void BenderQuad(
const BAvector &x ,
const BAvector &y ,
Fun fun ,
BAvector &g ,
BAvector &gx ,
BAvector &gxx )
{ // determine the base type
typedef typename BAvector::value_type Base;
// check that BAvector is a SimpleVector class
CheckSimpleVector<Base, BAvector>();
// declare the ADvector type
typedef CPPAD_TESTVECTOR(AD<Base>) ADvector;
// size of the x and y spaces
size_t n = size_t(x.size());
size_t m = size_t(y.size());
// check the size of gx and gxx
CPPAD_ASSERT_KNOWN(
g.size() == 1,
"BenderQuad: size of the vector g is not equal to 1"
);
CPPAD_ASSERT_KNOWN(
size_t(gx.size()) == n,
"BenderQuad: size of the vector gx is not equal to n"
);
CPPAD_ASSERT_KNOWN(
size_t(gxx.size()) == n * n,
"BenderQuad: size of the vector gxx is not equal to n * n"
);
// some temporary indices
size_t i, j;
// variable versions x
ADvector vx(n);
for(j = 0; j < n; j++)
vx[j] = x[j];
// declare the independent variables
Independent(vx);
// evaluate h = H(x, y)
ADvector h(m);
h = fun.h(vx, y);
// evaluate dy (x) = Newton step as a function of x through h only
ADvector dy(m);
dy = fun.dy(x, y, h);
// variable version of y
ADvector vy(m);
for(j = 0; j < m; j++)
vy[j] = y[j] + dy[j];
// evaluate G~ (x) = F [ x , y + dy(x) ]
ADvector gtilde(1);
gtilde = fun.f(vx, vy);
// AD function object that corresponds to G~ (x)
// We will make heavy use of this tape, so optimize it
ADFun<Base> Gtilde;
Gtilde.Dependent(vx, gtilde);
Gtilde.optimize();
// value of G(x)
g = Gtilde.Forward(0, x);
// initial forward direction vector as zero
BAvector dx(n);
for(j = 0; j < n; j++)
dx[j] = Base(0);
// weight, first and second order derivative values
BAvector dg(1), w(1), ddw(2 * n);
w[0] = 1.;
// Jacobian and Hessian of G(x) is equal Jacobian and Hessian of Gtilde
for(j = 0; j < n; j++)
{ // compute partials in x[j] direction
dx[j] = Base(1);
dg = Gtilde.Forward(1, dx);
gx[j] = dg[0];
// restore the dx vector to zero
dx[j] = Base(0);
// compute second partials w.r.t x[j] and x[l] for l = 1, n
ddw = Gtilde.Reverse(2, w);
for(i = 0; i < n; i++)
gxx[ i * n + j ] = ddw[ i * 2 + 1 ];
}
return;
}
void testDynamicFull(std::vector<ADCG>& u,
const std::vector<double>& x,
const std::vector<double>& xNorm,
const std::vector<double>& eqNorm,
size_t maxAssignPerFunc = 100,
double epsilonR = 1e-14,
double epsilonA = 1e-14) {
ASSERT_EQ(u.size(), x.size());
ASSERT_EQ(x.size(), xNorm.size());
using namespace std;
// use a special object for source code generation
CppAD::Independent(u);
for (size_t i = 0; i < u.size(); i++)
u[i] *= xNorm[i];
// dependent variable vector
std::vector<ADCG> Z = model(u);
if (eqNorm.size() > 0) {
ASSERT_EQ(Z.size(), eqNorm.size());
for (size_t i = 0; i < Z.size(); i++)
Z[i] /= eqNorm[i];
}
/**
* create the CppAD tape as usual
*/
// create f: U -> Z and vectors used for derivative calculations
ADFun<CGD> fun;
fun.Dependent(Z);
/**
* Create the dynamic library
* (generate and compile source code)
*/
ModelCSourceGen<double> compHelp(fun, _name + "dynamic");
compHelp.setCreateForwardZero(true);
compHelp.setCreateJacobian(true);
compHelp.setCreateHessian(true);
compHelp.setCreateSparseJacobian(true);
compHelp.setCreateSparseHessian(true);
compHelp.setCreateForwardOne(true);
compHelp.setCreateReverseOne(true);
compHelp.setCreateReverseTwo(true);
compHelp.setMaxAssignmentsPerFunc(maxAssignPerFunc);
ModelLibraryCSourceGen<double> compDynHelp(compHelp);
SaveFilesModelLibraryProcessor<double>::saveLibrarySourcesTo(compDynHelp, "sources_" + _name + "_1");
DynamicModelLibraryProcessor<double> p(compDynHelp);
GccCompiler<double> compiler;
DynamicLib<double>* dynamicLib = p.createDynamicLibrary(compiler);
/**
* test the library
*/
GenericModel<double>* model = dynamicLib->model(_name + "dynamic");
ASSERT_TRUE(model != nullptr);
testModelResults(*model, fun, x, epsilonR, epsilonA);
delete model;
delete dynamicLib;
}
bool old_usead_2(void)
{ bool ok = true;
using CppAD::NearEqual;
double eps = 10. * CppAD::numeric_limits<double>::epsilon();
// --------------------------------------------------------------------
// Create the ADFun<doulbe> r_
create_r();
// --------------------------------------------------------------------
// domain and range space vectors
size_t n = 3, m = 2;
vector< AD<double> > au(n), ax(n), ay(m);
au[0] = 0.0; // value of z_0 (t) = t, at t = 0
ax[1] = 0.0; // value of z_1 (t) = t^2/2, at t = 0
au[2] = 1.0; // final t
CppAD::Independent(au);
size_t M = 2; // number of r steps to take
ax[0] = au[0]; // value of z_0 (t) = t, at t = 0
ax[1] = au[1]; // value of z_1 (t) = t^2/2, at t = 0
AD<double> dt = au[2] / double(M); // size of each r step
ax[2] = dt;
for(size_t i_step = 0; i_step < M; i_step++)
{ size_t id = 0; // not used
solve_ode(id, ax, ay);
ax[0] = ay[0];
ax[1] = ay[1];
}
// create f: u -> y and stop tape recording
// y_0(t) = u_0 + t = u_0 + u_2
// y_1(t) = u_1 + u_0 * t + t^2 / 2 = u_1 + u_0 * u_2 + u_2^2 / 2
// where t = u_2
ADFun<double> f;
f.Dependent(au, ay);
// --------------------------------------------------------------------
// Check forward mode results
//
// zero order forward
vector<double> up(n), yp(m);
size_t q = 0;
double u0 = 0.5;
double u1 = 0.25;
double u2 = 0.75;
double check;
up[0] = u0;
up[1] = u1;
up[2] = u2;
yp = f.Forward(q, up);
check = u0 + u2;
ok &= NearEqual( yp[0], check, eps, eps);
check = u1 + u0 * u2 + u2 * u2 / 2.0;
ok &= NearEqual( yp[1], check, eps, eps);
//
// forward mode first derivative w.r.t t
q = 1;
up[0] = 0.0;
up[1] = 0.0;
up[2] = 1.0;
yp = f.Forward(q, up);
check = 1.0;
ok &= NearEqual( yp[0], check, eps, eps);
check = u0 + u2;
ok &= NearEqual( yp[1], check, eps, eps);
//
// forward mode second order Taylor coefficient w.r.t t
q = 2;
up[0] = 0.0;
up[1] = 0.0;
up[2] = 0.0;
yp = f.Forward(q, up);
check = 0.0;
ok &= NearEqual( yp[0], check, eps, eps);
check = 1.0 / 2.0;
ok &= NearEqual( yp[1], check, eps, eps);
// --------------------------------------------------------------------
// reverse mode derivatives of \partial_t y_1 (t)
vector<double> w(m * q), dw(n * q);
w[0 * q + 0] = 0.0;
w[1 * q + 0] = 0.0;
w[0 * q + 1] = 0.0;
w[1 * q + 1] = 1.0;
dw = f.Reverse(q, w);
// derivative of y_1(u) = u_1 + u_0 * u_2 + u_2^2 / 2, w.r.t. u
// is equal deritative of \partial_u2 y_1(u) w.r.t \partial_u2 u
check = u2;
ok &= NearEqual( dw[0 * q + 1], check, eps, eps);
check = 1.0;
ok &= NearEqual( dw[1 * q + 1], check, eps, eps);
check = u0 + u2;
ok &= NearEqual( dw[2 * q + 1], check, eps, eps);
// derivative of \partial_t y_1 w.r.t u = u_0 + t, w.r.t u
check = 1.0;
ok &= NearEqual( dw[0 * q + 0], check, eps, eps);
check = 0.0;
ok &= NearEqual( dw[1 * q + 0], check, eps, eps);
check = 1.0;
ok &= NearEqual( dw[2 * q + 0], check, eps, eps);
// --------------------------------------------------------------------
// forward mode sparsity pattern for the Jacobian
// f_u = [ 1, 0, 1 ]
// [ u_2, 1, u_2 ]
size_t i, j, p = n;
CppAD::vectorBool r(n * p), s(m * p);
// r = identity sparsity pattern
for(i = 0; i < n; i++)
for(j = 0; j < p; j++)
r[i*n +j] = (i == j);
s = f.ForSparseJac(p, r);
ok &= s[ 0 * p + 0] == true;
ok &= s[ 0 * p + 1] == false;
ok &= s[ 0 * p + 2] == true;
ok &= s[ 1 * p + 0] == true;
ok &= s[ 1 * p + 1] == true;
ok &= s[ 1 * p + 2] == true;
// --------------------------------------------------------------------
// reverse mode sparsity pattern for the Jacobian
q = m;
s.resize(q * m);
r.resize(q * n);
// s = identity sparsity pattern
for(i = 0; i < q; i++)
for(j = 0; j < m; j++)
s[i*m +j] = (i == j);
r = f.RevSparseJac(q, s);
ok &= r[ 0 * n + 0] == true;
ok &= r[ 0 * n + 1] == false;
ok &= r[ 0 * n + 2] == true;
ok &= r[ 1 * n + 0] == true;
ok &= r[ 1 * n + 1] == true;
ok &= r[ 1 * n + 2] == true;
// --------------------------------------------------------------------
// Hessian sparsity for y_1 (u) = u_1 + u_0 * u_2 + u_2^2 / 2
s.resize(m);
s[0] = false;
s[1] = true;
r.resize(n * n);
for(i = 0; i < n; i++)
for(j = 0; j < n; j++)
r[ i * n + j ] = (i == j);
CppAD::vectorBool h(n * n);
h = f.RevSparseHes(n, s);
ok &= h[0 * n + 0] == false;
ok &= h[0 * n + 1] == false;
ok &= h[0 * n + 2] == true;
ok &= h[1 * n + 0] == false;
ok &= h[1 * n + 1] == false;
ok &= h[1 * n + 2] == false;
ok &= h[2 * n + 0] == true;
ok &= h[2 * n + 1] == false;
ok &= h[2 * n + 2] == true;
// --------------------------------------------------------------------
destroy_r();
// Free all temporary work space associated with old_atomic objects.
// (If there are future calls to user atomic functions, they will
// create new temporary work space.)
CppAD::user_atomic<double>::clear();
return ok;
}
bool old_usead_1(void)
{ bool ok = true;
using CppAD::NearEqual;
double eps = 10. * CppAD::numeric_limits<double>::epsilon();
// --------------------------------------------------------------------
// Create the ADFun<doulbe> r_
create_r();
// --------------------------------------------------------------------
// Create the function f(x)
//
// domain space vector
size_t n = 1;
double x0 = 0.5;
vector< AD<double> > ax(n);
ax[0] = x0;
// declare independent variables and start tape recording
CppAD::Independent(ax);
// range space vector
size_t m = 1;
vector< AD<double> > ay(m);
// call user function and store reciprocal(x) in au[0]
vector< AD<double> > au(m);
size_t id = 0; // not used
reciprocal(id, ax, au); // u = 1 / x
// call user function and store reciprocal(u) in ay[0]
reciprocal(id, au, ay); // y = 1 / u = x
// create f: x -> y and stop tape recording
ADFun<double> f;
f.Dependent(ax, ay); // f(x) = x
// --------------------------------------------------------------------
// Check function value results
//
// check function value
double check = x0;
ok &= NearEqual( Value(ay[0]) , check, eps, eps);
// check zero order forward mode
size_t q;
vector<double> x_q(n), y_q(m);
q = 0;
x_q[0] = x0;
y_q = f.Forward(q, x_q);
ok &= NearEqual(y_q[0] , check, eps, eps);
// check first order forward mode
q = 1;
x_q[0] = 1;
y_q = f.Forward(q, x_q);
check = 1.;
ok &= NearEqual(y_q[0] , check, eps, eps);
// check second order forward mode
q = 2;
x_q[0] = 0;
y_q = f.Forward(q, x_q);
check = 0.;
ok &= NearEqual(y_q[0] , check, eps, eps);
// --------------------------------------------------------------------
// Check reverse mode results
//
// third order reverse mode
q = 3;
vector<double> w(m), dw(n * q);
w[0] = 1.;
dw = f.Reverse(q, w);
check = 1.;
ok &= NearEqual(dw[0] , check, eps, eps);
check = 0.;
ok &= NearEqual(dw[1] , check, eps, eps);
ok &= NearEqual(dw[2] , check, eps, eps);
// --------------------------------------------------------------------
// forward mode sparstiy pattern
size_t p = n;
CppAD::vectorBool r1(n * p), s1(m * p);
r1[0] = true; // compute sparsity pattern for x[0]
s1 = f.ForSparseJac(p, r1);
ok &= s1[0] == true; // f[0] depends on x[0]
// --------------------------------------------------------------------
// reverse mode sparstiy pattern
q = m;
CppAD::vectorBool s2(q * m), r2(q * n);
s2[0] = true; // compute sparsity pattern for f[0]
r2 = f.RevSparseJac(q, s2);
ok &= r2[0] == true; // f[0] depends on x[0]
// --------------------------------------------------------------------
// Hessian sparsity (using previous ForSparseJac call)
CppAD::vectorBool s3(m), h(p * n);
s3[0] = true; // compute sparsity pattern for f[0]
h = f.RevSparseJac(p, s3);
ok &= h[0] == true; // second partial of f[0] w.r.t. x[0] may be non-zero
// -----------------------------------------------------------------
// Free all memory associated with the object r_ptr
destroy_r();
// -----------------------------------------------------------------
// Free all temporary work space associated with old_atomic objects.
// (If there are future calls to user atomic functions, they will
// create new temporary work space.)
CppAD::user_atomic<double>::clear();
return ok;
}
