Fri Apr 26 13:29:11 2024 polynomial_conversion_test(): python version: 3.10.12 numpy version: 1.26.4 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) = -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_legendre01_matrix_test ( ): bernstein_to_legendre01_matrix() returns the matrix which maps polynomial coefficients from Bernstein form to Legendre01 form. [[ 0.2 0.2 0.2 0.2 0.2 ] [-0.4 -0.2 0. 0.2 0.4 ] [ 0.28571429 -0.14285714 -0.28571429 -0.14285714 0.28571429] [-0.1 0.2 0. -0.2 0.1 ] [ 0.01428571 -0.05714286 0.08571429 -0.05714286 0.01428571]] 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) = 1.000 P011(x) = -1.000 1.000 P012(x) = 1.000 -2.000 1.000 P013(x) = -1.000 3.000 -3.000 1.000 P014(x) = 1.000 -4.000 6.000 -4.000 1.000 P015(x) = -1.000 5.000 -10.000 10.000 -5.000 1.000 P016(x) = 1.000 -6.000 15.000 -20.000 15.000 -6.000 1.000 legendre01_to_bernstein_matrix_test ( ): legendre01_to_bernstein_matrix() returns the matrix which maps polynomial coefficients from Legendre01 form to Bernstein form. [[ 1. -1. 1. -1. 1. -1. ] [ 1. -0.6 -0.2 1.4 -3. 5. ] [ 1. -0.2 -0.8 0.8 2. -10. ] [ 1. 0.2 -0.8 -0.8 2. 10. ] [ 1. 0.6 -0.2 -1.4 -3. -5. ] [ 1. 1. 1. 1. 1. 1. ]] bernstein_legendre01_bernstein_test ( ): Convert a polynomial from Bernstein form to Legendre01 form and back. L2 difference = 5.347643783831372e-14 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 maps polynomial coefficients 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 maps polynomial coefficients from monomial form to Bernstein form. [[1. 1. 1. 1. 1. ] [0. 0.25 0.5 0.75 1. ] [0. 0. 0.16666667 0.5 1. ] [0. 0. 0. 0.25 1. ] [0. 0. 0. 0. 1. ]] bernstein_monomial_bernstein_test ( ): Convert a polynomial from Bernstein form to monomial form and back. L2 difference = 8.437317521139966e-13 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 = 6.205342290003078e-15 gegenbauer_to_monomial_test ( ): gegenbauer_to_monomial() converts a polynomial from Gegenbauer form to monomial form. Gegenbauer parameter alpha = 0.5 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 maps polynomial coefficients from Gegenbauer form to monomial form. alpha = 0.5 [[ 1. 0. -0.5 0. 0.375] [ 0. 1. 0. -1.5 0. ] [ 0. 0. 1.5 0. -3.75 ] [ 0. 0. 0. 2.5 0. ] [ 0. 0. 0. 0. 4.375]] monomial_to_gegenbauer_test ( ): monomial_to_gegenbauer() converts a polynomial from monomial form to Gegenbauer form. Gegenbauer parameter alpha = 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 maps polynomial coefficients from monomial form to Gegenbauer form. Gegenbauer parameter alpha = 0.5 [[1. 0. 0.33333333 0. ] [0. 1. 0. 0.6 ] [0. 0. 0.66666667 0. ] [0. 0. 0. 0.4 ]] gegenbauer_monomial_gegenbauer_test ( ): Convert a polynomial from Gegenbauer form to monomial form and back. Gegenbauer parameter alpha = 0.5 L2 difference = 3.6931565159455796e-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 maps polynomial coefficients 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 maps polynomial coefficients from monomial form to Hermite form. [[1. 0. 0.5 0. ] [0. 0.5 0. 0.75 ] [0. 0. 0.25 0. ] [0. 0. 0. 0.125]] hermite_monomial_hermite_test ( ): Convert a polynomial from Hermite form to monomial form and back. L2 difference = 1.2800031596840297e-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 maps polynomial coefficients from Laguerre form to monomial form. [[ 1. 1. 1. 1. 1. ] [ 0. -1. -2. -3. -4. ] [ 0. 0. 0.5 1.5 3. ] [ 0. 0. 0. -0.16666667 -0.66666667] [ 0. 0. 0. 0. 0.04166667]] 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 maps polynomial coefficients from monomial form to Laguerre form. [[ 1. 1. 2. 6.] [ 0. -1. -4. -18.] [ 0. 0. 2. 18.] [ 0. 0. 0. -6.]] laguerre_monomial_laguerre_test ( ): Convert a polynomial from Laguerre form to monomial form and back. L2 difference = 9.482290340753292e-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 maps polynomial coefficients from Legendre form to monomial form. [[ 1. 0. -0.5 -0. 0.375] [ 0. 1. 0. -1.5 -0. ] [ 0. 0. 1.5 0. -3.75 ] [ 0. 0. 0. 2.5 0. ] [ 0. 0. 0. 0. 4.375]] 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 maps polynomial coefficients from monomial form to Legendre form. [[1. 0. 0.33333333 0. ] [0. 1. 0. 0.6 ] [0. 0. 0.66666667 0. ] [0. 0. 0. 0.4 ]] legendre_monomial_legendre_test ( ): Convert a polynomial from Legendre form to monomial form and back. L2 difference = 2.5566305388572275e-14 polynomial_conversion_test(): Normal end of execution. Fri Apr 26 13:29:11 2024