%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% TABLES FOR WAVELET FILTERS ADAPTED TO LIFE ON AN INTERVAL. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% This file contains two sets of tables, both for wavelets adapted to the interval. The resulting wavelet bases on say [0,1] have the same number of vanishing moments (even as the edges) as the unperturbed interior wavelets. The first set of tables corresponds to a construction which was discovered independently by Albert Cohen, Ingrid Daubechies & Pierre Vial, by Bjorn Jawerth, and by Pierre-Gilles Lemarie . A first announcement of the construction appeared in A. Cohen, I. Daubechies, B. Jawerth and P. Vial, "Multiresolution analysis, wavelets and fast algorithms on the interval", Comptes Rendus, Acad. Sc. Paris 316 (serie 1) (1992) pp. 417-421. The full details of the construction have appeared in "Wavelets on the interval and fast wavelet transforms", by Albert Cohen, Ingrid Daubechies and Pierre Vial, in the first issue of Journal for Applied and Computational Harmonic Analysis, volume 1, 1993 (pp. 54-81). The second set of tables corresponds to an older construction of wavelet bases adapted to the interval, due to Yves Meyer, "Ondelettes sur l'intervalle", Revista Matematica Iberoamericana, 7 (1992) p. 115-133. The original paper of Y. Meyer did not give any tables corresponding to his construction; they are provided here. For a discussion of some advantages of the new construction over this first construction by Y. Mayer, see the J. ACHA paper mentioned above. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% TABLES FOR WAVELETS ON THE INTERVAL AS IN THE JOINT WORK OF ALBERT COHEN, INGRID DAUBECHIES AND PIERRE VIAL. (Tables computed by Albert Cohen) *************************************************************** What follows are tables for a special construction of wavelets on the interval. The number of scaling functions and the number of wavelets at a resolution level j are equal in this construction (and both equal to 2^j). The tables are carried out for different values of N (N = 2 to 8), which is the number of vanishing moments of the wavelets. For given N, we need to adapt the N outermost wavelets and scaling functions, both on the right and the left side of the interval; the 2^j-2N "interior" functions are untouched and are therefore the same as for the construction on the whole line. These are therefore associated with a pair of exact reconstruction filters. We have chosen the pair with length 2N (shortest length for which N vanishing moments are possible), and with phase closest to linear phase (exact linear phase is excluded, because these filters are orthonormal). At each edge we have computed the adapted filters corresponding to the adapted functions. Their lengths go from N+1 (for the one closest to the edge) to 3N-1 (closest to the interior), with increments of 2. The adapted filters are different for the left and right edges. The following illustrates how these adapted filters should be used. Suppose the data are represented by the following sequence of stars: * * * * * * * * * * .... We only consider the left edge here. The approximations at the next coarser scale will be obtained by applying low pass filters, and decimating, as usual. We represent the result as a sparser sequence of stars: original seq. : * * * * * * * * * ... coarser seq. : * * * * ..... In the case N=2, the interior filters have 4 taps, and we have 2 adapted filters for the edge, one with 3 and one with 5 taps. What this means is that the leftmost of the coarser sequence points is obtained by weighting the leftmost 3 points of the finer sequence with the 3-tap adapted filter (the first coefficient weighs the leftmost fine scale point, the 2nd coefficient the 2nd point, etc.); the second leftmost of the coarser sequence is similarly obtained by applying the 5 tap adapted filter to the 5 leftmost fine scale points. From then on, i.e. for the third leftmost coarse seq. point on (and until we get near the right edge, where the right coefficients take over) we use the "interior filters". The third coarse point e.g. is obtained by acting with the standard 4 tap filter on the fine scale points directly above it ( 2 to the right and 2 to the left). For larger N, one has to use the adapted tables for the N leftmost coarse points; from the (N+1)th, the interior filters take over. For any N, these tables can only be used if the data have at least 2N points; for less points the 2 edges interfere and these adapted tables are not sufficient. The whole procedure can of course be repeated, to lead to a decomposition in many scales, but it has to be stopped when the coarsest scale has strictly less than 2N points. (At this point, other adapted filters should take over; in any case, if we want the scaling functions at every level to generate all polynomials of degree less than or equal to N-1, then we can at most go one step further ...) The high pass filters work of course in exactly the same way. On the infinite line, the fact that the wavelets have N vanishing moments is expressed by the fact that ... 1 1 1 1 1 1 1 1 ... is invariant under the lowpass filtering + decimation operation, while ... 1 2 3 4 5 6 .... gets mapped into 1/2 times itself + multiple of .. 1 1 1 1 1 1 .. , etc. (similar statements for higher order polynomials). On the interval, it is not true, even though the wavelets have vanishing moments, that the sequence 1 1 1 ... 1 1 1 gets mapped, by the lowpass+decimation operations to a sequence 1 1 1 .. 1 1 1 of half the original length. (This is because the "adapted" low pass functions don't have integral 1.) Instead, there exist a1, a2, .. aN so that a1 a2 .. aN 1 1 1 1 1 ... gets mapped to a similar sequence (at the other end, we need to end with properly chosen bN, .. b2, b1 of course). This sequence a1 a2 .. aN 1 1 1 1 ... is therefore the sequence which maps to an all-zero sequence under the high-pass+decimation operation. In some applications (image analysis?) one would like the sequence 1 1 1 1 ... to have this property, however. To achieve this, one has to precondition the data. Before starting the decomposition, the N extreme values at the left have to be multiplied by a lower triangular matrix (the upper left corner triangle is zero), which will map the column vector 1 1 .. 1 to a1 a2 .. aN (and which will also do the appropriate thing with the higher order polynomials). See below for the detailed preconditioning scheme. This matrix is also given in the tables, as well as its inverse (needed after reconstruction), which is also a lower triangular matrix. Organization of the tables: For every N we have list of the lowpass filter coefficients used on the interior. (BEWARE: these should be normalized so that their sum equals sqrt(2). In some cases - which will be indicated - it isn't, and the normalization should be adapted to be in accordance with the "edge" coefficients; the "edge" coefficients are always normalized in L^2-sense, i.e. the sum of the squares of every group is 1). two columns with the lowpass adapted coefficients at the left, highpass coefficients at the right. there are N different filters; the shortest corresponds with the outermost point, the longest with the innermost of the adapted edge filters. two columns with N blocks, with N entries in the every block. These give the entries of the preconditioning matrix described above: left column for the matrix to apply to the data, right column for the inverse, to use at the end of the reconstruction (each block represents a column of the matrix in question). THE WHOLE THING IS GIVEN FOR THE LEFT EDGE AND THEN REPEATED FOR THE RIGHT EDGE. AT THE RIGHT EDGE : -The adapted filter coefficients have been obtained from the same program as the results at the left edge, except that the "interior" filter coefficients were listed in the opposite order. The filtering operation should thus be done symmetrically : in the case N=2, for example, the rightmost of the coarser sequence points is obtained by weighting the rightmost 3 points of the finer sequence with the 3-tap adapted filter (the first coeff. weighs the rightmost fine scale point, the 2nd coeff. the 2nd point, etc.); the second rightmost of the coarser sequence is similarly obtained by applying the 5 tap adapted filter to the 5 rightmost fine scale points. From then on, i.e. for the third rightmost coarse seq. point on (and until we get near the left edge, where the left coeff. take over) we use the "interior filters". -The preconditioning matrices are now upper triangular and their application does not require to "symmetrize" the data, i.e. to consider the rightmost point as the first point. The following scheme (corresponding to N=2) shows that the extreme points should be consider as standard column vectors on which the matrices are applied : Prec. Matrix Original Data Preconditioned Data Left | A 0 | a Aa | B C | b Ba+Cb c c d d e e f f | D E | g Dg+Ef right | 0 F | h Fh The inverse operation (after reconstruction) works in the same way. ************************************************************************ The interior coefficients in these tables were computed with Macsyma. The edge coefficients were then computed, using these interior filter coefficients, with a Fortran program using double precision. ************************************************************************ TABLES AT LEFT EDGE. %%%%%%%%%%%%%%%%%%%%%%%%% N=2 lowpass coefficients in the interior 0.482962913145 0.836516303738 0.224143868042 -0.129409522551 coefficients for the edge filters: 0.6033325119E+00 -0.7965435169E+00 0.6908955318E+00 0.5463927140E+00 -0.3983129977E+00 -0.2587922483E+00 0.3751746045E-01 0.1003722456E-01 0.4573276599E+00 0.1223510431E+00 0.8500881025E+00 0.2274281117E+00 0.2238203570E+00 -0.8366029212E+00 -0.1292227434E+00 0.4830129218E+00 entries for the triangular preconditioning matrix and its inverse: 0.3248940489E+00 0.3077926491E+01 0.3715801512E-01 -0.1142045672E+00 0.0000000000E+00 0.0000000000E+00 0.1001445405E+01 0.9985566812E+00 N=3 lowpass coefficients for the interior: .332670552950 .806891509311 .459877502118 -.135011020010 -.085441273882 .035226291882 coefficients for the edge filters: 0.3888997639E+00 0.5837809695E+00 -0.8820782813E-01 0.7936188402E+00 -0.8478413085E+00 0.1609551773E+00 0.3494874367E+00 -0.5884171124E-01 -0.6211483178E+00 -0.3493401824E+00 0.5225273932E+00 0.2989205572E+00 -0.2000080031E+00 -0.3283013439E+00 0.3378673486E+00 -0.3322637132E+00 -0.3997707705E+00 0.6982497200E+00 0.1648201297E+00 -0.2878789995E+00 -0.9587863831E-02 0.1015059001E-02 0.3712255319E-03 -0.3930133175E-04 0.3260097101E+00 -0.3451437111E-01 0.8016481645E+00 -0.8486981030E-01 0.4720552620E+00 0.1337307023E+00 -0.1400420809E+00 0.4604064538E+00 -0.8542510010E-01 -0.8068932216E+00 0.3521962365E-01 0.3326712589E+00 entries for the triangular preconditioning matrix described above, and its inverse: 0.1007941579E+00 0.9921209927E+01 -0.5929310244E+00 0.2752403722E+02 -0.1509649764E-01 -0.6946796955E+00 0.0000000000E+00 0.0000000000E+00 0.2137256653E+00 0.4678895250E+01 0.3068542369E-01 -0.1435467050E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.1000189333E+01 0.9998107029E+00 N=4 coefficients for the interior lowpass filter: (beware: these coefficients are normalized so that their sum is 2) 0.045570345896 - 0.0178247014417 - 0.140317624179 0.421234534204 1.13665824341 0.703739068656 - 0.0419109651251 - 0.107148901418 coefficients for the edge filters: 0.9097539258E+00 -0.7573970762E-01 0.4041658894E+00 0.3254391718E+00 0.8904031866E-01 -0.6843490805E+00 -0.1198419201E-01 0.6200442107E+00 -0.3042908414E-01 -0.1885851398E+00 -0.2728514077E+00 0.1665959592E+00 0.5090815232E+00 -0.4847843089E+00 0.6236424434E+00 0.3564635425E+00 0.4628400863E+00 0.4839896156E+00 0.2467476417E+00 -0.6057543651E+00 -0.1766953329E-01 0.3451833289E-01 -0.4517364549E-01 0.8824901639E-01 0.1261179286E+00 0.2082535326E+00 -0.2308557268E+00 -0.4018227932E+00 -0.5279923525E-01 -0.6872148762E-01 0.2192651713E+00 0.3302135113E+00 0.4634807211E+00 0.5580212962E+00 0.7001197140E+00 -0.5994974134E+00 0.4120325790E+00 -0.6909199198E-01 -0.2622276250E-01 0.2785356997E-01 -0.6704069413E-01 0.7120999037E-01 -0.2907980427E-01 0.6548500701E-01 0.5992807229E-01 -0.1349524295E+00 0.6176427778E-02 -0.1390873929E-01 -0.4021099904E-01 0.9055141946E-01 -0.3952587013E-01 0.8900857304E-01 -0.5259906257E-01 0.3733444476E+00 0.3289494480E+00 -0.8404653708E+00 0.7966378967E+00 0.3156849362E+00 0.4901130336E+00 0.1202976509E+00 -0.2943287768E-01 -0.1307020280E-01 -0.7524762313E-01 -0.3341507090E-01 entries for the triangular preconditioning matrix and its inverse: 0.2489911114E+01 0.4016207624E+00 -0.2752988536E+01 0.6592239446E+00 0.1687841447E+01 -0.1870967456E+00 -0.4022221173E+00 0.3352374610E-01 0.0000000000E+00 0.0000000000E+00 0.1677210550E+01 0.5962280646E+00 -0.7075375437E+00 0.3732739492E+00 0.1763544288E+00 -0.8158414568E-01 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.1130145142E+01 0.8848420994E+00 -0.6162121550E-01 0.5415219932E-01 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.1006885156E+01 0.9931619247E+00 N=5 coefficients for the interior lowpass filter: (beware: these are normalized so that their sum is 2) 0.0276321529578 - 0.0298424998687 - 0.247951362613 0.0234789231361 0.89658164838 1.02305296689 0.281990696854 - 0.0553441861166 0.0417468644215 0.0386547959548 coefficients for the edge filters: 0.9302490657E+00 0.2803062751E-01 0.3488878121E+00 -0.1899596351E+00 0.1098578445E+00 0.5126446690E+00 0.2701025958E-01 -0.6992703507E+00 0.7897329608E-02 0.4475860840E+00 0.7300852033E-02 -0.1049415950E+00 -0.3099501188E+00 -0.6736388320E-01 0.5987214008E+00 0.3342473230E+00 0.6208411495E+00 -0.5086311754E+00 0.3720164550E+00 0.1104945888E-01 0.1451060379E+00 0.6367318477E+00 0.6263262144E-02 -0.4656214411E+00 0.1687072021E-01 0.3800200446E-01 0.1562115518E-01 0.3518730685E-01 0.1138401479E+00 0.1327317986E+00 -0.3641831811E+00 -0.4544562923E+00 0.1228916167E-01 0.2604140629E+00 0.4117590210E+00 0.4050120843E+00 0.5954973448E+00 -0.8108043041E-02 0.5457944280E+00 -0.6031278756E+00 0.1756416185E+00 -0.3803908839E-01 -0.1751671276E-01 0.4149398330E+00 0.2376581050E-01 -0.5938666471E-01 0.2200554624E-01 -0.5498806769E-01 -0.4098816981E-01 -0.2828796750E-01 0.1431055982E+00 0.1003358539E+00 -0.6777711666E-01 -0.8695683128E-01 -0.1740980466E+00 -0.7322615732E-01 -0.9559132536E-01 0.9631505948E-01 0.1512981220E+00 0.2847632852E+00 0.6357421629E+00 -0.7284839004E+00 0.6823643465E+00 0.5708436334E+00 0.1963091141E+00 -0.5757775517E-02 -0.3301996982E-01 -0.1685142803E+00 0.2833562039E-01 0.2152759089E-01 0.2623688365E-01 0.1993310503E-01 0.7965029532E-02 0.1109055091E-01 -0.2796122002E-01 -0.3893335648E-01 0.1706238600E-01 0.2375776006E-01 0.2928655475E-01 0.4077875984E-01 0.2857806991E-02 0.3979226173E-02 -0.4686793277E-01 -0.6525916723E-01 -0.1702677471E+00 -0.3158187796E-01 0.3028147873E-01 -0.1797740855E+00 0.6351733467E+00 0.7214516731E+00 0.7207789094E+00 -0.6372838903E+00 0.1995469939E+00 0.1632013715E-01 -0.3864256419E-01 0.1755600827E+00 0.2947288315E-01 -0.2116688221E-01 0.2728991267E-01 -0.1959911299E-01 entries for the triangular preconditioning matrix and its inverse: 0.3743818971E+01 0.2671069322E+00 -0.6861305063E+01 0.1047409836E+01 0.7183286173E+01 -0.6066998614E+00 -0.3711751230E+01 0.2622361574E+00 0.7595392314E+00 -0.5336282441E-01 0.0000000000E+00 0.0000000000E+00 0.1749746932E+01 0.5715112179E+00 -0.1112386159E+01 0.5118280722E+00 0.5611031648E+00 -0.2021081048E+00 -0.1136294342E+00 0.3953339052E-01 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.1242099062E+01 0.8050887651E+00 -0.2151591879E+00 0.1662752175E+00 0.4303743724E-01 -0.3186979674E-01 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.1041780293E+01 0.9598952930E+00 -0.1641111826E-01 0.1572808312E-01 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.1001581378E+01 0.9984211186E+00 N=6 coefficients for the interior lowpass filter (Beware: they are normalized so that their sum is 2) - 0.0110318675094 0.00249992209279 0.06325056266 - 0.0297837512985 - 0.102724969862 0.477904371333 1.11389278393 0.694457972958 - 0.0683231215866 - 0.166863215412 0.00493661237185 0.0217847003266 coefficients for the edge filters: 0.9231184460E+00 -0.2321705918E-01 0.3781064509E+00 0.1171366871E+00 0.6815972396E-01 -0.3314072447E+00 -0.1063392935E-01 0.6083387113E+00 -0.9724819798E-02 -0.6313905276E+00 0.1297887318E-02 0.3213644020E+00 0.5723757426E-02 -0.6248310180E-01 -0.2868924125E+00 0.6092307458E-01 0.5940469387E+00 -0.2496185025E+00 0.6609604336E+00 0.4764189916E+00 0.3412988002E+00 -0.3565792957E+00 0.9716877076E-01 -0.2893047969E+00 -0.1860855577E-01 0.6336061692E+00 -0.4013700006E-01 -0.3069767199E+00 0.1537307481E-02 0.4772815467E-02 0.6783960390E-02 0.2106188350E-01 0.1472870932E+00 -0.1146309215E+00 -0.3468945123E+00 0.3715476805E+00 0.6221043773E-01 -0.4207564723E+00 0.4938022108E+00 -0.1034481165E+00 0.5849105895E+00 0.4067108104E+00 0.4598788833E+00 0.2977351919E+00 0.2274224529E+00 -0.6148599157E+00 -0.2788953680E-01 0.6853115007E-01 -0.6367943024E-01 0.1538100267E+00 0.2177711568E-02 -0.5448874481E-02 0.9609989671E-02 -0.2404525386E-01 -0.8324138021E-01 0.1150865862E+00 0.2035630921E+00 -0.2924528794E+00 -0.8289131955E-01 0.1456717540E+00 -0.1939904105E+00 0.2552553980E+00 -0.1908457968E-01 -0.1279750816E-02 0.2636403540E+00 -0.3051944288E+00 0.5123094150E+00 -0.4352292068E+00 0.6538041187E+00 0.7155631228E+00 0.3695601186E+00 -0.1145542755E+00 -0.3993953251E-01 -0.4300360725E-01 -0.9479455728E-01 -0.6987749084E-01 0.2986558645E-02 0.4395928052E-02 0.1317933842E-01 0.1939872286E-01 0.3164853364E-01 0.7165752442E-01 -0.8214471961E-01 -0.1869771835E+00 0.4327551059E-01 0.1021125523E+00 0.6830653932E-01 0.1533850430E+00 -0.4840048148E-02 -0.1330465569E-01 -0.7320834090E-01 -0.1616269775E+00 -0.5786918156E-01 -0.1222261416E+00 0.2055855208E-01 -0.2142989488E+00 0.4001944206E+00 0.8103733356E+00 0.7644983569E+00 -0.4058841524E+00 0.4653802512E+00 -0.1135045856E+00 -0.4686421163E-01 0.2621633969E-01 -0.1137136979E+00 0.6071714788E-01 0.3413297317E-02 -0.2015600401E-02 0.1506248690E-01 -0.8894611814E-02 -0.5550804971E-02 0.1092693197E-01 0.1471087926E-01 -0.2895882270E-01 -0.8859117912E-02 0.1743944876E-01 -0.1158923365E-01 0.2281376635E-01 0.1569832259E-02 -0.3090263591E-02 0.1157111171E-01 -0.2277809280E-01 0.7445526684E-02 -0.1465675051E-01 0.2902493903E-01 -0.8673422325E-01 -0.2999940975E-01 0.6576188609E-01 -0.6576340468E-01 0.4762105224E+00 0.3438258786E+00 -0.7968622388E+00 0.7867130346E+00 0.3399096026E+00 0.4895844920E+00 0.7597309556E-01 -0.4825468670E-01 -0.2118117647E-01 -0.1177993251E+00 -0.4513809001E-01 0.3488475665E-02 0.1772121221E-02 0.1539424027E-01 0.7820166308E-02 entries for the triangular preconditioning matrix and its inverse: 0.2691258238E+01 0.3715734097E+00 -0.4691390835E+01 0.7677024985E+00 0.5650878809E+01 -0.1862336274E+00 -0.4003610222E+01 0.4546833284E-01 0.1548107666E+01 -0.9293368857E-02 -0.2523403787E+00 0.1131936169E-02 0.0000000000E+00 0.0000000000E+00 0.2270666166E+01 0.4403993925E+00 -0.2346218035E+01 0.6446164864E+00 0.1686964492E+01 -0.2228021018E+00 -0.6557730032E+00 0.6332382245E-01 0.1069443363E+00 -0.8983535001E-02 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.1602926731E+01 0.6238588332E+00 -0.7485464376E+00 0.3995416825E+00 0.3030447729E+00 -0.1345491657E+00 -0.5083020320E-01 0.2195487513E-01 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.1168807480E+01 0.8555728955E+00 -0.1287884925E+00 0.1077442661E+00 0.2180567976E-01 -0.1782040660E-01 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.1022680347E+01 0.9778226434E+00 -0.7652542041E-02 0.7478034810E-02 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.1000641088E+01 0.9993593230E+00 N=7 coefficients for the interior lowpass filter: (Beware: they are normalized so that their sum is 2) 0.014521394762 0.00567134268574 - 0.152463871896 - 0.198056706807 0.408183939725 1.08578270981 0.758162601964 0.0246656594886 - 0.070078291222 0.0960147679355 0.043155452582 - 0.0178704316511 - 0.0014812259146 0.0037926585342 coefficients for the edge filters: 0.9426568713E+00 0.2111640418E-01 0.2691475418E+00 -0.3198838656E+00 0.1685897688E+00 0.5837712653E+00 0.9379442214E-01 -0.5101698301E+00 0.4001600171E-01 0.4662343677E+00 0.1057520816E-01 -0.2666472827E+00 -0.1804517915E-02 0.8683768041E-01 0.4620417362E-02 -0.1225652919E-01 -0.3237338194E+00 -0.3337831390E-01 0.6746802222E+00 0.3515528841E+00 0.5985769136E+00 -0.4361153142E+00 0.2331427899E+00 0.2303567833E-01 0.7615188825E-02 0.3942229572E+00 0.8787238208E-01 -0.5996924995E+00 0.1327822780E+00 0.3966958788E+00 -0.4208296665E-01 -0.1101295389E+00 -0.4763766998E-02 -0.2001792798E-02 0.1219755973E-01 0.5125562862E-02 -0.2713311808E-01 -0.6003418428E-01 -0.2899110477E+00 0.4010347311E+00 0.6661404639E-01 -0.2255897141E+00 0.7251175151E+00 -0.3612133157E+00 0.5750729858E+00 0.4028777516E+00 0.4362186445E-01 0.2083956160E+00 -0.1857980605E+00 -0.6015619432E+00 0.1201045634E+00 0.2500040680E+00 0.5011061230E-01 0.1224078560E+00 -0.2991531277E-01 -0.9490678016E-01 -0.1573393605E-02 -0.3494310966E-02 0.4028652635E-02 0.8947135057E-02 0.2428297386E-01 -0.9808774833E-02 -0.1012534619E-01 0.2839107988E-01 -0.1589124403E+00 0.2026374721E-02 -0.1400872185E+00 0.3959072389E-02 0.3332116140E+00 -0.1570876545E-01 0.7053065273E+00 -0.9207675872E-01 0.5793528972E+00 -0.5918868498E-02 0.3896614469E-02 0.5375286822E+00 -0.5955471765E-01 -0.7665446854E+00 0.7479188863E-01 0.2868941871E+00 0.3081374376E-01 0.1404254891E+00 -0.1340206604E-01 -0.1078898335E+00 -0.1047350551E-02 -0.4024427396E-02 0.2681726647E-02 0.1030449087E-01 0.2396415492E-02 0.1254105463E-02 -0.2199441967E-01 -0.1041703156E-01 0.3831273498E-01 0.1308623534E-01 0.8416826933E-02 0.7187262673E-02 -0.1404553727E+00 -0.3166691268E-01 -0.9975512873E-01 -0.1089545516E-01 0.2671255526E+00 0.5917635073E-01 0.7725679637E+00 0.4986270055E-01 0.5400947777E+00 0.1873760767E-01 0.1395136806E-01 -0.5366643035E+00 -0.4947167749E-01 0.7678225002E+00 0.6809969285E-01 -0.2885552645E+00 0.3044230228E-01 -0.1401119926E+00 -0.1259630803E-01 0.1078385285E+00 -0.1045026849E-02 0.4012411756E-02 0.2675776840E-02 -0.1027372499E-01 -0.9493922980E-03 -0.4169893239E-04 0.8445740060E-02 0.4623987716E-03 -0.8462283108E-02 -0.6221335658E-03 -0.3100522289E-02 0.1572706697E-03 0.2269052507E-01 0.2991444009E-02 -0.9675176425E-02 0.4406571767E-03 -0.1013545517E+00 -0.1220793447E-01 -0.1405275956E+00 -0.3060471910E-01 0.2877816730E+00 0.6783517122E-01 0.7686169120E+00 0.4959733828E-01 0.5358841401E+00 0.1742614880E-01 0.1743190445E-01 -0.5361004996E+00 -0.4949055461E-01 0.7677690648E+00 0.6785067390E-01 -0.2886325963E+00 0.3050565786E-01 -0.1400474616E+00 -0.1262873733E-01 0.1078086397E+00 -0.1047102354E-02 0.4010247499E-02 0.2681091142E-02 -0.1026818344E-01 0.1364120169E-03 0.3562754358E-04 -0.1153014522E-02 -0.3011395265E-03 0.1050196147E-02 0.2742856482E-03 0.6396328807E-03 0.1670567176E-03 -0.1940525665E-02 -0.5068179562E-03 0.1962825019E-02 0.5126423314E-03 0.9431646581E-02 0.2463316874E-02 0.4027633417E-02 0.1051919469E-02 -0.1076854888E+00 -0.1260408191E-01 -0.1401281648E+00 -0.3053643220E-01 0.2886799721E+00 0.6790539526E-01 0.7677614604E+00 0.4955094521E-01 0.5360881498E+00 0.1743687297E-01 0.1744975917E-01 -0.5360995353E+00 -0.4954996630E-01 0.7677648691E+00 0.6789074612E-01 -0.2886301380E+00 0.3051526119E-01 -0.1400473018E+00 -0.1263602514E-01 0.1078082911E+00 -0.1047379021E-02 0.4010246532E-02 0.2681799545E-02 -0.1026818096E-01 entries for the triangular preconditioning matrix and its inverse: 0.5804269091E+00 0.1722869812E+01 -0.7323447716E+00 0.5738683253E+01 0.2824499599E+01 -0.1245382394E+02 -0.2917456460E+01 0.7964976943E+01 0.1789930270E+01 -0.4649550414E+01 -0.6097284388E+00 0.1520565899E+01 0.8862324360E-01 -0.2151255312E+00 0.0000000000E+00 0.0000000000E+00 0.2198648442E+00 0.4548248738E+01 0.5966667693E+00 -0.4076684813E+01 -0.9937306950E-01 0.1227270380E+01 0.5522044783E-01 -0.6678395557E+00 -0.1473788829E-01 0.1967618134E+00 0.1693029724E-02 -0.2546662797E-01 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.6656852331E+00 0.1502211481E+01 0.1901881588E+00 -0.2856934692E+00 -0.1038800577E+00 0.1544684019E+00 0.3255433820E-01 -0.4820986746E-01 -0.4462431097E-02 0.6604466353E-02 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.1000032785E+01 0.9999672157E+00 -0.4315341245E-02 0.4305484704E-02 0.1542073127E-02 -0.1534917109E-02 -0.2143390832E-03 0.2132631237E-03 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.1002256439E+01 0.9977486406E+00 -0.1554134553E-02 0.1550217349E-02 0.2204062611E-03 -0.2197888501E-03 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.1000269825E+01 0.9997302475E+00 -0.7738658261E-04 0.7736527399E-04 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.1000005602E+01 0.9999943980E+00 N=8 coefficients for the interior lowpass filter: (beware: they are normalized so that their sum is 2) 0.00267279339281 - 0.000428394300246 - 0.0211456865284 0.00538638875377 0.0694904659113 - 0.0384935212634 - 0.0734625087609 0.515398670374 1.09910663054 0.68074534719 - 0.0866536154058 - 0.202648655286 0.0107586117505 0.0448236230437 - 0.000766690896228 - 0.0047834585115 coefficients for the edge filters: 0.9281136260E+00 -0.7274859222E-02 0.3668618286E+00 0.4042756257E-01 0.6266997447E-01 -0.1352706631E+00 -0.7647264163E-02 0.3196302046E+00 -0.5088004810E-02 -0.5501818613E+00 0.1171898539E-02 0.6205221664E+00 0.1656055473E-02 -0.4113728030E+00 -0.1929333000E-03 0.1430304841E+00 -0.1203653707E-02 -0.2044325554E-01 -0.2926634432E+00 0.2188690374E-01 0.6373078980E+00 -0.1065695633E+00 0.6452435440E+00 0.2843724182E+00 0.2965161471E+00 -0.4589840425E+00 0.5906254343E-01 0.3646732234E+00 -0.1366965641E-01 0.1447078292E+00 -0.1323318522E-01 -0.5672211027E+00 0.2213708145E-02 0.4500458402E+00 0.8306912600E-02 -0.1356216791E+00 -0.1892199826E-03 0.8474645355E-03 -0.1180561737E-02 0.5287413026E-02 0.1537394280E+00 0.4622773093E-01 -0.3933877381E+00 -0.1945832994E+00 0.1368645026E+00 0.3992968143E+00 0.6064470308E+00 -0.3762144385E+00 0.5685338138E+00 -0.7211460588E-01 0.3166230149E+00 0.4092764167E+00 0.9637901837E-01 0.5023569070E-01 -0.2215743488E-01 -0.5779911399E+00 -0.4105959919E-01 0.3834915553E+00 0.3062891878E-02 -0.1151747954E-01 0.1191510029E-01 -0.4999008246E-01 -0.2473506634E-03 0.7518452020E-03 -0.1543244666E-02 0.4690834793E-02 -0.9143117079E-01 -0.7950461567E-01 0.2571933236E+00 0.2823466127E+00 -0.1858137201E+00 -0.4114017970E+00 -0.2318000501E+00 0.1023384550E+00 0.1598859051E+00 0.3519831583E+00 0.4871009258E+00 -0.6162537699E-01 0.5734443542E+00 -0.4034315192E+00 0.4450618899E+00 -0.1544031905E+00 0.2033090498E+00 0.6034144392E+00 -0.3331081673E-01 -0.1069950598E+00 -0.6859620275E-01 -0.2019995950E+00 0.4406096842E-02 0.1468973030E-01 0.1763488599E-01 0.5758759998E-01 -0.3388224811E-03 -0.1171092606E-02 -0.2113946167E-02 -0.7306559816E-02 0.5709470789E-01 0.6367040385E-01 -0.1665850443E+00 -0.1917735089E+00 0.1454047216E+00 0.1859227361E+00 0.1015538648E+00 0.8760929009E-01 -0.1362852159E+00 -0.1698024241E+00 -0.1769345243E+00 -0.1650717698E+00 0.8596479652E-02 0.4044496899E-01 0.3062987789E+00 0.2651503207E+00 0.5431752460E+00 0.3382384364E+00 0.6140955155E+00 -0.7711604374E+00 0.3284966144E+00 0.2754111726E+00 -0.4723534035E-01 0.4710140765E-01 -0.1039762360E+00 0.2958356475E-01 0.6053819361E-02 -0.8186932177E-02 0.2473853830E-01 -0.2780308340E-01 -0.4480360998E-03 0.8002315701E-03 -0.2795340476E-02 0.4992722014E-02 -0.2771885178E-01 0.5905246892E-01 0.8389262409E-01 -0.1800708576E+00 -0.8147463473E-01 0.1795432638E+00 -0.3866640174E-01 0.7542773595E-01 0.7464550842E-01 -0.1632828547E+00 0.6920099668E-01 -0.1404076028E+00 -0.2231653624E-01 0.5304071283E-01 -0.1020129060E+00 0.2049015597E+00 -0.6275852804E-01 0.1129722066E+00 0.8683887629E-01 0.6297984646E-01 0.4540741128E+00 -0.7409643915E+00 0.7328223558E+00 0.5042713730E+00 0.4319437621E+00 0.7588728111E-01 -0.5734179466E-01 -0.4120932567E-01 -0.1314896433E+00 -0.8313424682E-01 0.7195965493E-02 0.5540498594E-02 0.2979946085E-01 0.2315912504E-01 -0.5190323961E-03 -0.3922287088E-03 -0.3238293222E-02 -0.2447152777E-02 0.8529185218E-02 0.1789547417E-01 -0.2624362023E-01 -0.5515123460E-01 0.2697489980E-01 0.5699017157E-01 0.9748173003E-02 0.1992423503E-01 -0.2431726904E-01 -0.5131208900E-01 -0.1901319060E-01 -0.3947317762E-01 0.8695522469E-02 0.1852759787E-01 0.2729552258E-01 0.5658785929E-01 0.1231155208E-01 0.2487421369E-01 0.9187597846E-02 0.5732429572E-01 -0.4745631970E-01 -0.1020173091E+00 -0.2924026466E-01 -0.4251128534E+00 0.3831732042E+00 0.8001954561E+00 0.7723764353E+00 -0.3763869007E+00 0.4743837775E+00 -0.6582574501E-01 -0.6082976218E-01 0.2842730285E-01 -0.1418145038E+00 0.5331847291E-01 0.7565491348E-02 -0.3918460367E-02 0.3149214931E-01 -0.1548884491E-01 -0.5401012058E-03 0.3080051475E-03 -0.3369743560E-02 0.1921673848E-02 -0.1148179452E-02 0.2054346689E-02 0.3567347972E-02 -0.6382774933E-02 -0.3784785333E-02 0.6771819551E-02 -0.1105680377E-02 0.1978304192E-02 0.3387180654E-02 -0.6060419089E-02 0.2395725348E-02 -0.4286482122E-02 -0.1281174092E-02 0.2292309675E-02 -0.3407989030E-02 0.6097652254E-02 -0.1283416571E-02 0.2296316381E-02 -0.9841020551E-02 0.2254192382E-01 0.6341196709E-02 -0.1213654065E-01 0.4619539219E-01 -0.1379967819E+00 -0.2943416082E-01 0.6522286075E-01 -0.5094613096E-01 0.4794644197E+00 0.3655480429E+00 -0.7789628537E+00 0.7770499808E+00 0.3646968778E+00 0.4810695095E+00 0.5250853492E-01 -0.6126039684E-01 -0.2724349082E-01 -0.1432436897E+00 -0.4923361338E-01 0.7606483137E-02 0.3810616823E-02 0.3168981524E-01 0.1496216731E-01 -0.5420982042E-03 -0.3029798461E-03 -0.3382203026E-02 -0.1890320507E-02 entries for the triangular preconditioning matrix and its inverse: 0.2810123818E+01 0.3558562059E+00 -0.6559223197E+01 0.8146829794E+00 0.1166265739E+02 -0.1366545660E+00 -0.1370803617E+02 -0.2512978838E-01 0.1057161896E+02 0.3435512306E-01 -0.5161014832E+01 -0.1989050428E-01 0.1450032681E+01 0.6413814665E-02 -0.1790147104E+00 -0.8795283072E-03 0.0000000000E+00 0.0000000000E+00 0.2865090274E+01 0.3490291420E+00 -0.4726642907E+01 0.7527005851E+00 0.5658991531E+01 -0.1741151174E+00 -0.4391120800E+01 0.2189754588E-01 0.2150489727E+01 0.7628539402E-02 -0.6053327281E+00 -0.4888651292E-02 0.7483245389E-01 0.8230905056E-03 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.2191756126E+01 0.4562551409E+00 -0.2253964453E+01 0.6427198947E+00 0.1808275069E+01 -0.2393601344E+00 -0.9018774144E+00 0.8134531543E-01 0.2565106244E+00 -0.1922603801E-01 -0.3190347407E-01 0.2116725807E-02 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.1600048291E+01 0.6249811369E+00 -0.8330291569E+00 0.4302638030E+00 0.4321721196E+00 -0.1746850867E+00 -0.1262794856E+00 0.4820621391E-01 0.1601926411E-01 -0.6049455037E-02 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.1210019309E+01 0.8264330929E+00 -0.2036886238E+00 0.1611623644E+00 0.6037258981E-01 -0.4551697161E-01 -0.7732501809E-02 0.5803277507E-02 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.1044505769E+01 0.9573905957E+00 -0.2609642521E-01 0.2489086650E-01 0.3366051566E-02 -0.3198214876E-02 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.1003760640E+01 0.9962534497E+00 -0.9726417449E-03 0.9689366947E-03 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.1000062955E+01 0.9999370493E+00 ***************************************************************** TABLES FOR THE RIGHT EDGE. &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& The coefficients for the interior filters are exactly the same as above for every value of N, so that we do not repeat them here. N=2 coefficients for the edge filters: 0.8705087534E+00 -0.2575129195E+00 0.4348969980E+00 0.8014229620E+00 0.2303890438E+00 -0.5398225007E+00 -0.1942334074E+00 0.3717189665E+00 0.1901514184E+00 -0.3639069596E+00 0.3749553316E+00 -0.7175799994E+00 0.7675566693E+00 0.4010695194E+00 0.4431490496E+00 0.2315575950E+00 entries for the triangular preconditioning matrix and its inverse: 0.1089843053E+01 0.9175633109E+00 0.0000000000E+00 0.0000000000E+00 -0.8008132342E+00 0.3505220326E+00 0.2096292884E+01 0.4770325785E+00 N=3 coefficients for the edge filters: 0.9096849943E+00 0.7221948764E-01 0.3823606559E+00 -0.4265622188E+00 0.1509872153E+00 0.8042331410E+00 0.5896101069E-01 -0.4074776976E+00 -0.2904078511E+00 -0.1535052307E+00 0.4189992290E+00 0.5223942379E+00 0.4969643721E+00 -0.9819800088E-01 0.4907578307E+00 -0.7678795743E+00 0.4643627674E+00 0.2985152397E+00 0.1914505442E+00 0.1230738317E+00 0.8183541840E-01 0.2294775484E+00 -0.1587582156E+00 -0.4451794444E+00 -0.9124735623E-01 -0.2558698912E+00 0.6042558204E-03 0.1694414802E-02 0.7702933610E-01 0.7598761510E+00 0.5200601778E+00 0.1391503267E+00 0.7642591993E+00 -0.2725472352E+00 0.3150938230E+00 -0.1123675716E+00 entries of the triangular preconditioning matrix and its inverse: 0.1055782528E+01 0.9471647557E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 -0.4658798302E+00 0.2539461793E+00 0.1737631796E+01 0.5754959149E+00 0.0000000000E+00 0.0000000000E+00 0.2417783151E+01 -0.1059694498E+00 -0.6663367942E+01 0.6796520006E+00 0.5642212524E+01 0.1772354366E+00 N=4 coefficients for the edge filters: 0.9154705188E+00 -0.1982779906E+00 0.3919142810E+00 0.6040677868E+00 0.5947771124E-01 -0.6495297603E+00 -0.2519180851E-01 0.4050309541E+00 0.6437934569E-01 -0.9924194741E-01 -0.2191626469E+00 -0.2726273506E+00 0.4488001781E+00 0.5092867484E+00 0.7540005084E+00 0.6811856626E-01 0.3937758157E+00 -0.6735345752E+00 -0.1581338944E+00 0.4499340827E+00 -0.1614201190E-01 0.2719065540E-01 0.4126840881E-01 -0.6951519362E-01 0.1290078289E-01 0.4581959340E-02 -0.1390716006E+00 0.3062032365E-01 0.2921367950E-01 0.1388737145E-01 0.4606168537E+00 -0.9504834999E-01 0.8164119742E+00 -0.3015815012E+00 0.2986473346E+00 0.8033636317E+00 -0.1027663536E+00 -0.4968427065E+00 -0.1257488211E-01 -0.2963204370E-01 0.3214874197E-01 0.7575680778E-01 -0.6775603652E-02 0.2880305124E-02 0.1913244129E-01 -0.8133189531E-02 -0.1770918425E-01 0.7528163799E-02 -0.6765916174E-01 0.2876186983E-01 -0.3023588481E-01 0.1285325684E-01 0.4977920821E+00 -0.9920191439E-01 0.8039495996E+00 -0.2977899841E+00 0.2977111011E+00 0.8037936841E+00 -0.9910804055E-01 -0.4976470524E+00 -0.1259895190E-01 -0.2963766018E-01 0.3221027840E-01 0.7577116678E-01 entries of the triangular preconditioning matrix and its inverse: 0.1000398078E+01 0.9996020804E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 -0.2241154296E-02 0.2235092825E-02 0.1002312956E+01 0.9976923812E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 -0.1844504727E-01 0.2335082980E-01 0.9170462790E-01 -0.1171759021E+00 0.7808176166E+00 0.1280708809E+01 0.0000000000E+00 0.0000000000E+00 -0.7373304912E-02 -0.2846460011E-02 -0.9310068502E-03 0.9005357890E-01 0.3767386370E+00 -0.9639839213E+00 0.5005192311E+00 0.1997925230E+01 N=5 coefficients of the edge filters: 0.6629994791E+00 0.2704377396E+00 0.5590853114E+00 -0.2099389697E+00 -0.3638895712E+00 0.6232723378E+00 -0.3190292420E+00 -0.6204577645E+00 -0.8577516141E-01 0.3239177989E+00 0.7938922949E-01 -0.6655879286E-01 -0.1615976602E+00 -0.4460509080E+00 0.7429922432E+00 0.2531551137E+00 0.5771521705E+00 -0.3811235714E+00 0.2773360273E+00 -0.2939476383E+00 0.1530007177E-01 0.6480763210E+00 -0.1063942878E+00 -0.2856775435E+00 -0.1216769629E-01 -0.4448843004E-01 0.1126647052E-01 0.4119330180E-01 0.2576681838E+00 -0.4091805529E+00 -0.3995181391E-01 0.1427046841E+00 0.1290658921E-01 0.2088087907E-01 0.4163708782E+00 -0.3899540483E+00 0.6469374504E+00 -0.2052536834E+00 0.5608421202E+00 0.7190940497E+00 0.4995700940E-02 -0.3116714966E+00 -0.1569482750E+00 -0.1763286609E-01 -0.2009485730E-01 -0.4039743821E-01 0.1860648984E-01 0.3740531781E-01 -0.8955158953E-01 -0.1414833249E+00 0.3895616532E-01 0.6067058589E-01 0.4751157158E-02 -0.1094361815E-01 -0.6596188737E-01 -0.1401642518E+00 0.1520881337E-01 -0.7844525367E-01 0.2466644601E+00 0.5612750679E-01 0.7199998123E+00 0.5913073605E+00 0.6131240289E+00 -0.7443064557E+00 0.1537319456E-01 0.1990571237E+00 -0.1721947543E+00 0.4730213481E-01 -0.2083858871E-01 0.3055544136E-01 0.1929513523E-01 -0.2829228895E-01 0.1546583496E-01 0.1104876084E-01 -0.6559247482E-02 -0.4685912973E-02 0.2728093541E-02 0.1948944437E-02 0.1830645747E-01 0.1307809574E-01 0.1708296448E-01 0.1220403484E-01 0.2156026058E-01 0.1540260595E-01 -0.3692524465E-01 -0.1737014260E+00 0.2045334663E+00 -0.1298838460E-01 0.7233635779E+00 0.6336000391E+00 0.6327590443E+00 -0.7243137518E+00 0.1649999072E-01 0.1992776018E+00 -0.1751674471E+00 0.3929252813E-01 -0.2109311508E-01 0.2952572161E-01 0.1953080958E-01 -0.2733883754E-01 entries of the triangular preconditioning matrix and its inverse: 0.1000413355E+01 0.9995868157E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 -0.4572991430E-02 0.4514077458E-02 0.1012632589E+01 0.9875250029E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.9186034191E-02 -0.8522720044E-02 -0.5149118250E-01 0.4842233071E-01 0.1050111166E+01 0.9522801325E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 -0.8653411835E-01 0.4412830877E-01 0.4462922645E+00 -0.2280710782E+00 -0.9332961770E+00 0.5124746278E+00 0.1734250554E+01 0.5766179504E+00 0.0000000000E+00 0.0000000000E+00 -0.6651201997E-01 0.2197171709E+00 0.3272287057E+00 -0.1071279051E+01 -0.6835308959E+00 0.2403809220E+01 0.1157116986E+00 -0.2710986078E+00 0.2461150317E+00 0.4063140690E+01 N=6 coefficients of the edge filters: 0.9236675275E+00 -0.5565971353E-01 0.3793343885E+00 0.2242498085E+00 0.4986459778E-01 -0.5135424238E+00 -0.1688947163E-01 0.6321916480E+00 -0.3311806998E-02 -0.4901838615E+00 0.2804629640E-02 0.2042322283E+00 -0.1237553624E-01 -0.3508415169E-01 -0.2831955072E+00 0.1057159278E+00 0.6209232596E+00 -0.3394364574E+00 0.6494435367E+00 0.4787854504E+00 0.3279016732E+00 -0.7187645472E-01 0.4613465423E-01 -0.5042780615E+00 -0.2201105042E-01 0.5796966704E+00 0.4772996268E-01 -0.2205355783E+00 0.1811083865E-02 -0.3313371482E-02 -0.7992103956E-02 0.1462152573E-01 0.1415889950E+00 0.1743290418E+00 -0.3264117354E+00 -0.4255531446E+00 0.5898718517E-01 0.2638047100E+00 0.5662575494E+00 0.3616438204E+00 0.6511436245E+00 -0.2644671055E+00 0.3434709841E+00 -0.4908547063E+00 -0.6897565912E-01 0.4962107578E+00 -0.2139852264E-01 0.6828427694E-01 0.4514540543E-01 -0.1606899475E+00 0.1807019829E-02 -0.5156673789E-02 -0.7974169836E-02 0.2275580595E-01 -0.4080929146E-01 0.3244709516E-02 0.1251977353E+00 0.5111253513E-03 -0.9208945297E-01 0.4381492218E-02 -0.1815441604E+00 -0.3035847066E-01 0.7492893632E-01 -0.3796933443E-01 0.4921890166E+00 0.7322186910E-01 0.7598885402E+00 0.3436818708E+00 0.3298535864E+00 -0.7867428461E+00 -0.6885203537E-01 0.4886190401E+00 -0.2056224689E-01 0.4823811158E-01 0.4357038095E-01 -0.1176377166E+00 0.1729458762E-02 -0.3491719268E-02 -0.7631901801E-02 0.1540855391E-01 0.1473338385E-01 -0.5211034254E-02 -0.3879928306E-01 0.1379054345E-01 0.3222685441E-01 -0.1172287487E-01 0.4181351746E-01 -0.1651839644E-01 -0.4470160402E-01 0.1484603300E-01 -0.1143592801E+00 0.4328769202E-01 -0.3079264597E-01 0.1491923547E-01 0.4953303341E+00 -0.7352728683E-01 0.7831063037E+00 -0.3353441076E+00 0.3365261769E+00 0.7880177709E+00 -0.7161554542E-01 -0.4916362852E+00 -0.2096645980E-01 -0.4832809329E-01 0.4445995152E-01 0.1180259590E+00 0.1762244193E-02 0.3492043263E-02 -0.7776580122E-02 -0.1540998367E-01 -0.2279778462E-02 0.1154376053E-02 0.5934267127E-02 -0.3004842779E-02 -0.4653920620E-02 0.2356533579E-02 -0.4697326198E-02 0.2378512204E-02 0.7905498252E-02 -0.4002984474E-02 0.1478426761E-01 -0.7486080223E-02 0.6356609850E-03 -0.3218698441E-03 -0.1184137622E+00 0.4493383491E-01 -0.4719524338E-01 0.2049260653E-01 0.4914056494E+00 -0.7279363945E-01 0.7873827096E+00 -0.3377604925E+00 0.3378777169E+00 0.7876649023E+00 -0.7256793624E-01 -0.4910841873E+00 -0.2105690525E-01 -0.4831332253E-01 0.4471373463E-01 0.1179951690E+00 0.1767573251E-02 0.3490782271E-02 -0.7800096641E-02 -0.1540441905E-01 entries of the triangular preconditioning matrix and its inverse: 0.1000078420E+01 0.9999215862E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 -0.9850976530E-03 0.9819736622E-03 0.1003102675E+01 0.9969069215E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.2633468462E-02 -0.2560290665E-02 -0.1664138984E-01 0.1623091263E-01 0.1022118540E+01 0.9783601031E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 -0.1429038400E-02 0.1388671224E-02 0.9368484963E-02 -0.9150173851E-02 -0.2392821028E-01 0.2393097496E-01 0.9782470759E+00 0.1022236636E+01 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.1195277199E-01 -0.1168953970E-01 -0.6711312742E-01 0.6542835502E-01 0.1479375368E+00 -0.1465646909E+00 -0.7026196422E-01 0.7358661282E-01 0.9760519092E+00 0.1024535673E+01 0.0000000000E+00 0.0000000000E+00 -0.1248032832E-01 0.2141640226E-01 0.7502310126E-01 -0.1275021840E+00 -0.1804736950E+00 0.3095551764E+00 0.1461500318E+00 -0.2545824950E+00 0.1504596966E+00 -0.2445553979E+00 0.6303329548E+00 0.1586463142E+01 N=7 coefficients for the edge filters: 0.9091449027E+00 0.1058599696E-01 0.4122956702E+00 -0.4261024318E-01 0.8463996964E-02 0.1626466305E+00 -0.4985469571E-01 -0.3983434261E+00 -0.2885243693E-01 0.6359366721E+00 -0.8468475604E-02 -0.5811383289E+00 0.9290995299E-03 0.2621339682E+00 0.2377975298E-02 -0.4571068446E-01 -0.2699308042E+00 -0.3369311938E-01 0.6287804833E+00 0.1173158297E+00 0.6425124921E+00 -0.3345684650E+00 0.3295936378E+00 0.4993594177E+00 0.9680040842E-01 -0.2270999192E+00 -0.1505090528E-02 -0.4092454872E+00 -0.2576996713E-01 0.5883989035E+00 -0.1663793375E-01 -0.2415648560E+00 0.7886583178E-03 0.4918478872E-02 0.2019348750E-02 0.1259369707E-01 0.2157402688E+00 -0.6868038150E-01 -0.3660961628E+00 0.2059784468E+00 0.9979560410E-01 -0.4260199250E+00 0.5343306371E+00 0.3030769028E+00 0.5651956498E+00 0.2528028219E+00 0.3984651316E+00 -0.2995453713E+00 0.2006608171E+00 -0.4153788373E+00 0.3790996947E-01 0.5783273640E+00 -0.5279896883E-01 -0.1200871578E+00 -0.3509616877E-01 -0.6583871196E-01 0.1600620645E-02 0.3864118919E-02 0.4098367097E-02 0.9894023233E-02 -0.1219999250E+00 0.1199301213E+00 0.2497494925E+00 -0.3021493088E+00 -0.1489636838E+00 0.4092549285E+00 -0.2314941689E+00 0.2642183651E-01 0.4306729538E-01 -0.3532455770E+00 0.3349988297E+00 -0.2065478346E+00 0.5170449138E+00 0.2227171845E+00 0.5314908191E+00 0.5240786066E+00 0.3984867666E+00 -0.2234158448E+00 0.1134176909E+00 -0.3876543947E+00 -0.8664578083E-01 0.1720771534E+00 -0.6206801690E-01 0.6600629896E-01 0.2555164772E-02 -0.5990160538E-02 0.6542464174E-02 -0.1533772348E-01 0.6643773700E-01 0.4081778499E-01 -0.1425076588E+00 -0.7665915987E-01 0.1150002072E+00 0.2089854289E-01 0.1110261320E+00 0.1140640809E+00 -0.5456405522E-01 0.1937409327E-01 -0.1403852745E+00 -0.1187989690E+00 -0.9002913124E-01 -0.1838791619E+00 0.9927107272E-01 -0.1133363121E+00 0.3252695570E+00 0.7805202816E+00 0.5955739150E+00 -0.5430653297E+00 0.6177120462E+00 0.6990288263E-01 0.2102093627E+00 -0.6927193818E-01 -0.1207077310E+00 0.6202160209E-01 -0.9029360085E-01 0.1264388999E-01 0.3498469159E-02 -0.2337275009E-02 0.8957782052E-02 -0.5984560439E-02 -0.2472698999E-01 0.1089534551E+00 0.5451727819E-01 -0.2418936349E+00 -0.4913268141E-01 0.2243741754E+00 -0.3543504434E-01 0.1488992192E+00 0.2981657384E-01 -0.1382661605E+00 0.5443081267E-01 -0.2312770306E+00 0.3080352023E-01 -0.1080114084E+00 -0.2311127518E-01 0.1488311123E+00 -0.2663146891E-01 0.2352279421E+00 -0.3986350788E-01 0.4020354092E+00 0.1012109980E+00 -0.7029809958E+00 0.5654368499E+00 -0.6175503239E-02 0.7419995864E+00 0.1485821868E+00 0.2730680885E+00 0.1174257523E+00 -0.1373359727E+00 -0.5325615968E-01 -0.1050857718E+00 -0.2772249506E-01 0.3942767529E-02 0.1737252935E-02 0.1009540190E-01 0.4448212190E-02 0.4060965940E-02 0.1545016950E-01 -0.9082349871E-02 -0.3455430249E-01 0.8675066430E-02 0.3300477019E-01 0.5263347825E-02 0.2002469773E-01 -0.5426164014E-02 -0.2064414148E-01 -0.8281419894E-02 -0.3150712024E-01 -0.2928559727E-02 -0.1114186730E-01 0.7407888982E-02 0.2818372382E-01 0.1392100926E-02 -0.5377738331E-01 0.2865053765E-01 0.1320738411E+00 0.5527738563E-01 0.2388167237E+00 -0.5250033174E-01 -0.7743478585E+00 0.2337385282E-01 0.5554662583E+00 0.5390029057E+00 -0.7133893666E-02 0.7666684946E+00 -0.5462109919E-01 0.2878132266E+00 -0.7104460368E-01 -0.1399692009E+00 0.3084906050E-01 -0.1077108034E+00 0.1309957900E-01 0.4008607630E-02 -0.1053633670E-02 0.1026398458E-01 -0.2697814488E-02 entries of the triangular preconditioning matrix and its inverse: 0.1000408431E+01 0.9995917354E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 -0.5293682422E-02 0.5202484794E-02 0.1017114208E+01 0.9831737600E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.1591493727E-01 -0.1341009335E-01 -0.1031512206E+00 0.8847321480E-01 0.1146285615E+01 0.8723829270E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 -0.3646661500E-01 0.1680436654E-01 0.2406286152E+00 -0.1136375469E+00 -0.6581590373E+00 0.3658356512E+00 0.1569466249E+01 0.6371592893E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.8620589496E-01 -0.7264200771E-02 -0.5839504132E+00 0.5536106388E-01 0.1663842388E+01 -0.2090053065E+00 -0.2536273536E+01 0.6450028470E+00 0.2505431179E+01 0.3991328951E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 -0.3341753604E+00 -0.3790478410E-02 0.2298323873E+01 0.1873956341E-01 -0.6712323867E+01 -0.2295905912E-01 0.1070192046E+02 -0.9239613787E-01 -0.9843372614E+01 0.7726440127E+00 0.5084895171E+01 0.1966608881E+00 0.0000000000E+00 0.0000000000E+00 0.1653022182E+00 0.3026314320E-01 -0.1367863363E+01 -0.1720350030E+00 0.4921932660E+01 0.4114532707E+00 -0.1002831667E+02 -0.6057060145E+00 0.1256338987E+02 0.5848923814E+00 -0.9758759367E+01 0.4444537862E+00 0.4318033378E+01 0.2315869083E+00 N=8 coefficients for the edge filters: 0.9280961080E+00 -0.1623137602E-01 0.3685482772E+00 0.7700181909E-01 0.5169019500E-01 -0.2216538064E+00 -0.1072856966E-01 0.4518914876E+00 -0.3547264354E-02 -0.5968036841E+00 0.1881724221E-02 0.5361053678E+00 0.2253426546E-03 -0.2972611580E+00 -0.4074549423E-03 0.9152878068E-01 0.2542121693E-02 -0.1206728019E-01 -0.2880715337E+00 0.3847998474E-01 0.6422316271E+00 -0.1590369267E+00 0.6540393284E+00 0.3562112107E+00 0.2730170577E+00 -0.4595861878E+00 0.4300012686E-01 0.1637283171E+00 -0.1532507378E-01 0.3534175472E+00 -0.3095082211E-02 -0.5814453781E+00 0.3081063250E-02 0.3686477291E+00 -0.1192117285E-01 -0.9703824753E-01 -0.2510321213E-03 -0.5800646631E-03 0.1566213637E-02 0.3619079426E-02 0.1554699662E+00 -0.7121179707E-01 -0.3928508188E+00 0.2523023478E+00 0.1655006354E+00 -0.4171714520E+00 0.6186900270E+00 0.2451267006E+00 0.5757733437E+00 0.2725111911E+00 0.2765573214E+00 -0.3518314346E+00 0.4215137090E-01 -0.2344734683E+00 -0.2022141803E-01 0.5903810045E+00 0.3170527734E-01 -0.3062645760E+00 0.2969565406E-02 -0.9326190637E-02 -0.1133537854E-01 0.4097674398E-01 -0.2472629557E-03 0.5916913076E-03 0.1542697449E-02 -0.3691619185E-02 -0.9273812077E-01 0.1179909741E+00 0.2525480154E+00 -0.3454318691E+00 -0.1903081753E+00 0.3669763444E+00 -0.2325263183E+00 0.8571956937E-01 0.1951123754E+00 -0.3733637204E+00 0.5747752998E+00 -0.1532441521E+00 0.6031889613E+00 0.3576146478E+00 0.3197987067E+00 0.3379298220E+00 -0.2318110629E-01 -0.4826776512E+00 -0.2335276594E-01 -0.1247229279E+00 0.3904642048E-01 0.2577717071E+00 0.3358324305E-02 0.1649336963E-01 -0.1296942483E-01 -0.6672983676E-01 -0.2744734004E-03 -0.1243663709E-02 0.1712466040E-02 0.7759337931E-02 0.4096472123E-01 0.9544232866E-02 -0.1240767851E+00 -0.2688549916E-01 0.1278114403E+00 0.3303656538E-01 0.7138489316E-01 -0.1099762148E-01 -0.1584871307E+00 -0.3331736763E-01 -0.1727866355E+00 0.3186523735E-01 0.1143640280E+00 0.7533252701E-01 0.5129116028E+00 -0.5202591621E-01 0.7137757767E+00 -0.3899644872E+00 0.3414317954E+00 0.7710342652E+00 -0.3881329228E-01 -0.4656907083E+00 -0.2526829049E-01 -0.6031146457E-01 0.4424255303E-01 0.1391049995E+00 0.3575822034E-02 0.7543265904E-02 -0.1394488775E-01 -0.3124469163E-01 -0.2875903358E-03 -0.5438414561E-03 0.1794303867E-02 0.3393079342E-02 -0.1790191282E-01 -0.5044968595E-02 0.5295161530E-01 0.1488052556E-01 -0.5704547538E-01 -0.1581581210E-01 -0.1894676577E-01 -0.6949272400E-02 0.6968256270E-01 0.2057861785E-01 0.4547075753E-01 0.1765306809E-01 -0.7337937479E-01 -0.1862118927E-01 -0.1444748191E+00 -0.4891212508E-01 -0.1409191494E-01 -0.1375364073E-01 0.4948704363E+00 0.5400109528E-01 0.7618895951E+00 0.3573536308E+00 0.3591100053E+00 -0.7782672053E+00 -0.4810103061E-01 0.4837479787E+00 -0.2674149513E-01 0.6134832074E-01 0.4783092078E-01 -0.1436058269E+00 0.3754819526E-02 -0.7612327455E-02 -0.1470868404E-01 0.3171165160E-01 -0.2997260590E-03 0.5426010792E-03 0.1870019815E-02 -0.3385340511E-02 0.4842573875E-02 0.2223331313E-02 -0.1435818114E-01 -0.6588142232E-02 0.1564773617E-01 0.7160556501E-02 0.3635704163E-02 0.1734300817E-02 -0.1807616145E-01 -0.8390109930E-02 -0.7951972463E-02 -0.3916508325E-02 0.2177252927E-01 0.9923280681E-02 0.3159516732E-01 0.1489081491E-01 -0.5393073080E-02 -0.2164190023E-02 -0.1454356948E+00 -0.5005924913E-01 -0.5484912621E-01 -0.2423995567E-01 0.4834662634E+00 0.5271872910E-01 0.7753953496E+00 0.3632737173E+00 0.3639514649E+00 -0.7773694792E+00 -0.5141318290E-01 0.4816288882E+00 -0.2717238099E-01 0.6128840935E-01 0.4899043649E-01 -0.1433368916E+00 0.3804055936E-02 -0.7609148826E-02 -0.1492982098E-01 0.3170285605E-01 -0.3026846009E-03 0.5422216523E-03 0.1888478444E-02 -0.3382973230E-02 -0.5886912723E-03 0.3289309542E-03 0.1750384584E-02 -0.9780261437E-03 -0.1931250902E-02 0.1079085355E-02 -0.3621632497E-03 0.2023585594E-03 0.2085884179E-02 -0.1165486300E-02 0.6409242844E-03 -0.3581158117E-03 -0.2736289413E-02 0.1528899888E-02 -0.3368917714E-02 0.1882379797E-02 0.1038171472E-02 -0.5800785496E-03 0.3193936333E-01 -0.1508848895E-01 0.6823471193E-02 -0.3370611049E-02 -0.1435014917E+00 0.4925184726E-01 -0.6098305316E-01 0.2705640950E-01 0.4814477634E+00 -0.5199195925E-01 0.7771077176E+00 -0.3643916717E+00 0.3644295324E+00 0.7771916813E+00 -0.5192289139E-01 -0.4813707824E+00 -0.2721779258E-01 -0.6127396434E-01 0.4913249792E-01 0.1432965635E+00 0.3808651449E-02 0.7607535473E-02 -0.1495173150E-01 -0.3169534309E-01 -0.3029170562E-03 -0.5421338829E-03 0.1889928755E-02 0.3382425628E-02 entries of the triangular preconditioning matrix and its inverse: 0.1000011417E+01 0.9999885829E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 -0.1885821248E-03 0.1884331061E-03 0.1000779405E+01 0.9992212023E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.6980138374E-03 -0.6895681425E-03 -0.5775869059E-02 0.5710508693E-02 0.1010657918E+01 0.9894544755E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 -0.1587420489E-02 0.1473040141E-02 0.1315517251E-01 -0.1221739122E-01 -0.4838107469E-01 0.4544822540E-01 0.1053305612E+01 0.9493920742E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.2302522936E-02 -0.1832761923E-02 -0.1919511889E-01 0.1530411869E-01 0.7113262876E-01 -0.5742370539E-01 -0.1541810491E+00 0.1326319561E+00 0.1103642518E+01 0.9060904992E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 -0.6297296878E-02 0.3996745292E-02 0.5008238228E-01 -0.3139508197E-01 -0.1744341513E+00 0.1085741195E+00 0.3478392588E+00 -0.2247406296E+00 -0.4139824420E+00 0.3061849704E+00 0.1225094612E+01 0.8162634872E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.1205751485E-01 -0.5357488581E-02 -0.9775783312E-01 0.4355462708E-01 0.3469638042E+00 -0.1557775571E+00 -0.7026319735E+00 0.3312968007E+00 0.8627444834E+00 -0.4752264599E+00 -0.6802055242E+00 0.4601200251E+00 0.1206700215E+01 0.8287062417E+00 0.0000000000E+00 0.0000000000E+00 -0.1638857751E-01 0.1062802918E-01 0.1318974327E+00 -0.8500762499E-01 -0.4651165383E+00 0.2996885100E+00 0.9374435384E+00 -0.6305890566E+00 -0.1161167601E+01 0.9184100559E+00 0.8600562361E+00 -0.8062512474E+00 -0.2230327919E+00 0.2486081011E+00 0.7434539179E+00 0.1345073280E+01 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% *************************************************************************** TABLES FOR WAVELETS ON THE INTERVAL IN THE CONSTRUCTION OF YVES MEYER (COMPUTED BY PIERRE VIAL) *************************************************************************** These tables correspond to a different construction for wavelets on the interval, due to Yves Meyer (Revista Matematica Iberoamericana, 7 (1992) p. 115-133). The details of how these tables were obtained, as well as graphs corresponding to the cases N=2 and N=4, can be found in "Wavelets on the interval and fast algorithms", by Albert Cohen, Ingrid Daubechies and Pierre Vial, to appear in Journal for Applied and Computational Harmonic Analysis (1993). The organization of these tables is as follows: - table of the interior filter coefficients for the different values of N. We have again chosen the filters with closest to linear phase, leading to "near-symmetric" scaling functions and wavelets. Note: the interior coefficients given are not always normalized so that their sum is sqrt(2). They should be renormalized before they are used. These interior filters are the same as in the first set of tables given above, but for some values of N their order has been inverted. This will mean that the graphs are mirror images. If you would like the same graphs (without mirroring), then you should invert the order of the interior coefficients, exchange the right edge table with the left edge table (for this value of N), and invert the order of all the edge coefficients in each subgroup as well. - table of edge coefficients for the scaling functions ("low pass" filters) at the left side, for N=2 to 8 - table of edge coefficients for the wavelet ("high pass" filters) at the left side, for N=2 to 8 - table of edge coefficients for the scaling functions ("low pass" filters) at the right side, for N=2 to 8 - table of edge coefficients for the wavelet ("high pass" filters) at the right side, for N=2 to 8 Note: the tables of the right side have been obtained by doing exactly the same computations, and listing the results in the same order, as for the left side tables, but with the order of the interior coefficients inverted. ************************************************************************** The interior coefficients in these tables were computed with Macsyma. The edge coefficients were then computed, using the interior filter coefficients, by means of a Fortran program using double precision for N=2,3,4,5 and quadruple precision for N=6,7,8 . *************************************************************************** INTERIOR COEFFICIENTS ********************* N=2 0.482962913145 0.836516303738 0.224143868042 -0.129409522551 N=3 .332670552950 .806891509311 .459877502118 -.135011020010 -.085441273882 .035226291882 N=4 (coefficients normalized so that their sum equals 2) - 0.107148901418 - 0.0419109651251 0.703739068656 1.13665824341 0.421234534204 - 0.140317624179 - 0.0178247014417 0.045570345896 N=5 (coefficients normalized so that their sum equals 2) 0.0386547959548 0.0417468644215 - 0.0553441861166 0.281990696854 1.02305296689 0.89658164838 0.0234789231361 - 0.247951362613 - 0.0298424998687 0.0276321529578 N=6 (coefficients normalized so that their sum equals 2) 0.0217847003266 0.00493661237185 - 0.166863215412 - 0.0683231215866 0.694457972958 1.11389278393 0.477904371333 - 0.102724969862 - 0.0297837512985 0.06325056266 0.00249992209279 - 0.0110318675094 N=7 (coefficients normalized so that their sum equals 2) 0.0037926585342 - 0.0014812259146 - 0.0178704316511 0.043155452582 0.0960147679355 - 0.070078291222 0.0246656594886 0.758162601964 1.08578270981 0.408183939725 - 0.198056706807 - 0.152463871896 0.00567134268574 0.014521394762 N=8 (coefficients normalized so that their sum equals 2) 0.00267279339281 - 0.000428394300246 - 0.0211456865284 0.00538638875377 0.0694904659113 - 0.0384935212634 - 0.0734625087609 0.515398670374 1.09910663054 0.68074534719 - 0.0866536154058 - 0.202648655286 0.0107586117505 0.0448236230437 - 0.000766690896228 - 0.0047834585115 **************************************** LEFT EDGE SCALING FUNCTION COEFFICIENTS *************************************** N=2 0.848528137424 - 0.529150262213 0.132287565553 0.212132034356 0.838525491562 - 0.484122918276 N=3 0.689047760315 0.724715933318 0.0306457241755 - 0.0291374408035 - 0.986047279405 0.161005005859 0.0172802631418 - 0.0164297845102 0.00443452721664 0.0208960300827 - 0.924034270866 0.380966943247 0.027026368393 - 0.0256962180001 0.0639688879804 0.381971870809 0.176750229211 0.404677356783 - 0.747429432607 0.308155135811 N=4 0.7983434920E+00 0.6022023488E+00 -0.3918024327E-01 0.5194149822E-01 -0.4817281609E+00 0.8739021503E+00 0.1774707150E-01 -0.2352740580E-01 -0.1232594861E+00 -0.6575127688E-01 -0.9620570014E-01 0.9850684416E+00 -0.2636405192E-01 0.3495099166E-01 0.8114147375E+00 0.4440233637E+00 0.3192581817E+00 0.1636579832E+00 -0.4282797155E-01 0.1094933054E+00 -0.1670338745E-01 0.2214378721E-01 -0.1643714751E-01 -0.1112580065E-01 0.2995602574E+00 0.2728668922E-01 0.8472064764E+00 -0.4270166998E+00 -0.3309408518E-01 0.8460780753E-01 0.2727915769E-02 -0.3616415322E-02 -0.5206157868E-01 -0.2836107693E-01 -0.4413123462E-01 -0.1285294872E-01 0.4543141690E+00 0.8282235028E+00 0.3000539798E+00 -0.1037443976E+00 -0.1262470890E-01 0.3227612835E-01 N=5 0.5149588736E+00 0.8572148847E+00 -0.7062608421E-01 0.4242755162E-01 -0.9680855135E+00 0.2366902992E+00 0.1166375834E+00 -0.7006826369E-01 0.2569251462E-01 0.1524482921E+00 -0.8988377800E+00 0.3868800469E+00 0.4678469852E+00 -0.2810519985E+00 0.8265463674E-01 0.5280457443E+00 0.8615307089E-01 -0.2053530811E+00 -0.4422572318E+00 0.4138613016E+00 -0.1341363044E+00 0.8058035557E-01 -0.3810281736E-01 -0.2103133707E+00 0.3026059798E-01 0.2107415482E+00 -0.8553851730E+00 -0.3335028061E+00 -0.1496490635E+00 0.1385649939E+00 -0.2809362553E+00 0.1687682052E+00 -0.4001455131E-01 -0.2777441959E+00 0.9006724682E-02 0.2482896416E+00 -0.9917949547E-01 0.8098971461E+00 -0.2582323890E+00 -0.1241046836E+00 -0.4791583558E-01 0.4436684941E-01 -0.8360649632E-01 0.5022533782E-01 -0.1533783538E-01 -0.9668361515E-01 -0.4952912706E-02 0.6191148032E-01 -0.5197035907E-01 0.2312568194E+00 0.6976664051E+00 0.6350643725E+00 0.1189068293E-01 -0.1727260340E+00 -0.2133407205E-01 0.1975391957E-01 -0.1591308791E-02 0.9559546817E-03 0.3515007474E-03 0.7914817671E-03 -0.1039035431E-02 -0.2096326217E-02 0.2722494187E-01 0.2963704669E-01 -0.3930998378E-01 0.1995579157E+00 0.7233513164E+00 0.6339755574E+00 0.1659420760E-01 -0.1753213559E+00 -0.2110191042E-01 0.1953895348E-01 N=6 0.8035811728E+00 -0.5951951771E+00 0.2409444375E+00 0.3253023901E+00 0.8139624945E+00 -0.4166403612E+00 -0.1713726513E+00 -0.2313725672E+00 0.2850349985E+00 0.2770986033E+00 0.5575844464E+00 -0.6694543662E+00 -0.2876454491E-02 -0.3883540664E-02 -0.5655242446E-01 -0.1151783354E+00 0.5730520088E+00 0.4076173301E+00 -0.4430745754E+00 -0.5409776766E+00 0.9214100804E-01 0.1244008388E+00 0.7306532844E-01 0.2931573652E+00 -0.1321263657E+00 -0.2417688989E-01 -0.3632781234E+00 0.6792063579E-01 0.1887648043E+00 -0.8333645213E+00 -0.1061491551E+00 -0.1433134304E+00 -0.2622879500E+00 -0.6856964195E+00 0.2766563635E+00 -0.8836692218E-01 0.3328884755E+00 0.1288342707E+00 0.5008585553E-01 -0.4619028205E+00 0.8828610310E-02 -0.3895963779E-01 -0.2023876977E-01 -0.2732464068E-01 0.4220601869E-01 0.4941654301E-01 0.3803171587E-01 0.8472554296E-01 0.1946516826E+00 -0.6992838718E-01 0.9438761468E+00 0.1295249721E+00 -0.7015973081E-01 0.1735085659E+00 0.4990121912E-02 -0.2202083175E-01 0.5456011297E-01 0.7366235691E-01 -0.1344279366E+00 -0.1735568822E+00 0.3102530241E-02 -0.1659152277E+00 -0.3869255752E+00 0.2453596290E+00 0.2217987487E+00 0.1874151629E+00 0.7052410111E+00 -0.3333463173E+00 -0.4413043778E-01 0.1047852370E+00 0.3298337216E-02 -0.1455518125E-01 -0.4678407876E-02 -0.6316382647E-02 0.3592640703E-03 -0.6935341643E-02 0.4493043023E-02 0.4405183141E-02 0.2315284183E-01 -0.9374856771E-02 -0.1151952189E+00 -0.4165806865E-01 0.4741171777E+00 0.7976083337E+00 0.3391664841E+00 -0.7534748748E-01 -0.2114679112E-01 0.4508434214E-01 0.1768528334E-02 -0.7804311311E-02 0.4182788817E-04 0.5647240556E-04 -0.3442465609E-04 0.1028288644E-05 0.1389588842E-03 0.7128147780E-04 -0.1053053091E-03 0.2899067329E-03 0.1541349274E-01 0.3547130473E-02 -0.1181216165E+00 -0.4823069885E-01 0.4910659254E+00 0.7876202163E+00 0.3379287356E+00 -0.7263467678E-01 -0.2106028481E-01 0.4472486618E-01 0.1767711923E-02 -0.7800708584E-02 N=7 0.7766665156E+00 0.6299119967E+00 -0.1148964921E+00 0.1416646431E+00 -0.9671641580E+00 0.1769842267E+00 -0.3218471381E-01 0.3968298692E-01 0.1563278738E+00 0.8016258409E+00 -0.5564532662E+00 0.1438984865E+00 0.2211311440E-01 -0.2726494430E-01 0.4246022560E-01 0.2682115073E+00 0.2563887092E+00 -0.5363572642E+00 -0.6324950327E+00 0.4142017603E+00 0.1199996300E-01 -0.1479566908E-01 -0.5636972038E-01 -0.2884098615E+00 -0.2710188640E+00 0.6266429769E+00 -0.5971809113E+00 0.2582226700E+00 0.5436350287E-01 0.1445242950E+00 0.4175845107E-02 -0.5148717734E-02 -0.7440855354E-02 -0.3382983614E-01 -0.3079310698E-01 0.7981928189E-01 0.5722707580E-01 0.2319141981E+00 -0.9107619432E+00 -0.3104299380E+00 0.3358655707E-01 0.8599791766E-01 -0.1031229858E+00 0.1271481897E+00 0.1056363589E-01 -0.1109935195E+00 -0.1694835353E+00 -0.1066751168E+00 0.3522103457E-01 0.1052218705E+00 -0.2477521992E-02 -0.9262193855E-01 -0.8918295201E+00 -0.3112729161E+00 0.3153823148E-01 0.8075320692E-01 -0.1636840253E+00 0.2018185116E+00 0.2397992313E-01 -0.1367621625E+00 -0.2287872293E+00 -0.2411625975E+00 0.1547745353E+00 0.1738003308E+00 -0.2203021645E+00 0.7991821052E+00 0.4097263186E-01 0.7425536593E-01 -0.2186097493E+00 -0.7664414437E-01 0.7725319564E-02 0.1978057424E-01 -0.5079391756E-01 0.6262769271E-01 0.6693967094E-02 -0.4652396311E-01 -0.7498687931E-01 -0.6670242581E-01 0.2830429724E-01 0.3953767158E-01 0.1915788427E-01 0.1080996941E+00 -0.9385371148E-01 0.5278533401E+00 0.7495761660E+00 0.2923381676E+00 -0.1429933474E+00 -0.1070457309E+00 0.4143065991E-02 0.1060826335E-01 -0.1495677487E-02 0.1844134781E-02 0.3796088187E-03 -0.3726476076E-03 -0.1313050363E-02 -0.4257093968E-02 0.4767087176E-02 0.2983259636E-02 -0.1353810327E-01 0.3517346347E-01 0.6457953904E-01 -0.4929701131E-01 0.1763779822E-01 0.5365060286E+00 0.7675636132E+00 0.2885569171E+00 -0.1400433929E+00 -0.1077912821E+00 0.4010358474E-02 0.1026846759E-01 -0.3038841290E-04 0.3746819061E-04 0.1201067262E-04 0.1591583744E-04 0.1765202958E-04 -0.5058087991E-04 -0.2976878538E-03 -0.5384490113E-03 0.2571676204E-02 -0.9401364213E-03 -0.1271271848E-01 0.3052112329E-01 0.6789733930E-01 -0.4954313507E-01 0.1743713195E-01 0.5361004301E+00 0.7677643255E+00 0.2886299560E+00 -0.1400472373E+00 -0.1078082259E+00 0.4010244932E-02 0.1026817686E-01 -0.4587815337E-07 0.5656667234E-07 0.1705493214E-07 0.1813824211E-07 0.3222871934E-07 -0.2080479474E-07 -0.2019192222E-06 -0.3625456178E-06 -0.1335197462E-06 0.6674082282E-07 0.2681764400E-02 -0.1047381271E-02 -0.1263630033E-01 0.3051551953E-01 0.6789269080E-01 -0.4955283591E-01 0.1744125510E-01 0.5361019173E+00 0.7677643170E+00 0.2886296318E+00 -0.1400472404E+00 -0.1078082377E+00 0.4010244872E-02 0.1026817671E-01 N=8 0.8145313640E+00 -0.5801195196E+00 0.2546778816E+00 0.3575868684E+00 0.3176080089E+00 -0.8404736527E+00 -0.2118740650E+00 -0.2974870959E+00 -0.5809146479E+00 -0.4102927684E+00 0.5953490052E+00 -0.7980217044E-01 0.7371113089E-01 0.1034959624E+00 0.3790561153E+00 0.2096111511E+00 0.5261835609E+00 -0.4930256875E+00 0.6765214691E-01 -0.5212625063E+00 -0.1657029358E-01 -0.2326593637E-01 0.2835607555E-01 -0.4204253027E-02 0.5232892196E-01 0.3363143855E+00 0.2707791658E+00 -0.2181631699E+00 0.1282592034E+00 -0.8632205676E+00 0.4725307654E-01 0.6634686747E-01 -0.1768605708E+00 -0.2428779496E-01 -0.1728053705E+00 -0.2496491113E+00 -0.1026485332E+00 -0.7015597057E-01 0.4504320556E+00 -0.6366908518E-01 -0.1272105456E+00 -0.7941822291E+00 -0.3150600071E+00 -0.4423679063E+00 0.4664265832E+00 -0.1074191330E+00 0.4591536250E-01 -0.1495306795E-01 0.3948485068E+00 0.2753380149E+00 -0.2521499192E+00 0.4757966099E-01 0.4479299855E-01 -0.3909345922E+00 -0.2305781603E-01 -0.1438599401E+00 -0.1628374040E+00 -0.2286359419E+00 0.1439556412E+00 -0.9221803771E-01 -0.1559638710E+00 -0.4526846422E+00 0.7680278703E-01 0.2798722613E+00 0.6073428962E+00 -0.1277567678E+00 0.7075076739E-02 0.4371314130E+00 0.1227511608E-01 0.4457322339E-01 -0.1100591484E-02 -0.6866696512E-02 0.1422343910E-01 0.1997077647E-01 -0.5755686815E-01 -0.8943575462E-02 -0.5113148256E-01 -0.2870337098E-01 -0.5044680204E-01 -0.7048754871E-01 0.7802410165E-01 -0.3357971353E-02 0.9574788820E+00 -0.6034410649E-01 -0.8780892537E-01 -0.2208827842E+00 0.1042138073E-01 0.4380269399E-01 -0.7294541741E-03 -0.4551135007E-02 -0.2847286228E-01 -0.3997803654E-01 0.1712399543E-01 -0.1916575373E-01 -0.2592997362E-01 0.5065243826E-02 0.4279291071E-01 -0.3263024185E-01 -0.3163483356E-01 0.1965128227E-01 0.1870478101E+00 -0.5633846528E-01 0.8568892098E+00 0.4372612498E+00 -0.6703059990E-01 -0.1500716835E+00 0.8519695716E-02 0.3506433161E-01 -0.6219669046E-03 -0.3880511557E-02 -0.1332967539E-01 -0.1871586512E-01 0.2153245326E-01 -0.3865012867E-02 0.4740812821E-02 0.3654642397E-02 0.1552794626E-01 0.1184719866E-01 -0.1683351520E-01 0.2573274217E-02 0.5123819976E-01 -0.3022844964E-01 -0.4903142965E-01 0.3621831839E+00 0.7774835776E+00 0.4809708581E+00 -0.6128478594E-01 -0.1432550194E+00 0.7610815937E-02 0.3170366925E-01 -0.5425512917E-03 -0.3385029882E-02 0.1198029623E-03 0.1682123545E-03 -0.4574159978E-03 -0.6498394141E-04 -0.5037600110E-03 -0.1039508974E-02 0.1793350305E-03 0.1895383041E-03 0.1581295871E-02 -0.2137732665E-03 -0.1495199763E-01 0.3830464294E-02 0.4910595228E-01 -0.2718959315E-01 -0.5195946631E-01 0.3644408152E+00 0.7771868548E+00 0.4813611500E+00 -0.6127351228E-01 -0.1432947954E+00 0.7607500914E-02 0.3169516934E-01 -0.5421324438E-03 -0.3382416650E-02 -0.1467161418E-04 -0.2060004793E-04 0.1949164967E-04 -0.5844488030E-05 0.7485554110E-06 0.9490983180E-05 -0.5287598342E-04 -0.9424653819E-05 0.1650150426E-06 -0.8931253371E-05 0.1889628005E-02 -0.3041026881E-03 -0.1495041138E-01 0.3806880495E-02 0.4913803765E-01 -0.2721895815E-01 -0.5194591141E-01 0.3644417925E+00 0.7771857621E+00 0.4813596873E+00 -0.6127335999E-01 -0.1432942437E+00 0.7607487339E-02 0.3169508789E-01 -0.5421323322E-03 -0.3382415953E-02 -0.1287522004E-07 -0.1807777568E-07 0.1467373756E-07 -0.6047676057E-08 -0.2557954799E-08 0.6767773484E-08 -0.4138623196E-07 -0.1152590396E-07 -0.7816962231E-09 -0.6457861266E-08 -0.1973430468E-08 -0.1721336728E-09 0.1889952080E-02 -0.3029230007E-03 -0.1495225720E-01 0.3808752194E-02 0.4913717957E-01 -0.2721903007E-01 -0.5194583809E-01 0.3644418949E+00 0.7771857517E+00 0.4813596513E+00 -0.6127335907E-01 -0.1432942384E+00 0.7607487325E-02 0.3169508781E-01 -0.5421323318E-03 -0.3382415951E-02 ********************************************************************* LEFT EDGE WAVELET COEFFICIENTS. ******************************* N=2 - 0.512347538298 - 0.821583836258 0.216506350947 - 0.125 N=3 0.720522830617 - 0.685061028561 0.0259917491699 - 0.101939535681, 0.0200641216304 - 0.00827216838973 0.0639675079235 - 0.0608192341872 0.151405112504 0.904072212264 - 0.0510574707719 - 0.18071490589 0.315790060572 - 0.130196008824 N=4 0.5979027428E+00 -0.7926434769E+00 -0.1659403671E-01 0.6477069526E-01 0.9713044594E-01 -0.1797030610E-01 -0.3192898087E-03 0.8162911886E-03 0.4823971249E-01 -0.6395169431E-01 0.3010034664E+00 0.1718883936E+00 -0.8873256413E+00 -0.3991915695E-01 0.2462565991E+00 -0.1524149055E+00 -0.9080945357E-02 0.2321619929E-01 -0.1162436086E-02 0.1541048928E-02 0.2218479707E-01 0.1208539488E-01 0.1880547055E-01 0.5476976811E-02 -0.8114432093E-01 -0.3089428579E+00 0.8028339176E+00 -0.4957693566E+00 -0.2962669767E-01 0.7574314021E-01 N=5 0.6182708675E+00 -0.3714168701E+00 -0.1886088129E+00 -0.5203639573E+00 0.1728721711E+00 0.3655404713E+00 0.9964278013E-01 0.2321755628E-02 0.8297752060E-04 -0.7683163866E-04 -0.9199155757E-01 0.5526253651E-01 0.1276201402E+00 0.4846229512E+00 0.3921178348E+00 0.7493106089E+00 0.1219411317E+00 -0.8181830470E-01 0.2258502019E-01 0.4446446219E-02 0.3345391169E-02 -0.3097607805E-02 -0.5206990422E-01 0.3128020722E-01 -0.1303591078E-01 -0.7446233534E-01 0.2030318262E-02 0.5628764191E-01 -0.1851188211E+00 0.7400777444E-02 0.6246714288E+00 -0.7215672985E+00 0.1975651316E+00 0.3986516515E-01 0.2939208418E-01 -0.2721509824E-01 -0.1137543931E-02 0.6833623070E-03 0.2512696118E-03 0.5657891708E-03 -0.7427524153E-03 -0.1498554635E-02 0.1946169563E-01 0.2118598397E-01 -0.1754541390E+00 -0.1648697186E-01 0.6339417098E+00 -0.7234098228E+00 0.1993922999E+00 0.3913868175E-01 0.2951943631E-01 -0.2733301778E-01 N=6 -0.4056098474E+00 -0.5476194186E+00 0.3345888248E+00 -0.8469145514E-02 0.2860429450E-02 0.4344317225E+00 -0.1793040681E+00 0.4501354334E+00 -0.7823562605E-02 -0.2169451337E-03 0.3443284776E-06 -0.1518815163E-05 -0.2714331420E+00 -0.3664656082E+00 0.8617650411E-01 -0.2747405494E+00 -0.5148935461E+00 -0.3097406490E+00 -0.2206953036E+00 -0.5444907507E+00 0.4953215623E-01 -0.2013924147E-01 -0.1989883688E-02 0.4859370755E-02 0.1437935110E-03 -0.6345441585E-03 -0.7388896229E-01 -0.9975850151E-01 0.1991481291E+00 0.2684432545E+00 -0.1045213665E-01 0.2405920775E+00 0.5401581689E+00 -0.3490563093E+00 -0.6165711214E-01 -0.1943705670E+00 0.5024780923E+00 -0.3169028187E+00 -0.3084242027E-01 0.7560970841E-01 0.2218060423E-02 -0.9788044508E-02 0.2329741271E-02 0.3145415646E-02 -0.1484555312E-03 0.3513131058E-02 -0.2412185766E-02 -0.2301643677E-02 -0.1162880173E-01 0.4467413223E-02 0.4333253688E-01 0.1764767584E-01 -0.6404967457E-01 -0.3432838094E+00 0.7870194497E+00 -0.4897071000E+00 -0.4826799594E-01 0.1178085687E+00 0.3490290194E-02 -0.1540224757E-01 -0.2118182730E-04 -0.2859787559E-04 0.1743279790E-04 -0.5207298811E-06 -0.7036938958E-04 -0.3609725256E-04 0.5332707089E-04 -0.1468100425E-03 -0.7805460453E-02 -0.1796282458E-02 0.4479149901E-01 0.2101925260E-01 -0.7264258737E-01 -0.3379188415E+00 0.7876414895E+00 -0.4910573861E+00 -0.4831174654E-01 0.1179901294E+00 0.3490712054E-02 -0.1540410920E-01 N=7 0.3969456608E+00 -0.4894245622E+00 -0.1235692328E+00 -0.2582101893E-01 -0.1328855813E+00 -0.1202996209E-01 0.3801419403E+00 0.6231415519E+00 0.1905526450E+00 0.5893964132E-02 0.1561741876E-03 0.6031669262E-05 -0.4927938364E-06 -0.1261756223E-05 -0.3233700290E+00 0.3987075576E+00 0.1351807407E+00 0.2096521373E+00 0.4833387568E+00 0.3720043480E+00 0.2556921125E+00 0.4668718999E+00 0.1373682453E+00 0.2872512719E-02 -0.1360874965E-02 -0.1949202336E-02 0.8743490990E-03 0.3629247193E-03 -0.2999653169E-04 -0.7680570657E-04 -0.2823703425E+00 0.3481559189E+00 0.2903665693E-01 -0.3033125208E+00 -0.4606818655E+00 -0.2824761359E+00 0.5936310480E-01 0.2414473445E+00 0.2265766807E+00 -0.4453082198E+00 0.3158425440E+00 -0.6883194783E-02 -0.3045582749E-01 -0.4030240270E-01 0.1788874193E-01 0.7517433396E-02 -0.6122399330E-03 -0.1567631908E-02 -0.5050738626E-02 0.6227440642E-02 0.1186122150E-02 -0.1781771641E-02 -0.5423430571E-02 -0.1518205990E-01 0.2487591795E-01 0.2339536126E-01 -0.1088432050E+00 0.1555511237E+00 0.2777338303E+00 -0.7671513525E+00 0.5369254850E+00 -0.1606926084E-01 -0.5015309817E-01 -0.6812578033E-01 0.3052715070E-01 0.1268650625E-01 -0.1047058590E-02 -0.2680979085E-02 -0.1153350842E-03 0.1422054166E-03 0.4560875753E-04 0.6053691674E-04 0.6687225073E-04 -0.1932039563E-03 -0.1135318214E-02 -0.2053589490E-02 0.9849438060E-02 -0.3601089889E-02 -0.1080997299E+00 0.1400686730E+00 0.2886474191E+00 -0.7677274911E+00 0.5360863094E+00 -0.1744690015E-01 -0.4955276912E-01 -0.6789145494E-01 0.3051552376E-01 0.1263634496E-01 -0.1047384658E-02 -0.2681813977E-02 -0.1756594007E-06 0.2165838647E-06 0.6530033661E-07 0.6944811113E-07 0.1233981379E-06 -0.7965760361E-07 -0.7731119139E-06 -0.1388121081E-05 -0.5112227575E-06 0.2555383959E-06 0.1026798462E-01 -0.4010231020E-02 -0.1078082259E+00 0.1400472648E+00 0.2886296214E+00 -0.7677643207E+00 0.5361019171E+00 -0.1744125426E-01 -0.4955283493E-01 -0.6789269348E-01 0.3051551317E-01 0.1263630340E-01 -0.1047384889E-02 -0.2681814568E-02 N=8 -0.2620979145E+00 -0.3680051517E+00 0.3007938848E+00 -0.1223236495E+00 -0.3815411480E-01 0.2223806092E+00 -0.7414398574E+00 -0.2856615192E+00 0.7435240137E-01 -0.3958129970E-01 -0.3312367172E-01 0.5296663936E-03 -0.2698631364E-04 0.4827845400E-07 -0.2405836391E-08 -0.1119370789E-07 -0.1530044792E-01 -0.2148297772E-01 -0.1411089928E+00 -0.6710033379E-01 -0.2754652268E+00 -0.5621677849E+00 -0.2521929541E+00 0.8489402134E-01 -0.5756119710E+00 -0.4252477763E+00 -0.1717046011E-02 0.4224061134E-03 -0.2349772977E-03 -0.4160927634E-03 0.3225252044E-04 0.1266155053E-03 -0.2565139468E-05 -0.1600415263E-04 0.1495099502E+00 0.2099231961E+00 0.1776433332E+00 0.2017476699E+00 0.4784490465E+00 0.5947478107E-01 -0.3620530588E+00 0.6528531425E+00 0.5286410695E-01 -0.2222121460E+00 0.5727745934E-01 -0.1143513897E+00 0.5375754041E-01 0.8506084034E-02 -0.4048226504E-02 -0.7458590086E-02 0.5621800279E-03 0.2220046324E-02 -0.4426269435E-04 -0.2761592227E-03 0.2437646831E-01 0.3422639182E-01 -0.4003214950E-01 0.6820587728E-02 -0.9838965803E-02 -0.9366231848E-02 -0.2696011202E-01 -0.2069757161E-01 0.3436761211E-01 -0.5103853901E-02 -0.1475095258E+00 0.6694319985E-01 0.4773719174E+00 -0.7755787502E+00 0.3636972524E+00 0.5218600648E-01 -0.2717665152E-01 -0.4912168611E-01 0.3801081650E-02 0.1492736485E-01 -0.3021310554E-03 -0.1885024820E-02 -0.2526109188E-03 -0.3546846973E-03 0.8694036319E-03 0.1010912744E-03 0.9035494282E-03 0.1885121065E-02 -0.4586723661E-03 -0.3637255134E-03 -0.2829586692E-02 0.3593205922E-03 0.3169382593E-01 -0.7649438160E-02 -0.1432336703E+00 0.6121586703E-01 0.4813866596E+00 -0.7771843511E+00 0.3644396836E+00 0.5194280857E-01 -0.2721872350E-01 -0.4913606047E-01 0.3808725019E-02 0.1495209647E-01 -0.3029202893E-03 -0.1889948926E-02 0.2622395072E-04 0.3682039585E-04 -0.3484560037E-04 0.1044400200E-04 -0.1346357753E-05 -0.1696820074E-04 0.9452329486E-04 0.1683706766E-04 -0.2973670447E-06 0.1596726796E-04 -0.3381844248E-02 0.5442476019E-03 0.3169178699E-01 -0.7604144409E-02 -0.1432957713E+00 0.6127323127E-01 0.4813597833E+00 -0.7771855710E+00 0.3644418761E+00 0.5194577328E-01 -0.2721902826E-01 -0.4913717014E-01 0.3808751988E-02 0.1495225819E-01 -0.3029205141E-03 -0.1889950329E-02 0.2304180410E-07 0.3235242306E-07 -0.2626045803E-07 0.1082307302E-07 0.4577834066E-08 -0.1211150005E-07 0.7406609086E-07 0.2062688911E-07 0.1399229053E-08 0.1155742488E-07 0.3531713891E-08 0.3080661641E-09 -0.3382419079E-02 0.5421367809E-03 0.3169508577E-01 -0.7607487647E-02 -0.1432942382E+00 0.6127335935E-01 0.4813596512E+00 -0.7771857518E+00 0.3644418948E+00 0.5194583812E-01 -0.2721902992E-01 -0.4913717967E-01 0.3808752014E-02 0.1495225834E-01 -0.3029205147E-03 -0.1889950333E-02 ************************************************************************** RIGHT EDGE SCALING FUNCTION COEFFICIENTS. ***************************************** N=2 0.848528137424 0.529150262213 - 0.132287565553 0.212132034356 0.838525491562 0.484122918276 N=3 0.889500699418 0.456933808921 - 0.198411021088 0.386241373662 0.832668382346 0.343677222149 0.0390630495665 - 0.0760429831027 - 0.143921176769 0.456707890812 0.807766275151 0.33303120718 - 0.000276799784313 0.000538838660959 0.0349752642807 - 0.085504178774 - 0.134969198046 0.459895243878 0.806892290508 0.332670875027 N=4 0.7629809303E+00 -0.6464209928E+00 0.1555526564E+00 0.1836012627E+00 0.4620817399E+00 -0.8535657052E+00 0.3793246643E+00 0.4477229057E+00 0.4284467089E+00 0.3973740378E+00 -0.2021221018E+00 -0.5228106220E+00 0.2385999808E+00 0.2816233343E+00 0.1056438723E+00 0.1612498770E+00 0.8548427132E+00 0.2929411663E+00 -0.3647382801E-01 -0.9324840384E-01 0.6526723701E-01 0.7703595299E-01 0.7744666349E-01 0.7039069048E-01 -0.6529437593E-01 0.2555397028E+00 0.8099281093E+00 0.4965300820E+00 -0.2995738718E-01 -0.7658857572E-01 0.1517778948E-02 0.1791458518E-02 -0.3127686151E-02 -0.1031248163E-02 0.3237561439E-01 -0.1322822647E-01 -0.9898430026E-01 0.2979273659E+00 0.8037308261E+00 0.4975940939E+00 -0.2963560969E-01 -0.7576592454E-01 N=5 0.9116496405E+00 0.4109682870E+00 -0.1759262671E+00 0.3902566773E+00 0.6301011968E+00 0.6478596732E+00 0.2825379610E-03 -0.6267530579E-03 0.4175827162E+00 -0.4056820940E+00 0.6289312762E+00 0.5152588582E+00 -0.5113299639E-01 0.1134281628E+00 0.4836999717E+00 -0.5526531145E+00 -0.2269223725E+00 -0.5499800740E+00 0.2214856571E+00 0.2051843068E+00 0.2756002147E-02 -0.6113630773E-02 -0.1460819570E+00 0.1465088170E+00 0.1654940540E+00 0.3172833766E-01 0.9500926016E+00 -0.1444971260E-01 0.1180200176E+00 0.1092786192E+00 0.1425700173E-01 -0.3162626148E-01 -0.7075177701E-01 0.9173486581E-01 -0.6745433251E-01 0.2118550693E+00 -0.1051600438E-01 0.9395202801E+00 0.1694709068E+00 -0.1464208651E+00 0.4001747247E-01 0.3705349502E-01 -0.1315787444E-02 0.2918807090E-02 0.1730939444E-01 -0.1895045515E-01 -0.1537869850E-02 -0.2706707215E-01 -0.1556669346E+00 -0.6193750436E-05 0.6330645158E+00 0.7286274296E+00 0.1987062136E+00 -0.3988654553E-01 0.2953429005E-01 0.2734677134E-01 -0.8561071719E-04 0.1899099809E-03 -0.9013424188E-06 -0.1367686226E-03 -0.3599933730E-03 0.3327378221E-03 0.1961899121E-01 -0.2117649690E-01 -0.1753299891E+00 0.1662647625E-01 0.6339762696E+00 0.7234044479E+00 0.1993976399E+00 -0.3913415866E-01 0.2951949191E-01 0.2733306926E-01 N=6 0.6512594203E+00 0.7588551689E+00 -0.6896282953E-01 0.5918480130E-01 -0.9848250307E+00 0.1478544768E+00 -0.1667727153E-01 0.1431265231E-01 0.1090239805E+00 0.7126760308E+00 -0.1719730277E+00 0.6709313982E+00 0.9785571254E-01 -0.8398105097E-01 0.6834310191E-02 0.1247808574E+00 0.7236789907E-01 -0.1108818957E+00 0.1804007431E+00 0.9579551851E+00 -0.5378738739E+00 0.4616103858E+00 0.2733949616E-01 -0.2535533852E+00 0.3484637175E+00 0.3309876136E+00 -0.2950887461E+00 0.1958019515E+00 0.6099724771E-01 0.2691738861E+00 -0.2335808916E+00 0.2004621729E+00 0.5067312783E-01 0.1483313327E+00 0.4193562472E+00 -0.6838768540E-01 0.8092621294E+00 -0.1702431983E+00 -0.5881963586E-01 -0.1104006534E+00 0.5469174586E-02 0.2413483588E-01 0.7905558067E-01 -0.6784653218E-01 -0.2413743535E-02 0.4795434784E-01 -0.2979345169E-01 -0.5477003063E-01 0.1575224560E+00 -0.5400590327E-01 0.8600210456E+00 0.4427411664E+00 -0.5350546863E-01 -0.1279990455E+00 0.3964078767E-02 0.1749302183E-01 0.4472356538E-01 -0.3838234812E-01 -0.1245771188E-02 0.2792643621E-01 -0.2285669131E-01 -0.3338969826E-01 0.4201463682E-01 -0.2161240035E-01 -0.6527800067E-01 0.3288435947E+00 0.7890314114E+00 0.4902682296E+00 -0.4839771981E-01 -0.1181080824E+00 0.3500297801E-02 0.1544640999E-01 -0.2366701878E-04 0.2031134472E-04 -0.3373738591E-03 -0.2266339823E-02 -0.2165041937E-02 0.1906206337E-02 -0.7087323880E-02 0.2020684368E-02 0.4460763770E-01 -0.2107187698E-01 -0.7263524048E-01 0.3379418668E+00 0.7876410397E+00 0.4910540301E+00 -0.4831177914E-01 -0.1179902457E+00 0.3490713064E-02 0.1540411365E-01 -0.1333785556E-05 0.1144672190E-05 0.4933806493E-06 0.2205985224E-05 -0.3259284258E-06 -0.2564526296E-05 -0.1197305244E-05 -0.1010124086E-06 -0.7800395608E-02 0.1767376409E-02 0.4472504864E-01 -0.2106027212E-01 -0.7263753168E-01 0.3379294037E+00 0.7876411418E+00 0.4910559454E+00 -0.4831174259E-01 -0.1179901111E+00 0.3490712084E-02 0.1540410933E-01 N=7 0.7004199839E+00 0.7137309340E+00 0.1053864722E-01 -0.1034210340E-01 0.6658963651E+00 0.7458981223E+00 -0.1757138133E+00 0.1724367832E+00 -0.1665581445E+00 0.1535673633E+00 -0.4422666014E+00 0.8321453685E+00 0.1613128649E+00 -0.1583044098E+00 -0.3601719723E+00 0.3170674120E+00 0.7182714497E+00 0.3180082506E+00 -0.1351100609E+00 0.2887289881E+00 0.2626733923E+00 -0.2577745821E+00 0.5300977359E-01 -0.5460956119E-01 -0.7894206983E-01 0.8761351181E-01 0.1138292645E+00 -0.8840156389E-02 0.1186027472E+00 0.9042968950E+00 -0.9906552530E-01 0.9721797156E-01 0.1575818939E+00 -0.1379327181E+00 0.2550022277E+00 0.1514595280E+00 0.8750776361E+00 0.6499770717E-01 0.2324452664E+00 -0.9349432145E-01 -0.4623379279E-01 0.1183889785E+00 -0.6250197855E-01 0.6133632819E-01 0.7570194334E-02 -0.5024723655E-02 0.2646032111E-01 -0.9402290802E-02 0.6149372377E-01 0.5681683063E-01 0.2562598477E-01 0.2756686809E-01 0.9366103730E+00 -0.3120657710E+00 -0.3336171928E-01 0.8542222229E-01 -0.4715917315E+00 0.4627966328E+00 -0.9443328396E-02 0.2151032037E-01 0.4754578984E-01 -0.1760708900E+00 -0.1591797424E+00 0.4829772924E+00 0.2074893977E+00 0.2895141132E+00 -0.4058619450E-01 0.1026407474E+00 0.3418617349E+00 -0.1182037757E+00 -0.1210726949E-01 0.3100049663E-01 -0.9439529077E-01 0.9263483604E-01 -0.7325279539E-01 0.6801412471E-01 -0.2325217040E-01 -0.7869955176E-01 -0.8937965975E-01 0.4016014208E-01 0.1328240580E+00 0.6204454273E-01 0.1623006055E+00 0.6626531984E+00 -0.6074912864E+00 0.2552288166E+00 0.1574205947E+00 -0.1004613457E+00 -0.4839078318E-02 0.1239039332E-01 0.1594142646E+00 -0.1564412180E+00 0.7441639637E-02 -0.1106491958E-01 -0.2825478866E-01 0.5459386943E-01 -0.9775758534E-02 -0.1478196128E+00 -0.1113587794E+00 -0.8536948628E-01 0.2751605400E+00 0.6421729864E+00 0.6324608023E+00 -0.1525303792E-01 -0.8448334026E-01 0.8762658370E-01 0.3318133734E-01 -0.1602650231E-01 -0.1102323809E-02 0.2822484916E-02 -0.6037533035E-02 0.5924934159E-02 0.1534054302E-02 -0.1202064256E-02 0.3182693183E-02 -0.2822206008E-03 0.8251845825E-02 0.6110061754E-02 0.6347460794E-02 0.1773857064E-02 -0.1077767325E+00 -0.1373538162E+00 0.2848100511E+00 0.7687892964E+00 0.5372655282E+00 0.1673410769E-01 -0.4968993169E-01 0.6802066194E-01 0.3052110650E-01 -0.1264613714E-01 -0.1047456655E-02 0.2681998325E-02 -0.2814830317E-04 0.2762334252E-04 -0.2993814193E-04 0.2750781612E-04 0.1564675966E-04 -0.1442059454E-04 0.2143345853E-04 -0.4969368764E-04 -0.5136649938E-04 0.2578289227E-04 0.1026729934E-01 0.4010109626E-02 -0.1078074809E+00 -0.1400480006E+00 0.2886301179E+00 0.7677642441E+00 0.5361017227E+00 0.1744136474E-01 -0.4955281693E-01 0.6789267353E-01 0.3051551282E-01 -0.1263630236E-01 -0.1047384891E-02 0.2681814574E-02 N=8 0.8154844606E+00 0.5787789687E+00 -0.1247831717E+00 0.1758162321E+00 -0.3656686728E+00 0.9054304139E+00 0.2997291603E-02 -0.4223105639E-02 0.1242773642E-01 0.6252204333E-02 -0.9904302529E+00 0.1372135453E+00 0.1966225161E-01 -0.2770359932E-01 -0.7546094737E+00 -0.2966686120E+00 0.3499437320E-01 0.3331775846E+00 -0.2987492141E+00 0.3740523778E+00 0.4323222764E-02 -0.6091308037E-02 0.7954572256E-01 0.3390409091E-01 0.9217898627E-01 0.6563318928E+00 0.3523462443E+00 -0.1251353548E+00 0.4042229670E+00 0.4999957374E+00 -0.2660208461E-01 0.3748164289E-01 -0.9461286592E-03 -0.1132648426E-01 -0.9275963658E-02 -0.6461897138E-01 0.1372894292E-01 0.6267297020E-01 0.2202320256E+00 -0.8389760645E-01 -0.1403041536E+00 0.9561140215E+00 0.2524537323E+00 -0.3557007197E+00 0.1516837508E-01 0.1099880629E+00 0.1862464672E-01 0.1115880939E+00 0.2254220157E-01 -0.4913049824E-02 -0.5563920979E+00 0.2664015938E+00 0.3095222627E+00 0.2269636732E+00 -0.8010927222E-01 0.4998095408E+00 0.2456578749E+00 -0.3461255340E+00 0.9925065785E-02 0.1050746034E+00 -0.4318903116E-01 -0.3334514090E+00 0.2290161361E+00 0.5487762846E+00 0.5044722993E+00 -0.1254772285E-02 0.1029941228E+00 -0.1417543694E+00 -0.2283734323E-01 0.2364674480E+00 -0.3231151084E-02 0.2015946352E-01 -0.2349913172E+00 0.3310966326E+00 -0.5311446508E-01 -0.1181288132E+00 -0.9603473986E-02 -0.4380266939E-01 0.2600141912E+00 0.8361504832E-01 0.2510639110E-01 -0.1008073945E+00 0.8418631631E+00 0.7567187201E-01 -0.5157252055E-01 -0.1011324247E+00 0.1353427731E-01 -0.5842857844E-01 -0.8943337330E-03 0.5579834492E-02 0.1175808867E+00 -0.1656684005E+00 0.2116820474E-01 0.5692304840E-01 -0.3212417295E-03 -0.1449706939E-01 0.7608433230E-02 0.8842036371E-01 -0.1106702915E+00 0.1150658911E+00 0.1320221928E+00 0.5853544071E-01 0.8673441259E+00 -0.3405381015E+00 -0.7026544508E-01 0.1612247059E+00 0.8814953584E-02 -0.3651364229E-01 -0.6354725161E-03 0.3964774371E-02 -0.1869200178E+00 0.2633654264E+00 -0.1715897751E-01 -0.8383072732E-01 -0.5454552299E-04 0.1716903650E-01 -0.2459571155E-01 -0.1067048762E+00 0.1392253947E+00 -0.1312182020E+00 -0.6903207429E-01 -0.6174129657E-01 0.4567820059E+00 0.6659677770E+00 0.4075238681E+00 -0.8959489682E-01 -0.3070551742E-01 0.5834412826E-01 0.4209662663E-02 -0.1666652373E-01 -0.3299795784E-03 0.2058774443E-02 -0.5983387981E-04 0.8430437497E-04 -0.7367030616E-03 -0.3221424476E-03 0.2377031466E-03 0.1801086072E-02 0.6525360795E-02 0.1852858079E-02 -0.1304362553E-01 0.4142993226E-02 0.2877868990E-01 0.7490490000E-02 -0.1429947491E+00 -0.6137476013E-01 0.4811678727E+00 0.7773035028E+00 0.3644701648E+00 -0.5200003920E-01 -0.2722180405E-01 0.4914754640E-01 0.3808981800E-02 -0.1495346270E-01 -0.3029283977E-03 0.1889999515E-02 0.2133198342E-03 -0.3005620786E-03 0.1154368505E-03 0.1343825608E-03 0.1922522728E-04 0.1082819743E-03 -0.9178438545E-03 -0.5253253664E-03 0.5862560755E-03 -0.1372988867E-03 -0.3162915788E-02 -0.5366827388E-03 0.3167918922E-01 0.7662389238E-02 -0.1433799225E+00 -0.6122357795E-01 0.4813668294E+00 0.7771700444E+00 0.3644410683E+00 -0.5194231988E-01 -0.2721896821E-01 0.4913678918E-01 0.3808752164E-02 -0.1495225825E-01 -0.3029205498E-03 0.1889950551E-02 -0.2204602645E-06 0.3106227586E-06 -0.2497015754E-06 -0.1915445903E-06 -0.3628131005E-07 -0.2161647330E-06 0.1096077744E-05 0.4502869954E-06 -0.6259648891E-06 0.1952007624E-06 -0.5855423375E-06 -0.5654617843E-08 -0.3382391093E-02 -0.5421772240E-03 0.3169514253E-01 0.7607457819E-02 -0.1432942434E+00 -0.6127334917E-01 0.4813596518E+00 0.7771857494E+00 0.3644418948E+00 -0.5194583784E-01 -0.2721902992E-01 0.4913717967E-01 0.3808752014E-02 -0.1495225834E-01 -0.3029205147E-03 0.1889950333E-02 ************************************************************************* RIGHT SIDE WAVELET COEFFICIENTS. ******************************** N=2 0.512347538298 - 0.821583836258 0.216506350946 0.125 N=3 - 0.409742284317 0.797634233593 - 0.419058128916 - 0.117669342504 0.0741631890253 0.0305764886814 - 0.00261427398522 0.00508913652903 0.330328738376 - 0.807556085169 0.460310974517 0.13519444871 - 0.0854338960798 - 0.0352232501168 N=4 -0.4071236735E+00 -0.4805345164E+00 0.7323866385E+00 0.2189246571E+00 0.1377492261E+00 0.6432723244E-02 -0.5725128723E-03 -0.1463677232E-02 -0.1510687974E+00 -0.1783088929E+00 -0.2220387683E+00 -0.1860863787E+00 0.4453190824E+00 -0.7578721319E+00 0.2811170011E+00 0.9317065817E-01 -0.1190456353E-01 -0.3043501623E-01 -0.3568796396E-02 -0.4212306878E-02 0.7354216552E-02 0.2424802855E-02 -0.7612569411E-01 0.3110390153E-01 0.4970737955E+00 -0.8039165747E+00 0.2978757587E+00 0.9927560396E-01 -0.1260377436E-01 -0.3222260742E-01 N=5 0.3667623662E+00 -0.8135877873E+00 0.3605867008E+00 0.2389793582E+00 0.1721476353E-01 -0.1262774479E+00 0.1354530290E-01 0.7338813977E-03 -0.1058396455E-03 -0.9800040389E-04 0.2440133283E-01 -0.5412939880E-01 0.1933279241E+00 -0.1487960520E+00 -0.7215807244E+00 0.6068591878E+00 0.1499494360E+00 -0.1537729673E+00 0.4017810927E-02 0.4249831221E-01 -0.5115722859E-02 -0.4736816190E-02 -0.2747616845E-02 0.6095029686E-02 0.2424194881E-01 -0.2799508244E-01 -0.5956481976E-02 -0.3440854634E-01 -0.1090515083E-01 -0.2236505386E+00 0.7232999959E+00 -0.6265589773E+00 0.1577095589E-01 0.1743929125E+00 -0.2107998910E-01 -0.1951865580E-01 -0.1197613924E-03 0.2656663148E-03 -0.1260893172E-05 -0.1913265215E-03 -0.5035970875E-03 0.4654691185E-03 0.2744513531E-01 -0.2962394021E-01 -0.3913691676E-01 -0.1993634542E+00 0.7234039987E+00 -0.6339835070E+00 0.1660226434E-01 0.1753282263E+00 -0.2110183265E-01 -0.1953888146E-01 N=6 0.4378023718E+00 -0.3757277153E+00 -0.6873475431E-01 -0.1032247812E+00 0.7266439214E+00 0.3259673475E+00 -0.1186803367E+00 -0.5853826628E-01 -0.3032048461E-03 -0.4670847828E-04 0.1703850068E-05 0.7518930104E-05 -0.9713836045E-01 0.8336541004E-01 0.1006861439E+00 0.5919694503E+00 0.3702101657E+00 -0.5544630394E+00 -0.4149317683E+00 -0.7460178119E-01 0.2790428530E-01 0.5912930318E-02 -0.1712035030E-02 -0.3636645827E-02 0.1436692465E-03 0.6339957943E-03 -0.8958975532E-01 0.7688709850E-01 0.1185119667E-02 -0.6467017684E-01 0.3743730652E-01 0.7423011440E-01 -0.1113332259E+00 0.5103740064E-01 0.4816519926E+00 -0.7799800339E+00 0.3345221160E+00 0.7239621136E-01 -0.2085354320E-01 -0.4433542083E-01 0.1748540164E-02 0.7716105825E-02 0.4166215409E-04 -0.3575500495E-04 0.6680919371E-03 0.4483753011E-02 0.4274088494E-02 -0.3773957888E-02 0.1399084946E-01 -0.3990648231E-02 -0.1177575130E+00 0.4833340703E-01 0.4910525706E+00 -0.7876666869E+00 0.3379295212E+00 0.7264103605E-01 -0.2106021362E-01 -0.4472460633E-01 0.1767709932E-02 0.7800699800E-02 0.2633834884E-05 -0.2260391508E-05 -0.9742819475E-06 -0.4356173277E-05 0.6436128145E-06 0.5064186603E-05 0.2364326456E-05 0.1994698649E-06 0.1540349180E-01 -0.3490049659E-02 -0.1179904012E+00 0.4831170232E-01 0.4910559595E+00 -0.7876411054E+00 0.3379294202E+00 0.7263751587E-01 -0.2106029251E-01 -0.4472490177E-01 0.1767711864E-02 0.7800708325E-02 N=7 0.3287269241E+00 -0.3225962277E+00 -0.3486576217E-01 0.2200880144E-01 -0.4013253310E+00 -0.8807413471E-01 0.7139363748E-01 0.7005967686E+00 0.2475030985E+00 -0.2451712749E+00 0.7181777146E-02 0.2499604984E-04 -0.8073680719E-08 -0.3908981471E-07 0.5957737342E-01 -0.5846626641E-01 0.4582097589E+00 -0.4107166017E+00 0.2022914839E+00 0.2997172270E+00 -0.3986325494E+00 -0.6261552962E-01 0.5532851486E+00 -0.1200134025E+00 0.1616443953E-01 -0.3615532478E-02 -0.1770925212E-02 0.1363254906E-02 0.5071037744E-04 -0.1298432110E-03 0.1154439687E-01 -0.1132909600E-01 -0.3933408112E+00 0.3508326132E+00 -0.1045297744E+00 -0.1942431291E+00 0.4053278706E-01 -0.3956498210E+00 0.7001774443E+00 -0.5344583491E-01 -0.6098922304E-02 -0.7677883475E-01 0.1158196639E+00 -0.4412947160E-01 -0.2089669169E-01 0.1616290641E-01 0.5971498449E-03 -0.1528993947E-02 0.3435795707E-01 -0.3371718752E-01 0.3919592661E-02 -0.4452130171E-02 -0.2728348640E-02 0.1439788762E-01 0.1012896303E-01 -0.3223449962E-01 -0.2185300516E-01 -0.2044704093E-01 0.6843499760E-01 0.2980333628E-01 0.4539318191E-01 -0.5452752162E+00 0.7607344157E+00 -0.2839752561E+00 -0.1395508493E+00 0.1071639975E+00 0.4000222290E-02 -0.1024251403E-01 -0.1619528496E-02 0.1589324589E-02 0.3554364827E-03 -0.2723954613E-03 0.8549575210E-03 -0.9551275473E-04 0.2187750783E-02 0.1520814609E-02 0.1580292226E-02 0.5022963426E-03 -0.1263138978E-01 -0.2981485818E-01 0.6690165825E-01 0.4983337040E-01 0.1775563260E-01 -0.5362889286E+00 0.7677311001E+00 -0.2885962362E+00 -0.1400458666E+00 0.1078059333E+00 0.4010225471E-02 -0.1026812703E-01 -0.7351578516E-05 0.7214472934E-05 -0.7819175985E-05 0.7184425358E-05 0.4086432729E-05 -0.3766364036E-05 0.5597958787E-05 -0.1297860916E-04 -0.1341567344E-04 0.6733817189E-05 0.2681585429E-02 0.1047349568E-02 -0.1263610581E-01 -0.3051571178E-01 0.6789282065E-01 0.4955281636E-01 0.1744120464E-01 -0.5361018885E+00 0.7677643218E+00 -0.2886296370E+00 -0.1400472405E+00 0.1078082380E+00 0.4010244871E-02 -0.1026817671E-01 N=8 0.2423397898E+00 -0.3414504387E+00 -0.1594658038E+00 0.3529902230E-01 0.1178925154E-02 0.5541735135E-02 -0.3397784131E+00 -0.6081576576E+00 0.3969712638E+00 -0.2244673049E+00 0.3235661995E+00 0.1864123221E-02 -0.3711413269E-03 0.1409795475E-06 0.1765799666E-07 -0.1432302065E-07 0.4513529643E-01 -0.6359445463E-01 0.4156183867E+00 0.1864214898E+00 0.8260455402E-01 0.5471723539E+00 -0.2060895161E+00 0.3195284622E+00 -0.1900505437E-01 -0.5728513561E+00 0.8401643267E-01 -0.7395446869E-02 -0.5473278975E-03 0.9194626204E-03 0.4880437220E-04 -0.2033336993E-03 -0.3477949227E-05 0.2169926352E-04 0.1250013206E+00 -0.1761235982E+00 -0.2969401780E+00 -0.6849590110E-01 0.1052599951E-01 0.9784281131E-01 0.7121369985E+00 -0.1923488214E+00 -0.1670869235E+00 -0.4966168654E+00 -0.1731874885E+00 -0.1213007854E-01 0.3720006761E-01 -0.2322200303E-01 -0.2923066799E-02 0.6878894624E-02 0.3616735843E-03 -0.1510315965E-02 -0.2565448314E-04 0.1600607975E-03 0.1176229912E+00 -0.1657277246E+00 0.1156398803E-01 0.5306159526E-01 -0.1350101618E-03 -0.1210974010E-01 0.8506023466E-02 0.6454872425E-01 -0.7545099201E-01 0.7860638961E-01 0.1423462206E-01 0.3160238725E-01 -0.6318521633E-01 -0.3456069087E+00 0.7552228032E+00 -0.4695151924E+00 -0.5958716642E-01 0.1395811538E+00 0.7391464073E-02 -0.3081345978E-01 -0.5261056159E-03 0.3282423723E-02 -0.1408148250E-03 0.1984044131E-03 0.3171629950E-03 0.7015727951E-04 -0.1485516761E-03 -0.1095011310E-02 -0.2896265919E-02 -0.6063657602E-03 0.6809567802E-02 -0.2202777079E-02 -0.1350306650E-01 -0.3747971165E-02 0.4898531345E-01 0.2723198199E-01 -0.5177607522E-01 -0.3645627219E+00 0.7771651866E+00 -0.4813205851E+00 -0.6127118296E-01 0.1432859367E+00 0.7607311222E-02 -0.3169412534E-01 -0.5421276476E-03 0.3382386726E-02 -0.1190143232E-03 0.1676880751E-03 -0.6429765381E-04 -0.7493111227E-04 -0.1071266241E-04 -0.6032714131E-04 0.5119585945E-03 0.2931623842E-03 -0.3270646712E-03 0.7655763607E-04 0.1767780640E-02 0.2998801694E-03 -0.1494339773E-01 -0.3839392904E-02 0.4918502279E-01 0.2719124334E-01 -0.5194987783E-01 -0.3644331897E+00 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