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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). c.[RRS5n[R"UR U5S-S- 5nUR U5S-S- nUS:XaUSUS'[ XEXS9n[R "[UR5U- S- 5n[URXq5"U5n[R"UURU5R5n [XR-US S 9 [XS S 9 g ) zA To avoid repetition of code the following function is provided. r(rrr:rr7bc_typer1r~rN)rNrUrr random_samplereyelenr5r design_matrixtoarrayrr6) rXr7rfrrrrr6 des_matr_def des_matr_csrs rZrun_design_matrix_testsHTestBSpline.test_design_matrix_bc_types..run_design_matrix_testss))''-C))!,r1B67A!!!$r)B.A*$u!%aaADs466{Q*+A"466103L"00151244;GI  L66115 A LU CrrrGr>clampednaturalrr< not-a-knotrrrN)r)rVrnrXr7bcs rZtest_design_matrix_bc_types'TestBSpline.test_design_matrix_bc_typessg D*  (B #A" -)q!QA #A, 7  q!A #A* 5rrr)FTrdegreerc [RRS5nURSUS--5n[R"U5[R "U5peUn[R [R"US- US- U5[R"XVSUS--5[R"US-US-U54n[R"[U5U- S- 5n [XXq5n [U "U5[R"XHXq5R55 [R"US- US- US-US-/5nU(d;[R "["5 [R"XHXq5 SSS5 g[U "U5[R"XHXq5R55 g!,(df  g=f)z;Test that design_matrix(x) is equivalent to BSpline(..)(x).rrkr1r<r2N)rNrUrrgaminamaxrrlrhrir rrjrkarrayrer rL) rVrrwrrxminxmaxr7r5r6bsplines rZ'test_design_matrix_same_as_BSpline_call3TestBSpline.test_design_matrix_same_as_BSpline_call;sxii##D)   bFQJ/ 0WWQZd  EE"++dQhq&9++d!vz*:;++dQhq&9: ; FF3q6A:> "!/ AJ--aACKKM HHdRi4#:tbyA Bz*%%aA;+*  %%aA;CCE +*s :G Gc[RRS5nSnSn[R"UR U5S-S- 5nUR U5S-S- n[ XEUS9n[ SS5HTnUSUnUSUn [R"UURU5R5n [XR-U S S 9 MV g) Nrrkr>rdrr7r1r?r~r) rNrUrrrgrrr rjr5rkrr6) rVrrXr7rrrr4xcycrms rZtest_design_matrix_x_shapes'TestBSpline.test_design_matrix_x_shapesWsii##D)   GGC%%a(2-2 3   a 2 % *!!!,q!A2AB2AB"00151244;GI  L6612E B rrct/SQn[R"SUS5R5n[U/SQ/SS9 g)N)r3r3r3rArBrCrCrCrAr>)g?gmਪ?gK}\UU?r@r~r)r rjrkr)rVr5des_matrs rZtest_design_matrix_t_shapes'TestBSpline.test_design_matrix_t_shapeshs7 ,((Q2::<;<" $rrc[RRS5nSnSn[R"UR U5S-S- 5nUR U5S-S- n[ XEUS9n[ [5 [R"XFRSSS2U5 SSS5 Sn/S Qn/S Qn[ [5 [R"XGU5 SSS5 g!,(df  NH=f!,(df  g=f) Nrrkr>rdrrr:r<)r@r3rArBrC@r) rNrUrrrgrrJrLr rjr5)rVrrXr7rrrr5s rZtest_design_matrix_asserts&TestBSpline.test_design_matrix_assertspsii##D)   GGC%%a(2-2 3   a 2 % *!!!,: &  ! !!VVDbD\1 5'  $  : &  ! !! *' & ' & ' &s?(C)C:) C7: Drf)rrrqrrsc[RRS5n[R"URS55nURS5nUS:XaUSUS'[ X4US9n[ R "XQS9n[R"SSS5n[U"U5U"U5SS 9 [X4US9n[URURSS 9 g) Nrrrrr:rfr1r^r) rNrUrrrr from_power_basisrlrrr6) rVrfrrrcbrrnbspl_news rZtest_from_power_basis!TestBSpline.test_from_power_basissii##D) GGCJJrN # JJrN j aDAbE w /''< [[Ar "2Ru5%aG< 7rrc[RRS5n[R"URS55nURS5URS5S--nUS:XaUSUS'[ X4US9n[ R "XQS9n[X4RUS9n[X4RUS9n[URURSUR--SS 9 g) Nrrr2rrr:rr^r) rNrUrrrr rrrrrr6) rVrfrrrrr bspl_new_real bspl_new_imags rZtest_from_power_basis_complex)TestBSpline.test_from_power_basis_complexsii##D) GGCJJrN # JJrNSZZ^b0 0 j aDAbE w /''<*1ffgF *1ffgF  "}2F FUSrrc[R"/SQ5n[R"/SQ5n[R"[ XSS9SS9n[ UR /SQSS9 g) a5 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=)r1r1r1r1r1rrr)r3r1r1r1r1r1r1r^rN)rNr{r rrrr6)rVrrrs rZtest_from_power_basis_exmp&TestBSpline.test_from_power_basis_exmpsM HH_ % HH_ %'' A)(L09; 7eDrrcR[R"SS/5n[R"S/5nURSS9 URSS9 [R"SSS5nURSS9 [ XSS9n[ U"U5[R "U5S-5 g)Nrr1rBFwriterkr4)rNr{setflagsrlr rry)rVr5r6rnrYs rZtest_read_onlyTestBSpline.test_read_onlys HHaV  HHcUO     [[Ar " %  a ""r||B/#56rrc<^[TS9nU4Sjn[SX25 g)Nr}cj>URup nTRX#X#*S- S5nU"U5 g)Nr1i')rdrl)rrYr5r7rnrWs rZ worker_fn/TestBSpline.test_concurrency..worker_fns3eeGA!QT1RT7E2B bErrrk)rcr()rVrWrYrs ` rZtest_concurrencyTestBSpline.test_concurrencys 2 &  I1rrcygwinz'threading.get_native_id not implemented)rr c f[5n[R"SSS5nU"U5n[R"5n[R "[ URSUS355SURRURRS9nURUSS&[R "[ URSUS355SURRURRS9nURUSS&XblXrl [U"U5U5 g) Nrr1rkr5z.datzw+)moderIrr6) rcrNrl threading get_native_idmemmapstrjoinr5rIrr6r)rVtmpdirrYrnrotidt_mmc_mms rZ test_memmapTestBSpline.test_memmaps ! [[Ar "R5%%'yyV[[1SE78t ssyy ;##QyyV[[1SE78t ssyy ;##Q"x(rrrHN)=rIrJrKrLr[rgrprurzrrskip_xp_backendsrrrrrrrrrrrrrrrr r rrrr$r.xfail_xp_backendsr6r<rCrPremark parametrizerrYr`rurrrrrrrrrxfailsysplatformrfrrMrHrrrZr.r.2sM!F )* >D  $l+OPk*KLgk2 /3MQ /A ;1 .E&W? ( 6? 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Useful only for testing! computes B(x; t[i],..., t[i+k+1]) rr1r3r@_naive_Brr7r4r5c1c2s rZr r s  Avda(!aC&(s1(c11v~ A$hQ3!$ '(1c1*@ @1Qx1qS6  G!AhlQs1uXA#. /(1c1Q32J J Grrc ^^^^^TTT:XaTmOURTT5S- mTTTs=::a TTS-::de eTT:aTTRST- :de[UUUUU4Sj[STS-555$)z5 Naive B-spline evaluation. Useful only for testing! r1rc3X># UHnTTU- [TTTU- T5-v M! g7fNr ).0rr6r4r7r5rs rZ _naive_eval..s-F 1q1vAqsA.. s'*) searchsortedrsumr)rr5r6r7rWr4s```` @rZrrs AaDy  OOAq !A % Q41 !A#    6a!''!*q.(( ( FFa1 F FFrrc^^^^TRSTS-- nUTS-:deTRSU:deTTTs=::a TU::de e[UUUU4Sj[U555$)z'Naive B-spline evaluation, another way.rr1c3L># UHnTU[TTUT5-v M g7frr rr4r6r7r5rs rZr _naive_eval_2..s%=Hqqthq!Q**H!$)rrr)rr5r6r7rWrXs```` rZrrsr  acA !8O8 771:?? Q41 !    =E!H= ==rrc[U5US-- nXCS-:deURSU:deSn[U5HCn[R"XXc-S-SS9"U5nXRU[ R "U5-- nME U$)Nr1rr@r<Fr)rirrr rrN nan_to_num)rr5r6r7rXsr4rYs rZr r s A!A#A !8O8 771:?? A 1X  ! !!ac!e*% @ C qTBMM!$ $$ Hrrc[R"[U55n[R"XS:US:-US:US:-US:US:*-/SSS/5nUR U5$)z*A linear B-spline function B(x | 0, 1, 2).rr<r1cgNr@rHrs rZB_012..sbrrcU$rrHr"s rZr#r$sArrc SU- $NrArHr"s rZr#r$sArr)rN atleast_1dr piecewiserT)rrWresults rZrrsv '*+A \\!1uQ/!VA.!VQ/1)+~FHF ::f rrc[R"[U55nUS:US:US:-US:/nUS:Xa SSS/nOUS:Xa SSS /nO[S U35e[R"XU5nU$) z0A quadratic B-spline function B(x | 0, 1, 2, 3).r1r<rcX-S- $r'rHr"s rZr#B_0123..s 13r6rrcSUS- S-- $)Ng?r2r<rHr"s rZr#r-s41T6A+-rrcSU- S-S- $)NrBr<rHr"s rZr#r-sBqD19q=rrcgNr3rHr"s rZr#r-2rrcg)NgrHr"s rZr#r-s3rrcgr1rHr"s rZr#r-r2rrznever be here: der=)rNr(r rLr))rrcondsfuncspiecess rZrrs '*+A UQUq1u%q1u -E ax!-(* .se455 \\!E *F Mrr#r>c&[RRS5n[R"URX-S-55nURU5nUR U5UR U5pT[ R "XEU5$)N{r1)rNrUrrrTr construct_fast)rXr7rWrr5r6s rZrcrcsj ))   $C  13q5!"A 1 A ::a="**Q-q  ! !! **rrc#v# URURp!URR5nUSUSS&USUS'[ X1U5v URR5nUSUSUS-&[ X1U5v URR5nUSX2*S- S&[ X1U5v g7f) zIncrease knot multiplicity.rrNr1r:)r6r7r5copyr )rYr6r7t1s rZrrs 33q B2Br"I VBrF "  B!uBt!H "  B2Br!tuI " sB7B9cV\rSrSrSrSrSrSrSrSr Sr S r S r S r S rS rg) TestInteropicn[R"SS[R-S5n[R"U5n[ X5nUR UR UR4UlXUsUl Ul Ul [R"SS[R-S5Ul [RUR UR UR 4n[R"XD45Ul[!UR URUR5Ulg)NrrCrr?)rNrlrrrr5r6r7rdrnrrYxnewc_dstackrr b2)rVrnrrYrs rZ setup_methodTestInterop.setup_method s [[BruuHb ) VVBZ r &CCacc?#%1 $&KK2bee8R0 UU133QSS= !))RH%!##tww,rrc URURURp2n[[ X5U"U5SSS9 [[ XR 5U"U5SSS9 [[ R"UVs/sHn[ XB5PM sn5U"U5SSS9 [[SS9 [ X5 SSS5 [[SURR55S-nURRU5nURXcR 4n[[ R"[ X55U"U5RU5SSS9 gs snf!,(df  N=f)Nr^r_zCalling splev.. with BSplinematchr1r)rErYrHrrrdrNrTrJrLrTrr6rA transposer5r7)rVrErYrHrrUrrds rZ test_splevTestInterop.test_splevsii d$e% 9dEE*$e% 9 #>AE!K#>?$e% 9 :-K L $OM5BDDII& '$ . 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VVBZ !Y ? !vh5I Jbdd/ !(>@ !*0F8(<>bdd/ !5F G !dXJ5G Hbdd/ !\ B !T :bdd/: & rF ;'XXrvvbz266":.QX 7b"Xb"X !e^ D !(>@bdd/ii##D) GGCJJAJ& ' JJQ1aLJ )zz!}bjjm1288I&'(288I&'( as < a ;bdd/1' &s  I44 Jcx[RRS5nSup4[R"URUS95nURUS9n[ XS5n[ XVXs5nUR U5n[UR XVU45upn [XX;5n [U RUSSS9 g)Nr)r>rrr~r_) rNrUrrrmake_interp_full_matrrTrrrr6) rVrWrr7rXry_nprrrrr5rYs rZtest_full_matrixTestInterp.test_full_matrixsii##D)wwszzqz)*zzqz!4# "4t 7 ZZ^bjj4t"45a qQ *Re%8rrc [RRS5nSn[SSS5GHn[ US- S- 5n[R "URSU455n[SUS-5HxnUSU*2US24==[R "URSX&- 455- ss'XVS2SU*24==[R "URSX&- 455- ss'Mz URXD45nXuSU2U*S24'URXD45nXU*S2SU24'[R "X245n [[XD*S- S55HAupjU S :a[R"XZS 9XSU 24'M'[R"XZS 9XU S24'MC URU5n [[XXU5[RRX[5S S 9 GM g) z Random elements in diagonal matrix with blocks in the left lower and right upper corners checking the implementation of Woodbury algorithm. rr> r<r1Nr:r)offsetr~r) rNrUrrintdiagflatr{rdiagonalrrlinalgsolve) rVrrXr7rrr4urlldrrYs rZ test_woodburyTestInterp.test_woodburys ii##D) q"aA!a%1%F CJJ1v./A1fqj)#A2#qr' bkk#**aZ*@AA "crc' bkk#**aZ*@AA *V,-B#%gvgwx V,-B#%vgh ! A!%! R"@Aq5!{{17A!eH!{{17AeH B  1 A /ra@IIOOA1 ?#!rrrHN)0rIrJrKrLrNrlrrnrrrrrrrerrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrr&rMrHrrrZrrs 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?rrrcURUR:XdeURURU-S-:XdeURn[R"XD4[RS9n[ U5HOnXnXrU:XaUnO[R "X'5S- n[ R"X#Xx5n XXhU- US-24'MQ [R"XQ5n U $)zAssemble an spline order k with knots t to interpolate y(x) using full matrices. Not-a-knot BC only. This routine is here for testing only (even though it's functional). r1rH) rrNr{rSrrr,evaluate_all_bsplslr") rrr5r7rXArrleftbbr6s rZrrs 66QVV   66QVVaZ!^ ## # A !rzz*A 1Xt Q4<D??1+a/D ' 'd 9 !!VDF]  A Hrrc:[[RXU45upnURnURU- S- n[R"XE4[R S9n[ U5HOnXnXU:XaUn O[R"X(5S- n [R"X#X5n XXyU- U S-24'MQ [R"URU5n [R"URU5n [R"X5n XU 44$)z,Make the least-square spline, full matrices.r1rH)rrNrTrr{rSrrr,r)dotTr*r")rrr5r7rrXr+rrr,r-rNYr6s rZmake_lsq_full_matrixr2s"**qQi(GA! A  QA !rzz*A 1Xt Q4<D??1+a/D ' 'd 9 !!VDF]  qssAA qssAA A !f9rrmethodnorm-eqqrc \rSrSr\R R S5rSurr \R"\R \55r \R \5r \ "\R"\ S\ SS5\ 5r\S5r\S5rS r\S 5r\S 5rS r\S 5rSr\S5r\S5r\S5r\S5r\S5r\R>RAS\!"\""SS555S5r#Sr$Sr%g)TestLSQir)r:r>rr:rcURURURUR4up#pE[ X#XE5upg[ X#XEUS9n[ URU5 URRURU- S- 4:XdeUup[RRXSS9un n [ URU 5 g)Nr3r1r:)rcond) rrr5r7r2rrr6rrrNr!lstsq) rVr3rrr5r7c0AYrYaarr rs rZ test_lstsqTestLSQ.test_lstsqsVVTVVTVVTVV3 a%aA1 A!v 6R ssyyQVVaZ!^----iioob2o6 Aq!R rrc /[URURURUR45QUR P7up4pVUR U5n[X4XVUS9n[X4XVXqS9n [URU RSS9 [URU RSS9 UR U R :Xdeg)Nr9wr3r~r) rrTrrr5r7ryrrr6) rVr3rWrrr5r7rCrYb_ws rZ test_weightsTestLSQ.test_weights!sHc"**tvvtvvtvv&>?GG a LLO A!v 6aAA=SUU/SUU/sscee||rrc 0/[URURURUR45QUR P7up#pE[ RRS5RURSS9nURU5n[X#XEUSS9n[X#XEUSS9n[X#XESS9n [URURSS 9 URURU RUR- 5S:5(aeg) Nrrrr4rBr5r9r~r)rrTrrr5r7rNrUrrrrrr6rabs) rVrWrrr5r7rCb_neb_qrb_no_ws rZtest_weights_sameTestLSQ.test_weights_same.sGc"**tvvtvvtvv&>?GG a II ! !$ ' / /QWWQZ / @ JJqMqQQyAqQQt< qD9U366"&&DFF!23e;<<<<rrr9r^r)rrTrr5r7rXrNrUrrrrr6r0r)rVr3rWrr5r7rXnrhsrrrYr4r-coefss rZtest_multiple_rhs_2TestLSQ.test_multiple_rhs_2EsGc"**tvvtvv&67GGG aii##D) JJQIJ & JJqM A!v 6T{$"!a1a4!v>" $5;7;aQ%'';78::ss/ $7s %DDcd/[URURUR45QURPUR P7up#pESn[ RRXV4S9nURU5n[X'X4SS9n[X'X4SS9n [URU RSS9 g)Nr>rr5r9r4r^r) rrTrr5r7rXrNrUrrr6) rVrWrr5r7rXrQrrJb_neqs rZtest_multiple_rhs_3TestLSQ.test_multiple_rhs_3TsGc"**tvvtvv&67GGG a II  1)  , JJqMqQ$7a9=e4rrc/[URURUR45QURP7up4nURUR S-5n[ X6XEUS9n[ X2RU5XEUS9n[ X2RU5XEUS9n [U"U5U"U5SU "U5--SSS9 g)N?@r9r2r^r_) rrTrr5r7rrrrr) rVr3rWrr5r7rrYrrs rZrTestLSQ.test_complex]s=3rzzDFFDFF#34! HHUOQXXe_ahhuo6 eafn # WR[u=rrc[R"SSS5nUSSS2nUSSS2n[US5n[X4USUS9 g)Nr:r1rr>r`)rNrlrr)rVr3rnrrr5s rZrTestLSQ.test_sliced_inputsI[[Q $ ssG ssG AqMa1V4rrc [R"S5R[5nUS-n[ US5n[R [R [R *4HnXSS'[[[X#XAS9 M g)N r<r>r:r9) rNrRrarfrrPrQrJrLr)rVr3rrr5rs rZtest_checkfiniteTestLSQ.test_checkfinitesd IIbM  ' qD AqM&&"&&266'*AbE *oqQ N+rrcURURURpCnURSS9 URSS9 URSS9 [ X#XAS9 g)NFr)rrr5r3)rrr5rrrbs rZrTestLSQ.test_read_onlysO&&$&&$&&a      !A5rrr7r1cURURp2[[R"USUSS5U5n[ X#XASS9n[ X#XASS9nUSSUSS-S- n[ U"U5U"U5S S 9 g) Nrr:rr4r`r5r1rAr^r)rrrrNrlrr)rVr7rrr5 spl_norm_eqspl_qrrns rZtest_qr_vs_norm_eqTestLSQ.test_qr_vs_norm_eqs~vvtvv1 BKK!aeQ/ 3%aA9E  qd;eafn # B%@rrcT[R"URS5n[R"URS5n[ URURUR SSS9n[ XUR SSS9nUSSUSS-S- n[ U"U5U"U5SS 9 g) Nr<r>r5r`r1r:rAr^r)rNrepeatrrrr5r)rVrrrspl_2rns rZtest_duplicatesTestLSQ.test_duplicatess IIdffa  IIdffa !DIdff$?eafn #b 5959rrrHN)&rIrJrKrLrNrUrrrXr7rrrrrlr5parametrize_lsq_methodsr?rErLrrSrWrr]rrjrrprrerrrrrwr|rMrHrrrZr7r7sv ))   %C DAq  1 A 1 A AaD!B%+Q/A ! !   =:: 0 05 M MM,55 > >55OO66 [[S$uQ{"34A5A:rrr7c4\rSrSrSrSr\S5rSrSr g) PackedMatrixia_A 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]``. cXlX lX0lURS:XdeURS:XdeURSURS:Xdeg)Nr<r1r)rrncrAr)rVrrrs rZ__init__PackedMatrix.__init__sQ vv{{{{awwqzV\\!_,,,rrcLURRSUR4$Nr)rrrrs rZrPackedMatrix.shapesvv||A''rrcn[R"UR5nURRSn[ URS5H_n[ UR URU- U5nURUSU24XURUURUU-24'Ma U$)Nr1r)rNr{rrrminrr)rVoutnelemr4nels rZtodensePackedMatrix.todenseshhtzz" Qsyy|$Adgg A.6C:>&&DSD/C4;;q>$++a.3"666 7% rr)rrrN) rIrJrKrL__doc__rpropertyrrrMrHrrrZrrs%-((rrrc RSSKJn U"S[RSS9nURnUR nUR nURupURSU:XdeUR5n UR5n [X(5Hn Xln [X5HnU[X5:a M'U"XS4XS45unnnUXS4'[SU 5H'n[UUXU4XU45uXU4'XUS- 4'M) SXS4'[U RS5H$n[UUXU4XU45uXU4'XU4'M& M M [[U RS55n[U [R"U[RS 9U5nUU 4$) zbThis is a python counterpart of the `_qr_reduce` routine, declared in interpolate/src/__fitpack.h r)get_lapack_funcslartg preferred)rIilp64r1r@r:rH)scipy.linalg.lapackrrNrSrrrrr@rrfprotarrr{int64)a_prstartrowrdlartgrrrrnzRrr4oirr6rrroffsR_ps rZ _qr_reduce_pyrs5 gRZZ{ KF A ZZF B GGEA 771:?? A B 8  YrACJQ!tWa1g.GAq!AdG1b\%+Aq!qD'1T7%C"Q$ac6"AeH288A;'%+Aq"T(B!tH%E"a4"T(( * aggaj! "D q"((4rxx8" =C 7Nrrc0X-X--nU*U-X--nXE4$)z@Givens rotate [a, b]. [aa] = [ c s] @ [a] [bb] [-s c] [b] rH)r6rrrYr>r-s rZrrs) #)B AB 6MrrcURnURup4URnURSURS:Xde[R"USU5nXS- X%S- S4- XeS- S4'[ US- SS5HGn[ XEU- 5nX'SU2S4XgS-Xx-2S4-RSS9n XU - X'S4- XgS4'MI U$)zxBacksubsitution solve upper triangular banded `R @ c = y.` `R` is in the "packed" format: `R[i, :]` is `a[i, i:i+k+1]` rNr1.r<r:r!)rrrrNrrrr) rrrrrrr6r4rsumms rZfpbackr s A GGEA B 771: ## # afAT7Q!tQwZ'AdCiL 2a4R "dmQsUD.!Ac!%in$55:::BdTka1g-S& ! Hrrc8\rSrSrSrSrSrSrSrSr Sr g ) TestGivensQRi4crSn[R"U[S9nUS-SSU-- -n[X25nX4XR4$)Nr>rHr1)rNrRrfr)rVrXr7rrr5s rZ_get_xytTestGivensQR._get_xyt7s@  IIau % qD1ac7N  Qzrrc VSnURU5up#pE[R"X$U5n[R"UR 55upxUR U-n URupXRSU- S- :XdeURSSUS-2n [R"U [RS9n URRXS-5n [XU 5nUSS2S4n[R "XX5 [#[R$"UR 5U-UR 5U- 5[R&"U5SS9 [#[R$"[)XSS2S4- 5[)XSS2S4-55[R&"U 5SS9 [R*"X5n[R,"UR.UR0X/XE[R2"U5U5un n[#UUSS2S4SS9 g) Nrkrr1rHr^rgvIh%L=-a=)rr rjr*r5rr0rindicesrNascontiguousarrayrdatarrr, qr_reducerminimumrrHr"rrrry)rVrXrrr5r7a_csrqrqTyrrrr+ry_c_fullc_bandedrs rZ test_vs_fullTestGivensQR.test_vs_full>s ]]1% a%%aA.uuU]]_%ccAg WWQZ!^a''''w!A#w'%%fBHH= JJ  qA# & B ' q$wZ1b-  199;?#$99;?457]]15EE S 3s1X~#6#&s1X~#689;s9KRW Y!!!addA1aRTU!QAU;rrcSnURU5up#pE[R"X$U5nURupxXRSU- S- :XdeURSSUS-2n [ R "U [ RS9n URRXuS-5n [XU5n USS2S4n [X5up[R"XX5 [U RU RSS9 [!U R"U R"SS9 U R$U R$:Xde[XSS9 g) Nrkrr1rHr^rF) check_dtype)rr rjrrrNrrrrrrr,rrrrrr)rVrXrrr5r7rrrrr+rrRRrs rZtest_py_vs_compiled TestGivensQR.test_py_vs_compiledas ]]1% a%%aA. WWQZ!^a''''w!A#w'%%fBHH= JJ  qA# & B ' q$wZq%1b.acc. 188?uu}}U+rrcSnURU5up#pE[R"SUS-[S9n[R "X$XV5upxn UR Sn [R"X$U5n XSS2S4-R5n U RRXS-45n U RSSUS-2R[R5n[X}SS9 [!X5 XR SU- S- :Xdeg)Nrkr1rHrr^r)rrNrRrfr, data_matrixrr rjtocsrrrrrarrr)rVrXrrr5r7rCr+rrrra_wA_offset_s rZtest_data_matrixTestGivensQR.test_data_matrix|s ]]1% a IIa1E * ,,Q18 2 GGAJ%%aA.Dz!((* XX  qA#h '++g1g&--bhh7E*(WWQZ!^a''''rrc SnURU5up#pE[RX3S-4n[R"X$U[R "U55upgn[ XgU5n [R"XgX5 [X5n [R"XhX#XE[R "U5U5un n [XSS9 g)Nrkr<r~r) rrNrFr,rryrrrr) rVrXrrr5r7r+rrrr6rrs rZ test_fpbackTestGivensQR.test_fpbacks ]]1% a EE!T'N ,,Q1bll1oF 2 B '1b, 1L??1!bll1oqIAqE*rrc SnURU5up#pE[R"US-4[S9nUHMn[ [ R "XEXqUS-5U5 [ [ R "XEXqSU-5U5 MO g)Nrkr1rHr<)rrNr{rfrr,r))rVrXrrr5r7 zero_arrayrs rZtest_evaluate_all_bspl#TestGivensQR.test_evaluate_all_bspls{ ]]1% aXXq1uhe4 D **1!a%@* N **1!A#>  LrrrHN) rIrJrKrLrrrrrrrMrHrrrZrr4s"!r@r2r1r:rz)``x`` and ``y`` length must be at least 5rL)rNrUrrrgrnormalrJrLrrr@rRrrer )rVrrXrrx_duplexception_messages rZtest_invalid_input&TestSmoothingSpline.test_invalid_inputsii##D)  GGC%%a(1,q0 1 qD266!a%= 1a4 '#**Ra*@ @: & !!qrU +' : & !!AB% +' : & !!))Aq/1 5': & !!DbD'1 -'1Iq : & !& ,' IIaL GGAJG ]]:-> ? !! '@ ?+' & & & & &' & ' &@ ?sHG;G "G2H H9 H% G G/2 H H H"% H3c[R"[S55nUSnUSnUSnSSS5 [WW5"U5n[ UWSSSS9 g!,(df  N.=f) a} 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.npzrry_GCVSPLN-C6?F)r`rar)rNloadrrr)rVrrrry_comprs rZtest_compare_with_GCVSPL,TestSmoothingSpline.test_compare_with_GCVSPLsgRWWY|, -S AS AJ'H . 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"qQ'1,,,zz!"*** VVX!1ra(A---zz!"*** VVX!q1ra(B... ]]:-= > JJra ?VVX22ra(B... ]]:-= > JJra ? > ? > ? >s1F"F F F"cSn/SQn/SQn[R"X2U5S:Xde[R"[SS9 [ R "X2U5 SSS5 /SQn[R"X2U5S:Xde[R"[SS9 [ R "X2U5 SSS5 g!,(df  Ni=f!,(df  g=f)Nr1)rrr1r<r<)rHrHrHr/Schoenberg-Whitney*rL)rrrr r rer rLrrrs rZtest_condition_5_x1xm TestFpchec.test_condition_5_x1xm s   qQ'2--- ]]:-B C JJqQ D qQ'2--- ]]:-B C JJqQ D C D C D CsB<C < C  CcSn/SQnSS/n[R"X2U5S:Xde[R"X2U5beg)Nr1)rrr1r1rg333333?r)r r rrrs rZtest_condition_5_k1TestFpchec.test_condition_5_k1 sE   #JqQ'1,,,zz!"***rrcSnS/US--S/-S/US---nS/S-n[R"X2U5S:Xde[R"[SS9 [ R "X2U5 SSS5 S/US--S/-S/US---nS/S-n[R"X2U5S:Xde[R"[SS9 [ R "X2U5 SSS5 g!,(df  N=f!,(df  g=f) Nr>rr1r<rr/rrLrrs rZtest_condition_5_1TestFpchec.test_condition_5_1 s  C1IOqc1Q3i ' CEqQ'2--- ]]:-B C JJqQ DC1IOqc1Q3i ' CEqQ'2--- ]]:-B C JJqQ D C D C D CsC* C;* C8; D cSnS/US--SS/-S/US---nS/S-S/-n[R"X2U5S:Xde[R"[S S 9 [ R "X2U5 SSS5 S/S-SS/-n[R"X2U5S:Xde[ R "X2U5beg!,(df  NQ=f) Nr>rr1r<rrHr?r/rrLrrs rZtest_condition_5_2TestFpchec.test_condition_5_2 s  C1IA !ac * E!GqcMqQ'2--- ]]:-B C JJqQ DE!Gq!f qQ'1,,,zz!"*** D Cs B>> C cSn/SQn/SQn[R"X2U5S:Xde[R"[SS9 [ R "X2U5 SSS5 g!,(df  g=f)Nr1) rrr<r>r?rrrr)r1r1r1@r,r,rr/rrLrrs rZtest_condition_5_3TestFpchec.test_condition_5_3 sT  ' )qQ'2--- ]]:-B C JJqQ D C Cs A"" A0rHN)rIrJrKrLr rrrrr r#r&r)r-rMrHrrrZrr s4   *!,  !>  +   + rrrc[R"XX"*5n[[U5S- 5Vs/sHoSXEXES-R 5PM nnX4SSn[[U55H%nXuS- nXe==U- ss'XeS-==U-ss'M' US==US- ss'[ [ U5[ U5SS9 Xd4$s snf)z)Split the knot interval into "runs". r1r:r<r^r)rNrrrirr) rr5r7 residualsrr4fpartscarriescarrys rZ_splitr4 s aG $B6;CGAI6F G6Fb1g&**,6FF G1R!G 3w<  Q U s u !  2J)B-JCKYe< :Hs#C cT[XX#5upESnSn[[U55H%nXXS-XX- S:dMXHU:dMUnXHnM' US:Xa [S5eXVXVS--S-S-n X n [R "X5n [R USU XU S4n U $)z Insert a new knot given reduals.ig}Ô%Ir1z5Internal error, please report it to SciPy developers.r<N)r4rrirLrNrr) rr5r7r0r1ridx_max fpart_maxr4 idx_newknotnew_knotidx_tt_news rZ _add_knotr< sa+JFGI 3v;  c7RU?Q 69y#8G I $PQQ;AI.2q8K~H OOA (E EE!FU)Xy0 1E Lrrc"\rSrSrSr\R RS/SQ5S5rSr Sr Sr S r S r S rS r\R RS /SQ5\R RS/SQ5S55rSrSrSrg)TestGenerateKnotsi c[R"S[S9nUS-SSU-- -nSn[R"S/US--S/US---5n[ XX4S9nU"U5U- S -nS S KJn URXX65n[XX65n [XS S 9 [ XX8S9n U "U5U- S -n URXX;5n [XX;5n [XS S 9 g)NrrHr>r3r1r@r)r7r5r<r_fitpack_repror^r) rNrRrfr{rrrAadd_knotr<r)rVrrr7r5r]r0_frnew_tnew_t_pyspl2 residuals2new_t2 new_t2_pys rZtest_split_add_knot%TestGenerateKnots.test_split_add_knot s IIau % qD2q1u:   HHbT1Q3Z2$!*, -aa-VaZ!O ; Q10Q10e4qq21gkA% a6a6 6rrr7rc URSURS9nURX2R-S- 5n[ [ X4USS95Sn[ X4USS9SnURXbRS9n[XVSS9 g)NrrHrr7rr:r^r) rRrSrrrr$rrTr)rVr7rWrrr5rs rZtest_s0TestGenerateKnots.test_s0 sy IIarzzI * FF1UU719  Q/ 0 4 AA #A & ZZ**Z -E*rrc SnURX!RS9nUS-n[[X4SSS95nUR [ [ R"U5S55n[USUSS9 g) NrkrHr>rrMr:r^r)rRrSrr$rTrrNrrVrWrXrrknotsros rZ test_s0_1TestGenerateKnots.test_s0_1 sd  IIazzI * qD^AA34::k"**Q-;<b 8%8rrc SnURU5nUS-n[[X4SSS95nUR[ [ R"U5S55n[ USUSS9 g)Nrr>rrMr:r^r)rRrr$rTrrNrrQs rZ test_s0_n20TestGenerateKnots.test_s0_n20 s]  IIaL qD^AA34::k"**Q-;<b 8%8rrc [R"S5nUS-n[[5 [ [ XSSSS95 SSS5 g!,(df  g=f)Nrkr>rr7rnest)rNrRrJrLrr$rVrrs rZ test_s0_nestTestGenerateKnots.test_s0_nest& s? IIbM qD : & QR8 9' & &s A  Ac URSURS9nURU[R-S- 5nSn[ [ X#USS95n/SQ/SQ/SQ/S Q/S Q/nUVs/sHoqRXqRS9PM nn[U5[U5:Xde[XV5Hup[XS S 9 M [X#USS9un n [US URU5S S 9 gs snf)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. rrHr>rrM)r@r@r@r@rrrr) r@r@r@r@rCrrrr r@r@r@r@rArCrrrr) r@r@r@r@rArCrrrrr) r@r@r@r@rArBrCrrrrrr^rr:N) rRrSrrNrrr$rTrirrr) rVrWrrr7rRwantedwantr5rrs rZ test_s_switchTestGenerateKnots.test_s_switch- s. IIarzzI * FF1RUU719  ^AA6726:>A   BHH**T*4H5zS[((('EA A .(d+1ab 2::a=u=Is+"C4cX[[S55n[XSSS9n[U5 g)Nrrr1)rr7)rrr$next)rVrgens rZr!TestGenerateKnots.test_list_inputY s$ qNQSA. 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