26 April 2024 8:20:08.763 AM polynomial_conversion_test(): Fortran90 version Test polynomial_conversion(). bernstein_to_legendre01_test ( ): bernstein_to_legendre01() converts a polynomial from Bernstein form to Legendre01 form. P010 P011 P012 P013 P014 P015 P016 B0(x) = 1.000 B1(x) = 0.500 0.500 B2(x) = 0.333 0.500 0.167 B3(x) = 0.250 0.450 0.250 0.050 B4(x) = 0.200 0.400 0.286 0.100 0.014 B5(x) = 0.167 0.357 0.298 0.139 0.036 0.004 B6(x) = 0.143 0.321 0.298 0.167 0.058 0.012 0.001 bernstein_to_legendre01_matrix_test ( ): bernstein_to_legendre01_matrix() returns the matrix which converts a polynomial from Bernstein form to Legendre01 form. A: 0.1667 0.1667 0.1667 0.1667 0.1667 0.1667 -0.3571 -0.2143 -0.0714 0.0714 0.2143 0.3571 0.2976 -0.0595 -0.2381 -0.2381 -0.0595 0.2976 -0.1389 0.1944 0.1111 -0.1111 -0.1944 0.1389 0.0357 -0.1071 0.0714 0.0714 -0.1071 0.0357 -0.0040 0.0198 -0.0397 0.0397 -0.0198 0.0040 legendre01_to_bernstein_test ( ): legendre01_to_bernstein() converts a polynomial from Legendre01 form to Bernstein form. B0(x) B1(x) B2(x) B3(x) B4(x) B5(x) B6(x) P010 = 1.00 P011 = -1.00 1.00 P012 = 1.00 -2.00 1.00 P013 = -1.00 3.00 -3.00 1.00 P014 = 1.00 -4.00 6.00 -4.00 1.00 P015 = -1.00 5.00 -10.00 10.00 -5.00 1.00 P016 = 1.00 -6.00 15.00 -20.00 15.00 -6.00 1.00 legendre01_to_bernstein_matrix_test ( ): legendre01_to_bernstein_matrix() returns the matrix which converts a polynomial from Legendre01 form to Bernstein form. A: 1.0000 -1.0000 1.0000 -1.0000 1.0000 -1.0000 1.0000 -0.6000 -0.2000 1.4000 -3.0000 5.0000 1.0000 -0.2000 -0.8000 0.8000 2.0000 -10.0000 1.0000 0.2000 -0.8000 -0.8000 2.0000 10.0000 1.0000 0.6000 -0.2000 -1.4000 -3.0000 -5.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 bernstein_legendre01_bernstein_test ( ): Convert a polynomial from Bernstein form to legendre01 form and back. L2 difference = 0.581045E-11 bernstein_to_monomial_test ( ): bernstein_to_monomial() converts a polynomial from Bernstein form to monomial form. X**0 X**1 X**2 X**3 X**4 X**5 X**6 B0(x) = 1.000 B1(x) = -1.000 1.000 B2(x) = 1.000 -2.000 1.000 B3(x) = -1.000 3.000 -3.000 1.000 B4(x) = 1.000 -4.000 6.000 -4.000 1.000 B5(x) = -1.000 5.000 -10.000 10.000 -5.000 1.000 B6(x) = 1.000 -6.000 15.000 -20.000 15.000 -6.000 1.000 bernstein_to_monomial_matrix_test ( ): bernstein_to_monomial_matrix() returns the matrix which converts a polynomial from Bernstein form to monomial form. A: 1.0000 -4.0000 6.0000 -4.0000 1.0000 0.0000 4.0000 -12.0000 12.0000 -4.0000 0.0000 0.0000 6.0000 -12.0000 6.0000 0.0000 0.0000 0.0000 4.0000 -4.0000 0.0000 0.0000 0.0000 0.0000 1.0000 monomial_to_bernstein_test ( ): monomial_to_bernstein() converts a polynomial from monomial form to Bernstein form. B0(x) B1(x) B2(x) B3(x) B4(x) B5(x) B6(x) X**0 = 1.00000 X**1 = 1.00000 1.00000 X**2 = 1.00000 1.00000 1.00000 X**3 = 1.00000 1.00000 1.00000 1.00000 X**4 = 1.00000 1.00000 1.00000 1.00000 1.00000 X**5 = 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 X**6 = 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 monomial_to_bernstein_matrix_test ( ): monomial_to_bernstein_matrix() returns the matrix which converts a polynomial from monomial form to Bernstein form. A: 1.0000 1.0000 1.0000 1.0000 1.0000 0.0000 0.2500 0.5000 0.7500 1.0000 0.0000 0.0000 0.1667 0.5000 1.0000 0.0000 0.0000 0.0000 0.2500 1.0000 0.0000 0.0000 0.0000 0.0000 1.0000 bernstein_monomial_bernstein_test ( ): Convert a polynomial from Bernstein form to monomial form and back. L2 difference = 0.141857E-11 chebyshev_to_monomial_test ( ): chebyshev_to_monomial() converts a polynomial from Chebyshev form to monomial form. X**0 X**1 X**2 X**3 X**4 X**5 X**6 T0(x) = 1.000 T1(x) = 0.000 1.000 T2(x) = -1.000 0.000 2.000 T3(x) = 0.000 -3.000 0.000 4.000 T4(x) = 1.000 0.000 -8.000 0.000 8.000 T5(x) = 0.000 5.000 0.000 -20.000 0.000 16.000 T6(x) = -1.000 0.000 18.000 0.000 -48.000 0.000 32.000 monomial_to_chebyshev_test ( ): monomial_to_chebyshev() converts a polynomial from monomial form to Chebyshev form. T0(x) T1(x) T2(x) T3(x) T4(x) T5(x) T6(x) X**0 = 2.00000 X**1 = 0.00000 1.00000 X**2 = 0.50000 0.00000 0.50000 X**3 = 0.00000 0.75000 0.00000 0.25000 X**4 = 0.37500 0.00000 0.50000 0.00000 0.12500 X**5 = 0.00000 0.62500 0.00000 0.31250 0.00000 0.06250 X**6 = 0.31250 0.00000 0.46875 0.00000 0.18750 0.00000 0.03125 chebyshev_monomial_chebyshev_test ( ): Convert a polynomial from Chebyshev form to monomial form and back. L2 difference = 0.384593E-15 gegenbauer_to_monomial_test ( ): gegenbauer_to_monomial() converts a polynomial from Gegenbauer form to monomial form. Gegenbauer parameter = 0.500000 X**0 X**1 X**2 X**3 X**4 X**5 X**6 C0(x) = 1.000 C1(x) = 0.000 1.000 C2(x) = -0.500 0.000 1.500 C3(x) = 0.000 -1.500 0.000 2.500 C4(x) = 0.375 0.000 -3.750 0.000 4.375 C5(x) = 0.000 1.875 0.000 -8.750 0.000 7.875 C6(x) = -0.312 0.000 6.562 0.000 -19.687 0.000 14.438 gegenbauer_to_monomial_matrix_test ( ): gegenbauer_to_monomial_matrix() returns the matrix which converts a polynomial from Gegenbauer form to monomial form. A: 1.0000 0.0000 -0.5000 0.0000 0.3750 0.0000 1.0000 0.0000 -1.5000 0.0000 0.0000 0.0000 1.5000 0.0000 -3.7500 0.0000 0.0000 0.0000 2.5000 0.0000 0.0000 0.0000 0.0000 0.0000 4.3750 monomial_to_gegenbauer_test ( ): monomial_to_gegenbauer() converts a polynomial from monomial form to Gegenbauer form. Gegenbauer parameter = 0.500000 C0(x) C1(x) C2(x) C3(x) C4(x) C5(x) C6(x) X**0 = 1.00000 X**1 = 0.00000 1.00000 X**2 = 0.33333 0.00000 0.66667 X**3 = 0.00000 0.60000 0.00000 0.40000 X**4 = 0.20000 0.00000 0.57143 0.00000 0.22857 X**5 = 0.00000 0.42857 0.00000 0.44444 0.00000 0.12698 X**6 = 0.14286 0.00000 0.47619 0.00000 0.31169 0.00000 0.06926 monomial_to_gegenbauer_matrix_test ( ): monomial_to_gegenbauer_matrix() returns the matrix which converts a polynomial from monomial form to Gegenbauer form. Gegenbauer parameter = 0.500000 A: 1.0000 0.0000 0.3333 0.0000 0.2000 0.0000 1.0000 0.0000 0.6000 0.0000 0.0000 0.0000 0.6667 0.0000 0.5714 0.0000 0.0000 0.0000 0.4000 0.0000 0.0000 0.0000 0.0000 0.0000 0.2286 gegenbauer_monomial_gegenbauer_test ( ): Convert a polynomial from Gegenbauer form to monomial form and back. Gegenbauer parameter = 0.500000 L2 difference = 0.171251E-13 hermite_to_monomial_test ( ): hermite_to_monomial() converts a polynomial from Hermite form to monomial form. X**0 X**1 X**2 X**3 X**4 X**5 X**6 H0(x) = 1.000 H1(x) = 0.000 2.000 H2(x) = -2.000 0.000 4.000 H3(x) = 0.000 -12.000 0.000 8.000 H4(x) = 12.000 0.000 -48.000 0.000 16.000 H5(x) = 0.000 120.000 0.000-160.000 0.000 32.000 H6(x) = -120.000 0.000 720.000 0.000-480.000 0.000 64.000 hermite_to_monomial_matrix_test ( ): hermite_to_monomial_matrix() returns the matrix which converts a polynomial from Hermite form to monomial form. A: 1.0000 0.0000 -2.0000 -0.0000 12.0000 0.0000 2.0000 0.0000 -12.0000 -0.0000 0.0000 0.0000 4.0000 0.0000 -48.0000 0.0000 0.0000 0.0000 8.0000 0.0000 0.0000 0.0000 0.0000 0.0000 16.0000 monomial_to_hermite_test ( ): monomial_to_hermite() converts a polynomial from monomial form to Hermite form. H0(x) H1(x) H2(x) H3(x) H4(x) H5(x) H6(x) X**0 = 1.00000 X**1 = 0.00000 0.50000 X**2 = 0.50000 0.00000 0.25000 X**3 = 0.00000 0.75000 0.00000 0.12500 X**4 = 0.75000 0.00000 0.75000 0.00000 0.06250 X**5 = 0.00000 1.87500 0.00000 0.62500 0.00000 0.03125 X**6 = 1.87500 0.00000 2.81250 0.00000 0.46875 0.00000 0.01562 monomial_to_hermite_matrix_test ( ): monomial_to_hermite_matrix() returns the matrix which converts a polynomial from monomial form to Hermite form. A: 1.0000 0.0000 0.5000 0.0000 0.7500 0.0000 0.5000 0.0000 0.7500 0.0000 0.0000 0.0000 0.2500 0.0000 0.7500 0.0000 0.0000 0.0000 0.1250 0.0000 0.0000 0.0000 0.0000 0.0000 0.0625 hermite_monomial_hermite_test ( ): Convert a polynomial from Hermite form to monomial form and back. L2 difference = 0.101353E-11 laguerre_to_monomial_test ( ): laguerre_to_monomial() converts a polynomial from Laguerre form to monomial form. X**0 X**1 X**2 X**3 X**4 X**5 X**6 L0(x) = 1.000 L1(x) = 1.000 -1.000 L2(x) = 1.000 -2.000 0.500 L3(x) = 1.000 -3.000 1.500 -0.167 L4(x) = 1.000 -4.000 3.000 -0.667 0.042 L5(x) = 1.000 -5.000 5.000 -1.667 0.208 -0.008 L6(x) = 1.000 -6.000 7.500 -3.333 0.625 -0.050 0.001 laguerre_to_monomial_matrix_test ( ): laguerre_to_monomial_matrix() returns the matrix which converts a polynomial from Laguerre form to monomial form. A: 1.0000 1.0000 1.0000 1.0000 1.0000 0.0000 -1.0000 -2.0000 -3.0000 -4.0000 0.0000 0.0000 0.5000 1.5000 3.0000 0.0000 0.0000 0.0000 -0.1667 -0.6667 0.0000 0.0000 0.0000 0.0000 0.0417 monomial_to_laguerre_test ( ): monomial_to_laguerre() converts a polynomial from monomial form to Laguerre form. L0(x) L1(x) L2(x) L3(x) L4(x) L5(x) L6(x) X**0 = 1.000 X**1 = 1.000 -1.000 X**2 = 2.000 -4.000 2.000 X**3 = 6.000 -18.00 18.00 -6.000 X**4 = 24.00 -96.00 144.0 -96.00 24.00 X**5 = 120.0 -600.0 1200. -1200. 600.0 -120.0 X**6 = 720.0 -4320. 0.1080E+05 -0.1440E+05 0.1080E+05 -4320. 720.0 monomial_to_laguerre_matrix_test ( ): monomial_to_laguerre_matrix() returns the matrix which converts a polynomial from monomial form to Laguerre form. A: 1.0000 1.0000 2.0000 6.0000 24.0000 0.0000 -1.0000 -4.0000 -18.0000 -96.0000 0.0000 0.0000 2.0000 18.0000 144.0000 0.0000 0.0000 0.0000 -6.0000 -96.0000 0.0000 0.0000 0.0000 0.0000 24.0000 laguerre_monomial_laguerre_test ( ): Convert a polynomial from Laguerre form to monomial form and back. L2 difference = 0.288274E-12 legendre_to_monomial_test ( ): legendre_to_monomial() converts a polynomial from Legendre form to monomial form. X**0 X**1 X**2 X**3 X**4 X**5 X**6 P0(x) = 1.000 P1(x) = 0.000 1.000 P2(x) = -0.500 0.000 1.500 P3(x) = 0.000 -1.500 0.000 2.500 P4(x) = 0.375 0.000 -3.750 0.000 4.375 P5(x) = 0.000 1.875 0.000 -8.750 0.000 7.875 P6(x) = -0.312 0.000 6.562 0.000 -19.688 0.000 14.438 legendre_to_monomial_matrix_test ( ): legendre_to_monomial_matrix() returns the matrix which converts a polynomial from Legendre form to monomial form. A: 1.0000 0.0000 -0.5000 -0.0000 0.3750 0.0000 1.0000 0.0000 -1.5000 -0.0000 0.0000 0.0000 1.5000 0.0000 -3.7500 0.0000 0.0000 0.0000 2.5000 0.0000 0.0000 0.0000 0.0000 0.0000 4.3750 monomial_to_legendre_test ( ): monomial_to_legendre() converts a polynomial from monomial form to Legendre form. P0(x) P1(x) P2(x) P3(x) P4(x) P5(x) P6(x) X**0 = 1.00000 X**1 = 0.00000 1.00000 X**2 = 0.33333 0.00000 0.66667 X**3 = 0.00000 0.60000 0.00000 0.40000 X**4 = 0.20000 0.00000 0.57143 0.00000 0.22857 X**5 = 0.00000 0.42857 0.00000 0.44444 0.00000 0.12698 X**6 = 0.14286 0.00000 0.47619 0.00000 0.31169 0.00000 0.06926 monomial_to_legendre_matrix_test ( ): monomial_to_legendre_matrix() returns the matrix which converts a polynomial from monomial form to Legendre_matrix form. A: 1.0000 0.0000 0.3333 0.0000 0.2000 0.0000 1.0000 0.0000 0.6000 0.0000 0.0000 0.0000 0.6667 0.0000 0.5714 0.0000 0.0000 0.0000 0.4000 0.0000 0.0000 0.0000 0.0000 0.0000 0.2286 legendre_monomial_legendre_test ( ): Convert a polynomial from Legendre form to monomial form and back. L2 difference = 0.182984E-13 polynomial_conversion_test(): Normal end of execution. 26 April 2024 8:20:08.763 AM