root/trunk/special-functions/fermi-dirac.lisp

;; Fermi-Dirac function.
;; Liam Healy, Sat Apr 22 2006 - 16:12
;; Time-stamp: <2008-02-16 21:37:25EST fermi-dirac.lisp>
;; $Id$

(in-package :gsl)

;;;;****************************************************************************
;;;; Complete Fermi-Dirac Integrals
;;;;****************************************************************************

(defmfun fermi-dirac-m1 (x)
  "gsl_sf_fermi_dirac_m1_e" ((x :double) (ret sf-result))
  :documentation                        ; FDL
  "The complete Fermi-Dirac integral with an index of -1. 
  This integral is given by F_{-1}(x) = e^x / (1 + e^x).")

(defmfun fermi-dirac-0 (x)
  "gsl_sf_fermi_dirac_0_e" ((x :double) (ret sf-result))
  :documentation                        ; FDL
  "The complete Fermi-Dirac integral with an index of 0. 
   This integral is given by F_0(x) = \ln(1 + e^x).")

(defmfun fermi-dirac-1 (x)
  "gsl_sf_fermi_dirac_1_e" ((x :double) (ret sf-result))
  :documentation                        ; FDL
  "The complete Fermi-Dirac integral with an index of 1,
   F_1(x) = \int_0^\infty dt (t /(\exp(t-x)+1)).")

(defmfun fermi-dirac-2 (x)
  "gsl_sf_fermi_dirac_2_e" ((x :double) (ret sf-result))
  :documentation                        ; FDL
  "The complete Fermi-Dirac integral with an index of 2,
   F_2(x) = (1/2) \int_0^\infty dt (t^2 /(\exp(t-x)+1)).")

(defmfun fermi-dirac-integral (j x)
  "gsl_sf_fermi_dirac_int_e" ((j :int) (x :double) (ret sf-result))
  :documentation                        ; FDL
  "The complete Fermi-Dirac integral with an integer index of j,
   F_j(x) = (1/\Gamma(j+1)) \int_0^\infty dt (t^j /(\exp(t-x)+1)).")

(defmfun fermi-dirac-m1/2 (x)
  "gsl_sf_fermi_dirac_mhalf_e" ((x :double) (ret sf-result))
  :documentation                        ; FDL
  "The complete Fermi-Dirac integral F_{-1/2}(x).")

(defmfun fermi-dirac-1/2 (x)
  "gsl_sf_fermi_dirac_half_e" ((x :double) (ret sf-result))
  :documentation                        ; FDL
  "The complete Fermi-Dirac integral F_{1/2}(x).")

(defmfun fermi-dirac-3/2 (x)
  "gsl_sf_fermi_dirac_3half_e" ((x :double) (ret sf-result))
  :documentation                        ; FDL
  "The complete Fermi-Dirac integral F_{3/2}(x).")

;;;;****************************************************************************
;;;; Incomplete Fermi-Dirac Integrals
;;;;****************************************************************************

(defmfun fermi-dirac-inc-0 (x b)
  "gsl_sf_fermi_dirac_inc_0_e" ((x :double) (b :double) (ret sf-result))
  :documentation                        ; FDL
  "The incomplete Fermi-Dirac integral with an index
  of zero, F_0(x,b) = \ln(1 + e^{b-x}) - (b-x).")

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

#|
(make-tests fermi-dirac
  (fermi-dirac-m1 0.5d0)
  (fermi-dirac-0 0.75d0)
  (fermi-dirac-1 -0.75d0)
  (fermi-dirac-2 0.25d0)
  (fermi-dirac-integral 5 12.35d0)
  (fermi-dirac-m1/2 2.0d0)
  (fermi-dirac-1/2 2.0d0)
  (fermi-dirac-3/2 2.0d0)
  (fermi-dirac-inc-0 2.0d0 0.5d0))
|#

(LISP-UNIT:DEFINE-TEST FERMI-DIRAC
  (LISP-UNIT::ASSERT-NUMERICAL-EQUAL
   (LIST 0.6224593312018546d0 4.040305821324309d-16)
   (MULTIPLE-VALUE-LIST (FERMI-DIRAC-M1 0.5d0)))
  (LISP-UNIT::ASSERT-NUMERICAL-EQUAL
   (LIST 1.1368710061148999d0 1.6653345369377348d-16)
   (MULTIPLE-VALUE-LIST (FERMI-DIRAC-0 0.75d0)))
  (LISP-UNIT::ASSERT-NUMERICAL-EQUAL
   (LIST 0.42589430612383183d0 5.594591187346375d-16)
   (MULTIPLE-VALUE-LIST (FERMI-DIRAC-1 -0.75d0)))
  (LISP-UNIT::ASSERT-NUMERICAL-EQUAL
   (LIST 1.1301630162645293d0 6.04246936785309d-16)
   (MULTIPLE-VALUE-LIST (FERMI-DIRAC-2 0.25d0)))
  (LISP-UNIT::ASSERT-NUMERICAL-EQUAL
   (LIST 6668.827087650077d0 2.1696654306572242d-10)
   (MULTIPLE-VALUE-LIST (FERMI-DIRAC-INTEGRAL 5 12.35d0)))
  (LISP-UNIT::ASSERT-NUMERICAL-EQUAL
   (LIST 1.4642945890876293d0 4.053118505064653d-15)
   (MULTIPLE-VALUE-LIST (FERMI-DIRAC-M1/2 2.0d0)))
  (LISP-UNIT::ASSERT-NUMERICAL-EQUAL
   (LIST 2.8237212774015843d0 2.909989668869937d-15)
   (MULTIPLE-VALUE-LIST (FERMI-DIRAC-1/2 2.0d0)))
  (LISP-UNIT::ASSERT-NUMERICAL-EQUAL
   (LIST 4.165414459868321d0 3.666976569654393d-15)
   (MULTIPLE-VALUE-LIST (FERMI-DIRAC-3/2 2.0d0)))
  (LISP-UNIT::ASSERT-NUMERICAL-EQUAL
   (LIST 1.7014132779827524d0 8.881784197001252d-16)
   (MULTIPLE-VALUE-LIST (FERMI-DIRAC-INC-0 2.0d0 0.5d0))))