26-Apr-2024 12:41:58 polynomial_conversion_test(): MATLAB/Octave version 6.4.0 Test polynomial_conversion(). bernstein_to_legendre01_test ( ) bernstein_to_legendre01() converts a polynomial from Bernstein form to Legendre01 form. X^0 X^1 X^2 X^3 X^4 X^5 X^6 P010(x) = 1.000 P011(x) = 0.500 0.500 P012(x) = 0.333 0.500 0.167 P013(x) = 0.250 0.450 0.250 0.050 P014(x) = 0.200 0.400 0.286 0.100 0.014 P015(x) = 0.167 0.357 0.298 0.139 0.036 0.004 P016(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 Legendre[0,1] form. 0.2000 0.2000 0.2000 0.2000 0.2000 -0.4000 -0.2000 0 0.2000 0.4000 0.2857 -0.1429 -0.2857 -0.1429 0.2857 -0.1000 0.2000 0 -0.2000 0.1000 0.0143 -0.0571 0.0857 -0.0571 0.0143 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(X) = 1.00000 P011(X) = -1.00000 1.00000 P012(X) = 1.00000 -2.00000 1.00000 P013(X) = -1.00000 3.00000 -3.00000 1.00000 P014(X) = 1.00000 -4.00000 6.00000 -4.00000 1.00000 P015(X) = -1.00000 5.00000 -10.00000 10.00000 -5.00000 1.00000 P016(X) = 1.00000 -6.00000 15.00000 -20.00000 15.00000 -6.00000 1.00000 legendre01_to_bernstein_matrix_test ( ) legendre01_to_bernstein_matrix() returns the matrix which converts a polynomial from Legendre[0,1] form to Bernstein form. 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 = 1.59467e-12 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. 1 -4 6 -4 1 0 4 -12 12 -4 0 0 6 -12 6 0 0 0 4 -4 0 0 0 0 1 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. 1.0000 1.0000 1.0000 1.0000 1.0000 0 0.2500 0.5000 0.7500 1.0000 0 0 0.1667 0.5000 1.0000 0 0 0 0.2500 1.0000 0 0 0 0 1.0000 bernstein_monomial_bernstein_test ( ) Convert a polynomial from Bernstein form to monomial form and back. L2 difference = 1.05086e-14 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 = 4.51794e-15 gegenbauer_to_monomial_test ( ) gegenbauer_to_monomial() converts a polynomial from Gegenbauer form to monomial form. Gegenbauer parameter = 0.5 X^0 X^1 X^2 X^3 X^4 X^5 X^6 H0(x) = 1.000 H1(x) = 0.000 1.000 H2(x) = -0.500 0.000 1.500 H3(x) = 0.000 -1.500 0.000 2.500 H4(x) = 0.375 0.000 -3.750 0.000 4.375 H5(x) = 0.000 1.875 0.000 -8.750 0.000 7.875 H6(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. alpha = 0.5 1.0000 0 -0.5000 0 0.3750 0 1.0000 0 -1.5000 0 0 0 1.5000 0 -3.7500 0 0 0 2.5000 0 0 0 0 0 4.3750 monomial_to_gegenbauer_test ( ) monomial_to_gegenbauer() converts a polynomial from monomial form to Gegenbauer form. Gegenbauer parameter = 0.5 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 = 0.5 1.0000 0 0.3333 0 0.2000 0 1.0000 0 0.6000 0 0 0 0.6667 0 0.5714 0 0 0 0.4000 0 0 0 0 0 0.2286 gegenbauer_monomial_gegenbauer_test ( ) Convert a polynomial from Gegenbauer form to monomial form and back. Gegenbauer parameter alpha = 0.5 L2 difference = 2.09176e-14 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. 1 0 -2 0 12 0 2 0 -12 0 0 0 4 0 -48 0 0 0 8 0 0 0 0 0 16 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. 1.0000 0 0.5000 0 0.7500 0 0.5000 0 0.7500 0 0 0 0.2500 0 0.7500 0 0 0 0.1250 0 0 0 0 0 0.0625 hermite_monomial_hermite_test ( ) Convert a polynomial from Hermite form to monomial form and back. L2 difference = 9.65052e-12 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. 1.0000 1.0000 1.0000 1.0000 1.0000 0 -1.0000 -2.0000 -3.0000 -4.0000 0 0 0.5000 1.5000 3.0000 0 0 0 -0.1667 -0.6667 0 0 0 0 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 = 1.0 X^1 = 1.0 -1.0 X^2 = 2.0 -4.0 2.0 X^3 = 6.0 -18.0 18.0 -6.0 X^4 = 24.0 -96.0 144.0 -96.0 24.0 X^5 = 120.0 -600.0 1200.0 -1200.0 600.0 -120.0 X^6 = 720.0 -4320.0 10800.0 -14400.0 10800.0 -4320.0 720.0 monomial_to_laguerre_matrix_test ( ) monomial_to_laguerre_matrix() returns the matrix which converts a polynomial from monomial form to Laguerre form. 1 1 2 6 24 0 -1 -4 -18 -96 0 0 2 18 144 0 0 0 -6 -96 0 0 0 0 24 laguerre_monomial_laguerre_test ( ) Convert a polynomial from Laguerre form to monomial form and back. L2 difference = 2.01529e-13 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. 1.0000 0 -0.5000 0 0.3750 0 1.0000 0 -1.5000 0 0 0 1.5000 0 -3.7500 0 0 0 2.5000 0 0 0 0 0 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 form. 1.0000 0 0.3333 0 0 1.0000 0 0.6000 0 0 0.6667 0 0 0 0 0.4000 legendre_monomial_legendre_test ( ) Convert a polynomial from Legendre form to monomial form and back. L2 difference = 2.04086e-14 polynomial_conversion_test ( ) Normal end of execution. 26-Apr-2024 12:41:58