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;; Psi (digamma) functions
;; Liam Healy, Mon May 1 2006 - 22:11
;; Time-stamp: <2008-07-10 21:42:08EDT psi.lisp>
(in-package :gsl)
;;;;****************************************************************************
;;;; Digamma Function
;;;;****************************************************************************
(defgeneric psi (x)
(:documentation "The psi, or digamma, function."))
(defmfun psi ((n integer))
"gsl_sf_psi_int_e" ((n :int) (ret sf-result))
:definition :method
:documentation ; FDL
"Domain: n integer, n > 0.")
(defmfun psi ((x float))
"gsl_sf_psi_e" ((x :double) (ret sf-result))
:definition :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)
(:documentation "The Trigamma function."))
(defmfun psi-1 ((n integer))
"gsl_sf_psi_1_int_e" ((n :int) (ret sf-result))
:definition :method
:documentation ; FDL
"Domain: n integer, n > 0.")
(defmfun psi-1 ((x float))
"gsl_sf_psi_1_e" ((x :double) (ret sf-result))
:definition :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))))