Computer Programs

NAME OR DESIGNATION OF PROGRAM, COMPUTER, DESCRIPTION OF PROBLEM OR FUNCTION, METHOD OF SOLUTION, RESTRICTIONS ON THE COMPLEXITY OF THE PROBLEM, TYPICAL RUNNING TIME, UNUSUAL FEATURES OF THE PROGRAM, RELATED AND AUXILIARY PROGRAMS, STATUS, REFERENCES, MACHINE REQUIREMENTS, LANGUAGE, OPERATING SYSTEM UNDER WHICH PROGRAM IS EXECUTED, OTHER PROGRAMMING OR OPERATING INFORMATION OR RESTRICTIONS, NAME AND ESTABLISHMENT OF AUTHOR, MATERIAL, CATEGORIES

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Program name | Package id | Status | Status date |
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FC,LSEI,WNNLS | NESC0909/01 | Tested | 27-FEB-1989 |

Machines used:

Package ID | Orig. computer | Test computer |
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NESC0909/01 | CDC 6600 | CDC CYBER 830 |

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3. DESCRIPTION OF PROBLEM OR FUNCTION

FC allows a user to fit dis- crete data, in a weighted least-squares sense, using piece-wise polynomial functions represented by B-splines on a given set of knots. In addition to the least-squares fitting of the data, equali- ty, inequality, and periodic constraints at a discrete, user-speci- fied set of points can be imposed on the fitted curve or its deriva- tives. The subprograms LSEI and WNNLS solve the linearly-constrained least-squares problem. LSEI solves the class of problem with general inequality constraints, and, if requested, obtains a covariance matrix of the solution parameters. WNNLS solves the class of problem with nonnegativity constraints. It is anticipated that most users will find LSEI suitable for their needs; however, users with inequa- lities that are single bounds on variables may wish to use WNNLS.

FC allows a user to fit dis- crete data, in a weighted least-squares sense, using piece-wise polynomial functions represented by B-splines on a given set of knots. In addition to the least-squares fitting of the data, equali- ty, inequality, and periodic constraints at a discrete, user-speci- fied set of points can be imposed on the fitted curve or its deriva- tives. The subprograms LSEI and WNNLS solve the linearly-constrained least-squares problem. LSEI solves the class of problem with general inequality constraints, and, if requested, obtains a covariance matrix of the solution parameters. WNNLS solves the class of problem with nonnegativity constraints. It is anticipated that most users will find LSEI suitable for their needs; however, users with inequa- lities that are single bounds on variables may wish to use WNNLS.

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4. METHOD OF SOLUTION

The discrete data are fit by a linear combina- tion of piece-wise polynomial curves which leads to a linear least- squares system of algebraic equations. Additional information is ex- pressed as a discrete set of linear inequality and equality cons- traints on the fitted curve which leads to a linearly-constrained least-squares system of algebraic equations. The solution of this system is the main computational problem solved.

The discrete data are fit by a linear combina- tion of piece-wise polynomial curves which leads to a linear least- squares system of algebraic equations. Additional information is ex- pressed as a discrete set of linear inequality and equality cons- traints on the fitted curve which leads to a linearly-constrained least-squares system of algebraic equations. The solution of this system is the main computational problem solved.

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6. TYPICAL RUNNING TIME

The sample driver required 0.3 seconds of CP time on a CDC6600, and less than 0.2 seconds of CP time on a CDC CYBER175.

The sample driver required 0.3 seconds of CP time on a CDC6600, and less than 0.2 seconds of CP time on a CDC CYBER175.

NESC0909/01

The test case included in this package was executed by NEA-DB on a CDC CYBER 830 computer in 0.5 seconds of CPU time.[ top ]

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10. REFERENCES

- Karen H. Haskell and Richard J. Hanson,

Selected Algorithms for the Linearly Constrained Least Squares

Problem - A User's Guide,

SAND78-1290, August 1979.

- Richard J. Hanson,

Constrained Least Squares Curve Fitting to Discrete Data Using B-

Splines - A Users Guide,

SAND78-1291, February 1979.

- FC,LSEI,WNNLS, NESC No. 909.6600, FC,LSEI,WNNLS Tape Description,

National Energy Software Center Note 81-37, May 21, 1981.

- Chuck L. Lawson, Richard J. Hanson, David R. Kincaid, and Fred T.

Krogh,

Basic Linear Algebra Subprograms for FORTRAN Usage,

SAND77-0898, October 1977 (also published in Association for Com-

puting Machinery, Transactions on Mathematical Software, Vol. 5,

No. 3, pp. 308-323, September 1979).

- C. de Boor,

Package for Calculating with B-Splines, Society for Industrial and Applied Mathematics Journal of Numerical Analysis, Vol. 14, No. 3, pp. 441-472, June 1977.

- Karen H. Haskell and Richard J. Hanson,

Selected Algorithms for the Linearly Constrained Least Squares

Problem - A User's Guide,

SAND78-1290, August 1979.

- Richard J. Hanson,

Constrained Least Squares Curve Fitting to Discrete Data Using B-

Splines - A Users Guide,

SAND78-1291, February 1979.

- FC,LSEI,WNNLS, NESC No. 909.6600, FC,LSEI,WNNLS Tape Description,

National Energy Software Center Note 81-37, May 21, 1981.

- Chuck L. Lawson, Richard J. Hanson, David R. Kincaid, and Fred T.

Krogh,

Basic Linear Algebra Subprograms for FORTRAN Usage,

SAND77-0898, October 1977 (also published in Association for Com-

puting Machinery, Transactions on Mathematical Software, Vol. 5,

No. 3, pp. 308-323, September 1979).

- C. de Boor,

Package for Calculating with B-Splines, Society for Industrial and Applied Mathematics Journal of Numerical Analysis, Vol. 14, No. 3, pp. 441-472, June 1977.

NESC0909/01, included references:

- Karen H. Haskell and Richard J. Hanson :Selected Algorithms for the Linearly Constrained Least Squares

Problem - A User's Guide

SAND78-1290 (August 1979)

- Richard J. Hanson :

Constrained Least Squares Curve Fitting to Discrete Data Using

B- Splines - A Users Guide

SAND78-1291 (February 1979)

- FC,LSEI,WNNLS Tape Description

NESC Note 81-37 (May 21, 1981)

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11. MACHINE REQUIREMENTS

37,000 (octal) words of storage are needed to execute the sample driver that is provided. The storage required is a linear function of the number of data points plus a quadratic function of the number of piecewise polynomial coefficients. The code is edited output produced by the FORTRAN preprocessor, FLECS.

37,000 (octal) words of storage are needed to execute the sample driver that is provided. The storage required is a linear function of the number of data points plus a quadratic function of the number of piecewise polynomial coefficients. The code is edited output produced by the FORTRAN preprocessor, FLECS.

NESC0909/01

60,000 (octal) words were required to run the test case on a CDC CYBER 830 computer.[ top ]

13. OPERATING SYSTEM UNDER WHICH PROGRAM IS EXECUTED

NOS 1.4 (CDC6600) SCOPE 2.1 (CDC7600), NOS 1.3 (CDC CYBER175).

NOS 1.4 (CDC6600) SCOPE 2.1 (CDC7600), NOS 1.3 (CDC CYBER175).

NESC0909/01

NOS2.5.1 (CDC CYBER 830).[ top ]

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NESC0909/01

File name | File description | Records |
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NESC0909_01.001 | Information file | 47 |

NESC0909_01.002 | JCL and control information | 13 |

NESC0909_01.003 | FC, LSEI, and WNNLS FORTRAN source | 5572 |

NESC0909_01.004 | Basic Linear Algebra Subprograms (BLAS) | 726 |

NESC0909_01.005 | Sample driver | 537 |

NESC0909_01.006 | Output sample problem | 80 |

Keywords: data processing, least square fit, numerical solution, optimization, polynomials, spline functions.