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    <innerclass refid="structlibecpint_1_1_five_index" prot="public">libecpint::FiveIndex</innerclass>
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    <innerclass refid="structlibecpint_1_1_gaussian_shell" prot="public">libecpint::GaussianShell</innerclass>
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    <innerclass refid="classlibecpint_1_1_radial_integral" prot="public">libecpint::RadialIntegral</innerclass>
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    <innerclass refid="structlibecpint_1_1_sum_term" prot="public">libecpint::SumTerm</innerclass>
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        <name>GCTYPE</name>
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          <name>ONEPOINT</name>
          <briefdescription>
<para>Described in Perez92. </para>
          </briefdescription>
          <detaileddescription>
          </detaileddescription>
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          <name>TWOPOINT</name>
          <briefdescription>
<para>Described in Perez93. </para>
          </briefdescription>
          <detaileddescription>
          </detaileddescription>
        </enumvalue>
        <briefdescription>
<para>Different choices of integration algorithm, see references. </para>
        </briefdescription>
        <detaileddescription>
        </detaileddescription>
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        </inbodydescription>
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        <definition>using libecpint::Pair = typedef std::tuple&lt;int, int&gt;</definition>
        <argsstring></argsstring>
        <name>Pair</name>
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        </briefdescription>
        <detaileddescription>
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        <type>std::tuple&lt; int, int, int &gt;</type>
        <definition>using libecpint::Triple = typedef std::tuple&lt;int, int, int&gt;</definition>
        <argsstring></argsstring>
        <name>Triple</name>
        <briefdescription>
        </briefdescription>
        <detaileddescription>
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        <type>std::tuple&lt; int, int, int, int, int &gt;</type>
        <definition>using libecpint::Quintuple = typedef std::tuple&lt;int, int, int, int, int&gt;</definition>
        <argsstring></argsstring>
        <name>Quintuple</name>
        <briefdescription>
        </briefdescription>
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        <type>std::tuple&lt; int, int, int, int, int, int, int &gt;</type>
        <definition>using libecpint::Heptuple = typedef std::tuple&lt;int, int, int, int, int, int, int&gt;</definition>
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        <name>Heptuple</name>
        <briefdescription>
        </briefdescription>
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        <type>double</type>
        <definition>double libecpint::FAC</definition>
        <argsstring>[MAX_FAC]</argsstring>
        <name>FAC</name>
        <briefdescription>
<para>Array of factorials. </para>
        </briefdescription>
        <detaileddescription>
        </detaileddescription>
        <inbodydescription>
        </inbodydescription>
        <location file="/Users/robertshaw/devfiles/libecpint/src/lib/mathutil.cpp" line="30" column="8" bodyfile="/Users/robertshaw/devfiles/libecpint/src/lib/mathutil.cpp" bodystart="30" bodyend="-1" declfile="/Users/robertshaw/devfiles/libecpint/include/libecpint/mathutil.hpp" declline="55" declcolumn="15"/>
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        <type>double</type>
        <definition>double libecpint::DFAC</definition>
        <argsstring>[MAX_DFAC]</argsstring>
        <name>DFAC</name>
        <briefdescription>
<para>Array of double factorials. </para>
        </briefdescription>
        <detaileddescription>
        </detaileddescription>
        <inbodydescription>
        </inbodydescription>
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        <argsstring></argsstring>
        <name>maxL</name>
        <initializer>= LIBECPINT_MAX_L</initializer>
        <briefdescription>
        </briefdescription>
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        <definition>const int libecpint::maxUnrol</definition>
        <argsstring></argsstring>
        <name>maxUnrol</name>
        <initializer>= LIBECPINT_MAX_UNROL</initializer>
        <briefdescription>
        </briefdescription>
        <detaileddescription>
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        </inbodydescription>
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        <type>const int</type>
        <definition>const int libecpint::maxN</definition>
        <argsstring></argsstring>
        <name>maxN</name>
        <initializer>= 15</initializer>
        <briefdescription>
        </briefdescription>
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        <definition>const int libecpint::CAX1</definition>
        <argsstring></argsstring>
        <name>CAX1</name>
        <initializer>= <ref refid="namespacelibecpint_1a6a8879ed7b1d299f2b2e92b105cce919" kindref="member">maxN</ref> + 1</initializer>
        <briefdescription>
        </briefdescription>
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        <definition>const int libecpint::CAX2</definition>
        <argsstring></argsstring>
        <name>CAX2</name>
        <initializer>= <ref refid="namespacelibecpint_1a02017a941eee202982bab7731ead620d" kindref="member">CAX1</ref> * (<ref refid="namespacelibecpint_1a190a564f849660c170e298aba2181d0a" kindref="member">maxL</ref> + 1)</initializer>
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        </briefdescription>
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        <type>const int</type>
        <definition>const int libecpint::CAX3</definition>
        <argsstring></argsstring>
        <name>CAX3</name>
        <initializer>= <ref refid="namespacelibecpint_1ae0ba3cdb903f3057f168bfaa5495bba0" kindref="member">CAX2</ref> * (<ref refid="namespacelibecpint_1a190a564f849660c170e298aba2181d0a" kindref="member">maxL</ref> + 1)</initializer>
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        <type>constexpr double</type>
        <definition>constexpr double libecpint::TWO_C_TOLERANCE</definition>
        <argsstring></argsstring>
        <name>TWO_C_TOLERANCE</name>
        <initializer>= 1E-12</initializer>
        <briefdescription>
        </briefdescription>
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        </detaileddescription>
        <inbodydescription>
        </inbodydescription>
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        <type>constexpr double</type>
        <definition>constexpr double libecpint::SMALL</definition>
        <argsstring></argsstring>
        <name>SMALL</name>
        <initializer>= 1.0E-7</initializer>
        <briefdescription>
<para>Numerical tolerance of z below which K_n(z) = { 1 (n=0), 0 otherwise }. </para>
        </briefdescription>
        <detaileddescription>
        </detaileddescription>
        <inbodydescription>
        </inbodydescription>
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        <type>constexpr int</type>
        <definition>constexpr int libecpint::TAYLOR_CUT</definition>
        <argsstring></argsstring>
        <name>TAYLOR_CUT</name>
        <initializer>= 5</initializer>
        <briefdescription>
<para>Order of local Taylor series to be used in Bessel function expansion. </para>
        </briefdescription>
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        </detaileddescription>
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        </inbodydescription>
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        <type>const std::string</type>
        <definition>const std::string libecpint::atom_names[109]</definition>
        <argsstring>[109]</argsstring>
        <name>atom_names</name>
        <initializer>= {&quot;h&quot;, &quot;he&quot;, &quot;li&quot;, &quot;be&quot;, &quot;b&quot;, &quot;c&quot;, &quot;n&quot;,
		&quot;o&quot;, &quot;f&quot;, &quot;ne&quot;, &quot;na&quot;, &quot;mg&quot;, &quot;al&quot;, &quot;si&quot;, &quot;p&quot;, &quot;s&quot;, &quot;cl&quot;, &quot;ar&quot;,
		&quot;k&quot;, &quot;ca&quot;, &quot;sc&quot;, &quot;ti&quot;, &quot;v&quot;, &quot;cr&quot;, &quot;mn&quot;, &quot;fe&quot;, &quot;co&quot;, &quot;ni&quot;, &quot;cu&quot;,
		&quot;zn&quot;, &quot;ga&quot;, &quot;ge&quot;, &quot;as&quot;, &quot;se&quot;, &quot;br&quot;, &quot;kr&quot;, &quot;rb&quot;, &quot;sr&quot;, &quot;y&quot;, &quot;zr&quot;,
		&quot;nb&quot;, &quot;mo&quot;, &quot;tc&quot;, &quot;ru&quot;, &quot;rh&quot;, &quot;pd&quot;, &quot;ag&quot;, &quot;cd&quot;, &quot;in&quot;, &quot;sn&quot;, &quot;sb&quot;,
		&quot;te&quot;, &quot;i&quot;, &quot;xe&quot;, &quot;cs&quot;, &quot;ba&quot;, &quot;la&quot;, &quot;ce&quot;, &quot;pr&quot;, &quot;nd&quot;, &quot;pm&quot;, &quot;sm&quot;,
		&quot;eu&quot;, &quot;gd&quot;, &quot;tb&quot;, &quot;dy&quot;, &quot;ho&quot;, &quot;er&quot;, &quot;tm&quot;, &quot;yb&quot;, &quot;lu&quot;, &quot;hf&quot;, &quot;ta&quot;,
		&quot;w&quot;, &quot;re&quot;, &quot;os&quot;, &quot;ir&quot;, &quot;pt&quot;, &quot;au&quot;, &quot;hg&quot;, &quot;tl&quot;, &quot;pb&quot;, &quot;bi&quot;, &quot;po&quot;,
		&quot;at&quot;, &quot;rn&quot;, &quot;fr&quot;, &quot;ra&quot;, &quot;ac&quot;, &quot;th&quot;, &quot;pa&quot;, &quot;u&quot;, &quot;np&quot;, &quot;pu&quot;, &quot;am&quot;,
		&quot;cm&quot;, &quot;bk&quot;, &quot;cf&quot;, &quot;es&quot;, &quot;fm&quot;, &quot;md&quot;, &quot;no&quot;, &quot;lr&quot;, &quot;rf&quot;, &quot;db&quot;, &quot;sg&quot;,
		&quot;bh&quot;, &quot;hs&quot;, &quot;mt&quot; }</initializer>
        <briefdescription>
<para>names of each atom in order of atomic number </para>
        </briefdescription>
        <detaileddescription>
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        <type>constexpr double</type>
        <definition>constexpr double libecpint::ROOT_PI</definition>
        <argsstring></argsstring>
        <name>ROOT_PI</name>
        <initializer>= 1.772453850905516</initializer>
        <briefdescription>
<para>square root of PI </para>
        </briefdescription>
        <detaileddescription>
        </detaileddescription>
        <inbodydescription>
        </inbodydescription>
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        <type>constexpr double</type>
        <definition>constexpr double libecpint::SINH_1</definition>
        <argsstring></argsstring>
        <name>SINH_1</name>
        <initializer>= 1.1752011936</initializer>
        <briefdescription>
        </briefdescription>
        <detaileddescription>
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        <inbodydescription>
        </inbodydescription>
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        <type>constexpr int</type>
        <definition>constexpr int libecpint::MAX_POW</definition>
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        <name>MAX_POW</name>
        <initializer>= 20</initializer>
        <briefdescription>
        </briefdescription>
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        </detaileddescription>
        <inbodydescription>
        </inbodydescription>
        <location file="/Users/robertshaw/devfiles/libecpint/include/libecpint/mathutil.hpp" line="53" column="15" bodyfile="/Users/robertshaw/devfiles/libecpint/include/libecpint/mathutil.hpp" bodystart="53" bodyend="-1"/>
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        <type>double(*</type>
        <definition>double(* libecpint::FAST_POW[23])(double)</definition>
        <argsstring>[23])(double)</argsstring>
        <name>FAST_POW</name>
        <briefdescription>
<para>Array of function pointers to hand-coded x**n routines. </para>
        </briefdescription>
        <detaileddescription>
        </detaileddescription>
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        </inbodydescription>
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        <type>const double</type>
        <definition>const double libecpint::GAMMA[30]</definition>
        <argsstring>[30]</argsstring>
        <name>GAMMA</name>
        <briefdescription>
        </briefdescription>
        <detaileddescription>
<para>Gamma function tabulation, where GAMMA[i] = Gamma((i+1)/2) e.g. GAMMA[0] = Gamma(1/2) = sqrt(Pi), GAMMA[1] = 0! = 1, GAMMA[2] = Gamma(3/2) = sqrt(Pi) / 2, etc. </para>
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        <type>constexpr double</type>
        <definition>constexpr double libecpint::MIN_EXP</definition>
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        <name>MIN_EXP</name>
        <initializer>= 0.002</initializer>
        <briefdescription>
        </briefdescription>
        <detaileddescription>
        </detaileddescription>
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        <type><ref refid="structlibecpint_1_1_two_index" kindref="compound">TwoIndex</ref>&lt; double &gt;</type>
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          <type>int</type>
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          <type>double</type>
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          <type>double</type>
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<para>Calculates real spherical harmonics S_lm(theta, phi) for all l, m up to lmax <parameterlist kind="param"><parameteritem>
<parameternamelist>
<parametername>lmax</parametername>
</parameternamelist>
<parameterdescription>
<para>- the maximum angular momentum needed </para>
</parameterdescription>
</parameteritem>
<parameteritem>
<parameternamelist>
<parametername>x</parametername>
</parameternamelist>
<parameterdescription>
<para>- cos(theta), where theta is the polar angle in spherical coordinates </para>
</parameterdescription>
</parameteritem>
<parameteritem>
<parameternamelist>
<parametername>phi</parametername>
</parameternamelist>
<parameterdescription>
<para>- the azimuth angle in spherical coordinates </para>
</parameterdescription>
</parameteritem>
</parameterlist>
<simplesect kind="return"><para>a matrix S(l, l+m) of the spherical harmonic values </para>
</simplesect>
</para>
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<para><parameterlist kind="param"><parameteritem>
<parameternamelist>
<parametername>mat</parametername>
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<parameterdescription>
<para>- a reference to a <ref refid="structlibecpint_1_1_two_index" kindref="compound">TwoIndex</ref> array </para>
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<simplesect kind="return"><para>the Frobenius norm of mat </para>
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          <type>std::ostream &amp;</type>
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          <param>
            <type>class Ch</type>
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          <param>
            <type>class Tr</type>
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          <param>
            <type>class...</type>
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            <defname>Args</defname>
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          <type>std::basic_ostream&lt; Ch, Tr &gt; &amp;</type>
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          <type>std::tuple&lt; Args... &gt; const &amp;</type>
          <declname>t</declname>
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          <param>
            <type>typename T</type>
          </param>
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        <type>int</type>
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        <name>check_file</name>
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          <type>std::string</type>
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        </param>
        <param>
          <type>std::vector&lt; T &gt; &amp;</type>
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<para>A helper function for tests that reads in a file of values and compares them to those provided by the test, returning 0 on success or 1 on failure.</para>
<para><parameterlist kind="templateparam"><parameteritem>
<parameternamelist>
<parametername>T</parametername>
</parameternamelist>
<parameterdescription>
<para>- the type of the value; must be pipeable from a stringstream. </para>
</parameterdescription>
</parameteritem>
</parameterlist>
<parameterlist kind="param"><parameteritem>
<parameternamelist>
<parametername>filename</parametername>
</parameternamelist>
<parameterdescription>
<para>- the file to read data from </para>
</parameterdescription>
</parameteritem>
<parameteritem>
<parameternamelist>
<parametername>results</parametername>
</parameternamelist>
<parameterdescription>
<para>- reference to the vector of calculated results </para>
</parameterdescription>
</parameteritem>
</parameterlist>
<simplesect kind="return"><para>0 if the results agree with the file within 0.00005%, 1 otherwise </para>
</simplesect>
</para>
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        </inbodydescription>
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    <detaileddescription>
    </detaileddescription>
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