Description of pinv_sol

pinv_sol

PURPOSE

PINV_SOL - Compute pseudoinverse solution.

SYNOPSIS

function x = pinv_sol(A,b,method)

DESCRIPTION

 PINV_SOL - Compute pseudoinverse solution.

  x = pinv_sol(A,b,method)

 Returns the pseudoinvers solution (= the minimum norm solution) to
 the linear equation Ax = b.

CROSS-REFERENCE INFORMATION

This function calls:

This function is called by:

• cgi_alloc CGI_ALLOC - Control allocation based on cascading generalized inverses.
• sls_alloc SLS_ALLOC - Control allocation using sequential least squares.

SOURCE CODE

0001 function x = pinv_sol(A,b,method)
0002   
0003 % PINV_SOL - Compute pseudoinverse solution.
0004 %
0005 %  x = pinv_sol(A,b,method)
0006 %
0007 % Returns the pseudoinvers solution (= the minimum norm solution) to
0008 % the linear equation Ax = b.
0009 
0010   if nargin < 3
0011     method = 1;
0012   end
0013   
0014   switch(method)
0015    case 1
0016     % -----------------------
0017     %  Use QR decomposition.
0018     % -----------------------
0019     if isempty(A)
0020       x = [];
0021       return
0022     end
0023   
0024     [Q1,R1,E] = qr(A',0);
0025     % Account for rank deficiency. The tolerance is 10 x tolerance
0026     % used in \. See qr documentation.
0027     tol = max(size(A))*10*eps*abs(R1(1,1));
0028     % Compute numerical rank.
0029     r = sum(abs(diag(R1))>tol);
0030     % Compute pseudoinverse solution.
0031     x = Q1(:,1:r)*(R1(1:r,:)'\b(E));
0032    case 2
0033     % -------------------------------------
0034     %  Use MATLAB's pseudoinverse command.
0035     % -------------------------------------
0036     x = pinv(A) * b;
0037    case 3
0038     % ------------------------
0039     %  Use SVD decomposition.
0040     % ------------------------
0041     % Adopted from pinv.m.
0042     [n,m] = size(A);
0043     if n > m
0044       % Ax = b is overdetermined.
0045       [U,S,V] = svd(A,0);
0046     else
0047       % Ax = b is underdetermined.
0048       [V,S,U] = svd(A',0);
0049     end
0050     s = diag(S);
0051     r = sum(s > .0000001);
0052     Sr_pinv = diag(1./s(1:r));
0053     x = V(:,1:r)*Sr_pinv*U(:,1:r)'*b;
0054   end

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