root/trunk/special-functions/psi.lisp

;; Psi (digamma) functions
;; Liam Healy, Mon May  1 2006 - 22:11
;; Time-stamp: <2008-02-16 22:43:28EST psi.lisp>
;; $Id$

(in-package :gsl)

;;;;****************************************************************************
;;;; Digamma Function
;;;;****************************************************************************

(defgeneric psi (x)
  ;; FDL
  (:documentation "The psi, or digamma, function."))

(defmfun psi  ((n integer))
  "gsl_sf_psi_int_e" ((n :int) (ret sf-result))
  :type :method
  :export t
  :documentation                        ; FDL
  "Domain: n integer, n > 0.")

(defmfun psi ((x float))
  "gsl_sf_psi_e" ((x :double) (ret sf-result))
  :type :method 
  :documentation                        ; FDL
  "Domain: x /= 0.0, -1.0, -2.0, ...")

(defmfun psi-1+iy (x)
  "gsl_sf_psi_1piy_e" ((x :double) (ret sf-result))
  :documentation                        ; FDL
  "The real part of the digamma function
  on the line 1+i y, Re[psi(1 + i y)].")

;;;;****************************************************************************
;;;; Trigamma Function
;;;;****************************************************************************

(defgeneric psi-1 (x)
  ;; FDL
  (:documentation "The Trigamma function."))

(defmfun psi-1 ((n integer))
  "gsl_sf_psi_1_int_e" ((n :int) (ret sf-result))
  :type :method 
  :documentation                        ; FDL
  "Domain: n integer, n > 0.")

(defmfun psi-1 ((x float))
  "gsl_sf_psi_1_e" ((x :double) (ret sf-result))
  :type :method
  :documentation                        ; FDL
  "Domain: x /= 0.0, -1.0, -2.0, ...")

;;;;****************************************************************************
;;;; Polygamma
;;;;****************************************************************************

(defmfun psi-n (m x)
  "gsl_sf_psi_n_e" ((m :int) (x :double) (ret sf-result))
  :documentation                        ; FDL
  "The polygamma function psi^{(m)}(x)} for m >= 0, x > 0.")

;;;;****************************************************************************
;;;; Examples and unit test
;;;;****************************************************************************

#|
(make-tests psi
  (psi 4)
  (psi 4.0d0)
  (psi-1+iy 2.0d0)
  (psi-1 4)
  (psi-1 4.0d0)
  (psi-n 2 4.0d0))
|#

(LISP-UNIT:DEFINE-TEST PSI
  (LISP-UNIT::ASSERT-NUMERICAL-EQUAL
   (LIST 1.2561176684318005d0 2.789141514262906d-16)
   (MULTIPLE-VALUE-LIST (PSI 4)))
  (LISP-UNIT::ASSERT-NUMERICAL-EQUAL
   (LIST 1.2561176684318005d0 2.846229783626858d-16)
   (MULTIPLE-VALUE-LIST (PSI 4.0d0)))
  (LISP-UNIT::ASSERT-NUMERICAL-EQUAL
   (LIST 0.7145915153739806d0 1.925418559790263d-14)
   (MULTIPLE-VALUE-LIST (PSI-1+IY 2.0d0)))
  (LISP-UNIT::ASSERT-NUMERICAL-EQUAL
   (LIST 0.2838229557371153d0 6.302135607530242d-17)
   (MULTIPLE-VALUE-LIST (PSI-1 4)))
  (LISP-UNIT::ASSERT-NUMERICAL-EQUAL
   (LIST 0.28382295573711525d0 1.764597970108467d-15)
   (MULTIPLE-VALUE-LIST (PSI-1 4.0d0)))
  (LISP-UNIT::ASSERT-NUMERICAL-EQUAL
   (LIST -0.0800397322451145d0 5.222647053360405d-16)
   (MULTIPLE-VALUE-LIST (PSI-N 2 4.0d0))))