Computer Programs
NESC0562 AMDLIBAE
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NESC0562 AMDLIBAE

AMDLIBAE, IBM 360 Subroutine Library, Special Function, Polynomials, Differential Equation

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1. NAME OR DESIGNATION OF PROGRAM:  AMDLIBAE
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2. COMPUTERS
To submit a request, click below on the link of the version you wish to order. Rules for end-users are available here.
Program name Package id Status Status date
AMDLIBAE NESC0562/01 Tested 01-MAR-1980

Machines used:

Package ID Orig. computer Test computer
NESC0562/01 IBM 3033 IBM 3033
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3. DESCRIPTION OF PROBLEM OR FUNCTION

AMDLIBAE is  a subset  of the

IBM 360 Subroutine Library at  the Applied Mathematics Division at

Argonne  National   Laboratory.   This  subset   includes  library

categories A-E:

IDENTIFICATION          DESCRIPTION

A152S A  MPA            Mult. prec. floating point arith. package

B156S A  ARSIN          Arcsine, arccosine

B158S A  DSIN/DCOS      DP sine, cosine

B159S A  DTAN/DCOT      DP tangent, cotangent

B252S A  SINH/COSH      Hyperbolic sine, cosine

B353S A  ALOG           SP logarithm

B354S A  DEXP           DP exponential

B355S A  DLOG           DP logarithm

B456S A  DCUBRT         DP cube root

B457S A  ARGPOWER       X**Y

B458S A  ARGFDXPD       DP X**Y

C150S F  DQD            Q. D. algorithm applied to a power series

C151S F  DCONF1         Eval. cont. fract. Q. D. of power series

C250S F  CUBIC          Roots of cubic polynomial equation

C251S F  QUARTIC        Roots of quartic polynomial equation

C252S F  RSSR           All roots of poly eqs. with real coef.

C253S F  POLDRV         Driver for C254S

C254S F  CPOLY          Roots arb. poly. Jenkins-Traub algorithm

C353S F1 CLEBSH         Ang. mom. coef. - Clebsch, Racah, Wigner

C365S A  ALGAMA         Logarithm of the gamma function

C366S A  DGAMMA/DLGAMA  DP gamma and log(gamma) functions

C368S F  EONE           Exponential integral E1

C370S F  BESJY          Bessel functions J and Y

C371S F  BESIK          Bessel functions I and K

C372S F  CHIPRB         Chi-square integral

C380S F  DRZETA         Long precision zeta, zeta-1 functions

C382S F  DCGAM          Long precision complex gamma

C383S A  DERF/DERFC     DP error function

C384S F  BFJ1           Bessel function J1

C385S F  COULMB         Regular Coulomb wave functions

C386S F1 DSGMAL         Coulomb phase shift

C387S F  BFJYR          Bessel functions J0,J1,Y0,Y1

C388S F  IRCOUL         LP irregular Coulomb wave functions

C389S F  GAMIN          Incomplete gamma function

C390S F  LQ             Assoc. Legendre functions of 2nd. kind

C392S A  DAERF          Inverse error function

C393S F  CDEONE         Modified complex exponential integral

D153S F  DROMB          Two-dimensional Romberg quadrature

D153S P  DROMBP         Two-dimensional Romberg quadrature

D158S F  ANC4           Adap. quad. using 4-th order Newton-Cotes

D158S P  ANC4P          Adap. quad. using 4-th order Newton-Cotes

D161S F  GAUSS          Arbitrary Gaussian weights and nodes

D162S F  SQUANK         Simpson's quad. used adaptively

D252S F  DDFSUB         DP Neville or Stoer sol. lin. dif. eqns.

D253S F  DDFSYS         Driver for D252S

D255S F  DFBND          Stoer sol. dif. eqs. with error bounds

D256S F  DFBDRV         Driver for D255S

D257S F  GEARDV         Gear's sol. of init. value problem

D452S F  ENDACE         Numerical derivatives real analytic fn.

E206S F  LSQPOL         Least squares weighted polynomial fit

E208S F1                Arbitrary function fit, least squares

E209S F  CALLSQ         Driver for E206S

E212S F                 General least squares fit + fnction eval.

E250S F  VA02A          Least squares funct. min. w/o derivatives

E252S F  MINMAX         Chebyshev line fit

E253S F                 Arbitrary functional fit II

E256S F  BGPOL          Least squares fit with polynomials

E257S F  BGLSSQ         Least squares fit with arbitrary function

E350S F  SMOOTH         Smoothing by cubic splines
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4. METHOD OF SOLUTION:
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5. RESTRICTIONS ON THE COMPLEXITY OF THE PROBLEM:
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6. TYPICAL RUNNING TIME:
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7. UNUSUAL FEATURES OF THE PROGRAM:
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8. RELATED AND AUXILIARY PROGRAMS

AMDLIBF (NESC  Abstract 563)  and
AMDLIBGZ (NESC Abstract 564).
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9. STATUS
Package ID Status date Status
NESC0562/01 01-MAR-1980 Tested at NEADB
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10. REFERENCES

- B.T. Smith:

  The ANL-AMD Subroutine Library (ACC 562, 563, and 564),

  ACC Programming Note 73-5 (September 1, 1972).

- ANL-AMD System/360 Library Subroutine Descriptions:

- K.E. Hillstrom:

  MPA, Multiple-precision Floating-point Arithmetic Package for the
  System/360

  ANL A152S (November 1971).

- W.J. Cody and K. Paciorek:

  ARGARSIN, OS/360 FORTRAN IV Systems Subroutine for Arcsine,

  Arccosine Function (Single Precision),

  ANL B156S, (February 1969).

- K. Hillstrom and J. Wang:

  DSIN/DCOS, OS/360 FORTRAN IV Compatible Routine for the Sine and

  Cosine Function

  ANL B158S (Ocotber 1969) Rev. (July 1975).

- K. Hillstrom and J. Wang:

  DTAN/DCOTAN, FORTRAN IV Compatible Routine for the Tangent and

  Cotangent Function

  ANL B159S (October 1969) Rev. (July 1975).

- W.J. Cody and K. Paciorek:

ARGSINH, OS/360 FORTRAN IV Library Routine for Hyperbolic Sine and    Cosine Functions (Single-precision)

  ANL B252S (February 1969).

- Nancy W. Clark:

  ALOG, OS/360 FORTRAN IV Systems Routine for Natural or Base 10 DP
  Logarithms

  ANL B353S (February 1969).

- Nancy Clark:

  DEXP, OS/360 FORTRAN IV Systems Routine for Double-precision E**X
  ANL B354S (February 1969).

- Nancy W. Clark:

  DLOG, FORTRAN IV Systems Routine for Natural or Base 10 DP

  Logarithms

  ANL B355S (February 1969).

- Kathleen A. Paciorek:

DOUBRT, System/360 Assembly Language Subroutine which Computes the    DP Cube Root of a Normalized DP Floating Point Argument

  ANL B456S (October 1967).

- Donald  F. Jordan and J. Cody:

  ARGPOWER, IBM S/360 FORTRAN IV Single-precision Power Function

  ANL B457S (January 1968) (Rev. February 1969 and October 1974).

- N.A. Clark, W.J. Cody, and K.A. Paciorek:

  ARGFDXPD, IBM S/360 FORTRAN IV DP Power Function

  ANL B458S (May 1969), Rev. (October 1974).

- H.C. Thacher, Jr. and Kathleen A. Paciorek:

  DQD, DP FORTRAN IV Quotient-Difference Algorithm

  ANL C150S (July 1969).

-H.C. Thacher, Jr. and Kathleen A. Paciorek:

  DCONF1, DP FORTRAN IV Routine to Evaluate an S-fraction

  ANL C151S (July 1969).

- Burton S. Garbow:

  CUBIC, Roots of Cubic Polynomial Equations

  ANL C250S (December 1967), Rev. (September 1977).

- Burton S. Garbow:

  QUARTI, Roots of Quartic Polynomial Equations

  ANL C251S (December 1967).

- Burton S. Garbow:

  RSSR, Zeroes of Polynomials with Real Coefficients

  ANL C252S (July 1968) Rev. (December 1968, April 1977).

- K. Paciorek:

  POLDRV, FORTRAN IV Double-precision Driver for ANL C254S

  ANL C253S (April 1969).

- Kathleen Paciorek:

  CPOLY,RPOLY,BNDZRO, A FORTRAN IV Double-precision Polynomial

  Rootfinder Package

  ANL C254S (April 1969).

- S. Pieper:

CLEBSH, Clebsch-Gordan, Racah, Wigner 3J, Wigner 6J, and Wigner 9J    Coefficients

  ANL C353S (June 1977).

- K. Hillstrom:

  ALGAMA, FORTRAN IV Compatible Routine for the Natural Log of the

  Real Gamma Function

  ANL C365S (March 1967).

- K. Hillstrom:

  DGAMMA/DLGAMA, OS/360 FORTRAN IV Compatible Routine for the Gamma
  Function and the Natural Log of the Gamma Function

  ANL C366S (May 1969) Rev. (April 1973 and November 1974).

- Donald F. Jordan:

  EONE, Exponential Integral

  ANL C368S (March 1968).

- Donald F. Jordan:

  BESJY,  Bessel Functions

  ANL C370S (October 1967).

- Donald F. Jordan:

  BESIK, Bessel Functions

  ANL C371S (November 1967).

- Kathleen Paciorek:

  CHIPRB, FORTRAN IV Double-precision Subroutine which Finds the

  Probability that X**2 for N Degrees of Freedom Exceeds X

  ANL C372S (January 1968).

- K. Hillstrom:

  DRZETA, FORTRAN IV (H) Routine for the Riemann Zeta Function

  ZETA(S) or ZETA(S)-1

  ANL C380S (October 1970).

- K. Hillstrom and H. Kuki:

  DCGAM/DCLGAM/CDGAMA/CDLGAM, OS/360 FORTRAN IV(H) Routine for the

  Double-precision Complex Gamma and Log Gamma Functions

  ANL C382S-1 (November 1970).

- K. Hillstrom and J. Wang:

  DERF/DERFC, OS/360 FORTRANIV Compatible Routine for the Error

  Function and the Complementary Error Function

  ANL C383S (March 1969) Rev. (July 1975).

- K. Hillstrom:

  BFJ1, OS/360 FORTRAN IV Routine for the Bessel Function of the

  First Kind and Order

  ANL C384S (April 1969).

- Kathleen A. Paciorek:

  COULMB, A DP FORTRAN IV Routine to Calculate Regular Coulomb Wave
  Functions

  ANL C385S (August 1969).

- K. Hillstrom:

  DSGMAL, OS/360 FORTRAN IV(H) Routine for the Coulomb Phase Shift

  SIGMAL(N), (L=0,1,2,...,N)

  ANL C386S-2 (July 1970) Rev. (January 1975).

- J. Gregory:

  BFJYR, OS/360 FORTRAN IV Routine for the Bessel Function of the

  First and Second Kind and of Order Zero and Order One

  ANL C387S (July 1970).

- A. Strecok and J. Wang:

  IRCOUL, Irregular Coulomb Wave Functions GL(N,P)

  ANL C388S (August 1970) Rev. (April 1976).

- A. Strecok:

  GAMIN, OS/360 FORTRAN IV (H) DP Routine for the Incomplete Gamma

  Function

  ANL C389S (January 1971).

- A. Strecok:

  LQ, A FORTRAN IV DP Routine for Associated Legendre Functions of

  the Second Kind

  ANL C390S (September 1971).

- P. Kinnucan and H. Kuki:

DAERF, A FORTRAN IV Double Precision Subroutine for the Inverses o    the Error Function, the Complemented Error Function and the

  Gaussian Function

  ANL C392S (July 1976).

- A. Strecok:

  CDEONE, Modified Complex Exponential Integral

  ANL C393S (May 1972) Rev. (September 1976).

- K. Hillstrom:

  DROMB, OS/360 FORTRAN IV Routine for Two-dimensional Romberg

  Quadrature

  ANL C153S (November 1968).

- K. Hillstrom:

DROMBP, OS/360 PL/I Routine for Two-dimensional Romberg Quadrature    ANL D153S-P (July 1970).

- K. Hillstrom:

  ANC4, OS/360 FORTRAN IV Routine for Adaptive Quadrature Using the
  4th Newton-Cotes Formula

  ANL D158S (November 1968).

- K. Hillstrom:

  ANC4P, PL/I Routine for Adaptive Quadrature Based on the Newton-

  Cotes 5-point Rule

  ANL D158S-P (July 1970).

- K. Hillstrom and J. Wang:

  GAUSS, OS/360 FORTRAN IV Routine for Gaussian Quadrature Formula

  Generation

  ANL D161S (December 1968) Rev. (September 1977).

- J.N. Lyness and K.E. Hillstrom:

  SQUANK, FORTRAN IV Routine for Adaptive Simpson Rule Quadrature

  ANL D162S (July 1970).

- Kathleen Paciorek:

  DDFSUB, FORTRAN IV Subroutine which Performs One DP Integration

  Step for a System of First-order Ordinary Differential Equations

  ANL D252S (September 1968).

- Kathleen Paciorek:

  DDFSYS, FORTRAN IV DP Routine which Provides Input/Output and

  Control for Use with the DP Ordinary Differential Equations

  ANL D253S (May 1967).

- Kathleen Paciorek:

  DFBND-DIFI, FORTRAN IV Double-precision Routines which Estimate

the Error in the Bulirsch-Stoer Method for Solution of a System of    First-order Ordinary Differential Equations

  ANL D255S (October 1969).

- Kathleen A. Paciorek:

  DFBDRV, FORTRAN IV DP Routine which Provides Input/Output and

  Control for Use with the DP Routines ANL D255S DFBND-DIFI to

  Integrate a System of First-order Ordinary Differential Equations
  ANL D256S (October 1969).

- A. C. HindmarshL

  GEARDV, Numerical Integration of an Initial Value Problem for a

  System of Ordinary Differential Equations

  ANL D257S (July 1975).

- J.N. Lyness:

ENDACE, Evaluate Numerical Differentiation and Corresponding Error    ANL D452S (August 1976).

- Kathleen Paciorek:

  LSQPOL, Least Square Polynomial Fit

  ANL E206S (September 1967).

- K. Szabo and K. Hillstrom:

  Arbitrary Functional Fit

  ANL E208S-1 (January 1970).

- K. Paciorek:

  CALLSQ, FORTRAN IV DP Routine which Provides Input/Output and

Control for Use with the DP Version of ANL E206S - LSQPOL to Do a   Least Square Polynomial  Fit

  ANL E209S (September 1967).

- J. B. Cohen:

A General Program for the Evaluation of an Arbitrary Function, and    for the Least Squares Determination of the Coefficients of a

  Function, Linear in the Coefficients, InvolvingOne or More

  Independent Variables

  ANL E212S (January 1967).

- Burton S. Garbow:

  VA02A,SV01A, Least Squares Functional Minimization without

  Derivatives

  ANL E250S (August 1968).

- Burton S. Garbow:

  MINMAX, Chebyshev Line Fit

  ANL E252S (October 1968).

- A. Meyer and I.K. Abu-Shumays:

  Arbitrary Functional Fit II

  ANL E253S (April 1969).

- K.E. Hillstrom and W.J. Cody:

BGPOL, Linear Least Squares Solution by Householder Transformation    ANL E256S (December 1971).

- K. E. Hillstrom and W. J. Cody:

  BGLSS, Least Squares Solutions of Systems of Linear Equations by

  Orthogonal Householder Transformations with Statistical

  Calculations

  ANL E257S (December 1971).

- Burton S. Garbow and B. Garbow:

  SMOOTH, Smoothing by Cubic Splines

  ANL E350S (December 1968) Rev. (April 1975).
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11. MACHINE REQUIREMENTS:
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12. PROGRAMMING LANGUAGE(S) USED
Package ID Computer language
NESC0562/01 FORTRAN-IV
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13. OPERATING SYSTEM UNDER WHICH PROGRAM IS EXECUTED:   OS/360 Release
19.6.
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14. OTHER PROGRAMMING OR OPERATING INFORMATION OR RESTRICTIONS:
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15. NAME AND ESTABLISHMENT OF AUTHOR

   Contact       Jesse Y. Wang, Program Librarian
                 Applied Mathematics Division
                 Argonne National Laboratory
                 9700 South Cass Avenue
                 Argonne, Illinois  60439
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16. MATERIAL AVAILABLE
NESC0562/01
File name File description Records
NESC0562_01.001 SOURCE (F4,EBCDIC) 20067
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17. CATEGORIES
  • P. General Mathematical and Computing System Routines

Keywords: differential equations, elementary functions, interpolation, polynomials, quadratures, special functions.