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>ring_synthesis</TITLE> 7<META NAME="description" CONTENT="ring_synthesis"> 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_rotate_alm.htm"> 29<LINK REL="previous" HREF="sub_ring_num.htm"> 30<LINK REL="next" HREF="sub_rotate_alm.htm"> 31</HEAD> 32 33<body text="#000000" bgcolor="#FFFFFA"> 34 35<DIV CLASS="navigation"><!--Navigation Panel--> 36<A 37 HREF="sub_ring_num.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_rotate_alm.htm"> 44<IMG WIDTH="37" HEIGHT="24" ALT="next" SRC="next.png"></A> 45<A ID="tex2html482" 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_ring_num.htm">ring_num</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_rotate_alm.htm">rotate_alm*</A> 57<B> Top:</B> <a href="main.htm">Main Page</a></DIV> 58<!--End of Navigation Panel--> 59 60<H1><A ID="SECTION9500"></A> 61<A ID="sub:ring_synthesis"></A> 62<BR> 63 64</H1> 65 66<P> 67<b><font size=+6><FONT COLOR="#CC0000">ring_synthesis</FONT></font></b><hr> 68Location in HEALPix directory tree: <a href="https://sourceforge.net/p/healpix/code/1005/tree/trunk/src/f90/mod/alm_tools.F90"><b>src/f90/mod/alm_tools.F90</b></a> 69 70<P> 71<hr><h1>FORMAT </h1><blockquote><h3>call <FONT COLOR="#CC0000">ring_synthesis</FONT>( 72<A HREF="#sub:ring_synthesis:nsmax">nsmax</A>, <A HREF="#sub:ring_synthesis:nlmax">nlmax</A>, <A HREF="#sub:ring_synthesis:nmmax">nmmax</A>, <A HREF="#sub:ring_synthesis:datain">datain</A>, <A HREF="#sub:ring_synthesis:nph">nph</A>, <A HREF="#sub:ring_synthesis:dataout">dataout</A>, <A HREF="#sub:ring_synthesis:kphi0">kphi0</A> 73)</h3></blockquote> 74 75<P> 76<hr><H1>ARGUMENTS</H1> 77 78<TABLE CELLPADDING=3 BORDER="1"> 79<TR><TH ALIGN="LEFT" VALIGN="TOP" WIDTH=200><SPAN CLASS="textbf">name & dimensionality</SPAN></TH> 80<TH ALIGN="LEFT" VALIGN="TOP" WIDTH=25><SPAN CLASS="textbf">kind</SPAN></TH> 81<TH ALIGN="LEFT" VALIGN="TOP" WIDTH=50><SPAN CLASS="textbf">in/out</SPAN></TH> 82<TH ALIGN="LEFT" VALIGN="TOP" WIDTH=175><SPAN CLASS="textbf">description</SPAN></TH> 83</TR> 84<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=200> </TD> 85<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=25> </TD> 86<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=50> </TD> 87<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=175> </TD> 88</TR> 89<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=200> 90nsmax<A ID="sub:ring_synthesis:nsmax"></A></TD> 91<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=25>I4B</TD> 92<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=50>IN</TD> 93<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=175><!-- MATH 94 $N_{\mathrm{side}}$ 95 --> 96<SPAN CLASS="MATH"><I>N</I><SUB>side</SUB></SPAN> of the map.</TD> 97</TR> 98<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=200>nlmax<A ID="sub:ring_synthesis:nlmax"></A></TD> 99<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=25>I4B</TD> 100<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=50>IN</TD> 101<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=175>Maximum <SPAN CLASS="MATH"><IMG STYLE="height: 1.69ex; vertical-align: -0.10ex; " SRC="sub_img21.png" 102 ALT="$\ell$"></SPAN> of the analysis.</TD> 103</TR> 104<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=200>nmmax<A ID="sub:ring_synthesis:nmmax"></A></TD> 105<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=25>I4B</TD> 106<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=50>IN</TD> 107<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=175>Maximum <SPAN CLASS="MATH"><I>m</I></SPAN> of the analysis.</TD> 108</TR> 109<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=200>nph<A ID="sub:ring_synthesis:nph"></A></TD> 110<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=25>I4B</TD> 111<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=50>IN</TD> 112<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=175>The number of points on the ring.</TD> 113</TR> 114<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=200>datain<A ID="sub:ring_synthesis:datain"></A>(0:nmmax)</TD> 115<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=25>DPC</TD> 116<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=50>IN</TD> 117<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=175>Fourier components as computed from the <SPAN CLASS="MATH"><I>a</I><SUB><I>lm</I></SUB></SPAN>.</TD> 118</TR> 119<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=200>dataout<A ID="sub:ring_synthesis:dataout"></A>(0:nph-1)</TD> 120<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=25>DP</TD> 121<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=50>OUT</TD> 122<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=175>Synthesized function values on the ring.</TD> 123</TR> 124<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=200>kphi0<A ID="sub:ring_synthesis:kphi0"></A></TD> 125<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=25>I4B</TD> 126<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=50>IN</TD> 127<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=175>0 if the first pixel on the ring is at 128 <SPAN CLASS="MATH"><IMG STYLE="height: 2.10ex; vertical-align: -0.55ex; " SRC="sub_img135.png" 129 ALT="$\phi=0$"></SPAN>; 1 otherwise.</TD> 130</TR> 131</TABLE> 132 133<P> 134<HR><H1>EXAMPLE:</H1> 135<tt>call ring_synthesis(64,128,128,datain,8,dataout,1) 136<BR></tt> 137<blockquote> 138This computes the inverse (complex-to-real) Fast Fourier Transform for 139the second ring from the pole, containing <SPAN CLASS="MATH">8</SPAN> pixels, for a map 140resolution of <!-- MATH 141 $N_{\mathrm{side}}=64$ 142 --> 143<SPAN CLASS="MATH"><I>N</I><SUB>side</SUB>=64</SPAN>. <SPAN CLASS="MATH">128</SPAN> complex Fourier 144compoments contribute to these 8 pixels. The value <SPAN CLASS="MATH"><I>kphi</I>0=1</SPAN> specifies 145that a phase factor needed to be applied to correctly 146rotate the ring into position on the <b>HEALPix</b> grid. 147</blockquote> 148 149<P> 150<hr><H1>MODULES & ROUTINES</H1><H3>This section lists the modules and routines used by <FONT COLOR="#CC0000">ring_synthesis</FONT>.</h3> 151 <DL COMPACT><DT> 152<B><SPAN CLASS="textbf">healpix_fft</SPAN></B> 153<DD>module. 154 </DL> 155 156<P> 157<hr><H1>RELATED ROUTINES</H1><h3>This section lists the routines related to <b><FONT COLOR="#CC0000">ring_synthesis</FONT></b></h3> 158 159 <DL COMPACT><DT> 160<B><A HREF="sub_ring_analysis.htm#sub:ring_analysis">ring_analysis</A></B> 161<DD>Forward transform, used in 162 <A HREF="sub_map2alm.htm#sub:map2alm">map2alm</A> and anafast 163 </DL> 164 165<P> 166 167<P> 168 169 170<P> 171 172<P> 173 174<DIV CLASS="navigation"><HR> 175<!--Navigation Panel--> 176<A 177 HREF="sub_ring_num.htm"> 178<IMG WIDTH="63" HEIGHT="24" ALT="previous" SRC="prev.png"></A> 179<A 180 HREF="sub_HEALPix_F90_subroutines.htm"> 181<IMG WIDTH="26" HEIGHT="24" ALT="up" SRC="up.png"></A> 182<A 183 HREF="sub_rotate_alm.htm"> 184<IMG WIDTH="37" HEIGHT="24" ALT="next" SRC="next.png"></A> 185<A ID="tex2html482" 186 HREF="sub_TABLE_CONTENTS.htm"> 187<IMG WIDTH="65" HEIGHT="24" ALT="contents" SRC="contents.png"></A> 188<BR> 189<B> Previous:</B> <A 190 HREF="sub_ring_num.htm">ring_num</A> 191 192<B>Up:</B> <A 193 HREF="sub_HEALPix_F90_subroutines.htm">HEALPix/F90 subroutines</A> 194 195<B> Next:</B> <A 196 HREF="sub_rotate_alm.htm">rotate_alm*</A> 197<B> Top:</B> <a href="main.htm">Main Page</a></DIV> 198<!--End of Navigation Panel--> 199<ADDRESS> 200Version 3.50, 2018-12-10 201</ADDRESS> 202</BODY> 203</HTML> 204
