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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. Only liaison officers are authorised to submit online requests. Rules for requesters 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.