr4rrrrr4r4rt) rKrfrrr7rr#rr2rr3r4)rSr4r4rwrrr`r,s rW%test_make_splrep_with_unequal_weightsz9_TestMakeSplrepBase.test_make_splrep_with_unequal_weightsps KK1RUU7B ' FF1I KK1c!f %QQ!t'Z2GI!Q!tq'Bs1v&ceeaS#%%']23AT +rkc d}tjddtjzd}tj|}tj||fj \}}|j jdusJ|j jdusJtjddt|}tj||fj \}} |j jdusJt|||dd |d k( } t|||d d| } || | t|||d d| } || | t|||d d| } || | t|||d d| } || | y) Nct|j|dttj|jdg|j dzzf|ddy)Nrr.rrt)rr2rKrr3r4)r,r`s rWcheckzO_TestMakeSplrepBase.test_make_splrep_with_non_c_contiguous_input..checksG CEE3q6 * BEE#%%!ceeAg"67F /rkrr9reFr.rr;rrrr) rKrfrrrrrrr7rr#) rSr4rrwrrrrw1rr`r,s rW,test_make_splrep_with_non_c_contiguous_inputz@_TestMakeSplrepBase.test_make_splrep_with_non_c_contiguous_inputs\ / KK1RUU7B ' FF1Iq!tBxx$$---xx$$--- KK1c!f %ad Axx$$---QQ!t'Z2GI"a17C c3!R17C c3!Q"7C c3"bB$!")+ c3rkc |tjddd}tjdtjz|z}|d|d}}d}d}tj|g|dzz|g|dzzz}t |||||||d| } t | tsJ| jjdd|dzzk(sJ| j|k(sJt| jd|dztj|g|dzzt| j|dz dtj|g|dzzy) Nrr.rer9r7r;r)xbxer4rr2rr4) rKrfrrrGr#rr r2rr4rrQ) rSr4r4rwrrrrr2r,s rW%test_make_splrep_impl_no_optimizationz9_TestMakeSplrepBase.test_make_splrep_impl_no_optimizations/ KK1b ! FF1ruu9q= !1quB   HHbTQU^rda!en4 5!Q2"qtW>#w'''uu{{1~a!e,,,uuzzdqs RZZA%?@!fg B41q5>(BCrkrU)r3rrDr)rerrr.rc ltjjd}tjdtj|j ddtj z|dz dtj zf}tj|tj|z}t||||jdk(\}}}t||||j} |dk(r|d k(r|jdk(s8t| j|d t| j|d| d z d yy) Nrrr9rrrrrrDr.rZrt)rKrRrrrrrrrrr4r#rr2r3 rSrUrrrwrr2r3r4r,s rW(test_make_splrep_matches_splrep_periodicz<_TestMakeSplrepBase.test_make_splrep_matches_splrep_periodicsii##C( EE!RWWS[[AIAE[BCQYN O FF1Iq !A)CE1a!Q!T\\:RAFt||z'A CEE15 1 CEE1Wqb1f:E :(Brkc  tjjd}tjdtj|j ddtj z|dz dtj zf}tj|tj|z}t||||jdk(\}}}t||||j|} t| j|d| dz d y) Nrrr9rrr)rr4r2r.rZrt)rKrRrrrrrrrrr4r#rr3rs rW"test_make_splrep_with_splrep_knotsz6_TestMakeSplrepBase.test_make_splrep_with_splrep_knotssii##C( EE!RWWS[[AIAE[BCQYN O FF1Iq !A)CE1a!Q!T\\Q?q1"q&z6rk)rrrr4rKrrrrarzr{rrr thread_unsaferrrrrrrrrrkrWrr sG 5Qn% [[S"45*6* 0 [[S"45&6& [[,,8 [[S),!-!(: [[YT(:; [[S/2 +3< + [[YT(:;+<+\ [[YT(:; [[S/2D3<D, [[S"34 [[S"56 ;75 ; [[S"34 [[S"567757rkrceZdZejj dgddZejj dgddZdZdZ dZ dZ d Z d Z d Zd Zd Zy)TestMakeSplrepr4rcddlm}|j\}}}tjdg|dzzddgzdg|dzzz}|||dddf|||}t |||||}dD]} t || || d y) NrFr.rBr@rr.rerrZrt) scipy.interpolate._fitpack_reprorrrKrGrr) rSr4rrwrrr2ff_drs rWtest_fitpack_FzTestMakeSplrep.test_fitpack_Fs 7.."1a HHaS!A#Y#s+qc1Q3i7 8 a1d7Q1 %aAq!$ 6A AaD#a&u 5 6rkcddlm}|j\}}}tjdg|dzzddgzdg|dzzz}tj |j dt}|||dddf||||}t||||||} t|||||} d D]B} t|| | | d tj| | | | d sBJy) Nrrr.rBr@rrErrrZrt) rrrrKrGrOrrrrr) rSr4rrwrrr2rfwfw_drrs rWtest_fitpack_F_with_weightsz*TestMakeSplrep.test_fitpack_F_with_weightss 7.."1a HHaS!A#Y#s+qc1Q3i7 8 IIaggaj . q!AtG*aA +q!Q1*aAq!$ @A BqE47 7{{3q647? ?? @rkc ddlmcm}tjj d}tj ddddtj|jddzddddf }t|d}}t|j||j}t||}|jd|d|zz dz k(sJt||d y) Nrrrrrr;r9rZrt)r interpolatertrKrRrrrrr7rrrrrr)rSrvrr2rUr4DD_denses rWtest_disc_matrixzTestMakeSplrep.test_disc_matrixs 76ii##E* EE!Q1bggckkqk&9:1*CEE>rkcbd}|j\}}}tt||||d}t||||}t|||||}t |j |j dt |j |j d|j|jk(sJy)Nr;rr7)r2r4rrZrt)rrr"r#rr2r3r4)rSr4rwrrr2rrs rWrzTestMakeSplrep.test_with_knotss .."1a 1Q/ 0 4q!qA.AqAa0 EGG%8 EGG%8zzUWW$$$rkcd}|j||j}|dz}d}t|||d}|jjdd|dzzk(sJy)NrerEr;r.rrr9)rOrPr#r2r)rSrTrUrwrr4r,s rWtest_no_internal_knotsz%TestMakeSplrep.test_no_internal_knots*s]  IIarzzI * qD !Q!q)uu{{1~AaC(((rkcd}|j||j}|dz}t||d}t||d}t |j |j dy)NrerEr;rMrZrt)rOrPr#r rr3)rSrTrUrwrr,rs rWrzTestMakeSplrep.test_default_s3sV  IIarzzI * qD!Q!$"1a1-uwwU3rkcd}tj|}|dz}tjt5}t ||dd}t ||dd}t|j|dttj|jdg|jdzzf|dddddtd k(sJy#1swYxYw) Nrr;rrrr.rrtr9)rKrOrarrrr#rr2rrr3r4r7)rSrUrwrr~r`r,s rWrzTestMakeSplrep.test_s_too_small<s  IIaL qD \\. ) 0QAe,Caa51C CEE3q6 * BEE#%%!ceeAg"67F 0  0 1v{{  0 0s A7CCcttjgdtj}tjgdtj}tjdg|jdztj}t t 5t |||dddddy#1swYyxYw) N)g4@gR9c@g ףp=e@gףp= Oi@gQm@gQo@g)\(p@gfffffq@gq= ףq@g(\Yr@g)\r@g(\r@gQs@gQ3s@g33333Gs@皙as@rghs@rE)gJ@gH@gLH@gffffffG@gE@g)\(D@gC@gB@g333333@@g<@g3333339@g5@g2@g,@g%@g@g @r=g5{2?rr9r)rr4r)rKrQrPrrGrIr#rs rWtest_issue_22704zTestMakeSplrep.test_issue_22704Js JJ%-/JJ 8 JJ&(ZZ 1 JJy1771:-RZZ @ : & . 1Q" - . . .s B..B7c^d\}}|j||j}|dz}t|||}t|||d}|jjdk(sJ|jjdk(sJt||dd|zz z|d}|jjdk(sJy)Nrer;rEr;rMrrr.)rOrPr#r3r) rSrTrUr4rwrr,rrs rWrzTestMakeSplrep.test_shapeXs1 IIarzzI * qD!Q!$AqA.uuzzQww||q   Aq1ac7{a48ww||q   rkcd\}}|j||j}|dz}t||dd}t||dd}|jjdk(sJ|jjdk(sJ|j j d||zdzk(sJ|j j dd|dzzk(sJy)NrrEr;rrr.r9)rOrPr#r3rr2r)rSrTrUr4rwrrrs rWtest_s0_vs_notzTestMakeSplrep.test_s0_vs_noths1 IIarzzI * qDAqA+AqA+ww||q   ww||q   ww}}Q1q519,,,ww}}Q1A;...rkN)rrrrarzr{rrrrrr rrrrrrrkrWrrs} [[S"45 66 6 [[S"45@6@ 0 ? %)4  .! /rkrc|eZdZdZej j dgddZej j dgddZdZ dZ ej j dd d gd Z ej j d gd ej j ddgdZ y)TestMakeSplrepPeriodicrr4rc|jddd}|jd}t|||d|j}|jj dd|dzzk(sJy)NrrerDrr.rr9)rfrr#r4r2r)rSr4rTrwrr,s rWr z-TestMakeSplrepPeriodic.test_no_internal_knots}s[ KK2r " GGEN!Q!q$,,?uu{{1~AaC(((rkcd}tjddtjz|}tj|tj|z}t |||d|j }t |||d|j }|jjdk(sJ|jjdk(sJ|jjd|d|zzk(sJy)Nrerr9rr.) rKrfrrrr#r4r3rr2r)rSr4rUrwrrrs rWrz%TestMakeSplrepPeriodic.test_s0_vs_nots  KK1RUU7A & FF1Iq !AqADLLAAqADLLAww||q   ww||q   ww}}Q1q1u9,,,rkcTd}dd|jz}}|j|||dz|j}|j|}t ||d|j }t t|||dd |j||j|z}t ||d |j }t t|||dd d |j|z|j|dzz}t ||d|j }t t|||dd y)Nrerr9r.rErrrrLr[rr0rr;) rrfrPrr#r4rrr)rSrTrrrVrwrr,s rW test_periodic_with_periodic_dataz7TestMakeSplrepPeriodic.test_periodic_with_periodic_datas !BEE'1 KK1a!e2::K 6 FF1I!Q$ =a qt$? FF1Iq !!Q%>a qt$? bffQiK"&&)A+ %!Q$ =a qt$?rkc d}ddtjz}}tj|||dz}tj|}t t 5t ||d|jdddy#1swYyxYw)Nrerr9r.rr)rKrrfrrGrIr#r4rs rW$test_periodic_with_non_periodic_dataz;TestMakeSplrepPeriodic.test_periodic_with_non_periodic_datasj !BEE'1 KK1a!e $ FF1I : & < 1dll ; < < TestMakeSplrepPeriodic.test_make_splrep_periodic_m_eq_2_k_eq_1s HHc3Z  HHc3Z $%EBHHc3Z t!Q!q*BQQ!a0 q5 CEE3q6 *ceeaS#%%']23A rkk_fp))r.-C6)r9r)r;gAȘrLc @d}tjdd|}tjdtjz|z}|\}}t ||||d}d} t ||dddf|d||} t j5t jdtt| d d| |z ftj||z ff|d z} ddd| j} tjd d g} | | }t|d|dy#1swYGxYw) Nrerr.r9rrrr5r>MbP?r=r0)rKrfrrrr rrrrr!rNr,rGr)rSrrrUrwrr4rr`fp0splinerbsx_checky_checks rWtest_fperiodic_basic_fitz/TestMakeSplrepPeriodic.test_fperiodic_basic_fits  KK1a  FF1ruu9q= !2QQ!+1a4j#a&A;  $ $ & T  ! !(N ;&#C!G rvvrAv6F'GUSA T ZZ((C:&W+ GAJ/ T Ts ADDN) rrrr4rarzr{r rrrrr'rrkrWrrxsG [[S"45)6) [[S"45 -6 -@"< [[S1e*-  .   [[V%QR [[S4&)0*S0rkrceZdZddefdZej jdgddZej jdgddZ dZ d Z d Z y ) TestMakeSplpreprer;c|j||j|jz|z }|j||j |g}|||fS)NrE)rOrPrrr)rSrr4rTrwrs rW_get_xykzTestMakeSplprep._get_xyksK IIarzzI *RUU 2Q 6 VVAYq "!Qwrkrrrr!rc 8d\}}tj|tjz|z }tj|tj|g}ddddd}t ||\\}}}} t ||\} } t| | d t| j|d t|||k(sJtj|j} t| j| d t| | t|||d | d y) Nrrrrrer,rrZrtr.r)rKrOrrrrr$rr2r7rQrr3r ) rSrrr4rwr num_knotsr2r3u_r,rrs rWtest_simple_vs_splprepz&TestMakeSplprep.test_simple_vs_splpreps1 IIaL255 1 $ VVAYq "%u=  Q Aq2a1%Q 2E* qu-1v1%%%ZZ]__r. A01aa03% ArkcT|j\}}}t|tsJtj|ddk(sJt ||\}}t tj ||\}}t|||t|d|ddt|dt|dk(sJt|d|dd|d|dk(sJtjt||tj|k(sJt||\}}t||dt|j|ddt|jj|dd|j|dk(sJ||jtj|k(sJttj ||\}}t||dt|j|ddt|jj|dd|j|dk(sJ||jtj|k(sJtt 5ttj |j|dddy#1swYyxYw)Nrr9r.rtrZr.)r+rrrKrrrQrr7rr$r2r3rr4rGrI) rSrrrr`rtck_au_ar,s rWtest_array_not_listz#TestMakeSplprep.test_array_not_lists(--/1a!T"""xx{1~"""aQRZZ]a0 s3Q'Aau53q6{c%(m+++Aau51vq!!!xxa &"((1+555a1%Q3U+uQxe4q6uua   1v||rxx{***bjjmq1Q3U+uQxe4q6uua   1v||rxx{*** : & / AA . / / /s *+JJ'c|jd|\}}}t|\}}t|||j|dy)NrerrTrZrtr+r$rrrSrTrwrr4r,rs rWtest_default_s_is_zeroz&TestMakeSplprep.test_default_s_is_zeros?--"-,1aaQA %8rkc|jd|\}}}t|d\}}t|d\}}t||dt|||j|dt|||j|d|j|jk(sJ|j j |j j k(sJy)Nrer7rr.rZrtr)r+r$rrrr3r) rSrTrwrr4ru_ispl_nu_ns rWtest_s_zero_vs_near_zeroz(TestMakeSplprep.test_s_zero_vs_near_zero%s--"-,1a!!q) s!!u- sSu-c BHHQKe<c BHHQKd;zzUZZ'''ww}} ---rkctjdt}tt5t |dddtt5t |ddddtt5t |ddddt |gd\}}t |gd\}}||jdk(sJt|||gd y#1swYxYw#1swYxYw#1swYpxYw) NrrErr.rrr.rrZrt) rKrOrrGrIrr$rr)rSrwr`r0r,rs rWrzTestMakeSplprep.test_1D2s IIau % : &  AJ : & ! a  !: & # c " #1#&RqcT*Q1v||v%%%A%0   ! ! # #s# CC$3C0C!$C-0C9N rrrrKr+rarzr{r1r5r:r?rrrkrWr)r)slqR  [[S"67A8A: [[S"67/8/B9 .1rkr)ceZdZddefdZej jdgddZej jdgddZ dZ d Z d Z y ) TestMakeSplprepPeriodicrer;c|jdd|jz||j}|j||j |g}|||fS)Nrr9rE)rfrrPrr)rSrUr4rTrwrs rWr+z TestMakeSplprepPeriodic._get_xykGsI KK1RUU7ARZZK 8 VVAYq "!QwrkrrrLrr0c d}tjddtjz|}tj|tj|g}ddddd}t ||d\\}}}} t ||d \} } t| | d t| j||k(sJt| | t|||d | ddy)Nrerr9rrrFr.rrrrZrtrr0r[) rKrfrrrrr$rr7r2r ) rSrrUrwrr/r2r3r4r0r,rs rWr1z.TestMakeSplprepPeriodic.test_simple_vs_splprepLs  KK1RUU7A & VVAYq ""Bb9  QA. Aq2a1j9Q 2E*355zYq\))) A 81aa 8 ;" 0rkc|j\}}}t|tsJtj|ddk(sJt ||d\}}t tj ||d\}}t|||t|d|ddt|dt|dk(sJt|d|dD]\}} t|| d|d|dk(sJtjt||tj|k(sJt||d\} }t||d| j|dk(sJ| |jtj|k(sJttj ||d\} }t||d| j|dk(sJ| |jtj|k(sJtt5ttj |j|ddddy#1swYyxYw) Nrr9r.rrtrZrr)r+rrrKrrrQrr7rrr$r4rGrIr) rSrrrr`rr3r4rrr,s rWr5z+TestMakeSplprepPeriodic.test_array_not_listes--/1a!T"""xx{1~"""aQ'QRZZ]aQ7 s3Q'Aau53q6{c%(m+++#a&%(+ 0FB B / 01vq!!!xxa &"((1+555a1j9Q3U+uua   1v||rxx{***bjjmq*EQ3U+uua   1v||rxx{*** : & C AAz B C C Cs ,H77Ic|jd|\}}}t|d\}}t|||j|dy)NrerUrTrrXrZrtr8r9s rWr:z.TestMakeSplprepPeriodic.test_default_s_is_zerosB--"-,1aa4QA %8rkc<|jd|\}}}t|dd\}}t|dd\}}t||d|j|} t||| dt||| d d |j|jk(sJy) NrerJrrrrrZrtrr0r[)r+r$rrr) rSrTrwrr4rr<r=r>y_arrs rWr?z0TestMakeSplprepPeriodic.test_s_zero_vs_near_zeros--"-,1a!!q*= s!!ujA sSu- c E6c E4@zzUZZ'''rkc$tjddtjzd}tj|}t t 5t |ddddt t 5t|dddddt t 5t|dddddt|gd d\}}||jd k(sJt|||gd y#1swYxYw#1swYzxYw#1swY`xYw) Nrr9rr.rrrrrZrArt) rKrfrrrGrIrr$rr)rSrwr,rs rWrzTestMakeSplprepPeriodic.test_1Ds KK1RUU7A & FF1I : &  A1  : & 5 a 4 5: & 7 c: 6 7qcUJ?Q1v||v%%%A%0   5 5 7 7s$ C.2C:D.C7:DDNrBrrkrWrDrDDsmqR  [[S"780900 [[S"78C9C<9 (1rkrDc,eZdZdZdZddZdZdZy) BatchSplinec tj||d}|jdd|_|j d|jdDcgc] }|||fi|c}|_||_ycc}wNr7)rKmoveaxisr _batch_shaper_splines_axis)rSrwrrr#kwargsyis rWrzBatchSpline.__init__se KK4 $GGCRL;<99RQS;UVR200V  Ws A.c|jDcgc] }|| }}tj||j|jz}|jr!tj |d|j S|Scc}wrQ)rTrKrrSrrRrU)rSrwr#rs rWr~zBatchSpline.__call__sc%)]] 36VAY 3 3 JJq$++agg5 612r{{1b$**-?a? 4sA<Nc|jDcgc]}|j|||}}tj||jScc}wr)rTrrKrrS)rSrrVrr#rs rWrzBatchSpline.integratesE?C}} MVV  aK 0 M Mzz!T..// NsA ctj|}|jDcgc]}|j|c}|_|Scc}wr)rdeepcopyrTrrSrrr#s rWrzBatchSpline.derivatives<mmD!>!$cnnQ&7S ""3q63q62 ""=3== =3==&;QRrkN) rrrrarzr{r rrrirrkrWr`r`s [[2 b !  $ % . Hi0 1 Hd+ ,    [[\+;< [[VZ0S1= Srkr`rrrb)zr<rorvrrrorrr}numpyrKscipy._lib._array_apirrrrrrscipy._lib.array_api_extra_libarray_api_extrarrar rGrr r r r rrrrrrrrrrrrrrrrscipy.sparse.linalgsparserscipy.interpolate._bsplinesrrrrrrr r!r"r#r$scipy.interpolate._fitpack_implr _fitpack_implr scipy._lib._utilr%scipy._lib._testutilsr&scipy.interpolate._ndbspliner'r(rHr)rCr*rzryr,rrrrrrrurr_rrr9rrr{rrrrr rrrBrDrfrrJrlrrrArgrorqrrrrrr)rDrOr`rrkrWrws1    )(*  !!EEBGG//&953-&;;//7_ )_ )_ )D7S$S$S$l6,$ G> $b+$_)_)D%&`?`?'`?F 88!++11(Y)X  (nLnLb* ()J3J3*J3^  7 :":"z9j4j4j4ZWGWGta a L(.>"ll#l^2,,^Q7Q7h;R/(R/ R/j;\00\0 \0~< h1h1!h1V< b1b1!b1J8$S$Srk