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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|$Adgg A.6C:>&&DSD/C4;;q>$++a.3"666 7% 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:?? 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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_GCVSPLsjRWWY|, -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 sUii##D)  GGC%%a(1,q0 1 qD266!a%= 1a4 '#**Ra*@ @2::1v&1#Aq)::eCjr:2C A FF1c#h  # #C ()!Q2Es1S6{QsV+,D53=1S612Hh $CCG)3$,R="2333rkN) rrrrIrOrUrarz fail_slowr\rrkrWrDrDs6 (>6Tp$* [[133rkrDc  |\ |\tz dz }|dzk\sJtz dz dzk\sJt fdt|D}tj|S)z-A naive 2D tensort product spline evaluation.r.c 3K|]9}tD])}||ft|zt |z+;ywr)rr) rixiyr3r4nytxtyrwrs rWrzbspline2..' sO7!"E"IbBi!Aq"b/)AaBO;,5<!s?A)r7rrrKrQ) rr2r3r4nxrrbrcrdrwrs `` @@@@@rWbspline2rf s DAq FB R1qB !A#II R1qB !A#II 77b 7 7C ::c?rkcb|dk(r|||cxkr ||dzkrdSdS|||z||k(rd}n)|||z |||z||z z t||dz ||z}|||zdz||dzk(rd}||zS|||zdz|z |||zdz||dzz z t||dz |dz|z}||zS)Nrr.r0r=rrs rWrr, sAvda(!AaC&(s1(c11v1~ !A$h1Q3!A$ '!AqsAq/ 91Qx1QqS6  7N!AhlQqs1uX!A#. /!AqsAaC2C C 7Nrkctz dz }|dzk\rt|k\sJtfdt|DS)Nr.c3FK|]}|t|zywrrhrs rWrzbspline..= s%6Xqta1am#Xr)r7rr)rwr2r3r4rUs```` rWrJrJ: sD A QA 1H3q6Q;' ' 6U1X6 66rkceZdZddZdZy) NdBSpline0ct|}|t|jksJ t|td|D|_td|D|_||_y#t$r |f|z}YGwxYw)aTensor product spline object. c[i1, i2, ..., id] * B(x1, i1) * B(x2, i2) * ... * B(xd, id) Parameters ---------- c : ndarray, shape (n1, n2, ..., nd, ...) b-spline coefficients t : tuple of 1D ndarrays knot vectors in directions 1, 2, ... d ``len(t[i]) == n[i] + k + 1`` k : int or length-d tuple of integers spline degrees. c3FK|]}tj|ywr)operatorindex)rkis rWrz&NdBSpline0.__init__..Y s6Abx~~b)As!c3RK|]}tj|t!yw)rEN)rKrQr)rtis rWrz&NdBSpline0.__init__..Z s?Qrrzz"E22Qs%'N)r7rrHr$r4r2r3)rSr2r3r4rs rWrzNdBSpline0.__init__A sx1vs177|###  F 6A66?Q??  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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) rSrTrwrr4rwantedwantr2rNrs rW test_s_switchzTestGenerateKnots.test_s_switch s. 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