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Thread: how do you solve a system of linear equations in ThinBasic?

  1. #11
    hi Bob and Dan
    Bob, Octave does much beter than thinBasic, Dan, I did change the script to make it work.
    anyway, you can also drop the first column in the matrix and just make the first coefficient = 1,
    (also decrease the size of the dimensions by one) the rest of the coefficients will differ
    slightly because of this change, but it approximates the gamma function almost as well, (it needs to be checked).

    example thinBasic script, look carefully for the changes.
    Uses "console"
    Uses "math"
    Const n = 6 
    Dim As Ext g = 5 
    Dim As Ext a(n,n), b(n,n), c(n,1) 
    Dim As Integer i, j 
    'for n = 6, the following sets up matrix a as: 
    ' [[ 1,   1/2, 1/3, 1/4,  1/5,  1/6 ] 
    ' [  1/2, 1/3, 1/4, 1/5,  1/6,  1/7 ] 
    ' [  1/3, 1/4, 1/5, 1/6,  1/7,  1/8 ] 
    ' [  1/4, 1/5, 1/6, 1/7,  1/8,  1/9 ] 
    ' [  1/5, 1/6, 1/7, 1/8,  1/9,  1/10 ] 
    ' [  1/6, 1/7, 1/8, 1/9,  1/10, 1/11 ]] 
     
    For i=1 To n
                           '<< note the change 
      For j=1 To n  '<< note the change
        a(i,j)=1/(i+j-1)  '<< note the change
      Next
    Next
    For i=1 To n 
      c(i,1) = Factorial(i-1)/((i+g-0.5)^(i-0.5)/Exp(i+g-0.5)*Sqr(2*M_PI))-1 '<< note the change
    Next
    MAT b() = INV(a()) 
    MAT a() = b() * c()
    Console_WriteLine "C( 1) = 1" 
    For i=1 To n 
      Console_WriteLine "C("&Str$(i+1)&") = "&a(i,1) 
    Next 
    Console_WriteLine "All done. Press any key to finish"
    Console_WaitKey
    
    here are the coefficients as calculated with Maple
    c[0] := 1
    c[1] := 76.180091728331374539146745
    c[2] := -86.505320289513654614503042
    c[3] := 24.014097921606006186204527
    c[4] := -1.2317386147754424755938420
    c[5] := .120745388047503859955038e-2
    c[6] := -.4868518292851569517614e-5
    Last edited by jack; 15-08-2011 at 02:34.

  2. #12
    thinBasic MVPs danbaron's Avatar
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    It seems that the new values disagree more with the values from Numerical Recipes.

    ' code -----------------------------------------------------------------------------
    
    Uses "console"
    Uses "math"
    Const n = 6
    Dim As Ext a(n), b(n), c(n)
    Dim As Integer i
    
    ' From Johan.
    
    a(1) = 76.1800917283313588
    a(2) = -86.5053202895132074
    a(3) = 24.0140979216034793
    a(4) = -1.23173861476925595
    a(5) = 1.2074538708475302 * 10^-3
    a(6) = -4.8685153615224408 * 10^-6
    
    ' From Numerical Recipes.
    
    b(1) =  76.18009172947146
    b(2) = -86.50532032941677
    b(3) =  24.01409824083091
    b(4) =  -1.231739572450155
    b(5) =   0.1208650973866179 * 10^-2
    b(6) =  -0.5395239384953 * 10^-5
    
    ' abs(difference).
    
    For i = 1 To n
    c(i) = Abs(a(i)-b(i))
    Next
    
    For i = 1 To n
    PrintL c(i)
    Next
    
    Console_WaitKey
    
    ' output ---------------------------------------------------------------------------
    
    1.14010120094709677E-9
    3.99035626000299182E-8
    3.19227430699633996E-7
    9.57680899050031287E-7
    1.19710301864880011E-6
    5.267240234305592E-7
    
    Last edited by danbaron; 15-08-2011 at 07:50.
    "You can't cheat an honest man. Never give a sucker an even break, or smarten up a chump." - W.C.Fields

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