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>create_alm*</TITLE> 7<META NAME="description" CONTENT="create_alm*"> 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_del_card.htm"> 29<LINK REL="previous" HREF="sub_coordsys2euler_zyz.htm"> 30<LINK REL="next" HREF="sub_del_card.htm"> 31</HEAD> 32 33<body text="#000000" bgcolor="#FFFFFA"> 34 35<DIV CLASS="navigation"><!--Navigation Panel--> 36<A 37 HREF="sub_coordsys2euler_zyz.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_del_card.htm"> 44<IMG WIDTH="37" HEIGHT="24" ALT="next" SRC="next.png"></A> 45<A ID="tex2html342" 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_coordsys2euler_zyz.htm">coordsys2euler_zyz</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_del_card.htm">del_card</A> 57<B> Top:</B> <a href="main.htm">Main Page</a></DIV> 58<!--End of Navigation Panel--> 59 60<H1><A ID="SECTION2500"></A> 61<A ID="sub:create_alm"></A> 62<BR> 63 64</H1> 65 66<P> 67<b><font size=+6><FONT COLOR="#CC0000">create_alm*</FONT></font></b><hr> 68<H3>This routine generates scalar (and tensor) <SPAN CLASS="MATH"><IMG STYLE="height: 1.46ex; vertical-align: -0.45ex; " SRC="sub_img6.png" 69 ALT="$a_{\ell m}$"></SPAN> for a temperature (and 70 polarisation) power spectrum read from an input FITS 71file. The <SPAN CLASS="MATH"><IMG STYLE="height: 1.46ex; vertical-align: -0.45ex; " SRC="sub_img6.png" 72 ALT="$a_{\ell m}$"></SPAN> are gaussian distributed with a zero mean, and their 73 amplitude is multiplied with the <SPAN CLASS="MATH"><IMG STYLE="height: 1.69ex; vertical-align: -0.10ex; " SRC="sub_img21.png" 74 ALT="$\ell$"></SPAN>-space window function of a gaussian 75 beam characterized by its FWHM or an arbitrary circular beam 76and a pixel window read from an external file.</H3> 77Location 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> 78 79<P> 80<hr><h1>FORMAT </h1><blockquote><h3>call <FONT COLOR="#CC0000">create_alm*</FONT>( 81<A HREF="#sub:create_alm:nsmax">nsmax</A>, <A HREF="#sub:create_alm:nlmax">nlmax</A>, <A HREF="#sub:create_alm:nmmax">nmmax</A>, <A HREF="#sub:create_alm:polar">polar</A>, <A HREF="#sub:create_alm:filename">filename</A>, <A HREF="#sub:create_alm:rng_handle">rng_handle</A>, <A HREF="#sub:create_alm:fwhm_arcmin">fwhm_arcmin</A>, <A HREF="#sub:create_alm:alm_TGC">alm_TGC</A>, <A HREF="#sub:create_alm:header">header</A><i><font color="#224422">[, 82<A HREF="#sub:create_alm:windowfile">windowfile</A>, <A HREF="#sub:create_alm:units">units</A>, <A HREF="#sub:create_alm:beam_file">beam_file</A>]</font></i> 83)</h3></blockquote> 84Arguments appearing in <i><font color="#224422">italic</font></i> are 85optional. 86 87<P> 88<hr><H1>ARGUMENTS</H1> 89 90<TABLE CELLPADDING=3 BORDER="1"> 91<TR><TH ALIGN="LEFT" VALIGN="TOP" WIDTH=185><SPAN CLASS="textbf">name & dimensionality</SPAN></TH> 92<TH ALIGN="LEFT" VALIGN="TOP" WIDTH=25><SPAN CLASS="textbf">kind</SPAN></TH> 93<TH ALIGN="LEFT" VALIGN="TOP" WIDTH=50><SPAN CLASS="textbf">in/out</SPAN></TH> 94<TH ALIGN="LEFT" VALIGN="TOP" WIDTH=190><SPAN CLASS="textbf">description</SPAN></TH> 95</TR> 96<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=185> </TD> 97<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=25> </TD> 98<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=50> </TD> 99<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=190> </TD> 100</TR> 101<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=185> 102nsmax<A ID="sub:create_alm:nsmax"></A></TD> 103<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=25>I4B</TD> 104<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=50>IN</TD> 105<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=190><!-- MATH 106 $N_{\mathrm{side}}$ 107 --> 108<SPAN CLASS="MATH"><I>N</I><SUB>side</SUB></SPAN> of the map to be synthetized from the <SPAN CLASS="MATH"><IMG STYLE="height: 1.46ex; vertical-align: -0.45ex; " SRC="sub_img6.png" 109 ALT="$a_{\ell m}$"></SPAN> 110 created by this routine.</TD> 111</TR> 112<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=185>nlmax<A ID="sub:create_alm:nlmax"></A></TD> 113<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=25>I4B</TD> 114<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=50>IN</TD> 115<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=190>maximum <SPAN CLASS="MATH"><IMG STYLE="height: 1.69ex; vertical-align: -0.10ex; " SRC="sub_img21.png" 116 ALT="$\ell$"></SPAN> value to be considered (MAX=<!-- MATH 117 $4N_{\mathrm{side}}$ 118 --> 119<SPAN CLASS="MATH">4<I>N</I><SUB>side</SUB></SPAN> 120if <A HREF="#sub:create_alm:windowfile"><TT>windowfile</TT></A> is provided).</TD> 121</TR> 122<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=185>nmmax<A ID="sub:create_alm:nmmax"></A></TD> 123<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=25>I4B</TD> 124<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=50>IN</TD> 125<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=190>maximum <SPAN CLASS="MATH"><I>m</I></SPAN> value for the <SPAN CLASS="MATH"><IMG STYLE="height: 1.46ex; vertical-align: -0.45ex; " SRC="sub_img6.png" 126 ALT="$a_{\ell m}$"></SPAN>.</TD> 127</TR> 128<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=185>polar<A ID="sub:create_alm:polar"></A></TD> 129<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=25>I4B</TD> 130<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=50>IN</TD> 131<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=190><SPAN CLASS="textbf">if set to 0</SPAN>, only Temperature (scalar) <SPAN CLASS="MATH"><IMG STYLE="height: 1.46ex; vertical-align: -0.45ex; " SRC="sub_img6.png" 132 ALT="$a_{\ell m}$"></SPAN> are 133generated using TT spectrum. <SPAN CLASS="textbf">If set to 1</SPAN>, 'conventional' polarization is added, based on EE, BB and TE spectra. <SPAN CLASS="textbf">If set to 2</SPAN>, and if 134the relevant information is in <TT>filename</TT>, polarization is generated 135assuming non-zero correlation of Curl (B) modes with Temperature (T) and Gradient 136(E) modes (TB and EB cross-spectra). Note that the <A HREF="./fac_synfast.htm#fac:synfast"><TT>synfast</TT></A> facility calls <FONT COLOR="#CC0000">create_alm*</FONT> with <TT>polar</TT>=0 <EM>or</EM> <TT>polar</TT>=1</TD> 137</TR> 138<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=185>filename<A ID="sub:create_alm:filename"></A>(LEN=<tt>filenamelen</tt>)</TD> 139<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=25>CHR</TD> 140<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=50>IN</TD> 141<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=190>name of FITS file containing power 142spectra in the order TT, [EE, BB, TE, [TB, EB]] (terms in brackets are optional, see <A HREF="#sub:create_alm:polar"><TT>polar</TT></A>)</TD> 143</TR> 144<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=185>rng_handle<A ID="sub:create_alm:rng_handle"></A></TD> 145<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=25><A HREF="sub_planck_rng_derived_type.htm#sub:planck_rng">planck_rng</A></TD> 146<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=50>INOUT</TD> 147<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=190>structure containing 148information necessary to continue a random sequence 149initiated <EM>previously</EM> with the 150subroutine <A HREF="sub_rand_init.htm#sub:rand_init"><TT>rand_init</TT></A>. Consecutive calls to <FONT COLOR="#CC0000">create_alm*</FONT> can be made after a 151single invocation to <A HREF="sub_rand_init.htm#sub:rand_init"><TT>rand_init</TT></A>.</TD> 152</TR> 153<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=185>fwhm_arcmin<A ID="sub:create_alm:fwhm_arcmin"></A></TD> 154<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=25>SP/ DP</TD> 155<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=50>IN</TD> 156<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=190>FWHM size of the gaussian beam in arcminutes.</TD> 157</TR> 158<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=185>alm_TGC<A ID="sub:create_alm:alm_TGC"></A>(1:p,0:nlmax,0:nmmax)</TD> 159<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=25>SPC/ DPC</TD> 160<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=50>OUT</TD> 161<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=190>complex <SPAN CLASS="MATH"><IMG STYLE="height: 1.46ex; vertical-align: -0.45ex; " SRC="sub_img6.png" 162 ALT="$a_{\ell m}$"></SPAN> values 163generated from the power spectrum in the FITS file. The first index here runs 164form 1:1 for temperature only, and 1:3 for polarisation. In the latter case, 1651=T, 2=E, 3=B.</TD> 166</TR> 167</TABLE> 168<TABLE CELLPADDING=3 BORDER="1"> 169<TR><TH ALIGN="LEFT" VALIGN="TOP" WIDTH=185><SPAN CLASS="textbf">name & dimensionality</SPAN></TH> 170<TH ALIGN="LEFT" VALIGN="TOP" WIDTH=25><SPAN CLASS="textbf">kind</SPAN></TH> 171<TH ALIGN="LEFT" VALIGN="TOP" WIDTH=50><SPAN CLASS="textbf">in/out</SPAN></TH> 172<TH ALIGN="LEFT" VALIGN="TOP" WIDTH=190><SPAN CLASS="textbf">description</SPAN></TH> 173</TR> 174<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=185> </TD> 175<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=25> </TD> 176<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=50> </TD> 177<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=190> </TD> 178</TR> 179<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=185> 180header<A ID="sub:create_alm:header"></A>(LEN=80),dimension(60)</TD> 181<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=25>CHR</TD> 182<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=50>OUT</TD> 183<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=190>part of header which 184will be included in the FITS-file containing the 185map synthesised from the <SPAN CLASS="MATH"><IMG STYLE="height: 1.46ex; vertical-align: -0.45ex; " SRC="sub_img6.png" 186 ALT="$a_{\ell m}$"></SPAN> which create_alm generates.</TD> 187</TR> 188<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=185><i><font color="#224422">windowfile<A ID="sub:create_alm:windowfile"></A></font></i>(LEN=<tt>filenamelen</tt>)</TD> 189<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=25>CHR</TD> 190<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=50>IN</TD> 191<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=190>full filename specification 192of the FITS file with the pixel window function (defined for <!-- MATH 193 $\ell\le4 N_{\mathrm{side}}$ 194 --> 195<SPAN CLASS="MATH"><IMG STYLE="height: 2.04ex; vertical-align: -0.45ex; " SRC="sub_img104.png" 196 ALT="$\ell\le4 N_{\mathrm{side}}$"></SPAN>)</TD> 197</TR> 198<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=185><i><font color="#224422">units<A ID="sub:create_alm:units"></A></font></i>(LEN=80),dimension(1:)</TD> 199<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=25>CHR</TD> 200<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=50>OUT</TD> 201<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=190>physical units of the created 202<SPAN CLASS="MATH"><IMG STYLE="height: 1.46ex; vertical-align: -0.45ex; " SRC="sub_img6.png" 203 ALT="$a_{\ell m}$"></SPAN> (square-root of the input power spectrum units).</TD> 204</TR> 205<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=185><i><font color="#224422">beam_file<A ID="sub:create_alm:beam_file"></A></font></i>(LEN=<tt>filenamelen</tt>)</TD> 206<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=25>CHR</TD> 207<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=50>IN</TD> 208<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=190>name of the file containing 209the (non necessarily gaussian) window function <SPAN CLASS="MATH"><IMG STYLE="height: 2.04ex; vertical-align: -0.45ex; " SRC="sub_img78.png" 210 ALT="$B_\ell$"></SPAN> of a circular beam. If present, it will override 211the argument <A HREF="#sub:create_alm:fwhm_arcmin"><TT>fwhm_arcmin</TT></A>.</TD> 212</TR> 213</TABLE> 214 215<P> 216<HR><H1>EXAMPLE:</H1> 217<tt>use alm_tools, only: create_alm 218<BR> 219use rngmod, only: rand_init, planck_rng 220<BR> 221type(planck_rng) :: rng_handle 222<BR> 223<BR> 224call rand_init(rng_handle, -1) 225<BR> 226call create_alm(64, 128, 128, 1, 'cl.fits', rng_handle, 5.0, alm_TGC, & 227<BR>& header, 'data/pixel_window_n0064.fits') 228<BR></tt> 229<blockquote> 230Creates scalar and tensor <SPAN CLASS="MATH"><IMG STYLE="height: 1.46ex; vertical-align: -0.45ex; " SRC="sub_img6.png" 231 ALT="$a_{\ell m}$"></SPAN> from the power spectrum given in the file 232`cl.fits'. The map to be created from these <SPAN CLASS="MATH"><IMG STYLE="height: 1.46ex; vertical-align: -0.45ex; " SRC="sub_img6.png" 233 ALT="$a_{\ell m}$"></SPAN> is assumed to have 234<!-- MATH 235 $N_{\mathrm{side}}=64$ 236 --> 237<SPAN CLASS="MATH"><I>N</I><SUB>side</SUB>=64</SPAN>. <SPAN CLASS="MATH"><IMG STYLE="height: 2.04ex; vertical-align: -0.45ex; " SRC="sub_img105.png" 238 ALT="$C_\ell$"></SPAN>s from the power spectrum are used up to an <SPAN CLASS="MATH"><IMG STYLE="height: 1.69ex; vertical-align: -0.10ex; " SRC="sub_img21.png" 239 ALT="$\ell$"></SPAN> value of 240128. 241Corresponding <SPAN CLASS="MATH"><IMG STYLE="height: 1.46ex; vertical-align: -0.45ex; " SRC="sub_img6.png" 242 ALT="$a_{\ell m}$"></SPAN> values up to l=128 and m=128 are created as gaussian distributed 243complex numbers. Their are drawn from a sequence of pseudo-random numbers 244initiated with a seed of -1. 245The produced <SPAN CLASS="MATH"><IMG STYLE="height: 1.46ex; vertical-align: -0.45ex; " SRC="sub_img6.png" 246 ALT="$a_{\ell m}$"></SPAN> are convolved with a gaussian beam of FWHM 5 arcminutes 247and a pixel window read from 'data/pixel_window_n0064.fits'. It is assumed that after the return 248from this routine, a map is generated from the created 249<SPAN CLASS="MATH"><IMG STYLE="height: 1.46ex; vertical-align: -0.45ex; " SRC="sub_img6.png" 250 ALT="$a_{\ell m}$"></SPAN>. For this purpose, <TT>header</TT> is updated with FITS format information 251describing the origin and history of these <SPAN CLASS="MATH"><IMG STYLE="height: 1.46ex; vertical-align: -0.45ex; " SRC="sub_img6.png" 252 ALT="$a_{\ell m}$"></SPAN>. 253</blockquote> 254 255<P> 256<hr><H1>MODULES & ROUTINES</H1><H3>This section lists the modules and routines used by <FONT COLOR="#CC0000">create_alm*</FONT>.</h3> 257 <DL COMPACT><DT> 258<B><SPAN CLASS="textbf">alm_tools</SPAN></B> 259<DD><u>module</u>, containing: 260 <DT> 261<B>pow2alm_units</B> 262<DD>routine to convert from power spectrum units to 263 <SPAN CLASS="MATH"><IMG STYLE="height: 1.46ex; vertical-align: -0.45ex; " SRC="sub_img6.png" 264 ALT="$a_{\ell m}$"></SPAN> units 265 <DT> 266<B><A HREF="sub_generate_beam.htm#sub:generate_beam">generate_beam</A></B> 267<DD>routine to generate beam window function 268 <DT> 269<B><A HREF="sub_pixel_window.htm#sub:pixel_window">pixel_window</A></B> 270<DD>routine to read in pixel window function 271 <DT> 272<B><SPAN CLASS="textbf">utilities</SPAN></B> 273<DD><u>module</u>, containing: 274 <DT> 275<B>die_alloc</B> 276<DD>routine that prints an error message if there is not enough space for allocation of variables. 277 <DT> 278<B><SPAN CLASS="textbf">fitstools</SPAN></B> 279<DD><u>module</u>, containing: 280 <DT> 281<B><A HREF="sub_fits2cl.htm#sub:fits2cl">fits2cl</A></B> 282<DD>routine to read a FITS 283 file containing a power spectrum. 284 <DT> 285<B><A HREF="sub_read_dbintab.htm#sub:read_dbintab">read_dbintab</A></B> 286<DD>routine to read a FITS-binary file containing the pixel window functions. 287 <DT> 288<B><SPAN CLASS="textbf">head_fits</SPAN></B> 289<DD><u>module</u>, containing: 290 <DT> 291<B><A HREF="sub_add_card.htm#sub:add_card">add_card</A></B> 292<DD>routine to add a keyword to a FITS header. 293 <DT> 294<B><A HREF="sub_get_card.htm#sub:get_card">get_card</A></B> 295<DD>routine to read a keyword value from 296 FITS header. 297 <DT> 298<B><A HREF="sub_merge_headers.htm#sub:merge_headers">merge_headers</A></B> 299<DD>routine to merge two FITS headers. 300<DT> 301<B><SPAN CLASS="textbf">rngmod</SPAN></B> 302<DD><u>module</u>, containing: 303 <DT> 304<B><A HREF="sub_rand_gauss.htm#sub:rand_gauss">rand_gauss</A></B> 305<DD>function which returns a gaussian distributed random 306 number. 307 </DL> 308 309<P> 310<hr><H1>RELATED ROUTINES</H1><h3>This section lists the routines related to <b><FONT COLOR="#CC0000">create_alm*</FONT></b></h3> 311 312 <DL COMPACT><DT> 313<B><A HREF="sub_rand_init.htm#sub:rand_init">rand_init</A></B> 314<DD>subroutine to initiate a random number sequence. 315 <DT> 316<B>synfast</B> 317<DD>executable using <FONT COLOR="#CC0000">create_alm*</FONT> to synthesize CMB maps from a given 318 power spectrum. 319 <DT> 320<B><A HREF="sub_alm2map.htm#sub:alm2map">alm2map</A></B> 321<DD>Routine to transform a set of <SPAN CLASS="MATH"><IMG STYLE="height: 1.46ex; vertical-align: -0.45ex; " SRC="sub_img6.png" 322 ALT="$a_{\ell m}$"></SPAN> created by <FONT COLOR="#CC0000">create_alm*</FONT> to a <b>HEALPix</b> map. 323 <DT> 324<B><A HREF="sub_alms2fits.htm#sub:alms2fits">alms2fits</A>, <A HREF="sub_dump_alms.htm#sub:dump_alms">dump_alms</A></B> 325<DD>Routines to save a set of <SPAN CLASS="MATH"><IMG STYLE="height: 1.46ex; vertical-align: -0.45ex; " SRC="sub_img6.png" 326 ALT="$a_{\ell m}$"></SPAN> in a FITS file. 327 </DL> 328 329<P> 330 331<P> 332 333 334<P> 335 336<P> 337 338<DIV CLASS="navigation"><HR> 339<!--Navigation Panel--> 340<A 341 HREF="sub_coordsys2euler_zyz.htm"> 342<IMG WIDTH="63" HEIGHT="24" ALT="previous" SRC="prev.png"></A> 343<A 344 HREF="sub_HEALPix_F90_subroutines.htm"> 345<IMG WIDTH="26" HEIGHT="24" ALT="up" SRC="up.png"></A> 346<A 347 HREF="sub_del_card.htm"> 348<IMG WIDTH="37" HEIGHT="24" ALT="next" SRC="next.png"></A> 349<A ID="tex2html342" 350 HREF="sub_TABLE_CONTENTS.htm"> 351<IMG WIDTH="65" HEIGHT="24" ALT="contents" SRC="contents.png"></A> 352<BR> 353<B> Previous:</B> <A 354 HREF="sub_coordsys2euler_zyz.htm">coordsys2euler_zyz</A> 355 356<B>Up:</B> <A 357 HREF="sub_HEALPix_F90_subroutines.htm">HEALPix/F90 subroutines</A> 358 359<B> Next:</B> <A 360 HREF="sub_del_card.htm">del_card</A> 361<B> Top:</B> <a href="main.htm">Main Page</a></DIV> 362<!--End of Navigation Panel--> 363<ADDRESS> 364Version 3.50, 2018-12-10 365</ADDRESS> 366</BODY> 367</HTML> 368
