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preglq.1
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preglq.1
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.\" ========================================================================
.\"
.IX Title "PREGLQ 1"
.TH PREGLQ 1 "2014-09-12" "SHTOOLS 3.0" "SHTOOLS 3.0"
.\" For nroff, turn off justification. Always turn off hyphenation; it makes
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.SH "PreGLQ"
.IX Header "PreGLQ"
.IP "PreGLQ \-" 9
.IX Item "PreGLQ -"
Calculate the weights and nodes used in integrating a function by Gauss-Legendre quadrature.
.SH "SYNOPSIS"
.IX Header "SYNOPSIS"
.IP "\s-1SUBROUTINE\s0 PreGLQ (" 20
.IX Item "SUBROUTINE PreGLQ ("
\&\s-1LOWER\s0, \s-1UPPER\s0, N, \s-1ZERO\s0, W )
.RS 4
.IP "REAL*8" 11
.IX Item "REAL*8"
\&\s-1LOWER\s0, \s-1UPPER\s0, \s-1ZERO\s0(N), W(N)
.IP "\s-1INTEGER\s0" 11
.IX Item "INTEGER"
N
.RE
.RS 4
.RE
.SH "DESCRIPTION"
.IX Header "DESCRIPTION"
\&\fIPreGLQ\fR will calculate the weights and zeros used to integrate a function using Gauss-Legendre quadrature. For N quadrature points, the integration will be exact if the function is a polynomial of degree 2N\-1, or less. The quadrature nodes correspond to the zeros of the Legendre polynomial of degree N. The number of quadrature points required to integrate a polynomial of degree L can be determined by a call to \fI\s-1NGLQ\s0\fR.
.PP
To integrate a function between the bounds \s-1LOWER\s0 and \s-1UPPER\s0 it is only necessary to calculate the sum of the function evaluated at the nodes \s-1ZERO\s0 multiplied by the weights.
.SH "ARGUMENTS"
.IX Header "ARGUMENTS"
.IP "\s-1LOWER\s0" 13
.IX Item "LOWER"
(input) REAL*8
.Sp
The lower bound of the integration.
.IP "\s-1UPPER\s0" 13
.IX Item "UPPER"
(input) REAL*8
.Sp
The upper bound of the integration.
.IP "N" 13
.IX Item "N"
(input) \s-1INTEGER\s0
.Sp
The number of integration points to use. This will integrate exactly a polynomial of degree 2*N\-1.
.IP "\s-1ZERO\s0" 13
.IX Item "ZERO"
(output) REAL*8, \s-1DIMENSION\s0 (N)
.Sp
The zeros used in the Gauss-Legendre quadrature.
.IP "W" 13
.IX Item "W"
(output) REAL*8, \s-1DIMENSION\s0 (N)
.Sp
The weights used in the Gauss-Legendre quadrature.
.SH "NOTES"
.IX Header "NOTES"
This is a slightly modified version of the algorithm that was published in \s-1NUMERICAL\s0 \s-1RECIPES\s0.
.SH "SEE ALSO"
.IX Header "SEE ALSO"
\&\fInglq\fR\|(1), \fInglqsh\fR\|(1), \fInglqshn\fR\|(1)
.PP
<http://shtools.ipgp.fr/>
.SH "REFERENCES"
.IX Header "REFERENCES"
Press, W.H., S.A. Teukolsky, W.T. Vetterling, and B.P. Flannery, Numerical Recipes in \s-1FORTRAN:\s0 The Art of Scientific Computing, 2nd ed., Cambridge Univ. Press, Cambridge, \s-1UK\s0, 1992.
.SH "COPYRIGHT AND LICENSE"
.IX Header "COPYRIGHT AND LICENSE"
Copyright 2012 by Mark Wieczorek <wieczor@ipgp.fr>.
.PP
This is free software; you can distribute and modify it under the terms of the revised \s-1BSD\s0 license.