Tue Oct 19 17:06:12 2021 r8poly_test(): Python version: 3.6.9 Test r8poly() r8_sign_test Python version: 3.6.9 r8_sign returns the sign of an R8. R8 r8_sign(R8) -1.2500 -1 -0.2500 -1 0.0000 1 0.5000 1 9.0000 1 r8_sign_test Normal end of execution. r82poly2_print_test r82poly2_print prints an R82POLY2, a quadratic polynomial in x and y. Coefficients a, b, c, d, e, f: 1 2 3 4 5 6 p(x,y) = 1 * x^2 + 2 * y^2 + 3 * xy + 4 * x + 5 * y + 6 r82poly2_print_test: Normal end of execution. r82poly2_type_test r82poly2_type determines the type of a second order equation in two variables. p(x,y) = 9 * x^2 + -4 * y^2 + 0 * xy + -36 * x + -24 * y + -36 Type = 1 The set of solutions forms a hyperbola. p(x,y) = 4 * x^2 + 1 * y^2 + -4 * xy + 3 * x + -4 * y + 1 Type = 2 The set of solutions forms a parabola. p(x,y) = 9 * x^2 + 16 * y^2 + 0 * xy + 36 * x + -32 * y + -92 Type = 3 The set of solutions forms an ellipse. p(x,y) = 1 * x^2 + 1 * y^2 + 0 * xy + -6 * x + -10 * y + 115 Type = 4 The set of solutions forms an imaginary ellipse. (There are no real solutions). p(x,y) = 0 * x^2 + 0 * y^2 + 1 * xy + 3 * x + -1 * y + -3 Type = 5 The set of solutions forms a pair of intersecting lines. p(x,y) = 1 * x^2 + 2 * y^2 + 0 * xy + -2 * x + 16 * y + 33 Type = 6 The set of solutions is a single point. p(x,y) = 0 * x^2 + 1 * y^2 + 0 * xy + 0 * x + -6 * y + 8 Type = 7 The set of solutions form a pair of distinct parallel lines. p(x,y) = 0 * x^2 + 1 * y^2 + 0 * xy + 0 * x + -6 * y + 10 Type = 8 The set of solutions forms a pair of imaginary parallel lines. (There are no real solutions). p(x,y) = 0 * x^2 + 1 * y^2 + 0 * xy + 0 * x + -2 * y + 1 Type = 9 The set of solutions forms a pair of coincident lines. p(x,y) = 0 * x^2 + 0 * y^2 + 0 * xy + 2 * x + -1 * y + 1 Type = 10 The set of solutions forms a single line. p(x,y) = 0 * x^2 + 0 * y^2 + 0 * xy + 0 * x + 0 * y + 0 Type = 11 The set of solutions is all space. p(x,y) = 0 * x^2 + 0 * y^2 + 0 * xy + 0 * x + 0 * y + 1 Type = 12 The set of solutions is empty. r82poly2_type_test: Normal end of execution. r8mat_inverse_3d_test r8mat_inverse_3d inverts a 3 by 3 matrix. Matrix A to be inverted: Col: 0 1 2 Row 0 : 1 2 3 1 : 4 5 6 2 : 7 8 0 Inverse matrix B: Col: 0 1 2 Row 0 : -1.77778 0.888889 -0.111111 1 : 1.55556 -0.777778 0.222222 2 : -0.111111 0.222222 -0.111111 Product C = A * B: Col: 0 1 2 Row 0 : 1 -1.11022e-16 0 1 : 5.55112e-16 1 0 2 : 1.77636e-15 -8.88178e-16 1 r8mat_inverse_3d_test: Normal end of execution. r8mat_print_test Python version: 3.6.9 r8mat_print prints an R8MAT. Here is an R8MAT: Col: 0 1 2 3 4 Row 0 : 11 12 13 14 15 1 : 21 22 23 24 25 2 : 31 32 33 34 35 3 : 41 42 43 44 45 Col: 5 Row 0 : 16 1 : 26 2 : 36 3 : 46 r8mat_print_test: Normal end of execution. r8mat_print_some_test Python version: 3.6.9 r8mat_print_some prints some of an R8MAT. Here is an R8MAT: Col: 3 4 5 Row 0 : 14 15 16 1 : 24 25 26 2 : 34 35 36 r8mat_print_some_test: Normal end of execution. r8poly_add_test Python version: 3.6.9 r8poly_add adds two R8POLY's. Polynomial A: p(x) = 5.5 * x^5 + 4.4 * x^4 + 3.3 * x^3 + 2.2 * x^2 + 1.1 * x Polynomial B: p(x) = - 5.5 * x^5 + 8.3 * x^3 + 7.2 * x^2 - 2.1 * x + 1 Polynomial C = A+B: p(x) = 4.4 * x^4 + 11.6 * x^3 + 9.4 * x^2 - 1 * x + 1 r8poly_add_test: Normal end of execution. r8poly_ant_coef_test r8poly_ant_coef() computes the coefficients of the antiderivative of a polynomial Polynomial p(x): p(x) = 1 * x^5 + 2 * x^4 + 3 * x^3 + 4 * x^2 + 5 * x + 6 Antideriv(p(x)): p(x) = 0.166667 * x^6 + 0.4 * x^5 + 0.75 * x^4 + 1.33333 * x^3 + 2.5 * x^2 + 6 * x r8poly_ant_coef_test: Normal end of execution. r8poly_ant_value_test Python version: 3.6.9 r8poly_ant_value evaluates the antiderivative of a polynomial at a point using a naive method. The polynomial coefficients: p(x) = 1 * x^4 - 10 * x^3 + 35 * x^2 - 50 * x + 24 I X antiP(X) 0 0.0000 0 1 0.3333 5.62428 2 0.6667 7.87819 3 1.0000 8.36667 4 1.3333 8.15144 5 1.6667 7.84979 6 2.0000 7.73333 7 2.3333 7.82675 8 2.6667 8.00658 9 3.0000 8.1 10 3.3333 7.98354 11 3.6667 7.68189 12 4.0000 7.46667 13 4.3333 7.95514 14 4.6667 10.2091 15 5.0000 15.8333 r8poly_ant_value_test: Normal end of execution. r8poly_degree_test Python version: 3.6.9 r8poly_degree determines the degree of an R8POLY. The R8POLY: p(x) = 4 * x^3 + 3 * x^2 + 2 * x + 1 Dimensioned degree = 3, Actual degree = 3 The R8POLY: p(x) = 3 * x^2 + 2 * x + 1 Dimensioned degree = 3, Actual degree = 2 The R8POLY: p(x) = 4 * x^3 + 2 * x + 1 Dimensioned degree = 3, Actual degree = 3 The R8POLY: p(x) = 1 Dimensioned degree = 3, Actual degree = 0 The R8POLY: p(x) = 0 Dimensioned degree = 3, Actual degree = 0 r8poly_degree_test: Normal end of execution. r8poly_deriv_test r8poly_deriv computes the coefficients of the derivative of a polynomial. The initial polynomial p(x) = 1 * x^4 - 10 * x^3 + 35 * x^2 - 50 * x + 24 The derivative of order 0 p(x) = 1 * x^4 - 10 * x^3 + 35 * x^2 - 50 * x + 24 The derivative of order 1 p(x) = 4 * x^3 - 30 * x^2 + 70 * x - 50 The derivative of order 2 p(x) = 12 * x^2 - 60 * x + 70 The derivative of order 3 p(x) = 24 * x - 60 The derivative of order 4 p(x) = 0 r8poly_division_test Python version: 3.6.9 r8poly_division computes the quotient and remainder for polynomial division. The polynomial to be divided, A: p(x) = 1 * x^3 + 2 * x^2 - 5 * x - 6 The divisor polynomial, B: p(x) = 1 * x - 2 The quotient polynomial, Q: p(x) = 1 * x^2 + 4 * x + 3 The remainder polynomial, R: p(x) = 0 The polynomial to be divided, A: p(x) = 1 * x^4 + 3 * x^3 + 2 * x^2 + 5 * x - 2 The divisor polynomial, B: p(x) = 1 * x^2 + 1 * x - 3 The quotient polynomial, Q: p(x) = 1 * x^2 + 2 * x + 3 The remainder polynomial, R: p(x) = 8 * x + 7 The polynomial to be divided, A: p(x) = 1 * x^3 - 2 * x^2 - 4 The divisor polynomial, B: p(x) = 1 * x - 3 The quotient polynomial, Q: p(x) = 1 * x^2 + 1 * x + 3 The remainder polynomial, R: p(x) = 5 r8poly_division_test: Normal end of execution. r8poly_lagrange_0_test r8poly_lagrange_0 evaluates the Lagrange factor W(X) at a point. The number of data points is 5 Abscissas: 0: 0 1: 1 2: 2 3: 3 4: 4 X W(X) 0.000000 0.000000e+00 0.222222 3.224441e+00 0.444444 3.489983e+00 0.666667 2.304527e+00 0.888889 7.207573e-01 1.111111 -5.988247e-01 1.333333 -1.316872e+00 1.555556 -1.356162e+00 1.777778 -8.345611e-01 2.000000 0.000000e+00 2.222222 8.345611e-01 2.444444 1.356162e+00 2.666667 1.316872e+00 2.888889 5.988247e-01 3.111111 -7.207573e-01 3.333333 -2.304527e+00 3.555556 -3.489983e+00 3.777778 -3.224441e+00 4.000000 0.000000e+00 r8poly_lagrange_0_test: Normal end of execution. r8poly_lagrange_1_test r8poly_lagrange_1 evaluates the Lagrange factor W(X) at a point. The number of data points is 5 Abscissas: 0: 0 1: 1 2: 2 3: 3 4: 4 X W(X) 0.000000 24.000000 0.222222 6.536199 0.444444 -3.020271 0.666667 -6.864198 0.888889 -6.897729 1.111111 -4.730376 1.333333 -1.679012 1.555556 1.232129 1.777778 3.271453 2.000000 4.000000 2.222222 3.271453 2.444444 1.232129 2.666667 -1.679012 2.888889 -4.730376 3.111111 -6.897729 3.333333 -6.864198 3.555556 -3.020271 3.777778 6.536199 4.000000 24.000000 r8poly_lagrange_1_test: Normal end of execution. r8poly_lagrange_2_test r8poly_lagrange_2 evaluates the Lagrange factor W"(X) at a point. The number of data points is 5 Abscissas: 0: 0 1: 1 2: 2 3: 3 4: 4 X W"(X) 0.000000 -1.000000e+02 0.222222 -5.903978e+01 0.444444 -2.861454e+01 0.666667 -7.407407e+00 0.888889 5.898491e+00 1.111111 1.262003e+01 1.333333 1.407407e+01 1.555556 1.157750e+01 1.777778 6.447188e+00 2.000000 0.000000e+00 2.222222 -6.447188e+00 2.444444 -1.157750e+01 2.666667 -1.407407e+01 2.888889 -1.262003e+01 3.111111 -5.898491e+00 3.333333 7.407407e+00 3.555556 2.861454e+01 3.777778 5.903978e+01 4.000000 1.000000e+02 r8poly_lagrange_2_test: Normal end of execution. r8poly_lagrange_coef_test r8poly_lagrange_coef returns the coefficients for a Lagrange basis polynomial. Abscissas: 0: 1 1: 2 2: 3 3: 4 4: 5 The Lagrange basis polynomial: p(x) = 0.0416667 * x^4 - 0.583333 * x^3 + 2.95833 * x^2 - 6.41667 * x + 5 The Lagrange basis polynomial: p(x) = - 0.166667 * x^4 + 2.16667 * x^3 - 9.83333 * x^2 + 17.8333 * x - 10 The Lagrange basis polynomial: p(x) = 0.25 * x^4 - 3 * x^3 + 12.25 * x^2 - 19.5 * x + 10 The Lagrange basis polynomial: p(x) = - 0.166667 * x^4 + 1.83333 * x^3 - 6.83333 * x^2 + 10.1667 * x - 5 The Lagrange basis polynomial: p(x) = 0.0416667 * x^4 - 0.416667 * x^3 + 1.45833 * x^2 - 2.08333 * x + 1 r8poly_lagrange_coef_test: Normal end of execution. r8poly_lagrange_factor_test r8poly_lagrange_factor evaluates the Lagrange factor W(X) at a point. For this test, we use 5 functions. Abscissas: 0: 0 1: 0.8 2: 1.6 3: 2.4 4: 3.2 X W(X) W(X) 4.500000 131.818050 274.542900 4.000000 39.321600 112.230400 3.500000 5.925150 32.142900 3.000000 -1.108800 2.030400 2.500000 -0.267750 -2.857100 2.000000 0.460800 0.230400 1.500000 -0.160650 1.542900 1.000000 -0.369600 -1.169600 0.500000 0.846450 -2.657100 0.000000 0.000000 9.830400 r8poly_lagrange_factor_test: Normal end of execution. r8poly_lagrange_value_test r8poly_lagrange_value() evaluates a Lagrange interpolating polynomial at a point. Number of data points = #d 5 Abscissas: 0: 0 1: 1 2: 2 3: 3 4: 4 Here are the values of the functions at several points: X L1 L2 L3 L4 L5 0.000000 1.000000 0.000000 -0.000000 0.000000 -0.000000 0.500000 0.273438 1.093750 -0.546875 0.218750 -0.039062 1.000000 -0.000000 1.000000 0.000000 -0.000000 0.000000 1.500000 -0.039062 0.468750 0.703125 -0.156250 0.023438 2.000000 0.000000 -0.000000 1.000000 0.000000 -0.000000 2.500000 0.023438 -0.156250 0.703125 0.468750 -0.039062 3.000000 -0.000000 0.000000 -0.000000 1.000000 0.000000 3.500000 -0.039062 0.218750 -0.546875 1.093750 0.273438 4.000000 0.000000 -0.000000 0.000000 -0.000000 1.000000 And the derivatives: X L1 L2 L3 L4 L5 0.000000 -2.083333 4.000000 -3.000000 1.333333 -0.250000 0.500000 -0.916667 0.708333 0.375000 -0.208333 0.041667 1.000000 -0.250000 -0.833333 1.500000 -0.500000 0.083333 1.500000 0.041667 -1.125000 1.125000 -0.041667 0.000000 2.000000 0.083333 -0.666667 0.000000 0.666667 -0.083333 2.500000 0.000000 0.041667 -1.125000 1.125000 -0.041667 3.000000 -0.083333 0.500000 -1.500000 0.833333 0.250000 3.500000 -0.041667 0.208333 -0.375000 -0.708333 0.916667 4.000000 0.250000 -1.333333 3.000000 -4.000000 2.083333 r8poly_lagrange_value_test: Normal end of execution. r8poly_multiply_test Python version: 3.6.9 r8poly_multiply multiplies two polynomials. The factor A: p(x) = 1 * x + 1 The factor B: p(x) = - 1 * x + 1 The product C = A*B: p(x) = - 1 * x^2 + 1 The factor A: p(x) = 3 * x^2 + 2 * x + 1 The factor B: p(x) = - 2 * x + 1 The product C = A*B: p(x) = - 6 * x^3 - 1 * x^2 + 1 r8poly_multiply_test: Normal end of execution. r8poly_power_test Python version: 3.6.9 r8poly_power takes a polynomial to a power. The polynomial A: p(x) = - 1 * x + 2 Raised to the power 3: p(x) = - 1 * x^3 + 6 * x^2 - 12 * x + 8 The polynomial A: p(x) = 1 * x^2 + 1 * x Raised to the power 2: p(x) = 1 * x^4 + 2 * x^3 + 1 * x^2 r8poly_power_test Normal end of execution. r8poly_print_test Python version: 3.6.9 r8poly_print prints an R8POLY. The R8POLY: p(x) = 9 * x^5 + 0.78 * x^4 + 56 * x^2 - 3.4 * x + 12 The R8POLY: p(x) = 0.78 * x^4 + 56 * x^2 - 3.4 * x + 12 The R8POLY: p(x) = 12 The R8POLY: p(x) = 0 r8poly_print_test: Normal end of execution. r8poly_shift_test r8poly_shift shifts an R8POLY p(x) to q(z) where z=scale*x+shift. p(x): p(x) = 2 * x^2 - 1 * x + 6 z = scale * x + shift Scale = 2 Shift = 3 q(z): p(x) = 0.5 * x^2 - 3.5 * x + 12 Expected q(z): p(x) = 0.5 * x^2 - 3.5 * x + 12 r8poly_shift_test: Normal end of execution. r8poly_value_test Python version: 3.6.9 r8poly_value evaluates a polynomial at a point using a naive method. The polynomial coefficients: p(x) = 1 * x^4 - 10 * x^3 + 35 * x^2 - 50 * x + 24 I X P(X) 0 0.0000 24 1 0.3333 10.8642 2 0.6667 3.45679 3 1.0000 0 4 1.3333 -0.987654 5 1.6667 -0.691358 6 2.0000 0 7 2.3333 0.493827 8 2.6667 0.493827 9 3.0000 0 10 3.3333 -0.691358 11 3.6667 -0.987654 12 4.0000 0 13 4.3333 3.45679 14 4.6667 10.8642 15 5.0000 24 r8poly_value_test: Normal end of execution. r8poly_value_horner_test Python version: 3.6.9 r8poly_value_horner evaluates a polynomial at a point using Horners method. The polynomial coefficients: p(x) = 1 * x^4 - 10 * x^3 + 35 * x^2 - 50 * x + 24 I X P(X) 0 0.0000 24 1 0.3333 10.8642 2 0.6667 3.45679 3 1.0000 0 4 1.3333 -0.987654 5 1.6667 -0.691358 6 2.0000 0 7 2.3333 0.493827 8 2.6667 0.493827 9 3.0000 0 10 3.3333 -0.691358 11 3.6667 -0.987654 12 4.0000 0 13 4.3333 3.45679 14 4.6667 10.8642 15 5.0000 24 r8poly_value_horner_test: Normal end of execution. r8poly_values_horner_test Python version: 3.6.9 r8poly_values_horner evaluates a polynomial at a point, using Horner's method. The polynomial: p(x) = 1 * x^4 - 10 * x^3 + 35 * x^2 - 50 * x + 24 X, P(X): 0: 0 24 1: 0.333333 10.8642 2: 0.666667 3.45679 3: 1 0 4: 1.33333 -0.987654 5: 1.66667 -0.691358 6: 2 0 7: 2.33333 0.493827 8: 2.66667 0.493827 9: 3 0 10: 3.33333 -0.691358 11: 3.66667 -0.987654 12: 4 0 13: 4.33333 3.45679 14: 4.66667 10.8642 15: 5 24 r8poly_values_horner_test: Normal end of execution. r8poly2_ex_test r8poly2_ex finds the extreme value of a parabola determined by three points. Parabolic coefficients: A = 2.000000, B = -4.000000, C = 10.000000 Point 1: (1,8) Point 1: (2,10) Point 1: (3,16) r8poly2_ex returns XMIN = 1.000000, YMIN = 8.000000 r8poly2_ex_test: Normal end of execution. r8poly2_ex2_test r8poly2_ex2 finds the extreme value of a parabola determined by three points. Parabolic coefficients: A = 2.000000, B = -4.000000, C = 10.000000 Point 1: (1,8) Point 1: (2,10) Point 1: (3,16) r8poly2_ex2 returns XMIN = 1.000000, YMIN = 8.000000 and A = 2.000000, B = -4.000000, C = 10.000000 r8poly2_ex2_test: Normal end of execution. r8poly2_root_test r8poly2_root finds quadratic equation roots. A B C R1.real R1.imag R2.real R2.imag 2.0000 -2.0000 -24.0000 4.0000 -0.0000 -3.0000 0.0000 1.0000 -20.0000 100.0000 10.0000 -0.0000 10.0000 0.0000 1.0000 -2.0000 10.0000 1.0000 3.0000 1.0000 -3.0000 r8poly2_root_test Normal end of execution. r8poly2_rroot_test r8poly2_rroot finds the real parts of quadratic equation roots. A B C R1 R2 2.0000 -2.0000 -24.0000 4.0000 -3.0000 1.0000 -20.0000 100.0000 10.0000 10.0000 1.0000 -2.0000 10.0000 1.0000 1.0000 1.0000 0.0000 1.0000 -0.0000 -0.0000 1.0000 -6.0000 10.0000 3.0000 3.0000 r8poly2_rroot_test Normal end of execution. r8poly2_val_test r8poly2_val evaluates a parabola given 3 data points. Our parabola will be 2*x^2 + 3 * x + 1. Case 1: 3 distinct data points: -1.000000 0.000000 1.000000 6.000000 3.000000 28.000000 Sampled data: X, Y, Y, Y" 0.000000 1.000000 3.000000 4.000000 1.000000 6.000000 7.000000 4.000000 2.000000 15.000000 11.000000 4.000000 3.000000 28.000000 15.000000 4.000000 Case 2: X1=X2, X3 distinct: -1.000000 0.000000 -1.000000 -1.000000 3.000000 28.000000 Sampled data: X, Y, Y, Y" 0.000000 1.000000 3.000000 4.000000 1.000000 6.000000 7.000000 4.000000 2.000000 15.000000 11.000000 4.000000 3.000000 28.000000 15.000000 4.000000 Case 3: X1=X2=X3: -1.000000 0.000000 -1.000000 -1.000000 -1.000000 4.000000 Sampled data: X, Y, Y, Y" 0.000000 1.000000 3.000000 4.000000 1.000000 6.000000 7.000000 4.000000 2.000000 15.000000 11.000000 4.000000 3.000000 28.000000 15.000000 4.000000 r8poly2_val_test: Normal end of execution. r8poly2_val2_test r8poly2_val2 evaluates parabolas through 3 points in a table Our data tables will actually be parabolas: A: 2*x^2 + 3 * x + 1. B: 4*x^2 - 2 * x + 5. 0 0.000000 1.000000 5.000000 1 2.000000 15.000000 17.000000 2 4.000000 45.000000 61.000000 3 6.000000 91.000000 137.000000 4 8.000000 153.000000 245.000000 Interpolated data: LEFT, X, Y1, Y2 1 1.000000 6.000000 7.000000 2 3.000000 28.000000 35.000000 3 5.000000 66.000000 95.000000 3 7.000000 120.000000 187.000000 3 9.000000 190.000000 311.000000 r8poly2_val2_test: Normal end of execution. r8poly3_root_test r8poly3_root finds roots of cubic equations. Polynomial coefficients: A = 1.000000, B = -6.000000, C = 11.000000, D = -6.000000 Roots: 1.000000 0.000000 3.000000 0.000000 2.000000 0.000000 Polynomial coefficients: A = 9.000000, B = -36.000000, C = 54.000000, D = -27.000000 Roots: 1.000000 0.000000 1.500000 0.866025 1.500000 -0.866025 Polynomial coefficients: A = 1.000000, B = -5.000000, C = 8.000000, D = -4.000000 Roots: 1.000000 0.000000 2.000000 0.000000 2.000000 -0.000000 Polynomial coefficients: A = 1.000000, B = -8.000000, C = 25.000000, D = -26.000000 Roots: 2.000000 0.000000 3.000000 2.000000 3.000000 -2.000000 r8poly3_root_test Normal end of execution. r8poly4_root_test r8poly4_root finds roots of quartic equations. A = 1.000000 B = -10.000000 C = 35.000000 D = -50.000000 E = 24.000000 Roots: 4.000000 0.000000 1.000000 0.000000 3.000000 0.000000 2.000000 0.000000 A = 1.000000 B = -5.000000 C = 1.000000 D = 21.000000 E = -18.000000 Roots: 3.000000 0.000000 3.000000 0.000000 1.000000 0.000000 -2.000000 0.000000 A = 1.000000 B = -22.000000 C = 141.000000 D = -220.000000 E = 100.000000 Roots: 10.000000 0.000000 10.000000 0.000000 1.000000 0.000000 1.000000 0.000000 A = 1.000000 B = -16.000000 C = 72.000000 D = -128.000000 E = 80.000000 Roots: 10.000000 0.000000 2.000000 0.000000 2.000000 0.000000 2.000000 0.000000 A = 1.000000 B = -20.000000 C = 150.000000 D = -500.000000 E = 625.000000 Roots: 5.000000 0.000000 5.000000 0.000000 5.000000 0.000000 5.000000 0.000000 A = 1.000000 B = 2.000000 C = 1.000000 D = 8.000000 E = -12.000000 Roots: -0.000000 2.000000 -0.000000 -2.000000 1.000000 0.000000 -3.000000 0.000000 A = 1.000000 B = 0.000000 C = 13.000000 D = 0.000000 E = 36.000000 Roots: 0.000000 3.000000 0.000000 2.000000 0.000000 -2.000000 -0.000000 -3.000000 r8poly4_root_test Normal end of execution. r8vec_even_test r8vec_even computes N evenly spaced values between XLO and XHI. XLO = 0.000000 XHI = 99.000000 while N = 10 Resulting array: 0: 0 1: 11 2: 22 3: 33 4: 44 5: 55 6: 66 7: 77 8: 88 9: 99 r8vec_even_test: Normal end of execution. r8vec_even_select_test r8vec_even_select returns the I-th of N evenly spaced values between XLO and XHI. XLO = 0.000000 XHI = 99.000000 while N = 10 X(2) = 11 X(5) = 44 X(8) = 77 r8vec_even_select_test: Normal end of execution. r8vec_indicator1_test Python version: 3.6.9 r8vec_indicator1 returns the 1-based indicator matrix. The 1-based indicator vector: 0: 1 1: 2 2: 3 3: 4 4: 5 5: 6 6: 7 7: 8 8: 9 9: 10 r8vec_indicator1_test Normal end of execution. r8vec_is_distinct_test Python version: 3.6.9 r8vec_is_distinct computes the maximum entry in an R8VEC. Input vector: 0: 1 1: 2 2: 5 3: 3 4: 4 Array entries are distinct. Input vector: 0: 1 1: 2 2: 5 3: 2 4: 4 Array entries are NOT distinct. r8vec_is_distinct_test: Normal end of execution. r8vec_is_zero_test Python version: 3.6.9 r8vec_is_zero is TRUE if an R8VEC contains only zero entries. X: 0 1 0 X contains at least one nonzero entry. X: 0 0 0 X contains only zero entries. X: -3 -99 -87.3 X contains at least one nonzero entry. r8vec_is_zero_test Normal end of execution. r8vec_linspace_test Python version: 3.6.9 r8vec_linspace returns evenly spaced values between A and B. The linspace vector: 0: 10 1: 12.5 2: 15 3: 17.5 4: 20 r8vec_linspace_test Normal end of execution. r8vec_print_test Python version: 3.6.9 Test r8vec_print(), which prints an R8VEC. Use r8vec_print(): 0: 123.456 1: 5e-06 2: -1e+06 3: 3.14159 Use python print(): [ 1.23456000e+02 5.00000000e-06 -1.00000000e+06 3.14159265e+00] r8vec_print_test: Normal end of execution. r8vec_transpose_print_test Python version: 3.6.9 r8vec_transpose_print() prints an R8VEC "tranposed", that is, placing multiple entries on a line. The vector X: 1 2.1 3.2 4.3 5.4 6.5 7.6 8.7 9.8 10.9 11 r8vec_transpose_print_test Normal end of execution. r8vec2_print_test Python version: 3.6.9 r8vec2_print() prints a pair of R8VEC's. Print a pair of R8VEC's: 0: 0 0 1: 0.2 0.04 2: 0.4 0.16 3: 0.6 0.36 4: 0.8 0.64 5: 1 1 r8vec2_print_test: Normal end of execution. roots_to_r8poly_test Python version: 3.6.9 roots_to_r8poly is given N real roots, and constructs the coefficient vector of the corresponding polynomial. N real roots: 0: 1 1: -4 2: 3 3: 0 4: 3 The polynomial: p(x) = 1 * x^5 - 3 * x^4 - 13 * x^3 + 51 * x^2 - 36 * x roots_to_r8poly_test: Normal end of execution. r8poly_test(): Normal end of execution. Tue Oct 19 17:06:12 2021