returnValue ExportGaussElim::setupSolveReuseComplete( ExportFunction& _solveReuse, ExportVariable& _bPerm ) {
ExportIndex run1( "i" );
ExportIndex run2( "j" );
ExportIndex tmp_index1( "index1" );
ExportIndex tmp_index2( "index2" );
ExportVariable tmp( "tmp_var", 1, 1, _bPerm.getType(), ACADO_LOCAL, true );
_solveReuse.addIndex( run1 );
_solveReuse.addIndex( run2 );
_solveReuse.addIndex( tmp_index1 );
_solveReuse.addIndex( tmp_index2 );
_solveReuse.addDeclaration(tmp);
uint run3;
if (nRightHandSides <= 0)
return ACADOERROR(RET_INVALID_OPTION);
ExportForLoop loop1( run1, 0, dim );
loop1 << run2.getName() << " = " << rk_perm.getFullName() << "[" << run1.getName() << "]*" << toString(nRightHandSides) << ";\n";
for( run3 = 0; run3 < nRightHandSides; run3++ ) {
loop1 << _bPerm.get( run1,run3 ) << " = b[" << run2.getName() << "+" << toString(run3) << "];\n";
}
_solveReuse.addStatement( loop1 );
ExportForLoop loop2( run2, 1, dim ); // row run2
loop2.addStatement( tmp_index1 == run2*nRightHandSides );
ExportForLoop loop3( run1, 0, run2 ); // column run1
loop3.addStatement( tmp_index2 == run1*nRightHandSides );
loop3.addStatement( tmp == A.getElement(run2,run1) );
for( run3 = 0; run3 < nRightHandSides; run3++ ) {
// loop3.addStatement( _bPerm.getElement( run2,run3 ) += tmp * _bPerm.getElement( run1,run3 ) );
loop3 << _bPerm.getFullName() << "[" << tmp_index1.getName() << "+" << toString(run3) << "] += " << tmp.getName() << "*" << _bPerm.getFullName() << "[" << tmp_index2.getName() << "+" << toString(run3) << "];\n";
}
loop2.addStatement( loop3 );
_solveReuse.addStatement( loop2 );
// Solve the upper triangular system of equations:
ExportForLoop loop4( run1, dim-1, -1, -1 );
loop4.addStatement( tmp_index1 == run1*nRightHandSides );
ExportForLoop loop5( run2, dim-1, run1, -1 );
loop5.addStatement( tmp_index2 == run2*nRightHandSides );
loop5.addStatement( tmp == A.getElement( run1,run2 ) );
for( run3 = 0; run3 < nRightHandSides; run3++ ) {
// loop5.addStatement( _bPerm.getElement( run1,run3 ) -= tmp * _bPerm.getElement( run2,run3 ) );
loop5 << _bPerm.getFullName() << "[" << tmp_index1.getName() << "+" << toString(run3) << "] -= " << tmp.getName() << "*" << _bPerm.getFullName() << "[" << tmp_index2.getName() << "+" << toString(run3) << "];\n";
}
loop4.addStatement( loop5 );
loop4 << tmp.getName() << " = 1.0/A[" << run1.getName() << "*" << toString(dim+1) << "];\n";
for( run3 = 0; run3 < nRightHandSides; run3++ ) {
// loop4 << _bPerm.get( run1,run3 ) << " = " << _bPerm.get( run1,run3 ) << "*" << tmp.getName() << ";\n";
loop4 << _bPerm.getFullName() << "[" << tmp_index1.getName() << "+" << toString(run3) << "] = " << tmp.getName() << "*" << _bPerm.getFullName() << "[" << tmp_index1.getName() << "+" << toString(run3) << "];\n";
}
_solveReuse.addStatement( loop4 );
_solveReuse.addStatement( b == _bPerm );
return SUCCESSFUL_RETURN;
}
returnValue ExportGaussElim::setupSolveReuseTranspose( ExportFunction& _solveReuse, ExportVariable& _bPerm ) {
ExportIndex run1( "i" );
ExportIndex run2( "j" );
ExportVariable tmp( "tmp_var", 1, 1, _bPerm.getType(), ACADO_LOCAL, true );
_solveReuse.addIndex( run1 );
_solveReuse.addIndex( run2 );
_solveReuse.addDeclaration(tmp);
_solveReuse.addStatement( _bPerm == b_trans );
ExportForLoop loop2( run2, 0, dim ); // row run2
ExportForLoop loop3( run1, 0, run2 ); // column run1
loop3.addStatement( _bPerm.getRow(run2) -= A.getElement(run1,run2)*_bPerm.getRow(run1) );
loop2.addStatement( loop3 );
loop2 << tmp.getName() << " = 1.0/A[" << run2.getName() << "*" << toString(dim+1) << "];\n";
loop2.addStatement( _bPerm.getRow(run2) == _bPerm.getRow(run2)*tmp );
_solveReuse.addStatement( loop2 );
// Solve the upper triangular system of equations:
ExportForLoop loop4( run1, dim-1, -1, -1 );
ExportForLoop loop5( run2, dim-1, run1, -1 );
loop5.addStatement( _bPerm.getRow(run1) += A.getElement(run2,run1)*_bPerm.getRow(run2) );
loop4.addStatement( loop5 );
_solveReuse.addStatement( loop4 );
// The permutation now happens HERE!
ExportForLoop loop1( run1, 0, dim );
loop1 << run2.getName() << " = " << rk_perm.getFullName() << "[" << run1.getName() << "];\n";
loop1.addStatement( b_trans.getRow(run2) == _bPerm.getRow(run1) );
_solveReuse.addStatement( loop1 );
return SUCCESSFUL_RETURN;
}
returnValue ExportGaussElim::setupFactorization( ExportFunction& _solve, ExportVariable& _swap, ExportVariable& _determinant, const string& absF ) {
uint run1, run2, run3;
ExportIndex i( "i" );
_solve.addIndex( i );
ExportIndex j( "j" );
ExportIndex k( "k" );
ExportVariable indexMax( "indexMax", 1, 1, INT, ACADO_LOCAL, true );
ExportVariable intSwap( "intSwap", 1, 1, INT, ACADO_LOCAL, true );
ExportVariable valueMax( "valueMax", 1, 1, REAL, ACADO_LOCAL, true );
ExportVariable temp( "temp", 1, 1, REAL, ACADO_LOCAL, true );
if( !UNROLLING ) {
_solve.addIndex( j );
_solve.addIndex( k );
_solve.addDeclaration( indexMax );
if( REUSE ) _solve.addDeclaration( intSwap );
_solve.addDeclaration( valueMax );
_solve.addDeclaration( temp );
}
// initialise rk_perm (the permutation vector)
if( REUSE ) {
ExportForLoop loop1( i,0,dim );
loop1 << rk_perm.get( 0,i ) << " = " << i.getName() << ";\n";
_solve.addStatement( loop1 );
}
_solve.addStatement( _determinant == 1 );
if( UNROLLING || dim <= 5 ) {
// Start the factorization:
for( run1 = 0; run1 < (dim-1); run1++ ) {
// Search for pivot in column run1:
for( run2 = run1+1; run2 < dim; run2++ ) {
// add the test (if or else if):
stringstream test;
if( run2 == (run1+1) ) {
test << "if(";
} else {
test << "else if(";
}
test << absF << "(A[" << toString( run2*dim+run1 ) << "]) > " << absF << "(A[" << toString( run1*dim+run1 ) << "])";
for( run3 = run1+1; run3 < dim; run3++ ) {
if( run3 != run2) {
test << " && " << absF << "(A[" << toString( run2*dim+run1 ) << "]) > " << absF << "(A[" << toString( run3*dim+run1 ) << "])";
}
}
test << ") {\n";
_solve.addStatement( test.str() );
// do the row swaps:
// for A:
for( run3 = 0; run3 < dim; run3++ ) {
_solve.addStatement( _swap == A.getSubMatrix( run1,run1+1,run3,run3+1 ) );
_solve.addStatement( A.getSubMatrix( run1,run1+1,run3,run3+1 ) == A.getSubMatrix( run2,run2+1,run3,run3+1 ) );
_solve.addStatement( A.getSubMatrix( run2,run2+1,run3,run3+1 ) == _swap );
}
if( REUSE ) { // rk_perm also needs to be updated if it needs to be possible to reuse the factorization
_solve.addStatement( intSwap == rk_perm.getCol( run1 ) );
_solve.addStatement( rk_perm.getCol( run1 ) == rk_perm.getCol( run2 ) );
_solve.addStatement( rk_perm.getCol( run2 ) == intSwap );
}
_solve.addStatement( "}\n" );
}
// potentially needed row swaps are done
_solve.addLinebreak();
// update of the next rows:
for( run2 = run1+1; run2 < dim; run2++ ) {
_solve << "A[" << toString( run2*dim+run1 ) << "] = -A[" << toString( run2*dim+run1 ) << "]/A[" << toString( run1*dim+run1 ) << "];\n";
_solve.addStatement( A.getSubMatrix( run2,run2+1,run1+1,dim ) += A.getSubMatrix( run2,run2+1,run1,run1+1 ) * A.getSubMatrix( run1,run1+1,run1+1,dim ) );
_solve.addLinebreak();
}
_solve.addStatement( _determinant == _determinant*A.getSubMatrix(run1,run1+1,run1,run1+1) );
_solve.addLinebreak();
}
_solve.addStatement( _determinant == _determinant*A.getSubMatrix(dim-1,dim,dim-1,dim) );
_solve.addLinebreak();
}
else { // without UNROLLING:
_solve << "for( i=0; i < (" << toString( dim-1 ) << "); i++ ) {\n";
_solve << " indexMax = i;\n";
_solve << " valueMax = " << absF << "(A[i*" << toString( dim ) << "+i]);\n";
_solve << " for( j=(i+1); j < " << toString( dim ) << "; j++ ) {\n";
_solve << " temp = " << absF << "(A[j*" << toString( dim ) << "+i]);\n";
_solve << " if( temp > valueMax ) {\n";
_solve << " indexMax = j;\n";
_solve << " valueMax = temp;\n";
_solve << " }\n";
_solve << " }\n";
_solve << " if( indexMax > i ) {\n";
ExportForLoop loop2( k,0,dim );
loop2 << " " << _swap.getFullName() << " = A[i*" << toString( dim ) << "+" << k.getName() << "];\n";
loop2 << " A[i*" << toString( dim ) << "+" << k.getName() << "] = A[indexMax*" << toString( dim ) << "+" << k.getName() << "];\n";
loop2 << " A[indexMax*" << toString( dim ) << "+" << k.getName() << "] = " << _swap.getFullName() << ";\n";
_solve.addStatement( loop2 );
if( REUSE ) {
_solve << " " << intSwap.getFullName() << " = " << rk_perm.getFullName() << "[i];\n";
_solve << " " << rk_perm.getFullName() << "[i] = " << rk_perm.getFullName() << "[indexMax];\n";
_solve << " " << rk_perm.getFullName() << "[indexMax] = " << intSwap.getFullName() << ";\n";
}
_solve << " }\n";
_solve << " " << _determinant.getFullName() << " *= A[i*" << toString( dim ) << "+i];\n";
_solve << " for( j=i+1; j < " << toString( dim ) << "; j++ ) {\n";
_solve << " A[j*" << toString( dim ) << "+i] = -A[j*" << toString( dim ) << "+i]/A[i*" << toString( dim ) << "+i];\n";
_solve << " for( k=i+1; k < " << toString( dim ) << "; k++ ) {\n";
_solve << " A[j*" << toString( dim ) << "+k] += A[j*" << toString( dim ) << "+i] * A[i*" << toString( dim ) << "+k];\n";
_solve << " }\n";
_solve << " }\n";
_solve << "}\n";
_solve << _determinant.getFullName() << " *= A[" << toString( (dim-1)*dim+(dim-1) ) << "];\n";
}
_solve << _determinant.getFullName() << " = " << absF << "(" << _determinant.getFullName() << ");\n";
return SUCCESSFUL_RETURN;
}