NSWC
Naval Surface Warfare Center Mathematical Library

NSWC is a FORTRAN90 library which contains an extensive collection of mathematical software, compiled by Alfred Morris.

Languages:

NSWC is available in a FORTRAN90 version.

Related Data and Programs:

BLAS1, a FORTRAN90 library which contains basic linear algebra routines for vector-vector operations, combining the single and double precision, real and complex arithmetic libraries.

EISPACK, a FORTRAN90 library which carries out eigenvalue computations; superseded by LAPACK;

FFTPACK5.1, a FORTRAN90 library which implements the Fast Fourier Transform using single precision arithmetic, by Paul Swarztrauber and Dick Valent;

FN, a FORTRAN90 library which approximates elementary and special functions using Chebyshev polynomials, by Wayne Fullerton.

LINPACK_S, a FORTRAN90 library which solves linear systems using single precision real arithmetic;

TEST_VALUES, a FORTRAN90 library which supplies test values of various mathematical functions.

Software Compiler and Maintainter:

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

Source Code:

• nswc.f90, the source code.

Examples and Tests:

• nswc_test.f90, a sample calling program.
• nswc_test.txt, output from the sample calling program.

List of Routines:

• 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 A*x + x*B = c.
• ABSLV1 solves the real matrix equation a*x + x*b = 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 for positive argument and high order.
• ASJY computes Bessel functions J and Y for positive argument and high order.
• ASSGN solves the assignment problem.
• ASSGN1 solves the square assignment problem.
• ATN calculates complex function atn(z) = z*atan(z) using double precision.
• BADD adds real banded matrices
• BALANC balances a real matrix before eigenvalue calculations.
• BALBAK is a translation of the algol procedure balbak,
• BALINV inverts the similarity transforms used by BALANC.
• BANFAC computes the LU factorization of a banded matrix.
• BANSLV solves a linear system factored by BANFAC.
• 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 computes the Cholesky factorization of a banded matrix.
• BCHSLV solves a linear system factored by BCHFAC.
• BCORR evaluates a correction term used to approximate log ( gamma ( x ) ).
• BESI computes a sequence of I Bessel functions.
• BESI0_VALUES returns some values of the I0 Bessel function for testing.
• BESI1_VALUES returns some values of the I1 Bessel function for testing.
• BESIN_VALUES returns some values of the IN Bessel function for testing.
• BESJ computes a sequence of J Bessel functions.
• BESJ0_VALUES returns some values of the J0 Bessel function for testing.
• BESJ1_VALUES returns some values of the J1 Bessel function for testing.
• BESJN_VALUES returns some values of the JN Bessel function for testing.
• BETA computes the Beta function.
• BETA_INC_VALUES returns some values of the incomplete 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 a block triangular linear system.
• BLKTRI ???
• BLND ???
• BLSQ solves a linear system using least squares.
• BPOSE transposes a real banded matrix.
• BPROD multiplies 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 converts 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
• CI_VALUES returns some values of the cosine integral function.
• CIN computes the integral of (1-cos(t))/t on (0,x)
• CIN_VALUES returns some values of the cosine integral function.
• CIRCV: circular coverage and circular error functions
• CK calculates the complete elliptic integral f(k) for complex modulus K.
• CKE calculates the complete elliptic integrals f(k) and e(k)
• CKM calculates the modified Bessel function of the second kind
• 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
• CLOC2 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.
• 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 the matrix exponential.
• DMFIT constructs a least-squares multinomial fit to given data
• DMPROD: product of double precision matrices
• 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 finds the minimizing combination of Gauss-Newton and gradient steps.
• 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
• E1_VALUES returns some values of the exponential integral function EI(X).
• EI_VALUES returns some values of the exponential integral function EI(X).
• 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
• ERF_VALUES returns some values of the ERF or "error" function for testing.
• 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)
• EULER_CONSTANT returns the value of the Euler-Mascheroni constant.
• 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)
• FRESNEL evaluates the real Fresnel integrals
• FRESNEL_COS_VALUES returns some values of the Fresnel cosine integral function.
• FRESNEL_SIN_VALUES returns some values of the Fresnel sine integral function.
• 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 evaluates the Gamma function for a real argument.
• GAMMA_INC_VALUES returns some values of the incomplete Gamma function.
• 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 evaluates of the natural logarithm of X for X >= 15.
• GNRTP is a utility routine used by MFIT.
• GRAT1 evaluates 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 of a finite planar set
• HYBRD find a zero of n nonlinear functions in n variables
• I_SWAP swaps two integer values.
• 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 evalues the incomplete Beta function for A and B >= 0.5.
• ITERT computes the next estimate of the solution of an integral equation.
• 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
• JACOBI_SN_VALUES returns some values of the Jacobi SN function.
• 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 solves A*X = 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
• MTABLE 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 a closed polygonal curve.
• 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
• PI returns the value of pi.
• PI1 computes a feasible solution to the current knapsack 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 a real quadratic polynomial.
• QELG: epsilon algorithm
• QFORM produces the explicit QR factorization of a matrix.
• QK15I: integration rule
• QK15I1: integration rule
• QK21F: integration rules
• QPSRT: ordering routine
• QRFAC computes a QR factorization using Householder transformations.
• QRSOLV solves a rectangular linear system A*x=b 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 is a lower level routine used by RFFTB1.
• RADB3 is a lower level routine used by RFFTB1.
• RADB4 is a lower level routine used by RFFTB1.
• RADB5 is a lower level routine used by RFFTB1.
• RADBG is a lower level routine used by RFFTB1.
• R_PI returns the value of pi.
• RADF2 is a lower level routine used by RFFTF1.
• RADF3 is a lower level routine used by RFFTF1.
• RADF4 is a lower level routine used by RFFTF1.
• RADF5 is a lower level routine used by RFFTF1.
• RADFG is a lower level routine used by RFFTF1.
• 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)
• RMAT_PRINT prints a real matrix.
• 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 to reorder the elements of A.
• R_SWAP swaps two real values.
• SADD: addition of sparse real matrices
• SAMAX returns the maximum absolute value of the entries in a vector.
• 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 evaluates the sine integral function for a given X.
• SI_VALUES returns some values of the sine integral function.
• 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
• TIMESTAMP prints the current YMDHMS date as a time stamp.
• 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

You can go up one level to the FORTRAN90 source codes.