TEST_INT_2D\
Quadrature Tests for 2D Finite Intervals {#test_int_2d-quadrature-tests-for-2d-finite-intervals align=”center”}
========================================
TEST_INT_2D is a C++ program which evaluates test integrands.
The test integrands would normally be used to testing 2D 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 current set of problems is:
- integral on [0,1]x[0,1] of f(x,y) = 1 / ( 1 - x * y ); singular
at [1,1].
- integral on [-1,1]x[-1,1] of f(x,y) = 1 / sqrt ( 1 - x * x *
y * y ); singular at [1,1], [1,-1], [-1,1], [-1,-1];
- integral on [-1,1]x[-1,1] of f(x,y) = 1 / sqrt ( 2 - x - y );
singular at [1,1];
- integral on [-1,1]x[-1,1] of f(x,y) = 1 / sqrt ( 3 - x - 2 * y
); singular along the line y = ( 3 - x ) / 2.
- integral on [0,1]x[0,1] of f(x,y) = sqrt ( x * y ); singular
along the lines y = 0 and x = 0.
- integral on [-1,1]x[-1,1] of f(x,y) = abs ( x * x + y * y -
1/4 ); nondifferentiable along x*x+y*y=1/4.
- integral on [0,1]x[0,1] of f(x,y) = sqrt ( abs ( x - y ) );
nondifferentiable along y = x.
- integral on [0,5]x[0,5] of f(x,y) = exp ( - ( (x-4)\^2 +
(y-1)\^2 ) ), highly localized near (4,1).
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 #5, we have the routines:
- P05_FUN evaluates the integrand for problem 5.
- P05_LIM returns the integration limits for problem 5.
- P05_EXACT returns the exact integral for problem 5.
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 2 instead, you simply change the “05” to “02”
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.
Licensing: {#licensing align=”center”}
The computer code and data files described and made available on this
web page are distributed under the GNU LGPL
license.
Languages: {#languages align=”center”}
TEST_INT_2D is available in a C
version and a C++
version and a FORTRAN90
version and a FORTRAN77
version and a MATLAB
version.
TEST_INT, a C++ library which
defines test integrands for 1D quadrature rules.
TEST_INT_HERMITE,
a C++ library which defines some test integration problems over infinite
intervals.
TEST_INT_LAGUERRE,
a C++ library which defines test integrands for integration over
[ALPHA,+oo).
Reference: {#reference align=”center”}
- Gwynne Evans,\
Practical Numerical Integration,\
Wiley, 1993,\
ISBN: 047193898X,\
LC: QA299.3E93.
Source Code: {#source-code align=”center”}
Examples and Tests: {#examples-and-tests align=”center”}
List of Routines: {#list-of-routines align=”center”}
- LEGENDRE_DR_COMPUTE: Gauss-Legendre quadrature by
Davis-Rabinowitz method.
- P00_EXACT returns the exact integral for any problem.
- P00_FUN evaluates the integrand for any problem.
- P00_LIM returns the integration limits for any problem.
- P00_PROBLEM_NUM returns the number of test integration
problems.
- P01_EXACT returns the exact integral for problem 1.
- P01_FUN evaluates the integrand for problem 1.
- P01_LIM returns the integration limits for problem 1.
- P02_EXACT returns the exact integral for problem 2.
- P02_FUN evaluates the integrand for problem 2.
- P02_LIM returns the integration limits for problem 2.
- P03_EXACT returns the exact integral for problem 3.
- P03_FUN evaluates the integrand for problem 3.
- P03_LIM returns the integration limits for problem 3.
- P04_EXACT returns the exact integral for problem 4.
- P04_FUN evaluates the integrand for problem 4.
- P04_LIM returns the integration limits for problem 4.
- P05_EXACT returns the exact integral for problem 5.
- P05_FUN evaluates the integrand for problem 5.
- P05_LIM returns the integration limits for problem 5.
- P06_EXACT returns the exact integral for problem 6.
- P06_FUN evaluates the integrand for problem 6.
- P06_LIM returns the integration limits for problem 6.
- P07_EXACT returns the exact integral for problem 7.
- P07_FUN evaluates the integrand for problem 7.
- P07_LIM returns the integration limits for problem 7.
- P08_EXACT returns the exact integral for problem 8.
- P08_FUN evaluates the integrand for problem 8.
- P08_LIM returns the integration limits for problem 8.
- R8_ABS returns the absolute value of an R8.
- R8_CSEVL evaluates a Chebyshev series.
- R8_ERF evaluates the error function of an R8 argument.
- R8_ERFC evaluates the co-error function of an R8 argument.
- R8_INITS initializes a Chebyshev series.
- R8_MACH returns double precision real machine constants.
- R8MAT_UNIFORM_01 returns a unit pseudorandom R8MAT.
- R8VEC_SUM returns the sum of an R8VEC.
- TIMESTAMP prints the current YMDHMS date as a time stamp.
You can go up one level to the C++ source codes.
Last revised on 18 September 2011.