NSWC: Naval Surface Warfare Center Mathematical Library

NSWC is an extensive collection of mathematical software.

The NSWC library was compiled by:

Alfred H Morris, Jr,
Engineering and Information Systems Department,
Naval Surface Warfare Center,
Dahlgren, Virginia, 22448-5000.

Files you may copy include:

nswc.f90, the source code.
nswc_prb.f90, a sample calling program.
nswc_prb.out, output from the sample calling program.

The list of routines includes:

ABCON calculates the abscissa of convergence of a given function
ABCON1 calculates the abscissa of convergence of a given function
ABSLV solves the real matrix equation ax + xb = c.
ABSLV1 solves the real matrix equation ax + xb = c.
ACOND tests whether X lies to the right of the abscissa of convergence
ACONDF is the function integrated along the x-axis in ACOND.
ACONDG is the function integrated along the line x = c in ACOND.
ADAPT computes a piecewise polynomial approximation.
ADAPT1 computes a piecewise polynomial approximation
ADCHK checks for discarding interval, applies various tests
ADCOMP computes the piecewise polynomial approximation on the current interval.
ADPUT puts intervals on the stack or discards them.
ADSET checks the input data and initializes the computation.
ADTAKE takes an active interval off the top of the stack.
ADTRAN converts polynomial representation from divided difference to power form.
AI evaluates the Airy function.
AIA calculates the Airy function and its derivative.
AIE computes the scaled Airy function.
AII calculates the Airy function ai and its derivative aip
AIMP computes the Airy modulus and phase for x >= 1
AIRM calculates the Airy functions ai and bi and their
AIRY_VALUES returns some values of the Airy function for testing.
ALGDIV computes ln(gamma(b)/gamma(a+b)) when b >= 8
ALLOT checks for sufficiency the declared dimensions of the
ALNREL evaluates the function ln(1 + a)
AORD reorders the elements of a so that abs(a(i)) <= abs(a(i+1))
ARCEBE performs the backward elimination step in the solution phase of arceco.
ARCEBM performs the backward modification step in the solution phase of arceco.
ARCEBS performs the backward solution step in the solution phase of arceco.
ARCECO solves the linear system a*x = b where a is
ARCEDC supervises the modified alternate row and column decomposition
ARCEFE performs the forward elimination step in the solution phase of arceco.
ARCEFM performs the forward modification step in the solution phase of arceco.
ARCEFS performs the forward solution step in the solution phase of arceco.
ARCEPC performs nclpiv column eliminations on the matrices topblk and botblk
ARCEPR performs nrwpiv row eliminations on the matrix block
ARCESL supervises the solution of the linear system
ARTNQ ??? looks like a variation of the arc-tangent function.
ASIK computes bessel functions i and k
ASJY computes bessel functions j and y
ASSGN solves the assignment problem.
ASSGN1 solves the square assignment problem.
ATN calculates complex function atn(z) = z*atan(z) using double precision.
BADD carries out addition of real banded matrices
BALANC balances a real matrix before eigenvalue calculations.
BALBAK is a translation of the algol procedure balbak,
BALINV ???
BANFAC ???
BANSLV ???
BASIZ finds the size of a basis required for polynomial approximation.
BASYM carries out asymptotic expansion for ix(a,b) for large a and b.
BCHFAC ???
BCHSLV ???
BCORR evaluates a correction term used to approximate log ( gamma ( x ) ).
BESI ???
BESJ ???
BETA computes the Beta function.
BETA_VALUES returns some values of the Beta function for testing.
BETALN evaluates the logarithm of the beta function
BFRAC continued fraction expansion for ix(a,b) when a,b > 1.
BGRAT asymptotic expansion for ix(a,b) when a is larger than b.
BI evaluation of the Airy function BI(X).
BIA calculates the airy function bi and its derivative bip for
BIE computes the scaled Airy function BI(X).
BII calculates the airy function bi and its derivative bip
BIM calculates the modified bessel function of the first kind
BJM calculates the bessel function of the first kind
BLKORD reorders a sparse matrix into block triangular form
BLKTR1 solves the linear system
BLKTRI ???
BLND ???
BLSQ ???
BPOSE transposition of real banded matrices
BPROD multiplication of real banded matrices
BPSER power series expansion for evaluating ix(a,b) when b <= 1
BRATIO evaluates the incomplete beta function ix(a,b)
BRCMP1 evaluates exp(mu) * (x**a*y**b/beta(a,b))
BRCOMP evaluates x**a*y**b/beta(a,b)
BSL2 produces the b-spline coefficients bcoef of the piecewise
BSLV employs gauss elimination with row interchanges to solve
BSLV1 employs gauss elimination with row interchanges to solve
BSPEV evaluation of b-splines
BSPP conversion from b-spline representation to pp representation
BSRH ???
BSSLI modified bessel function of integral order
BSSLJ ordinary bessel function of integral order
BSSLK modified bessel function of integral order
BSSLY ordinary bessel function of integral order
BSTRP produces the b-spline coeff.s bcoef of the piecewise
BSUBT subtraction of real banded matrices
BTPRD product of a real vector and a real banded matrix
BTPRD1 setting y = x*a + y where a is a real banded matrix and
BTSLV ???
BUP evaluation of ix(a,b) - ix(a+n,b) where n is a positive integer.
BUPD backtracking step updating
BVIP performs bivariate interpolation when the pro-
BVIP2 performs smooth surface fitting when the pro-
BVPRD product of a real banded matrix and a real vector
BVPRD1 sets y = a*x + y where a is a banded matrix, x and y are vectors.
CAI calculates the airy function ai and its derivative aip
CALCSC calculates scalar quantities used to
CALCT computes t = -p(s)/h(s)
CAUCHY computes a lower bound bnd on the moduli of the zeros
CAXPY: constant times a vector plus a vector.
CBABK2 is a translation of the algol procedure
CBADD: addition of complex banded matrices
CBAL is a translation of the algol procedure
CBCRT computes the roots of the real polynomial
CBFA factors a complex band matrix by elimination.
CBI calculates the airy function bi and its derivative bip
CBPOSE: transposition of complex banded matrices
CBPROD: multiplication of complex banded matrices
CBRT: cube root of a real number
CBSL solves the complex band system a*x = b or trans(a)*x = b
CBSLV employs gauss elimination with row interchanges to solve
CBSLV1 employs gauss elimination with row interchanges to solve
CBSPL: cubic spline interpolation
CBSSLJ: ordinary bessel function of first kind
CBSSLK: calculation of the modified bessel function of the
CBSUBT: subtraction of complex banded matrices
CBTPD: product of a complex vector and a complex banded matrix
CBTPD1: setting y = x*a + y where a is a complex banded matrix and
CBVPD: product of a complex banded matrix and a complex vector
CBVPD1: setting y = a*x + y where a is a complex banded matrix and
CCOPY copies a vector, x, to a vector, y.
CDET: evaluation of the determinant of a-xi where a is an nxn matrix,
CDIVID: double precision complex division c = a/b avoiding overflow
CDOTC: forms the dot product of two vectors, conjugating the first vector.
CDOTU: forms the dot product of two vectors.
CEEZ determines the coefficients c1, c2, and c3
CEIG: eigenvalues of complex matrices
CEIGV: eigenvalues and eigenvectors of complex matrices
CERF: computation of the complex error function
CERFC: computation of the complex coerror function
CERR: compute the approximation error at point t
CEXPLI: evaluation of the complex exponential integral
CFLECT: reflects z with respect to the origin if real(z)
CFOD defines coefficients needed in the integrator package sfode
CFRNLI: computation of the complex fresnel integral e(z)
CGAMMA: evaluation of the complex gamma and loggamma functions
CGECO factors a complex matrix by gaussian elimination
CGEDI computes the determinant and inverse of a matrix
CGEFA factors a complex matrix by gaussian elimination.
CGESL solves the complex system
CHEBY: rational chebychev approximation of continuous functions
CHEBY1 ???
CHKPRM checks the input parameters for errors
CHKSNG checks if the pde sepell must solve is a singular operator
CIN computes the integral of (1-cos(t))/t on (0,x) by means
CIRCV: circular coverage and circular error functions
CK calculates the complete elliptic integral f(k)
CKE calculates the complete elliptic integrals f(k)
CKM calculates the modified bessel function of the second
CKML calculates the modified bessel function of the second
CKPROD: kronecker product of complex matrices a and b
CL1 ???
CLE: solution of complex linear equations with reduced storage
CLI: computation of the complex logarithmic integral
CLOC determines if two arrays begin at the same spot.
CLUIMP tries to improve the solution of a complex linear system.
CMADD: addition of complex matrices
CMADJ copies the complex conjugate transpose of a matrix.
CMCONJ copies the conjugate of a complex matrix.
CMCOPY copies a complex matrix.
CMCVBS: conversion of complex matrices from banded to sparse form
CMCVSB: conversion of complex matrices from sparse to banded form
CMIMAG ???
CMPROD: product of complex matrices
CMREAL ???
CMSLV: partial pivot gauss procedure for inverting complex matrices
CMSLV1: partial pivot gauss procedure for inverting complex matrices
CMSUBT: subtraction of complex matrices
CMTMS: product of complex matrices
CNSPIV uses sparse gaussian elimination with
COMPB computes the roots of the b polynomials using tqlrt0,
COMQR is a translation of a unitary analogue of the
COMQR2 is a translation of a unitary analogue of the
CONEW updates the value of the condition number in iegs.
CONSTR constructs the elements of a 3 by 3
CORTH is a translation of a complex analogue of
COS0: computation of cos(x*pi/2) for abs(x) <= 0.5
COS1: evaluation of cos(x*pi)
COSQB: ???
COSQB1: ???
COSQF
COSQF1: ???
COSQI ???
COVAR uses results from the orthogonal decomposition
CPABS: evaluation of sqrt(x*x + y*y)
CPOSE: transposing a sparse complex matrix
CPOSE1: transposing a sparse complex matrix
CPROD0 applies a sequence of matrix operations to the vector x and
CPRODP applies a sequence of matrix operations to the vector x and
CPSC: evaluation of complex power series coefficients or derivatives.
CPSI: evaluation of the complex digamma function
CQEXT: epsilon algorithm
CQZHES is a modification of the eispack subroutine
CQZIT is a modification of the eispack subroutine qzit.
CREC: complex reciprocal u + i*v = 1/(x + i*y)
CROUT: procedure for inverting matrices and solving equations
CROUT1: crout procedure for inverting matrices
CSADD: addition of sparse complex matrices
CSCAL: scales a vector by a constant.
CSCOPY: copying a sparse complex matrix
CSEVL: evaluate the n term chebyshev series a at x.
CSIMAG: imaginary part of a sparse complex matrix
CSINT: integrating a cubic spline
CSINT1: integrating a cubic spline
CSINT2: integrating a cubic spline
CSLOOP: closed curve cubic spline fitting in n-dimensional space
CSLOP1: closed curve cubic spline fitting in n-dimensional space
CSLV: solution of complex sparse matrices
CSLV1 solves a factored system of complex sparse matrices.
CSLVMP: solution of complex linear equations with iterative improvement
CSPLU employs gaussian elimination with column interchanges
CSPROD: multiplication of sparse complex matrices
CSPSLV: solution of complex sparse matrices
CSREAL: real part of a sparse complex matrix
CSROT: applies a plane rotation, where the cos and sin (c and s) are real
CSSCAL: scales a complex vector by a real constant.
CSSUBT: subtraction of sparse complex matrices
CSVDC is a subroutine to reduce a complex nxp matrix x by
CSWAP interchanges two vectors.
CTIP transposes a rectangular matrix in situ.
CTPOSE makes a transposed copy of a complex matrix.
CTPRD: product of a vector and a sparse matrix
CTPRD1: set y = x*a + y where a is a sparse matrix and x,y are vectors
CTRANS finds the complex conjugate of an input matrix.
CTSLV: solution of complex sparse matrices
CTSLV1: ???
CUBRUL: basic cubature rule pair over a triangle
CUBTRI: adaptive cubature over a triangle
CURV1 determines the parameters necessary to
CURV2 interpolates a curve at a given point
CURVD differentiates a curve at a given point
CURVI integrates a curve specified by a spline
CVBC: conversion of complex matrices from banded to standard form
CVBR: conversion of real matrices from banded to standard form
CVCB: conversion of complex matrices from standard to banded form
CVCB1: conversion of complex matrices from standard to banded form
CVCS: ???
CVDS: ???
CVPRD: product of a sparse matrix and a vector
CVPRD1: set y = a*x + y where a is a sparse matrix and x,y are vectors
CVRB: conversion of real matrices from standard to banded form
CVRB1: conversion of real matrices from standard to banded form
CVRS: ???
CVSC ???
CVSD: ???
CVSR: ???
CXP: computation of exp(-r*(pi/2)*i)
CYCHG ???
DABSLV solves the real matrix equation ax + xb = c.
DABSV1 solves the real matrix equation ax + xb = c.
DAORD is used to reorder the elements of the double precision array a
DARTNQ ???
DASUM takes the sum of the absolute values.
DAWSON computes single precision values of dawsons integral,
DAWSON_VALUES returns some values of Dawson's integral for testing.
DAXPY: constant times a vector plus a vector.
DBABK forms the eigenvectors of a real general matrix by back transforming
DBAL balances a double precision real matrix and isolates eigenvalues.
DBALNV ???
DBCORR: evaluation of del(a) + del(b0) - del(a) + b0)
DBETLN: evaluation of the logarithm of the beta function
DCBABK forms the eigenvectors of a double precision complex matrix
DCBAL balances a double precision complex matrix and isolates eigenvalues.
DCBCRT computes the roots of a real cubic polynomial
DCBRT: cube root of a number.
DCEIG: eigenvalues of double precision complex matrices
DCEIGV: eigenvalues and eigenvectors of double precision complex matrices
DCERF: computation of the complex error function
DCERFC: computation of the complex coerror function
DCFACT decomposes a complex matrix by partial pivot gauss elimination
DCGAMA evaluates the complex gamma and loggamma functions
DCMINV inverts a matrix using the lu decomposition obtained by dcfact.
DCMQR2: eigenvalues/vectors of double precision complex upper hessenberg matrix
DCMSLV: partial pivot gauss procedure for double precision complex equations.
DCOMQR: eigenvalues of a double precision complex upper hessenberg matrix
DCOPY copies a vector, x, to a vector, y.
DCORTH reduces a double precision complex matrix to upper hessenberg form.
DCPABS: evaluation of sqrt(x*x + y*y)
DCPLY1 is a utility routine used by dcpoly.
DCPOLY finds the zeros of a complex polynomial.
DCPSC: evaluation of complex power series coefficients or derivatives.
DCPSI: evaluation of the complex digamma function
DCREC: complex reciprocal u + i*v = 1/(x + i*y)
DCSEVL: evaluate the n term chebyshev series a at x.
DCSOL: solution of system of m equations a*x = b factored by dcfact.
DCSQRT computes the square root of a double precision complex number.
DDOT forms the dot product of two vectors.
DDSORT uses the shell sorting procedure to reorder the elements of a
DE1 solves an ordinary differential equation set up by ode.
DE1E evalutes the exponential integral.
DEC: matrix triangularization by gaussian elimination.
DECBT: block-tridiagonal matrix decomposition routine.
DECOM2: ???
DEFER: ???
DEI evaluates the exponential integral
DEI0 evaluates ei(x) near a zero.
DEI1: double precision evaluation of exp(-x)*ei(x)
DEIG: eigenvalues of double precision matrices
DEIGV: eigenvalues and eigenvectors of double precision matrices
DELLPI: elliptic integrals of the first and second kinds
DEPI: elliptic integral of the third kind
DERF: the error function
DERFC: the complementary error function
DERFC1: evaluation of the complementary error function
DESUM: evaluation of exp(mu + x)
DET evaluates the determinant of a-xi where a is an nxn matrix,
DGAM1 evaluates 1/gamma(1 + x) - 1 for -0.5 <= x <= 1.5
DGAMLN evaluates ln(gamma(a)) for positive a
DGAMMA evaluates the gamma function.
DGECO factors a double precision matrix by gaussian elimination
DGEDI computes the determinant and inverse of a matrix
DGEFA factors a double precision matrix by gaussian elimination.
DGESL solves the double precision system a * x = b or trans(a) * x = b
DGMLN1: evaluation of ln(gamma(1 + x)) for -0.5 <= x <= 1.5
DGNRTP is a utility routine used by dmfit.
DGSMLN: evaluation of the function ln(gamma(a + b))
DH12 contructs or applies a single householder transformation.
DHFTI solves a linear least squares problem.
DHFTI2 solves a linear least squares problem.
DHQR finds the eigenvalues of a double precision upper hessenberg matrix
DHQR2 finds eigenvalues/vectors of a double precision upper hessenberg matrix
DILOGARITHM evaluates the dilogarithm function.
DILOGARITHM_VALUES returns some values of the dilogarithm function for testing.
DINCDG is a utility routine used by dgnrtp.
DISORT uses the shell sorting procedure to reorder the elements of a
DKPROD: kronecker product of double precision matrices a and b
DLGDIV: computation of ln(gamma(b)/gamma(a+b)) for b >= 10
DLLSQ: ???
DLNREL: evaluation of the function ln(1 + a)
DLOC determines if two double precision arrays begin at the same location.
DMADD: addition of double precision matrices
DMCOPY copies a double precision array.
DMCVFS: ???
DMCVSF: ???
DMEVAL evaluates the least-squares multinomial fit produced by dmfit.
DMEVL1 performs the main work of evaluating the fitting multinomial
DMEXP computes exp(a) and stores it in z where a is a matrix
DMFIT constructs a least-squares multinomial fit to given data
DMPROD: product of double precision matrices
DMSLV: matrix factorization and computation of rcond
DMSUBT: subtraction of double precision matrices
DMTMS: product of double precision matrices
DNRM2: euclidean norm of the n-vector stored in dx()
DNSPIV uses sparse gaussian elimination with column interchanges
DOGLEG optimally combines the gauss-newton and gradient directions.
DORSOL: least squares solution of a linear system
DORTH reduces a matrix to upper hessenberg form.
DORTHO: orthogonal transformation of a rectangular matrix to triangular form.
DORTRN accumulates the orthogonal similarity transformations
DPADD: addition of double precision polynomials
DPCHOL: cholesky matrix factorization.
DPCOPY: copying double precision polynomials
DPDEL: computation of the function del(x) for x >= 10
DPDET: evaluation of the determinant of a-xi
DPDIV: division of double precision polynomials
DPINV: computation of the inverse of the power series
DPLE: solution of linear equations with reduced storage
DPLPWR: set b = a**r where a is a double precision polynomial
DPMPAR provides the double precision machine constants for the computer
DPMULT: multiplication of double precision polynomials
DPOSE: transposing a sparse double precision matrix
DPOSE1: transposing a sparse double precision matrix
DPPDI: determinant and inverse of a symmetric positive definite matrix
DPPFA factors a symmetric positive definite matrix stored in packed form.
DPPSL solves the double precision symmetric positive definite system a * x = b
DPSI: evaluation of the digamma function
DPSI0: taylor series expansion of psi(x) around a zero.
DPSLV: partial pivot solution of a*x = b
DPSUBT: subtraction of double precision polynomials
DQAGI: integration over infinite intervals
DQAGIE: integration over infinite intervals
DQAGS: computation of a definite integral
DQAGSE: computation of a definite integral
DQDCRT computes the roots of a quadratic polynomial
DQELG implements the epsilon algorithm.
DQK15I approximates an integral on an infinite interval.
DQK21 approximates an integral over a finite interval.
DQPSRT maintains the sorted order of the local error estimates.
DQTCRT computes the roots of a real quartic polynomial
DRCVL1 evaluates an elliptic integral.
DRDVAL computes the incomplete elliptic integral of the second kind
DREXP: evaluation of the function exp(x) - 1
DRFVAL: computes the incomplete elliptic integral of the first kind
DRJVAL computes the incomplete elliptic integral of the third kind
DRLOG: evaluation of the function x - 1 - ln(x)
DRLOG1: evaluation of the function x - ln(1 + x)
DROT applies a plane rotation.
DROTG constructs a givens rotation.
DRPLY1 is called by drpoly.
DRPOLY finds the zeros of a real polynomial.
DRTRN1 accumulates the orthogonal similarity transformations used
DSADD: addition of sparse double precision matrices
DSCAL scales a vector by a constant.
DSCALD carries out the data-scaling which is defined by dscalp.
DSCALP finds scaling parameter(s) for the problem.
DSCHUR transforms a hessenberg matrix into schur form.
DSCOPY copies a sparse double precision matrix
DSHSLV solves the matrix equation ax + xb = c
DSLV: solution of double precision sparse equations
DSLV1 is called by DSLV.
DSMSLV: matrix factorization and computation of rcond
DSORT uses the shell sorting procedure to reorder the elements of a
DSPCO factors a double precision symmetric matrix stored in packed form
DSPDI computes the determinant, inertia and inverse of a symmetric matrix.
DSPFA factors a double precision symmetric matrix stored in packed form
DSPLU employs gaussian elimination with column interchanges
DSPROD: multiplication of sparse double precision matrices
DSPSL solves the double precision symmetric system a * x = b
DSPSLV: solution of double precision sparse equations
DSSUBT: subtraction of sparse double precision matrices
DSTOR2: storage of double precision information into memory
DSVDC computes the singular value decomposition of a matrix.
DSVPRD: ???
DSWAP interchanges two vectors.
DSYMSV solves the matrix equation transpose(a)*x + x*a = c
DTASLV solves the real matrix equation transpose(a)*x + x*a = c
DTASV1 solves the real matrix equation transpose(a)*x + x*a = c
DTIP: transposition of a rectangular matrix in situ.
DTOPLX: solution of the toeplitz system of equations
DTPOSE makes a transposed copy of a double precision matrix.
DTPRD: product of a vector and a sparse matrix
DTPRD1: set y = x*a + y where a is a sparse matrix and x,y are vectors
DTSLV: solution of double precision sparse equations
DTSLV1: solve yu = b by forward substitution
DVPRD: product of a sparse matrix and a vector
DVPRD1: set y = a*x + y where a is a sparse matrix and x,y are vectors
DXFN approximates the third and fourth x derivatives of u at a mesh point.
DXPARG estimates the largest possible exponent for dexp.
DYCHG: ???
DYFN approximates the third and fourth y partial derivatives of u
EIG computes the eigenvalues of a real matrix.
EIG1: eigenvalues of real matrices
EIGV: eigenvalues and eigenvectors of real matrices
EIGV1: eigenvalues and eigenvectors of real matrices
EKL computes the complete elliptic integrals f(k), f(l), e(k), e(l)
EKM computes the complete elliptic integrals f(k) and e(k)
ELLPF calculates the Jacobi elliptic functions sn(u,k), cn(u,k), and dn(u,k).
ELLPI: real elliptic integrals of the first and second kinds
ELMHES transforms a real general matrix to upper Hessenberg form.
ELMHS0 reduces a matrix to upper hessenberg form using stabilized elementary transforms.
ELPFC1 calculates the elliptic functions sn(u,k), cn(u,k), dn(u,k)
ELTRAN accumulates the stabilized elementary similarity transformations used
ELTRN0 accumulates the stabilized elementary similarity transformations
ENORM computes the Euclidean norm of a vector.
EPI: real elliptic integral of the third kind
ERF: evaluation of the real error function
ERF0: evaluation of erf(a) for 0 <= a <= 4
ERFC: evaluation of the complementary error function
ERFC0: evaluation of erfc(a) for 0 <= a <= 4.
ERFC1: evaluation of the complementary error function
ERFC2: evaluation of erfc(x) for abs(x) <= 4.0
ERFCM2: calculation of erfc(z) using the taylor series
ERFINV: evaluation of the inverse error function
ERREV: bounds the error in evaluating the polynomial by the horner
ERRINT does a four point integration rule for the
ESUM: evaluation of exp(mu + x)
EXPARG returns the largest "safe" argument of the exponential function.
EXPLI computes the exponential integrals
FDJAC1 computes a forward-difference approximation
FDJAC2 computes a forward-difference approximation
FEHL: fehlberg fourth-fifth order runge-kutta method
FFT ???
FFT1: ???
FMIN: golden section minimization of a function f(t)
FRNL: evaluation of the real fresnel integrals
FSTOCD: find central difference approximation g to the first derivative
FSTOFD: find forward difference approximation g to the first derivative
FUPD: forward step updating
FXDEC: fixed step coordinate descent procedure / one iteration
FXSHFR computes up to l2 fixed shift k-polynomials,
FXSHFT computes l2 fixed-shift h polynomials and tests for convergence.
GAM1: computation of 1/gamma(a+1) - 1 for -0.5 <= a <= 1.5
GAMINV: inverse incomplete gamma ratio function
GAMLN: evaluation of ln(gamma(a)) for positive a
GAMLN1: evaluation of ln(gamma(1 + a)) for -0.2 <= a <= 1.25
GAMMA: evaluation of the gamma function for real arguments
GAMMA_VALUES returns some values of the Gamma function for testing.
GERK: fehlberg 4,5 order runge-kutta method with global error assessment
GERKS: fehlberg 4,5 order runge-kutta method with global error assessment
GLOG: evaluation of ln(x) for x >= 15
GNRTP is a utility routine used by mfit.
GRAT1: evaluation of the incomplete gamma ratio functions p(a,x) and q(a,x)
GRATIO: evaluation of the incomplete gamma ratio functions p(a,x) and q(a,x)
GSUMLN: evaluation of the function ln(gamma(a + b))
H12 constructs or applies a householder transformation: q = i + u*(u**t)/b
HBRD finds a zero of n nonlinear functions in n variables
HC finds one or more hamiltonian circuits in a directed graph
HC1 is a utility routine used by hc to find hamilton circuits.
HFTI solves a linear least squares problem
HFTI2 solves a linear least squares problem
HQR finds the eigenvalues of a real upper hessenberg matrix by the qr method.
HQR2 finds the eigenvalues and eigenvectors of a real upper hessenberg matrix
HSTART computes a starting step size for solving initial value problems
HTRP: hermite interpolation
HULL computes the convex hull for a finite planar set
HYBRD find a zero of n nonlinear functions in n variables
IA calculates the modified bessel function of the first kind
ICAMAX finds the index of element having max. absolute value.
IDAMAX finds the index of element having max. absolute value.
IDCLDP selects several data points that are closest to each of the data points.
IDGRID organizes grid points for surface fitting by sorting them
IDLCTN determines what triangle a given point belongs to.
IDPDRV estimates first and second partial derivatives at the data points.
IDPTIP performs pointwise interpolation or extrapolation.
IDTANG performs triangulation.
IDXCHG determines whether or not the exchange of two triangles is necessary
IEGS controls the solution of the integral equation.
IESLV solves an integral equation.
IMC calculates the modified bessel function of the first kind
IMTQL1 finds the eigenvalues of a symmetric tridiagonal matrix
IMTQL2 finds the eigenvalues and eigenvectors of a symmetric tridiagonal matrix
INCDG is a utility routine for gnrtp, and is not called by the user.
INDXA ???
INDXB ???
INDXC ???
INFCTR factors n into its prime powers, npower in number.
INTRP is used by step1 to evaluate the interpolating polynomial at a point.
INTRVL seeks to bracket a value using an array of increasing values.
INTYD approximates the solution and derivatives at t by polynomial interpolation.
IPATH finds the start and end vertices of the largest path of implied arcs.
IPMPAR provides the integer machine constants for the computer that is used.
ISAMAX finds the index of the vector element of maximum absolute value.
ISHELL uses the shell sort to reorder the elements of a
ISUBX ???
ITERT calculates one iterate xm given the initial guess xmz.
IUPD updates for implied arc
JA calculates the bessel function of the first kind for orders 1/3, 2/3, -1/3, and -2/3
JAIRY computes the airy function and its derivative for jbess
JMC calculates the bessel function of the first kind for orders 1/3, 2/3, -1/3, and -2/3
JROT premultiplies an upper hessenberg matrix by a jacobian rotation.
KA calculates the modified bessel function of the second
KL computes the complete elliptic integrals f(k) and f(l) for
KM computes the complete elliptic integral f(k) for a given
KML calculates the modified bessel function of the second kind for orders
KPROD is a kronecker product of real matrices a and b
KROUT is a crout procedure for inverting matrices and solving equations
KURV1 determines the parameters of a spline under tension
KURV2 maps the interval (0.,1.) onto a curve in the plane.
KURVP1 determines the parameters of a spline under tension
KURVP2 performs the interval (0.,1.) onto a closed plane curve.
L2SLV computes least squares solutions to over/under-determined systems.
LAINV calculates the inverse laplace transform of a given function
LAINV1 is used by lainv.
LE: solution of linear equations with reduced storage
LEAVE sets all necessary parameters for leaving iegaus.
LGRNGN: lagrangian normalization factors
LGRNGV: lagrangian function evaluation
LGRNGX: lagrangian polynomial expansion
LLSQ: ???
LLSQMP ???
LLTSLV: solution of ax = b where a has the form l(l-transpose)
LMDIF minimizes the sum of the squares of m nonlinear functions in n variables
LMDIFF minimize the sum of the squares of m functions in n variables
LMPAR determines a parameter for a least squares problem.
LNSRCH finds a next newton iterate by line search
LNSYS: solve ax = b where a is a matrix of order n.
LOCPT locates a point inside, on, or outside a closed polygonal path.
LOGAM: computation of ln(gamma(x)) for x = n/2 where n is an integer
LOPCMP: evaluation of a cubic spline closed curve in n-space
LOPDF: evaluation and differentiation of a cubic spline closed curve in n-space
LPDP determines vectors w and z which minimize ||w|| with g*w+h*z >= y.
LSEI solves a linearly constrained least squares problem
LSI is a companion subprogram to lsei( ).
LSOD1 is called by stfode to solve ordinary differential equations.
LTRP performs Lagrange interpolation.
LUIMP improves the solution of a linear system by iterative refinement.
MACH computes single and double precision machine constants.
MACH1 evaluates single precision machine constants.
MACH2 computes double precision environment constants.
MADD computes the sum of two real matrices.
MC13D: ???
MC31E ???
MC21A ???
MC21B ???
MCOPY copies a real matrix.
MCVBS: conversion of real matrices from banded to sparse form
MCVDR copies a double precision matrix into a real matrix.
MCVFS ???
MCVRC copies a real matrix into the real part of a complex matrix.
MCVRD copies a real matrix into a double precision matrix.
MCVSB: conversion of real matrices from sparse to banded form
MCVSF ???
MEVAL evaluates the least-squares multinomial fit produced by mfit.
MEVAL1 performs the main work of evaluating the fitting multinomial
MEXP computes the matrix exponential.
MFFT: ???
MFFT1 ???
MFIT constructs a least-squares orthogonal multinomial fit to data.
MINSOL orthogonalizes the array usol with respect to the constant array in
MKP solves a 0-1 multiple knapsack problem of n items and m knapsacks.
MKP1 carries out the solution of a knapsack problem.
MPLNMV: multiplex polynomial evaluation
MPROD computes the product of real matrices.
MSLV factors and solves a system of linear equations.
MSUBT: subtraction of real matrices
NTABLE tabulates JP and KJ for each J.
MTMS: product of real matrices
MTPRD: product of a vector and a sparse matrix
MTPRD1: set y = x*a + y where a is a sparse matrix and x,y are vectors
MVPRD: product of a sparse matrix and a vector
MVPRD1 set y = a*x + y where a is a sparse matrix and x,y are vectors
NEWEST computes new estimates of the quadratic coefficients
NEWTON computes the divided differences array as follows
NEXTH calculates the next shifted H polynomial.
NEXTK computes the next k polynomials using the scalars computed in calcsc.
NORMLZ computes the euclidean norm of x.
NOSHFT computes the derivative polynomial as the initial h polynomial
NPIVOT: matrix inversion/equation solving without pivot search
NRNG is a Gaussian random number generator.
NSPIV1 uses sparse gaussian elimination with
NSTERP uses the values of xn(1:n) to calculate the nystrom interpolates
NSURF2 maps values onto a surface at every point of a grid
ODE integrates a system of first order differential equations.
OPCHK1 checks input for reasonableness
OPSTP: unconstrained minimization stopping criteria
OPTDRV: driver for non-linear optimization problem
OPTF: interface to minimization package
ORIMP improves an approximate least squares solution of a linear system.
ORSOL computes the least squares solution of a factored linear system.
ORTHES reduces a matrix to upper hessenberg form.
ORTHG orthogonalizes the array usol with respect to
ORTHO orthogonally transforms an m by n matrix to upper triangular form.
ORTHOS: orthonormal polynomial synthesis
ORTHOV: orthonormal polynomial evaluation
ORTHOX: orthonormal polynomial expansion
ORTRAN accumulates the orthogonal similarity
ORTRN1 accumulates the orthogonal similarity
PADD: addition of real polynomials
PARC: parametric computation of the upper bounds.
PAREA computes the area bounded by the closed polygonal curve which passes
PCHOL computes the inverse of a positive definite symmetric matrix in packed form.
PCOEFF ???
PDEDGE ???
PDIV: division of real polynomials
PEQ: weierstrass p-function in the equianharmonic case
PEQ1: first derivative of weierstrass p-function in the
PFIT: unweighted least squares polynomial fit
PL1 computes a feasible solution to the current problem.
PINV: computation of the inverse of the power series
PJAC sets up the iteration matrix (involving the jacobian) for the
PKILL: elliptical coverage function
PKILL3: elliptical coverage function
PLCOPY: copying real polynomials
PLEM: weierstrass p-function in the lemniscatic case
PLEM1: first derivative of weierstrass p-function in the
PLPWR: set b = a**r where a is a real polynomial
PMULT: multiplication of real polynomials
PNDF: evaluate the normal probability density function.
PNINV: evaluation of the inverse normal distribution function
POCA ???
POLYDD evaluates the current polynomial piece represented
POLYEV evaluates a polynomial p at s by the horner recurrence algo.,
PPADD computes the eigenvalues of the periodic tridiagonal matrix
PPSGF: ???
PPSPF: ???
PPVAL evaluates a piecewise polynomial at the
PROD0 applies a sequence of matrix operations to the vector x and
PRODP applies a sequence of matrix operations to the vector x and
PSGF ???
PSI evalulates the digamma function.
PSI_VALUES returns some values of the Psi or Digamma function for testing.
PSUBT: subtraction of real polynomials
QAGI approximates an integral over an infinite interval.
QAGI1 approximates an integral over an infinite interval.
QAGIE approximates an integral over an infinite interval.
QAGIE1 approximates an integral over an infinite interval.
QAGS approximates an integral.
QAGSE approximates an integral.
QDCRT computes the roots of the real polynomial
QELG: epsilon algorithm
QFORM accumulates the m by n q factor from its factored form.
QK15I: integration rule
QK15I1: integration rule
QK21F: integration rules
QPSRT: ordering routine
QRFAC computes the qr factorization of an m by n matrix.
QRSOLV solves a*x=b, d*x=0 in the least squares sense.
QRUPDT finds an orthogonal matrix (q*) and an upper triangular
QSUBA computes the integral of f(x) from a to b where the
QTCRT computes the roots of the real polynomial
QUAD attempts to calculate the integral of f(x)
QUADIT: variable-shift k-polynomial iteration for a
QUADPL calculate the zeros of the quadratic a*z**2+b1*z+c.
QUADSD divides p by the quadratic 1,u,v placing the
QURV1 determines the parameters necessary to
QURV2 performs the mapping of points in the
R1MPYQ multiplies a matrix by a sequence of givens rotations.
R1UPDT updates the r factor of a qr factorization, following a rank 1 update.
radb2 ???
radb3 ???
radb4 ???
radb5 ???
radbg: ???
radf2 ???
radf3 ???
radf4 ???
radf5 ???
radfg ???
RADIX sets ibeta = the radix of the floating point arithmetic
RARC removes the arc (ia,ib) from a graph.
RBND computes error bounds and cluster counts
RCOMP evaluates exp(-x)*x**a/gamma(a)
RCVAL1 computes the integral
RDVAL computes the incomplete elliptic integral of the second kind
REALIT: variable-shift h polynomial iteration for a real zero.
REXP evaluates exp(x) - 1
RFFTB ???
RFFTB1 ???
RFFTF ???
RFFTF1 ???
RFFTI ???
RFFTI1 ???
RFVAL computes the incomplete elliptic integral of the first kind
RISORT uses the shell sorting procedure to reorder the elements of a
RJVAL computes the incomplete elliptic integral of the third kind
RK: fourth order runge-kutta procedure for solving dy=f(t,y)
RK8: eighth order runge-kutta procedure for solving dy=f(t,y)
RKF45: fehlberg fourth-fifth order runge-kutta method
RKFS: fehlberg fourth-fifth order runge-kutta method
RLOC determines if two real arrays begin at the same location.
RLOG: evaluation of the function x - 1 - ln(x)
RLOG1: evaluation of the function x - ln(1 + x)
RMIN computes the minimum relative error for an integral equation.
RNDERR computes the rounding error committed when the sum x+a is formed.
RNRM computes the maximum norm of x or x-y.
ROT3 ???
ROTA ???
RPOSE transposes a sparse real matrix
RPOSE1 transposes a sparse real matrix where the rows are interchanged
RRSORT uses the shell sorting procedure to reorder the elements of a
RSCO restores from rsav and isav the contents of common block debdf1,
RSCOPY: copying a sparse real matrix
RSLV factors and solves a set of real sparse linear equations.
RSLV1 solves a factored system of sparse linear equations.
RSORT uses the shell sorting procedure is to reorder the elements of a
R_SWAP swaps two real values.
SADD: addition of sparse real matrices
SASUM sums the absolute values of the entries of a vector.
SAXPY adds a constant times one vector to another.
SCALCP returns a scale factor to multiply the coefficients of the polynomial.
SCALDN carries out the data-scaling defined by scalpm.
SCALEX rescales the variables
SCALPM finds scaling parameter(s) for the problem.
SCASUM takes the sum of the absolute values of a complex vector
SCD computes the elliptic functions sn(u,k), cn(u,k), and dn(u,k)
SCDF computes sn(u,k), cn(u,k), and dn(u,k) for real u and k
SCDJ computes sn(u,k), cn(u,k), and dn(u,k) for real u and k
SCDM calculates sn(u,k), cn(u,k), and dn(u,k) for "small" u and 0<= k <= 1.
SCHUR factors an upper hessenberg matrix into schur form.
SCNRM2: unitary norm of a complex n-vector
SCOMP evaluates a cubic spline at the abscissas in xi.
SCOMP1 evaluates a cubic spline at the abscissas in xi.
SCOMP2 evaluates a cubic spline at the abscissas in xi.
SCONJ computates the conjugate of a sparse complex matrix.
SCOPY copies one real vector into another.
SCVDR ???
SCVRC computes a + bi for the sparse real matrices a and b
SCVRD ???
SDOT forms the dot product of two vectors.
SECFAC updates the hessian by the bfgs factored method.
SEIG: eigenvalues of a symmetric real matrix.
SEIG1: eigenvalues of symmetric real matrices
SEIGV: eigenvalues and eigenvectors of symmetric real matrices
SEIGV1: eigenvalues and eigenvectors of symmetric real matrices
SEPDE: solution of separable elliptic partial differential equations
SEPEL1 sets up vectors and arrays for input to blktri
SEPELL solves a separable elliptic pde on a rectangular domain.
SEVAL evaluates a cubic spline and its first and second derivatives
SEVAL1 evaluates a cubic spline and its first and second derivatives
SEVAL2 evaluates a cubic spline and its first and second derivatives
SFFT: multivariate complex fourier transform, computed in place
SFODE ???
SFODE1 ???
SGBFA factors a real band matrix by elimination.
SGBSL solves a real banded system factored by SGBCO or SGBFA.
SGECO factors a real matrix and estimates its condition number.
SGEDI computes the determinant and inverse of a matrix factored by SGECO or SGEFA.
SGEFA factors a real matrix.
SGESL solves a real general linear system A * X = B.
SHELL uses the shell sorting procedure to reorder the elements of a
SHELL2 uses the shell sorting procedure to reorder the elements of a
SHRSLV solves the matrix equation ax + xb = c
SI computes the integral of sin(t)/t on (0,x)
SIGMA1 computes an upper bound ub on the best final solution
SIN0: computation of sin(x*pi/2) for abs(x) <= 0.5
SIN1: evaluation of sin(x*pi)
SINQB: ???
SINQF: ???
SKNP solves the 0-1 single knapsack problem
SKNP1 solves the 0-1 single knapsack problem
SLV: partial pivot solution of a*x = b
SLVMP: solution of real linear equations with iterative improvement
SLVS solves the linear system in the iteration scheme for sfode.
SMADD adds two real symmetric storage matrices.
SMCOPY copies a real symmetric storage matrix.
SMPLX: simplex procedure for solving linear programming problems
SMPLX1: utility routine called by smplx.
SMPROD ???
SMSLV: matrix factorization and computation of rcond
SMSUBT: ???
SNBFA factors a real band matrix by elimination.
SNBSL solves the real band system a*x = b or trans(a)*x = b
SNHCSH approximates sinh(x)-x, cosh(x)-1 and cosh(x)-1-x*x/2.
SNRM2 computes the Euclidean norm of a vector.
SOL: solution of linear system, a*x = b.
SOLBT: solution of block-tridiagonal linear system.
SOLVE2:
SOLVE3 is called only by solve2.
SPFIT: least squares cubic spline fitting
SPLIFT fits an interpolating cubic spline to data.
SPLSQ finds a solution x to a variety of systems of linear equations.
SPLU employs gaussian elimination with column interchanges
SPMPAR provides the single precision machine constants for the computer
SPORD orders the rows of an mxn sparse matrix a,ia,ja
SPPDI: determinant and inverse of a real symmetric positive definite matrix
SPPFA factors a real symmetric positive definite matrix stored in packed form.
SPPSL solves the real symmetric positive definite system a * x = b
SPROD: multiplication of sparse real matrices
SPSLV: solution of real sparse equations
SQUIN2 finds a right solvent of the matrix equation ax**2 + bx + c = 0.
SQUINT breaks down the work array into smaller pieces.
SRCH calculates an upper bound for the smallest number x such that a
SROT applies a plane rotation.
SROTG constructs a Givens plane rotation.
SROTM applies a modified givens transformation.
SROTMG constructs a modified givens transformation.
SSCAL scales a vector by a constant.
SSPCO factors a real symmetric matrix stored in packed form
SSPDI: determinant, inertia and inverse of a real symmetric matrix
SSPFA factors a real symmetric matrix stored in packed form
SSPLX: simplex procedure for solving linear programming problems
SSPLX1 is a utility routine called by ssplx.
SSPSL solves the real symmetric system a * x = b
SSUBT: subtraction of sparse real matrices
SSVDC computes the singular value decomposition of a rectangular matrix.
SSWAP interchanges two vectors.
STEP1 is used by subroutine ode to take an integration step.
STFODE solves stiff ode's.
STLSQ finds a solution x to a variety of systems of linear equations.
STOD performs one step of the integration of an initial value problem
STORE2: storage of single precision information into memory
SURF determines parameters for an interpolatory surface on a rectangular grid.
SURF2 evaluates an interpolating surface at a given coordinate pair.
SVCO stores in rsav and isav the contents of common block debdf1,
SVPRD: ???
SYMSLV solves the matrix equation transpose(a)*x + x*a = c
TASLV solves the real matrix equation transpose(a)*x + x*a = c
TASLV1 solves the real matrix equation transpose(a)*x + x*a = c
TERMS computes the diagonal and superdiagonal
TIP: transposition of a rectangular matrix in situ.
TMPROD ???
TOPLX: solution of the toeplitz system of equations
TPOSE ???
TQL2 is a translation of the algol procedure tql2,
TQLRAT is a translation of the algol procedure tqlrat,
TQLRT0 is a modification of the eispack subroutine tqlrat.
TRED1 is a translation of the algol procedure tred1,
TRED2 is a translation of the algol procedure tred2,
TRED3 is a translation of the algol procedure tred3,
TRISLV backsolves a system of the form uy + vyl = f,
TRISP solves for a non-zero eigenvector corresponding to the zero eigenvalue
TRP ???
TSLV: solution of real sparse equations
TSLV1 solves yu = b by forward substitution
URNG: uniform random number generator
VALR2 ???
VNORM computes the maximum norm of the vector v(*) of length ncomp and
VNWRMS computes the weighted root-mean-square norm
VRSHFT carries out the third stage iteration.
WANDT returns weights and abscissas for gauss-legendre quadrature.
WNLIT is a companion subprogram to wnnls( ).
WNLSM is a companion subprogram to wnnls( ).
WNNLS solves a linearly constrained least squares problem.
WPFIT: weighted least squares polynomial fit
XCOND tests whether x lies to the right of all singularities of the complex
XCONDX is the real part of the integrand in xcond.
XCONDY is the imaginary part of integrand in xcond.
XL1 uses a modification of the simplex method of linear programming
YCHG ???
ZEROIN finds a zero of the function f(x) in the interval (ax,bx)
ZZZJAC is a dummy jacobian subroutine

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Last revised on 18 May 2001.