| ofs | hex dump | ascii |
|---|---|---|
| 0000 | cb 0d 0d 0a 00 00 00 00 0d fd a7 68 51 cc 00 00 e3 00 00 00 00 00 00 00 00 00 00 00 00 05 00 00 | ...........hQ................... |
| 0020 | 00 00 00 00 00 f3 c2 01 00 00 97 00 64 00 5a 00 64 01 64 02 6c 01 5a 02 64 01 64 02 6c 03 6d 04 | ............d.Z.d.d.l.Z.d.d.l.m. |
| 0040 | 5a 05 01 00 64 01 64 03 6c 06 6d 07 5a 07 01 00 64 04 64 05 6c 08 6d 09 5a 0a 01 00 64 04 64 06 | Z...d.d.l.m.Z...d.d.l.m.Z...d.d. |
| 0060 | 6c 0b 6d 0c 5a 0c 01 00 67 00 64 07 a2 01 5a 0d 65 0a 6a 1c 00 00 00 00 00 00 00 00 00 00 00 00 | l.m.Z...g.d...Z.e.j............. |
| 0080 | 00 00 00 00 00 00 5a 0f 64 08 84 00 5a 10 64 09 84 00 5a 11 02 00 65 02 6a 24 00 00 00 00 00 00 | ......Z.d...Z.d...Z...e.j$...... |
| 00a0 | 00 00 00 00 00 00 00 00 00 00 00 00 64 0a 64 0b 67 02 ab 01 00 00 00 00 00 00 5a 13 02 00 65 02 | ............d.d.g.........Z...e. |
| 00c0 | 6a 24 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 64 01 67 01 ab 01 00 00 00 00 00 00 | j$..................d.g......... |
| 00e0 | 5a 14 02 00 65 02 6a 24 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 64 04 67 01 ab 01 | Z...e.j$..................d.g... |
| 0100 | 00 00 00 00 00 00 5a 15 02 00 65 02 6a 24 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 | ......Z...e.j$.................. |
| 0120 | 64 01 64 04 67 02 ab 01 00 00 00 00 00 00 5a 16 64 0c 84 00 5a 17 64 0d 84 00 5a 18 64 0e 84 00 | d.d.g.........Z.d...Z.d...Z.d... |
| 0140 | 5a 19 64 0f 84 00 5a 1a 64 10 84 00 5a 1b 64 11 84 00 5a 1c 64 12 84 00 5a 1d 64 26 64 13 84 01 | Z.d...Z.d...Z.d...Z.d...Z.d&d... |
| 0160 | 5a 1e 64 27 64 14 84 01 5a 1f 64 04 67 00 64 01 64 04 64 01 66 05 64 15 84 01 5a 20 64 28 64 16 | Z.d'd...Z.d.g.d.d.d.f.d...Z.d(d. |
| 0180 | 84 01 5a 21 64 17 84 00 5a 22 64 18 84 00 5a 23 64 19 84 00 5a 24 64 1a 84 00 5a 25 64 1b 84 00 | ..Z!d...Z"d...Z#d...Z$d...Z%d... |
| 01a0 | 5a 26 64 1c 84 00 5a 27 64 1d 84 00 5a 28 64 29 64 1e 84 01 5a 29 64 1f 84 00 5a 2a 64 20 84 00 | Z&d...Z'd...Z(d)d...Z)d...Z*d... |
| 01c0 | 5a 2b 64 21 84 00 5a 2c 64 22 84 00 5a 2d 64 23 84 00 5a 2e 02 00 47 00 64 24 84 00 64 25 65 0c | Z+d!..Z,d"..Z-d#..Z...G.d$..d%e. |
| 01e0 | ab 03 00 00 00 00 00 00 5a 2f 79 02 29 2a 61 2e 05 00 00 0a 3d 3d 3d 3d 3d 3d 3d 3d 3d 3d 3d 3d | ........Z/y.)*a.....============ |
| 0200 | 3d 3d 3d 3d 3d 3d 3d 3d 3d 3d 3d 3d 3d 3d 3d 3d 3d 3d 3d 3d 3d 3d 3d 3d 3d 3d 3d 3d 3d 3d 3d 3d | ================================ |
| 0220 | 3d 3d 3d 3d 3d 3d 3d 3d 3d 3d 3d 3d 3d 3d 3d 3d 3d 3d 3d 3d 3d 3d 3d 0a 48 65 72 6d 69 74 65 45 | =======================.HermiteE |
| 0240 | 20 53 65 72 69 65 73 2c 20 22 50 72 6f 62 61 62 69 6c 69 73 74 73 22 20 28 3a 6d 6f 64 3a 60 6e | .Series,."Probabilists".(:mod:`n |
| 0260 | 75 6d 70 79 2e 70 6f 6c 79 6e 6f 6d 69 61 6c 2e 68 65 72 6d 69 74 65 5f 65 60 29 0a 3d 3d 3d 3d | umpy.polynomial.hermite_e`).==== |
| 0280 | 3d 3d 3d 3d 3d 3d 3d 3d 3d 3d 3d 3d 3d 3d 3d 3d 3d 3d 3d 3d 3d 3d 3d 3d 3d 3d 3d 3d 3d 3d 3d 3d | ================================ |
| 02a0 | 3d 3d 3d 3d 3d 3d 3d 3d 3d 3d 3d 3d 3d 3d 3d 3d 3d 3d 3d 3d 3d 3d 3d 3d 3d 3d 3d 3d 3d 3d 3d 0a | ===============================. |
| 02c0 | 0a 54 68 69 73 20 6d 6f 64 75 6c 65 20 70 72 6f 76 69 64 65 73 20 61 20 6e 75 6d 62 65 72 20 6f | .This.module.provides.a.number.o |
| 02e0 | 66 20 6f 62 6a 65 63 74 73 20 28 6d 6f 73 74 6c 79 20 66 75 6e 63 74 69 6f 6e 73 29 20 75 73 65 | f.objects.(mostly.functions).use |
| 0300 | 66 75 6c 20 66 6f 72 0a 64 65 61 6c 69 6e 67 20 77 69 74 68 20 48 65 72 6d 69 74 65 5f 65 20 73 | ful.for.dealing.with.Hermite_e.s |
| 0320 | 65 72 69 65 73 2c 20 69 6e 63 6c 75 64 69 6e 67 20 61 20 60 48 65 72 6d 69 74 65 45 60 20 63 6c | eries,.including.a.`HermiteE`.cl |
| 0340 | 61 73 73 20 74 68 61 74 0a 65 6e 63 61 70 73 75 6c 61 74 65 73 20 74 68 65 20 75 73 75 61 6c 20 | ass.that.encapsulates.the.usual. |
| 0360 | 61 72 69 74 68 6d 65 74 69 63 20 6f 70 65 72 61 74 69 6f 6e 73 2e 20 20 28 47 65 6e 65 72 61 6c | arithmetic.operations...(General |
| 0380 | 20 69 6e 66 6f 72 6d 61 74 69 6f 6e 0a 6f 6e 20 68 6f 77 20 74 68 69 73 20 6d 6f 64 75 6c 65 20 | .information.on.how.this.module. |
| 03a0 | 72 65 70 72 65 73 65 6e 74 73 20 61 6e 64 20 77 6f 72 6b 73 20 77 69 74 68 20 73 75 63 68 20 70 | represents.and.works.with.such.p |
| 03c0 | 6f 6c 79 6e 6f 6d 69 61 6c 73 20 69 73 20 69 6e 20 74 68 65 0a 64 6f 63 73 74 72 69 6e 67 20 66 | olynomials.is.in.the.docstring.f |
| 03e0 | 6f 72 20 69 74 73 20 22 70 61 72 65 6e 74 22 20 73 75 62 2d 70 61 63 6b 61 67 65 2c 20 60 6e 75 | or.its."parent".sub-package,.`nu |
| 0400 | 6d 70 79 2e 70 6f 6c 79 6e 6f 6d 69 61 6c 60 29 2e 0a 0a 43 6c 61 73 73 65 73 0a 2d 2d 2d 2d 2d | mpy.polynomial`)...Classes.----- |
| 0420 | 2d 2d 0a 2e 2e 20 61 75 74 6f 73 75 6d 6d 61 72 79 3a 3a 0a 20 20 20 3a 74 6f 63 74 72 65 65 3a | --....autosummary::....:toctree: |
| 0440 | 20 67 65 6e 65 72 61 74 65 64 2f 0a 0a 20 20 20 48 65 72 6d 69 74 65 45 0a 0a 43 6f 6e 73 74 61 | .generated/.....HermiteE..Consta |
| 0460 | 6e 74 73 0a 2d 2d 2d 2d 2d 2d 2d 2d 2d 0a 2e 2e 20 61 75 74 6f 73 75 6d 6d 61 72 79 3a 3a 0a 20 | nts.---------....autosummary::.. |
| 0480 | 20 20 3a 74 6f 63 74 72 65 65 3a 20 67 65 6e 65 72 61 74 65 64 2f 0a 0a 20 20 20 68 65 72 6d 65 | ..:toctree:.generated/.....herme |
| 04a0 | 64 6f 6d 61 69 6e 0a 20 20 20 68 65 72 6d 65 7a 65 72 6f 0a 20 20 20 68 65 72 6d 65 6f 6e 65 0a | domain....hermezero....hermeone. |
| 04c0 | 20 20 20 68 65 72 6d 65 78 0a 0a 41 72 69 74 68 6d 65 74 69 63 0a 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d | ...hermex..Arithmetic.---------- |
| 04e0 | 0a 2e 2e 20 61 75 74 6f 73 75 6d 6d 61 72 79 3a 3a 0a 20 20 20 3a 74 6f 63 74 72 65 65 3a 20 67 | ....autosummary::....:toctree:.g |
| 0500 | 65 6e 65 72 61 74 65 64 2f 0a 0a 20 20 20 68 65 72 6d 65 61 64 64 0a 20 20 20 68 65 72 6d 65 73 | enerated/.....hermeadd....hermes |
| 0520 | 75 62 0a 20 20 20 68 65 72 6d 65 6d 75 6c 78 0a 20 20 20 68 65 72 6d 65 6d 75 6c 0a 20 20 20 68 | ub....hermemulx....hermemul....h |
| 0540 | 65 72 6d 65 64 69 76 0a 20 20 20 68 65 72 6d 65 70 6f 77 0a 20 20 20 68 65 72 6d 65 76 61 6c 0a | ermediv....hermepow....hermeval. |
| 0560 | 20 20 20 68 65 72 6d 65 76 61 6c 32 64 0a 20 20 20 68 65 72 6d 65 76 61 6c 33 64 0a 20 20 20 68 | ...hermeval2d....hermeval3d....h |
| 0580 | 65 72 6d 65 67 72 69 64 32 64 0a 20 20 20 68 65 72 6d 65 67 72 69 64 33 64 0a 0a 43 61 6c 63 75 | ermegrid2d....hermegrid3d..Calcu |
| 05a0 | 6c 75 73 0a 2d 2d 2d 2d 2d 2d 2d 2d 0a 2e 2e 20 61 75 74 6f 73 75 6d 6d 61 72 79 3a 3a 0a 20 20 | lus.--------....autosummary::... |
| 05c0 | 20 3a 74 6f 63 74 72 65 65 3a 20 67 65 6e 65 72 61 74 65 64 2f 0a 0a 20 20 20 68 65 72 6d 65 64 | .:toctree:.generated/.....hermed |
| 05e0 | 65 72 0a 20 20 20 68 65 72 6d 65 69 6e 74 0a 0a 4d 69 73 63 20 46 75 6e 63 74 69 6f 6e 73 0a 2d | er....hermeint..Misc.Functions.- |
| 0600 | 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 0a 2e 2e 20 61 75 74 6f 73 75 6d 6d 61 72 79 3a 3a 0a 20 | -------------....autosummary::.. |
| 0620 | 20 20 3a 74 6f 63 74 72 65 65 3a 20 67 65 6e 65 72 61 74 65 64 2f 0a 0a 20 20 20 68 65 72 6d 65 | ..:toctree:.generated/.....herme |
| 0640 | 66 72 6f 6d 72 6f 6f 74 73 0a 20 20 20 68 65 72 6d 65 72 6f 6f 74 73 0a 20 20 20 68 65 72 6d 65 | fromroots....hermeroots....herme |
| 0660 | 76 61 6e 64 65 72 0a 20 20 20 68 65 72 6d 65 76 61 6e 64 65 72 32 64 0a 20 20 20 68 65 72 6d 65 | vander....hermevander2d....herme |
| 0680 | 76 61 6e 64 65 72 33 64 0a 20 20 20 68 65 72 6d 65 67 61 75 73 73 0a 20 20 20 68 65 72 6d 65 77 | vander3d....hermegauss....hermew |
| 06a0 | 65 69 67 68 74 0a 20 20 20 68 65 72 6d 65 63 6f 6d 70 61 6e 69 6f 6e 0a 20 20 20 68 65 72 6d 65 | eight....hermecompanion....herme |
| 06c0 | 66 69 74 0a 20 20 20 68 65 72 6d 65 74 72 69 6d 0a 20 20 20 68 65 72 6d 65 6c 69 6e 65 0a 20 20 | fit....hermetrim....hermeline... |
| 06e0 | 20 68 65 72 6d 65 32 70 6f 6c 79 0a 20 20 20 70 6f 6c 79 32 68 65 72 6d 65 0a 0a 53 65 65 20 61 | .herme2poly....poly2herme..See.a |
| 0700 | 6c 73 6f 0a 2d 2d 2d 2d 2d 2d 2d 2d 0a 60 6e 75 6d 70 79 2e 70 6f 6c 79 6e 6f 6d 69 61 6c 60 0a | lso.--------.`numpy.polynomial`. |
| 0720 | 0a e9 00 00 00 00 4e 29 01 da 14 6e 6f 72 6d 61 6c 69 7a 65 5f 61 78 69 73 5f 69 6e 64 65 78 e9 | ......N)...normalize_axis_index. |
| 0740 | 01 00 00 00 29 01 da 09 70 6f 6c 79 75 74 69 6c 73 29 01 da 0b 41 42 43 50 6f 6c 79 42 61 73 65 | ....)...polyutils)...ABCPolyBase |
| 0760 | 29 1f da 09 68 65 72 6d 65 7a 65 72 6f da 08 68 65 72 6d 65 6f 6e 65 da 06 68 65 72 6d 65 78 da | )...hermezero..hermeone..hermex. |
| 0780 | 0b 68 65 72 6d 65 64 6f 6d 61 69 6e da 09 68 65 72 6d 65 6c 69 6e 65 da 08 68 65 72 6d 65 61 64 | .hermedomain..hermeline..hermead |
| 07a0 | 64 da 08 68 65 72 6d 65 73 75 62 da 09 68 65 72 6d 65 6d 75 6c 78 da 08 68 65 72 6d 65 6d 75 6c | d..hermesub..hermemulx..hermemul |
| 07c0 | da 08 68 65 72 6d 65 64 69 76 da 08 68 65 72 6d 65 70 6f 77 da 08 68 65 72 6d 65 76 61 6c da 08 | ..hermediv..hermepow..hermeval.. |
| 07e0 | 68 65 72 6d 65 64 65 72 da 08 68 65 72 6d 65 69 6e 74 da 0a 68 65 72 6d 65 32 70 6f 6c 79 da 0a | hermeder..hermeint..herme2poly.. |
| 0800 | 70 6f 6c 79 32 68 65 72 6d 65 da 0e 68 65 72 6d 65 66 72 6f 6d 72 6f 6f 74 73 da 0b 68 65 72 6d | poly2herme..hermefromroots..herm |
| 0820 | 65 76 61 6e 64 65 72 da 08 68 65 72 6d 65 66 69 74 da 09 68 65 72 6d 65 74 72 69 6d da 0a 68 65 | evander..hermefit..hermetrim..he |
| 0840 | 72 6d 65 72 6f 6f 74 73 da 08 48 65 72 6d 69 74 65 45 da 0a 68 65 72 6d 65 76 61 6c 32 64 da 0a | rmeroots..HermiteE..hermeval2d.. |
| 0860 | 68 65 72 6d 65 76 61 6c 33 64 da 0b 68 65 72 6d 65 67 72 69 64 32 64 da 0b 68 65 72 6d 65 67 72 | hermeval3d..hermegrid2d..hermegr |
| 0880 | 69 64 33 64 da 0d 68 65 72 6d 65 76 61 6e 64 65 72 32 64 da 0d 68 65 72 6d 65 76 61 6e 64 65 72 | id3d..hermevander2d..hermevander |
| 08a0 | 33 64 da 0e 68 65 72 6d 65 63 6f 6d 70 61 6e 69 6f 6e da 0a 68 65 72 6d 65 67 61 75 73 73 da 0b | 3d..hermecompanion..hermegauss.. |
| 08c0 | 68 65 72 6d 65 77 65 69 67 68 74 63 01 00 00 00 00 00 00 00 00 00 00 00 06 00 00 00 03 00 00 00 | hermeweightc.................... |
| 08e0 | f3 aa 00 00 00 97 00 74 01 00 00 00 00 00 00 00 00 6a 02 00 00 00 00 00 00 00 00 00 00 00 00 00 | .......t.........j.............. |
| 0900 | 00 00 00 00 00 7c 00 67 01 ab 01 00 00 00 00 00 00 5c 01 00 00 7d 00 74 05 00 00 00 00 00 00 00 | .....|.g.........\...}.t........ |
| 0920 | 00 7c 00 ab 01 00 00 00 00 00 00 64 01 7a 0a 00 00 7d 01 64 02 7d 02 74 07 00 00 00 00 00 00 00 | .|.........d.z...}.d.}.t........ |
| 0940 | 00 7c 01 64 03 64 03 ab 03 00 00 00 00 00 00 44 00 5d 1a 00 00 7d 03 74 09 00 00 00 00 00 00 00 | .|.d.d.........D.]...}.t........ |
| 0960 | 00 74 0b 00 00 00 00 00 00 00 00 7c 02 ab 01 00 00 00 00 00 00 7c 00 7c 03 19 00 00 00 ab 02 00 | .t.........|.........|.|........ |
| 0980 | 00 00 00 00 00 7d 02 8c 1c 04 00 7c 02 53 00 29 04 61 a5 03 00 00 0a 20 20 20 20 70 6f 6c 79 32 | .....}.....|.S.).a.........poly2 |
| 09a0 | 68 65 72 6d 65 28 70 6f 6c 29 0a 0a 20 20 20 20 43 6f 6e 76 65 72 74 20 61 20 70 6f 6c 79 6e 6f | herme(pol)......Convert.a.polyno |
| 09c0 | 6d 69 61 6c 20 74 6f 20 61 20 48 65 72 6d 69 74 65 20 73 65 72 69 65 73 2e 0a 0a 20 20 20 20 43 | mial.to.a.Hermite.series.......C |
| 09e0 | 6f 6e 76 65 72 74 20 61 6e 20 61 72 72 61 79 20 72 65 70 72 65 73 65 6e 74 69 6e 67 20 74 68 65 | onvert.an.array.representing.the |
| 0a00 | 20 63 6f 65 66 66 69 63 69 65 6e 74 73 20 6f 66 20 61 20 70 6f 6c 79 6e 6f 6d 69 61 6c 20 28 72 | .coefficients.of.a.polynomial.(r |
| 0a20 | 65 6c 61 74 69 76 65 0a 20 20 20 20 74 6f 20 74 68 65 20 22 73 74 61 6e 64 61 72 64 22 20 62 61 | elative.....to.the."standard".ba |
| 0a40 | 73 69 73 29 20 6f 72 64 65 72 65 64 20 66 72 6f 6d 20 6c 6f 77 65 73 74 20 64 65 67 72 65 65 20 | sis).ordered.from.lowest.degree. |
| 0a60 | 74 6f 20 68 69 67 68 65 73 74 2c 20 74 6f 20 61 6e 0a 20 20 20 20 61 72 72 61 79 20 6f 66 20 74 | to.highest,.to.an.....array.of.t |
| 0a80 | 68 65 20 63 6f 65 66 66 69 63 69 65 6e 74 73 20 6f 66 20 74 68 65 20 65 71 75 69 76 61 6c 65 6e | he.coefficients.of.the.equivalen |
| 0aa0 | 74 20 48 65 72 6d 69 74 65 20 73 65 72 69 65 73 2c 20 6f 72 64 65 72 65 64 0a 20 20 20 20 66 72 | t.Hermite.series,.ordered.....fr |
| 0ac0 | 6f 6d 20 6c 6f 77 65 73 74 20 74 6f 20 68 69 67 68 65 73 74 20 64 65 67 72 65 65 2e 0a 0a 20 20 | om.lowest.to.highest.degree..... |
| 0ae0 | 20 20 50 61 72 61 6d 65 74 65 72 73 0a 20 20 20 20 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 | ..Parameters.....----------..... |
| 0b00 | 70 6f 6c 20 3a 20 61 72 72 61 79 5f 6c 69 6b 65 0a 20 20 20 20 20 20 20 20 31 2d 44 20 61 72 72 | pol.:.array_like.........1-D.arr |
| 0b20 | 61 79 20 63 6f 6e 74 61 69 6e 69 6e 67 20 74 68 65 20 70 6f 6c 79 6e 6f 6d 69 61 6c 20 63 6f 65 | ay.containing.the.polynomial.coe |
| 0b40 | 66 66 69 63 69 65 6e 74 73 0a 0a 20 20 20 20 52 65 74 75 72 6e 73 0a 20 20 20 20 2d 2d 2d 2d 2d | fficients......Returns.....----- |
| 0b60 | 2d 2d 0a 20 20 20 20 63 20 3a 20 6e 64 61 72 72 61 79 0a 20 20 20 20 20 20 20 20 31 2d 44 20 61 | --.....c.:.ndarray.........1-D.a |
| 0b80 | 72 72 61 79 20 63 6f 6e 74 61 69 6e 69 6e 67 20 74 68 65 20 63 6f 65 66 66 69 63 69 65 6e 74 73 | rray.containing.the.coefficients |
| 0ba0 | 20 6f 66 20 74 68 65 20 65 71 75 69 76 61 6c 65 6e 74 20 48 65 72 6d 69 74 65 0a 20 20 20 20 20 | .of.the.equivalent.Hermite...... |
| 0bc0 | 20 20 20 73 65 72 69 65 73 2e 0a 0a 20 20 20 20 53 65 65 20 41 6c 73 6f 0a 20 20 20 20 2d 2d 2d | ...series.......See.Also.....--- |
| 0be0 | 2d 2d 2d 2d 2d 0a 20 20 20 20 68 65 72 6d 65 32 70 6f 6c 79 0a 0a 20 20 20 20 4e 6f 74 65 73 0a | -----.....herme2poly......Notes. |
| 0c00 | 20 20 20 20 2d 2d 2d 2d 2d 0a 20 20 20 20 54 68 65 20 65 61 73 79 20 77 61 79 20 74 6f 20 64 6f | ....-----.....The.easy.way.to.do |
| 0c20 | 20 63 6f 6e 76 65 72 73 69 6f 6e 73 20 62 65 74 77 65 65 6e 20 70 6f 6c 79 6e 6f 6d 69 61 6c 20 | .conversions.between.polynomial. |
| 0c40 | 62 61 73 69 73 20 73 65 74 73 0a 20 20 20 20 69 73 20 74 6f 20 75 73 65 20 74 68 65 20 63 6f 6e | basis.sets.....is.to.use.the.con |
| 0c60 | 76 65 72 74 20 6d 65 74 68 6f 64 20 6f 66 20 61 20 63 6c 61 73 73 20 69 6e 73 74 61 6e 63 65 2e | vert.method.of.a.class.instance. |
| 0c80 | 0a 0a 20 20 20 20 45 78 61 6d 70 6c 65 73 0a 20 20 20 20 2d 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 | ......Examples.....--------..... |
| 0ca0 | 3e 3e 3e 20 69 6d 70 6f 72 74 20 6e 75 6d 70 79 20 61 73 20 6e 70 0a 20 20 20 20 3e 3e 3e 20 66 | >>>.import.numpy.as.np.....>>>.f |
| 0cc0 | 72 6f 6d 20 6e 75 6d 70 79 2e 70 6f 6c 79 6e 6f 6d 69 61 6c 2e 68 65 72 6d 69 74 65 5f 65 20 69 | rom.numpy.polynomial.hermite_e.i |
| 0ce0 | 6d 70 6f 72 74 20 70 6f 6c 79 32 68 65 72 6d 65 0a 20 20 20 20 3e 3e 3e 20 70 6f 6c 79 32 68 65 | mport.poly2herme.....>>>.poly2he |
| 0d00 | 72 6d 65 28 6e 70 2e 61 72 61 6e 67 65 28 34 29 29 0a 20 20 20 20 61 72 72 61 79 28 5b 20 20 32 | rme(np.arange(4)).....array([..2 |
| 0d20 | 2e 2c 20 20 31 30 2e 2c 20 20 20 32 2e 2c 20 20 20 33 2e 5d 29 0a 0a 20 20 20 20 72 04 00 00 00 | .,..10.,...2.,...3.])......r.... |
| 0d40 | 72 02 00 00 00 e9 ff ff ff ff 29 06 da 02 70 75 da 09 61 73 5f 73 65 72 69 65 73 da 03 6c 65 6e | r.........)...pu..as_series..len |
| 0d60 | da 05 72 61 6e 67 65 72 0c 00 00 00 72 0e 00 00 00 29 04 da 03 70 6f 6c da 03 64 65 67 da 03 72 | ..ranger....r....)...pol..deg..r |
| 0d80 | 65 73 da 01 69 73 04 00 00 00 20 20 20 20 fa 61 2f 68 6f 6d 65 2f 62 6c 61 63 6b 68 61 6f 2f 75 | es..is.........a/home/blackhao/u |
| 0da0 | 69 75 63 2d 63 6f 75 72 73 65 2d 67 72 61 70 68 2f 2e 76 65 6e 76 2f 6c 69 62 2f 70 79 74 68 6f | iuc-course-graph/.venv/lib/pytho |
| 0dc0 | 6e 33 2e 31 32 2f 73 69 74 65 2d 70 61 63 6b 61 67 65 73 2f 6e 75 6d 70 79 2f 70 6f 6c 79 6e 6f | n3.12/site-packages/numpy/polyno |
| 0de0 | 6d 69 61 6c 2f 68 65 72 6d 69 74 65 5f 65 2e 70 79 72 16 00 00 00 72 16 00 00 00 61 00 00 00 73 | mial/hermite_e.pyr....r....a...s |
| 0e00 | 5a 00 00 00 80 00 f4 4e 01 00 0d 0f 8f 4c 89 4c 98 23 98 15 d3 0c 1f 81 45 80 53 dc 0a 0d 88 63 | Z......N.....L.L.#......E.S....c |
| 0e20 | 8b 28 90 51 89 2c 80 43 d8 0a 0b 80 43 dc 0d 12 90 33 98 02 98 42 d3 0d 1f f2 00 01 05 2f 88 01 | .(.Q.,.C....C....3...B......./.. |
| 0e40 | dc 0e 16 94 79 a0 13 93 7e a0 73 a8 31 a1 76 d3 0e 2e 89 03 f0 03 01 05 2f e0 0b 0e 80 4a f3 00 | ....y...~.s.1.v........./....J.. |
| 0e60 | 00 00 00 63 01 00 00 00 00 00 00 00 00 00 00 00 07 00 00 00 03 00 00 00 f3 20 01 00 00 97 00 64 | ...c...........................d |
| 0e80 | 01 64 02 6c 00 6d 01 7d 01 6d 02 7d 02 6d 03 7d 03 01 00 74 09 00 00 00 00 00 00 00 00 6a 0a 00 | .d.l.m.}.m.}.m.}...t.........j.. |
| 0ea0 | 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 7c 00 67 01 ab 01 00 00 00 00 00 00 5c 01 00 | .................|.g.........\.. |
| 0ec0 | 00 7d 00 74 0d 00 00 00 00 00 00 00 00 7c 00 ab 01 00 00 00 00 00 00 7d 04 7c 04 64 01 6b 28 00 | .}.t.........|.........}.|.d.k(. |
| 0ee0 | 00 72 02 7c 00 53 00 7c 04 64 03 6b 28 00 00 72 02 7c 00 53 00 7c 00 64 04 19 00 00 00 7d 05 7c | .r.|.S.|.d.k(..r.|.S.|.d.....}.| |
| 0f00 | 00 64 05 19 00 00 00 7d 06 74 0f 00 00 00 00 00 00 00 00 7c 04 64 01 7a 0a 00 00 64 01 64 05 ab | .d.....}.t.........|.d.z...d.d.. |
| 0f20 | 03 00 00 00 00 00 00 44 00 5d 28 00 00 7d 07 7c 05 7d 08 02 00 7c 03 7c 00 7c 07 64 03 7a 0a 00 | .......D.](..}.|.}...|.|.|.d.z.. |
| 0f40 | 00 19 00 00 00 7c 06 7c 07 64 01 7a 0a 00 00 7a 05 00 00 ab 02 00 00 00 00 00 00 7d 05 02 00 7c | .....|.|.d.z...z...........}...| |
| 0f60 | 01 7c 08 02 00 7c 02 7c 06 ab 01 00 00 00 00 00 00 ab 02 00 00 00 00 00 00 7d 06 8c 2a 04 00 02 | .|...|.|.................}..*... |
| 0f80 | 00 7c 01 7c 05 02 00 7c 02 7c 06 ab 01 00 00 00 00 00 00 ab 02 00 00 00 00 00 00 53 00 29 06 61 | .|.|...|.|.................S.).a |
| 0fa0 | 05 04 00 00 0a 20 20 20 20 43 6f 6e 76 65 72 74 20 61 20 48 65 72 6d 69 74 65 20 73 65 72 69 65 | .........Convert.a.Hermite.serie |
| 0fc0 | 73 20 74 6f 20 61 20 70 6f 6c 79 6e 6f 6d 69 61 6c 2e 0a 0a 20 20 20 20 43 6f 6e 76 65 72 74 20 | s.to.a.polynomial.......Convert. |
| 0fe0 | 61 6e 20 61 72 72 61 79 20 72 65 70 72 65 73 65 6e 74 69 6e 67 20 74 68 65 20 63 6f 65 66 66 69 | an.array.representing.the.coeffi |
| 1000 | 63 69 65 6e 74 73 20 6f 66 20 61 20 48 65 72 6d 69 74 65 20 73 65 72 69 65 73 2c 0a 20 20 20 20 | cients.of.a.Hermite.series,..... |
| 1020 | 6f 72 64 65 72 65 64 20 66 72 6f 6d 20 6c 6f 77 65 73 74 20 64 65 67 72 65 65 20 74 6f 20 68 69 | ordered.from.lowest.degree.to.hi |
| 1040 | 67 68 65 73 74 2c 20 74 6f 20 61 6e 20 61 72 72 61 79 20 6f 66 20 74 68 65 20 63 6f 65 66 66 69 | ghest,.to.an.array.of.the.coeffi |
| 1060 | 63 69 65 6e 74 73 0a 20 20 20 20 6f 66 20 74 68 65 20 65 71 75 69 76 61 6c 65 6e 74 20 70 6f 6c | cients.....of.the.equivalent.pol |
| 1080 | 79 6e 6f 6d 69 61 6c 20 28 72 65 6c 61 74 69 76 65 20 74 6f 20 74 68 65 20 22 73 74 61 6e 64 61 | ynomial.(relative.to.the."standa |
| 10a0 | 72 64 22 20 62 61 73 69 73 29 20 6f 72 64 65 72 65 64 0a 20 20 20 20 66 72 6f 6d 20 6c 6f 77 65 | rd".basis).ordered.....from.lowe |
| 10c0 | 73 74 20 74 6f 20 68 69 67 68 65 73 74 20 64 65 67 72 65 65 2e 0a 0a 20 20 20 20 50 61 72 61 6d | st.to.highest.degree.......Param |
| 10e0 | 65 74 65 72 73 0a 20 20 20 20 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 63 20 3a 20 61 72 72 | eters.....----------.....c.:.arr |
| 1100 | 61 79 5f 6c 69 6b 65 0a 20 20 20 20 20 20 20 20 31 2d 44 20 61 72 72 61 79 20 63 6f 6e 74 61 69 | ay_like.........1-D.array.contai |
| 1120 | 6e 69 6e 67 20 74 68 65 20 48 65 72 6d 69 74 65 20 73 65 72 69 65 73 20 63 6f 65 66 66 69 63 69 | ning.the.Hermite.series.coeffici |
| 1140 | 65 6e 74 73 2c 20 6f 72 64 65 72 65 64 0a 20 20 20 20 20 20 20 20 66 72 6f 6d 20 6c 6f 77 65 73 | ents,.ordered.........from.lowes |
| 1160 | 74 20 6f 72 64 65 72 20 74 65 72 6d 20 74 6f 20 68 69 67 68 65 73 74 2e 0a 0a 20 20 20 20 52 65 | t.order.term.to.highest.......Re |
| 1180 | 74 75 72 6e 73 0a 20 20 20 20 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 70 6f 6c 20 3a 20 6e 64 61 72 | turns.....-------.....pol.:.ndar |
| 11a0 | 72 61 79 0a 20 20 20 20 20 20 20 20 31 2d 44 20 61 72 72 61 79 20 63 6f 6e 74 61 69 6e 69 6e 67 | ray.........1-D.array.containing |
| 11c0 | 20 74 68 65 20 63 6f 65 66 66 69 63 69 65 6e 74 73 20 6f 66 20 74 68 65 20 65 71 75 69 76 61 6c | .the.coefficients.of.the.equival |
| 11e0 | 65 6e 74 20 70 6f 6c 79 6e 6f 6d 69 61 6c 0a 20 20 20 20 20 20 20 20 28 72 65 6c 61 74 69 76 65 | ent.polynomial.........(relative |
| 1200 | 20 74 6f 20 74 68 65 20 22 73 74 61 6e 64 61 72 64 22 20 62 61 73 69 73 29 20 6f 72 64 65 72 65 | .to.the."standard".basis).ordere |
| 1220 | 64 20 66 72 6f 6d 20 6c 6f 77 65 73 74 20 6f 72 64 65 72 20 74 65 72 6d 0a 20 20 20 20 20 20 20 | d.from.lowest.order.term........ |
| 1240 | 20 74 6f 20 68 69 67 68 65 73 74 2e 0a 0a 20 20 20 20 53 65 65 20 41 6c 73 6f 0a 20 20 20 20 2d | .to.highest.......See.Also.....- |
| 1260 | 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 70 6f 6c 79 32 68 65 72 6d 65 0a 0a 20 20 20 20 4e 6f 74 65 | -------.....poly2herme......Note |
| 1280 | 73 0a 20 20 20 20 2d 2d 2d 2d 2d 0a 20 20 20 20 54 68 65 20 65 61 73 79 20 77 61 79 20 74 6f 20 | s.....-----.....The.easy.way.to. |
| 12a0 | 64 6f 20 63 6f 6e 76 65 72 73 69 6f 6e 73 20 62 65 74 77 65 65 6e 20 70 6f 6c 79 6e 6f 6d 69 61 | do.conversions.between.polynomia |
| 12c0 | 6c 20 62 61 73 69 73 20 73 65 74 73 0a 20 20 20 20 69 73 20 74 6f 20 75 73 65 20 74 68 65 20 63 | l.basis.sets.....is.to.use.the.c |
| 12e0 | 6f 6e 76 65 72 74 20 6d 65 74 68 6f 64 20 6f 66 20 61 20 63 6c 61 73 73 20 69 6e 73 74 61 6e 63 | onvert.method.of.a.class.instanc |
| 1300 | 65 2e 0a 0a 20 20 20 20 45 78 61 6d 70 6c 65 73 0a 20 20 20 20 2d 2d 2d 2d 2d 2d 2d 2d 0a 20 20 | e.......Examples.....--------... |
| 1320 | 20 20 3e 3e 3e 20 66 72 6f 6d 20 6e 75 6d 70 79 2e 70 6f 6c 79 6e 6f 6d 69 61 6c 2e 68 65 72 6d | ..>>>.from.numpy.polynomial.herm |
| 1340 | 69 74 65 5f 65 20 69 6d 70 6f 72 74 20 68 65 72 6d 65 32 70 6f 6c 79 0a 20 20 20 20 3e 3e 3e 20 | ite_e.import.herme2poly.....>>>. |
| 1360 | 68 65 72 6d 65 32 70 6f 6c 79 28 5b 20 20 32 2e 2c 20 20 31 30 2e 2c 20 20 20 32 2e 2c 20 20 20 | herme2poly([..2.,..10.,...2.,... |
| 1380 | 33 2e 5d 29 0a 20 20 20 20 61 72 72 61 79 28 5b 30 2e 2c 20 20 31 2e 2c 20 20 32 2e 2c 20 20 33 | 3.]).....array([0.,..1.,..2.,..3 |
| 13a0 | 2e 5d 29 0a 0a 20 20 20 20 72 04 00 00 00 29 03 da 07 70 6f 6c 79 61 64 64 da 08 70 6f 6c 79 6d | .])......r....)...polyadd..polym |
| 13c0 | 75 6c 78 da 07 70 6f 6c 79 73 75 62 e9 02 00 00 00 e9 fe ff ff ff 72 27 00 00 00 29 08 da 0a 70 | ulx..polysub..........r'...)...p |
| 13e0 | 6f 6c 79 6e 6f 6d 69 61 6c 72 33 00 00 00 72 34 00 00 00 72 35 00 00 00 72 28 00 00 00 72 29 00 | olynomialr3...r4...r5...r(...r). |
| 1400 | 00 00 72 2a 00 00 00 72 2b 00 00 00 29 09 da 01 63 72 33 00 00 00 72 34 00 00 00 72 35 00 00 00 | ..r*...r+...)...cr3...r4...r5... |
| 1420 | da 01 6e da 02 63 30 da 02 63 31 72 2f 00 00 00 da 03 74 6d 70 73 09 00 00 00 20 20 20 20 20 20 | ..n..c0..c1r/.....tmps.......... |
| 1440 | 20 20 20 72 30 00 00 00 72 15 00 00 00 72 15 00 00 00 90 00 00 00 73 b0 00 00 00 80 00 f7 4c 01 | ...r0...r....r........s.......L. |
| 1460 | 00 05 37 d1 04 36 e4 0a 0c 8f 2c 89 2c 98 01 90 73 d3 0a 1b 81 43 80 51 dc 08 0b 88 41 8b 06 80 | ..7..6....,.,...s....C.Q....A... |
| 1480 | 41 d8 07 08 88 41 82 76 d8 0f 10 88 08 d8 07 08 88 41 82 76 d8 0f 10 88 08 e0 0d 0e 88 72 89 55 | A....A.v.........A.v.........r.U |
| 14a0 | 88 02 d8 0d 0e 88 72 89 55 88 02 e4 11 16 90 71 98 31 91 75 98 61 a0 12 d3 11 24 f2 00 03 09 2c | ......r.U......q.1.u.a....$...., |
| 14c0 | 88 41 d8 12 14 88 43 d9 11 18 98 11 98 31 98 71 99 35 99 18 a0 32 a8 11 a8 51 a9 15 a1 3c d3 11 | .A....C......1.q.5...2...Q...<.. |
| 14e0 | 30 88 42 d9 11 18 98 13 99 68 a0 72 9b 6c d3 11 2b 89 42 f0 07 03 09 2c f1 08 00 10 17 90 72 99 | 0.B......h.r.l..+.B....,......r. |
| 1500 | 38 a0 42 9b 3c d3 0f 28 d0 08 28 72 31 00 00 00 67 00 00 00 00 00 00 f0 bf e7 00 00 00 00 00 00 | 8.B.<..(..(r1...g............... |
| 1520 | f0 3f 63 02 00 00 00 00 00 00 00 00 00 00 00 04 00 00 00 03 00 00 00 f3 66 00 00 00 97 00 7c 01 | .?c.....................f.....|. |
| 1540 | 64 01 6b 37 00 00 72 17 74 01 00 00 00 00 00 00 00 00 6a 02 00 00 00 00 00 00 00 00 00 00 00 00 | d.k7..r.t.........j............. |
| 1560 | 00 00 00 00 00 00 7c 00 7c 01 67 02 ab 01 00 00 00 00 00 00 53 00 74 01 00 00 00 00 00 00 00 00 | ......|.|.g.........S.t......... |
| 1580 | 6a 02 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 7c 00 67 01 ab 01 00 00 00 00 00 00 | j...................|.g......... |
| 15a0 | 53 00 29 02 61 f5 02 00 00 0a 20 20 20 20 48 65 72 6d 69 74 65 20 73 65 72 69 65 73 20 77 68 6f | S.).a.........Hermite.series.who |
| 15c0 | 73 65 20 67 72 61 70 68 20 69 73 20 61 20 73 74 72 61 69 67 68 74 20 6c 69 6e 65 2e 0a 0a 20 20 | se.graph.is.a.straight.line..... |
| 15e0 | 20 20 50 61 72 61 6d 65 74 65 72 73 0a 20 20 20 20 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 | ..Parameters.....----------..... |
| 1600 | 6f 66 66 2c 20 73 63 6c 20 3a 20 73 63 61 6c 61 72 73 0a 20 20 20 20 20 20 20 20 54 68 65 20 73 | off,.scl.:.scalars.........The.s |
| 1620 | 70 65 63 69 66 69 65 64 20 6c 69 6e 65 20 69 73 20 67 69 76 65 6e 20 62 79 20 60 60 6f 66 66 20 | pecified.line.is.given.by.``off. |
| 1640 | 2b 20 73 63 6c 2a 78 60 60 2e 0a 0a 20 20 20 20 52 65 74 75 72 6e 73 0a 20 20 20 20 2d 2d 2d 2d | +.scl*x``.......Returns.....---- |
| 1660 | 2d 2d 2d 0a 20 20 20 20 79 20 3a 20 6e 64 61 72 72 61 79 0a 20 20 20 20 20 20 20 20 54 68 69 73 | ---.....y.:.ndarray.........This |
| 1680 | 20 6d 6f 64 75 6c 65 27 73 20 72 65 70 72 65 73 65 6e 74 61 74 69 6f 6e 20 6f 66 20 74 68 65 20 | .module's.representation.of.the. |
| 16a0 | 48 65 72 6d 69 74 65 20 73 65 72 69 65 73 20 66 6f 72 0a 20 20 20 20 20 20 20 20 60 60 6f 66 66 | Hermite.series.for.........``off |
| 16c0 | 20 2b 20 73 63 6c 2a 78 60 60 2e 0a 0a 20 20 20 20 53 65 65 20 41 6c 73 6f 0a 20 20 20 20 2d 2d | .+.scl*x``.......See.Also.....-- |
| 16e0 | 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 6e 75 6d 70 79 2e 70 6f 6c 79 6e 6f 6d 69 61 6c 2e 70 6f 6c 79 | ------.....numpy.polynomial.poly |
| 1700 | 6e 6f 6d 69 61 6c 2e 70 6f 6c 79 6c 69 6e 65 0a 20 20 20 20 6e 75 6d 70 79 2e 70 6f 6c 79 6e 6f | nomial.polyline.....numpy.polyno |
| 1720 | 6d 69 61 6c 2e 63 68 65 62 79 73 68 65 76 2e 63 68 65 62 6c 69 6e 65 0a 20 20 20 20 6e 75 6d 70 | mial.chebyshev.chebline.....nump |
| 1740 | 79 2e 70 6f 6c 79 6e 6f 6d 69 61 6c 2e 6c 65 67 65 6e 64 72 65 2e 6c 65 67 6c 69 6e 65 0a 20 20 | y.polynomial.legendre.legline... |
| 1760 | 20 20 6e 75 6d 70 79 2e 70 6f 6c 79 6e 6f 6d 69 61 6c 2e 6c 61 67 75 65 72 72 65 2e 6c 61 67 6c | ..numpy.polynomial.laguerre.lagl |
| 1780 | 69 6e 65 0a 20 20 20 20 6e 75 6d 70 79 2e 70 6f 6c 79 6e 6f 6d 69 61 6c 2e 68 65 72 6d 69 74 65 | ine.....numpy.polynomial.hermite |
| 17a0 | 2e 68 65 72 6d 6c 69 6e 65 0a 0a 20 20 20 20 45 78 61 6d 70 6c 65 73 0a 20 20 20 20 2d 2d 2d 2d | .hermline......Examples.....---- |
| 17c0 | 2d 2d 2d 2d 0a 20 20 20 20 3e 3e 3e 20 66 72 6f 6d 20 6e 75 6d 70 79 2e 70 6f 6c 79 6e 6f 6d 69 | ----.....>>>.from.numpy.polynomi |
| 17e0 | 61 6c 2e 68 65 72 6d 69 74 65 5f 65 20 69 6d 70 6f 72 74 20 68 65 72 6d 65 6c 69 6e 65 0a 20 20 | al.hermite_e.import.hermeline... |
| 1800 | 20 20 3e 3e 3e 20 66 72 6f 6d 20 6e 75 6d 70 79 2e 70 6f 6c 79 6e 6f 6d 69 61 6c 2e 68 65 72 6d | ..>>>.from.numpy.polynomial.herm |
| 1820 | 69 74 65 5f 65 20 69 6d 70 6f 72 74 20 68 65 72 6d 65 6c 69 6e 65 2c 20 68 65 72 6d 65 76 61 6c | ite_e.import.hermeline,.hermeval |
| 1840 | 0a 20 20 20 20 3e 3e 3e 20 68 65 72 6d 65 76 61 6c 28 30 2c 68 65 72 6d 65 6c 69 6e 65 28 33 2c | .....>>>.hermeval(0,hermeline(3, |
| 1860 | 20 32 29 29 0a 20 20 20 20 33 2e 30 0a 20 20 20 20 3e 3e 3e 20 68 65 72 6d 65 76 61 6c 28 31 2c | .2)).....3.0.....>>>.hermeval(1, |
| 1880 | 68 65 72 6d 65 6c 69 6e 65 28 33 2c 20 32 29 29 0a 20 20 20 20 35 2e 30 0a 0a 20 20 20 20 72 02 | hermeline(3,.2)).....5.0......r. |
| 18a0 | 00 00 00 29 02 da 02 6e 70 da 05 61 72 72 61 79 29 02 da 03 6f 66 66 da 03 73 63 6c 73 02 00 00 | ...)...np..array)...off..scls... |
| 18c0 | 00 20 20 72 30 00 00 00 72 0b 00 00 00 72 0b 00 00 00 db 00 00 00 73 2f 00 00 00 80 00 f0 42 01 | ...r0...r....r........s/......B. |
| 18e0 | 00 08 0b 88 61 82 78 dc 0f 11 8f 78 89 78 98 13 98 63 98 0a d3 0f 23 d0 08 23 e4 0f 11 8f 78 89 | ....a.x....x.x...c....#..#....x. |
| 1900 | 78 98 13 98 05 8b 7f d0 08 1e 72 31 00 00 00 63 01 00 00 00 00 00 00 00 00 00 00 00 05 00 00 00 | x.........r1...c................ |
| 1920 | 03 00 00 00 f3 40 00 00 00 97 00 74 01 00 00 00 00 00 00 00 00 6a 02 00 00 00 00 00 00 00 00 00 | .....@.....t.........j.......... |
| 1940 | 00 00 00 00 00 00 00 00 00 74 04 00 00 00 00 00 00 00 00 74 06 00 00 00 00 00 00 00 00 7c 00 ab | .........t.........t.........|.. |
| 1960 | 03 00 00 00 00 00 00 53 00 29 01 61 7a 06 00 00 0a 20 20 20 20 47 65 6e 65 72 61 74 65 20 61 20 | .......S.).az........Generate.a. |
| 1980 | 48 65 72 6d 69 74 65 45 20 73 65 72 69 65 73 20 77 69 74 68 20 67 69 76 65 6e 20 72 6f 6f 74 73 | HermiteE.series.with.given.roots |
| 19a0 | 2e 0a 0a 20 20 20 20 54 68 65 20 66 75 6e 63 74 69 6f 6e 20 72 65 74 75 72 6e 73 20 74 68 65 20 | .......The.function.returns.the. |
| 19c0 | 63 6f 65 66 66 69 63 69 65 6e 74 73 20 6f 66 20 74 68 65 20 70 6f 6c 79 6e 6f 6d 69 61 6c 0a 0a | coefficients.of.the.polynomial.. |
| 19e0 | 20 20 20 20 2e 2e 20 6d 61 74 68 3a 3a 20 70 28 78 29 20 3d 20 28 78 20 2d 20 72 5f 30 29 20 2a | .......math::.p(x).=.(x.-.r_0).* |
| 1a00 | 20 28 78 20 2d 20 72 5f 31 29 20 2a 20 2e 2e 2e 20 2a 20 28 78 20 2d 20 72 5f 6e 29 2c 0a 0a 20 | .(x.-.r_1).*.....*.(x.-.r_n),... |
| 1a20 | 20 20 20 69 6e 20 48 65 72 6d 69 74 65 45 20 66 6f 72 6d 2c 20 77 68 65 72 65 20 74 68 65 20 3a | ...in.HermiteE.form,.where.the.: |
| 1a40 | 6d 61 74 68 3a 60 72 5f 6e 60 20 61 72 65 20 74 68 65 20 72 6f 6f 74 73 20 73 70 65 63 69 66 69 | math:`r_n`.are.the.roots.specifi |
| 1a60 | 65 64 20 69 6e 20 60 72 6f 6f 74 73 60 2e 0a 20 20 20 20 49 66 20 61 20 7a 65 72 6f 20 68 61 73 | ed.in.`roots`......If.a.zero.has |
| 1a80 | 20 6d 75 6c 74 69 70 6c 69 63 69 74 79 20 6e 2c 20 74 68 65 6e 20 69 74 20 6d 75 73 74 20 61 70 | .multiplicity.n,.then.it.must.ap |
| 1aa0 | 70 65 61 72 20 69 6e 20 60 72 6f 6f 74 73 60 20 6e 20 74 69 6d 65 73 2e 0a 20 20 20 20 46 6f 72 | pear.in.`roots`.n.times......For |
| 1ac0 | 20 69 6e 73 74 61 6e 63 65 2c 20 69 66 20 32 20 69 73 20 61 20 72 6f 6f 74 20 6f 66 20 6d 75 6c | .instance,.if.2.is.a.root.of.mul |
| 1ae0 | 74 69 70 6c 69 63 69 74 79 20 74 68 72 65 65 20 61 6e 64 20 33 20 69 73 20 61 20 72 6f 6f 74 20 | tiplicity.three.and.3.is.a.root. |
| 1b00 | 6f 66 0a 20 20 20 20 6d 75 6c 74 69 70 6c 69 63 69 74 79 20 32 2c 20 74 68 65 6e 20 60 72 6f 6f | of.....multiplicity.2,.then.`roo |
| 1b20 | 74 73 60 20 6c 6f 6f 6b 73 20 73 6f 6d 65 74 68 69 6e 67 20 6c 69 6b 65 20 5b 32 2c 20 32 2c 20 | ts`.looks.something.like.[2,.2,. |
| 1b40 | 32 2c 20 33 2c 20 33 5d 2e 20 54 68 65 0a 20 20 20 20 72 6f 6f 74 73 20 63 61 6e 20 61 70 70 65 | 2,.3,.3]..The.....roots.can.appe |
| 1b60 | 61 72 20 69 6e 20 61 6e 79 20 6f 72 64 65 72 2e 0a 0a 20 20 20 20 49 66 20 74 68 65 20 72 65 74 | ar.in.any.order.......If.the.ret |
| 1b80 | 75 72 6e 65 64 20 63 6f 65 66 66 69 63 69 65 6e 74 73 20 61 72 65 20 60 63 60 2c 20 74 68 65 6e | urned.coefficients.are.`c`,.then |
| 1ba0 | 0a 0a 20 20 20 20 2e 2e 20 6d 61 74 68 3a 3a 20 70 28 78 29 20 3d 20 63 5f 30 20 2b 20 63 5f 31 | .........math::.p(x).=.c_0.+.c_1 |
| 1bc0 | 20 2a 20 48 65 5f 31 28 78 29 20 2b 20 2e 2e 2e 20 2b 20 20 63 5f 6e 20 2a 20 48 65 5f 6e 28 78 | .*.He_1(x).+.....+..c_n.*.He_n(x |
| 1be0 | 29 0a 0a 20 20 20 20 54 68 65 20 63 6f 65 66 66 69 63 69 65 6e 74 20 6f 66 20 74 68 65 20 6c 61 | )......The.coefficient.of.the.la |
| 1c00 | 73 74 20 74 65 72 6d 20 69 73 20 6e 6f 74 20 67 65 6e 65 72 61 6c 6c 79 20 31 20 66 6f 72 20 6d | st.term.is.not.generally.1.for.m |
| 1c20 | 6f 6e 69 63 0a 20 20 20 20 70 6f 6c 79 6e 6f 6d 69 61 6c 73 20 69 6e 20 48 65 72 6d 69 74 65 45 | onic.....polynomials.in.HermiteE |
| 1c40 | 20 66 6f 72 6d 2e 0a 0a 20 20 20 20 50 61 72 61 6d 65 74 65 72 73 0a 20 20 20 20 2d 2d 2d 2d 2d | .form.......Parameters.....----- |
| 1c60 | 2d 2d 2d 2d 2d 0a 20 20 20 20 72 6f 6f 74 73 20 3a 20 61 72 72 61 79 5f 6c 69 6b 65 0a 20 20 20 | -----.....roots.:.array_like.... |
| 1c80 | 20 20 20 20 20 53 65 71 75 65 6e 63 65 20 63 6f 6e 74 61 69 6e 69 6e 67 20 74 68 65 20 72 6f 6f | .....Sequence.containing.the.roo |
| 1ca0 | 74 73 2e 0a 0a 20 20 20 20 52 65 74 75 72 6e 73 0a 20 20 20 20 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 | ts.......Returns.....-------.... |
| 1cc0 | 20 6f 75 74 20 3a 20 6e 64 61 72 72 61 79 0a 20 20 20 20 20 20 20 20 31 2d 44 20 61 72 72 61 79 | .out.:.ndarray.........1-D.array |
| 1ce0 | 20 6f 66 20 63 6f 65 66 66 69 63 69 65 6e 74 73 2e 20 20 49 66 20 61 6c 6c 20 72 6f 6f 74 73 20 | .of.coefficients...If.all.roots. |
| 1d00 | 61 72 65 20 72 65 61 6c 20 74 68 65 6e 20 60 6f 75 74 60 20 69 73 20 61 0a 20 20 20 20 20 20 20 | are.real.then.`out`.is.a........ |
| 1d20 | 20 72 65 61 6c 20 61 72 72 61 79 2c 20 69 66 20 73 6f 6d 65 20 6f 66 20 74 68 65 20 72 6f 6f 74 | .real.array,.if.some.of.the.root |
| 1d40 | 73 20 61 72 65 20 63 6f 6d 70 6c 65 78 2c 20 74 68 65 6e 20 60 6f 75 74 60 20 69 73 20 63 6f 6d | s.are.complex,.then.`out`.is.com |
| 1d60 | 70 6c 65 78 0a 20 20 20 20 20 20 20 20 65 76 65 6e 20 69 66 20 61 6c 6c 20 74 68 65 20 63 6f 65 | plex.........even.if.all.the.coe |
| 1d80 | 66 66 69 63 69 65 6e 74 73 20 69 6e 20 74 68 65 20 72 65 73 75 6c 74 20 61 72 65 20 72 65 61 6c | fficients.in.the.result.are.real |
| 1da0 | 20 28 73 65 65 20 45 78 61 6d 70 6c 65 73 0a 20 20 20 20 20 20 20 20 62 65 6c 6f 77 29 2e 0a 0a | .(see.Examples.........below)... |
| 1dc0 | 20 20 20 20 53 65 65 20 41 6c 73 6f 0a 20 20 20 20 2d 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 6e 75 | ....See.Also.....--------.....nu |
| 1de0 | 6d 70 79 2e 70 6f 6c 79 6e 6f 6d 69 61 6c 2e 70 6f 6c 79 6e 6f 6d 69 61 6c 2e 70 6f 6c 79 66 72 | mpy.polynomial.polynomial.polyfr |
| 1e00 | 6f 6d 72 6f 6f 74 73 0a 20 20 20 20 6e 75 6d 70 79 2e 70 6f 6c 79 6e 6f 6d 69 61 6c 2e 6c 65 67 | omroots.....numpy.polynomial.leg |
| 1e20 | 65 6e 64 72 65 2e 6c 65 67 66 72 6f 6d 72 6f 6f 74 73 0a 20 20 20 20 6e 75 6d 70 79 2e 70 6f 6c | endre.legfromroots.....numpy.pol |
| 1e40 | 79 6e 6f 6d 69 61 6c 2e 6c 61 67 75 65 72 72 65 2e 6c 61 67 66 72 6f 6d 72 6f 6f 74 73 0a 20 20 | ynomial.laguerre.lagfromroots... |
| 1e60 | 20 20 6e 75 6d 70 79 2e 70 6f 6c 79 6e 6f 6d 69 61 6c 2e 68 65 72 6d 69 74 65 2e 68 65 72 6d 66 | ..numpy.polynomial.hermite.hermf |
| 1e80 | 72 6f 6d 72 6f 6f 74 73 0a 20 20 20 20 6e 75 6d 70 79 2e 70 6f 6c 79 6e 6f 6d 69 61 6c 2e 63 68 | romroots.....numpy.polynomial.ch |
| 1ea0 | 65 62 79 73 68 65 76 2e 63 68 65 62 66 72 6f 6d 72 6f 6f 74 73 0a 0a 20 20 20 20 45 78 61 6d 70 | ebyshev.chebfromroots......Examp |
| 1ec0 | 6c 65 73 0a 20 20 20 20 2d 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 3e 3e 3e 20 66 72 6f 6d 20 6e 75 | les.....--------.....>>>.from.nu |
| 1ee0 | 6d 70 79 2e 70 6f 6c 79 6e 6f 6d 69 61 6c 2e 68 65 72 6d 69 74 65 5f 65 20 69 6d 70 6f 72 74 20 | mpy.polynomial.hermite_e.import. |
| 1f00 | 68 65 72 6d 65 66 72 6f 6d 72 6f 6f 74 73 2c 20 68 65 72 6d 65 76 61 6c 0a 20 20 20 20 3e 3e 3e | hermefromroots,.hermeval.....>>> |
| 1f20 | 20 63 6f 65 66 20 3d 20 68 65 72 6d 65 66 72 6f 6d 72 6f 6f 74 73 28 28 2d 31 2c 20 30 2c 20 31 | .coef.=.hermefromroots((-1,.0,.1 |
| 1f40 | 29 29 0a 20 20 20 20 3e 3e 3e 20 68 65 72 6d 65 76 61 6c 28 28 2d 31 2c 20 30 2c 20 31 29 2c 20 | )).....>>>.hermeval((-1,.0,.1),. |
| 1f60 | 63 6f 65 66 29 0a 20 20 20 20 61 72 72 61 79 28 5b 30 2e 2c 20 30 2e 2c 20 30 2e 5d 29 0a 20 20 | coef).....array([0.,.0.,.0.])... |
| 1f80 | 20 20 3e 3e 3e 20 63 6f 65 66 20 3d 20 68 65 72 6d 65 66 72 6f 6d 72 6f 6f 74 73 28 28 2d 31 6a | ..>>>.coef.=.hermefromroots((-1j |
| 1fa0 | 2c 20 31 6a 29 29 0a 20 20 20 20 3e 3e 3e 20 68 65 72 6d 65 76 61 6c 28 28 2d 31 6a 2c 20 31 6a | ,.1j)).....>>>.hermeval((-1j,.1j |
| 1fc0 | 29 2c 20 63 6f 65 66 29 0a 20 20 20 20 61 72 72 61 79 28 5b 30 2e 2b 30 2e 6a 2c 20 30 2e 2b 30 | ),.coef).....array([0.+0.j,.0.+0 |
| 1fe0 | 2e 6a 5d 29 0a 0a 20 20 20 20 29 04 72 28 00 00 00 da 0a 5f 66 72 6f 6d 72 6f 6f 74 73 72 0b 00 | .j])......).r(....._fromrootsr.. |
| 2000 | 00 00 72 0f 00 00 00 29 01 da 05 72 6f 6f 74 73 73 01 00 00 00 20 72 30 00 00 00 72 17 00 00 00 | ..r....)...rootss.....r0...r.... |
| 2020 | 72 17 00 00 00 02 01 00 00 73 18 00 00 00 80 00 f4 6a 01 00 0c 0e 8f 3d 89 3d 9c 19 a4 48 a8 65 | r........s.......j.....=.=...H.e |
| 2040 | d3 0b 34 d0 04 34 72 31 00 00 00 63 02 00 00 00 00 00 00 00 00 00 00 00 04 00 00 00 03 00 00 00 | ..4..4r1...c.................... |
| 2060 | f3 2e 00 00 00 97 00 74 01 00 00 00 00 00 00 00 00 6a 02 00 00 00 00 00 00 00 00 00 00 00 00 00 | .......t.........j.............. |
| 2080 | 00 00 00 00 00 7c 00 7c 01 ab 02 00 00 00 00 00 00 53 00 29 01 61 f0 03 00 00 0a 20 20 20 20 41 | .....|.|.........S.).a.........A |
| 20a0 | 64 64 20 6f 6e 65 20 48 65 72 6d 69 74 65 20 73 65 72 69 65 73 20 74 6f 20 61 6e 6f 74 68 65 72 | dd.one.Hermite.series.to.another |
| 20c0 | 2e 0a 0a 20 20 20 20 52 65 74 75 72 6e 73 20 74 68 65 20 73 75 6d 20 6f 66 20 74 77 6f 20 48 65 | .......Returns.the.sum.of.two.He |
| 20e0 | 72 6d 69 74 65 20 73 65 72 69 65 73 20 60 63 31 60 20 2b 20 60 63 32 60 2e 20 20 54 68 65 20 61 | rmite.series.`c1`.+.`c2`...The.a |
| 2100 | 72 67 75 6d 65 6e 74 73 0a 20 20 20 20 61 72 65 20 73 65 71 75 65 6e 63 65 73 20 6f 66 20 63 6f | rguments.....are.sequences.of.co |
| 2120 | 65 66 66 69 63 69 65 6e 74 73 20 6f 72 64 65 72 65 64 20 66 72 6f 6d 20 6c 6f 77 65 73 74 20 6f | efficients.ordered.from.lowest.o |
| 2140 | 72 64 65 72 20 74 65 72 6d 20 74 6f 0a 20 20 20 20 68 69 67 68 65 73 74 2c 20 69 2e 65 2e 2c 20 | rder.term.to.....highest,.i.e.,. |
| 2160 | 5b 31 2c 32 2c 33 5d 20 72 65 70 72 65 73 65 6e 74 73 20 74 68 65 20 73 65 72 69 65 73 20 60 60 | [1,2,3].represents.the.series.`` |
| 2180 | 50 5f 30 20 2b 20 32 2a 50 5f 31 20 2b 20 33 2a 50 5f 32 60 60 2e 0a 0a 20 20 20 20 50 61 72 61 | P_0.+.2*P_1.+.3*P_2``.......Para |
| 21a0 | 6d 65 74 65 72 73 0a 20 20 20 20 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 63 31 2c 20 63 32 | meters.....----------.....c1,.c2 |
| 21c0 | 20 3a 20 61 72 72 61 79 5f 6c 69 6b 65 0a 20 20 20 20 20 20 20 20 31 2d 44 20 61 72 72 61 79 73 | .:.array_like.........1-D.arrays |
| 21e0 | 20 6f 66 20 48 65 72 6d 69 74 65 20 73 65 72 69 65 73 20 63 6f 65 66 66 69 63 69 65 6e 74 73 20 | .of.Hermite.series.coefficients. |
| 2200 | 6f 72 64 65 72 65 64 20 66 72 6f 6d 20 6c 6f 77 20 74 6f 0a 20 20 20 20 20 20 20 20 68 69 67 68 | ordered.from.low.to.........high |
| 2220 | 2e 0a 0a 20 20 20 20 52 65 74 75 72 6e 73 0a 20 20 20 20 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 6f | .......Returns.....-------.....o |
| 2240 | 75 74 20 3a 20 6e 64 61 72 72 61 79 0a 20 20 20 20 20 20 20 20 41 72 72 61 79 20 72 65 70 72 65 | ut.:.ndarray.........Array.repre |
| 2260 | 73 65 6e 74 69 6e 67 20 74 68 65 20 48 65 72 6d 69 74 65 20 73 65 72 69 65 73 20 6f 66 20 74 68 | senting.the.Hermite.series.of.th |
| 2280 | 65 69 72 20 73 75 6d 2e 0a 0a 20 20 20 20 53 65 65 20 41 6c 73 6f 0a 20 20 20 20 2d 2d 2d 2d 2d | eir.sum.......See.Also.....----- |
| 22a0 | 2d 2d 2d 0a 20 20 20 20 68 65 72 6d 65 73 75 62 2c 20 68 65 72 6d 65 6d 75 6c 78 2c 20 68 65 72 | ---.....hermesub,.hermemulx,.her |
| 22c0 | 6d 65 6d 75 6c 2c 20 68 65 72 6d 65 64 69 76 2c 20 68 65 72 6d 65 70 6f 77 0a 0a 20 20 20 20 4e | memul,.hermediv,.hermepow......N |
| 22e0 | 6f 74 65 73 0a 20 20 20 20 2d 2d 2d 2d 2d 0a 20 20 20 20 55 6e 6c 69 6b 65 20 6d 75 6c 74 69 70 | otes.....-----.....Unlike.multip |
| 2300 | 6c 69 63 61 74 69 6f 6e 2c 20 64 69 76 69 73 69 6f 6e 2c 20 65 74 63 2e 2c 20 74 68 65 20 73 75 | lication,.division,.etc.,.the.su |
| 2320 | 6d 20 6f 66 20 74 77 6f 20 48 65 72 6d 69 74 65 20 73 65 72 69 65 73 0a 20 20 20 20 69 73 20 61 | m.of.two.Hermite.series.....is.a |
| 2340 | 20 48 65 72 6d 69 74 65 20 73 65 72 69 65 73 20 28 77 69 74 68 6f 75 74 20 68 61 76 69 6e 67 20 | .Hermite.series.(without.having. |
| 2360 | 74 6f 20 22 72 65 70 72 6f 6a 65 63 74 22 20 74 68 65 20 72 65 73 75 6c 74 20 6f 6e 74 6f 0a 20 | to."reproject".the.result.onto.. |
| 2380 | 20 20 20 74 68 65 20 62 61 73 69 73 20 73 65 74 29 20 73 6f 20 61 64 64 69 74 69 6f 6e 2c 20 6a | ...the.basis.set).so.addition,.j |
| 23a0 | 75 73 74 20 6c 69 6b 65 20 74 68 61 74 20 6f 66 20 22 73 74 61 6e 64 61 72 64 22 20 70 6f 6c 79 | ust.like.that.of."standard".poly |
| 23c0 | 6e 6f 6d 69 61 6c 73 2c 0a 20 20 20 20 69 73 20 73 69 6d 70 6c 79 20 22 63 6f 6d 70 6f 6e 65 6e | nomials,.....is.simply."componen |
| 23e0 | 74 2d 77 69 73 65 2e 22 0a 0a 20 20 20 20 45 78 61 6d 70 6c 65 73 0a 20 20 20 20 2d 2d 2d 2d 2d | t-wise."......Examples.....----- |
| 2400 | 2d 2d 2d 0a 20 20 20 20 3e 3e 3e 20 66 72 6f 6d 20 6e 75 6d 70 79 2e 70 6f 6c 79 6e 6f 6d 69 61 | ---.....>>>.from.numpy.polynomia |
| 2420 | 6c 2e 68 65 72 6d 69 74 65 5f 65 20 69 6d 70 6f 72 74 20 68 65 72 6d 65 61 64 64 0a 20 20 20 20 | l.hermite_e.import.hermeadd..... |
| 2440 | 3e 3e 3e 20 68 65 72 6d 65 61 64 64 28 5b 31 2c 20 32 2c 20 33 5d 2c 20 5b 31 2c 20 32 2c 20 33 | >>>.hermeadd([1,.2,.3],.[1,.2,.3 |
| 2460 | 2c 20 34 5d 29 0a 20 20 20 20 61 72 72 61 79 28 5b 32 2e 2c 20 20 34 2e 2c 20 20 36 2e 2c 20 20 | ,.4]).....array([2.,..4.,..6.,.. |
| 2480 | 34 2e 5d 29 0a 0a 20 20 20 20 29 02 72 28 00 00 00 da 04 5f 61 64 64 a9 02 72 3c 00 00 00 da 02 | 4.])......).r(....._add..r<..... |
| 24a0 | 63 32 73 02 00 00 00 20 20 72 30 00 00 00 72 0c 00 00 00 72 0c 00 00 00 3a 01 00 00 f3 15 00 00 | c2s......r0...r....r....:....... |
| 24c0 | 00 80 00 f4 4a 01 00 0c 0e 8f 37 89 37 90 32 90 72 8b 3f d0 04 1a 72 31 00 00 00 63 02 00 00 00 | ....J.....7.7.2.r.?...r1...c.... |
| 24e0 | 00 00 00 00 00 00 00 00 04 00 00 00 03 00 00 00 f3 2e 00 00 00 97 00 74 01 00 00 00 00 00 00 00 | .......................t........ |
| 2500 | 00 6a 02 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 7c 00 7c 01 ab 02 00 00 00 00 00 | .j...................|.|........ |
| 2520 | 00 53 00 29 01 61 fd 03 00 00 0a 20 20 20 20 53 75 62 74 72 61 63 74 20 6f 6e 65 20 48 65 72 6d | .S.).a.........Subtract.one.Herm |
| 2540 | 69 74 65 20 73 65 72 69 65 73 20 66 72 6f 6d 20 61 6e 6f 74 68 65 72 2e 0a 0a 20 20 20 20 52 65 | ite.series.from.another.......Re |
| 2560 | 74 75 72 6e 73 20 74 68 65 20 64 69 66 66 65 72 65 6e 63 65 20 6f 66 20 74 77 6f 20 48 65 72 6d | turns.the.difference.of.two.Herm |
| 2580 | 69 74 65 20 73 65 72 69 65 73 20 60 63 31 60 20 2d 20 60 63 32 60 2e 20 20 54 68 65 0a 20 20 20 | ite.series.`c1`.-.`c2`...The.... |
| 25a0 | 20 73 65 71 75 65 6e 63 65 73 20 6f 66 20 63 6f 65 66 66 69 63 69 65 6e 74 73 20 61 72 65 20 66 | .sequences.of.coefficients.are.f |
| 25c0 | 72 6f 6d 20 6c 6f 77 65 73 74 20 6f 72 64 65 72 20 74 65 72 6d 20 74 6f 20 68 69 67 68 65 73 74 | rom.lowest.order.term.to.highest |
| 25e0 | 2c 20 69 2e 65 2e 2c 0a 20 20 20 20 5b 31 2c 32 2c 33 5d 20 72 65 70 72 65 73 65 6e 74 73 20 74 | ,.i.e.,.....[1,2,3].represents.t |
| 2600 | 68 65 20 73 65 72 69 65 73 20 60 60 50 5f 30 20 2b 20 32 2a 50 5f 31 20 2b 20 33 2a 50 5f 32 60 | he.series.``P_0.+.2*P_1.+.3*P_2` |
| 2620 | 60 2e 0a 0a 20 20 20 20 50 61 72 61 6d 65 74 65 72 73 0a 20 20 20 20 2d 2d 2d 2d 2d 2d 2d 2d 2d | `.......Parameters.....--------- |
| 2640 | 2d 0a 20 20 20 20 63 31 2c 20 63 32 20 3a 20 61 72 72 61 79 5f 6c 69 6b 65 0a 20 20 20 20 20 20 | -.....c1,.c2.:.array_like....... |
| 2660 | 20 20 31 2d 44 20 61 72 72 61 79 73 20 6f 66 20 48 65 72 6d 69 74 65 20 73 65 72 69 65 73 20 63 | ..1-D.arrays.of.Hermite.series.c |
| 2680 | 6f 65 66 66 69 63 69 65 6e 74 73 20 6f 72 64 65 72 65 64 20 66 72 6f 6d 20 6c 6f 77 20 74 6f 0a | oefficients.ordered.from.low.to. |
| 26a0 | 20 20 20 20 20 20 20 20 68 69 67 68 2e 0a 0a 20 20 20 20 52 65 74 75 72 6e 73 0a 20 20 20 20 2d | ........high.......Returns.....- |
| 26c0 | 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 6f 75 74 20 3a 20 6e 64 61 72 72 61 79 0a 20 20 20 20 20 20 20 | ------.....out.:.ndarray........ |
| 26e0 | 20 4f 66 20 48 65 72 6d 69 74 65 20 73 65 72 69 65 73 20 63 6f 65 66 66 69 63 69 65 6e 74 73 20 | .Of.Hermite.series.coefficients. |
| 2700 | 72 65 70 72 65 73 65 6e 74 69 6e 67 20 74 68 65 69 72 20 64 69 66 66 65 72 65 6e 63 65 2e 0a 0a | representing.their.difference... |
| 2720 | 20 20 20 20 53 65 65 20 41 6c 73 6f 0a 20 20 20 20 2d 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 68 65 | ....See.Also.....--------.....he |
| 2740 | 72 6d 65 61 64 64 2c 20 68 65 72 6d 65 6d 75 6c 78 2c 20 68 65 72 6d 65 6d 75 6c 2c 20 68 65 72 | rmeadd,.hermemulx,.hermemul,.her |
| 2760 | 6d 65 64 69 76 2c 20 68 65 72 6d 65 70 6f 77 0a 0a 20 20 20 20 4e 6f 74 65 73 0a 20 20 20 20 2d | mediv,.hermepow......Notes.....- |
| 2780 | 2d 2d 2d 2d 0a 20 20 20 20 55 6e 6c 69 6b 65 20 6d 75 6c 74 69 70 6c 69 63 61 74 69 6f 6e 2c 20 | ----.....Unlike.multiplication,. |
| 27a0 | 64 69 76 69 73 69 6f 6e 2c 20 65 74 63 2e 2c 20 74 68 65 20 64 69 66 66 65 72 65 6e 63 65 20 6f | division,.etc.,.the.difference.o |
| 27c0 | 66 20 74 77 6f 20 48 65 72 6d 69 74 65 0a 20 20 20 20 73 65 72 69 65 73 20 69 73 20 61 20 48 65 | f.two.Hermite.....series.is.a.He |
| 27e0 | 72 6d 69 74 65 20 73 65 72 69 65 73 20 28 77 69 74 68 6f 75 74 20 68 61 76 69 6e 67 20 74 6f 20 | rmite.series.(without.having.to. |
| 2800 | 22 72 65 70 72 6f 6a 65 63 74 22 20 74 68 65 20 72 65 73 75 6c 74 0a 20 20 20 20 6f 6e 74 6f 20 | "reproject".the.result.....onto. |
| 2820 | 74 68 65 20 62 61 73 69 73 20 73 65 74 29 20 73 6f 20 73 75 62 74 72 61 63 74 69 6f 6e 2c 20 6a | the.basis.set).so.subtraction,.j |
| 2840 | 75 73 74 20 6c 69 6b 65 20 74 68 61 74 20 6f 66 20 22 73 74 61 6e 64 61 72 64 22 0a 20 20 20 20 | ust.like.that.of."standard"..... |
| 2860 | 70 6f 6c 79 6e 6f 6d 69 61 6c 73 2c 20 69 73 20 73 69 6d 70 6c 79 20 22 63 6f 6d 70 6f 6e 65 6e | polynomials,.is.simply."componen |
| 2880 | 74 2d 77 69 73 65 2e 22 0a 0a 20 20 20 20 45 78 61 6d 70 6c 65 73 0a 20 20 20 20 2d 2d 2d 2d 2d | t-wise."......Examples.....----- |
| 28a0 | 2d 2d 2d 0a 20 20 20 20 3e 3e 3e 20 66 72 6f 6d 20 6e 75 6d 70 79 2e 70 6f 6c 79 6e 6f 6d 69 61 | ---.....>>>.from.numpy.polynomia |
| 28c0 | 6c 2e 68 65 72 6d 69 74 65 5f 65 20 69 6d 70 6f 72 74 20 68 65 72 6d 65 73 75 62 0a 20 20 20 20 | l.hermite_e.import.hermesub..... |
| 28e0 | 3e 3e 3e 20 68 65 72 6d 65 73 75 62 28 5b 31 2c 20 32 2c 20 33 2c 20 34 5d 2c 20 5b 31 2c 20 32 | >>>.hermesub([1,.2,.3,.4],.[1,.2 |
| 2900 | 2c 20 33 5d 29 0a 20 20 20 20 61 72 72 61 79 28 5b 30 2e 2c 20 30 2e 2c 20 30 2e 2c 20 34 2e 5d | ,.3]).....array([0.,.0.,.0.,.4.] |
| 2920 | 29 0a 0a 20 20 20 20 29 02 72 28 00 00 00 da 04 5f 73 75 62 72 49 00 00 00 73 02 00 00 00 20 20 | )......).r(....._subrI...s...... |
| 2940 | 72 30 00 00 00 72 0d 00 00 00 72 0d 00 00 00 62 01 00 00 72 4b 00 00 00 72 31 00 00 00 63 01 00 | r0...r....r....b...rK...r1...c.. |
| 2960 | 00 00 00 00 00 00 00 00 00 00 06 00 00 00 03 00 00 00 f3 5c 01 00 00 97 00 74 01 00 00 00 00 00 | ...................\.....t...... |
| 2980 | 00 00 00 6a 02 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 7c 00 67 01 ab 01 00 00 00 | ...j...................|.g...... |
| 29a0 | 00 00 00 5c 01 00 00 7d 00 74 05 00 00 00 00 00 00 00 00 7c 00 ab 01 00 00 00 00 00 00 64 01 6b | ...\...}.t.........|.........d.k |
| 29c0 | 28 00 00 72 0a 7c 00 64 02 19 00 00 00 64 02 6b 28 00 00 72 02 7c 00 53 00 74 07 00 00 00 00 00 | (..r.|.d.....d.k(..r.|.S.t...... |
| 29e0 | 00 00 00 6a 08 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 74 05 00 00 00 00 00 00 00 | ...j...................t........ |
| 2a00 | 00 7c 00 ab 01 00 00 00 00 00 00 64 01 7a 00 00 00 7c 00 6a 0a 00 00 00 00 00 00 00 00 00 00 00 | .|.........d.z...|.j............ |
| 2a20 | 00 00 00 00 00 00 00 ac 03 ab 02 00 00 00 00 00 00 7d 01 7c 00 64 02 19 00 00 00 64 02 7a 05 00 | .................}.|.d.....d.z.. |
| 2a40 | 00 7c 01 64 02 3c 00 00 00 7c 00 64 02 19 00 00 00 7c 01 64 01 3c 00 00 00 74 0d 00 00 00 00 00 | .|.d.<...|.d.....|.d.<...t...... |
| 2a60 | 00 00 00 64 01 74 05 00 00 00 00 00 00 00 00 7c 00 ab 01 00 00 00 00 00 00 ab 02 00 00 00 00 00 | ...d.t.........|................ |
| 2a80 | 00 44 00 5d 23 00 00 7d 02 7c 00 7c 02 19 00 00 00 7c 01 7c 02 64 01 7a 00 00 00 3c 00 00 00 7c | .D.]#..}.|.|.....|.|.d.z...<...| |
| 2aa0 | 01 7c 02 64 01 7a 0a 00 00 78 02 78 02 19 00 00 00 7c 00 7c 02 19 00 00 00 7c 02 7a 05 00 00 7a | .|.d.z...x.x.....|.|.....|.z...z |
| 2ac0 | 0d 00 00 63 03 63 02 3c 00 00 00 8c 25 04 00 7c 01 53 00 29 04 61 fd 02 00 00 4d 75 6c 74 69 70 | ...c.c.<....%..|.S.).a....Multip |
| 2ae0 | 6c 79 20 61 20 48 65 72 6d 69 74 65 20 73 65 72 69 65 73 20 62 79 20 78 2e 0a 0a 20 20 20 20 4d | ly.a.Hermite.series.by.x.......M |
| 2b00 | 75 6c 74 69 70 6c 79 20 74 68 65 20 48 65 72 6d 69 74 65 20 73 65 72 69 65 73 20 60 63 60 20 62 | ultiply.the.Hermite.series.`c`.b |
| 2b20 | 79 20 78 2c 20 77 68 65 72 65 20 78 20 69 73 20 74 68 65 20 69 6e 64 65 70 65 6e 64 65 6e 74 0a | y.x,.where.x.is.the.independent. |
| 2b40 | 20 20 20 20 76 61 72 69 61 62 6c 65 2e 0a 0a 0a 20 20 20 20 50 61 72 61 6d 65 74 65 72 73 0a 20 | ....variable........Parameters.. |
| 2b60 | 20 20 20 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 63 20 3a 20 61 72 72 61 79 5f 6c 69 6b 65 | ...----------.....c.:.array_like |
| 2b80 | 0a 20 20 20 20 20 20 20 20 31 2d 44 20 61 72 72 61 79 20 6f 66 20 48 65 72 6d 69 74 65 20 73 65 | .........1-D.array.of.Hermite.se |
| 2ba0 | 72 69 65 73 20 63 6f 65 66 66 69 63 69 65 6e 74 73 20 6f 72 64 65 72 65 64 20 66 72 6f 6d 20 6c | ries.coefficients.ordered.from.l |
| 2bc0 | 6f 77 20 74 6f 0a 20 20 20 20 20 20 20 20 68 69 67 68 2e 0a 0a 20 20 20 20 52 65 74 75 72 6e 73 | ow.to.........high.......Returns |
| 2be0 | 0a 20 20 20 20 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 6f 75 74 20 3a 20 6e 64 61 72 72 61 79 0a 20 | .....-------.....out.:.ndarray.. |
| 2c00 | 20 20 20 20 20 20 20 41 72 72 61 79 20 72 65 70 72 65 73 65 6e 74 69 6e 67 20 74 68 65 20 72 65 | .......Array.representing.the.re |
| 2c20 | 73 75 6c 74 20 6f 66 20 74 68 65 20 6d 75 6c 74 69 70 6c 69 63 61 74 69 6f 6e 2e 0a 0a 20 20 20 | sult.of.the.multiplication...... |
| 2c40 | 20 53 65 65 20 41 6c 73 6f 0a 20 20 20 20 2d 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 68 65 72 6d 65 | .See.Also.....--------.....herme |
| 2c60 | 61 64 64 2c 20 68 65 72 6d 65 73 75 62 2c 20 68 65 72 6d 65 6d 75 6c 2c 20 68 65 72 6d 65 64 69 | add,.hermesub,.hermemul,.hermedi |
| 2c80 | 76 2c 20 68 65 72 6d 65 70 6f 77 0a 0a 20 20 20 20 4e 6f 74 65 73 0a 20 20 20 20 2d 2d 2d 2d 2d | v,.hermepow......Notes.....----- |
| 2ca0 | 0a 20 20 20 20 54 68 65 20 6d 75 6c 74 69 70 6c 69 63 61 74 69 6f 6e 20 75 73 65 73 20 74 68 65 | .....The.multiplication.uses.the |
| 2cc0 | 20 72 65 63 75 72 73 69 6f 6e 20 72 65 6c 61 74 69 6f 6e 73 68 69 70 20 66 6f 72 20 48 65 72 6d | .recursion.relationship.for.Herm |
| 2ce0 | 69 74 65 0a 20 20 20 20 70 6f 6c 79 6e 6f 6d 69 61 6c 73 20 69 6e 20 74 68 65 20 66 6f 72 6d 0a | ite.....polynomials.in.the.form. |
| 2d00 | 0a 20 20 20 20 2e 2e 20 6d 61 74 68 3a 3a 0a 0a 20 20 20 20 20 20 20 20 78 50 5f 69 28 78 29 20 | ........math::..........xP_i(x). |
| 2d20 | 3d 20 28 50 5f 7b 69 20 2b 20 31 7d 28 78 29 20 2b 20 69 50 5f 7b 69 20 2d 20 31 7d 28 78 29 29 | =.(P_{i.+.1}(x).+.iP_{i.-.1}(x)) |
| 2d40 | 29 0a 0a 20 20 20 20 45 78 61 6d 70 6c 65 73 0a 20 20 20 20 2d 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 | )......Examples.....--------.... |
| 2d60 | 20 3e 3e 3e 20 66 72 6f 6d 20 6e 75 6d 70 79 2e 70 6f 6c 79 6e 6f 6d 69 61 6c 2e 68 65 72 6d 69 | .>>>.from.numpy.polynomial.hermi |
| 2d80 | 74 65 5f 65 20 69 6d 70 6f 72 74 20 68 65 72 6d 65 6d 75 6c 78 0a 20 20 20 20 3e 3e 3e 20 68 65 | te_e.import.hermemulx.....>>>.he |
| 2da0 | 72 6d 65 6d 75 6c 78 28 5b 31 2c 20 32 2c 20 33 5d 29 0a 20 20 20 20 61 72 72 61 79 28 5b 32 2e | rmemulx([1,.2,.3]).....array([2. |
| 2dc0 | 2c 20 20 37 2e 2c 20 20 32 2e 2c 20 20 33 2e 5d 29 0a 0a 20 20 20 20 72 04 00 00 00 72 02 00 00 | ,..7.,..2.,..3.])......r....r... |
| 2de0 | 00 a9 01 da 05 64 74 79 70 65 29 07 72 28 00 00 00 72 29 00 00 00 72 2a 00 00 00 72 40 00 00 00 | .....dtype).r(...r)...r*...r@... |
| 2e00 | da 05 65 6d 70 74 79 72 50 00 00 00 72 2b 00 00 00 29 03 72 39 00 00 00 da 03 70 72 64 72 2f 00 | ..emptyrP...r+...).r9.....prdr/. |
| 2e20 | 00 00 73 03 00 00 00 20 20 20 72 30 00 00 00 72 0e 00 00 00 72 0e 00 00 00 8a 01 00 00 73 b7 00 | ..s.......r0...r....r........s.. |
| 2e40 | 00 00 80 00 f4 4e 01 00 0b 0d 8f 2c 89 2c 98 01 90 73 d3 0a 1b 81 43 80 51 e4 07 0a 88 31 83 76 | .....N.....,.,...s....C.Q....1.v |
| 2e60 | 90 11 82 7b 90 71 98 11 91 74 98 71 92 79 d8 0f 10 88 08 e4 0a 0c 8f 28 89 28 94 33 90 71 93 36 | ...{.q...t.q.y.........(.(.3.q.6 |
| 2e80 | 98 41 91 3a a0 51 a7 57 a1 57 d4 0a 2d 80 43 d8 0d 0e 88 71 89 54 90 41 89 58 80 43 88 01 81 46 | .A.:.Q.W.W..-.C....q.T.A.X.C...F |
| 2ea0 | d8 0d 0e 88 71 89 54 80 43 88 01 81 46 dc 0d 12 90 31 94 63 98 21 93 66 d3 0d 1d f2 00 02 05 1f | ....q.T.C...F....1.c.!.f........ |
| 2ec0 | 88 01 d8 15 16 90 71 91 54 88 03 88 41 90 01 89 45 89 0a d8 08 0b 88 41 90 01 89 45 8b 0a 90 61 | ......q.T...A...E......A...E...a |
| 2ee0 | 98 01 91 64 98 51 91 68 d1 08 1e 8c 0a f0 05 02 05 1f f0 06 00 0c 0f 80 4a 72 31 00 00 00 63 02 | ...d.Q.h................Jr1...c. |
| 2f00 | 00 00 00 00 00 00 00 00 00 00 00 07 00 00 00 03 00 00 00 f3 ea 01 00 00 97 00 74 01 00 00 00 00 | ..........................t..... |
| 2f20 | 00 00 00 00 6a 02 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 7c 00 7c 01 67 02 ab 01 | ....j...................|.|.g... |
| 2f40 | 00 00 00 00 00 00 5c 02 00 00 7d 00 7d 01 74 05 00 00 00 00 00 00 00 00 7c 00 ab 01 00 00 00 00 | ......\...}.}.t.........|....... |
| 2f60 | 00 00 74 05 00 00 00 00 00 00 00 00 7c 01 ab 01 00 00 00 00 00 00 6b 44 00 00 72 05 7c 01 7d 02 | ..t.........|.........kD..r.|.}. |
| 2f80 | 7c 00 7d 03 6e 04 7c 00 7d 02 7c 01 7d 03 74 05 00 00 00 00 00 00 00 00 7c 02 ab 01 00 00 00 00 | |.}.n.|.}.|.}.t.........|....... |
| 2fa0 | 00 00 64 01 6b 28 00 00 72 0b 7c 02 64 02 19 00 00 00 7c 03 7a 05 00 00 7d 04 64 02 7d 00 6e 8c | ..d.k(..r.|.d.....|.z...}.d.}.n. |
| 2fc0 | 74 05 00 00 00 00 00 00 00 00 7c 02 ab 01 00 00 00 00 00 00 64 03 6b 28 00 00 72 11 7c 02 64 02 | t.........|.........d.k(..r.|.d. |
| 2fe0 | 19 00 00 00 7c 03 7a 05 00 00 7d 04 7c 02 64 01 19 00 00 00 7c 03 7a 05 00 00 7d 00 6e 6d 74 05 | ....|.z...}.|.d.....|.z...}.nmt. |
| 3000 | 00 00 00 00 00 00 00 00 7c 02 ab 01 00 00 00 00 00 00 7d 05 7c 02 64 04 19 00 00 00 7c 03 7a 05 | ........|.........}.|.d.....|.z. |
| 3020 | 00 00 7d 04 7c 02 64 05 19 00 00 00 7c 03 7a 05 00 00 7d 00 74 07 00 00 00 00 00 00 00 00 64 06 | ..}.|.d.....|.z...}.t.........d. |
| 3040 | 74 05 00 00 00 00 00 00 00 00 7c 02 ab 01 00 00 00 00 00 00 64 01 7a 00 00 00 ab 02 00 00 00 00 | t.........|.........d.z......... |
| 3060 | 00 00 44 00 5d 37 00 00 7d 06 7c 04 7d 07 7c 05 64 01 7a 0a 00 00 7d 05 74 09 00 00 00 00 00 00 | ..D.]7..}.|.}.|.d.z...}.t....... |
| 3080 | 00 00 7c 02 7c 06 0b 00 19 00 00 00 7c 03 7a 05 00 00 7c 00 7c 05 64 01 7a 0a 00 00 7a 05 00 00 | ..|.|.......|.z...|.|.d.z...z... |
| 30a0 | ab 02 00 00 00 00 00 00 7d 04 74 0b 00 00 00 00 00 00 00 00 7c 07 74 0d 00 00 00 00 00 00 00 00 | ........}.t.........|.t......... |
| 30c0 | 7c 00 ab 01 00 00 00 00 00 00 ab 02 00 00 00 00 00 00 7d 00 8c 39 04 00 74 0b 00 00 00 00 00 00 | |.................}..9..t....... |
| 30e0 | 00 00 7c 04 74 0d 00 00 00 00 00 00 00 00 7c 00 ab 01 00 00 00 00 00 00 ab 02 00 00 00 00 00 00 | ..|.t.........|................. |
| 3100 | 53 00 29 07 61 5a 04 00 00 0a 20 20 20 20 4d 75 6c 74 69 70 6c 79 20 6f 6e 65 20 48 65 72 6d 69 | S.).aZ........Multiply.one.Hermi |
| 3120 | 74 65 20 73 65 72 69 65 73 20 62 79 20 61 6e 6f 74 68 65 72 2e 0a 0a 20 20 20 20 52 65 74 75 72 | te.series.by.another.......Retur |
| 3140 | 6e 73 20 74 68 65 20 70 72 6f 64 75 63 74 20 6f 66 20 74 77 6f 20 48 65 72 6d 69 74 65 20 73 65 | ns.the.product.of.two.Hermite.se |
| 3160 | 72 69 65 73 20 60 63 31 60 20 2a 20 60 63 32 60 2e 20 20 54 68 65 20 61 72 67 75 6d 65 6e 74 73 | ries.`c1`.*.`c2`...The.arguments |
| 3180 | 0a 20 20 20 20 61 72 65 20 73 65 71 75 65 6e 63 65 73 20 6f 66 20 63 6f 65 66 66 69 63 69 65 6e | .....are.sequences.of.coefficien |
| 31a0 | 74 73 2c 20 66 72 6f 6d 20 6c 6f 77 65 73 74 20 6f 72 64 65 72 20 22 74 65 72 6d 22 20 74 6f 20 | ts,.from.lowest.order."term".to. |
| 31c0 | 68 69 67 68 65 73 74 2c 0a 20 20 20 20 65 2e 67 2e 2c 20 5b 31 2c 32 2c 33 5d 20 72 65 70 72 65 | highest,.....e.g.,.[1,2,3].repre |
| 31e0 | 73 65 6e 74 73 20 74 68 65 20 73 65 72 69 65 73 20 60 60 50 5f 30 20 2b 20 32 2a 50 5f 31 20 2b | sents.the.series.``P_0.+.2*P_1.+ |
| 3200 | 20 33 2a 50 5f 32 60 60 2e 0a 0a 20 20 20 20 50 61 72 61 6d 65 74 65 72 73 0a 20 20 20 20 2d 2d | .3*P_2``.......Parameters.....-- |
| 3220 | 2d 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 63 31 2c 20 63 32 20 3a 20 61 72 72 61 79 5f 6c 69 6b 65 | --------.....c1,.c2.:.array_like |
| 3240 | 0a 20 20 20 20 20 20 20 20 31 2d 44 20 61 72 72 61 79 73 20 6f 66 20 48 65 72 6d 69 74 65 20 73 | .........1-D.arrays.of.Hermite.s |
| 3260 | 65 72 69 65 73 20 63 6f 65 66 66 69 63 69 65 6e 74 73 20 6f 72 64 65 72 65 64 20 66 72 6f 6d 20 | eries.coefficients.ordered.from. |
| 3280 | 6c 6f 77 20 74 6f 0a 20 20 20 20 20 20 20 20 68 69 67 68 2e 0a 0a 20 20 20 20 52 65 74 75 72 6e | low.to.........high.......Return |
| 32a0 | 73 0a 20 20 20 20 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 6f 75 74 20 3a 20 6e 64 61 72 72 61 79 0a | s.....-------.....out.:.ndarray. |
| 32c0 | 20 20 20 20 20 20 20 20 4f 66 20 48 65 72 6d 69 74 65 20 73 65 72 69 65 73 20 63 6f 65 66 66 69 | ........Of.Hermite.series.coeffi |
| 32e0 | 63 69 65 6e 74 73 20 72 65 70 72 65 73 65 6e 74 69 6e 67 20 74 68 65 69 72 20 70 72 6f 64 75 63 | cients.representing.their.produc |
| 3300 | 74 2e 0a 0a 20 20 20 20 53 65 65 20 41 6c 73 6f 0a 20 20 20 20 2d 2d 2d 2d 2d 2d 2d 2d 0a 20 20 | t.......See.Also.....--------... |
| 3320 | 20 20 68 65 72 6d 65 61 64 64 2c 20 68 65 72 6d 65 73 75 62 2c 20 68 65 72 6d 65 6d 75 6c 78 2c | ..hermeadd,.hermesub,.hermemulx, |
| 3340 | 20 68 65 72 6d 65 64 69 76 2c 20 68 65 72 6d 65 70 6f 77 0a 0a 20 20 20 20 4e 6f 74 65 73 0a 20 | .hermediv,.hermepow......Notes.. |
| 3360 | 20 20 20 2d 2d 2d 2d 2d 0a 20 20 20 20 49 6e 20 67 65 6e 65 72 61 6c 2c 20 74 68 65 20 28 70 6f | ...-----.....In.general,.the.(po |
| 3380 | 6c 79 6e 6f 6d 69 61 6c 29 20 70 72 6f 64 75 63 74 20 6f 66 20 74 77 6f 20 43 2d 73 65 72 69 65 | lynomial).product.of.two.C-serie |
| 33a0 | 73 20 72 65 73 75 6c 74 73 20 69 6e 20 74 65 72 6d 73 0a 20 20 20 20 74 68 61 74 20 61 72 65 20 | s.results.in.terms.....that.are. |
| 33c0 | 6e 6f 74 20 69 6e 20 74 68 65 20 48 65 72 6d 69 74 65 20 70 6f 6c 79 6e 6f 6d 69 61 6c 20 62 61 | not.in.the.Hermite.polynomial.ba |
| 33e0 | 73 69 73 20 73 65 74 2e 20 20 54 68 75 73 2c 20 74 6f 20 65 78 70 72 65 73 73 0a 20 20 20 20 74 | sis.set...Thus,.to.express.....t |
| 3400 | 68 65 20 70 72 6f 64 75 63 74 20 61 73 20 61 20 48 65 72 6d 69 74 65 20 73 65 72 69 65 73 2c 20 | he.product.as.a.Hermite.series,. |
| 3420 | 69 74 20 69 73 20 6e 65 63 65 73 73 61 72 79 20 74 6f 20 22 72 65 70 72 6f 6a 65 63 74 22 20 74 | it.is.necessary.to."reproject".t |
| 3440 | 68 65 0a 20 20 20 20 70 72 6f 64 75 63 74 20 6f 6e 74 6f 20 73 61 69 64 20 62 61 73 69 73 20 73 | he.....product.onto.said.basis.s |
| 3460 | 65 74 2c 20 77 68 69 63 68 20 6d 61 79 20 70 72 6f 64 75 63 65 20 22 75 6e 69 6e 74 75 69 74 69 | et,.which.may.produce."unintuiti |
| 3480 | 76 65 22 20 28 62 75 74 0a 20 20 20 20 63 6f 72 72 65 63 74 29 20 72 65 73 75 6c 74 73 3b 20 73 | ve".(but.....correct).results;.s |
| 34a0 | 65 65 20 45 78 61 6d 70 6c 65 73 20 73 65 63 74 69 6f 6e 20 62 65 6c 6f 77 2e 0a 0a 20 20 20 20 | ee.Examples.section.below....... |
| 34c0 | 45 78 61 6d 70 6c 65 73 0a 20 20 20 20 2d 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 3e 3e 3e 20 66 72 | Examples.....--------.....>>>.fr |
| 34e0 | 6f 6d 20 6e 75 6d 70 79 2e 70 6f 6c 79 6e 6f 6d 69 61 6c 2e 68 65 72 6d 69 74 65 5f 65 20 69 6d | om.numpy.polynomial.hermite_e.im |
| 3500 | 70 6f 72 74 20 68 65 72 6d 65 6d 75 6c 0a 20 20 20 20 3e 3e 3e 20 68 65 72 6d 65 6d 75 6c 28 5b | port.hermemul.....>>>.hermemul([ |
| 3520 | 31 2c 20 32 2c 20 33 5d 2c 20 5b 30 2c 20 31 2c 20 32 5d 29 0a 20 20 20 20 61 72 72 61 79 28 5b | 1,.2,.3],.[0,.1,.2]).....array([ |
| 3540 | 31 34 2e 2c 20 20 31 35 2e 2c 20 20 32 38 2e 2c 20 20 20 37 2e 2c 20 20 20 36 2e 5d 29 0a 0a 20 | 14.,..15.,..28.,...7.,...6.])... |
| 3560 | 20 20 20 72 04 00 00 00 72 02 00 00 00 72 36 00 00 00 72 37 00 00 00 72 27 00 00 00 e9 03 00 00 | ...r....r....r6...r7...r'....... |
| 3580 | 00 29 07 72 28 00 00 00 72 29 00 00 00 72 2a 00 00 00 72 2b 00 00 00 72 0d 00 00 00 72 0c 00 00 | .).r(...r)...r*...r+...r....r... |
| 35a0 | 00 72 0e 00 00 00 29 08 72 3c 00 00 00 72 4a 00 00 00 72 39 00 00 00 da 02 78 73 72 3b 00 00 00 | .r....).r<...rJ...r9.....xsr;... |
| 35c0 | da 02 6e 64 72 2f 00 00 00 72 3d 00 00 00 73 08 00 00 00 20 20 20 20 20 20 20 20 72 30 00 00 00 | ..ndr/...r=...s............r0... |
| 35e0 | 72 0f 00 00 00 72 0f 00 00 00 bf 01 00 00 73 11 01 00 00 80 00 f4 4e 01 00 10 12 8f 7c 89 7c 98 | r....r........s.......N.....|.|. |
| 3600 | 52 a0 12 98 48 d3 0f 25 81 48 80 52 88 12 e4 07 0a 88 32 83 77 94 13 90 52 93 17 d2 07 18 d8 0c | R...H..%.H.R......2.w...R....... |
| 3620 | 0e 88 01 d8 0d 0f 89 02 e0 0c 0e 88 01 d8 0d 0f 88 02 e4 07 0a 88 31 83 76 90 11 82 7b d8 0d 0e | ......................1.v...{... |
| 3640 | 88 71 89 54 90 42 89 59 88 02 d8 0d 0e 89 02 dc 09 0c 88 51 8b 16 90 31 8a 1b d8 0d 0e 88 71 89 | .q.T.B.Y...........Q...1......q. |
| 3660 | 54 90 42 89 59 88 02 d8 0d 0e 88 71 89 54 90 42 89 59 89 02 e4 0d 10 90 11 8b 56 88 02 d8 0d 0e | T.B.Y......q.T.B.Y........V..... |
| 3680 | 88 72 89 55 90 52 89 5a 88 02 d8 0d 0e 88 72 89 55 90 52 89 5a 88 02 dc 11 16 90 71 9c 23 98 61 | .r.U.R.Z......r.U.R.Z......q.#.a |
| 36a0 | 9b 26 a0 31 99 2a d3 11 25 f2 00 04 09 2e 88 41 d8 12 14 88 43 d8 11 13 90 61 91 16 88 42 dc 11 | .&.1.*..%......A....C....a...B.. |
| 36c0 | 19 98 21 98 51 98 42 99 25 a0 22 99 2a a0 62 a8 42 b0 11 a9 46 a1 6d d3 11 34 88 42 dc 11 19 98 | ..!.Q.B.%.".*.b.B...F.m..4.B.... |
| 36e0 | 23 9c 79 a8 12 9b 7d d3 11 2d 89 42 f0 09 04 09 2e f4 0a 00 0c 14 90 42 9c 09 a0 22 9b 0d d3 0b | #.y...}..-.B...........B...".... |
| 3700 | 26 d0 04 26 72 31 00 00 00 63 02 00 00 00 00 00 00 00 00 00 00 00 05 00 00 00 03 00 00 00 f3 38 | &..&r1...c.....................8 |
| 3720 | 00 00 00 97 00 74 01 00 00 00 00 00 00 00 00 6a 02 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 | .....t.........j................ |
| 3740 | 00 00 00 74 04 00 00 00 00 00 00 00 00 7c 00 7c 01 ab 03 00 00 00 00 00 00 53 00 29 01 61 38 05 | ...t.........|.|.........S.).a8. |
| 3760 | 00 00 0a 20 20 20 20 44 69 76 69 64 65 20 6f 6e 65 20 48 65 72 6d 69 74 65 20 73 65 72 69 65 73 | .......Divide.one.Hermite.series |
| 3780 | 20 62 79 20 61 6e 6f 74 68 65 72 2e 0a 0a 20 20 20 20 52 65 74 75 72 6e 73 20 74 68 65 20 71 75 | .by.another.......Returns.the.qu |
| 37a0 | 6f 74 69 65 6e 74 2d 77 69 74 68 2d 72 65 6d 61 69 6e 64 65 72 20 6f 66 20 74 77 6f 20 48 65 72 | otient-with-remainder.of.two.Her |
| 37c0 | 6d 69 74 65 20 73 65 72 69 65 73 0a 20 20 20 20 60 63 31 60 20 2f 20 60 63 32 60 2e 20 20 54 68 | mite.series.....`c1`./.`c2`...Th |
| 37e0 | 65 20 61 72 67 75 6d 65 6e 74 73 20 61 72 65 20 73 65 71 75 65 6e 63 65 73 20 6f 66 20 63 6f 65 | e.arguments.are.sequences.of.coe |
| 3800 | 66 66 69 63 69 65 6e 74 73 20 66 72 6f 6d 20 6c 6f 77 65 73 74 0a 20 20 20 20 6f 72 64 65 72 20 | fficients.from.lowest.....order. |
| 3820 | 22 74 65 72 6d 22 20 74 6f 20 68 69 67 68 65 73 74 2c 20 65 2e 67 2e 2c 20 5b 31 2c 32 2c 33 5d | "term".to.highest,.e.g.,.[1,2,3] |
| 3840 | 20 72 65 70 72 65 73 65 6e 74 73 20 74 68 65 20 73 65 72 69 65 73 0a 20 20 20 20 60 60 50 5f 30 | .represents.the.series.....``P_0 |
| 3860 | 20 2b 20 32 2a 50 5f 31 20 2b 20 33 2a 50 5f 32 60 60 2e 0a 0a 20 20 20 20 50 61 72 61 6d 65 74 | .+.2*P_1.+.3*P_2``.......Paramet |
| 3880 | 65 72 73 0a 20 20 20 20 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 63 31 2c 20 63 32 20 3a 20 | ers.....----------.....c1,.c2.:. |
| 38a0 | 61 72 72 61 79 5f 6c 69 6b 65 0a 20 20 20 20 20 20 20 20 31 2d 44 20 61 72 72 61 79 73 20 6f 66 | array_like.........1-D.arrays.of |
| 38c0 | 20 48 65 72 6d 69 74 65 20 73 65 72 69 65 73 20 63 6f 65 66 66 69 63 69 65 6e 74 73 20 6f 72 64 | .Hermite.series.coefficients.ord |
| 38e0 | 65 72 65 64 20 66 72 6f 6d 20 6c 6f 77 20 74 6f 0a 20 20 20 20 20 20 20 20 68 69 67 68 2e 0a 0a | ered.from.low.to.........high... |
| 3900 | 20 20 20 20 52 65 74 75 72 6e 73 0a 20 20 20 20 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 5b 71 75 6f | ....Returns.....-------.....[quo |
| 3920 | 2c 20 72 65 6d 5d 20 3a 20 6e 64 61 72 72 61 79 73 0a 20 20 20 20 20 20 20 20 4f 66 20 48 65 72 | ,.rem].:.ndarrays.........Of.Her |
| 3940 | 6d 69 74 65 20 73 65 72 69 65 73 20 63 6f 65 66 66 69 63 69 65 6e 74 73 20 72 65 70 72 65 73 65 | mite.series.coefficients.represe |
| 3960 | 6e 74 69 6e 67 20 74 68 65 20 71 75 6f 74 69 65 6e 74 20 61 6e 64 0a 20 20 20 20 20 20 20 20 72 | nting.the.quotient.and.........r |
| 3980 | 65 6d 61 69 6e 64 65 72 2e 0a 0a 20 20 20 20 53 65 65 20 41 6c 73 6f 0a 20 20 20 20 2d 2d 2d 2d | emainder.......See.Also.....---- |
| 39a0 | 2d 2d 2d 2d 0a 20 20 20 20 68 65 72 6d 65 61 64 64 2c 20 68 65 72 6d 65 73 75 62 2c 20 68 65 72 | ----.....hermeadd,.hermesub,.her |
| 39c0 | 6d 65 6d 75 6c 78 2c 20 68 65 72 6d 65 6d 75 6c 2c 20 68 65 72 6d 65 70 6f 77 0a 0a 20 20 20 20 | memulx,.hermemul,.hermepow...... |
| 39e0 | 4e 6f 74 65 73 0a 20 20 20 20 2d 2d 2d 2d 2d 0a 20 20 20 20 49 6e 20 67 65 6e 65 72 61 6c 2c 20 | Notes.....-----.....In.general,. |
| 3a00 | 74 68 65 20 28 70 6f 6c 79 6e 6f 6d 69 61 6c 29 20 64 69 76 69 73 69 6f 6e 20 6f 66 20 6f 6e 65 | the.(polynomial).division.of.one |
| 3a20 | 20 48 65 72 6d 69 74 65 20 73 65 72 69 65 73 20 62 79 20 61 6e 6f 74 68 65 72 0a 20 20 20 20 72 | .Hermite.series.by.another.....r |
| 3a40 | 65 73 75 6c 74 73 20 69 6e 20 71 75 6f 74 69 65 6e 74 20 61 6e 64 20 72 65 6d 61 69 6e 64 65 72 | esults.in.quotient.and.remainder |
| 3a60 | 20 74 65 72 6d 73 20 74 68 61 74 20 61 72 65 20 6e 6f 74 20 69 6e 20 74 68 65 20 48 65 72 6d 69 | .terms.that.are.not.in.the.Hermi |
| 3a80 | 74 65 0a 20 20 20 20 70 6f 6c 79 6e 6f 6d 69 61 6c 20 62 61 73 69 73 20 73 65 74 2e 20 20 54 68 | te.....polynomial.basis.set...Th |
| 3aa0 | 75 73 2c 20 74 6f 20 65 78 70 72 65 73 73 20 74 68 65 73 65 20 72 65 73 75 6c 74 73 20 61 73 20 | us,.to.express.these.results.as. |
| 3ac0 | 61 20 48 65 72 6d 69 74 65 0a 20 20 20 20 73 65 72 69 65 73 2c 20 69 74 20 69 73 20 6e 65 63 65 | a.Hermite.....series,.it.is.nece |
| 3ae0 | 73 73 61 72 79 20 74 6f 20 22 72 65 70 72 6f 6a 65 63 74 22 20 74 68 65 20 72 65 73 75 6c 74 73 | ssary.to."reproject".the.results |
| 3b00 | 20 6f 6e 74 6f 20 74 68 65 20 48 65 72 6d 69 74 65 0a 20 20 20 20 62 61 73 69 73 20 73 65 74 2c | .onto.the.Hermite.....basis.set, |
| 3b20 | 20 77 68 69 63 68 20 6d 61 79 20 70 72 6f 64 75 63 65 20 22 75 6e 69 6e 74 75 69 74 69 76 65 22 | .which.may.produce."unintuitive" |
| 3b40 | 20 28 62 75 74 20 63 6f 72 72 65 63 74 29 20 72 65 73 75 6c 74 73 3b 20 73 65 65 0a 20 20 20 20 | .(but.correct).results;.see..... |
| 3b60 | 45 78 61 6d 70 6c 65 73 20 73 65 63 74 69 6f 6e 20 62 65 6c 6f 77 2e 0a 0a 20 20 20 20 45 78 61 | Examples.section.below.......Exa |
| 3b80 | 6d 70 6c 65 73 0a 20 20 20 20 2d 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 3e 3e 3e 20 66 72 6f 6d 20 | mples.....--------.....>>>.from. |
| 3ba0 | 6e 75 6d 70 79 2e 70 6f 6c 79 6e 6f 6d 69 61 6c 2e 68 65 72 6d 69 74 65 5f 65 20 69 6d 70 6f 72 | numpy.polynomial.hermite_e.impor |
| 3bc0 | 74 20 68 65 72 6d 65 64 69 76 0a 20 20 20 20 3e 3e 3e 20 68 65 72 6d 65 64 69 76 28 5b 20 31 34 | t.hermediv.....>>>.hermediv([.14 |
| 3be0 | 2e 2c 20 20 31 35 2e 2c 20 20 32 38 2e 2c 20 20 20 37 2e 2c 20 20 20 36 2e 5d 2c 20 5b 30 2c 20 | .,..15.,..28.,...7.,...6.],.[0,. |
| 3c00 | 31 2c 20 32 5d 29 0a 20 20 20 20 28 61 72 72 61 79 28 5b 31 2e 2c 20 32 2e 2c 20 33 2e 5d 29 2c | 1,.2]).....(array([1.,.2.,.3.]), |
| 3c20 | 20 61 72 72 61 79 28 5b 30 2e 5d 29 29 0a 20 20 20 20 3e 3e 3e 20 68 65 72 6d 65 64 69 76 28 5b | .array([0.])).....>>>.hermediv([ |
| 3c40 | 20 31 35 2e 2c 20 20 31 37 2e 2c 20 20 32 38 2e 2c 20 20 20 37 2e 2c 20 20 20 36 2e 5d 2c 20 5b | .15.,..17.,..28.,...7.,...6.],.[ |
| 3c60 | 30 2c 20 31 2c 20 32 5d 29 0a 20 20 20 20 28 61 72 72 61 79 28 5b 31 2e 2c 20 32 2e 2c 20 33 2e | 0,.1,.2]).....(array([1.,.2.,.3. |
| 3c80 | 5d 29 2c 20 61 72 72 61 79 28 5b 31 2e 2c 20 32 2e 5d 29 29 0a 0a 20 20 20 20 29 03 72 28 00 00 | ]),.array([1.,.2.]))......).r(.. |
| 3ca0 | 00 da 04 5f 64 69 76 72 0f 00 00 00 72 49 00 00 00 73 02 00 00 00 20 20 72 30 00 00 00 72 10 00 | ..._divr....rI...s......r0...r.. |
| 3cc0 | 00 00 72 10 00 00 00 01 02 00 00 73 18 00 00 00 80 00 f4 56 01 00 0c 0e 8f 37 89 37 94 38 98 52 | ..r........s.......V.....7.7.8.R |
| 3ce0 | a0 12 d3 0b 24 d0 04 24 72 31 00 00 00 63 03 00 00 00 00 00 00 00 00 00 00 00 06 00 00 00 03 00 | ....$..$r1...c.................. |
| 3d00 | 00 00 f3 3a 00 00 00 97 00 74 01 00 00 00 00 00 00 00 00 6a 02 00 00 00 00 00 00 00 00 00 00 00 | ...:.....t.........j............ |
| 3d20 | 00 00 00 00 00 00 00 74 04 00 00 00 00 00 00 00 00 7c 00 7c 01 7c 02 ab 04 00 00 00 00 00 00 53 | .......t.........|.|.|.........S |
| 3d40 | 00 29 01 61 88 03 00 00 52 61 69 73 65 20 61 20 48 65 72 6d 69 74 65 20 73 65 72 69 65 73 20 74 | .).a....Raise.a.Hermite.series.t |
| 3d60 | 6f 20 61 20 70 6f 77 65 72 2e 0a 0a 20 20 20 20 52 65 74 75 72 6e 73 20 74 68 65 20 48 65 72 6d | o.a.power.......Returns.the.Herm |
| 3d80 | 69 74 65 20 73 65 72 69 65 73 20 60 63 60 20 72 61 69 73 65 64 20 74 6f 20 74 68 65 20 70 6f 77 | ite.series.`c`.raised.to.the.pow |
| 3da0 | 65 72 20 60 70 6f 77 60 2e 20 54 68 65 0a 20 20 20 20 61 72 67 75 6d 65 6e 74 20 60 63 60 20 69 | er.`pow`..The.....argument.`c`.i |
| 3dc0 | 73 20 61 20 73 65 71 75 65 6e 63 65 20 6f 66 20 63 6f 65 66 66 69 63 69 65 6e 74 73 20 6f 72 64 | s.a.sequence.of.coefficients.ord |
| 3de0 | 65 72 65 64 20 66 72 6f 6d 20 6c 6f 77 20 74 6f 20 68 69 67 68 2e 0a 20 20 20 20 69 2e 65 2e 2c | ered.from.low.to.high......i.e., |
| 3e00 | 20 5b 31 2c 32 2c 33 5d 20 69 73 20 74 68 65 20 73 65 72 69 65 73 20 20 60 60 50 5f 30 20 2b 20 | .[1,2,3].is.the.series..``P_0.+. |
| 3e20 | 32 2a 50 5f 31 20 2b 20 33 2a 50 5f 32 2e 60 60 0a 0a 20 20 20 20 50 61 72 61 6d 65 74 65 72 73 | 2*P_1.+.3*P_2.``......Parameters |
| 3e40 | 0a 20 20 20 20 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 63 20 3a 20 61 72 72 61 79 5f 6c 69 | .....----------.....c.:.array_li |
| 3e60 | 6b 65 0a 20 20 20 20 20 20 20 20 31 2d 44 20 61 72 72 61 79 20 6f 66 20 48 65 72 6d 69 74 65 20 | ke.........1-D.array.of.Hermite. |
| 3e80 | 73 65 72 69 65 73 20 63 6f 65 66 66 69 63 69 65 6e 74 73 20 6f 72 64 65 72 65 64 20 66 72 6f 6d | series.coefficients.ordered.from |
| 3ea0 | 20 6c 6f 77 20 74 6f 0a 20 20 20 20 20 20 20 20 68 69 67 68 2e 0a 20 20 20 20 70 6f 77 20 3a 20 | .low.to.........high......pow.:. |
| 3ec0 | 69 6e 74 65 67 65 72 0a 20 20 20 20 20 20 20 20 50 6f 77 65 72 20 74 6f 20 77 68 69 63 68 20 74 | integer.........Power.to.which.t |
| 3ee0 | 68 65 20 73 65 72 69 65 73 20 77 69 6c 6c 20 62 65 20 72 61 69 73 65 64 0a 20 20 20 20 6d 61 78 | he.series.will.be.raised.....max |
| 3f00 | 70 6f 77 65 72 20 3a 20 69 6e 74 65 67 65 72 2c 20 6f 70 74 69 6f 6e 61 6c 0a 20 20 20 20 20 20 | power.:.integer,.optional....... |
| 3f20 | 20 20 4d 61 78 69 6d 75 6d 20 70 6f 77 65 72 20 61 6c 6c 6f 77 65 64 2e 20 54 68 69 73 20 69 73 | ..Maximum.power.allowed..This.is |
| 3f40 | 20 6d 61 69 6e 6c 79 20 74 6f 20 6c 69 6d 69 74 20 67 72 6f 77 74 68 20 6f 66 20 74 68 65 20 73 | .mainly.to.limit.growth.of.the.s |
| 3f60 | 65 72 69 65 73 0a 20 20 20 20 20 20 20 20 74 6f 20 75 6e 6d 61 6e 61 67 65 61 62 6c 65 20 73 69 | eries.........to.unmanageable.si |
| 3f80 | 7a 65 2e 20 44 65 66 61 75 6c 74 20 69 73 20 31 36 0a 0a 20 20 20 20 52 65 74 75 72 6e 73 0a 20 | ze..Default.is.16......Returns.. |
| 3fa0 | 20 20 20 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 63 6f 65 66 20 3a 20 6e 64 61 72 72 61 79 0a 20 20 | ...-------.....coef.:.ndarray... |
| 3fc0 | 20 20 20 20 20 20 48 65 72 6d 69 74 65 20 73 65 72 69 65 73 20 6f 66 20 70 6f 77 65 72 2e 0a 0a | ......Hermite.series.of.power... |
| 3fe0 | 20 20 20 20 53 65 65 20 41 6c 73 6f 0a 20 20 20 20 2d 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 68 65 | ....See.Also.....--------.....he |
| 4000 | 72 6d 65 61 64 64 2c 20 68 65 72 6d 65 73 75 62 2c 20 68 65 72 6d 65 6d 75 6c 78 2c 20 68 65 72 | rmeadd,.hermesub,.hermemulx,.her |
| 4020 | 6d 65 6d 75 6c 2c 20 68 65 72 6d 65 64 69 76 0a 0a 20 20 20 20 45 78 61 6d 70 6c 65 73 0a 20 20 | memul,.hermediv......Examples... |
| 4040 | 20 20 2d 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 3e 3e 3e 20 66 72 6f 6d 20 6e 75 6d 70 79 2e 70 6f | ..--------.....>>>.from.numpy.po |
| 4060 | 6c 79 6e 6f 6d 69 61 6c 2e 68 65 72 6d 69 74 65 5f 65 20 69 6d 70 6f 72 74 20 68 65 72 6d 65 70 | lynomial.hermite_e.import.hermep |
| 4080 | 6f 77 0a 20 20 20 20 3e 3e 3e 20 68 65 72 6d 65 70 6f 77 28 5b 31 2c 20 32 2c 20 33 5d 2c 20 32 | ow.....>>>.hermepow([1,.2,.3],.2 |
| 40a0 | 29 0a 20 20 20 20 61 72 72 61 79 28 5b 32 33 2e 2c 20 20 32 38 2e 2c 20 20 34 36 2e 2c 20 20 31 | ).....array([23.,..28.,..46.,..1 |
| 40c0 | 32 2e 2c 20 20 20 39 2e 5d 29 0a 0a 20 20 20 20 29 03 72 28 00 00 00 da 04 5f 70 6f 77 72 0f 00 | 2.,...9.])......).r(....._powr.. |
| 40e0 | 00 00 29 03 72 39 00 00 00 da 03 70 6f 77 da 08 6d 61 78 70 6f 77 65 72 73 03 00 00 00 20 20 20 | ..).r9.....pow..maxpowers....... |
| 4100 | 72 30 00 00 00 72 11 00 00 00 72 11 00 00 00 2f 02 00 00 73 1a 00 00 00 80 00 f4 44 01 00 0c 0e | r0...r....r..../...s.......D.... |
| 4120 | 8f 37 89 37 94 38 98 51 a0 03 a0 58 d3 0b 2e d0 04 2e 72 31 00 00 00 63 04 00 00 00 00 00 00 00 | .7.7.8.Q...X......r1...c........ |
| 4140 | 00 00 00 00 07 00 00 00 03 00 00 00 f3 be 02 00 00 97 00 74 01 00 00 00 00 00 00 00 00 6a 02 00 | ...................t.........j.. |
| 4160 | 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 7c 00 64 01 64 02 ac 03 ab 03 00 00 00 00 00 | .................|.d.d.......... |
| 4180 | 00 7d 00 7c 00 6a 04 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 6a 06 00 00 00 00 00 | .}.|.j...................j...... |
| 41a0 | 00 00 00 00 00 00 00 00 00 00 00 00 00 64 04 76 00 72 1f 7c 00 6a 09 00 00 00 00 00 00 00 00 00 | .............d.v.r.|.j.......... |
| 41c0 | 00 00 00 00 00 00 00 00 00 74 00 00 00 00 00 00 00 00 00 6a 0a 00 00 00 00 00 00 00 00 00 00 00 | .........t.........j............ |
| 41e0 | 00 00 00 00 00 00 00 ab 01 00 00 00 00 00 00 7d 00 74 0d 00 00 00 00 00 00 00 00 6a 0e 00 00 00 | ...............}.t.........j.... |
| 4200 | 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 7c 01 64 05 ab 02 00 00 00 00 00 00 7d 04 74 0d 00 | ...............|.d.........}.t.. |
| 4220 | 00 00 00 00 00 00 00 6a 0e 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 7c 03 64 06 ab | .......j...................|.d.. |
| 4240 | 02 00 00 00 00 00 00 7d 05 7c 04 64 07 6b 02 00 00 72 0b 74 11 00 00 00 00 00 00 00 00 64 08 ab | .......}.|.d.k...r.t.........d.. |
| 4260 | 01 00 00 00 00 00 00 82 01 74 13 00 00 00 00 00 00 00 00 7c 05 7c 00 6a 14 00 00 00 00 00 00 00 | .........t.........|.|.j........ |
| 4280 | 00 00 00 00 00 00 00 00 00 00 00 ab 02 00 00 00 00 00 00 7d 05 7c 04 64 07 6b 28 00 00 72 02 7c | ...................}.|.d.k(..r.| |
| 42a0 | 00 53 00 74 01 00 00 00 00 00 00 00 00 6a 16 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 | .S.t.........j.................. |
| 42c0 | 00 7c 00 7c 05 64 07 ab 03 00 00 00 00 00 00 7d 00 74 19 00 00 00 00 00 00 00 00 7c 00 ab 01 00 | .|.|.d.........}.t.........|.... |
| 42e0 | 00 00 00 00 00 7d 06 7c 04 7c 06 6b 5c 00 00 72 08 7c 00 64 09 64 01 1a 00 64 07 7a 05 00 00 53 | .....}.|.|.k\..r.|.d.d...d.z...S |
| 4300 | 00 74 1b 00 00 00 00 00 00 00 00 7c 04 ab 01 00 00 00 00 00 00 44 00 5d 60 00 00 7d 07 7c 06 64 | .t.........|.........D.]`..}.|.d |
| 4320 | 01 7a 0a 00 00 7d 06 7c 00 7c 02 7a 12 00 00 7d 00 74 01 00 00 00 00 00 00 00 00 6a 1c 00 00 00 | .z...}.|.|.z...}.t.........j.... |
| 4340 | 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 7c 06 66 01 7c 00 6a 1e 00 00 00 00 00 00 00 00 00 | ...............|.f.|.j.......... |
| 4360 | 00 00 00 00 00 00 00 00 00 64 01 64 09 1a 00 7a 00 00 00 7c 00 6a 04 00 00 00 00 00 00 00 00 00 | .........d.d...z...|.j.......... |
| 4380 | 00 00 00 00 00 00 00 00 00 ac 0a ab 02 00 00 00 00 00 00 7d 08 74 1b 00 00 00 00 00 00 00 00 7c | ...................}.t.........| |
| 43a0 | 06 64 07 64 0b ab 03 00 00 00 00 00 00 44 00 5d 10 00 00 7d 09 7c 09 7c 00 7c 09 19 00 00 00 7a | .d.d.........D.]...}.|.|.|.....z |
| 43c0 | 05 00 00 7c 08 7c 09 64 01 7a 0a 00 00 3c 00 00 00 8c 12 04 00 7c 08 7d 00 8c 62 04 00 74 01 00 | ...|.|.d.z...<.......|.}..b..t.. |
| 43e0 | 00 00 00 00 00 00 00 6a 16 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 7c 00 64 07 7c | .......j...................|.d.| |
| 4400 | 05 ab 03 00 00 00 00 00 00 7d 00 7c 00 53 00 29 0c 61 25 07 00 00 0a 20 20 20 20 44 69 66 66 65 | .........}.|.S.).a%........Diffe |
| 4420 | 72 65 6e 74 69 61 74 65 20 61 20 48 65 72 6d 69 74 65 5f 65 20 73 65 72 69 65 73 2e 0a 0a 20 20 | rentiate.a.Hermite_e.series..... |
| 4440 | 20 20 52 65 74 75 72 6e 73 20 74 68 65 20 73 65 72 69 65 73 20 63 6f 65 66 66 69 63 69 65 6e 74 | ..Returns.the.series.coefficient |
| 4460 | 73 20 60 63 60 20 64 69 66 66 65 72 65 6e 74 69 61 74 65 64 20 60 6d 60 20 74 69 6d 65 73 20 61 | s.`c`.differentiated.`m`.times.a |
| 4480 | 6c 6f 6e 67 0a 20 20 20 20 60 61 78 69 73 60 2e 20 20 41 74 20 65 61 63 68 20 69 74 65 72 61 74 | long.....`axis`...At.each.iterat |
| 44a0 | 69 6f 6e 20 74 68 65 20 72 65 73 75 6c 74 20 69 73 20 6d 75 6c 74 69 70 6c 69 65 64 20 62 79 20 | ion.the.result.is.multiplied.by. |
| 44c0 | 60 73 63 6c 60 20 28 74 68 65 0a 20 20 20 20 73 63 61 6c 69 6e 67 20 66 61 63 74 6f 72 20 69 73 | `scl`.(the.....scaling.factor.is |
| 44e0 | 20 66 6f 72 20 75 73 65 20 69 6e 20 61 20 6c 69 6e 65 61 72 20 63 68 61 6e 67 65 20 6f 66 20 76 | .for.use.in.a.linear.change.of.v |
| 4500 | 61 72 69 61 62 6c 65 29 2e 20 54 68 65 20 61 72 67 75 6d 65 6e 74 0a 20 20 20 20 60 63 60 20 69 | ariable)..The.argument.....`c`.i |
| 4520 | 73 20 61 6e 20 61 72 72 61 79 20 6f 66 20 63 6f 65 66 66 69 63 69 65 6e 74 73 20 66 72 6f 6d 20 | s.an.array.of.coefficients.from. |
| 4540 | 6c 6f 77 20 74 6f 20 68 69 67 68 20 64 65 67 72 65 65 20 61 6c 6f 6e 67 20 65 61 63 68 0a 20 20 | low.to.high.degree.along.each... |
| 4560 | 20 20 61 78 69 73 2c 20 65 2e 67 2e 2c 20 5b 31 2c 32 2c 33 5d 20 72 65 70 72 65 73 65 6e 74 73 | ..axis,.e.g.,.[1,2,3].represents |
| 4580 | 20 74 68 65 20 73 65 72 69 65 73 20 60 60 31 2a 48 65 5f 30 20 2b 20 32 2a 48 65 5f 31 20 2b 20 | .the.series.``1*He_0.+.2*He_1.+. |
| 45a0 | 33 2a 48 65 5f 32 60 60 0a 20 20 20 20 77 68 69 6c 65 20 5b 5b 31 2c 32 5d 2c 5b 31 2c 32 5d 5d | 3*He_2``.....while.[[1,2],[1,2]] |
| 45c0 | 20 72 65 70 72 65 73 65 6e 74 73 20 60 60 31 2a 48 65 5f 30 28 78 29 2a 48 65 5f 30 28 79 29 20 | .represents.``1*He_0(x)*He_0(y). |
| 45e0 | 2b 20 31 2a 48 65 5f 31 28 78 29 2a 48 65 5f 30 28 79 29 0a 20 20 20 20 2b 20 32 2a 48 65 5f 30 | +.1*He_1(x)*He_0(y).....+.2*He_0 |
| 4600 | 28 78 29 2a 48 65 5f 31 28 79 29 20 2b 20 32 2a 48 65 5f 31 28 78 29 2a 48 65 5f 31 28 79 29 60 | (x)*He_1(y).+.2*He_1(x)*He_1(y)` |
| 4620 | 60 20 69 66 20 61 78 69 73 3d 30 20 69 73 20 60 60 78 60 60 20 61 6e 64 20 61 78 69 73 3d 31 0a | `.if.axis=0.is.``x``.and.axis=1. |
| 4640 | 20 20 20 20 69 73 20 60 60 79 60 60 2e 0a 0a 20 20 20 20 50 61 72 61 6d 65 74 65 72 73 0a 20 20 | ....is.``y``.......Parameters... |
| 4660 | 20 20 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 63 20 3a 20 61 72 72 61 79 5f 6c 69 6b 65 0a | ..----------.....c.:.array_like. |
| 4680 | 20 20 20 20 20 20 20 20 41 72 72 61 79 20 6f 66 20 48 65 72 6d 69 74 65 5f 65 20 73 65 72 69 65 | ........Array.of.Hermite_e.serie |
| 46a0 | 73 20 63 6f 65 66 66 69 63 69 65 6e 74 73 2e 20 49 66 20 60 63 60 20 69 73 20 6d 75 6c 74 69 64 | s.coefficients..If.`c`.is.multid |
| 46c0 | 69 6d 65 6e 73 69 6f 6e 61 6c 0a 20 20 20 20 20 20 20 20 74 68 65 20 64 69 66 66 65 72 65 6e 74 | imensional.........the.different |
| 46e0 | 20 61 78 69 73 20 63 6f 72 72 65 73 70 6f 6e 64 20 74 6f 20 64 69 66 66 65 72 65 6e 74 20 76 61 | .axis.correspond.to.different.va |
| 4700 | 72 69 61 62 6c 65 73 20 77 69 74 68 20 74 68 65 0a 20 20 20 20 20 20 20 20 64 65 67 72 65 65 20 | riables.with.the.........degree. |
| 4720 | 69 6e 20 65 61 63 68 20 61 78 69 73 20 67 69 76 65 6e 20 62 79 20 74 68 65 20 63 6f 72 72 65 73 | in.each.axis.given.by.the.corres |
| 4740 | 70 6f 6e 64 69 6e 67 20 69 6e 64 65 78 2e 0a 20 20 20 20 6d 20 3a 20 69 6e 74 2c 20 6f 70 74 69 | ponding.index......m.:.int,.opti |
| 4760 | 6f 6e 61 6c 0a 20 20 20 20 20 20 20 20 4e 75 6d 62 65 72 20 6f 66 20 64 65 72 69 76 61 74 69 76 | onal.........Number.of.derivativ |
| 4780 | 65 73 20 74 61 6b 65 6e 2c 20 6d 75 73 74 20 62 65 20 6e 6f 6e 2d 6e 65 67 61 74 69 76 65 2e 20 | es.taken,.must.be.non-negative.. |
| 47a0 | 28 44 65 66 61 75 6c 74 3a 20 31 29 0a 20 20 20 20 73 63 6c 20 3a 20 73 63 61 6c 61 72 2c 20 6f | (Default:.1).....scl.:.scalar,.o |
| 47c0 | 70 74 69 6f 6e 61 6c 0a 20 20 20 20 20 20 20 20 45 61 63 68 20 64 69 66 66 65 72 65 6e 74 69 61 | ptional.........Each.differentia |
| 47e0 | 74 69 6f 6e 20 69 73 20 6d 75 6c 74 69 70 6c 69 65 64 20 62 79 20 60 73 63 6c 60 2e 20 20 54 68 | tion.is.multiplied.by.`scl`...Th |
| 4800 | 65 20 65 6e 64 20 72 65 73 75 6c 74 20 69 73 0a 20 20 20 20 20 20 20 20 6d 75 6c 74 69 70 6c 69 | e.end.result.is.........multipli |
| 4820 | 63 61 74 69 6f 6e 20 62 79 20 60 60 73 63 6c 2a 2a 6d 60 60 2e 20 20 54 68 69 73 20 69 73 20 66 | cation.by.``scl**m``...This.is.f |
| 4840 | 6f 72 20 75 73 65 20 69 6e 20 61 20 6c 69 6e 65 61 72 20 63 68 61 6e 67 65 20 6f 66 0a 20 20 20 | or.use.in.a.linear.change.of.... |
| 4860 | 20 20 20 20 20 76 61 72 69 61 62 6c 65 2e 20 28 44 65 66 61 75 6c 74 3a 20 31 29 0a 20 20 20 20 | .....variable..(Default:.1)..... |
| 4880 | 61 78 69 73 20 3a 20 69 6e 74 2c 20 6f 70 74 69 6f 6e 61 6c 0a 20 20 20 20 20 20 20 20 41 78 69 | axis.:.int,.optional.........Axi |
| 48a0 | 73 20 6f 76 65 72 20 77 68 69 63 68 20 74 68 65 20 64 65 72 69 76 61 74 69 76 65 20 69 73 20 74 | s.over.which.the.derivative.is.t |
| 48c0 | 61 6b 65 6e 2e 20 28 44 65 66 61 75 6c 74 3a 20 30 29 2e 0a 0a 20 20 20 20 52 65 74 75 72 6e 73 | aken..(Default:.0).......Returns |
| 48e0 | 0a 20 20 20 20 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 64 65 72 20 3a 20 6e 64 61 72 72 61 79 0a 20 | .....-------.....der.:.ndarray.. |
| 4900 | 20 20 20 20 20 20 20 48 65 72 6d 69 74 65 20 73 65 72 69 65 73 20 6f 66 20 74 68 65 20 64 65 72 | .......Hermite.series.of.the.der |
| 4920 | 69 76 61 74 69 76 65 2e 0a 0a 20 20 20 20 53 65 65 20 41 6c 73 6f 0a 20 20 20 20 2d 2d 2d 2d 2d | ivative.......See.Also.....----- |
| 4940 | 2d 2d 2d 0a 20 20 20 20 68 65 72 6d 65 69 6e 74 0a 0a 20 20 20 20 4e 6f 74 65 73 0a 20 20 20 20 | ---.....hermeint......Notes..... |
| 4960 | 2d 2d 2d 2d 2d 0a 20 20 20 20 49 6e 20 67 65 6e 65 72 61 6c 2c 20 74 68 65 20 72 65 73 75 6c 74 | -----.....In.general,.the.result |
| 4980 | 20 6f 66 20 64 69 66 66 65 72 65 6e 74 69 61 74 69 6e 67 20 61 20 48 65 72 6d 69 74 65 20 73 65 | .of.differentiating.a.Hermite.se |
| 49a0 | 72 69 65 73 20 64 6f 65 73 20 6e 6f 74 0a 20 20 20 20 72 65 73 65 6d 62 6c 65 20 74 68 65 20 73 | ries.does.not.....resemble.the.s |
| 49c0 | 61 6d 65 20 6f 70 65 72 61 74 69 6f 6e 20 6f 6e 20 61 20 70 6f 77 65 72 20 73 65 72 69 65 73 2e | ame.operation.on.a.power.series. |
| 49e0 | 20 54 68 75 73 20 74 68 65 20 72 65 73 75 6c 74 20 6f 66 20 74 68 69 73 0a 20 20 20 20 66 75 6e | .Thus.the.result.of.this.....fun |
| 4a00 | 63 74 69 6f 6e 20 6d 61 79 20 62 65 20 22 75 6e 69 6e 74 75 69 74 69 76 65 2c 22 20 61 6c 62 65 | ction.may.be."unintuitive,".albe |
| 4a20 | 69 74 20 63 6f 72 72 65 63 74 3b 20 73 65 65 20 45 78 61 6d 70 6c 65 73 20 73 65 63 74 69 6f 6e | it.correct;.see.Examples.section |
| 4a40 | 0a 20 20 20 20 62 65 6c 6f 77 2e 0a 0a 20 20 20 20 45 78 61 6d 70 6c 65 73 0a 20 20 20 20 2d 2d | .....below.......Examples.....-- |
| 4a60 | 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 3e 3e 3e 20 66 72 6f 6d 20 6e 75 6d 70 79 2e 70 6f 6c 79 6e 6f | ------.....>>>.from.numpy.polyno |
| 4a80 | 6d 69 61 6c 2e 68 65 72 6d 69 74 65 5f 65 20 69 6d 70 6f 72 74 20 68 65 72 6d 65 64 65 72 0a 20 | mial.hermite_e.import.hermeder.. |
| 4aa0 | 20 20 20 3e 3e 3e 20 68 65 72 6d 65 64 65 72 28 5b 20 31 2e 2c 20 20 31 2e 2c 20 20 31 2e 2c 20 | ...>>>.hermeder([.1.,..1.,..1.,. |
| 4ac0 | 20 31 2e 5d 29 0a 20 20 20 20 61 72 72 61 79 28 5b 31 2e 2c 20 20 32 2e 2c 20 20 33 2e 5d 29 0a | .1.]).....array([1.,..2.,..3.]). |
| 4ae0 | 20 20 20 20 3e 3e 3e 20 68 65 72 6d 65 64 65 72 28 5b 2d 30 2e 32 35 2c 20 20 31 2e 2c 20 20 31 | ....>>>.hermeder([-0.25,..1.,..1 |
| 4b00 | 2e 2f 32 2e 2c 20 20 31 2e 2f 33 2e 2c 20 20 31 2e 2f 34 20 5d 2c 20 6d 3d 32 29 0a 20 20 20 20 | ./2.,..1./3.,..1./4.],.m=2)..... |
| 4b20 | 61 72 72 61 79 28 5b 31 2e 2c 20 20 32 2e 2c 20 20 33 2e 5d 29 0a 0a 20 20 20 20 72 04 00 00 00 | array([1.,..2.,..3.])......r.... |
| 4b40 | 54 a9 02 da 05 6e 64 6d 69 6e da 04 63 6f 70 79 fa 0d 3f 62 42 68 48 69 49 6c 4c 71 51 70 50 7a | T....ndmin..copy..?bBhHiIlLqQpPz |
| 4b60 | 17 74 68 65 20 6f 72 64 65 72 20 6f 66 20 64 65 72 69 76 61 74 69 6f 6e fa 08 74 68 65 20 61 78 | .the.order.of.derivation..the.ax |
| 4b80 | 69 73 72 02 00 00 00 7a 2c 54 68 65 20 6f 72 64 65 72 20 6f 66 20 64 65 72 69 76 61 74 69 6f 6e | isr....z,The.order.of.derivation |
| 4ba0 | 20 6d 75 73 74 20 62 65 20 6e 6f 6e 2d 6e 65 67 61 74 69 76 65 4e 72 4f 00 00 00 72 27 00 00 00 | .must.be.non-negativeNrO...r'... |
| 4bc0 | 29 10 72 40 00 00 00 72 41 00 00 00 72 50 00 00 00 da 04 63 68 61 72 da 06 61 73 74 79 70 65 da | ).r@...rA...rP.....char..astype. |
| 4be0 | 06 64 6f 75 62 6c 65 72 28 00 00 00 da 07 5f 61 73 5f 69 6e 74 da 0a 56 61 6c 75 65 45 72 72 6f | .doubler(....._as_int..ValueErro |
| 4c00 | 72 72 03 00 00 00 da 04 6e 64 69 6d da 08 6d 6f 76 65 61 78 69 73 72 2a 00 00 00 72 2b 00 00 00 | rr......ndim..moveaxisr*...r+... |
| 4c20 | 72 51 00 00 00 da 05 73 68 61 70 65 29 0a 72 39 00 00 00 da 01 6d 72 43 00 00 00 da 04 61 78 69 | rQ.....shape).r9.....mrC.....axi |
| 4c40 | 73 da 03 63 6e 74 da 05 69 61 78 69 73 72 3a 00 00 00 72 2f 00 00 00 da 03 64 65 72 da 01 6a 73 | s..cnt..iaxisr:...r/.....der..js |
| 4c60 | 0a 00 00 00 20 20 20 20 20 20 20 20 20 20 72 30 00 00 00 72 13 00 00 00 72 13 00 00 00 54 02 00 | ..............r0...r....r....T.. |
| 4c80 | 00 73 4f 01 00 00 80 00 f4 6a 01 00 09 0b 8f 08 89 08 90 11 98 21 a0 24 d4 08 27 80 41 d8 07 08 | .sO......j...........!.$..'.A... |
| 4ca0 | 87 77 81 77 87 7c 81 7c 90 7f d1 07 26 d8 0c 0d 8f 48 89 48 94 52 97 59 91 59 d3 0c 1f 88 01 dc | .w.w.|.|....&....H.H.R.Y.Y...... |
| 4cc0 | 0a 0c 8f 2a 89 2a 90 51 d0 18 31 d3 0a 32 80 43 dc 0c 0e 8f 4a 89 4a 90 74 98 5a d3 0c 28 80 45 | ...*.*.Q..1..2.C....J.J.t.Z..(.E |
| 4ce0 | d8 07 0a 88 51 82 77 dc 0e 18 d0 19 47 d3 0e 48 d0 08 48 dc 0c 20 a0 15 a8 01 af 06 a9 06 d3 0c | ....Q.w.....G..H..H............. |
| 4d00 | 2f 80 45 e0 07 0a 88 61 82 78 d8 0f 10 88 08 e4 08 0a 8f 0b 89 0b 90 41 90 75 98 61 d3 08 20 80 | /.E....a.x.............A.u.a.... |
| 4d20 | 41 dc 08 0b 88 41 8b 06 80 41 d8 07 0a 88 61 82 78 d8 0f 10 90 12 90 21 88 75 90 71 89 79 d0 08 | A....A...A....a.x......!.u.q.y.. |
| 4d40 | 18 e4 11 16 90 73 93 1a f2 00 06 09 14 88 41 d8 10 11 90 41 91 05 88 41 d8 0c 0d 90 13 89 48 88 | .....s........A....A...A......H. |
| 4d60 | 41 dc 12 14 97 28 91 28 98 41 98 34 a0 21 a7 27 a1 27 a8 21 a8 22 a0 2b d1 1b 2d b0 51 b7 57 b1 | A....(.(.A.4.!.'.'.!.".+..-.Q.W. |
| 4d80 | 57 d4 12 3d 88 43 dc 15 1a 98 31 98 61 a0 12 93 5f f2 00 01 0d 26 90 01 d8 1d 1e a0 11 a0 31 a1 | W..=.C....1.a..._....&........1. |
| 4da0 | 14 99 58 90 03 90 41 98 01 91 45 92 0a f0 03 01 0d 26 e0 10 13 89 41 f0 0d 06 09 14 f4 0e 00 09 | ..X...A...E......&....A......... |
| 4dc0 | 0b 8f 0b 89 0b 90 41 90 71 98 25 d3 08 20 80 41 d8 0b 0c 80 48 72 31 00 00 00 63 06 00 00 00 00 | ......A.q.%....A....Hr1...c..... |
| 4de0 | 00 00 00 00 00 00 00 09 00 00 00 03 00 00 00 f3 90 04 00 00 97 00 74 01 00 00 00 00 00 00 00 00 | ......................t......... |
| 4e00 | 6a 02 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 7c 00 64 01 64 02 ac 03 ab 03 00 00 | j...................|.d.d....... |
| 4e20 | 00 00 00 00 7d 00 7c 00 6a 04 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 6a 06 00 00 | ....}.|.j...................j... |
| 4e40 | 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 64 04 76 00 72 1f 7c 00 6a 09 00 00 00 00 00 00 | ................d.v.r.|.j....... |
| 4e60 | 00 00 00 00 00 00 00 00 00 00 00 00 74 00 00 00 00 00 00 00 00 00 6a 0a 00 00 00 00 00 00 00 00 | ............t.........j......... |
| 4e80 | 00 00 00 00 00 00 00 00 00 00 ab 01 00 00 00 00 00 00 7d 00 74 01 00 00 00 00 00 00 00 00 6a 0c | ..................}.t.........j. |
| 4ea0 | 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 7c 02 ab 01 00 00 00 00 00 00 73 03 7c 02 | ..................|.........s.|. |
| 4ec0 | 67 01 7d 02 74 0f 00 00 00 00 00 00 00 00 6a 10 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 | g.}.t.........j................. |
| 4ee0 | 00 00 7c 01 64 05 ab 02 00 00 00 00 00 00 7d 06 74 0f 00 00 00 00 00 00 00 00 6a 10 00 00 00 00 | ..|.d.........}.t.........j..... |
| 4f00 | 00 00 00 00 00 00 00 00 00 00 00 00 00 00 7c 05 64 06 ab 02 00 00 00 00 00 00 7d 07 7c 06 64 07 | ..............|.d.........}.|.d. |
| 4f20 | 6b 02 00 00 72 0b 74 13 00 00 00 00 00 00 00 00 64 08 ab 01 00 00 00 00 00 00 82 01 74 15 00 00 | k...r.t.........d...........t... |
| 4f40 | 00 00 00 00 00 00 7c 02 ab 01 00 00 00 00 00 00 7c 06 6b 44 00 00 72 0b 74 13 00 00 00 00 00 00 | ......|.........|.kD..r.t....... |
| 4f60 | 00 00 64 09 ab 01 00 00 00 00 00 00 82 01 74 01 00 00 00 00 00 00 00 00 6a 16 00 00 00 00 00 00 | ..d...........t.........j....... |
| 4f80 | 00 00 00 00 00 00 00 00 00 00 00 00 7c 03 ab 01 00 00 00 00 00 00 64 07 6b 37 00 00 72 0b 74 13 | ............|.........d.k7..r.t. |
| 4fa0 | 00 00 00 00 00 00 00 00 64 0a ab 01 00 00 00 00 00 00 82 01 74 01 00 00 00 00 00 00 00 00 6a 16 | ........d...........t.........j. |
| 4fc0 | 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 7c 04 ab 01 00 00 00 00 00 00 64 07 6b 37 | ..................|.........d.k7 |
| 4fe0 | 00 00 72 0b 74 13 00 00 00 00 00 00 00 00 64 0b ab 01 00 00 00 00 00 00 82 01 74 19 00 00 00 00 | ..r.t.........d...........t..... |
| 5000 | 00 00 00 00 7c 07 7c 00 6a 16 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 ab 02 00 00 | ....|.|.j....................... |
| 5020 | 00 00 00 00 7d 07 7c 06 64 07 6b 28 00 00 72 02 7c 00 53 00 74 01 00 00 00 00 00 00 00 00 6a 1a | ....}.|.d.k(..r.|.S.t.........j. |
| 5040 | 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 7c 00 7c 07 64 07 ab 03 00 00 00 00 00 00 | ..................|.|.d......... |
| 5060 | 7d 00 74 1d 00 00 00 00 00 00 00 00 7c 02 ab 01 00 00 00 00 00 00 64 07 67 01 7c 06 74 15 00 00 | }.t.........|.........d.g.|.t... |
| 5080 | 00 00 00 00 00 00 7c 02 ab 01 00 00 00 00 00 00 7a 0a 00 00 7a 05 00 00 7a 00 00 00 7d 02 74 1f | ......|.........z...z...z...}.t. |
| 50a0 | 00 00 00 00 00 00 00 00 7c 06 ab 01 00 00 00 00 00 00 44 00 5d cc 00 00 7d 08 74 15 00 00 00 00 | ........|.........D.]...}.t..... |
| 50c0 | 00 00 00 00 7c 00 ab 01 00 00 00 00 00 00 7d 09 7c 00 7c 04 7a 12 00 00 7d 00 7c 09 64 01 6b 28 | ....|.........}.|.|.z...}.|.d.k( |
| 50e0 | 00 00 72 2c 74 01 00 00 00 00 00 00 00 00 6a 20 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 | ..r,t.........j................. |
| 5100 | 00 00 7c 00 64 07 19 00 00 00 64 07 6b 28 00 00 ab 01 00 00 00 00 00 00 72 11 7c 00 64 07 78 02 | ..|.d.....d.k(..........r.|.d.x. |
| 5120 | 78 02 19 00 00 00 7c 02 7c 08 19 00 00 00 7a 0d 00 00 63 03 63 02 3c 00 00 00 8c 44 74 01 00 00 | x.....|.|.....z...c.c.<....Dt... |
| 5140 | 00 00 00 00 00 00 6a 22 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 7c 09 64 01 7a 00 | ......j"..................|.d.z. |
| 5160 | 00 00 66 01 7c 00 6a 24 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 64 01 64 0c 1a 00 | ..f.|.j$..................d.d... |
| 5180 | 7a 00 00 00 7c 00 6a 04 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 ac 0d ab 02 00 00 | z...|.j......................... |
| 51a0 | 00 00 00 00 7d 0a 7c 00 64 07 19 00 00 00 64 07 7a 05 00 00 7c 0a 64 07 3c 00 00 00 7c 00 64 07 | ....}.|.d.....d.z...|.d.<...|.d. |
| 51c0 | 19 00 00 00 7c 0a 64 01 3c 00 00 00 74 1f 00 00 00 00 00 00 00 00 64 01 7c 09 ab 02 00 00 00 00 | ....|.d.<...t.........d.|....... |
| 51e0 | 00 00 44 00 5d 13 00 00 7d 0b 7c 00 7c 0b 19 00 00 00 7c 0b 64 01 7a 00 00 00 7a 0b 00 00 7c 0a | ..D.]...}.|.|.....|.d.z...z...|. |
| 5200 | 7c 0b 64 01 7a 00 00 00 3c 00 00 00 8c 15 04 00 7c 0a 64 07 78 02 78 02 19 00 00 00 7c 02 7c 08 | |.d.z...<.......|.d.x.x.....|.|. |
| 5220 | 19 00 00 00 74 27 00 00 00 00 00 00 00 00 7c 03 7c 0a ab 02 00 00 00 00 00 00 7a 0a 00 00 7a 0d | ....t'........|.|.........z...z. |
| 5240 | 00 00 63 03 63 02 3c 00 00 00 7c 0a 7d 00 8c ce 04 00 74 01 00 00 00 00 00 00 00 00 6a 1a 00 00 | ..c.c.<...|.}.....t.........j... |
| 5260 | 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 7c 00 64 07 7c 07 ab 03 00 00 00 00 00 00 7d 00 | ................|.d.|.........}. |
| 5280 | 7c 00 53 00 29 0e 61 4f 0d 00 00 0a 20 20 20 20 49 6e 74 65 67 72 61 74 65 20 61 20 48 65 72 6d | |.S.).aO........Integrate.a.Herm |
| 52a0 | 69 74 65 5f 65 20 73 65 72 69 65 73 2e 0a 0a 20 20 20 20 52 65 74 75 72 6e 73 20 74 68 65 20 48 | ite_e.series.......Returns.the.H |
| 52c0 | 65 72 6d 69 74 65 5f 65 20 73 65 72 69 65 73 20 63 6f 65 66 66 69 63 69 65 6e 74 73 20 60 63 60 | ermite_e.series.coefficients.`c` |
| 52e0 | 20 69 6e 74 65 67 72 61 74 65 64 20 60 6d 60 20 74 69 6d 65 73 20 66 72 6f 6d 0a 20 20 20 20 60 | .integrated.`m`.times.from.....` |
| 5300 | 6c 62 6e 64 60 20 61 6c 6f 6e 67 20 60 61 78 69 73 60 2e 20 41 74 20 65 61 63 68 20 69 74 65 72 | lbnd`.along.`axis`..At.each.iter |
| 5320 | 61 74 69 6f 6e 20 74 68 65 20 72 65 73 75 6c 74 69 6e 67 20 73 65 72 69 65 73 20 69 73 0a 20 20 | ation.the.resulting.series.is... |
| 5340 | 20 20 2a 2a 6d 75 6c 74 69 70 6c 69 65 64 2a 2a 20 62 79 20 60 73 63 6c 60 20 61 6e 64 20 61 6e | ..**multiplied**.by.`scl`.and.an |
| 5360 | 20 69 6e 74 65 67 72 61 74 69 6f 6e 20 63 6f 6e 73 74 61 6e 74 2c 20 60 6b 60 2c 20 69 73 20 61 | .integration.constant,.`k`,.is.a |
| 5380 | 64 64 65 64 2e 0a 20 20 20 20 54 68 65 20 73 63 61 6c 69 6e 67 20 66 61 63 74 6f 72 20 69 73 20 | dded......The.scaling.factor.is. |
| 53a0 | 66 6f 72 20 75 73 65 20 69 6e 20 61 20 6c 69 6e 65 61 72 20 63 68 61 6e 67 65 20 6f 66 20 76 61 | for.use.in.a.linear.change.of.va |
| 53c0 | 72 69 61 62 6c 65 2e 20 20 28 22 42 75 79 65 72 0a 20 20 20 20 62 65 77 61 72 65 22 3a 20 6e 6f | riable...("Buyer.....beware":.no |
| 53e0 | 74 65 20 74 68 61 74 2c 20 64 65 70 65 6e 64 69 6e 67 20 6f 6e 20 77 68 61 74 20 6f 6e 65 20 69 | te.that,.depending.on.what.one.i |
| 5400 | 73 20 64 6f 69 6e 67 2c 20 6f 6e 65 20 6d 61 79 20 77 61 6e 74 20 60 73 63 6c 60 0a 20 20 20 20 | s.doing,.one.may.want.`scl`..... |
| 5420 | 74 6f 20 62 65 20 74 68 65 20 72 65 63 69 70 72 6f 63 61 6c 20 6f 66 20 77 68 61 74 20 6f 6e 65 | to.be.the.reciprocal.of.what.one |
| 5440 | 20 6d 69 67 68 74 20 65 78 70 65 63 74 3b 20 66 6f 72 20 6d 6f 72 65 20 69 6e 66 6f 72 6d 61 74 | .might.expect;.for.more.informat |
| 5460 | 69 6f 6e 2c 0a 20 20 20 20 73 65 65 20 74 68 65 20 4e 6f 74 65 73 20 73 65 63 74 69 6f 6e 20 62 | ion,.....see.the.Notes.section.b |
| 5480 | 65 6c 6f 77 2e 29 20 20 54 68 65 20 61 72 67 75 6d 65 6e 74 20 60 63 60 20 69 73 20 61 6e 20 61 | elow.)..The.argument.`c`.is.an.a |
| 54a0 | 72 72 61 79 20 6f 66 0a 20 20 20 20 63 6f 65 66 66 69 63 69 65 6e 74 73 20 66 72 6f 6d 20 6c 6f | rray.of.....coefficients.from.lo |
| 54c0 | 77 20 74 6f 20 68 69 67 68 20 64 65 67 72 65 65 20 61 6c 6f 6e 67 20 65 61 63 68 20 61 78 69 73 | w.to.high.degree.along.each.axis |
| 54e0 | 2c 20 65 2e 67 2e 2c 20 5b 31 2c 32 2c 33 5d 0a 20 20 20 20 72 65 70 72 65 73 65 6e 74 73 20 74 | ,.e.g.,.[1,2,3].....represents.t |
| 5500 | 68 65 20 73 65 72 69 65 73 20 60 60 48 5f 30 20 2b 20 32 2a 48 5f 31 20 2b 20 33 2a 48 5f 32 60 | he.series.``H_0.+.2*H_1.+.3*H_2` |
| 5520 | 60 20 77 68 69 6c 65 20 5b 5b 31 2c 32 5d 2c 5b 31 2c 32 5d 5d 0a 20 20 20 20 72 65 70 72 65 73 | `.while.[[1,2],[1,2]].....repres |
| 5540 | 65 6e 74 73 20 60 60 31 2a 48 5f 30 28 78 29 2a 48 5f 30 28 79 29 20 2b 20 31 2a 48 5f 31 28 78 | ents.``1*H_0(x)*H_0(y).+.1*H_1(x |
| 5560 | 29 2a 48 5f 30 28 79 29 20 2b 20 32 2a 48 5f 30 28 78 29 2a 48 5f 31 28 79 29 20 2b 0a 20 20 20 | )*H_0(y).+.2*H_0(x)*H_1(y).+.... |
| 5580 | 20 32 2a 48 5f 31 28 78 29 2a 48 5f 31 28 79 29 60 60 20 69 66 20 61 78 69 73 3d 30 20 69 73 20 | .2*H_1(x)*H_1(y)``.if.axis=0.is. |
| 55a0 | 60 60 78 60 60 20 61 6e 64 20 61 78 69 73 3d 31 20 69 73 20 60 60 79 60 60 2e 0a 0a 20 20 20 20 | ``x``.and.axis=1.is.``y``....... |
| 55c0 | 50 61 72 61 6d 65 74 65 72 73 0a 20 20 20 20 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 63 20 | Parameters.....----------.....c. |
| 55e0 | 3a 20 61 72 72 61 79 5f 6c 69 6b 65 0a 20 20 20 20 20 20 20 20 41 72 72 61 79 20 6f 66 20 48 65 | :.array_like.........Array.of.He |
| 5600 | 72 6d 69 74 65 5f 65 20 73 65 72 69 65 73 20 63 6f 65 66 66 69 63 69 65 6e 74 73 2e 20 49 66 20 | rmite_e.series.coefficients..If. |
| 5620 | 63 20 69 73 20 6d 75 6c 74 69 64 69 6d 65 6e 73 69 6f 6e 61 6c 0a 20 20 20 20 20 20 20 20 74 68 | c.is.multidimensional.........th |
| 5640 | 65 20 64 69 66 66 65 72 65 6e 74 20 61 78 69 73 20 63 6f 72 72 65 73 70 6f 6e 64 20 74 6f 20 64 | e.different.axis.correspond.to.d |
| 5660 | 69 66 66 65 72 65 6e 74 20 76 61 72 69 61 62 6c 65 73 20 77 69 74 68 20 74 68 65 0a 20 20 20 20 | ifferent.variables.with.the..... |
| 5680 | 20 20 20 20 64 65 67 72 65 65 20 69 6e 20 65 61 63 68 20 61 78 69 73 20 67 69 76 65 6e 20 62 79 | ....degree.in.each.axis.given.by |
| 56a0 | 20 74 68 65 20 63 6f 72 72 65 73 70 6f 6e 64 69 6e 67 20 69 6e 64 65 78 2e 0a 20 20 20 20 6d 20 | .the.corresponding.index......m. |
| 56c0 | 3a 20 69 6e 74 2c 20 6f 70 74 69 6f 6e 61 6c 0a 20 20 20 20 20 20 20 20 4f 72 64 65 72 20 6f 66 | :.int,.optional.........Order.of |
| 56e0 | 20 69 6e 74 65 67 72 61 74 69 6f 6e 2c 20 6d 75 73 74 20 62 65 20 70 6f 73 69 74 69 76 65 2e 20 | .integration,.must.be.positive.. |
| 5700 | 28 44 65 66 61 75 6c 74 3a 20 31 29 0a 20 20 20 20 6b 20 3a 20 7b 5b 5d 2c 20 6c 69 73 74 2c 20 | (Default:.1).....k.:.{[],.list,. |
| 5720 | 73 63 61 6c 61 72 7d 2c 20 6f 70 74 69 6f 6e 61 6c 0a 20 20 20 20 20 20 20 20 49 6e 74 65 67 72 | scalar},.optional.........Integr |
| 5740 | 61 74 69 6f 6e 20 63 6f 6e 73 74 61 6e 74 28 73 29 2e 20 20 54 68 65 20 76 61 6c 75 65 20 6f 66 | ation.constant(s)...The.value.of |
| 5760 | 20 74 68 65 20 66 69 72 73 74 20 69 6e 74 65 67 72 61 6c 20 61 74 0a 20 20 20 20 20 20 20 20 60 | .the.first.integral.at.........` |
| 5780 | 60 6c 62 6e 64 60 60 20 69 73 20 74 68 65 20 66 69 72 73 74 20 76 61 6c 75 65 20 69 6e 20 74 68 | `lbnd``.is.the.first.value.in.th |
| 57a0 | 65 20 6c 69 73 74 2c 20 74 68 65 20 76 61 6c 75 65 20 6f 66 20 74 68 65 20 73 65 63 6f 6e 64 0a | e.list,.the.value.of.the.second. |
| 57c0 | 20 20 20 20 20 20 20 20 69 6e 74 65 67 72 61 6c 20 61 74 20 60 60 6c 62 6e 64 60 60 20 69 73 20 | ........integral.at.``lbnd``.is. |
| 57e0 | 74 68 65 20 73 65 63 6f 6e 64 20 76 61 6c 75 65 2c 20 65 74 63 2e 20 20 49 66 20 60 60 6b 20 3d | the.second.value,.etc...If.``k.= |
| 5800 | 3d 20 5b 5d 60 60 20 28 74 68 65 0a 20 20 20 20 20 20 20 20 64 65 66 61 75 6c 74 29 2c 20 61 6c | =.[]``.(the.........default),.al |
| 5820 | 6c 20 63 6f 6e 73 74 61 6e 74 73 20 61 72 65 20 73 65 74 20 74 6f 20 7a 65 72 6f 2e 20 20 49 66 | l.constants.are.set.to.zero...If |
| 5840 | 20 60 60 6d 20 3d 3d 20 31 60 60 2c 20 61 20 73 69 6e 67 6c 65 0a 20 20 20 20 20 20 20 20 73 63 | .``m.==.1``,.a.single.........sc |
| 5860 | 61 6c 61 72 20 63 61 6e 20 62 65 20 67 69 76 65 6e 20 69 6e 73 74 65 61 64 20 6f 66 20 61 20 6c | alar.can.be.given.instead.of.a.l |
| 5880 | 69 73 74 2e 0a 20 20 20 20 6c 62 6e 64 20 3a 20 73 63 61 6c 61 72 2c 20 6f 70 74 69 6f 6e 61 6c | ist......lbnd.:.scalar,.optional |
| 58a0 | 0a 20 20 20 20 20 20 20 20 54 68 65 20 6c 6f 77 65 72 20 62 6f 75 6e 64 20 6f 66 20 74 68 65 20 | .........The.lower.bound.of.the. |
| 58c0 | 69 6e 74 65 67 72 61 6c 2e 20 28 44 65 66 61 75 6c 74 3a 20 30 29 0a 20 20 20 20 73 63 6c 20 3a | integral..(Default:.0).....scl.: |
| 58e0 | 20 73 63 61 6c 61 72 2c 20 6f 70 74 69 6f 6e 61 6c 0a 20 20 20 20 20 20 20 20 46 6f 6c 6c 6f 77 | .scalar,.optional.........Follow |
| 5900 | 69 6e 67 20 65 61 63 68 20 69 6e 74 65 67 72 61 74 69 6f 6e 20 74 68 65 20 72 65 73 75 6c 74 20 | ing.each.integration.the.result. |
| 5920 | 69 73 20 2a 6d 75 6c 74 69 70 6c 69 65 64 2a 20 62 79 20 60 73 63 6c 60 0a 20 20 20 20 20 20 20 | is.*multiplied*.by.`scl`........ |
| 5940 | 20 62 65 66 6f 72 65 20 74 68 65 20 69 6e 74 65 67 72 61 74 69 6f 6e 20 63 6f 6e 73 74 61 6e 74 | .before.the.integration.constant |
| 5960 | 20 69 73 20 61 64 64 65 64 2e 20 28 44 65 66 61 75 6c 74 3a 20 31 29 0a 20 20 20 20 61 78 69 73 | .is.added..(Default:.1).....axis |
| 5980 | 20 3a 20 69 6e 74 2c 20 6f 70 74 69 6f 6e 61 6c 0a 20 20 20 20 20 20 20 20 41 78 69 73 20 6f 76 | .:.int,.optional.........Axis.ov |
| 59a0 | 65 72 20 77 68 69 63 68 20 74 68 65 20 69 6e 74 65 67 72 61 6c 20 69 73 20 74 61 6b 65 6e 2e 20 | er.which.the.integral.is.taken.. |
| 59c0 | 28 44 65 66 61 75 6c 74 3a 20 30 29 2e 0a 0a 20 20 20 20 52 65 74 75 72 6e 73 0a 20 20 20 20 2d | (Default:.0).......Returns.....- |
| 59e0 | 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 53 20 3a 20 6e 64 61 72 72 61 79 0a 20 20 20 20 20 20 20 20 48 | ------.....S.:.ndarray.........H |
| 5a00 | 65 72 6d 69 74 65 5f 65 20 73 65 72 69 65 73 20 63 6f 65 66 66 69 63 69 65 6e 74 73 20 6f 66 20 | ermite_e.series.coefficients.of. |
| 5a20 | 74 68 65 20 69 6e 74 65 67 72 61 6c 2e 0a 0a 20 20 20 20 52 61 69 73 65 73 0a 20 20 20 20 2d 2d | the.integral.......Raises.....-- |
| 5a40 | 2d 2d 2d 2d 0a 20 20 20 20 56 61 6c 75 65 45 72 72 6f 72 0a 20 20 20 20 20 20 20 20 49 66 20 60 | ----.....ValueError.........If.` |
| 5a60 | 60 6d 20 3c 20 30 60 60 2c 20 60 60 6c 65 6e 28 6b 29 20 3e 20 6d 60 60 2c 20 60 60 6e 70 2e 6e | `m.<.0``,.``len(k).>.m``,.``np.n |
| 5a80 | 64 69 6d 28 6c 62 6e 64 29 20 21 3d 20 30 60 60 2c 20 6f 72 0a 20 20 20 20 20 20 20 20 60 60 6e | dim(lbnd).!=.0``,.or.........``n |
| 5aa0 | 70 2e 6e 64 69 6d 28 73 63 6c 29 20 21 3d 20 30 60 60 2e 0a 0a 20 20 20 20 53 65 65 20 41 6c 73 | p.ndim(scl).!=.0``.......See.Als |
| 5ac0 | 6f 0a 20 20 20 20 2d 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 68 65 72 6d 65 64 65 72 0a 0a 20 20 20 | o.....--------.....hermeder..... |
| 5ae0 | 20 4e 6f 74 65 73 0a 20 20 20 20 2d 2d 2d 2d 2d 0a 20 20 20 20 4e 6f 74 65 20 74 68 61 74 20 74 | .Notes.....-----.....Note.that.t |
| 5b00 | 68 65 20 72 65 73 75 6c 74 20 6f 66 20 65 61 63 68 20 69 6e 74 65 67 72 61 74 69 6f 6e 20 69 73 | he.result.of.each.integration.is |
| 5b20 | 20 2a 6d 75 6c 74 69 70 6c 69 65 64 2a 20 62 79 20 60 73 63 6c 60 2e 0a 20 20 20 20 57 68 79 20 | .*multiplied*.by.`scl`......Why. |
| 5b40 | 69 73 20 74 68 69 73 20 69 6d 70 6f 72 74 61 6e 74 20 74 6f 20 6e 6f 74 65 3f 20 20 53 61 79 20 | is.this.important.to.note?..Say. |
| 5b60 | 6f 6e 65 20 69 73 20 6d 61 6b 69 6e 67 20 61 20 6c 69 6e 65 61 72 20 63 68 61 6e 67 65 20 6f 66 | one.is.making.a.linear.change.of |
| 5b80 | 0a 20 20 20 20 76 61 72 69 61 62 6c 65 20 3a 6d 61 74 68 3a 60 75 20 3d 20 61 78 20 2b 20 62 60 | .....variable.:math:`u.=.ax.+.b` |
| 5ba0 | 20 69 6e 20 61 6e 20 69 6e 74 65 67 72 61 6c 20 72 65 6c 61 74 69 76 65 20 74 6f 20 60 78 60 2e | .in.an.integral.relative.to.`x`. |
| 5bc0 | 20 20 54 68 65 6e 0a 20 20 20 20 3a 6d 61 74 68 3a 60 64 78 20 3d 20 64 75 2f 61 60 2c 20 73 6f | ..Then.....:math:`dx.=.du/a`,.so |
| 5be0 | 20 6f 6e 65 20 77 69 6c 6c 20 6e 65 65 64 20 74 6f 20 73 65 74 20 60 73 63 6c 60 20 65 71 75 61 | .one.will.need.to.set.`scl`.equa |
| 5c00 | 6c 20 74 6f 0a 20 20 20 20 3a 6d 61 74 68 3a 60 31 2f 61 60 20 2d 20 70 65 72 68 61 70 73 20 6e | l.to.....:math:`1/a`.-.perhaps.n |
| 5c20 | 6f 74 20 77 68 61 74 20 6f 6e 65 20 77 6f 75 6c 64 20 68 61 76 65 20 66 69 72 73 74 20 74 68 6f | ot.what.one.would.have.first.tho |
| 5c40 | 75 67 68 74 2e 0a 0a 20 20 20 20 41 6c 73 6f 20 6e 6f 74 65 20 74 68 61 74 2c 20 69 6e 20 67 65 | ught.......Also.note.that,.in.ge |
| 5c60 | 6e 65 72 61 6c 2c 20 74 68 65 20 72 65 73 75 6c 74 20 6f 66 20 69 6e 74 65 67 72 61 74 69 6e 67 | neral,.the.result.of.integrating |
| 5c80 | 20 61 20 43 2d 73 65 72 69 65 73 20 6e 65 65 64 73 0a 20 20 20 20 74 6f 20 62 65 20 22 72 65 70 | .a.C-series.needs.....to.be."rep |
| 5ca0 | 72 6f 6a 65 63 74 65 64 22 20 6f 6e 74 6f 20 74 68 65 20 43 2d 73 65 72 69 65 73 20 62 61 73 69 | rojected".onto.the.C-series.basi |
| 5cc0 | 73 20 73 65 74 2e 20 20 54 68 75 73 2c 20 74 79 70 69 63 61 6c 6c 79 2c 0a 20 20 20 20 74 68 65 | s.set...Thus,.typically,.....the |
| 5ce0 | 20 72 65 73 75 6c 74 20 6f 66 20 74 68 69 73 20 66 75 6e 63 74 69 6f 6e 20 69 73 20 22 75 6e 69 | .result.of.this.function.is."uni |
| 5d00 | 6e 74 75 69 74 69 76 65 2c 22 20 61 6c 62 65 69 74 20 63 6f 72 72 65 63 74 3b 20 73 65 65 0a 20 | ntuitive,".albeit.correct;.see.. |
| 5d20 | 20 20 20 45 78 61 6d 70 6c 65 73 20 73 65 63 74 69 6f 6e 20 62 65 6c 6f 77 2e 0a 0a 20 20 20 20 | ...Examples.section.below....... |
| 5d40 | 45 78 61 6d 70 6c 65 73 0a 20 20 20 20 2d 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 3e 3e 3e 20 66 72 | Examples.....--------.....>>>.fr |
| 5d60 | 6f 6d 20 6e 75 6d 70 79 2e 70 6f 6c 79 6e 6f 6d 69 61 6c 2e 68 65 72 6d 69 74 65 5f 65 20 69 6d | om.numpy.polynomial.hermite_e.im |
| 5d80 | 70 6f 72 74 20 68 65 72 6d 65 69 6e 74 0a 20 20 20 20 3e 3e 3e 20 68 65 72 6d 65 69 6e 74 28 5b | port.hermeint.....>>>.hermeint([ |
| 5da0 | 31 2c 20 32 2c 20 33 5d 29 20 23 20 69 6e 74 65 67 72 61 74 65 20 6f 6e 63 65 2c 20 76 61 6c 75 | 1,.2,.3]).#.integrate.once,.valu |
| 5dc0 | 65 20 30 20 61 74 20 30 2e 0a 20 20 20 20 61 72 72 61 79 28 5b 31 2e 2c 20 31 2e 2c 20 31 2e 2c | e.0.at.0......array([1.,.1.,.1., |
| 5de0 | 20 31 2e 5d 29 0a 20 20 20 20 3e 3e 3e 20 68 65 72 6d 65 69 6e 74 28 5b 31 2c 20 32 2c 20 33 5d | .1.]).....>>>.hermeint([1,.2,.3] |
| 5e00 | 2c 20 6d 3d 32 29 20 23 20 69 6e 74 65 67 72 61 74 65 20 74 77 69 63 65 2c 20 76 61 6c 75 65 20 | ,.m=2).#.integrate.twice,.value. |
| 5e20 | 26 20 64 65 72 69 76 20 30 20 61 74 20 30 0a 20 20 20 20 61 72 72 61 79 28 5b 2d 30 2e 32 35 20 | &.deriv.0.at.0.....array([-0.25. |
| 5e40 | 20 20 20 20 20 2c 20 20 31 2e 20 20 20 20 20 20 20 20 2c 20 20 30 2e 35 20 20 20 20 20 20 20 2c | .....,..1.........,..0.5......., |
| 5e60 | 20 20 30 2e 33 33 33 33 33 33 33 33 2c 20 20 30 2e 32 35 20 20 20 20 20 20 5d 29 20 23 20 6d 61 | ..0.33333333,..0.25......]).#.ma |
| 5e80 | 79 20 76 61 72 79 0a 20 20 20 20 3e 3e 3e 20 68 65 72 6d 65 69 6e 74 28 5b 31 2c 20 32 2c 20 33 | y.vary.....>>>.hermeint([1,.2,.3 |
| 5ea0 | 5d 2c 20 6b 3d 31 29 20 23 20 69 6e 74 65 67 72 61 74 65 20 6f 6e 63 65 2c 20 76 61 6c 75 65 20 | ],.k=1).#.integrate.once,.value. |
| 5ec0 | 31 20 61 74 20 30 2e 0a 20 20 20 20 61 72 72 61 79 28 5b 32 2e 2c 20 31 2e 2c 20 31 2e 2c 20 31 | 1.at.0......array([2.,.1.,.1.,.1 |
| 5ee0 | 2e 5d 29 0a 20 20 20 20 3e 3e 3e 20 68 65 72 6d 65 69 6e 74 28 5b 31 2c 20 32 2c 20 33 5d 2c 20 | .]).....>>>.hermeint([1,.2,.3],. |
| 5f00 | 6c 62 6e 64 3d 2d 31 29 20 23 20 69 6e 74 65 67 72 61 74 65 20 6f 6e 63 65 2c 20 76 61 6c 75 65 | lbnd=-1).#.integrate.once,.value |
| 5f20 | 20 30 20 61 74 20 2d 31 0a 20 20 20 20 61 72 72 61 79 28 5b 2d 31 2e 2c 20 20 31 2e 2c 20 20 31 | .0.at.-1.....array([-1.,..1.,..1 |
| 5f40 | 2e 2c 20 20 31 2e 5d 29 0a 20 20 20 20 3e 3e 3e 20 68 65 72 6d 65 69 6e 74 28 5b 31 2c 20 32 2c | .,..1.]).....>>>.hermeint([1,.2, |
| 5f60 | 20 33 5d 2c 20 6d 3d 32 2c 20 6b 3d 5b 31 2c 20 32 5d 2c 20 6c 62 6e 64 3d 2d 31 29 0a 20 20 20 | .3],.m=2,.k=[1,.2],.lbnd=-1).... |
| 5f80 | 20 61 72 72 61 79 28 5b 20 31 2e 38 33 33 33 33 33 33 33 2c 20 20 30 2e 20 20 20 20 20 20 20 20 | .array([.1.83333333,..0......... |
| 5fa0 | 2c 20 20 30 2e 35 20 20 20 20 20 20 20 2c 20 20 30 2e 33 33 33 33 33 33 33 33 2c 20 20 30 2e 32 | ,..0.5.......,..0.33333333,..0.2 |
| 5fc0 | 35 20 20 20 20 20 20 5d 29 20 23 20 6d 61 79 20 76 61 72 79 0a 0a 20 20 20 20 72 04 00 00 00 54 | 5......]).#.may.vary......r....T |
| 5fe0 | 72 5e 00 00 00 72 61 00 00 00 7a 18 74 68 65 20 6f 72 64 65 72 20 6f 66 20 69 6e 74 65 67 72 61 | r^...ra...z.the.order.of.integra |
| 6000 | 74 69 6f 6e 72 62 00 00 00 72 02 00 00 00 7a 2d 54 68 65 20 6f 72 64 65 72 20 6f 66 20 69 6e 74 | tionrb...r....z-The.order.of.int |
| 6020 | 65 67 72 61 74 69 6f 6e 20 6d 75 73 74 20 62 65 20 6e 6f 6e 2d 6e 65 67 61 74 69 76 65 7a 1e 54 | egration.must.be.non-negativez.T |
| 6040 | 6f 6f 20 6d 61 6e 79 20 69 6e 74 65 67 72 61 74 69 6f 6e 20 63 6f 6e 73 74 61 6e 74 73 7a 16 6c | oo.many.integration.constantsz.l |
| 6060 | 62 6e 64 20 6d 75 73 74 20 62 65 20 61 20 73 63 61 6c 61 72 2e 7a 15 73 63 6c 20 6d 75 73 74 20 | bnd.must.be.a.scalar.z.scl.must. |
| 6080 | 62 65 20 61 20 73 63 61 6c 61 72 2e 4e 72 4f 00 00 00 29 14 72 40 00 00 00 72 41 00 00 00 72 50 | be.a.scalar.NrO...).r@...rA...rP |
| 60a0 | 00 00 00 72 63 00 00 00 72 64 00 00 00 72 65 00 00 00 da 08 69 74 65 72 61 62 6c 65 72 28 00 00 | ...rc...rd...re.....iterabler(.. |
| 60c0 | 00 72 66 00 00 00 72 67 00 00 00 72 2a 00 00 00 72 68 00 00 00 72 03 00 00 00 72 69 00 00 00 da | .rf...rg...r*...rh...r....ri.... |
| 60e0 | 04 6c 69 73 74 72 2b 00 00 00 da 03 61 6c 6c 72 51 00 00 00 72 6a 00 00 00 72 12 00 00 00 29 0c | .listr+.....allrQ...rj...r....). |
| 6100 | 72 39 00 00 00 72 6b 00 00 00 da 01 6b da 04 6c 62 6e 64 72 43 00 00 00 72 6c 00 00 00 72 6d 00 | r9...rk.....k..lbndrC...rl...rm. |
| 6120 | 00 00 72 6e 00 00 00 72 2f 00 00 00 72 3a 00 00 00 72 3d 00 00 00 72 70 00 00 00 73 0c 00 00 00 | ..rn...r/...r:...r=...rp...s.... |
| 6140 | 20 20 20 20 20 20 20 20 20 20 20 20 72 30 00 00 00 72 14 00 00 00 72 14 00 00 00 a5 02 00 00 73 | ............r0...r....r........s |
| 6160 | 1a 02 00 00 80 00 f4 62 02 00 09 0b 8f 08 89 08 90 11 98 21 a0 24 d4 08 27 80 41 d8 07 08 87 77 | .......b...........!.$..'.A....w |
| 6180 | 81 77 87 7c 81 7c 90 7f d1 07 26 d8 0c 0d 8f 48 89 48 94 52 97 59 91 59 d3 0c 1f 88 01 dc 0b 0d | .w.|.|....&....H.H.R.Y.Y........ |
| 61a0 | 8f 3b 89 3b 90 71 8c 3e d8 0d 0e 88 43 88 01 dc 0a 0c 8f 2a 89 2a 90 51 d0 18 32 d3 0a 33 80 43 | .;.;.q.>....C......*.*.Q..2..3.C |
| 61c0 | dc 0c 0e 8f 4a 89 4a 90 74 98 5a d3 0c 28 80 45 d8 07 0a 88 51 82 77 dc 0e 18 d0 19 48 d3 0e 49 | ....J.J.t.Z..(.E....Q.w.....H..I |
| 61e0 | d0 08 49 dc 07 0a 88 31 83 76 90 03 82 7c dc 0e 18 d0 19 39 d3 0e 3a d0 08 3a dc 07 09 87 77 81 | ..I....1.v...|.....9..:..:....w. |
| 6200 | 77 88 74 83 7d 98 01 d2 07 19 dc 0e 18 d0 19 31 d3 0e 32 d0 08 32 dc 07 09 87 77 81 77 88 73 83 | w.t.}..........1..2..2....w.w.s. |
| 6220 | 7c 90 71 d2 07 18 dc 0e 18 d0 19 30 d3 0e 31 d0 08 31 dc 0c 20 a0 15 a8 01 af 06 a9 06 d3 0c 2f | |.q........0..1..1............./ |
| 6240 | 80 45 e0 07 0a 88 61 82 78 d8 0f 10 88 08 e4 08 0a 8f 0b 89 0b 90 41 90 75 98 61 d3 08 20 80 41 | .E....a.x.............A.u.a....A |
| 6260 | dc 08 0c 88 51 8b 07 90 31 90 23 98 13 9c 73 a0 31 9b 76 99 1c d1 12 26 d1 08 26 80 41 dc 0d 12 | ....Q...1.#...s.1.v....&..&.A... |
| 6280 | 90 33 8b 5a f2 00 0c 05 14 88 01 dc 0c 0f 90 01 8b 46 88 01 d8 08 09 88 53 89 08 88 01 d8 0b 0c | .3.Z.............F......S....... |
| 62a0 | 90 01 8a 36 94 62 97 66 91 66 98 51 98 71 99 54 a0 51 99 59 d4 16 27 d8 0c 0d 88 61 8b 44 90 41 | ...6.b.f.f.Q.q.T.Q.Y..'....a.D.A |
| 62c0 | 90 61 91 44 89 4c 8c 44 e4 12 14 97 28 91 28 98 41 a0 01 99 45 98 38 a0 61 a7 67 a1 67 a8 61 a8 | .a.D.L.D....(.(.A...E.8.a.g.g.a. |
| 62e0 | 62 a0 6b d1 1b 31 b8 11 bf 17 b9 17 d4 12 41 88 43 d8 15 16 90 71 91 54 98 41 91 58 88 43 90 01 | b.k..1........A.C....q.T.A.X.C.. |
| 6300 | 89 46 d8 15 16 90 71 91 54 88 43 90 01 89 46 dc 15 1a 98 31 98 61 93 5b f2 00 01 0d 2c 90 01 d8 | .F....q.T.C...F....1.a.[....,... |
| 6320 | 1d 1e 98 71 99 54 a0 51 a8 11 a1 55 99 5e 90 03 90 41 98 01 91 45 92 0a f0 03 01 0d 2c e0 0c 0f | ...q.T.Q...U.^...A...E......,... |
| 6340 | 90 01 8b 46 90 61 98 01 91 64 9c 58 a0 64 a8 43 d3 1d 30 d1 16 30 d1 0c 30 8b 46 d8 10 13 89 41 | ...F.a...d.X.d.C..0..0..0.F....A |
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| 6380 | 00 00 00 63 03 00 00 00 00 00 00 00 00 00 00 00 06 00 00 00 03 00 00 00 f3 92 02 00 00 97 00 74 | ...c...........................t |
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| 63c0 | 01 64 02 ac 03 ab 03 00 00 00 00 00 00 7d 01 7c 01 6a 04 00 00 00 00 00 00 00 00 00 00 00 00 00 | .d...........}.|.j.............. |
| 63e0 | 00 00 00 00 00 6a 06 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 64 04 76 00 72 1f 7c | .....j...................d.v.r.| |
| 6400 | 01 6a 09 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 74 00 00 00 00 00 00 00 00 00 6a | .j...................t.........j |
| 6420 | 0a 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 ab 01 00 00 00 00 00 00 7d 01 74 0d 00 | ...........................}.t.. |
| 6440 | 00 00 00 00 00 00 00 7c 00 74 0e 00 00 00 00 00 00 00 00 74 10 00 00 00 00 00 00 00 00 66 02 ab | .......|.t.........t.........f.. |
| 6460 | 02 00 00 00 00 00 00 72 15 74 01 00 00 00 00 00 00 00 00 6a 12 00 00 00 00 00 00 00 00 00 00 00 | .......r.t.........j............ |
| 6480 | 00 00 00 00 00 00 00 7c 00 ab 01 00 00 00 00 00 00 7d 00 74 0d 00 00 00 00 00 00 00 00 7c 00 74 | .......|.........}.t.........|.t |
| 64a0 | 00 00 00 00 00 00 00 00 00 6a 14 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 ab 02 00 | .........j...................... |
| 64c0 | 00 00 00 00 00 72 2d 7c 02 72 2b 7c 01 6a 17 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 | .....r-|.r+|.j.................. |
| 64e0 | 00 7c 01 6a 18 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 64 05 7c 00 6a 1a 00 00 00 | .|.j...................d.|.j.... |
| 6500 | 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 7a 05 00 00 7a 00 00 00 ab 01 00 00 00 00 00 00 7d | ...............z...z...........} |
| 6520 | 01 74 1d 00 00 00 00 00 00 00 00 7c 01 ab 01 00 00 00 00 00 00 64 01 6b 28 00 00 72 08 7c 01 64 | .t.........|.........d.k(..r.|.d |
| 6540 | 06 19 00 00 00 7d 03 64 06 7d 04 6e 69 74 1d 00 00 00 00 00 00 00 00 7c 01 ab 01 00 00 00 00 00 | .....}.d.}.nit.........|........ |
| 6560 | 00 64 07 6b 28 00 00 72 0b 7c 01 64 06 19 00 00 00 7d 03 7c 01 64 01 19 00 00 00 7d 04 6e 50 74 | .d.k(..r.|.d.....}.|.d.....}.nPt |
| 6580 | 1d 00 00 00 00 00 00 00 00 7c 01 ab 01 00 00 00 00 00 00 7d 05 7c 01 64 08 19 00 00 00 7d 03 7c | .........|.........}.|.d.....}.| |
| 65a0 | 01 64 09 19 00 00 00 7d 04 74 1f 00 00 00 00 00 00 00 00 64 0a 74 1d 00 00 00 00 00 00 00 00 7c | .d.....}.t.........d.t.........| |
| 65c0 | 01 ab 01 00 00 00 00 00 00 64 01 7a 00 00 00 ab 02 00 00 00 00 00 00 44 00 5d 20 00 00 7d 06 7c | .........d.z...........D.]...}.| |
| 65e0 | 03 7d 07 7c 05 64 01 7a 0a 00 00 7d 05 7c 01 7c 06 0b 00 19 00 00 00 7c 04 7c 05 64 01 7a 0a 00 | .}.|.d.z...}.|.|.......|.|.d.z.. |
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| 6620 | 03 7c 04 7c 00 7a 05 00 00 7a 00 00 00 53 00 29 0b 61 1c 0a 00 00 0a 20 20 20 20 45 76 61 6c 75 | .|.|.z...z...S.).a.........Evalu |
| 6640 | 61 74 65 20 61 6e 20 48 65 72 6d 69 74 65 45 20 73 65 72 69 65 73 20 61 74 20 70 6f 69 6e 74 73 | ate.an.HermiteE.series.at.points |
| 6660 | 20 78 2e 0a 0a 20 20 20 20 49 66 20 60 63 60 20 69 73 20 6f 66 20 6c 65 6e 67 74 68 20 60 60 6e | .x.......If.`c`.is.of.length.``n |
| 6680 | 20 2b 20 31 60 60 2c 20 74 68 69 73 20 66 75 6e 63 74 69 6f 6e 20 72 65 74 75 72 6e 73 20 74 68 | .+.1``,.this.function.returns.th |
| 66a0 | 65 20 76 61 6c 75 65 3a 0a 0a 20 20 20 20 2e 2e 20 6d 61 74 68 3a 3a 20 70 28 78 29 20 3d 20 63 | e.value:.........math::.p(x).=.c |
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| 66e0 | 2e 2e 20 2b 20 63 5f 6e 20 2a 20 48 65 5f 6e 28 78 29 0a 0a 20 20 20 20 54 68 65 20 70 61 72 61 | ...+.c_n.*.He_n(x)......The.para |
| 6700 | 6d 65 74 65 72 20 60 78 60 20 69 73 20 63 6f 6e 76 65 72 74 65 64 20 74 6f 20 61 6e 20 61 72 72 | meter.`x`.is.converted.to.an.arr |
| 6720 | 61 79 20 6f 6e 6c 79 20 69 66 20 69 74 20 69 73 20 61 20 74 75 70 6c 65 20 6f 72 20 61 0a 20 20 | ay.only.if.it.is.a.tuple.or.a... |
| 6740 | 20 20 6c 69 73 74 2c 20 6f 74 68 65 72 77 69 73 65 20 69 74 20 69 73 20 74 72 65 61 74 65 64 20 | ..list,.otherwise.it.is.treated. |
| 6760 | 61 73 20 61 20 73 63 61 6c 61 72 2e 20 49 6e 20 65 69 74 68 65 72 20 63 61 73 65 2c 20 65 69 74 | as.a.scalar..In.either.case,.eit |
| 6780 | 68 65 72 20 60 78 60 0a 20 20 20 20 6f 72 20 69 74 73 20 65 6c 65 6d 65 6e 74 73 20 6d 75 73 74 | her.`x`.....or.its.elements.must |
| 67a0 | 20 73 75 70 70 6f 72 74 20 6d 75 6c 74 69 70 6c 69 63 61 74 69 6f 6e 20 61 6e 64 20 61 64 64 69 | .support.multiplication.and.addi |
| 67c0 | 74 69 6f 6e 20 62 6f 74 68 20 77 69 74 68 0a 20 20 20 20 74 68 65 6d 73 65 6c 76 65 73 20 61 6e | tion.both.with.....themselves.an |
| 67e0 | 64 20 77 69 74 68 20 74 68 65 20 65 6c 65 6d 65 6e 74 73 20 6f 66 20 60 63 60 2e 0a 0a 20 20 20 | d.with.the.elements.of.`c`...... |
| 6800 | 20 49 66 20 60 63 60 20 69 73 20 61 20 31 2d 44 20 61 72 72 61 79 2c 20 74 68 65 6e 20 60 60 70 | .If.`c`.is.a.1-D.array,.then.``p |
| 6820 | 28 78 29 60 60 20 77 69 6c 6c 20 68 61 76 65 20 74 68 65 20 73 61 6d 65 20 73 68 61 70 65 20 61 | (x)``.will.have.the.same.shape.a |
| 6840 | 73 20 60 78 60 2e 20 20 49 66 0a 20 20 20 20 60 63 60 20 69 73 20 6d 75 6c 74 69 64 69 6d 65 6e | s.`x`...If.....`c`.is.multidimen |
| 6860 | 73 69 6f 6e 61 6c 2c 20 74 68 65 6e 20 74 68 65 20 73 68 61 70 65 20 6f 66 20 74 68 65 20 72 65 | sional,.then.the.shape.of.the.re |
| 6880 | 73 75 6c 74 20 64 65 70 65 6e 64 73 20 6f 6e 20 74 68 65 0a 20 20 20 20 76 61 6c 75 65 20 6f 66 | sult.depends.on.the.....value.of |
| 68a0 | 20 60 74 65 6e 73 6f 72 60 2e 20 49 66 20 60 74 65 6e 73 6f 72 60 20 69 73 20 74 72 75 65 20 74 | .`tensor`..If.`tensor`.is.true.t |
| 68c0 | 68 65 20 73 68 61 70 65 20 77 69 6c 6c 20 62 65 20 63 2e 73 68 61 70 65 5b 31 3a 5d 20 2b 0a 20 | he.shape.will.be.c.shape[1:].+.. |
| 68e0 | 20 20 20 78 2e 73 68 61 70 65 2e 20 49 66 20 60 74 65 6e 73 6f 72 60 20 69 73 20 66 61 6c 73 65 | ...x.shape..If.`tensor`.is.false |
| 6900 | 20 74 68 65 20 73 68 61 70 65 20 77 69 6c 6c 20 62 65 20 63 2e 73 68 61 70 65 5b 31 3a 5d 2e 20 | .the.shape.will.be.c.shape[1:].. |
| 6920 | 4e 6f 74 65 20 74 68 61 74 0a 20 20 20 20 73 63 61 6c 61 72 73 20 68 61 76 65 20 73 68 61 70 65 | Note.that.....scalars.have.shape |
| 6940 | 20 28 2c 29 2e 0a 0a 20 20 20 20 54 72 61 69 6c 69 6e 67 20 7a 65 72 6f 73 20 69 6e 20 74 68 65 | .(,).......Trailing.zeros.in.the |
| 6960 | 20 63 6f 65 66 66 69 63 69 65 6e 74 73 20 77 69 6c 6c 20 62 65 20 75 73 65 64 20 69 6e 20 74 68 | .coefficients.will.be.used.in.th |
| 6980 | 65 20 65 76 61 6c 75 61 74 69 6f 6e 2c 20 73 6f 0a 20 20 20 20 74 68 65 79 20 73 68 6f 75 6c 64 | e.evaluation,.so.....they.should |
| 69a0 | 20 62 65 20 61 76 6f 69 64 65 64 20 69 66 20 65 66 66 69 63 69 65 6e 63 79 20 69 73 20 61 20 63 | .be.avoided.if.efficiency.is.a.c |
| 69c0 | 6f 6e 63 65 72 6e 2e 0a 0a 20 20 20 20 50 61 72 61 6d 65 74 65 72 73 0a 20 20 20 20 2d 2d 2d 2d | oncern.......Parameters.....---- |
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| 6a40 | 74 6f 20 61 6e 20 6e 64 61 72 72 61 79 2c 20 6f 74 68 65 72 77 69 73 65 0a 20 20 20 20 20 20 20 | to.an.ndarray,.otherwise........ |
| 6a60 | 20 69 74 20 69 73 20 6c 65 66 74 20 75 6e 63 68 61 6e 67 65 64 20 61 6e 64 20 74 72 65 61 74 65 | .it.is.left.unchanged.and.treate |
| 6a80 | 64 20 61 73 20 61 20 73 63 61 6c 61 72 2e 20 49 6e 20 65 69 74 68 65 72 20 63 61 73 65 2c 20 60 | d.as.a.scalar..In.either.case,.` |
| 6aa0 | 78 60 0a 20 20 20 20 20 20 20 20 6f 72 20 69 74 73 20 65 6c 65 6d 65 6e 74 73 20 6d 75 73 74 20 | x`.........or.its.elements.must. |
| 6ac0 | 73 75 70 70 6f 72 74 20 61 64 64 69 74 69 6f 6e 20 61 6e 64 20 6d 75 6c 74 69 70 6c 69 63 61 74 | support.addition.and.multiplicat |
| 6ae0 | 69 6f 6e 20 77 69 74 68 0a 20 20 20 20 20 20 20 20 77 69 74 68 20 74 68 65 6d 73 65 6c 76 65 73 | ion.with.........with.themselves |
| 6b00 | 20 61 6e 64 20 77 69 74 68 20 74 68 65 20 65 6c 65 6d 65 6e 74 73 20 6f 66 20 60 63 60 2e 0a 20 | .and.with.the.elements.of.`c`... |
| 6b20 | 20 20 20 63 20 3a 20 61 72 72 61 79 5f 6c 69 6b 65 0a 20 20 20 20 20 20 20 20 41 72 72 61 79 20 | ...c.:.array_like.........Array. |
| 6b40 | 6f 66 20 63 6f 65 66 66 69 63 69 65 6e 74 73 20 6f 72 64 65 72 65 64 20 73 6f 20 74 68 61 74 20 | of.coefficients.ordered.so.that. |
| 6b60 | 74 68 65 20 63 6f 65 66 66 69 63 69 65 6e 74 73 20 66 6f 72 20 74 65 72 6d 73 20 6f 66 0a 20 20 | the.coefficients.for.terms.of... |
| 6b80 | 20 20 20 20 20 20 64 65 67 72 65 65 20 6e 20 61 72 65 20 63 6f 6e 74 61 69 6e 65 64 20 69 6e 20 | ......degree.n.are.contained.in. |
| 6ba0 | 63 5b 6e 5d 2e 20 49 66 20 60 63 60 20 69 73 20 6d 75 6c 74 69 64 69 6d 65 6e 73 69 6f 6e 61 6c | c[n]..If.`c`.is.multidimensional |
| 6bc0 | 20 74 68 65 0a 20 20 20 20 20 20 20 20 72 65 6d 61 69 6e 69 6e 67 20 69 6e 64 69 63 65 73 20 65 | .the.........remaining.indices.e |
| 6be0 | 6e 75 6d 65 72 61 74 65 20 6d 75 6c 74 69 70 6c 65 20 70 6f 6c 79 6e 6f 6d 69 61 6c 73 2e 20 49 | numerate.multiple.polynomials..I |
| 6c00 | 6e 20 74 68 65 20 74 77 6f 0a 20 20 20 20 20 20 20 20 64 69 6d 65 6e 73 69 6f 6e 61 6c 20 63 61 | n.the.two.........dimensional.ca |
| 6c20 | 73 65 20 74 68 65 20 63 6f 65 66 66 69 63 69 65 6e 74 73 20 6d 61 79 20 62 65 20 74 68 6f 75 67 | se.the.coefficients.may.be.thoug |
| 6c40 | 68 74 20 6f 66 20 61 73 20 73 74 6f 72 65 64 20 69 6e 0a 20 20 20 20 20 20 20 20 74 68 65 20 63 | ht.of.as.stored.in.........the.c |
| 6c60 | 6f 6c 75 6d 6e 73 20 6f 66 20 60 63 60 2e 0a 20 20 20 20 74 65 6e 73 6f 72 20 3a 20 62 6f 6f 6c | olumns.of.`c`......tensor.:.bool |
| 6c80 | 65 61 6e 2c 20 6f 70 74 69 6f 6e 61 6c 0a 20 20 20 20 20 20 20 20 49 66 20 54 72 75 65 2c 20 74 | ean,.optional.........If.True,.t |
| 6ca0 | 68 65 20 73 68 61 70 65 20 6f 66 20 74 68 65 20 63 6f 65 66 66 69 63 69 65 6e 74 20 61 72 72 61 | he.shape.of.the.coefficient.arra |
| 6cc0 | 79 20 69 73 20 65 78 74 65 6e 64 65 64 20 77 69 74 68 20 6f 6e 65 73 0a 20 20 20 20 20 20 20 20 | y.is.extended.with.ones......... |
| 6ce0 | 6f 6e 20 74 68 65 20 72 69 67 68 74 2c 20 6f 6e 65 20 66 6f 72 20 65 61 63 68 20 64 69 6d 65 6e | on.the.right,.one.for.each.dimen |
| 6d00 | 73 69 6f 6e 20 6f 66 20 60 78 60 2e 20 53 63 61 6c 61 72 73 20 68 61 76 65 20 64 69 6d 65 6e 73 | sion.of.`x`..Scalars.have.dimens |
| 6d20 | 69 6f 6e 20 30 0a 20 20 20 20 20 20 20 20 66 6f 72 20 74 68 69 73 20 61 63 74 69 6f 6e 2e 20 54 | ion.0.........for.this.action..T |
| 6d40 | 68 65 20 72 65 73 75 6c 74 20 69 73 20 74 68 61 74 20 65 76 65 72 79 20 63 6f 6c 75 6d 6e 20 6f | he.result.is.that.every.column.o |
| 6d60 | 66 20 63 6f 65 66 66 69 63 69 65 6e 74 73 20 69 6e 0a 20 20 20 20 20 20 20 20 60 63 60 20 69 73 | f.coefficients.in.........`c`.is |
| 6d80 | 20 65 76 61 6c 75 61 74 65 64 20 66 6f 72 20 65 76 65 72 79 20 65 6c 65 6d 65 6e 74 20 6f 66 20 | .evaluated.for.every.element.of. |
| 6da0 | 60 78 60 2e 20 49 66 20 46 61 6c 73 65 2c 20 60 78 60 20 69 73 20 62 72 6f 61 64 63 61 73 74 0a | `x`..If.False,.`x`.is.broadcast. |
| 6dc0 | 20 20 20 20 20 20 20 20 6f 76 65 72 20 74 68 65 20 63 6f 6c 75 6d 6e 73 20 6f 66 20 60 63 60 20 | ........over.the.columns.of.`c`. |
| 6de0 | 66 6f 72 20 74 68 65 20 65 76 61 6c 75 61 74 69 6f 6e 2e 20 20 54 68 69 73 20 6b 65 79 77 6f 72 | for.the.evaluation...This.keywor |
| 6e00 | 64 20 69 73 20 75 73 65 66 75 6c 0a 20 20 20 20 20 20 20 20 77 68 65 6e 20 60 63 60 20 69 73 20 | d.is.useful.........when.`c`.is. |
| 6e20 | 6d 75 6c 74 69 64 69 6d 65 6e 73 69 6f 6e 61 6c 2e 20 54 68 65 20 64 65 66 61 75 6c 74 20 76 61 | multidimensional..The.default.va |
| 6e40 | 6c 75 65 20 69 73 20 54 72 75 65 2e 0a 0a 20 20 20 20 52 65 74 75 72 6e 73 0a 20 20 20 20 2d 2d | lue.is.True.......Returns.....-- |
| 6e60 | 2d 2d 2d 2d 2d 0a 20 20 20 20 76 61 6c 75 65 73 20 3a 20 6e 64 61 72 72 61 79 2c 20 61 6c 67 65 | -----.....values.:.ndarray,.alge |
| 6e80 | 62 72 61 5f 6c 69 6b 65 0a 20 20 20 20 20 20 20 20 54 68 65 20 73 68 61 70 65 20 6f 66 20 74 68 | bra_like.........The.shape.of.th |
| 6ea0 | 65 20 72 65 74 75 72 6e 20 76 61 6c 75 65 20 69 73 20 64 65 73 63 72 69 62 65 64 20 61 62 6f 76 | e.return.value.is.described.abov |
| 6ec0 | 65 2e 0a 0a 20 20 20 20 53 65 65 20 41 6c 73 6f 0a 20 20 20 20 2d 2d 2d 2d 2d 2d 2d 2d 0a 20 20 | e.......See.Also.....--------... |
| 6ee0 | 20 20 68 65 72 6d 65 76 61 6c 32 64 2c 20 68 65 72 6d 65 67 72 69 64 32 64 2c 20 68 65 72 6d 65 | ..hermeval2d,.hermegrid2d,.herme |
| 6f00 | 76 61 6c 33 64 2c 20 68 65 72 6d 65 67 72 69 64 33 64 0a 0a 20 20 20 20 4e 6f 74 65 73 0a 20 20 | val3d,.hermegrid3d......Notes... |
| 6f20 | 20 20 2d 2d 2d 2d 2d 0a 20 20 20 20 54 68 65 20 65 76 61 6c 75 61 74 69 6f 6e 20 75 73 65 73 20 | ..-----.....The.evaluation.uses. |
| 6f40 | 43 6c 65 6e 73 68 61 77 20 72 65 63 75 72 73 69 6f 6e 2c 20 61 6b 61 20 73 79 6e 74 68 65 74 69 | Clenshaw.recursion,.aka.syntheti |
| 6f60 | 63 20 64 69 76 69 73 69 6f 6e 2e 0a 0a 20 20 20 20 45 78 61 6d 70 6c 65 73 0a 20 20 20 20 2d 2d | c.division.......Examples.....-- |
| 6f80 | 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 3e 3e 3e 20 66 72 6f 6d 20 6e 75 6d 70 79 2e 70 6f 6c 79 6e 6f | ------.....>>>.from.numpy.polyno |
| 6fa0 | 6d 69 61 6c 2e 68 65 72 6d 69 74 65 5f 65 20 69 6d 70 6f 72 74 20 68 65 72 6d 65 76 61 6c 0a 20 | mial.hermite_e.import.hermeval.. |
| 6fc0 | 20 20 20 3e 3e 3e 20 63 6f 65 66 20 3d 20 5b 31 2c 32 2c 33 5d 0a 20 20 20 20 3e 3e 3e 20 68 65 | ...>>>.coef.=.[1,2,3].....>>>.he |
| 6fe0 | 72 6d 65 76 61 6c 28 31 2c 20 63 6f 65 66 29 0a 20 20 20 20 33 2e 30 0a 20 20 20 20 3e 3e 3e 20 | rmeval(1,.coef).....3.0.....>>>. |
| 7000 | 68 65 72 6d 65 76 61 6c 28 5b 5b 31 2c 32 5d 2c 5b 33 2c 34 5d 5d 2c 20 63 6f 65 66 29 0a 20 20 | hermeval([[1,2],[3,4]],.coef)... |
| 7020 | 20 20 61 72 72 61 79 28 5b 5b 20 33 2e 2c 20 31 34 2e 5d 2c 0a 20 20 20 20 20 20 20 20 20 20 20 | ..array([[.3.,.14.],............ |
| 7040 | 5b 33 31 2e 2c 20 35 34 2e 5d 5d 29 0a 0a 20 20 20 20 72 04 00 00 00 4e 72 5e 00 00 00 72 61 00 | [31.,.54.]])......r....Nr^...ra. |
| 7060 | 00 00 29 01 72 04 00 00 00 72 02 00 00 00 72 36 00 00 00 72 37 00 00 00 72 27 00 00 00 72 54 00 | ..).r....r....r6...r7...r'...rT. |
| 7080 | 00 00 29 10 72 40 00 00 00 72 41 00 00 00 72 50 00 00 00 72 63 00 00 00 72 64 00 00 00 72 65 00 | ..).r@...rA...rP...rc...rd...re. |
| 70a0 | 00 00 da 0a 69 73 69 6e 73 74 61 6e 63 65 da 05 74 75 70 6c 65 72 73 00 00 00 da 07 61 73 61 72 | ....isinstance..tuplers.....asar |
| 70c0 | 72 61 79 da 07 6e 64 61 72 72 61 79 da 07 72 65 73 68 61 70 65 72 6a 00 00 00 72 68 00 00 00 72 | ray..ndarray..reshaperj...rh...r |
| 70e0 | 2a 00 00 00 72 2b 00 00 00 29 08 da 01 78 72 39 00 00 00 da 06 74 65 6e 73 6f 72 72 3b 00 00 00 | *...r+...)...xr9.....tensorr;... |
| 7100 | 72 3c 00 00 00 72 56 00 00 00 72 2f 00 00 00 72 3d 00 00 00 73 08 00 00 00 20 20 20 20 20 20 20 | r<...rV...r/...r=...s........... |
| 7120 | 20 72 30 00 00 00 72 12 00 00 00 72 12 00 00 00 1d 03 00 00 73 35 01 00 00 80 00 f4 46 02 00 09 | .r0...r....r........s5......F... |
| 7140 | 0b 8f 08 89 08 90 11 98 21 a0 24 d4 08 27 80 41 d8 07 08 87 77 81 77 87 7c 81 7c 90 7f d1 07 26 | ........!.$..'.A....w.w.|.|....& |
| 7160 | d8 0c 0d 8f 48 89 48 94 52 97 59 91 59 d3 0c 1f 88 01 dc 07 11 90 21 94 65 9c 54 90 5d d4 07 23 | ....H.H.R.Y.Y.........!.e.T.]..# |
| 7180 | dc 0c 0e 8f 4a 89 4a 90 71 8b 4d 88 01 dc 07 11 90 21 94 52 97 5a 91 5a d4 07 20 a1 56 d8 0c 0d | ....J.J.q.M......!.R.Z.Z....V... |
| 71a0 | 8f 49 89 49 90 61 97 67 91 67 a0 04 a0 71 a7 76 a1 76 a1 0d d1 16 2d d3 0c 2e 88 01 e4 07 0a 88 | .I.I.a.g.g...q.v.v....-......... |
| 71c0 | 31 83 76 90 11 82 7b d8 0d 0e 88 71 89 54 88 02 d8 0d 0e 89 02 dc 09 0c 88 51 8b 16 90 31 8a 1b | 1.v...{....q.T...........Q...1.. |
| 71e0 | d8 0d 0e 88 71 89 54 88 02 d8 0d 0e 88 71 89 54 89 02 e4 0d 10 90 11 8b 56 88 02 d8 0d 0e 88 72 | ....q.T......q.T........V......r |
| 7200 | 89 55 88 02 d8 0d 0e 88 72 89 55 88 02 dc 11 16 90 71 9c 23 98 61 9b 26 a0 31 99 2a d3 11 25 f2 | .U......r.U......q.#.a.&.1.*..%. |
| 7220 | 00 04 09 1e 88 41 d8 12 14 88 43 d8 11 13 90 61 91 16 88 42 d8 11 12 90 41 90 32 91 15 98 12 98 | .....A....C....a...B....A.2..... |
| 7240 | 72 a0 41 99 76 99 1d d1 11 26 88 42 d8 11 14 90 72 98 41 91 76 91 1c 89 42 f0 09 04 09 1e f0 0a | r.A.v....&.B....r.A.v...B....... |
| 7260 | 00 0c 0e 90 02 90 51 91 06 89 3b d0 04 16 72 31 00 00 00 63 03 00 00 00 00 00 00 00 00 00 00 00 | ......Q...;...r1...c............ |
| 7280 | 06 00 00 00 03 00 00 00 f3 3a 00 00 00 97 00 74 01 00 00 00 00 00 00 00 00 6a 02 00 00 00 00 00 | .........:.....t.........j...... |
| 72a0 | 00 00 00 00 00 00 00 00 00 00 00 00 00 74 04 00 00 00 00 00 00 00 00 7c 02 7c 00 7c 01 ab 04 00 | .............t.........|.|.|.... |
| 72c0 | 00 00 00 00 00 53 00 29 01 61 18 06 00 00 0a 20 20 20 20 45 76 61 6c 75 61 74 65 20 61 20 32 2d | .....S.).a.........Evaluate.a.2- |
| 72e0 | 44 20 48 65 72 6d 69 74 65 45 20 73 65 72 69 65 73 20 61 74 20 70 6f 69 6e 74 73 20 28 78 2c 20 | D.HermiteE.series.at.points.(x,. |
| 7300 | 79 29 2e 0a 0a 20 20 20 20 54 68 69 73 20 66 75 6e 63 74 69 6f 6e 20 72 65 74 75 72 6e 73 20 74 | y).......This.function.returns.t |
| 7320 | 68 65 20 76 61 6c 75 65 73 3a 0a 0a 20 20 20 20 2e 2e 20 6d 61 74 68 3a 3a 20 70 28 78 2c 79 29 | he.values:.........math::.p(x,y) |
| 7340 | 20 3d 20 5c 73 75 6d 5f 7b 69 2c 6a 7d 20 63 5f 7b 69 2c 6a 7d 20 2a 20 48 65 5f 69 28 78 29 20 | .=.\sum_{i,j}.c_{i,j}.*.He_i(x). |
| 7360 | 2a 20 48 65 5f 6a 28 79 29 0a 0a 20 20 20 20 54 68 65 20 70 61 72 61 6d 65 74 65 72 73 20 60 78 | *.He_j(y)......The.parameters.`x |
| 7380 | 60 20 61 6e 64 20 60 79 60 20 61 72 65 20 63 6f 6e 76 65 72 74 65 64 20 74 6f 20 61 72 72 61 79 | `.and.`y`.are.converted.to.array |
| 73a0 | 73 20 6f 6e 6c 79 20 69 66 20 74 68 65 79 20 61 72 65 0a 20 20 20 20 74 75 70 6c 65 73 20 6f 72 | s.only.if.they.are.....tuples.or |
| 73c0 | 20 61 20 6c 69 73 74 73 2c 20 6f 74 68 65 72 77 69 73 65 20 74 68 65 79 20 61 72 65 20 74 72 65 | .a.lists,.otherwise.they.are.tre |
| 73e0 | 61 74 65 64 20 61 73 20 61 20 73 63 61 6c 61 72 73 20 61 6e 64 20 74 68 65 79 0a 20 20 20 20 6d | ated.as.a.scalars.and.they.....m |
| 7400 | 75 73 74 20 68 61 76 65 20 74 68 65 20 73 61 6d 65 20 73 68 61 70 65 20 61 66 74 65 72 20 63 6f | ust.have.the.same.shape.after.co |
| 7420 | 6e 76 65 72 73 69 6f 6e 2e 20 49 6e 20 65 69 74 68 65 72 20 63 61 73 65 2c 20 65 69 74 68 65 72 | nversion..In.either.case,.either |
| 7440 | 20 60 78 60 0a 20 20 20 20 61 6e 64 20 60 79 60 20 6f 72 20 74 68 65 69 72 20 65 6c 65 6d 65 6e | .`x`.....and.`y`.or.their.elemen |
| 7460 | 74 73 20 6d 75 73 74 20 73 75 70 70 6f 72 74 20 6d 75 6c 74 69 70 6c 69 63 61 74 69 6f 6e 20 61 | ts.must.support.multiplication.a |
| 7480 | 6e 64 20 61 64 64 69 74 69 6f 6e 20 62 6f 74 68 0a 20 20 20 20 77 69 74 68 20 74 68 65 6d 73 65 | nd.addition.both.....with.themse |
| 74a0 | 6c 76 65 73 20 61 6e 64 20 77 69 74 68 20 74 68 65 20 65 6c 65 6d 65 6e 74 73 20 6f 66 20 60 63 | lves.and.with.the.elements.of.`c |
| 74c0 | 60 2e 0a 0a 20 20 20 20 49 66 20 60 63 60 20 69 73 20 61 20 31 2d 44 20 61 72 72 61 79 20 61 20 | `.......If.`c`.is.a.1-D.array.a. |
| 74e0 | 6f 6e 65 20 69 73 20 69 6d 70 6c 69 63 69 74 6c 79 20 61 70 70 65 6e 64 65 64 20 74 6f 20 69 74 | one.is.implicitly.appended.to.it |
| 7500 | 73 20 73 68 61 70 65 20 74 6f 20 6d 61 6b 65 0a 20 20 20 20 69 74 20 32 2d 44 2e 20 54 68 65 20 | s.shape.to.make.....it.2-D..The. |
| 7520 | 73 68 61 70 65 20 6f 66 20 74 68 65 20 72 65 73 75 6c 74 20 77 69 6c 6c 20 62 65 20 63 2e 73 68 | shape.of.the.result.will.be.c.sh |
| 7540 | 61 70 65 5b 32 3a 5d 20 2b 20 78 2e 73 68 61 70 65 2e 0a 0a 20 20 20 20 50 61 72 61 6d 65 74 65 | ape[2:].+.x.shape.......Paramete |
| 7560 | 72 73 0a 20 20 20 20 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 78 2c 20 79 20 3a 20 61 72 72 | rs.....----------.....x,.y.:.arr |
| 7580 | 61 79 5f 6c 69 6b 65 2c 20 63 6f 6d 70 61 74 69 62 6c 65 20 6f 62 6a 65 63 74 73 0a 20 20 20 20 | ay_like,.compatible.objects..... |
| 75a0 | 20 20 20 20 54 68 65 20 74 77 6f 20 64 69 6d 65 6e 73 69 6f 6e 61 6c 20 73 65 72 69 65 73 20 69 | ....The.two.dimensional.series.i |
| 75c0 | 73 20 65 76 61 6c 75 61 74 65 64 20 61 74 20 74 68 65 20 70 6f 69 6e 74 73 20 60 60 28 78 2c 20 | s.evaluated.at.the.points.``(x,. |
| 75e0 | 79 29 60 60 2c 0a 20 20 20 20 20 20 20 20 77 68 65 72 65 20 60 78 60 20 61 6e 64 20 60 79 60 20 | y)``,.........where.`x`.and.`y`. |
| 7600 | 6d 75 73 74 20 68 61 76 65 20 74 68 65 20 73 61 6d 65 20 73 68 61 70 65 2e 20 49 66 20 60 78 60 | must.have.the.same.shape..If.`x` |
| 7620 | 20 6f 72 20 60 79 60 20 69 73 20 61 20 6c 69 73 74 0a 20 20 20 20 20 20 20 20 6f 72 20 74 75 70 | .or.`y`.is.a.list.........or.tup |
| 7640 | 6c 65 2c 20 69 74 20 69 73 20 66 69 72 73 74 20 63 6f 6e 76 65 72 74 65 64 20 74 6f 20 61 6e 20 | le,.it.is.first.converted.to.an. |
| 7660 | 6e 64 61 72 72 61 79 2c 20 6f 74 68 65 72 77 69 73 65 20 69 74 20 69 73 20 6c 65 66 74 0a 20 20 | ndarray,.otherwise.it.is.left... |
| 7680 | 20 20 20 20 20 20 75 6e 63 68 61 6e 67 65 64 20 61 6e 64 20 69 66 20 69 74 20 69 73 6e 27 74 20 | ......unchanged.and.if.it.isn't. |
| 76a0 | 61 6e 20 6e 64 61 72 72 61 79 20 69 74 20 69 73 20 74 72 65 61 74 65 64 20 61 73 20 61 20 73 63 | an.ndarray.it.is.treated.as.a.sc |
| 76c0 | 61 6c 61 72 2e 0a 20 20 20 20 63 20 3a 20 61 72 72 61 79 5f 6c 69 6b 65 0a 20 20 20 20 20 20 20 | alar......c.:.array_like........ |
| 76e0 | 20 41 72 72 61 79 20 6f 66 20 63 6f 65 66 66 69 63 69 65 6e 74 73 20 6f 72 64 65 72 65 64 20 73 | .Array.of.coefficients.ordered.s |
| 7700 | 6f 20 74 68 61 74 20 74 68 65 20 63 6f 65 66 66 69 63 69 65 6e 74 20 6f 66 20 74 68 65 20 74 65 | o.that.the.coefficient.of.the.te |
| 7720 | 72 6d 0a 20 20 20 20 20 20 20 20 6f 66 20 6d 75 6c 74 69 2d 64 65 67 72 65 65 20 69 2c 6a 20 69 | rm.........of.multi-degree.i,j.i |
| 7740 | 73 20 63 6f 6e 74 61 69 6e 65 64 20 69 6e 20 60 60 63 5b 69 2c 6a 5d 60 60 2e 20 49 66 20 60 63 | s.contained.in.``c[i,j]``..If.`c |
| 7760 | 60 20 68 61 73 0a 20 20 20 20 20 20 20 20 64 69 6d 65 6e 73 69 6f 6e 20 67 72 65 61 74 65 72 20 | `.has.........dimension.greater. |
| 7780 | 74 68 61 6e 20 74 77 6f 20 74 68 65 20 72 65 6d 61 69 6e 69 6e 67 20 69 6e 64 69 63 65 73 20 65 | than.two.the.remaining.indices.e |
| 77a0 | 6e 75 6d 65 72 61 74 65 20 6d 75 6c 74 69 70 6c 65 0a 20 20 20 20 20 20 20 20 73 65 74 73 20 6f | numerate.multiple.........sets.o |
| 77c0 | 66 20 63 6f 65 66 66 69 63 69 65 6e 74 73 2e 0a 0a 20 20 20 20 52 65 74 75 72 6e 73 0a 20 20 20 | f.coefficients.......Returns.... |
| 77e0 | 20 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 76 61 6c 75 65 73 20 3a 20 6e 64 61 72 72 61 79 2c 20 63 | .-------.....values.:.ndarray,.c |
| 7800 | 6f 6d 70 61 74 69 62 6c 65 20 6f 62 6a 65 63 74 0a 20 20 20 20 20 20 20 20 54 68 65 20 76 61 6c | ompatible.object.........The.val |
| 7820 | 75 65 73 20 6f 66 20 74 68 65 20 74 77 6f 20 64 69 6d 65 6e 73 69 6f 6e 61 6c 20 70 6f 6c 79 6e | ues.of.the.two.dimensional.polyn |
| 7840 | 6f 6d 69 61 6c 20 61 74 20 70 6f 69 6e 74 73 20 66 6f 72 6d 65 64 20 77 69 74 68 0a 20 20 20 20 | omial.at.points.formed.with..... |
| 7860 | 20 20 20 20 70 61 69 72 73 20 6f 66 20 63 6f 72 72 65 73 70 6f 6e 64 69 6e 67 20 76 61 6c 75 65 | ....pairs.of.corresponding.value |
| 7880 | 73 20 66 72 6f 6d 20 60 78 60 20 61 6e 64 20 60 79 60 2e 0a 0a 20 20 20 20 53 65 65 20 41 6c 73 | s.from.`x`.and.`y`.......See.Als |
| 78a0 | 6f 0a 20 20 20 20 2d 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 68 65 72 6d 65 76 61 6c 2c 20 68 65 72 | o.....--------.....hermeval,.her |
| 78c0 | 6d 65 67 72 69 64 32 64 2c 20 68 65 72 6d 65 76 61 6c 33 64 2c 20 68 65 72 6d 65 67 72 69 64 33 | megrid2d,.hermeval3d,.hermegrid3 |
| 78e0 | 64 0a 20 20 20 20 a9 03 72 28 00 00 00 da 06 5f 76 61 6c 6e 64 72 12 00 00 00 a9 03 72 7d 00 00 | d.......r(....._valndr......r}.. |
| 7900 | 00 da 01 79 72 39 00 00 00 73 03 00 00 00 20 20 20 72 30 00 00 00 72 1d 00 00 00 72 1d 00 00 00 | ...yr9...s.......r0...r....r.... |
| 7920 | 7a 03 00 00 73 1a 00 00 00 80 00 f4 50 01 00 0c 0e 8f 39 89 39 94 58 98 71 a0 21 a0 51 d3 0b 27 | z...s.......P.....9.9.X.q.!.Q..' |
| 7940 | d0 04 27 72 31 00 00 00 63 03 00 00 00 00 00 00 00 00 00 00 00 06 00 00 00 03 00 00 00 f3 3a 00 | ..'r1...c.....................:. |
| 7960 | 00 00 97 00 74 01 00 00 00 00 00 00 00 00 6a 02 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 | ....t.........j................. |
| 7980 | 00 00 74 04 00 00 00 00 00 00 00 00 7c 02 7c 00 7c 01 ab 04 00 00 00 00 00 00 53 00 29 01 61 a6 | ..t.........|.|.|.........S.).a. |
| 79a0 | 06 00 00 0a 20 20 20 20 45 76 61 6c 75 61 74 65 20 61 20 32 2d 44 20 48 65 72 6d 69 74 65 45 20 | ........Evaluate.a.2-D.HermiteE. |
| 79c0 | 73 65 72 69 65 73 20 6f 6e 20 74 68 65 20 43 61 72 74 65 73 69 61 6e 20 70 72 6f 64 75 63 74 20 | series.on.the.Cartesian.product. |
| 79e0 | 6f 66 20 78 20 61 6e 64 20 79 2e 0a 0a 20 20 20 20 54 68 69 73 20 66 75 6e 63 74 69 6f 6e 20 72 | of.x.and.y.......This.function.r |
| 7a00 | 65 74 75 72 6e 73 20 74 68 65 20 76 61 6c 75 65 73 3a 0a 0a 20 20 20 20 2e 2e 20 6d 61 74 68 3a | eturns.the.values:.........math: |
| 7a20 | 3a 20 70 28 61 2c 62 29 20 3d 20 5c 73 75 6d 5f 7b 69 2c 6a 7d 20 63 5f 7b 69 2c 6a 7d 20 2a 20 | :.p(a,b).=.\sum_{i,j}.c_{i,j}.*. |
| 7a40 | 48 5f 69 28 61 29 20 2a 20 48 5f 6a 28 62 29 0a 0a 20 20 20 20 77 68 65 72 65 20 74 68 65 20 70 | H_i(a).*.H_j(b)......where.the.p |
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| 7a80 | 70 61 69 72 73 20 66 6f 72 6d 65 64 20 62 79 20 74 61 6b 69 6e 67 0a 20 20 20 20 60 61 60 20 66 | pairs.formed.by.taking.....`a`.f |
| 7aa0 | 72 6f 6d 20 60 78 60 20 61 6e 64 20 60 62 60 20 66 72 6f 6d 20 60 79 60 2e 20 54 68 65 20 72 65 | rom.`x`.and.`b`.from.`y`..The.re |
| 7ac0 | 73 75 6c 74 69 6e 67 20 70 6f 69 6e 74 73 20 66 6f 72 6d 20 61 20 67 72 69 64 20 77 69 74 68 0a | sulting.points.form.a.grid.with. |
| 7ae0 | 20 20 20 20 60 78 60 20 69 6e 20 74 68 65 20 66 69 72 73 74 20 64 69 6d 65 6e 73 69 6f 6e 20 61 | ....`x`.in.the.first.dimension.a |
| 7b00 | 6e 64 20 60 79 60 20 69 6e 20 74 68 65 20 73 65 63 6f 6e 64 2e 0a 0a 20 20 20 20 54 68 65 20 70 | nd.`y`.in.the.second.......The.p |
| 7b20 | 61 72 61 6d 65 74 65 72 73 20 60 78 60 20 61 6e 64 20 60 79 60 20 61 72 65 20 63 6f 6e 76 65 72 | arameters.`x`.and.`y`.are.conver |
| 7b40 | 74 65 64 20 74 6f 20 61 72 72 61 79 73 20 6f 6e 6c 79 20 69 66 20 74 68 65 79 20 61 72 65 0a 20 | ted.to.arrays.only.if.they.are.. |
| 7b60 | 20 20 20 74 75 70 6c 65 73 20 6f 72 20 61 20 6c 69 73 74 73 2c 20 6f 74 68 65 72 77 69 73 65 20 | ...tuples.or.a.lists,.otherwise. |
| 7b80 | 74 68 65 79 20 61 72 65 20 74 72 65 61 74 65 64 20 61 73 20 61 20 73 63 61 6c 61 72 73 2e 20 49 | they.are.treated.as.a.scalars..I |
| 7ba0 | 6e 20 65 69 74 68 65 72 0a 20 20 20 20 63 61 73 65 2c 20 65 69 74 68 65 72 20 60 78 60 20 61 6e | n.either.....case,.either.`x`.an |
| 7bc0 | 64 20 60 79 60 20 6f 72 20 74 68 65 69 72 20 65 6c 65 6d 65 6e 74 73 20 6d 75 73 74 20 73 75 70 | d.`y`.or.their.elements.must.sup |
| 7be0 | 70 6f 72 74 20 6d 75 6c 74 69 70 6c 69 63 61 74 69 6f 6e 0a 20 20 20 20 61 6e 64 20 61 64 64 69 | port.multiplication.....and.addi |
| 7c00 | 74 69 6f 6e 20 62 6f 74 68 20 77 69 74 68 20 74 68 65 6d 73 65 6c 76 65 73 20 61 6e 64 20 77 69 | tion.both.with.themselves.and.wi |
| 7c20 | 74 68 20 74 68 65 20 65 6c 65 6d 65 6e 74 73 20 6f 66 20 60 63 60 2e 0a 0a 20 20 20 20 49 66 20 | th.the.elements.of.`c`.......If. |
| 7c40 | 60 63 60 20 68 61 73 20 66 65 77 65 72 20 74 68 61 6e 20 74 77 6f 20 64 69 6d 65 6e 73 69 6f 6e | `c`.has.fewer.than.two.dimension |
| 7c60 | 73 2c 20 6f 6e 65 73 20 61 72 65 20 69 6d 70 6c 69 63 69 74 6c 79 20 61 70 70 65 6e 64 65 64 20 | s,.ones.are.implicitly.appended. |
| 7c80 | 74 6f 0a 20 20 20 20 69 74 73 20 73 68 61 70 65 20 74 6f 20 6d 61 6b 65 20 69 74 20 32 2d 44 2e | to.....its.shape.to.make.it.2-D. |
| 7ca0 | 20 54 68 65 20 73 68 61 70 65 20 6f 66 20 74 68 65 20 72 65 73 75 6c 74 20 77 69 6c 6c 20 62 65 | .The.shape.of.the.result.will.be |
| 7cc0 | 20 63 2e 73 68 61 70 65 5b 32 3a 5d 20 2b 0a 20 20 20 20 78 2e 73 68 61 70 65 2e 0a 0a 20 20 20 | .c.shape[2:].+.....x.shape...... |
| 7ce0 | 20 50 61 72 61 6d 65 74 65 72 73 0a 20 20 20 20 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 78 | .Parameters.....----------.....x |
| 7d00 | 2c 20 79 20 3a 20 61 72 72 61 79 5f 6c 69 6b 65 2c 20 63 6f 6d 70 61 74 69 62 6c 65 20 6f 62 6a | ,.y.:.array_like,.compatible.obj |
| 7d20 | 65 63 74 73 0a 20 20 20 20 20 20 20 20 54 68 65 20 74 77 6f 20 64 69 6d 65 6e 73 69 6f 6e 61 6c | ects.........The.two.dimensional |
| 7d40 | 20 73 65 72 69 65 73 20 69 73 20 65 76 61 6c 75 61 74 65 64 20 61 74 20 74 68 65 20 70 6f 69 6e | .series.is.evaluated.at.the.poin |
| 7d60 | 74 73 20 69 6e 20 74 68 65 0a 20 20 20 20 20 20 20 20 43 61 72 74 65 73 69 61 6e 20 70 72 6f 64 | ts.in.the.........Cartesian.prod |
| 7d80 | 75 63 74 20 6f 66 20 60 78 60 20 61 6e 64 20 60 79 60 2e 20 20 49 66 20 60 78 60 20 6f 72 20 60 | uct.of.`x`.and.`y`...If.`x`.or.` |
| 7da0 | 79 60 20 69 73 20 61 20 6c 69 73 74 20 6f 72 0a 20 20 20 20 20 20 20 20 74 75 70 6c 65 2c 20 69 | y`.is.a.list.or.........tuple,.i |
| 7dc0 | 74 20 69 73 20 66 69 72 73 74 20 63 6f 6e 76 65 72 74 65 64 20 74 6f 20 61 6e 20 6e 64 61 72 72 | t.is.first.converted.to.an.ndarr |
| 7de0 | 61 79 2c 20 6f 74 68 65 72 77 69 73 65 20 69 74 20 69 73 20 6c 65 66 74 0a 20 20 20 20 20 20 20 | ay,.otherwise.it.is.left........ |
| 7e00 | 20 75 6e 63 68 61 6e 67 65 64 20 61 6e 64 2c 20 69 66 20 69 74 20 69 73 6e 27 74 20 61 6e 20 6e | .unchanged.and,.if.it.isn't.an.n |
| 7e20 | 64 61 72 72 61 79 2c 20 69 74 20 69 73 20 74 72 65 61 74 65 64 20 61 73 20 61 20 73 63 61 6c 61 | darray,.it.is.treated.as.a.scala |
| 7e40 | 72 2e 0a 20 20 20 20 63 20 3a 20 61 72 72 61 79 5f 6c 69 6b 65 0a 20 20 20 20 20 20 20 20 41 72 | r......c.:.array_like.........Ar |
| 7e60 | 72 61 79 20 6f 66 20 63 6f 65 66 66 69 63 69 65 6e 74 73 20 6f 72 64 65 72 65 64 20 73 6f 20 74 | ray.of.coefficients.ordered.so.t |
| 7e80 | 68 61 74 20 74 68 65 20 63 6f 65 66 66 69 63 69 65 6e 74 73 20 66 6f 72 20 74 65 72 6d 73 20 6f | hat.the.coefficients.for.terms.o |
| 7ea0 | 66 0a 20 20 20 20 20 20 20 20 64 65 67 72 65 65 20 69 2c 6a 20 61 72 65 20 63 6f 6e 74 61 69 6e | f.........degree.i,j.are.contain |
| 7ec0 | 65 64 20 69 6e 20 60 60 63 5b 69 2c 6a 5d 60 60 2e 20 49 66 20 60 63 60 20 68 61 73 20 64 69 6d | ed.in.``c[i,j]``..If.`c`.has.dim |
| 7ee0 | 65 6e 73 69 6f 6e 0a 20 20 20 20 20 20 20 20 67 72 65 61 74 65 72 20 74 68 61 6e 20 74 77 6f 20 | ension.........greater.than.two. |
| 7f00 | 74 68 65 20 72 65 6d 61 69 6e 69 6e 67 20 69 6e 64 69 63 65 73 20 65 6e 75 6d 65 72 61 74 65 20 | the.remaining.indices.enumerate. |
| 7f20 | 6d 75 6c 74 69 70 6c 65 20 73 65 74 73 20 6f 66 0a 20 20 20 20 20 20 20 20 63 6f 65 66 66 69 63 | multiple.sets.of.........coeffic |
| 7f40 | 69 65 6e 74 73 2e 0a 0a 20 20 20 20 52 65 74 75 72 6e 73 0a 20 20 20 20 2d 2d 2d 2d 2d 2d 2d 0a | ients.......Returns.....-------. |
| 7f60 | 20 20 20 20 76 61 6c 75 65 73 20 3a 20 6e 64 61 72 72 61 79 2c 20 63 6f 6d 70 61 74 69 62 6c 65 | ....values.:.ndarray,.compatible |
| 7f80 | 20 6f 62 6a 65 63 74 0a 20 20 20 20 20 20 20 20 54 68 65 20 76 61 6c 75 65 73 20 6f 66 20 74 68 | .object.........The.values.of.th |
| 7fa0 | 65 20 74 77 6f 20 64 69 6d 65 6e 73 69 6f 6e 61 6c 20 70 6f 6c 79 6e 6f 6d 69 61 6c 20 61 74 20 | e.two.dimensional.polynomial.at. |
| 7fc0 | 70 6f 69 6e 74 73 20 69 6e 20 74 68 65 20 43 61 72 74 65 73 69 61 6e 0a 20 20 20 20 20 20 20 20 | points.in.the.Cartesian......... |
| 7fe0 | 70 72 6f 64 75 63 74 20 6f 66 20 60 78 60 20 61 6e 64 20 60 79 60 2e 0a 0a 20 20 20 20 53 65 65 | product.of.`x`.and.`y`.......See |
| 8000 | 20 41 6c 73 6f 0a 20 20 20 20 2d 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 68 65 72 6d 65 76 61 6c 2c | .Also.....--------.....hermeval, |
| 8020 | 20 68 65 72 6d 65 76 61 6c 32 64 2c 20 68 65 72 6d 65 76 61 6c 33 64 2c 20 68 65 72 6d 65 67 72 | .hermeval2d,.hermeval3d,.hermegr |
| 8040 | 69 64 33 64 0a 20 20 20 20 a9 03 72 28 00 00 00 da 07 5f 67 72 69 64 6e 64 72 12 00 00 00 72 82 | id3d.......r(....._gridndr....r. |
| 8060 | 00 00 00 73 03 00 00 00 20 20 20 72 30 00 00 00 72 1f 00 00 00 72 1f 00 00 00 a5 03 00 00 73 1a | ...s.......r0...r....r........s. |
| 8080 | 00 00 00 80 00 f4 58 01 00 0c 0e 8f 3a 89 3a 94 68 a0 01 a0 31 a0 61 d3 0b 28 d0 04 28 72 31 00 | ......X.....:.:.h...1.a..(..(r1. |
| 80a0 | 00 00 63 04 00 00 00 00 00 00 00 00 00 00 00 07 00 00 00 03 00 00 00 f3 3c 00 00 00 97 00 74 01 | ..c.....................<.....t. |
| 80c0 | 00 00 00 00 00 00 00 00 6a 02 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 74 04 00 00 | ........j...................t... |
| 80e0 | 00 00 00 00 00 00 7c 03 7c 00 7c 01 7c 02 ab 05 00 00 00 00 00 00 53 00 29 01 61 77 06 00 00 0a | ......|.|.|.|.........S.).aw.... |
| 8100 | 20 20 20 20 45 76 61 6c 75 61 74 65 20 61 20 33 2d 44 20 48 65 72 6d 69 74 65 5f 65 20 73 65 72 | ....Evaluate.a.3-D.Hermite_e.ser |
| 8120 | 69 65 73 20 61 74 20 70 6f 69 6e 74 73 20 28 78 2c 20 79 2c 20 7a 29 2e 0a 0a 20 20 20 20 54 68 | ies.at.points.(x,.y,.z).......Th |
| 8140 | 69 73 20 66 75 6e 63 74 69 6f 6e 20 72 65 74 75 72 6e 73 20 74 68 65 20 76 61 6c 75 65 73 3a 0a | is.function.returns.the.values:. |
| 8160 | 0a 20 20 20 20 2e 2e 20 6d 61 74 68 3a 3a 20 70 28 78 2c 79 2c 7a 29 20 3d 20 5c 73 75 6d 5f 7b | ........math::.p(x,y,z).=.\sum_{ |
| 8180 | 69 2c 6a 2c 6b 7d 20 63 5f 7b 69 2c 6a 2c 6b 7d 20 2a 20 48 65 5f 69 28 78 29 20 2a 20 48 65 5f | i,j,k}.c_{i,j,k}.*.He_i(x).*.He_ |
| 81a0 | 6a 28 79 29 20 2a 20 48 65 5f 6b 28 7a 29 0a 0a 20 20 20 20 54 68 65 20 70 61 72 61 6d 65 74 65 | j(y).*.He_k(z)......The.paramete |
| 81c0 | 72 73 20 60 78 60 2c 20 60 79 60 2c 20 61 6e 64 20 60 7a 60 20 61 72 65 20 63 6f 6e 76 65 72 74 | rs.`x`,.`y`,.and.`z`.are.convert |
| 81e0 | 65 64 20 74 6f 20 61 72 72 61 79 73 20 6f 6e 6c 79 20 69 66 0a 20 20 20 20 74 68 65 79 20 61 72 | ed.to.arrays.only.if.....they.ar |
| 8200 | 65 20 74 75 70 6c 65 73 20 6f 72 20 61 20 6c 69 73 74 73 2c 20 6f 74 68 65 72 77 69 73 65 20 74 | e.tuples.or.a.lists,.otherwise.t |
| 8220 | 68 65 79 20 61 72 65 20 74 72 65 61 74 65 64 20 61 73 20 61 20 73 63 61 6c 61 72 73 20 61 6e 64 | hey.are.treated.as.a.scalars.and |
| 8240 | 0a 20 20 20 20 74 68 65 79 20 6d 75 73 74 20 68 61 76 65 20 74 68 65 20 73 61 6d 65 20 73 68 61 | .....they.must.have.the.same.sha |
| 8260 | 70 65 20 61 66 74 65 72 20 63 6f 6e 76 65 72 73 69 6f 6e 2e 20 49 6e 20 65 69 74 68 65 72 20 63 | pe.after.conversion..In.either.c |
| 8280 | 61 73 65 2c 20 65 69 74 68 65 72 0a 20 20 20 20 60 78 60 2c 20 60 79 60 2c 20 61 6e 64 20 60 7a | ase,.either.....`x`,.`y`,.and.`z |
| 82a0 | 60 20 6f 72 20 74 68 65 69 72 20 65 6c 65 6d 65 6e 74 73 20 6d 75 73 74 20 73 75 70 70 6f 72 74 | `.or.their.elements.must.support |
| 82c0 | 20 6d 75 6c 74 69 70 6c 69 63 61 74 69 6f 6e 20 61 6e 64 0a 20 20 20 20 61 64 64 69 74 69 6f 6e | .multiplication.and.....addition |
| 82e0 | 20 62 6f 74 68 20 77 69 74 68 20 74 68 65 6d 73 65 6c 76 65 73 20 61 6e 64 20 77 69 74 68 20 74 | .both.with.themselves.and.with.t |
| 8300 | 68 65 20 65 6c 65 6d 65 6e 74 73 20 6f 66 20 60 63 60 2e 0a 0a 20 20 20 20 49 66 20 60 63 60 20 | he.elements.of.`c`.......If.`c`. |
| 8320 | 68 61 73 20 66 65 77 65 72 20 74 68 61 6e 20 33 20 64 69 6d 65 6e 73 69 6f 6e 73 2c 20 6f 6e 65 | has.fewer.than.3.dimensions,.one |
| 8340 | 73 20 61 72 65 20 69 6d 70 6c 69 63 69 74 6c 79 20 61 70 70 65 6e 64 65 64 20 74 6f 20 69 74 73 | s.are.implicitly.appended.to.its |
| 8360 | 0a 20 20 20 20 73 68 61 70 65 20 74 6f 20 6d 61 6b 65 20 69 74 20 33 2d 44 2e 20 54 68 65 20 73 | .....shape.to.make.it.3-D..The.s |
| 8380 | 68 61 70 65 20 6f 66 20 74 68 65 20 72 65 73 75 6c 74 20 77 69 6c 6c 20 62 65 20 63 2e 73 68 61 | hape.of.the.result.will.be.c.sha |
| 83a0 | 70 65 5b 33 3a 5d 20 2b 0a 20 20 20 20 78 2e 73 68 61 70 65 2e 0a 0a 20 20 20 20 50 61 72 61 6d | pe[3:].+.....x.shape.......Param |
| 83c0 | 65 74 65 72 73 0a 20 20 20 20 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 78 2c 20 79 2c 20 7a | eters.....----------.....x,.y,.z |
| 83e0 | 20 3a 20 61 72 72 61 79 5f 6c 69 6b 65 2c 20 63 6f 6d 70 61 74 69 62 6c 65 20 6f 62 6a 65 63 74 | .:.array_like,.compatible.object |
| 8400 | 0a 20 20 20 20 20 20 20 20 54 68 65 20 74 68 72 65 65 20 64 69 6d 65 6e 73 69 6f 6e 61 6c 20 73 | .........The.three.dimensional.s |
| 8420 | 65 72 69 65 73 20 69 73 20 65 76 61 6c 75 61 74 65 64 20 61 74 20 74 68 65 20 70 6f 69 6e 74 73 | eries.is.evaluated.at.the.points |
| 8440 | 0a 20 20 20 20 20 20 20 20 60 28 78 2c 20 79 2c 20 7a 29 60 2c 20 77 68 65 72 65 20 60 78 60 2c | .........`(x,.y,.z)`,.where.`x`, |
| 8460 | 20 60 79 60 2c 20 61 6e 64 20 60 7a 60 20 6d 75 73 74 20 68 61 76 65 20 74 68 65 20 73 61 6d 65 | .`y`,.and.`z`.must.have.the.same |
| 8480 | 20 73 68 61 70 65 2e 20 20 49 66 0a 20 20 20 20 20 20 20 20 61 6e 79 20 6f 66 20 60 78 60 2c 20 | .shape...If.........any.of.`x`,. |
| 84a0 | 60 79 60 2c 20 6f 72 20 60 7a 60 20 69 73 20 61 20 6c 69 73 74 20 6f 72 20 74 75 70 6c 65 2c 20 | `y`,.or.`z`.is.a.list.or.tuple,. |
| 84c0 | 69 74 20 69 73 20 66 69 72 73 74 20 63 6f 6e 76 65 72 74 65 64 0a 20 20 20 20 20 20 20 20 74 6f | it.is.first.converted.........to |
| 84e0 | 20 61 6e 20 6e 64 61 72 72 61 79 2c 20 6f 74 68 65 72 77 69 73 65 20 69 74 20 69 73 20 6c 65 66 | .an.ndarray,.otherwise.it.is.lef |
| 8500 | 74 20 75 6e 63 68 61 6e 67 65 64 20 61 6e 64 20 69 66 20 69 74 20 69 73 6e 27 74 20 61 6e 0a 20 | t.unchanged.and.if.it.isn't.an.. |
| 8520 | 20 20 20 20 20 20 20 6e 64 61 72 72 61 79 20 69 74 20 69 73 20 20 74 72 65 61 74 65 64 20 61 73 | .......ndarray.it.is..treated.as |
| 8540 | 20 61 20 73 63 61 6c 61 72 2e 0a 20 20 20 20 63 20 3a 20 61 72 72 61 79 5f 6c 69 6b 65 0a 20 20 | .a.scalar......c.:.array_like... |
| 8560 | 20 20 20 20 20 20 41 72 72 61 79 20 6f 66 20 63 6f 65 66 66 69 63 69 65 6e 74 73 20 6f 72 64 65 | ......Array.of.coefficients.orde |
| 8580 | 72 65 64 20 73 6f 20 74 68 61 74 20 74 68 65 20 63 6f 65 66 66 69 63 69 65 6e 74 20 6f 66 20 74 | red.so.that.the.coefficient.of.t |
| 85a0 | 68 65 20 74 65 72 6d 20 6f 66 0a 20 20 20 20 20 20 20 20 6d 75 6c 74 69 2d 64 65 67 72 65 65 20 | he.term.of.........multi-degree. |
| 85c0 | 69 2c 6a 2c 6b 20 69 73 20 63 6f 6e 74 61 69 6e 65 64 20 69 6e 20 60 60 63 5b 69 2c 6a 2c 6b 5d | i,j,k.is.contained.in.``c[i,j,k] |
| 85e0 | 60 60 2e 20 49 66 20 60 63 60 20 68 61 73 20 64 69 6d 65 6e 73 69 6f 6e 0a 20 20 20 20 20 20 20 | ``..If.`c`.has.dimension........ |
| 8600 | 20 67 72 65 61 74 65 72 20 74 68 61 6e 20 33 20 74 68 65 20 72 65 6d 61 69 6e 69 6e 67 20 69 6e | .greater.than.3.the.remaining.in |
| 8620 | 64 69 63 65 73 20 65 6e 75 6d 65 72 61 74 65 20 6d 75 6c 74 69 70 6c 65 20 73 65 74 73 20 6f 66 | dices.enumerate.multiple.sets.of |
| 8640 | 0a 20 20 20 20 20 20 20 20 63 6f 65 66 66 69 63 69 65 6e 74 73 2e 0a 0a 20 20 20 20 52 65 74 75 | .........coefficients.......Retu |
| 8660 | 72 6e 73 0a 20 20 20 20 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 76 61 6c 75 65 73 20 3a 20 6e 64 61 | rns.....-------.....values.:.nda |
| 8680 | 72 72 61 79 2c 20 63 6f 6d 70 61 74 69 62 6c 65 20 6f 62 6a 65 63 74 0a 20 20 20 20 20 20 20 20 | rray,.compatible.object......... |
| 86a0 | 54 68 65 20 76 61 6c 75 65 73 20 6f 66 20 74 68 65 20 6d 75 6c 74 69 64 69 6d 65 6e 73 69 6f 6e | The.values.of.the.multidimension |
| 86c0 | 61 6c 20 70 6f 6c 79 6e 6f 6d 69 61 6c 20 6f 6e 20 70 6f 69 6e 74 73 20 66 6f 72 6d 65 64 20 77 | al.polynomial.on.points.formed.w |
| 86e0 | 69 74 68 0a 20 20 20 20 20 20 20 20 74 72 69 70 6c 65 73 20 6f 66 20 63 6f 72 72 65 73 70 6f 6e | ith.........triples.of.correspon |
| 8700 | 64 69 6e 67 20 76 61 6c 75 65 73 20 66 72 6f 6d 20 60 78 60 2c 20 60 79 60 2c 20 61 6e 64 20 60 | ding.values.from.`x`,.`y`,.and.` |
| 8720 | 7a 60 2e 0a 0a 20 20 20 20 53 65 65 20 41 6c 73 6f 0a 20 20 20 20 2d 2d 2d 2d 2d 2d 2d 2d 0a 20 | z`.......See.Also.....--------.. |
| 8740 | 20 20 20 68 65 72 6d 65 76 61 6c 2c 20 68 65 72 6d 65 76 61 6c 32 64 2c 20 68 65 72 6d 65 67 72 | ...hermeval,.hermeval2d,.hermegr |
| 8760 | 69 64 32 64 2c 20 68 65 72 6d 65 67 72 69 64 33 64 0a 20 20 20 20 72 80 00 00 00 a9 04 72 7d 00 | id2d,.hermegrid3d.....r......r}. |
| 8780 | 00 00 72 83 00 00 00 da 01 7a 72 39 00 00 00 73 04 00 00 00 20 20 20 20 72 30 00 00 00 72 1e 00 | ..r......zr9...s........r0...r.. |
| 87a0 | 00 00 72 1e 00 00 00 d4 03 00 00 73 1c 00 00 00 80 00 f4 54 01 00 0c 0e 8f 39 89 39 94 58 98 71 | ..r........s.......T.....9.9.X.q |
| 87c0 | a0 21 a0 51 a8 01 d3 0b 2a d0 04 2a 72 31 00 00 00 63 04 00 00 00 00 00 00 00 00 00 00 00 07 00 | .!.Q....*..*r1...c.............. |
| 87e0 | 00 00 03 00 00 00 f3 3c 00 00 00 97 00 74 01 00 00 00 00 00 00 00 00 6a 02 00 00 00 00 00 00 00 | .......<.....t.........j........ |
| 8800 | 00 00 00 00 00 00 00 00 00 00 00 74 04 00 00 00 00 00 00 00 00 7c 03 7c 00 7c 01 7c 02 ab 05 00 | ...........t.........|.|.|.|.... |
| 8820 | 00 00 00 00 00 53 00 29 01 61 26 07 00 00 0a 20 20 20 20 45 76 61 6c 75 61 74 65 20 61 20 33 2d | .....S.).a&........Evaluate.a.3- |
| 8840 | 44 20 48 65 72 6d 69 74 65 45 20 73 65 72 69 65 73 20 6f 6e 20 74 68 65 20 43 61 72 74 65 73 69 | D.HermiteE.series.on.the.Cartesi |
| 8860 | 61 6e 20 70 72 6f 64 75 63 74 20 6f 66 20 78 2c 20 79 2c 20 61 6e 64 20 7a 2e 0a 0a 20 20 20 20 | an.product.of.x,.y,.and.z....... |
| 8880 | 54 68 69 73 20 66 75 6e 63 74 69 6f 6e 20 72 65 74 75 72 6e 73 20 74 68 65 20 76 61 6c 75 65 73 | This.function.returns.the.values |
| 88a0 | 3a 0a 0a 20 20 20 20 2e 2e 20 6d 61 74 68 3a 3a 20 70 28 61 2c 62 2c 63 29 20 3d 20 5c 73 75 6d | :.........math::.p(a,b,c).=.\sum |
| 88c0 | 5f 7b 69 2c 6a 2c 6b 7d 20 63 5f 7b 69 2c 6a 2c 6b 7d 20 2a 20 48 65 5f 69 28 61 29 20 2a 20 48 | _{i,j,k}.c_{i,j,k}.*.He_i(a).*.H |
| 88e0 | 65 5f 6a 28 62 29 20 2a 20 48 65 5f 6b 28 63 29 0a 0a 20 20 20 20 77 68 65 72 65 20 74 68 65 20 | e_j(b).*.He_k(c)......where.the. |
| 8900 | 70 6f 69 6e 74 73 20 60 60 28 61 2c 20 62 2c 20 63 29 60 60 20 63 6f 6e 73 69 73 74 20 6f 66 20 | points.``(a,.b,.c)``.consist.of. |
| 8920 | 61 6c 6c 20 74 72 69 70 6c 65 73 20 66 6f 72 6d 65 64 20 62 79 20 74 61 6b 69 6e 67 0a 20 20 20 | all.triples.formed.by.taking.... |
| 8940 | 20 60 61 60 20 66 72 6f 6d 20 60 78 60 2c 20 60 62 60 20 66 72 6f 6d 20 60 79 60 2c 20 61 6e 64 | .`a`.from.`x`,.`b`.from.`y`,.and |
| 8960 | 20 60 63 60 20 66 72 6f 6d 20 60 7a 60 2e 20 54 68 65 20 72 65 73 75 6c 74 69 6e 67 20 70 6f 69 | .`c`.from.`z`..The.resulting.poi |
| 8980 | 6e 74 73 20 66 6f 72 6d 0a 20 20 20 20 61 20 67 72 69 64 20 77 69 74 68 20 60 78 60 20 69 6e 20 | nts.form.....a.grid.with.`x`.in. |
| 89a0 | 74 68 65 20 66 69 72 73 74 20 64 69 6d 65 6e 73 69 6f 6e 2c 20 60 79 60 20 69 6e 20 74 68 65 20 | the.first.dimension,.`y`.in.the. |
| 89c0 | 73 65 63 6f 6e 64 2c 20 61 6e 64 20 60 7a 60 20 69 6e 0a 20 20 20 20 74 68 65 20 74 68 69 72 64 | second,.and.`z`.in.....the.third |
| 89e0 | 2e 0a 0a 20 20 20 20 54 68 65 20 70 61 72 61 6d 65 74 65 72 73 20 60 78 60 2c 20 60 79 60 2c 20 | .......The.parameters.`x`,.`y`,. |
| 8a00 | 61 6e 64 20 60 7a 60 20 61 72 65 20 63 6f 6e 76 65 72 74 65 64 20 74 6f 20 61 72 72 61 79 73 20 | and.`z`.are.converted.to.arrays. |
| 8a20 | 6f 6e 6c 79 20 69 66 20 74 68 65 79 0a 20 20 20 20 61 72 65 20 74 75 70 6c 65 73 20 6f 72 20 61 | only.if.they.....are.tuples.or.a |
| 8a40 | 20 6c 69 73 74 73 2c 20 6f 74 68 65 72 77 69 73 65 20 74 68 65 79 20 61 72 65 20 74 72 65 61 74 | .lists,.otherwise.they.are.treat |
| 8a60 | 65 64 20 61 73 20 61 20 73 63 61 6c 61 72 73 2e 20 49 6e 0a 20 20 20 20 65 69 74 68 65 72 20 63 | ed.as.a.scalars..In.....either.c |
| 8a80 | 61 73 65 2c 20 65 69 74 68 65 72 20 60 78 60 2c 20 60 79 60 2c 20 61 6e 64 20 60 7a 60 20 6f 72 | ase,.either.`x`,.`y`,.and.`z`.or |
| 8aa0 | 20 74 68 65 69 72 20 65 6c 65 6d 65 6e 74 73 20 6d 75 73 74 20 73 75 70 70 6f 72 74 0a 20 20 20 | .their.elements.must.support.... |
| 8ac0 | 20 6d 75 6c 74 69 70 6c 69 63 61 74 69 6f 6e 20 61 6e 64 20 61 64 64 69 74 69 6f 6e 20 62 6f 74 | .multiplication.and.addition.bot |
| 8ae0 | 68 20 77 69 74 68 20 74 68 65 6d 73 65 6c 76 65 73 20 61 6e 64 20 77 69 74 68 20 74 68 65 20 65 | h.with.themselves.and.with.the.e |
| 8b00 | 6c 65 6d 65 6e 74 73 0a 20 20 20 20 6f 66 20 60 63 60 2e 0a 0a 20 20 20 20 49 66 20 60 63 60 20 | lements.....of.`c`.......If.`c`. |
| 8b20 | 68 61 73 20 66 65 77 65 72 20 74 68 61 6e 20 74 68 72 65 65 20 64 69 6d 65 6e 73 69 6f 6e 73 2c | has.fewer.than.three.dimensions, |
| 8b40 | 20 6f 6e 65 73 20 61 72 65 20 69 6d 70 6c 69 63 69 74 6c 79 20 61 70 70 65 6e 64 65 64 20 74 6f | .ones.are.implicitly.appended.to |
| 8b60 | 0a 20 20 20 20 69 74 73 20 73 68 61 70 65 20 74 6f 20 6d 61 6b 65 20 69 74 20 33 2d 44 2e 20 54 | .....its.shape.to.make.it.3-D..T |
| 8b80 | 68 65 20 73 68 61 70 65 20 6f 66 20 74 68 65 20 72 65 73 75 6c 74 20 77 69 6c 6c 20 62 65 20 63 | he.shape.of.the.result.will.be.c |
| 8ba0 | 2e 73 68 61 70 65 5b 33 3a 5d 20 2b 0a 20 20 20 20 78 2e 73 68 61 70 65 20 2b 20 79 2e 73 68 61 | .shape[3:].+.....x.shape.+.y.sha |
| 8bc0 | 70 65 20 2b 20 7a 2e 73 68 61 70 65 2e 0a 0a 20 20 20 20 50 61 72 61 6d 65 74 65 72 73 0a 20 20 | pe.+.z.shape.......Parameters... |
| 8be0 | 20 20 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 78 2c 20 79 2c 20 7a 20 3a 20 61 72 72 61 79 | ..----------.....x,.y,.z.:.array |
| 8c00 | 5f 6c 69 6b 65 2c 20 63 6f 6d 70 61 74 69 62 6c 65 20 6f 62 6a 65 63 74 73 0a 20 20 20 20 20 20 | _like,.compatible.objects....... |
| 8c20 | 20 20 54 68 65 20 74 68 72 65 65 20 64 69 6d 65 6e 73 69 6f 6e 61 6c 20 73 65 72 69 65 73 20 69 | ..The.three.dimensional.series.i |
| 8c40 | 73 20 65 76 61 6c 75 61 74 65 64 20 61 74 20 74 68 65 20 70 6f 69 6e 74 73 20 69 6e 20 74 68 65 | s.evaluated.at.the.points.in.the |
| 8c60 | 0a 20 20 20 20 20 20 20 20 43 61 72 74 65 73 69 61 6e 20 70 72 6f 64 75 63 74 20 6f 66 20 60 78 | .........Cartesian.product.of.`x |
| 8c80 | 60 2c 20 60 79 60 2c 20 61 6e 64 20 60 7a 60 2e 20 20 49 66 20 60 78 60 2c 20 60 79 60 2c 20 6f | `,.`y`,.and.`z`...If.`x`,.`y`,.o |
| 8ca0 | 72 20 60 7a 60 20 69 73 20 61 0a 20 20 20 20 20 20 20 20 6c 69 73 74 20 6f 72 20 74 75 70 6c 65 | r.`z`.is.a.........list.or.tuple |
| 8cc0 | 2c 20 69 74 20 69 73 20 66 69 72 73 74 20 63 6f 6e 76 65 72 74 65 64 20 74 6f 20 61 6e 20 6e 64 | ,.it.is.first.converted.to.an.nd |
| 8ce0 | 61 72 72 61 79 2c 20 6f 74 68 65 72 77 69 73 65 20 69 74 20 69 73 0a 20 20 20 20 20 20 20 20 6c | array,.otherwise.it.is.........l |
| 8d00 | 65 66 74 20 75 6e 63 68 61 6e 67 65 64 20 61 6e 64 2c 20 69 66 20 69 74 20 69 73 6e 27 74 20 61 | eft.unchanged.and,.if.it.isn't.a |
| 8d20 | 6e 20 6e 64 61 72 72 61 79 2c 20 69 74 20 69 73 20 74 72 65 61 74 65 64 20 61 73 20 61 0a 20 20 | n.ndarray,.it.is.treated.as.a... |
| 8d40 | 20 20 20 20 20 20 73 63 61 6c 61 72 2e 0a 20 20 20 20 63 20 3a 20 61 72 72 61 79 5f 6c 69 6b 65 | ......scalar......c.:.array_like |
| 8d60 | 0a 20 20 20 20 20 20 20 20 41 72 72 61 79 20 6f 66 20 63 6f 65 66 66 69 63 69 65 6e 74 73 20 6f | .........Array.of.coefficients.o |
| 8d80 | 72 64 65 72 65 64 20 73 6f 20 74 68 61 74 20 74 68 65 20 63 6f 65 66 66 69 63 69 65 6e 74 73 20 | rdered.so.that.the.coefficients. |
| 8da0 | 66 6f 72 20 74 65 72 6d 73 20 6f 66 0a 20 20 20 20 20 20 20 20 64 65 67 72 65 65 20 69 2c 6a 20 | for.terms.of.........degree.i,j. |
| 8dc0 | 61 72 65 20 63 6f 6e 74 61 69 6e 65 64 20 69 6e 20 60 60 63 5b 69 2c 6a 5d 60 60 2e 20 49 66 20 | are.contained.in.``c[i,j]``..If. |
| 8de0 | 60 63 60 20 68 61 73 20 64 69 6d 65 6e 73 69 6f 6e 0a 20 20 20 20 20 20 20 20 67 72 65 61 74 65 | `c`.has.dimension.........greate |
| 8e00 | 72 20 74 68 61 6e 20 74 77 6f 20 74 68 65 20 72 65 6d 61 69 6e 69 6e 67 20 69 6e 64 69 63 65 73 | r.than.two.the.remaining.indices |
| 8e20 | 20 65 6e 75 6d 65 72 61 74 65 20 6d 75 6c 74 69 70 6c 65 20 73 65 74 73 20 6f 66 0a 20 20 20 20 | .enumerate.multiple.sets.of..... |
| 8e40 | 20 20 20 20 63 6f 65 66 66 69 63 69 65 6e 74 73 2e 0a 0a 20 20 20 20 52 65 74 75 72 6e 73 0a 20 | ....coefficients.......Returns.. |
| 8e60 | 20 20 20 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 76 61 6c 75 65 73 20 3a 20 6e 64 61 72 72 61 79 2c | ...-------.....values.:.ndarray, |
| 8e80 | 20 63 6f 6d 70 61 74 69 62 6c 65 20 6f 62 6a 65 63 74 0a 20 20 20 20 20 20 20 20 54 68 65 20 76 | .compatible.object.........The.v |
| 8ea0 | 61 6c 75 65 73 20 6f 66 20 74 68 65 20 74 77 6f 20 64 69 6d 65 6e 73 69 6f 6e 61 6c 20 70 6f 6c | alues.of.the.two.dimensional.pol |
| 8ec0 | 79 6e 6f 6d 69 61 6c 20 61 74 20 70 6f 69 6e 74 73 20 69 6e 20 74 68 65 20 43 61 72 74 65 73 69 | ynomial.at.points.in.the.Cartesi |
| 8ee0 | 61 6e 0a 20 20 20 20 20 20 20 20 70 72 6f 64 75 63 74 20 6f 66 20 60 78 60 20 61 6e 64 20 60 79 | an.........product.of.`x`.and.`y |
| 8f00 | 60 2e 0a 0a 20 20 20 20 53 65 65 20 41 6c 73 6f 0a 20 20 20 20 2d 2d 2d 2d 2d 2d 2d 2d 0a 20 20 | `.......See.Also.....--------... |
| 8f20 | 20 20 68 65 72 6d 65 76 61 6c 2c 20 68 65 72 6d 65 76 61 6c 32 64 2c 20 68 65 72 6d 65 67 72 69 | ..hermeval,.hermeval2d,.hermegri |
| 8f40 | 64 32 64 2c 20 68 65 72 6d 65 76 61 6c 33 64 0a 20 20 20 20 72 85 00 00 00 72 88 00 00 00 73 04 | d2d,.hermeval3d.....r....r....s. |
| 8f60 | 00 00 00 20 20 20 20 72 30 00 00 00 72 20 00 00 00 72 20 00 00 00 01 04 00 00 73 1c 00 00 00 80 | .......r0...r....r........s..... |
| 8f80 | 00 f4 5e 01 00 0c 0e 8f 3a 89 3a 94 68 a0 01 a0 31 a0 61 a8 11 d3 0b 2b d0 04 2b 72 31 00 00 00 | ..^.....:.:.h...1.a....+..+r1... |
| 8fa0 | 63 02 00 00 00 00 00 00 00 00 00 00 00 05 00 00 00 03 00 00 00 f3 aa 01 00 00 97 00 74 01 00 00 | c...........................t... |
| 8fc0 | 00 00 00 00 00 00 6a 02 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 7c 01 64 01 ab 02 | ......j...................|.d... |
| 8fe0 | 00 00 00 00 00 00 7d 02 7c 02 64 02 6b 02 00 00 72 0b 74 05 00 00 00 00 00 00 00 00 64 03 ab 01 | ......}.|.d.k...r.t.........d... |
| 9000 | 00 00 00 00 00 00 82 01 74 07 00 00 00 00 00 00 00 00 6a 08 00 00 00 00 00 00 00 00 00 00 00 00 | ........t.........j............. |
| 9020 | 00 00 00 00 00 00 7c 00 64 04 64 05 ac 06 ab 03 00 00 00 00 00 00 64 07 7a 00 00 00 7d 00 7c 02 | ......|.d.d...........d.z...}.|. |
| 9040 | 64 05 7a 00 00 00 66 01 7c 00 6a 0a 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 7a 00 | d.z...f.|.j...................z. |
| 9060 | 00 00 7d 03 7c 00 6a 0c 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 7d 04 74 07 00 00 | ..}.|.j...................}.t... |
| 9080 | 00 00 00 00 00 00 6a 0e 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 7c 03 7c 04 ac 08 | ......j...................|.|... |
| 90a0 | ab 02 00 00 00 00 00 00 7d 05 7c 00 64 02 7a 05 00 00 64 05 7a 00 00 00 7c 05 64 02 3c 00 00 00 | ........}.|.d.z...d.z...|.d.<... |
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| 9100 | 00 00 19 00 00 00 7c 00 7a 05 00 00 7c 05 7c 06 64 09 7a 0a 00 00 19 00 00 00 7c 06 64 05 7a 0a | ......|.z...|.|.d.z.......|.d.z. |
| 9120 | 00 00 7a 05 00 00 7a 0a 00 00 7c 05 7c 06 3c 00 00 00 8c 21 04 00 74 07 00 00 00 00 00 00 00 00 | ..z...z...|.|.<....!..t......... |
| 9140 | 6a 12 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 7c 05 64 02 64 0a ab 03 00 00 00 00 | j...................|.d.d....... |
| 9160 | 00 00 53 00 29 0b 61 31 06 00 00 50 73 65 75 64 6f 2d 56 61 6e 64 65 72 6d 6f 6e 64 65 20 6d 61 | ..S.).a1...Pseudo-Vandermonde.ma |
| 9180 | 74 72 69 78 20 6f 66 20 67 69 76 65 6e 20 64 65 67 72 65 65 2e 0a 0a 20 20 20 20 52 65 74 75 72 | trix.of.given.degree.......Retur |
| 91a0 | 6e 73 20 74 68 65 20 70 73 65 75 64 6f 2d 56 61 6e 64 65 72 6d 6f 6e 64 65 20 6d 61 74 72 69 78 | ns.the.pseudo-Vandermonde.matrix |
| 91c0 | 20 6f 66 20 64 65 67 72 65 65 20 60 64 65 67 60 20 61 6e 64 20 73 61 6d 70 6c 65 20 70 6f 69 6e | .of.degree.`deg`.and.sample.poin |
| 91e0 | 74 73 0a 20 20 20 20 60 78 60 2e 20 54 68 65 20 70 73 65 75 64 6f 2d 56 61 6e 64 65 72 6d 6f 6e | ts.....`x`..The.pseudo-Vandermon |
| 9200 | 64 65 20 6d 61 74 72 69 78 20 69 73 20 64 65 66 69 6e 65 64 20 62 79 0a 0a 20 20 20 20 2e 2e 20 | de.matrix.is.defined.by......... |
| 9220 | 6d 61 74 68 3a 3a 20 56 5b 2e 2e 2e 2c 20 69 5d 20 3d 20 48 65 5f 69 28 78 29 2c 0a 0a 20 20 20 | math::.V[...,.i].=.He_i(x),..... |
| 9240 | 20 77 68 65 72 65 20 60 60 30 20 3c 3d 20 69 20 3c 3d 20 64 65 67 60 60 2e 20 54 68 65 20 6c 65 | .where.``0.<=.i.<=.deg``..The.le |
| 9260 | 61 64 69 6e 67 20 69 6e 64 69 63 65 73 20 6f 66 20 60 56 60 20 69 6e 64 65 78 20 74 68 65 20 65 | ading.indices.of.`V`.index.the.e |
| 9280 | 6c 65 6d 65 6e 74 73 20 6f 66 0a 20 20 20 20 60 78 60 20 61 6e 64 20 74 68 65 20 6c 61 73 74 20 | lements.of.....`x`.and.the.last. |
| 92a0 | 69 6e 64 65 78 20 69 73 20 74 68 65 20 64 65 67 72 65 65 20 6f 66 20 74 68 65 20 48 65 72 6d 69 | index.is.the.degree.of.the.Hermi |
| 92c0 | 74 65 45 20 70 6f 6c 79 6e 6f 6d 69 61 6c 2e 0a 0a 20 20 20 20 49 66 20 60 63 60 20 69 73 20 61 | teE.polynomial.......If.`c`.is.a |
| 92e0 | 20 31 2d 44 20 61 72 72 61 79 20 6f 66 20 63 6f 65 66 66 69 63 69 65 6e 74 73 20 6f 66 20 6c 65 | .1-D.array.of.coefficients.of.le |
| 9300 | 6e 67 74 68 20 60 60 6e 20 2b 20 31 60 60 20 61 6e 64 20 60 56 60 20 69 73 20 74 68 65 0a 20 20 | ngth.``n.+.1``.and.`V`.is.the... |
| 9320 | 20 20 61 72 72 61 79 20 60 60 56 20 3d 20 68 65 72 6d 65 76 61 6e 64 65 72 28 78 2c 20 6e 29 60 | ..array.``V.=.hermevander(x,.n)` |
| 9340 | 60 2c 20 74 68 65 6e 20 60 60 6e 70 2e 64 6f 74 28 56 2c 20 63 29 60 60 20 61 6e 64 0a 20 20 20 | `,.then.``np.dot(V,.c)``.and.... |
| 9360 | 20 60 60 68 65 72 6d 65 76 61 6c 28 78 2c 20 63 29 60 60 20 61 72 65 20 74 68 65 20 73 61 6d 65 | .``hermeval(x,.c)``.are.the.same |
| 9380 | 20 75 70 20 74 6f 20 72 6f 75 6e 64 6f 66 66 2e 20 54 68 69 73 20 65 71 75 69 76 61 6c 65 6e 63 | .up.to.roundoff..This.equivalenc |
| 93a0 | 65 20 69 73 0a 20 20 20 20 75 73 65 66 75 6c 20 62 6f 74 68 20 66 6f 72 20 6c 65 61 73 74 20 73 | e.is.....useful.both.for.least.s |
| 93c0 | 71 75 61 72 65 73 20 66 69 74 74 69 6e 67 20 61 6e 64 20 66 6f 72 20 74 68 65 20 65 76 61 6c 75 | quares.fitting.and.for.the.evalu |
| 93e0 | 61 74 69 6f 6e 20 6f 66 20 61 20 6c 61 72 67 65 0a 20 20 20 20 6e 75 6d 62 65 72 20 6f 66 20 48 | ation.of.a.large.....number.of.H |
| 9400 | 65 72 6d 69 74 65 45 20 73 65 72 69 65 73 20 6f 66 20 74 68 65 20 73 61 6d 65 20 64 65 67 72 65 | ermiteE.series.of.the.same.degre |
| 9420 | 65 20 61 6e 64 20 73 61 6d 70 6c 65 20 70 6f 69 6e 74 73 2e 0a 0a 20 20 20 20 50 61 72 61 6d 65 | e.and.sample.points.......Parame |
| 9440 | 74 65 72 73 0a 20 20 20 20 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 78 20 3a 20 61 72 72 61 | ters.....----------.....x.:.arra |
| 9460 | 79 5f 6c 69 6b 65 0a 20 20 20 20 20 20 20 20 41 72 72 61 79 20 6f 66 20 70 6f 69 6e 74 73 2e 20 | y_like.........Array.of.points.. |
| 9480 | 54 68 65 20 64 74 79 70 65 20 69 73 20 63 6f 6e 76 65 72 74 65 64 20 74 6f 20 66 6c 6f 61 74 36 | The.dtype.is.converted.to.float6 |
| 94a0 | 34 20 6f 72 20 63 6f 6d 70 6c 65 78 31 32 38 0a 20 20 20 20 20 20 20 20 64 65 70 65 6e 64 69 6e | 4.or.complex128.........dependin |
| 94c0 | 67 20 6f 6e 20 77 68 65 74 68 65 72 20 61 6e 79 20 6f 66 20 74 68 65 20 65 6c 65 6d 65 6e 74 73 | g.on.whether.any.of.the.elements |
| 94e0 | 20 61 72 65 20 63 6f 6d 70 6c 65 78 2e 20 49 66 20 60 78 60 20 69 73 0a 20 20 20 20 20 20 20 20 | .are.complex..If.`x`.is......... |
| 9500 | 73 63 61 6c 61 72 20 69 74 20 69 73 20 63 6f 6e 76 65 72 74 65 64 20 74 6f 20 61 20 31 2d 44 20 | scalar.it.is.converted.to.a.1-D. |
| 9520 | 61 72 72 61 79 2e 0a 20 20 20 20 64 65 67 20 3a 20 69 6e 74 0a 20 20 20 20 20 20 20 20 44 65 67 | array......deg.:.int.........Deg |
| 9540 | 72 65 65 20 6f 66 20 74 68 65 20 72 65 73 75 6c 74 69 6e 67 20 6d 61 74 72 69 78 2e 0a 0a 20 20 | ree.of.the.resulting.matrix..... |
| 9560 | 20 20 52 65 74 75 72 6e 73 0a 20 20 20 20 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 76 61 6e 64 65 72 | ..Returns.....-------.....vander |
| 9580 | 20 3a 20 6e 64 61 72 72 61 79 0a 20 20 20 20 20 20 20 20 54 68 65 20 70 73 65 75 64 6f 2d 56 61 | .:.ndarray.........The.pseudo-Va |
| 95a0 | 6e 64 65 72 6d 6f 6e 64 65 20 6d 61 74 72 69 78 2e 20 54 68 65 20 73 68 61 70 65 20 6f 66 20 74 | ndermonde.matrix..The.shape.of.t |
| 95c0 | 68 65 20 72 65 74 75 72 6e 65 64 20 6d 61 74 72 69 78 20 69 73 0a 20 20 20 20 20 20 20 20 60 60 | he.returned.matrix.is.........`` |
| 95e0 | 78 2e 73 68 61 70 65 20 2b 20 28 64 65 67 20 2b 20 31 2c 29 60 60 2c 20 77 68 65 72 65 20 54 68 | x.shape.+.(deg.+.1,)``,.where.Th |
| 9600 | 65 20 6c 61 73 74 20 69 6e 64 65 78 20 69 73 20 74 68 65 20 64 65 67 72 65 65 20 6f 66 20 74 68 | e.last.index.is.the.degree.of.th |
| 9620 | 65 0a 20 20 20 20 20 20 20 20 63 6f 72 72 65 73 70 6f 6e 64 69 6e 67 20 48 65 72 6d 69 74 65 45 | e.........corresponding.HermiteE |
| 9640 | 20 70 6f 6c 79 6e 6f 6d 69 61 6c 2e 20 20 54 68 65 20 64 74 79 70 65 20 77 69 6c 6c 20 62 65 20 | .polynomial...The.dtype.will.be. |
| 9660 | 74 68 65 20 73 61 6d 65 20 61 73 0a 20 20 20 20 20 20 20 20 74 68 65 20 63 6f 6e 76 65 72 74 65 | the.same.as.........the.converte |
| 9680 | 64 20 60 78 60 2e 0a 0a 20 20 20 20 45 78 61 6d 70 6c 65 73 0a 20 20 20 20 2d 2d 2d 2d 2d 2d 2d | d.`x`.......Examples.....------- |
| 96a0 | 2d 0a 20 20 20 20 3e 3e 3e 20 69 6d 70 6f 72 74 20 6e 75 6d 70 79 20 61 73 20 6e 70 0a 20 20 20 | -.....>>>.import.numpy.as.np.... |
| 96c0 | 20 3e 3e 3e 20 66 72 6f 6d 20 6e 75 6d 70 79 2e 70 6f 6c 79 6e 6f 6d 69 61 6c 2e 68 65 72 6d 69 | .>>>.from.numpy.polynomial.hermi |
| 96e0 | 74 65 5f 65 20 69 6d 70 6f 72 74 20 68 65 72 6d 65 76 61 6e 64 65 72 0a 20 20 20 20 3e 3e 3e 20 | te_e.import.hermevander.....>>>. |
| 9700 | 78 20 3d 20 6e 70 2e 61 72 72 61 79 28 5b 2d 31 2c 20 30 2c 20 31 5d 29 0a 20 20 20 20 3e 3e 3e | x.=.np.array([-1,.0,.1]).....>>> |
| 9720 | 20 68 65 72 6d 65 76 61 6e 64 65 72 28 78 2c 20 33 29 0a 20 20 20 20 61 72 72 61 79 28 5b 5b 20 | .hermevander(x,.3).....array([[. |
| 9740 | 31 2e 2c 20 2d 31 2e 2c 20 20 30 2e 2c 20 20 32 2e 5d 2c 0a 20 20 20 20 20 20 20 20 20 20 20 5b | 1.,.-1.,..0.,..2.],............[ |
| 9760 | 20 31 2e 2c 20 20 30 2e 2c 20 2d 31 2e 2c 20 2d 30 2e 5d 2c 0a 20 20 20 20 20 20 20 20 20 20 20 | .1.,..0.,.-1.,.-0.],............ |
| 9780 | 5b 20 31 2e 2c 20 20 31 2e 2c 20 20 30 2e 2c 20 2d 32 2e 5d 5d 29 0a 0a 20 20 20 20 72 2d 00 00 | [.1.,..1.,..0.,.-2.]])......r-.. |
| 97a0 | 00 72 02 00 00 00 7a 18 64 65 67 20 6d 75 73 74 20 62 65 20 6e 6f 6e 2d 6e 65 67 61 74 69 76 65 | .r....z.deg.must.be.non-negative |
| 97c0 | 4e 72 04 00 00 00 29 02 72 60 00 00 00 72 5f 00 00 00 e7 00 00 00 00 00 00 00 00 72 4f 00 00 00 | Nr....).r`...r_............rO... |
| 97e0 | 72 36 00 00 00 72 27 00 00 00 29 0a 72 28 00 00 00 72 66 00 00 00 72 67 00 00 00 72 40 00 00 00 | r6...r'...).r(...rf...rg...r@... |
| 9800 | 72 41 00 00 00 72 6a 00 00 00 72 50 00 00 00 72 51 00 00 00 72 2b 00 00 00 72 69 00 00 00 29 07 | rA...rj...rP...rQ...r+...ri...). |
| 9820 | 72 7d 00 00 00 72 2d 00 00 00 da 04 69 64 65 67 da 04 64 69 6d 73 da 04 64 74 79 70 da 01 76 72 | r}...r-.....ideg..dims..dtyp..vr |
| 9840 | 2f 00 00 00 73 07 00 00 00 20 20 20 20 20 20 20 72 30 00 00 00 72 18 00 00 00 72 18 00 00 00 33 | /...s...........r0...r....r....3 |
| 9860 | 04 00 00 73 e5 00 00 00 80 00 f4 5a 01 00 0c 0e 8f 3a 89 3a 90 63 98 35 d3 0b 21 80 44 d8 07 0b | ...s.......Z.....:.:.c.5..!.D... |
| 9880 | 88 61 82 78 dc 0e 18 d0 19 33 d3 0e 34 d0 08 34 e4 08 0a 8f 08 89 08 90 11 98 14 a0 51 d4 08 27 | .a.x.....3..4..4............Q..' |
| 98a0 | a8 23 d1 08 2d 80 41 d8 0c 10 90 31 89 48 88 3b 98 11 9f 17 99 17 d1 0b 20 80 44 d8 0b 0c 8f 37 | .#..-.A....1.H.;..........D....7 |
| 98c0 | 89 37 80 44 dc 08 0a 8f 08 89 08 90 14 98 54 d4 08 22 80 41 d8 0b 0c 88 71 89 35 90 31 89 39 80 | .7.D..........T..".A....q.5.1.9. |
| 98e0 | 41 80 61 81 44 d8 07 0b 88 61 82 78 d8 0f 10 88 01 88 21 89 04 dc 11 16 90 71 98 24 a0 11 99 28 | A.a.D....a.x......!......q.$...( |
| 9900 | d3 11 23 f2 00 01 09 37 88 41 d8 14 15 90 61 98 21 91 65 91 48 98 71 91 4c a0 31 a0 51 a8 11 a1 | ..#....7.A....a.!.e.H.q.L.1.Q... |
| 9920 | 55 a1 38 a8 71 b0 31 a9 75 d1 23 35 d1 14 35 88 41 88 61 8a 44 f0 03 01 09 37 e4 0b 0d 8f 3b 89 | U.8.q.1.u.#5..5.A.a.D....7....;. |
| 9940 | 3b 90 71 98 21 98 52 d3 0b 20 d0 04 20 72 31 00 00 00 63 03 00 00 00 00 00 00 00 00 00 00 00 05 | ;.q.!.R......r1...c............. |
| 9960 | 00 00 00 03 00 00 00 f3 48 00 00 00 97 00 74 01 00 00 00 00 00 00 00 00 6a 02 00 00 00 00 00 00 | ........H.....t.........j....... |
| 9980 | 00 00 00 00 00 00 00 00 00 00 00 00 74 04 00 00 00 00 00 00 00 00 74 04 00 00 00 00 00 00 00 00 | ............t.........t......... |
| 99a0 | 66 02 7c 00 7c 01 66 02 7c 02 ab 03 00 00 00 00 00 00 53 00 29 01 61 6f 06 00 00 50 73 65 75 64 | f.|.|.f.|.........S.).ao...Pseud |
| 99c0 | 6f 2d 56 61 6e 64 65 72 6d 6f 6e 64 65 20 6d 61 74 72 69 78 20 6f 66 20 67 69 76 65 6e 20 64 65 | o-Vandermonde.matrix.of.given.de |
| 99e0 | 67 72 65 65 73 2e 0a 0a 20 20 20 20 52 65 74 75 72 6e 73 20 74 68 65 20 70 73 65 75 64 6f 2d 56 | grees.......Returns.the.pseudo-V |
| 9a00 | 61 6e 64 65 72 6d 6f 6e 64 65 20 6d 61 74 72 69 78 20 6f 66 20 64 65 67 72 65 65 73 20 60 64 65 | andermonde.matrix.of.degrees.`de |
| 9a20 | 67 60 20 61 6e 64 20 73 61 6d 70 6c 65 0a 20 20 20 20 70 6f 69 6e 74 73 20 60 60 28 78 2c 20 79 | g`.and.sample.....points.``(x,.y |
| 9a40 | 29 60 60 2e 20 54 68 65 20 70 73 65 75 64 6f 2d 56 61 6e 64 65 72 6d 6f 6e 64 65 20 6d 61 74 72 | )``..The.pseudo-Vandermonde.matr |
| 9a60 | 69 78 20 69 73 20 64 65 66 69 6e 65 64 20 62 79 0a 0a 20 20 20 20 2e 2e 20 6d 61 74 68 3a 3a 20 | ix.is.defined.by.........math::. |
| 9a80 | 56 5b 2e 2e 2e 2c 20 28 64 65 67 5b 31 5d 20 2b 20 31 29 2a 69 20 2b 20 6a 5d 20 3d 20 48 65 5f | V[...,.(deg[1].+.1)*i.+.j].=.He_ |
| 9aa0 | 69 28 78 29 20 2a 20 48 65 5f 6a 28 79 29 2c 0a 0a 20 20 20 20 77 68 65 72 65 20 60 60 30 20 3c | i(x).*.He_j(y),......where.``0.< |
| 9ac0 | 3d 20 69 20 3c 3d 20 64 65 67 5b 30 5d 60 60 20 61 6e 64 20 60 60 30 20 3c 3d 20 6a 20 3c 3d 20 | =.i.<=.deg[0]``.and.``0.<=.j.<=. |
| 9ae0 | 64 65 67 5b 31 5d 60 60 2e 20 54 68 65 20 6c 65 61 64 69 6e 67 20 69 6e 64 69 63 65 73 20 6f 66 | deg[1]``..The.leading.indices.of |
| 9b00 | 0a 20 20 20 20 60 56 60 20 69 6e 64 65 78 20 74 68 65 20 70 6f 69 6e 74 73 20 60 60 28 78 2c 20 | .....`V`.index.the.points.``(x,. |
| 9b20 | 79 29 60 60 20 61 6e 64 20 74 68 65 20 6c 61 73 74 20 69 6e 64 65 78 20 65 6e 63 6f 64 65 73 20 | y)``.and.the.last.index.encodes. |
| 9b40 | 74 68 65 20 64 65 67 72 65 65 73 20 6f 66 0a 20 20 20 20 74 68 65 20 48 65 72 6d 69 74 65 45 20 | the.degrees.of.....the.HermiteE. |
| 9b60 | 70 6f 6c 79 6e 6f 6d 69 61 6c 73 2e 0a 0a 20 20 20 20 49 66 20 60 60 56 20 3d 20 68 65 72 6d 65 | polynomials.......If.``V.=.herme |
| 9b80 | 76 61 6e 64 65 72 32 64 28 78 2c 20 79 2c 20 5b 78 64 65 67 2c 20 79 64 65 67 5d 29 60 60 2c 20 | vander2d(x,.y,.[xdeg,.ydeg])``,. |
| 9ba0 | 74 68 65 6e 20 74 68 65 20 63 6f 6c 75 6d 6e 73 20 6f 66 20 60 56 60 0a 20 20 20 20 63 6f 72 72 | then.the.columns.of.`V`.....corr |
| 9bc0 | 65 73 70 6f 6e 64 20 74 6f 20 74 68 65 20 65 6c 65 6d 65 6e 74 73 20 6f 66 20 61 20 32 2d 44 20 | espond.to.the.elements.of.a.2-D. |
| 9be0 | 63 6f 65 66 66 69 63 69 65 6e 74 20 61 72 72 61 79 20 60 63 60 20 6f 66 20 73 68 61 70 65 0a 20 | coefficient.array.`c`.of.shape.. |
| 9c00 | 20 20 20 28 78 64 65 67 20 2b 20 31 2c 20 79 64 65 67 20 2b 20 31 29 20 69 6e 20 74 68 65 20 6f | ...(xdeg.+.1,.ydeg.+.1).in.the.o |
| 9c20 | 72 64 65 72 0a 0a 20 20 20 20 2e 2e 20 6d 61 74 68 3a 3a 20 63 5f 7b 30 30 7d 2c 20 63 5f 7b 30 | rder.........math::.c_{00},.c_{0 |
| 9c40 | 31 7d 2c 20 63 5f 7b 30 32 7d 20 2e 2e 2e 20 2c 20 63 5f 7b 31 30 7d 2c 20 63 5f 7b 31 31 7d 2c | 1},.c_{02}.....,.c_{10},.c_{11}, |
| 9c60 | 20 63 5f 7b 31 32 7d 20 2e 2e 2e 0a 0a 20 20 20 20 61 6e 64 20 60 60 6e 70 2e 64 6f 74 28 56 2c | .c_{12}..........and.``np.dot(V, |
| 9c80 | 20 63 2e 66 6c 61 74 29 60 60 20 61 6e 64 20 60 60 68 65 72 6d 65 76 61 6c 32 64 28 78 2c 20 79 | .c.flat)``.and.``hermeval2d(x,.y |
| 9ca0 | 2c 20 63 29 60 60 20 77 69 6c 6c 20 62 65 20 74 68 65 20 73 61 6d 65 0a 20 20 20 20 75 70 20 74 | ,.c)``.will.be.the.same.....up.t |
| 9cc0 | 6f 20 72 6f 75 6e 64 6f 66 66 2e 20 54 68 69 73 20 65 71 75 69 76 61 6c 65 6e 63 65 20 69 73 20 | o.roundoff..This.equivalence.is. |
| 9ce0 | 75 73 65 66 75 6c 20 62 6f 74 68 20 66 6f 72 20 6c 65 61 73 74 20 73 71 75 61 72 65 73 0a 20 20 | useful.both.for.least.squares... |
| 9d00 | 20 20 66 69 74 74 69 6e 67 20 61 6e 64 20 66 6f 72 20 74 68 65 20 65 76 61 6c 75 61 74 69 6f 6e | ..fitting.and.for.the.evaluation |
| 9d20 | 20 6f 66 20 61 20 6c 61 72 67 65 20 6e 75 6d 62 65 72 20 6f 66 20 32 2d 44 20 48 65 72 6d 69 74 | .of.a.large.number.of.2-D.Hermit |
| 9d40 | 65 45 0a 20 20 20 20 73 65 72 69 65 73 20 6f 66 20 74 68 65 20 73 61 6d 65 20 64 65 67 72 65 65 | eE.....series.of.the.same.degree |
| 9d60 | 73 20 61 6e 64 20 73 61 6d 70 6c 65 20 70 6f 69 6e 74 73 2e 0a 0a 20 20 20 20 50 61 72 61 6d 65 | s.and.sample.points.......Parame |
| 9d80 | 74 65 72 73 0a 20 20 20 20 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 78 2c 20 79 20 3a 20 61 | ters.....----------.....x,.y.:.a |
| 9da0 | 72 72 61 79 5f 6c 69 6b 65 0a 20 20 20 20 20 20 20 20 41 72 72 61 79 73 20 6f 66 20 70 6f 69 6e | rray_like.........Arrays.of.poin |
| 9dc0 | 74 20 63 6f 6f 72 64 69 6e 61 74 65 73 2c 20 61 6c 6c 20 6f 66 20 74 68 65 20 73 61 6d 65 20 73 | t.coordinates,.all.of.the.same.s |
| 9de0 | 68 61 70 65 2e 20 54 68 65 20 64 74 79 70 65 73 0a 20 20 20 20 20 20 20 20 77 69 6c 6c 20 62 65 | hape..The.dtypes.........will.be |
| 9e00 | 20 63 6f 6e 76 65 72 74 65 64 20 74 6f 20 65 69 74 68 65 72 20 66 6c 6f 61 74 36 34 20 6f 72 20 | .converted.to.either.float64.or. |
| 9e20 | 63 6f 6d 70 6c 65 78 31 32 38 20 64 65 70 65 6e 64 69 6e 67 20 6f 6e 0a 20 20 20 20 20 20 20 20 | complex128.depending.on......... |
| 9e40 | 77 68 65 74 68 65 72 20 61 6e 79 20 6f 66 20 74 68 65 20 65 6c 65 6d 65 6e 74 73 20 61 72 65 20 | whether.any.of.the.elements.are. |
| 9e60 | 63 6f 6d 70 6c 65 78 2e 20 53 63 61 6c 61 72 73 20 61 72 65 20 63 6f 6e 76 65 72 74 65 64 20 74 | complex..Scalars.are.converted.t |
| 9e80 | 6f 0a 20 20 20 20 20 20 20 20 31 2d 44 20 61 72 72 61 79 73 2e 0a 20 20 20 20 64 65 67 20 3a 20 | o.........1-D.arrays......deg.:. |
| 9ea0 | 6c 69 73 74 20 6f 66 20 69 6e 74 73 0a 20 20 20 20 20 20 20 20 4c 69 73 74 20 6f 66 20 6d 61 78 | list.of.ints.........List.of.max |
| 9ec0 | 69 6d 75 6d 20 64 65 67 72 65 65 73 20 6f 66 20 74 68 65 20 66 6f 72 6d 20 5b 78 5f 64 65 67 2c | imum.degrees.of.the.form.[x_deg, |
| 9ee0 | 20 79 5f 64 65 67 5d 2e 0a 0a 20 20 20 20 52 65 74 75 72 6e 73 0a 20 20 20 20 2d 2d 2d 2d 2d 2d | .y_deg].......Returns.....------ |
| 9f00 | 2d 0a 20 20 20 20 76 61 6e 64 65 72 32 64 20 3a 20 6e 64 61 72 72 61 79 0a 20 20 20 20 20 20 20 | -.....vander2d.:.ndarray........ |
| 9f20 | 20 54 68 65 20 73 68 61 70 65 20 6f 66 20 74 68 65 20 72 65 74 75 72 6e 65 64 20 6d 61 74 72 69 | .The.shape.of.the.returned.matri |
| 9f40 | 78 20 69 73 20 60 60 78 2e 73 68 61 70 65 20 2b 20 28 6f 72 64 65 72 2c 29 60 60 2c 20 77 68 65 | x.is.``x.shape.+.(order,)``,.whe |
| 9f60 | 72 65 0a 20 20 20 20 20 20 20 20 3a 6d 61 74 68 3a 60 6f 72 64 65 72 20 3d 20 28 64 65 67 5b 30 | re.........:math:`order.=.(deg[0 |
| 9f80 | 5d 2b 31 29 2a 28 64 65 67 5b 31 5d 2b 31 29 60 2e 20 20 54 68 65 20 64 74 79 70 65 20 77 69 6c | ]+1)*(deg[1]+1)`...The.dtype.wil |
| 9fa0 | 6c 20 62 65 20 74 68 65 20 73 61 6d 65 0a 20 20 20 20 20 20 20 20 61 73 20 74 68 65 20 63 6f 6e | l.be.the.same.........as.the.con |
| 9fc0 | 76 65 72 74 65 64 20 60 78 60 20 61 6e 64 20 60 79 60 2e 0a 0a 20 20 20 20 53 65 65 20 41 6c 73 | verted.`x`.and.`y`.......See.Als |
| 9fe0 | 6f 0a 20 20 20 20 2d 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 68 65 72 6d 65 76 61 6e 64 65 72 2c 20 | o.....--------.....hermevander,. |
| a000 | 68 65 72 6d 65 76 61 6e 64 65 72 33 64 2c 20 68 65 72 6d 65 76 61 6c 32 64 2c 20 68 65 72 6d 65 | hermevander3d,.hermeval2d,.herme |
| a020 | 76 61 6c 33 64 0a 20 20 20 20 a9 03 72 28 00 00 00 da 0f 5f 76 61 6e 64 65 72 5f 6e 64 5f 66 6c | val3d.......r(....._vander_nd_fl |
| a040 | 61 74 72 18 00 00 00 29 03 72 7d 00 00 00 72 83 00 00 00 72 2d 00 00 00 73 03 00 00 00 20 20 20 | atr....).r}...r....r-...s....... |
| a060 | 72 30 00 00 00 72 21 00 00 00 72 21 00 00 00 70 04 00 00 73 23 00 00 00 80 00 f4 58 01 00 0c 0e | r0...r!...r!...p...s#......X.... |
| a080 | d7 0b 1d d1 0b 1d 9c 7b ac 4b d0 1e 38 b8 31 b8 61 b8 26 c0 23 d3 0b 46 d0 04 46 72 31 00 00 00 | .......{.K..8.1.a.&.#..F..Fr1... |
| a0a0 | 63 04 00 00 00 00 00 00 00 00 00 00 00 06 00 00 00 03 00 00 00 f3 54 00 00 00 97 00 74 01 00 00 | c.....................T.....t... |
| a0c0 | 00 00 00 00 00 00 6a 02 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 74 04 00 00 00 00 | ......j...................t..... |
| a0e0 | 00 00 00 00 74 04 00 00 00 00 00 00 00 00 74 04 00 00 00 00 00 00 00 00 66 03 7c 00 7c 01 7c 02 | ....t.........t.........f.|.|.|. |
| a100 | 66 03 7c 03 ab 03 00 00 00 00 00 00 53 00 29 01 61 05 07 00 00 50 73 65 75 64 6f 2d 56 61 6e 64 | f.|.........S.).a....Pseudo-Vand |
| a120 | 65 72 6d 6f 6e 64 65 20 6d 61 74 72 69 78 20 6f 66 20 67 69 76 65 6e 20 64 65 67 72 65 65 73 2e | ermonde.matrix.of.given.degrees. |
| a140 | 0a 0a 20 20 20 20 52 65 74 75 72 6e 73 20 74 68 65 20 70 73 65 75 64 6f 2d 56 61 6e 64 65 72 6d | ......Returns.the.pseudo-Vanderm |
| a160 | 6f 6e 64 65 20 6d 61 74 72 69 78 20 6f 66 20 64 65 67 72 65 65 73 20 60 64 65 67 60 20 61 6e 64 | onde.matrix.of.degrees.`deg`.and |
| a180 | 20 73 61 6d 70 6c 65 0a 20 20 20 20 70 6f 69 6e 74 73 20 60 60 28 78 2c 20 79 2c 20 7a 29 60 60 | .sample.....points.``(x,.y,.z)`` |
| a1a0 | 2e 20 49 66 20 60 6c 60 2c 20 60 6d 60 2c 20 60 6e 60 20 61 72 65 20 74 68 65 20 67 69 76 65 6e | ..If.`l`,.`m`,.`n`.are.the.given |
| a1c0 | 20 64 65 67 72 65 65 73 20 69 6e 20 60 78 60 2c 20 60 79 60 2c 20 60 7a 60 2c 0a 20 20 20 20 74 | .degrees.in.`x`,.`y`,.`z`,.....t |
| a1e0 | 68 65 6e 20 48 65 68 65 20 70 73 65 75 64 6f 2d 56 61 6e 64 65 72 6d 6f 6e 64 65 20 6d 61 74 72 | hen.Hehe.pseudo-Vandermonde.matr |
| a200 | 69 78 20 69 73 20 64 65 66 69 6e 65 64 20 62 79 0a 0a 20 20 20 20 2e 2e 20 6d 61 74 68 3a 3a 20 | ix.is.defined.by.........math::. |
| a220 | 56 5b 2e 2e 2e 2c 20 28 6d 2b 31 29 28 6e 2b 31 29 69 20 2b 20 28 6e 2b 31 29 6a 20 2b 20 6b 5d | V[...,.(m+1)(n+1)i.+.(n+1)j.+.k] |
| a240 | 20 3d 20 48 65 5f 69 28 78 29 2a 48 65 5f 6a 28 79 29 2a 48 65 5f 6b 28 7a 29 2c 0a 0a 20 20 20 | .=.He_i(x)*He_j(y)*He_k(z),..... |
| a260 | 20 77 68 65 72 65 20 60 60 30 20 3c 3d 20 69 20 3c 3d 20 6c 60 60 2c 20 60 60 30 20 3c 3d 20 6a | .where.``0.<=.i.<=.l``,.``0.<=.j |
| a280 | 20 3c 3d 20 6d 60 60 2c 20 61 6e 64 20 60 60 30 20 3c 3d 20 6a 20 3c 3d 20 6e 60 60 2e 20 20 54 | .<=.m``,.and.``0.<=.j.<=.n``...T |
| a2a0 | 68 65 20 6c 65 61 64 69 6e 67 0a 20 20 20 20 69 6e 64 69 63 65 73 20 6f 66 20 60 56 60 20 69 6e | he.leading.....indices.of.`V`.in |
| a2c0 | 64 65 78 20 74 68 65 20 70 6f 69 6e 74 73 20 60 60 28 78 2c 20 79 2c 20 7a 29 60 60 20 61 6e 64 | dex.the.points.``(x,.y,.z)``.and |
| a2e0 | 20 74 68 65 20 6c 61 73 74 20 69 6e 64 65 78 20 65 6e 63 6f 64 65 73 0a 20 20 20 20 74 68 65 20 | .the.last.index.encodes.....the. |
| a300 | 64 65 67 72 65 65 73 20 6f 66 20 74 68 65 20 48 65 72 6d 69 74 65 45 20 70 6f 6c 79 6e 6f 6d 69 | degrees.of.the.HermiteE.polynomi |
| a320 | 61 6c 73 2e 0a 0a 20 20 20 20 49 66 20 60 60 56 20 3d 20 68 65 72 6d 65 76 61 6e 64 65 72 33 64 | als.......If.``V.=.hermevander3d |
| a340 | 28 78 2c 20 79 2c 20 7a 2c 20 5b 78 64 65 67 2c 20 79 64 65 67 2c 20 7a 64 65 67 5d 29 60 60 2c | (x,.y,.z,.[xdeg,.ydeg,.zdeg])``, |
| a360 | 20 74 68 65 6e 20 74 68 65 20 63 6f 6c 75 6d 6e 73 0a 20 20 20 20 6f 66 20 60 56 60 20 63 6f 72 | .then.the.columns.....of.`V`.cor |
| a380 | 72 65 73 70 6f 6e 64 20 74 6f 20 74 68 65 20 65 6c 65 6d 65 6e 74 73 20 6f 66 20 61 20 33 2d 44 | respond.to.the.elements.of.a.3-D |
| a3a0 | 20 63 6f 65 66 66 69 63 69 65 6e 74 20 61 72 72 61 79 20 60 63 60 20 6f 66 0a 20 20 20 20 73 68 | .coefficient.array.`c`.of.....sh |
| a3c0 | 61 70 65 20 28 78 64 65 67 20 2b 20 31 2c 20 79 64 65 67 20 2b 20 31 2c 20 7a 64 65 67 20 2b 20 | ape.(xdeg.+.1,.ydeg.+.1,.zdeg.+. |
| a3e0 | 31 29 20 69 6e 20 74 68 65 20 6f 72 64 65 72 0a 0a 20 20 20 20 2e 2e 20 6d 61 74 68 3a 3a 20 63 | 1).in.the.order.........math::.c |
| a400 | 5f 7b 30 30 30 7d 2c 20 63 5f 7b 30 30 31 7d 2c 20 63 5f 7b 30 30 32 7d 2c 2e 2e 2e 20 2c 20 63 | _{000},.c_{001},.c_{002},....,.c |
| a420 | 5f 7b 30 31 30 7d 2c 20 63 5f 7b 30 31 31 7d 2c 20 63 5f 7b 30 31 32 7d 2c 2e 2e 2e 0a 0a 20 20 | _{010},.c_{011},.c_{012},....... |
| a440 | 20 20 61 6e 64 20 20 60 60 6e 70 2e 64 6f 74 28 56 2c 20 63 2e 66 6c 61 74 29 60 60 20 61 6e 64 | ..and..``np.dot(V,.c.flat)``.and |
| a460 | 20 60 60 68 65 72 6d 65 76 61 6c 33 64 28 78 2c 20 79 2c 20 7a 2c 20 63 29 60 60 20 77 69 6c 6c | .``hermeval3d(x,.y,.z,.c)``.will |
| a480 | 20 62 65 20 74 68 65 0a 20 20 20 20 73 61 6d 65 20 75 70 20 74 6f 20 72 6f 75 6e 64 6f 66 66 2e | .be.the.....same.up.to.roundoff. |
| a4a0 | 20 54 68 69 73 20 65 71 75 69 76 61 6c 65 6e 63 65 20 69 73 20 75 73 65 66 75 6c 20 62 6f 74 68 | .This.equivalence.is.useful.both |
| a4c0 | 20 66 6f 72 20 6c 65 61 73 74 20 73 71 75 61 72 65 73 0a 20 20 20 20 66 69 74 74 69 6e 67 20 61 | .for.least.squares.....fitting.a |
| a4e0 | 6e 64 20 66 6f 72 20 74 68 65 20 65 76 61 6c 75 61 74 69 6f 6e 20 6f 66 20 61 20 6c 61 72 67 65 | nd.for.the.evaluation.of.a.large |
| a500 | 20 6e 75 6d 62 65 72 20 6f 66 20 33 2d 44 20 48 65 72 6d 69 74 65 45 0a 20 20 20 20 73 65 72 69 | .number.of.3-D.HermiteE.....seri |
| a520 | 65 73 20 6f 66 20 74 68 65 20 73 61 6d 65 20 64 65 67 72 65 65 73 20 61 6e 64 20 73 61 6d 70 6c | es.of.the.same.degrees.and.sampl |
| a540 | 65 20 70 6f 69 6e 74 73 2e 0a 0a 20 20 20 20 50 61 72 61 6d 65 74 65 72 73 0a 20 20 20 20 2d 2d | e.points.......Parameters.....-- |
| a560 | 2d 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 78 2c 20 79 2c 20 7a 20 3a 20 61 72 72 61 79 5f 6c 69 6b | --------.....x,.y,.z.:.array_lik |
| a580 | 65 0a 20 20 20 20 20 20 20 20 41 72 72 61 79 73 20 6f 66 20 70 6f 69 6e 74 20 63 6f 6f 72 64 69 | e.........Arrays.of.point.coordi |
| a5a0 | 6e 61 74 65 73 2c 20 61 6c 6c 20 6f 66 20 74 68 65 20 73 61 6d 65 20 73 68 61 70 65 2e 20 54 68 | nates,.all.of.the.same.shape..Th |
| a5c0 | 65 20 64 74 79 70 65 73 20 77 69 6c 6c 0a 20 20 20 20 20 20 20 20 62 65 20 63 6f 6e 76 65 72 74 | e.dtypes.will.........be.convert |
| a5e0 | 65 64 20 74 6f 20 65 69 74 68 65 72 20 66 6c 6f 61 74 36 34 20 6f 72 20 63 6f 6d 70 6c 65 78 31 | ed.to.either.float64.or.complex1 |
| a600 | 32 38 20 64 65 70 65 6e 64 69 6e 67 20 6f 6e 20 77 68 65 74 68 65 72 0a 20 20 20 20 20 20 20 20 | 28.depending.on.whether......... |
| a620 | 61 6e 79 20 6f 66 20 74 68 65 20 65 6c 65 6d 65 6e 74 73 20 61 72 65 20 63 6f 6d 70 6c 65 78 2e | any.of.the.elements.are.complex. |
| a640 | 20 53 63 61 6c 61 72 73 20 61 72 65 20 63 6f 6e 76 65 72 74 65 64 20 74 6f 20 31 2d 44 0a 20 20 | .Scalars.are.converted.to.1-D... |
| a660 | 20 20 20 20 20 20 61 72 72 61 79 73 2e 0a 20 20 20 20 64 65 67 20 3a 20 6c 69 73 74 20 6f 66 20 | ......arrays......deg.:.list.of. |
| a680 | 69 6e 74 73 0a 20 20 20 20 20 20 20 20 4c 69 73 74 20 6f 66 20 6d 61 78 69 6d 75 6d 20 64 65 67 | ints.........List.of.maximum.deg |
| a6a0 | 72 65 65 73 20 6f 66 20 74 68 65 20 66 6f 72 6d 20 5b 78 5f 64 65 67 2c 20 79 5f 64 65 67 2c 20 | rees.of.the.form.[x_deg,.y_deg,. |
| a6c0 | 7a 5f 64 65 67 5d 2e 0a 0a 20 20 20 20 52 65 74 75 72 6e 73 0a 20 20 20 20 2d 2d 2d 2d 2d 2d 2d | z_deg].......Returns.....------- |
| a6e0 | 0a 20 20 20 20 76 61 6e 64 65 72 33 64 20 3a 20 6e 64 61 72 72 61 79 0a 20 20 20 20 20 20 20 20 | .....vander3d.:.ndarray......... |
| a700 | 54 68 65 20 73 68 61 70 65 20 6f 66 20 74 68 65 20 72 65 74 75 72 6e 65 64 20 6d 61 74 72 69 78 | The.shape.of.the.returned.matrix |
| a720 | 20 69 73 20 60 60 78 2e 73 68 61 70 65 20 2b 20 28 6f 72 64 65 72 2c 29 60 60 2c 20 77 68 65 72 | .is.``x.shape.+.(order,)``,.wher |
| a740 | 65 0a 20 20 20 20 20 20 20 20 3a 6d 61 74 68 3a 60 6f 72 64 65 72 20 3d 20 28 64 65 67 5b 30 5d | e.........:math:`order.=.(deg[0] |
| a760 | 2b 31 29 2a 28 64 65 67 5b 31 5d 2b 31 29 2a 28 64 65 67 5b 32 5d 2b 31 29 60 2e 20 20 54 68 65 | +1)*(deg[1]+1)*(deg[2]+1)`...The |
| a780 | 20 64 74 79 70 65 20 77 69 6c 6c 0a 20 20 20 20 20 20 20 20 62 65 20 74 68 65 20 73 61 6d 65 20 | .dtype.will.........be.the.same. |
| a7a0 | 61 73 20 74 68 65 20 63 6f 6e 76 65 72 74 65 64 20 60 78 60 2c 20 60 79 60 2c 20 61 6e 64 20 60 | as.the.converted.`x`,.`y`,.and.` |
| a7c0 | 7a 60 2e 0a 0a 20 20 20 20 53 65 65 20 41 6c 73 6f 0a 20 20 20 20 2d 2d 2d 2d 2d 2d 2d 2d 0a 20 | z`.......See.Also.....--------.. |
| a7e0 | 20 20 20 68 65 72 6d 65 76 61 6e 64 65 72 2c 20 68 65 72 6d 65 76 61 6e 64 65 72 33 64 2c 20 68 | ...hermevander,.hermevander3d,.h |
| a800 | 65 72 6d 65 76 61 6c 32 64 2c 20 68 65 72 6d 65 76 61 6c 33 64 0a 20 20 20 20 72 92 00 00 00 29 | ermeval2d,.hermeval3d.....r....) |
| a820 | 04 72 7d 00 00 00 72 83 00 00 00 72 89 00 00 00 72 2d 00 00 00 73 04 00 00 00 20 20 20 20 72 30 | .r}...r....r....r-...s........r0 |
| a840 | 00 00 00 72 22 00 00 00 72 22 00 00 00 9f 04 00 00 73 28 00 00 00 80 00 f4 5a 01 00 0c 0e d7 0b | ...r"...r".......s(......Z...... |
| a860 | 1d d1 0b 1d 9c 7b ac 4b bc 1b d0 1e 45 c8 01 c8 31 c8 61 c0 79 d0 52 55 d3 0b 56 d0 04 56 72 31 | .....{.K....E...1.a.y.RU..V..Vr1 |
| a880 | 00 00 00 63 06 00 00 00 00 00 00 00 00 00 00 00 09 00 00 00 03 00 00 00 f3 40 00 00 00 97 00 74 | ...c.....................@.....t |
| a8a0 | 01 00 00 00 00 00 00 00 00 6a 02 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 74 04 00 | .........j...................t.. |
| a8c0 | 00 00 00 00 00 00 00 7c 00 7c 01 7c 02 7c 03 7c 04 7c 05 ab 07 00 00 00 00 00 00 53 00 29 01 61 | .......|.|.|.|.|.|.........S.).a |
| a8e0 | ac 15 00 00 0a 20 20 20 20 4c 65 61 73 74 20 73 71 75 61 72 65 73 20 66 69 74 20 6f 66 20 48 65 | .........Least.squares.fit.of.He |
| a900 | 72 6d 69 74 65 20 73 65 72 69 65 73 20 74 6f 20 64 61 74 61 2e 0a 0a 20 20 20 20 52 65 74 75 72 | rmite.series.to.data.......Retur |
| a920 | 6e 20 74 68 65 20 63 6f 65 66 66 69 63 69 65 6e 74 73 20 6f 66 20 61 20 48 65 72 6d 69 74 65 45 | n.the.coefficients.of.a.HermiteE |
| a940 | 20 73 65 72 69 65 73 20 6f 66 20 64 65 67 72 65 65 20 60 64 65 67 60 20 74 68 61 74 20 69 73 0a | .series.of.degree.`deg`.that.is. |
| a960 | 20 20 20 20 74 68 65 20 6c 65 61 73 74 20 73 71 75 61 72 65 73 20 66 69 74 20 74 6f 20 74 68 65 | ....the.least.squares.fit.to.the |
| a980 | 20 64 61 74 61 20 76 61 6c 75 65 73 20 60 79 60 20 67 69 76 65 6e 20 61 74 20 70 6f 69 6e 74 73 | .data.values.`y`.given.at.points |
| a9a0 | 20 60 78 60 2e 20 49 66 0a 20 20 20 20 60 79 60 20 69 73 20 31 2d 44 20 74 68 65 20 72 65 74 75 | .`x`..If.....`y`.is.1-D.the.retu |
| a9c0 | 72 6e 65 64 20 63 6f 65 66 66 69 63 69 65 6e 74 73 20 77 69 6c 6c 20 61 6c 73 6f 20 62 65 20 31 | rned.coefficients.will.also.be.1 |
| a9e0 | 2d 44 2e 20 49 66 20 60 79 60 20 69 73 20 32 2d 44 0a 20 20 20 20 6d 75 6c 74 69 70 6c 65 20 66 | -D..If.`y`.is.2-D.....multiple.f |
| aa00 | 69 74 73 20 61 72 65 20 64 6f 6e 65 2c 20 6f 6e 65 20 66 6f 72 20 65 61 63 68 20 63 6f 6c 75 6d | its.are.done,.one.for.each.colum |
| aa20 | 6e 20 6f 66 20 60 79 60 2c 20 61 6e 64 20 74 68 65 20 72 65 73 75 6c 74 69 6e 67 0a 20 20 20 20 | n.of.`y`,.and.the.resulting..... |
| aa40 | 63 6f 65 66 66 69 63 69 65 6e 74 73 20 61 72 65 20 73 74 6f 72 65 64 20 69 6e 20 74 68 65 20 63 | coefficients.are.stored.in.the.c |
| aa60 | 6f 72 72 65 73 70 6f 6e 64 69 6e 67 20 63 6f 6c 75 6d 6e 73 20 6f 66 20 61 20 32 2d 44 20 72 65 | orresponding.columns.of.a.2-D.re |
| aa80 | 74 75 72 6e 2e 0a 20 20 20 20 54 68 65 20 66 69 74 74 65 64 20 70 6f 6c 79 6e 6f 6d 69 61 6c 28 | turn......The.fitted.polynomial( |
| aaa0 | 73 29 20 61 72 65 20 69 6e 20 74 68 65 20 66 6f 72 6d 0a 0a 20 20 20 20 2e 2e 20 6d 61 74 68 3a | s).are.in.the.form.........math: |
| aac0 | 3a 20 20 70 28 78 29 20 3d 20 63 5f 30 20 2b 20 63 5f 31 20 2a 20 48 65 5f 31 28 78 29 20 2b 20 | :..p(x).=.c_0.+.c_1.*.He_1(x).+. |
| aae0 | 2e 2e 2e 20 2b 20 63 5f 6e 20 2a 20 48 65 5f 6e 28 78 29 2c 0a 0a 20 20 20 20 77 68 65 72 65 20 | ....+.c_n.*.He_n(x),......where. |
| ab00 | 60 6e 60 20 69 73 20 60 64 65 67 60 2e 0a 0a 20 20 20 20 50 61 72 61 6d 65 74 65 72 73 0a 20 20 | `n`.is.`deg`.......Parameters... |
| ab20 | 20 20 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 78 20 3a 20 61 72 72 61 79 5f 6c 69 6b 65 2c | ..----------.....x.:.array_like, |
| ab40 | 20 73 68 61 70 65 20 28 4d 2c 29 0a 20 20 20 20 20 20 20 20 78 2d 63 6f 6f 72 64 69 6e 61 74 65 | .shape.(M,).........x-coordinate |
| ab60 | 73 20 6f 66 20 74 68 65 20 4d 20 73 61 6d 70 6c 65 20 70 6f 69 6e 74 73 20 60 60 28 78 5b 69 5d | s.of.the.M.sample.points.``(x[i] |
| ab80 | 2c 20 79 5b 69 5d 29 60 60 2e 0a 20 20 20 20 79 20 3a 20 61 72 72 61 79 5f 6c 69 6b 65 2c 20 73 | ,.y[i])``......y.:.array_like,.s |
| aba0 | 68 61 70 65 20 28 4d 2c 29 20 6f 72 20 28 4d 2c 20 4b 29 0a 20 20 20 20 20 20 20 20 79 2d 63 6f | hape.(M,).or.(M,.K).........y-co |
| abc0 | 6f 72 64 69 6e 61 74 65 73 20 6f 66 20 74 68 65 20 73 61 6d 70 6c 65 20 70 6f 69 6e 74 73 2e 20 | ordinates.of.the.sample.points.. |
| abe0 | 53 65 76 65 72 61 6c 20 64 61 74 61 20 73 65 74 73 20 6f 66 20 73 61 6d 70 6c 65 0a 20 20 20 20 | Several.data.sets.of.sample..... |
| ac00 | 20 20 20 20 70 6f 69 6e 74 73 20 73 68 61 72 69 6e 67 20 74 68 65 20 73 61 6d 65 20 78 2d 63 6f | ....points.sharing.the.same.x-co |
| ac20 | 6f 72 64 69 6e 61 74 65 73 20 63 61 6e 20 62 65 20 66 69 74 74 65 64 20 61 74 20 6f 6e 63 65 20 | ordinates.can.be.fitted.at.once. |
| ac40 | 62 79 0a 20 20 20 20 20 20 20 20 70 61 73 73 69 6e 67 20 69 6e 20 61 20 32 44 2d 61 72 72 61 79 | by.........passing.in.a.2D-array |
| ac60 | 20 74 68 61 74 20 63 6f 6e 74 61 69 6e 73 20 6f 6e 65 20 64 61 74 61 73 65 74 20 70 65 72 20 63 | .that.contains.one.dataset.per.c |
| ac80 | 6f 6c 75 6d 6e 2e 0a 20 20 20 20 64 65 67 20 3a 20 69 6e 74 20 6f 72 20 31 2d 44 20 61 72 72 61 | olumn......deg.:.int.or.1-D.arra |
| aca0 | 79 5f 6c 69 6b 65 0a 20 20 20 20 20 20 20 20 44 65 67 72 65 65 28 73 29 20 6f 66 20 74 68 65 20 | y_like.........Degree(s).of.the. |
| acc0 | 66 69 74 74 69 6e 67 20 70 6f 6c 79 6e 6f 6d 69 61 6c 73 2e 20 49 66 20 60 64 65 67 60 20 69 73 | fitting.polynomials..If.`deg`.is |
| ace0 | 20 61 20 73 69 6e 67 6c 65 20 69 6e 74 65 67 65 72 0a 20 20 20 20 20 20 20 20 61 6c 6c 20 74 65 | .a.single.integer.........all.te |
| ad00 | 72 6d 73 20 75 70 20 74 6f 20 61 6e 64 20 69 6e 63 6c 75 64 69 6e 67 20 74 68 65 20 60 64 65 67 | rms.up.to.and.including.the.`deg |
| ad20 | 60 27 74 68 20 74 65 72 6d 20 61 72 65 20 69 6e 63 6c 75 64 65 64 20 69 6e 20 74 68 65 0a 20 20 | `'th.term.are.included.in.the... |
| ad40 | 20 20 20 20 20 20 66 69 74 2e 20 46 6f 72 20 4e 75 6d 50 79 20 76 65 72 73 69 6f 6e 73 20 3e 3d | ......fit..For.NumPy.versions.>= |
| ad60 | 20 31 2e 31 31 2e 30 20 61 20 6c 69 73 74 20 6f 66 20 69 6e 74 65 67 65 72 73 20 73 70 65 63 69 | .1.11.0.a.list.of.integers.speci |
| ad80 | 66 79 69 6e 67 20 74 68 65 0a 20 20 20 20 20 20 20 20 64 65 67 72 65 65 73 20 6f 66 20 74 68 65 | fying.the.........degrees.of.the |
| ada0 | 20 74 65 72 6d 73 20 74 6f 20 69 6e 63 6c 75 64 65 20 6d 61 79 20 62 65 20 75 73 65 64 20 69 6e | .terms.to.include.may.be.used.in |
| adc0 | 73 74 65 61 64 2e 0a 20 20 20 20 72 63 6f 6e 64 20 3a 20 66 6c 6f 61 74 2c 20 6f 70 74 69 6f 6e | stead......rcond.:.float,.option |
| ade0 | 61 6c 0a 20 20 20 20 20 20 20 20 52 65 6c 61 74 69 76 65 20 63 6f 6e 64 69 74 69 6f 6e 20 6e 75 | al.........Relative.condition.nu |
| ae00 | 6d 62 65 72 20 6f 66 20 74 68 65 20 66 69 74 2e 20 53 69 6e 67 75 6c 61 72 20 76 61 6c 75 65 73 | mber.of.the.fit..Singular.values |
| ae20 | 20 73 6d 61 6c 6c 65 72 20 74 68 61 6e 0a 20 20 20 20 20 20 20 20 74 68 69 73 20 72 65 6c 61 74 | .smaller.than.........this.relat |
| ae40 | 69 76 65 20 74 6f 20 74 68 65 20 6c 61 72 67 65 73 74 20 73 69 6e 67 75 6c 61 72 20 76 61 6c 75 | ive.to.the.largest.singular.valu |
| ae60 | 65 20 77 69 6c 6c 20 62 65 20 69 67 6e 6f 72 65 64 2e 20 54 68 65 0a 20 20 20 20 20 20 20 20 64 | e.will.be.ignored..The.........d |
| ae80 | 65 66 61 75 6c 74 20 76 61 6c 75 65 20 69 73 20 6c 65 6e 28 78 29 2a 65 70 73 2c 20 77 68 65 72 | efault.value.is.len(x)*eps,.wher |
| aea0 | 65 20 65 70 73 20 69 73 20 74 68 65 20 72 65 6c 61 74 69 76 65 20 70 72 65 63 69 73 69 6f 6e 20 | e.eps.is.the.relative.precision. |
| aec0 | 6f 66 0a 20 20 20 20 20 20 20 20 74 68 65 20 66 6c 6f 61 74 20 74 79 70 65 2c 20 61 62 6f 75 74 | of.........the.float.type,.about |
| aee0 | 20 32 65 2d 31 36 20 69 6e 20 6d 6f 73 74 20 63 61 73 65 73 2e 0a 20 20 20 20 66 75 6c 6c 20 3a | .2e-16.in.most.cases......full.: |
| af00 | 20 62 6f 6f 6c 2c 20 6f 70 74 69 6f 6e 61 6c 0a 20 20 20 20 20 20 20 20 53 77 69 74 63 68 20 64 | .bool,.optional.........Switch.d |
| af20 | 65 74 65 72 6d 69 6e 69 6e 67 20 6e 61 74 75 72 65 20 6f 66 20 72 65 74 75 72 6e 20 76 61 6c 75 | etermining.nature.of.return.valu |
| af40 | 65 2e 20 57 68 65 6e 20 69 74 20 69 73 20 46 61 6c 73 65 20 28 74 68 65 0a 20 20 20 20 20 20 20 | e..When.it.is.False.(the........ |
| af60 | 20 64 65 66 61 75 6c 74 29 20 6a 75 73 74 20 74 68 65 20 63 6f 65 66 66 69 63 69 65 6e 74 73 20 | .default).just.the.coefficients. |
| af80 | 61 72 65 20 72 65 74 75 72 6e 65 64 2c 20 77 68 65 6e 20 54 72 75 65 20 64 69 61 67 6e 6f 73 74 | are.returned,.when.True.diagnost |
| afa0 | 69 63 0a 20 20 20 20 20 20 20 20 69 6e 66 6f 72 6d 61 74 69 6f 6e 20 66 72 6f 6d 20 74 68 65 20 | ic.........information.from.the. |
| afc0 | 73 69 6e 67 75 6c 61 72 20 76 61 6c 75 65 20 64 65 63 6f 6d 70 6f 73 69 74 69 6f 6e 20 69 73 20 | singular.value.decomposition.is. |
| afe0 | 61 6c 73 6f 20 72 65 74 75 72 6e 65 64 2e 0a 20 20 20 20 77 20 3a 20 61 72 72 61 79 5f 6c 69 6b | also.returned......w.:.array_lik |
| b000 | 65 2c 20 73 68 61 70 65 20 28 60 4d 60 2c 29 2c 20 6f 70 74 69 6f 6e 61 6c 0a 20 20 20 20 20 20 | e,.shape.(`M`,),.optional....... |
| b020 | 20 20 57 65 69 67 68 74 73 2e 20 49 66 20 6e 6f 74 20 4e 6f 6e 65 2c 20 74 68 65 20 77 65 69 67 | ..Weights..If.not.None,.the.weig |
| b040 | 68 74 20 60 60 77 5b 69 5d 60 60 20 61 70 70 6c 69 65 73 20 74 6f 20 74 68 65 20 75 6e 73 71 75 | ht.``w[i]``.applies.to.the.unsqu |
| b060 | 61 72 65 64 0a 20 20 20 20 20 20 20 20 72 65 73 69 64 75 61 6c 20 60 60 79 5b 69 5d 20 2d 20 79 | ared.........residual.``y[i].-.y |
| b080 | 5f 68 61 74 5b 69 5d 60 60 20 61 74 20 60 60 78 5b 69 5d 60 60 2e 20 49 64 65 61 6c 6c 79 20 74 | _hat[i]``.at.``x[i]``..Ideally.t |
| b0a0 | 68 65 20 77 65 69 67 68 74 73 20 61 72 65 0a 20 20 20 20 20 20 20 20 63 68 6f 73 65 6e 20 73 6f | he.weights.are.........chosen.so |
| b0c0 | 20 74 68 61 74 20 74 68 65 20 65 72 72 6f 72 73 20 6f 66 20 74 68 65 20 70 72 6f 64 75 63 74 73 | .that.the.errors.of.the.products |
| b0e0 | 20 60 60 77 5b 69 5d 2a 79 5b 69 5d 60 60 20 61 6c 6c 20 68 61 76 65 20 74 68 65 0a 20 20 20 20 | .``w[i]*y[i]``.all.have.the..... |
| b100 | 20 20 20 20 73 61 6d 65 20 76 61 72 69 61 6e 63 65 2e 20 20 57 68 65 6e 20 75 73 69 6e 67 20 69 | ....same.variance...When.using.i |
| b120 | 6e 76 65 72 73 65 2d 76 61 72 69 61 6e 63 65 20 77 65 69 67 68 74 69 6e 67 2c 20 75 73 65 0a 20 | nverse-variance.weighting,.use.. |
| b140 | 20 20 20 20 20 20 20 60 60 77 5b 69 5d 20 3d 20 31 2f 73 69 67 6d 61 28 79 5b 69 5d 29 60 60 2e | .......``w[i].=.1/sigma(y[i])``. |
| b160 | 20 20 54 68 65 20 64 65 66 61 75 6c 74 20 76 61 6c 75 65 20 69 73 20 4e 6f 6e 65 2e 0a 0a 20 20 | ..The.default.value.is.None..... |
| b180 | 20 20 52 65 74 75 72 6e 73 0a 20 20 20 20 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 63 6f 65 66 20 3a | ..Returns.....-------.....coef.: |
| b1a0 | 20 6e 64 61 72 72 61 79 2c 20 73 68 61 70 65 20 28 4d 2c 29 20 6f 72 20 28 4d 2c 20 4b 29 0a 20 | .ndarray,.shape.(M,).or.(M,.K).. |
| b1c0 | 20 20 20 20 20 20 20 48 65 72 6d 69 74 65 20 63 6f 65 66 66 69 63 69 65 6e 74 73 20 6f 72 64 65 | .......Hermite.coefficients.orde |
| b1e0 | 72 65 64 20 66 72 6f 6d 20 6c 6f 77 20 74 6f 20 68 69 67 68 2e 20 49 66 20 60 79 60 20 77 61 73 | red.from.low.to.high..If.`y`.was |
| b200 | 20 32 2d 44 2c 0a 20 20 20 20 20 20 20 20 74 68 65 20 63 6f 65 66 66 69 63 69 65 6e 74 73 20 66 | .2-D,.........the.coefficients.f |
| b220 | 6f 72 20 74 68 65 20 64 61 74 61 20 69 6e 20 63 6f 6c 75 6d 6e 20 6b 20 20 6f 66 20 60 79 60 20 | or.the.data.in.column.k..of.`y`. |
| b240 | 61 72 65 20 69 6e 20 63 6f 6c 75 6d 6e 0a 20 20 20 20 20 20 20 20 60 6b 60 2e 0a 0a 20 20 20 20 | are.in.column.........`k`....... |
| b260 | 5b 72 65 73 69 64 75 61 6c 73 2c 20 72 61 6e 6b 2c 20 73 69 6e 67 75 6c 61 72 5f 76 61 6c 75 65 | [residuals,.rank,.singular_value |
| b280 | 73 2c 20 72 63 6f 6e 64 5d 20 3a 20 6c 69 73 74 0a 20 20 20 20 20 20 20 20 54 68 65 73 65 20 76 | s,.rcond].:.list.........These.v |
| b2a0 | 61 6c 75 65 73 20 61 72 65 20 6f 6e 6c 79 20 72 65 74 75 72 6e 65 64 20 69 66 20 60 60 66 75 6c | alues.are.only.returned.if.``ful |
| b2c0 | 6c 20 3d 3d 20 54 72 75 65 60 60 0a 0a 20 20 20 20 20 20 20 20 2d 20 72 65 73 69 64 75 61 6c 73 | l.==.True``..........-.residuals |
| b2e0 | 20 2d 2d 20 73 75 6d 20 6f 66 20 73 71 75 61 72 65 64 20 72 65 73 69 64 75 61 6c 73 20 6f 66 20 | .--.sum.of.squared.residuals.of. |
| b300 | 74 68 65 20 6c 65 61 73 74 20 73 71 75 61 72 65 73 20 66 69 74 0a 20 20 20 20 20 20 20 20 2d 20 | the.least.squares.fit.........-. |
| b320 | 72 61 6e 6b 20 2d 2d 20 74 68 65 20 6e 75 6d 65 72 69 63 61 6c 20 72 61 6e 6b 20 6f 66 20 74 68 | rank.--.the.numerical.rank.of.th |
| b340 | 65 20 73 63 61 6c 65 64 20 56 61 6e 64 65 72 6d 6f 6e 64 65 20 6d 61 74 72 69 78 0a 20 20 20 20 | e.scaled.Vandermonde.matrix..... |
| b360 | 20 20 20 20 2d 20 73 69 6e 67 75 6c 61 72 5f 76 61 6c 75 65 73 20 2d 2d 20 73 69 6e 67 75 6c 61 | ....-.singular_values.--.singula |
| b380 | 72 20 76 61 6c 75 65 73 20 6f 66 20 74 68 65 20 73 63 61 6c 65 64 20 56 61 6e 64 65 72 6d 6f 6e | r.values.of.the.scaled.Vandermon |
| b3a0 | 64 65 20 6d 61 74 72 69 78 0a 20 20 20 20 20 20 20 20 2d 20 72 63 6f 6e 64 20 2d 2d 20 76 61 6c | de.matrix.........-.rcond.--.val |
| b3c0 | 75 65 20 6f 66 20 60 72 63 6f 6e 64 60 2e 0a 0a 20 20 20 20 20 20 20 20 46 6f 72 20 6d 6f 72 65 | ue.of.`rcond`...........For.more |
| b3e0 | 20 64 65 74 61 69 6c 73 2c 20 73 65 65 20 60 6e 75 6d 70 79 2e 6c 69 6e 61 6c 67 2e 6c 73 74 73 | .details,.see.`numpy.linalg.lsts |
| b400 | 71 60 2e 0a 0a 20 20 20 20 57 61 72 6e 73 0a 20 20 20 20 2d 2d 2d 2d 2d 0a 20 20 20 20 52 61 6e | q`.......Warns.....-----.....Ran |
| b420 | 6b 57 61 72 6e 69 6e 67 0a 20 20 20 20 20 20 20 20 54 68 65 20 72 61 6e 6b 20 6f 66 20 74 68 65 | kWarning.........The.rank.of.the |
| b440 | 20 63 6f 65 66 66 69 63 69 65 6e 74 20 6d 61 74 72 69 78 20 69 6e 20 74 68 65 20 6c 65 61 73 74 | .coefficient.matrix.in.the.least |
| b460 | 2d 73 71 75 61 72 65 73 20 66 69 74 20 69 73 0a 20 20 20 20 20 20 20 20 64 65 66 69 63 69 65 6e | -squares.fit.is.........deficien |
| b480 | 74 2e 20 54 68 65 20 77 61 72 6e 69 6e 67 20 69 73 20 6f 6e 6c 79 20 72 61 69 73 65 64 20 69 66 | t..The.warning.is.only.raised.if |
| b4a0 | 20 60 60 66 75 6c 6c 20 3d 20 46 61 6c 73 65 60 60 2e 20 20 54 68 65 0a 20 20 20 20 20 20 20 20 | .``full.=.False``...The......... |
| b4c0 | 77 61 72 6e 69 6e 67 73 20 63 61 6e 20 62 65 20 74 75 72 6e 65 64 20 6f 66 66 20 62 79 0a 0a 20 | warnings.can.be.turned.off.by... |
| b4e0 | 20 20 20 20 20 20 20 3e 3e 3e 20 69 6d 70 6f 72 74 20 77 61 72 6e 69 6e 67 73 0a 20 20 20 20 20 | .......>>>.import.warnings...... |
| b500 | 20 20 20 3e 3e 3e 20 77 61 72 6e 69 6e 67 73 2e 73 69 6d 70 6c 65 66 69 6c 74 65 72 28 27 69 67 | ...>>>.warnings.simplefilter('ig |
| b520 | 6e 6f 72 65 27 2c 20 6e 70 2e 65 78 63 65 70 74 69 6f 6e 73 2e 52 61 6e 6b 57 61 72 6e 69 6e 67 | nore',.np.exceptions.RankWarning |
| b540 | 29 0a 0a 20 20 20 20 53 65 65 20 41 6c 73 6f 0a 20 20 20 20 2d 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 | )......See.Also.....--------.... |
| b560 | 20 6e 75 6d 70 79 2e 70 6f 6c 79 6e 6f 6d 69 61 6c 2e 63 68 65 62 79 73 68 65 76 2e 63 68 65 62 | .numpy.polynomial.chebyshev.cheb |
| b580 | 66 69 74 0a 20 20 20 20 6e 75 6d 70 79 2e 70 6f 6c 79 6e 6f 6d 69 61 6c 2e 6c 65 67 65 6e 64 72 | fit.....numpy.polynomial.legendr |
| b5a0 | 65 2e 6c 65 67 66 69 74 0a 20 20 20 20 6e 75 6d 70 79 2e 70 6f 6c 79 6e 6f 6d 69 61 6c 2e 70 6f | e.legfit.....numpy.polynomial.po |
| b5c0 | 6c 79 6e 6f 6d 69 61 6c 2e 70 6f 6c 79 66 69 74 0a 20 20 20 20 6e 75 6d 70 79 2e 70 6f 6c 79 6e | lynomial.polyfit.....numpy.polyn |
| b5e0 | 6f 6d 69 61 6c 2e 68 65 72 6d 69 74 65 2e 68 65 72 6d 66 69 74 0a 20 20 20 20 6e 75 6d 70 79 2e | omial.hermite.hermfit.....numpy. |
| b600 | 70 6f 6c 79 6e 6f 6d 69 61 6c 2e 6c 61 67 75 65 72 72 65 2e 6c 61 67 66 69 74 0a 20 20 20 20 68 | polynomial.laguerre.lagfit.....h |
| b620 | 65 72 6d 65 76 61 6c 20 3a 20 45 76 61 6c 75 61 74 65 73 20 61 20 48 65 72 6d 69 74 65 20 73 65 | ermeval.:.Evaluates.a.Hermite.se |
| b640 | 72 69 65 73 2e 0a 20 20 20 20 68 65 72 6d 65 76 61 6e 64 65 72 20 3a 20 70 73 65 75 64 6f 20 56 | ries......hermevander.:.pseudo.V |
| b660 | 61 6e 64 65 72 6d 6f 6e 64 65 20 6d 61 74 72 69 78 20 6f 66 20 48 65 72 6d 69 74 65 20 73 65 72 | andermonde.matrix.of.Hermite.ser |
| b680 | 69 65 73 2e 0a 20 20 20 20 68 65 72 6d 65 77 65 69 67 68 74 20 3a 20 48 65 72 6d 69 74 65 45 20 | ies......hermeweight.:.HermiteE. |
| b6a0 | 77 65 69 67 68 74 20 66 75 6e 63 74 69 6f 6e 2e 0a 20 20 20 20 6e 75 6d 70 79 2e 6c 69 6e 61 6c | weight.function......numpy.linal |
| b6c0 | 67 2e 6c 73 74 73 71 20 3a 20 43 6f 6d 70 75 74 65 73 20 61 20 6c 65 61 73 74 2d 73 71 75 61 72 | g.lstsq.:.Computes.a.least-squar |
| b6e0 | 65 73 20 66 69 74 20 66 72 6f 6d 20 74 68 65 20 6d 61 74 72 69 78 2e 0a 20 20 20 20 73 63 69 70 | es.fit.from.the.matrix......scip |
| b700 | 79 2e 69 6e 74 65 72 70 6f 6c 61 74 65 2e 55 6e 69 76 61 72 69 61 74 65 53 70 6c 69 6e 65 20 3a | y.interpolate.UnivariateSpline.: |
| b720 | 20 43 6f 6d 70 75 74 65 73 20 73 70 6c 69 6e 65 20 66 69 74 73 2e 0a 0a 20 20 20 20 4e 6f 74 65 | .Computes.spline.fits.......Note |
| b740 | 73 0a 20 20 20 20 2d 2d 2d 2d 2d 0a 20 20 20 20 54 68 65 20 73 6f 6c 75 74 69 6f 6e 20 69 73 20 | s.....-----.....The.solution.is. |
| b760 | 74 68 65 20 63 6f 65 66 66 69 63 69 65 6e 74 73 20 6f 66 20 74 68 65 20 48 65 72 6d 69 74 65 45 | the.coefficients.of.the.HermiteE |
| b780 | 20 73 65 72 69 65 73 20 60 70 60 20 74 68 61 74 0a 20 20 20 20 6d 69 6e 69 6d 69 7a 65 73 20 74 | .series.`p`.that.....minimizes.t |
| b7a0 | 68 65 20 73 75 6d 20 6f 66 20 74 68 65 20 77 65 69 67 68 74 65 64 20 73 71 75 61 72 65 64 20 65 | he.sum.of.the.weighted.squared.e |
| b7c0 | 72 72 6f 72 73 0a 0a 20 20 20 20 2e 2e 20 6d 61 74 68 3a 3a 20 45 20 3d 20 5c 73 75 6d 5f 6a 20 | rrors.........math::.E.=.\sum_j. |
| b7e0 | 77 5f 6a 5e 32 20 2a 20 7c 79 5f 6a 20 2d 20 70 28 78 5f 6a 29 7c 5e 32 2c 0a 0a 20 20 20 20 77 | w_j^2.*.|y_j.-.p(x_j)|^2,......w |
| b800 | 68 65 72 65 20 74 68 65 20 3a 6d 61 74 68 3a 60 77 5f 6a 60 20 61 72 65 20 74 68 65 20 77 65 69 | here.the.:math:`w_j`.are.the.wei |
| b820 | 67 68 74 73 2e 20 54 68 69 73 20 70 72 6f 62 6c 65 6d 20 69 73 20 73 6f 6c 76 65 64 20 62 79 0a | ghts..This.problem.is.solved.by. |
| b840 | 20 20 20 20 73 65 74 74 69 6e 67 20 75 70 20 74 68 65 20 28 74 79 70 69 63 61 6c 6c 79 29 20 6f | ....setting.up.the.(typically).o |
| b860 | 76 65 72 64 65 74 65 72 6d 69 6e 65 64 20 6d 61 74 72 69 78 20 65 71 75 61 74 69 6f 6e 0a 0a 20 | verdetermined.matrix.equation... |
| b880 | 20 20 20 2e 2e 20 6d 61 74 68 3a 3a 20 56 28 78 29 20 2a 20 63 20 3d 20 77 20 2a 20 79 2c 0a 0a | ......math::.V(x).*.c.=.w.*.y,.. |
| b8a0 | 20 20 20 20 77 68 65 72 65 20 60 56 60 20 69 73 20 74 68 65 20 70 73 65 75 64 6f 20 56 61 6e 64 | ....where.`V`.is.the.pseudo.Vand |
| b8c0 | 65 72 6d 6f 6e 64 65 20 6d 61 74 72 69 78 20 6f 66 20 60 78 60 2c 20 74 68 65 20 65 6c 65 6d 65 | ermonde.matrix.of.`x`,.the.eleme |
| b8e0 | 6e 74 73 20 6f 66 20 60 63 60 0a 20 20 20 20 61 72 65 20 74 68 65 20 63 6f 65 66 66 69 63 69 65 | nts.of.`c`.....are.the.coefficie |
| b900 | 6e 74 73 20 74 6f 20 62 65 20 73 6f 6c 76 65 64 20 66 6f 72 2c 20 61 6e 64 20 74 68 65 20 65 6c | nts.to.be.solved.for,.and.the.el |
| b920 | 65 6d 65 6e 74 73 20 6f 66 20 60 79 60 20 61 72 65 20 74 68 65 0a 20 20 20 20 6f 62 73 65 72 76 | ements.of.`y`.are.the.....observ |
| b940 | 65 64 20 76 61 6c 75 65 73 2e 20 20 54 68 69 73 20 65 71 75 61 74 69 6f 6e 20 69 73 20 74 68 65 | ed.values...This.equation.is.the |
| b960 | 6e 20 73 6f 6c 76 65 64 20 75 73 69 6e 67 20 74 68 65 20 73 69 6e 67 75 6c 61 72 20 76 61 6c 75 | n.solved.using.the.singular.valu |
| b980 | 65 0a 20 20 20 20 64 65 63 6f 6d 70 6f 73 69 74 69 6f 6e 20 6f 66 20 60 56 60 2e 0a 0a 20 20 20 | e.....decomposition.of.`V`...... |
| b9a0 | 20 49 66 20 73 6f 6d 65 20 6f 66 20 74 68 65 20 73 69 6e 67 75 6c 61 72 20 76 61 6c 75 65 73 20 | .If.some.of.the.singular.values. |
| b9c0 | 6f 66 20 60 56 60 20 61 72 65 20 73 6f 20 73 6d 61 6c 6c 20 74 68 61 74 20 74 68 65 79 20 61 72 | of.`V`.are.so.small.that.they.ar |
| b9e0 | 65 0a 20 20 20 20 6e 65 67 6c 65 63 74 65 64 2c 20 74 68 65 6e 20 61 20 60 7e 65 78 63 65 70 74 | e.....neglected,.then.a.`~except |
| ba00 | 69 6f 6e 73 2e 52 61 6e 6b 57 61 72 6e 69 6e 67 60 20 77 69 6c 6c 20 62 65 20 69 73 73 75 65 64 | ions.RankWarning`.will.be.issued |
| ba20 | 2e 20 54 68 69 73 20 6d 65 61 6e 73 20 74 68 61 74 0a 20 20 20 20 74 68 65 20 63 6f 65 66 66 69 | ..This.means.that.....the.coeffi |
| ba40 | 63 69 65 6e 74 20 76 61 6c 75 65 73 20 6d 61 79 20 62 65 20 70 6f 6f 72 6c 79 20 64 65 74 65 72 | cient.values.may.be.poorly.deter |
| ba60 | 6d 69 6e 65 64 2e 20 55 73 69 6e 67 20 61 20 6c 6f 77 65 72 20 6f 72 64 65 72 20 66 69 74 0a 20 | mined..Using.a.lower.order.fit.. |
| ba80 | 20 20 20 77 69 6c 6c 20 75 73 75 61 6c 6c 79 20 67 65 74 20 72 69 64 20 6f 66 20 74 68 65 20 77 | ...will.usually.get.rid.of.the.w |
| baa0 | 61 72 6e 69 6e 67 2e 20 20 54 68 65 20 60 72 63 6f 6e 64 60 20 70 61 72 61 6d 65 74 65 72 20 63 | arning...The.`rcond`.parameter.c |
| bac0 | 61 6e 20 61 6c 73 6f 20 62 65 0a 20 20 20 20 73 65 74 20 74 6f 20 61 20 76 61 6c 75 65 20 73 6d | an.also.be.....set.to.a.value.sm |
| bae0 | 61 6c 6c 65 72 20 74 68 61 6e 20 69 74 73 20 64 65 66 61 75 6c 74 2c 20 62 75 74 20 74 68 65 20 | aller.than.its.default,.but.the. |
| bb00 | 72 65 73 75 6c 74 69 6e 67 20 66 69 74 20 6d 61 79 20 62 65 0a 20 20 20 20 73 70 75 72 69 6f 75 | resulting.fit.may.be.....spuriou |
| bb20 | 73 20 61 6e 64 20 68 61 76 65 20 6c 61 72 67 65 20 63 6f 6e 74 72 69 62 75 74 69 6f 6e 73 20 66 | s.and.have.large.contributions.f |
| bb40 | 72 6f 6d 20 72 6f 75 6e 64 6f 66 66 20 65 72 72 6f 72 2e 0a 0a 20 20 20 20 46 69 74 73 20 75 73 | rom.roundoff.error.......Fits.us |
| bb60 | 69 6e 67 20 48 65 72 6d 69 74 65 45 20 73 65 72 69 65 73 20 61 72 65 20 70 72 6f 62 61 62 6c 79 | ing.HermiteE.series.are.probably |
| bb80 | 20 6d 6f 73 74 20 75 73 65 66 75 6c 20 77 68 65 6e 20 74 68 65 20 64 61 74 61 20 63 61 6e 0a 20 | .most.useful.when.the.data.can.. |
| bba0 | 20 20 20 62 65 20 61 70 70 72 6f 78 69 6d 61 74 65 64 20 62 79 20 60 60 73 71 72 74 28 77 28 78 | ...be.approximated.by.``sqrt(w(x |
| bbc0 | 29 29 20 2a 20 70 28 78 29 60 60 2c 20 77 68 65 72 65 20 60 60 77 28 78 29 60 60 20 69 73 20 74 | )).*.p(x)``,.where.``w(x)``.is.t |
| bbe0 | 68 65 20 48 65 72 6d 69 74 65 45 0a 20 20 20 20 77 65 69 67 68 74 2e 20 49 6e 20 74 68 61 74 20 | he.HermiteE.....weight..In.that. |
| bc00 | 63 61 73 65 20 74 68 65 20 77 65 69 67 68 74 20 60 60 73 71 72 74 28 77 28 78 5b 69 5d 29 29 60 | case.the.weight.``sqrt(w(x[i]))` |
| bc20 | 60 20 73 68 6f 75 6c 64 20 62 65 20 75 73 65 64 0a 20 20 20 20 74 6f 67 65 74 68 65 72 20 77 69 | `.should.be.used.....together.wi |
| bc40 | 74 68 20 64 61 74 61 20 76 61 6c 75 65 73 20 60 60 79 5b 69 5d 2f 73 71 72 74 28 77 28 78 5b 69 | th.data.values.``y[i]/sqrt(w(x[i |
| bc60 | 5d 29 29 60 60 2e 20 54 68 65 20 77 65 69 67 68 74 20 66 75 6e 63 74 69 6f 6e 20 69 73 0a 20 20 | ]))``..The.weight.function.is... |
| bc80 | 20 20 61 76 61 69 6c 61 62 6c 65 20 61 73 20 60 68 65 72 6d 65 77 65 69 67 68 74 60 2e 0a 0a 20 | ..available.as.`hermeweight`.... |
| bca0 | 20 20 20 52 65 66 65 72 65 6e 63 65 73 0a 20 20 20 20 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 | ...References.....----------.... |
| bcc0 | 20 2e 2e 20 5b 31 5d 20 57 69 6b 69 70 65 64 69 61 2c 20 22 43 75 72 76 65 20 66 69 74 74 69 6e | ....[1].Wikipedia,."Curve.fittin |
| bce0 | 67 22 2c 0a 20 20 20 20 20 20 20 20 20 20 20 68 74 74 70 73 3a 2f 2f 65 6e 2e 77 69 6b 69 70 65 | g",............https://en.wikipe |
| bd00 | 64 69 61 2e 6f 72 67 2f 77 69 6b 69 2f 43 75 72 76 65 5f 66 69 74 74 69 6e 67 0a 0a 20 20 20 20 | dia.org/wiki/Curve_fitting...... |
| bd20 | 45 78 61 6d 70 6c 65 73 0a 20 20 20 20 2d 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 3e 3e 3e 20 69 6d | Examples.....--------.....>>>.im |
| bd40 | 70 6f 72 74 20 6e 75 6d 70 79 20 61 73 20 6e 70 0a 20 20 20 20 3e 3e 3e 20 66 72 6f 6d 20 6e 75 | port.numpy.as.np.....>>>.from.nu |
| bd60 | 6d 70 79 2e 70 6f 6c 79 6e 6f 6d 69 61 6c 2e 68 65 72 6d 69 74 65 5f 65 20 69 6d 70 6f 72 74 20 | mpy.polynomial.hermite_e.import. |
| bd80 | 68 65 72 6d 65 66 69 74 2c 20 68 65 72 6d 65 76 61 6c 0a 20 20 20 20 3e 3e 3e 20 78 20 3d 20 6e | hermefit,.hermeval.....>>>.x.=.n |
| bda0 | 70 2e 6c 69 6e 73 70 61 63 65 28 2d 31 30 2c 20 31 30 29 0a 20 20 20 20 3e 3e 3e 20 72 6e 67 20 | p.linspace(-10,.10).....>>>.rng. |
| bdc0 | 3d 20 6e 70 2e 72 61 6e 64 6f 6d 2e 64 65 66 61 75 6c 74 5f 72 6e 67 28 29 0a 20 20 20 20 3e 3e | =.np.random.default_rng().....>> |
| bde0 | 3e 20 65 72 72 20 3d 20 72 6e 67 2e 6e 6f 72 6d 61 6c 28 73 63 61 6c 65 3d 31 2e 2f 31 30 2c 20 | >.err.=.rng.normal(scale=1./10,. |
| be00 | 73 69 7a 65 3d 6c 65 6e 28 78 29 29 0a 20 20 20 20 3e 3e 3e 20 79 20 3d 20 68 65 72 6d 65 76 61 | size=len(x)).....>>>.y.=.hermeva |
| be20 | 6c 28 78 2c 20 5b 31 2c 20 32 2c 20 33 5d 29 20 2b 20 65 72 72 0a 20 20 20 20 3e 3e 3e 20 68 65 | l(x,.[1,.2,.3]).+.err.....>>>.he |
| be40 | 72 6d 65 66 69 74 28 78 2c 20 79 2c 20 32 29 0a 20 20 20 20 61 72 72 61 79 28 5b 31 2e 30 32 32 | rmefit(x,.y,.2).....array([1.022 |
| be60 | 38 34 31 39 36 2c 20 32 2e 30 30 30 33 32 38 30 35 2c 20 32 2e 39 39 39 37 38 34 35 37 5d 29 20 | 84196,.2.00032805,.2.99978457]). |
| be80 | 23 20 6d 61 79 20 76 61 72 79 0a 0a 20 20 20 20 29 03 72 28 00 00 00 da 04 5f 66 69 74 72 18 00 | #.may.vary......).r(....._fitr.. |
| bea0 | 00 00 29 06 72 7d 00 00 00 72 83 00 00 00 72 2d 00 00 00 da 05 72 63 6f 6e 64 da 04 66 75 6c 6c | ..).r}...r....r-.....rcond..full |
| bec0 | da 01 77 73 06 00 00 00 20 20 20 20 20 20 72 30 00 00 00 72 19 00 00 00 72 19 00 00 00 cf 04 00 | ..ws..........r0...r....r....... |
| bee0 | 00 73 20 00 00 00 80 00 f4 46 04 00 0c 0e 8f 37 89 37 94 3b a0 01 a0 31 a0 63 a8 35 b0 24 b8 01 | .s.......F.....7.7.;...1.c.5.$.. |
| bf00 | d3 0b 3a d0 04 3a 72 31 00 00 00 63 01 00 00 00 00 00 00 00 00 00 00 00 0b 00 00 00 03 00 00 00 | ..:..:r1...c.................... |
| bf20 | f3 00 03 00 00 97 00 74 01 00 00 00 00 00 00 00 00 6a 02 00 00 00 00 00 00 00 00 00 00 00 00 00 | .......t.........j.............. |
| bf40 | 00 00 00 00 00 7c 00 67 01 ab 01 00 00 00 00 00 00 5c 01 00 00 7d 00 74 05 00 00 00 00 00 00 00 | .....|.g.........\...}.t........ |
| bf60 | 00 7c 00 ab 01 00 00 00 00 00 00 64 01 6b 02 00 00 72 0b 74 07 00 00 00 00 00 00 00 00 64 02 ab | .|.........d.k...r.t.........d.. |
| bf80 | 01 00 00 00 00 00 00 82 01 74 05 00 00 00 00 00 00 00 00 7c 00 ab 01 00 00 00 00 00 00 64 01 6b | .........t.........|.........d.k |
| bfa0 | 28 00 00 72 21 74 09 00 00 00 00 00 00 00 00 6a 0a 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 | (..r!t.........j................ |
| bfc0 | 00 00 00 7c 00 64 03 19 00 00 00 0b 00 7c 00 64 04 19 00 00 00 7a 0b 00 00 67 01 67 01 ab 01 00 | ...|.d.......|.d.....z...g.g.... |
| bfe0 | 00 00 00 00 00 53 00 74 05 00 00 00 00 00 00 00 00 7c 00 ab 01 00 00 00 00 00 00 64 04 7a 0a 00 | .....S.t.........|.........d.z.. |
| c000 | 00 7d 01 74 09 00 00 00 00 00 00 00 00 6a 0c 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 | .}.t.........j.................. |
| c020 | 00 7c 01 7c 01 66 02 7c 00 6a 0e 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 ac 05 ab | .|.|.f.|.j...................... |
| c040 | 02 00 00 00 00 00 00 7d 02 74 09 00 00 00 00 00 00 00 00 6a 10 00 00 00 00 00 00 00 00 00 00 00 | .......}.t.........j............ |
| c060 | 00 00 00 00 00 00 00 64 06 64 06 74 09 00 00 00 00 00 00 00 00 6a 12 00 00 00 00 00 00 00 00 00 | .......d.d.t.........j.......... |
| c080 | 00 00 00 00 00 00 00 00 00 74 09 00 00 00 00 00 00 00 00 6a 14 00 00 00 00 00 00 00 00 00 00 00 | .........t.........j............ |
| c0a0 | 00 00 00 00 00 00 00 7c 01 64 04 7a 0a 00 00 64 03 64 07 ab 03 00 00 00 00 00 00 ab 01 00 00 00 | .......|.d.z...d.d.............. |
| c0c0 | 00 00 00 7a 0b 00 00 66 02 ab 01 00 00 00 00 00 00 7d 03 74 08 00 00 00 00 00 00 00 00 6a 16 00 | ...z...f.........}.t.........j.. |
| c0e0 | 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 6a 19 00 00 00 00 00 00 00 00 00 00 00 00 00 | .................j.............. |
| c100 | 00 00 00 00 00 7c 03 ab 01 00 00 00 00 00 00 64 08 64 08 64 07 85 03 19 00 00 00 7d 03 7c 02 6a | .....|.........d.d.d.......}.|.j |
| c120 | 1b 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 64 07 ab 01 00 00 00 00 00 00 64 04 64 | ...................d.........d.d |
| c140 | 08 7c 01 64 04 7a 00 00 00 85 03 19 00 00 00 7d 04 7c 02 6a 1b 00 00 00 00 00 00 00 00 00 00 00 | .|.d.z.........}.|.j............ |
| c160 | 00 00 00 00 00 00 00 64 07 ab 01 00 00 00 00 00 00 7c 01 64 08 7c 01 64 04 7a 00 00 00 85 03 19 | .......d.........|.d.|.d.z...... |
| c180 | 00 00 00 7d 05 74 09 00 00 00 00 00 00 00 00 6a 12 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 | ...}.t.........j................ |
| c1a0 | 00 00 00 74 09 00 00 00 00 00 00 00 00 6a 14 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 | ...t.........j.................. |
| c1c0 | 00 64 04 7c 01 ab 02 00 00 00 00 00 00 ab 01 00 00 00 00 00 00 7c 04 64 09 3c 00 00 00 7c 04 7c | .d.|.................|.d.<...|.| |
| c1e0 | 05 64 09 3c 00 00 00 7c 02 64 08 64 08 85 02 64 07 66 02 78 02 78 02 19 00 00 00 7c 03 7c 00 64 | .d.<...|.d.d...d.f.x.x.....|.|.d |
| c200 | 08 64 07 1a 00 7a 05 00 00 7c 00 64 07 19 00 00 00 7a 0b 00 00 7a 17 00 00 63 03 63 02 3c 00 00 | .d...z...|.d.....z...z...c.c.<.. |
| c220 | 00 7c 02 53 00 29 0a 61 66 02 00 00 0a 20 20 20 20 52 65 74 75 72 6e 20 74 68 65 20 73 63 61 6c | .|.S.).af........Return.the.scal |
| c240 | 65 64 20 63 6f 6d 70 61 6e 69 6f 6e 20 6d 61 74 72 69 78 20 6f 66 20 63 2e 0a 0a 20 20 20 20 54 | ed.companion.matrix.of.c.......T |
| c260 | 68 65 20 62 61 73 69 73 20 70 6f 6c 79 6e 6f 6d 69 61 6c 73 20 61 72 65 20 73 63 61 6c 65 64 20 | he.basis.polynomials.are.scaled. |
| c280 | 73 6f 20 74 68 61 74 20 74 68 65 20 63 6f 6d 70 61 6e 69 6f 6e 20 6d 61 74 72 69 78 20 69 73 0a | so.that.the.companion.matrix.is. |
| c2a0 | 20 20 20 20 73 79 6d 6d 65 74 72 69 63 20 77 68 65 6e 20 60 63 60 20 69 73 20 61 6e 20 48 65 72 | ....symmetric.when.`c`.is.an.Her |
| c2c0 | 6d 69 74 65 45 20 62 61 73 69 73 20 70 6f 6c 79 6e 6f 6d 69 61 6c 2e 20 54 68 69 73 20 70 72 6f | miteE.basis.polynomial..This.pro |
| c2e0 | 76 69 64 65 73 0a 20 20 20 20 62 65 74 74 65 72 20 65 69 67 65 6e 76 61 6c 75 65 20 65 73 74 69 | vides.....better.eigenvalue.esti |
| c300 | 6d 61 74 65 73 20 74 68 61 6e 20 74 68 65 20 75 6e 73 63 61 6c 65 64 20 63 61 73 65 20 61 6e 64 | mates.than.the.unscaled.case.and |
| c320 | 20 66 6f 72 20 62 61 73 69 73 0a 20 20 20 20 70 6f 6c 79 6e 6f 6d 69 61 6c 73 20 74 68 65 20 65 | .for.basis.....polynomials.the.e |
| c340 | 69 67 65 6e 76 61 6c 75 65 73 20 61 72 65 20 67 75 61 72 61 6e 74 65 65 64 20 74 6f 20 62 65 20 | igenvalues.are.guaranteed.to.be. |
| c360 | 72 65 61 6c 20 69 66 0a 20 20 20 20 60 6e 75 6d 70 79 2e 6c 69 6e 61 6c 67 2e 65 69 67 76 61 6c | real.if.....`numpy.linalg.eigval |
| c380 | 73 68 60 20 69 73 20 75 73 65 64 20 74 6f 20 6f 62 74 61 69 6e 20 74 68 65 6d 2e 0a 0a 20 20 20 | sh`.is.used.to.obtain.them...... |
| c3a0 | 20 50 61 72 61 6d 65 74 65 72 73 0a 20 20 20 20 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 63 | .Parameters.....----------.....c |
| c3c0 | 20 3a 20 61 72 72 61 79 5f 6c 69 6b 65 0a 20 20 20 20 20 20 20 20 31 2d 44 20 61 72 72 61 79 20 | .:.array_like.........1-D.array. |
| c3e0 | 6f 66 20 48 65 72 6d 69 74 65 45 20 73 65 72 69 65 73 20 63 6f 65 66 66 69 63 69 65 6e 74 73 20 | of.HermiteE.series.coefficients. |
| c400 | 6f 72 64 65 72 65 64 20 66 72 6f 6d 20 6c 6f 77 20 74 6f 20 68 69 67 68 0a 20 20 20 20 20 20 20 | ordered.from.low.to.high........ |
| c420 | 20 64 65 67 72 65 65 2e 0a 0a 20 20 20 20 52 65 74 75 72 6e 73 0a 20 20 20 20 2d 2d 2d 2d 2d 2d | .degree.......Returns.....------ |
| c440 | 2d 0a 20 20 20 20 6d 61 74 20 3a 20 6e 64 61 72 72 61 79 0a 20 20 20 20 20 20 20 20 53 63 61 6c | -.....mat.:.ndarray.........Scal |
| c460 | 65 64 20 63 6f 6d 70 61 6e 69 6f 6e 20 6d 61 74 72 69 78 20 6f 66 20 64 69 6d 65 6e 73 69 6f 6e | ed.companion.matrix.of.dimension |
| c480 | 73 20 28 64 65 67 2c 20 64 65 67 29 2e 0a 20 20 20 20 72 36 00 00 00 7a 2e 53 65 72 69 65 73 20 | s.(deg,.deg)......r6...z.Series. |
| c4a0 | 6d 75 73 74 20 68 61 76 65 20 6d 61 78 69 6d 75 6d 20 64 65 67 72 65 65 20 6f 66 20 61 74 20 6c | must.have.maximum.degree.of.at.l |
| c4c0 | 65 61 73 74 20 31 2e 72 02 00 00 00 72 04 00 00 00 72 4f 00 00 00 72 3e 00 00 00 72 27 00 00 00 | east.1.r....r....rO...r>...r'... |
| c4e0 | 4e 2e 29 0e 72 28 00 00 00 72 29 00 00 00 72 2a 00 00 00 72 67 00 00 00 72 40 00 00 00 72 41 00 | N.).r(...r)...r*...rg...r@...rA. |
| c500 | 00 00 da 05 7a 65 72 6f 73 72 50 00 00 00 da 06 68 73 74 61 63 6b da 04 73 71 72 74 da 06 61 72 | ....zerosrP.....hstack..sqrt..ar |
| c520 | 61 6e 67 65 da 08 6d 75 6c 74 69 70 6c 79 da 0a 61 63 63 75 6d 75 6c 61 74 65 72 7c 00 00 00 29 | ange..multiply..accumulater|...) |
| c540 | 06 72 39 00 00 00 72 3a 00 00 00 da 03 6d 61 74 72 43 00 00 00 da 03 74 6f 70 da 03 62 6f 74 73 | .r9...r:.....matrC.....top..bots |
| c560 | 06 00 00 00 20 20 20 20 20 20 72 30 00 00 00 72 23 00 00 00 72 23 00 00 00 55 05 00 00 73 55 01 | ..........r0...r#...r#...U...sU. |
| c580 | 00 00 80 00 f4 2c 00 0b 0d 8f 2c 89 2c 98 01 90 73 d3 0a 1b 81 43 80 51 dc 07 0a 88 31 83 76 90 | .....,....,.,...s....C.Q....1.v. |
| c5a0 | 01 82 7a dc 0e 18 d0 19 49 d3 0e 4a d0 08 4a dc 07 0a 88 31 83 76 90 11 82 7b dc 0f 11 8f 78 89 | ..z.....I..J..J....1.v...{....x. |
| c5c0 | 78 98 31 98 51 99 34 98 25 a0 21 a0 41 a1 24 99 2c 98 1e d0 18 28 d3 0f 29 d0 08 29 e4 08 0b 88 | x.1.Q.4.%.!.A.$.,....(..)..).... |
| c5e0 | 41 8b 06 90 11 89 0a 80 41 dc 0a 0c 8f 28 89 28 90 41 90 71 90 36 a0 11 a7 17 a1 17 d4 0a 29 80 | A.......A....(.(.A.q.6........). |
| c600 | 43 dc 0a 0c 8f 29 89 29 90 52 98 12 9c 62 9f 67 99 67 a4 62 a7 69 a1 69 b0 01 b0 41 b1 05 b0 71 | C....).).R...b.g.g.b.i.i...A...q |
| c620 | b8 22 d3 26 3d d3 1e 3e d1 19 3e d0 14 3f d3 0a 40 80 43 dc 0a 0c 8f 2b 89 2b d7 0a 20 d1 0a 20 | .".&=..>..>..?..@.C....+.+...... |
| c640 | a0 13 d3 0a 25 a1 64 a8 02 a0 64 d1 0a 2b 80 43 d8 0a 0d 8f 2b 89 2b 90 62 8b 2f 98 21 98 28 98 | ....%.d...d..+.C....+.+.b./.!.(. |
| c660 | 51 a0 11 99 55 98 28 d1 0a 23 80 43 d8 0a 0d 8f 2b 89 2b 90 62 8b 2f 98 21 98 28 98 51 a0 11 99 | Q...U.(..#.C....+.+.b./.!.(.Q... |
| c680 | 55 98 28 d1 0a 23 80 43 dc 0f 11 8f 77 89 77 94 72 97 79 91 79 a0 11 a0 41 93 7f d3 0f 27 80 43 | U.(..#.C....w.w.r.y.y...A....'.C |
| c6a0 | 88 03 81 48 d8 0f 12 80 43 88 03 81 48 d8 04 07 8a 01 88 32 88 05 83 4a 90 23 98 01 98 23 98 32 | ...H....C...H......2...J.#...#.2 |
| c6c0 | 98 06 91 2c a0 11 a0 32 a1 15 d1 12 26 d1 04 26 83 4a d8 0b 0e 80 4a 72 31 00 00 00 63 01 00 00 | ...,...2....&..&.J....Jr1...c... |
| c6e0 | 00 00 00 00 00 00 00 00 00 05 00 00 00 03 00 00 00 f3 66 01 00 00 97 00 74 01 00 00 00 00 00 00 | ..................f.....t....... |
| c700 | 00 00 6a 02 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 7c 00 67 01 ab 01 00 00 00 00 | ..j...................|.g....... |
| c720 | 00 00 5c 01 00 00 7d 00 74 05 00 00 00 00 00 00 00 00 7c 00 ab 01 00 00 00 00 00 00 64 01 6b 1a | ..\...}.t.........|.........d.k. |
| c740 | 00 00 72 21 74 07 00 00 00 00 00 00 00 00 6a 08 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 | ..r!t.........j................. |
| c760 | 00 00 67 00 7c 00 6a 0a 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 ac 02 ab 02 00 00 | ..g.|.j......................... |
| c780 | 00 00 00 00 53 00 74 05 00 00 00 00 00 00 00 00 7c 00 ab 01 00 00 00 00 00 00 64 03 6b 28 00 00 | ....S.t.........|.........d.k(.. |
| c7a0 | 72 20 74 07 00 00 00 00 00 00 00 00 6a 08 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 | r.t.........j................... |
| c7c0 | 7c 00 64 04 19 00 00 00 0b 00 7c 00 64 01 19 00 00 00 7a 0b 00 00 67 01 ab 01 00 00 00 00 00 00 | |.d.......|.d.....z...g......... |
| c7e0 | 53 00 74 0d 00 00 00 00 00 00 00 00 7c 00 ab 01 00 00 00 00 00 00 64 05 64 05 64 06 85 03 64 05 | S.t.........|.........d.d.d...d. |
| c800 | 64 05 64 06 85 03 66 02 19 00 00 00 7d 01 74 0f 00 00 00 00 00 00 00 00 6a 10 00 00 00 00 00 00 | d.d...f.....}.t.........j....... |
| c820 | 00 00 00 00 00 00 00 00 00 00 00 00 7c 01 ab 01 00 00 00 00 00 00 7d 02 7c 02 6a 13 00 00 00 00 | ............|.........}.|.j..... |
| c840 | 00 00 00 00 00 00 00 00 00 00 00 00 00 00 ab 00 00 00 00 00 00 00 01 00 7c 02 53 00 29 07 61 ea | ........................|.S.).a. |
| c860 | 05 00 00 0a 20 20 20 20 43 6f 6d 70 75 74 65 20 74 68 65 20 72 6f 6f 74 73 20 6f 66 20 61 20 48 | ........Compute.the.roots.of.a.H |
| c880 | 65 72 6d 69 74 65 45 20 73 65 72 69 65 73 2e 0a 0a 20 20 20 20 52 65 74 75 72 6e 20 74 68 65 20 | ermiteE.series.......Return.the. |
| c8a0 | 72 6f 6f 74 73 20 28 61 2e 6b 2e 61 2e 20 22 7a 65 72 6f 73 22 29 20 6f 66 20 74 68 65 20 70 6f | roots.(a.k.a.."zeros").of.the.po |
| c8c0 | 6c 79 6e 6f 6d 69 61 6c 0a 0a 20 20 20 20 2e 2e 20 6d 61 74 68 3a 3a 20 70 28 78 29 20 3d 20 5c | lynomial.........math::.p(x).=.\ |
| c8e0 | 73 75 6d 5f 69 20 63 5b 69 5d 20 2a 20 48 65 5f 69 28 78 29 2e 0a 0a 20 20 20 20 50 61 72 61 6d | sum_i.c[i].*.He_i(x).......Param |
| c900 | 65 74 65 72 73 0a 20 20 20 20 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 63 20 3a 20 31 2d 44 | eters.....----------.....c.:.1-D |
| c920 | 20 61 72 72 61 79 5f 6c 69 6b 65 0a 20 20 20 20 20 20 20 20 31 2d 44 20 61 72 72 61 79 20 6f 66 | .array_like.........1-D.array.of |
| c940 | 20 63 6f 65 66 66 69 63 69 65 6e 74 73 2e 0a 0a 20 20 20 20 52 65 74 75 72 6e 73 0a 20 20 20 20 | .coefficients.......Returns..... |
| c960 | 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 6f 75 74 20 3a 20 6e 64 61 72 72 61 79 0a 20 20 20 20 20 20 | -------.....out.:.ndarray....... |
| c980 | 20 20 41 72 72 61 79 20 6f 66 20 74 68 65 20 72 6f 6f 74 73 20 6f 66 20 74 68 65 20 73 65 72 69 | ..Array.of.the.roots.of.the.seri |
| c9a0 | 65 73 2e 20 49 66 20 61 6c 6c 20 74 68 65 20 72 6f 6f 74 73 20 61 72 65 20 72 65 61 6c 2c 0a 20 | es..If.all.the.roots.are.real,.. |
| c9c0 | 20 20 20 20 20 20 20 74 68 65 6e 20 60 6f 75 74 60 20 69 73 20 61 6c 73 6f 20 72 65 61 6c 2c 20 | .......then.`out`.is.also.real,. |
| c9e0 | 6f 74 68 65 72 77 69 73 65 20 69 74 20 69 73 20 63 6f 6d 70 6c 65 78 2e 0a 0a 20 20 20 20 53 65 | otherwise.it.is.complex.......Se |
| ca00 | 65 20 41 6c 73 6f 0a 20 20 20 20 2d 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 6e 75 6d 70 79 2e 70 6f | e.Also.....--------.....numpy.po |
| ca20 | 6c 79 6e 6f 6d 69 61 6c 2e 70 6f 6c 79 6e 6f 6d 69 61 6c 2e 70 6f 6c 79 72 6f 6f 74 73 0a 20 20 | lynomial.polynomial.polyroots... |
| ca40 | 20 20 6e 75 6d 70 79 2e 70 6f 6c 79 6e 6f 6d 69 61 6c 2e 6c 65 67 65 6e 64 72 65 2e 6c 65 67 72 | ..numpy.polynomial.legendre.legr |
| ca60 | 6f 6f 74 73 0a 20 20 20 20 6e 75 6d 70 79 2e 70 6f 6c 79 6e 6f 6d 69 61 6c 2e 6c 61 67 75 65 72 | oots.....numpy.polynomial.laguer |
| ca80 | 72 65 2e 6c 61 67 72 6f 6f 74 73 0a 20 20 20 20 6e 75 6d 70 79 2e 70 6f 6c 79 6e 6f 6d 69 61 6c | re.lagroots.....numpy.polynomial |
| caa0 | 2e 68 65 72 6d 69 74 65 2e 68 65 72 6d 72 6f 6f 74 73 0a 20 20 20 20 6e 75 6d 70 79 2e 70 6f 6c | .hermite.hermroots.....numpy.pol |
| cac0 | 79 6e 6f 6d 69 61 6c 2e 63 68 65 62 79 73 68 65 76 2e 63 68 65 62 72 6f 6f 74 73 0a 0a 20 20 20 | ynomial.chebyshev.chebroots..... |
| cae0 | 20 4e 6f 74 65 73 0a 20 20 20 20 2d 2d 2d 2d 2d 0a 20 20 20 20 54 68 65 20 72 6f 6f 74 20 65 73 | .Notes.....-----.....The.root.es |
| cb00 | 74 69 6d 61 74 65 73 20 61 72 65 20 6f 62 74 61 69 6e 65 64 20 61 73 20 74 68 65 20 65 69 67 65 | timates.are.obtained.as.the.eige |
| cb20 | 6e 76 61 6c 75 65 73 20 6f 66 20 74 68 65 20 63 6f 6d 70 61 6e 69 6f 6e 0a 20 20 20 20 6d 61 74 | nvalues.of.the.companion.....mat |
| cb40 | 72 69 78 2c 20 52 6f 6f 74 73 20 66 61 72 20 66 72 6f 6d 20 74 68 65 20 6f 72 69 67 69 6e 20 6f | rix,.Roots.far.from.the.origin.o |
| cb60 | 66 20 74 68 65 20 63 6f 6d 70 6c 65 78 20 70 6c 61 6e 65 20 6d 61 79 20 68 61 76 65 20 6c 61 72 | f.the.complex.plane.may.have.lar |
| cb80 | 67 65 0a 20 20 20 20 65 72 72 6f 72 73 20 64 75 65 20 74 6f 20 74 68 65 20 6e 75 6d 65 72 69 63 | ge.....errors.due.to.the.numeric |
| cba0 | 61 6c 20 69 6e 73 74 61 62 69 6c 69 74 79 20 6f 66 20 74 68 65 20 73 65 72 69 65 73 20 66 6f 72 | al.instability.of.the.series.for |
| cbc0 | 20 73 75 63 68 0a 20 20 20 20 76 61 6c 75 65 73 2e 20 52 6f 6f 74 73 20 77 69 74 68 20 6d 75 6c | .such.....values..Roots.with.mul |
| cbe0 | 74 69 70 6c 69 63 69 74 79 20 67 72 65 61 74 65 72 20 74 68 61 6e 20 31 20 77 69 6c 6c 20 61 6c | tiplicity.greater.than.1.will.al |
| cc00 | 73 6f 20 73 68 6f 77 20 6c 61 72 67 65 72 0a 20 20 20 20 65 72 72 6f 72 73 20 61 73 20 74 68 65 | so.show.larger.....errors.as.the |
| cc20 | 20 76 61 6c 75 65 20 6f 66 20 74 68 65 20 73 65 72 69 65 73 20 6e 65 61 72 20 73 75 63 68 20 70 | .value.of.the.series.near.such.p |
| cc40 | 6f 69 6e 74 73 20 69 73 20 72 65 6c 61 74 69 76 65 6c 79 0a 20 20 20 20 69 6e 73 65 6e 73 69 74 | oints.is.relatively.....insensit |
| cc60 | 69 76 65 20 74 6f 20 65 72 72 6f 72 73 20 69 6e 20 74 68 65 20 72 6f 6f 74 73 2e 20 49 73 6f 6c | ive.to.errors.in.the.roots..Isol |
| cc80 | 61 74 65 64 20 72 6f 6f 74 73 20 6e 65 61 72 20 74 68 65 20 6f 72 69 67 69 6e 20 63 61 6e 0a 20 | ated.roots.near.the.origin.can.. |
| cca0 | 20 20 20 62 65 20 69 6d 70 72 6f 76 65 64 20 62 79 20 61 20 66 65 77 20 69 74 65 72 61 74 69 6f | ...be.improved.by.a.few.iteratio |
| ccc0 | 6e 73 20 6f 66 20 4e 65 77 74 6f 6e 27 73 20 6d 65 74 68 6f 64 2e 0a 0a 20 20 20 20 54 68 65 20 | ns.of.Newton's.method.......The. |
| cce0 | 48 65 72 6d 69 74 65 45 20 73 65 72 69 65 73 20 62 61 73 69 73 20 70 6f 6c 79 6e 6f 6d 69 61 6c | HermiteE.series.basis.polynomial |
| cd00 | 73 20 61 72 65 6e 27 74 20 70 6f 77 65 72 73 20 6f 66 20 60 78 60 20 73 6f 20 74 68 65 0a 20 20 | s.aren't.powers.of.`x`.so.the... |
| cd20 | 20 20 72 65 73 75 6c 74 73 20 6f 66 20 74 68 69 73 20 66 75 6e 63 74 69 6f 6e 20 6d 61 79 20 73 | ..results.of.this.function.may.s |
| cd40 | 65 65 6d 20 75 6e 69 6e 74 75 69 74 69 76 65 2e 0a 0a 20 20 20 20 45 78 61 6d 70 6c 65 73 0a 20 | eem.unintuitive.......Examples.. |
| cd60 | 20 20 20 2d 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 3e 3e 3e 20 66 72 6f 6d 20 6e 75 6d 70 79 2e 70 | ...--------.....>>>.from.numpy.p |
| cd80 | 6f 6c 79 6e 6f 6d 69 61 6c 2e 68 65 72 6d 69 74 65 5f 65 20 69 6d 70 6f 72 74 20 68 65 72 6d 65 | olynomial.hermite_e.import.herme |
| cda0 | 72 6f 6f 74 73 2c 20 68 65 72 6d 65 66 72 6f 6d 72 6f 6f 74 73 0a 20 20 20 20 3e 3e 3e 20 63 6f | roots,.hermefromroots.....>>>.co |
| cdc0 | 65 66 20 3d 20 68 65 72 6d 65 66 72 6f 6d 72 6f 6f 74 73 28 5b 2d 31 2c 20 30 2c 20 31 5d 29 0a | ef.=.hermefromroots([-1,.0,.1]). |
| cde0 | 20 20 20 20 3e 3e 3e 20 63 6f 65 66 0a 20 20 20 20 61 72 72 61 79 28 5b 30 2e 2c 20 32 2e 2c 20 | ....>>>.coef.....array([0.,.2.,. |
| ce00 | 30 2e 2c 20 31 2e 5d 29 0a 20 20 20 20 3e 3e 3e 20 68 65 72 6d 65 72 6f 6f 74 73 28 63 6f 65 66 | 0.,.1.]).....>>>.hermeroots(coef |
| ce20 | 29 0a 20 20 20 20 61 72 72 61 79 28 5b 2d 31 2e 2c 20 20 30 2e 2c 20 20 31 2e 5d 29 20 23 20 6d | ).....array([-1.,..0.,..1.]).#.m |
| ce40 | 61 79 20 76 61 72 79 0a 0a 20 20 20 20 72 04 00 00 00 72 4f 00 00 00 72 36 00 00 00 72 02 00 00 | ay.vary......r....rO...r6...r... |
| ce60 | 00 4e 72 27 00 00 00 29 0a 72 28 00 00 00 72 29 00 00 00 72 2a 00 00 00 72 40 00 00 00 72 41 00 | .Nr'...).r(...r)...r*...r@...rA. |
| ce80 | 00 00 72 50 00 00 00 72 23 00 00 00 da 02 6c 61 da 07 65 69 67 76 61 6c 73 da 04 73 6f 72 74 29 | ..rP...r#.....la..eigvals..sort) |
| cea0 | 03 72 39 00 00 00 72 6b 00 00 00 da 01 72 73 03 00 00 00 20 20 20 72 30 00 00 00 72 1b 00 00 00 | .r9...rk.....rs.......r0...r.... |
| cec0 | 72 1b 00 00 00 7d 05 00 00 73 99 00 00 00 80 00 f4 66 01 00 0b 0d 8f 2c 89 2c 98 01 90 73 d3 0a | r....}...s.......f.....,.,...s.. |
| cee0 | 1b 81 43 80 51 dc 07 0a 88 31 83 76 90 11 82 7b dc 0f 11 8f 78 89 78 98 02 a0 21 a7 27 a1 27 d4 | ..C.Q....1.v...{....x.x...!.'.'. |
| cf00 | 0f 2a d0 08 2a dc 07 0a 88 31 83 76 90 11 82 7b dc 0f 11 8f 78 89 78 98 21 98 41 99 24 98 15 a0 | .*..*....1.v...{....x.x.!.A.$... |
| cf20 | 11 a0 31 a1 14 99 1c 98 0e d3 0f 27 d0 08 27 f4 06 00 09 17 90 71 d3 08 19 99 24 98 42 98 24 a1 | ..1........'..'......q....$.B.$. |
| cf40 | 04 a0 22 a0 04 98 2a d1 08 25 80 41 dc 08 0a 8f 0a 89 0a 90 31 8b 0d 80 41 d8 04 05 87 46 81 46 | .."...*..%.A........1...A....F.F |
| cf60 | 84 48 d8 0b 0c 80 48 72 31 00 00 00 63 02 00 00 00 00 00 00 00 00 00 00 00 0a 00 00 00 03 00 00 | .H....Hr1...c................... |
| cf80 | 00 f3 16 02 00 00 97 00 7c 01 64 01 6b 28 00 00 72 5a 74 01 00 00 00 00 00 00 00 00 6a 02 00 00 | ........|.d.k(..rZt.........j... |
| cfa0 | 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 7c 00 6a 04 00 00 00 00 00 00 00 00 00 00 00 00 | ................|.j............. |
| cfc0 | 00 00 00 00 00 00 64 02 74 01 00 00 00 00 00 00 00 00 6a 06 00 00 00 00 00 00 00 00 00 00 00 00 | ......d.t.........j............. |
| cfe0 | 00 00 00 00 00 00 74 01 00 00 00 00 00 00 00 00 6a 06 00 00 00 00 00 00 00 00 00 00 00 00 00 00 | ......t.........j............... |
| d000 | 00 00 00 00 64 03 74 00 00 00 00 00 00 00 00 00 6a 08 00 00 00 00 00 00 00 00 00 00 00 00 00 00 | ....d.t.........j............... |
| d020 | 00 00 00 00 7a 05 00 00 ab 01 00 00 00 00 00 00 ab 01 00 00 00 00 00 00 7a 0b 00 00 ab 02 00 00 | ....z...................z....... |
| d040 | 00 00 00 00 53 00 64 04 7d 02 64 05 74 01 00 00 00 00 00 00 00 00 6a 06 00 00 00 00 00 00 00 00 | ....S.d.}.d.t.........j......... |
| d060 | 00 00 00 00 00 00 00 00 00 00 74 01 00 00 00 00 00 00 00 00 6a 06 00 00 00 00 00 00 00 00 00 00 | ..........t.........j........... |
| d080 | 00 00 00 00 00 00 00 00 64 03 74 00 00 00 00 00 00 00 00 00 6a 08 00 00 00 00 00 00 00 00 00 00 | ........d.t.........j........... |
| d0a0 | 00 00 00 00 00 00 00 00 7a 05 00 00 ab 01 00 00 00 00 00 00 ab 01 00 00 00 00 00 00 7a 0b 00 00 | ........z...................z... |
| d0c0 | 7d 03 74 0b 00 00 00 00 00 00 00 00 7c 01 ab 01 00 00 00 00 00 00 7d 04 74 0d 00 00 00 00 00 00 | }.t.........|.........}.t....... |
| d0e0 | 00 00 7c 01 64 02 7a 0a 00 00 ab 01 00 00 00 00 00 00 44 00 5d 49 00 00 7d 05 7c 02 7d 06 7c 03 | ..|.d.z...........D.]I..}.|.}.|. |
| d100 | 0b 00 74 01 00 00 00 00 00 00 00 00 6a 06 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 | ..t.........j................... |
| d120 | 7c 04 64 05 7a 0a 00 00 7c 04 7a 0b 00 00 ab 01 00 00 00 00 00 00 7a 05 00 00 7d 02 7c 06 7c 03 | |.d.z...|.z...........z...}.|.|. |
| d140 | 7c 00 7a 05 00 00 74 01 00 00 00 00 00 00 00 00 6a 06 00 00 00 00 00 00 00 00 00 00 00 00 00 00 | |.z...t.........j............... |
| d160 | 00 00 00 00 64 05 7c 04 7a 0b 00 00 ab 01 00 00 00 00 00 00 7a 05 00 00 7a 00 00 00 7d 03 7c 04 | ....d.|.z...........z...z...}.|. |
| d180 | 64 05 7a 0a 00 00 7d 04 8c 4b 04 00 7c 02 7c 03 7c 00 7a 05 00 00 7a 00 00 00 53 00 29 06 61 85 | d.z...}..K..|.|.|.z...z...S.).a. |
| d1a0 | 02 00 00 0a 20 20 20 20 45 76 61 6c 75 61 74 65 20 61 20 6e 6f 72 6d 61 6c 69 7a 65 64 20 48 65 | ........Evaluate.a.normalized.He |
| d1c0 | 72 6d 69 74 65 45 20 70 6f 6c 79 6e 6f 6d 69 61 6c 2e 0a 0a 20 20 20 20 43 6f 6d 70 75 74 65 20 | rmiteE.polynomial.......Compute. |
| d1e0 | 74 68 65 20 76 61 6c 75 65 20 6f 66 20 74 68 65 20 6e 6f 72 6d 61 6c 69 7a 65 64 20 48 65 72 6d | the.value.of.the.normalized.Herm |
| d200 | 69 74 65 45 20 70 6f 6c 79 6e 6f 6d 69 61 6c 20 6f 66 20 64 65 67 72 65 65 20 60 60 6e 60 60 0a | iteE.polynomial.of.degree.``n``. |
| d220 | 20 20 20 20 61 74 20 74 68 65 20 70 6f 69 6e 74 73 20 60 60 78 60 60 2e 0a 0a 0a 20 20 20 20 50 | ....at.the.points.``x``........P |
| d240 | 61 72 61 6d 65 74 65 72 73 0a 20 20 20 20 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 78 20 3a | arameters.....----------.....x.: |
| d260 | 20 6e 64 61 72 72 61 79 20 6f 66 20 64 6f 75 62 6c 65 2e 0a 20 20 20 20 20 20 20 20 50 6f 69 6e | .ndarray.of.double..........Poin |
| d280 | 74 73 20 61 74 20 77 68 69 63 68 20 74 6f 20 65 76 61 6c 75 61 74 65 20 74 68 65 20 66 75 6e 63 | ts.at.which.to.evaluate.the.func |
| d2a0 | 74 69 6f 6e 0a 20 20 20 20 6e 20 3a 20 69 6e 74 0a 20 20 20 20 20 20 20 20 44 65 67 72 65 65 20 | tion.....n.:.int.........Degree. |
| d2c0 | 6f 66 20 74 68 65 20 6e 6f 72 6d 61 6c 69 7a 65 64 20 48 65 72 6d 69 74 65 45 20 66 75 6e 63 74 | of.the.normalized.HermiteE.funct |
| d2e0 | 69 6f 6e 20 74 6f 20 62 65 20 65 76 61 6c 75 61 74 65 64 2e 0a 0a 20 20 20 20 52 65 74 75 72 6e | ion.to.be.evaluated.......Return |
| d300 | 73 0a 20 20 20 20 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 76 61 6c 75 65 73 20 3a 20 6e 64 61 72 72 | s.....-------.....values.:.ndarr |
| d320 | 61 79 0a 20 20 20 20 20 20 20 20 54 68 65 20 73 68 61 70 65 20 6f 66 20 74 68 65 20 72 65 74 75 | ay.........The.shape.of.the.retu |
| d340 | 72 6e 20 76 61 6c 75 65 20 69 73 20 64 65 73 63 72 69 62 65 64 20 61 62 6f 76 65 2e 0a 0a 20 20 | rn.value.is.described.above..... |
| d360 | 20 20 4e 6f 74 65 73 0a 20 20 20 20 2d 2d 2d 2d 2d 0a 20 20 20 20 54 68 69 73 20 66 75 6e 63 74 | ..Notes.....-----.....This.funct |
| d380 | 69 6f 6e 20 69 73 20 6e 65 65 64 65 64 20 66 6f 72 20 66 69 6e 64 69 6e 67 20 74 68 65 20 47 61 | ion.is.needed.for.finding.the.Ga |
| d3a0 | 75 73 73 20 70 6f 69 6e 74 73 20 61 6e 64 20 69 6e 74 65 67 72 61 74 69 6f 6e 0a 20 20 20 20 77 | uss.points.and.integration.....w |
| d3c0 | 65 69 67 68 74 73 20 66 6f 72 20 68 69 67 68 20 64 65 67 72 65 65 73 2e 20 54 68 65 20 76 61 6c | eights.for.high.degrees..The.val |
| d3e0 | 75 65 73 20 6f 66 20 74 68 65 20 73 74 61 6e 64 61 72 64 20 48 65 72 6d 69 74 65 45 20 66 75 6e | ues.of.the.standard.HermiteE.fun |
| d400 | 63 74 69 6f 6e 73 0a 20 20 20 20 6f 76 65 72 66 6c 6f 77 20 77 68 65 6e 20 6e 20 3e 3d 20 32 30 | ctions.....overflow.when.n.>=.20 |
| d420 | 37 2e 0a 0a 20 20 20 20 72 02 00 00 00 72 04 00 00 00 72 36 00 00 00 72 8c 00 00 00 72 3e 00 00 | 7.......r....r....r6...r....r>.. |
| d440 | 00 29 07 72 40 00 00 00 72 98 00 00 00 72 6a 00 00 00 72 9d 00 00 00 da 02 70 69 da 05 66 6c 6f | .).r@...r....rj...r......pi..flo |
| d460 | 61 74 72 2b 00 00 00 29 07 72 7d 00 00 00 72 3a 00 00 00 72 3b 00 00 00 72 3c 00 00 00 72 56 00 | atr+...).r}...r:...r;...r<...rV. |
| d480 | 00 00 72 2f 00 00 00 72 3d 00 00 00 73 07 00 00 00 20 20 20 20 20 20 20 72 30 00 00 00 da 13 5f | ..r/...r=...s...........r0....._ |
| d4a0 | 6e 6f 72 6d 65 64 5f 68 65 72 6d 69 74 65 5f 65 5f 6e 72 ac 00 00 00 bd 05 00 00 73 e3 00 00 00 | normed_hermite_e_nr........s.... |
| d4c0 | 80 00 f0 36 00 08 09 88 41 82 76 dc 0f 11 8f 77 89 77 90 71 97 77 91 77 a0 01 a4 42 a7 47 a1 47 | ...6....A.v....w.w.q.w.w...B.G.G |
| d4e0 | ac 42 af 47 a9 47 b0 41 bc 02 bf 05 b9 05 b1 49 d3 2c 3e d3 24 3f d1 20 3f d3 0f 40 d0 08 40 e0 | .B.G.G.A.......I.,>.$?..?..@..@. |
| d500 | 09 0b 80 42 d8 09 0b 8c 62 8f 67 89 67 94 62 97 67 91 67 98 61 a4 22 a7 25 a1 25 99 69 d3 16 28 | ...B....b.g.g.b.g.g.a.".%.%.i..( |
| d520 | d3 0e 29 d1 09 29 80 42 dc 09 0e 88 71 8b 18 80 42 dc 0d 12 90 31 90 71 91 35 8b 5c f2 00 04 05 | ..)..).B....q...B....1.q.5.\.... |
| d540 | 16 88 01 d8 0e 10 88 03 d8 0e 10 88 53 94 32 97 37 91 37 98 42 a0 12 99 47 a0 72 99 3e d3 13 2a | ............S.2.7.7.B...G.r.>..* |
| d560 | d1 0d 2a 88 02 d8 0d 10 90 32 98 01 91 36 9c 42 9f 47 99 47 a0 42 a8 12 a1 47 d3 1c 2c d1 13 2c | ..*......2...6.B.G.G.B...G..,.., |
| d580 | d1 0d 2c 88 02 d8 0d 0f 90 23 89 58 89 02 f0 09 04 05 16 f0 0a 00 0c 0e 90 02 90 51 91 06 89 3b | ..,......#.X...............Q...; |
| d5a0 | d0 04 16 72 31 00 00 00 63 01 00 00 00 00 00 00 00 00 00 00 00 05 00 00 00 03 00 00 00 f3 68 02 | ...r1...c.....................h. |
| d5c0 | 00 00 97 00 74 01 00 00 00 00 00 00 00 00 6a 02 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 | ....t.........j................. |
| d5e0 | 00 00 7c 00 64 01 ab 02 00 00 00 00 00 00 7d 01 7c 01 64 02 6b 1a 00 00 72 0b 74 05 00 00 00 00 | ..|.d.........}.|.d.k...r.t..... |
| d600 | 00 00 00 00 64 03 ab 01 00 00 00 00 00 00 82 01 74 07 00 00 00 00 00 00 00 00 6a 08 00 00 00 00 | ....d...........t.........j..... |
| d620 | 00 00 00 00 00 00 00 00 00 00 00 00 00 00 64 02 67 01 7c 00 7a 05 00 00 64 04 67 01 7a 00 00 00 | ..............d.g.|.z...d.g.z... |
| d640 | ab 01 00 00 00 00 00 00 7d 02 74 0b 00 00 00 00 00 00 00 00 7c 02 ab 01 00 00 00 00 00 00 7d 03 | ........}.t.........|.........}. |
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| d840 | 69 74 65 45 20 71 75 61 64 72 61 74 75 72 65 2e 0a 0a 20 20 20 20 43 6f 6d 70 75 74 65 73 20 74 | iteE.quadrature.......Computes.t |
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| d880 | 20 47 61 75 73 73 2d 48 65 72 6d 69 74 65 45 20 71 75 61 64 72 61 74 75 72 65 2e 0a 20 20 20 20 | .Gauss-HermiteE.quadrature...... |
| d8a0 | 54 68 65 73 65 20 73 61 6d 70 6c 65 20 70 6f 69 6e 74 73 20 61 6e 64 20 77 65 69 67 68 74 73 20 | These.sample.points.and.weights. |
| d8c0 | 77 69 6c 6c 20 63 6f 72 72 65 63 74 6c 79 20 69 6e 74 65 67 72 61 74 65 20 70 6f 6c 79 6e 6f 6d | will.correctly.integrate.polynom |
| d8e0 | 69 61 6c 73 20 6f 66 0a 20 20 20 20 64 65 67 72 65 65 20 3a 6d 61 74 68 3a 60 32 2a 64 65 67 20 | ials.of.....degree.:math:`2*deg. |
| d900 | 2d 20 31 60 20 6f 72 20 6c 65 73 73 20 6f 76 65 72 20 74 68 65 20 69 6e 74 65 72 76 61 6c 20 3a | -.1`.or.less.over.the.interval.: |
| d920 | 6d 61 74 68 3a 60 5b 2d 5c 69 6e 66 2c 20 5c 69 6e 66 5d 60 0a 20 20 20 20 77 69 74 68 20 74 68 | math:`[-\inf,.\inf]`.....with.th |
| d940 | 65 20 77 65 69 67 68 74 20 66 75 6e 63 74 69 6f 6e 20 3a 6d 61 74 68 3a 60 66 28 78 29 20 3d 20 | e.weight.function.:math:`f(x).=. |
| d960 | 5c 65 78 70 28 2d 78 5e 32 2f 32 29 60 2e 0a 0a 20 20 20 20 50 61 72 61 6d 65 74 65 72 73 0a 20 | \exp(-x^2/2)`.......Parameters.. |
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| da40 | 72 72 61 79 0a 20 20 20 20 20 20 20 20 31 2d 44 20 6e 64 61 72 72 61 79 20 63 6f 6e 74 61 69 6e | rray.........1-D.ndarray.contain |
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| de60 | ab 01 00 00 00 00 00 00 7d 01 7c 01 53 00 29 03 61 c3 01 00 00 57 65 69 67 68 74 20 66 75 6e 63 | ........}.|.S.).a....Weight.func |
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| dec0 | 6d 61 74 68 3a 60 5c 65 78 70 28 2d 78 5e 32 2f 32 29 60 20 61 6e 64 20 74 68 65 20 69 6e 74 65 | math:`\exp(-x^2/2)`.and.the.inte |
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 |
index : uiuc-course-graph.git | |
| Unnamed repository; edit this file 'description' to name the repository. | Ubuntu |
| summaryrefslogtreecommitdiff |
path: root/.venv/lib/python3.12/site-packages/numpy/polynomial/__pycache__/hermite_e.cpython-312.pyc
blob: dbd433b1683b4fdff51ff2d70f3998c380cf525c (plain)