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 Two-Dimensional 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 Semi-infinite 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 200-400 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
0-1 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
N-Dimensional 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
|B-Splines ................................................487
|Finding the Interval that Contains a Point - INTRVL ......489
|Evaluation and Differentiation of Piecewise Polynomial
| from its B-Spline Representation - BVAL .............491
|Evaluation of the Indefinite Integral of a Piecewise
| Polynomial from its B-spline representation - BVALI..493
Conversion of Piecewise Polynomials from B-Spline 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 B-Spline Piecewise Polynomial Interpolation -
| BSTRP2 ..............................................517
|Bivariate B-Spline Piecewise Polynomial Least Squares
| Fitting - BSLSQ2 ....................................519
|Evaluation and Differentiation of Bivariate Piecewise
| Polynomials from their B-Spline 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
Fourth-Order Runge-Kutta - RK ............................571
Eighth-Order Runge-Kutta - RK8 ...........................573


Partial Differential Equations


Separable Second-Order 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 Chi-Square
| Distribution - RGAM, DRGAM ..........................595
|Beta Random Number Generator - RBETA, DRBETA .............597
|F-Distribution Random Number Generator - FRAN, DFRAN .....599
|Student t-Distribution Random Number Generator -
| TRAN, DTRAN .........................................601
|First Order Markov Random Number Generator - RMK1,DRMK1 ..603