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- Log ----------------------------------------------------------------- commit 7c5a3186070096ee93e16f2ddf51b2c84e7c5895 Author: Raymond Toy rtoy@google.com Date: Wed Apr 11 09:18:31 2012 -0700

Correct some comments, remove unused code.

diff --git a/qd-bessel.lisp b/qd-bessel.lisp index 367b847..0197e7f 100644 --- a/qd-bessel.lisp +++ b/qd-bessel.lisp @@ -37,7 +37,7 @@

;; B[k](p) = 1/2^(k+3/2)*integrate(exp(-p*u)*u^(k-1/2),u,0,1) ;; = 1/2^(k+3/2)/p^(k+1/2)*integrate(t^(k-1/2)*exp(-t),t,0,p) -;; = 1/2^(k+3/2)/p^(k+1/2) * g(k+1/2, p) +;; = 1/2^(k+3/2)/p^(k+1/2) * G(k+1/2, p) ;; ;; where G(a,z) is the lower incomplete gamma function. ;; @@ -109,6 +109,12 @@ ;; = conj(B[k](%i*z). ;; ;; Hence I(-%i*z, v) = conj(I(%i*z, v)) when both z and v are real. +;; +;; Also note that when v is an integer of the form (2*m+1)/2, then +;; r[2*k+1](-2*%i*v) = r[2*k+1](-%i*(2*m+1)) +;; = -%i*(2*m+1)*product(-(2*m+1)^2+(2*j-1)^2, j, 1, k) +;; so the product is zero when k >= m and the series I(p, q) is +;; finite. (defun exp-arc-i (p q) (let* ((sqrt2 (sqrt (float 2 (realpart p)))) (exp/p/sqrt2 (/ (exp (- p)) p sqrt2)) @@ -144,14 +150,9 @@ (format t " sum - ~S~%" sum)))))

(defun exp-arc-i-2 (p q) - (let* ((sqrt2 (sqrt (float 2 (realpart p)))) - (exp/p/sqrt2 (/ (exp (- p)) p sqrt2)) - (v (* #c(0 -2) q)) + (let* ((v (* #c(0 -2) q)) (v2 (expt v 2)) (eps (epsilon (realpart p)))) - (when *debug-exparc* - (format t "sqrt2 = ~S~%" sqrt2) - (format t "exp/p/sqrt2 = ~S~%" exp/p/sqrt2)) (do* ((k 0 (1+ k)) (bk (bk 0 p) (bk k p)) @@ -162,6 +163,12 @@ (* ratio bk)) (sum term (+ sum term))) ((< (abs term) (* (abs sum) eps)) + (when *debug-exparc* + (format t "Final k= ~D~%" k) + (format t " bk = ~S~%" bk) + (format t " ratio = ~S~%" ratio) + (format t " term = ~S~%" term) + (format t " sum - ~S~%" sum)) (* sum #c(0 2) (/ (exp p) q))) (when *debug-exparc* (format t "k = ~D~%" k)

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Summary of changes: qd-bessel.lisp | 21 ++++++++++++++------- 1 files changed, 14 insertions(+), 7 deletions(-)

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