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<body><h1>Numerical Recipes Routines by Chapter and Section</h1>
Chapter number links jump to the corresponding place in the
book Table of Contents. (Click on the Chapter number to get back.)
Routine name links jump to the listing
of the program. Example links jump to an example program that
shows the use of the routine.<p>
<h3><a name="C1"></A><A HREF="toc.htm#C1">Chapter
1</a></h3>
<menu>
<li>[1.0]
<a href="recipes/flmoon.cpp"><b>flmoon</b></a> calculate phases of the moon by date
(<a href="examples/xflmoon.cpp">example</a>)<li>[1.1]
<a href="recipes/julday.cpp"><b>julday</b></a> Julian Day number from calendar date
(<a href="examples/xjulday.cpp">example</a>)<li>[1.1]
<a href="recipes/badluk.cpp"><b>badluk</b></a> Friday the 13th when the moon is full
<li>[1.1]
<a href="recipes/caldat.cpp"><b>caldat</b></a> calendar date from Julian day number
(<a href="examples/xcaldat.cpp">example</a>)</menu>
<h3><a name="C2"></A><A HREF="toc.htm#C2">Chapter
2</a></h3>
<menu>
<li>[2.1]
<a href="recipes/gaussj.cpp"><b>gaussj</b></a> Gauss-Jordan matrix inversion and linear equation solution
(<a href="examples/xgaussj.cpp">example</a>)<li>[2.3]
<a href="recipes/ludcmp.cpp"><b>ludcmp</b></a> linear equation solution, LU decomposition
(<a href="examples/xludcmp.cpp">example</a>)<li>[2.3]
<a href="recipes/lubksb.cpp"><b>lubksb</b></a> linear equation solution, backsubstitution
(<a href="examples/xlubksb.cpp">example</a>)<li>[2.4]
<a href="recipes/tridag.cpp"><b>tridag</b></a> solution of tridiagonal systems
(<a href="examples/xtridag.cpp">example</a>)<li>[2.4]
<a href="recipes/banmul.cpp"><b>banmul</b></a> multiply vector by band diagonal matrix
(<a href="examples/xbanmul.cpp">example</a>)<li>[2.4]
<a href="recipes/bandec.cpp"><b>bandec</b></a> band diagonal systems, decomposition
(<a href="examples/xbandec.cpp">example</a>)<li>[2.4]
<a href="recipes/banbks.cpp"><b>banbks</b></a> band diagonal systems, backsubstitution
<li>[2.5]
<a href="recipes/mprove.cpp"><b>mprove</b></a> linear equation solution, iterative improvement
(<a href="examples/xmprove.cpp">example</a>)<li>[2.6]
<a href="recipes/svbksb.cpp"><b>svbksb</b></a> singular value backsubstitution
(<a href="examples/xsvbksb.cpp">example</a>)<li>[2.6]
<a href="recipes/svdcmp.cpp"><b>svdcmp</b></a> singular value decomposition of a matrix
(<a href="examples/xsvdcmp.cpp">example</a>)<li>[2.6]
<a href="recipes/pythag.cpp"><b>pythag</b></a> calculate (a^2+b^2)^{1/2} without overflow
<li>[2.7]
<a href="recipes/cyclic.cpp"><b>cyclic</b></a> solution of cyclic tridiagonal systems
(<a href="examples/xcyclic.cpp">example</a>)<li>[2.7]
<a href="recipes/sprsin.cpp"><b>sprsin</b></a> convert matrix to sparse format
(<a href="examples/xsprsin.cpp">example</a>)<li>[2.7]
<a href="recipes/sprsax.cpp"><b>sprsax</b></a> product of sparse matrix and vector
(<a href="examples/xsprsax.cpp">example</a>)<li>[2.7]
<a href="recipes/sprstx.cpp"><b>sprstx</b></a> product of transpose sparse matrix and vector
(<a href="examples/xsprstx.cpp">example</a>)<li>[2.7]
<a href="recipes/sprstp.cpp"><b>sprstp</b></a> transpose of sparse matrix
(<a href="examples/xsprstp.cpp">example</a>)<li>[2.7]
<a href="recipes/sprspm.cpp"><b>sprspm</b></a> pattern multiply two sparse matrices
(<a href="examples/xsprspm.cpp">example</a>)<li>[2.7]
<a href="recipes/sprstm.cpp"><b>sprstm</b></a> threshold multiply two sparse matrices
(<a href="examples/xsprstm.cpp">example</a>)<li>[2.7]
<a href="recipes/linbcg.cpp"><b>linbcg</b></a> biconjugate gradient solution of sparse systems
(<a href="examples/xlinbcg.cpp">example</a>)<li>[2.7]
<a href="recipes/snrm.cpp"><b>snrm </b></a> used by linbcg for vector norm
<li>[2.7]
<a href="recipes/atimes.cpp"><b>atimes</b></a> used by linbcg for sparse multiplication
<li>[2.7]
<a href="recipes/asolve.cpp"><b>asolve</b></a> used by linbcg for preconditioner
<li>[2.8]
<a href="recipes/vander.cpp"><b>vander</b></a> solve Vandermonde systems
(<a href="examples/xvander.cpp">example</a>)<li>[2.8]
<a href="recipes/toeplz.cpp"><b>toeplz</b></a> solve Toeplitz systems
(<a href="examples/xtoeplz.cpp">example</a>)<li>[2.9]
<a href="recipes/choldc.cpp"><b>choldc</b></a> Cholesky decomposition
<li>[2.9]
<a href="recipes/cholsl.cpp"><b>cholsl</b></a> Cholesky backsubstitution
(<a href="examples/xcholsl.cpp">example</a>)<li>[2.10]
<a href="recipes/qrdcmp.cpp"><b>qrdcmp</b></a> QR decomposition
(<a href="examples/xqrdcmp.cpp">example</a>)<li>[2.10]
<a href="recipes/qrsolv.cpp"><b>qrsolv</b></a> QR backsubstitution
(<a href="examples/xqrsolv.cpp">example</a>)<li>[2.10]
<a href="recipes/rsolv.cpp"><b>rsolv</b></a> right triangular backsubstitution
<li>[2.10]
<a href="recipes/qrupdt.cpp"><b>qrupdt</b></a> update a QR decomposition
(<a href="examples/xqrupdt.cpp">example</a>)<li>[2.10]
<a href="recipes/rotate.cpp"><b>rotate</b></a> Jacobi rotation used by qrupdt
</menu>
<h3><a name="C3"></A><A HREF="toc.htm#C3">Chapter
3</a></h3>
<menu>
<li>[3.1]
<a href="recipes/polint.cpp"><b>polint</b></a> polynomial interpolation
(<a href="examples/xpolint.cpp">example</a>)<li>[3.2]
<a href="recipes/ratint.cpp"><b>ratint</b></a> rational function interpolation
(<a href="examples/xratint.cpp">example</a>)<li>[3.3]
<a href="recipes/spline.cpp"><b>spline</b></a> construct a cubic spline
(<a href="examples/xspline.cpp">example</a>)<li>[3.3]
<a href="recipes/splint.cpp"><b>splint</b></a> cubic spline interpolation
(<a href="examples/xsplint.cpp">example</a>)<li>[3.4]
<a href="recipes/locate.cpp"><b>locate</b></a> search an ordered table by bisection
(<a href="examples/xlocate.cpp">example</a>)<li>[3.4]
<a href="recipes/hunt.cpp"><b>hunt</b></a> search a table when calls are correlated
(<a href="examples/xhunt.cpp">example</a>)<li>[3.5]
<a href="recipes/polcoe.cpp"><b>polcoe</b></a> polynomial coefficients from table of values
(<a href="examples/xpolcoe.cpp">example</a>)<li>[3.5]
<a href="recipes/polcof.cpp"><b>polcof</b></a> polynomial coefficients from table of values
(<a href="examples/xpolcof.cpp">example</a>)<li>[3.6]
<a href="recipes/polin2.cpp"><b>polin2</b></a> two-dimensional polynomial interpolation
(<a href="examples/xpolin2.cpp">example</a>)<li>[3.6]
<a href="recipes/bcucof.cpp"><b>bcucof</b></a> construct two-dimensional bicubic
(<a href="examples/xbcucof.cpp">example</a>)<li>[3.6]
<a href="recipes/bcuint.cpp"><b>bcuint</b></a> two-dimensional bicubic interpolation
(<a href="examples/xbcuint.cpp">example</a>)<li>[3.6]
<a href="recipes/splie2.cpp"><b>splie2</b></a> construct two-dimensional spline
(<a href="examples/xsplie2.cpp">example</a>)<li>[3.6]
<a href="recipes/splin2.cpp"><b>splin2</b></a> two-dimensional spline interpolation
(<a href="examples/xsplin2.cpp">example</a>)</menu>
<h3><a name="C4"></A><A HREF="toc.htm#C4">Chapter
4</a></h3>
<menu>
<li>[4.2]
<a href="recipes/trapzd.cpp"><b>trapzd</b></a> trapezoidal rule
(<a href="examples/xtrapzd.cpp">example</a>)<li>[4.2]
<a href="recipes/qtrap.cpp"><b>qtrap</b></a> integrate using trapezoidal rule
(<a href="examples/xqtrap.cpp">example</a>)<li>[4.2]
<a href="recipes/qsimp.cpp"><b>qsimp</b></a> integrate using Simpson's rule
(<a href="examples/xqsimp.cpp">example</a>)<li>[4.3]
<a href="recipes/qromb.cpp"><b>qromb</b></a> integrate using Romberg adaptive method
(<a href="examples/xqromb.cpp">example</a>)<li>[4.4]
<a href="recipes/midpnt.cpp"><b>midpnt</b></a> extended midpoint rule
(<a href="examples/xmidpnt.cpp">example</a>)<li>[4.4]
<a href="recipes/qromo.cpp"><b>qromo</b></a> integrate using open Romberg adaptive method
(<a href="examples/xqromo.cpp">example</a>)<li>[4.4]
<a href="recipes/midinf.cpp"><b>midinf</b></a> integrate a function on a semi-infinite interval
<li>[4.4]
<a href="recipes/midsql.cpp"><b>midsql</b></a> integrate a function with lower square-root singularity
<li>[4.4]
<a href="recipes/midsqu.cpp"><b>midsqu</b></a> integrate a function with upper square-root singularity
<li>[4.4]
<a href="recipes/midexp.cpp"><b>midexp</b></a> integrate a function that decreases exponentially
<li>[4.5]
<a href="recipes/qgaus.cpp"><b>qgaus</b></a> integrate a function by Gaussian quadratures
(<a href="examples/xqgaus.cpp">example</a>)<li>[4.5]
<a href="recipes/gauleg.cpp"><b>gauleg</b></a> Gauss-Legendre weights and abscissas
(<a href="examples/xgauleg.cpp">example</a>)<li>[4.5]
<a href="recipes/gaulag.cpp"><b>gaulag</b></a> Gauss-Laguerre weights and abscissas
(<a href="examples/xgaulag.cpp">example</a>)<li>[4.5]
<a href="recipes/gauher.cpp"><b>gauher</b></a> Gauss-Hermite weights and abscissas
(<a href="examples/xgauher.cpp">example</a>)<li>[4.5]
<a href="recipes/gaujac.cpp"><b>gaujac</b></a> Gauss-Jacobi weights and abscissas
(<a href="examples/xgaujac.cpp">example</a>)<li>[4.5]
<a href="recipes/gaucof.cpp"><b>gaucof</b></a> quadrature weights from orthogonal polynomials
(<a href="examples/xgaucof.cpp">example</a>)<li>[4.5]
<a href="recipes/orthog.cpp"><b>orthog</b></a> construct nonclassical orthogonal polynomials
(<a href="examples/xorthog.cpp">example</a>)<li>[4.6]
<a href="recipes/quad3d.cpp"><b>quad3d</b></a> integrate a function over a three-dimensional space
(<a href="examples/xquad3d.cpp">example</a>)</menu>
<h3><a name="C5"></A><A HREF="toc.htm#C5">Chapter
5</a></h3>
<menu>
<li>[5.1]
<a href="recipes/eulsum.cpp"><b>eulsum</b></a> sum a series by Euler--van Wijngaarden algorithm
(<a href="examples/xeulsum.cpp">example</a>)<li>[5.3]
<a href="recipes/ddpoly.cpp"><b>ddpoly</b></a> evaluate a polynomial and its derivatives
(<a href="examples/xddpoly.cpp">example</a>)<li>[5.3]
<a href="recipes/poldiv.cpp"><b>poldiv</b></a> divide one polynomial by another
(<a href="examples/xpoldiv.cpp">example</a>)<li>[5.3]
<a href="recipes/ratval.cpp"><b>ratval</b></a> evaluate a rational function
<li>[5.7]
<a href="recipes/dfridr.cpp"><b>dfridr</b></a> numerical derivative by Ridders' method
(<a href="examples/xdfridr.cpp">example</a>)<li>[5.8]
<a href="recipes/chebft.cpp"><b>chebft</b></a> fit a Chebyshev polynomial to a function
(<a href="examples/xchebft.cpp">example</a>)<li>[5.8]
<a href="recipes/chebev.cpp"><b>chebev</b></a> Chebyshev polynomial evaluation
(<a href="examples/xchebev.cpp">example</a>)<li>[5.9]
<a href="recipes/chder.cpp"><b>chder</b></a> derivative of a function already Chebyshev fitted
(<a href="examples/xchder.cpp">example</a>)<li>[5.9]
<a href="recipes/chint.cpp"><b>chint</b></a> integrate a function already Chebyshev fitted
(<a href="examples/xchint.cpp">example</a>)<li>[5.10]
<a href="recipes/chebpc.cpp"><b>chebpc</b></a> polynomial coefficients from a Chebyshev fit
(<a href="examples/xchebpc.cpp">example</a>)<li>[5.10]
<a href="recipes/pcshft.cpp"><b>pcshft</b></a> polynomial coefficients of a shifted polynomial
(<a href="examples/xpcshft.cpp">example</a>)<li>[5.11]
<a href="recipes/pccheb.cpp"><b>pccheb</b></a> inverse of chebpc; use to economize power series
(<a href="examples/xpccheb.cpp">example</a>)<li>[5.12]
<a href="recipes/pade.cpp"><b>pade</b></a> Pade approximant from power series coefficients
(<a href="examples/xpade.cpp">example</a>)<li>[5.13]
<a href="recipes/ratlsq.cpp"><b>ratlsq</b></a> rational fit by least-squares method
(<a href="examples/xratlsq.cpp">example</a>)</menu>
<h3><a name="C6"></A><A HREF="toc.htm#C6">Chapter
6</a></h3>
<menu>
<li>[6.1]
<a href="recipes/gammln.cpp"><b>gammln</b></a> logarithm of gamma function
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