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boost c++ librariesNSWC Mathematics Subroutine Library
NSWC LIBRARY TABLE OF CONTENTS
Elementary Operations
Machine Constants Q SPMPAR, DPMPAR, IPPMAR .................3 Argument Bounds for the Exponential Function   EPSLN, EXPARG, DEPSLN, DXPARG..........................5 Sorting Lists Q ISHELL, SHELL, AORD, RISORT, SHELL2, DSORT,  DAORD, DISORT, DDSORT, QSORTI, QSORTR, QSORTD, IORDER,  RORDER, DORDER ........................................7 Cube Root  CBRT, DCBRT ...................................11 Four Quadrant Arctangent  ARTNQ, DARTNQ...................11 Length of a TwoDimensional Vector  CPABS, DCPABS ........11 Reciprocal of a Complex Number  CREC, DCREC ..............13 Division of a Complex Number  CDVI,DIVID..................13 Square Root of a Double Precision Complex Number  DCSQR...13 Conversion of Polar to Cartesian Coordinates Q POCA .......15 Conversion of Cartesian to Polar Coordinates  CAPO .......15 Rotation of Axes  ROTA ...................................15 Planar Givens Rotations  SROTG, DROTG ....................17 Three Dimension Rotations  ROT3 ..........................19 Rotation of a Point on the Unit Sphere to the North Pole  CONSTR ...............................................21 Computation of the Angle Between Two Vectors  ANG ........23 Trigonometric Functions  SIN1, COS1, DSIN1, DCOS1 ........25 Hyperbolic Sine and Cosine Functions SNHCSH ...............27 Exponentials Q REXP, DREXP ................................29 Logarithms  ALNREL, RLOG, RLOG1, DLNREL, DRLOG, DRLOG1 ...31
Geometry
Determining if a Point is Inside or Outside a Polygon  LOCPT ................................................33 Intersection of a Straight Line and Polygonal Path  PFIND.35 The Convex Hull for a Finite Planar Set Q HULL ............37 Areas of Planar Polygons  PAREA ..........................39 Hamiltonian Circuits  HC .................................41
Special Functions
Error Function  CERF, CERFC, ERF, ERFC, ERFC1, DCERF, DCERFC, DERF, DERFC, DERFC1 ...........................45 Inverse Error Function  ERFI, DERFI ......................51 Difference of Error Function  AERF, DAERF ................53 Normal Probability Distribution Function  PNDF ...........55 Inverse Normal Probability Distribution Function  PNI,DPNI ..............................................57 Dawson's Integral  DAW, DPDAW ............................59 Complex Fresnel Integral  CFRNLI .........................61 Real Fresnel Integrals  FRNL .............................63 Exponential Integral Function  CEXPLI, EXPLI, DEI, DEI1 ..65 Sine and Cosine Integral Functions  SI, CIN ..............69 Exponential Exponential Integral Function  CEXEXI ........71 Dilogarithm Function  CLI, ALI ...........................73 Gamma Function  CGAMMA, GAMMA, GAMLN, DCGAMA, DGAMMA, DGAMLN .......................................75 Digamma Function  CPSI, PSI, DCPSI, DPSI .................79 Derivatives of the Digamma Function  PSIDF ...............81 Incomplete Gamma Ratio Functions  GRATIO, RCOMP, DGRAT, DRCOMP ...............................................83 Inverse Incomplete Gamma Ratio Function  GAMINV, DGINV ...85 Logarithm of the Beta Function Q BETALN, DBETLN ...........87 Incomplete Beta Function  BRATIO, ISUBX, BRCOMP ..........89 Bessel Function Jv(z)  CBSSLJ,BSSLJ, BESJ ................91 Bessel Function Yv(z)  BSSLY .............................93 Modified Bessel Function Iv(Z)  CBSSLI, BSSLI, BESI ......95 Modified Bessel Function Kv(z)  CBESK, CBSSLK, BSSLK .....97 Airy Functions  CAI, CBI, AI, AIE, BI, BIE ...............99 Complete Complex Elliptic Integrals of the First and Second Kinds  CK, CKE ..............................103 Real Elliptic Integrals of the First and Second Kinds  ELLPI, RFVAL, RDVAL, DELLPI, DRFVAL, DRDVAL .........107 Real Elliptic Integrals of the Third Kind  EPI, RJVAL, DEPI, DRJVAL ............................111 Jacobian Elliptic Functions  ELLPF, ELPFC1 ..............115 Weierstrass Elliptic Function for the Equianharmonic and Lemniscatic Cases  PEQ, PEQ1, PLEM, PLEM1 ......119 Integral of the Bivariate Density Function over Arbitrary Polygons and Semiinfinite Angular Regions  VALR2 ..123 Circular Coverage Function  CIRCV .......................125 Elliptical Coverage Function Q PKILL .....................127
Polynomials
Copying Polynomials  PLCOPY, DPCOPY .....................129 Addition of Polynomials  PADD, DPADD ....................131 Subtraction of Polynomials  PSUBT, DPSUBST ..............133 Multiplication of Polynomials  PMULT, DPMULT ............135 Division of Polynomials Q PDIV, DPDIV ....................137 Real Powers of Polynomials  PLPWR, DPLPWR ...............139 Inverses of Power Series  PINV, DPINV ...................141 Derivatives and Integrals of Polynomials  MPLNMV ........143 Evaluation of Chebyshev Expansions  CSEVL, DCSEVL .......145 Lagrange Polynomials Q LGRNGN, LGRNGV, LRGNGX ............147 Orthogonal Polynomials on Finite Sets  ORTHOS, ORTHOV, ORTHOX ..............................................149
Solutions of Nonlinear Equations
Zeros of Continuous Functions  ZEROIN, DZERO ............151 Solution of Systems of Nonlinear Equations  HBRD ........153 Solutions of Quadratic, Cubic, and Quartic Equations  QDCRT, CBCRT, QTCRT, DQDCRT, DCBCRT, DQTCRT ........155 Double Precision Roots of Polynomials  DRPOLY, DCPOLY ...157 Accuracy of the Roots of Polynomial  RBND, CBND .........159
Vectors
Copying Vectors Q SCOPY, DCOPY, CCOPY ....................161 Interchanging Vectors  SSWAP, DSWAP, CSWAP ..............163 Planar Rotation of Vectors  SROT, DROT, CSROT ...........165 Modified Givens Rotations  SROTMG, DROTMG, SROTM, DROTM .167 Dot Products of Vectors  SDOT, DDOT, CDOTC, CDOTU .......171 Scaling Vectors  SSCAL, DSCAL, CSCAL, CSSCAL ............173 Vector Addition  SAXPY, DAXPY, CAXPY ....................175 Ll Norm of a Vector  SASUM, DASUM, SCASUM ...............177 L2 Norm of a Vector Q SNRM2, DNRM2, SCNRM2 ...............179 L0 Norm of a Vector  ISAMAX, IDAMAX, ICAMAX .............181
Matrices
Packing and Unpacking Symmetric Matrices  MCVFS, DMCVFS, MCVSF, DMCVSF .......................................183 Conversion of Real Matrices to and from Double Precision Form  MCVRD, MDCVDR ................................185 Storage of Real Matrices in the Complex Matrix Format  MCVRC ...............................................187 The Real and Imaginary Parts of a Complex Matrix  CMREAL, CMIMAG.......................................189 Copying matrices  MCOPY, SMCOPY, DMCOPY, CMCOPY .........191 Computation of the Conjugate of a Complex Matrix  CMCONJ.193 Transposing Matrices Q TPOSE, DTPOSE, CTPOSE, TIP, DTIP, CTIP ..........................................195 Computing Adjoints of Complex Matrices  CMADJ, CTRANS ...197 Matrix Addition  MADD, SMADD, DMADD, CMADD ..............199 Matrix Subtraction  MSUBT, SMSUBT, DMSUBT, CMSUBT .......201 Matrix Multiplication  MTMS, DMTMS, CMTMS, MPROD, DMPROD, CMPROD ......................................203 Product of a Packed Symmetric Matrix and a Vector  SVPRD, DSVPRD .......................................205 Transpose Matrix Products  TMPROD .......................207 Symmetric Matrix Products  SMPROD .......................209 Kronecker Product of Matrices  KPROD, DKPROD, CKPROD ....211 Rank of a Real Matrix  RNK, DRNK ........................213 Inverting General Real Matrices and Solving General  Systems of Real Linear Equations  CROUT,KROUT,  NPIVOT, MSLV, DMSLV, MSLV1, DMSLV1 ............... 215 Solutions of Real Equations with Iterative Improvement  SLVMP ...............................................221 Solutions of Almost Block Diagonal Systems of Linear Equations  ARCECO, ARCESL ..........................223 Solution of Almost Block Tridiagonal Systems of Linear Equations Q BTSLV ...................................225 Inverting Symmetric Real Matrices and Solving Symmetric Systems of Real Linear Equations  SMSLV, DSMSLV ....227 Inverting Positive Definite Symmetric Matrices and Solving Positive Definite Symmetric Systems of Linear Equations  PCHOL,DPCHOL .....................231 Solution of Toeplitz Systems of Linear Equations  TOPLX, DTOPLX .......................................233 Inverting General Complex Matrices and Solving General Systems of Complex Linear Equations  CMSLV, CMSLV1, DCMSLV ...............................235 Solution of Complex Equations with Iterative Improvement  CSLVMP ..............................................239 Singular Value Decomposition of a Matrix  SSVDC,DSVDC, CSVDC ...............................................241 Evaluation of the Characteristic Polynomial of a Matrix  DET, DPDET, CDET ...........................243 Solution of the Matrix Equation AX + XB = C  ABSLV, DABSLV .......................................245 Solution of the Matrix Equation AtX + XA = C where C is Symmetric  TASLV, DTASLV ...........................247 Solution of the Matrix Equation  AX2 + BX + C = O  SQUINT ..............................................249 Exponential of a Real Matrix  MEXP, DMEXP ...............251
Large Dense Systems of Linear Equations
Solving systems of 200400 Linear Equations  LE, DPLE, CLE .......................................253
Banded Matrices
Band Matrix Storage ......................................255 Conversion of Banded Matrices to and from the  Standard Format  CVBR, CVBD, CVBC, CVRB,  CVDB, CVCB, CVRB1,CVDB1, CVCB1 ......................257 Conversion of Banded Matrices to and from Sparse Form   MCVBS, DMCVBS, CMCVBS, MCVSB, DMCVSB, CMCVSB ....... 259 Conversion of Banded Real Matrices to and from  Double Precision Form  BCVRD, BCVDR ............... 261 The Real and Imaginary Parts of a Banded  Complex Matrix  BREAL, BIMAG .................... 263 Computing A + Bi for Banded Real Matrices A and B  BCVR..265 Transposing Banded Matrices Q BPOSE, DBPOSE, CBPOSE ......267 Addition of Banded Matrices  BADD, DBADD, CBADD .........269 Subtraction of Banded Matrices  BSUBT, DBSUBT, CBSUBT ...271 Multiplication of Banded Matrices  BPROD,DBPROD,CBPROD ..273 Product of a Real Banded Matrix and Vector  BVPRD, BVPRD1, BTPRD, BTPRD1 .................. 275 Product of a Double Precision Banded Matrix and Vector  DBVPD, DBVPD1, DBTPD, DBTPD1 ........................277 Product of a Complex Banded Matrix and Vector  CBVPD, CBVPD1, CBTPD, CBTPD1 ..................... 279 L1 Norm of a Real Banded Matrix  B1NRM, DB1NRM ..........281 L0 Norm of a Real Banded Matrix  BNRM, DBNRM ............283 Solution of Banded Systems of Real Linear Equations  BSLV, BSLV1 .........................................285 Computation of the Condition Number of a Real  Banded Matrix  B1CND ...............................287 Double Precision Solution of Banded Systems of  Real Linear Equations  DBSLV, DBSLV1 ...............289 Computation of the Condition Number of a Double Precision Banded Matrix  DB1CND .............291 Solution of Banded Systems of Complex Linear Equations  CBSLV, CBSLV1 .......................................293
Sparse Matrices
Storage of Sparse Matrices ...............................295 Conversion of Sparse Matrices to and from the Standard Format  CVRS, CVDS, CVCS, CVSR, CVSD, CVSC .........297 Conversion of Spase Real Matrices to and from Double Precision Form  SCVRD, SCVDR ................299 The Real and Imaginary Parts of a Sparse Complex Matrix  CSREAL, CSIMAG ......................................301 Computing A + Bi for Sparse Real Matrices A and B Q SCVRC ...............................................303 Copying Sparse Matrices  RSCOPY, DSCOPY, CSCOPY ........305 Computing Conjugates of Sparse Complex Matrices  SCONJ ..307 Transposing Sparse Real Matrices  RPSOE, RPOSE1 .........309 Transposing Sparse Double Precision Matrices  DPOSE, DPOSE1 .......................................311 Transposing Sparse Complex Matrices  CPOSE, CPOSE1 ......313 Addition of Sparse Matrices  SADD, DSADD, CSADD .........315 Subtraction of Sparse Matrices Q SSUBT, DSSUBT, CSSUBT ...317 Multiplication of Sparse Matrices  SPROD,DSPROD,CSPROD ..319 Product of a Real Sparse Matrix and Vector  MVPRD, MVPRD1, MTPRD, MTPRD1 ........................321 Product of a Double Precision Sparse Matrix and Vector Q DVPRD, DVPRD1, DTPRD, DTPRD1 ........................323 Product of a Complex Sparse Matrix and Vector  CVPRD, CVPRD1, CTPRD, CTPRD1 ........................325 L1 Norm of a Sparse Real Matrix  S1NRM, DS1NRM ..........327 L0 Norm of a Sparse Real Matrix  SNRM, DSNRM ............329 Ordering the Rows of a Sparse Matrix by Increasing Length Q SPORD ...........................331 Reordering Sparse Matrix into Block Triangular Form Q BLKORD ..............................................333 Solution of Sparse Systems of Real Linear Equations  SPSLV, RSLV, TSLV ...................................335 Computation of the Condition Number of a Real  Sparse Matrix  S1CND ...............................339 Double Precision Solution of Sparse Systems of Real Linear Equation  DSPSLV, DSLV, DTSLV ..........341 Computation of the Condition Number of a  Double Precision Sparse Matrix  DS1CND .............345 Solution of Sparse Systems of Complex Linear Equations  CSPSLV, CSLV, CTSLV .................................347
Eigenvalues and Eigenvectors
Computation of Eigenvalues of General Real Matrices  EIG, EIG1 ................................... .......351 Computation of Eigenvalues and Eigenvectors of General Real Matrices  EIGV, EIGV1 .................353 Double Precision Computation of Eigenvalues of Real Matrices  DEIG ................................355 Double Precision Computation of Eigenvalues and Eigenvectors of Real Matrices  DEIGV ...............357 Computation of Eigenvalues of Symmetric Real Matrices  SEIG, SEIG1 .........................................359 Computation of Eigenvalues and Eigenvectors of Symmetric Real Matrices  SEIGV, SEIGV1 .............361 Double Precision Computation of Eigenvalues of  Symmetric Real Matrices  DSEIG .....................363 Double Precision Computation of Eigenvalues and  Eigenvectors of Symmetric Real Matrices  DSEIGV ....365 Computation of Eigenvalues of Complex Matrices  CEIG ....367 Computation of Eigenvalues and Eigenvectors of Complex Matrices  CEIGV ............................369 Double Precision Computation of Eigenvalues of Complex Matrices  DCEIG ............................371 Double Precision Computation of Eigenvalues and Eigenvectors of Complex Matrices  DCEIGV ...........373
L1 Solution of Linear Equations
L1 Solution of Systems of Linear Equations with Equality and Inequality Constraints  CL1 ....................375
Least Squares Solution of Linear Equations
Least Squares Solution of Systems of Linear Equations   LLSQ, LSQR, HFTI, HFTI2 .......................... 377 Least Squares Solution of Overdetermined Systems of Linear Equations with Iterative Improvement  LLSQMP .......383 Double Precision Least Squares Solution of Systems of  Linear Equations  DLLSQ, DLSQR, DHFTI, DHFTI2 .....385 Least Squares Solution of Systems of Linear Equations with Equality and Inequality Constraints  LSEI ..........391 Least Squares Solution of Systems of Linear Equations with Equality and Nonnegativity Constraints  WNNLS ......395 Least Squares Iterative Improvement Solution of Systems of Linear Equations with Equality Constraints  L2SLV ..399 Iterative Least Squares Solution of Banded Linear Equations  BLSQ ...................................403 Iterative Least Squares Solution of Sparse Linear Equations  SPLSQ, STLSQ ...........................405
Optimization
Minimization of Functions of a Single Variable  FMIN ....407 Minimization of Functions of n Variable  OPTF ...........409 Unconstrained Minimum of the Sum of Squares of Nonlinear Functions Q LMDIFF ..................................411 Linear Programming  SMPLX, SSPLX ........................413 The Assignment Problem  ASSGN ...........................417 01 Knapsack Problem MKP .................................419
Transforms
Inversion of the Laplace Transform  LAINV ...............421 Fast Fourier Transform  FFT, FFTl .......................425 Multivariate Fast Fourier Transform  MFFT, MFFTl ........427 Discrete Cosine and Sine Transforms  COSQI, COSQB, COSQF, SINQB, SINQF .................................429
Approximation of Functions
Rational Minimax Approximation of Functions Q CHEBY ......433 Lp Approximation of Functions Q ADAPT ....................435 Calculation of the Taylor Series of Complex Analytic Function  CPSC, DCPSC .....................439
Curve Fitting
Linear Interpolation  TRP ...............................443 Lagrange Interpolation Q LTRP ............................445 Hermite Interpolation  HTRP .............................447 Conversion of Real Polynomials from Newton to Taylor Series Form  PCOEFF ................................449 Least Squares Polynomial Fit  PFIT ......................451 Weighted Least Squares Polynomial Fit  WPFIT.............453 Cubic Spline Interpolation  CBSPL, SPLIFT ...............455 Weighted Least Squares Cubic Spline Fit  SPFIT ..........457 Least Squares Cubic Spline Fitting with Equality and  Inequality Constraints  CSPFIT .....................459 Cubic Spline Evaluation  SCOMP, SCOMP1, SCOMP2 ..........461 Cubic Spline Evaluation and Differentiation  SEVAL, SEVAL1, SEVAL2 ..............................463 Integrals of Cubic Spline  CSINT, CSINT1, CSINT2 ........465 Periodic Cubic Spline Interpolation  PDSPL ..............467 Least Squares Periodic Cubic Spline Fitting  PDFIT ......469 Periodic Cubic Spline Evaluation and Differentiation   PSCMP, PSEVL ........................................471 NDimensional Cubic Spline Closed Curve Fitting  CSLOOP, LOPCMP, LOPDF ..............................473 Spline under Tension Interpolation  CURV1 ...............475 Spline under Tension Evaluation  CURV2 ..................477 Differentiation and Integrals of Splines under Tension Q CURVD, CURVI .......................................479 Two Dimensional Spline under Tension Curve Fitting  KURV1, KURV2 .......................................481 Two Dimensional Spline under Tension Closed Curve fitting  KURVP1,KURVP2 ............................483 Three Dimensional Spline under Tension Curve Fitting  QURV1, QURV2 .......................................485 BSplines ................................................487 Finding the Interval that Contains a Point  INTRVL ......489 Evaluation and Differentiation of Piecewise Polynomial  from its BSpline Representation  BVAL .............491 Evaluation of the Indefinite Integral of a Piecewise  Polynomial from its Bspline representation  BVALI..493 Conversion of Piecewise Polynomials from BSpline to Taylor Series Form  BSPP ..........................495 Evaluation of Piecewise Polynomials from their Taylor Series Representation  PPVAL .......................497 Piecewise Polynomial Interpolation  BSTRP ...............499 Weighted Least Squares Piecewise Polynomial Fitting   BSLSQ ...............................................501 Least Squares Piecewise Polynomial Fitting with  Equality and Inequality Constraints  BFIT ..........503
Surface Fitting over Rectangular Grids
Bicubic Splines and Bisplines under Tension ..............505 Weighted Least Squares Bicubic Spline Fitting  SPFIT2 ...507 Evaluation and Differentiation of Bicubic Splines   CSURF, CSURF1, CSRF, CSRF2 ..........................509 Bispline under Tension Surface Interpolation  SURF ......513 Bispline under Tension Evaluation  SURF2, NSURF2 ........515 Bivariate BSpline Piecewise Polynomial Interpolation   BSTRP2 ..............................................517 Bivariate BSpline Piecewise Polynomial Least Squares  Fitting  BSLSQ2 ....................................519 Evaluation and Differentiation of Bivariate Piecewise  Polynomials from their BSpline Representation   BVAL2................................................521
Surface Fitting over Arbitrarily Positioned Data Points
Surface Interpolation for Arbitrarily Positioned  Data Points  TRMESH, GRADG, GRADL, SFVAL, SFVAL2 ...523
Manifold Fitting
Weighted Least Squares Fitting with Polynomials of n Variables  MFIT, DMFIT, MEVAL, DMEVAL .............527
Numerical Integration
Evaluation of Integrals over Finite Intervals   QAGS, QXGS, QSUBA, DQAGS, DQXGS .....................531 Evaluation of Integrals over Infinite Intervals  QAGI, DQAGI .........................................539 Evaluation of Double Integrals over Triangles Q CUBTRI ...543
Integral Equations
Solution of Fredholm Integral Equations of the Second Kind  IESLV .......................................545
Ordinary Differential Equations/Initial Value Problems
The Initial Value Solvers  Introductory Comments ........549 Adaptive Adams Solution of Nonstiff Differential Equations  ODE .....................................551 Adaptive Block RKF Solution of Nonstiff Differential Equations  BRKF45 ..................................555 Adaptive RFK Solution of Nonstiff Differential Equations  RFK45 ..................................559 Adaptive RFK Solution of Nonstiff Differebtial Equations with Global Error Estimation  GERK .................563 Adaptive Solution of Stiff Differential Equations  SFODE, SFODE1 .......................................567 FourthOrder RungeKutta  RK ............................571 EighthOrder RungeKutta  RK8 ...........................573
Partial Differential Equations
Separable SecondOrder Elliptic Equations on Rectangular Domains  SEPDE ...................................575
Discrete Random Number Generation
Uniform Random Selection of Values from a Finite Set of  Integers  URGET ....................................579
Continuous Random Number Generation
Uniform Random Number Generator  URNG, DURNG.............581 Generating Points Uniformly in a Square  URNG2, DURNG2 ..583 Generating Points Uniformly in a Circle  RCIR, DRCIR ....585 Normal Random Number Generator  RNOR, DRNOR,  NRNG, DNRNG .........................................587 Multivariate Normal Random Vector Generator   NRVG, DNRVG, NRVG1, DNRVG1 ..........................589 Exponential Random Number Generator  RANEXP, DRNEXP .....593 Gamma Random Number Generator and the ChiSquare  Distribution  RGAM, DRGAM ..........................595 Beta Random Number Generator  RBETA, DRBETA .............597 FDistribution Random Number Generator  FRAN, DFRAN .....599 Student tDistribution Random Number Generator   TRAN, DTRAN .........................................601 First Order Markov Random Number Generator  RMK1,DRMK1 ..603
Special Functions Mathematical LibraryGNU MP ( C# Wrapper) <( arbitrary precisiion library, LGPL Edited by user 30 May 2014 02:28:27(UTC)
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