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<h1 id="preglq">PreGLQ</h1>
<p>Calculate the weights and nodes used in integrating a function by Gauss-Legendre quadrature.</p>
<h1 id="usage">Usage</h1>
<p>call PreGLQ (<code>lower</code>, <code>upper</code>, <code>n</code>, <code>zero</code>, <code>w</code>, <code>exitstatus</code>)</p>
<h1 id="parameters">Parameters</h1>
<dl>
<dt><code>lower</code> : input, real*8</dt>
<dd>The lower bound of the integration.
</dd>
<dt><code>upper</code> : input, real*8</dt>
<dd>The upper bound of the integration.
</dd>
<dt><code>n</code> : input, integer</dt>
<dd>The number of integration points to use. This will integrate exactly a polynomial of degree <code>2n-1</code>.
</dd>
<dt><code>zero</code> : output, real*8, dimension (<code>n</code>)</dt>
<dd>The zeros used in the Gauss-Legendre quadrature.
</dd>
<dt><code>w</code> : output, real*8, dimension (<code>n</code>)</dt>
<dd>The weights used in the Gauss-Legendre quadrature.
</dd>
<dt><code>exitstatus</code> : output, optional, integer</dt>
<dd>If present, instead of executing a STOP when an error is encountered, the variable exitstatus will be returned describing the error. 0 = No errors; 1 = Improper dimensions of input array; 2 = Improper bounds for input variable; 3 = Error allocating memory; 4 = File IO error.
</dd>
</dl>
<h1 id="description">Description</h1>
<p><code>PreGLQ</code> will calculate the weights and zeros used to integrate a function using Gauss-Legendre quadrature. For <code>n</code> quadrature points, the integration will be exact if the function is a polynomial of degree <code>2n-1</code>, or less. The quadrature nodes correspond to the zeros of the Legendre polynomial of degree <code>n</code>. The number of quadrature points required to integrate a polynomial of degree <code>L</code> is <code>ceiling((L+1)/2)</code>.</p>
<p>To integrate a function between the bounds <code>lower</code> and <code>upper</code> it is only necessary to calculate the sum of the function evaluated at the nodes <code>zero</code> multiplied by the weights.</p>
<p>This is a slightly modified version of the algorithm that was published in NUMERICAL RECIPES.</p>
<h1 id="references">References</h1>
<p>Press, W.H., S.A. Teukolsky, W.T. Vetterling, and B.P. Flannery, Numerical Recipes in FORTRAN: The Art of Scientific Computing, 2nd ed., Cambridge Univ. Press, Cambridge, UK, 1992.</p>
<h1 id="see-also">See also</h1>
<p><a href="shglq.html">shglq</a></p>
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