/**
* Extract the gradient from my_matrixfun()
*/
void test_matrix(){
std::cout << "== test_matrix() ==" << std::endl;
// use with normal floats
Eigen::VectorXd a(3),b(3);
a.setLinSpaced(0.,1.);
b.setLinSpaced(1.,2.);
double c = my_matrixfun(a,b);
std::cout << "Result: " << c << std::endl;
// use with AutoDiffScalar
typedef Eigen::AutoDiffScalar<Eigen::VectorXd> AScalar;
typedef Eigen::Matrix<AScalar,Eigen::Dynamic,1> AVector;
AVector Aa(a.size()),Ab(b.size());
// copy value from non-active example
for(int i=0;i<a.size();i++)Aa(i).value() = a(i);
for(int i=0;i<b.size();i++)Ab(i).value() = b(i);
// initialize derivative vectors
const int derivative_num = a.size() + b.size();
int derivative_idx = 0;
for(int i=0;i<Aa.size();i++){
Aa(i).derivatives() =
Eigen::VectorXd::Unit(derivative_num, derivative_idx);
derivative_idx++;
}
for(int i=0;i<Ab.size();i++){
Ab(i).derivatives() =
Eigen::VectorXd::Unit(derivative_num, derivative_idx);
derivative_idx++;
}
AScalar Ac = my_matrixfun(Aa,Ab);
std::cout << "Result: " << Ac.value() << std::endl;
std::cout << "Gradient: " <<
Ac.derivatives().transpose() << std::endl;
}
int main()
{
const int sz=7;
CArray A(sz);
A(0) = complex<float>(1,2);
A(1) = complex<float>(3,4);
Array<float,1> Ar = real(A);
BZTEST(int(Ar(0)) == 1 && int(Ar(1)) == 3);
Array<float,1> Ai = imag(A);
BZTEST(int(Ai(0)) == 2 && int(Ai(1)) == 4);
CArray Ac(sz);
Ac = conj(A);
BZTEST(Ac(0) == complex<float>(1,-2));
BZTEST(Ac(1) == complex<float>(3,-4));
Array<float,1> Ab(sz);
Ab = abs(A);
BZTEST(fabs(Ab(0) - 2.236068) < eps);
BZTEST(fabs(Ab(1) - 5.0) < eps);
Ab = arg(A);
BZTEST(fabs(Ab(0) - atan(2.0)) < eps);
BZTEST(fabs(Ab(1) - atan(4.0/3.0)) < eps);
Array<float,1> r(sz), theta(sz);
r(0) = 4.0f;
r(1) = 15.0f;
theta(0) = float(3.141592/3.0);
theta(1) = float(3.0*3.141592/2.0);
Ac = blitz::polar(r,theta);
BZTEST(fabs(real(Ac(0)) - 2) < eps);
BZTEST(fabs(imag(Ac(0)) - 3.4641012) < eps);
BZTEST(fabs(real(Ac(1)) - 0.0) < eps);
BZTEST(fabs(imag(Ac(1)) + 15.0) < eps);
Array<complex<long double>,1> A11(5),B11(5),C11(5);
A11=1,2,3,4,5;
B11=1,2,3,4,5;
C11=A11+B11;
BZTEST(fabs(real(C11(0)) - 2.) < eps);
C11=A11/B11;
BZTEST(fabs(real(C11(1)) - 1.) < eps);
C11=1.0l/A11;
BZTEST(fabs(real(C11(2)) - 1/3.) < eps);
C11=A11/1.0l;
BZTEST(fabs(real(C11(3)) - 4.) < eps);
C11=complex<long double>(0,1)/A11;
BZTEST(fabs(imag(C11(4)) - 1/5.) < eps);
C11=A11/complex<long double>(0,1);
BZTEST(fabs(imag(C11(0)) - -1.) < eps);
return 0;
}
/**
* Generating the gradient and the hessian from my_matrixfun
*/
void test_matrix_twice(){
std::cout << "== test_matrix_twice() ==" << std::endl;
// use with normal floats
Eigen::VectorXd a(3),b(3);
a.setLinSpaced(0.,1.);
b.setLinSpaced(1.,2.);
double c = my_matrixfun(a,b);
std::cout << "Result: " << c << std::endl;
// use with AutoDiffScalar
typedef Eigen::Matrix<double,Eigen::Dynamic,1> inner_derivative_type;
typedef Eigen::AutoDiffScalar<inner_derivative_type> inner_active_scalar;
typedef Eigen::Matrix<inner_active_scalar,Eigen::Dynamic,1> outer_derivative_type;
typedef Eigen::AutoDiffScalar<outer_derivative_type> outer_active_scalar;
typedef Eigen::Matrix<outer_active_scalar,Eigen::Dynamic,1> AVector;
AVector Aa(a.size()),Ab(b.size());
// copy value from non-active example
for(int i=0;i<a.size();i++)Aa(i).value().value() = a(i);
for(int i=0;i<b.size();i++)Ab(i).value().value() = b(i);
// initialize derivative vectors
const int derivative_num = a.size() + b.size();
int derivative_idx = 0;
for(int i=0;i<Aa.size();i++){
init_twice_active_var(Aa(i),derivative_num,derivative_idx);
derivative_idx++;
}
for(int i=0;i<Ab.size();i++){
init_twice_active_var(Ab(i),derivative_num,derivative_idx);
derivative_idx++;
}
outer_active_scalar Ac = my_matrixfun(Aa,Ab);
std::cout << "Result: " << Ac.value().value() << std::endl;
std::cout << "Gradient: " <<
Ac.value().derivatives().transpose() << std::endl;
std::cout << "Hessian" << std::endl;
Eigen::MatrixXd hessian(Ac.derivatives().size(),Ac.derivatives().size());
for(int idx=0;idx<Ac.derivatives().size();idx++){
hessian.middleRows(idx,1) =
Ac.derivatives()(idx).derivatives().transpose();
}
std::cout << hessian << std::endl;
}
/**
* This describes the basic use of Eigen::AutoDiffScalar
*/
void basic_use_autodiff_scalar(){
std::cout << "== basic_use_autodiff_scalar() ==" << std::endl;
typedef Eigen::AutoDiffScalar<Eigen::VectorXd> AScalar;
// AScalar stores a scalar and a derivative vector.
// Instantiate an AutoDiffScalar variable with a normal Scalar
double s = 0.3;
AScalar As(s);
// Get the value from the Instance
std::cout << "value: " << As.value() << std::endl;
// The derivative vector
As.derivatives(); // gives you a reference of
// the contained derivative vector
// Resize the derivative vector
As.derivatives().resize(2);
/**
* Important note:
* All ActiveScalars which are used in one computation must have
* either a common derivative vector length or a zero-length
* derivative vector.
*/
// Set the initial derivative vector
As.derivatives() = Eigen::VectorXd::Unit(2,0);
std::cout << "Derivative vector : " <<
As.derivatives().transpose() << std::endl;
// Instantiate another AScalar
AScalar Ab(4);
Ab.derivatives() = Eigen::VectorXd::Unit(2,1);
// Do the most simple calculation
AScalar Ac = As * Ab;
std::cout << "Result/Ac.value()" << Ac.value() << std::endl;
std::cout << "Gradient: " << Ac.derivatives().transpose() << std::endl;
}
void BlockMatrixTest::testOperators1()
{
std::cout << "--> Test: operators1." <<std::endl;
double tol = 1e-10;
SP::SiconosMatrix Ab(new BlockMatrix(m, 2, 3));
SP::SiconosMatrix Cb(new BlockMatrix(*Ab));
SP::SiconosMatrix A(new SimpleMatrix(5, 7));
for (unsigned int i = 0; i < 5 ; ++i)
for (unsigned int j = 0; j < 7; ++j)
(*A)(i, j) = i + j;
double a = 2.3;
int a1 = 2;
// Block *= scal or /= scal
*Cb *= a;
for (unsigned int i = 0; i < Cb->size(0); ++i)
for (unsigned int j = 0 ; j < Cb->size(1); ++j)
CPPUNIT_ASSERT_EQUAL_MESSAGE("testOperators1: ", fabs((*Cb)(i, j) - a * (*Ab)(i, j)) < tol , true);
*Cb *= a1;
for (unsigned int i = 0; i < Cb->size(0); ++i)
for (unsigned int j = 0 ; j < Cb->size(1); ++j)
CPPUNIT_ASSERT_EQUAL_MESSAGE("testOperators1: ", fabs((*Cb)(i, j) - a1 * a * (*Ab)(i, j)) < tol , true);
*Cb /= a;
for (unsigned int i = 0; i < Cb->size(0); ++i)
for (unsigned int j = 0 ; j < Cb->size(1); ++j)
CPPUNIT_ASSERT_EQUAL_MESSAGE("testOperators1: ", fabs((*Cb)(i, j) - a1 * (*Ab)(i, j)) < tol , true);
*Cb /= a1;
for (unsigned int i = 0; i < Cb->size(0); ++i)
for (unsigned int j = 0 ; j < Cb->size(1); ++j)
CPPUNIT_ASSERT_EQUAL_MESSAGE("testOperators1: ", fabs((*Cb)(i, j) - (*Ab)(i, j)) < tol , true);
// Block += Simple
*Cb += *A;
for (unsigned int i = 0; i < Cb->size(0); ++i)
for (unsigned int j = 0 ; j < Cb->size(1); ++j)
CPPUNIT_ASSERT_EQUAL_MESSAGE("testOperators1: ", fabs((*Cb)(i, j) - (*Ab)(i, j) - (*A)(i, j)) < tol , true);
// Block -= Block
*Cb -= *Ab;
for (unsigned int i = 0; i < Cb->size(0); ++i)
for (unsigned int j = 0 ; j < Cb->size(1); ++j)
CPPUNIT_ASSERT_EQUAL_MESSAGE("testOperators1: ", fabs((*Cb)(i, j) - (*A)(i, j)) < tol , true);
// Block += Block
*Cb += *Ab;
for (unsigned int i = 0; i < Cb->size(0); ++i)
for (unsigned int j = 0 ; j < Cb->size(1); ++j)
CPPUNIT_ASSERT_EQUAL_MESSAGE("testOperators1: ", fabs((*Cb)(i, j) - (*Ab)(i, j) - (*A)(i, j)) < tol , true);
// Block -= Simple
*Cb -= *A;
for (unsigned int i = 0; i < Cb->size(0); ++i)
for (unsigned int j = 0 ; j < Cb->size(1); ++j)
CPPUNIT_ASSERT_EQUAL_MESSAGE("testOperators1: ", fabs((*Cb)(i, j) - (*Ab)(i, j)) < tol , true);
std::cout << "--> test operators1 ended with success." <<std::endl;
}
