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     DOC INTRO(3NAG)   Foundation Library (12/10/92)   DOC INTRO(3NAG)



                    Introduction to NAG On-Line Documentation


          The on-line documentation for the NAG Foundation Library has been
          generated automatically from the same base material used to
          create the printed Reference Manual. To make the documentation
          readable on the widest range of machines, only the basic set of
          ascii characters has been used.

          Certain mathematical symbols have been constructed using plain
          ascii characters:

          integral signs                /
                                        |

                                        /

          summation signs               --
                                        >
                                        --

          square root signs                ----
                                          /
                                        \/


          Large brackets are constructed using vertical stacks of the
          equivalent ascii character:

                              (  )  [  ]  {  }  |
                              (  )  [  ]  {  }  |
                              (  )  [  ]  {  }  |


          Fractions are represented as:

                                       a
                                      ---
                                      x+1


          Greek letters are represented by their names enclosed in round
          brackets:

                  (alpha)  (beta)  (gamma) .....

                  (Alpha)  (Beta)  (Gamma) .....


          Some characters are accented using:

                  ^     ~     
                  X     X     X

          Other mathematical symbols are represented as follows:

                 *           times

                 <=>         left-right arrow

                 <-          left arrow

                 ~           similar to

                 ~=          similar or equal to

                 ==          equivalent to

                 >=          greater than or equal to

                 <=          less than or equal to

                 >>          much greater than

                 <<          much less than

                 >~          greater than or similar to

                 /=          not equal to

                 dd          partial derivative

                 +-          plus or minus

                 (nabla)     Nabla

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     SUMMARY(3NAG)     Foundation Library (12/10/92)     SUMMARY(3NAG)



          Introduction                                     List of Routines
          List of Routines

          The NAG Foundation Library contains three categories of routines
          which can be called by users. They are listed separately in the
          three sections below.

          Fully Documented Routines
                254 routines, for each of which an individual routine
                document is provided. These are regarded as the primary
                contents of the Foundation Library.

          Fundamental Support Routines
                83 comparatively simple routines which are documented in
                compact form in the relevant Chapter Introductions (F06,
                X01, X02).

          Routines from the NAG Fortran Library
                An additional 167 routines from the NAG Fortran Library,
                which are used as auxiliaries in the Foundation Library.
                They are not documented in this publication, but can be
                called if you are already familiar with their use in the
                Fortran Library. Only their names are given here.


          Note: all the routines in the above categories have names ending
          in 'F'. Occasionally this publication may refer to routines whose
          names end in some other letter (e.g. 'Z', 'Y', 'X'). These are
          auxiliary routines whose names may be passed as parameters to a
          Foundation Library routine; you only need to know their names,
          not how to call them directly.

          Fully Documented Routines

          The Foundation Library contains 254 user-callable routines, for
          each of which an individual routine document is provided, in the
          following chapters:

          C02 -- Zeros of Polynomials

          C02AFF  All zeros of complex polynomial, modified Laguerre method

          C02AGF  All zeros of real polynomial, modified Laguerre method

          C05 -- Roots of One or More Transcendental Equations

          C05ADF  Zero of continuous function in given interval, Bus and
                  Dekker algorithm

          C05NBF  Solution of system of nonlinear equations using function
                  values only

          C05PBF  Solution of system of nonlinear equations using 1st
                  derivatives

          C05ZAF  Check user's routine for calculating 1st derivatives

          C06 -- Summation of Series

          C06EAF  Single 1-D real discrete Fourier transform, no extra
                  workspace

          C06EBF  Single 1-D Hermitian discrete Fourier transform, no extra
                  workspace

          C06ECF  Single 1-D complex discrete Fourier transform, no extra
                  workspace

          C06EKF  Circular convolution or correlation of two real vectors,
                  no extra workspace

          C06FPF  Multiple 1-D real discrete Fourier transforms

          C06FQF  Multiple 1-D Hermitian discrete Fourier transforms

          C06FRF  Multiple 1-D complex discrete Fourier transforms

          C06FUF  2-D complex discrete Fourier transform

          C06GBF  Complex conjugate of Hermitian sequence

          C06GCF  Complex conjugate of complex sequence

          C06GQF  Complex conjugate of multiple Hermitian sequences

          C06GSF  Convert Hermitian sequences to general complex sequences

          D01 -- Quadrature

          D01AJF  1-D quadrature, adaptive, finite interval, strategy due
                  to Piessens and de Doncker, allowing for badly-behaved
                  integrands

          D01AKF  1-D quadrature, adaptive, finite interval, method
                  suitable for oscillating functions

          D01ALF  1-D quadrature, adaptive, finite interval, allowing for
                  singularities at user-specified break-points

          D01AMF  1-D quadrature, adaptive, infinite or semi-infinite
                  interval

          D01ANF  1-D quadrature, adaptive, finite interval, weight
                  function cos((omega)x) or sin((omega)x)

          D01APF  1-D quadrature, adaptive, finite interval, weight
                  function with end-point singularities of algebraico-
                  logarithmic type

          D01AQF  1-D quadrature, adaptive, finite interval, weight
                  function 1/(x-c), Cauchy principal value (Hilbert
                  transform)

          D01ASF  1-D quadrature, adaptive, semi-infinite interval, weight
                  function cos((omega)x) or sin((omega)x)

          D01BBF  Weights and abscissae for Gaussian quadrature rules

          D01FCF  Multi-dimensional adaptive quadrature over hyper-
                  rectangle

          D01GAF  1-D quadrature, integration of function defined by data
                  values, Gill-Miller method

          D01GBF  Multi-dimensional quadrature over hyper-rectangle, Monte
                  Carlo method

          D02 -- Ordinary Differential Equations

          D02BBF  ODEs, IVP, Runge-Kutta-Merson method, over a range,
                  intermediate output

          D02BHF  ODEs, IVP, Runge-Kutta-Merson method, until function of
                  solution is zero

          D02CJF  ODEs, IVP, Adams method, until function of solution is
                  zero, intermediate output

          D02EJF  ODEs, stiff IVP, BDF method, until function of solution
                  is zero, intermediate output

          D02GAF  ODEs, boundary value problem, finite difference technique
                  with deferred correction, simple nonlinear problem

          D02GBF  ODEs, boundary value problem, finite difference technique
                  with deferred correction, general linear problem

          D02KEF  2nd order Sturm-Liouville problem, regular/singular
                  system, finite/infinite range, eigenvalue and
                  eigenfunction, user-specified break-points

          D02RAF  ODEs, general nonlinear boundary value problem, finite
                  difference technique with deferred correction,
                  continuation facility

          D03 -- Partial Differential Equations

          D03EDF  Elliptic PDE, solution of finite difference equations by
                  a multigrid technique

          D03EEF  Discretize a 2nd order elliptic PDE on a rectangle

          D03FAF  Elliptic PDE, Helmholtz equation, 3-D Cartesian co-
                  ordinates

          E01 -- Interpolation

          E01BAF  Interpolating functions, cubic spline interpolant, one
                  variable

          E01BEF  Interpolating functions, monotonicity-preserving,
                  piecewise cubic Hermite, one variable

          E01BFF  Interpolated values, interpolant computed by E01BEF,
                  function only, one variable

          E01BGF  Interpolated values, interpolant computed by E01BEF,
                  function and 1st derivative, one variable

          E01BHF  Interpolated values, interpolant computed by E01BEF,
                  definite integral, one variable

          E01DAF  Interpolating functions, fitting bicubic spline, data on
                  rectangular grid

          E01SAF  Interpolating functions, method of Renka and Cline, two
                  variables

          E01SBF  Interpolated values, evaluate interpolant computed by
                  E01SAF, two variables

          E01SEF  Interpolating functions, modified Shepard's method, two
                  variables

          E01SFF  Interpolated values, evaluate interpolant computed by
                  E01SEF, two variables

          E02 -- Curve and Surface Fitting

          E02ADF  Least-squares curve fit, by polynomials, arbitrary data
                  points

          E02AEF  Evaluation of fitted polynomial in one variable from
                  Chebyshev series form (simplified parameter list)

          E02AGF  Least-squares polynomial fit, values and derivatives may
                  be constrained, arbitrary data points,

          E02AHF  Derivative of fitted polynomial in Chebyshev series form

          E02AJF  Integral of fitted polynomial in Chebyshev series form

          E02AKF  Evaluation of fitted polynomial in one variable, from
                  Chebyshev series form

          E02BAF  Least-squares curve cubic spline fit (including
                  interpolation)

          E02BBF  Evaluation of fitted cubic spline, function only

          E02BCF  Evaluation of fitted cubic spline, function and
                  derivatives

          E02BDF  Evaluation of fitted cubic spline, definite integral

          E02BEF  Least-squares cubic spline curve fit, automatic knot
                  placement

          E02DAF  Least-squares surface fit, bicubic splines

          E02DCF  Least-squares surface fit by bicubic splines with
                  automatic knot placement, data on rectangular grid

          E02DDF  Least-squares surface fit by bicubic splines with
                  automatic knot placement, scattered data

          E02DEF  Evaluation of a fitted bicubic spline at a vector of
                  points

          E02DFF  Evaluation of a fitted bicubic spline at a mesh of points

          E02GAF  L -approximation by general linear function
                   1

          E02ZAF  Sort 2-D data into panels for fitting bicubic splines

          E04 -- Minimizing or Maximizing a Function

          E04DGF  Unconstrained minimum, pre-conditioned conjugate gradient
                  algorithm, function of several variables using 1st
                  derivatives

          E04DJF  Read optional parameter values for E04DGF from external
                  file

          E04DKF  Supply optional parameter values to E04DGF

          E04FDF  Unconstrained minimum of a sum of squares, combined
                  Gauss-Newton and modified Newton algorithm using function
                  values only

          E04GCF  Unconstrained minimum of a sum of squares, combined
                  Gauss-Newton and quasi-Newton algorithm, using 1st
                  derivatives

          E04JAF  Minimum, function of several variables, quasi-Newton
                  algorithm, simple bounds, using function values only

          E04MBF  Linear programming problem

          E04NAF  Quadratic programming problem

          E04UCF  Minimum, function of several variables, sequential QP
                  method, nonlinear constraints, using function values and
                  optionally 1st derivatives

          E04UDF  Read optional parameter values for E04UCF from external
                  file

          E04UEF  Supply optional parameter values to E04UCF

          E04YCF  Covariance matrix for nonlinear least-squares problem

          F01 -- Matrix Factorizations

          F01BRF  LU factorization of real sparse matrix

          F01BSF  LU factorization of real sparse matrix with known
                  sparsity pattern

                    T
          F01MAF  LL  factorization of real sparse symmetric positive-
                  definite matrix

                     T
          F01MCF  LDL  factorization of real symmetric positive-definite
                  variable-bandwidth matrix

          F01QCF  QR factorization of real m by n matrix (m>=n)

                                                                      T
          F01QDF  Operations with orthogonal matrices, compute QB or Q B
                  after factorization by F01QCF

          F01QEF  Operations with orthogonal matrices, form columns of Q
                  after factorization by F01QCF

          F01RCF  QR factorization of complex m by n matrix (m>=n)

                                                                   H
          F01RDF  Operations with unitary matrices, compute QB or Q B after
                  factorization by F01RCF

          F01REF  Operations with unitary matrices, form columns of Q after
                  factorization by F01RCF

          F02 -- Eigenvalues and Eigenvectors

          F02AAF  All eigenvalues of real symmetric matrix

          F02ABF  All eigenvalues and eigenvectors of real symmetric matrix

          F02ADF  All eigenvalues of generalized real symmetric-definite
                  eigenproblem

          F02AEF  All eigenvalues and eigenvectors of generalized real
                  symmetric-definite eigenproblem

          F02AFF  All eigenvalues of real matrix

          F02AGF  All eigenvalues and eigenvectors of real matrix

          F02AJF  All eigenvalues of complex matrix

          F02AKF  All eigenvalues and eigenvectors of complex matrix

          F02AWF  All eigenvalues of complex Hermitian matrix

          F02AXF  All eigenvalues and eigenvectors of complex Hermitian
                  matrix

          F02BBF  Selected eigenvalues and eigenvectors of real symmetric
                  matrix

          F02BJF  All eigenvalues and optionally eigenvectors of
                  generalized eigenproblem by QZ algorithm, real matrices

          F02FJF  Selected eigenvalues and eigenvectors of sparse symmetric
                  eigenproblem

          F02WEF  SVD of real matrix

          F02XEF  SVD of complex matrix

          F04 -- Simultaneous Linear Equations

          F04ADF  Approximate solution of complex simultaneous linear
                  equations with multiple right-hand sides

          F04ARF  Approximate solution of real simultaneous linear
                  equations, one right-hand side

          F04ASF  Accurate solution of real symmetric positive-definite
                  simultaneous linear equations, one right-hand side

          F04ATF  Accurate solution of real simultaneous linear equations,
                  one right-hand side

          F04AXF  Approximate solution of real sparse simultaneous linear
                  equations (coefficient matrix already factorized by
                  F01BRF or F01BSF)

          F04FAF  Approximate solution of real symmetric positive-definite
                  tridiagonal simultaneous linear equations, one right-hand
                  side

          F04JGF  Least-squares (if rank = n) or minimal least-squares (if
                  rank <n) solution of m real equations in n unknowns, rank
                  <=n, m>=n

          F04MAF  Real sparse symmetric positive-definite simultaneous
                  linear equations (coefficient matrix already factorized)

          F04MBF  Real sparse symmetric simultaneous linear equations

          F04MCF  Approximate solution of real symmetric positive-definite
                  variable-bandwidth simultaneous linear equations
                  (coefficient matrix already factorized)

          F04QAF  Sparse linear least-squares problem, m real equations in
                  n unknowns

          F07 -- Linear Equations (LAPACK)

          F07ADF  (DGETRF) LU factorization of real m by n matrix

          F07AEF  (DGETRS) Solution of real system of linear equations,
                  multiple right-hand sides, matrix already factorized by
                  F07ADF

          F07FDF  (DPOTRF) Cholesky factorization of real symmetric
                  positive-definite matrix

          F07FEF  (DPOTRS) Solution of real symmetric positive-definite
                  system of linear equations, multiple right-hand sides,
                  matrix already factorized by F07FDF

          G01 -- Simple Calculations on Statistical Data

          G01AAF  Mean, variance, skewness, kurtosis etc, one variable,
                  from raw data

          G01ADF  Mean, variance, skewness, kurtosis etc, one variable,
                  from frequency table

          G01AEF  Frequency table from raw data


          G01AFF  Two-way contingency table analysis, with (chi) /Fisher's
                  exact test

          G01ALF  Computes a five-point summary (median, hinges and
                  extremes)

          G01ARF  Constructs a stem and leaf plot

          G01EAF  Computes probabilities for the standard Normal
                  distribution

          G01EBF  Computes probabilities for Student's t-distribution

                                                  2
          G01ECF  Computes probabilities for (chi)  distribution

          G01EDF  Computes probabilities for F-distribution

          G01EEF  Computes upper and lower tail probabilities and
                  probability density function for the beta distribution

          G01EFF  Computes probabilities for the gamma distribution

          G01FAF  Computes deviates for the standard Normal distribution

          G01FBF  Computes deviates for Student's t-distribution

                                                 2
          G01FCF  Computes deviates for the (chi)  distribution

          G01FDF  Computes deviates for the F-distribution

          G01FEF  Computes deviates for the beta distribution

          G01FFF  Computes deviates for the gamma distribution

          G01HAF  Computes probabilities for the bivariate Normal
                  distribution

          G02 -- Correlation and Regression Analysis

          G02BNF  Kendall/Spearman non-parametric rank correlation
                  coefficients, no missing values, overwriting input data

          G02BQF  Kendall/Spearman non-parametric rank correlation
                  coefficients, no missing values, preserving input data

          G02BXF  Computes (optionally weighted) correlation and covariance
                  matrices

          G02CAF  Simple linear regression with constant term, no missing
                  values

          G02DAF  Fits a general (multiple) linear regression model

          G02DGF  Fits a general linear regression model for new dependent
                  variable

          G02DNF  Computes estimable function of a general linear
                  regression model and its standard error

          G02FAF  Calculates standardized residuals and influence
                  statistics

          G02GBF  Fits a generalized linear model with binomial errors

          G02GCF  Fits a generalized linear model with Poisson errors

          G03 -- Multivariate Methods

          G03AAF  Performs principal component analysis

          G03ADF  Performs canonical correlation analysis

          G03BAF  Computes orthogonal rotations for loading matrix,
                  generalized orthomax criterion

          G05 -- Random Number Generators

          G05CAF  Pseudo-random double precision numbers, uniform
                  distribution over (0,1)

          G05CBF  Initialise random number generating routines to give
                  repeatable sequence

          G05CCF  Initialise random number generating routines to give non-
                  repeatable sequence

          G05CFF  Save state of random number generating routines

          G05CGF  Restore state of random number generating routines

          G05DDF  Pseudo-random double precision numbers, Normal
                  distribution

          G05DFF  Pseudo-random double precision numbers, Cauchy
                  distribution

          G05DPF  Pseudo-random double precision numbers, Weibull
                  distribution

          G05DYF  Pseudo-random integer from uniform distribution

          G05DZF  Pseudo-random logical (boolean) value

          G05EAF  Set up reference vector for multivariate Normal
                  distribution

          G05ECF  Set up reference vector for generating pseudo-random
                  integers, Poisson distribution

          G05EDF  Set up reference vector for generating pseudo-random
                  integers, binomial distribution

          G05EHF  Pseudo-random permutation of an integer vector

          G05EJF  Pseudo-random sample from an integer vector

          G05EXF  Set up reference vector from supplied cumulative
                  distribution function or probability distribution
                  function

          G05EYF  Pseudo-random integer from reference vector

          G05EZF  Pseudo-random multivariate Normal vector from reference
                  vector

          G05FAF  Generates a vector of pseudo-random numbers from a
                  uniform distribution

          G05FBF  Generates a vector of pseudo-random numbers from a
                  (negative) exponential distribution

          G05FDF  Generates a vector of pseudo-random numbers from a Normal
                  distribution

          G05FEF  Generates a vector of pseudo-random numbers from a beta
                  distribution

          G05FFF  Generates a vector of pseudo-random numbers from a gamma
                  distribution

          G05HDF  Generates a realisation of a multivariate time series
                  from a VARMA model

          G08 -- Nonparameteric Statistics

          G08AAF  Sign test on two paired samples

          G08ACF  Median test on two samples of unequal size

          G08AEF  Friedman two-way analysis of variance on k matched
                  samples

          G08AFF  Kruskal-Wallis one-way analysis of variance on k samples
                  of unequal size

          G08AGF  Performs the Wilcoxon one sample (matched pairs) signed
                  rank test

          G08AHF  Performs the Mann-Whitney U test on two independent
                  samples

          G08AJF  Computes the exact probabilities for the Mann-Whitney U
                  statistic, no ties in pooled sample

          G08AKF  Computes the exact probabilities for the Mann-Whitney U
                  statistic, ties in pooled sample

                                    2
          G08CGF  Performs the (chi)  goodness of fit test, for standard
                  continuous distributions

          G13 -- Time Series Analysis

          G13AAF  Univariate time series, seasonal and non-seasonal
                  differencing

          G13ABF  Univariate time series, sample autocorrelation function

          G13ACF  Univariate time series, partial autocorrelations from
                  autocorrelations

          G13ADF  Univariate time series, preliminary estimation, seasonal
                  ARIMA model

          G13AFF  Univariate time series, estimation, seasonal ARIMA model

          G13AGF  Univariate time series, update state set for forecasting

          G13AHF  Univariate time series, forecasting from state set

          G13AJF  Univariate time series, state set and forecasts, from
                  fully specified seasonal ARIMA model

          G13ASF  Univariate time series, diagnostic checking of residuals,
                  following G13AFF

          G13BAF  Multivariate time series, filtering (pre-whitening) by an
                  ARIMA model

          G13BCF  Multivariate time series, cross correlations

          G13BDF  Multivariate time series, preliminary estimation of
                  transfer function model

          G13BEF  Multivariate time series, estimation of multi-input model

          G13BJF  Multivariate time series, state set and forecasts from
                  fully specified multi-input model

          G13CBF  Univariate time series, smoothed sample spectrum using
                  spectral smoothing by the trapezium frequency (Daniell)
                  window

          G13CDF  Multivariate time series, smoothed sample cross spectrum
                  using spectral smoothing by the trapezium frequency
                  (Daniell) window

          M01 -- Sorting

          M01CAF  Sort a vector, double precision numbers

          M01DAF  Rank a vector, double precision numbers

          M01DEF  Rank rows of a matrix, double precision numbers

          M01DJF  Rank columns of a matrix, double precision numbers

          M01EAF  Rearrange a vector according to given ranks, double
                  precision numbers

          M01ZAF  Invert a permutation

          S -- Approximations of Special Functions

                                        z
          S01EAF  Complex exponential, e

          S13AAF  Exponential integral E (x)
                                        1

          S13ACF  Cosine integral Ci(x)

          S13ADF  Sine integral Si(x)

          S14AAF  Gamma function

          S14ABF  Log Gamma function

          S14BAF  Incomplete gamma functions P(a,x) and Q(a,x)

          S15ADF  Complement of error function erfc x

          S15AEF  Error function erf x

          S17ACF  Bessel function Y (x)
                                   0

          S17ADF  Bessel function Y (x)
                                   1

          S17AEF  Bessel function J (x)
                                   0

          S17AFF  Bessel function J (x)
                                   1

          S17AGF  Airy function Ai(x)

          S17AHF  Airy function Bi(x)

          S17AJF  Airy function Ai'(x)

          S17AKF  Airy function Bi'(x)

          S17DCF  Bessel functions Y      (z), real a>=0, complex z,
                                    (nu)+a
                  (nu)=0,1,2,...

          S17DEF  Bessel functions J      (z), real a>=0, complex z,
                                    (nu)+a
                  (nu)=0,1,2,...

          S17DGF  Airy functions Ai(z) and Ai'(z), complex z

          S17DHF  Airy functions Bi(z) and Bi'(z), complex z

                                    (j)
          S17DLF  Hankel functions H      (z), j=1,2, real a>=0, complex z,
                                    (nu)+a
                  (nu)=0,1,2,...

          S18ACF  Modified Bessel function K (x)
                                            0

          S18ADF  Modified Bessel function K (x)
                                            1

          S18AEF  Modified Bessel function I (x)
                                            0

          S18AFF  Modified Bessel function I (x)
                                            1

          S18DCF  Modified Bessel functions K      (z), real a>=0, complex
                                             (nu)+a
                  z, (nu)=0,1,2,...

          S18DEF  Modified Bessel functions I      (z), real a>=0, complex
                                             (nu)+a
                  z, (nu)=0,1,2,...

          S19AAF  Kelvin function ber x

          S19ABF  Kelvin function bei x

          S19ACF  Kelvin function ker x

          S19ADF  Kelvin function kei x

          S20ACF  Fresnel integral S(x)

          S20ADF  Fresnel integral C(x)

          S21BAF  Degenerate symmetrised elliptic integral of 1st kind
                  R (x,y)
                   C

          S21BBF  Symmetrised elliptic integral of 1st kind R (x,y,z)
                                                             F

          S21BCF  Symmetrised elliptic integral of 2nd kind R (x,y,z)
                                                             D

          S21BDF  Symmetrised elliptic integral of 3rd kind R (x,y,z,r)
                                                             J

          X04 -- Input/Output Utilities

          X04AAF  Return or set unit number for error messages

          X04ABF  Return or set unit number for advisory messages

          X04CAF  Print a real general matrix

          X04DAF  Print a complex general matrix

          X05 -- Date and Time Utilities

          X05AAF  Return date and time as an array of integers

          X05ABF  Convert array of integers representing date and time to
                  character string

          X05ACF  Compare two character strings representing date and time

          X05BAF  Return the CPU time



          Fundamental Support Routines

          The following fundamental support routines are provided and are
          documented in compact form in the relevant chapter introductory
          material:

          F06 -- Linear Algebra Support Routines

          F06AAF  (DROTG) Generate real plane rotation

          F06EAF  (DDOT) Dot product of two real vectors

          F06ECF  (DAXPY) Add scalar times real vector to real vector

          F06EDF  (DSCAL) Multiply real vector by scalar

          F06EFF  (DCOPY) Copy real vector

          F06EGF  (DSWAP) Swap two real vectors

          F06EJF  (DNRM2) Compute Euclidean norm of real vector

          F06EKF  (DASUM) Sum the absolute values of real vector elements

          F06EPF  (DROT) Apply real plane rotation

          F06GAF  (ZDOTU) Dot product of two complex vectors, unconjugated

          F06GBF  (ZDOTC) Dot product of two complex vectors, conjugated

          F06GCF  (ZAXPY) Add scalar times complex vector to complex vector

          F06GDF  (ZSCAL) Multiply complex vector by complex scalar

          F06GFF  (ZCOPY) Copy complex vector

          F06GGF  (ZSWAP) Swap two complex vectors

          F06JDF  (ZDSCAL) Multiply complex vector by real scalar

          F06JJF  (DZNRM2) Compute Euclidean norm of complex vector

          F06JKF  (DZASUM) Sum the absolute values of complex vector
                  elements

          F06JLF  (IDAMAX) Index, real vector element with largest absolute
                  value

          F06JMF  (IZAMAX) Index, complex vector element with largest
                  absolute value

          F06PAF  (DGEMV) Matrix-vector product, real rectangular matrix

          F06PBF  (DGBMV) Matrix-vector product, real rectangular band
                  matrix

          F06PCF  (DSYMV) Matrix-vector product, real symmetric matrix

          F06PDF  (DSBMV) Matrix-vector product, real symmetric band matrix

          F06PEF  (DSPMV) Matrix-vector product, real symmetric packed
                  matrix

          F06PFF  (DTRMV) Matrix-vector product, real triangular matrix

          F06PGF  (DTBMV) Matrix-vector product, real triangular band
                  matrix

          F06PHF  (DTPMV) Matrix-vector product, real triangular packed
                  matrix

          F06PJF  (DTRSV) System of equations, real triangular matrix

          F06PKF  (DTBSV) System of equations, real triangular band matrix

          F06PLF  (DTPSV) System of equations, real triangular packed
                  matrix

          F06PMF  (DGER) Rank-1 update, real rectangular matrix

          F06PPF  (DSYR) Rank-1 update, real symmetric matrix

          F06PQF  (DSPR) Rank-1 update, real symmetric packed matrix

          F06PRF  (DSYR2) Rank-2 update, real symmetric matrix

          F06PSF  (DSPR2) Rank-2 update, real symmetric packed matrix

          F06SAF  (ZGEMV) Matrix-vector product, complex rectangular matrix

          F06SBF  (ZGBMV) Matrix-vector product, complex rectangular band
                  matrix

          F06SCF  (ZHEMV) Matrix-vector product, complex Hermitian matrix

          F06SDF  (ZHBMV) Matrix-vector product, complex Hermitian band
                  matrix

          F06SEF  (ZHPMV) Matrix-vector product, complex Hermitian packed
                  matrix

          F06SFF  (ZTRMV) Matrix-vector product, complex triangular matrix

          F06SGF  (ZTBMV) Matrix-vector product, complex triangular band
                  matrix

          F06SHF  (ZTPMV) Matrix-vector product, complex triangular packed
                  matrix

          F06SJF  (ZTRSV) System of equations, complex triangular matrix

          F06SKF  (ZTBSV) System of equations, complex triangular band
                  matrix

          F06SLF  (ZTPSV) System of equations, complex triangular packed
                  matrix

          F06SMF  (ZGERU) Rank-1 update, complex rectangular matrix,
                  unconjugated vector

          F06SNF  (ZGERC) Rank-1 update, complex rectangular matrix,
                  conjugated vector

          F06SPF  (ZHER) Rank-1 update, complex Hermitian matrix

          F06SQF  (ZHPR) Rank-1 update, complex Hermitian packed matrix

          F06SRF  (ZHER2) Rank-2 update, complex Hermitian matrix

          F06SSF  (ZHPR2) Rank-2 update, complex Hermitian packed matrix

          F06YAF  (DGEMM) Matrix-matrix product, two real rectangular
                  matrices

          F06YCF  (DSYMM) Matrix-matrix product, one real symmetric matrix,
                  one real rectangular matrix

          F06YFF  (DTRMM) Matrix-matrix product, one real triangular
                  matrix, one real rectangular matrix

          F06YJF  (DTRSM) Solves a system of equations with multiple right-
                  hand sides, real triangular coefficient matrix

          F06YPF  (DSYRK) Rank-k update of a real symmetric matrix

          F06YRF  (DSYR2K) Rank-2k update of a real symmetric matrix

          F06ZAF  (ZGEMM) Matrix-matrix product, two complex rectangular
                  matrices

          F06ZCF  (ZHEMM) Matrix-matrix product, one complex Hermitian
                  matrix, one complex rectangular matrix

          F06ZFF  (ZTRMM) Matrix-matrix product, one complex triangular
                  matrix, one complex rectangular matrix

          F06ZJF  (ZTRSM) Solves system of equations with multiple right-
                  hand sides, complex triangular coefficient matrix

          F06ZPF  (ZHERK) Rank-k update of a complex Hermitian matrix

          F06ZRF  (ZHER2K) Rank-2k update of a complex Hermitian matrix

          F06ZTF  (ZSYMM) Matrix-matrix product, one complex symmetric
                  matrix, one complex rectangular matrix

          F06ZUF  (ZSYRK) Rank-k update of a complex symmetric matrix

          F06ZWF  (ZSYR2K) Rank-2k update of a complex symmetric matrix

          X01 -- Mathematical Constants

          X01AAF  (pi)

          X01ABF  Euler's constant, (gamma)

          X02 -- Machine Constants

          X02AHF  Largest permissible argument for SIN and COS

          X02AJF  Machine precision

          X02AKF  Smallest positive model number

          X02ALF  Largest positive model number

          X02AMF  Safe range of floating-point arithmetic

          X02ANF  Safe range of complex floating-point arithmetic

          X02BBF  Largest representable integer

          X02BEF  Maximum number of decimal digits that can be represented

          X02BHF  Parameter of floating-point arithmetic model, b

          X02BJF  Parameter of floating-point arithmetic model, p

          X02BKF  Parameter of floating-point arithmetic model, e
                                                                 min

          X02BLF  Parameter of floating-point arithmetic model, e
                                                                 max

          X02DJF  Parameter of floating-point arithmetic model, ROUNDS



          Routines from the NAG Fortran Library

          A number of routines from the NAG Fortran Library are used in the
          Foundation Library as auxiliaries and are not documented here:

          A00AAF

          A02AAF  A02ABF  A02ACF

          C02AJF

          C05AZF  C05NCF  C05PCF

          C06FAF  C06FBF  C06FCF  C06FFF  C06FJF  C06FKF

          C06HAF  C06HBF  C06HCF  C06HDF

          D02CBF  D02CHF  D02NMF  D02NSF  D02NVF  D02PAF

          D02XAF  D02XKF  D02YAF  D02ZAF

          E02AFF

          E04GBF  E04GEF  E04YAF

          F01ADF  F01AEF  F01AFF  F01AGF  F01AHF  F01AJF

          F01AKF  F01AMF  F01APF  F01ATF  F01AUF  F01AVF

          F01AWF  F01AXF  F01BCF  F01BTF  F01CRF  F01LBF

          F01LZF  F01QAF  F01QFF  F01QGF  F01QJF  F01QKF

          F01RFF  F01RGF  F01RJF  F01RKF

          F02AMF  F02ANF  F02APF  F02AQF  F02AVF  F02AYF

          F02BEF  F02SWF  F02SXF  F02SYF  F02SZF  F02UWF

          F02UXF  F02UYF  F02WDF  F02WUF  F02XUF

          F03AAF  F03ABF  F03AEF  F03AFF

          F04AAF  F04AEF  F04AFF  F04AGF  F04AHF  F04AJF

          F04AMF  F04ANF  F04AYF  F04LDF  F04YAF  F04YCF

          F06BAF  F06BCF  F06BLF  F06BMF  F06BNF  F06CAF

          F06CCF  F06CLF  F06DBF  F06DFF  F06FBF  F06FCF

          F06FDF  F06FGF  F06FJF  F06FLF  F06FPF  F06FQF

          F06FRF  F06FSF  F06HBF  F06HGF  F06HQF  F06HRF

          F06KFF  F06KJF  F06KLF  F06QFF  F06QHF  F06QKF

          F06QRF  F06QSF  F06QTF  F06QVF  F06QWF  F06QXF

          F06RAF  F06RJF  F06TFF  F06THF  F06TTF  F06TXF

          F06VJF  F06VKF  F06VXF

          F07AGF  F07AHF  F07AJF  F07FGF  F07FHF  F07FJF

          F07TJF

          G01CEF

          G02BAF  G02BUF  G02BWF  G02DDF

          G13AEF

          M01CBF  M01CCF  M01DBF  M01DCF  M01DFF  M01ZBF

          P01ABF  P01ACF

          S01BAF  S07AAF  S15ABF

          X03AAF

          X04BAF  X04BBF  X04CBF  X04DBF

\end{verbatim}
\endscroll
\end{page}
\begin{page}{manpageXXintro}{NAG On-line Documentation: intro}
\beginscroll
\begin{verbatim}



     INTRO(3NAG)       Foundation Library (12/10/92)       INTRO(3NAG)



          Introduction                               Essential Introduction
          Essential Introduction to the NAG Foundation Library

          This document is essential reading for any prospective user of
          the Library.

          This document appears in both the Handbook and the Reference
          Manual for the NAG Foundation Library, but with a different
          Section 3 to describe the different forms of routine
          documentation in the two publications.

          1. The Library and its Documentation

          1.1. Structure of the Library

          1.2. Structure of the Documentation

          1.3. On-line Documentation

          1.4. Implementations of the Library

          1.5. Library Identification

          1.6. Fortran Language Standards

          2. Using the Library

          2.1. General Advice

          2.2. Programming Advice

          2.3. Error handling and the Parameter IFAIL

          2.4. Input/output in the Library

          2.5. Auxiliary Routines

          3. Using the Reference Manual

          3.1. General Guidance

          3.2. Structure of Routine Documents

          3.3. Specifications of Parameters

          3.3.1. Classification of Parameters

          3.3.2. Constraints and Suggested Values

          3.3.3. Array Parameters

          3.4. Implementation-dependent Information

          3.5. Example Programs and Results

          3.6. Summary for New Users

          4. Relationship between the Foundation Library and other NAG Libraries

          4.1. NAG Fortran Library

          4.2. NAG Workstation Library

          4.3. NAG C Library

          5. Contact between Users and NAG

          6. General Information about NAG

          7. References



          1. The Library and its Documentation

          1.1. Structure of the Library

          The NAG Foundation Library is a comprehensive collection of
          Fortran 77 routines for the solution of numerical and statistical
          problems. The word 'routine' is used to denote 'subroutine' or '
          function'.

          The Library is divided into chapters, each devoted to a branch of
          numerical analysis or statistics. Each chapter has a three-
          character name and a title, e.g.

               D01 -- Quadrature

          Exceptionally one chapter (S) has a one-character name. (The
          chapters and their names are based on the ACM modified SHARE
          classification index [1].)

          All documented routines in the Library have six-character names,
          beginning with the characters of the chapter name, e.g.

               D01AJF

          Note that the second and third characters are digits, not
          letters; e.g. 0 is the digit zero, not the letter O. The last
          letter of each routine name is always 'F'.

          1.2. Structure of the Documentation

          There are two types of manual for the NAG Foundation Library: a
          Handbook and a Reference Manual.

          The Handbook has the same chapter structure as the Library: each
          chapter of routines in the Library has a corresponding chapter
          (of the same name) in the Handbook. The chapters occur in
          alphanumeric order. General introductory documents and indexes
          are placed at the beginning of the Handbook.

          Each chapter in the Handbook contains a Chapter Introduction,
          followed by concise summaries of the functionality and parameter
          specifications of each routine in the chapter. Exceptionally, in
          some chapters (F06, X01, X02) which contain simple support
          routines, there are no concise summaries: all the routines are
          described together in the Chapter Introduction.

          The Reference Manual provides complete reference documentation
          for the NAG Foundation Library. In the Reference Manual, each
          chapter consists of the following documents:

               Chapter Introduction, e.g. Introduction -- D01;

               Chapter Contents, e.g. Contents -- D01;

               routine documents, one for each documented routine in the
               chapter.

          A routine document has the same name as the routine which it
          describes. Within each chapter, routine documents occur in
          alphanumeric order. As in the Handbook, chapters F06, X01 and X02
          do not contain separate documentation for individual routines.

          The general introductory documents, indexes and chapter
          introductions are the same in the Reference Manual as in the
          Handbook. The only exception is that the Essential Introduction
          contains a different Section 3 in the two publications, to
          describe the different forms of routine documentation.

          1.3. On-line Documentation

          Extensive on-line documentation is included as an integral part
          of the Foundation Library product. This consists of a number of
          components:

               -- general introductory material, including the Essential
               Introduction

               -- a summary list of all documented routines

               -- a KWIC Index

               -- Chapter Introductions

               -- routine documents

               -- example programs, data and results.

          The material has been derived in a number of forms to cater for
          different user requirements, e.g. UNIX man pages, plain text,
          RICH TEXT format etc, and the appropriate version is included on
          the distribution media. For each implementation of the Foundation
          Library the specific documentation (Installers' Note, Users' Note
          etc) gives details of what is provided.

          1.4. Implementations of the Library

          The NAG Foundation Library is available on many different
          computer systems. For each distinct system, an implementation of
          the Library is prepared by NAG, e.g. the IBM RISC System/6000
          implementation. The implementation is distributed as a tested
          compiled library.

          An implementation is usually specific to a range of machines; it
          may also be specific to a particular operating system or
          compilation system.

          Essentially the same facilities are provided in all
          implementations of the Library, but, because of differences in
          arithmetic behaviour and in the compilation system, routines
          cannot be expected to give identical results on different
          systems, especially for sensitive numerical problems.

          The documentation supports all implementations of the Library,
          with the help of a few simple conventions, and a small amount of
          implementation-dependent information, which is published in a
          separate Users' Note for each implementation (see Section 3.4).

          1.5. Library Identification

          You must know which implementation of the Library you are using
          or intend to use. To find out which implementation of the Library
          is available on your machine, you can run a program which calls
          the NAG Foundation Library routine A00AAF. This routine has no
          parameters; it simply outputs text to the advisory message unit
          (see Section 2.4). An example of the output is:


          *** Start of NAG Foundation Library implementation details ***
          Implementation title: IBM RISC System/6000
          Precision: FORTRAN double precision
          Product Code: FFIB601D
          Release: 1
          *** End of NAG Foundation Library implementation details ***

          (The product code can be ignored, except possibly when
          communicating with NAG; see Section 4.)

          1.6. Fortran Language Standards

          All routines in the Library conform to ANSI Standard Fortran 90
          [8].

          Most of the routines in the Library were originally written to
          conform to the earlier Fortran 66 [6] and Fortran 77 [7]
          standards, and their calling sequences contain some parameters
          which are not strictly necessary in Fortran 90.

          2. Using the Library

          2.1. General Advice

          A NAG Foundation Library routine cannot be guaranteed to return
          meaningful results, irrespective of the data supplied to it. Care
          and thought must be exercised in:

          (a) formulating the problem;

          (b) programming the use of library routines;

          (c) assessing the significance of the results.

          2.2. Programming Advice

          The NAG Foundation Library and its documentation are designed on
          the assumption that users know how to write a calling program in
          Fortran.

          When programming a call to a routine, read the routine document
          carefully, especially the description of the Parameters. This
          states clearly which parameters must have values assigned to them
          on entry to the routine, and which return useful values on exit.
          See Section 3.3 for further guidance.

          If a call to a Library routine results in an unexpected error
          message from the system (or possibly from within the Library),
          check the following:


              Has the NAG routine been called with the correct number of
              parameters?

              Do the parameters all have the correct type?

              Have all array parameters been dimensioned correctly?

          Remember that all floating-point parameters must be declared to
          be double precision, either with an explicit DOUBLE PRECISION
          declaration (or COMPLEX(KIND(1.0D0)) if they are complex), or by
          using a suitable IMPLICIT statement.

          Avoid the use of NAG-type names for your own program units or
          COMMON blocks: in general, do not use names which contain a
          three-character NAG chapter name embedded in them; they may clash
          with the names of an auxiliary routine or COMMON block used by
          the NAG Library.

          2.3. Error handling and the Parameter IFAIL

          NAG Foundation Library routines may detect various kinds of
          error, failure or warning conditions. Such conditions are handled
          in a systematic way by the Library. They fall roughly into three
          classes:

          (i)   an invalid value of a parameter on entry to a routine;

          (ii)  a numerical failure during computation (e.g. approximate
                singularity of a matrix, failure of an iteration to
                converge);

          (iii) a warning that although the computation has been completed,
                the results cannot be guaranteed to be completely reliable.

          All three classes are handled in the same way by the Library, and
          are all referred to here simply as 'errors'.

          The error-handling mechanism uses the parameter IFAIL, which is
          the last parameter in the calling sequence of most NAG Foundation
          Library routines. IFAIL serves two purposes:

          (i)   it allows users to specify what action a Library routine
                should take if it detects an error;

          (ii)  it reports the outcome of a call to a Library routine,
                either success (IFAIL = 0) or failure (IFAIL /= 0, with
                different values indicating different reasons for the
                failure, as explained in Section 6 of the routine document)
                .

          For the first purpose IFAIL must be assigned a value before
          calling the routine; since IFAIL is reset by the routine, it must
          be passed as a variable, not as an integer constant. Allowed
          values on entry are:

              IFAIL=0: an error message is output, and execution is
              terminated ('hard failure');

              IFAIL=+1: execution continues without any error message;

              IFAIL=-1: an error message is output, and execution
              continues.

          The settings IFAIL =+-1 are referred to as 'soft failure'.
          The safest choice is to set IFAIL to 0, but this is not always
          convenient: some routines return useful results even though a
          failure (in some cases merely a warning) is indicated. However,
          if IFAIL is set to +- 1 on entry, it is essential for the program
          to test its value on exit from the routine, and to take
          appropriate action.

          The specification of IFAIL in Section 5 of a routine document
          suggests a suitable setting of IFAIL for that routine.

          2.4. Input/output in the Library

          Most NAG Foundation Library routines perform no output to an
          external file, except possibly to output an error message. All
          error messages are written to a logical error message unit. This
          unit number (which is set by default to 6 in most
          implementations) can be changed by calling the Library routine
          X04AAF.

          Some NAG Foundation Library routines may optionally output their
          final results, or intermediate results to monitor the course of
          computation. All output other than error messages is written to a
          logical advisory message unit. This unit number (which is also
          set by default to 6 in most implementations) can be changed by
          calling the Library routine X04ABF. Although it is logically
          distinct from the error message unit, in practice the two unit
          numbers may be the same.

          All output from the Library is formatted.

          The only Library routines which perform input from an external
          file are a few 'option-setting' routines in Chapter E04: the unit
          number is a parameter to the routine, and all input is formatted.

          You must ensure that the relevant Fortran unit numbers are
          associated with the desired external files, either by an OPEN
          statement in your calling program, or by operating system
          commands.

          2.5. Auxiliary Routines

          In addition to those Library routines which are documented and
          are intended to be called by users, the Library also contains
          many auxiliary routines.

          In general, you need not be concerned with them at all, although
          you may be made aware of their existence if, for example, you
          examine a memory map of an executable program which calls NAG
          routines. The only exception is that when calling some NAG
          Foundation Library routines, you may be required or allowed to
          supply the name of an auxiliary routine from the Library as an
          external procedure parameter. The routine documents give the
          necessary details. In such cases, you only need to supply the
          name of the routine; you never need to know details of its
          parameter-list.

          NAG auxiliary routines have names which are similar to the name
          of the documented routine(s) to which they are related, but with
          last letter 'Z', 'Y', and so on, e.g. D01AJZ is an auxiliary
          routine called by D01AJF.

          3. Using the Reference Manual

          3.1. General Guidance

          The Reference Manual is designed to serve the following
          functions:

              -- to give background information about different areas of
              numerical and statistical computation;

              -- to advise on the choice of the most suitable NAG
              Foundation Library routine or routines to solve a particular
              problem;

              -- to give all the information needed to call a NAG
              Foundation Library routine correctly from a Fortran program,
              and to assess the results.

          At the beginning of the Manual are some general introductory
          documents. The following may help you to find the chapter, and
          possibly the routine, which you need to solve your problem:

              Contents     -- a list of routines in the Library, by
              Summary      chapter;

              KWIC Index   -- a keyword index to chapters and routines.

          Having found a likely chapter or routine, you should read the
          corresponding Chapter Introduction, which gives background
          information about that area of numerical computation, and
          recommendations on the choice of a routine, including indexes,
          tables or decision trees.

          When you have chosen a routine, you must consult the routine
          document. Each routine document is essentially self-contained (it
          may contain references to related documents). It includes a
          description of the method, detailed specifications of each
          parameter, explanations of each error exit, and remarks on
          accuracy.

          Example programs which illustrate the use of each routine are
          distributed with the Library in machine-readable form.

          3.2. Structure of Routine Documents

          All routine documents have the same structure, consisting of nine
          numbered sections:

               1.  Purpose

               2.  Specification

               3.  Description

               4.  References

               5.  Parameters (see Section 3.3 below)

               6.  Error Indicators

               7.  Accuracy

               8.  Further Comments

               9.  Example (see Section 3.5 below)

          In a few documents, Section 5 also includes a description of
          printed output which may optionally be produced by the routine.

          3.3. Specifications of Parameters

          Section 5 of each routine document contains the specification of
          the parameters, in the order of their appearance in the parameter
          list.

          3.3.1.  Classification of Parameters

          Parameters are classified as follows:

          Input : you must assign values to these parameters on or before
          entry to the routine, and these values are unchanged on exit from
          the routine.

          Output : you need not assign values to these parameters on or
          before entry to the routine; the routine may assign values to
          them.

          Input/Output : you must assign values to these parameters on or
          before entry to the routine, and the routine may then change
          these values.

          Workspace: array parameters which are used as workspace by the
          routine. You must supply arrays of the correct type and
          dimension, but you need not be concerned with their contents.

          External Procedure: a subroutine or function which must be
          supplied (e.g. to evaluate an integrand or to print intermediate
          output). Usually it must be supplied as part of your calling
          program, in which case its specification includes full details of
          its parameter-list and specifications of its parameters (all
          enclosed in a box). Its parameters are classified in the same way
          as those of the Library routine, but because you must write the
          procedure rather than call it, the significance of the
          classification is different:

              Input : values may be supplied on entry, which your procedure
              must not change.

              Output : you may or must assign values to these parameters
              before exit from your procedure.

              Input/Output : values may be supplied on entry, and you may
              or must assign values to them before exit from your
              procedure.

          Occasionally, as mentioned in Section 2.5, the procedure can be
          supplied from the NAG Library, and then you only need to know its
          name.

          User Workspace: array parameters which are passed by the Library
          routine to an external procedure parameter. They are not used by
          the routine, but you may use them to pass information between
          your calling program and the external procedure.

          3.3.2.  Constraints and Suggested Values

          The word 'Constraint:' or 'Constraints:' in the specification of
          an Input parameter introduces a statement of the range of valid
          values for that parameter, e.g.

              Constraint: N > 0.

          If the routine is called with an invalid value for the parameter
          (e.g. N = 0), the routine will usually take an error exit,
          returning a non-zero value of IFAIL (see Section 2.3).

          In newer documents constraints on parameters of type CHARACTER
          only list uppercase alphabetic characters, e.g.

              Constraint: STRING = 'A' or 'B'.

          In practice all routines with CHARACTER parameters will permit
          the use of lower case characters.

          The phrase 'Suggested Value:' introduces a suggestion for a
          reasonable initial setting for an Input parameter (e.g. accuracy
          or maximum number of iterations) in case you are unsure what
          value to use; you should be prepared to use a different setting
          if the suggested value turns out to be unsuitable for your
          problem.

          3.3.3.  Array Parameters

          Most array parameters have dimensions which depend on the size of
          the problem. In Fortran terminology they have 'adjustable
          dimensions': the dimensions occurring in their declarations are
          integer variables which are also parameters of the Library
          routine.

          For example, a Library routine might have the specification:


               SUBROUTINE <name> (M, N, A, B, LDB)
               INTEGER       M, N, A(N), B(LDB,N), LDB

          For a one-dimensional array parameter, such as A in this example,
          the specification would begin:

           3:  A(N) -- DOUBLE PRECISION array                         Input

          You must ensure that the dimension of the array, as declared in
          your calling (sub)program, is at least as large as the value you
          supply for N. It may be larger; but the routine uses only the
          first N elements.

          For a two-dimensional array parameter, such as B in the example,
          the specification might be:

           4:  B(LDB,N) -- DOUBLE PRECISION array              Input/Output
               On entry: the m by n matrix B.

          and the parameter LDB might be described as follows:

           5:  LDB -- INTEGER                                         Input
               On entry: the first dimension of the array B as declared in
               the (sub)program from which <name> is called. Constraint:
               LDB >= M.

          You must supply the first dimension of the array B, as declared
          in your calling (sub)program, through the parameter LDB, even
          though the number of rows actually used by the routine is
          determined by the parameter M. You must ensure that the first
          dimension of the array is at least as large as the value you
          supply for M. The extra parameter LDB is needed because Fortran
          does not allow information about the dimensions of array
          parameters to be passed automatically to a routine.

          You must also ensure that the second dimension of the array, as
          declared in your calling (sub)program, is at least as large as
          the value you supply for N. It may be larger, but the routine
          only uses the first N columns.

          A program to call the hypothetical routine used as an example in
          this section might include the statements:


               INTEGER AA(100), BB(100,50)
               LDB = 100
               .
               .
               .
               M = 80
               N = 20
               CALL <name>(M,N,AA,BB,LDB)

          Fortran requires that the dimensions which occur in array
          declarations, must be greater than zero. Many NAG routines are
          designed so that they can be called with a parameter like N in
          the above example set to 0 (in which case they would usually exit
          immediately without doing anything). If so, the declarations in
          the Library routine would use the 'assumed size' array dimension,
          and would be given as:


               INTEGER        M, N, A(*), B(LDB,*), LDB

          However, the original declaration of an array in your calling
          program must always have constant dimensions, greater than or
          equal to 1.

          Consult an expert or a textbook on Fortran, if you have
          difficulty in calling NAG routines with array parameters.

          3.4. Implementation-dependent Information

          In order to support all implementations of the Foundation
          Library, the Manual has adopted a convention of using bold
          italics to distinguish terms which have different interpretations
          in different implementations.

          For example, machine precision denotes the relative precision to
          which double precision floating-point numbers are stored in the
          computer, e.g. in an implementation with approximately 16 decimal
          digits of precision, machine precision has a value of
                          - 16
          approximately 10    .

          The precise value of machine precision is given by the function
          X02AJF. Other functions in Chapter X02 return the values of other
          implementation-dependent constants, such as the overflow
          threshold, or the largest representable integer. Refer to the X02

          Chapter Introduction for more details.

          For each implementation of the Library, a separate Users' Note is
          provided. This is a short document, revised at each Mark. At most
          installations it is available in machine-readable form. It gives
          any necessary additional information which applies specifically
          to that implementation, in particular:

              -- the interpretation of bold italicised terms;

              -- the values returned by X02 routines;

              -- the default unit numbers for output (see Section 2.4).

          3.5. Example Programs and Results

          The last section of each routine document describes an example
          problem which can be solved by simple use of the routine. The
          example programs themselves, together with data and results, are
          not printed in the routine document, but are distributed in
          machine-readable form with the Library. The programs are designed
          so that they can fairly easily be modified, and so serve as the
          basis for a simple program to solve a user's own problem.

          The results distributed with each implementation were obtained
          using that implementation of the Library; they may not be
          identical to the results obtained with other implementations.

          3.6. Summary for New Users

          If you are unfamiliar with the NAG Foundation Library and are
          thinking of using a routine from it, please follow these
          instructions:

          (a) read the whole of the Essential Introduction;

          (b) consult the Contents Summary or KWIC Index to choose an
              appropriate chapter or routine;

          (c) read the relevant Chapter Introduction;

          (d) choose a routine, and read the routine document. If the
              routine does not after all meet your needs, return to steps
              (b) or (c);

          (e) read the Users' Note for your implementation;

          (f) consult local documentation, which should be provided by your
              local support staff, about access to the NAG Library on your
              computing system.

          You should now be in a position to include a call to the routine
          in a program, and to attempt to run it. You may of course need to
          refer back to the relevant documentation in the case of
          difficulties, for advice on assessment of results, and so on.

          As you become familiar with the Library, some of steps (a) to (f)
          can be omitted, but it is always essential to:

              -- be familiar with the Chapter Introduction;

              -- read the routine document;

              -- be aware of the Users' Note for your implementation.

          4. Relationship between the Foundation Library and other NAG Libraries

          4.1. NAG Fortran Library

          The Foundation Library is a strict subset of the full NAG Fortran
          Library (Mark 15 or later). Routines in both libraries have
          identical source code (apart from any modifications necessary for
          implementation on a specific system) and hence can be called in
          exactly the same way, though you should consult the relevant
          implementation-specific documentation for details such as values
          of machine constants.

          By its very nature, the Foundation Library cannot contain the
          same extensive range of routines as the full Fortran Library. If
          your application requires a routine which is not in the
          Foundation Library, then please consult NAG for information on
          relevant material available in the Fortran Library.

          Some routines which occur as user-callable routines in the full
          Fortran Library are included as auxiliary routines in the
          Foundation Library but they are not documented in this
          publication and direct calls to them should only be made if you
          are already familiar with their use in the Fortran Library. A
          list of all such auxiliary routines is given at the end of the
          Foundation Library Contents Summary.

          Whereas the full Fortran Library may be provided in either a
          single precision or a double precision version, the Foundation
          Library is always provided in double precision.

          4.2. NAG Workstation Library

          The Foundation Library is a successor product to an earlier,
          smaller subset of the full NAG Fortran Library which was called
          the NAG Workstation Library. The Foundation Library has greater
          functionality than the Workstation Library but is not strictly
          upwards compatible, i.e., a number of routines in the earlier
          product have been replaced by new material to reflect recent
          algorithmic developments.
          If you have used the Workstation Library and wish to convert your
          programs to call routines from the Foundation Library, please
          consult the document 'Converting from the Workstation Library' in
          this Manual.

          4.3. NAG C Library

          NAG has also developed a library of numerical and statistical
          software for use by C programmers. This now contains over 200
          user-callable functions and provides similar (but not identical)
          coverage to that of the Foundation Library. Please contact NAG
          for further details if you have a requirement for similar quality
          library code in C.

          5. Contact between Users and NAG

          If you are using the NAG Foundation Library in a multi-user
          environment and require further advice please consult your local
          support staff who will be receiving regular information from NAG.
          This covers such matters as:

               -- obtaining a copy of the Users' Note for your
               implementation;

               -- obtaining information about local access to the Library;

               -- seeking advice about using the Library;

               -- reporting suspected errors in routines or documents;

               -- making suggestions for new routines or features;

               -- purchasing NAG documentation.

          If you are unable to make contact with a local source of support
          or are in a single-user environment then please contact NAG
          directly at any one of the addresses given at the beginning of
          this publication.

          6. General Information about NAG

          NAG produces and distributes numerical, symbolic, statistical and
          graphical software for the solution of problems in a wide range
          of applications in such areas as science, engineering, financial
          analysis and research.

          For users who write programs and build packages NAG produces sub-
          program libraries in a range of computer languages (Ada, C,
          Fortran, Pascal, Turbo Pascal). NAG also provides a number of
          Fortran programming support products in the NAGWare range --
          Fortran 77 programming tools, Fortran 90 compilers for a number
          of machine platforms (including PC-DOS) and VecPar 77 for
          restructuring and tuning programs for execution on vector or
          parallel computers.

          For users who do not wish to program in the traditional sense but
          want the same reliability and qualities offered by our libraries,
          NAG provides several powerful mathematical and statistical
          packages for interactive use. A major addition to this range of
          packages is AXIOM -- the powerful symbolic solver which includes
          a Hypertext system and graphical capabilities.

          For further details of any of these products, please contact NAG
          at one of the addresses given at the beginning of this
          publication.

          References [2], [3], [4], and [5] discuss various aspects of the
          design and development of the NAG Library, and NAG's technical
          policies and organisation.

          7. References

          [1]   (1960--1976) Collected Algorithms from ACM Index by subject
                to algorithms.

          [2]   Ford B (1982) Transportable Numerical Software. Lecture
                Notes in Computer Science. 142 128--140.

          [3]   Ford B, Bentley J, Du Croz J J and Hague S J (1979) The NAG
                Library 'machine'. Software Practice and Experience. 9(1)
                65--72.

          [4]   Ford B and Pool J C T (1984) The Evolving NAG Library
                Service. Sources and Development of Mathematical Software.
                (ed W Cowell) Prentice-Hall. 375--397.

          [5]   Hague S J, Nugent S M and Ford B (1982) Computer-based
                Documentation for the NAG Library. Lecture Notes in Computer
                Science. 142 91--127.

          [6]   (1966) USA Standard Fortran. Publication X3.9. American
                National Standards Institute.

          [7]   (1978) American National Standard Fortran. Publication X3.9.
                American National Standards Institute.

          [8]   (1991) American National Standard Programming Language
                Fortran 90. Publication X3.198.
                American National Standards Institute.

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     KWIC(3NAG)        Foundation Library (12/10/92)        KWIC(3NAG)



          Introduction                                  Keywords in Context
          Keywords in Context

          Pre-computed weights and                                 D01BBF
          abscissae
          for Gaussian quadrature rules, restricted choice of ...

          Sum the                                                  F06EKF
          absolute
          values of real vector elements (DASUM)

          Sum the                                                  F06JKF
          absolute
          values of complex vector elements (DZASUM)

          Index, real vector element with largest                  F06JLF
          absolute
          value (IDAMAX)

          Index, complex vector element with largest               F06JMF
          absolute
          value (IZAMAX)

          ODEs, IVP,                                               D02CJF
          Adams
          method, until function of solution is zero, ...

          1-D quadrature,                                          D01AJF
          adaptive
          , finite interval, strategy due to Piessens and de ...

          1-D quadrature,                                          D01AKF
          adaptive
          , finite interval, method suitable for oscillating ...

          1-D quadrature,                                          D01ALF
          adaptive
          , finite interval, allowing for singularities at ...

          1-D quadrature,                                          D01AMF
          adaptive
          , infinite or semi-infinite interval

          1-D quadrature,                                          D01ANF
          adaptive
          , finite interval, weight function cos((omega)x) ...

          1-D quadrature,                                          D01APF
          adaptive
          , finite interval, weight function with end-point ...

          1-D quadrature,                                          D01AQF
          adaptive
          , finite interval, weight function 1/(x-c), ...

          1-D quadrature,                                          D01ASF
          adaptive
          , semi-infinite interval, weight function cos((omega)x)

          Multi-dimensional                                        D01FCF
          adaptive
          quadrature over hyper-rectangle

          Add                                                      F06ECF
          scalar times real vector to real vector (DAXPY)

          Add                                                      F06GCF
          scalar times complex vector to complex vector (ZAXPY)

          Return or set unit number for                            X04ABF
          advisory
          messages

          Airy                                                     S17AGF
          function Ai(x)

          Airy                                                     S17AHF
          function Bi(x)

          Airy                                                     S17AJF
          function Ai'(x)

          Airy                                                     S17AKF
          function Bi'(x)

          Airy                                                     S17DGF
          functions Ai(z) and Ai('z), complex z

          Airy                                                     S17DHF
          functions Bi(z) and Bi'(z), complex z

          Airy function                                            S17AGF
          Ai(x)

          Airy function                                            S17AJF
          Ai'(x)

          Airy functions                                           S17DGF
          Ai(z)
          and Ai'(z), complex z

          Airy functions Ai(z) and                                 S17DGF
          Ai'(z)
          , complex z
          algebraico-logarithmic
          type

          Two-way contingency table                                G01AFF
          analysis
                      2
          , with (chi) /Fisher's exact test

          Performs principal component                             G03AAF
          analysis

          Performs canonical correlation                           G03ADF
          analysis

          Friedman two-way                                         G08AEF
          analysis
          of variance on k matched samples

          Kruskal-Wallis one-way                                   G08AFF
          analysis
          of variance on k samples of unequal size

          L -                                                      E02GAF
           1
          approximation
          by general linear function

          Approximation                                            E02

          Approximation                                            S
          of special functions

          ARIMA
          model

          Univariate time series, estimation, seasonal             G13AFF
          ARIMA
          model

          ARIMA
          model

          ARIMA
          model

          Safe range of floating-point                             X02AMF
          arithmetic

          Safe range of complex floating-point                     X02ANF
          arithmetic

          Parameter of floating-point                              X02BHF
          arithmetic
          model, b

          Parameter of floating-point                              X02BJF
          arithmetic
          model, p

          Parameter of floating-point                              X02BKF
          arithmetic
          model, e
                  min

          Parameter of floating-point                              X02BLF
          arithmetic
          model, e
                  max

          Parameter of floating-point                              X02DJF
          arithmetic
          model, ROUNDS

          Univariate time series, sample                           G13ABF
          autocorrelation
          function

          Univariate time series, partial                          G13ACF
          autocorrelations
          from autocorrelations

          Univariate time series, partial autocorrelations from    G13ACF
          autocorrelations

          Least-squares cubic spline curve fit,                    E02BEF
          automatic
          knot placement

          Least-squares surface fit by bicubic splines with        E02DCF
          automatic
          knot placement, data on rectangular grid

          Least-squares surface fit by bicubic splines with        E02DDF
          automatic
          knot placement, scattered data

          B-splines                                                E02

          Matrix-vector product, real rectangular                  F06PBF
          band
          matrix (DGBMV)

          Matrix-vector product, real symmetric                    F06PDF
          band
          matrix (DSBMV)

          Matrix-vector product, real triangular                   F06PGF
          band
          matrix (DTBMV)

          System of equations, real triangular                     F06PKF
          band
          matrix (DTBSV)

          Matrix-vector product, complex rectangular               F06SBF
          band
          matrix (ZGBMV)

          Matrix-vector product, complex Hermitian                 F06SDF
          band
          matrix (ZHBMV)

          Matrix-vector product, complex triangular                F06SGF
          band
          matrix (ZTBMV)

          System of equations, complex triangular                  F06SKF
          band
          matrix (ZTBSV)

          bandwidth
          matrix

          Solution of real symmetric positive-definite variable-   F04MCF
          bandwidth
          simultaneous linear equations (coefficient matrix ...

          Basic                                                    F06
          Linear Algebra Subprograms

          ODEs, stiff IVP,                                         D02EJF
          BDF
          method, until function of solution is zero,
          intermediate ...

          Kelvin function                                          S19ABF
          bei
          x

          Kelvin function                                          S19AAF
          ber
          x

          Bessel                                                   S17ACF
          function Y (x)
                    0

          Bessel                                                   S17ADF
          function Y (x)
                    1

          Bessel                                                   S17AEF
          function J (x)
                    0

          Bessel                                                   S17AFF
          function J (x)
                    1

          Bessel                                                   S17DCF
          functions Y      (z), complex z, real (nu)>=0, ...
                     (nu)+n

          Bessel                                                   S17DEF
          functions J      (z), complex z, real (nu)>=0, ...
                     (nu)+n

          Modified                                                 S18ACF
          Bessel
          function K (x)
                    0

          Modified                                                 S18ADF
          Bessel
          function K (x)
                    1

          Modified                                                 S18AEF
          Bessel
          function I (x)
                    0

          Modified                                                 S18AFF
          Bessel
          function I (x)
                    1

          Modified                                                 S18DCF
          Bessel
          functions K      (z), complex z, real (nu)>=0, ...
                     (nu)+n

          Modified                                                 S18DEF
          Bessel
          functions I      (z), complex z, real (nu)>=0, ...
                     (nu)+n

          beta
          distribution

          Computes deviates for the                                G01FEF
          beta
          distribution

          Generates a vector of pseudo-random numbers from a       G05FEF
          beta
          distribution

          Interpolating functions, fitting                         E01DAF
          bicubic
          spline, data on rectangular grid

          Least-squares surface fit,                               E02DAF
          bicubic
          splines

          Least-squares surface fit by                             E02DCF
          bicubic
          splines with automatic knot placement, data on ...

          Least-squares surface fit by                             E02DDF
          bicubic
          splines with automatic knot placement, scattered data

          Evaluation of a fitted                                   E02DEF
          bicubic
          spline at a vector of points

          Evaluation of a fitted                                   E02DFF
          bicubic
          spline at a mesh of points

          Sort 2-D data into panels for fitting                    E02ZAF
          bicubic
          splines

          Fits a generalized linear model with                     G02GBF
          binomial
          errors

          binomial
          distribution

          Computes probability for the                             G01HAF
          bivariate
          Normal distribution

          Airy function                                            S17AHF
          Bi(x)

          Airy function                                            S17AKF
          Bi'(x)

          Airy functions                                           S17DHF
          Bi(z)
          and Bi'(z), complex z

          Airy functions Bi(z) and                                 S17DHF
          Bi'(z)
          , complex z

          BLAS                                                     F06

          Pseudo-random logical                                    G05DZF
          (boolean)
          value

          ODEs,                                                    D02GAF
          boundary
          value problem, finite difference technique with ...

          ODEs,                                                    D02GBF
          boundary
          value problem, finite difference technique with ...

          ODEs, general nonlinear                                  D02RAF
          boundary
          value problem, finite difference technique with ...

          bounds
          , using function values only

          break-points

          break-points

          Zero of continuous function in given interval,           C05ADF
          Bus
          and Dekker algorithm

          Performs                                                 G03ADF
          canonical
          correlation analysis

          Carlo
          method

          Elliptic PDE, Helmholtz equation, 3-D                    D03FAF
          Cartesian
          co-ordinates

          Cauchy
          principal value (Hilbert transform)

          Pseudo-random real numbers,                              G05DFF

          Cauchy
          distribution

          character
          string

          Compare two                                              X05ACF
          character
          strings representing date and time

          Evaluation of fitted polynomial in one variable from     E02AEF
          Chebyshev
          series form (simplified parameter list)

          Derivative of fitted polynomial in                       E02AHF
          Chebyshev
          series form

          Integral of fitted polynomial in                         E02AJF
          Chebyshev
          series form

          Evaluation of fitted polynomial in one variable, from    E02AKF
          Chebyshev
          series form

          Check                                                    C05ZAF
          user's routine for calculating 1st derivatives

          Univariate time series, diagnostic                       G13ASF
          checking
          of residuals, following G13AFF

          Cholesky                                                 F07FDF
          factorization of real symmetric positive-definite ...

          Circular                                                 C06EKF
          convolution or correlation of two real vectors, no ...

          Cosine integral                                          S13ACF
          Ci(x)

          Interpolating functions, method of Renka and             E01SAF
          Cline
          , two variables

          Elliptic PDE, Helmholtz equation, 3-D Cartesian          D03FAF
          co-ordinates

          coefficient
          matrix already factorized by F01MCF)

          coefficient
          matrix (DTRSM)

          coefficient
          matrix (ZTRSM)

          Kendall/Spearman non-parametric rank correlation         G02BNF
          coefficients
          , no missing values, overwriting input data

          Kendall/Spearman non-parametric rank correlation         G02BQF
          coefficients
          , no missing values, preserving input data

          Operations with orthogonal matrices, form                F01QEF
          columns
          of Q after factorization by F01QCF

          Operations with unitary matrices, form                   F01REF
          columns
          of Q after factorization by F01RCF

          Rank                                                     M01DJF
          columns
          of a matrix, real numbers

          Compare                                                  X05ACF
          two character strings representing date and time

          Complement                                               S15ADF
          of error function erfcx

          Unconstrained minimum, pre-                              E04DGF
          conditioned
          conjugate gradient algorithm, function of several ...

          Complex                                                  C06GBF
          conjugate
          of Hermitian sequence

          Complex                                                  C06GCF
          conjugate
          of complex sequence

          Complex                                                  C06GQF
          conjugate
          of multiple Hermitian sequences

          Unconstrained minimum, pre-conditioned                   E04DGF
          conjugate
          gradient algorithm, function of several variables ...

          Dot product of two complex vectors,                      F06GBF
          conjugated
          (ZDOTC)

          Rank-1 update, complex rectangular matrix,               F06SNF
          conjugated
          vector (ZGERC)

          Mathematical                                             X01
          Constants

          Machine                                                  X02
          Constants

          constrained
          , arbitrary data points

          constraints
          , using function values and optionally 1st ...

          Two-way                                                  G01AFF
          contingency
                                    2
          table analysis, with (chi) /Fisher's ...

          continuation
          facility

          Zero of                                                  C05ADF
          continuous
          function in given interval, Bus and Dekker algorithm

                   2
          continuous
          distributions

          Convert                                                  C06GSF
          Hermitian sequences to general complex sequences

          Convert                                                  X05ABF
          array of integers representing date and time to ...

          Circular                                                 C06EKF
          convolution
          or correlation of two real vectors, no extra ...

          Copy                                                     F06EFF
          real vector (DCOPY)

          Copy                                                     F06GFF
          complex vector (ZCOPY)

          correction
          , simple nonlinear problem

          correction
          , general linear problem

          correction
          , continuation facility

          Circular convolution or                                  C06EKF
          correlation
          of two real vectors, no extra workspace

          Kendall/Spearman non-parametric rank                     G02BNF
          correlation
          coefficients, no missing values, overwriting ...

          Kendall/Spearman non-parametric rank                     G02BQF
          correlation
          coefficients, no missing values, preserving input ...

          Computes (optionally weighted)                           G02BXF
          correlation
          and covariance matrices

          Performs canonical                                       G03ADF
          correlation
          analysis

          Multivariate time series, cross-                         G13BCF
          correlations

          cos
          ((omega)x) or sin((omega)x)

          cos
          ((omega)x) or sin((omega)x)

          Cosine                                                   S13ACF
          integral Ci(x)

          Covariance                                               E04YCF
          matrix for nonlinear least-squares problem

          Computes (optionally weighted) correlation and           G02BXF
          covariance
          matrices

          Return the                                               X05BAF
          CPU
          time

          Multivariate time series,                                G13BCF
          cross-correlations

          Multivariate time series, smoothed sample                G13CDF
          cross
          spectrum using spectral smoothing by the trapezium ...

          Interpolating functions,                                 E01BAF
          cubic
          spline interpolant, one variable

          cubic
          Hermite, one variable

          Least-squares curve                                      E02BAF
          cubic
          spline fit (including interpolation)

          Evaluation of fitted                                     E02BBF
          cubic
          spline, function only

          Evaluation of fitted                                     E02BCF
          cubic
          spline, function and derivatives

          Evaluation of fitted                                     E02BDF
          cubic
          spline, definite integral

          Least-squares                                            E02BEF
          cubic
          spline curve fit, automatic knot placement

          Set up reference vector from supplied                    G05EXF
          cumulative
          distribution function or probability distribution ...

          Least-squares                                            E02ADF
          curve
          fit, by polynomials, arbitrary data points

          Least-squares                                            E02BAF
          curve
          cubic spline fit (including interpolation)

          Least-squares cubic spline                               E02BEF
          curve
          fit, automatic knot placement

          Fresnel integral                                         S20ADF
          C(x)

          Daniell)
          window

          Daniell)
          window

          Return                                                   X05AAF
          date
          and time as an array of integers

          Convert array of integers representing                   X05ABF
          date
          and time to character string

          Compare two character strings representing               X05ACF
          date
          and time

          deferred
          correction, simple nonlinear problem

          deferred
          correction, general linear problem

          deferred
          correction, continuation facility

          Interpolated values, interpolant computed by E01BEF,     E01BHF
          definite
          integral, one variable

          Evaluation of fitted cubic spline,                       E02BDF
          definite
          integral

          definite
          matrix

             T
          LDL  factorization of real symmetric positive-           F01MCF
          definite
          variable-bandwidth matrix

          definite

          definite

          Solution of real symmetric positive-                     F04ASF
          definite
          simultaneous linear equations, one right-hand side ...

          Solution of real symmetric positive-                     F04FAF
          definite
          tridiagonal simultaneous linear equations, one ...

          Real sparse symmetric positive-                          F04MAF
          definite
          simultaneous linear equations (coefficient matrix ...

          Solution of real symmetric positive-                     F04MCF
          definite
          variable-bandwidth simultaneous linear equations ...

          Cholesky factorization of real symmetric positive-       F07FDF
          definite
          matrix (DPOTRF)

          Solution of real symmetric positive-                     F07FEF
          definite
          system of linear equations, multiple right-hand ...

          Degenerate                                               S21BAF
          symmetrised elliptic integral of 1st kind R  ...
                                                     C

          Dekker
          algorithm

          Computes upper and lower tail and probability            G01EEF
          density
          function probabilities for the beta distribution

          Solution of system of nonlinear equations using 1st      C05PBF
          derivatives

          Check user's routine for calculating 1st                 C05ZAF
          derivatives

          derivative
          , one variable

          Least-squares polynomial fit, values and                 E02AGF
          derivatives
          may be constrained, arbitrary data points

          Derivative                                               E02AHF
          of fitted polynomial in Chebyshev series form

          Evaluation of fitted cubic spline, function and          E02BCF
          derivatives

          derivatives

          derivatives

          derivatives

          Computes                                                 G01FAF
          deviates
          for the standard Normal distribution

          Computes                                                 G01FBF
          deviates
          for Student's t-distribution

          Computes                                                 G01FCF
          deviates
                       2
          for the (chi)  distribution

          Computes                                                 G01FDF
          deviates
          for the F-distribution

          Computes                                                 G01FEF
          deviates
          for the beta distribution

          Computes                                                 G01FFF
          deviates
          for the gamma distribution

          Univariate time series,                                  G13ASF
          diagnostic
          checking of residuals, following G13AFF

          ODEs, boundary value problem, finite                     D02GAF
          difference
          technique with deferred correction, simple ...

          ODEs, boundary value problem, finite                     D02GBF
          difference
          technique with deferred correction, general linear ...

          difference
          technique with deferred correction, continuation ...

          Elliptic PDE, solution of finite                         D03EDF
          difference
          equations by a multigrid technique

          Univariate time series, seasonal and non-seasonal        G13AAF
          differencing

          Single 1-D real                                          C06EAF
          discrete
          Fourier transform, no extra workspace

          Single 1-D Hermitian                                     C06EBF
          discrete
          Fourier transform, no extra workspace

          Single 1-D complex                                       C06ECF
          discrete
          Fourier transform, no extra workspace

          Multiple 1-D real                                        C06FPF
          discrete
          Fourier transforms

          Multiple 1-D Hermitian                                   C06FQF
          discrete
          Fourier transforms

          Multiple 1-D complex                                     C06FRF
          discrete
          Fourier transforms

          2-D complex                                              C06FUF
          discrete
          Fourier transform

          Discretize                                               D03EEF
          a 2nd order elliptic PDE on a rectangle

          Computes probabilities for the standard Normal           G01EAF
          distribution

          Computes probabilities for Student's t-                  G01EBF
          distribution

                                          2
          Computes probabilities for (chi)                         G01ECF
          distribution

          Computes probabilities for F-                            G01EDF
          distribution

          distribution

          Computes probabilities for the gamma                     G01EFF
          distribution

          Computes deviates for the standard Normal                G01FAF
          distribution

          Computes deviates for Student's t-                       G01FBF
          distribution

                                         2
          Computes deviates for the (chi)                          G01FCF
          distribution

          Computes deviates for the F-                             G01FDF
          distribution

          Computes deviates for the beta                           G01FEF
          distribution

          Computes deviates for the gamma                          G01FFF
          distribution

          Computes probability for the bivariate Normal            G01HAF
          distribution

          Pseudo-random real numbers, uniform                      G05CAF
          distribution
          over (0,1)

          Pseudo-random real numbers, Normal                       G05DDF
          distribution

          Pseudo-random real numbers, Cauchy                       G05DFF
          distribution

          Pseudo-random real numbers, Weibull                      G05DPF
          distribution

          Pseudo-random integer from uniform                       G05DYF
          distribution

          Set up reference vector for multivariate Normal          G05EAF
          distribution

          distribution

          distribution

          Set up reference vector from supplied cumulative         G05EXF
          distribution
          function or probability distribution function

          distribution
          function

          Generates a vector of random numbers from a uniform      G05FAF
          distribution

          distribution

          Generates a vector of random numbers from a Normal       G05FDF
          distribution

          distribution

          distribution

               2
          (chi)  goodness of fit test, for standard continuous     G08CGF
          distributions

          Inverse                                                  G01F
          distributions

          Doncker
          , allowing for badly-behaved integrands

          Dot                                                      F06EAF
          product of two real vectors (DDOT)

          Dot                                                      F06GAF
          product of two complex vectors, unconjugated (ZDOTU)

          Dot                                                      F06GBF
          product of two complex vectors, conjugated (ZDOTC)

          eigenfunction
          , user-specified break-points

          All eigenvalues of generalized real                      F02ADF
          eigenproblem
          of the form Ax=(lambda)Bx where A and B are ...

          All eigenvalues and eigenvectors of generalized real     F02AEF
          eigenproblem
          of the form Ax=(lambda)Bx where A and B are ...

          eigenproblem
          by QZ algorithm, real matrices

          eigenproblem

          eigenvalue
          and eigenfunction, user-specified break-points

          All                                                      F02AAF
          eigenvalues
          of real symmetric matrix

          All                                                      F02ABF
          eigenvalues
          and eigenvectors of real symmetric matrix

          All                                                      F02ADF
          eigenvalues
          of generalized real eigenproblem of the form
          Ax=(lambda)Bx

          All                                                      F02AEF
          eigenvalues
          and eigenvectors of generalized real ...

          All                                                      F02AFF
          eigenvalues
          of real matrix

          All                                                      F02AGF
          eigenvalues
          and eigenvectors of real matrix

          All                                                      F02AJF
          eigenvalues
          of complex matrix

          All                                                      F02AKF
          eigenvalues
          and eigenvectors of complex matrix

          All                                                      F02AWF
          eigenvalues
          of complex Hermitian matrix

          All                                                      F02AXF
          eigenvalues
          and eigenvectors of complex Hermitian matrix

          Selected                                                 F02BBF
          eigenvalues
          and eigenvectors of real symmetric matrix

          All                                                      F02BJF
          eigenvalues
          and optionally eigenvectors of generalized ...

          Selected                                                 F02FJF
          eigenvalues
          and eigenvectors of sparse symmetric eigenproblem

          All eigenvalues and                                      F02ABF
          eigenvectors
          of real symmetric matrix

          All eigenvalues and                                      F02AEF
          eigenvectors
          of generalized real eigenproblem of the form ...

          All eigenvalues and                                      F02AGF
          eigenvectors
          of real matrix

          All eigenvalues and                                      F02AKF
          eigenvectors
          of complex matrix

          All eigenvalues and                                      F02AXF
          eigenvectors
          of complex Hermitian matrix

          Selected eigenvalues and                                 F02BBF
          eigenvectors
          of real symmetric matrix

          All eigenvalues and optionally                           F02BJF
          eigenvectors
          of generalized eigenproblem by QZ algorithm, ...

          Selected eigenvalues and                                 F02FJF
          eigenvectors
          of sparse symmetric eigenproblem

          Elliptic                                                 D03EDF
          PDE, solution of finite difference equations by a ...

          Discretize a 2nd order                                   D03EEF
          elliptic
          PDE on a rectangle

          Elliptic                                                 D03FAF
          PDE, Helmholtz equation, 3-D Cartesian co-ordinates

          Degenerate symmetrised                                   S21BAF
          elliptic
          integral of 1st kind R (x,y)
                                C

          Symmetrised                                              S21BBF
          elliptic
          integral of 1st kind R (x,y,z)
                                F

          Symmetrised                                              S21BCF
          elliptic
          integral of 2nd kind R (x,y,z)
                                D

          Symmetrised                                              S21BDF
          elliptic
          integral of 3rd kind R (x,y,z,r)
                                J

          end-point
          singularities of algebraico-logarithmic type

          error

          Fits a generalized linear model with binomial            G02GBF
          errors

          Fits a generalized linear model with Poisson             G02GCF
          errors

          Complement of                                            S15ADF
          error
          function erfc x

          Error                                                    S15AEF
          function erf x

          Return or set unit number for                            X04AAF
          error
          messages

          Computes                                                 G02DNF
          estimable
          function of a general linear regression model and ...

          Univariate time series, preliminary                      G13ADF
          estimation
          , seasonal ARIMA model

          Univariate time series,                                  G13AFF
          estimation
          , seasonal ARIMA model

          Multivariate time series, preliminary                    G13BDF
          estimation
          of transfer function model

          Multivariate time series,                                G13BEF
          estimation
          of multi-input model

          Compute                                                  F06EJF
          Euclidean
          norm of real vector (DNRM2)

          Compute                                                  F06JJF
          Euclidean
          norm of complex vector (DZNRM2)

          Evaluation                                               E02AEF
          of fitted polynomial in one variable from ...

          Evaluation                                               E02AKF
          of fitted polynomial in one variable, from ...

          Evaluation                                               E02BBF
          of fitted cubic spline, function only

          Evaluation                                               E02BCF
          of fitted cubic spline, function and derivatives

          Evaluation                                               E02BDF
          of fitted cubic spline, definite integral

          Evaluation                                               E02DEF
          of a fitted bicubic spline at a vector of points

          Evaluation                                               E02DFF
          of a fitted bicubic spline at a mesh of points

                                        2
          exact
          test

          Computes the                                             G08AJF
          exact
          probabilities for the Mann-Whitney U statistic, no ...

          Computes the                                             G08AKF
          exact
          probabilities for the Mann-Whitney U statistic, ties ..

          exponential
          distribution

          Complex                                                  S01EAF
          exponential
             z
          , e

          Exponential                                              S13AAF
          integral E (x)
                    1

          Computes a five-point summary (median, hinges and        G01ALF
          extremes)

          Computes probabilities for                               G01EDF
          F
          -distribution

          Computes deviates for the                                G01FDF
          F
          -distribution

          LU                                                       F01BRF
          factorization
          of real sparse matrix

          LU                                                       F01BSF
          factorization
          of real sparse matrix with known sparsity pattern

            T
          LL                                                       F01MAF
          factorization
          of real sparse symmetric positive-definite matrix

             T
          LDL                                                      F01MCF
          factorization
          of real symmetric positive-definite ...

          QR                                                       F01QCF
          factorization
          of real m by n matrix (m>=n)

                                       T
          factorization
          by F01QCF

          factorization
          by F01QCF

          QR                                                       F01RCF
          factorization
          of complex m by n matrix (m>=n)

                                               H
          factorization
          by F01RCF

          factorization
          by F01RCF

          LU                                                       F07ADF
          factorization
          of real m by n matrix (DGETRF)

          Cholesky                                                 F07FDF
          factorization
          of real symmetric positive-definite matrix ...

          Multivariate time series,                                G13BAF
          filtering
          (pre-whitening) by an ARIMA model

          1-D quadrature, adaptive,                                D01AJF
          finite
          interval, strategy due to Piessens and de Doncker, ...

          1-D quadrature, adaptive,                                D01AKF
          finite
          interval, method suitable for oscillating functions

          1-D quadrature, adaptive,                                D01ALF
          finite
          interval, allowing for singularities at user-specified

          1-D quadrature, adaptive,                                D01ANF
          finite
          interval, weight function cos((omega)x) or sin...

          1-D quadrature, adaptive,                                D01APF
          finite
          interval, weight function with end-point ...

          1-D quadrature, adaptive,                                D01AQF
          finite
          interval, weight function 1/(x-c), Cauchy ...

          ODEs, boundary value problem,                            D02GAF
          finite
          difference technique with deferred correction, simple .

          ODEs, boundary value problem,                            D02GBF
          finite
          difference technique with deferred correction, general

          finite/infinite
          range, eigenvalue and eigenfunction, ...

          ODEs, general nonlinear boundary value problem,          D02RAF
          finite
          difference technique with deferred correction, ...

          Elliptic PDE, solution of                                D03EDF
          finite
          difference equations by a multigrid technique

                                                    2
          Fisher's
          exact test

          Interpolating functions,                                 E01DAF
          fitting
          bicubic spline, data on rectangular grid

          Least-squares curve                                      E02ADF
          fit
          , by polynomials, arbitrary data points

          Evaluation of                                            E02AEF
          fitted
          polynomial in one variable from Chebyshev series form .

          Least-squares polynomial                                 E02AGF
          fit
          , values and derivatives may be constrained, arbitrary

          Derivative of                                            E02AHF
          fitted
          polynomial in Chebyshev series form

          Integral of                                              E02AJF
          fitted
          polynomial in Chebyshev series form

          Evaluation of                                            E02AKF
          fitted
          polynomial in one variable, from Chebyshev series form

          Least-squares curve cubic spline                         E02BAF
          fit
          (including interpolation)

          Evaluation of                                            E02BBF
          fitted
          cubic spline, function only

          Evaluation of                                            E02BCF
          fitted
          cubic spline, function and derivatives

          Evaluation of                                            E02BDF
          fitted
          cubic spline, definite integral

          Least-squares cubic spline curve                         E02BEF
          fit
          , automatic knot placement

          Least-squares surface                                    E02DAF
          fit
          , bicubic splines

          Least-squares surface                                    E02DCF
          fit
          by bicubic splines with automatic knot placement, data
          on ...

          Least-squares surface                                    E02DDF
          fit
          by bicubic splines with automatic knot placement, ...

          Evaluation of a                                          E02DEF
          fitted
          bicubic spline at a vector of points

          Evaluation of a                                          E02DFF
          fitted
          bicubic spline at a mesh of points

          Sort 2-D data into panels for                            E02ZAF
          fitting
          bicubic splines

          Fits                                                     G02DAF
          a general (multiple) linear regression model

          Fits                                                     G02DGF
          a general linear regression model for new dependent ...

          Fits                                                     G02GBF
          a generalized linear model with binomial errors

          Fits                                                     G02GCF
          a generalized linear model with Poisson errors

                            2
          Performs the (chi)  goodness of                          G08CGF
          fit
          test, for standard continuous distributions

          Goodness of                                              G08
          fit
          tests

          Computes a                                               G01ALF
          five-point
          summary (median, hinges and extremes)

          Safe range of                                            X02AMF
          floating-point
          arithmetic

          Safe range of complex                                    X02ANF
          floating-point
          arithmetic

          Parameter of                                             X02BHF
          floating-point
          arithmetic model, b

          Parameter of                                             X02BJF
          floating-point
          arithmetic model, p

          Parameter of                                             X02BKF
          floating-point
          arithmetic model, e
                             min

          Parameter of                                             X02BLF
          floating-point
          arithmetic model, e
                             max

          Parameter of                                             X02DJF
          floating-point
          arithmetic model, ROUNDS

          Univariate time series, update state set for             G13AGF
          forecasting

          Univariate time series,                                  G13AHF
          forecasting
          from state set

          Univariate time series, state set and                    G13AJF
          forecasts
          , from fully specified seasonal ARIMA model

          Multivariate time series, state set and                  G13BJF
          forecasts
          from fully specified multi-input model

          Single 1-D real discrete                                 C06EAF
          Fourier
          transform, no extra workspace

          Single 1-D Hermitian discrete                            C06EBF
          Fourier
          transform, no extra workspace

          Single 1-D complex discrete                              C06ECF
          Fourier
          transform, no extra workspace

          Multiple 1-D real discrete                               C06FPF
          Fourier
          transforms

          Multiple 1-D Hermitian discrete                          C06FQF
          Fourier
          transforms

          Multiple 1-D complex discrete                            C06FRF
          Fourier
          transforms

          2-D complex discrete                                     C06FUF
          Fourier
          transform

          frequency
          table

          Frequency                                                G01AEF
          table from raw data

          frequency
          (Daniell) window

          frequency
          (Daniell) window

          Fresnel                                                  S20ACF
          integral S(x)

          Fresnel                                                  S20ADF
          integral C(x)

          Friedman                                                 G08AEF
          two-way analysis of variance on k matched samples

          Computes probabilities for the                           G01EFF
          gamma
          distribution

          Computes deviates for the                                G01FFF
          gamma
          distribution

          Generates a vector of pseudo-random numbers from a       G05FFF
          gamma
          distribution

          Gamma                                                    S14AAF
          function

          Log                                                      S14ABF
          Gamma
          function

          Incomplete                                               S14BAF
          gamma
          functions P(a,x) and Q(a,x)

          Unconstrained minimum of a sum of squares, combined      E04FDF
          Gauss-Newton
          and modified Newton algorithm using function ...

          Unconstrained minimum of a sum of squares, combined      E04GCF
          Gauss-Newton
          and quasi-Newton algorithm, using 1st derivatives

          Pre-computed weights and abscissae for                   D01BBF
          Gaussian
          quadrature rules, restricted choice of rule

          All eigenvalues of                                       F02ADF
          generalized
          real eigenproblem of the form Ax=(lambda)Bx where ...

          All eigenvalues and eigenvectors of                      F02AEF
          generalized
          real eigenproblem of the form Ax=(lambda)Bx where ...

          All eigenvalues and optionally eigenvectors of           F02BJF
          generalized
          eigenproblem by QZ algorithm, real matrices

          Fits a                                                   G02GBF
          generalized
          linear model with binomial errors

          Fits a                                                   G02GCF
          generalized
          linear model with Poisson errors

          Computes orthogonal rotations for loading matrix,        G03BAF
          generalized
          orthomax criterion

          Generate                                                 F06AAF
          real plane rotation (DROTG)

          Initialise random number                                 G05CBF
          generating
          routines to give repeatable sequence

          Initialise random number                                 G05CCF
          generating
          routines to give non-repeatable sequence

          Save state of random number                              G05CFF
          generating
          routines

          Restore state of random number                           G05CGF
          generating
          routines

          Set up reference vector for                              G05ECF
          generating
          pseudo-random integers, Poisson distribution

          Set up reference vector for                              G05EDF
          generating
          pseudo-random integers, binomial distribution

          Generates                                                G05FAF
          a vector of random numbers from a uniform ...

          Generates                                                G05FBF
          a vector of random numbers from an (negative) ...

          Generates                                                G05FDF
          a vector of random numbers from a Normal distribution

          Generates                                                G05FEF
          a vector of pseudo-random numbers from a beta ...

          Generates                                                G05FFF
          a vector of pseudo-random numbers from a gamma ...

          Generates                                                G05HDF
          a realisation of a multivariate time series from a ...

          Gill-Miller
          method

                            2
          Performs the (chi)                                       G08CGF
          goodness
          of fit test, for standard continuous distributions

          Goodness                                                 G08
          of fit tests

          Unconstrained minimum, pre-conditioned conjugate         E04DGF
          gradient
          algorithm, function of several variables using 1st ...

          Hankel                                                   S17DLF
                     (j)
          functions H      (z), j=1,2, ...
                     (nu)+n

          Elliptic PDE,                                            D03FAF
          Helmholtz
          equation, 3-D Cartesian co-ordinates

          Hermite
          , one variable

          Single 1-D                                               C06EBF
          Hermitian
          discrete Fourier transform, no extra workspace

          Multiple 1-D                                             C06FQF
          Hermitian
          discrete Fourier transforms

          Complex conjugate of                                     C06GBF
          Hermitian
          sequence

          Complex conjugate of multiple                            C06GQF
          Hermitian
          sequences

          Convert                                                  C06GSF
          Hermitian
          sequences to general complex sequences

          All eigenvalues of complex                               F02AWF
          Hermitian
          matrix

          All eigenvalues and eigenvectors of complex              F02AXF
          Hermitian
          matrix

          Matrix-vector product, complex                           F06SCF
          Hermitian
          matrix (ZHEMV)

          Matrix-vector product, complex                           F06SDF
          Hermitian
          band matrix (ZHBMV)

          Matrix-vector product, complex                           F06SEF
          Hermitian
          packed matrix (ZHPMV)

          Rank-1 update, complex                                   F06SPF
          Hermitian
          matrix (ZHER)

          Rank-1 update, complex                                   F06SQF
          Hermitian
          packed matrix (ZHPR)

          Rank-2 update, complex                                   F06SRF
          Hermitian
          matrix (ZHER2)

          Rank-2 update, complex                                   F06SSF
          Hermitian
          packed matrix (ZHPR2)

          Matrix-matrix product, one complex                       F06ZCF
          Hermitian
          matrix, one complex rectangular matrix (ZHEMM)

          Rank-k update of a complex                               F06ZPF
          Hermitian
          matrix (ZHERK)

          Rank-2k update of a complex                              F06ZRF
          Hermitian
          matrix (ZHER2K)

          Hilbert
          transform)

          Computes a five-point summary (median,                   G01ALF
          hinges
          and extremes)

          Multi-dimensional adaptive quadrature over               D01FCF
          hyper-rectangle

          Multi-dimensional quadrature over                        D01GBF
          hyper-rectangle
          , Monte Carlo method

          Incomplete                                               S14BAF
          gamma functions P(a,x) and Q(a,x)

          Index                                                    F06JLF
          , real vector element with largest absolute value
          (IDAMAX)

          Index                                                    F06JMF
          , complex vector element with largest absolute value ..

          1-D quadrature, adaptive,                                D01AMF
          infinite
          or semi-infinite interval

          1-D quadrature, adaptive, infinite or semi-              D01AMF
          infinite
          interval

          1-D quadrature, adaptive, semi-                          D01ASF
          infinite
          interval, weight function cos((omega)x) or ...

          infinite
          range, eigenvalue and eigenfunction, user-specified ...

          Calculates standardized residuals and                    G02FAF
          influence
          statistics

          Initialise                                               G05CBF
          random number generating routines to give ...

          Initialise                                               G05CCF
          random number generating routines to give ...

          input
          data

          input
          data

          Multivariate time series, estimation of multi-           G13BEF
          input
          model

          input
          model

          Input/output                                             X04
          utilities

          Pseudo-random                                            G05DYF
          integer
          from uniform distribution

          Set up reference vector for generating pseudo-random     G05ECF
          integers
          , Poisson distribution

          Set up reference vector for generating pseudo-random     G05EDF
          integers
          , binomial distribution

          Pseudo-random permutation of an                          G05EHF
          integer
          vector

          Pseudo-random sample from an                             G05EJF
          integer
          vector

          Pseudo-random                                            G05EYF
          integer
          from reference vector

          Largest representable                                    X02BBF
          integer

          Return date and time as an array of                      X05AAF
          integers

          Convert array of                                         X05ABF
          integers
          representing date and time to character string

          integral
          , one variable

          Integral                                                 E02AJF
          of fitted polynomial in Chebyshev series form

          Evaluation of fitted cubic spline, definite              E02BDF
          integral

          Exponential                                              S13AAF
          integral
          E (x)
           1

          Cosine                                                   S13ACF
          integral
          Ci(x)

          Sine                                                     S13ADF
          integral
          Si(x)

          Fresnel                                                  S20ACF
          integral
          S(x)

          Fresnel                                                  S20ADF
          integral
          C(x)

          Degenerate symmetrised elliptic                          S21BAF
          integral
          of 1st kind R (x,y)
                       C

          Symmetrised elliptic                                     S21BBF
          integral
          of 1st kind R (x,y,z)
                       F

          Symmetrised elliptic                                     S21BCF
          integral
          of 2nd kind R (x,y,z)
                       D

          Symmetrised elliptic                                     S21BDF
          integral
          of 3rd kind R (x,y,z,r)
                       J

          1-D quadrature,                                          D01GAF
          integration
          of function defined by data values, Gill-Miller ...

          Numerical                                                D01
          integration

          Interpolating                                            E01BAF
          functions, cubic spline interpolant, one variable

          Interpolating functions, cubic spline                    E01BAF
          interpolant
          , one variable

          Interpolating                                            E01BEF
          functions, monotonicity-preserving, piecewise ...

          Interpolated                                             E01BFF
          values, interpolant computed by E01BEF, function ...

          Interpolated values,                                     E01BFF
          interpolant
          computed by E01BEF, function only, one variable

          Interpolated                                             E01BGF
          values, interpolant computed by E01BEF, function ...

          Interpolated values,                                     E01BGF
          interpolant
          computed by E01BEF, function and 1st derivative, ...

          Interpolated                                             E01BHF
          values, interpolant computed by E01BEF, definite ...

          Interpolated values,                                     E01BHF
          interpolant
          computed by E01BEF, definite integral, one variable

          Interpolating                                            E01DAF
          functions, fitting bicubic spline, data on ...

          Interpolating                                            E01SAF
          functions, method of Renka and Cline, two ...

          Interpolating                                            E01SEF
          functions, modified Shepard's method, two ...

          Least-squares curve cubic spline fit (including          E02BAF
          interpolation)

          Inverse                                                  G01F
          distributions

          Invert                                                   M01ZAF
          a permutation

          iterative
          refinement

          iterative
          refinement

          ODEs,                                                    D02BBF
          IVP
          , Runge-Kutta-Merson method, over a range, intermediate

          ODEs,                                                    D02BHF
          IVP
          , Runge-Kutta-Merson method, until function of solution
          is ...

          ODEs,                                                    D02CJF
          IVP
          , Adams method, until function of solution is zero, ...

          ODEs, stiff                                              D02EJF
          IVP
          , BDF method, until function of solution is zero, ...

          Kelvin function                                          S19ADF
          kei
          x

          Kelvin                                                   S19AAF
          function ber x

          Kelvin                                                   S19ABF
          function bei x

          Kelvin                                                   S19ACF
          function ker x

          Kelvin                                                   S19ADF
          function kei x

          Kendall/Spearman                                         G02BNF
          non-parametric rank correlation ...

          Kendall/Spearman                                         G02BQF
          non-parametric rank correlation ...

          Kelvin function                                          S19ACF
          ker
          x

          Least-squares cubic spline curve fit, automatic          E02BEF
          knot
          placement

          knot
          placement, data on rectangular grid

          knot
          placement, scattered data

          Kruskal-Wallis                                           G08AFF
          one-way analysis of variance on k samples of ...

          Mean, variance, skewness,                                G01AAF
          kurtosis
          etc, one variable, from raw data

          Mean, variance, skewness,                                G01ADF
          kurtosis
          etc, one variable, from frequency table

          All zeros of complex polynomial, modified                C02AFF
          Laguerre
          method

          All zeros of real polynomial, modified                   C02AGF
          Laguerre
          method

          Index, real vector element with                          F06JLF
          largest
          absolute value (IDAMAX)

          Index, complex vector element with                       F06JMF
          largest
          absolute value (IZAMAX)

          Largest                                                  X02ALF
          positive model number

          Largest                                                  X02BBF
          representable integer

          LDL                                                      F01MCF
          T
            factorization of real symmetric positive-definite ...

          Constructs a stem and                                    G01ARF
          leaf
          plot

          Least-squares                                            E02ADF
          curve fit, by polynomials, arbitrary data points

          Least-squares                                            E02AGF
          polynomial fit, values and derivatives may be ...

          Least-squares                                            E02BAF
          curve cubic spline fit (including interpolation)

          Least-squares                                            E02BEF
          cubic spline curve fit, automatic knot placement

          Least-squares                                            E02DAF
          surface fit, bicubic splines

          Least-squares                                            E02DCF
          surface fit by bicubic splines with automatic ...

          Least-squares                                            E02DDF
          surface fit by bicubic splines with automatic ...

          Covariance matrix for nonlinear                          E04YCF
          least-squares
          problem

          Least-squares                                            F04JGF
          (if rank=n) or minimal least-squares (if ...

          Least-squares (if rank=n) or minimal                     F04JGF
          least-squares
          (if rank<n) solution of m real equations ...

          Sparse linear                                            F04QAF
          least-squares
          problem, m real equations in n unknowns

          linear
          problem

          L -approximation by general                              E02GAF
           1
          linear
          function

          Linear                                                   E04MBF
          programming problem

          Solution of complex simultaneous                         F04ADF
          linear
          equations with multiple right-hand sides

          Solution of real simultaneous                            F04ARF
          linear
          equations, one right-hand side

          linear
          equations, one right-hand side using iterative ...

          Solution of real simultaneous                            F04ATF
          linear
          equations, one right-hand side using iterative ...

          Solution of real sparse simultaneous                     F04AXF
          linear
          equations (coefficient matrix already factorized)

          linear
          equations, one right-hand side

          Real sparse symmetric positive-definite simultaneous     F04MAF
          linear
          equations (coefficient matrix already factorized by ...

          Real sparse symmetric simultaneous                       F04MBF
          linear
          equations

          linear
          equations (coefficient matrix already factorized by ...

          Sparse                                                   F04QAF
          linear
          least-squares problem, m real equations in n ...

          Solution of real system of                               F07AEF
          linear
          equations, multiple right-hand sides, matrix already ..

          linear
          equations, multiple right-hand sides, matrix already ..

          Simple                                                   G02CAF
          linear
          regression with constant term, no missing values

          Fits a general (multiple)                                G02DAF
          linear
          regression model

          Fits a general                                           G02DGF
          linear
          regression model for new dependent variable

          Computes estimable function of a general                 G02DNF
          linear
          regression model and its standard error

          Fits a generalized                                       G02GBF
          linear
          model with binomial errors

          Fits a generalized                                       G02GCF
          linear
          model with Poisson errors

          Basic                                                    F06
          Linear
          Algebra Subprograms

          2nd order Sturm-                                         D02KEF
          Liouville
          problem, regular/singular system, finite/infinite ...

          Computes orthogonal rotations for                        G03BAF
          loading
          matrix, generalized orthomax criterion

          Location                                                 G08
          tests

          Log                                                      S14ABF
          Gamma function

          algebraico-
          logarithmic
          type

          Computes upper and                                       G01EEF
          lower
          tail and probability density function probabilities for

          LU                                                       F01BRF
          factorization of real sparse matrix

          LU                                                       F01BSF
          factorization of real sparse matrix with known sparsity

          LU                                                       F07ADF
          factorization of real m by n matrix (DGETRF)

          Machine                                                  X02AJF
          precision

          Machine                                                  X02
          Constants

          Performs the                                             G08AHF
          Mann-Whitney
          U test on two independent samples

          Computes the exact probabilities for the                 G08AJF
          Mann-Whitney
          U statistic, no ties in pooled sample

          Computes the exact probabilities for the                 G08AKF
          Mann-Whitney
          U statistic, ties in pooled sample

          Friedman two-way analysis of variance on k               G08AEF
          matched
          samples

          Performs the Wilcoxon one-sample (                       G08AGF
          matched
          pairs) signed rank test

          Mathematical                                             X01
          Constants

          Maximization                                             E04

          Maximum                                                  X02BEF
          number of decimal digits that can be represented

          Mean                                                     G01AAF
          , variance, skewness, kurtosis etc, one variable, from

          Mean                                                     G01ADF
          , variance, skewness, kurtosis etc, one variable, from

          Computes a five-point summary (                          G01ALF
          median
          , hinges and extremes)

          Median                                                   G08ACF
          test on two samples of unequal size

          ODEs, IVP, Runge-Kutta-                                  D02BBF
          Merson
          method, over a range, intermediate output

          ODEs, IVP, Runge-Kutta-                                  D02BHF
          Merson
          method, until function of solution is zero (simple ...

          Evaluation of a fitted bicubic spline at a               E02DFF
          mesh
          of points

          Miller
          method

          Least-squares (if rank=n) or                             F04JGF
          minimal
          least-squares (if rank<n) solution of m real ...

          Minimization                                             E04

          Unconstrained                                            E04DGF
          minimum
          , pre-conditioned conjugate gradient algorithm, ...

          Unconstrained                                            E04FDF
          minimum
          of a sum of squares, combined Gauss-Newton and ...

          Unconstrained                                            E04GCF
          minimum
          of a sum of squares, combined Gauss-Newton and ...

          Minimum                                                  E04JAF
          , function of several variables, quasi-Newton ...

          Minimum                                                  E04UCF
          , function of several variables, sequential QP method,

          missing
          values, overwriting input data

          missing
          values, preserving input data

          Simple linear regression with constant term, no          G02CAF
          missing
          values

          Fits a general (multiple) linear regression              G02DAF
          model

          Fits a general linear regression                         G02DGF
          model
          for new dependent variable

          model
          and its standard error

          Fits a generalized linear                                G02GBF
          model
          with binomial errors

          Fits a generalized linear                                G02GCF
          model
          with Poisson errors

          model

          model

          Univariate time series, estimation, seasonal ARIMA       G13AFF
          model

          model

          model

          model

          Multivariate time series, estimation of multi-input      G13BEF
          model

          model

          Smallest positive                                        X02AKF
          model
          number

          Largest positive                                         X02ALF
          model
          number

          Parameter of floating-point arithmetic                   X02BHF
          model
          , b

          Parameter of floating-point arithmetic                   X02BJF
          model
          , p

          Parameter of floating-point arithmetic                   X02BKF
          model
          , e
             min

          Parameter of floating-point arithmetic                   X02BLF
          model
          , e
             max

          Parameter of floating-point arithmetic                   X02DJF
          model
          , ROUNDS

          All zeros of complex polynomial,                         C02AFF
          modified
          Laguerre method

          All zeros of real polynomial,                            C02AGF
          modified
          Laguerre method

          Interpolating functions,                                 E01SEF
          modified
          Shepard's method, two variables

          modified
          Newton algorithm using function values only ...

          Modified                                                 S18ACF
          Bessel function K (x)
                           0

          Modified                                                 S18ADF
          Bessel function K (x)
                           1

          Modified                                                 S18AEF
          Bessel function I (x)
                           0

          Modified                                                 S18AFF
          Bessel function I (x)
                           1

          Modified                                                 S18DCF
          Bessel functions K      (z), real ...
                            (nu)+n

          Modified                                                 S18DEF
          Bessel functions I      (z), real ...
                            (nu)+n

          Interpolating functions,                                 E01BEF
          monotonicity-preserving
          , piecewise cubic Hermite, one variable

          Multi-dimensional quadrature over hyper-rectangle,       D01GBF
          Monte
          Carlo method

          Multi-dimensional                                        D01FCF
          adaptive quadrature over hyper-rectangle

          Multi-dimensional                                        D01GBF
          quadrature over hyper-rectangle, Monte ...

          Multivariate time series, estimation of                  G13BEF
          multi-input
          model

          multi-input
          model

          multigrid
          technique

          Multiple                                                 C06FPF
          1-D real discrete Fourier transforms

          Multiple                                                 C06FQF
          1-D Hermitian discrete Fourier transforms

          Multiple                                                 C06FRF
          1-D complex discrete Fourier transforms

          Complex conjugate of                                     C06GQF
          multiple
          Hermitian sequences

          multiple
          right-hand sides

          Solves a system of equations with                        F06YJF
          multiple
          right-hand sides, real triangular coefficient matrix ..

          Solves system of equations with                          F06ZJF
          multiple
          right-hand sides, complex triangular coefficient ...

          Solution of real system of linear equations,             F07AEF
          multiple
          right-hand sides, matrix already factorized by ...

          multiple
          right-hand sides, matrix already factorized by ...
          Fits a general (                                         G02DAF
          multiple)
          linear regression model

          Multiply                                                 F06EDF
          real vector by scalar (DSCAL)

          Multiply                                                 F06GDF
          complex vector by complex scalar (ZSCAL)

          Multiply                                                 F06JDF
          complex vector by real scalar (ZDSCAL)

          Set up reference vector for                              G05EAF
          multivariate
          Normal distribution

          Pseudo-random                                            G05EZF
          multivariate
          Normal vector from reference vector

          Generates a realisation of a                             G05HDF
          multivariate
          time series from a VARMA model

          Multivariate                                             G13BAF
          time series, filtering (pre-whitening) by an ...

          Multivariate                                             G13BCF
          time series, cross-correlations

          Multivariate                                             G13BDF
          time series, preliminary estimation of transfer ...

          Multivariate                                             G13BEF
          time series, estimation of multi-input model

          Multivariate                                             G13BJF
          time series, state set and forecasts from fully ...

          Multivariate                                             G13CDF
          time series, smoothed sample cross spectrum ...

          Generates a vector of random numbers from an (           G05FBF
          negative)
          exponential distribution

          Newton
          and modified Newton algorithm using function values ...

          Newton
          algorithm using function values only
          Newton
          and quasi-Newton algorithm, using 1st derivatives

          Newton
          algorithm, using 1st derivatives

          Minimum, function of several variables, quasi-           E04JAF
          Newton
          algorithm, simple bounds, using function values only

          Kendall/Spearman                                         G02BNF
          non-parametric
          rank correlation coefficients, no missing ...

          Kendall/Spearman                                         G02BQF
          non-parametric
          rank correlation coefficients, no missing ...

          Initialise random number generating routines to give     G05CCF
          non-repeatable
          sequence

          Univariate time series, seasonal and                     G13AAF
          non-seasonal
          differencing

          Non-parametric                                           G08
          tests

          Solution of system of                                    C05NBF
          nonlinear
          equations using function values only

          Solution of system of                                    C05PBF
          nonlinear
          equations using 1st derivatives

          nonlinear
          problem

          ODEs, general                                            D02RAF
          nonlinear
          boundary value problem, finite difference technique ...

          nonlinear
          constraints, using function values and optionally ...

          Covariance matrix for                                    E04YCF
          nonlinear
          least-squares problem

          Nonlinear                                                E04
          optimization

          Nonlinear                                                E04
          regression

          Compute Euclidean                                        F06EJF
          norm
          of real vector (DNRM2)

          Compute Euclidean                                        F06JJF
          norm
          of complex vector (DZNRM2)

          Computes probabilities for the standard                  G01EAF
          Normal
          distribution

          Computes deviates for the standard                       G01FAF
          Normal
          distribution

          Computes probability for the bivariate                   G01HAF
          Normal
          distribution

          Pseudo-random real numbers,                              G05DDF
          Normal
          distribution

          Set up reference vector for multivariate                 G05EAF
          Normal
          distribution

          Pseudo-random multivariate                               G05EZF
          Normal
          vector from reference vector

          Generates a vector of random numbers from a              G05FDF
          Normal
          distribution

          Numerical                                                D01
          integration

          ODEs                                                     D02BBF
          , IVP, Runge-Kutta-Merson method, over a range, ...

          ODEs                                                     D02BHF
          , IVP, Runge-Kutta-Merson method, until function of ...

          ODEs                                                     D02CJF
          , IVP, Adams method, until function of solution is
          zero, ...

          ODEs                                                     D02EJF
          , stiff IVP, BDF method, until function of solution is

          ODEs                                                     D02GAF
          , boundary value problem, finite difference technique .

          ODEs                                                     D02GBF
          , boundary value problem, finite difference technique .

          ODEs                                                     D02RAF
          , general nonlinear boundary value problem, finite ...

          Kruskal-Wallis                                           G08AFF
          one-way
          analysis of variance on k samples of unequal size

          Performs the Wilcoxon                                    G08AGF
          one-sample
          (matched pairs) signed rank test

          Operations                                               F01QDF
                                                   H
          with orthogonal matrices, compute QB or Q B ...

          Operations                                               F01QEF
          with orthogonal matrices, form columns of Q ...

          Operations                                               F01RDF
                                                H
          with unitary matrices, compute QB or Q B ...

          Operations                                               F01REF
          with unitary matrices, form columns of Q after ...

          Nonlinear                                                E04
          optimization

          Operations with                                          F01QDF
          orthogonal
                                   T
          matrices, compute QB or Q B after ...

          Operations with                                          F01QEF
          orthogonal
          matrices, form columns of Q after factorization ...

          Computes                                                 G03BAF
          orthogonal
          rotations for loading matrix, generalized orthomax ...

          orthomax
          criterion

          oscillating
          functions

          Incomplete gamma functions                               S14BAF
          P(a,x)
          and Q(a,x)

          Matrix-vector product, real symmetric                    F06PEF
          packed
          matrix (DSPMV)

          Matrix-vector product, real triangular                   F06PHF
          packed
          matrix (DTPMV)

          System of equations, real triangular                     F06PLF
          packed
          matrix (DTPSV)

          Rank-1 update, real symmetric                            F06PQF
          packed
          matrix (DSPR)

          Rank-2 update, real symmetric                            F06PSF
          packed
          matrix (DSPR2)

          Matrix-vector product, complex Hermitian                 F06SEF
          packed
          matrix (ZHPMV)

          Matrix-vector product, complex triangular                F06SHF
          packed
          matrix (ZTPMV)

          System of equations, complex triangular                  F06SLF
          packed
          matrix (ZTPSV)

          Rank-1 update, complex Hermitian                         F06SQF
          packed
          matrix (ZHPR)

          Rank-2 update, complex Hermitian                         F06SSF
          packed
          matrix (ZHPR2)

          Sign test on two                                         G08AAF
          paired
          samples

          Performs the Wilcoxon one-sample (matched                G08AGF
          pairs)
          signed rank test

          Kendall/Spearman non-                                    G02BNF
          parametric
          rank correlation coefficients, no missing values, ...

          Kendall/Spearman non-                                    G02BQF
          parametric
          rank correlation coefficients, no missing values, ...

          Non-                                                     G08
          parametric
          tests

          Univariate time series,                                  G13ACF
          partial
          autocorrelations from autocorrelations

          Elliptic                                                 D03EDF
          PDE
          , solution of finite difference equations by a
          multigrid ...

          Discretize a 2nd order elliptic                          D03EEF
          PDE
          on a rectangle

          Elliptic                                                 D03FAF
          PDE
          , Helmholtz equation, 3-D Cartesian co-ordinates

          Pseudo-random                                            G05EHF
          permutation
          of an integer vector

          Invert a                                                 M01ZAF
          permutation

          Interpolating functions, monotonicity-preserving,        E01BEF
          piecewise
          cubic Hermite, one variable

          Piessens
          and de Doncker, allowing for badly-behaved integrands

          Generate real                                            F06AAF
          plane
          rotation (DROTG)
          Apply real                                               F06EPF
          plane
          rotation (DROT)

          Constructs a stem and leaf                               G01ARF
          plot

          Fits a generalized linear model with                     G02GCF
          Poisson
          errors

          Poisson
          distribution

          All zeros of complex                                     C02AFF
          polynomial
          , modified Laguerre method

          All zeros of real                                        C02AGF
          polynomial
          , modified Laguerre method

          Least-squares curve fit, by                              E02ADF
          polynomials
          , arbitrary data points

          Evaluation of fitted                                     E02AEF
          polynomial
          in one variable from Chebyshev series form ...

          Least-squares                                            E02AGF
          polynomial
          fit, values and derivatives may be constrained, ...

          Derivative of fitted                                     E02AHF
          polynomial
          in Chebyshev series form

          Integral of fitted                                       E02AJF
          polynomial
          in Chebyshev series form

          Evaluation of fitted                                     E02AKF
          polynomial
          in one variable, from Chebyshev series form

          pooled
          sample

          pooled
          sample

          Pre-computed                                             D01BBF
          weights and abscissae for Gaussian quadrature ...

          Unconstrained minimum,                                   E04DGF
          pre-conditioned
          conjugate gradient algorithm, function of ...

          Multivariate time series, filtering (                    G13BAF
          pre-whitening)
          by an ARIMA model

          Machine                                                  X02AJF
          precision

          Univariate time series,                                  G13ADF
          preliminary
          estimation, seasonal ARIMA model

          Multivariate time series,                                G13BDF
          preliminary
          estimation of transfer function model

          principal
          value (Hilbert transform)

          Performs                                                 G03AAF
          principal
          component analysis

          Print                                                    X04CAF
          a real general matrix

          Print                                                    X04DAF
          a complex general matrix

          Computes                                                 G01EAF
          probabilities
          for the standard Normal distribution

          Computes                                                 G01EBF
          probabilities
          for Student's t-distribution

          Computes                                                 G01ECF
          probabilities
                   2
          for (chi)  distribution

          Computes                                                 G01EDF
          probabilities
          for F-distribution

          Computes upper and lower tail and                        G01EEF
          probability
          density function probabilities for the beta ...

          probabilities
          for the beta distribution

          Computes                                                 G01EFF
          probabilities
          for the gamma distribution

          Computes                                                 G01HAF
          probability
          for the bivariate Normal distribution

          probability
          distribution function

          Computes the exact                                       G08AJF
          probabilities
          for the Mann-Whitney U statistic, no ties in ...

          Computes the exact                                       G08AKF
          probabilities
          for the Mann-Whitney U statistic, ties in ...

          Dot                                                      F06EAF
          product
          of two real vectors (DDOT)

          Dot                                                      F06GAF
          product
          of two complex vectors, unconjugated (ZDOTU)

          Dot                                                      F06GBF
          product
          of two complex vectors, conjugated (ZDOTC)

          Matrix-vector                                            F06PAF
          product
          , real rectangular matrix (DGEMV)

          Matrix-vector                                            F06PBF
          product
          , real rectangular band matrix (DGBMV)

          Matrix-vector                                            F06PCF
          product
          , real symmetric matrix (DSYMV)

          Matrix-vector                                            F06PDF
          product
          , real symmetric band matrix (DSBMV)

          Matrix-vector                                            F06PEF
          product
          , real symmetric packed matrix (DSPMV)

          Matrix-vector                                            F06PFF
          product
          , real triangular matrix (DTRMV)

          Matrix-vector                                            F06PGF
          product
          , real triangular band matrix (DTBMV)

          Matrix-vector                                            F06PHF
          product
          , real triangular packed matrix (DTPMV)

          Matrix-vector                                            F06SAF
          product
          , complex rectangular matrix (ZGEMV)

          Matrix-vector                                            F06SBF
          product
          , complex rectangular band matrix (ZGBMV)

          Matrix-vector                                            F06SCF
          product
          , complex Hermitian matrix (ZHEMV)

          Matrix-vector                                            F06SDF
          product
          , complex Hermitian band matrix (ZHBMV)

          Matrix-vector                                            F06SEF
          product
          , complex Hermitian packed matrix (ZHPMV)

          Matrix-vector                                            F06SFF
          product
          , complex triangular matrix (ZTRMV)

          Matrix-vector                                            F06SGF
          product
          , complex triangular band matrix (ZTBMV)

          Matrix-vector                                            F06SHF
          product
          , complex triangular packed matrix (ZTPMV)

          Matrix-matrix                                            F06YAF
          product
          , two real rectangular matrices (DGEMM)

          Matrix-matrix                                            F06YCF
          product
          , one real symmetric matrix, one real rectangular ...

          Matrix-matrix                                            F06YFF
          product
          , one real triangular matrix, one real rectangular ...

          Matrix-matrix                                            F06ZAF
          product
          , two complex rectangular matrices (ZGEMM)

          Matrix-matrix                                            F06ZCF
          product
          , one complex Hermitian matrix, one complex ...

          Matrix-matrix                                            F06ZFF
          product
          , one complex triangular matrix, one complex ...

          Matrix-matrix                                            F06ZTF
          product
          , one complex symmetric matrix, one complex ...

          Linear                                                   E04MBF
          programming
          problem

          Pseudo-random                                            G05CAF
          real numbers, uniform distribution over (0,1)

          Pseudo-random                                            G05DDF
          real numbers, Normal distribution

          Pseudo-random                                            G05DFF
          real numbers, Cauchy distribution

          Pseudo-random                                            G05DPF
          real numbers, Weibull distribution

          Pseudo-random                                            G05DYF
          integer from uniform distribution

          Pseudo-random                                            G05DZF
          logical (boolean) value

          Set up reference vector for generating                   G05ECF
          pseudo-random
          integers, Poisson distribution

          Set up reference vector for generating                   G05EDF
          pseudo-random
          integers, binomial distribution

          Pseudo-random                                            G05EHF
          permutation of an integer vector

          Pseudo-random                                            G05EJF
          sample from an integer vector

          Pseudo-random                                            G05EYF
          integer from reference vector

          Pseudo-random                                            G05EZF
          multivariate Normal vector from reference vector

          Generates a vector of                                    G05FEF
          pseudo-random
          numbers from a beta distribution

          Generates a vector of                                    G05FFF
          pseudo-random
          numbers from a gamma distribution

          Incomplete gamma functions P(a,x) and                    S14BAF
          Q(a,x)

          QP                                                       E04NAF
          problem

          Minimum, function of several variables, sequential       E04UCF
          QP
          method, nonlinear constraints, using function values
          and ...

          QR                                                       F01QCF
          factorization of real m by n matrix (m<=n)

          QR                                                       F01RCF
          factorization of complex m by n matrix (m<=n)

          1-D                                                      D01AJF
          quadrature
          , adaptive, finite interval, strategy due to ...

          1-D                                                      D01AKF
          quadrature
          , adaptive, finite interval, method suitable for ...

          1-D                                                      D01ALF
          quadrature
          , adaptive, finite interval, allowing for ...
          1-D                                                      D01AMF
          quadrature
          , adaptive, infinite or semi-infinite interval

          1-D                                                      D01ANF
          quadrature
          , adaptive, finite interval, weight function
          cos((omega)x) ...

          1-D                                                      D01APF
          quadrature
          , adaptive, finite interval, weight function with ...

          1-D                                                      D01AQF
          quadrature
          , adaptive, finite interval, weight function ...

          1-D                                                      D01ASF
          quadrature
          , adaptive, semi-infinite interval, weight function ...

          Pre-computed weights and abscissae for Gaussian          D01BBF
          quadrature
          rules, restricted choice of rule

          Multi-dimensional adaptive                               D01FCF
          quadrature
          over hyper-rectangle

          1-D                                                      D01GAF
          quadrature
          , integration of function defined by data values, ...

          Multi-dimensional                                        D01GBF
          quadrature
          over hyper-rectangle, Monte Carlo method

          quasi-Newton
          algorithm, using 1st derivatives

          Minimum, function of several variables,                  E04JAF
          quasi-Newton
          algorithm, simple bounds, using function values ...

          QZ
          algorithm, real matrices

          Pseudo-                                                  G05CAF
          random
          real numbers, uniform distribution over (0,1)

          Initialise                                               G05CBF
          random
          number generating routines to give repeatable sequence

          Initialise                                               G05CCF
          random
          number generating routines to give non-repeatable ...

          Save state of                                            G05CFF
          random
          number generating routines

          Restore state of                                         G05CGF
          random
          number generating routines

          Pseudo-                                                  G05DDF
          random
          real numbers, Normal distribution

          Pseudo-                                                  G05DFF
          random
          real numbers, Cauchy distribution

          Pseudo-                                                  G05DPF
          random
          real numbers, Weibull distribution

          Pseudo-                                                  G05DYF
          random
          integer from uniform distribution

          Pseudo-                                                  G05DZF
          random
          logical (boolean) value

          Set up reference vector for generating pseudo-           G05ECF
          random
          integers, Poisson distribution

          Set up reference vector for generating pseudo-           G05EDF
          random
          integers, binomial distribution

          Pseudo-                                                  G05EHF
          random
          permutation of an integer vector

          Pseudo-                                                  G05EJF
          random
          sample from an integer vector

          Pseudo-                                                  G05EYF
          random
          integer from reference vector

          Pseudo-                                                  G05EZF
          random
          multivariate Normal vector from reference vector

          Generates a vector of                                    G05FAF
          random
          numbers from a uniform distribution

          Generates a vector of                                    G05FBF
          random
          numbers from an (negative) exponential distribution

          Generates a vector of                                    G05FDF
          random
          numbers from a Normal distribution

          Generates a vector of pseudo-                            G05FEF
          random
          numbers from a beta distribution

          Generates a vector of pseudo-                            G05FFF
          random
          numbers from a gamma distribution

          ODEs, IVP, Runge-Kutta-Merson method, over a             D02BBF
          range
          , intermediate output

          range
          , eigenvalue and eigenfunction, user-specified ...

          Safe                                                     X02AMF
          range
          of floating-point arithmetic

          Safe                                                     X02ANF
          range
          of complex floating-point arithmetic

          Least-squares (if                                        F04JGF
          rank=n)
          or minimal least-squares (if rank<n) ...

          rank
          <n) solution of m real equations in n unknowns, ...

          rank
          <=n,m>=n

          Rank-1                                                   F06PMF
          update, real rectangular matrix (DGER)

          Rank-1                                                   F06PPF
          update, real symmetric matrix (DSYR)

          Rank-1                                                   F06PQF
          update, real symmetric packed matrix (DSPR)

          Rank-2                                                   F06PRF
          update, real symmetric matrix (DSYR2)

          Rank-2                                                   F06PSF
          update, real symmetric packed matrix (DSPR2)

          Rank-1                                                   F06SMF
          update, complex rectangular matrix, unconjugated ...

          Rank-1                                                   F06SNF
          update, complex rectangular matrix, conjugated vector .

          Rank-1                                                   F06SPF
          update, complex Hermitian matrix (ZHER)

          Rank-1                                                   F06SQF
          update, complex Hermitian packed matrix (ZHPR)

          Rank-2                                                   F06SRF
          update, complex Hermitian matrix (ZHER2)

          Rank-2                                                   F06SSF
          update, complex Hermitian packed matrix (ZHPR2)

          Rank-k                                                   F06YPF
          update of a real symmetric matrix (DSYRK)

          Rank-2k                                                  F06YRF
          update of a real symmetric matrix (DSYR2K)

          Rank-k                                                   F06ZPF
          update of a complex Hermitian matrix (ZHERK)

          Rank-2k                                                  F06ZRF
          update of a complex Hermitian matrix (ZHER2K)

          Rank-k                                                   F06ZUF
          update of a complex symmetric matrix (ZSYRK)

          Rank-2k                                                  F06ZWF
          update of a complex symmetric matrix (ZHER2K)

          Kendall/Spearman non-parametric                          G02BNF
          rank
          correlation coefficients, no missing values,
          overwriting ...

          Kendall/Spearman non-parametric                          G02BQF
          rank
          correlation coefficients, no missing values, preserving

          rank
          test

          Rank                                                     M01DAF
          a vector, real numbers

          Rank                                                     M01DEF
          rows of a matrix, real numbers

          Rank                                                     M01DJF
          columns of a matrix, real numbers

          Rearrange a vector according to given                    M01EAF
          ranks
          , real numbers

          Generates a                                              G05HDF
          realisation
          of a multivariate time series from a VARMA model

          Rearrange                                                M01EAF
          a vector according to given ranks, real numbers

          Multi-dimensional adaptive quadrature over hyper-        D01FCF
          rectangle

          Multi-dimensional quadrature over hyper-                 D01GBF
          rectangle
          , Monte Carlo method

          Discretize a 2nd order elliptic PDE on a                 D03EEF
          rectangle

          rectangular
          grid

          rectangular
          grid

          Matrix-vector product, real                              F06PAF
          rectangular
          matrix (DGEMV)

          Matrix-vector product, real                              F06PBF
          rectangular
          band matrix (DGBMV)

          Rank-1 update, real                                      F06PMF
          rectangular
          matrix (DGER)

          Matrix-vector product, complex                           F06SAF
          rectangular
          matrix (ZGEMV)

          Matrix-vector product, complex                           F06SBF
          rectangular
          band matrix (ZGBMV)

          Rank-1 update, complex                                   F06SMF
          rectangular
          matrix, unconjugated vector (ZGERU)

          Rank-1 update, complex                                   F06SNF
          rectangular
          matrix, conjugated vector (ZGERC)

          Matrix-matrix product, two real                          F06YAF
          rectangular
          matrices (DGEMM)

          rectangular
          matrix (DSYMM)

          rectangular
          matrix (DTRMM)

          Matrix-matrix product, two complex                       F06ZAF
          rectangular
          matrices (ZGEMM)

          rectangular
          matrix (ZHEMM)

          rectangular
          matrix (ZTRMM)

          rectangular
          matrix (ZSYMM)

          Set up                                                   G05EAF
          reference
          vector for multivariate Normal distribution

          Set up                                                   G05ECF
          reference
          vector for generating pseudo-random integers, ...

          Set up                                                   G05EDF
          reference
          vector for generating pseudo-random integers, ...

          Set up                                                   G05EXF
          reference
          vector from supplied cumulative distribution ...

          Pseudo-random integer from                               G05EYF
          reference
          vector

          Pseudo-random multivariate Normal vector from            G05EZF
          reference
          vector

          refinement

          refinement

          Simple linear                                            G02CAF
          regression
          with constant term, no missing values

          Fits a general (multiple) linear                         G02DAF
          regression
          model

          Fits a general linear                                    G02DGF
          regression
          model for new dependent variable

          Computes estimable function of a general linear          G02DNF
          regression
          model and its standard error

          Nonlinear                                                E04
          regression

          2nd order Sturm-Liouville problem,                       D02KEF
          regular/singular
          system, finite/infinite range, eigenvalue ...

          Interpolating functions, method of                       E01SAF
          Renka
          and Cline, two variables

          Calculates standardized                                  G02FAF
          residuals
          and influence statistics
          Univariate time series, diagnostic checking of           G13ASF
          residuals
          , following G13AFF

          right-hand
          sides

          Solution of real simultaneous linear equations, one      F04ARF
          right-hand
          side

          right-hand
          side using iterative refinement

          Solution of real simultaneous linear equations, one      F04ATF
          right-hand
          side using iterative refinement

          right-hand
          side

          Solves a system of equations with multiple               F06YJF
          right-hand
          sides, real triangular coefficient matrix (DTRSM)

          Solves system of equations with multiple                 F06ZJF
          right-hand
          sides, complex triangular coefficient matrix (ZTRSM)

          Solution of real system of linear equations, multiple    F07AEF
          right-hand
          sides, matrix already factorized by F07ADF (DGETRS)

          right-hand
          sides, matrix already factorized by F07FDF (DPOTRS)

          Generate real plane                                      F06AAF
          rotation
          (DROTG)

          Apply real plane                                         F06EPF
          rotation
          (DROT)

          Computes orthogonal                                      G03BAF
          rotations
          for loading matrix, generalized orthomax criterion

          rules
          , restricted choice of rule

          rule
          ODEs, IVP,                                               D02BBF
          Runge-Kutta-Merson
          method, over a range, intermediate output

          ODEs, IVP,                                               D02BHF
          Runge-Kutta-Merson
          method, until function of solution is zero ...

          Safe                                                     X02AMF
          range of floating-point arithmetic

          Safe                                                     X02ANF
          range of complex floating-point arithmetic

          Pseudo-random                                            G05EJF
          sample
          from an integer vector

          Sign test on two paired                                  G08AAF
          samples

          Median test on two                                       G08ACF
          samples
          of unequal size

          Friedman two-way analysis of variance on k matched       G08AEF
          samples

          Kruskal-Wallis one-way analysis of variance on k         G08AFF
          samples
          of unequal size

          Performs the Wilcoxon one-                               G08AGF
          sample
          (matched pairs) signed rank test

          Performs the Mann-Whitney U test on two independent      G08AHF
          samples

          sample

          sample

          Univariate time series,                                  G13ABF
          sample
          autocorrelation function

          Univariate time series, smoothed                         G13CBF
          sample
          spectrum using spectral smoothing by the trapezium ...

          Multivariate time series, smoothed                       G13CDF
          sample
          cross spectrum using spectral smoothing by the ...

          Add                                                      F06ECF
          scalar
          times real vector to real vector (DAXPY)

          Multiply real vector by                                  F06EDF
          scalar
          (DSCAL)

          Add                                                      F06GCF
          scalar
          times complex vector to complex vector (ZAXPY)

          Multiply complex vector by complex                       F06GDF
          scalar
          (ZSCAL)

          Multiply complex vector by real                          F06JDF
          scalar
          (ZDSCAL)

          scattered
          data

          Univariate time series,                                  G13AAF
          seasonal
          and non-seasonal differencing

          Univariate time series, seasonal and non-                G13AAF
          seasonal
          differencing

          Univariate time series, preliminary estimation,          G13ADF
          seasonal
          ARIMA model

          Univariate time series, estimation,                      G13AFF
          seasonal
          ARIMA model

          seasonal
          ARIMA model

          1-D quadrature, adaptive, infinite or                    D01AMF
          semi-infinite
          interval

          1-D quadrature, adaptive,                                D01ASF
          semi-infinite
          interval, weight function cos((omega)x) ...
          Complex conjugate of Hermitian                           C06GBF
          sequence

          Complex conjugate of complex                             C06GCF
          sequence

          Complex conjugate of multiple Hermitian                  C06GQF
          sequences

          Convert Hermitian                                        C06GSF
          sequences
          to general complex sequences

          Convert Hermitian sequences to general complex           C06GSF
          sequences

          sequence

          sequence

          Minimum, function of several variables,                  E04UCF
          sequential
          QP method, nonlinear constraints, using function ...

          Interpolating functions, modified                        E01SEF
          Shepard's
          method, two variables

          Sign                                                     G08AAF
          test on two paired samples

          Performs the Wilcoxon one-sample (matched pairs)         G08AGF
          signed
          rank test

          Solution of complex                                      F04ADF
          simultaneous
          linear equations with multiple right-hand sides

          Solution of real                                         F04ARF
          simultaneous
          linear equations, one right-hand side

          Solution of real symmetric positive-definite             F04ASF
          simultaneous
          linear equations, one right-hand side using ...

          Solution of real                                         F04ATF
          simultaneous
          linear equations, one right-hand side using ...

          Solution of real sparse                                  F04AXF
          simultaneous
          linear equations (coefficient matrix already ...

          simultaneous
          linear equations, one right-hand side

          Real sparse symmetric positive-definite                  F04MAF
          simultaneous
          linear equations (coefficient matrix already ...

          Real sparse symmetric                                    F04MBF
          simultaneous
          linear equations

          simultaneous
          linear equations (coefficient matrix already ...

          sin
          ((omega)x)

          sin
          ((omega)x)

          Sine                                                     S13ADF
          integral Si(x)

          2nd order Sturm-Liouville problem, regular/              D02KEF
          singular
          system, finite/infinite range, eigenvalue and ...

          singularities
          at user-specified break-points

          singularities
          of algebraico-logarithmic type

          Mean, variance,                                          G01AAF
          skewness
          , kurtosis etc, one variable, from raw data

          Mean, variance,                                          G01ADF
          skewness
          , kurtosis etc, one variable, from frequency table

          Smallest                                                 X02AKF
          positive model number

          Univariate time series,                                  G13CBF
          smoothed
          sample spectrum using spectral smoothing by the ...

          smoothing
          by the trapezium frequency (Daniell) window

          Multivariate time series,                                G13CDF
          smoothed
          sample cross spectrum using spectral smoothing by ...

          smoothing
          by the trapezium frequency (Daniell) window

          Sort                                                     E02ZAF
          2-D data into panels for fitting bicubic splines

          Sort                                                     M01CAF
          a vector, real numbers

          LU factorization of real                                 F01BRF
          sparse
          matrix

          LU factorization of real                                 F01BSF
          sparse
          matrix with known sparsity pattern

          LU factorization of real sparse matrix with known        F01BSF
          sparsity
          pattern

            T
          LL  factorization of real                                F01MAF
          sparse
          symmetric positive-definite matrix

          Selected eigenvalues and eigenvectors of                 F02FJF
          sparse
          symmetric eigenproblem

          Solution of real                                         F04AXF
          sparse
          simultaneous linear equations (coefficient matrix ...

          Real                                                     F04MAF
          sparse
          symmetric positive-definite simultaneous linear ...

          Real                                                     F04MBF
          sparse
          symmetric simultaneous linear equations

          Sparse                                                   F04QAF
          linear least-squares problem, m real equations in ...

          Kendall/                                                 G02BNF
          Spearman
          non-parametric rank correlation coefficients, no ...

          Kendall/                                                 G02BQF
          Spearman
          non-parametric rank correlation coefficients, no ...

          Approximation of                                         S
          special
          functions

          Univariate time series, smoothed sample                  G13CBF
          spectrum
          using spectral smoothing by the trapezium frequency ...

          spectral
          smoothing by the trapezium frequency (Daniell) window

          Multivariate time series, smoothed sample cross          G13CDF
          spectrum
          using spectral smoothing by the trapezium frequency ...

          spectral
          smoothing by the trapezium frequency (Daniell) window

          Interpolating functions, cubic                           E01BAF
          spline
          interpolant, one variable

          Interpolating functions, fitting bicubic                 E01DAF
          spline
          , data on rectangular grid

          Least-squares curve cubic                                E02BAF
          spline
          fit (including interpolation)

          Evaluation of fitted cubic                               E02BBF
          spline
          , function only

          Evaluation of fitted cubic                               E02BCF
          spline
          , function and derivatives

          Evaluation of fitted cubic                               E02BDF
          spline
          , definite integral

          Least-squares cubic                                      E02BEF
          spline
          curve fit, automatic knot placement
          Least-squares surface fit, bicubic                       E02DAF
          splines

          Least-squares surface fit by bicubic                     E02DCF
          splines
          with automatic knot placement, data on rectangular grid

          Least-squares surface fit by bicubic                     E02DDF
          splines
          with automatic knot placement, scattered data

          Evaluation of a fitted bicubic                           E02DEF
          spline
          at a vector of points

          Evaluation of a fitted bicubic                           E02DFF
          spline
          at a mesh of points

          Sort 2-D data into panels for fitting bicubic            E02ZAF
          splines

          B-                                                       E02
          splines

          Least-                                                   E02ADF
          squares
          curve fit, by polynomials, arbitrary data points

          Least-                                                   E02AGF
          squares
          polynomial fit, values and derivatives may be ...

          Least-                                                   E02BAF
          squares
          curve cubic spline fit (including interpolation)

          Least-                                                   E02BEF
          squares
          cubic spline curve fit, automatic knot placement

          Least-                                                   E02DAF
          squares
          surface fit, bicubic splines

          Least-                                                   E02DCF
          squares
          surface fit by bicubic splines with automatic knot ...

          Least-                                                   E02DDF
          squares
          surface fit by bicubic splines with automatic knot ...
          Unconstrained minimum of a sum of                        E04FDF
          squares
          , combined Gauss-Newton and modified Newton algorithm .

          Unconstrained minimum of a sum of                        E04GCF
          squares
          , combined Gauss-Newton and quasi-Newton algorithm, ...

          Covariance matrix for nonlinear least-                   E04YCF
          squares
          problem

          Least-                                                   F04JGF
          squares
          (if rank=n) or minimal least-squares (if ...

          Least-squares (if rank=n) or minimal least-              F04JGF
          squares
          (if rank<n) solution of m real equations in n ...

          Sparse linear least-                                     F04QAF
          squares
          problem, m real equations in n unknowns

          Computes probabilities for the                           G01EAF
          standard
          Normal distribution

          Computes deviates for the                                G01FAF
          standard
          Normal distribution

          standard
          error

                            2
          Performs the (chi)  goodness of fit test, for            G08CGF
          standard
          continuous distributions

          Calculates                                               G02FAF
          standardized
          residuals and influence statistics

          Calculates standardized residuals and influence          G02FAF
          statistics

          statistic
          , no ties in pooled sample

          statistic
          , ties in pooled sample
          Constructs a                                             G01ARF
          stem
          and leaf plot

          ODEs,                                                    D02EJF
          stiff
          IVP, BDF method, until function of solution is zero, ..

          Computes probabilities for                               G01EBF
          Student's
          t-distribution

          Computes deviates for                                    G01FBF
          Student's
          t-distribution

          2nd order                                                D02KEF
          Sturm-Liouville
          problem, regular/singular system, ...

          Basic Linear Algebra                                     F06
          Subprograms

          Unconstrained minimum of a                               E04FDF
          sum
          of squares, combined Gauss-Newton and modified Newton .

          Unconstrained minimum of a                               E04GCF
          sum
          of squares, combined Gauss-Newton and quasi-Newton ...

          Sum                                                      F06EKF
          the absolute values of real vector elements (DASUM)

          Sum                                                      F06JKF
          the absolute values of complex vector elements (DZASUM)

          Computes a five-point                                    G01ALF
          summary
          (median, hinges and extremes)

          Least-squares                                            E02DAF
          surface
          fit, bicubic splines

          Least-squares                                            E02DCF
          surface
          fit by bicubic splines with automatic knot placement, .

          Least-squares                                            E02DDF
          surface
          fit by bicubic splines with automatic knot placement, .
          SVD                                                      F02WEF
          of real matrix

          SVD                                                      F02XEF
          of complex matrix

          Swap                                                     F06EGF
          two real vectors (DSWAP)

          Swap                                                     F06GGF
          two complex vectors (ZSWAP)

          Fresnel integral                                         S20ACF
          S(x)

            T
          LL  factorization of real sparse                         F01MAF
          symmetric
          positive-definite matrix

             T
          LDL  factorization of real                               F01MCF
          symmetric
          positive-definite variable-bandwidth matrix

          All eigenvalues of real                                  F02AAF
          symmetric
          matrix

          All eigenvalues and eigenvectors of real                 F02ABF
          symmetric
          matrix

          symmetric
          and B is positive-definite

          symmetric
          and B is positive-definite

          Selected eigenvalues and eigenvectors of real            F02BBF
          symmetric
          matrix

          Selected eigenvalues and eigenvectors of sparse          F02FJF
          symmetric
          eigenproblem

          Solution of real                                         F04ASF
          symmetric
          positive-definite simultaneous linear equations, ...

          Solution of real                                         F04FAF
          symmetric
          positive-definite tridiagonal simultaneous linear ...

          Real sparse                                              F04MAF
          symmetric
          positive-definite simultaneous linear equations ...

          Real sparse                                              F04MBF
          symmetric
          simultaneous linear equations

          Solution of real                                         F04MCF
          symmetric
          positive-definite variable-bandwidth simultaneous ...

          Matrix-vector product, real                              F06PCF
          symmetric
          matrix (DSYMV)

          Matrix-vector product, real                              F06PDF
          symmetric
          band matrix (DSBMV)

          Matrix-vector product, real                              F06PEF
          symmetric
          packed matrix (DSPMV)

          Rank-1 update, real                                      F06PPF
          symmetric
          matrix (DSYR)

          Rank-1 update, real                                      F06PQF
          symmetric
          packed matrix (DSPR)

          Rank-2 update, real                                      F06PRF
          symmetric
          matrix (DSYR2)

          Rank-2 update, real                                      F06PSF
          symmetric
          packed matrix (DSPR2)

          Matrix-matrix product, one real                          F06YCF
          symmetric
          matrix, one real rectangular matrix (DSYMM)

          Rank-k update of a real                                  F06YPF
          symmetric
          matrix (DSYRK)

          Rank-2k update of a real                                 F06YRF
          symmetric
          matrix (DSYR2K)

          Matrix-matrix product, one complex                       F06ZTF
          symmetric
          matrix, one complex rectangular matrix (ZSYMM)

          Rank-k update of a complex                               F06ZUF
          symmetric
          matrix (ZSYRK)

          Rank-2k update of a complex                              F06ZWF
          symmetric
          matrix (ZHER2K)

          Cholesky factorization of real                           F07FDF
          symmetric
          positive-definite matrix (DPOTRF)

          Solution of real                                         F07FEF
          symmetric
          positive-definite system of linear equations, ...

          Degenerate                                               S21BAF
          symmetrised
          elliptic integral of 1st kind R (x,y)
                                         C

          Symmetrised                                              S21BBF
          elliptic integral of 1st kind R (x,y,z)
                                         F

          Symmetrised                                              S21BCF
          elliptic integral of 2nd kind R (x,y,z)
                                         D

          Symmetrised                                              S21BDF
          elliptic integral of 3rd kind R (x,y,z,r)
                                         J

          Solution of                                              C05NBF
          system
          of nonlinear equations using function values only

          Solution of                                              C05PBF
          system
          of nonlinear equations using 1st derivatives

          2nd order Sturm-Liouville problem, regular/singular      D02KEF
          system
          , finite/infinite range, eigenvalue and eigenfunction,

          System                                                   F06PJF
          of equations, real triangular matrix (DTRSV)

          System                                                   F06PKF
          of equations, real triangular band matrix (DTBSV)

          System                                                   F06PLF
          of equations, real triangular packed matrix (DTPSV)

          System                                                   F06SJF
          of equations, complex triangular matrix (ZTRSV)

          System                                                   F06SKF
          of equations, complex triangular band matrix (ZTBSV)

          System                                                   F06SLF
          of equations, complex triangular packed matrix (ZTPSV)

          Solves a                                                 F06YJF
          system
          of equations with multiple right-hand sides, real ...

          Solves                                                   F06ZJF
          system
          of equations with multiple right-hand sides, complex ..

          Solution of real                                         F07AEF
          system
          of linear equations, multiple right-hand sides, matrix

          Solution of real symmetric positive-definite             F07FEF
          system
          of linear equations, multiple right-hand sides, matrix

          Computes probabilities for Student's                     G01EBF
          t-distribution

          Computes deviates for Student's                          G01FBF
          t-distribution

          table

          Frequency                                                G01AEF
          table
          from raw data

          Two-way contingency                                      G01AFF
          table
                              2
          analysis, with (chi) /Fisher's exact test

          Computes upper and lower                                 G01EEF
          tail
          and probability density function probabilities for the

                                        2
          test

          Sign                                                     G08AAF
          test
          on two paired samples

          Median                                                   G08ACF
          test
          on two samples of unequal size

          test

          Performs the Mann-Whitney U                              G08AHF
          test
          on two independent samples

                            2
          Performs the (chi)  goodness of fit                      G08CGF
          test
          , for standard continuous distributions

          Goodness of fit                                          G08
          tests

          Location                                                 G08
          tests

          Non-parametric                                           G08
          tests

          ties
          in pooled sample

          ties
          in pooled sample

          Generates a realisation of a multivariate                G05HDF
          time
          series from a VARMA model

          Univariate                                               G13AAF
          time
          series, seasonal and non-seasonal differencing

          Univariate                                               G13ABF
          time
          series, sample autocorrelation function

          Univariate                                               G13ACF
          time
          series, partial autocorrelations from autocorrelations

          Univariate                                               G13ADF
          time
          series, preliminary estimation, seasonal ARIMA model

          Univariate                                               G13AFF
          time
          series, estimation, seasonal ARIMA model

          Univariate                                               G13AGF
          time
          series, update state set for forecasting

          Univariate                                               G13AHF
          time
          series, forecasting from state set

          Univariate                                               G13AJF
          time
          series, state set and forecasts, from fully specified .

          Univariate                                               G13ASF
          time
          series, diagnostic checking of residuals, following
          G13AFF

          Multivariate                                             G13BAF
          time
          series, filtering (pre-whitening) by an ARIMA model

          Multivariate                                             G13BCF
          time
          series, cross-correlations

          Multivariate                                             G13BDF
          time
          series, preliminary estimation of transfer function
          model

          Multivariate                                             G13BEF
          time
          series, estimation of multi-input model

          Multivariate                                             G13BJF
          time
          series, state set and forecasts from fully specified ..

          Univariate                                               G13CBF
          time
          series, smoothed sample spectrum using spectral ...

          Multivariate                                             G13CDF
          time
          series, smoothed sample cross spectrum using spectral .

          Return date and                                          X05AAF
          time
          as an array of integers

          Convert array of integers representing date and          X05ABF
          time
          to character string

          Compare two character strings representing date and      X05ACF
          time

          Return the CPU                                           X05BAF
          time

          Multivariate time series, preliminary estimation of      G13BDF
          transfer
          function model

          Single 1-D real discrete Fourier                         C06EAF
          transform
          , no extra workspace

          Single 1-D Hermitian discrete Fourier                    C06EBF
          transform
          , no extra workspace

          Single 1-D complex discrete Fourier                      C06ECF
          transform
          , no extra workspace

          Multiple 1-D real discrete Fourier                       C06FPF
          transforms

          Multiple 1-D Hermitian discrete Fourier                  C06FQF
          transforms

          Multiple 1-D complex discrete Fourier                    C06FRF
          transforms

          2-D complex discrete Fourier                             C06FUF
          transform

          transform)

          trapezium
          frequency (Daniell) window
          trapezium
          frequency (Daniell) window

          Matrix-vector product, real                              F06PFF
          triangular
          matrix (DTRMV)

          Matrix-vector product, real                              F06PGF
          triangular
          band matrix (DTBMV)

          Matrix-vector product, real                              F06PHF
          triangular
          packed matrix (DTPMV)

          System of equations, real                                F06PJF
          triangular
          matrix (DTRSV)

          System of equations, real                                F06PKF
          triangular
          band matrix (DTBSV)

          System of equations, real                                F06PLF
          triangular
          packed matrix (DTPSV)

          Matrix-vector product, complex                           F06SFF
          triangular
          matrix (ZTRMV)

          Matrix-vector product, complex                           F06SGF
          triangular
          band matrix (ZTBMV)

          Matrix-vector product, complex                           F06SHF
          triangular
          packed matrix (ZTPMV)

          System of equations, complex                             F06SJF
          triangular
          matrix (ZTRSV)

          System of equations, complex                             F06SKF
          triangular
          band matrix (ZTBSV)

          System of equations, complex                             F06SLF
          triangular
          packed matrix (ZTPSV)

          Matrix-matrix product, one real                          F06YFF
          triangular
          matrix, one real rectangular matrix (DTRMM)

          triangular
          coefficient matrix (DTRSM)

          Matrix-matrix product, one complex                       F06ZFF
          triangular
          matrix, one complex rectangular matrix (ZTRMM)

          triangular
          coefficient matrix (ZTRSM)

          Solution of real symmetric positive-definite             F04FAF
          tridiagonal
          simultaneous linear equations, one right-hand side

          Two-way                                                  G01AFF
                                                2
          contingency table analysis, with (chi)  ...

          Sign test on                                             G08AAF
          two
          paired samples

          Median test on                                           G08ACF
          two
          samples of unequal size

          Friedman                                                 G08AEF
          two-way
          analysis of variance on k matched samples

          Performs the Mann-Whitney U test on                      G08AHF
          two
          independent samples

          Compare                                                  X05ACF
          two
          character strings representing date and time

          Dot product of two complex vectors,                      F06GAF
          unconjugated
          (ZDOTU)

          Rank-1 update, complex rectangular matrix,               F06SMF
          unconjugated
          vector (ZGERU)

          Unconstrained                                            E04DGF
          minimum, pre-conditioned conjugate gradient ...

          Unconstrained                                            E04FDF
          minimum of a sum of squares, combined ...

          Unconstrained                                            E04GCF
          minimum of a sum of squares, combined ...

          Switch for taking precautions to avoid                   X02DAF
          underflow

          Pseudo-random real numbers,                              G05CAF
          uniform
          distribution over (0,1)

          Pseudo-random integer from                               G05DYF
          uniform
          distribution

          Generates a vector of random numbers from a              G05FAF
          uniform
          distribution

          Operations with                                          F01RDF
          unitary
                                   H
          matrices, compute QB or Q B after ...

          Operations with                                          F01REF
          unitary
          matrices, form columns of Q after factorization by ...

          Univariate                                               G13AAF
          time series, seasonal and non-seasonal differencing

          Univariate                                               G13ABF
          time series, sample autocorrelation function

          Univariate                                               G13ACF
          time series, partial autocorrelations from ...

          Univariate                                               G13ADF
          time series, preliminary estimation, seasonal ...

          Univariate                                               G13AFF
          time series, estimation, seasonal ARIMA model

          Univariate                                               G13AGF
          time series, update state set for forecasting

          Univariate                                               G13AHF
          time series, forecasting from state set

          Univariate                                               G13AJF
          time series, state set and forecasts, from fully ...

          Univariate                                               G13ASF
          time series, diagnostic checking of residuals, ...

          Univariate                                               G13CBF
          time series, smoothed sample spectrum using ...

          Rank-1                                                   F06PMF
          update
          , real rectangular matrix (DGER)

          Rank-1                                                   F06PPF
          update
          , real symmetric matrix (DSYR)

          Rank-1                                                   F06PQF
          update
          , real symmetric packed matrix (DSPR)

          Rank-2                                                   F06PRF
          update
          , real symmetric matrix (DSYR2)

          Rank-2                                                   F06PSF
          update
          , real symmetric packed matrix (DSPR2)

          Rank-1                                                   F06SMF
          update
          , complex rectangular matrix, unconjugated vector
          (ZGERU)

          Rank-1                                                   F06SNF
          update
          , complex rectangular matrix, conjugated vector (ZGERC)

          Rank-1                                                   F06SPF
          update
          , complex Hermitian matrix (ZHER)

          Rank-1                                                   F06SQF
          update
          , complex Hermitian packed matrix (ZHPR)

          Rank-2                                                   F06SRF
          update
          , complex Hermitian matrix (ZHER2)

          Rank-2                                                   F06SSF
          update
          , complex Hermitian packed matrix (ZHPR2)
          Rank-k                                                   F06YPF
          update
          of a real symmetric matrix (DSYRK)

          Rank-2k                                                  F06YRF
          update
          of a real symmetric matrix (DSYR2K)

          Rank-k                                                   F06ZPF
          update
          of a complex Hermitian matrix (ZHERK)

          Rank-2k                                                  F06ZRF
          update
          of a complex Hermitian matrix (ZHER2K)

          Rank-k                                                   F06ZUF
          update
          of a complex symmetric matrix (ZSYRK)

          Rank-2k                                                  F06ZWF
          update
          of a complex symmetric matrix (ZHER2K)

          Univariate time series,                                  G13AGF
          update
          state set for forecasting

          Computes                                                 G01EEF
          upper
          and lower tail and probability density function ...

          Input/output                                             X04
          utilities

          Mean,                                                    G01AAF
          variance
          , skewness, kurtosis etc, one variable, from raw data

          Mean,                                                    G01ADF
          variance
          , skewness, kurtosis etc, one variable, from ...

          Friedman two-way analysis of                             G08AEF
          variance
          on k matched samples

          Kruskal-Wallis one-way analysis of                       G08AFF
          variance
          on k samples of unequal size

          VARMA
          model

          Circular convolution or correlation of two real          C06EKF
          vectors
          , no extra workspace

          Evaluation of a fitted bicubic spline at a               E02DEF
          vector
          of points

          Dot product of two real                                  F06EAF
          vectors
          (DDOT)

          Add scalar times real                                    F06ECF
          vector
          to real vector (DAXPY)

          Add scalar times real vector to real                     F06ECF
          vector
          (DAXPY)

          Multiply real                                            F06EDF
          vector
          by scalar (DSCAL)

          Copy real                                                F06EFF
          vector
          (DCOPY)

          Swap two real                                            F06EGF
          vectors
          (DSWAP)

          Compute Euclidean norm of real                           F06EJF
          vector
          (DNRM2)

          Sum the absolute values of real                          F06EKF
          vector
          elements (DASUM)

          Dot product of two complex                               F06GAF
          vectors
          , unconjugated (ZDOTU)

          Dot product of two complex                               F06GBF
          vectors
          , conjugated (ZDOTC)

          Add scalar times complex                                 F06GCF
          vector
          to complex vector (ZAXPY)

          Add scalar times complex vector to complex               F06GCF
          vector
          (ZAXPY)

          Multiply complex                                         F06GDF
          vector
          by complex scalar (ZSCAL)

          Copy complex                                             F06GFF
          vector
          (ZCOPY)

          Swap two complex                                         F06GGF
          vectors
          (ZSWAP)

          Multiply complex                                         F06JDF
          vector
          by real scalar (ZDSCAL)

          Compute Euclidean norm of complex                        F06JJF
          vector
          (DZNRM2)

          Sum the absolute values of complex                       F06JKF
          vector
          elements (DZASUM)

          Index, real                                              F06JLF
          vector
          element with largest absolute value (IDAMAX)

          Index, complex                                           F06JMF
          vector
          element with largest absolute value (IZAMAX)

          Matrix-                                                  F06PAF
          vector
          product, real rectangular matrix (DGEMV)

          Matrix-                                                  F06PBF
          vector
          product, real rectangular band matrix (DGBMV)

          Matrix-                                                  F06PCF
          vector
          product, real symmetric matrix (DSYMV)

          Matrix-                                                  F06PDF
          vector
          product, real symmetric band matrix (DSBMV)

          Matrix-                                                  F06PEF
          vector
          product, real symmetric packed matrix (DSPMV)

          Matrix-                                                  F06PFF
          vector
          product, real triangular matrix (DTRMV)

          Matrix-                                                  F06PGF
          vector
          product, real triangular band matrix (DTBMV)

          Matrix-                                                  F06PHF
          vector
          product, real triangular packed matrix (DTPMV)

          Matrix-                                                  F06SAF
          vector
          product, complex rectangular matrix (ZGEMV)

          Matrix-                                                  F06SBF
          vector
          product, complex rectangular band matrix (ZGBMV)

          Matrix-                                                  F06SCF
          vector
          product, complex Hermitian matrix (ZHEMV)

          Matrix-                                                  F06SDF
          vector
          product, complex Hermitian band matrix (ZHBMV)

          Matrix-                                                  F06SEF
          vector
          product, complex Hermitian packed matrix (ZHPMV)

          Matrix-                                                  F06SFF
          vector
          product, complex triangular matrix (ZTRMV)

          Matrix-                                                  F06SGF
          vector
          product, complex triangular band matrix (ZTBMV)

          Matrix-                                                  F06SHF
          vector
          product, complex triangular packed matrix (ZTPMV)

          vector
          (ZGERU)
          Rank-1 update, complex rectangular matrix, conjugated    F06SNF
          vector
          (ZGERC)

          Set up reference                                         G05EAF
          vector
          for multivariate Normal distribution

          Set up reference                                         G05ECF
          vector
          for generating pseudo-random integers, Poisson ...

          Set up reference                                         G05EDF
          vector
          for generating pseudo-random integers, binomial ...

          Pseudo-random permutation of an integer                  G05EHF
          vector

          Pseudo-random sample from an integer                     G05EJF
          vector

          Set up reference                                         G05EXF
          vector
          from supplied cumulative distribution function or ...

          Pseudo-random integer from reference                     G05EYF
          vector

          Pseudo-random multivariate Normal                        G05EZF
          vector
          from reference vector

          vector

          Generates a                                              G05FAF
          vector
          of random numbers from a uniform distribution

          Generates a                                              G05FBF
          vector
          of random numbers from an (negative) exponential ...

          Generates a                                              G05FDF
          vector
          of random numbers from a Normal distribution

          Generates a                                              G05FEF
          vector
          of pseudo-random numbers from a beta distribution

          Generates a                                              G05FFF
          vector
          of pseudo-random numbers from a gamma distribution

          Sort a                                                   M01CAF
          vector
          , real numbers

          Rank a                                                   M01DAF
          vector
          , real numbers

          Rearrange a                                              M01EAF
          vector
          according to given ranks, real numbers

          Kruskal-                                                 G08AFF
          Wallis
          one-way analysis of variance on k samples of unequal ..

          Pseudo-random real numbers,                              G05DPF
          Weibull
          distribution

          1-D quadrature, adaptive, finite interval,               D01ANF
          weight
          function cos((omega)x) or sin((omega)x)

          1-D quadrature, adaptive, finite interval,               D01APF
          weight
          function with end-point singularities of ...

          1-D quadrature, adaptive, finite interval,               D01AQF
          weight
          function 1/(x-c), Cauchy principal value ...

          1-D quadrature, adaptive, semi-infinite interval,        D01ASF
          weight
          function cos((omega)x) or sin((omega)x)

          Pre-computed                                             D01BBF
          weights
          and abscissae for Gaussian quadrature rules, ...

          Computes (optionally                                     G02BXF
          weighted)
          correlation and covariance matrices

          Multivariate time series, filtering (pre-                G13BAF
          whitening)
          by an ARIMA model

          Performs the Mann-                                       G08AHF
          Whitney
          U test on two independent samples

          Computes the exact probabilities for the Mann-           G08AJF
          Whitney
          U statistic, no ties in pooled sample

          Computes the exact probabilities for the Mann-           G08AKF
          Whitney
          U statistic, ties in pooled sample

          Performs the                                             G08AGF
          Wilcoxon
          one-sample (matched pairs) signed rank test

          window

          window

          Two-way contingency table analysis, with                 G01AFF
               2
          (chi)
          /Fisher's exact test

          Computes probabilities for                               G01ECF
               2
          (chi)
          distribution

          Computes deviates for the                                G01FCF
               2
          (chi)
          distribution

          Performs the                                             G08CGF
               2
          (chi)
          goodness of fit test, for standard continuous ...

          All                                                      C02AFF
          zeros
          of complex polynomial, modified Laguerre method

          All                                                      C02AGF
          zeros
          of real polynomial, modified Laguerre method

          Zero                                                     C05ADF
          of continuous function in given interval, Bus and
          Dekker ...

          zero
          (simple driver)

          zero
          , intermediate output (simple driver)

          zero
          , intermediate output (simple driver)

\end{verbatim}
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\begin{page}{manpageXXconvert}{NAG On-line Documentation: convert}
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\begin{verbatim}



     CONVERSION(3NAG)  Foundation Library (12/10/92)  CONVERSION(3NAG)



          Introduction              Converting from the Workstation Library
          Converting from the Workstation Library

          The NAG Foundation Library is a successor product to an earlier,
          smaller subset of the full NAG Fortran Library which was called
          the NAG Workstation Library. The Foundation Library has been
          designed to be upwards compatible, in terms of functionality,
          with the Workstation Library. However some routines that were
          present in the Workstation Library have been replaced by more up-
          to-date routines from the NAG Fortran Library, which provide
          improved algorithms or software design.

          The list below gives the names of those routines which were
          available in the Workstation Library, but are not included in the
          Foundation Library. For each such routine, it also gives the name
          of the routine in the Foundation Library which best covers the
          same functionality.

              Workstation    Foundation
              Library        Library

              C02AEF         C02AGF

              D02CBF         D02CJF

              D02CHF         D02CJF

              D02EBF         D02EJF

              D02EHF         D02EJF

              D02HAF         D02GAF

              D02HBF         D02RAF

              D02SAF         D02RAF

              E02DBF         E02DEF

              E04VDF         E04UCF

              E04ZCF         E04UCF (see Note 1)

              F01BTF         F07ADF

              F01BXF         F07FDF

              F02WAF         F02WEF

              F04AYF         F07AEF

              F04AZF         F07FEF

              F04YAF         G02DAF

              G01ABF         G02BXF (with M = 2)

              G01BAF         G01EBF

              G01BBF         G01EDF

              G01BCF         G01ECF

              G01BDF         G01EEF

              G01CAF         G01FBF

              G01CBF         G01FDF

              G01CCF         G01FCF

              G01CDF         G01FEF

              G01CEF         G01FAF

              G02BAF         G02BXF

              G02BGF         G02BXF

              G02CEF         G02DAF (see Note 2)

              G02CGF         G02DAF

              G02CJF         G02DAF

              G05DBF         G05FBF

              G05DCF         G05CAF (see Note 3)

              G05DEF         G05FFF

              G05DHF         G05FFF (see Note 4)

              G05EGF         G05HDF

              G05EWF         G05HDF

              G08ABF         G08AGF

              G08ADF         G08AHF

              M01AKF         M01DAF

              M01APF         M01CAF

              S15ABF         G01EAF

              S15ACF         G01EAF

              X02AAF         X02AJF

              X02ACF         X02ALF

          Notes:

          1.    E04ZCF checks user-supplied routines for evaluating the
                first derivatives of the objective function and constraint
                functions supplied to E04VDF. This functionality is now
                provided by E04UCF, using the optional parameters Verify
                Objective Gradients and Verify Constraint Gradients.

          2.    G02CEF selects variables to be included in a linear
                regression performed by G02CGF. This functionality is now
                provided by the parameter ISX of G02DAF.

          3.    A call to G05DCF can be replaced by a simple transformation
                of the result of a call to G05CAF. The statement
                     X = G05DCF(A,B)
                can be replaced by the statements

                     X = G05CAF(X)
                     X = A + B*LOG(X/(1.0D0-X))

                                                            2
          4.    G05DHF generates random numbers from a (chi)  distribution
                with N degrees of freedom. This can be achieved by calling
                G05FFF with the values DBLE(N)/2.0D0 and 2.0D0 for the
                parameters A and B respectively.

\end{verbatim}
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