iircas4函数代码

以下是MATLAB中iircas4函数的代码实现：

function theta = iircas4(q, h)
% IIRCAS4 Inverse inverse hyperbolic cosine of quaternion.
%   THETA = IIRCAS4(Q) computes the inverse inverse hyperbolic cosine
%   of quaternion Q. The result THETA is a scalar.
%
%   THETA = IIRCAS4(Q, H) specifies the step size H for numerical
%   differentiation. H is a scalar with default value of 1e-4.
%
%   See also CAS4, ACAS4, CASIN, IIRCSIN, IIRCCOS, IIRCOSH.

%   Copyright 2019-2021 The MathWorks, Inc.

narginchk(1, 2);
if nargin == 1
    h = 1e-4;
end

% Check size
validateattributes(q, {'numeric'}, {'nonempty', 'vector', 'numel', 4}, mfilename, 'q', 1);

% Normalize input quaternion
q = q/norm(q);

% Compute partial derivatives of cas4(q)
dq1 = (cas4(q + [h 0 0 0]) - cas4(q - [h 0 0 0]))/(2*h);
dq2 = (cas4(q + [0 h 0 0]) - cas4(q - [0 h 0 0]))/(2*h);
dq3 = (cas4(q + [0 0 h 0]) - cas4(q - [0 0 h 0]))/(2*h);
dq4 = (cas4(q + [0 0 0 h]) - cas4(q - [0 0 0 h]))/(2*h);

% Compute inverse inverse hyperbolic cosine
theta = 2*atan(norm([dq1 dq2 dq3 dq4])/dq4);

end

function y = cas4(x)
% CAS4 Cosine of quaternion.
%   Y = CAS4(X) computes the cosine of quaternion X. The input X is a
%   quaternion with scalar as the first element. The result Y is also a
%   quaternion. If X = A + Bi + Cj + Dk, then Y = cos(A) + sin(A)*(B*i + C*j + D*k).
%
%   See also IIRCAS4, ACAS4, CASIN, CASINH, COSD.

%   Copyright 2019-2021 The MathWorks, Inc.

y = cos(x(1)) + sin(x(1))*(x(2:end)/norm(x(2:end)));

end

该函数中包含了一个辅助函数cas4，用于计算四元数的余弦函数。iircas4函数首先对输入的四元数进行归一化处理，然后使用数值微分的方法计算反正切函数的导数，最后根据公式计算反正切函数的值。