June 2018 Update
This commit is contained in:
Ingy döt Net
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5278 changed files with 84726 additions and 14379 deletions
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@ -3,13 +3,13 @@ package main
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import (
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"fmt"
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"github.com/gonum/matrix/mat64"
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"gonum.org/v1/gonum/mat"
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)
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func cholesky(order int, elements []float64) fmt.Formatter {
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t := mat64.NewTriDense(order, false, nil)
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t.Cholesky(mat64.NewSymDense(order, elements), false)
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return mat64.Formatted(t)
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var c mat.Cholesky
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c.Factorize(mat.NewSymDense(order, elements))
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return mat.Formatted(c.LTo(nil))
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}
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func main() {
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@ -0,0 +1,6 @@
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chol[A_] :=
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Module[{L},
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L[k_, k_] := L[k, k] = Sqrt[A[[k, k]] - Sum[L[k, j]^2, {j, 1, k-1}]];
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L[i_, k_] := L[i, k] = L[k, k]^-1 (A[[i, k]] - Sum[L[i, j] L[k, j], {j, 1, k-1}]);
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PadRight[Table[L[i, j], {i, Length[A]}, {j, i}]]
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]
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@ -1,51 +1,49 @@
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/*REXX program performs the Cholesky decomposition on a square matrix. */
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niner = '25 15 -5' , /*define a 3x3 matrix. */
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/*REXX program performs the Cholesky decomposition on a square matrix & displays results*/
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niner = '25 15 -5' , /*define a 3x3 matrix with elements. */
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'15 18 0' ,
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'-5 0 11'
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call Cholesky niner
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hexer = 18 22 54 42, /*define a 4x4 matrix. */
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hexer = 18 22 54 42, /*define a 4x4 matrix with elements. */
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22 70 86 62,
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54 86 174 134,
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42 62 134 106
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call Cholesky hexer
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exit /*stick a fork in it, we're all done. */
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/*────────────────────────────────────────────────────────────────────────────*/
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Cholesky: procedure; parse arg mat; say; say; call tell 'input matrix',mat
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do r=1 for ord
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do c=1 for r; $=0; do i=1 for c-1; $=$+!.r.i*!.c.i; end /*i*/
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if r=c then !.r.r=sqrt(!.r.r-$)
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else !.r.c=1/!.c.c*(@.r.c-$)
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end /*c*/
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end /*r*/
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exit /*stick a fork in it, we're all done. */
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/*──────────────────────────────────────────────────────────────────────────────────────*/
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Cholesky: procedure; parse arg mat; say; say; call tell 'input array',mat
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do r=1 for ord
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do c=1 for r; $=0; do i=1 for c-1; $= $ + !.r.i * !.c.i; end /*i*/
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if r=c then !.r.r= sqrt(!.r.r - $) / 1
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else !.r.c= 1 / !.c.c * (@.r.c - $)
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end /*c*/
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end /*r*/
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call tell 'Cholesky factor',,!.,'─'
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return
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/*────────────────────────────────────────────────────────────────────────────*/
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err: say; say; say '***error***!'; say; say arg(1); say; say; exit 13
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/*────────────────────────────────────────────────────────────────────────────*/
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tell: parse arg hdr,x,y,sep; #=0; if sep=='' then sep='═'
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dPlaces= 5 /*# decimal places past the decimal point*/
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width =10 /*width of field used to display elements*/
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/*──────────────────────────────────────────────────────────────────────────────────────*/
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err: say; say; say '***error***!'; say; say arg(1); say; say; exit 13
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/*──────────────────────────────────────────────────────────────────────────────────────*/
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tell: parse arg hdr,x,y,sep; #=0; if sep=='' then sep= '═'
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dPlaces= 5 /*# dec. places past the decimal point.*/
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width =10 /*field width used to display elements.*/
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if y=='' then !.=0
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else do row=1 for ord; do col=1 for ord; x=x !.row.col; end; end
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else do row=1 for ord; do col=1 for ord; x=x !.row.col; end; end
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w=words(x)
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do ord=1 until ord**2>=w; end /*a fast way to find matrix's order*/
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do ord=1 until ord**2>=w; end /*a fast way to find the matrix's order*/
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say
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if ord**2\==w then call err "matrix elements don't form a square matrix."
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say center(hdr, ((width+1)*w)%ord, sep)
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say center(hdr, ((width + 1) * w) % ord, sep)
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say
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do row=1 for ord; z=
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do col=1 for ord; #=#+1
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@.row.col=word(x,#)
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if col<=row then !.row.col=@.row.col
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z=z right( format(@.row.col,, dPlaces) / 1, width)
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end /*col*/
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say z
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do row=1 for ord; z=
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do col=1 for ord; #= # + 1
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@.row.col= word(x, #)
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if col<=row then !.row.col= @.row.col
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z=z right( format(@.row.col, , dPlaces) / 1, width)
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end /*col*/ /* ↑↑↑ */
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say z /* └┴┴──◄──normalization for zero*/
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end /*row*/
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return
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/*────────────────────────────────────────────────────────────────────────────*/
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sqrt: procedure; parse arg x; if x=0 then return 0; d=digits(); i=; m.=9
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numeric digits 9; numeric form; h=d+6; if x<0 then do; x=-x; i='i'; end
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parse value format(x,2,1,,0) 'E0' with g 'E' _ .; g=g*.5'e'_%2
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do j=0 while h>9; m.j=h; h=h%2+1; end /*j*/
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do k=j+5 to 0 by -1; numeric digits m.k; g=(g+x/g)*.5; end /*k*/
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numeric digits d; return (g/1)i /*make complex if X < 0.*/
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/*──────────────────────────────────────────────────────────────────────────────────────*/
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sqrt: procedure; parse arg x; if x=0 then return 0; d=digits(); numeric digits; h=d+6
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numeric form; m.=9; parse value format(x,2,1,,0) 'E0' with g 'E' _ .; g=g*.5'e'_ %2
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do j=0 while h>9; m.j=h; h=h%2+1; end /*j*/
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do k=j+5 to 0 by -1; numeric digits m.k; g=(g+x/g)*.5; end /*k*/; return g
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45
Task/Cholesky-decomposition/Ring/cholesky-decomposition.ring
Normal file
45
Task/Cholesky-decomposition/Ring/cholesky-decomposition.ring
Normal file
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@ -0,0 +1,45 @@
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# Project : Cholesky decomposition
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# Date : 2017/11/12
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# Author : Gal Zsolt (~ CalmoSoft ~)
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# Email : <calmosoft@gmail.com>
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load "stdlib.ring"
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decimals(5)
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m1 = [[25, 15, -5],
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[15, 18, 0],
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[-5, 0, 11]]
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cholesky(m1)
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printarray(m1)
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see nl
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m2 = [[18, 22, 54, 42],
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[22, 70, 86, 62],
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[54, 86, 174, 134],
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[42, 62, 134, 106]]
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cholesky(m2)
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printarray(m2)
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func cholesky(a)
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l = newlist(len(a), len(a))
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for i = 1 to len(a)
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for j = 1 to i
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s = 0
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for k = 1 to j
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s = s + l[i][k] * l[j][k]
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next
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if i = j
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l[i][j] = sqrt(a[i][i] - s)
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else
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l[i][j] = (a[i][j] - s) / l[j][j]
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ok
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next
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next
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a = l
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func printarray(a)
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for row = 1 to len(a)
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for col = 1 to len(a)
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see "" + a[row][col] + " "
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next
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see nl
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next
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@ -0,0 +1,19 @@
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a = [25 15 -5; 15 18 0; -5 0 11];
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chol(a)
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ans =
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5. 3. -1.
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0. 3. 1.
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0. 0. 3.
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a = [18 22 54 42; 22 70 86 62;
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54 86 174 134; 42 62 134 106];
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chol(a)
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ans =
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4.2426407 5.1854497 12.727922 9.8994949
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0. 6.5659052 3.0460385 1.6245539
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0. 0. 1.6497422 1.849711
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0. 0. 0. 1.3926212
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