30 April 2009 11:19:57 AM PIECEWISE_LINEAR_PRODUCT_INTEGRAL_PRB C++ version Tests for PIECEWISE_LINEAR_PRODUCT_INTEGRAL. TEST01 Test PIECEWISE_LINEAR_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 1 0 0 1 2 2.33333 2.33333 1 3 8.66667 8.66667 1 4 21 21 1 5 41.3333 41.3333 TEST02 Test PIECEWISE_LINEAR_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 1 0 0 1 2 2.33333 2.33333 1 3 8.66667 8.66667 1 4 21 21 1 5 41.3333 41.3333 TEST03 Test PIECEWISE_LINEAR_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 0 0 0 -0 0 0.523599 0.247447 0.247447 0.25 0 1.0472 0.743259 0.743259 0.75 0 1.5708 0.990786 0.990786 1 0 2.0944 0.743259 0.743259 0.75 0 2.61799 0.247447 0.247447 0.25 0 3.14159 -2.56739e-15 4.23652e-16 -0 TEST04 Test PIECEWISE_LINEAR_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 PIECEWISE_LINEAR_PRODUCT_INTEGRAL_PRB Normal end of execution. 30 April 2009 11:19:57 AM