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zm_opt_qp.c
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zm_opt_qp.c
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/* ZM - Z's Mathematics Toolbox
* Copyright (C) 1998 Tomomichi Sugihara (Zhidao)
*
* zm_opt_qp - optimization tools: quadratic programming.
*/
#include <zm/zm_opt.h>
/* calculation of a quadratic value. */
double zQuadraticValue(zMat q, zVec c, zVec x)
{
int i, j, n;
double val;
n = zVecSize( x );
if( !zMatIsSqr(q) ){
ZRUNERROR( ZM_ERR_NONSQR_MAT );
return 0;
}
if( zMatRowSize(q) != n ){
ZRUNERROR( ZM_ERR_SIZMIS_MATVEC );
return 0;
}
if( zVecSize(c) != n ){
ZRUNERROR( ZM_ERR_SIZMIS_VEC );
return 0;
}
for( val=0, i=0; i<n; i++ ){
for( j=0; j<n; j++ )
val += 0.5*zMatElemNC(q,i,j)*zVecElemNC(x,i)*zVecElemNC(x,j);
val += zVecElemNC(c,i)*zVecElemNC(x,i);
}
return val;
}
#if 0
/* quadratic programming solver. */
/* NOTE: this function is to be deleted due to mathematical illegality. */
bool zQPSolve(zMat q, zVec c, zMat a, zVec b, zVec ans, double *cost)
{
int i, j, m, n;
zMat d;
zVec f, y;
n = zVecSize( ans );
m = b ? zVecSize( b ) : 0;
if( !zMatIsSqr(q) || zMatRowSize(q)!=n ){
ZRUNERROR( ZM_ERR_SIZMIS_MAT );
return false;
}
if( c && zVecSize(c)!=n ){
ZRUNERROR( ZM_ERR_SIZMIS_VEC );
return false;
}
if( a && zMatColSize(a) == 0 )
a = NULL;
if( a && ( zMatColSize(a)!=n || zMatRowSize(a)!=m ) ){
ZRUNERROR( ZM_ERR_SIZMIS_MATVEC );
return false;
}
d = zMatAllocSqr( n+m );
f = zVecAlloc( n+m );
y = zVecAlloc( n+m );
for( i=0; i<n; i++ ){
for( j=0; j<n; j++ )
zMatSetElemNC( d, i, j,
0.5*( zMatElemNC( q, i, j )+zMatElemNC( q, j, i ) ) );
if( c ) zVecSetElemNC( f, i,-zVecElemNC( c, i ) );
}
for( i=0; i<m; i++ ){
for( j=0; j<n; j++ ){
zMatSetElemNC( d, n+i, j, zMatElemNC( a, i, j ) );
zMatSetElemNC( d, j, n+i, zMatElemNC( a, i, j ) );
}
zVecSetElemNC( f, n+i, zVecElemNC( b, i ) );
}
zLESolveGauss( d, f, y );
for( i=0; i<n; i++ )
zVecSetElemNC( ans, i, zVecElemNC( y, i ) );
zMatFree( d );
zVecFreeAO( 2, f, y );
if( cost ) *cost = zQuadraticValue( q, c, ans );
return true;
}
#endif
/* transform a quadratic programming problem to a linear complementary problem. */
static bool _zQP2LCP(zMat q, zVec c, zMat a, zVec b, zMat *lm, zVec *lq, zVec *z)
{
int i, j;
*lm = zMatAllocSqr( zMatRowSizeNC(q) + zMatRowSize(a) );
*lq = zVecAlloc( zVecSizeNC(c) + zVecSize(b) );
*z = zVecAlloc( zVecSizeNC(c) + zVecSize(b) );
if( !*lm || !*lq || !*z ){
ZALLOCERROR();
zMatFree( *lm );
zVecFree( *lq );
zVecFree( *z );
return false;
}
zMatPut( *lm, 0, 0, q );
zMatPut( *lm, zMatRowSizeNC(q), 0, a );
for( i=0; i<zMatRowSize(a); i++ )
for( j=0; j<zMatColSize(a); j++ )
zMatSetElemNC( *lm, j, i+zMatColSizeNC(q), -zMatElemNC(a,i,j) );
zVecPut( *lq, 0, c );
for( i=0; i<zVecSize(b); i++ )
zVecSetElemNC( *lq, zVecSizeNC(c)+i, -zVecElemNC(b,i) );
return true;
}
/* define quadratic programming problem solver */
#define zQPSolverDef( name ) \
bool zQPSolve##name(zMat q, zVec c, zMat a, zVec b, zVec ans, double *cost)\
{\
zMat lm;\
zVec lq, z;\
bool ret = false;\
\
if( !_zQP2LCP( q, c, a, b, &lm, &lq, &z ) ) return false;\
\
if( zLCPSolve##name( lm, lq, NULL, z ) ){\
zVecGet( z, 0, ans );\
if( cost ) *cost = zQuadraticValue( q, c, ans );\
ret = true;\
}\
zMatFree( lm );\
zVecFree( lq );\
zVecFree( z );\
return ret;\
}
/* solve quadratic programming problem with Lemke's method. */
zQPSolverDef( Lemke )
/* solve quadratic programming problem with interior-point method. */
zQPSolverDef( IP )
/* quadratic programming solver by conjugate gradient method. */
double zCGSolve(zMat q, zVec c, zVec ans, int iter)
{
zVec d, g, qd;
double a, b, s, result;
int i = 0;
d = zVecAlloc( zVecSizeNC(ans) );
g = zVecAlloc( zVecSizeNC(ans) );
qd= zVecAlloc( zVecSizeNC(ans) );
if( !d || !g || !qd ) goto TERMINATE;
zMulMatVec( q, ans, g );
zVecAddDRC( g, c );
if( zVecIsTiny( g ) ) goto TERMINATE;
zVecCopy( g, d );
ZITERINIT( iter );
for( i=0; i<iter; i++ ){
zMulMatVecNC( q, d, qd );
s = zVecInnerProd( d, qd );
a = zVecInnerProd( d, g ) / s;
zVecCatNCDRC( ans, -a, d );
zVecCatNCDRC( g, -a, qd );
if( zVecIsTiny( g ) ) goto TERMINATE;
b = zVecInnerProd( g, qd ) / s;
zVecCat( g, b, d, d );
}
ZITERWARN( iter );
TERMINATE:
result = zQuadraticValue( q, c, ans );
zVecFreeAO( 3, d, g, qd );
return result;
}