orthoval
Orthogonal evaluation.
Syntax
F = orthoval(x, input4eval, varargin)
Description
F = orthoval(itauobject, input4eval, varargin) performs an
orthogonal evaluation at x, depending on the type of input
and evaluation. See examples.
Inputs
x = independent tau variable (itau object).
input4eval = input for evaluation (double scalar, vector or matrix).
Inputs (optional) select only one.
'coef' = coefficients of sum(a_iP_i) (double vector).
'j' = j-th polynomial (integer scalar).
'difforder' = derivative order (integer scalar).
Output
F = polynomial evaluation (double scalar, vector, matrix).
Examples
% Creating itau object:
x = itau('ChebyshevT', [1 2], 10);
% Evaluate a vector vec in a linear combination sum(a_iP_i(vec)):
vec = 0:0.001:1; orthoval(x, vec, 'coef', [1 3 2 4 3 2 1]);
% Evaluate a vector vec at a P_j(vec) polynomial:
vec = 0:0.001:1; orthoval(x, vec, 'j', 2);
% Evaluate a matrix A in a linear combination sum(a_iP_i(A)):
A = [1 2 3;1 4 2;1 2 3]; orthoval(x, A, 'coef', [1 2 3 4 3 2 1])
% Evaluate a matrix A in an especified P_j(A) polynomial:
A = [1 2 3;1 4 2;1 2 3]; orthoval(x, A, 'j', 2);
% Evaluate each derivative d(P_i(val))/dx of the basis (without sum):
val = 0.5; orthoval(x, val, 'difforder', 0);
See also
orthovalv, orthovalvj, orthovalM, orthovalMj and orthovald.
F = orthoval(itauobject, input4eval, varargin) performs an orthogonal evaluation at x, depending on the type of input and evaluation. See examples.
Inputs
x = independent tau variable (itau object).
input4eval = input for evaluation (double scalar, vector or matrix).
Inputs (optional) select only one.
'coef' = coefficients of sum(a_iP_i) (double vector).
'j' = j-th polynomial (integer scalar).
'difforder' = derivative order (integer scalar).
Output
F = polynomial evaluation (double scalar, vector, matrix).
Examples
% Creating itau object:
x = itau('ChebyshevT', [1 2], 10);
% Evaluate a vector vec in a linear combination sum(a_iP_i(vec)):
vec = 0:0.001:1; orthoval(x, vec, 'coef', [1 3 2 4 3 2 1]);
% Evaluate a vector vec at a P_j(vec) polynomial:
vec = 0:0.001:1; orthoval(x, vec, 'j', 2);
% Evaluate a matrix A in a linear combination sum(a_iP_i(A)):
A = [1 2 3;1 4 2;1 2 3]; orthoval(x, A, 'coef', [1 2 3 4 3 2 1])
% Evaluate a matrix A in an especified P_j(A) polynomial:
A = [1 2 3;1 4 2;1 2 3]; orthoval(x, A, 'j', 2);
% Evaluate each derivative d(P_i(val))/dx of the basis (without sum):
val = 0.5; orthoval(x, val, 'difforder', 0);
See also
orthovalv, orthovalvj, orthovalM, orthovalMj and orthovald.
'coef' = coefficients of sum(a_iP_i) (double vector). 'j' = j-th polynomial (integer scalar). 'difforder' = derivative order (integer scalar).
Output
F = polynomial evaluation (double scalar, vector, matrix).
Examples
% Creating itau object:
x = itau('ChebyshevT', [1 2], 10);
% Evaluate a vector vec in a linear combination sum(a_iP_i(vec)):
vec = 0:0.001:1; orthoval(x, vec, 'coef', [1 3 2 4 3 2 1]);
% Evaluate a vector vec at a P_j(vec) polynomial:
vec = 0:0.001:1; orthoval(x, vec, 'j', 2);
% Evaluate a matrix A in a linear combination sum(a_iP_i(A)):
A = [1 2 3;1 4 2;1 2 3]; orthoval(x, A, 'coef', [1 2 3 4 3 2 1])
% Evaluate a matrix A in an especified P_j(A) polynomial:
A = [1 2 3;1 4 2;1 2 3]; orthoval(x, A, 'j', 2);
% Evaluate each derivative d(P_i(val))/dx of the basis (without sum):
val = 0.5; orthoval(x, val, 'difforder', 0);
See also
orthovalv, orthovalvj, orthovalM, orthovalMj and orthovald.
% Creating itau object: x = itau('ChebyshevT', [1 2], 10); % Evaluate a vector vec in a linear combination sum(a_iP_i(vec)): vec = 0:0.001:1; orthoval(x, vec, 'coef', [1 3 2 4 3 2 1]); % Evaluate a vector vec at a P_j(vec) polynomial: vec = 0:0.001:1; orthoval(x, vec, 'j', 2); % Evaluate a matrix A in a linear combination sum(a_iP_i(A)): A = [1 2 3;1 4 2;1 2 3]; orthoval(x, A, 'coef', [1 2 3 4 3 2 1]) % Evaluate a matrix A in an especified P_j(A) polynomial: A = [1 2 3;1 4 2;1 2 3]; orthoval(x, A, 'j', 2); % Evaluate each derivative d(P_i(val))/dx of the basis (without sum): val = 0.5; orthoval(x, val, 'difforder', 0);