From mboxrd@z Thu Jan 1 00:00:00 1970 Return-Path: Received: (qmail 16324 invoked by alias); 17 Dec 2001 16:52:05 -0000 Mailing-List: contact gsl-discuss-help@sources.redhat.com; run by ezmlm Precedence: bulk List-Subscribe: List-Archive: List-Post: List-Help: , Sender: gsl-discuss-owner@sources.redhat.com Received: (qmail 16305 invoked from network); 17 Dec 2001 16:52:04 -0000 Received: from unknown (HELO shadow.nrl.navy.mil) (132.250.121.160) by sources.redhat.com with SMTP; 17 Dec 2001 16:52:04 -0000 Received: by shadow.nrl.navy.mil (Postfix, from userid 1114) id 6A0283F8B; Mon, 17 Dec 2001 11:52:14 -0500 (EST) From: Liam Healy MIME-Version: 1.0 Content-Type: multipart/mixed; boundary="JS4nK3gBIr" Content-Transfer-Encoding: 7bit Message-ID: <15390.8891.712402.651008@shadow.nrl.navy.mil> Date: Wed, 19 Dec 2001 13:20:00 -0000 To: gsl-discuss@sources.redhat.com Subject: Elliptic integral and function X-Mailer: VM 6.72 under 21.1 (patch 8) "Bryce Canyon" XEmacs Lucid Reply-To: Liam Healy X-SW-Source: 2001/txt/msg00139.txt.bz2 --JS4nK3gBIr Content-Type: text/plain; charset=us-ascii Content-Description: message body text Content-Transfer-Encoding: 7bit Content-length: 524 My understanding is that the Jacobi elliptic function is the inverse of the elliptic function. That is, sn(K(k),k) = 1 cn(K(k),k) = 0 dn(K(k),k) = sqrt(1-k^2) see http://mathworld.wolfram.com/JacobiEllipticFunctions.html but when I try this I get e.g. gsltest 0.5 k= 0.50000000000000 K(k)= 1.68575035481260 sn= 0.99289175131682 cn= 0.11902088122262 dn= 0.71209759519570 all three of these seem wrong. My driver program is attached. What is wrong here? Thank you for any light you can shed on this. Liam --JS4nK3gBIr Content-Type: text/plain Content-Description: C source code to drive elliptic integrals and functions. Content-Disposition: inline; filename="gsltest.c" Content-Transfer-Encoding: 7bit Content-length: 962 /* ******************************************************** */ /* file: gsltest.c */ /* description: Test the GSL */ /* date: Mon Dec 17 2001 - 10:09 */ /* author: Liam Healy */ /* modified: Mon Dec 17 2001 - 11:45 */ /* ******************************************************** */ /* Compile with: gcc gsltest.c -lgslcblas -lgsl -o gsltest Run: source ~/bin/libpath /usr/local/lib/ gsltest */ #include #include #include #include int main(int argc, char *argv[]) { double k, kk; double sn, cn, dn; int ret; k = atof(argv[1]); kk = gsl_sf_ellint_Kcomp (k, GSL_PREC_DOUBLE); ret = gsl_sf_elljac_e (kk, k, &sn, &cn, &dn); printf("k=%18.14f K(k)=%18.14f\n",k,kk); printf("sn=%18.14f cn=%18.14f dn=%18.14f\n",sn,cn,dn); } --JS4nK3gBIr-- From mboxrd@z Thu Jan 1 00:00:00 1970 From: Liam Healy To: gsl-discuss@sources.redhat.com Subject: Elliptic integral and function Date: Wed, 19 Dec 2001 13:20:00 -0000 Message-ID: <15390.8891.712402.651008@shadow.nrl.navy.mil> X-SW-Source: 2001/msg00815.html Message-ID: <20011219132000.FJwCURTH8A_-nRcbXmlD7EhxRx7S0UGRcLvzF_FlJNs@z> My understanding is that the Jacobi elliptic function is the inverse of the elliptic function. That is, sn(K(k),k) = 1 cn(K(k),k) = 0 dn(K(k),k) = sqrt(1-k^2) see http://mathworld.wolfram.com/JacobiEllipticFunctions.html but when I try this I get e.g. gsltest 0.5 k= 0.50000000000000 K(k)= 1.68575035481260 sn= 0.99289175131682 cn= 0.11902088122262 dn= 0.71209759519570 all three of these seem wrong. My driver program is attached. What is wrong here? Thank you for any light you can shed on this. Liam From mboxrd@z Thu Jan 1 00:00:00 1970 Return-Path: Received: (qmail 16324 invoked by alias); 17 Dec 2001 16:52:05 -0000 Mailing-List: contact gsl-discuss-help@sources.redhat.com; run by ezmlm Precedence: bulk List-Subscribe: List-Archive: List-Post: List-Help: , Sender: gsl-discuss-owner@sources.redhat.com Received: (qmail 16305 invoked from network); 17 Dec 2001 16:52:04 -0000 Received: from unknown (HELO shadow.nrl.navy.mil) (132.250.121.160) by sources.redhat.com with SMTP; 17 Dec 2001 16:52:04 -0000 Received: by shadow.nrl.navy.mil (Postfix, from userid 1114) id 6A0283F8B; Mon, 17 Dec 2001 11:52:14 -0500 (EST) From: Liam Healy MIME-Version: 1.0 Content-Type: multipart/mixed; boundary="JS4nK3gBIr" Content-Transfer-Encoding: 7bit Message-ID: <15390.8891.712402.651008@shadow.nrl.navy.mil> Date: Sat, 08 Dec 2001 10:51:00 -0000 To: gsl-discuss@sources.redhat.com Subject: Elliptic integral and function X-Mailer: VM 6.72 under 21.1 (patch 8) "Bryce Canyon" XEmacs Lucid Reply-To: Liam Healy X-SW-Source: 2001-q4/txt/msg00139.txt.bz2 Message-ID: <20011208105100.TfjXfPoGi4ccoEOYtLyIbk8vX4xTBlPsWEI-fMJpFSE@z> --JS4nK3gBIr Content-Type: text/plain; charset=us-ascii Content-Description: message body text Content-Transfer-Encoding: 7bit Content-length: 524 My understanding is that the Jacobi elliptic function is the inverse of the elliptic function. That is, sn(K(k),k) = 1 cn(K(k),k) = 0 dn(K(k),k) = sqrt(1-k^2) see http://mathworld.wolfram.com/JacobiEllipticFunctions.html but when I try this I get e.g. gsltest 0.5 k= 0.50000000000000 K(k)= 1.68575035481260 sn= 0.99289175131682 cn= 0.11902088122262 dn= 0.71209759519570 all three of these seem wrong. My driver program is attached. What is wrong here? Thank you for any light you can shed on this. Liam --JS4nK3gBIr Content-Type: text/plain Content-Description: C source code to drive elliptic integrals and functions. Content-Disposition: inline; filename="gsltest.c" Content-Transfer-Encoding: 7bit Content-length: 962 /* ******************************************************** */ /* file: gsltest.c */ /* description: Test the GSL */ /* date: Mon Dec 17 2001 - 10:09 */ /* author: Liam Healy */ /* modified: Mon Dec 17 2001 - 11:45 */ /* ******************************************************** */ /* Compile with: gcc gsltest.c -lgslcblas -lgsl -o gsltest Run: source ~/bin/libpath /usr/local/lib/ gsltest */ #include #include #include #include int main(int argc, char *argv[]) { double k, kk; double sn, cn, dn; int ret; k = atof(argv[1]); kk = gsl_sf_ellint_Kcomp (k, GSL_PREC_DOUBLE); ret = gsl_sf_elljac_e (kk, k, &sn, &cn, &dn); printf("k=%18.14f K(k)=%18.14f\n",k,kk); printf("sn=%18.14f cn=%18.14f dn=%18.14f\n",sn,cn,dn); } --JS4nK3gBIr-- From mboxrd@z Thu Jan 1 00:00:00 1970 From: Liam Healy To: gsl-discuss@sources.redhat.com Subject: Elliptic integral and function Date: Mon, 17 Dec 2001 08:52:00 -0000 Message-ID: <15390.8891.712402.651008@shadow.nrl.navy.mil> X-SW-Source: 2001-q4/msg00158.html Message-ID: <20011217085200.vWVAPyRNH3thLIduYKj9f68g6zFntAzKbWxUbqssLss@z> My understanding is that the Jacobi elliptic function is the inverse of the elliptic function. That is, sn(K(k),k) = 1 cn(K(k),k) = 0 dn(K(k),k) = sqrt(1-k^2) see http://mathworld.wolfram.com/JacobiEllipticFunctions.html but when I try this I get e.g. gsltest 0.5 k= 0.50000000000000 K(k)= 1.68575035481260 sn= 0.99289175131682 cn= 0.11902088122262 dn= 0.71209759519570 all three of these seem wrong. My driver program is attached. What is wrong here? Thank you for any light you can shed on this. Liam