Utilities

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Utilities

X x findplaces P 1 - : k 0 : 12 mat n 1 X length range X n el x ≡ P k k 1 + : el n : continue if for P 31 line :

X R removerows V 0 X cols matrix : r 1 X rows range R r findplaces 1 - ≡ V V X r row stack : continue if for V 31 line :

SVD Decomposition using dn library A tol MSVD S U V' 13 mat A dn_LinAlgSVD transpose : U - S V' - transpose 13 mat eval 21 line :

Null space A tol null U S V 13 mat A tol MSVD : r S tol > vectorize sum eval : V 1 V rows range r 1 + (V cols range el 31 line :

A null A TOL null 11 line :

rat

X# product P# 1 : x# X# P# x# P# * : for P# 31 line :

gcd of two numbers a b gcd x a abs : y b abs : 12 mat x 0 ≠ (y 0 ≠ (& x y > x x y mod : y y x mod : if while x y + 31 line :

gcd of an array. A gcd g A 1 el : k 2 A length range g g A k el gcd : for g 31 line :

lcm of two numbers a b lcm a b * a b gcd / 11 line :

lcm of an array A lcm l A 1 el : k 2 A length range l l A k el lcm : for l 31 line :

rat returns two integer matrices so that vectorize(N/D) is close to X in the sense that abs(N./D - X) <= tol*abs(X).
The rational approximations are generated by truncating continued fraction expansions. X tol rat N X X - : D N : T tol X normi * : 13 mat j 1 X length range x X j el : k 0 : C 2 identity : 13 mat Iters 110000 range k k 1 + : d x trunc : x x d - : C C d 121 mat * C 1 col augment eval : C 11 el C 21 el / X j el - abs T < (x 0 ≡ (| break x 1 x / : if 51 line for N j el C 21 el sign C 11 el * : D j el C 21 el abs : 12 mat 31 line for N D 12 mat eval 31 line :

X rat X TOL rat 11 line :

Try to find integers values from a vector of rationals. A tol ratint X A abs vectorize : m X min eval : (tol > 0 m X max eval : k 1 X length range m X k el > (X k el tol > (& m X k el : continue if for 21 line if N D 12 mat A m / rat : D lcm N D / vectorize * eval 41 line :

A ratint A TOL ratint 11 line :

Chem Bal

Molecular mass from a compound. R ChemMass R IsString X R ChemAtoms : M 0 : 12 mat k 1 X rows range M M X k 2 el MolW X k 1 el 1 findrows 2 el * + : for M g mol / * 31 line A R : k 1 A length range A k el A k el ChemMass : for A 31 line if 11 line :

MolW H 1.0079 He 4.0026 Li 6.941 Be 9.0122 B 10.81 C 12.011 N 14.0067 O 15.9994 F 18.9984 Ne 20.179 Na 22.9898 Mg 24.305 Al 26.9815 Si 28.086 P 30.9738 S 32.06 Cl 35.453 Ar 39.948 K 39.098 Ca 40.08 Sc 44.9559 Ti 47.9 V 50.9414 Cr 51.996 Mn 54.938 Fe 55.847 Co 58.9332 Ni 58.7 Cu 63.546 Zn 65.38 Ga 69.72 Ge 72.59 As 74.9216 Se 78.96 Br 79.904 Kr 83.8 Rb 85.4678 Sr 87.62 Yt 88.9059 Zr 91.22 Nb 92.9064 Mo 95.94 Tc 98.9062 Ru 101.07 Rh 102.9055 Pd 106.4 Ag 107.868 Cd 112.4 In 114.82 Sn 118.69 Sb 121.75 Te 127.6 I 126.9045 Xe 131.3 Cs 132.9054 Ba 137.34 La 138.9055 Ce 140.12 Pr 140.9077 Nd 144.24 Pm 147 Sm 150.4 Eu 151.96 Gd 157.25 Tb 158.9254 Dy 162.5 Ho 164.9304 Er 167.26 Tm 168.9342 Yt 173.04 Lu 174.97 Hf 178.49 Ta 180.9479 W 183.85 Re 186.207 Os 190.2 Ir 192.22 Pt 195.09 Au 196.9665 Hg 200.59 Tl 204.37 Pb 207.2 Bi 208.9804 Po 210 At 210 Rn 222 Fr 223 Ra 226.0254 Ac 227 Th 232.0381 Pa 231.0359 U 238.029 Np 237.0482 Pu 244 Am 243 Cm 247 Bk 247 Cf 251 Es 254 Fm 257 Md 258 No 259 Lr 262 Rf 261 Db 262 Sg 266 Bh 264 Hs 277 Mt 268 Q 01102 mat :

UChars ABCDEFGHIJKLMNOPQRSTUVWXYZ :

LChars abcdefghijklmnopqrstuvwxyz :

NChars .1234567890 :

Compostion from a chemical formula Σ ChemAtoms Σ IsString k 1 : r 0 : M 0 : S Σ strrep concat : 14 mat S S + Q strrep - Qn strrep : str (aq) (s) (l) (g) 14 mat S S str strrep : for a b s S a b substr : S (findstr 1 - ≡ k S strlen < UChars k 1 s findstr 1 - ≡ j 1 : NChars k j + 1 s findstr 1 - ≠ j j 1 + : while Digits M r 2 el k j s str2num : k k j + : 13 mat 31 line LChars k 1 + 1 s findstr 1 - ≡ UChar M r r 1 + : 1 el k 1 s : M r 2 el 1 : k k 1 + : 14 mat LChar M r r 1 + : 1 el k 2 s : M r 2 el 1 : k k 2 + : 14 mat if if while r 1 M rows range M r 1 el Qn ≡ Neg charges M r 1 el Q : M r 2 el M r 2 el - : 13 mat continue if for 21 line α S (findstr 1 el : β S) findstr 1 el : 12 mat j 0 : NChars β j + 1 + 1 s findstr 1 - ≠ j j 1 + : while M α 1 + β α - 1 - s ChemAtoms : j 0 ≡ 0 M M 1 col β 1 + j s str2num M 2 col * augment : if str β j + 1 + S strlen β - j - s : M M 1 α 1 - s str concat ChemAtoms stack eval : 71 line if r 0 : r M rows < Combine duplicates r r 1 + : 12 mat P M 1 col M r 1 el findplaces : (r 11 mat ≠ M r 2 el M P 2 el sum : M M P 2 P length range el removerows : 21 line continue if 21 line while 71 line M Σ augment : k 1 Σ length range A Σ k el ChemAtoms : r 1 A rows range R 1 M rows 1 + (range R M rows > (M R 1 el A r 1 el ≡ (| break continue if for M R 1 el A r 1 el : M R k 1 + el A r 2 el : 31 line for 21 line for 21 line if M 21 line :

Balance a chemical equation R ra ChemBal R rows 1 ≡ A R ChemAtoms : A R : if B A 2 A rows 2 A cols submatrix : C B null : 12 mat ra 0 ≡ C C ratint : C C ra * 0 round vectorize eval : if S C cols 1 matrix C transpose augment : r c N C r c el abs 1 ≡ C r c el abs num2str concat if : c 1 C cols range check 0 : b 12 mat : 12 mat χ 2 A cols range r 2 A rows range A r χ el A r χ el S χ el * : for check check A 2 A rows range χ el sum (+ eval : 21 line for b k str b k el 1 b k el strlen 3 - substr : r 1 C rows range ChemSign C r c el * 0 < b 1 el b 1 el r c N A 1 r 1 + el + concat : b 2 el b 2 el r c N A 1 r 1 + el + concat : if for S c 1 el b 1 str -> b 2 str concat strrep : check 0 ≡ 0 S c 1 el ERROR: S c 1 el concat : if 61 line for S 71 line :

Last is for charges Q

R ChemBal R 0 ChemBal 11 line :

ChemSign 1 :

TOL 1012 -^:

Examples

Balancing equations using null space

R KAu(CN)4 KAu(CN)2Cl2 KHCl2 Fe4(CN)12Fe3(CN)6 PtCl3(H2O)7 15 mat :

Example

R R Pt2(NH3)4(C5H4ON)2(NO3)2(H2O)2 K3.99Fe(CN)6 HAuCl3 NO2 14 mat augment :

Function call

A R ChemAtoms :

B R ChemBal :

A KAu(CN)4 KAu(CN)2Cl2 KHCl2 Fe4(CN)12Fe3(CN)6 PtCl3(H2O)7 Pt2(NH3)4(C5H4ON)2(NO3)2(H2O)2 K3.99Fe(CN)6 HAuCl3 NO2 C 42018010600 N 4201808601 K 111000 3.99 00 Au 110000010 Cl 022030030 H 00101424010 Fe 000700100 O 0000710002 Pt 0000120001010 mat

B 1 el -> strsplit 2793 KAu(CN)4 + 5179 KAu(CN)2Cl2 + 3200 KHCl2 + 400 Fe4(CN)12Fe3(CN)6 + 2386 PtCl3(H2O)7 1193 Pt2(NH3)4(C5H4ON)2(NO3)2(H2O)2 + 2800 K3.99Fe(CN)6 + 7972 HAuCl3 + 2386 NO2 21 mat

By "hand", main math involved:

B A 210 range 210 range el null :

N D 12 mat B B abs vectorize min / rat :

C D lcm N D / vectorize * :

Results

B 0.2457 - 0.4556 - 0.2815 - 0.0352 - 0.2099 - 0.1049 0.2463 0.7013 0.2099 91 mat

C 2793 - 5179 - 3200 - 400 - 2386 - 119328007972238691 mat

R transpose KAu(CN)4 KAu(CN)2Cl2 KHCl2 Fe4(CN)12Fe3(CN)6 PtCl3(H2O)7 Pt2(NH3)4(C5H4ON)2(NO3)2(H2O)2 K3.99Fe(CN)6 HAuCl3 NO2 91 mat

R Yb4(CN)12Yb3(CN)6 CsRu(CN)2F2 CsRu(CN)4 CsHF2 PtF3(H2O)7 15 mat :

Example

R R Pt2(NH3)4(C5H4ON)2(NO3)2(H2O)2 Cs3.99Yb(CN)6 HRuF2.97 NO2 14 mat augment :

Function call

A R ChemAtoms :

B R ChemBal :

A Yb4(CN)12Yb3(CN)6 CsRu(CN)2F2 CsRu(CN)4 CsHF2 PtF3(H2O)7 Pt2(NH3)4(C5H4ON)2(NO3)2(H2O)2 Cs3.99Yb(CN)6 HRuF2.97 NO2 C 18240010600 N 1824008601 Yb 700000100 Cs 011100 3.99 00 Ru 011000010 F 0202300 2.97 0 H 00011424010 O 0000710002 Pt 0000120001010 mat

B 1 el -> strsplit 39600 Yb4(CN)12Yb3(CN)6 + 508735 CsRu(CN)2F2 + 288465 CsRu(CN)4 + 308828 CsHF2 + 244186 PtF3(H2O)7 122093 Pt2(NH3)4(C5H4ON)2(NO3)2(H2O)2 + 277200 Cs3.99Yb(CN)6 + 797200 HRuF2.97 + 244186 NO2 21 mat

By "hand", main math involved:

B A 210 range 210 range el null :

N D 12 mat B B abs vectorize min / rat :

C D lcm N D / vectorize * :

Results

B 0.0349 - 0.4487 - 0.2544 - 0.2724 - 0.2154 - 0.1077 0.2445 0.7031 0.2154 91 mat

C 39600 - 508735 - 288465 - 308828 - 244186 - 12209327720079720024418691 mat

R transpose Yb4(CN)12Yb3(CN)6 CsRu(CN)2F2 CsRu(CN)4 CsHF2 PtF3(H2O)7 Pt2(NH3)4(C5H4ON)2(NO3)2(H2O)2 Cs3.99Yb(CN)6 HRuF2.97 NO2 91 mat

Alvaro