L i'ddlZddlZddlZddlZddlZddlZddlZddlm Z ddl m Z m Z ddl mZddl Z ddlmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZm Z m!Z!ddl"m#Z$ddl%m&cm#Z'ddl(m)Z)m*Z*m+Z+m,Z,m-Z-ddlm.Z.m/Z/m0Z0ddl1m2cm3Z4ddl5m6Z6dd l7m8Z8dd l9m:Z:dd lm;Z<dd lm=Z>dd lm?Z?GddZ@GddZAdZBdZCdZDdZEdZFdZGdJdZHdKdZIdZJGddZKGddZLdZMdLd ZNe jjd!d"d#gZQGd$d%ZRGd&d'ZSdMd(ZTd)ZUd*ZVGd+d,ZWd-ZXGd.d/ZYd0ZZd1Z[d2Z\Gd3d4Z]Gd5d6Z^Gd7d8Z_Gd9d:Z`d;Zad<ZbGd=d>Zcd?ZdGd@dAZeGdBdCZfGdDdEZgGdFdGZhGdHdIZiy)NN)suppress_warnings)xp_assert_equalxp_assert_close)raises)BSplineBPolyPPolymake_interp_splinemake_lsq_splinesplevsplrepsplprepsplder splantidersprootsplintinsert CubicSpline NdBSplinemake_smoothing_splineRegularGridInterpolator) _not_a_knot_augknt_woodbury_algorithm_periodic_knots_make_interp_per_full_matr)generate_knots make_splrep make_splprep) AxisError)_run_concurrent_barrier) make_ndbspl) _dfitpack) _bsplines)_dierckxceZdZdZdZdZdZdZdZdZ dZ d Z d Z d Z d Zd ZdZdZdZdZdZdZdZdZdZdZdZdZdZdZdZdZe jBjEde#dd d!Z$d"Z%e jBjLd#Z'e jBjEd$gd%e jBjEd&e#d'd(Z(d)Z)d*Z*d+Z+e jBjEd,gd-d.Z,e jBjEd,gd-d/Z-d0Z.d1Z/e jBjLd2Z0d3Z1y4)5 TestBSplinec tttftfit ddgdgdt j d5tttfit dt jgdgddddtttfit dt jgdgdtttfit ddgdgdtttfit dgdggdgdtttfit gd dgdtttfit gd ddgd tttfit gd gd dtttfit gd gd dtttfit gdgdd d\}}t j||zdzt j}t jj|}t|||}t||jt||j||jk(sJy#1swYxYw)N??rtckignore)invalidrr)rr)r4r4)r8r+@@@)r+r+r+cubic@)r8rr)r)r4r6)r+r)r) r6dtype) assert_raises TypeError ValueErrorrdictnperrstatenaninfarangefloat64randomrr-r.r/)selfnr/r-r.bs k/mnt/ssd/data/python-lab/Trading/venv/lib/python3.12/site-packages/scipy/interpolate/tests/test_bsplines.py test_ctorzTestBSpline.test_ctor*sy*-w 1!SbTQ/ 1 [[ * S *g RBFF tq1Q R Sj'NTQKB41-MNj'JTQGtq-IJj'MTaS1#J2$!-LM j'KTI!-JKj' <RH: < i O1\WM Oi K1\SI K j' B, a@ B1 IIac!e2:: . II  Q  Aq! 133133ACCxx; S Ss 3I  Ic2t}|j}t|j|dddt|j|ddd|j |dk(sJt jt5d|_dddy#1swYyxYw)NrV瞯<atolrtolr)r4foo) _make_random_splinetckrr-r.r/pytestrAttributeError)rMrOrYs rPtest_tckzTestBSpline.test_tckMs}  !eeSV%e<SV%e<ssc!f}}]]> * AE   s <B  Bctjddd}tddgdgd}t||tj|dztgdddgd}t||tj |d kdd y) Nrr) r:r,)rffffff?r)r6r7r_r;)rFlinspacerr ones_likewhererMxxrOs rP test_degree_0zTestBSpline.test_degree_0Ysu [[Ar " q!f *"r||B/#56 lq!f 2"rxxT 3<=c<gd}gd}d}t|||}tjddd}t|dt |z|dt |dz zz|dt |dz zz||d tt ||||f||d y) Nr5r)r4r6r)r62rr4+=rU)rrFr`rB_012r )rMr-r.r/rOxs rP test_degree_1zTestBSpline.test_degree_1bs    Aq!  KK1b !!U1X !U1Q3Z7!A$uQqSz/I!5 *a!Q+QqT>rfcd}tjdg|dzzdg|dzzz}tjgd}t|jddddg}t |||}tj ddd}t ||d ||d d t t||||f||d y) Nr6rr)r+r9r:r;r2gr9r^T extrapolaterjrk)rFasarrayrreshaperr`rr )rMr/r-r.bpbsplrds rPtest_bernsteinzTestBSpline.test_bernsteinms  JJsAaCyA3!9, - JJ' ( 199R#aV ,q!Q [[b" %240RT2 @b1a),Ru .rfc Bt}|j\}}}tj|||| dz d}||}|Dcgc]}t ||||}}t ||d|Dcgc]}t ||||} }t || dycc}wcc}wNr)rirjrk)rXrYrFr` _naive_evalr _naive_eval_2) rMrOr-r.r/rdy_brmy_ny_n2s rPtest_rndm_naive_evalz TestBSpline.test_rndm_naive_eval{s !%%1a [[1q!Aw +e0231{1aA&33Su-356a aAq)66T. 47s B1Bc t}|j\}}}tj|||| dz d}t ||t ||||fdyryrXrYrFr`rr rMrOr-r.r/rds rPtest_rndm_splevzTestBSpline.test_rndm_splevsV  !%%1a [[1q!Aw +"uR!Q3%@rfctjjd}tj|jd}|jd}t ||}t |}|j |j}}tj|||| dz d}t||t||dy)Nr)Prjrk) rFrL RandomStatesortr rr-r/r`rr ) rMrngrmyrYrOr-r/rds rPtest_rndm_splrepzTestBSpline.test_rndm_splrepsii##D) GGCJJrN # JJrNQl SMssACC1 [[1q!Aw +"uR~E:rfc<t}tj|j|_tj|j |j |j |j dz d}t||tj|y)Nr)d)rXrFrar.r`r-r/r)rMrOrds rPtest_rndm_unityzTestBSpline.test_rndm_unityse  !ll133 [[QSS133tAv; 4"r||B/0rfcVtjjd}d\}}tj|j|}|j|ddf}t |||}|||| dz }}|||z |jdzz} || j dk(sJy) Nrr6sizer)r6r7)r6r7rrr)rFrLrrrshape) rMrrNr/r-r.rOtmtprds rPtest_vectorizationzTestBSpline.test_vectorizationsii##D)1 GGCJJqM " JJQ1IJ & Aq! 1q!AwB 27cjj33 3u{{o---rfc 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)!r6r)r2rrirjrk) rFrLrrr_rr`rr ) rMrrNr/r-r.c_padrOb_paddtrds rP test_len_czTestBSpline.test_len_cs ii##D)1 GGCJJqs1u% & JJqMaAaC()1a#WQq%95 rUQqT\ [[1AbEBJ 3"uRyu5"uR!Q3%@"uR!UA7eDrfc t}|j\}}}|||| dz }}dD])}t|||g|||dz|dz g|dd+y)Nr)TF绽|=& .>Hz>rTrXrYr) rMnum_parallel_threadsrOr-_r/rrextraps rPtest_endpointszTestBSpline.test_endpointsss  !%%1a1q!AwB# WF Ar2h/rEz2:6?dQU W Wrfc t}|j\}}}t|||dz| dz dz |||dz| dz dzdy)Nr)rrrkr)rMrrOr-rr/s rPtest_continuityzTestBSpline.test_continuitys\  !%%1a!AaC1+-.!AaC1+2E0F rfc Pt}|j\}}}|d|dz }tj|||z || dz |zd}|||k||| dz kz}t |||d|||dt ||dt ||||fdy) Nr2rr)riTrqF)extr)rMrOr-r.r/rrdmasks rP test_extrapzTestBSpline.test_extraps  !%%1a rUQqT\ [[1AqbdGbL" 5!r b1aRT7l+ "T(5"T(6 8 "$/b1a)+ -rfct}|j\}}}|ddz |ddzg}||}tjtj|rJy)Nrr)r2)rXrYrFallisnan)rMrOr-rr/rdyys rPtest_default_extrapzTestBSpline.test_default_extrapsY  !%%1adQh" " rU66"((2,''''rfc 4tjjd}tj|jd}|jd}d}t |||d}|j |dzz }|d|d z }tj |||z |||zd }|||||z ||||z zz} t||t| |||fgd }|||||z ||||z zz} t||d|| d y) Nrr7r6periodicrqr)r2rri)r2r?r)T) rFrLrrrrr`rr r) rMrr-r.r/rOrNrrdxys rPtest_periodic_extrapz TestBSpline.test_periodic_extrapsii##D) GGCJJqM " JJqM  Aq! 4 FFa!e  rUQqT\ [[1AaD2Ir 2 qTR!A$Y1Q4!A$;/ /"uR!Q34 qTR!A$Y1Q4!A$;/ /"*5q7NOrfct}|j\}}}tj|||f}t j |||| d}t ||||ddy)NrrjrT)rXrYr from_splinerFr`r)rMrOr-r.r/pprds rP test_ppolyzTestBSpline.test_ppolysa  !%%1a   1ay ) [[1q!uc *"r"vE>rfcjt}|j\}}}tj|d|dd}tj||f}t d|dzD])}t ||||f|}t||||d+t|||dztj|dy) Nrr2rir)dernurjrk) rXrYrFr`rranger r zeros_like)rMrOr-r.r/rdryds rPtest_derivative_rndmz TestBSpline.test_derivative_rndms  !%%1a [[1qub ) UU2q5\AaC= ;CrAq!9#.B B" E : ; "1 r}}R'8uErfcd}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)Nr4) r2r2rr)r)r6r7rrrrrrrr)r)r6r7rrrg2H@gη@r6r7r)r)rFrLrrrrsrallclose) rMr/r-rr.rOrmx0x1s rPtest_derivative_jumpsz!TestBSpline.test_derivative_jumps sP  2ii##D) EE!Q 1 q!+ , Aq!  JJ| $!AF)e+,!AF)e+, .;;q{AgJ777ZZA "u*+"u*+ - ZZA ;;qe2Ab5jQ4GHHH;;qUq11QY13EFFFFrfc tjddd}tjgd}t ||t ||j |j|jfdt ||t|dtjgd}tjd d d }t ||tj|d k||zd |z d zdy)Nr2r7rrr)r4r6)r-rjrkrr)r)r4rr4r^r)r9) rFr`r basis_elementrr r-r.r/B_0123rbrcs rPtest_basis_element_quadraticz(TestBSpline.test_basis_element_quadratic's [[Q #  ! !L 1"b133QSS/2 @"r  0  ! !L 1 [[Ar ""aBB 3% Arfc t}|j\}}}tj|||| dz d}t ||t ||||dy)Nr)rrjrk)rXrYrFr`r_sum_basis_elementsrs rPtest_basis_element_rndmz#TestBSpline.test_basis_element_rndm4sU  !%%1a [[1q!Aw +"22q!Q?eLrfct}|j\}}}|dz}t|||}t||jj|}t||jj |}t j|||| dz d}t||j||dt||j ||dy)Ny?@r)rrjrk) rXrYrr.realimagrFr`r) rMrOr-r.r/ccb_reb_imrds rP test_cmplxzTestBSpline.test_cmplx:s  !%%1a (^ Ar1 q!##((A&q!##((A& [[1q!Aw +" DH59" DH59rfctjgd}tj|tjsJy)Nr)rrrFrrHrMrOs rPtest_nanzTestBSpline.test_nanGs,  ! !, /xx"&& """rfctd}|j\}}}t|||}tj|||| dz d}t d|D].}|j }t|||||dd0y)Nrr/r)r-q=rT)rXrYrrFr`r derivativer)rMrOr-r.r/b0rdjs rPtest_derivative_methodz"TestBSpline.test_derivative_methodLs ! $%%1a Q1  [[1q!Aw +q! FA A Br1Iqu5u E Frfct}|j\}}}tj|||| dz d}t |j j |||ddtj|||f}tj||f}t|||}t |j j |||ddy)Nr)rrjrT) rXrYrFr`rantiderivativerc_dstackrrs rPtest_antiderivative_methodz&TestBSpline.test_antiderivative_methodUs  !%%1a [[1q!Aw +7((*557;"E 7 EE!Q'N IIq!f  Aq! 7((*557;"E 7rfc  tjgd}t|jddt j dt|jddt j dt|jddt j dt|jddt j dt|jddd t j dt|jddd t j dt|jddd t j dt|jddd t j t jdd|jd |_ |j}t j |d |dz }t|jdd |t|jd dt j d|zt|jd d|t|jddt j d |zt|jddt j |d|dz t|jddt j |d|dz |d z|dz t|jddt j |d|dz |d z|dz t|jddt j |d|dz |d z|dz d|zzt|jddt j |d|dz t|jd dt j |d|dz t|jdd t j |d|d z d|zz y)Nr3rr)rr2r8TrqFrr4iii?r6g+@rir7) rrr integraterFrs_implrrYrrr)rMrOi period_ints rP test_integralzTestBSpline.test_integralcsI  ! !) , Aq)2::c?; Aq)2::h+?@ Aq)2::d+;<  B*BJJsO< Bt  @#   ZZ!qt ,  Aq):6 Aq)2::b:o+FG B+Z8 B+RZZJ-GH C- 1S6AcF?3 5 C+ 1Q4!A$;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#?@ Brfcgd}t||}d|_tj|}dD]1\}}t |j |||j ||3y)Nr5r))r)rr)r )r rrr rrr)rMrmrOprrs rPtest_integrate_ppolyz TestBSpline.test_integrate_ppolys`  q! $"   a 5 1FB AKKB/KKB/ 1 1rfctjgd}dD]C}|jdd|}t|tj sJ|j dk(rCJy)Nr3rrr)rq)rrr isinstancerFndarrayndim)rMrOrrress rPtest_integrate_0D_alwaysz$TestBSpline.test_integrate_0D_alwayssY  ! !) ,( !K++a +.BN)__name__ __module__ __qualname__rfrPBrs rfr )rr)r4r4)rr __class__rr)rMr rOs rPtest_subclassingzTestBSpline.test_subclassingsg   OOL ){{a||~''1,,,!++q000rfaxisrr7c d\}}tjdd||zdz}gd}|dz}|j||t|}tjj d}|j |}t ||||} | jj||f|d|z||dzdzk(sJ|j d } | | j|d|| jz||dzdzk(sJ|j dz |jfD]$} ttt fit|||| &t ||||jt ||||jd t ||||jt ||||jd fD]} | j| jk(rJy) Nrrr)rrrr7rrrr)r-r.r/rr4)rFr`rtuplerLrrr.rrrBr rErrr) rMrrNr/r-shpos_axisrr.rOxpaxb1s rP test_axiszTestBSpline.test_axiss1 KK1a!eai ( !8 (A 2Yii##D) JJBJ  Aq!$ 'ssyyR\Ob(m;b!oMMMM ZZ "u{{b(mbhh6HQJKHHHHFF7Q;' :B )W : 1QR8 : : 1a.99;1a.99!<1a.==?1a.==a@B %B77aff$ $$  %rfcd}gd}tjgdgdg}t|||d}t||d|}t||d|}t|d |d |d gy) Nr4)rr)r4r6r7rr)r2r4rr2)r4rr)r2rrr)r=)rFarrayrr)rMr/r-r.splspl0spl1s rP test_neg_axiszTestBSpline.test_neg_axissn  ! HHnm4 5aAB'q!A$"q!A$"C49d3i"89rfcd}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(rrr2rr/bc_typer)rjrkN)rFrLrr random_sampler eyelenr-r design_matrixtoarrayrr.) rNr/r%rrmrrvr. des_matr_def des_matr_csrs rPrun_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 Crfr?r6clampednaturalrr4 not-a-knotrrrN)r)rMr-rNr/bcs rPtest_design_matrix_bc_typesz'TestBSpline.test_design_matrix_bc_typess| D*  ( .B #Aq" - .q!Q 8A #Aq, 7 8 q! 6A #Aq* 5 6rfrr)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).rr^r)r4rN)rFrLrr&aminamaxrr`r'r(rrr)r*rrZrrD) rMrrr4rrmxminxmaxr/r-r.bsplines rP'test_design_matrix_same_as_BSpline_callz3TestBSpline.test_design_matrix_same_as_BSpline_callsii##D)   bFQJ/ 0WWQZd  EE"++dQhq&9++dD!vz*:;++dQhq&9: ; FF3q6A:> "!Q;/ AJ--aA{CKKM HHdRi4#:tbyA Bz* <%%aA{; < <  %%aA{;CCE  < .worker_fns8eeGAq!QqT1aRT7E2B bErfr^)rXr!)rMrOrYs rPtest_concurrencyzTestBSpline.test_concurrencys !  Iq1rfc nt}tjddd}||}tj}tj t |jd|dd|jj|jj}|j|ddtj t |jd|dd|jj|jj}|j|dd||_||_ t|||y) Nrr)r^r-z.datzw+)moderArr.) rXrFr` threading get_native_idmemmapstrjoinr-rArr.r)rMtmpdirrOrdexpectedtidt_mmc_mms rP test_memmapzTestBSpline.test_memmaps ! [[Ar "R5%%'yyV[[1SE78t ssyy ;##QyyV[[1SE78t ssyy ;##Q"x(rfN)2rr r rQr\rernrwrrrrrrrrrrrrrrrrrrrrrrrrrZmark parametrizerrr  thread_unsafer3r;r?rBrErKrOrQrVrZrgr rfrPr'r'(s!F > ? . /A ;1 .E&W -(P$? FG4 AM :# F 7&BP 1!1 [[VU2q\2%3%:: [[(6(6T [[],EF [[XuQx01G4C"$+$ [[Y)CD 8D 8 [[Y)CD TD TE& 7 [[ 2 2)rfr'c>eZdZejj dgddZejj dgddZdZejj dgd d Z ejj d d d gdZ dZ dZ y ) TestInsertxval)r8r+r=r7@@c4tjd}tj|dz}t||d}t ||}|j |}t |j|jdt |j|jd|j dz d||dk7r|n|dd}tj|d|dd|ddzzf}t ||||dtj|dz}t||d} t|tj||fd} | j |} t | j|jdt | jtj|j |j| j |jfd||dk7r|n|dd}tj|d|dd|ddzzf}t | || |dy) Nrr6rrSrkr)r2r) rFrJsinr r insert_knotrr-r.r/rcosr) rMrmrmrrspl_1fspl_1rdy1spl_y1spl_yyspl_yy1s rP test_insertzTestInsert.test_inserts IIaL FF1IqL A+c"%6)CEE6!8!45A!B%-QQsV UU2sAabEAcrFN++ ,Br7VVAY\#ArQ/#AruuQU|q9$$T* 5777 255)>)@)@)/););D)A)C)C*D$EKP R!B%-QQsV UU2sAabEAcrFN++ ,r GBKer)rr6r4)lowhighrrrrrSrk)rFrL default_rngruniformrrrr) rMrrNr/r-r.rxvrurds rPtest_insert_randomzTestInsert.test_insert_randomsii##E*1 GGCKKQqSUK+ , KKaAYK 'aA [[QqsV!QBqD'[ 2# [[QqsV!QBqD'[ ;Br7rfr) r皙?r9r;@@@gffffff@roc  tjd}tj|dz}t||d}t |ddi}|j |}t ||jd\}}} t|j|d t|jd| d z |d| d z d tjjd jd d d} t|| t| ||| fd y)Nrr6rrrrTperrSrkr)rrr)r)rFrJrqr rrrrrYrr-r.rLrrr ) rMrrmrrYrrutfcfr/rds rPtest_insert_periodiczTestInsert.test_insert_periodics IIaL FF1IqLQQs3 3#2swwD1 B%0!A5QBqD > YY " "4 ( 0 0QQR 0 Hb 5b"a[#9FrfrrNrctjddztjz}tj|tj|}}t ||d|zzd}||_t ||d}||_t ||d}||_d}|j|} |j|} |j|} t| j| jdt| j| jdt| j| jd| jzzdy) Nrr4r*r6r @rSrk) rFrJpirqrsr rrrrrr-r.) rMrrrmy_rey_imrspl_respl_imrruspl_1respl_1ims rP test_complexzTestInsert.test_complexs IIaLN255 VVAYq d D2d7Na8%#Atq1(#Atq1( #$$R($$R(77R \!9Frfcd}d}tjdg|dzzgdzdg|dzzz}tjt||z dz }t |||d}t t 5t||||fd dddt t 5|j|dddy#1swY3xYw#1swYyxYw) Nrr6rr)r4r6r7rrrrqTr) rFronesr(rrBrDrrr)rMrr/r-r.rs rP+test_insert_periodic_too_few_internal_knotsz6TestInsert.test_insert_periodic_too_few_internal_knotss  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) Nr6rr)rrr2rr|)rFrrr(rrBrDrr)rMr/r-r.rs rPtest_insert_no_extrapz TestInsert.test_insert_no_extrap$s  HHaS!A#Y-QqS 9 : GGCFQJN #aA : & OOB  : &  OOA  : & $ OOAO # $ $      $ $s$.CC)C5C&)C25C>) rr r rZrhrirzr~rrrrrr rfrPrlrls [[V%AB=C=@ [[C 8 8 8 [[T$8 G G [[]T:,>?G@G, ( $rfrlc dd}dD]S}t|}tt|D].\}}|||td|dzD]}||||dd0Uy)Nc |j\}}}tj|}tj|ddz d|dd|ddzz|ddzf}t t ||||f||||||d|d|j y) Nrrrr)r2zder = z k = )rUrVerr_msg)rYrFuniquerrr r/) rOrrrUrVr-r.r/rms rP check_splevz,test_knots_multiplicity..check_splev8s%%1a IIaL EE!A$s(C122A/2s: ;a!QC0!As)se6!##.G Irfr)r4r6r7rrr)r)rrjrj)rX enumerate_make_multiplesr)rr/rOrrrs rPtest_knots_multiplicityr4ssI6 ! $q12 6EAr A Q!} 6B3u5 6 66rfcb|dk(r|||cxkr ||dzkrdSdS|||z||k(rd}n)|||z |||z||z z t||dz ||z}|||zdz||dzk(rd}||zS|||zdz|z |||zdz||dzz z t||dz |dz|z}||zS)zw Naive way to compute B-spline basis functions. Useful only for testing! computes B(x; t[i],..., t[i+k+1]) rr)r+r8_naive_Brmr/rr-c1c2s rPrrKs  Avda(!AaC&(s1(c11v1~ !A$h1Q3!A$ '(1ac1a*@ @1Qx1QqS6  G!AhlQqs1uX!A#. /(1ac1Q32J J Grfck(rntjdz cxkr dzksJJk\rtz ksJtfdt ddzDS)z= Naive B-spline evaluation. Useful only for testing! r)c3RK|]}|z t|z z ywNr).0rr.rr/r-rms rP z_naive_eval..hs-F1q1vAqsA..Fs$'r)rF searchsortedr(sumr)rmr-r.r/rs````@rPrzrz^s AaDy  OOAq !A % Q41 !A#    6a#a&1*n$ $ Fa1 F FFrfctdzz }|dzk\sJt|k\sJcxkr |ksJJtfdt|DS)z'Naive B-spline evaluation, another way.r)c3FK|]}|t|zywrrrrr.r/r-rms rPrz _naive_eval_2..qs%=qqthq!Q**=!r(rrrmr-r.r/rNs```` rPr{r{ksi A!A#A !8O8 q6Q;; Q41 !    =E!H= ==rfct||dzz }||dzk\sJt||k\sJd}t|D]F}tj||||zdzd|}|||t j |zz }H|S)Nr)r8r4Frq)r(rrrrF nan_to_num)rmr-r.r/rNsrrOs rPrrts A!A#A !8O8 q6Q;; A 1X% @G ! !!Aac!e*% @ C QqTBMM!$ $$% Hrfctj|}tj||dk|dkDz|dk\|dkz|dk\|dkzgdddgS)z+ A linear B-spline function B(x | 0, 1, 2).rr4r)cy)Nr8r rms rPzB_012..rfc|Srr rs rPrzB_012..sArfc d|z SNr9r rs rPrzB_012..s Arf)rF atleast_1d piecewisers rPrlrlse aA <<QUq1u-!VA.!VQ/1)+~F HHrfctj|}|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)r4rc||zdz Srr rs rPrzB_0123..s1Q3r6rfcd|dz dzz S)Ng?rr4r rs rPrzB_0123..s41T6A+-rfcd|z dzdz S)Nr:r4r rs rPrzB_0123..sBqD19q=rfcyNr+r rs rPrzB_0123..rrfcy)Ngr rs rPrzB_0123..rrfcyrr rs rPrzB_0123..rrfznever be here: der=)rFrrDr)rmrcondsfuncspiecess rPrrs aA UQUq1u%q1u -E ax!-(* .se455 \\!UE *F Mrfctjjd}tj|j||zdz}|j|}t j |||S)N{r))rFrLrrrconstruct_fast)rNr/rr-r.s rPrXrXsW ))   $C  1Q3q5!"A 1 A  ! !!Q **rfc#K|j|j}}|jj}|d|dd|d|d<t ||||jj}|d|d|dzt ||||jj}|d|| dz dt |||yw) zIncrease knot multiplicity.rrNr)r2)r.r/r-copyr)rOr.r/t1s rPrrs 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)rFr`rrsr r-r.r/rYrdrrOxnewrrrrb2)rMrdrrOrs rP setup_methodzTestInterop.setup_methods [[BruuHb ) VVBZ r2 &CCacc?#%r1 $&KK2bee8R0 UU133QSS= !))RH%!##tww,rfc  |j|j|j}}}tt ||||ddtt ||j ||ddtt j|Dcgc]}t ||c}||ddttd5t ||dddttd|jjdz}|jj|}|j||j f}tt jt ||||j|ddycc}w#1swYxYw)NrSrTzCalling splev.. with BSplinematchr)r)rrOrrr rYrFrsrBrDrrr.r transposer-r/)rMrrOrrmrrrYs rP 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)NrrSrkr)r4T) full_output)rdrr rrr r) rMrmrrYr-r.r/tck_frrrOs rP test_splrepzTestInterop.test_splrepsww1Ql,,q!$1aA.A.1v{{ 1$7q!Qa!%0a!%0Qx1}}1c]2E* SM1Q4e,rfc&|j|j}}tj||f}t t 5t ||dddt t 5tj ||dddt td5t |dd|dddddt td5tj |dd|dddddy#1swYxYw#1swYxxYw#1swYXxYw#1swYyxYw)Nm > k must holdrr6) rdrrFrrBrDr rrC)rMrmry2s rPtest_splrep_errorszTestInterop.test_splrep_errorssww1 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) Nrr@r6rrSrkrT)rr) rFrJrKrtrrrrsr ) rMrmrOurYu1b_fu_frs rP test_splprepzTestInterop.test_splpreps IIb + 3 3F ;qz1--"R 2E* 5A;/? 5C=115A&a1$? cAq!3U+ 5c?3QUCrfctjdjd}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 unpackrrr#r6)numr) >Ir >KrzInvalid inputs)r)r6r4r7)rg333333?g?r)) rFrJrtrBrDrrr`rC)rMrmrs rPtest_splprep_errorszTestInterop.test_splprep_errorssy 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)rrr=rrrTzCalling sproot.. with BSplinerri)mestr)r4r)r6r4r7rrk)rOrrFrrrrr-r.r/rBrDrrsrr)rMrOrrootsc2rrrs rP test_sprootzTestInterop.test_sproot3s2-.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)rjF)rUcheck_0dzCalling splint.. with BSplinerr4)r6r4)rU check_shape)rOrrrrYrrBrDr.rrFrsr-r/r)rMrOrrintegrs rP test_splintzTestInterop.test_splintDs2q!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)rhrSrkr4)rOrr(r-r.rrFrzerosrrrr/rrrrrMrOctb_crNbdtck_ds rP test_splderzTestInterop.test_splderXs&&$''" 0AQSSCH$B##((*CAveeC2%#))AB-*?!@@A 0AY acchhj#qss%;<eAhU;eAhU;ttuQx'''!"g...!%/// 0 0rfc |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 )rOrr(r-r.rrFrrrrrr/rrrrrs rPtest_splantiderzTestInterop.test_splantideris&&$''" 0AQSSCH$B##((*CAveeC2%#))AB-*?!@@A 0]((!##((*c133)?@eAhU;eAhU;ttuQx'''!"g...!%/// 0 0rfc|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)Nr4rr)rSrkrr)rOrrdr-rrr.r/rr rrrrrrrFrs) rMrOrrdrtnbntck_nrrtck_n2bn2s rPrzzTestInterop.test_insertzsbFFDGGTWWr2 CCHHM !##a&133qs8# $2qM6"qssACCo#>Eb" b%(u 6"g&&&%'''5# $ TT^^BqrFTM *RTT2rtt,-Rn  5V#45??1aHBe -#w'''&%(((rfN)rr r rrrrrrrr rrrzr rfrPrrs= -H6-0' D%:C"H(0"0")rfrceZdZejddej zZejeZdZ dZ dZ e jjdgddZe jjdgdd Zd Zd Ze jjdgd d ZdZdZdZe jjdgddZdZdZdZdZdZe jj;ddZdZdZ dZ!dZ"dZ#d Z$d!Z%d"Z&e jjdgd#d$Z'd%Z(d&Z)d'Z*d(Z+d)Z,y*)+ TestInterpr8r9ctt5t|j|jddddy#1swYyxYw)Nr=r)rBrCr rdrrMs rPtest_non_int_orderzTestInterp.test_non_int_orders3 9 % 8 tww3 7 8 8 8s #<Ac2t|j|jd}t||j|jddt|j|jdd}t||j|jddy)NrrrjrTr2r/rr rdrrrs rP test_order_0zTestInterp.test_order_0d tww1 5$'' DGG%eD tww12 >$'' DGG%eDrfc2t|j|jd}t||j|jddt|j|jdd}t||j|jddy)Nr)rrjrTr2r#r$rs rP test_linearzTestInterp.test_linearr&rfr/rc|gd}gd}ttd5t|||dddy#1swYyxYw)Nrr)r4r6r7r)rr)r4r6r7rrrz Shapes of xrrrBrDr rMr/rmrs rPtest_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)r4r6r7r*zx to not have duplicatesrr)rr4r)r6r7rzExpect x to be a 1D strictly)r)r2)rBrDr rFrsrtr,s rP test_broken_xzTestInterp.test_broken_xs   :-G H * q!q ) *  :-K L * q!q ) *  JJqM ! !' * :-K L * q!q ) * * * * * *  * *s#B.B:C.B7:CCcdD]L}t|j|j|}t||j|jddNy)Nr4r6r7rrrrjrTr$)rMr/rOs rPtest_not_a_knotzTestInterp.test_not_a_knotsC# IA"477DGGQ7A AdggJe% H IrfcZt|j|jdd}t||j|jddt ddD]:}t||jd|||jd |d <t|j|jddd }t||j|jddt ddD]:}t||jd|||jd |d <y) Nrrr$rjrTr)rrr2dy=rkr/r%r)r rdrrr)rMrOrs rP test_periodiczTestInterp.test_periodics tww1j I$'' DGG%eDq! SA AdggajQ/4772;11EE R S tww1jr R$'' DGG%eDq! SA AdggajQ/4772;11EE R Srfr1cd}tjjd}tj|j |dz}|j |dz}|d|d<t |||d}t |||d y) Nrrr^rr2rrr$rjrk)rFrLrrr&r r)rMr/rNrrmrrOs rPtest_periodic_randomzTestInterp.test_periodic_randoms} ii##D) GGC%%a(2- .   a 3 &u! q!q* =!ae,rfch|jjd}tjj d}|j |dztj z}tj|}d|d<dtj z|d<tjd|f}tj||d<tj||d<t||ddd }t|D] }t||||dd|fd "t||d||dd y) Nrrr4r8r2r)rrr5rjrk)rdrrFrLrr&rrrrqrsr rr)rMrNrrmrrOrs rPtest_periodic_axiszTestInterp.test_periodic_axiss GGMM! ii##D)   a 1 $ruu , GGAJ!BEE " HHaV vvay!vvay! q!q*1 Eq :A AadGQq!tW5 9 :!A$1R56rfc0tjjd}d}d}tj|j |}|j |}|ddz |d<t t 5t|||ddddy#1swYyxYw) Nrrrr2r)rrr$)rFrLrrr&rBrDr )rMrr/rNrmrs rPtest_periodic_points_exceptionz)TestInterp.test_periodic_points_exceptionsii##D)   GGC%%a( )   a uqy! : & > q!q* = > > >s 3B  BcPtjjd}d}d}tj|j |}|j |}tj |d|zz}t t5t||||ddddy#1swYyxYw)Nrr6rr4r) rFrLrrr&rrBrDr )rMrr/rNrmrr-s rPtest_periodic_knots_exceptionz(TestInterp.test_periodic_knots_exceptionsii##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) Nrr$T)rr/rjrkr)rrr)r rdrr r rr)rMr/rOrYrrs rPtest_periodic_splevzTestInterp.test_periodic_splevs tww1j ITWWdgg415DGGS!QtwwZe4q! ?A!,C C477q!1 > ?rfc 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) Nr6rr$rGrjrkrr^rr2r) r rdrrrrFrLrrr&)rMrOcubrrNrmrs rPtest_periodic_cubiczTestInterp.test_periodic_cubics tww1j I$''477J?$'' CLu=ii##D)  GGC%%a(2- .   a 3 &u! q!q* =!Q 3!c!f51rfcTdt|j|jd}t|jt |j|jt j fd}t||j||jdy)Nr6rr$c t|Sr)rz)rmr.r/r-s rPrz6TestInterp.test_periodic_full_matrix..*sK1a$;rfrjrk)r rdrrrrF vectorizer)rMrOrr.r/r-s @@@rPtest_periodic_full_matrixz$TestInterp.test_periodic_full_matrix#su  tww1j I DGGQ ' &twwA > \\; <$'' BtwwKes  y7)u twwUEN K$'' DGG%eD Adggaj!$4a Q6G#HI E!HQKq!#=>UQV Xx&u twwUEN K$'' DGG%eDrfc |d\}}tj|jtj}tj|}ddg}ddg}t |||||f}t |||ddt tj||d d ||d d gtj|D cgc]\}} |  c} }t tj||d d ||d d gtj|D cgc]\}} |  c} }ycc} }wcc} }w) N)rr)r)g()r4r)rI)r4r:r$rjrTrr)r4r2)rFrJastyperKrqr rrs) rMr/rNrmrrOrPrOrvals rPtest_quintic_derivszTestInterp.test_quintic_derivsMs1 IIaL   + FF1IF#'" q!q5%. A!ae%8 AadAJ!A$ #;< #?IRC#?@ B AaeQK1R5!#=> #?IRC#?@ B$@#?s > D2 D8unstable)reasoncd}t|j|}ddg}t|j|j|||df}t ||j|jddy)Nr6rM)r4r;rGrjrT)rrdr rr)rMr/r-rOrOs rPtest_cubic_deriv_unstablez$TestInterp.test_cubic_deriv_unstableZs[  DGGQ '" twwAt} M$'' DGG%eDrfc:d}tj|jdf|dzz|jdd|jddzdz |jdf|dzzf}t|j|j||dgdgf}t ||j|jdd t ||jddtj d d t ||jddtj d d y) Nr4rr)r2r9rNrGrjrTr8rk)rFrrdr rrrs)rMr/r-rOs rPtest_knots_not_data_sitesz$TestInterp.test_knots_not_data_sitesis  EE4771:-1%7712;"-3772;.!A#&' ( twwA)/6('; = $'' DGG%eD$''!*a("**S/F$''"+q)2::c?Grfcd}ddg}ddg}t|||dgdgf}tjdd}|dz}t|||ddy) Nr6r8r+r)r8rMrGrjrT)r rFr`r)rMr/rmrrOrdrs rPtest_minimum_points_and_derivz(TestInterp.test_minimum_points_and_derivxs_  H H q!Q'WI0F G [[R  U"rE:rfcgdx}}tt5t||dgdfdddtt5t||ddddtt5t||dgdddtt5t||ddddd\}}tt5t||||fdddy#1swYxYw#1swYxYw#1swYuxYw#1swY[xYw#1swYyxYw)N)r+r4r6r7rrr]rG*)r]r]r+rMrmrlrs rPtest_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(tjd}|dz}dgdg}}ttd5t ||||fddddgdg}}ttd 5t ||||fdddy#1swY:xYw#1swYyxYw) Nrr4)rrr)rzBad boundary conditions at 0.rrG)irzBad boundary conditions at 6.)rFrJrBrDr ras rPtest_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 5sA<"B<BBcd}|j}|jd|jzz}dgdg}}t|||||f}t|||ddt||dd |dd ddd t||d d |dd ddd d D]%}t|||}t|||dd'y)Nr6r*)r)y@)r)y@@rGrjrTrr)FrJr2rr)r)rdrr r)rMr/rdrrOrPrOs rPrzTestInterp.test_complexs  WW WWs477{ "!zK=u r2q5%. A"rE: beQKq!5uu   bfaL%(1+E  ?A"2rQ/A AbE2E > ?rfctjdjt}tjdjt}dD]}t |||}||y)Nr^rr)rFrJrSintr )rMrmrr/rOs rP test_int_xyzTestInterp.test_int_xysX IIbM  % IIbM  % A"1a1-A aD rfc|tjddd}|ddd}|ddd}dD]}t|||y)Nr2r)rrrr)rFr`r )rMrdrmrr/s rPtest_sliced_inputzTestInterp.test_sliced_inputsI [[Q $ ssG ssG *A q!q ) *rfctjdjt}|dz}tjtj tj fD]}||d<t tt||y)Nr^r4r2) rFrJrSfloatrHrIrBrDr rMrmrzs rPtest_check_finitezTestInterp.test_check_finitesa IIbM  ' qD&&"&&266'* @AAbE *&8!Q ? @rf)r)r4r6rcvttd}|Dcgc]}|dz }}t|||ycc}w)Nr^r4r)listrr )rMr/rmars rPtest_list_inputzTestInterp.test_list_inputs9 rO aQT  1a1% s 6ctjtj|jtj|jf}dddgfg}dddgfg}t |j|d||f}t ||j|dd t ||jd d|d ddd t ||jd d|d ddd y) Nr)r+r9r:r;r6r$rjrTrr2)rFrrqrdrsr r)rMrrOrPrOs rPtest_multiple_rhszTestInterp.test_multiple_rhss UU266$''?BFF477O3 4b"Xb"X twwa% H$'' BU?$''!*a(%(1+EN$''"+q)58A;UOrfctjjd}d\}}tj|j|}|j|dddf}t |||}|j j |dddfk(sJd|jdfg}d|jdfg}t |||||f }|j j ||zdz dddfk(sJy) Nrr6rrrrrr)rrrrG)rFrLrrr r.r) rMrr/rNrmrrOd_ld_rs rP test_shapeszTestInterp.test_shapessii##D)1 GGCJJAJ& ' JJQ1aLJ ) q!Q 'ssyyQ1aL(((3::i()*3::i()* q!Qc ;ssyyQUQY1a0000rfc|tj|j}t|j|dd}t|j|ddgdgf}t |j |j dt|j|dd}t|j|ddgdgf}t |j |j dt|j|d d }t|j|d dd gf}t |j |j dt|j|dd }t|j|dd}t |j |j dt t5t|j|dd dddtjtj|jtj|jf}dddgfg}d ddgfg}t|j|d||f}t|j|dd}t |j |j dtjjd}d\}}tj|j|} |j|dddf} dtjdfg} dtjdfg} t| | || | f}t| | |d}t |j |j dy#1swYxYw)Nr6r0r$rNrSrk)r0r/rfr4)Nr/r]r1typor)r8r.rr{rrrrr|rGr/)rFrqrdr rr.rBrDrrsrLrrr) rMrrrrOrPrr/rNrmrr}r~s rPtest_string_aliaseszTestInterp.test_string_aliasess VVDGG_ q) D qF8fX:N Obdd/ q(>@ q*0F8(<>bdd/ q:K L q4(:L Mbdd/ q, G q$ ?bdd/: & A twwa @ AUU266$''?BFF477O3 4b"Xb"X q5%. I q(>@bdd/ii##D)1 GGCJJAJ& ' JJQ1aLJ )288I&'(288I&'( 1a#s < 1a ;bdd// A As L11L;c<tjjd}d\}}tj|j|}|j|}t ||}t ||||}t ||||}t|j|ddy)Nr)r6rrrjrT) rFrLrrrr make_interp_full_matrrr.) rMrr/rNrmrr-rOrs rPtest_full_matrixzTestInterp.test_full_matrix-sii##D)1 GGCJJAJ& ' JJAJ  1  q!Q * "1aA .Re%8rfc tjjd}d}tdddD]}t |dz dz }tj |jd|f}td|dzD]x}|d| |dfxxtj |jd||z fz cc<||dd| fxxtj |jd||z fz cc<z|j||f}||d|| df<|j||f}||| dd|f<tj ||f} tt|| dz dD]G\}} | d krtj|| | |d| f<*tj|| | || df<I|j|} tt| ||| |tjj|| d y) z Random elements in diagonal matrix with blocks in the left lower and right upper corners checking the implementation of Woodbury algorithm. rr6 r4r)Nr2r)offsetrjrk) rFrLrrrkdiagflatrrdiagonalrrlinalgsolve) rMrrNr/rrvrurlldrrOs rP test_woodburyzTestInterp.test_woodbury8s ii##D) q"a ?A!a%1%F CJJ1v./A1fqj) B#A2#qr' bkk#**aQZ*@AA !"crc' bkk#**aQZ*@AA  BVV,-B#%Agvgwx VV,-B#%Avgh !Q A!%! R"@A 81q5!{{1Q7Aa!eH!{{1Q7AaeH  8  1 A /2r1a@IIOOAq1 ?# ?rfN)-rr r rFr`rrdrqrr!r%r(rZrhrir-r/r2r6r8r:r<r>r@rCrGrKrQrUxfailrYr[r^rdrgrrlrnrsrwryrrrrr rfrPrrs RBEE "B B8E E  [[S,/*0*  [[S,/ *0 *I S [[S"45-6- 7 > 7 [[S,/ ?0 ?2 = " E B [[j) E* E H ;5. 5?**@ [[S,/&0& P 110f 9?rfrc|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)r@) rrFrrKrrr%evaluate_all_bsplslr) rmrr-r/rNArrmleftbbr.s rPrrUs 66QVV   66QVVaZ!^ ## # A !Qrzz*A 1X !t 1Q4<D??1d+a/D ' '1dD 9 !T!VDF]  ! AA HrfcFttj|||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)r@)maprFrsrrrKrrr%rdotTrr)rmrr-r/r}rNrrrmrrr Yr.s rPmake_lsq_full_matrixrqs "**q!Qi(GAq! A  QA !Qrzz*A 1X !t 1Q4<D??1d+a/D ' '1dD 9 !T!VDF]  ! qssAA qssAA AA q!f9rfmethodnorm-eqqrc eZdZejj dZd\ZZejej eZ ej eZ e eje de ddeZedZedZdZed Zed Zd Zed Zd ZedZedZedZedZedZej<j?de e!dddZ"dZ#y)TestLSQr)rr6rr2rc|j|j|j|jf\}}}}t ||||\}}t |||||}t |j||jj|j|z dz fk(sJ|\} } tjj| |d\} } } } t |j| y)Nrr)r2)rcond) rmrr-r/rr rr.rrrFrlstsq) rMrrmrr-r/c0AYrOaarrrs rP test_lstsqzTestLSQ.test_lstsqsVVTVVTVVTVV3 1a%aAq1B Aq!Qv 6R ssyyQVVaZ!^----Biioob!2o6 Aq!R rfc|j|j|j|jf\}}}}t j |}t |||||}t ||||||}t|j|jdt|j|jd|j|jk(sJy)Nrwrrjrk) rmrr-r/rFrar rr.) rMrrmrr-r/rrOb_ws rP test_weightszTestLSQ.test_weightssVVTVVTVVTVV3 1a LLO Aq!Qv 6aAqAf=SUU/SUU/sscee||rfc|j|j|j|jf\}}}}tj j dj|jd}t|||||d}t|||||d}t||||d}t|j|jd t j|j|jd rJy) Nrrrrrrrrjrk) rmrr-r/rFrLrrrr rr.r) rMrmrr-r/rb_neb_qrb_no_ws rPtest_weights_samezTestLSQ.test_weights_samesVVTVVTVVTVV3 1a II ! !$ ' / /QWWQZ / @q!QQyAq!QQt< Aq!D9U3;;vxxe<<<$$ E$K8q2a57789;;qss/ $8s DDc6|j|j|j|jf\}}}}d}tj j ||f}t ||||d}t ||||d}t|j|jdy)Nr6rrrrrSrk) rmr-r/rNrFrLr rr.) rMrmr-r/rNrrrb_neqs rPtest_multiple_rhs_3zTestLSQ.test_multiple_rhs_3sVVTVVTVVTVV3 1a II  1d)  ,q!Q$71a9=e4rfc@|j|j|j}}}|jdz}t |||||}t ||j |||}t ||j |||}t||||d||zzddy)N?@rr*rSrT)rmr-r/rr rrr) rMrrmr-r/r>rOrrs rPrzTestLSQ.test_complexs&&$&&$&&a1 VVx  Ar1a 7q"''1a?q"''1a?!d1gDG 3%eLrfcb|j|j|j}}}|jdz}t j ||fd}t ||||}t ||j||}t ||j||}t||||d||zzddt j ||fd}t ||||}t ||j||}t ||j||}t||||d||zzddy)Nrr)rr*rSrT) rmr-r/rrFstackr rrr)rMrmr-r/r>rOrrs rPtest_complex_2zTestLSQ.test_complex_2s &&$&&$&&a1 VVx  XXr2hQ ' Ar1a (q"''1a0q"''1a0!d1gDG 3%eLXXr2hQ ' Ar1a (q"''1a0q"''1a0!d1gDG 3%eLrfctjdjt}tjdjt}t |d}t |||d|y)Nr^r)rr/r)rFrJrSrkrr rMrrmrr-s rPrlzTestLSQ.test_int_xysM IIbM  % IIbM  % AO1a1V4rfctjdtj}tjdtj}t|d}t |||d|}t |j t |j t |j t d|}|dd|ddzdz }t||||d y) Nr^r@r)rrr2r9rSrk)rFrJfloat32rr rSrpr)rMrrmrr-spl_f32spl_f64x2s rP test_f32_xyzTestLSQ.test_f32_xy s IIb + IIb + AO!!QQv>! HHUOQXXe_ahhuo6 eafn # WR[u=rfctjddd}|ddd}|ddd}t|d}t|||d|y)Nr2r)rr6r)rFr`rr )rMrrdrmrr-s rPrnzTestLSQ.test_sliced_inputsK[[Q $ ssG ssG AqM1a1V4rfc tjdjt}|dz}t |d}tj tj tj fD] }||d<ttt||||"y)N r4r6r2r) rFrJrSrprrHrIrBrDr )rMrrmrr-rrs rPtest_checkfinitezTestLSQ.test_checkfinite!sq IIbM  ' qD AqM&&"&&266'* OAAbE *oq!Qv N Orfc|j|j|j}}}|jd|jd|jdt ||||y)NFrS)rmrr-r)rmrr-rUr rs rPrVzTestLSQ.test_read_only,sU&&$&&$&&a1      !qAf5rfr/r)c|j|j}}ttj|d|dd|}t ||||d}t ||||d}|dd|ddzdz }t ||||d y) Nrr2rrrrr)r9rSrk)rmrrrFr`r r)rMr/rmrr- spl_norm_eqspl_qrrds rPtest_qr_vs_norm_eqzTestLSQ.test_qr_vs_norm_eq5svvtvv1 BKK!aeQ/ 3%aA9E  AqAd;eafn # B%@rfcdtj|jd}tj|jd}t |j|j|j dd}t |||j dd}|dd|ddzdz }t ||||d y) Nr4r6rrr)r2r9rSrk)rFrepeatrmrr r-r)rMrmrruspl_2rds rPtest_duplicateszTestLSQ.test_duplicates@s IIdffa  IIdffa !DI1dff$?eafn #b 5959rfN)$rr r rFrLrrrNr/rrmrrr`r-parametrize_lsq_methodsrrrryrrrrrlrrnrrVrZrhrirurrrr rfrPrrsz ))   %C DAq 1 A 1 A  AaD!B%+Q/A ! !   =22 0 05 M MM,55 > >55OO66 [[S$uQ{"34A5A:rfrc,eZdZdZdZedZdZy) PackedMatrixasA simplified CSR format for when non-zeros in each row are consecutive. Assuming that each row of an `(m, nc)` matrix 1) only has `nz` non-zeros, and 2) these non-zeros are consecutive, we only store an `(m, nz)` matrix of non-zeros and a 1D array of row offsets. This way, a row `i` of the original matrix A is ``A[i, offset[i]: offset[i] + nz]``. c||_||_||_|jdk(sJ|jdk(sJ|jd|jdk(sJy)Nr4r)r)rvrncrr)rMrvrrs rP__init__zPackedMatrix.__init__TsW vv{{{{awwqzV\\!_,,,rfcL|jjd|jfS)Nr)rvrrr s rPrzPackedMatrix.shape]svv||A''rfcjtj|j}|jjd}t |jdD]_}t |j |j|z |}|j|d|f|||j||j||zf<a|S)Nr)r)rFrrrvrminrr)rMoutnelemrnels rPtodensezPackedMatrix.todenseashhtzz" Qsyy|$ JAdgg A.6C:>&&DSD/C4;;q>$++a.3"666 7 J rfN)rr r __doc__rpropertyrrr rfrPrrKs%-((rfrc 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)r8r2r@)scipy.linalg.lapackrrvrrrrrrfprotarurrFrint64)a_prstartrowrrvrrr}nzRrvroirr.rrcrboffsR_ps rP _qr_reduce_pyrjs+ 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 7Nrfc8||z||zz}| |z||zz}||fS)zLGivens rotate [a, b]. [aa] = [ c s] @ [a] [bb] [-s c] [b] r )r.rrvrOrrs rPrrs1 A#!)B A!B r6Mrfc|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).r4r2r)rvrrrFrrrr) rrrrrrr.rrsumms rPfpbackrs A GGEAr B 771: ## # afART7Qr!tQwZ'AbdCiL 2a4R ."bdm!QsUD.!Aac!C%in$55:::BdTka1g-!S& . Hrfc*eZdZdZdZdZdZdZy) TestGivensQRc|d}tj|t}|dzdd|zz z}t||}||||fS)Nr6r@r))rFrJrpr)rMrNr/rmrr-s rP_get_xytzTestGivensQR._get_xytsF  IIau % qD1ac7N 1 !Qzrfc <d}|j|\}}}}tj|||}tj|j \}}|j |z} |j\} } | |jd|z dz k(sJ|jdd|dz} tj| tj} |jj| |dz} t| | | }|dddf}tj | | | |t#tj$|j |z|j |z tj&|dt#tj$t)| |dddfz t)| |dddfztj&| dtj*|| }tj,|j.|j0|}t#||dddfdy) Nr^rr)r@rSrkgvIh%L=-a=)rrr)rrrrrindicesrFascontiguousarrayrdatartrr% qr_reducerminimumrabsrrrvr)rMrNrmrr-r/a_csrqrcqTyr}rrrry_c_fullc_bandeds rP test_vs_fullzTestGivensQR.test_vs_fulls ]]1% 1a%%aA.uuU]]_%1ccAg 2QWWQZ!^a''''w!A#w'%%fBHH= JJ  q!A# & FB ' q$wZ1fb"-  199;?#$99;?457]]15EE S 3sR1X~#6#&sR1X~#689;s9KRW Y!S!??133b1AU;rfcd}|j|\}}}}tj|||}|j\}}||jd|z dz k(sJ|jdd|dz} t j | t j} |jj||dz} t| | |} |dddf} t| | \} }tj| | || t| j| jdt!| j"| j"d| j$| j$k(sJt|| dy) Nr^rr)r@rSrkF) check_dtype)rrr)rrrFrrrrtrrr%rrrvrrr)rMrNrmrr-r/rr}rrrrr RRrs rPtest_py_vs_compiledz TestGivensQR.test_py_vs_compileds, ]]1% 1a%%aA. 2QWWQZ!^a''''w!A#w'%%fBHH= JJ  q!A# & FB ' q$wZq"%B1fb2.acc. 188?uu}}BU+rfc6d}|j|\}}}}tjd|dzt}t j ||||\}}} |j d} tj|||} | |dddfzj} | jj| |dzf} | jdd|dzjtj}t|| dt!||| |j d|z dz k(sJy)Nr^r)r@rrSrk)rrFrJrpr% data_matrixrrr)tocsrrrtrrSrrr)rMrNrmrr-r/rrrrr}ra_wA_offset_s rPtest_data_matrixzTestGivensQR.test_data_matrixs ]]1% 1a IIa1E * ,,Q1a8 62 GGAJ%%aA.qDz!((* XX  q!A#h '++g1g&--bhh72E*(QWWQZ!^a''''rfcnd}|j|\}}}}tj||dzf}tj|||tj |\}}}t |||} tj||||t| |} tj|||} t| | dy)Nr^r4rjrk) rrFrr%rrarrrr) rMrNrmrr-r/rrrrr.rs rP test_fpbackzTestGivensQR.test_fpbacks ]]1% 1a EE!QT'N ,,Q1bll1oF 62 FB '1fb!, 1aL __QA &AE*rfN)rr r rr rrrr rfrPrrs! ? ( !!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.npzrmry_GCVSPLNg-C6?F)rUrVr)rFloadr!rr)rMrrmrr*y_comprs rPtest_compare_with_GCVSPLz,TestSmoothingSpline.test_compare_with_GCVSPLEsqRWWY|, - (S AS AJ'H  ( .'1-a0 4US ( (s AA#ctjjd}d}tj|j |dzdz }|dztj d|zz|dzz|j dd|z}t||d}t||dd }tj|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. rrr7r4r6r8r)lamr0rGrr2rSrkN) rFrLrrr&rqr%rr r`r)rMrrNrmr spline_GCV spline_interpgrids rPtest_non_regularized_casez-TestSmoothingSpline.test_non_regularized_case}s ii##D)  GGC%%a(1,q0 1 qD266!a%= 1a4 '#**Ra*@ @*1aR8 *1aIF {{1Q42A. 4(%d+" $rfr4cJtjjd}d}tj|j |dzdz }|dztj d|zz|dzz|j dd|z}t||}|jtdd D]u}tj|}d ||<t|||}t|||||z } t|||||z } | | ksdtd | d d | d y)Nrrr7r4r6r8rr^rg>@zJSpline with weights should be closer to the points than the original one: z.4z < ) rFrLrrr&rqr%rchoicerrrrD) rMrrNrmrrindrspl_worigweighteds rPtest_weighted_smoothing_splinez2TestSmoothingSpline.test_weighted_smoothing_splines.ii##D)  GGC%%a(1,q0 1 qD266!a%= 1a4 '#**Ra*@ @#Aq)::eCjr:2 3C AAcF)!Q2Es1S6{QsV+,D53=1S612Hh $CCG)3$,R="233 3rfN) rr r r(r-r3rZrh fail_slowr:r rfrPr#r#"s6(>6Tp$& [[133rfr#c  |\ |\tz dz }|dzk\sJtz dz dzk\sJt fdt|D}tj|S)z-A naive 2D tensort product spline evaluation.r)c 3K|]9}tD])}||ft|zt |z+;ywr)rr ) rixiyr.r/nytxtyrmrs rPrzbspline2..sU7E"I7&(Bi!Aq"b/)AaBO;7;7s?A)r(rrrFrs) rr-r.r/nxrr@rArBrmrs `` @@@@@rPbspline2rDs DAq FB R1qB !A#II R1qB !A#II 77b 7 7C ::c?rfcb|dk(r|||cxkr ||dzkrdSdS|||z||k(rd}n)|||z |||z||z z t||dz ||z}|||zdz||dzk(rd}||zS|||zdz|z |||zdz||dzz z t||dz |dz|z}||zS)Nrr)r+r8r rs rPr r sAvda(!AaC&(s1(c11v1~ !A$h1Q3!A$ '!AqsAq/ 91Qx1QqS6  7N!AhlQqs1uX!A#. /!AqsAaC2C C 7Nrfctz dz }|dzk\rt|k\sJtfdt|DS)Nr)c3FK|]}|t|zywrrFrs rPrzbspline..s$6qta1am#6rrrs```` rPr:r:sD A QA 1H3q6Q;' ' 6U1X6 66rfceZdZddZdZy) NdBSpline0ct|}|t|jksJ t|td|D|_td|D|_||_y#t$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 rPrz&NdBSpline0.__init__..s6bx~~b)6s!c3RK|]}tj|t!yw)r@N)rFrsrp)rtis rPrz&NdBSpline0.__init__..s?rrzz"E22?s%'N)r(rrCrr/r-r.)rMr-r.r/rs rPrzNdBSpline0.__init__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) r(r-rr/rFrr itertoolsproductr.prodr rs) rMrmrrrtdxdr/resultitersidxterms rP__call__zNdBSpline0.__call__s466{1v~~JtOt 4AVVAY!Bq ARU{!r2.2!ad8r/R!QZ/ // //Q4191B! !3 33 4 !H rr)rrrjrkr) rFrLrrrrrrr) rMrrNr/n_trr-r.rOnbxis rPtest_1DzTestNdBSpline.test_1D sii##E*1 GGCKKQUQYK/ 0 KKaYK ' Aq!  tQ " [[b[ !2ag;"E +"QW+$$!aggaj(AAAArfc tjd}|dz}t||d}|dzd|zz}t||d}|j|jf}|jdddf|jdddfz}||dfS)Nrr6rr4rFrJr r-r.rMrmrry_1rut2rs rP make_2d_casezTestNdBSpline.make_2d_case s IIaL qD A+dQqSj"1cQ/eeUWW  UU1d7^eggdAg. .2qyrfcftjd}|dz}t||d}tjddz}|dzd|zz}t||d}|j|jf}|jdddf|jdddfz}|||j |j fS)Nrr6rrrr4)rFrJr r-r.r/rhs rP make_2d_mixedzTestNdBSpline.make_2d_mixed, s IIaL qD A+ IIaL3 dQqSj"1cQ/eeUWW  UU1d7^eggdAg. .2suuegg%%rfc gd}|j\}}}|Dcgc]\}}|dz|dzd|zzz}}}ttj|Dcgc]}t ||||c}tj|ddt ||d} | |j t|fk(sJt| ||dtj|}tj|d <ttj| |tjgd tjjd } | jd dz}| |} | j dk(sJ|jdj\}}t| j!|dz|dzd|zzzdycc}}wcc}w)Nrr=)r=r))rrr6r4Frjr rUrrkri)TFFr)r7r6r4rr)r7r6)r2r4)rkrrFrsrDrrr(rHrrrLrrrtrravel) rMrdrjrr/rmrtargetrbspl2rrYs rPtest_2D_separablezTestNdBSpline.test_2D_separable; s /%%' B467&1a!Q$!Q$1*%77  b#IHRR$;#IJ 6*$)" $ "bA&Ry3r7+---b U ,ZZ^664r+RZZ8L-MNii##E* [[i[ (1 ,r||v%%%zz'"$$1 11qs +% 978$Js GG cd}gd}|Dcgc]\}}|dz|dzd|zzz}}}|j\}}}tj||||f} d} t|| d} | | } t|||| } | jdk(sJt | | gdzd | |jtj|dd | j j|dzk(sJt | |tj|dddfd d | jd}t||d}|| } | jdk(sJt | | | g| | ggd ||jtj|dd |j j|dzk(sJt ||tj|ddddfd d ycc}}w)Nr4ror6rprr7r7rjrkr2FgvIh%,=rqrrr4r4)r4r4) rkrFrrrrr.rsrt)rMrrdrmrrsrjrr/c2_4rbspl2_4rY val_singlec2_22bspl2_22s rPtest_2D_separable_2z!TestNdBSpline.test_2D_separable_2\ s /467&1a!Q$!Q$1*%77%%' Byy"b"b)* B*)Yr2q)"- ||t####q(u 6 r{  BHHRL"$5 8N$NNNN bjj&8D&A$)" $  \*R!,"||v%%%$j1$j139> @  "" Sb!HJJ$4$4TU$;;< =< bjj&8D$&G$)" $E8sGcgd}|Dcgc]\}}|dz|dzd|zzz}}}|Dcgc] }|d|zz }}|j\}}}|dz}tj||||f} d} t|| d} | | } t|||| } | jdk(sJt | | gd zd ycc}}wcc}w) Nror6r4y@rrprrwr7rjrk)rkrFrrrr)rMrdrmrrsr-rjrr/ryrrzrYr{s rPtest_2D_separable_2_complexz)TestNdBSpline.test_2D_separable_2_complex s /467&1a!Q$!Q$1*%77$*+q!bd(++%%' B 6]yy"b"b)* B*)Yr2q)"- ||t####q(u 68+s B>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)Nrr6rrrrr7r)r)r+r+rjrkr)rr4皙?g?@) rFrLrrrrrrrrDr) rMrr/rArBr.rrdrs rPtest_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" $Cs7E c|j\}}}}gd}|Dcgc]\}}|dz|dzd|zzz}}}t||||f} | |jt|fk(sJt | ||dycc}}w)N)ffffff?r)r=g333333@)rrr6r4rrjrk)rmrrr(r) rMrjrkxkyrdrmrrsrts rP test_2D_mixedzTestNdBSpline.test_2D_mixed s++-BB 1467&1a!Q$!Q$1*%77"bRH-Ry3r7+---b U ,8sBc |j\}}}}gd}t||||f}||d}t||D cgc]\}} d|dzz| dzd| zzzc} }d||d }t||D cgc]\}} d|dzzd| zdzzc} }d||d }t||D cgc]\}} |dz| dzd| zzzc} }dtt5||d }dddtt5||d }dddycc} }wcc} }wcc} }w#1swY>xYw#1swYyxYw) Nrrrfrr6r4rjrkr)r))rr)r2rr2rr))rmrrrBrD) rMrjrrrrdrtrrmrs rPtest_2D_derivativez TestNdBSpline.test_2D_derivative sa++-BB 1"bRH-B6";=>41a1a41a4!A#:.>U LB6"8:;11a41Q37+;% IB6"9;<AAA!,<5 J: & (w'C (: & +z*C + +?<= ( ( + +s)D <D& 6D, * D2 D>2D;>Ec 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)r4r6rrrr6rr7r)rrrrjrk) rFrLrrrrrrrrJr rMrrrrArBr.rdrtbspl2_0rs rPtest_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) Nrrrr6rr4rjrk)rFrJr r.rr-r/rrTrUranyrrtr) rMrmrspl_xspl_yrrvvaluesrgirvrOrdbxis rPtest_tx_neq_tyzTestNdBSpline.test_tx_neq_ty sM IIaL IIaL3 "1ada0"1adQqSjA6 WWQW a 0 0%''577+R%''5771CDQ$4AqD1Q3Ja#88%q!ff5!*!2!21a!8 9Aq!f 9 92h88C=$$&&&SW51 FLL16F :s<E6ctjd}|dz}t||d}|dzd|zz}t||d}|dzd|zzdz}t||d}|j|j|jf}|jddddf|jddddfz|jddddfz} || dfS)Nrr6rr4r)rg) rMrmrrriruy_2rrjrs rP make_3d_casezTestNdBSpline.make_3d_case s IIaL qD A+dQqSj"1cQ/dQqSj1n"1cQ/eeUWWegg &eeAtTM"ggdAtm$%ggdD!m$%2qyrfctjjd}|jddz\}}}|dz|dzd|zzz|dzd|zzdzz}|j \}}}t ||d} t |||D cgc]} | } } | | } | jd k(sJt| |d ycc} w) Nrr6r?rrr6r4r)r)r?rjrk) rFrLrrrrziprr) rMrrmrrrrst3c3r/bspl3rrdrYs rPtest_3D_separablezTestNdBSpline.test_3D_separable sii##E*++7++a/1aAA!$1qs Q7%%' B"bA&Q1 &Aa & &r||u$$$U3's B=c|j\}}}t||d}tjj d}|j ddz\}}}t |||D cgc]} | } } t|| dd|d zz|dzd |zzz|dzd|zzd zzd t|| d d|z|dzd |zzz|dzd|zzd zzd t|| dd|zd|d zzd zz|dzd|zzd zzd t|| dd|zd|d zzd zzdzd t|| dtjt| d ycc} w)Nr6rrrrr)r)rrrr4r)rjrk)r4rrr)r4r)r)r4r)r6)r4r)r7) rrrFrLrrrrrr() rMrrr/rrrmrrrrrds rPtest_3D_derivativez TestNdBSpline.test_3D_derivative s%%' B"bA&ii##E*++7++a/1aQ1 &Aa & &bY/!Q$!Q$1*-A!a@u N bY/!q!tacz*adQqSj1n=E K bY/!qAvz*adQqSj1n=E K bY/!qAvz*a0u > bY/R) 7's* E/c jtjjd}d}tjddddtj|j ddzddddf }tjddddtj|j ddzddddf }tjddddtj|j ddzddddf }|j |j |z dz |j |z dz |j |z dz f}t|||f|| }t|||f|| }d } t|| || d tjgd gdgdf} t|| | D cgc] } ||  c} d ycc} w)Nrr6rrrrr7r)r)r+r+r)rjrkrrg?rgffffff?) rFrLrrrrrrrJrr) rMrr/rArBtzr.rspl_0rdrs rPtest_3D_randomzTestNdBSpline.test_3D_random) sii##E*  UU1aArwws{{{':;a?Aq!K L UU1aArwws{{{':;a?Aq!K L UU1aArwws{{{':;a?Aq!K L KKbggaik27719Q; ! DK ER a1-BB<a0 Br7 UU;""#$ 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)Nrr6rrrrr7r)r*rrrrrjrk) rFrLrrrrrrrrrr) rMrr/rArBrr.rrrrds rPtest_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 @rf cls_extrapNT call_extrapcR|j\}}}t||d|}gdgdgd} }}ttj||| f\}}} t ||| D cgc]} | } } |dz|dzd|zzz| dzd| zzdzz} || |} t | | d ycc} w Nr6)r/rr)r2r)rrrn)r2g@r4r)rqrjrkrrrrFrsrr)rMrrrrr/rrmrrrrrdrsrYs rPtest_extrapolate_3D_separablez+TestNdBSpline.test_extrapolate_3D_separableO 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)rMrrrr/rrrrmrrrrrdrsrYs rPtest_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)Nr6r)rr)r)rrrn)r2rrr4r)Frqrr2rjrk)rrrrFrsrrr) rMrrr/rrmrrrrrdrsrYs rP#test_extrapolate_false_3D_separablez1TestNdBSpline.test_extrapolate_false_3D_separablep 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)Nr6rrr)r4rrrrnr2rrjrk) rrrFrsrHrrrr) rMrrr/rrmrrrrrdrsrrYs rP 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)Nrr6r6rr7rr2r4r)rrrrrjrk)rFrLrrrrflags c_contiguousrrrrrJrrs rPtest_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;"#$2cc7BssG,aB8<b1gr#A#w/r2h?b /122 @2s:G c|j\}}}t||d}tdD]}d||j_d|j_t||d}|d|dk(sJy)Nr6rFrh)rrrr writeable)rMrrr/rrbspl3_s rP test_readonlyzTestNdBSpline.test_readonly sy%%' B"bA&q *A$)BqEKK ! *"2rQ'Y6)#4444rfcr|j\}}}tjgdgdg}t|||j |||}tj|||||g}|j d|j dk(sJt |j|jdtt5tjgd||gdzdddttd5tjd d gg||gdzdddy#1swYBxYw#1swYyxYw) Nrh)r7rrrgؗҜ ? 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) Nrr6rrrrr7r)rcLtjgdgdgdf}||y)Nrrr)rFr)rrrds rPrYz1TestNdBSpline.test_concurrency..worker_fn s&{&&'(B Grfr^) rFrLrrrrrrr!) rMrr/rArBrr.rrYs rPrZzTestNdBSpline.test_concurrency s+ii##E*  UU1aArwws{{{':;a?Aq!K L UU1aArwws{{{':;a?Aq!K L UU1aArwws{{{':;a?Aq!K L KKbggaik27719Q; ! DK ER a1-  Is3rf)rr r rerkrmrur~rrrrrrrrrrrrZrhrirrrrrrrrjrZr rfrPr`r` sB"  &9B($V6&$&,+2@ G(& 47,G&@& [[\D$<8 [[]T4L9 4:9 4 [[X |'DE4F4 @ 4$@2 5 9 [[44rfr`c<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)Nrrr6r4r)rrSrkr4rrT)rlinearrrj) rFrJrTrUr"rrrr r.scipy.interpolater) rMrmrrrvrOrdrvrrrRGIrs rPtest_2D_separable_simplez#TestMakeND.test_2D_separable_simple s1 IIaL IIaL3 1d7Q!Q$1*dAg!66!*!2!21a!8 9Aq!f 9 9Aq66Q/R&,,.u=#1ada0"1adQqSjA6 WWQW a 0 0DFFQ7 E1a&&2Bb6:s&D?ctjd}tjd}tj||Dcgc] \}}||f }}}|dddfdz|dzd|zzdddfz}tj||||f}t ||f|dt j}||} tj||||fjt} | jdk(sJt| jddd| d|jd } t ||f| dt j}||} | jd k(sJt| jdddd| jd dycc}}w) Nrr6r4r/solver)$r7r7rjrkrx)rr4r4) rFrJrTrUrr"sslspsolverSrprrrt) rMrmrrvrOrdrvalues4rvrYrsvalues22s rPtest_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 r/)rr)r6r))r)r6rc~tjd}tjddz}tj||Dcgc] \}}||f }}}|dzdddf|dzd|zzdddfz}t ||f||t j }t|||jdycc}}w) Nrrrr6r4rrSrk) rFrJrTrUr"rrrrr) rMr/rmrrvrOrdrrvs rPrzTestMakeND.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)Nrrr2r6r4r)r)rFrJrHrBrDr")rMrmrrs rP test_2D_nanszTestMakeND.test_2D_nans s IIaL IIaL3 "1d7Q!Q$1*dAg!66 : & - A! , - - -s /B  Bc tjgd}tjgd}tjgdgdgdgdgdgdg}|||fS)N)rr9r:r;rr)r)r4r)r4r)r))r)r4r6r4r)r))r)r4r4r4r)r))rFrrqs rP_get_sample_2d_datazTestMakeND._get_sample_2d_data sR HH. / HH. / HH""""""   !Qwrfc|j\}}}t||f|d}t||f|d}tjgdgdgj }t ||||dy) Nr)rrrr)gffffff@g333333@rffffff @333333?r6r)rrr;rDr+r6rjrkrr"rrFrrrrMrmrrrrvrrds rPtest_2D_vs_RGI_linearz TestMakeND.test_2D_vs_RGI_linear- sq**,1aAq61*%q!faA XX66899:  R#b'6rfc|j\}}}t||f|dtj}t ||f|d}t j gdgdgj}t||||dy) Nr6r cubic_legacyrrrrjrk rr"rrrrFrrrrs rPtest_2D_vs_RGI_cubiczTestMakeND.test_2D_vs_RGI_cubic7 sw**,1aAq61#++>%q!faG XX66899:  R#b'6rfrc|j\}}}t||f|d|d}t||f|d}tjgdgdgj }t ||||dd y) Nr6gư>)r/rrVrrrrrjrrTr)rMrrmrrrrvrrds rPtest_2D_vs_RGI_cubic_iterativez)TestMakeND.test_2D_vs_RGI_cubic_iterativeA sy **,1aAq61&tD%q!faG XX66899:  R#b'DArfc|j\}}}t||f|dtj}t ||f|d}t j gdgdgj}t||||dy) Nrrquintic_legacyrrrrjrkrrs rPtest_2D_vs_RGI_quinticz!TestMakeND.test_2D_vs_RGI_quinticP sx**,1aAq61#++>%q!fa8HI XX66899:  R#b'6rfzk, meth))r)r)r6r)rrctjjd}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@rrrrrrrgffffff?rr>rrjrk) rFrLrcumsumrr"rrrr) rMr/methrndmrmrrrrrvrrds rPtest_3D_random_vs_RGIz TestMakeND.test_3D_random_vs_RGIZ syy$$V, IIdlll* + IIdlll* + IIdlll* +9-Aq!9f#++F%q!QiE YY  3Sw  ?R#b'6rfc:|j\}}}ddi}ttd5t||f|fddi|dddttd5t||ft j ||ffddi|dddy#1swYJxYw#1swYyxYw)Nmaxiterr)rrr/r6)rrBrDr"rFr)rMrmrrr solver_argss rPtest_solver_err_not_convergedz(TestMakeND.test_solver_err_not_convergedj 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)rr r rrrZrhrirrrrrrgmresgcrotmkrrrrr rfrPrr s7(B4 [[S"JK>L>- 77 [[X 3;;'?@ BA B7 [[N 7 7GrfrcHeZdZdZdZdZdZdZdZdZ dZ d Z d Z y ) TestFpcheccd}tjdjdd}tjd}tjt d5t j|||dddtjt d5t j|||dddy#1swYExYw#1swYyxYw)Nr)rr4rz 1D sequencer)rFrJrtrZrrD_bfpcheckrMr/r-rms rP test_1D_x_tzTestFpchec.test_1D_x_tw 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)Nr6r4r)r?r^z Need k+1*r) rFrJdfitpackfpchecrZrrDrr)rMr/rNr}r-rms rPtest_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) Nr6rr)r4r)r)r4r6r7rr2rz Last k knots*rzFirst k knots*rrrrrrZrrD)rMr/r-rmtts rPtest_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) Nr6rr)r4rr)r4r6rr7rzInternal knots*r)rrrrrZrrDrs rPtest_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) Nr6rr)rrr#zOut of bounds*rr2r )rMr/r-rmrds rPtest_condition_4zTestFpchec.test_condition_4 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)r4r4)rrrriSchoenberg-Whitney*r)rrrrrrZrrDrrrs rPtest_condition_5_x1xmz TestFpchec.test_condition_5_x1xm 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)rrrrrs rPtest_condition_5_k1zTestFpchec.test_condition_5_k1 sI   #Jq!Q'1,,,zz!Q"***rfcd}dg|dzzdgzdg|dzzz}dgdz}tj|||dk(sJtjtd5t j |||ddddg|dzzdgzdg|dzzz}dgdz}tj|||dk(sJtjtd5t j |||dddy#1swY~xYw#1swYyxYw) Nr6rr)r4rrirrrrs rPtest_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) Nr6rr)r4rrr7rirrrrs rPtest_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)) rrr4r6r7rrrr)r)r)r)@rrrnrirrrrs rPtest_condition_5_3zTestFpchec.test_condition_5_3 s`  ' )q!Q'2--- ]]:-B C JJq!Q    s A##A,N) rr r rr r rrrrrrr r rfrPrrt s4   *!,  !>  +   + rfrctj|||| }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)r2r4rSrk)rFrrr(rr) rmr-r/ residualsr>rfpartscarriescarrys rP_splitr& 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.r4N)r&rr(rDrFrr) rmr-r/r"r#r>idx_max fpart_maxr idx_newknotnew_knotidx_tt_news rP _add_knotr.. s1a+JFBGI 3v; " ac7RU?Q 6!9y#8Gq I" $PQQg;GAI.2q8K~H OOAx (E EE!FU)Xqy0 1E LrfcFeZdZdZej j dgddZdZdZ dZ dZ d Z d Z d Zej j d gd ej j dgddZej j dZy)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)Nrr@r6r+r)r8ro)r/r-r4r_fitpack_reprorSrk) rFrJrprr rr3add_knotr.r)rMrmrr/r-rr"_frnew_tnew_t_pyspl2 residuals2new_t2 new_t2_pys rPtest_split_add_knotz%TestGenerateKnots.test_split_add_knotF s IIau % qD2q1u:   HHbT1Q3Z2$!*, -aa1-VaZ!O ; Q1i0Q1i0xe4q!qE21gkA% a:6a:6  6rfr/rctjdtj}tj|tjzdz }t t |||dd}t|||dd}t||dy)Nrr@rr/rr2rSrk) rFrJrKrqrrurr r)rMr/rmrr-r s rPtest_s0zTestGenerateKnots.test_s0^ sk IIarzz * FF1RUU719  1Q/ 0 4 AqA #A &2E*rfcd}tj|}|dz}tt||dd}t |dt |ddy)Nr^r6rr>r2rSrkrFrJrurrrrMrNrmrknotss rP test_s0_1zTestGenerateKnots.test_s0_1g sI  IIaL qD^AqA34b ;q!#45Arfcd}tj|}|dz}tt||dd}t |dt |ddy)Nrr6rr>r2rSrkrArBs rP test_s0_n20zTestGenerateKnots.test_s0_n20o sI  IIaL qD^AqA34b ;q!#45Arfc tjd}|dz}tt5t t ||ddddddy#1swYyxYw)Nr^r6rr/rnest)rFrJrBrDrurrMrmrs rP test_s0_nestzTestGenerateKnots.test_s0_nestv sJ IIbM qD : & : 1QR8 9 : : :s A  Actjd}tj|tjzdz }d}t t |||d}gdgdgdgdgd g}t |t |k(sJt||D]\}}t||d t|||d\}}}t|d |d y )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. rr6rr>)r8r8r8r8rorororo) r8r8r8r8r;rorororo r8r8r8r8r9r;rorororo) r8r8r8r8r9r;rrorororo) r8r8r8r8r9r:r;rDrrorororSrkr2N) rFrJrqrrurr(rrr ) rMrmrr/rCwantedr-r rs rP test_s_switchzTestGenerateKnots.test_s_switch} s. IIaL FF1RUU719  ^AqA6726:>A  5zS[(((' /EAr Ar . /Ad+1ab 151rfc`ttd}t||dd}t|y)Nrrr))rr/)rurrnext)rMrmgens rPrwz!TestGenerateKnots.test_list_input s& qNQSA. S rfc Ttjd}tj|tjzdz }d}t t ||d|d}t |dgdd tt5t t ||dd dddy#1swYyxYw) Nrrr6r^rHr2rMrSrkr7)r/rI) rFrJrqrrurrrBrD)rMrmrrrCs rP test_nestzTestGenerateKnots.test_nest s IIaL FF1RUU719  ^AqA<=b @u N: & 4 12 3 4 4 4s <BB'c tjd}tj|tjzdz }t t 5t t||tjddddt t 5t t||tjd dddy#1swYMxYw#1swYyxYw)Nrr?r) rFrJrqrrBrDrurrrJs rPrzTestGenerateKnots.test_weights s IIaL FF1RUU719  : & 8 1 " 6 7 8: & 6 1 4 5 6 6 8 8 6 6s+C,CCCnpts)rrirr)rg{Gz?rctjjd}dtj|j |z}tj |tj zdz tj|dz dz z}d}t||||d}tt||||d }t||d y) Nrr^rrr4r6r>rr2rSrk) rFrLrrrrqrexpr rurr) rMrrWrrmrr/r-r s rPtest_vs_splrepz TestGenerateKnots.test_vs_splrep syy$$U+ rwwt|||./ / FF1RUU72: !A# !2 2  1a1 "1 % .Aa0 1" 5AE*rfc8d}tj|}|dz}tt||dd}t 5}|j t }t||dd}t|dk(sJ dddt|ddy#1swYxYw)Nr6Jz5r>r)r2r) rFrJrurrrecordRuntimeWarningr r(r)rMrNrmrrCsuprcrYs rPtest_s_too_smallz"TestGenerateKnots.test_s_too_small s  IIaL qD^AqA78   C >*AAe,Cq6Q; ;  b 3q6*   s 5BBN)rr r r<rZrhrir?rDrFrKrOrwrTrrZrjrar rfrPr0r0E s70 [[S/2+3+BB:)2V 46 [[V]3 [[S.1+24+" [[ + +rfr0cZ|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<$|||z |ztj|z z}|S)zStraitforward way to compute the discontinuity matrix. For testing ONLY. This routine returns a dense matrix, while `_fitpack_repro.disc` returns a packed one. rr)r4Nrrr@) rrFrrr'emptyrprmath factorial) r-r/rNdeltanrintrQtiir}matrrs rP disc_naiverj sD  A a!eaiL1Q4 E !GaKE 1Q3qs1uB ))B C!HH1II(266!a%!)$a(3A 88U1Waggaj) 7D 1aggaj! $,!Q$!AaCF)+QT1W , U5[1 t~~a0 00D KrfceZdZdZddZdZy)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|_ ddl m}t|j!||j#|_|jdk(sJ||jz} tj&| t j(|j$jdf|_||_y)Nr@r)rr2)rmrr-r/rFrarprrrr'ra_denserr3rdiscrb_denserrrr) rMrmrr-r/rrrnr5rs rPrzF_dense.__init__ s 12au-vv{{a<'!RVVAGGAJNQ$67;A>40 ;#SXXa^4<<> vv{{ Z%%BHHT\\%7%7%:;;<rfctj|j|j|z f}ddlm}m}||d\}}|j|jz}|jd}||d|d|f|d|} t|j| |j} tj|jdz| |j|j z dzz} | |_| |j$z S)Nr)rreconomic)r\r)r4)rFrrnrp scipy.linalgrrrrrrr-r/rrrmrrr) rMrabrrrrcqyrr.rfps rPr]zF_dense.__call__ s YY dllQ&67 8 +":&1 SS477] WWQZ !CRC"H+r#2w 'dffa( VVDFFAITVVtvv!5 99 :DFF{rfr)rr r rrr]r rfrPrlrl s,rfrlceZdZdZdZdZdZdZdZdZ dZ d Z e jjd Zd Zd Zd Zy)TestMakeSplrepctjddd}tjddd}tt5t ||dddtt5t ddddddtt5tj |j dddf}t ||ddddtj d}tt5t ||d z|d dddtj d }tt5t ||d z|d dddtj |jddf}tt5t ||d z|d dddtt5t |ddd |d zddddtt5t ||d zd d dddtt5t ||d zd dddtt5t ||d zd dddddtt5t ||d zdddddtt5t tjdtjdddddy#1swYjxYw#1swYQxYw#1swYxYw#1swYxYw#1swYxYw#1swYoxYw#1swYMxYw#1swY0xYw#1swYxYw#1swYxYw#1swYxYw#1swYyxYw)Nrr^r?rr)r4rrr6)rrr2r=r>)r/rIr)rrIr ) rFr`rBrDrrrrrCrJrMrmrrs rPtest_input_errorsz TestMakeSplrep.test_input_errors1 s KK2r " KK2r " : &  1  : & % 1 $ %: & %Aq)*A 1 $ % GGBK : & - 1a41 , -WWR[L : & - 1a41 , - GGQWWQZO $ : & - 1a41 , -: & . $B$A - .9 % / 1a43# . /: & ' 1a42 & ': & 5 1a411 4 5: & / 1a412 . /: & ;  ! biilc : ; ;a   % % % %  - -  - -  - - . . / / ' ' 5 5 / / ; ;s J3"K2K &K&K'4K4L L7L L( L455M3J=K  KK$'K14K>L LL%(L14L=M ctjddd}tj|dzdz dz}d}d}tjdg|dzzd d gzdg|dzzz}|||||fS) Nrrr?gQ @r4r6gq@H&?r)r=r;)rFr`rqr)rMrmrr/rr s rP _get_xyktzTestMakeSplrep._get_xykth sy KK1b ! VVAdFQJ  "   XXqc1Q3i3*,sAaCy8 9!Q2~rfcddlm}|j\}}}}}|||dddf|||}t|||||}dD]} t || || dy)NrFr)r^rrSrk) scipy.interpolate._fitpack_reprorrrlr) rMrrmrr/rr-ff_drs rPtest_fitpack_FzTestMakeSplrep.test_fitpack_Fq sj6( 1aA a1d7Q1 %aAq!$ 6A AaD#a&u 5 6rfcddlm}|j\}}}}}tj|j dt }|||dddf||||}t||||||} t|||||} dD]B} t|| | | dtj| | | | dsBJy)Nrrr@rVrrSrk) rrrrFrJrrprlrr) rMrrmrr/rr-rfwfw_drrs rPtest_fitpack_F_with_weightsz*TestMakeSplrep.test_fitpack_F_with_weights{ s6( 1aA IIaggaj . q!AtG*aA +q!Q1*aAq!$ @A BqE47 7{{3q647? ?? @rfc ddlmcm}tjj d}tj ddddtj|jddzddddf }t|d}}t|j||j}t||}|jd|d|zz dz k(sJt||d y) Nrrrrrr6r4rSrk)r interpolater3rFrLrrrrr(rrorrjrr)rMr5rr-rNr/DD_denses rPtest_disc_matrixzTestMakeSplrep.test_disc_matrix s 76ii##E* EE!Q1bggckkqk&9:1rSrk) rrFrr rrrr.r) rMrmrr/rr r-r.rs rPtest_simple_vs_splrepz$TestMakeSplrep.test_simple_vs_splrep s)1aB XXqc1Q3i3*,sAaCy8 9q!qA&!A17||!Q!q)+355::E:rfcb|j\}}}}}tt||||d}t||||}t|||||}t |j |j dt |j |j d|j|jk(sJy)Nr>r2)r-r/rrSrk)rrurrrr-r.r/) rMrmrr/rrr-spl_autospl_ts rPtest_with_knotszTestMakeSplrep.test_with_knots s( 1aA 1Q/ 0 4q!qA.AqAa0 EGG%8 EGG%8zzUWW$$$rfcd}tj|}|dz}d}t|||d}|jjdd|dzzk(sJy)Nr^r6r)r>rr4)rFrJrr-r)rMrNrmrr/rs rPtest_no_internal_knotsz%TestMakeSplrep.test_no_internal_knots sT  IIaL qD !Q!q)uu{{1~AaC(((rfcd}tj|}|dz}t||d}t||d}t |j |j dy)Nr^r6rrSrk)rFrJrr rr.)rMrNrmrrspl_is rPtest_default_szTestMakeSplrep.test_default_s sM  IIaL qD!Q!$"1a1-uwwU3rfcd}tj|}|dz}t5}|jt}t ||dd}t ||dd}t|dk(sJt|j|dttj|jdg|jdzzf|dd dddy#1swYyxYw) Nr\r6r]r>r4rr)rrk)rFrJrr^r_r rr(rr-rrr.r/)rMrNrmrr`rcrYrs rPrazTestMakeSplrep.test_s_too_small s  IIaL qD   0C >*AAe,Caa51Cq6Q; ; CEE3q6 * BEE#%%!ceeAg"67F 0  0 0 0s BC  Ccttjgdtj}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@r@)gJ@gH@gLH@gffffffG@gE@g)\(D@gC@gB@g333333@@g<@g3333339@g5@g2@g,@g%@g@g @r8g5{2?rr4r)rr/r)rFrsrKrrBrDrr|s rPtest_issue_22704zTestMakeSplrep.test_issue_22704 s JJ%-/JJ 8 JJ&(ZZ 1 JJy1771:-RZZ @ : & . 1Q" - . . .s B..B7cNd\}}tj|}|dz}t|||}t|||d}|jjdk(sJ|jjdk(sJt||dd|zz z|d}|jjdk(sJy)Nr^r6r6rh㈵>r>r))rFrJrr.r)rMrNr/rmrrrurs rP test_shapezTestMakeSplrep.test_shape s1 IIaL qD!Q!$AqA.uuzzQww||q   Aq1ac7{a48ww||q   rfczd\}}tj|}|dz}t||dd}t||dd}|jjdk(sJ|jjdk(sJ|j j d||zdzk(sJ|j j dd|dzzk(sJy)Nrr6rr>r)r4)rFrJrr.rr-r)rMrNr/rmrrrus rPtest_s0_vs_notzTestMakeSplrep.test_s0_vs_not s1 IIaL qDAqA+AqA+ww||q   ww||q   ww}}Q1q519,,,ww}}Q1A;...rfN)rr r r}rrrrrrrrrZrhrjrarrrr rfrPrxrx0 s^5;n6 @ 0; %)4 [[ 0 0 .! /rfrxceZdZd dZej j dgddZej j dgddZdZ dZ dZ y ) TestMakeSplprepctj|tjz|z }tj|tj|g}|||fSr)rFrJrrqrs)rMr}r/rmrs rP_get_xykzTestMakeSplprep._get_xyk sB IIaL255 1 $ VVAYq "!QwrfrrrgMbP?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) Nrr\rr{r^rrzrSrkr)r)rFrJrrqrsrrrr-r(rsrr.r) rMrr}r/rmr num_knotsr-r.u_rrrs rPtest_simple_vs_splprepz&TestMakeSplprep.test_simple_vs_splpreps1 IIaL255 1 $ VVAYq "%u=  Q Aq2a1%Q 2E* qu-1v1%%%ZZ]__r. A01aa03% Arfc||j\}}}t|tsJtj|ddk(sJt ||\}}t tj ||\}}t|||t|d|ddt|dt|dk(sJt|d|dD]\}} t|| d|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(sJt!t"5ttj |j|dddy#1swYyxYw)Nrr4rzrkrSr))rrrurFrrrsrr(rr rr-r.rr/rBrD) rMrrrrYrtck_au_arrrs rPtest_array_not_listz#TestMakeSplprep.test_array_not_list"sB--/1a!T"""xx{1~"""aQRZZ]a0 s3Q'Aau53q6{c%(m+++#a&%(+ 0FB B / 01vq!!!xxa &"((1+555a1%Q3U+uQxe4q6uua   1v||rxx{***bjjmq1Q3U+uQxe4q6uua   1v||rxx{*** : & / AA . / / /s >+J22J;ct|jd\}}}t|\}}t|||dy)Nr^r|rSrk)rrr)rMrmrr/rrs rPtest_default_s_is_zeroz&TestMakeSplprep.test_default_s_is_zeroEs5--"-%1aaQA.rfcp|jd\}}}t|d\}}t|d\}}t||dt|||dt|||d|j|jk(sJ|jj |jj k(sJy)Nr^r|rrzrSrkr)rrrrr.r)rMrmrr/ru_ispl_nu_ns rPtest_s_zero_vs_near_zeroz(TestMakeSplprep.test_s_zero_vs_near_zeroKs--"-%1a!!q) s!!u- sSu-c AE2c AD1zzUZZ'''ww}} ---rfctjdt}tt5t |dddtt5t |ddddtt5t |ddddt |gd\}}t |gd\}}||jdk(sJt|||gd y#1swYxYw#1swYxYw#1swYpxYw) Nrr@rrzrr)r)rrSrk) rFrJrprBrDrrrr)rMrmrYrrrs rPrezTestMakeSplprep.test_1DXs IIau % : &  AJ : & ! a  !: & # c " #1#&RqcT*Q1v||v%%%A%0   ! ! # #s# CC$3C0C!$C-0C9Nr) rr r rrZrhrirrrrrer rfrPrr se  [[S"67A8A: [[S"67 /8 /D/ .1rfrc,eZdZdZdZddZdZdZy) BatchSplinec tj||d}|jdd|_|j d|jdDcgc] }|||fi|c}|_||_ycc}wNr2)rFmoveaxisr _batch_shapert_splines_axis)rMrmrrsplinekwargsyis rPrzBatchSpline.__init__lse KK4 $GGCRL;<99RQS;UVR200V  Ws A.c|jDcgc] }|| }}tj||j|jz}|jr!tj |d|j S|Scc}wr)rrFrtrrrr)rMrmrrs rPr]zBatchSpline.__call__rsc%)]] 36VAY 3 3 JJq$++agg5 612r{{1b$**-?a? 4sA<Nc|jDcgc]}|j|||}}tj||jScc}wr)rrrFrtr)rMrvrOrrrrs rPrzBatchSpline.integratewsE?C}} MVV  aK 0 M Mzz!T..// NsA ctj|}|jDcgc]}|j|c}|_|Scc}wr)rdeepcopyrrrMrrrs rPrzBatchSpline.derivative{s<mmD!>!$cnnQ&7S ""3q63q62 ""=3== =3==&;QRrfN) rr r rZrhrir rr rr rfrPrrs [[2 b !  $ % . Hi0 1 Hd+ ,    [[\+;< [[VZ0S1= Srfrr)#r6r^r)jrrMrTrdr]rnumpyrF numpy.testingrscipy._lib._array_apirrrZrrBrrrr r r r r rrrrrrrrrrrsrrscipy.sparse.linalgsparserscipy.interpolate._bsplinesrrrrrrrrscipy.interpolate._fitpack_implr _fitpack_implrscipy._lib._utilr scipy._lib._testutilsr!scipy.interpolate._ndbspliner"r#rr$rr%r'rlrrrzr{rrlrrXrrrrrrhrirrrrrrrr!r#rDr r:rJr`rrr&r.r0rjrlrxrrrr rfrPrs   +B*  !!EEHG//&953-&y )y )xM$M$`6.& G> H$+$_)_)D}?}?@ 88!++11(Y)X  (d+d+N* F3F3V  7 :":"zL4L4^WGWGta a L(.a+a+H2++\K/K/\i1i1X8$S$Srf