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07-Oct-2025 22:17:44

lagrange_test():
  MATLAB/Octave version 9.11.0.2358333 (R2021b) Update 7
  Test lagrange().

lagrange_basis_coef_test():
  lagrange_basis_coef() returns the coefficients
  for a Lagrange basis polynomial.

  Abscissas:

     1:           -3
     2:           -2
     3:           -1
     4:            0
     5:            1
     6:            2
     7:            3

  L(1)(x): = 
     +0.001389 * x^6
     -0.004167 * x^5
     -0.006944 * x^4
     +0.020833 * x^3
     +0.005556 * x^2
     -0.016667 * x

  L(2)(x): = 
     -0.008333 * x^6
     +0.016667 * x^5
     +0.083333 * x^4
     -0.166667 * x^3
     -0.075000 * x^2
     +0.150000 * x

  L(3)(x): = 
     +0.020833 * x^6
     -0.020833 * x^5
     -0.270833 * x^4
     +0.270833 * x^3
     +0.750000 * x^2
     -0.750000 * x

  L(4)(x): = 
     -0.027778 * x^6
     +0.388889 * x^4
     +0.000000 * x^3
     -1.361111 * x^2
     -0.000000 * x
     +1.000000

  L(5)(x): = 
     +0.020833 * x^6
     +0.020833 * x^5
     -0.270833 * x^4
     -0.270833 * x^3
     +0.750000 * x^2
     +0.750000 * x

  L(6)(x): = 
     -0.008333 * x^6
     -0.016667 * x^5
     +0.083333 * x^4
     +0.166667 * x^3
     -0.075000 * x^2
     -0.150000 * x

  L(7)(x): = 
     +0.001389 * x^6
     +0.004167 * x^5
     -0.006944 * x^4
     -0.020833 * x^3
     +0.005556 * x^2
     +0.016667 * x

lagrange_basis_value_test():
  lagrange_basis_value() evaluates Lagrange basis polynomials.
  Graphics saved as "lagrange_basis_value.png"

lagrange_basis_deriv_test():
  lagrange_basis_deriv() evaluates the derivative of a
  Lagrange basis polynomial.
  Graphics saved as "lagrange_basis_deriv.png"

lagrange_basis_deriv2_test():
  lagrange_basis_deriv2() evaluates the second derivative
  of a Lagrange basis polynomial.
  Graphics saved as "lagrange_basis_deriv2.png"

lagrange_basis_antideriv_test():
  lagrange_basis_antideriv() evaluates the antiderivative
  of a Lagrange basis polynomial.

pcof_antideriv =

         0
         0
    0.0750
   -0.0250
   -0.0417
    0.0167
    0.0028
   -0.0012

  Graphics saved as "lagrange_basis_antideriv.png"

lagrange_test():
  Normal end of execution.

07-Oct-2025 22:17:51