c0-2 (Numerical Recipes in C)

Computer Programsby Chapter and Sectionflmoonjuldaybadlukcaldatcalculate phases of the moon by dateJulian Day number from calendar dateFriday the 13th when the moon is fullcalendar date from Julian day number2.1gaussj2.32.32.42.42.42.42.52.62.62.62.72.72.72.72.72.72.72.72.72.72.72.82.82.92.92.102.102.102.102.10ludcmplubksbtridagbanmulbandecbanbksmprovesvbksbsvdcmppythagcyclicsprsinsprsaxsprstxsprstpsprspmsprstmlinbcgsnrmatimesasolvevandertoeplzcholdccholslqrdcmpqrsolvrsolvqrupdtrotateGauss-Jordan matrix inversion and linear equationsolutionlinear equation solution, LU decompositionlinear equation solution, backsubstitutionsolution of tridiagonal systemsmultiply vector by band diagonal matrixband diagonal systems, decompositionband diagonal systems, backsubstitutionlinear equation solution, iterative improvementsingular value backsubstitutionsingular value decomposition of a matrixcalculate (a2 + b2 )1/2 without overflowsolution of cyclic tridiagonal systemsconvert matrix to sparse formatproduct of sparse matrix and vectorproduct of transpose sparse matrix and vectortranspose of sparse matrixpattern multiply two sparse matricesthreshold multiply two sparse matricesbiconjugate gradient solution of sparse systemsused by linbcg for vector normused by linbcg for sparse multiplicationused by linbcg for preconditionersolve Vandermonde systemssolve Toeplitz systemsCholesky decompositionCholesky backsubstitutionQR decompositionQR backsubstitutionright triangular backsubstitutionupdate a QR decompositionJacobi rotation used by qrupdt3.13.23.33.33.4polintratintsplinesplintlocatepolynomial interpolationrational function interpolationconstruct a cubic splinecubic spline interpolationsearch an ordered table by bisectionxixSample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521-43108-5)Copyright (C) 1988-1992 by Cambridge University Press.Programs Copyright (C) 1988-1992 by Numerical Recipes Software.Permission is granted for internet users to make one paper copy for their own personal use.

Further reproduction, or any copying of machinereadable files (including this one) to any servercomputer, is strictly prohibited. To order Numerical Recipes books,diskettes, or CDROMsvisit website http://www.nr.com or call 1-800-872-7423 (North America only),or send email to trade@cup.cam.ac.uk (outside North America).1.01.11.11.1xxComputer Programs by Chapter and Sectionhuntpolcoepolcofpolin2bcucofbcuintsplie2splin2search a table when calls are correlatedpolynomial coefficients from table of valuespolynomial coefficients from table of valuestwo-dimensional polynomial interpolationconstruct two-dimensional bicubictwo-dimensional bicubic interpolationconstruct two-dimensional splinetwo-dimensional spline interpolation4.24.24.24.34.44.44.44.44.44.44.54.54.54.54.54.54.54.6trapzdqtrapqsimpqrombmidpntqromomidinfmidsqlmidsqumidexpqgausgauleggaulaggauhergaujacgaucoforthogquad3dtrapezoidal ruleintegrate using trapezoidal ruleintegrate using Simpson’s ruleintegrate using Romberg adaptive methodextended midpoint ruleintegrate using open Romberg adaptive methodintegrate a function on a semi-infinite intervalintegrate a function with lower square-root singularityintegrate a function with upper square-root singularityintegrate a function that decreases exponentiallyintegrate a function by Gaussian quadraturesGauss-Legendre weights and abscissasGauss-Laguerre weights and abscissasGauss-Hermite weights and abscissasGauss-Jacobi weights and abscissasquadrature weights from orthogonal polynomialsconstruct nonclassical orthogonal polynomialsintegrate a function over a three-dimensional space5.15.35.35.35.75.85.85.95.95.105.105.115.125.13eulsumddpolypoldivratvaldfridrchebftchebevchderchintchebpcpcshftpcchebpaderatlsqsum a series by Euler–van Wijngaarden algorithmevaluate a polynomial and its derivativesdivide one polynomial by anotherevaluate a rational functionnumerical derivative by Ridders’ methodfit a Chebyshev polynomial to a functionChebyshev polynomial evaluationderivative of a function already Chebyshev fittedintegrate a function already Chebyshev fittedpolynomial coefficients from a Chebyshev fitpolynomial coefficients of a shifted polynomialinverse of chebpc; use to economize power seriesPadé approximant from power series coefficientsrational fit by least-squares method6.16.16.16.1gammlnfactrlbicofactlnlogarithm of gamma functionfactorial functionbinomial coefficients functionlogarithm of factorial functionSample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521-43108-5)Copyright (C) 1988-1992 by Cambridge University Press.Programs Copyright (C) 1988-1992 by Numerical Recipes Software.Permission is granted for internet users to make one paper copy for their own personal use.

Further reproduction, or any copying of machinereadable files (including this one) to any servercomputer, is strictly prohibited. To order Numerical Recipes books,diskettes, or CDROMsvisit website http://www.nr.com or call 1-800-872-7423 (North America only),or send email to trade@cup.cam.ac.uk (outside North America).3.43.53.53.63.63.63.63.6Computer Programs by Chapter and Sectionxxibetagammpgammqgsergcferfferffcerfccexpinteibetaibetacfbessj0bessy0bessj1bessy1bessybessjbessi0bessk0bessi1bessk1besskbessibessjybeschbbessikairysphbesplgndrfrenelcisidawsonrfrdrjrcellfelleellpisncndnhypgeohypserhypdrvbeta functionincomplete gamma functioncomplement of incomplete gamma functionseries used by gammp and gammqcontinued fraction used by gammp and gammqerror functioncomplementary error functioncomplementary error function, concise routineexponential integral Enexponential integral Eiincomplete beta functioncontinued fraction used by betaiBessel function J0Bessel function Y0Bessel function J1Bessel function Y1Bessel function Y of general integer orderBessel function J of general integer ordermodified Bessel function I0modified Bessel function K0modified Bessel function I1modified Bessel function K1modified Bessel function K of integer ordermodified Bessel function I of integer orderBessel functions of fractional orderChebyshev expansion used by bessjymodified Bessel functions of fractional orderAiry functionsspherical Bessel functions jn and ynLegendre polynomials, associated (spherical harmonics)Fresnel integrals S(x) and C(x)cosine and sine integrals Ci and SiDawson’s integralCarlson’s elliptic integral of the first kindCarlson’s elliptic integral of the second kindCarlson’s elliptic integral of the third kindCarlson’s degenerate elliptic integralLegendre elliptic integral of the first kindLegendre elliptic integral of the second kindLegendre elliptic integral of the third kindJacobian elliptic functionscomplex hypergeometric functioncomplex hypergeometric function, series evaluationcomplex hypergeometric function, derivative of7.17.1ran0ran1random deviate by Park and Miller minimal standardrandom deviate, minimal standard plus shuffleSample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521-43108-5)Copyright (C) 1988-1992 by Cambridge University Press.Programs Copyright (C) 1988-1992 by Numerical Recipes Software.Permission is granted for internet users to make one paper copy for their own personal use.

Further reproduction, or any copying of machinereadable files (including this one) to any servercomputer, is strictly prohibited. To order Numerical Recipes books,diskettes, or CDROMsvisit website http://www.nr.com or call 1-800-872-7423 (North America only),or send email to trade@cup.cam.ac.uk (outside North America).6.16.26.26.26.26.26.26.26.36.36.46.46.56.56.56.56.56.56.66.66.66.66.66.66.76.76.76.76.76.86.96.96.106.116.116.116.116.116.116.116.116.126.126.12xxiiComputer Programs by Chapter and Sectionran2ran3expdevgasdevgamdevpoidevbnldevirbit1irbit2psdesran4sobseqvegasrebinmiserranptrandom deviate by L’Ecuyer long period plus shufflerandom deviate by Knuth subtractive methodexponential random deviatesnormally distributed random deviatesgamma-law distribution random deviatesPoisson distributed random deviatesbinomial distributed random deviatesrandom bit sequencerandom bit sequence“pseudo-DES” hashing of 64 bitsrandom deviates from DES-like hashingSobol’s quasi-random sequenceadaptive multidimensional Monte Carlo integrationsample rebinning used by vegasrecursive multidimensional Monte Carlo integrationget random point, used by miser8.18.18.18.28.28.38.48.48.48.58.58.58.68.6piksrtpiksr2shellsortsort2hpsortindexxsort3rankselectseliphpseleclasseclazzsort an array by straight insertionsort two arrays by straight insertionsort an array by Shell’s methodsort an array by quicksort methodsort two arrays by quicksort methodsort an array by heapsort methodconstruct an index for an arraysort, use an index to sort 3 or more arraysconstruct a rank table for an arrayfind the N th largest in an arrayfind the N th largest, without altering an arrayfind M largest values, without altering an arraydetermine equivalence classes from listdetermine equivalence classes from procedure9.09.19.19.19.29.29.29.39.49.49.59.5scrshozbraczbrakrtbisrtflsprtseczriddrzbrentrtnewtrtsafelaguerzroots9.59.5zrhqrqrootgraph a function to search for rootsoutward search for brackets on rootsinward search for brackets on rootsfind root of a function by bisectionfind root of a function by false-positionfind root of a function by secant methodfind root of a function by Ridders’ methodfind root of a function by Brent’s methodfind root of a function by Newton-Raphsonfind root of a function by Newton-Raphson and bisectionfind a root of a polynomial by Laguerre’s methodroots of a polynomial by Laguerre’s method withdeflationroots of a polynomial by eigenvalue methodscomplex or double root of a polynomial, BairstowSample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521-43108-5)Copyright (C) 1988-1992 by Cambridge University Press.Programs Copyright (C) 1988-1992 by Numerical Recipes Software.Permission is granted for internet users to make one paper copy for their own personal use.