# test_int

test_int, an Octave code which evaluates test integrands.

The test integrands would normally be used to testing one dimensional quadrature software. It is possible to invoke a particular function by number, or to try out all available functions, as demonstrated in the sample calling program.

The library includes not just the integrand, but also the interval of integration, and the exact value of the integral. Thus, for each integrand function, three subroutines are supplied. For instance, for function #9, we have the routines:

• P09_FUN evaluates the integrand for problem 9.
• P09_LIM returns the integration limits for problem 9.
• P09_EXACT returns the exact integral for problem 9.
So once you have the calling sequences for these routines, you can easily evaluate the function, or integrate it between the appropriate limits, or compare your estimate of the integral to the exact value.

Moreover, since the same interface is used for each function, if you wish to work with problem 16 instead, you simply change the "09" to "16" in your routine calls.

If you wish to call all of the functions, then you simply use the generic interface, which again has three subroutines, but which requires you to specify the problem number as an extra input argument:

• P00_FUN evaluates the integrand for any problem.
• P00_LIM returns the integration limits for any problem.
• P00_EXACT returns the exact integral for any problem.

Finally, some demonstration routines are built in for simple quadrature methods. These routines include

• P00_GAUSS_LEGENDRE
• P00_EVEN
• P00_HALTON
• P00_MIDPOINT
• P00_MONTECARLO
• P00_SIMPSON
• P00_TRAPEZOID
and can be used with any of the sample integrands.

### Languages:

test_int is available in a C version and a C++ version and a Fortran90 version and a MATLAB version and an Octave version and a Python version.

### Related Data and Programs:

test_int_2d, an Octave code which defines test integrands for 2D quadrature rules.

### Reference:

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An Introduction to Numerical Analysis,
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LC: QA297.A94.1989.
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Algorithm 446: Ten Subroutines for the Manipulation of Chebyshev Series,
Communications of the ACM,
Volume 16, 1973, pages 254-256.
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A Method for Numerical Integration on an Automatic Computer,
Numerische Mathematik,
Volume 2, Number 1, December 1960, pages 197-205.
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Projects in Scientific Computing,
Springer, 2005,
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LC: Q183.9.C733.
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Methods of Numerical Integration,
Second Edition,
Dover, 2007,
ISBN: 0486453391,
LC: QA299.3.D28.
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LC: QA299.3E5.
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Chebyshev Polynomials in Numerical Analysis,
Oxford Press, 1968,
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On the efficiency of certain quasi-random sequences of points in evaluating multi-dimensional integrals,
Numerische Mathematik,
Volume 2, Number 1, December 1960, pages 84-90.
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Computer Approximations,
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in Mathematical Software,
edited by John Rice,
ISBN: 012587250X,
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QUADPACK: A Subroutine Package for Automatic Integration,
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LC: QA299.3.Q36.
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Table of a Weierstrass Continuous Nondifferentiable Function,
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