computer science

MINPACK

MINPACK is a computer science topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand MINPACK rather than just read about it. In short: MINPACK is a library of Fortran subroutines for the solving of systems of nonlinear equations, or the least-squares minimization of the residual of a set of linear or nonlinear equations. MINPACK, along with other similar libraries such as LINPACK and EISPACK, originated from the Mathematics and Computer Science Division Software (MCS) of Argonne National Laboratory.

Key takeaways

MINPACK belongs to computer science; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect MINPACK to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of MINPACK from memory before moving on to harder problems.

Reference excerpt

MINPACK is a library of Fortran subroutines for the solving of systems of nonlinear equations, or the least-squares minimization of the residual of a set of linear or nonlinear equations. MINPACK, along with other similar libraries such as LINPACK and EISPACK, originated from the Mathematics and Computer Science Division Software (MCS) of Argonne National Laboratory. Written by Jorge Moré, Burt Garbow, and Ken Hillstrom, MINPACK is free and designed to be highly portable, robust and reliable. The quality of its implementation of the Levenberg–Marquardt algorithm is attested by Dennis and Schnabel. Five algorithmic paths each include a core subroutine and a driver routine. The algorithms proceed either from an analytic specification of the Jacobian matrix or directly from the problem functions. The paths include facilities for systems of equations with a banded Jacobian matrix, for least-squares problems with a large amount of data, and for checking the consistency of the Jacobian matrix with the functions. MINPACK has become available in other languages via translations and wrappers, and remains widely used. For example, it is used in the SciPy package for its least-square solver, and has also been translated to C.

See also List of open-source mathematical libraries

References Maurice R. Garbow sr, and K. E. Hillstrom, User Guide for MINPACK-1, Argonne National Laboratory Report ANL-80-74, Argonne, Ill., 1980. J. J. Moré, D. C. Sorensen, K. E. Hillstrom, and Maurice R. Garbow sr, The MINPACK Project, in Sources and Development of Mathematical Software, W. J. Cowell, ed., Prentice-Hall, pages 88–111, 1984.

External links Netlib download site User Guide for MINPACK-1, Chapters 1 to 3, from J. J. Moré website User Guide for MINPACK-1, Chapter 4, from J. J. Moré website

Worked examples

Example 1 — a first encounter with MINPACK

Start with the simplest possible case. Write down what MINPACK claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In computer science, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to MINPACK before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about MINPACK ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of MINPACK

In research: MINPACK appears in computer science research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses MINPACK in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: MINPACK is common in secondary-school and first-year university syllabi. It links to neighbouring topics Fortran libraries, Numerical software, so understanding it makes those chapters shorter.
In everyday life: Look for MINPACK outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study MINPACK in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what MINPACK means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain MINPACK out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is MINPACK in simple terms?

Why does MINPACK matter?

Because it connects several computer science ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study MINPACK?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on MINPACK.