Quadrature test



Keywords: quadrature test
Description: QUADRATURE_TEST is a MATLAB program which reads three files that define a quadrature rule, applies the quadrature rule to a set of test integrals, and reports the results. The quadrature rule is

QUADRATURE_TEST is a MATLAB program which reads three files that define a quadrature rule, applies the quadrature rule to a set of test integrals, and reports the results.

The quadrature rule is defined by three text files:
  1. the "X" file lists the abscissas (N rows, M columns);
  2. the "W" file lists the weights (N rows);
  3. the "R" file lists the integration region corners (2 rows, M columns);
For more on quadrature rules, see the QUADRATURE_RULES listing below. The list of integrand functions includes:
  1. f(x) = ( sum ( x(1:m) ) )**2;
  2. f(x) = ( sum ( 2 * x(1:m) - 1 ) )**4;
  3. f(x) = ( sum ( x(1:m) ) )**5;
  4. f(x) = ( sum ( 2 * x(1:m) - 1 ) )**6;
  5. f(x) = 1 / ( 1 + sum ( 2 * x(1:m) ) );
  6. f(x) = product ( 2 * abs ( 2 * x(1:m) - 1 ) );
  7. f(x) = product ( pi / 2 ) * sin ( pi * x(1:m) );
  8. f(x) = ( sin ( (pi/4) * sum ( x(1:m) ) ) )**2;
  9. f(x) = exp ( sum ( c(1:m) * x(1:m) ) );
  10. f(x) = sum ( abs ( x(1:m) - 0.5 ) );
  11. f(x) = exp ( sum ( abs ( 2 * x(1:m) - 1 ) ) );
  12. f(x) = product ( 1 quadrature_test ( 'prefix ' ) where prefix the common prefix for the files containing the abscissa (X), weight (W) and region (R) information of the quadrature rule;

The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.

NINT_EXACTNESS. a MATLAB program which demonstrates how to measure the polynomial exactness of a multidimensional quadrature rule.

QUADRATURE_RULES. a dataset directory which contains a description and examples of quadrature rules defined by a set of "X", "W" and "R" files.

QUADRATURE_TEST_2D. a MATLAB program which reads files defining a 2D quadrature rule, and applies them to all the test integrals defined by TEST_INT_2D.

STROUD. a MATLAB library which contains quadrature rules for a variety of unusual areas, surfaces and volumes in 2D, 3D and N-dimensions.

TEST_NINT. a MATLAB library which defines a set of integrand functions to be used for testing multidimensional quadrature rules and routines.

TESTPACK. a MATLAB library which defines a set of integrands used to test multidimensional quadrature.

Chebyshev Approximations for the Natural Logarithm of the Gamma Function, Mathematics of Computation,

Volume 5016, 2003, pages 161-172.
  • John Hart, Ward Cheney, Charles Lawson, Hans Maehly, Charles Mesztenyi, John Rice, Henry Thatcher, Christoph Witzgall, CC_D6_LEVEL3 is a Clenshaw-Curtis sparse grid quadrature rule in dimension 6 of level 3, 389 points.
    • cc_d6_level3_x.txt. the "X" file.
    • cc_d6_level3_w.txt. the "W" file.
    • cc_d6_level3_r.txt. the "R" file.
    • cc_d6_level3_test.txt. the test results.
    CC_D6_LEVEL4 is a Clenshaw-Curtis sparse grid quadrature rule in dimension 6 of level 4, 1457 points.
    • cc_d6_level4_x.txt. the "X" file.
    • cc_d6_level4_w.txt. the "W" file.
    • cc_d6_level4_r.txt. the "R" file.
    • cc_d6_level4_test.txt. the test results.
    CC_D6_LEVEL5 is a Clenshaw-Curtis sparse grid quadrature rule in dimension 6 of level 5, 4865 points.
    • cc_d6_level5_x.txt. the "X" file.
    • cc_d6_level5_w.txt. the "W" file.
    • cc_d6_level5_r.txt. the "R" file.
    • cc_d6_level5_test.txt. the test results.






    Photogallery Quadrature test:


    Stereo test tone oscillator.jpg


    hpGEM: tests/unit/Integration/QuadratureRules ...


    Encoder Test Jig


    Untitled Document


    hpGEM: tests/unit/Integration/QuadratureRules ...


    Ensemble RX II Builders' Notes


    Assess Quadrature-Demodulator Noise Figure Using Vector Signal ...


    Manuval


    Em ii lab manual 28.10.08 latest


    MARS SDR Buildathon - Elmer Stations


    VHDL code for quadrature encoder receiver module | Dew.Ninja


    Doubly Adaptive Quadrature Routines Based on NewtonCotes Rules ...


    TRF3722 | IQ Modulator | Broadband RF/IF | Online datasheet


    A discussion of a new error estimate for adaptive quadrature ...


    Ensemble II VHF RX Builders' Notes


    Quadrature and the development of orientation selective cortical ...


    Linear v Quadrature coils - Questions and Answers in MRI


    Analysis and design of quadrature oscillators


    Amplitude modulated pseudo random binary signal | Home Repair


    Ies electrical engineering - electrical machines