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