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<a href="gaussmod_8f90.html">Go to the documentation of this file.</a><div class="fragment"><pre class="fragment"><a name="l00001"></a>00001 <span class="comment">! =================</span>
<a name="l00002"></a>00002 <span class="comment">! SUBROUTINE INIGAU</span>
<a name="l00003"></a>00003 <span class="comment">! =================</span>
<a name="l00004"></a>00004 
<a name="l00005"></a><a class="code" href="gaussmod_8f90.html#a841a2f8e9025371eddc985235e1831ab">00005</a> <span class="keyword">subroutine </span><a class="code" href="gaussmod_8f90.html#a841a2f8e9025371eddc985235e1831ab">inigau</a>(klat,pz0,pzw)        ! pz0 &amp; pzw are (kind=8) reals !!!
<a name="l00006"></a>00006 <span class="keyword">implicit none</span>
<a name="l00007"></a>00007 <span class="keywordtype">integer</span>                  :: klat       <span class="comment">! Number of Gaussian latitudes</span>
<a name="l00008"></a>00008 <span class="keywordtype">real (kind=8)</span>            :: pz0(klat)  <span class="comment">! Gaussian abscissas</span>
<a name="l00009"></a>00009 <span class="keywordtype">real (kind=8)</span>            :: pzw(klat)  <span class="comment">! Gaussian weights</span>
<a name="l00010"></a>00010 <span class="keywordtype">integer</span>                  :: jlat       <span class="comment">! Latitudinal loop index</span>
<a name="l00011"></a>00011 <span class="keywordtype">integer</span>                  :: jiter      <span class="comment">! Iteration loop index</span>
<a name="l00012"></a>00012 <span class="keywordtype">integer</span>      , <span class="keywordtype">parameter</span> :: NITER = 50 <span class="comment">! Maximum # of iterations</span>
<a name="l00013"></a>00013 <span class="keywordtype">real (kind=8)</span>, <span class="keywordtype">parameter</span> :: PI    =  3.14159265358979_8
<a name="l00014"></a>00014 <span class="keywordtype">real (kind=8)</span>, <span class="keywordtype">parameter</span> :: ZEPS  =  1.0e-16 <span class="comment">! Convergence criterion</span>
<a name="l00015"></a>00015 <span class="keywordtype">real (kind=8)</span> :: z0,z1,z2,z3,z4,z5
<a name="l00016"></a>00016 <span class="keywordtype">real (kind=8)</span> :: ql,qld
<a name="l00017"></a>00017 
<a name="l00018"></a>00018 <span class="comment">! Compute Gaussian abscissas &amp; weights</span>
<a name="l00019"></a>00019 
<a name="l00020"></a>00020 z0 = PI / (2*klat+1)
<a name="l00021"></a>00021 z1 = 1.0_8 / (klat*klat*8)
<a name="l00022"></a>00022 z4 = 2.0_8 / (klat*klat)
<a name="l00023"></a>00023 
<a name="l00024"></a>00024 <span class="keyword">do</span> jlat = 1 , klat/2
<a name="l00025"></a>00025    z2 = z0 * (2*jlat - 0.5_8)
<a name="l00026"></a>00026    z2 = cos(z2 + z1 / tan(z2))
<a name="l00027"></a>00027    <span class="keyword">do</span> jiter = 1 , NITER
<a name="l00028"></a>00028       z3 = ql(klat,z2) * qld(klat,z2)
<a name="l00029"></a>00029       z2 = z2 - z3
<a name="l00030"></a>00030       <span class="keyword">if</span> (abs(z3) &lt; ZEPS) exit <span class="comment">! converged</span>
<a name="l00031"></a>00031    <span class="keyword">enddo</span> <span class="comment">! jiter</span>
<a name="l00032"></a>00032    z5 = ql(klat-1,z2) / sqrt(klat - 0.5_8)
<a name="l00033"></a>00033    pz0(jlat) = z2
<a name="l00034"></a>00034    pzw(jlat) = z4 * (1.0_8 - z2 * z2) / (z5 * z5)
<a name="l00035"></a>00035    pz0(klat-jlat+1) = -z2
<a name="l00036"></a>00036    pzw(klat-jlat+1) = pzw(jlat)
<a name="l00037"></a>00037 <span class="keyword">enddo</span> <span class="comment">! jlat</span>
<a name="l00038"></a>00038 
<a name="l00039"></a>00039 return
<a name="l00040"></a>00040 <span class="keyword">end subroutine inigau</span>
<a name="l00041"></a>00041 
<a name="l00042"></a>00042 <span class="comment">! ===========</span>
<a name="l00043"></a>00043 <span class="comment">! FUNCTION QL</span>
<a name="l00044"></a>00044 <span class="comment">! ===========</span>
<a name="l00045"></a>00045 
<a name="l00046"></a><a class="code" href="gaussmod_8f90.html#a278a9f628839bb589bfb00f5ece28891">00046</a> <span class="keyword">real (kind=8) </span><span class="keyword">function </span><a class="code" href="gaussmod_8f90.html#a278a9f628839bb589bfb00f5ece28891">ql</a>(k,p)
<a name="l00047"></a>00047 <span class="keyword">implicit none</span>
<a name="l00048"></a>00048 <span class="keywordtype">integer</span>      , <span class="keywordtype">intent(IN)</span> :: k
<a name="l00049"></a>00049 <span class="keywordtype">real (kind=8)</span>, <span class="keywordtype">intent(IN)</span> :: p
<a name="l00050"></a>00050 <span class="keywordtype">real (kind=8)</span> :: z0,z1,z2,z3,z4
<a name="l00051"></a>00051 <span class="keywordtype">integer</span> :: j
<a name="l00052"></a>00052 z0 = acos(p)
<a name="l00053"></a>00053 z1 = 1.0
<a name="l00054"></a>00054 z2 = 0.0
<a name="l00055"></a>00055 <span class="keyword">do</span> j = k , 0 , -2
<a name="l00056"></a>00056    z3 = z1 * cos(z0 * j)
<a name="l00057"></a>00057    z2 = z2 + z3
<a name="l00058"></a>00058    z4 = (k-j+1) * (k+j) * 0.5_8
<a name="l00059"></a>00059    z1 = z1 * z4 / (z4 + (j-1))
<a name="l00060"></a>00060 <span class="keyword">enddo</span> <span class="comment">! j</span>
<a name="l00061"></a>00061 <span class="keyword">if</span> (mod(k,2) == 0) z2 = z2 - 0.5_8 * z3
<a name="l00062"></a>00062 
<a name="l00063"></a>00063 z0 = sqrt(2.0_8)
<a name="l00064"></a>00064 <span class="keyword">do</span> j = 1 ,k
<a name="l00065"></a>00065    z0 = z0 * sqrt(1.0_8 - 0.25_8 / (j*j))
<a name="l00066"></a>00066 <span class="keyword">enddo</span> <span class="comment">! j</span>
<a name="l00067"></a>00067 <a class="code" href="gaussmod_8f90.html#a278a9f628839bb589bfb00f5ece28891">ql</a> = z0 * z2
<a name="l00068"></a>00068 return
<a name="l00069"></a>00069 <span class="keyword">end function ql</span>
<a name="l00070"></a>00070 
<a name="l00071"></a>00071 <span class="comment">! ============</span>
<a name="l00072"></a>00072 <span class="comment">! FUNCTION QLD</span>
<a name="l00073"></a>00073 <span class="comment">! ============</span>
<a name="l00074"></a>00074 
<a name="l00075"></a><a class="code" href="gaussmod_8f90.html#a8911e98641c97beec648f8d593306b39">00075</a> <span class="keyword">real (kind=8) </span><span class="keyword">function </span><a class="code" href="gaussmod_8f90.html#a8911e98641c97beec648f8d593306b39">qld</a>(k,p)
<a name="l00076"></a>00076 <span class="keyword">implicit none</span>
<a name="l00077"></a>00077 <span class="keywordtype">integer</span>      , <span class="keywordtype">intent(IN)</span> :: k
<a name="l00078"></a>00078 <span class="keywordtype">real (kind=8)</span>, <span class="keywordtype">intent(IN)</span> :: p
<a name="l00079"></a>00079 <span class="keywordtype">real (kind=8)</span> :: z
<a name="l00080"></a>00080 <span class="keywordtype">real (kind=8)</span> :: ql
<a name="l00081"></a>00081 
<a name="l00082"></a>00082 z = p * ql(k,p) - sqrt((k + k + 1.0_8) / (k + k - 1.0_8)) * ql(k-1,p)
<a name="l00083"></a>00083 <a class="code" href="gaussmod_8f90.html#a8911e98641c97beec648f8d593306b39">qld</a> = (p * p - 1.0_8) / (k * z)
<a name="l00084"></a>00084 
<a name="l00085"></a>00085 return
<a name="l00086"></a>00086 <span class="keyword">end function qld</span>
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