﻿ doubly stochastic matrix calculator doubly stochastic matrix calculator Update 2017-07-27
document for function doublStochMat() and jkCheck2() and robinMatrixf()
decimal to fraction calculator decimalFraction ; Unicode
doubly stochastic matrix program code follow next textbook.
The Cauchy-Schwarz Master Class   J. Michael Steele   ★★★★★ ;
This file is personal home work. No one proofread. Cannot promise correctness.
If you suspect any view point wrong, please ask a math expert near by.
Freeman 2009-06-19-10-46
Example ;
α more average and β more diverse both descending order
 α seq. α more average α=dsm*β OK 0.688... β seq. β more diverse β=dsm*α NO decimal
RUN 11 ☞ , output 0.9333333333333332
Box11 output doubly stochastic Matrix ; , ,

Box12 doubly stochastic Matrix HTML table ;

α sequence notEqual β sequence, doubly stochastic matrix let α and β equal. α=DSM*β
Box13 ; verify ; ≺ ≻ ≼ ≽ ≾ ≿ ⊀ ⊁ more

Box14

Box15 debug ; debug off, fast output to box11

QBboxc15.value='' ;
document for function doublStochMat() and jkCheck2() and robinMatrixf()

<a name=decimalFraction>
decimal to fraction Box16 input, Box17 output
Another file is better, it has Real number calculator http://freeman2.com/dec2frac.htm
if set answer if find then PI=3.141592653589793 output 22/7
Box16 input ; Box16 input, Box17 output

, , RUN 22 ☞ ☜ decimal only; [ minusEqual ]
Box17 output ; RUN 23 ► ◄ text OK
 control Run loop up to max. iteration. max0 default 1000000 panel answer if find accuracy zero6 default .000000
Irrational input need control panel . Rational decimal no need.
QBboxc17.value='' ; stochMat[ ] ; QBspanDrawMat.innerHTML='' ; QBspanAlert1.innerHTML=''
function decimal2fraction(arg1,arg2,arg3) ; function text0to9fraction(in0,arg2)
function doublStochMat( ) ; function d2f()

<a name=UnicodeSymbol>
UnicodeSymbol : ℂ ℍ ℕ ℙ ℚ ℝ ℤ ℽ ℾ ℿ ⅀ ⅅ ⅆ ⅇ ⅈ ⅉ ; × ÷ ° ◦ º ¹ ² ³
≦ ≠ ≧ ＜ ＝ ＞ ± ≡ ≈ ≌ ≒ ∏ ∑ √ ∛ ∜ ∝ → ∞ ∈ ∀ ∂ ⊥ ∃ ∋ ∆ ∇ ⊿ ∟ ∠ ∫ ∬ ∭ ∮ ∥
≺ ≻ ≼ ≽ ≾ ≿ ⊀ ⊁ ≭ ≮ ≯ ≰ ≱ ≲ ≳ ≴ ≵ ≶ ≷ ≸ ≹ ∧ ∨ ∩ ∪ ∴ ∵ ∶ ∷ ⊂ ⊃ ⊄ ⊅ ⊆ ⊇
Α Β Γ Δ Ε Ζ Η Θ Ι Κ Λ Μ Ν Ξ Ο Π Ρ ΢ Σ Τ Υ Φ Χ Ψ Ω , ＋ － ＊ ／
α β γ δ ε ζ η θ ι κ λ μ ν ξ ο π ρ ς σ τ υ φ χ ψ ω
2017-06-20-20-44 Liu,Hsinhan access en.wikipedia.org
https://en.wikipedia.org/wiki/List_of_mathematical_symbols
en.wikipedia.org-wiki-List_of_mathematical_symbols.htm
∧,⇒,−,∖,√,≥,≤,∓,⋅,⁄,⇔,∈,ℤ,ℝ,φ,π,∑,∫, ,∮,∯,∰,…,⋯,⋮,⋰,⋱,∴,∵,≠
˜ ,∝,∞,■,□,∎,▮,‣,≈,≃,≅,♎,≒,△,≡,≜,≝,≐,↔,≪,≫,≦,≧,≺,≻,◅,▻,→,⊃,⊆
⊂,∩,ℕ,ℚ,⊇,∪,↦,•,⊧,∨,⊢,⟨,⟩,ψ,α,β,–,‖,⌊,⌉,⌋,⌈,ℂ,∗,∣,∤,∥,∦,⋕,⊥
∃,≀,↯,※,⇐,⊕,⊻,∐,′,∀,∂,∉,∌,∋,ℍ,ω,○,∘,∅,ℙ,†,⊤,—,⊗,⋉,⋊,⋈,​,ℵ,ℶ
δ,∆,⊖,Δ,ƒ,∇,∏,σ,

<a name=diversAverag>
Example total treasure=30, member=5, treasure distribution is next
[30,0,0,0,0] ≻ [15,15,0,0,0] ≻ [10,10,10,0,0] ≻ [7.5,7.5,7.5,7.5,0] ≻ [6,6,6,6,6]
most diverse is [30,0,0,0,0] ; most average is [6,6,6,6,6] ; 30+0+0+0+0=6+6+6+6+6

<a name=pictureChar>
Picture characters 册=book (phone book below public telephone) ; 目=eye ; 口=mouth ;

middle 田 a place carry cargo. Bird view this car look like 車) ; 艸=grass,weed. a606211119

<a name="textbook"> (local)
Program http://freeman2.com/jsmajor2.htm
Program http://freeman2.com/dbstochm.htm
use book written by Professor J. Michael Steele
The Cauchy-Schwarz Master Class 　★★★★★
as textbook. Program code is written base on
textbook page 198 to page 201.
Liu,Hsinhan study notes tute0047.htm
http://freeman2.com/tute0047.htm
doubly stochastic matrix program document tute0069.htm
http://freeman2.com/tute0069.htm

<a name="strangePage">
This is a strange page. This page work on off line computer.
page as a strange page try if you can find out why?.
If many other freeman2.com calculator page not work
on your computer. Do not be surprised. They all work fine
before Liu,Hsinhan upload to freeman2.com .
2017-06-13-18-29

<a name="sortnumb">
Sort number not text string

Box71 accept only numbers, not name list, not non-number string.
 Box 71, input number sequence 0.556 -0.145 0.302e3 -0.305e2 -0.088 Box 72, output answer Click [Output New Index] to get permutation matrix Click [Sorted Seq. 321] to get sorted data number
This file sort numbers, not for sort text; upsidedown text ok.
2009-07-15-11-18 start sortNumb()
2009-07-15-18-40 done sortNumb()
2009-09-29-20-50 done upsidedown()
```
<a name="docA001">
2017-06-13-18-36 start
2017-06-09 Liu, HsinHan paid attention to
http://freeman2.com/jsmajor2.htm
jsmajor2.htm work on LiuHH's off line
computer, but not work on online computer.
LiuHH decide re-write jsmajor2.htm and
rename file as
http://freeman2.com/dbstochm.htm

<a name="docA002">
function doublStochMat() work on offline
Acer1 computer. Verify doubly stochastic
matrix get expected result. Matrix all
column sum to one, all row sum to one.
α_vector=doublStochMatrix*β_vector OK. Since
dbstochm.htm is different from jsmajor2.htm
2017-06-13-16-26 LiuHH take dbstochm.htm
to online Acer2 computer test run. But
get all kind errors.
offline Acer1 computer work correctly
online Acer2 computer get all kind errors.
<a name="docA003">
WHY? LiuHH do not expect to debug in short
time. Is it trouble only in Acer2 computer ?
Is it trouble only in offline Acer1 computer ?
Is it trouble in whole world user's computer ?
LiuHH do not know !!
Upload dbstochm.htm as a strange file,
NOT as a doubly stochastic matrix calculator
Hope someone find out why.
If many other freeman2.com calculator page
not work on reader's computer. Do not be
surprised. They all work fine before LiuHH
2017-06-13-18-56

<a name="docA004"> Update 2017-06-17
2017-06-16-21-16
Update 2017-06-17 added Box15 debug checkbox.
Default no debug output, allow faster answer.
Update 2017-06-17 added Date/Time stamp below
HTML table. Look like next line.
doublStochMat() Date/Time: 2017-06-16-21-14-31.700, elapse=0.002 sec.
Update 2017-06-17 move strange page message to
[a name="strangePage"]
Update 2017-06-17 deleted useless javascript
functions. Before LiuHH upload, Update 2017-06-17
work correctly in offline Acer1 computer.
2017-06-16-21-24

<a name="docA005">
2017-06-19-19-29
Update 2017-06-20 added decimal to fraction
calculator change 0.0754716981132076 to 4/53 .
allow doubly stochastic matrix calculator
output both decimal and fraction.
2017-06-19-19-38

<a name="docA006">
2017-06-21-09-00
Update 2017-06-21
change quotient to fraction
change Quotient to Fraction
At first, Liu,Hsinhan refer to ℂ ℍ ℕ ℙ ℚ ℝ ℤ
in which ℚ=integer1/integer2 decide use quotient.
Later find out the translation
[[
106,06,20,17,54
C:\\$fm\math\mathterm\mterm007.txt

C:\\$fm\math\mathterm\mterm004.txt

]]
and find online use "decimal to fraction calculator"
2017-06-21 decide change to correct term.
2017-06-21-09-05

<a name="docA007">
2017-07-11-14-51
Update 2017-07-12 added example  button. If
α8 = [2.5, 2.4, 1.5, 1.5, 0.1]
β8 = [3.0, 2.6, 1.2, 1.0, 0.2]
both α8 and β8 have five elements,
both α8 and β8 have total sum 8. These
two condition do NOT grantee majorization
relation that is α8⊀β8 and α8⊁β8 . Because
require 3.0+2.6+1.2+1.0 ≧ 2.5+2.4+1.5+1.5
but 7.8 ≧ 7.9 is not true.
If switch α β role and define
α9 = [3.0, 2.6, 1.2, 1.0, 0.2]
β9 = [2.5, 2.4, 1.5, 1.5, 0.1]
first element fail. Because require
2.5 ≧ 3.0 , but 2.5 ≧ 3.0 is not true.

document for function doublStochMat() and
jkCheck2() and robinMatrixf()
2017-07-11-15-43

<a name="docA008">
2017-07-12-15-04
Update 2017-07-12 modified
function decimal2fraction()
2017-07-12-11-40
use α=[ 5 2.5 2.25 1.25 1]
use β=[ 6  2   2    2   0]
fraction output, 2/1029 become 3/1029,
verify doubly stochastic matrix fail

Update 2017-07-12 change from
Because
parseInt(1.9999999999999997)=1
parseInt(1.99999999999999997)=2
See
http://freeman2.com/dec2frac.htm#docF031b
for more explanation.
2017-07-12-15-12

<a name="docA009">
2017-07-15-19-15
Update 2017-07-16 has minor change, move
http://freeman2.com/dbstoch1.htm
2017-07-15-19-20

<a name="docA010">
2017-07-27-18-10
Update 2017-07-27 change function bye09() error.
error code line change to new a607211645 line.
//if(nine0<0)nine0--; // negative integer minus one
if(in09<0)nine0--; //a607211645
After correction, program change -0.99999999999
to -1 . (Error code change to +1)
2017-07-27-18-13

[=][][]```

Javascript index
http://freeman2.com/jsindex2.htm   local
Save graph code to same folder as htm files.
http://freeman2.com/jsgraph2.js   local

File name jsmajor2.htm means
JavaScript MAJORization English (2)

doubly stochastic matrix : 雙隨機(矩)陣 //a606131521

Majorization transformation between two sequences.
http://freeman2.com/jsmajor2.htm

Chinese version doubly stochastic matrix calculator

http://freeman2.com/dbstoch1.htm