08-Jan-2022 09:02:57

pwl_product_integral_test():
  MATLAB/Octave version 9.8.0.1380330 (R2020a) Update 2
  Test pwl_product_integral().

pwl_PRODUCT_INTEGRAL_TEST01
  Test pwl_PRODUCT_INTEGRAL on a very simple problem.
  F and G are both defined over a single common
  interval, so that F(X) = G(X) = X.

           A           B      Integral        Exact

    1.000000    1.000000    0.000000        0.000000
    1.000000    2.000000    2.333333        2.333333
    1.000000    3.000000    8.666667        8.666667
    1.000000    4.000000   21.000000       21.000000
    1.000000    5.000000   41.333333       41.333333

pwl_PRODUCT_INTEGRAL_TEST02
  Test pwl_PRODUCT_INTEGRAL on a simple problem.
  F and G are both defined over separate, multiple
  intervals, but still true that F(X) = G(X) = X.

           A           B      Integral        Exact

    1.000000    1.000000        0.000000        0.000000
    1.000000    2.000000        2.333333        2.333333
    1.000000    3.000000        8.666667        8.666667
    1.000000    4.000000       21.000000       21.000000
    1.000000    5.000000       41.333333       41.333333

pwl_PRODUCT_INTEGRAL_TEST03
  Test pwl_PRODUCT_INTEGRAL on a simple problem.
  F and G are defined over separate, multiple
  intervals.

  F(X) interpolates SIN(X),
  G(X) interpolates 2*COS(X).

  We compare:

  INTEGRAL, our value for the integral,
  QUAD, a quadrature estimate for the integral, and
  CLOSE, the value of the integral of 2*COS(X)*SIN(X)

           A           B      Integral        Quad            Close

    0.000000    0.000000        0.000000        0.000000       -0.000000
    0.000000    0.523599        0.247447        0.247447        0.250000
    0.000000    1.047198        0.743259        0.743259        0.750000
    0.000000    1.570796        0.990786        0.990786        1.000000
    0.000000    2.094395        0.743259        0.743259        0.750000
    0.000000    2.617994        0.247447        0.247447        0.250000
    0.000000    3.141593       -0.000000        0.000000       -0.000000

pwl_PRODUCT_INTEGRAL_TEST04
  Test pwl_PRODUCT_INTEGRAL.
  The nodes are at 0, 1, and 2.
  F(X) = ( 0, 1, 0 ).
  G(X) = ( 1, 0, 0 ).

  Integral F(X) * F(X) dx = 0.666667
  Integral F(X) * G(X) dx = 0.166667
  Integral G(X) * G(X) dx = 0.333333

pwl_product_integral_test():
  Normal end of execution.

08-Jan-2022 09:02:57