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Thomas Baruchel 2022-09-15 19:56:45 +02:00
parent 7c695b47eb
commit 40fc24500d
1 changed files with 7 additions and 25 deletions
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32
carleman.lisp
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@ -28,24 +28,6 @@
; look for the compiled file like "convolution.o" and from now on:
; load("carleman.o")$
; Usage
; -----
; Two functions are provided here:
; * carleman(v)
; * carleman_diag(v)
; The most important is the second one.
;
; Both functions compute the Carleman matrix of a function given as
; a list of coefficients from its Taylor expansion at 0.
; For instance: carleman([0,2,1,0,0,0,0,0]); for f(x)=x^2+2x
;
; The size of resulting matrices will match the length of the initial list.
;
; The second function returns the diagonalized Carleman matrix as a list
; of three matrices whose dot product is the Carleman matrix.
; Compute the Carleman matrix for series whose coefficients are in v.
; Return a list of lists.
; The vector v contains Maxima objects, but the car '(mlist simp) should
@ -62,7 +44,7 @@
(addn
(loop for a in x
for b in u
collect (mul a b))) s))
collect (mul a b)) NIL) s))
finally (return s))
collect u)))
@ -84,7 +66,7 @@
(addn
(loop for e in x
for f in u
collect (mul e f)))
collect (mul e f)) NIL)
(sub d1 d2)) x)
for d2 = (div d1 d) then (div d2 d)
finally (setf (cdr z) r)
@ -115,7 +97,7 @@
(addn
(loop for e in x
for f in u
collect (mul e f)))
collect (mul e f)) NIL)
(sub d1 d2)) (cdr y))
finally (return (append q x)))))
@ -128,7 +110,7 @@
(defun $carleman (v)
(simplifya (cons '($matrix)
(mapcar #'(lambda (x) (simplify (cons '(mlist) x)))
(carleman (cdr v))))))
(carleman (cdr v)))) NIL))
; Let M be the Carleman matrix of a function having 0 as a fixed point
; (ie. f(0)=0) and f'(0) not in {0, 1} ; now, V(M) is such
@ -148,13 +130,13 @@
; left part
(simplifya
(cons '($matrix) (mapcar #'(lambda (x) (simplify (cons '(mlist) x)))
(carleman-diag-left m d))))
(carleman-diag-left m d))) NIL)
; diagonal matrix
(simplifya
(cons '($matrix) (mapcar #'(lambda (x) (simplify (cons '(mlist) x)))
(carleman-diag-middle m d))))
(carleman-diag-middle m d))) NIL)
; right part
(simplifya
(cons '($matrix) (mapcar #'(lambda (x) (simplify (cons '(mlist) x)))
(carleman-diag-right m d))))))))
(carleman-diag-right m d))) NIL)) NIL)))