void ForSparseJacSet(
bool transpose ,
size_t q ,
const VectorSet& r ,
VectorSet& s ,
size_t total_num_var ,
CppAD::vector<size_t>& dep_taddr ,
CppAD::vector<size_t>& ind_taddr ,
CppAD::player<Base>& play ,
CPPAD_INTERNAL_SPARSE_SET& for_jac_sparsity )
{
// temporary indices
size_t i, j;
std::set<size_t>::const_iterator itr;
// range and domain dimensions for F
size_t m = dep_taddr.size();
size_t n = ind_taddr.size();
CPPAD_ASSERT_KNOWN(
q > 0,
"RevSparseJac: q is not greater than zero"
);
CPPAD_ASSERT_KNOWN(
size_t(r.size()) == n || transpose,
"RevSparseJac: size of r is not equal to n and transpose is false."
);
CPPAD_ASSERT_KNOWN(
size_t(r.size()) == q || ! transpose,
"RevSparseJac: size of r is not equal to q and transpose is true."
);
// allocate memory for the requested sparsity calculation
for_jac_sparsity.resize(total_num_var, q);
// set values corresponding to independent variables
if( transpose )
{ for(i = 0; i < q; i++)
{ // add the elements that are present
itr = r[i].begin();
while( itr != r[i].end() )
{ j = *itr++;
CPPAD_ASSERT_KNOWN(
j < n,
"ForSparseJac: transpose is true and element of the set\n"
"r[j] has value greater than or equal n."
);
CPPAD_ASSERT_UNKNOWN( ind_taddr[j] < total_num_var );
// operator for j-th independent variable
CPPAD_ASSERT_UNKNOWN( play.GetOp( ind_taddr[j] ) == InvOp );
for_jac_sparsity.add_element( ind_taddr[j], i);
}
}
}
else
{ for(i = 0; i < n; i++)
{ CPPAD_ASSERT_UNKNOWN( ind_taddr[i] < total_num_var );
// ind_taddr[i] is operator taddr for i-th independent variable
CPPAD_ASSERT_UNKNOWN( play.GetOp( ind_taddr[i] ) == InvOp );
// add the elements that are present
itr = r[i].begin();
while( itr != r[i].end() )
{ j = *itr++;
CPPAD_ASSERT_KNOWN(
j < q,
"ForSparseJac: an element of the set r[i] "
"has value greater than or equal q."
);
for_jac_sparsity.add_element( ind_taddr[i], j);
}
}
}
// evaluate the sparsity patterns
ForJacSweep(
n,
total_num_var,
&play,
for_jac_sparsity
);
// return values corresponding to dependent variables
CPPAD_ASSERT_UNKNOWN( size_t(s.size()) == m || transpose );
CPPAD_ASSERT_UNKNOWN( size_t(s.size()) == q || ! transpose );
for(i = 0; i < m; i++)
{ CPPAD_ASSERT_UNKNOWN( dep_taddr[i] < total_num_var );
// extract results from for_jac_sparsity
// and add corresponding elements to sets in s
CPPAD_ASSERT_UNKNOWN( for_jac_sparsity.end() == q );
for_jac_sparsity.begin( dep_taddr[i] );
j = for_jac_sparsity.next_element();
while( j < q )
{ if( transpose )
s[j].insert(i);
else s[i].insert(j);
j = for_jac_sparsity.next_element();
}
}
}
void ForSparseJacBool(
bool transpose ,
size_t q ,
const VectorSet& r ,
VectorSet& s ,
size_t total_num_var ,
CppAD::vector<size_t>& dep_taddr ,
CppAD::vector<size_t>& ind_taddr ,
CppAD::player<Base>& play ,
sparse_pack& for_jac_sparsity )
{
// temporary indices
size_t i, j;
// range and domain dimensions for F
size_t m = dep_taddr.size();
size_t n = ind_taddr.size();
CPPAD_ASSERT_KNOWN(
q > 0,
"ForSparseJac: q is not greater than zero"
);
CPPAD_ASSERT_KNOWN(
size_t(r.size()) == n * q,
"ForSparseJac: size of r is not equal to\n"
"q times domain dimension for ADFun object."
);
// allocate memory for the requested sparsity calculation result
for_jac_sparsity.resize(total_num_var, q);
// set values corresponding to independent variables
for(i = 0; i < n; i++)
{ CPPAD_ASSERT_UNKNOWN( ind_taddr[i] < total_num_var );
// ind_taddr[i] is operator taddr for i-th independent variable
CPPAD_ASSERT_UNKNOWN( play.GetOp( ind_taddr[i] ) == InvOp );
// set bits that are true
if( transpose )
{ for(j = 0; j < q; j++) if( r[ j * n + i ] )
for_jac_sparsity.add_element( ind_taddr[i], j);
}
else
{ for(j = 0; j < q; j++) if( r[ i * q + j ] )
for_jac_sparsity.add_element( ind_taddr[i], j);
}
}
// evaluate the sparsity patterns
ForJacSweep(
n,
total_num_var,
&play,
for_jac_sparsity
);
// return values corresponding to dependent variables
CPPAD_ASSERT_UNKNOWN( size_t(s.size()) == m * q );
for(i = 0; i < m; i++)
{ CPPAD_ASSERT_UNKNOWN( dep_taddr[i] < total_num_var );
// extract the result from for_jac_sparsity
if( transpose )
{ for(j = 0; j < q; j++)
s[ j * m + i ] = false;
}
else
{ for(j = 0; j < q; j++)
s[ i * q + j ] = false;
}
CPPAD_ASSERT_UNKNOWN( for_jac_sparsity.end() == q );
for_jac_sparsity.begin( dep_taddr[i] );
j = for_jac_sparsity.next_element();
while( j < q )
{ if( transpose )
s[j * m + i] = true;
else s[i * q + j] = true;
j = for_jac_sparsity.next_element();
}
}
}
/**
* Accessor to vertices.
* @return pointer to vertices collection.
*/
VectorSet* getVertices()
{
VectorSet* newVertices = new VectorSet();
for(unsigned i = 0; i < vertices.size(); i++)
newVertices->push_back(vertices[i]);
return newVertices;
}
/**
* Method is used to rotate solid by vectors and angle.
* @param a is rotate vector.
* @param b is rotate vector.
* @param angle is rotate angle value.
*/
void Rotate(const Vector& a, const Vector& b, float angle)
{
for(unsigned i = 0; i < vertices.size(); i++)
{
Vector v = vertices[i];
v = VectorRotate(v, a, b, angle);
vertices[i] = v;
}
}
/**
* Method is used to translate solid by vector.
* @param t is translate vector.
*/
void Translate(const Vector& t)
{
for(unsigned i = 0; i < vertices.size(); i++)
{
Vector v = vertices[i];
v = v + t;
vertices[i] = v;
}
}
/**
* Method is used to scale solid by vector.
* @param s id scale vector.
*/
void Scale(const Vector& s)
{
for(unsigned i = 0; i < vertices.size(); i++)
{
Vector v = vertices[i];
v = VectorScale(v, s);
vertices[i] = v;
}
}
void sparsity_user2internal(
sparse_set& internal ,
const VectorSet& user ,
size_t n_row ,
size_t n_col ,
bool transpose )
{ CPPAD_ASSERT_UNKNOWN( n_row == size_t(user.size()) );
CPPAD_ASSERT_KNOWN(
size_t( user.size() ) == n_row,
"Size of this vector of sets sparsity pattern is not equal "
"the range dimension for the corresponding function."
);
size_t i, j;
std::set<size_t>::const_iterator itr;
// transposed pattern case
if( transpose )
{ internal.resize(n_col, n_row);
for(i = 0; i < n_row; i++)
{ itr = user[i].begin();
while(itr != user[i].end())
{ j = *itr++;
CPPAD_ASSERT_UNKNOWN( j < n_col );
internal.add_element(j, i);
}
}
return;
}
// same pattern case
internal.resize(n_row, n_col);
for(i = 0; i < n_row; i++)
{ itr = user[i].begin();
while(itr != user[i].end())
{ j = *itr++;
CPPAD_ASSERT_UNKNOWN( j < n_col );
internal.add_element(i, j);
}
}
return;
}
void solve()
{
borderSquares[xFace]->clear();
borderSquares[yFace]->clear();
borderSquares[zFace]->clear();
for (vector<Face*>::iterator iter = faces.begin(); iter != faces.end(); iter++)
{
// derive all Squares of this face
Face* f = *iter;
// unsigned int startTime = getMicroSecs();
// cout << "deriveSquares: ";
f->deriveSquares();
// cout << (getMicroSecs() - startTime) << endl;
// put all squares of faces with the same orientation together
VectorSet* squares = borderSquares[f->orientation];
for(VectorSet::iterator iter = f->squares.begin(); iter != f->squares.end(); iter++)
{
Vertex v = *iter;
squares->insert(v);
}
}
VectorSet::iterator iter = borderSquares[zFace]->begin();
Vertex min = *iter;
while(iter != borderSquares[zFace]->end())
{
if(*iter < min)
min = *iter;
iter++;
}
blocks.clear();
blocks.insert(min);
// unsigned int startTime = getMicroSecs();
// cout << "collectBlocks: ";
collectBlocks(min);
// cout << (getMicroSecs() - startTime) << endl;
cout << "The bulk is composed of " << blocks.size() << " units.\n";
}
void RevSparseHesSet(
bool transpose ,
size_t q ,
const VectorSet& s ,
VectorSet& h ,
size_t num_var ,
CppAD::vector<size_t>& dep_taddr ,
CppAD::vector<size_t>& ind_taddr ,
CppAD::player<Base>& play ,
CPPAD_INTERNAL_SPARSE_SET& for_jac_sparsity )
{
// temporary indices
size_t i, j;
std::set<size_t>::const_iterator itr;
// check VectorSet is Simple Vector class with sets for elements
CheckSimpleVector<std::set<size_t>, VectorSet>(
one_element_std_set<size_t>(), two_element_std_set<size_t>()
);
// range and domain dimensions for F
# ifndef NDEBUG
size_t m = dep_taddr.size();
# endif
size_t n = ind_taddr.size();
CPPAD_ASSERT_KNOWN(
q == for_jac_sparsity.end(),
"RevSparseHes: q is not equal to its value\n"
"in the previous call to ForSparseJac with this ADFun object."
);
CPPAD_ASSERT_KNOWN(
s.size() == 1,
"RevSparseHes: size of s is not equal to one."
);
// Array that will hold reverse Jacobian dependency flag.
// Initialize as true for the dependent variables.
pod_vector<bool> RevJac;
RevJac.extend(num_var);
for(i = 0; i < num_var; i++)
RevJac[i] = false;
itr = s[0].begin();
while( itr != s[0].end() )
{ i = *itr++;
CPPAD_ASSERT_KNOWN(
i < m,
"RevSparseHes: an element of the set s[0] has value "
"greater than or equal m"
);
CPPAD_ASSERT_UNKNOWN( dep_taddr[i] < num_var );
RevJac[ dep_taddr[i] ] = true;
}
// vector of sets that will hold reverse Hessain values
CPPAD_INTERNAL_SPARSE_SET rev_hes_sparsity;
rev_hes_sparsity.resize(num_var, q);
// compute the Hessian sparsity patterns
RevHesSweep(
n,
num_var,
&play,
for_jac_sparsity,
RevJac.data(),
rev_hes_sparsity
);
// return values corresponding to independent variables
// j is index corresponding to reverse mode partial
CPPAD_ASSERT_UNKNOWN( size_t(h.size()) == q || transpose );
CPPAD_ASSERT_UNKNOWN( size_t(h.size()) == n || ! transpose );
for(j = 0; j < n; j++)
{ CPPAD_ASSERT_UNKNOWN( ind_taddr[j] < num_var );
CPPAD_ASSERT_UNKNOWN( ind_taddr[j] == j + 1 );
CPPAD_ASSERT_UNKNOWN( play.GetOp( ind_taddr[j] ) == InvOp );
// extract the result from rev_hes_sparsity
// and add corresponding elements to result sets in h
CPPAD_ASSERT_UNKNOWN( rev_hes_sparsity.end() == q );
rev_hes_sparsity.begin(j+1);
i = rev_hes_sparsity.next_element();
while( i < q )
{ if( transpose )
h[j].insert(i);
else h[i].insert(j);
i = rev_hes_sparsity.next_element();
}
}
return;
}
void RevSparseHesBool(
bool transpose ,
size_t q ,
const VectorSet& s ,
VectorSet& h ,
size_t num_var ,
CppAD::vector<size_t>& dep_taddr ,
CppAD::vector<size_t>& ind_taddr ,
CppAD::player<Base>& play ,
sparse_pack& for_jac_sparsity )
{
// temporary indices
size_t i, j;
// check Vector is Simple VectorSet class with bool elements
CheckSimpleVector<bool, VectorSet>();
// range and domain dimensions for F
size_t m = dep_taddr.size();
size_t n = ind_taddr.size();
CPPAD_ASSERT_KNOWN(
q == for_jac_sparsity.end(),
"RevSparseHes: q is not equal to its value\n"
"in the previous call to ForSparseJac with this ADFun object."
);
CPPAD_ASSERT_KNOWN(
size_t(s.size()) == m,
"RevSparseHes: size of s is not equal to\n"
"range dimension for ADFun object."
);
// Array that will hold reverse Jacobian dependency flag.
// Initialize as true for the dependent variables.
pod_vector<bool> RevJac;
RevJac.extend(num_var);
for(i = 0; i < num_var; i++)
RevJac[i] = false;
for(i = 0; i < m; i++)
{ CPPAD_ASSERT_UNKNOWN( dep_taddr[i] < num_var );
RevJac[ dep_taddr[i] ] = s[i];
}
// vector of sets that will hold reverse Hessain values
sparse_pack rev_hes_sparsity;
rev_hes_sparsity.resize(num_var, q);
// compute the Hessian sparsity patterns
RevHesSweep(
n,
num_var,
&play,
for_jac_sparsity,
RevJac.data(),
rev_hes_sparsity
);
// return values corresponding to independent variables
CPPAD_ASSERT_UNKNOWN( size_t(h.size()) == n * q );
for(j = 0; j < n; j++)
{ for(i = 0; i < q; i++)
{ if( transpose )
h[ j * q + i ] = false;
else h[ i * n + j ] = false;
}
}
// j is index corresponding to reverse mode partial
for(j = 0; j < n; j++)
{ CPPAD_ASSERT_UNKNOWN( ind_taddr[j] < num_var );
// ind_taddr[j] is operator taddr for j-th independent variable
CPPAD_ASSERT_UNKNOWN( ind_taddr[j] == j + 1 );
CPPAD_ASSERT_UNKNOWN( play.GetOp( ind_taddr[j] ) == InvOp );
// extract the result from rev_hes_sparsity
CPPAD_ASSERT_UNKNOWN( rev_hes_sparsity.end() == q );
rev_hes_sparsity.begin(j + 1);
i = rev_hes_sparsity.next_element();
while( i < q )
{ if( transpose )
h[ j * q + i ] = true;
else h[ i * n + j ] = true;
i = rev_hes_sparsity.next_element();
}
}
return;
}
void ADFun<Base>::SparseJacobianCase(
const std::set<size_t>& set_type ,
const VectorBase& x ,
const VectorSet& p ,
VectorBase& jac )
{
typedef CppAD::vector<size_t> SizeVector;
typedef CppAD::vectorBool VectorBool;
size_t i, j, k;
size_t m = Range();
size_t n = Domain();
// some values
const Base zero(0);
const Base one(1);
// check VectorSet is Simple Vector class with sets for elements
CheckSimpleVector<std::set<size_t>, VectorSet>(
one_element_std_set<size_t>(), two_element_std_set<size_t>()
);
// check VectorBase is Simple Vector class with Base type elements
CheckSimpleVector<Base, VectorBase>();
CPPAD_ASSERT_KNOWN(
x.size() == n,
"SparseJacobian: size of x not equal domain dimension for f"
);
CPPAD_ASSERT_KNOWN(
p.size() == m,
"SparseJacobian: using sets and size of p "
"not equal range dimension for f"
);
CPPAD_ASSERT_UNKNOWN(jac.size() == m * n);
// point at which we are evaluating the Jacobian
Forward(0, x);
// initialize the return value
for(i = 0; i < m; i++)
for(j = 0; j < n; j++)
jac[i * n + j] = zero;
// create a copy of the transpose sparsity pattern
VectorSet q(n);
std::set<size_t>::const_iterator itr_i, itr_j;
for(i = 0; i < m; i++)
{ itr_j = p[i].begin();
while( itr_j != p[i].end() )
{ j = *itr_j++;
q[j].insert(i);
}
}
if( n <= m )
{ // use forward mode ----------------------------------------
// initial coloring
SizeVector color(n);
for(j = 0; j < n; j++)
color[j] = j;
// See GreedyPartialD2Coloring Algorithm Section 3.6.2 of
// Graph Coloring in Optimization Revisited by
// Assefaw Gebremedhin, Fredrik Maane, Alex Pothen
VectorBool forbidden(n);
for(j = 0; j < n; j++)
{ // initial all colors as ok for this column
for(k = 0; k < n; k++)
forbidden[k] = false;
// for each row connected to column j
itr_i = q[j].begin();
while( itr_i != q[j].end() )
{ i = *itr_i++;
// for each column connected to row i
itr_j = p[i].begin();
while( itr_j != p[i].end() )
{ // if this is not j, forbid it
k = *itr_j++;
forbidden[ color[k] ] = (k != j);
}
}
k = 0;
while( forbidden[k] && k < n )
{ k++;
CPPAD_ASSERT_UNKNOWN( k < n );
}
color[j] = k;
}
size_t n_color = 1;
for(k = 0; k < n; k++)
n_color = std::max(n_color, color[k] + 1);
// direction vector for calls to forward
VectorBase dx(n);
// location for return values from Reverse
VectorBase dy(m);
// loop over colors
size_t c;
for(c = 0; c < n_color; c++)
{ // determine all the colums with this color
for(j = 0; j < n; j++)
{ if( color[j] == c )
dx[j] = one;
else dx[j] = zero;
}
// call forward mode for all these columns at once
dy = Forward(1, dx);
// set the corresponding components of the result
for(j = 0; j < n; j++) if( color[j] == c )
{ itr_i = q[j].begin();
while( itr_i != q[j].end() )
{ i = *itr_i++;
jac[i * n + j] = dy[i];
}
}
}
}
else
{ // use reverse mode ----------------------------------------
// initial coloring
SizeVector color(m);
for(i = 0; i < m; i++)
color[i] = i;
// See GreedyPartialD2Coloring Algorithm Section 3.6.2 of
// Graph Coloring in Optimization Revisited by
// Assefaw Gebremedhin, Fredrik Maane, Alex Pothen
VectorBool forbidden(m);
for(i = 0; i < m; i++)
{ // initial all colors as ok for this row
for(k = 0; k < m; k++)
forbidden[k] = false;
// for each column connected to row i
itr_j = p[i].begin();
while( itr_j != p[i].end() )
{ j = *itr_j++;
// for each row connected to column j
itr_i = q[j].begin();
while( itr_i != q[j].end() )
{ // if this is not i, forbid it
k = *itr_i++;
forbidden[ color[k] ] = (k != i);
}
}
k = 0;
while( forbidden[k] && k < m )
{ k++;
CPPAD_ASSERT_UNKNOWN( k < n );
}
color[i] = k;
}
size_t n_color = 1;
for(k = 0; k < m; k++)
n_color = std::max(n_color, color[k] + 1);
// weight vector for calls to reverse
VectorBase w(m);
// location for return values from Reverse
VectorBase dw(n);
// loop over colors
size_t c;
for(c = 0; c < n_color; c++)
{ // determine all the rows with this color
for(i = 0; i < m; i++)
{ if( color[i] == c )
w[i] = one;
else w[i] = zero;
}
// call reverse mode for all these rows at once
dw = Reverse(1, w);
// set the corresponding components of the result
for(i = 0; i < m; i++) if( color[i] == c )
{ itr_j = p[i].begin();
while( itr_j != p[i].end() )
{ j = *itr_j++;
jac[i * n + j] = dw[j];
}
}
}
}
}
void RevSparseJacBool(
size_t p ,
const VectorSet& s ,
VectorSet& r ,
size_t total_num_var ,
CppAD::vector<size_t>& dep_taddr ,
CppAD::vector<size_t>& ind_taddr ,
CppAD::player<Base>& play )
{
// temporary indices
size_t i, j;
// check VectorSet is Simple Vector class with bool elements
CheckSimpleVector<bool, VectorSet>();
// range and domain dimensions for F
size_t m = dep_taddr.size();
size_t n = ind_taddr.size();
CPPAD_ASSERT_KNOWN(
p > 0,
"RevSparseJac: p (first argument) is not greater than zero"
);
CPPAD_ASSERT_KNOWN(
s.size() == p * m,
"RevSparseJac: s (second argument) length is not equal to\n"
"p (first argument) times range dimension for ADFun object."
);
// vector of sets that will hold the results
sparse_pack var_sparsity;
var_sparsity.resize(total_num_var, p);
// The sparsity pattern corresponding to the dependent variables
for(i = 0; i < m; i++)
{ CPPAD_ASSERT_UNKNOWN( dep_taddr[i] < total_num_var );
for(j = 0; j < p; j++) if( s[ i * m + j ] )
var_sparsity.add_element( dep_taddr[i], j );
}
// evaluate the sparsity patterns
RevJacSweep(
n,
total_num_var,
&play,
var_sparsity
);
// return values corresponding to dependent variables
CPPAD_ASSERT_UNKNOWN( r.size() == p * n );
for(j = 0; j < n; j++)
{ CPPAD_ASSERT_UNKNOWN( ind_taddr[j] == (j+1) );
// ind_taddr[j] is operator taddr for j-th independent variable
CPPAD_ASSERT_UNKNOWN( play.GetOp( ind_taddr[j] ) == InvOp );
// extract the result from var_sparsity
for(i = 0; i < p; i++)
r[ i * n + j ] = false;
CPPAD_ASSERT_UNKNOWN( var_sparsity.end() == p );
var_sparsity.begin(j+1);
i = var_sparsity.next_element();
while( i < p )
{ r[ i * n + j ] = true;
i = var_sparsity.next_element();
}
}
}
void RevSparseJacSet(
bool transpose ,
bool dependency ,
size_t q ,
const VectorSet& r ,
VectorSet& s ,
size_t total_num_var ,
CppAD::vector<size_t>& dep_taddr ,
CppAD::vector<size_t>& ind_taddr ,
CppAD::player<Base>& play )
{
// temporary indices
size_t i, j;
std::set<size_t>::const_iterator itr;
// check VectorSet is Simple Vector class with sets for elements
CheckSimpleVector<std::set<size_t>, VectorSet>(
one_element_std_set<size_t>(), two_element_std_set<size_t>()
);
// domain dimensions for F
size_t n = ind_taddr.size();
size_t m = dep_taddr.size();
CPPAD_ASSERT_KNOWN(
q > 0,
"RevSparseJac: q is not greater than zero"
);
CPPAD_ASSERT_KNOWN(
size_t(r.size()) == q || transpose,
"RevSparseJac: size of r is not equal to q and transpose is false."
);
CPPAD_ASSERT_KNOWN(
size_t(r.size()) == m || ! transpose,
"RevSparseJac: size of r is not equal to m and transpose is true."
);
// vector of lists that will hold the results
CPPAD_INTERNAL_SPARSE_SET var_sparsity;
var_sparsity.resize(total_num_var, q);
// The sparsity pattern corresponding to the dependent variables
if( transpose )
{ for(i = 0; i < m; i++)
{ itr = r[i].begin();
while(itr != r[i].end())
{ j = *itr++;
CPPAD_ASSERT_KNOWN(
j < q,
"RevSparseJac: transpose is true and element of the set\n"
"r[i] has value greater than or equal q."
);
CPPAD_ASSERT_UNKNOWN( dep_taddr[i] < total_num_var );
var_sparsity.add_element( dep_taddr[i], j );
}
}
}
else
{ for(i = 0; i < q; i++)
{ itr = r[i].begin();
while(itr != r[i].end())
{ j = *itr++;
CPPAD_ASSERT_KNOWN(
j < m,
"RevSparseJac: transpose is false and element of the set\n"
"r[i] has value greater than or equal range dimension."
);
CPPAD_ASSERT_UNKNOWN( dep_taddr[j] < total_num_var );
var_sparsity.add_element( dep_taddr[j], i );
}
}
}
// evaluate the sparsity patterns
RevJacSweep(
dependency,
n,
total_num_var,
&play,
var_sparsity
);
// return values corresponding to dependent variables
CPPAD_ASSERT_UNKNOWN( size_t(s.size()) == q || transpose );
CPPAD_ASSERT_UNKNOWN( size_t(s.size()) == n || ! transpose );
for(j = 0; j < n; j++)
{ CPPAD_ASSERT_UNKNOWN( ind_taddr[j] == (j+1) );
// ind_taddr[j] is operator taddr for j-th independent variable
CPPAD_ASSERT_UNKNOWN( play.GetOp( ind_taddr[j] ) == InvOp );
CPPAD_ASSERT_UNKNOWN( var_sparsity.end() == q );
var_sparsity.begin(j+1);
i = var_sparsity.next_element();
while( i < q )
{ if( transpose )
s[j].insert(i);
else s[i].insert(j);
i = var_sparsity.next_element();
}
}
}
void RevSparseJacBool(
bool transpose ,
bool dependency ,
size_t q ,
const VectorSet& r ,
VectorSet& s ,
size_t total_num_var ,
CppAD::vector<size_t>& dep_taddr ,
CppAD::vector<size_t>& ind_taddr ,
CppAD::player<Base>& play )
{
// temporary indices
size_t i, j;
// check VectorSet is Simple Vector class with bool elements
CheckSimpleVector<bool, VectorSet>();
// range and domain dimensions for F
size_t m = dep_taddr.size();
size_t n = ind_taddr.size();
CPPAD_ASSERT_KNOWN(
q > 0,
"RevSparseJac: q is not greater than zero"
);
CPPAD_ASSERT_KNOWN(
size_t(r.size()) == q * m,
"RevSparseJac: size of r is not equal to\n"
"q times range dimension for ADFun object."
);
// vector of sets that will hold the results
sparse_pack var_sparsity;
var_sparsity.resize(total_num_var, q);
// The sparsity pattern corresponding to the dependent variables
for(i = 0; i < m; i++)
{ CPPAD_ASSERT_UNKNOWN( dep_taddr[i] < total_num_var );
if( transpose )
{ for(j = 0; j < q; j++) if( r[ j * m + i ] )
var_sparsity.add_element( dep_taddr[i], j );
}
else
{ for(j = 0; j < q; j++) if( r[ i * q + j ] )
var_sparsity.add_element( dep_taddr[i], j );
}
}
// evaluate the sparsity patterns
RevJacSweep(
dependency,
n,
total_num_var,
&play,
var_sparsity
);
// return values corresponding to dependent variables
CPPAD_ASSERT_UNKNOWN( size_t(s.size()) == q * n );
for(j = 0; j < n; j++)
{ CPPAD_ASSERT_UNKNOWN( ind_taddr[j] == (j+1) );
// ind_taddr[j] is operator taddr for j-th independent variable
CPPAD_ASSERT_UNKNOWN( play.GetOp( ind_taddr[j] ) == InvOp );
// extract the result from var_sparsity
if( transpose )
{ for(i = 0; i < q; i++)
s[ j * q + i ] = false;
}
else
{ for(i = 0; i < q; i++)
s[ i * n + j ] = false;
}
CPPAD_ASSERT_UNKNOWN( var_sparsity.end() == q );
var_sparsity.begin(j+1);
i = var_sparsity.next_element();
while( i < q )
{ if( transpose )
s[ j * q + i ] = true;
else s[ i * n + j ] = true;
i = var_sparsity.next_element();
}
}
}
void ADFun<Base>::ForSparseHesCase(
const std::set<size_t>& set_type ,
const VectorSet& r ,
const VectorSet& s ,
VectorSet& h )
{ size_t n = Domain();
# ifndef NDEBUG
size_t m = Range();
# endif
std::set<size_t>::const_iterator itr_1;
//
// check VectorSet is Simple Vector class with sets for elements
CheckSimpleVector<std::set<size_t>, VectorSet>(
local::one_element_std_set<size_t>(), local::two_element_std_set<size_t>()
);
CPPAD_ASSERT_KNOWN(
r.size() == 1,
"ForSparseHes: size of s is not equal to one."
);
CPPAD_ASSERT_KNOWN(
s.size() == 1,
"ForSparseHes: size of s is not equal to one."
);
//
// sparsity pattern corresponding to r
local::sparse_list for_jac_pattern;
for_jac_pattern.resize(num_var_tape_, n + 1);
itr_1 = r[0].begin();
while( itr_1 != r[0].end() )
{ size_t i = *itr_1++;
CPPAD_ASSERT_UNKNOWN( ind_taddr_[i] < n + 1 );
// ind_taddr_[i] is operator taddr for i-th independent variable
CPPAD_ASSERT_UNKNOWN( play_.GetOp( ind_taddr_[i] ) == local::InvOp );
//
for_jac_pattern.add_element( ind_taddr_[i], ind_taddr_[i] );
}
// compute forward Jacobiain sparsity pattern
bool dependency = false;
local::ForJacSweep(
dependency,
n,
num_var_tape_,
&play_,
for_jac_pattern
);
// sparsity pattern correspnding to s
local::sparse_list rev_jac_pattern;
rev_jac_pattern.resize(num_var_tape_, 1);
itr_1 = s[0].begin();
while( itr_1 != s[0].end() )
{ size_t i = *itr_1++;
CPPAD_ASSERT_KNOWN(
i < m,
"ForSparseHes: an element of the set s[0] has value "
"greater than or equal m"
);
CPPAD_ASSERT_UNKNOWN( dep_taddr_[i] < num_var_tape_ );
rev_jac_pattern.add_element( dep_taddr_[i], 0);
}
//
// compute reverse sparsity pattern for dependency analysis
// (note that we are only want non-zero derivatives not true dependency)
local::RevJacSweep(
dependency,
n,
num_var_tape_,
&play_,
rev_jac_pattern
);
//
// vector of sets that will hold reverse Hessain values
local::sparse_list for_hes_pattern;
for_hes_pattern.resize(n+1, n+1);
//
// compute the Hessian sparsity patterns
local::ForHesSweep(
n,
num_var_tape_,
&play_,
for_jac_pattern,
rev_jac_pattern,
for_hes_pattern
);
// return values corresponding to independent variables
// j is index corresponding to reverse mode partial
h.resize(n);
CPPAD_ASSERT_UNKNOWN( for_hes_pattern.end() == n+1 );
for(size_t i = 0; i < n; i++)
{ CPPAD_ASSERT_UNKNOWN( ind_taddr_[i] == i + 1 );
CPPAD_ASSERT_UNKNOWN( play_.GetOp( ind_taddr_[i] ) == local::InvOp );
// extract the result from for_hes_pattern
local::sparse_list::const_iterator itr_2(for_hes_pattern, ind_taddr_[i] );
size_t j = *itr_2;
while( j < for_hes_pattern.end() )
{ CPPAD_ASSERT_UNKNOWN( 0 < j )
h[i].insert(j-1);
j = *(++itr_2);
}
}
}
void ADFun<Base>::ForSparseHesCase(
bool set_type ,
const VectorSet& r ,
const VectorSet& s ,
VectorSet& h )
{ size_t n = Domain();
size_t m = Range();
//
// check Vector is Simple VectorSet class with bool elements
CheckSimpleVector<bool, VectorSet>();
//
CPPAD_ASSERT_KNOWN(
size_t(r.size()) == n,
"ForSparseHes: size of r is not equal to\n"
"domain dimension for ADFun object."
);
CPPAD_ASSERT_KNOWN(
size_t(s.size()) == m,
"ForSparseHes: size of s is not equal to\n"
"range dimension for ADFun object."
);
//
// sparsity pattern corresponding to r
local::sparse_pack for_jac_pattern;
for_jac_pattern.resize(num_var_tape_, n + 1);
for(size_t i = 0; i < n; i++)
{ CPPAD_ASSERT_UNKNOWN( ind_taddr_[i] < n + 1 );
// ind_taddr_[i] is operator taddr for i-th independent variable
CPPAD_ASSERT_UNKNOWN( play_.GetOp( ind_taddr_[i] ) == local::InvOp );
//
if( r[i] )
for_jac_pattern.add_element( ind_taddr_[i], ind_taddr_[i] );
}
// compute forward Jacobiain sparsity pattern
bool dependency = false;
local::ForJacSweep(
dependency,
n,
num_var_tape_,
&play_,
for_jac_pattern
);
// sparsity pattern correspnding to s
local::sparse_pack rev_jac_pattern;
rev_jac_pattern.resize(num_var_tape_, 1);
for(size_t i = 0; i < m; i++)
{ CPPAD_ASSERT_UNKNOWN( dep_taddr_[i] < num_var_tape_ );
if( s[i] )
rev_jac_pattern.add_element( dep_taddr_[i], 0);
}
// compute reverse sparsity pattern for dependency analysis
// (note that we are only want non-zero derivatives not true dependency)
local::RevJacSweep(
dependency,
n,
num_var_tape_,
&play_,
rev_jac_pattern
);
// vector of sets that will hold the forward Hessain values
local::sparse_pack for_hes_pattern;
for_hes_pattern.resize(n+1, n+1);
//
// compute the Hessian sparsity patterns
local::ForHesSweep(
n,
num_var_tape_,
&play_,
for_jac_pattern,
rev_jac_pattern,
for_hes_pattern
);
// initialize return values corresponding to independent variables
h.resize(n * n);
for(size_t i = 0; i < n; i++)
{ for(size_t j = 0; j < n; j++)
h[ i * n + j ] = false;
}
// copy to result pattern
CPPAD_ASSERT_UNKNOWN( for_hes_pattern.end() == n+1 );
for(size_t i = 0; i < n; i++)
{ // ind_taddr_[i] is operator taddr for i-th independent variable
CPPAD_ASSERT_UNKNOWN( ind_taddr_[i] == i + 1 );
CPPAD_ASSERT_UNKNOWN( play_.GetOp( ind_taddr_[i] ) == local::InvOp );
// extract the result from for_hes_pattern
local::sparse_pack::const_iterator itr(for_hes_pattern, ind_taddr_[i] );
size_t j = *itr;
while( j < for_hes_pattern.end() )
{ CPPAD_ASSERT_UNKNOWN( 0 < j )
h[ i * n + (j-1) ] = true;
j = *(++itr);
}
}
}
void RevSparseJacSet(
size_t p ,
const VectorSet& s ,
VectorSet& r ,
size_t total_num_var ,
CppAD::vector<size_t>& dep_taddr ,
CppAD::vector<size_t>& ind_taddr ,
CppAD::player<Base>& play )
{
// temporary indices
size_t i, j;
std::set<size_t>::const_iterator itr;
// check VectorSet is Simple Vector class with sets for elements
static std::set<size_t> two, three;
if( two.empty() )
{ two.insert(2);
three.insert(3);
}
CPPAD_ASSERT_UNKNOWN( two.size() == 1 );
CPPAD_ASSERT_UNKNOWN( three.size() == 1 );
CheckSimpleVector<std::set<size_t>, VectorSet>(two, three);
// range and domain dimensions for F
size_t m = dep_taddr.size();
size_t n = ind_taddr.size();
CPPAD_ASSERT_KNOWN(
p > 0,
"RevSparseJac: p (first argument) is not greater than zero"
);
CPPAD_ASSERT_KNOWN(
s.size() == p,
"RevSparseJac: s (second argument) length is not equal to "
"p (first argument)."
);
// vector of sets that will hold the results
sparse_set var_sparsity;
var_sparsity.resize(total_num_var, p);
// The sparsity pattern corresponding to the dependent variables
for(i = 0; i < p; i++)
{ itr = s[i].begin();
while(itr != s[i].end())
{ j = *itr++;
CPPAD_ASSERT_KNOWN(
j < m,
"RevSparseJac: an element of the set s[i] "
"has value greater than or equal m."
);
CPPAD_ASSERT_UNKNOWN( dep_taddr[j] < total_num_var );
var_sparsity.add_element( dep_taddr[j], i );
}
}
// evaluate the sparsity patterns
RevJacSweep(
n,
total_num_var,
&play,
var_sparsity
);
// return values corresponding to dependent variables
CPPAD_ASSERT_UNKNOWN( r.size() == p );
for(j = 0; j < n; j++)
{ CPPAD_ASSERT_UNKNOWN( ind_taddr[j] == (j+1) );
// ind_taddr[j] is operator taddr for j-th independent variable
CPPAD_ASSERT_UNKNOWN( play.GetOp( ind_taddr[j] ) == InvOp );
// extract result from rev_hes_sparsity
// and add corresponding elements to sets in r
CPPAD_ASSERT_UNKNOWN( var_sparsity.end() == p );
var_sparsity.begin(j+1);
i = var_sparsity.next_element();
while( i < p )
{ r[i].insert(j);
i = var_sparsity.next_element();
}
}
}
void ADFun<Base>::SparseJacobianCase(
bool set_type ,
const VectorBase& x ,
const VectorSet& p ,
VectorBase& jac )
{
typedef CppAD::vector<size_t> SizeVector;
typedef CppAD::vectorBool VectorBool;
size_t i, j, k;
size_t m = Range();
size_t n = Domain();
// some values
const Base zero(0);
const Base one(1);
// check VectorSet is Simple Vector class with bool elements
CheckSimpleVector<bool, VectorSet>();
// check VectorBase is Simple Vector class with Base type elements
CheckSimpleVector<Base, VectorBase>();
CPPAD_ASSERT_KNOWN(
x.size() == n,
"SparseJacobian: size of x not equal domain dimension for f"
);
CPPAD_ASSERT_KNOWN(
p.size() == m * n,
"SparseJacobian: using bool values and size of p "
" not equal range dimension times domain dimension for f"
);
CPPAD_ASSERT_UNKNOWN(jac.size() == m * n);
// point at which we are evaluating the Jacobian
Forward(0, x);
// initialize the return value
for(i = 0; i < m; i++)
for(j = 0; j < n; j++)
jac[i * n + j] = zero;
if( n <= m )
{ // use forward mode ----------------------------------------
// initial coloring
SizeVector color(n);
for(j = 0; j < n; j++)
color[j] = j;
// See GreedyPartialD2Coloring Algorithm Section 3.6.2 of
// Graph Coloring in Optimization Revisited by
// Assefaw Gebremedhin, Fredrik Maane, Alex Pothen
VectorBool forbidden(n);
for(j = 0; j < n; j++)
{ // initial all colors as ok for this column
for(k = 0; k < n; k++)
forbidden[k] = false;
// for each row that is connected to column j
for(i = 0; i < m; i++) if( p[i * n + j] )
{ // for each column that is connected to row i
for(k = 0; k < n; k++)
if( p[i * n + k] & (j != k) )
forbidden[ color[k] ] = true;
}
k = 0;
while( forbidden[k] && k < n )
{ k++;
CPPAD_ASSERT_UNKNOWN( k < n );
}
color[j] = k;
}
size_t n_color = 1;
for(k = 0; k < n; k++)
n_color = std::max(n_color, color[k] + 1);
// direction vector for calls to forward
VectorBase dx(n);
// location for return values from Reverse
VectorBase dy(m);
// loop over colors
size_t c;
for(c = 0; c < n_color; c++)
{ // determine all the colums with this color
for(j = 0; j < n; j++)
{ if( color[j] == c )
dx[j] = one;
else dx[j] = zero;
}
// call forward mode for all these columns at once
dy = Forward(1, dx);
// set the corresponding components of the result
for(j = 0; j < n; j++) if( color[j] == c )
{ for(i = 0; i < m; i++)
if( p[ i * n + j ] )
jac[i * n + j] = dy[i];
}
}
}
else
{ // use reverse mode ----------------------------------------
// initial coloring
SizeVector color(m);
for(i = 0; i < m; i++)
color[i] = i;
// See GreedyPartialD2Coloring Algorithm Section 3.6.2 of
// Graph Coloring in Optimization Revisited by
// Assefaw Gebremedhin, Fredrik Maane, Alex Pothen
VectorBool forbidden(m);
for(i = 0; i < m; i++)
{ // initial all colors as ok for this row
for(k = 0; k < m; k++)
forbidden[k] = false;
// for each column that is connected to row i
for(j = 0; j < n; j++) if( p[i * n + j] )
{ // for each row that is connected to column j
for(k = 0; k < m; k++)
if( p[k * n + j] & (i != k) )
forbidden[ color[k] ] = true;
}
k = 0;
while( forbidden[k] && k < m )
{ k++;
CPPAD_ASSERT_UNKNOWN( k < n );
}
color[i] = k;
}
size_t n_color = 1;
for(k = 0; k < m; k++)
n_color = std::max(n_color, color[k] + 1);
// weight vector for calls to reverse
VectorBase w(m);
// location for return values from Reverse
VectorBase dw(n);
// loop over colors
size_t c;
for(c = 0; c < n_color; c++)
{ // determine all the rows with this color
for(i = 0; i < m; i++)
{ if( color[i] == c )
w[i] = one;
else w[i] = zero;
}
// call reverse mode for all these rows at once
dw = Reverse(1, w);
// set the corresponding components of the result
for(i = 0; i < m; i++) if( color[i] == c )
{ for(j = 0; j < n; j++)
if( p[ i * n + j ] )
jac[i * n + j] = dw[j];
}
}
}
}