Harjoitus 5
Ratkaisut palautettava viimeistään luennolla 1.3.
1.Johda sinille muotoa (a+bx+cx2)/(1+dx+ex2) oleva Pad\'en approksimaatio.
2. Oletetaan, että taulukossa ra on planeetan rektaskensio vuoden jokaiselle päivälle klo 0 UTC. Tee aliohjelma, joka laskee lineaarisella interpoloinnilla rektaskension mielivaltaiselle kellonajalle. Aliohjelma saa parametrinaan ko.\ päivää vastaavan taulukon indeksin ja ajan tunteina. Testaa, että aliohjelma toimii myös, kun rektaskensio muuttuu 24 -> 0 tai 0 -> 24. (Testiaineistona voit käyttää lopussa olevaa taulukkoa, jossa on Venuksen rektaskensiot ja deklinaatiot vuodelle 2001.)
3.Määrittele vektorien käsittelyyn sopiva tietotyyppi vector. Kirjoita aliohjelmat, jotka laskevat skalaaritulon, vektoritulon, skalaarikolmitulon ja vektorikolmitulon.
4. Tee ohjelma, joka sovittaa suoran f(x)=a+bx annettuun aineistoon (xi, yi), poistaa pisteet, joiden etäisyys suorasta on suurempi kuin 3R, missä
R = \sqrt( (1/n) \sum (yi - f(xi))2 ),
ja sovittaa uuden suoran puhdistettuun aineistoon.
2000 12 28 21.69681 -15.6543 2000 12 29 21.76857 -15.2361 2000 12 30 21.83978 -14.8125 2000 12 31 21.91044 -14.3836 2001 1 1 21.98054 -13.9498 2001 1 2 22.05009 -13.5113 2001 1 3 22.11908 -13.0683 2001 1 4 22.18750 -12.6210 2001 1 5 22.25537 -12.1697 2001 1 6 22.32267 -11.7146 2001 1 7 22.38940 -11.2559 2001 1 8 22.45556 -10.7939 2001 1 9 22.52115 -10.3289 2001 1 10 22.58617 -9.8609 2001 1 11 22.65062 -9.3904 2001 1 12 22.71449 -8.9174 2001 1 13 22.77779 -8.4423 2001 1 14 22.84051 -7.9652 2001 1 15 22.90265 -7.4863 2001 1 16 22.96422 -7.0059 2001 1 17 23.02519 -6.5242 2001 1 18 23.08558 -6.0414 2001 1 19 23.14538 -5.5578 2001 1 20 23.20458 -5.0736 2001 1 21 23.26317 -4.5889 2001 1 22 23.32114 -4.1040 2001 1 23 23.37850 -3.6193 2001 1 24 23.43522 -3.1347 2001 1 25 23.49129 -2.6508 2001 1 26 23.54671 -2.1675 2001 1 27 23.60145 -1.6853 2001 1 28 23.65551 -1.2044 2001 1 29 23.70887 -0.7249 2001 1 30 23.76151 -0.2472 2001 1 31 23.81341 0.2286 2001 2 1 23.86455 0.7020 2001 2 2 23.91491 1.1730 2001 2 3 23.96447 1.6411 2001 2 4 0.01320 2.1062 2001 2 5 0.06108 2.5679 2001 2 6 0.10807 3.0259 2001 2 7 0.15416 3.4800 2001 2 8 0.19930 3.9299 2001 2 9 0.24348 4.3753 2001 2 10 0.28666 4.8159 2001 2 11 0.32881 5.2514 2001 2 12 0.36989 5.6815 2001 2 13 0.40986 6.1059 2001 2 14 0.44870 6.5242 2001 2 15 0.48635 6.9361 2001 2 16 0.52277 7.3413 2001 2 17 0.55792 7.7394 2001 2 18 0.59175 8.1300 2001 2 19 0.62420 8.5127 2001 2 20 0.65523 8.8871 2001 2 21 0.68478 9.2528 2001 2 22 0.71279 9.6093 2001 2 23 0.73920 9.9561 2001 2 24 0.76396 10.2927 2001 2 25 0.78698 10.6185 2001 2 26 0.80822 10.9331 2001 2 27 0.82760 11.2358 2001 2 28 0.84507 11.5259 2001 3 1 0.86054 11.8029 2001 3 2 0.87396 12.0661 2001 3 3 0.88526 12.3148 2001 3 4 0.89439 12.5481 2001 3 5 0.90127 12.7654 2001 3 6 0.90585 12.9659 2001 3 7 0.90809 13.1488 2001 3 8 0.90795 13.3132 2001 3 9 0.90539 13.4584 2001 3 10 0.90039 13.5836 2001 3 11 0.89293 13.6879 2001 3 12 0.88302 13.7707 2001 3 13 0.87067 13.8312 2001 3 14 0.85590 13.8688 2001 3 15 0.83876 13.8827 2001 3 16 0.81930 13.8726 2001 3 17 0.79759 13.8378 2001 3 18 0.77373 13.7781 2001 3 19 0.74782 13.6932 2001 3 20 0.71998 13.5830 2001 3 21 0.69038 13.4477 2001 3 22 0.65916 13.2873 2001 3 23 0.62652 13.1025 2001 3 24 0.59264 12.8937 2001 3 25 0.55774 12.6618 2001 3 26 0.52204 12.4078 2001 3 27 0.48578 12.1330 2001 3 28 0.44920 11.8388 2001 3 29 0.41254 11.5269 2001 3 30 0.37605 11.1989 2001 3 31 0.33998 10.8569 2001 4 1 0.30458 10.5029 2001 4 2 0.27007 10.1391 2001 4 3 0.23669 9.7678 2001 4 4 0.20466 9.3911 2001 4 5 0.17416 9.0114 2001 4 6 0.14540 8.6309 2001 4 7 0.11853 8.2519 2001 4 8 0.09371 7.8764 2001 4 9 0.07107 7.5065 2001 4 10 0.05070 7.1441 2001 4 11 0.03271 6.7908 2001 4 12 0.01715 6.4482 2001 4 13 0.00408 6.1178 2001 4 14 23.99352 5.8006 2001 4 15 23.98550 5.4979 2001 4 16 23.98001 5.2104 2001 4 17 23.97704 4.9390 2001 4 18 23.97656 4.6841 2001 4 19 23.97854 4.4463 2001 4 20 23.98294 4.2259 2001 4 21 23.98972 4.0231 2001 4 22 23.99880 3.8381 2001 4 23 0.01015 3.6707 2001 4 24 0.02368 3.5211 2001 4 25 0.03934 3.3890 2001 4 26 0.05706 3.2744 2001 4 27 0.07677 3.1769 2001 4 28 0.09841 3.0963 2001 4 29 0.12190 3.0323 2001 4 30 0.14718 2.9845 2001 5 1 0.17419 2.9527 2001 5 2 0.20286 2.9365 2001 5 3 0.23313 2.9355 2001 5 4 0.26495 2.9492 2001 5 5 0.29825 2.9775 2001 5 6 0.33299 3.0197 2001 5 7 0.36910 3.0756 2001 5 8 0.40653 3.1446 2001 5 9 0.44523 3.2265 2001 5 10 0.48516 3.3208 2001 5 11 0.52626 3.4271 2001 5 12 0.56849 3.5449 2001 5 13 0.61180 3.6738 2001 5 14 0.65614 3.8134 2001 5 15 0.70149 3.9634 2001 5 16 0.74779 4.1233 2001 5 17 0.79502 4.2926 2001 5 18 0.84313 4.4710 2001 5 19 0.89209 4.6581 2001 5 20 0.94186 4.8536 2001 5 21 0.99243 5.0569 2001 5 22 1.04376 5.2678 2001 5 23 1.09581 5.4859 2001 5 24 1.14858 5.7108 2001 5 25 1.20203 5.9421 2001 5 26 1.25613 6.1795 2001 5 27 1.31088 6.4227 2001 5 28 1.36626 6.6713 2001 5 29 1.42223 6.9250 2001 5 30 1.47880 7.1836 2001 5 31 1.53595 7.4466 2001 6 1 1.59367 7.7138 2001 6 2 1.65194 7.9850 2001 6 3 1.71075 8.2598 2001 6 4 1.77010 8.5379 2001 6 5 1.82998 8.8190 2001 6 6 1.89038 9.1030 2001 6 7 1.95128 9.3894 2001 6 8 2.01269 9.6781 2001 6 9 2.07460 9.9687 2001 6 10 2.13699 10.2609 2001 6 11 2.19987 10.5546 2001 6 12 2.26322 10.8494 2001 6 13 2.32705 11.1451 2001 6 14 2.39134 11.4413 2001 6 15 2.45609 11.7379 2001 6 16 2.52130 12.0346 2001 6 17 2.58696 12.3310 2001 6 18 2.65306 12.6270 2001 6 19 2.71961 12.9223 2001 6 20 2.78660 13.2166 2001 6 21 2.85402 13.5097 2001 6 22 2.92187 13.8014 2001 6 23 2.99015 14.0913 2001 6 24 3.05885 14.3792 2001 6 25 3.12798 14.6649 2001 6 26 3.19752 14.9482 2001 6 27 3.26748 15.2289 2001 6 28 3.33786 15.5066 2001 6 29 3.40865 15.7812 2001 6 30 3.47986 16.0525 2001 7 1 3.55149 16.3202 2001 7 2 3.62352 16.5841 2001 7 3 3.69597 16.8440 2001 7 4 3.76883 17.0998 2001 7 5 3.84210 17.3511 2001 7 6 3.91578 17.5977 2001 7 7 3.98986 17.8396 2001 7 8 4.06434 18.0763 2001 7 9 4.13922 18.3078 2001 7 10 4.21449 18.5339 2001 7 11 4.29015 18.7542 2001 7 12 4.36620 18.9687 2001 7 13 4.44263 19.1771 2001 7 14 4.51943 19.3792 2001 7 15 4.59660 19.5749 2001 7 16 4.67413 19.7638 2001 7 17 4.75202 19.9460 2001 7 18 4.83025 20.1211 2001 7 19 4.90882 20.2889 2001 7 20 4.98772 20.4494 2001 7 21 5.06695 20.6023 2001 7 22 5.14648 20.7475 2001 7 23 5.22631 20.8848 2001 7 24 5.30644 21.0140 2001 7 25 5.38685 21.1351 2001 7 26 5.46753 21.2478 2001 7 27 5.54848 21.3521 2001 7 28 5.62968 21.4477 2001 7 29 5.71112 21.5346 2001 7 30 5.79280 21.6127 2001 7 31 5.87470 21.6818 2001 8 1 5.95682 21.7419 2001 8 2 6.03914 21.7928 2001 8 3 6.12164 21.8344 2001 8 4 6.20433 21.8667 2001 8 5 6.28718 21.8895 2001 8 6 6.37019 21.9028 2001 8 7 6.45334 21.9066 2001 8 8 6.53663 21.9006 2001 8 9 6.62002 21.8850 2001 8 10 6.70352 21.8596 2001 8 11 6.78711 21.8244 2001 8 12 6.87078 21.7794 2001 8 13 6.95451 21.7245 2001 8 14 7.03829 21.6597 2001 8 15 7.12210 21.5850 2001 8 16 7.20594 21.5004 2001 8 17 7.28978 21.4058 2001 8 18 7.37361 21.3014 2001 8 19 7.45743 21.1871 2001 8 20 7.54121 21.0630 2001 8 21 7.62494 20.9290 2001 8 22 7.70862 20.7853 2001 8 23 7.79222 20.6318 2001 8 24 7.87575 20.4687 2001 8 25 7.95918 20.2959 2001 8 26 8.04251 20.1136 2001 8 27 8.12573 19.9219 2001 8 28 8.20883 19.7207 2001 8 29 8.29181 19.5102 2001 8 30 8.37464 19.2905 2001 8 31 8.45734 19.0616 2001 9 1 8.53989 18.8237 2001 9 2 8.62228 18.5769 2001 9 3 8.70451 18.3213 2001 9 4 8.78658 18.0569 2001 9 5 8.86847 17.7840 2001 9 6 8.95019 17.5026 2001 9 7 9.03172 17.2129 2001 9 8 9.11308 16.9150 2001 9 9 9.19424 16.6090 2001 9 10 9.27522 16.2951 2001 9 11 9.35601 15.9734 2001 9 12 9.43660 15.6440 2001 9 13 9.51699 15.3072 2001 9 14 9.59719 14.9631 2001 9 15 9.67720 14.6118 2001 9 16 9.75700 14.2535 2001 9 17 9.83660 13.8884 2001 9 18 9.91601 13.5167 2001 9 19 9.99522 13.1384 2001 9 20 10.07424 12.7539 2001 9 21 10.15306 12.3632 2001 9 22 10.23169 11.9666 2001 9 23 10.31014 11.5643 2001 9 24 10.38841 11.1563 2001 9 25 10.46650 10.7429 2001 9 26 10.54442 10.3244 2001 9 27 10.62217 9.9007 2001 9 28 10.69977 9.4722 2001 9 29 10.77721 9.0391 2001 9 30 10.85451 8.6014 2001 10 1 10.93167 8.1594 2001 10 2 11.00869 7.7133 2001 10 3 11.08560 7.2633 2001 10 4 11.16239 6.8096 2001 10 5 11.23907 6.3522 2001 10 6 11.31566 5.8916 2001 10 7 11.39215 5.4277 2001 10 8 11.46857 4.9609 2001 10 9 11.54491 4.4912 2001 10 10 11.62119 4.0190 2001 10 11 11.69741 3.5444 2001 10 12 11.77359 3.0676 2001 10 13 11.84974 2.5888 2001 10 14 11.92586 2.1082 2001 10 15 12.00196 1.6260 2001 10 16 12.07805 1.1424 2001 10 17 12.15414 0.6576 2001 10 18 12.23024 0.1719 2001 10 19 12.30637 -0.3146 2001 10 20 12.38252 -0.8016 2001 10 21 12.45871 -1.2890 2001 10 22 12.53495 -1.7765 2001 10 23 12.61125 -2.2640 2001 10 24 12.68763 -2.7512 2001 10 25 12.76408 -3.2379 2001 10 26 12.84063 -3.7239 2001 10 27 12.91728 -4.2091 2001 10 28 12.99405 -4.6931 2001 10 29 13.07094 -5.1758 2001 10 30 13.14797 -5.6571 2001 10 31 13.22514 -6.1365 2001 11 1 13.30247 -6.6141 2001 11 2 13.37997 -7.0895 2001 11 3 13.45765 -7.5626 2001 11 4 13.53552 -8.0331 2001 11 5 13.61359 -8.5008 2001 11 6 13.69187 -8.9655 2001 11 7 13.77037 -9.4270 2001 11 8 13.84910 -9.8851 2001 11 9 13.92806 -10.3395 2001 11 10 14.00727 -10.7901 2001 11 11 14.08674 -11.2365 2001 11 12 14.16646 -11.6787 2001 11 13 14.24646 -12.1163 2001 11 14 14.32673 -12.5491 2001 11 15 14.40728 -12.9770 2001 11 16 14.48813 -13.3996 2001 11 17 14.56926 -13.8168 2001 11 18 14.65070 -14.2282 2001 11 19 14.73244 -14.6338 2001 11 20 14.81450 -15.0333 2001 11 21 14.89686 -15.4264 2001 11 22 14.97955 -15.8129 2001 11 23 15.06256 -16.1926 2001 11 24 15.14589 -16.5653 2001 11 25 15.22955 -16.9308 2001 11 26 15.31355 -17.2888 2001 11 27 15.39787 -17.6391 2001 11 28 15.48253 -17.9816 2001 11 29 15.56752 -18.3159 2001 11 30 15.65285 -18.6420 2001 12 1 15.73850 -18.9596 2001 12 2 15.82449 -19.2684 2001 12 3 15.91081 -19.5684 2001 12 4 15.99746 -19.8592 2001 12 5 16.08443 -20.1407 2001 12 6 16.17172 -20.4127 2001 12 7 16.25932 -20.6750 2001 12 8 16.34724 -20.9275 2001 12 9 16.43545 -21.1699 2001 12 10 16.52395 -21.4021 2001 12 11 16.61274 -21.6239 2001 12 12 16.70181 -21.8351 2001 12 13 16.79113 -22.0356 2001 12 14 16.88071 -22.2252 2001 12 15 16.97053 -22.4037 2001 12 16 17.06058 -22.5711 2001 12 17 17.15084 -22.7272 2001 12 18 17.24130 -22.8719 2001 12 19 17.33195 -23.0050 2001 12 20 17.42276 -23.1264 2001 12 21 17.51374 -23.2361 2001 12 22 17.60485 -23.3340 2001 12 23 17.69609 -23.4199 2001 12 24 17.78744 -23.4938 2001 12 25 17.87888 -23.5557 2001 12 26 17.97039 -23.6054 2001 12 27 18.06196 -23.6430 2001 12 28 18.15357 -23.6684 2001 12 29 18.24521 -23.6815 2001 12 30 18.33685 -23.6824 2001 12 31 18.42848 -23.6711 2002 1 1 18.52009 -23.6475 2002 1 2 18.61165 -23.6117 2002 1 3 18.70315 -23.5637