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+--- Thread: 41 MCODE - Hermite and Lagrange Polynomials (/thread-2712.html)
41 MCODE - Hermite and Lagrange Polynomials - Ángel Martin - 12-25-2014 06:00 PM
As usual when you thought a project was done new ideas pop up that just can't be ignored... like this sweet & short MCODE implementation for the Hermite and Lagrange orthogonal polynomials using the recurrence approach - as an afterthought to be included in the SandMatrix module.
Code:
0D4 "T" Hermite Polynomials
04D "M" n,x in {Y,X}
048 "H" Ángel Martin
284 CLRF 7
02B JNC +05
0C7 "G" Legendre Polynomials
045 "E" n,x in {Y,X}
04C "L" Ángel Martin
288 SETF 7
1A5 ?NC XQ Check for valid entries
100 ->4069 [CHKST2] - sets DEC mode
04E C=0 ALL
35C PT=12 C= 1
050 LD@PT- 1
168 WRIT 5(M)
0F8 READ 3(X) x
10E A=C ALL
28C ?FSET 7 Legendre?
01D ?NC XQ no, ergo Hermite
060 ->1807 [AD2_10]
1A8 WRIT 6(N) 2x or x
0B8 READ 2(Y) n
088 SETF 5 do integer portion
0ED ?NC XQ leaves result in 13-digit form
064 ->193B [INTFRC] - doesn't need DEC
070 N=C ALL update counter
2FA ?C#0 M n = 0?
18B JNC +49d yes, result in (5)M
009 ?NC XQ {A,B} = {A,B}-1
060 ->1802 [SUBONE]
2FA ?C#0 M was n=1 ?
19B JNC +51d yes, result in (6)N
28C ?FSET 7 Legendre?
025 ?NC XQ No, 2 (n-1)
060 ->1809 [AD1-10 ]
178 READ 5(M) H(n-2)
13D ?NC XQ
060 ->184F [MP1_10]
2BE C=-C-1 MS sign change
11E A=C MS ditto in 13-digit form
089 ?NC XQ
064 ->1922 [STSCR]
28C ?FSET 7 Legendre?
05B JNC +11d
0B0 C=N ALL n
10E A=C ALL
01D ?NC XQ 2n
060 ->1807 [AD2_10]
009 ?NC XQ 2n-1
060 ->1802 [SUBONE]
0F8 READ 3(X) x
13D ?NC XQ (2n-1)*x
060 ->184F [MP1_10]
02B JNC +05
0F8 READ 3(X) x
10E A=C ALL
01D ?NC XQ 2x
060 ->1807 [AD2_10]
1B8 READ 6(N) H(n-1) or: P(n-1)
168 WRIT 5(M) the new H(n-2) / P(n-2)
13D ?NC XQ 2x* H(n-1) or: (2n-1)*x*P(n-1)
060 ->184F [MP1_10]
0D1 ?NC XQ recall first term
064 ->1934 [RCSCR]
031 ?NC XQ add to complete it
060 ->180C [AD2-13]
28C ?FSET 7 Legendre?
023 JNC +04 no, skip
0B0 C=N ALL n
269 ?NC XQ
060 ->189A [DV1-10]
1A8 WRIT 6(N) the new H(n-1)
0B0 C=N ALL
1FD ?NC XQ {A,B} = C-1
100 ->407F [DECC10] - sets DEC
273 JNC - 50d
178 READ 5(M)
070 N=C ALL parameter passing
260 SETHEX
3AD PORT DEP: Abandon ship
08C GO in orderly fashion
13E ->AD3E [NFRX2]
1B8 READ 6(N)
3D3 JNC -06Only valid for integer orders. More complex formulas exist for non-integer cases, see JM Baillard's pages for details:
http://hp41programs.yolasite.com/orthopoly.php
Note that the listing above is for a sub-function sitting in a bank-switched page.
Comments and suggestions for improvement are welcome.
Enjoy, as usual ;-)