Changeset 78801d6381aaaf4f21967582680f26889582db60

Timestamp:

04/15/12 10:50:16 (13 months ago)

Author:

Raymond Toy <toy.raymond@…>

Children:

8c5195a87137fd61952a175a5dae676c70b480ef, 581a0a08f04a985424c09b6a7b3661d2eb58c3e9

Parents:

5566bc397937c2e8979ee6847e8f59f279f1f643

git-committer:

Raymond Toy <toy.raymond@…> (04/15/12 10:50:16)

Message:

• Add comments for integer-bessel-j-exp-arc.
• Simplify sum-an so we stop the sum when the terms no longer contribute to the sum.
• Change big-n. This still needs work.

Files:

• qd-bessel.lisp (modified) (4 diffs)

qd-bessel.lisp

@@ -180 +180 @@
 
 
-;;
+;; Not really just for Bessel J for integer orders, but in that case,
+;; this is all that's needed to compute Bessel J.  For other values,
+;; this is just part of the computation needed.
+;;
+;; Compute
+;;
+;;  1/(2*%pi) * (exp(-%i*v*%pi/2) * I(%i*z, v) + exp(%i*v*%pi/2) * I(-%i*z, v))
 (defun integer-bessel-j-exp-arc (v z)
   (let* ((iz (* #c(0 1) z))
@@ -258 +264 @@
 ;; sum(exp(-k*z)*a[n](k,v), k, 1, N)
 ;;
+#+nil
 (defun sum-an (big-n n v z)
   (let ((sum 0))
@@ -265 +272 @@
                           (an n k v))))
     sum))
+
+;; Like above, but we just stop when the terms no longer contribute to
+;; the sum.
+(defun sum-an (big-n n v z)
+  (let ((eps (epsilon (realpart z))))
+    (do* ((k 1 (+ 1 k))
+          (term (* (exp (- (* k z)))
+                   (an n k v))
+                (* (exp (- (* k z)))
+                   (an n k v)))
+          (sum term (+ sum term)))
+         ((or (<= (abs term) (* eps (abs sum)))
+              (> k big-n))
+          sum))))
 
 ;; SUM-AB computes the series
@@ -400 +421 @@
           (t
            ;; Need to fine-tune the value of big-n.
-           (let ((big-n 100)
+           (let ((big-n 10)
                  (vpi (* v (float-pi (realpart z)))))
              (+ (integer-bessel-j-exp-arc v z)