first commit with current lessons

10-04/optQf.m

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+function v = optQf( Q , q )
+
+%function v = optQf( Q , q )
+%
+% Given the data structure encoding a Quadratic function
+%
+%  f( x ) = (1/2) x^T * Q * x + q * x
+%
+% returns the value of f() in the "putative minimum" (or maximum), i.e.,
+% the point
+%
+%   xStar = Q \ -q;
+%
+% Input:
+%
+% - Q ([ n x n ] real symmetric matrix, not necessarily positive
+%   semidefinite): the quadratic part of f
+%
+% - q ([ n x 1 ] real column vector): the linear part of f
+%
+% Output:
+%
+% - f( xStar )
+%
+%{
+ =======================================
+ Author: Antonio Frangioni
+ Date: 30-09-22
+ Version 0.10
+ Copyright Antonio Frangioni
+ =======================================
+%}
+
+if ~ isreal( Q )
+   error( 'Q not a real matrix' );
+end
+
+n = size( Q , 1 );
+
+if n <= 1
+   error( 'Q is too small' );
+end
+
+if n ~= size( Q , 2 )
+   error( 'Q is not square' );
+end
+
+if ~ isreal( q )
+   error( 'q not a real vector' );
+end
+
+if size( q , 2 ) ~= 1
+   error( 'q is not a (column) vector' );
+end
+
+if size( q , 1 ) ~= n
+   error( 'q size does not match with Q' );
+end
+
+% "solve the problem" - - - - - - - - - - - - - - - - - - - - - - - - - - -
+% ignore if Q is singular
+
+xStar = Q \ -q;
+
+v = 0.5 * xStar' * Q * xStar + q' * xStar;
+
+end