Chilton::ACL::Harwell Subroutine Library

Harwell Subroutine Library

1973

The Harwell Subroutine Library was a library of subprograms which are called by a user written program. Complete programs are not included in the library although some of the library routines are in fact packages of more than one subprogram. The principle language was FORTRAN.

The library was composed mainly of mathematical and numerical analysis routines. These were in the main been written by members of the Numerical Analysis Group, past and present, and were of a high standard, A few of the routines were derived from sources outside Harwell and acknowledgements are made to that effect in the catalogue entries.

The principle function of the library was to provide Harwell computer users with good numerical facilities.

The library started life in 1963 and was first used on the IBM 7030 (STRETCH) computer at Aldermaston and later the Chilton Atlas and then Harwell's IBM 360 computers.

In 1967 the concept of having both single and double precision versions of routines was introduced.

The catalogue contains a complete list of routines that make up the library giving details of purpose, method and attributes. The details given are brief and only intended to be sufficient for a potential user to decide which of the routines, if any, are suitable for his particular problem. The routines are listed in alphabetical order by year and the classification used for routine names is such that the list for each year falls naturally into sections associated with different classes of problem. There are some exceptions and general topics, such as data fitting, are covered by routines spread throughout the list.

The first letter of a routine name indicates the section it belongs to:

D  Differential Equations
E  Algebraic eigen values and eigen vector problems
F  Mathematical functions, random numbers and Fourier transforms
G  Geometrical problems
I  Integer valued functions
K  Sorting
L  Linear and dynamic programming
M  Problems in linear algebra
N  Nonlinear equation problems
O  Input and output facilities
P  Polynomial and rational function problems
Q  Numerical integration
S  Functions of statistics
T  Interpolation and general approximation of functions
V  Optimization and nonlinear data fitting problems
Z  Non-FORTRAN system facilities

The list below is sorted in order of the last time the routine was updated. Fuller descriptions are available in the Harwell Subroutine Library manual.

Routines in machine code for the 360 series have been omitted. Names or routines that appear to be missing often indicate that the routine has become redundant because of a later addition. The date given is the last time the routine was updated.

D B Russell and P Hallowell were at the Atlas Computer Laboratory. Most of the other authors were permanent members of Harwell. There were some routines provided by visitors and in a few cases they originated in the SHARE Library.

Name	Year	Author	Description
DA01A	1963	D McVicar	To integrate a set of first order differential equations
EA02A	1963	E J York	Given a real symmetric matrix A and an estimate λ_e of one of its eigenvalues, will find to a given accuracy the eigen value nearest to λ_e
EA03A	1963	J Soper	Given a real symmetric matrix A, finds all its eigen values λ_i and eigenvectors x_i
FC03A	1963	S Marlow	To compute values of the Gamma function
FC05A	1963	S Marlow	To compute values of the Beta function
FC10A	1963	S Marlow	Computes the real and imaginary part of the Fresnel integral
FC11A	1963	S Marlow	To compute values of the exponential integral
FF01A	1963	S Marlow	Computes values of the Bessel functions J₀(x) and Y₀(x)
FF02A	1963	S Marlow	Computes values of the Bessel functions J₁(x) and Y₁(x)
FF05A	1963	F R A Hopgood	Given x ≥ 0, computes the value of the spherical Bessel functions
MA01B	1963	E J York	To solve a system of n linear algebraic equations in n unknowns with one or more right-hand sides
MB02A	1963	G Packham	To evaluate the adjoint matrix of an n by n real matrix where A may be singular
MC06A	1963	M Osbourne	Applies the Gram-Schmidt orthogonalization process to n vectors in an m dimensional space
ME02A	1963	E J York	Given an Hermitian matrix and a complex vector, compute the complex product
OA01A	1963	E J York	To print out an m by n matrix in an easily read format
PA01A	1963	SHARE	To find all the real and complex roots of a polynomial with real coefficients
PA02A	1963	M J Hopper	To find all the real roots of a polynomial with real coefficients that fall within a given interval
PA03A	1963	H Simmonds	To find all the roots of a cubic polynomial
PA04A	1963	M Lancefield	To find the number of real roots above, below and within a specified interval
PA05A	1963	S Marlow	To find all the roots of a quartic polynomial
PE01A	1963	S Marlow	Calculates the coefficients of a polynomial given the coefficients of its expansion in terms of Chebyshev polynomials
PE03A	1963	C Brittain	Given the coefficients of a polynomial calculates the coefficients of its expansion in terms of Chebyshev polynomials
PE04A	1963	A T Sinden	Given a function f(x) in a range, find a rational approximation
QA02A	1963	M J D Powell	To evaluate the integral of f(x) between a and b to a specified absolute accuracy
QA03A	1963	M J D Powell	To tabulate an integral function
QB01A	1963	F R A Hopgood	To evaluate a 1 to 6 dimensional integral using user-specified quadrature method at each dimension: Simpson's rule, Gauss quadrature or a quadrature based on Chebyshev polynomials at
TA01A	1963	M J D Powell	To compute and print out a table of differences of a function when the function is given at equal intervals
TB01A	1963	A G Hearn	To interpolate the value of an even function f(x)=f(-x) given n+1 function values
TB02A	1963	A G Hearn	To interpolate the value of a function given n+1 function values
VA03A	1963	M J D Powell	Reduces the problem of finding the minimum of a function of n variables to that of finding a minimum of a function of one variable many times
VB03A	1963	M J D Powell	To minimise a sum of squares of m functions of n variables when values of the derivatives are available
VB06A	1963	M J D Powell	To calculate a least square fit to given data by a cubic spline which has knots specified by the user and subject to smoothing conditions imposed
VC01A	1963	E J York	To calculate a best weighted least square fit to given data by a polynomial of specified degree
FC01A	1964	A Bailey	To evaluate the function e^{-z²erfc(-iz) for complex z}
FF06A	1964	S Marlow	Given x > 0, computes values of all the Bessel functions ber(x), bei(x), ker(x), kei(x), ber'(x), bei'(x), ker'(x), kei'(x)
GA01A	1964	A Hearn	Calculate the cartesian coordinates x,y,z of a point given in spherical coordinates or vice versa
GA02A	1964	D Miller	Calculates the area bounded by a contour f(x,y)=c
ID02A	1964	A Gavan	Finds K the HCF of two given integers
ID03A	1964	A Bailey	Calculates the number of seconds between two given times given in years, months, days and hours
KC01A	1964	D Willis	Given a set of intervals on the real line, the routine finds the smallest set of disjoint intervals
KC02A	1964	D Willis	Given two set of non-overlapping intervals the routine merges the two sets together
MA07A	1964	D B Russell	To solve a system of n linear equations in n unknown when the equation coefficient matrix is band structured
MA08A	1964	M J Hopper	Forms the normal equations of the linear least squares problem
MA09A	1964	M J Hopper	Solves the linear least square problem by the so-called normal equation method
MA10A	1964	M J Hopper	To solve a system of n linear algebraic equations in n unknowns
MB01B	1964	L Morgan	To compute the inverse matrix of of an n by n real matrix
MB04A	1964	M J D Powell	Given A^-1 the inverse matrix of a partitioned n by n real symmetric matrix where A₁ is (n-1) by (n-1) top left, A₂ is a row matrix (bottom left), A₂ ^T is top right and bottom right is a scalar, calculates the (n-1) by (n-1) inverse matrix of A₁
MB05A	1964	M J D Powell	As above but calculates the inverse of A
MC07A	1964	M J D Powell	Given an n by n real symmetric matrix, calculates the coefficients of its characteristic polynomial
MD03A	1964	M J D Powell	To evaluate the determinant of an n by n real symmetric matrix
PC02A	1964	L Morgan	Given n+1 points, calculates the coefficients of the polynomial that passes through them
PE06A	1964	L Morgan	Given a polynomial C(x) of degree K finds the coefficients of the Pade approximation
PE07A	1964	S Northcliffe	To compute the value of a polynomial P(x) of degree n which is expresses as a linear combination of orthogonal polynomials
PE08A	1964	S Northcliffe	To obtain the coefficients of a polynomial expressed as a linear combination of orthogonal polynomials
SV01A	1964	M J D Powell	To extract from a minimization of a sum of squares an approximation to the variance-covariance matrix
TB03A	1964	D Miller	Calculates the coefficients of the piece-wise cubic function which interpolates n+1 given function values at specified points
VA02A	1964	M J D Powell	To minimize a sum of squares of m functions of n variables
VA04A	1964	M J D Powell	To find the minimum of a general function of n variables
VD01A	1964	M J D Powell	To find a minimum of a general function of one variable
VD02A	1964	M J D Powell	To find a minimum of a general function of one variable within a specified accuracy
DD01A	1965	P Hallowell	To solve the two point boundary value problem for the second order linear differential equation
DD02A	1965	P Hallowell	To solve the two point boundary value problem for the second order non-linear differential equation
DP01A	1965	P Hallowell	To solve the two point boundary value problem for the linear parabolic partial differential equation
EB04A	1965	P Hallowell	Finds all the eigenvalues, real and complex of a real upper Hessenberg matrix
EC02A	1965	E J York	Finds all the eigenvalues of a tri-diagonal Hermitian matrix
MA11B	1965	M J Hopper	To solve an over-determined system of m linear algebraic equations in n unknowns>
QC02AD	1965	A R Curtis	To find weights and zeros for Gaussian type quadrature of integrals of the form e^-xf(x) between 0 and infinity
TA02A	1965	D B Russell	To evaluate the divided differences of a function f(x) tabulated at a set of points not necessarily equally spaced
TA03A	1965	D B Russell	To evaluate the central differences of a function f(x) tabulated at equal intervals
TD01A	1965	P Hallowell	To estimate first or second derivatives given a table of function values and finite differences
DP02A	1966	P Hallowell	To solve the two point boundary value problem for the non-linear parabolic partial differential equation
EB05A	1966	M Reynolds	Given a real upper Hessenberg matrix A and one of its eigenvalues λ, finds the corresponding eigenvector
FC13A	1966	A R Curtis	To compute values of Dawson's integral
FF03A	1966	S Marlow	Computes values of the Bessel functions I₀(x) and K₀(x)
FF04A	1966	S Marlow	Computes values of the Bessel functions I₁(x) and K₁(x)
GA04A	1966	M Ruffle	Computes the solid angle subtended by a disc of unit radius from a general point in the plane perpendicular to the plane of the disc
KB01A	1966	M Reynolds	To sort an array of numbers into ascending order
KB02A	1966	M Reynolds	To sort an array of numbers into descending order
KB03A	1966	M Reynolds	To sort an array of numbers into ascending order maintaining an index array to preserve a record of the original order
KB04A	1966	M Reynolds	To sort an array of numbers into descending order maintaining an index array to preserve a record of the original order
LA01A	1966	M J Hopper	Solve the general linear programming problem
MA12A	1966	M Reynolds	To solve a system of n linear algebraic equations in n unknowns where the coefficient matrix is upper Hessenberg
MC04B	1966		Transform n by n real symmetric matrix in to a tri-diagonal matrix having the same eigen values
MC08A	1966	E J York	Transform an n by n matrix to an upper Hessenberg matrix
ME01B	1966		Transform an n by n Hermitian matrix into a tri-diagonal matrix having the same eigenvalues
ME04A	1966		To solve a system of n complex linear algebraic equations in n unknowns
PD03A	1966	A R Curtis	Given a polynomial in x, calculate the coefficients of the polynomial under a change of variable
PE11A	1966	S Marlow	Given m values of a function f(x) calculates the nth degree minimax polynomial
QM01A	1966	D Green	Evaluate the value of an n dimensional integral to a specified accuracy by a Monte Carlo method
TG01A	1966	M J D Powell	To compute the values of a cubic spline defined over a given range in the standard format
TG01B	1966	M J Hopper	To compute the value of a cubic spline given in terms of its knot points and its values and first derivative values
VB05B	1966	M J D Powell	To calculate the best weighted least squares fit to given data by a cubic spline with the number of knots specified by the user
ZE01A	1966	A R Curtis	To estimate the rounding errors generated in floating point arithmetic
DINT	1967	R C F McLatchie	Returns the double precision point value of the integer part of a real double precision floating point number
EB01A	1967	E J York, M Reynolds	Finds all the eigenvalues and eigenvectors of a general real matrix
FA01AS	1967	R C F McLatchie	Generate uniformly distributed pseudo-random numbers
FA02AS	1967		To return the signed fractional part of a real floating point number
FB01A	1967	S Marlow	Compute values of the complete elliptic integrals of the 1st and 2nd kind
FB02A	1967	L Morgan	Compute values of the incomplete elliptic integrals of the 1st and 2nd kind
FB03a	1967	M Ruffle	Compute values of the complete elliptic integral of the 3rd kind
FT01A	1967	A R Curtis	Calculates discrete Fourier transforms
GA03A	1967	E J York	Constructs a system of plane contours f(x,y) = c_k for k=1,..,N over a specified rectangular region
OD01A	1967	D McVicar	To allow a FORTRAN programmer to read or write paper tape
OD02A	1967	R Garside	To allow a FORTRAN programmer to read or write Dectape
ON01B	1967	M Ruffle	To provide a free format input facility for the FORTRAN user
PC01A	1967	W E Hart	To calculate the coefficients of a polynomial given all its roots, the roots must be real
PE05AD	1967	A R Curtis	Given a smooth function in a range finds a weighted rational approximation
VC03A	1967	M J D Powell	To calculate a smooth weighted least square fit to given data by a cubic spline
MA14A	1968	M J Hopper	To calculate a least square solution to an over-determined system of m linear equations in n unknowns
NS03A	1968	M J D Powell	To solve a system of n non-linear equations in n unknowns
OA02A	1968	M J Hopper	To print out contents of a single dimensional array in tabular form
ON02A	1968	R C F McLatchie	Given a data card containing numeric data items constructs the FORTRAN format required to read the numbers from the card
QD01A	1968	W E Hart	To evaluate integrals of the form f(t) sin xt dt between a and b and the cosine equivalent
FG01A	1969	J Soper	To compute the various vector coupling coefficients (3-j, 6-j, 9-j etc)
OC01A	1969	A R Curtis	To produce a graph of several dependent variables against an independent variable on a lineprinter
VA05A	1969	M J D Powell	To minimise a sum of squares of m functions in n variables
VE01A	1969	R Fletcher	To find the minimum of a general function subject to a number of linear inequality constraints
DC01AD	1970	A R Curtis, A B Smith	A package of routines to integrate a system of first order ordinary differential equations
DC02AD	1970	A R Curtis	A package of routines to integrate a system of first order ordinary differential equations
EA07C	1970	J K Reid	Given a real symmetric matrix A, find all its eigen vectors λ_i and eigenvectors x_i
EA08C	1970	J K Reid	Given a real symmetric matrix A, find all its eigen vectors
EA09C	1970	J K Reid	Find all the eigenvalues of a real tri-diagonal symmetric matrix. The QR algorithm with shifts is used
LA02A	1970	R Fletcher	To find a feasible point to a set of linear constraints
MA07B	1970	J K Reid	To solve a system of n linear algebraic equations where the equation coefficient matrix has a band structure
MA16A	1970	J K Reid	To solve a system of n linear algebraic equations in n unknowns when the coefficient matrix is symmetric positive definite and is very large and sparse
MB10A	1970	M J D Powell	To calculate the generalized inverse of an m by n rectangular matrix
MB11A	1970	M J D Powell	As MB10A where the rank of A is equal to m
OA03A	1970	M J Hopper	To print out in tabular form the contents of two single dimensional arrays
PD02A	1970	M J Hopper	To give the first m terms of the Taylor series expansion of functions of a given polynomial
SA02A	1970	D G Papworth	To evaluate the one-sided cumulative distribution function of Student's distribution
SA03A	1970	D G Papworth	To evaluate the complement of the cumulative distribution function of the variance ratio distribution
TB04A	1970	J K Reid	Given function values at a set of points, find a cubic spline that interpolates the function values
TB05A	1970	J K Reid	Given function values at a set of points, find a periodic cubic spline that interpolates the function values
VA06A	1970	M J D Powell	To calculate the minimum of a general function of n values when values of the derivatives can be provided
VE02A	1970	R Fletcher	To find a minimum of a quadratic function subject to linear constraints
EC06C	1971	S Marlow	Given a complex Hermitian matrix, finds all its eigenvalues and eigenvectors
EC07C	1971	S Marlow	Given a complex Hermitian matrix, finds all its eigenvalues and eigenvectors with a defined constraint
EC08C	1971	S Marlow	Finds all the eigen values of a complex Hermitian tri-diagonal matrix
FA03A	1971	A B Smith	Generate pseudo-random numbers from a Gaussian distribution with mean zero and standard deviation specified by the user
FD01AS	1971	M Hopper	Given an integer n will compute 2ⁿ
FD01BS	1971	M Hopper	Given an integer n will compute 16ⁿ
MA18A	1971	A R Curtis, J K Reid	To solve a system of n linear algebraic equations when the coefficient matrix is large and sparse
MA21A	1971	S Marlow, J K Reid	Given an n by n matrix a) solves the system of algebraic equations b) computes the inverse matrix c) computes the value of the determinant
MA22A	1971	S Marlow, J K Reid	Given a symmetric positive definite n by n matrix a) solves the system of linear equations b) computes the inverse matrix c) computes the value of the determinant
MA23A	1971	S Marlow, J K Reid	Given a complex n by n matrix and a complex right hand side, solve the complex linear equations, compute the inverse or evaluate the determinant
MA24A	1971	S Marlow, J K Reid	Given a complex Hermitian n by n matrix and a complex right hand side, solve the complex linear equations, compute the inverse or evaluate the determinant
MC10A	1971	J K Reid	Calculates scaling factors for the rows and columns of an n by n real matrix
MC12A	1971	A R Curtis	Calculates scaling factors for the rows and columns of an n by n real sparse matrix
ME06AS	1971	S Marlow	To evaluate the sum of a complex constant c and an inner product of two complex vectors accumulating intermediate results double length
ME07A	1971	S Marlow	Calculates scaling factors for the rows and columns of an n by n complex matrix
ME08A	1971	S Marlow	Transforms an n by n complex Hermitian matrix to a tri-diagonal Hermitian matrix
OB01A	1971	A R Curtis	Simple editing facilities for the modification of source code
SA01A	1971	M J Hopper, J Hedger	To evaluate the cumulative chi-squared probability function
VA07A	1971	R Fletcher	To minimise a sum of squares of m functions of n variables when the values of the derivatives are available
VA11A	1971	M D Hebden	To calculate the minimum of a general function of n variables when values of both the first and second derivatives can be provided
VE03A	1971	R Fletcher	To find the minimum of a general function satisfying a set of linear constraints
DA02A	1972	A R Curtis, A B Smith	To integrate a set of first order differential equations
EA11A	1972	S Marlow	Calculates all the eigenvalues λ_i and eigenvector x_i of the system Ax_i=λ_iBx_i
GA05A	1972	J K Reid	To efficiently determine whether a point (x,y) is interior or exterior to a given closed region
KB11A	1972	M J Hopper	To sort n numbers from an array of m numbers
MA15C	1972	J K Reid	To sole a system of n linear algebraic equations in n unknowns where the coefficient matrix is band structured, symmetric and positive definite
MA17A	1972	J K Reid	To solve a system of n linear algebraic equations in n unknowns when the coefficient matrix is large and sparse and symmetric positive definite
MA20A	1972	I Barrowdale	To solve an over-determined system of m linear equations in n unknowns
MC09A	1972	J K Reid	Given a sparse matrix stored in a compact form evaluates the matrix-vector products
NB01A	1972	M J D Powell	To find a real zero of a continuous function f(x) in a given interval
NS03A	1972	J K Reid	To solve a system of m non-linear equations in n unknowns
OB11A	1972	S Marlow, M J D Powell	To draw on the graph plotter a smooth, tangentially continuous curve
OB12A	1972	S Marlow, M J D Powell	To draw on the graph plotter a cubic spline defined by its knots
QA04A	1972	I G A Robinson, A B Smith	To evaluate the integral of f(x) between a and b to a specified relative or absolute accuracy
QA05A	1972	C de Boor modified by A R Curtis	To evaluate the integral f(x) between a and b to a specified accuracy which may be relative or absolute
TD02A	1972	J K Reid	Given n functions, evaluates an approximation to the Jacobian matrix
TS01A	1972	M J D Powell	Finds a cubic spline approximation to a given smooth function within a prescribed accuracy
VA08A	1972	R Fletcher	To find the minimum of a general function of n variables when values of the derivatives can be provided
VA09A	1972	R Fletcher	To find the minimum of a general function of n variables when values of the derivatives can be provided
VA10A	1972	R Fletcher	To find the minimum of a general function of n variables when the function is differentiable although values of the derivatives are not required
VB01A	1972	R Fletcher	To calculate the best least squares fit to given data
VC04A	1972	J Ledger	To fit a straight line to data