1<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN"> 2 3<!--Converted with LaTeX2HTML 2018.3 (Released July 19, 2018) --> 4<HTML lang="EN"> 5<HEAD> 6<TITLE>coordsys2euler_zyz</TITLE> 7<META NAME="description" CONTENT="coordsys2euler_zyz"> 8<META NAME="keywords" CONTENT="subroutines"> 9<META NAME="resource-type" CONTENT="document"> 10<META NAME="distribution" CONTENT="global"> 11 12<META HTTP-EQUIV="Content-Type" CONTENT="text/html; charset=utf-8"> 13<META NAME="viewport" CONTENT="width=device-width, initial-scale=1.0"> 14<META NAME="Generator" CONTENT="LaTeX2HTML v2018.3"> 15 <link rel='apple-touch-icon' sizes='180x180' href='images/favicons/apple-touch-icon.png?v=2017'> 16 <link rel='icon' type='image/png' sizes='32x32' href='images/favicons/favicon-32x32.png?v=2017'> 17 <link rel='icon' type='image/png' sizes='16x16' href='images/favicons/favicon-16x16.png?v=2017'> 18 <link rel='manifest' href='images/favicons/manifest.json?v=2017'> 19 <link rel='mask-icon' href='images/favicons/safari-pinned-tab.svg?v=2017' color='#5bbad5'> 20 <link rel='shortcut icon' href='images/favicons/favicon.ico?v=2017'> 21 <meta name='apple-mobile-web-app-title' content='HEALPix'> 22 <meta name='application-name' content='HEALPix'> 23 <meta name='msapplication-config' content='images/favicons/browserconfig.xml?v=2017'> 24 <meta name='theme-color' content='#ffffff'> 25 26<LINK REL="STYLESHEET" HREF="subroutines.css"> 27 28<LINK REL="next" HREF="sub_create_alm.htm"> 29<LINK REL="previous" HREF="sub_convert_ring2nest.htm"> 30<LINK REL="next" HREF="sub_create_alm.htm"> 31</HEAD> 32 33<body text="#000000" bgcolor="#FFFFFA"> 34 35<DIV CLASS="navigation"><!--Navigation Panel--> 36<A 37 HREF="sub_convert_ring2nest.htm"> 38<IMG WIDTH="63" HEIGHT="24" ALT="previous" SRC="prev.png"></A> 39<A 40 HREF="sub_HEALPix_F90_subroutines.htm"> 41<IMG WIDTH="26" HEIGHT="24" ALT="up" SRC="up.png"></A> 42<A 43 HREF="sub_create_alm.htm"> 44<IMG WIDTH="37" HEIGHT="24" ALT="next" SRC="next.png"></A> 45<A ID="tex2html340" 46 HREF="sub_TABLE_CONTENTS.htm"> 47<IMG WIDTH="65" HEIGHT="24" ALT="contents" SRC="contents.png"></A> 48<BR> 49<B> Previous:</B> <A 50 HREF="sub_convert_ring2nest.htm">convert_ring2nest*</A> 51 52<B>Up:</B> <A 53 HREF="sub_HEALPix_F90_subroutines.htm">HEALPix/F90 subroutines</A> 54 55<B> Next:</B> <A 56 HREF="sub_create_alm.htm">create_alm*</A> 57<B> Top:</B> <a href="main.htm">Main Page</a></DIV> 58<!--End of Navigation Panel--> 59 60<H1><A ID="SECTION2400"></A> 61<A ID="sub:coordsys2euler_zyz"></A> 62<BR> 63 64</H1> 65 66<P> 67<b><font size=+6><FONT COLOR="#CC0000">coordsys2euler_zyz</FONT></font></b><hr> 68<H3>This routine returns the three Euler angles <!-- MATH 69 $\psi, \theta, \varphi$ 70 --> 71<SPAN CLASS="MATH"><IMG STYLE="height: 2.16ex; vertical-align: -0.55ex; " SRC="sub_img100.png" 72 ALT="$\psi, \theta, \varphi 73$"></SPAN>, corresponding to a rotation between standard astronomical 74coordinate systems. This angles can then be used in rotate_alm</H3> 75Location in HEALPix directory tree: <a href="https://sourceforge.net/p/healpix/code/1005/tree/trunk/src/f90/mod/coord_v_convert.f90"><b>src/f90/mod/coord_v_convert.f90</b></a> 76 77<P> 78<hr><h1>FORMAT </h1><blockquote><h3>call <FONT COLOR="#CC0000">coordsys2euler_zyz</FONT>( 79<A HREF="#sub:coordsys2euler_zyz:iepoch">iepoch</A>, <A HREF="#sub:coordsys2euler_zyz:oepoch">oepoch</A>, <A HREF="#sub:coordsys2euler_zyz:isys">isys</A>, <A HREF="#sub:coordsys2euler_zyz:osys">osys</A>, <A HREF="#sub:coordsys2euler_zyz:psi">psi</A>, <A HREF="#sub:coordsys2euler_zyz:theta">theta</A>, <A HREF="#sub:coordsys2euler_zyz:phi">phi</A> 80)</h3></blockquote> 81 82<P> 83<hr><H1>ARGUMENTS</H1> 84 85<TABLE CELLPADDING=3 BORDER="1"> 86<TR><TH ALIGN="LEFT" VALIGN="TOP" WIDTH=130><SPAN CLASS="textbf">name & dimensionality</SPAN></TH> 87<TH ALIGN="LEFT" VALIGN="TOP" WIDTH=25><SPAN CLASS="textbf">kind</SPAN></TH> 88<TH ALIGN="LEFT" VALIGN="TOP" WIDTH=45><SPAN CLASS="textbf">in/out</SPAN></TH> 89<TH ALIGN="LEFT" VALIGN="TOP" WIDTH=250><SPAN CLASS="textbf">description</SPAN></TH> 90</TR> 91<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=130> </TD> 92<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=25> </TD> 93<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=45> </TD> 94<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=250> </TD> 95</TR> 96<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=130> 97iepoch<A ID="sub:coordsys2euler_zyz:iepoch"></A></TD> 98<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=25>DP</TD> 99<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=45>IN</TD> 100<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=250>epoch of the input astronomical coordinate system.</TD> 101</TR> 102<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=130>oepoch<A ID="sub:coordsys2euler_zyz:oepoch"></A></TD> 103<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=25>DP</TD> 104<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=45>IN</TD> 105<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=250>epoch of the output astronomical coordinate system.</TD> 106</TR> 107<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=130>isys<A ID="sub:coordsys2euler_zyz:isys"></A>(len=*)</TD> 108<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=25>CHR</TD> 109<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=45>IN</TD> 110<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=250>input coordinate system, should be one of 'E'=Ecliptic, 'G'=Galactic, 'C'/'Q'=Celestial/eQuatorial.</TD> 111</TR> 112<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=130>osys<A ID="sub:coordsys2euler_zyz:osys"></A>(len=*)</TD> 113<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=25>CHR</TD> 114<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=45>IN</TD> 115<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=250>output coordinate system, same choice as above.</TD> 116</TR> 117<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=130>psi<A ID="sub:coordsys2euler_zyz:psi"></A></TD> 118<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=25>DP</TD> 119<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=45>OUT</TD> 120<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=250>first Euler angle: rotation <SPAN CLASS="MATH"><IMG STYLE="height: 2.10ex; vertical-align: -0.55ex; " SRC="sub_img101.png" 121 ALT="$\psi$"></SPAN> about the z-axis.</TD> 122</TR> 123<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=130>theta<A ID="sub:coordsys2euler_zyz:theta"></A></TD> 124<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=25>DP</TD> 125<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=45>OUT</TD> 126<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=250>second Euler angle: rotation <SPAN CLASS="MATH"><IMG STYLE="height: 1.69ex; vertical-align: -0.10ex; " SRC="sub_img102.png" 127 ALT="$\theta$"></SPAN> about the original 128(unrotated) y-axis;</TD> 129</TR> 130<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=130>phi<A ID="sub:coordsys2euler_zyz:phi"></A></TD> 131<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=25>DP</TD> 132<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=45>OUT</TD> 133<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=250>third Euler angle: rotation <SPAN CLASS="MATH"><IMG STYLE="height: 1.57ex; vertical-align: -0.55ex; " SRC="sub_img103.png" 134 ALT="$\varphi$"></SPAN> about the original (unrotated) z-axis;</TD> 135</TR> 136</TABLE> 137 138<P> 139<HR><H1>EXAMPLE:</H1> 140<tt>use coord_v_convert, only: coordsys2euler_zyz 141<BR> 142use alm_tools, only: rotate_alm 143<BR>... 144<BR> 145call coordsys2euler_zyz(2000.0_dp, 2000.0_dp, 'E', 'G', psi, theta, phi) 146<BR> 147call rotate_alm(64, alm_TGC, psi, theta, phi) 148<BR></tt> 149<blockquote> 150Rotate the <SPAN CLASS="MATH"><IMG STYLE="height: 1.46ex; vertical-align: -0.45ex; " SRC="sub_img6.png" 151 ALT="$a_{\ell m}$"></SPAN> from Ecliptic to Galactic coordinates. 152</blockquote> 153 154<P> 155<hr><H1>RELATED ROUTINES</H1><h3>This section lists the routines related to <b><FONT COLOR="#CC0000">coordsys2euler_zyz</FONT></b></h3> 156 157 <DL COMPACT><DT> 158<B><A HREF="sub_rotate_alm.htm#sub:rotate_alm">rotate_alm</A></B> 159<DD>apply arbitrary sky rotation to a 160 set of <SPAN CLASS="MATH"><IMG STYLE="height: 1.46ex; vertical-align: -0.45ex; " SRC="sub_img6.png" 161 ALT="$a_{\ell m}$"></SPAN> coefficients. 162 <DT> 163<B><A HREF="sub_xcc_v_convert.htm#sub:xcc_v_convert">xcc_v_convert</A></B> 164<DD>rotates a 3D coordinate 165vector from one astronomical coordinate system to another. 166 </DL> 167 168<P> 169 170<P> 171 172 173<P> 174 175<P> 176 177<DIV CLASS="navigation"><HR> 178<!--Navigation Panel--> 179<A 180 HREF="sub_convert_ring2nest.htm"> 181<IMG WIDTH="63" HEIGHT="24" ALT="previous" SRC="prev.png"></A> 182<A 183 HREF="sub_HEALPix_F90_subroutines.htm"> 184<IMG WIDTH="26" HEIGHT="24" ALT="up" SRC="up.png"></A> 185<A 186 HREF="sub_create_alm.htm"> 187<IMG WIDTH="37" HEIGHT="24" ALT="next" SRC="next.png"></A> 188<A ID="tex2html340" 189 HREF="sub_TABLE_CONTENTS.htm"> 190<IMG WIDTH="65" HEIGHT="24" ALT="contents" SRC="contents.png"></A> 191<BR> 192<B> Previous:</B> <A 193 HREF="sub_convert_ring2nest.htm">convert_ring2nest*</A> 194 195<B>Up:</B> <A 196 HREF="sub_HEALPix_F90_subroutines.htm">HEALPix/F90 subroutines</A> 197 198<B> Next:</B> <A 199 HREF="sub_create_alm.htm">create_alm*</A> 200<B> Top:</B> <a href="main.htm">Main Page</a></DIV> 201<!--End of Navigation Panel--> 202<ADDRESS> 203Version 3.50, 2018-12-10 204</ADDRESS> 205</BODY> 206</HTML> 207
