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- Log ----------------------------------------------------------------- commit 147fa2c7aa5e99988a7c3fb35800865d22efbc51 Author: Raymond Toy toy.raymond@gmail.com Date: Fri Mar 11 23:11:32 2011 -0500

Add tests for contagion support.

diff --git a/rt-tests.lisp b/rt-tests.lisp index 85f9b95..7635611 100644 --- a/rt-tests.lisp +++ b/rt-tests.lisp @@ -864,3 +864,68 @@ (true #q1.797210352103388311159883738420485817340818994823477337395512429419599q0)) (check-accuracy 212 rd true)) nil) + +;; Test some of the contagion stuff. + +(rt:deftest oct.carlson-rf.contagion.1 + ;; Rf(0,2,1) = integrate(1/sqrt(1-s^4), s, 0 ,1) + ;; = 1/4*beta(1/2,1/2) + ;; = sqrt(%pi)/4*gamma(1/4)/gamma(3/4) + (let ((rf (carlson-rf 0 2 1)) + (true 1.31102877714605990523241979494d0)) + (check-accuracy 23 rf true)) + nil) + +(rt:deftest oct.carlson-rf.contagion.1d + ;; Rf(0,2,1) = integrate(1/sqrt(1-s^4), s, 0 ,1) + ;; = 1/4*beta(1/2,1/2) + ;; = sqrt(%pi)/4*gamma(1/4)/gamma(3/4) + (let ((rf (carlson-rf 0d0 2 1)) + (true 1.31102877714605990523241979494d0)) + (check-accuracy 53 rf true)) + nil) + +(rt:deftest oct.carlson-rf.contagion.2d + ;; Rf(0,2,1) = integrate(1/sqrt(1-s^4), s, 0 ,1) + ;; = 1/4*beta(1/2,1/2) + ;; = sqrt(%pi)/4*gamma(1/4)/gamma(3/4) + (let ((rf (carlson-rf 0 2d0 1)) + (true 1.31102877714605990523241979494d0)) + (check-accuracy 53 rf true)) + nil) + +(rt:deftest oct.carlson-rf.contagion.3d + ;; Rf(0,2,1) = integrate(1/sqrt(1-s^4), s, 0 ,1) + ;; = 1/4*beta(1/2,1/2) + ;; = sqrt(%pi)/4*gamma(1/4)/gamma(3/4) + (let ((rf (carlson-rf 0 2 1d0)) + (true 1.31102877714605990523241979494d0)) + (check-accuracy 53 rf true)) + nil) + +(rt:deftest oct.carlson-rf.contagion.1q + ;; Rf(0,2,1) = integrate(1/sqrt(1-s^4), s, 0 ,1) + ;; = 1/4*beta(1/2,1/2) + ;; = sqrt(%pi)/4*gamma(1/4)/gamma(3/4) + (let ((rf (carlson-rf #q0q0 2 1)) + (true #q1.311028777146059905232419794945559706841377475715811581408410851900395q0)) + (check-accuracy 212 rf true)) + nil) + +(rt:deftest oct.carlson-rf.contagion.2q + ;; Rf(0,2,1) = integrate(1/sqrt(1-s^4), s, 0 ,1) + ;; = 1/4*beta(1/2,1/2) + ;; = sqrt(%pi)/4*gamma(1/4)/gamma(3/4) + (let ((rf (carlson-rf 0 #q2q0 1)) + (true #q1.311028777146059905232419794945559706841377475715811581408410851900395q0)) + (check-accuracy 212 rf true)) + nil) + +(rt:deftest oct.carlson-rf.contagion.3q + ;; Rf(0,2,1) = integrate(1/sqrt(1-s^4), s, 0 ,1) + ;; = 1/4*beta(1/2,1/2) + ;; = sqrt(%pi)/4*gamma(1/4)/gamma(3/4) + (let ((rf (carlson-rf 0 2 #q1q0)) + (true #q1.311028777146059905232419794945559706841377475715811581408410851900395q0)) + (check-accuracy 212 rf true)) + nil) \ No newline at end of file

commit e2d8d63c0c06c474f32b76ebbb7e4cde44aac736 Author: Raymond Toy toy.raymond@gmail.com Date: Fri Mar 11 22:57:40 2011 -0500

Clean up float-contagion stuff; use it in Carlson routines.

o FLOAT-CONTAGION now only returns the real type, not a complex type. o Add APPLY-CONTAGION to make the specified conversion. This handle complex numbers and makes the components have the specified precision. o Change uses of contagion stuff to use APPLY-CONTAGION. o Use the contagion stuff in CARLSON-RD and CARLSON-RF.

diff --git a/qd-elliptic.lisp b/qd-elliptic.lisp index 6c8070a..342290e 100644 --- a/qd-elliptic.lisp +++ b/qd-elliptic.lisp @@ -72,12 +72,16 @@ (single-float 'single-float) (double-float 'double-float) (qd-real 'qd-real)))) - (if complexp - (if (eq max-type 'qd-real) - 'qd-complex - `(cl:complex ,max-type)) - max-type))) - + max-type)) + +(defun apply-contagion (number precision) + (etypecase number + ((or cl:real qd-real) + (coerce number precision)) + ((or cl:complex qd-complex) + (complex (coerce (realpart number) precision) + (coerce (imagpart number) precision))))) + ;;; Jacobian elliptic functions

(defun ascending-transform (u m) @@ -282,9 +286,10 @@ "Compute Carlson's Rf function:

Rf(x, y, z) = 1/2*integrate((t+x)^(-1/2)*(t+y)^(-1/2)*(t+z)^(-1/2), t, 0, inf)" - (let* ((xn x) - (yn y) - (zn z) + (let* ((precision (float-contagion x y z)) + (xn (apply-contagion x precision)) + (yn (apply-contagion y precision)) + (zn (apply-contagion z precision)) (a (/ (+ xn yn zn) 3)) (epslon (/ (max (abs (- a xn)) (abs (- a yn)) @@ -333,9 +338,10 @@ "Compute Carlson's Rd function:

Rd(x,y,z) = integrate(3/2*(t+x)^(-1/2)*(t+y)^(-1/2)*(t+z)^(-3/2), t, 0, inf)" - (let* ((xn x) - (yn y) - (zn z) + (let* ((precision (float-contagion x y z)) + (xn (apply-contagion x precision)) + (yn (apply-contagion y precision)) + (zn (apply-contagion z precision)) (a (/ (+ xn yn (* 3 zn)) 5)) (epslon (/ (max (abs (- a xn)) (abs (- a yn)) @@ -348,20 +354,20 @@ xnroot ynroot znroot lam) (loop while (> (* power4 epslon) (abs an)) do - (setf xnroot (sqrt xn)) - (setf ynroot (sqrt yn)) - (setf znroot (sqrt zn)) - (setf lam (+ (* xnroot ynroot) - (* xnroot znroot) - (* ynroot znroot))) - (setf sigma (+ sigma (/ power4 - (* znroot (+ zn lam))))) - (setf power4 (* power4 1/4)) - (setf xn (* (+ xn lam) 1/4)) - (setf yn (* (+ yn lam) 1/4)) - (setf zn (* (+ zn lam) 1/4)) - (setf an (* (+ an lam) 1/4)) - (incf n)) + (setf xnroot (sqrt xn)) + (setf ynroot (sqrt yn)) + (setf znroot (sqrt zn)) + (setf lam (+ (* xnroot ynroot) + (* xnroot znroot) + (* ynroot znroot))) + (setf sigma (+ sigma (/ power4 + (* znroot (+ zn lam))))) + (setf power4 (* power4 1/4)) + (setf xn (* (+ xn lam) 1/4)) + (setf yn (* (+ yn lam) 1/4)) + (setf zn (* (+ zn lam) 1/4)) + (setf an (* (+ an lam) 1/4)) + (incf n)) ;; c1=-3/14,c2=1/6,c3=9/88,c4=9/22,c5=-3/22,c6=-9/52,c7=3/26 (let* ((xndev (/ (* (- a x) power4) an)) (yndev (/ (* (- a y) power4) an)) @@ -384,9 +390,9 @@ (* 3/20 ee2 ee4) (* 45/272 ee2 ee2 ee3) (* -9/68 (+ (* ee2 ee5) (* ee3 ee4)))))) - (+ (* 3 sigma) - (/ (* power4 s) - (expt an 3/2)))))) + (+ (* 3 sigma) + (/ (* power4 s) + (expt an 3/2))))))

;; Complete elliptic integral of the first kind. This can be computed ;; from Carlson's Rf function: @@ -403,7 +409,7 @@ (/ (float +pi+ m) 2)) (t (let ((precision (float-contagion m))) - (carlson-rf (coerce 0 precision) (- 1 m) (coerce 1 precision)))))) + (carlson-rf 0 (- 1 m) 1)))))

;; Elliptic integral of the first kind. This is computed using ;; Carlson's Rf function: @@ -416,8 +422,8 @@

Note for the complete elliptic integral, you can use elliptic-k" (let* ((precision (float-contagion x m)) - (x (coerce x precision)) - (m (coerce m precision))) + (x (apply-contagion x precision)) + (m (apply-contagion m precision))) (cond ((and (realp m) (realp x)) (cond ((> m 1) ;; A&S 17.4.15 @@ -425,7 +431,7 @@ ;; F(phi|m) = 1/sqrt(m)*F(theta|1/m) ;; ;; with sin(theta) = sqrt(m)*sin(phi) - (/ (elliptic-f (cl:asin (* (sqrt m) (sin x))) (/ m)) + (/ (elliptic-f (asin (* (sqrt m) (sin x))) (/ m)) (sqrt m))) ((< m 0) ;; A&S 17.4.17 @@ -445,7 +451,7 @@ ;; ;; F(phi,1) = log(sec(phi)+tan(phi)) ;; = log(tan(pi/4+pi/2)) - (log (cl:tan (+ (/ x 2) (/ (float-pi x) 4))))) + (log (tan (+ (/ x 2) (/ (float-pi x) 4))))) ((minusp x) (- (elliptic-f (- x) m))) ((> x (float-pi x)) @@ -462,7 +468,7 @@ (carlson-rf (* cos-x cos-x) (* (- 1 (* k sin-x)) (+ 1 (* k sin-x))) - 1.0)))) + 1)))) ((< x (float-pi x)) (+ (* 2 (elliptic-k m)) (elliptic-f (- x (float pi x)) m))))) @@ -485,8 +491,8 @@

E(phi, m) = integrate(sqrt(1-m*sin(x)^2), x, 0, phi)" (let* ((precision (float-contagion phi m)) - (phi (coerce phi precision)) - (m (coerce m precision))) + (phi (apply-contagion phi precision)) + (m (apply-contagion m precision))) (cond ((= m 0) ;; A&S 17.4.23 phi) @@ -500,10 +506,10 @@ E(phi, m) = integrate(sqrt(1-m*sin(x)^2), x, 0, phi)" (y (* (- 1 (* k sin-phi)) (+ 1 (* k sin-phi))))) (- (* sin-phi - (carlson-rf (* cos-phi cos-phi) y (coerce 1 precision))) + (carlson-rf (* cos-phi cos-phi) y 1)) (* (/ m 3) (expt sin-phi 3) - (carlson-rd (* cos-phi cos-phi) y (coerce 1 precision))))))))) + (carlson-rd (* cos-phi cos-phi) y 1))))))))

;; Complete elliptic integral of second kind. ;; @@ -513,17 +519,16 @@ E(phi, m) = integrate(sqrt(1-m*sin(x)^2), x, 0, phi)" "Complete elliptic integral of the second kind:

E(m) = integrate(sqrt(1-m*sin(x)^2), x, 0, %pi/2)" - (let ((precision (float-contagion m))) - (cond ((= m 0) - ;; A&S 17.4.23 - (/ (float-pi m) 2)) - ((= m 1) - ;; A&S 17.4.25 - (coerce 1 precision)) - (t - (let* ((k (sqrt m)) - (y (* (- 1 k) - (+ 1 k)))) - (- (carlson-rf 0.0 y 1.0) - (* (/ m 3) - (carlson-rd 0.0 y 1.0)))))))) + (cond ((= m 0) + ;; A&S 17.4.23 + (/ (float-pi m) 2)) + ((= m 1) + ;; A&S 17.4.25 + (float 1 m)) + (t + (let* ((k (sqrt m)) + (y (* (- 1 k) + (+ 1 k)))) + (- (carlson-rf 0 y 1) + (* (/ m 3) + (carlson-rd 0 y 1)))))))

-----------------------------------------------------------------------

Summary of changes: qd-elliptic.lisp | 111 ++++++++++++++++++++++++++++-------------------------- rt-tests.lisp | 65 +++++++++++++++++++++++++++++++ 2 files changed, 123 insertions(+), 53 deletions(-)

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