/// resize
void resize(size_t nr, size_t nc, size_t nnz)
{ nr_ = nr;
nc_ = nc;
nnz_ = nnz;
row_.resize(nnz);
col_.resize(nnz);
}
/// return the index vectors I_{k,ell} and J_{k,ell}
/// (simple representation uses I[i] = i and J[j] = j)
virtual void index(size_t k, size_t ell, SizeVector& I, SizeVector& J)
{ assert( I.size() >= m_ + 1 );
assert( J.size() >= n_ );
for(size_t i = 0; i <= m_; i++)
I[i] = i;
for(size_t j = 0; j < n_; j++)
J[j] = j;
}
void
DataType::coreSizes(size_t parentOffset,
SizeVector &sizes,
SizeVector &offsets) const
{
sizes.push_back(objectSize());
offsets.push_back( parentOffset );
}
/// assignment
void operator=(const sparse_rc& pattern)
{ nr_ = pattern.nr_;
nc_ = pattern.nc_;
nnz_ = pattern.nnz_;
// simple vector assignment requires vectors to have same size
row_.resize(nnz_);
col_.resize(nnz_);
row_ = pattern.row_;
col_ = pattern.col_;
}
FunctionCallPtr
Interpreter::newFunctionCall (const std::string &functionName)
{
Lock lock (_data->mutex);
//
// Calling a CTL function with variable-size array arguments
// from C++ is not supported.
//
const SymbolInfoPtr info = symtab().lookupSymbol (functionName);
if (!info)
THROW (ArgExc, "Cannot find CTL function " << functionName << ".");
if (!info->isFunction())
THROW (TypeExc, "CTL object " << functionName << " is not a function "
"(it is of type " << info->type()->asString() << ").");
const FunctionTypePtr fType = info->type();
const ParamVector ¶meters = fType->parameters();
for (int i = parameters.size() - 1; i >= 0; --i)
{
const Param ¶m = parameters[i];
ArrayTypePtr aType = param.type.cast<ArrayType>();
if(aType)
{
SizeVector sizes;
aType->sizes (sizes);
for (int j = 0; j < sizes.size(); j++)
{
if (sizes[j] == 0)
THROW (ArgExc, "CTL function " << functionName << " "
"has a variable-size array "
"argument, " << param.name << ", and can "
"only be called by another CTL function.");
}
}
}
return newFunctionCallInternal (info, functionName);
}
Game::Game(Dimension dimensioncount, SizeVector dimensions, NullTimer *timer, ProgramOptions opts):
timer(timer), dimensions(dimensions), dimensioncount(dimensioncount),
allpositions_initialised(false), minecount(0), flagcount(0), pressedcount(0),
state(GAMESTATE_INIT), window(NULL), opts(opts) {
assert(dimensions.size() == dimensioncount);
assert(dimensioncount > 0);
this->inittiles(0);
}
void LuInvert(
const SizeVector &ip,
const SizeVector &jp,
const FloatVector &LU,
FloatVector &B )
{ size_t k; // column index in X
size_t p; // index along diagonal in LU
size_t i; // row index in LU and X
typedef typename FloatVector::value_type Float;
// check numeric type specifications
CheckNumericType<Float>();
// check simple vector class specifications
CheckSimpleVector<Float, FloatVector>();
CheckSimpleVector<size_t, SizeVector>();
Float etmp;
size_t n = ip.size();
CPPAD_ASSERT_KNOWN(
size_t(jp.size()) == n,
"Error in LuInvert: jp must have size equal to n * n"
);
CPPAD_ASSERT_KNOWN(
size_t(LU.size()) == n * n,
"Error in LuInvert: Lu must have size equal to n * m"
);
size_t m = size_t(B.size()) / n;
CPPAD_ASSERT_KNOWN(
size_t(B.size()) == n * m,
"Error in LuSolve: B must have size equal to a multiple of n"
);
// temporary storage for reordered solution
FloatVector x(n);
// loop over equations
for(k = 0; k < m; k++)
{ // invert the equation c = L * b
for(p = 0; p < n; p++)
{ // solve for c[p]
etmp = B[ ip[p] * m + k ] / LU[ ip[p] * n + jp[p] ];
B[ ip[p] * m + k ] = etmp;
// subtract off effect on other variables
for(i = p+1; i < n; i++)
B[ ip[i] * m + k ] -=
etmp * LU[ ip[i] * n + jp[p] ];
}
// invert the equation x = U * c
p = n;
while( p > 0 )
{ --p;
etmp = B[ ip[p] * m + k ];
x[ jp[p] ] = etmp;
for(i = 0; i < p; i++ )
B[ ip[i] * m + k ] -=
etmp * LU[ ip[i] * n + jp[p] ];
}
// copy reordered solution into B
for(i = 0; i < n; i++)
B[i * m + k] = x[i];
}
return;
}
int LuFactor(SizeVector &ip, SizeVector &jp, FloatVector &LU) //
{
// type of the elements of LU //
typedef typename FloatVector::value_type Float; //
// check numeric type specifications
CheckNumericType<Float>();
// check simple vector class specifications
CheckSimpleVector<Float, FloatVector>();
CheckSimpleVector<size_t, SizeVector>();
size_t i, j; // some temporary indices
const Float zero( 0 ); // the value zero as a Float object
size_t imax; // row index of maximum element
size_t jmax; // column indx of maximum element
Float emax; // maximum absolute value
size_t p; // count pivots
int sign; // sign of the permutation
Float etmp; // temporary element
Float pivot; // pivot element
// -------------------------------------------------------
size_t n = ip.size();
CPPAD_ASSERT_KNOWN(
size_t(jp.size()) == n,
"Error in LuFactor: jp must have size equal to n"
);
CPPAD_ASSERT_KNOWN(
size_t(LU.size()) == n * n,
"Error in LuFactor: LU must have size equal to n * m"
);
// -------------------------------------------------------
// initialize row and column order in matrix not yet pivoted
for(i = 0; i < n; i++)
{ ip[i] = i;
jp[i] = i;
}
// initialize the sign of the permutation
sign = 1;
// ---------------------------------------------------------
// Reduce the matrix P to L * U using n pivots
for(p = 0; p < n; p++)
{ // determine row and column corresponding to element of
// maximum absolute value in remaining part of P
imax = jmax = n;
emax = zero;
for(i = p; i < n; i++)
{ for(j = p; j < n; j++)
{ CPPAD_ASSERT_UNKNOWN(
(ip[i] < n) & (jp[j] < n)
);
etmp = LU[ ip[i] * n + jp[j] ];
// check if maximum absolute value so far
if( AbsGeq (etmp, emax) )
{ imax = i;
jmax = j;
emax = etmp;
}
}
}
CPPAD_ASSERT_KNOWN(
(imax < n) & (jmax < n) ,
"LuFactor can't determine an element with "
"maximum absolute value.\n"
"Perhaps original matrix contains not a number or infinity.\n"
"Perhaps your specialization of AbsGeq is not correct."
);
if( imax != p )
{ // switch rows so max absolute element is in row p
i = ip[p];
ip[p] = ip[imax];
ip[imax] = i;
sign = -sign;
}
if( jmax != p )
{ // switch columns so max absolute element is in column p
j = jp[p];
jp[p] = jp[jmax];
jp[jmax] = j;
sign = -sign;
}
// pivot using the max absolute element
pivot = LU[ ip[p] * n + jp[p] ];
// check for determinant equal to zero
if( pivot == zero )
{ // abort the mission
return 0;
}
// Reduce U by the elementary transformations that maps
// LU( ip[p], jp[p] ) to one. Only need transform elements
// above the diagonal in U and LU( ip[p] , jp[p] ) is
// corresponding value below diagonal in L.
for(j = p+1; j < n; j++)
LU[ ip[p] * n + jp[j] ] /= pivot;
// Reduce U by the elementary transformations that maps
// LU( ip[i], jp[p] ) to zero. Only need transform elements
// above the diagonal in U and LU( ip[i], jp[p] ) is
// corresponding value below diagonal in L.
for(i = p+1; i < n; i++ )
{ etmp = LU[ ip[i] * n + jp[p] ];
for(j = p+1; j < n; j++)
{ LU[ ip[i] * n + jp[j] ] -=
etmp * LU[ ip[p] * n + jp[j] ];
}
}
}
return sign;
}
void UCK::makePathMatrix(const PairVector& e, SizeVector& sp, const Size e_size)
{
std::vector<Size>* line;
// create bond-matrix, because Floyd's Algorithm requires a reachability matrix
SizeVector* bond_matrix;
line = new vector<Size>;
bond_matrix = new SizeVector;
// initialize bond-matrix with 0 at every position
for (Size i = 0; i != e_size; ++i)
{
line->clear();
for(Size j = 0; j != e_size; ++j)
{
line->push_back(0);
}
bond_matrix->push_back(*line);
}
// proceed all edges and set corresponding position in bond_matrix to 1
for (Size i = 0; i != e.size(); ++i)
{
(*bond_matrix)[e[i].first][e[i].second] = 1;
}
// initialize sp-matrix
for(Size i = 0; i != bond_matrix->size(); ++i)
{
line->clear();
for(Size j = 0; j != bond_matrix->size(); ++j)
{
if (i == j) // distance from a node to itself = 0
{
line->push_back(0);
}
else if((*bond_matrix)[i][j] == 1) // if an edge exists between node i and j,
{
line->push_back(1); // the distance between them is 1
}
else
{
line->push_back(std::numeric_limits<Index>::max()); // otherwise the distance is set to infinity
}
}
sp.push_back(*line);
}
// Floyd's Algorithm
for(Size i = 0; i != sp.size(); ++i)
{
for(Size j = 0; j != sp.size(); ++j)
{
for(Size k = 0; k != sp.size(); k++)
{
if(sp[j][k] > (sp[j][i] + sp[i][k]))
{
sp[j][k] = (sp[j][i] + sp[i][k]);
}
}
}
}
delete bond_matrix;
delete line;
return;
}
int LuRatio(SizeVector &ip, SizeVector &jp, ADvector &LU, AD<Base> &ratio) //
{
typedef ADvector FloatVector; //
typedef AD<Base> Float; //
// check numeric type specifications
CheckNumericType<Float>();
// check simple vector class specifications
CheckSimpleVector<Float, FloatVector>();
CheckSimpleVector<size_t, SizeVector>();
size_t i, j; // some temporary indices
const Float zero( 0 ); // the value zero as a Float object
size_t imax; // row index of maximum element
size_t jmax; // column indx of maximum element
Float emax; // maximum absolute value
size_t p; // count pivots
int sign; // sign of the permutation
Float etmp; // temporary element
Float pivot; // pivot element
// -------------------------------------------------------
size_t n = size_t(ip.size());
CPPAD_ASSERT_KNOWN(
size_t(jp.size()) == n,
"Error in LuFactor: jp must have size equal to n"
);
CPPAD_ASSERT_KNOWN(
size_t(LU.size()) == n * n,
"Error in LuFactor: LU must have size equal to n * m"
);
// -------------------------------------------------------
// initialize row and column order in matrix not yet pivoted
for(i = 0; i < n; i++)
{ ip[i] = i;
jp[i] = i;
}
// initialize the sign of the permutation
sign = 1;
// initialize the ratio //
ratio = Float(1); //
// ---------------------------------------------------------
// Reduce the matrix P to L * U using n pivots
for(p = 0; p < n; p++)
{ // determine row and column corresponding to element of
// maximum absolute value in remaining part of P
imax = jmax = n;
emax = zero;
for(i = p; i < n; i++)
{ for(j = p; j < n; j++)
{ CPPAD_ASSERT_UNKNOWN(
(ip[i] < n) & (jp[j] < n)
);
etmp = LU[ ip[i] * n + jp[j] ];
// check if maximum absolute value so far
if( AbsGeq (etmp, emax) )
{ imax = i;
jmax = j;
emax = etmp;
}
}
}
for(i = p; i < n; i++) //
{ for(j = p; j < n; j++) //
{ etmp = abs(LU[ ip[i] * n + jp[j] ] / emax); //
ratio = //
CondExpGt(etmp, ratio, etmp, ratio); //
} //
} //
CPPAD_ASSERT_KNOWN(
(imax < n) & (jmax < n) ,
"AbsGeq must return true when second argument is zero"
);
if( imax != p )
{ // switch rows so max absolute element is in row p
i = ip[p];
ip[p] = ip[imax];
ip[imax] = i;
sign = -sign;
}
if( jmax != p )
{ // switch columns so max absolute element is in column p
j = jp[p];
jp[p] = jp[jmax];
jp[jmax] = j;
sign = -sign;
}
// pivot using the max absolute element
pivot = LU[ ip[p] * n + jp[p] ];
// check for determinant equal to zero
if( pivot == zero )
{ // abort the mission
return 0;
}
// Reduce U by the elementary transformations that maps
// LU( ip[p], jp[p] ) to one. Only need transform elements
// above the diagonal in U and LU( ip[p] , jp[p] ) is
// corresponding value below diagonal in L.
for(j = p+1; j < n; j++)
LU[ ip[p] * n + jp[j] ] /= pivot;
// Reduce U by the elementary transformations that maps
// LU( ip[i], jp[p] ) to zero. Only need transform elements
// above the diagonal in U and LU( ip[i], jp[p] ) is
// corresponding value below diagonal in L.
for(i = p+1; i < n; i++ )
{ etmp = LU[ ip[i] * n + jp[p] ];
for(j = p+1; j < n; j++)
{ LU[ ip[i] * n + jp[j] ] -=
etmp * LU[ ip[p] * n + jp[j] ];
}
}
}
return sign;
}
/// sizing constructor
/// Eigen vector is ambiguous for row_(0), col_(0) so use default ctor
sparse_rc(size_t nr, size_t nc, size_t nnz)
: nr_(nr), nc_(nc), nnz_(nnz)
{ row_.resize(nnz);
col_.resize(nnz);
}
void color_general_cppad(
const SetVector& pattern ,
const SizeVector& row ,
const SizeVector& col ,
CppAD::vector<size_t>& color )
{
size_t K = row.size();
size_t m = pattern.n_set();
size_t n = pattern.end();
CPPAD_ASSERT_UNKNOWN( size_t( col.size() ) == K );
CPPAD_ASSERT_UNKNOWN( size_t( color.size() ) == m );
// We define the set of rows, columns, and pairs that appear
// by the set ( row[k], col[k] ) for k = 0, ... , K-1.
// initialize rows that appear
CppAD::vector<bool> row_appear(m);
for(size_t i = 0; i < m; i++)
row_appear[i] = false;
// rows and columns that appear
SetVector c2r_appear, r2c_appear;
c2r_appear.resize(n, m);
r2c_appear.resize(m, n);
for(size_t k = 0; k < K; k++)
{ CPPAD_ASSERT_UNKNOWN( pattern.is_element(row[k], col[k]) );
row_appear[ row[k] ] = true;
c2r_appear.post_element(col[k], row[k]);
r2c_appear.post_element(row[k], col[k]);
}
// process posts
for(size_t j = 0; j < n; ++j)
c2r_appear.process_post(j);
for(size_t i = 0; i < m; ++i)
r2c_appear.process_post(i);
// for each column, which rows are non-zero and do not appear
SetVector not_appear;
not_appear.resize(n, m);
for(size_t i = 0; i < m; i++)
{ typename SetVector::const_iterator pattern_itr(pattern, i);
size_t j = *pattern_itr;
while( j != pattern.end() )
{ if( ! c2r_appear.is_element(j , i) )
not_appear.post_element(j, i);
j = *(++pattern_itr);
}
}
// process posts
for(size_t j = 0; j < n; ++j)
not_appear.process_post(j);
// initial coloring
color.resize(m);
size_t ell = 0;
for(size_t i = 0; i < m; i++)
{ if( row_appear[i] )
color[i] = ell++;
else
color[i] = m;
}
/*
See GreedyPartialD2Coloring Algorithm Section 3.6.2 of
Graph Coloring in Optimization Revisited by
Assefaw Gebremedhin, Fredrik Maane, Alex Pothen
The algorithm above was modified (by Brad Bell) to take advantage of the
fact that only the entries (subset of the sparsity pattern) specified by
row and col need to be computed.
*/
CppAD::vector<bool> forbidden(m);
for(size_t i = 1; i < m; i++) // for each row that appears
if( color[i] < m )
{
// initial all colors as ok for this row
// (value of forbidden for ell > initial color[i] does not matter)
for(ell = 0; ell <= color[i]; ell++)
forbidden[ell] = false;
// -----------------------------------------------------
// Forbid colors for which this row would destroy results:
//
// for each column that is non-zero for this row
typename SetVector::const_iterator pattern_itr(pattern, i);
size_t j = *pattern_itr;
while( j != pattern.end() )
{ // for each row that appears with this column
typename SetVector::const_iterator c2r_itr(c2r_appear, j);
size_t r = *c2r_itr;
while( r != c2r_appear.end() )
{ // if this is not the same row, forbid its color
if( (r < i) & (color[r] < m) )
forbidden[ color[r] ] = true;
r = *(++c2r_itr);
}
j = *(++pattern_itr);
}
// -----------------------------------------------------
// Forbid colors that destroy results needed for this row.
//
// for each column that appears with this row
typename SetVector::const_iterator r2c_itr(r2c_appear, i);
j = *r2c_itr;
while( j != r2c_appear.end() )
{ // For each row that is non-zero for this column
// (the appear rows have already been checked above).
typename SetVector::const_iterator not_itr(not_appear, j);
size_t r = *not_itr;
while( r != not_appear.end() )
{ // if this is not the same row, forbid its color
if( (r < i) & (color[r] < m) )
forbidden[ color[r] ] = true;
r = *(++not_itr);
}
j = *(++r2c_itr);
}
// pick the color with smallest index
ell = 0;
while( forbidden[ell] )
{ ell++;
CPPAD_ASSERT_UNKNOWN( ell <= color[i] );
}
color[i] = ell;
}
return;
}
void ADFun<Base,RecBase>::subgraph_jac_rev(
const BoolVector& select_domain ,
const BoolVector& select_range ,
const BaseVector& x ,
sparse_rcv<SizeVector, BaseVector>& matrix_out )
{ size_t m = Range();
size_t n = Domain();
//
// point at which we are evaluating Jacobian
Forward(0, x);
//
// nnz and row, column, and row_major vectors for subset
local::pod_vector<size_t> row_out;
local::pod_vector<size_t> col_out;
local::pod_vector_maybe<Base> val_out;
//
// initialize reverse mode computation on subgraphs
subgraph_reverse(select_domain);
//
// memory used to hold subgraph_reverse results
BaseVector dw;
SizeVector col;
//
// loop through selected independent variables
for(size_t i = 0; i < m; ++i) if( select_range[i] )
{ // compute Jacobian and sparsity for this dependent variable
size_t q = 1;
subgraph_reverse(q, i, col, dw);
CPPAD_ASSERT_UNKNOWN( size_t( dw.size() ) == n );
//
// offset for this dependent variable
size_t index = row_out.size();
CPPAD_ASSERT_UNKNOWN( col_out.size() == index );
CPPAD_ASSERT_UNKNOWN( val_out.size() == index );
//
// extend vectors to hold results for this dependent variable
size_t col_size = size_t( col.size() );
row_out.extend( col_size );
col_out.extend( col_size );
val_out.extend( col_size );
//
// store results for this dependent variable
for(size_t c = 0; c < col_size; ++c)
{ row_out[index + c] = i;
col_out[index + c] = col[c];
val_out[index + c] = dw[ col[c] ];
}
}
//
// create sparsity pattern corresponding to row_out, col_out
size_t nr = m;
size_t nc = n;
size_t nnz = row_out.size();
sparse_rc<SizeVector> pattern(nr, nc, nnz);
for(size_t k = 0; k < nnz; ++k)
pattern.set(k, row_out[k], col_out[k]);
//
// create sparse matrix
sparse_rcv<SizeVector, BaseVector> matrix(pattern);
for(size_t k = 0; k < nnz; ++k)
matrix.set(k, val_out[k]);
//
// return matrix
matrix_out = matrix;
//
return;
}
bool abs_min_linear(
size_t level ,
size_t n ,
size_t m ,
size_t s ,
const DblVector& g_hat ,
const DblVector& g_jac ,
const DblVector& bound ,
const DblVector& epsilon ,
const SizeVector& maxitr ,
DblVector& delta_x )
// END PROTOTYPE
{ using std::fabs;
bool ok = true;
double inf = std::numeric_limits<double>::infinity();
//
CPPAD_ASSERT_KNOWN(
level <= 4,
"abs_min_linear: level is not less that or equal 4"
);
CPPAD_ASSERT_KNOWN(
size_t(epsilon.size()) == 2,
"abs_min_linear: size of epsilon not equal to 2"
);
CPPAD_ASSERT_KNOWN(
size_t(maxitr.size()) == 2,
"abs_min_linear: size of maxitr not equal to 2"
);
CPPAD_ASSERT_KNOWN(
m == 1,
"abs_min_linear: m is not equal to 1"
);
CPPAD_ASSERT_KNOWN(
size_t(delta_x.size()) == n,
"abs_min_linear: size of delta_x not equal to n"
);
CPPAD_ASSERT_KNOWN(
size_t(bound.size()) == n,
"abs_min_linear: size of bound not equal to n"
);
CPPAD_ASSERT_KNOWN(
size_t(g_hat.size()) == m + s,
"abs_min_linear: size of g_hat not equal to m + s"
);
CPPAD_ASSERT_KNOWN(
size_t(g_jac.size()) == (m + s) * (n + s),
"abs_min_linear: size of g_jac not equal to (m + s)*(n + s)"
);
CPPAD_ASSERT_KNOWN(
size_t(bound.size()) == n,
"abs_min_linear: size of bound is not equal to n"
);
if( level > 0 )
{ std::cout << "start abs_min_linear\n";
CppAD::abs_print_mat("bound", n, 1, bound);
CppAD::abs_print_mat("g_hat", m + s, 1, g_hat);
CppAD::abs_print_mat("g_jac", m + s, n + s, g_jac);
}
// partial y(x, u) w.r.t x (J in reference)
DblVector py_px(n);
for(size_t j = 0; j < n; j++)
py_px[ j ] = g_jac[ j ];
//
// partial y(x, u) w.r.t u (Y in reference)
DblVector py_pu(s);
for(size_t j = 0; j < s; j++)
py_pu[ j ] = g_jac[ n + j ];
//
// partial z(x, u) w.r.t x (Z in reference)
DblVector pz_px(s * n);
for(size_t i = 0; i < s; i++)
{ for(size_t j = 0; j < n; j++)
{ pz_px[ i * n + j ] = g_jac[ (n + s) * (i + m) + j ];
}
}
// partial z(x, u) w.r.t u (L in reference)
DblVector pz_pu(s * s);
for(size_t i = 0; i < s; i++)
{ for(size_t j = 0; j < s; j++)
{ pz_pu[ i * s + j ] = g_jac[ (n + s) * (i + m) + n + j ];
}
}
// initailize delta_x
for(size_t j = 0; j < n; j++)
delta_x[j] = 0.0;
//
// value of approximation for g(x, u) at current delta_x
DblVector g_tilde = CppAD::abs_eval(n, m, s, g_hat, g_jac, delta_x);
//
// value of sigma at delta_x = 0; i.e., sign( z(x, u) )
CppAD::vector<double> sigma(s);
for(size_t i = 0; i < s; i++)
sigma[i] = CppAD::sign( g_tilde[m + i] );
//
// current set of cutting planes
DblVector C(maxitr[0] * n), c(maxitr[0]);
//
//
size_t n_plane = 0;
for(size_t itr = 0; itr < maxitr[0]; itr++)
{
// Equation (5), Propostion 3.1 of reference
// dy_dx = py_px + py_pu * Sigma * (I - pz_pu * Sigma)^-1 * pz_px
//
// tmp_ss = I - pz_pu * Sigma
DblVector tmp_ss(s * s);
for(size_t i = 0; i < s; i++)
{ for(size_t j = 0; j < s; j++)
tmp_ss[i * s + j] = - pz_pu[i * s + j] * sigma[j];
tmp_ss[i * s + i] += 1.0;
}
// tmp_sn = (I - pz_pu * Sigma)^-1 * pz_px
double logdet;
DblVector tmp_sn(s * n);
LuSolve(s, n, tmp_ss, pz_px, tmp_sn, logdet);
//
// tmp_sn = Sigma * (I - pz_pu * Sigma)^-1 * pz_px
for(size_t i = 0; i < s; i++)
{ for(size_t j = 0; j < n; j++)
tmp_sn[i * n + j] *= sigma[i];
}
// dy_dx = py_px + py_pu * Sigma * (I - pz_pu * Sigma)^-1 * pz_px
DblVector dy_dx(n);
for(size_t j = 0; j < n; j++)
{ dy_dx[j] = py_px[j];
for(size_t k = 0; k < s; k++)
dy_dx[j] += py_pu[k] * tmp_sn[ k * n + j];
}
//
// check for case where derivative of hyperplane is zero
// (in convex case, this is the minimizer)
bool near_zero = true;
for(size_t j = 0; j < n; j++)
near_zero &= std::fabs( dy_dx[j] ) < epsilon[1];
if( near_zero )
{ if( level > 0 )
std::cout << "end abs_min_linear: local derivative near zero\n";
return true;
}
// value of hyperplane at delta_x
double plane_at_zero = g_tilde[0];
// value of hyperplane at 0
for(size_t j = 0; j < n; j++)
plane_at_zero -= dy_dx[j] * delta_x[j];
//
// add a cutting plane with value g_tilde[0] at delta_x
// and derivative dy_dx
c[n_plane] = plane_at_zero;
for(size_t j = 0; j < n; j++)
C[n_plane * n + j] = dy_dx[j];
++n_plane;
//
// variables for cutting plane problem are (dx, w)
// c[i] + C[i,:]*dx <= w
DblVector b_box(n_plane), A_box(n_plane * (n + 1));
for(size_t i = 0; i < n_plane; i++)
{ b_box[i] = c[i];
for(size_t j = 0; j < n; j++)
A_box[i * (n+1) + j] = C[i * n + j];
A_box[i *(n+1) + n] = -1.0;
}
// w is the objective
DblVector c_box(n + 1);
for(size_t i = 0; i < size_t(c_box.size()); i++)
c_box[i] = 0.0;
c_box[n] = 1.0;
//
// d_box
DblVector d_box(n+1);
for(size_t j = 0; j < n; j++)
d_box[j] = bound[j];
d_box[n] = inf;
//
// solve the cutting plane problem
DblVector xout_box(n + 1);
size_t level_box = 0;
if( level > 0 )
level_box = level - 1;
ok &= CppAD::lp_box(
level_box,
A_box,
b_box,
c_box,
d_box,
maxitr[1],
xout_box
);
if( ! ok )
{ if( level > 0 )
{ CppAD::abs_print_mat("delta_x", n, 1, delta_x);
std::cout << "end abs_min_linear: lp_box failed\n";
}
return false;
}
//
// check for convergence
double max_diff = 0.0;
for(size_t j = 0; j < n; j++)
{ double diff = delta_x[j] - xout_box[j];
max_diff = std::max( max_diff, std::fabs(diff) );
}
//
// check for descent in value of approximation objective
DblVector delta_new(n);
for(size_t j = 0; j < n; j++)
delta_new[j] = xout_box[j];
DblVector g_new = CppAD::abs_eval(n, m, s, g_hat, g_jac, delta_new);
if( level > 0 )
{ std::cout << "itr = " << itr << ", max_diff = " << max_diff
<< ", y_cur = " << g_tilde[0] << ", y_new = " << g_new[0]
<< "\n";
CppAD::abs_print_mat("delta_new", n, 1, delta_new);
}
//
g_tilde = g_new;
delta_x = delta_new;
//
// value of sigma at new delta_x; i.e., sign( z(x, u) )
for(size_t i = 0; i < s; i++)
sigma[i] = CppAD::sign( g_tilde[m + i] );
//
if( max_diff < epsilon[0] )
{ if( level > 0 )
std::cout << "end abs_min_linear: change in delta_x near zero\n";
return true;
}
}
if( level > 0 )
std::cout << "end abs_min_linear: maximum number of iterations exceeded\n";
return false;
}