starpac/starpac.html

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    <title>
      STARPAC - Statistical Data Analysis Library
    </title>
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    <h1 align = "center">
      STARPAC <br> Statistical Data Analysis Library
    </h1>

    <hr>

    <p>
      <b>STARPAC</b> 
      is a FORTRAN90 library which
      contains a number of routines for statistical data analysis.
    </p>

    <p>
      <b>STARPAC</b> uses a COMMON block and EQUIVALENCE statements
      in order to make workspace storage available to its routines.
      This scheme assumes that an integer is stored in one word.
      When compiling this program with <b>G95</b>, it may be necessary
      to include the <b>-i4</b> switch, to guarantee that integers
      are stored in 4 bytes = one word.  Otherwise, routines that
      rely on the workspace storage system will fail.
    </p>

    <h3 align = "center">
      Languages:
    </h3>

    <p>
      <b>STARPAC</b> is available in
      <a href = "../../f77_src/starpac/starpac.html">a FORTRAN77 version</a> and
      <a href = "../../f_src/starpac/starpac.html">a FORTRAN90 version</a>.
    </p>

    <h3 align = "center">
      Related Data and Programs:
    </h3>

    <p>
      <a href = "../../f_src/blas1/blas1.html">
      BLAS1</a>,
      a FORTRAN90 library which
      implements the
      Basic Linear Algebra Subprograms, Level 1, and which are
      called by <b>STARPAC</b>.
    </p>

    <p>
      <a href = "../../f_src/machine/machine.html">
      MACHINE</a>,
      a FORTRAN90 library which 
      tabulates the values
      of certain machine-specific arithmetic quantities, and which are
      called by <b>STARPAC</b>.
    </p>

    <p>
      <a href = "../../f_src/nl2sol/nl2sol.html">
      NL2SOL</a>, 
      a FORTRAN90 library which
      minimizes the
      sum of squares of a set of nonlinear functions, and which is
      called by <b>STARPAC</b>.
    </p>

    <p>
      <a href = "../../f_src/prob/prob.html">
      PROB</a>, 
      a FORTRAN90 library which
      computes the PDF, CDF, inverse CDF, and sampling various statistical
      distributions.
    </p>

    <p>
      <a href = "../../f_src/uniform/uniform.html">
      UNIFORM</a>,
      a FORTRAN90 library which
      carries out uniform sampling of real, complex or integer data.
    </p>

    <p>
      <a href = "../../f_src/xerror/xerror.html">
      XERROR</a>,
      a FORTRAN90 library which
      carries out error handling.
    </p>

    <h3 align = "center">
      Reference:
    </h3>

    <p>
      <ol>
        <li>
          Milton Abramowitz, Irene Stegun,<br>
          Handbook of Mathematical Functions,<br>
          National Bureau of Standards, 1964,<br>
          LC: QA47.A34,<br>
          ISBN: 0-486-61272-4.
        </li>
        <li>
          Peter Bloomfield,<br>
          Fourier Analysis of Time Series - An Introduction,<br>
          Wiley, 2000,<br>
          ISBN: 0471889482,<br>
          LC: QA280.B59.
        </li>
        <li>
          Nancy Bosten, Thomas Aird,<br>
          Remark on Algorithm 179, <br>
          Communications of the ACM,<br>
          Volume 17, page 153, 1974.
        </li>
        <li>
          George Box, Gwilym Jenkins,<br>
          Time Series Analysis: Forecasting and Control,<br>
          Prentice Hall, 1991,<br>
          ISBN: 0139051007,<br>
          LC: QA280.B67.
        </li>
        <li>
          Kenneth Brown,<br>
          A Quadratically Convergent Newton-like Method Based upon 
          Gaussian Elimination,<br>
          SIAM Journal on Numerical Analysis,<br>
          Volume 6, pages 560-569, 1969.
        </li>
        <li>
          Peter Businger, Gene Golub,<br>
          Linear Least Squares Solutions by Householder Transformations,<br>
          Numerische Mathematik,<br>
          Volume 7, pages 269-276, 1965.
        </li>
        <li>
          Alan Cline, Cleve Moler, Pete Stewart, James Wilkinson,<br>
          An Estimate of the Condition Number of a Matrix,<br>
          Technical Report TM-310,<br>
          Applied Math Division,<br>
          Argonne National Laboratory, 1977.
        </li>
        <li>
          John Dennis, David Gay, Roy Welsch,<br>
          Algorithm 573:
          An Adaptive Nonlinear Least-Squares Algorithm,<br>
          ACM Transactions on Mathematical Software,<br>
          Volume 7, Number 3, 1981, pages 367-383.
        </li>
        <li>
          Janet Donaldson, Peter Tryon,<br>
          User's Guide to STARPAC,<br>
          The Standards Time Series and Regression Package,<br> 
          NIST, Boulder, Colorado, 1987.
        </li>
        <li>
          Jack Dongarra, Jim Bunch, Cleve Moler, Pete Stewart,<br>
          LINPACK User's Guide,<br>
          SIAM, 1979,<br>
          ISBN13: 978-0-898711-72-1,<br>
          LC: QA214.L56.
        </li>
        <li>
          Norman Draper, Harry Smith,<br>
          Applied Regression Analysis,<br>
          Wiley, 1998,<br>
          ISBN: 978-0471170822,<br>
          LC: QA278.2.D7.
        </li>
        <li>
          Merran Evans, Nicholas Hastings, Brian Peacock,<br>
          Statistical Distributions,<br>
          Wiley, 2000,<br>
          ISBN: 0471371246,<br>
          LC: QA273.6E92.
        </li>
        <li>
          Enrico Federghi,<br>
          Extended Tables of the Percentage Points of Student's
          T-Distribution,<br>
          Journal of the American Statistical Association,<br>
          Volume 54, Number 287, 1959, pages 683-688.
        </li>
        <li>
          Phyllis Fox, Andrew Hall, Norman Schryer,<br>
          Algorithm 528,
          A Framework for a Portable Library,<br>
          ACM Transactions on Mathematical Software,<br>
          Volume 4, Number 2, June 1978, pages 177-188.
        </li>
        <li>
          Walter Gautschi,<br>
          Algorithm 542:
          Incomplete Gamma Functions,<br>
          ACM Transactions on Mathematical Software,<br>
          Volume 5, Number 4, December 1979, pages 382-489.
        </li>
        <li>
          David Gay,<br>
          Computing Optimal Locally Constrained Steps,<br>
          SIAM Journal on Scientific and Statistical Computing,<br>
          Volume 2, Number 2, pages 186-197, 1981.
        </li>
        <li>
          Philip Gill, Walter Murray,<br>
          Algorithms for the Solution of the 
          Non-linear Least-squares Problem, <br>
          SIAM Journal on Numerical Analysis,<br>
          Volume 15, Number 5, pages 977-991, 1978.
        </li>
        <li>
          Steven Goldfeld, Richard Quandt, Hale Trotter,<br>
          Maximization by Quadratic Hill-climbing,<br>
          Econometrica,<br>
          Volume 34, pages 541-551, 1966.
        </li>
        <li>
          MD Hebden,<br>
          An Algorithm for Minimization using Exact Second Derivatives,<br>
          Report TP515,<br>
          Theoretical Physics Division,<br>
          AERE, Harwell, Oxon., England, 1973.
        </li>
        <li>
          DC Hoaglin,<br>
          Theoretical Properties of Congruential Random-Number Generators,
          An Empirical View,<br>
          Memorandum NS-340,<br>
          Department of Statistics,<br>
          Harvard University, 1976.
        </li>
        <li>
          Gwilym Jenkins, Donald Watts,<br>
          Spectral Analysis and its Applications,<br>
          Holden-Day, 1968,<br>
          ISBN: 1892803038,<br>
          LC: QA280.J45.
        </li>
        <li>
          Norman Johnson, Samuel Kotz, Narayanaswamy Balakrishnan,<br>
          Continuous Univariate Distributions,<br>
          Second edition,<br>
          Wiley, 1994,<br>
          ISBN: 0471584940,<br>
          LC: QA273.6.J6
        </li>
        <li>
          Donald Knuth,<br>
          The Art of Computer Programming,<br>
          Volume 2, Seminumerical Algorithms,<br> 
          Third Edition,<br>
          Addison Wesley, 1997,<br>
          ISBN: 0201896842,<br>
          LC: QA76.6.K64.
        </li>
        <li>
          Charles Lawson, Richard Hanson,<br>
          Solving Least Squares Problems,<br>
          SIAM, 1995,<br>
          ISBN: 0898713560,<br>
          LC: QA275.L38.
        </li>
        <li>
          Charles Lawson, Richard Hanson, David Kincaid, Fred Krogh,<br>
          Algorithm 539:
          Basic Linear Algebra Subprograms for Fortran Usage,<br>
          ACM Transactions on Mathematical Software,<br>
          Volume 5, Number 3, September 1979, pages 308-323.
        </li>
        <li>
          George Marsaglia, Wai Wan Tsang,<br>
          A fast, easily implemented method for sampling from decreasing or
          symmetric unimodal density functions,<br>
          SIAM Journal of Scientific and Statistical Computing,<br>
          Volume 5, 1983, pages 349-359.
        </li>
        <li>
          Jorge More,<br>
          The Levenberg-Marquardt Algorithm, Implementation and Theory,<br>
          in Springer Lecture Notes in Mathematics, Number 630,<br>
          edited by G A Watson,<br>
          Springer, 1978.
        </li>
        <li>
          Donald Owen, <br>
          Handbook of Statistical Tables,<br>
          Addison-Wesley, 1962.
        </li>
        <li>
          Egon Pearson, Herman Hartley, <br>
          Biometrika Tables for Statisticians, <br>
          Cambridge, 1970,<br>
          ISBN: 978-0852647004.
        </li>
        <li>
          Michael Powell,<br>
          A Fortran Subroutine for Solving Systems of Nonlinear 
          Algebraic Equations,<br>
          in Numerical Methods for Nonlinear Algebraic Equations,<br>
          edited by Philip Rabinowitz,<br>
          Gordon and Breach, 1970,<br>
          ISBN13: 978-0677142302,<br>
          LC: QA218.N85.
        </li>
        <li>
          CS Smith,<br>
          Multiplicative Pseudo-Random Number Generators with Prime Modulus,<br>
          Journal of the Association for Computing Machinery,<br>
          Volume 19, pages 586-593, 1971.
        </li>
        <li>
          Richard Varga,<br>
          Minimal Gerschgorin Sets,<br>
          Pacific Journal of Mathematics,<br>
          Volume 15, pages 719-729, 1965.
        </li>
        <li>
          Max Waldmeier,<br>
          The Sunspot-Activity in the Years 1610-1960,<br>
          Shulthess, 1961,<br>
          LC: QB525.W34.
        </li>
        <li>
          Martin Wilk, Ram Gnanadesikan, Marilyn Huyett,<br>
          Probability Plots for the Gamma Distribution,<br>
          Technometrics,<br>
          Volume 4, Number 1, 1962, pages 1-15,
        </li>
      </ol>
    </p>

    <h3 align = "center">
      Source Code:
    </h3>

    <p>
      <ul>
        <li>
          <a href = "starpac.f90">starpac.f90</a>, 
          the source code.
        </li>
        <li>
          <a href = "starpac.csh">starpac.csh</a>, 
          commands to compile the source code.
        </li>
      </ul>
    </p>

    <h3 align = "center">
      Examples and Tests:
    </h3>

    <p>
      <ul>
        <li>
          <a href = "starpac_prb.f90">starpac_prb.f90</a>, 
          a sample calling program.
        </li>
        <li>
          <a href = "starpac_prb.csh">starpac_prb.csh</a>, 
          commands to compile, link and run the sample calling program.
        </li>
        <li>
          <a href = "starpac_prb_output.txt">starpac_prb_output.txt</a>, 
          the output from a run of the sample calling program.
        </li>
      </ul>
    </p>

    <h3 align = "center">
      List of Routines:
    </h3>

    <p>
      <ul>
        <li>
          <b>ABSCOM</b> counts the entries of | V(1:N) - W(1:N) | greater than ABSTOL.
        </li>
        <li>
          <b>ACCDIG</b> returns the number of accurate digits in an approximation to X.
        </li>
        <li>
          <b>ACFD</b> computes autocorrelations and partial autocorrelations.
        </li>
        <li>
          <b>ACFDTL</b> prints titles for ACORRD.
        </li>
        <li>
          <b>ACFER</b> does error checking for the ACF routines.
        </li>
        <li>
          <b>ACF</b> is the simple interface to the autocorrelations routines.
        </li>
        <li>
          <b>ACFF</b> computes autocorrelations of a time series using an FFT.
        </li>
        <li>
          <b>ACFFS</b> uses an FFT with ACVF estimates for autocorrelations of a time series.
        </li>
        <li>
          <b>ACFLST</b> lists the autocorrelations and other information.
        </li>
        <li>
          <b>ACFM</b> computes autocorrelations of a time series with missing data.
        </li>
        <li>
          <b>ACFMN</b> computes autocorrelations of a time series.
        </li>
        <li>
          <b>ACFMNF</b> computes autocorrelations of a time series.
        </li>
        <li>
          <b>ACFMNM</b> computes autocorrelations of a time series with missing data.
        </li>
        <li>
          <b>ACFMS</b> is the user interface for autocorrelations of a time series with missing data.
        </li>
        <li>
          <b>ACFOUT</b> prints autocorrelations.
        </li>
        <li>
          <b>ACFSD</b> computes the standard error of autocorrelations.
        </li>
        <li>
          <b>ACFSDM</b> computes the standard error of autocorrelations with missing data.
        </li>
        <li>
          <b>ACFS</b> computes autocorrelations with computed ACVF estimates.
        </li>
        <li>
          <b>ACVF</b> computes the autocovariance function of a series.
        </li>
        <li>
          <b>ACVFF</b> computes the ACVF of a series using two FFT passes.
        </li>
        <li>
          <b>ACVFM</b> computes autocovariance when missing data is involved.
        </li>
        <li>
          <b>ADJLMT</b> corrects the plot limits when all observations are equal.
        </li>
        <li>
          <b>AIMEC</b> is the user interface for ARIMA estimation.
        </li>
        <li>
          <b>AIME</b> is the user interface for ARIMA estimation, control call.
        </li>
        <li>
          <b>AIMES</b> is the user interface for ARIMA estimation, long call.
        </li>
        <li>
          <b>AIMF</b> is the user interface for ARIMA estimation, short call.
        </li>
        <li>
          <b>AIMFS</b> is the user interface for ARIMA estimation, control call.
        </li>
        <li>
          <b>AIMX1</b> sets the starting parameter values for AIMX.
        </li>
        <li>
          <b>ALBETA</b> computes the logarithm of the Beta function.
        </li>
        <li>
          <b>ALGAMS</b> evaluates the log of the absolute value of the Gamma function.
        </li>
        <li>
          <b>ALNGAM</b> computes the logarithm of the absolute value of the Gamma function.
        </li>
        <li>
          <b>ALNREL</b> evaluates log ( 1 + X ) with relative error control.
        </li>
        <li>
          <b>AMDRV</b> estimates the jacobian matrix.
        </li>
        <li>
          <b>AMEAN</b> computes the arithmetic mean of a series.
        </li>
        <li>
          <b>AMEANM</b> computes the arithmetic mean of a series with missing data.
        </li>
        <li>
          <b>AMECNT</b> is the control routine for nonlinear least squares regression.
        </li>
        <li>
          <b>AMEDRV</b> is the control routine for nonlinear least squares regression.
        </li>
        <li>
          <b>AMEER</b> checks errors for the nonlinear least squares estimation.
        </li>
        <li>
          <b>AMEFIN</b> analyzes nonlinear least squares estimates after they are computed.
        </li>
        <li>
          <b>AMEHDR</b> prints headings for nonlinear least squares estimation.
        </li>
        <li>
          <b>AMEISM</b> prints an initial summary for nonlinear least squares routines.
        </li>
        <li>
          <b>AMEMN</b> is the control routine for using the NL2 software package.
        </li>
        <li>
          <b>AMEOUT</b> prints the final summary output from ARIMA estimation.
        </li>
        <li>
          <b>AMEPT1</b> prints data summary for nonlinear least squares routines.
        </li>
        <li>
          <b>AMEPT2</b> prints four standardized residual plots.
        </li>
        <li>
          <b>AMESTP</b> controls the step size selection.
        </li>
        <li>
          <b>AMFCNT</b> is the control routine for ARIMA forecasting.
        </li>
        <li>
          <b>AMFER</b> checks errors for nonlinear least squares estimation.
        </li>
        <li>
          <b>AMFHDR</b> prints headers for nonlinear least squares estimation.
        </li>
        <li>
          <b>AMFMN</b> computes and prints ARIMA forecasts.
        </li>
        <li>
          <b>AMFOUT</b> produces ARIMA forecasting output.
        </li>
        <li>
          <b>AMLST1</b> prints parameters for the ARIMA routine.
        </li>
        <li>
          <b>AMLST</b> prints parameter summaries from ARIMA forecasting.
        </li>
        <li>
          <b>AOS</b> computes autoregressive model order selection statistics.
        </li>
        <li>
          <b>AOSLST</b> lists the autoregressive model order selection statistics.
        </li>
        <li>
          <b>AOV1ER</b> does preliminary checks on input to the one-way family.
        </li>
        <li>
          <b>AOV1</b> is a user interface to AOV1MN, one-way analysis of variance.
        </li>
        <li>
          <b>AOV1HD</b> prints headers for the one-way ANOVA family.
        </li>
        <li>
          <b>AOV1MN</b> computes results for analysis of a one-way classification.
        </li>
        <li>
          <b>AOV1S</b> is a user interface for AOV1MN, one-way analysis of variance.
        </li>
        <li>
          <b>AOV1XP</b> prints storage for one-way family exerciser.
        </li>
        <li>
          <b>ARCOEF</b> uses Durbin's method for autoregression coefficients with order lag.
        </li>
        <li>
          <b>ARFLT</b> performs autoregressive filtering.
        </li>
        <li>
          <b>ASSESS</b> assesses a candidate step.
        </li>
        <li>
          <b>AXPBY:</b> SZ(1:N) = SA * SX(1:N) + SB * SY(1:N).
        </li>
        <li>
          <b>BACKOP</b> computes the number of back order terms for an ARIMA model.
        </li>
        <li>
          <b>BETAI</b> computes the incomplete Beta ratio.
        </li>
        <li>
          <b>BFSDRV</b> is the driver for time series Fourier spectrum analysis.
        </li>
        <li>
          <b>BFSER</b> checks errors for time series Fourier univariate spectrum analysis.
        </li>
        <li>
          <b>BFS:</b> short interface for time series Fourier bivariate spectrum analysis.
        </li>
        <li>
          <b>BFSF:</b> short interface for time series Fourier bivariate spectrum analysis.
        </li>
        <li>
          <b>BFSFS:</b> long interface for time series Fourier bivariate spectrum analysis.
        </li>
        <li>
          <b>BFSLAG:</b> lag window truncation points for Fourier bivariate spectral analysis.
        </li>
        <li>
          <b>BFSM:</b> short interface for time series bivariate Fourier spectrum analysis.
        </li>
        <li>
          <b>BFSMN</b> computes square coherency and phase components of a bivariate spectrum.
        </li>
        <li>
          <b>BFSMS:</b> long interface for BFS analysis with missing observations.
        </li>
        <li>
          <b>BFSMV:</b> short interface for BFS analysis, missing observations, covariances.
        </li>
        <li>
          <b>BFSMVS:</b> long interface for BFS analysis, missing observations, covariances.
        </li>
        <li>
          <b>BFSS:</b> long call for time series bivariate Fourier spectrum analysis.
        </li>
        <li>
          <b>BFSV:</b> short call for BFS analysis, with covariance input rather than series.
        </li>
        <li>
          <b>BFSVS:</b> long call for BFS analsys with covariances input rather than series.
        </li>
        <li>
          <b>CCFER</b> does error checking for CCF routines.
        </li>
        <li>
          <b>CCF</b> computes the cross-correlation of two time series.
        </li>
        <li>
          <b>CCFF</b> computes the cross-correlation of two time series by Singleton's FFT.
        </li>
        <li>
          <b>CCFFS</b> computes multivariate cross-correlations and covariances by FFT.
        </li>
        <li>
          <b>CCFLST</b> lists cross-correlations, standard errors, and summary information.
        </li>
        <li>
          <b>CCFM</b> computes cross-correlation of two series with missing data.
        </li>
        <li>
          <b>CCFMN</b> is the main routine for cross-correlations.
        </li>
        <li>
          <b>CCFMNF</b> is the main routine for cross-correlations using an FFT.
        </li>
        <li>
          <b>CCFMNM</b> is the main routine for cross-correlations with missing data.
        </li>
        <li>
          <b>CCFMS</b> is a user routine for multivariate cross-correlations.
        </li>
        <li>
          <b>CCFOUT</b> prints cross-correlations and standard errors.
        </li>
        <li>
          <b>CCFSD</b> is the main routine for computing standard error of cross-correlations.
        </li>
        <li>
          <b>CCFSDM:</b> standard error of cross-correlations with missing data.
        </li>
        <li>
          <b>CCFS</b> is the user routine for multivariate cross-correlations.
        </li>
        <li>
          <b>CCFXP</b> lists results for the time series cross-correlation routines.
        </li>
        <li>
          <b>CCVF</b> computes the cross covariance function between two series.
        </li>
        <li>
          <b>CCVFF</b> computes the cross covariance function between two series.
        </li>
        <li>
          <b>CCVFM</b> computes the cross covariance function of two series with missing data.
        </li>
        <li>
          <b>CDFCHI</b> computes the CDF for the Chi Square distribution.
        </li>
        <li>
          <b>CDFF</b> computes the CDF for the F distribution.
        </li>
        <li>
          <b>CDFNML</b> computes the CDF for the standard normal distribution.
        </li>
        <li>
          <b>CDFT</b> computes the CDF for Student's T distribution.
        </li>
        <li>
          <b>CENTER</b> centers an observed series.
        </li>
        <li>
          <b>CHIRHO</b> computes the Chi Square statistic and its probability.
        </li>
        <li>
          <b>CMPFD</b> computes a finite difference derivative.
        </li>
        <li>
          <b>CNTR</b> centers the input seriers about its mean.
        </li>
        <li>
          <b>CORRER</b> checks for errors in the input parameters.
        </li>
        <li>
          <b>CORR:</b> short call to correlation family of routines.
        </li>
        <li>
          <b>CORRHD</b> prints headers for the correlation family.
        </li>
        <li>
          <b>CORRMN</b> is the main routine in the correlation family.
        </li>
        <li>
          <b>CORRS</b> is the user routine for the correlation, with a long call interface.
        </li>
        <li>
          <b>CORRXP</b> prints stored output returned from CORRS.
        </li>
        <li>
          <b>COVCLC</b> computes the covariance matrix for NL2ITR.
        </li>
        <li>
          <b>CPYASF</b> copies a symmetric matrix stored rowwise into rectangular storage.
        </li>
        <li>
          <b>CPYMSS</b> copies an N by M matrix.
        </li>
        <li>
          <b>CPYVII</b> copies an integer vector.
        </li>
        <li>
          <b>CSEVL</b> evaluates a Chebyshev series.
        </li>
        <li>
          <b>D1MACH</b> returns double precision machine constants.
        </li>
        <li>
          <b>DCKCNT</b> controls the derivative checking process.
        </li>
        <li>
          <b>DCKCRV</b> checks whether high curvature caused poor derivative approximation.
        </li>
        <li>
          <b>DCKDRV</b> is the driver to the derivative checking routines.
        </li>
        <li>
          <b>DCKER</b> does error checking for the derivative checking routines.
        </li>
        <li>
          <b>DCKFPA</b> checks if arithmetic precision causes poor derivative approximation.
        </li>
        <li>
          <b>DCKHDR</b> prints page headers for the derivative checking routines.
        </li>
        <li>
          <b>DCKLS1</b> sets up a problem for testing the step size selection family.
        </li>
        <li>
          <b>DCKLSC</b> is the user routine for comparing analytic and numeric derivatives.
        </li>
        <li>
          <b>DCKLS</b> is the user routine for comparing analytic and numeric derivatives.
        </li>
        <li>
          <b>DCKMN</b> is the main routine for checking analytic versus numeric derivatives.
        </li>
        <li>
          <b>DCKOUT</b> prints results from the derivative checking routine.
        </li>
        <li>
          <b>DCKZRO</b> rechecks derivative errors where the analytic derivative is zero.
        </li>
        <li>
          <b>DCOEF</b> expands a difference filter.
        </li>
        <li>
          <b>DEMDRV</b> is the driver routine to demodulate a series.
        </li>
        <li>
          <b>DEMOD</b> demodulates a series at a given frequency.
        </li>
        <li>
          <b>DEMODS</b> demodulates a series at a given frequency.
        </li>
        <li>
          <b>DEMODU</b> demodulates a series at a given frequency.
        </li>
        <li>
          <b>DEMORD</b> sets up the data for the phase plots.
        </li>
        <li>
          <b>DEMOUT</b> prints output for the time series demodulation routines.
        </li>
        <li>
          <b>DFAULT</b> supplies default values to IV and V.
        </li>
        <li>
          <b>DFBW</b> computes degrees of freedom and bandwidth for a given lag window.
        </li>
        <li>
          <b>DFBWM</b> computes DOF and BW for a given lag window with missing data.
        </li>
        <li>
          <b>DIFC</b> expands a difference filter and performs difference filtering.
        </li>
        <li>
          <b>DIF</b> performs a first difference filtering operation.
        </li>
        <li>
          <b>DIFMC</b> expands a difference filter and performs the difference filter.
        </li>
        <li>
          <b>DIFM</b> performs a first difference filter for a series with missing data.
        </li>
        <li>
          <b>DIFSER</b> performs a differencing operation on a series.
        </li>
        <li>
          <b>DOTC</b> computes the dot product of two series, centered about their means.
        </li>
        <li>
          <b>DOTCM</b> computes the dot product of series with missing data.
        </li>
        <li>
          <b>DOTPRD</b> returns the inner product of two vectors.
        </li>
        <li>
          <b>DRV1A</b> derivative function for NLS family exerciser subroutine MDL1.
        </li>
        <li>
          <b>DRV1B</b> is an INCORRECT derivative function for the NLS exerciser MDL1.
        </li>
        <li>
          <b>DRV2</b> is a derivative function for the NLS exerciser routine MD12.
        </li>
        <li>
          <b>DRV3</b> is the derivative function for NLS family exerciser subroutine MDL3.
        </li>
        <li>
          <b>DRV4A</b> is a (correct) derivative for testing derivative checking routines.
        </li>
        <li>
          <b>DRV4B</b> is an (incorrect) derivative for testing derivative checking routines.
        </li>
        <li>
          <b>DRV</b> is a dummy derivative function for the NLS family.
        </li>
        <li>
          <b>DUPDAT</b> updates the scale vector for NL2ITR.
        </li>
        <li>
          <b>E9RINT</b> stores the current error message or prints the old one.
        </li>
        <li>
          <b>ECVF</b> prints an error message if missing data affects the covariance lags.
        </li>
        <li>
          <b>EHDR</b> prints the heading for the error checking routines.
        </li>
        <li>
          <b>EIAGE</b> ensures that "not too many" vectors are below a given lower bound.
        </li>
        <li>
          <b>EIAGEP</b> prints the error messages for ERAGT and ERAGTM.
        </li>
        <li>
          <b>EISEQ</b> prints an error message if NVAL is not equal to NEQ.
        </li>
        <li>
          <b>EISGE</b> prints a warning if NVAL is less than NMIN.
        </li>
        <li>
          <b>EISII</b> warns if an integer value does not lie within a given range.
        </li>
        <li>
          <b>EISLE</b> warns if an integer is greater than a given maximum.
        </li>
        <li>
          <b>EISRNG</b> warns if ISEED is not a suitable random number seed.
        </li>
        <li>
          <b>EIVEO</b> checks whether all vector entries are even (or odd).
        </li>
        <li>
          <b>EIVEQ</b> warns if the vector does not have at least NEQMN entries equal to IVAL.
        </li>
        <li>
          <b>EIVII</b> warns if too many values are outside given limits.
        </li>
        <li>
          <b>ENFFT</b> checks that NFFT is suitable for the Singleton FFT routine.
        </li>
        <li>
          <b>EPRINT</b> prints the last error message, if any.
        </li>
        <li>
          <b>ERAGT</b> warns if too many values are less than a lower bound.
        </li>
        <li>
          <b>ERAGTM</b> warns if too many values are less than or equal to a lower bound.
        </li>
        <li>
          <b>ERAGTP</b> prints the error messages for ERAGT and ERAGTM.
        </li>
        <li>
          <b>ERDF</b> checks the values that specify differencing on a time series.
        </li>
        <li>
          <b>ERFC</b> evaluates the complementary error function.
        </li>
        <li>
          <b>ERF</b> evaluates the error function.
        </li>
        <li>
          <b>ERIODD</b> warns if the value of NVAL is inconsistent.
        </li>
        <li>
          <b>ERSEI</b> warns if a value is not between given limits.
        </li>
        <li>
          <b>ERSGE</b> warns if a value is not greater than or equal to a minimum value.
        </li>
        <li>
          <b>ERSGT</b> warns if the input value is not greater than a specified minumum.
        </li>
        <li>
          <b>ERSIE</b> warns if a value is not within a specified range.
        </li>
        <li>
          <b>ERSII</b> warns if the input value is not within the given range.
        </li>
        <li>
          <b>ERSLF</b> checks the definition of a symmetric linear filter.
        </li>
        <li>
          <b>ERSLFS</b> checks values specifying a symmetric linear filter for a time series.
        </li>
        <li>
          <b>ERVGT</b> ensures that "most" values are greater than a specified lower bound.
        </li>
        <li>
          <b>ERVGTM</b> ensures that "most" values are greater than a specified lower bound.
        </li>
        <li>
          <b>ERVGTP</b> prints the error messages for ERVGT and ERVGTM.
        </li>
        <li>
          <b>ERVII</b> checks for vector values outside given limits.
        </li>
        <li>
          <b>ERVWT</b> checks user-supplied weights.
        </li>
        <li>
          <b>ETAMDL</b> computes noise and number of good digits in model routine results.
        </li>
        <li>
          <b>EXTEND</b> returns the I-th term in a series.
        </li>
        <li>
          <b>FACTOR</b> factors an integer.
        </li>
        <li>
          <b>FDUMP</b> is a dummy version of the dump routine called by XERRWV.
        </li>
        <li>
          <b>FFTCT</b> does a cosine transform of n=2*n2 symmetric data points.
        </li>
        <li>
          <b>FFT</b> is a multivariate complex Fourier transform.
        </li>
        <li>
          <b>FFTLEN</b> computes the value of NFFT for the Singleton FFT routine.
        </li>
        <li>
          <b>FFTR</b> is the user-callable routine for the Fourier transform of a series.
        </li>
        <li>
          <b>FITEXT</b> checks whether the fit is exact to machine precision.
        </li>
        <li>
          <b>FITPT1</b> prints the data summary for nonlinear least squares routines.
        </li>
        <li>
          <b>FITPT2</b> prints the four standardized residual plots.
        </li>
        <li>
          <b>FITSXP</b> generates reporst for least squares exerciser returned storage.
        </li>
        <li>
          <b>FITXSP</b> generates reports for least squares exerciser returned storage.
        </li>
        <li>
          <b>FIXPRT</b> sets the character array 'FIXED'.
        </li>
        <li>
          <b>FLTAR</b> filters an input series using an autoregressive filter.
        </li>
        <li>
          <b>FLTARM</b> filters a series with missing data, using an autoregressive filter.
        </li>
        <li>
          <b>FLTMA</b> filters a series using a simple moving average filter.
        </li>
        <li>
          <b>FLTMD</b> applies a modified Daniel filter to a symmetric series.
        </li>
        <li>
          <b>FTLSL</b> filters an input series.
        </li>
        <li>
          <b>GAMI</b> evaluates the incomplete Gamma function.
        </li>
        <li>
          <b>GAMIT</b> evaluates Tricomi's incomplete Gamma function.
        </li>
        <li>
          <b>GAMLIM</b> calculates the legal range of input arguments for the Gamma function.
        </li>
        <li>
          <b>GAMMA</b> evaluates the Gamma function.
        </li>
        <li>
          <b>GAMR</b> computes the reciprocal of the Gamma function.
        </li>
        <li>
          <b>GENI</b> assigns an arithmetic sequence of values into an integer vector.
        </li>
        <li>
          <b>GENR</b> puts an arithmetic sequence of values into a real vector.
        </li>
        <li>
          <b>GETPI</b> returns the value of PI.
        </li>
        <li>
          <b>GFAEST</b> computes the gain of an autoregressive linear filter.
        </li>
        <li>
          <b>GFARF:</b> short call to compute gain function of autoregressive filter.
        </li>
        <li>
          <b>GFARFS:</b> short call to compute gain function of autoregressive filter.
        </li>
        <li>
          <b>GFORD</b> produces ordinants for the gain function plots.
        </li>
        <li>
          <b>GFOUT</b> produces the gain function plots.
        </li>
        <li>
          <b>GFSEST:</b> gain function of symmetric linear filter with given frequencies.
        </li>
        <li>
          <b>GFSLF:</b> short call for gain function of symmetric linear filter.
        </li>
        <li>
          <b>GFSLFS:</b> short call for gain function of symmetric linear filter.
        </li>
        <li>
          <b>GMEAN</b> computes the geometric mean of a series.
        </li>
        <li>
          <b>GQTSTP</b> computes the Goldfeld-Quandt-Trotter step by More-Hebden technique.
        </li>
        <li>
          <b>HIPASS</b> carries out a high-pass filtering of a series.
        </li>
        <li>
          <b>HISTC:</b> long call for producing a histogram.
        </li>
        <li>
          <b>HIST:</b> short call for producing a histogram.
        </li>
        <li>
          <b>HPCOEF</b> computes hi-pass filter given K-term low pass filter coefficients.
        </li>
        <li>
          <b>HPFLT</b> compute high pass filter coefficients corresponding to a low pass filter.
        </li>
        <li>
          <b>HSTER</b> does error checking for the HIST family of histogram routines.
        </li>
        <li>
          <b>HSTMN</b> is the main routine for producing histograms.
        </li>
        <li>
          <b>I1MACH</b> returns integer machine constants.
        </li>
        <li>
          <b>I8SAVE</b> returns the current error number or recovery switch.
        </li>
        <li>
          <b>ICNTI</b> counts the number of occurences of a value in an integer vector.
        </li>
        <li>
          <b>ICOPY</b> copies an integer vector.
        </li>
        <li>
          <b>IMDCON</b> returns integer machine-dependent constants.
        </li>
        <li>
          <b>INITS</b> initializes an orthogonal series.
        </li>
        <li>
          <b>INPERL</b> computes the number of elements that can be printed on one line.
        </li>
        <li>
          <b>IPGDV</b> produces coordinates for the spectral plots.
        </li>
        <li>
          <b>IPGM:</b> short call to compute the integrated periodogram of a series.
        </li>
        <li>
          <b>IPGMN</b> computes the integrated periodogram.
        </li>
        <li>
          <b>IPGMP</b> is the user routine for integrated periodograms of a series (short call).
        </li>
        <li>
          <b>IPGMPS</b> is the user routine for the integrated periodogram of a series (long call).
        </li>
        <li>
          <b>IPGMS</b> is the user routine fo the integrated periodogram of a series (long call).
        </li>
        <li>
          <b>IPGORD</b> produces coordinates for the spectral plots.
        </li>
        <li>
          <b>IPGOUT</b> produces the integrated periodogram plots.
        </li>
        <li>
          <b>IPRINT</b> sets the logical unit for printed output.
        </li>
        <li>
          <b>ISAMAX</b> indexes the real array element of maximum absolute value.
        </li>
        <li>
          <b>ITSMRY</b> prints an iteration summary.
        </li>
        <li>
          <b>J4SAVE</b> saves and recalls data needed by the XERROR error library.
        </li>
        <li>
          <b>LDSCMP</b> computes storage needed for arrays.
        </li>
        <li>
          <b>LINVRT</b> computes the inverse of a lower triangular matrix.
        </li>
        <li>
          <b>LITVMU</b> solves L' * X = Y, where L is a lower triangular matrix.
        </li>
        <li>
          <b>LIVMUL</b> solves L * X = Y, where L is a lower triangular matrix.
        </li>
        <li>
          <b>LLCNT</b> is the controlling subroutine for linear least squares.
        </li>
        <li>
          <b>LLCNTG</b> is the controlling subroutine for general linear least squares.
        </li>
        <li>
          <b>LLCNTP</b> is the controlling subroutine for polynomial linear least squares.
        </li>
        <li>
          <b>LLER</b> is the error checking routine for the linear least squares routines.
        </li>
        <li>
          <b>LLHDRG:</b> page headings for the unrestricted linear least squares routines.
        </li>
        <li>
          <b>LLHDRP:</b> page headings for polynomial linear least squares routines.
        </li>
        <li>
          <b>LLS</b> is the general linear model least squares fit routine.
        </li>
        <li>
          <b>LLSMN:</b> main program for the linear least squares fitting.
        </li>
        <li>
          <b>LLSP</b> does an unweighted polynomial model least squares fit.
        </li>
        <li>
          <b>LLSPS</b> does an unweighted polynomial model least squares fit.
        </li>
        <li>
          <b>LLSPW</b> does a weighted polynomial model least squares fit.
        </li>
        <li>
          <b>LLSPWS</b> computes a weighted polynomial model least squares fit.
        </li>
        <li>
          <b>LLSS</b> computes an unweighted linear model least squares fit.
        </li>
        <li>
          <b>LLSW</b> computes a weighted linear model least squares fit.
        </li>
        <li>
          <b>LLSWS</b> performs a general linear model weighted least squares fit.
        </li>
        <li>
          <b>LMSTEP</b> computes a Levenberg-Marquardt step by More-Hebden techniques.
        </li>
        <li>
          <b>LOGLMT</b> adjusts plot limits for log plots, and computes log axis labels.
        </li>
        <li>
          <b>LOPASS</b> carries out a low-pass filtering of a series.
        </li>
        <li>
          <b>LPCOEF</b> computes a least squares approximation to an ideal low pass filter.
        </li>
        <li>
          <b>LPFLT</b> computes the low-pass filter coefficients.
        </li>
        <li>
          <b>LSAME</b> returns TRUE if CA is the same letter as CB regardless of case.
        </li>
        <li>
          <b>LSQRT</b> computes the Cholesky factor of a lower triangular matrix.
        </li>
        <li>
          <b>LSTLAG</b> finds the last computable lag value.
        </li>
        <li>
          <b>LSTVCF</b> prints N elements of a masked array.
        </li>
        <li>
          <b>LSTVEC</b> prints indices and values of a real vector.
        </li>
        <li>
          <b>LSVMIN</b> estimates the smallest singular value of a lower triangular matrix.
        </li>
        <li>
          <b>LTSQAR</b> sets A to the lower triangle of L' * L.
        </li>
        <li>
          <b>MADJ</b> is a sample jacobian routine.
        </li>
        <li>
          <b>MADR</b> is a sample residual routine.
        </li>
        <li>
          <b>MAFLT</b> performs a moving average filtering operation.
        </li>
        <li>
          <b>MATPRF</b> prints a square matrix stored in symmetric form.
        </li>
        <li>
          <b>MATPRT</b> is a matrix printing routine.
        </li>
        <li>
          <b>MDFLT</b> is a user routine for a modified Daniels filter of symmetric series.
        </li>
        <li>
          <b>MDL1</b> is the model function for an NLS exerciser.
        </li>
        <li>
          <b>MDL2</b> is a model function for an NLS exerciser.
        </li>
        <li>
          <b>MDL3</b> is a model function for an NLS exerciser.
        </li>
        <li>
          <b>MDL4</b> is a model routine for step size and derivative checking routines.
        </li>
        <li>
          <b>MDLTS1</b> is the user callable routine for estimating box-jenkins arima models.
        </li>
        <li>
          <b>MDLTS2</b> is the model routine for Pack's specification of box-jenkins models.
        </li>
        <li>
          <b>MDLTS3</b> is the user callable routine for estimating box-jenkins arima models.
        </li>
        <li>
          <b>MGS</b> solves a linear system using modified Gram-Schmidt algorithm.
        </li>
        <li>
          <b>MODSUM</b> prints the model summary for the ARIMA routines.
        </li>
        <li>
          <b>MPPC</b> produces a simple page plot with multiple Y-axis values.
        </li>
        <li>
          <b>MPP</b> produces a simple page plot with multiple Y-axis values.
        </li>
        <li>
          <b>MPPL</b> produces a simple page plot with multiple Y-axis values, and log option.
        </li>
        <li>
          <b>MPPMC:</b> produce a page plot with multiply Y-axis values, and missing data.
        </li>
        <li>
          <b>MPPM:</b> produce a page plot with multiple Y-axis values and missing data.
        </li>
        <li>
          <b>MPPML:</b> plot multiple Y-axis values with missing data, log option.
        </li>
        <li>
          <b>MSGX</b> prints the returned and expected values for the error flag IERR.
        </li>
        <li>
          <b>MULTBP</b> multiplies two difference factors from a Box-Jenkins time series model.
        </li>
        <li>
          <b>MVCHK</b> checks whether the input value equals the flag value for missing data.
        </li>
        <li>
          <b>MVPC</b> produces a vertical plot with multiple Y-axis values.
        </li>
        <li>
          <b>MVP</b> produces a vertical plot with multiple Y-axis values.
        </li>
        <li>
          <b>MVPL</b> produces a vertical plot with multiple y-axis values (log plot option).
        </li>
        <li>
          <b>MVPMC:</b> vertical plot with missing data and multiple y-axis values (long call).
        </li>
        <li>
          <b>MVPM:</b> vertical plot with missing data and multiple y-axis values (short call).
        </li>
        <li>
          <b>MVPML:</b> vertical plot with missing data and multiple y-axis values (log option).
        </li>
        <li>
          <b>NCHOSE</b> combines difference factors from a Box-Jenkins time series model.
        </li>
        <li>
          <b>NL2ITR</b> carries out iterations for NL2SOL.
        </li>
        <li>
          <b>NL2SNO</b> is like NL2SOL, but uses a finite difference jacobian.
        </li>
        <li>
          <b>NL2SOL</b> minimizes a nonlinear sum of squares using an analytic jacobian.
        </li>
        <li>
          <b>NL2X</b> tests nl2sol and nl2sno on madsen example.
        </li>
        <li>
          <b>NLCMP</b> computes statistics for the NLS family when weights are involved.
        </li>
        <li>
          <b>NLCNTA:</b> controlling routine for NLS regression with analytic derivatives.
        </li>
        <li>
          <b>NLCNT</b> controlling subroutine for nonlinear least squares regression.
        </li>
        <li>
          <b>NLCNTN</b> controlling routine for NLS regression with approximate derivatives.
        </li>
        <li>
          <b>NLDRVA</b> computes the analytic derivative matrix from the user DERIV routine.
        </li>
        <li>
          <b>NLDRVN</b> approximates the derivative matrix.
        </li>
        <li>
          <b>NLER</b> does error checking routine for nonlinear least squares estimation.
        </li>
        <li>
          <b>NLERR</b> sets the error flag ierr based on the convergence code returned by NL2.
        </li>
        <li>
          <b>NLFIN</b> completes the NLS analysis once the estimates have been found.
        </li>
        <li>
          <b>NLHDRA</b> prints headings for NLS estimation using analytic derivatives.
        </li>
        <li>
          <b>NLHDRN</b> prints headings for NLS estimation using approximate derivatives.
        </li>
        <li>
          <b>NLINIT</b> initializes the NLS routines.
        </li>
        <li>
          <b>NLISM</b> prints an initial summary for the nonlinear least squares routines.
        </li>
        <li>
          <b>NLITRP</b> prints iteration reports for nonlinear least squares regression.
        </li>
        <li>
          <b>NLMN:</b> controlling routine for nonlinear least squares regression.
        </li>
        <li>
          <b>NLOUT</b> prints the final summary report for nonlinear least squares routines.
        </li>
        <li>
          <b>NLSC:</b> NLS regression, approximate derivatives (control call)
        </li>
        <li>
          <b>NLSDC:</b> NLS regression, analytic derivatives, user parameters.
        </li>
        <li>
          <b>NLSD:</b> nonlinear least squares regression, analytic derivatives (short call).
        </li>
        <li>
          <b>NLSDS:</b> NLS regression, analytic derivatives, user parameters.
        </li>
        <li>
          <b>NLS:</b> NLS regression with numeric derivatives, short call.
        </li>
        <li>
          <b>NLSKL</b> prints warning messages for the nonlinear least squares routines.
        </li>
        <li>
          <b>NLSPK</b> packs the unmasked elements of one vector into another.
        </li>
        <li>
          <b>NLSS:</b> interface for nonlinear least squares reqression, approximate derivatives.
        </li>
        <li>
          <b>NLSUPK</b> unpacks a vector into another, using a mask vector.
        </li>
        <li>
          <b>NLSWC:</b> nonlinear least squares regression with weights and approximate derivatives.
        </li>
        <li>
          <b>NLSWDC:</b> NLS regression, analytic derivatives, weights, user parameters.
        </li>
        <li>
          <b>NLSWD:</b> NLS regression, analytic derivatives, weights (short call).
        </li>
        <li>
          <b>NLSWDS:</b> NLS regression with analytic derivatives, weights, user parameters.
        </li>
        <li>
          <b>NLSW:</b> NLS regression with approximate derivatives and weights.
        </li>
        <li>
          <b>NLSWS:</b> NLS regression with approximate derivatives and weights.
        </li>
        <li>
          <b>NLSX1</b> sets the starting parameter values for NLSX.
        </li>
        <li>
          <b>NLSX2</b> sets a problem for testing the NLS family.
        </li>
        <li>
          <b>NRANDC</b> generates pseudorandom normally distributed values.
        </li>
        <li>
          <b>NRAND</b> generates pseudorandom normally distributed values.
        </li>
        <li>
          <b>OANOVA</b> computes and prints analysis of variance.
        </li>
        <li>
          <b>OBSSM2</b> lists the data summary for the arima estimation routines.
        </li>
        <li>
          <b>OBSSUM</b> lists the data summary for the least squares subroutines.
        </li>
        <li>
          <b>PARCHK</b> checks the NL2SOL parameters.
        </li>
        <li>
          <b>PARZEN</b> computes and stores the Parzen lag window.
        </li>
        <li>
          <b>PGMEST</b> computes the periodogram estimates.
        </li>
        <li>
          <b>PGM</b> is the user callable routine for the raw periodogram of a series.
        </li>
        <li>
          <b>PGMMN</b> is the main routine for computing the raw periodogram.
        </li>
        <li>
          <b>PGMS</b> computes the (raw) periodogram of a series (long call).
        </li>
        <li>
          <b>PGORD</b> produces coordinates for the periodogram plot.
        </li>
        <li>
          <b>PGOUT</b> produces the periodogram plots.
        </li>
        <li>
          <b>PLINE</b> defines one line of a plot string for the vertical plot routines.
        </li>
        <li>
          <b>PLTCHK</b> checks for errors for the multiple plot routines.
        </li>
        <li>
          <b>PLTPLX</b> computes the point location in the plot string.
        </li>
        <li>
          <b>PLTSYM</b> supplies the plot symbol for the plot line.
        </li>
        <li>
          <b>POLAR</b> converts complex numbers from Cartesian to polar representation.
        </li>
        <li>
          <b>PPC</b> produces a simple page plot (long call).
        </li>
        <li>
          <b>PPCNT</b> is the controling routine for user called page plot routines.
        </li>
        <li>
          <b>PP</b> is the user callable routine which produces a simple page plot (short call).
        </li>
        <li>
          <b>PPCHFS</b> computes the percentage points of the Chi Square distribution.
        </li>
        <li>
          <b>PPFF</b> computes the percentage points for the F distribution.
        </li>
        <li>
          <b>PPFNML</b> computes the percentage points of the normal distribution.
        </li>
        <li>
          <b>PPFT</b> computes the percentage points of the Student's T distribution.
        </li>
        <li>
          <b>PPL</b> produces a simple page plot (log option).
        </li>
        <li>
          <b>PPLMT</b> sets the plot limits for page plots with missing values.
        </li>
        <li>
          <b>PPMC</b> produces a simple page plot for data with missing observations (long call).
        </li>
        <li>
          <b>PPM</b> produces a simple page plot for data with missing observations (short call).
        </li>
        <li>
          <b>PPML</b> plots data with missing observations (log option).
        </li>
        <li>
          <b>PPMN</b> is the main routine for page plots.
        </li>
        <li>
          <b>PRTCNT</b> sets up the print control parameters.
        </li>
        <li>
          <b>QAPPLY</b> applies orthogonal transformation to the residual R.
        </li>
        <li>
          <b>QRFACT</b> computes the QR decomposition of a matrix.
        </li>
        <li>
          <b>R1MACH</b> returns single precision machine constants.
        </li>
        <li>
          <b>R9GMIT</b> computes Tricomi's incomplete gamma function for small X.
        </li>
        <li>
          <b>R9LGIC</b> compute the log complementary incomplete gamma function.
        </li>
        <li>
          <b>R9LGIT</b> computes the log of Tricomi's incomplete Gamma function.
        </li>
        <li>
          <b>R9LGMC</b> computes the log Gamma correction factor.
        </li>
        <li>
          <b>RANDN</b> returns normal random numbers.
        </li>
        <li>
          <b>RANDU</b> returns uniform random numbers.
        </li>
        <li>
          <b>RANKO</b> puts the rank of N X's in the vector R.
        </li>
        <li>
          <b>REALTR</b> computes the forward or inverse Fourier transform of real data.
        </li>
        <li>
          <b>RELCOM</b> computes the difference between V(I) and W(I) relative to RELTOL.
        </li>
        <li>
          <b>RELDST</b> computes the relative difference between two real values.
        </li>
        <li>
          <b>REPCK</b> reformats the data in D for the N by NPAR format used by NLCMP.
        </li>
        <li>
          <b>RMDCON</b> returns machine constants.
        </li>
        <li>
          <b>RPTMUL</b> multiplies the R factor times a vector X.
        </li>
        <li>
          <b>S88FMT</b> writes an integer into a string.
        </li>
        <li>
          <b>SAMPLE</b> creates a new series by sampling every K-th item of the input.
        </li>
        <li>
          <b>SASUM</b> takes the sum of the absolute values of a real vector.
        </li>
        <li>
          <b>SAXPY</b> adds a real constant times one vector to another.
        </li>
        <li>
          <b>SCOPY</b> copies one real vector into another.
        </li>
        <li>
          <b>SDOT</b> forms the dot product of two real vectors.
        </li>
        <li>
          <b>SETERR</b> sets the error number and prints the error message.
        </li>
        <li>
          <b>SETESL</b> computes the smallest suitable value of NFFT for given N and Singleton FFT.
        </li>
        <li>
          <b>SETFRQ</b> computes the frequencies at which the spectrum is to be estimated.
        </li>
        <li>
          <b>SETIV</b> sets the entries of an integer vector to a value.
        </li>
        <li>
          <b>SETLAG</b> sets the number of autocorrelations to be computed.
        </li>
        <li>
          <b>SETRA</b> sets the entries of a real array to a given value.
        </li>
        <li>
          <b>SETROW</b> selects the row used by the derivative checking procedure.
        </li>
        <li>
          <b>SETRV</b> sets the elements of a real vector to a value.
        </li>
        <li>
          <b>SLFLT</b> applies a symmetric filter to a series.
        </li>
        <li>
          <b>SLUPDT</b> updates a symmetric matrix A so that A * STEP = Y.
        </li>
        <li>
          <b>SLVMUL</b> sets Y = S * X, where S is a P by P symmetric matrix.
        </li>
        <li>
          <b>SMACH</b> computes machine parameters for single precision arithmetic.
        </li>
        <li>
          <b>SMPLY</b> samples every K-th observation from a series.
        </li>
        <li>
          <b>SNRM2</b> computes the Euclidean norm of a real vector.
        </li>
        <li>
          <b>SPCCK</b> analyzes ordinates for the spectal semi-log plots.
        </li>
        <li>
          <b>SPPC</b> produces a simple page plot with user control of plot symbols (long call).
        </li>
        <li>
          <b>SPP</b> produces a simple page plot with user control of plot symbols (short call).
        </li>
        <li>
          <b>SPPL</b> produces a simple page plot with user control of plot symbols (log option).
        </li>
        <li>
          <b>SPPLTC:</b> confidence interval and bandwidth coordinates for spectrum plots.
        </li>
        <li>
          <b>SPTLTD</b> sets various y axis limits for decibel spectrum plots.
        </li>
        <li>
          <b>SPPLTL</b> sets various y axis limits for decibel spectrum plots.
        </li>
        <li>
          <b>SPPMC:</b> page plot with user plot symbols and missing observations (long call).
        </li>
        <li>
          <b>SPPM</b> page plot with user plot symbols and missing observations (short call).
        </li>
        <li>
          <b>SPPML:</b> page plot with user plot symbols and missing observations (log option).
        </li>
        <li>
          <b>SROT</b> applies a real plane rotation.
        </li>
        <li>
          <b>SROTG</b> constructs a real Givens plane rotation.
        </li>
        <li>
          <b>SRTIR</b> sorts an integer array IR on a key array A.
        </li>
        <li>
          <b>SRTIRR</b> sorts arrays A, IR and RR based on values in A.
        </li>
        <li>
          <b>SRTRI</b> sorts array A on integer array IR.
        </li>
        <li>
          <b>SRTRRI</b> sorts the array IR, A and RR, based on values in IR.
        </li>
        <li>
          <b>SSCAL</b> scales a real vector by a constant.
        </li>
        <li>
          <b>SSIDI</b> computes the determinant, inertia and inverse of a real symmetric matrix.
        </li>
        <li>
          <b>SSIFA</b> factors a real symmetric matrix.
        </li>
        <li>
          <b>SSWAP</b> interchanges two real vectors.
        </li>
        <li>
          <b>STAT1</b> computes statistics for a sorted vector.
        </li>
        <li>
          <b>STAT1W</b> computes statistics for a sorted vector with weights.
        </li>
        <li>
          <b>STAT2</b> computes statistics that do not require sorted data.
        </li>
        <li>
          <b>STAT2W</b> computes statistics on an unsorted, weighted vector.
        </li>
        <li>
          <b>STATER</b> does error checking for the STAT family of routines.
        </li>
        <li>
          <b>STAT</b> computes 53 statistics for an unweighted vector.
        </li>
        <li>
          <b>STATS</b> computes 53 different statistics for an unweighted vector.
        </li>
        <li>
          <b>STATW</b> computes 53 statistics for a weighted vector.
        </li>
        <li>
          <b>STATWS</b> computes 53 statistics for a weighted vector.
        </li>
        <li>
          <b>STKCLR</b> clears the stack for framework area manipulation routines.
        </li>
        <li>
          <b>STKGET</b> allocates space on an integer stack.
        </li>
        <li>
          <b>STKREL</b> de-allocates the last allocations made in the stack.
        </li>
        <li>
          <b>STKSET</b> initializes the stack to NITMES of type ITYPE.
        </li>
        <li>
          <b>STKST</b> returns statistics on the state of the stack.
        </li>
        <li>
          <b>STOPX</b> is called to stop execution.
        </li>
        <li>
          <b>STPADJ</b> adjusts the selected step sizes to optimal values.
        </li>
        <li>
          <b>STPAMO</b> is a dummy routine for the arima estimation routines.
        </li>
        <li>
          <b>STPCNT</b> controls the stepsize selection process.
        </li>
        <li>
          <b>STPDRV</b> is the driver for selecting forward difference step sizes.
        </li>
        <li>
          <b>STPER</b> does error checking for the stepsize selection routines.
        </li>
        <li>
          <b>STPHDR</b> prints page headings for the stepsize selection routines.
        </li>
        <li>
          <b>STPLS1</b> sets a test problem for the step size selection family.
        </li>
        <li>
          <b>STPLS2</b> sets a test problem for the step size selection family.
        </li>
        <li>
          <b>STPLSC</b> selects step sizes for forward difference estimates of derivatives.
        </li>
        <li>
          <b>STPLS</b> selects step sizes for estimating derivatives in NLS routines.
        </li>
        <li>
          <b>STPMN:</b> main routine for numerical derivative step size selection.
        </li>
        <li>
          <b>STPOUT</b> prints results for the step size selection routines.
        </li>
        <li>
          <b>STPSEL</b> selects new step sizes until no further improvement can be made.
        </li>
        <li>
          <b>STRCO</b> estimates the condition of a real triangular matrix.
        </li>
        <li>
          <b>STRDI</b> computes the determinant and inverse of a real triangular matrix.
        </li>
        <li>
          <b>SUMBS</b> finds a zero or value closest to zero in a sorted vector.
        </li>
        <li>
          <b>SUMDS</b> sums unweighted powers of differences from the mean of a sorted vector.
        </li>
        <li>
          <b>SUMID</b> sums I * ( X(I) - XMEAN ).
        </li>
        <li>
          <b>SUMIDW:</b> dot product of I and ( X(I) - XMEANW ).
        </li>
        <li>
          <b>SUMOT</b> reports the computation of 53 selected statistics.
        </li>
        <li>
          <b>SUMSS</b> calculates the sum of powers and mean for a sorted vector.
        </li>
        <li>
          <b>SUMTS</b> calculates unweighted trimmed mean for a sorted vector.
        </li>
        <li>
          <b>SUMWDS</b> calculates sums of powers of differences from the weighted mean.
        </li>
        <li>
          <b>SUMWSS</b> calculates weighted and unweighted sums of powers and the mean.
        </li>
        <li>
          <b>SUMWTS</b> calculates weighted and unweighted means for a sorted vector.
        </li>
        <li>
          <b>SVPC</b> produces a vertical plot with user plot symbols (long call).
        </li>
        <li>
          <b>SVP:</b> vertical plot with user plot symbols (short call).
        </li>
        <li>
          <b>SVPL</b> produces a vertical log plot with user control of the plot symbol.
        </li>
        <li>
          <b>SVPMC:</b> vertical plot with missing data and user plot symbols (long call).
        </li>
        <li>
          <b>SVPM:</b> vertical plot with missing data and user plot symbols (short call).
        </li>
        <li>
          <b>SVPML:</b> vertical plot with missing data and user plot symbols (log plot option).
        </li>
        <li>
          <b>TAPER</b> applies a split-cosine-bell taper to a centered observed series.
        </li>
        <li>
          <b>TIMESTAMP</b> prints the current YMDHMS date as a time stamp.
        </li>
        <li>
          <b>UAS</b> is the user callable routine for autoregressive spectrum estimation.
        </li>
        <li>
          <b>UASCFT</b> computes autoregressive coefficients using Durbin's method.
        </li>
        <li>
          <b>UASDV</b> is the driver for computing the autoregressive and Fourier spectrums.
        </li>
        <li>
          <b>UASER:</b> error checks for time series Fourier univariate spectrum analysis.
        </li>
        <li>
          <b>UASET</b> calculates the autoregressive spectrum.
        </li>
        <li>
          <b>UASF</b> is the user callable routine for autoregressive spectrum estimation.
        </li>
        <li>
          <b>UASFS:</b> interface for autoregressive spectrum estimation using the FFT (long call).
        </li>
        <li>
          <b>UASORD</b> produces coordinates for the spectrum plots.
        </li>
        <li>
          <b>UASOUT</b> produces the spectrum plots for the autoregressive spectrum estimates.
        </li>
        <li>
          <b>UASS:</b> user interface for autoregressive spectrum estimation (long call).
        </li>
        <li>
          <b>UASVAR</b> computes the variance for a given series and autoregressive model.
        </li>
        <li>
          <b>UASV</b> is the user routine for autoregressive spectrum estimation.
        </li>
        <li>
          <b>UASVS</b> is a user routine for autoregressive spectrum estimation.
        </li>
        <li>
          <b>UFPARM</b> is a dummy version of the optional user function for NL2SOL.
        </li>
        <li>
          <b>UFSDRV</b> is the controlling routine for time series Fourier spectrum analysis.
        </li>
        <li>
          <b>UFSET</b> checks errors for time series Fourier univariate spectrum analysis.
        </li>
        <li>
          <b>UFSEST</b> computes the spectra and the confidence limits.
        </li>
        <li>
          <b>UFS:</b> user routine for time series Fourier spectrum analysis (short call).
        </li>
        <li>
          <b>UFSF:</b> user routine for Fourier spectrum analysis using fft (short call).
        </li>
        <li>
          <b>UFSFS:</b> user routine for Fourier spectrum analysis using the fft (long call).
        </li>
        <li>
          <b>UFSLAG</b> computes the lag window truncation points for spectrum analysis.
        </li>
        <li>
          <b>UFSM:</b> user routine for Fourier spectrum analysis with missing data (short call).
        </li>
        <li>
          <b>UFSMN</b> computes autocorrelations and partial autocorrelations of a time series.
        </li>
        <li>
          <b>UFSMS:</b> time series Fourier spectrum analysis with missing data (long call).
        </li>
        <li>
          <b>UFSMV:</b> Fourier spectrum analysis, missing data, user ACVF values (short call).
        </li>
        <li>
          <b>UFSMVS:</b> time series Fourier spectrum analysis with missing data (long call).
        </li>
        <li>
          <b>UFSOUT</b> produces the Fourier bivariate spectrum output.
        </li>
        <li>
          <b>UFSPCV</b> produces coordinates for the spectrum plots.
        </li>
        <li>
          <b>UFSS:</b> time series Fourier spectrum analysis (long call).
        </li>
        <li>
          <b>UFSV:</b> Fourier spectrum analysis, user supplied ACVF values (short call).
        </li>
        <li>
          <b>UFSVS:</b> Fourier spectrum analysis and user supplied acvf values (long call).
        </li>
        <li>
          <b>V2NORM</b> computes the L2 norm of a vector.
        </li>
        <li>
          <b>VCOPY</b> copies a vector.
        </li>
        <li>
          <b>VCVOTF</b> prints the variance-covariance matrix.
        </li>
        <li>
          <b>VCVOUT</b> prints the variance-covariance matrix.
        </li>
        <li>
          <b>VERSP</b> prints the version number.
        </li>
        <li>
          <b>VP</b> is the user callable routine which produces a vertical plot (short call).
        </li>
        <li>
          <b>VPC</b> is the user callable routine which produces a vertical plot (long call).
        </li>
        <li>
          <b>VPCNT</b> is the controlling routine for user-called vertical plots
        </li>
        <li>
          <b>VPHEAD</b> prints the heading for the vertical plot output.
        </li>
        <li>
          <b>VPL</b> is the user callable routine which produces a vertical log plot.
        </li>
        <li>
          <b>VPLMT</b> sets the plot limits for vertical plots
        </li>
        <li>
          <b>VPM</b> produces a vertical plot with missing data (short call).
        </li>
        <li>
          <b>VPMC</b> produces a vertical plot with missing data (long call).
        </li>
        <li>
          <b>VPML</b> produces a vertical plot with missing data (log plot option).
        </li>
        <li>
          <b>VPMN</b> produces vertical plots.
        </li>
        <li>
          <b>XERABT</b> aborts execution of the program.
        </li>
        <li>
          <b>XERBLA</b> is an error handler for the LAPACK routines.
        </li>
        <li>
          <b>XERCLR</b> resets the current error number to zero.
        </li>
        <li>
          <b>XERCTL</b> gives the user control over handling individual errors.
        </li>
        <li>
          <b>XERPRT</b> prints an error message.
        </li>
        <li>
          <b>XERROR</b> processes a diagnostic message.
        </li>
        <li>
          <b>XERRWV</b> processes a diagnostic message.
        </li>
        <li>
          <b>XERSAV</b> records that an error has occurred.
        </li>
        <li>
          <b>XGETF</b> returns the current error control flag.
        </li>
        <li>
          <b>XGETUA</b> determines the units to which error messages are being sent.
        </li>
        <li>
          <b>XSETF</b> sets the error control flag.
        </li>
      </ul>
    </p>

    <p>
      You can go up one level to <a href = "../f_src.html">
      the FORTRAN90 source codes</a>.
    </p>

    <hr>

    <i>
      Last revised on 19 May 2007.
    </i>

    <!-- John Burkardt -->
 
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