SparseVector Basis::eval(const DenseVector &x) const
{
// Set correct starting size and values: one element of 1.
SparseMatrix tv1(1,1); //tv1.resize(1);
tv1.reserve(1);
tv1.insert(0,0) = 1;
SparseMatrix tv2 = tv1;
// Evaluate all basisfunctions in each dimension i and generate the tensor product of the function values
for (int dim = 0; dim < x.size(); dim++)
{
SparseVector xi = bases.at(dim).evaluate(x(dim));
// Avoid matrix copy
if (dim % 2 == 0)
{
tv1 = kroneckerProduct(tv2, xi); // tv1 = tv1 x xi
}
else
{
tv2 = kroneckerProduct(tv1, xi); // tv2 = tv1 x xi
}
}
// Return correct vector
if (tv1.size() == numBasisFunctions())
{
return tv1;
}
return tv2;
}
SparseVector kroneckerProductVectors(const std::vector<SparseVector> &vectors)
{
// Create two temp matrices
SparseMatrix temp1(1,1);
temp1.insert(0,0) = 1;
SparseMatrix temp2 = temp1;
// Multiply from left
int counter = 0;
for (const auto &vec : vectors)
{
// Avoid copy
if (counter % 2 == 0)
temp1 = kroneckerProduct(temp2, vec);
else
temp2 = kroneckerProduct(temp1, vec);
++counter;
}
// Return correct product
if (counter % 2 == 0)
return temp2;
return temp1;
}
// Old implementation of Jacobian
DenseMatrix BSplineBasis::evalBasisJacobianOld(DenseVector &x) const
{
// Jacobian basis matrix
DenseMatrix J; J.setZero(getNumBasisFunctions(), numVariables);
// Calculate partial derivatives
for (unsigned int i = 0; i < numVariables; i++)
{
// One column in basis jacobian
DenseVector bi; bi.setOnes(1);
for (unsigned int j = 0; j < numVariables; j++)
{
DenseVector temp = bi;
DenseVector xi;
if (j == i)
{
// Differentiated basis
xi = bases.at(j).evaluateFirstDerivative(x(j));
}
else
{
// Normal basis
xi = bases.at(j).evaluate(x(j));
}
bi = kroneckerProduct(temp, xi);
}
// Fill out column
J.block(0,i,bi.rows(),1) = bi.block(0,0,bi.rows(),1);
}
return J;
}
/*
* Calculate coefficients of B-spline representing a multivariate polynomial
*
* The polynomial f(x), with x in R^n, has m terms on the form
* f(x) = c(0)*x(0)^E(0,0)*x(1)^E(0,1)*...*x(n-1)^E(0,n-1)
* +c(1)*x(0)^E(1,0)*x(1)^E(1,1)*...*x(n-1)^E(1,n-1)
* +...
* +c(m-1)*x(0)^E(m-1,0)*x(1)^E(m-1,1)*...*x(n-1)^E(m-1,n-1)
* where c in R^m is a vector with coefficients for each of the m terms,
* and E in N^(mxn) is a matrix with the exponents of each variable in each of the m terms,
* e.g. the first row of E defines the first term with variable exponents E(0,0) to E(0,n-1).
*
* Note: E must be a matrix of nonnegative integers
*/
DenseMatrix getBSplineBasisCoefficients(DenseVector c, DenseMatrix E, std::vector<double> lb, std::vector<double> ub)
{
unsigned int dim = E.cols();
unsigned int terms = E.rows();
assert(dim >= 1); // At least one variable
assert(terms >= 1); // At least one term (assumes that c is a column vector)
assert(terms == c.rows());
assert(dim == lb.size());
assert(dim == ub.size());
// Get highest power of each variable
DenseVector powers = E.colwise().maxCoeff();
// Store in std vector
std::vector<unsigned int> powers2;
for (unsigned int i = 0; i < powers.size(); ++i)
powers2.push_back(powers(i));
// Calculate tensor product transformation matrix T
DenseMatrix T = getTransformationMatrix(powers2, lb, ub);
// Compute power basis coefficients (lambda vector)
SparseMatrix L(T.cols(),1);
L.setZero();
for (unsigned int i = 0; i < terms; i++)
{
SparseMatrix Li(1,1);
Li.insert(0,0) = 1;
for (unsigned int j = 0; j < dim; j++)
{
int e = E(i,j);
SparseVector li(powers(j)+1);
li.reserve(1);
li.insert(e) = 1;
SparseMatrix temp = Li;
Li = kroneckerProduct(temp, li);
}
L += c(i)*Li;
}
// Compute B-spline coefficients
DenseMatrix C = T*L;
return C;
}
SparseMatrix Basis::evalBasisJacobian(DenseVector &x) const
{
// Jacobian basis matrix
SparseMatrix J(numBasisFunctions(), numVariables);
//J.setZero(numBasisFunctions(), numInputs);
// Calculate partial derivatives
for (unsigned int i = 0; i < numVariables; i++)
{
// One column in basis jacobian
SparseMatrix Ji(1,1);
Ji.insert(0,0) = 1;
for (unsigned int j = 0; j < numVariables; j++)
{
SparseMatrix temp = Ji;
SparseMatrix xi;
if (j == i)
{
// Differentiated basis
xi = bases.at(j).evaluateDerivative(x(j),1);
}
else
{
// Normal basis
xi = bases.at(j).evaluate(x(j));
}
Ji = kroneckerProduct(temp, xi);
//myKroneckerProduct(temp,xi,Ji);
//Ji = kroneckerProduct(Ji, xi).eval();
}
// Fill out column
for (int k = 0; k < Ji.outerSize(); ++k)
for (SparseMatrix::InnerIterator it(Ji,k); it; ++it)
{
if (it.value() != 0)
J.insert(it.row(),i) = it.value();
}
//J.block(0,i,Ji.rows(),1) = bi.block(0,0,Ji.rows(),1);
}
J.makeCompressed();
return J;
}
/*
* Calculates the reparameterization matrix that changes the domain from [0,1] to [a,b]
*/
DenseMatrix getReparameterizationMatrixND(std::vector<unsigned int> degrees, std::vector<double> lb, std::vector<double> ub)
{
unsigned int dim = degrees.size();
assert(dim >= 1); // At least one variable
assert(dim == lb.size());
assert(dim == ub.size());
// Calculate tensor product transformation matrix T
SparseMatrix R(1,1);
R.insert(0,0) = 1;
for (unsigned int i = 0; i < dim; i++)
{
SparseMatrix temp(R);
unsigned int deg = degrees.at(i);
DenseMatrix Ri = getReparameterizationMatrix1D(deg, lb.at(i), ub.at(i));
R = kroneckerProduct(temp, Ri);
}
return R;
}
/*
* Transformation matrix taking a power basis to a B-spline basis
*/
DenseMatrix getTransformationMatrix(std::vector<unsigned int> degrees, std::vector<double> lb, std::vector<double> ub)
{
unsigned int dim = degrees.size();
assert(dim >= 1); // At least one variable
assert(dim == lb.size());
assert(dim == ub.size());
// Calculate tensor product transformation matrix T
SparseMatrix T(1,1);
T.insert(0,0) = 1;
for (unsigned int i = 0; i < dim; i++)
{
SparseMatrix temp(T);
unsigned int deg = degrees.at(i);
DenseMatrix Mi = getBSplineToPowerBasisMatrix1D(deg);
DenseMatrix Ri = getReparameterizationMatrix1D(deg, lb.at(i), ub.at(i));
DenseMatrix Ti = Mi.colPivHouseholderQr().solve(Ri);
T = kroneckerProduct(temp, Ti);
}
return T;
}
/*
* Returns the Hessian evaluated at x.
* The Hessian is an n x n matrix,
* where n is the dimension of x.
*/
DenseMatrix BSpline::evalHessian(DenseVector x) const
{
checkInput(x);
#ifndef NDEBUG
if (!pointInDomain(x))
throw Exception("BSpline::evalHessian: Evaluation at point outside domain.");
#endif // NDEBUG
DenseMatrix H;
H.setZero(1,1);
DenseMatrix identity = DenseMatrix::Identity(numVariables, numVariables);
DenseMatrix caug = kroneckerProduct(identity, coefficients.transpose());
DenseMatrix DB = basis.evalBasisHessian(x);
H = caug*DB;
// Fill in upper triangular of Hessian
for (size_t i = 0; i < numVariables; ++i)
for (size_t j = i+1; j < numVariables; ++j)
H(i,j) = H(j,i);
return H;
}
void test_kronecker_product()
{
// DM = dense matrix; SM = sparse matrix
Matrix<double, 2, 3> DM_a;
MatrixXd DM_b(3,2);
SparseMatrix<double> SM_a(2,3);
SparseMatrix<double> SM_b(3,2);
SM_a.insert(0,0) = DM_a(0,0) = -0.4461540300782201;
SM_a.insert(0,1) = DM_a(0,1) = -0.8057364375283049;
SM_a.insert(0,2) = DM_a(0,2) = 0.3896572459516341;
SM_a.insert(1,0) = DM_a(1,0) = -0.9076572187376921;
SM_a.insert(1,1) = DM_a(1,1) = 0.6469156566545853;
SM_a.insert(1,2) = DM_a(1,2) = -0.3658010398782789;
SM_b.insert(0,0) = DM_b(0,0) = 0.9004440976767099;
SM_b.insert(0,1) = DM_b(0,1) = -0.2368830858139832;
SM_b.insert(1,0) = DM_b(1,0) = -0.9311078389941825;
SM_b.insert(1,1) = DM_b(1,1) = 0.5310335762980047;
SM_b.insert(2,0) = DM_b(2,0) = -0.1225112806872035;
SM_b.insert(2,1) = DM_b(2,1) = 0.5903998022741264;
SparseMatrix<double,RowMajor> SM_row_a(SM_a), SM_row_b(SM_b);
// test kroneckerProduct(DM_block,DM,DM_fixedSize)
Matrix<double, 6, 6> DM_fix_ab;
DM_fix_ab(0,0)=37.0;
kroneckerProduct(DM_a.block(0,0,2,3),DM_b,DM_fix_ab);
CALL_SUBTEST(check_kronecker_product(DM_fix_ab));
// test kroneckerProduct(DM,DM,DM_block)
MatrixXd DM_block_ab(10,15);
DM_block_ab(0,0)=37.0;
kroneckerProduct(DM_a,DM_b,DM_block_ab.block(2,5,6,6));
CALL_SUBTEST(check_kronecker_product(DM_block_ab.block(2,5,6,6)));
// test kroneckerProduct(DM,DM,DM)
MatrixXd DM_ab(1,5);
DM_ab(0,0)=37.0;
kroneckerProduct(DM_a,DM_b,DM_ab);
CALL_SUBTEST(check_kronecker_product(DM_ab));
// test kroneckerProduct(SM,DM,SM)
SparseMatrix<double> SM_ab(1,20);
SM_ab.insert(0,0)=37.0;
kroneckerProduct(SM_a,DM_b,SM_ab);
CALL_SUBTEST(check_kronecker_product(SM_ab));
SparseMatrix<double,RowMajor> SM_ab2(10,3);
SM_ab2.insert(0,0)=37.0;
kroneckerProduct(SM_a,DM_b,SM_ab2);
CALL_SUBTEST(check_kronecker_product(SM_ab2));
// test kroneckerProduct(DM,SM,SM)
SM_ab.insert(0,0)=37.0;
kroneckerProduct(DM_a,SM_b,SM_ab);
CALL_SUBTEST(check_kronecker_product(SM_ab));
SM_ab2.insert(0,0)=37.0;
kroneckerProduct(DM_a,SM_b,SM_ab2);
CALL_SUBTEST(check_kronecker_product(SM_ab2));
// test kroneckerProduct(SM,SM,SM)
SM_ab.resize(2,33);
SM_ab.insert(0,0)=37.0;
kroneckerProduct(SM_a,SM_b,SM_ab);
CALL_SUBTEST(check_kronecker_product(SM_ab));
SM_ab2.resize(5,11);
SM_ab2.insert(0,0)=37.0;
kroneckerProduct(SM_a,SM_b,SM_ab2);
CALL_SUBTEST(check_kronecker_product(SM_ab2));
// test kroneckerProduct(SM,SM,SM) with sparse pattern
SM_a.resize(4,5);
SM_b.resize(3,2);
SM_a.resizeNonZeros(0);
SM_b.resizeNonZeros(0);
SM_a.insert(1,0) = -0.1;
SM_a.insert(0,3) = -0.2;
SM_a.insert(2,4) = 0.3;
SM_a.finalize();
SM_b.insert(0,0) = 0.4;
SM_b.insert(2,1) = -0.5;
SM_b.finalize();
SM_ab.resize(1,1);
SM_ab.insert(0,0)=37.0;
kroneckerProduct(SM_a,SM_b,SM_ab);
CALL_SUBTEST(check_sparse_kronecker_product(SM_ab));
// test dimension of result of kroneckerProduct(DM,DM,DM)
MatrixXd DM_a2(2,1);
MatrixXd DM_b2(5,4);
MatrixXd DM_ab2;
kroneckerProduct(DM_a2,DM_b2,DM_ab2);
CALL_SUBTEST(check_dimension(DM_ab2,2*5,1*4));
DM_a2.resize(10,9);
DM_b2.resize(4,8);
kroneckerProduct(DM_a2,DM_b2,DM_ab2);
CALL_SUBTEST(check_dimension(DM_ab2,10*4,9*8));
}
SparseMatrix BSplineBasis::evalBasisHessian(DenseVector &x) const
{
// Hessian basis matrix
/* Hij = B1 x ... x DBi x ... x DBj x ... x Bn
* (Hii = B1 x ... x DDBi x ... x Bn)
* Where B are basis functions evaluated at x,
* DB are the derivative of the basis functions,
* and x is the kronecker product.
* Hij is in R^(numBasisFunctions x 1)
* so that basis hessian H is in R^(numBasisFunctions*numInputs x numInputs)
* The real B-spline Hessian is calculated as (c^T x 1^(numInputs x 1))*H
*/
SparseMatrix H(getNumBasisFunctions()*numVariables, numVariables);
//H.setZero(numBasisFunctions()*numInputs, numInputs);
// Calculate partial derivatives
// Utilizing that Hessian is symmetric
// Filling out lower left triangular
for (unsigned int i = 0; i < numVariables; i++) // row
{
for (unsigned int j = 0; j <= i; j++) // col
{
// One column in basis jacobian
SparseMatrix Hi(1,1);
Hi.insert(0,0) = 1;
for (unsigned int k = 0; k < numVariables; k++)
{
SparseMatrix temp = Hi;
SparseMatrix Bk;
if (i == j && k == i)
{
// Diagonal element
Bk = bases.at(k).evaluateDerivative(x(k),2);
}
else if (k == i || k == j)
{
Bk = bases.at(k).evaluateDerivative(x(k),1);
}
else
{
Bk = bases.at(k).evaluate(x(k));
}
Hi = kroneckerProduct(temp, Bk);
}
// Fill out column
for (int k = 0; k < Hi.outerSize(); ++k)
for (SparseMatrix::InnerIterator it(Hi,k); it; ++it)
{
if (it.value() != 0)
{
int row = i*getNumBasisFunctions()+it.row();
int col = j;
H.insert(row,col) = it.value();
}
}
}
}
H.makeCompressed();
return H;
}
bool ConstraintBSpline::controlPointBoundsDeduction() const
{
// Get variable bounds
auto xlb = bspline.getDomainLowerBound();
auto xub = bspline.getDomainUpperBound();
// Use these instead?
// for (unsigned int i = 0; i < bspline.getNumVariables(); i++)
// {
// xlb.at(i) = variables.at(i)->getLowerBound();
// xub.at(i) = variables.at(i)->getUpperBound();
// }
double lowerBound = variables.back()->getLowerBound(); // f(x) = y > lowerBound
double upperBound = variables.back()->getUpperBound(); // f(x) = y < upperBound
// Get knot vectors and basis degrees
auto knotVectors = bspline.getKnotVectors();
auto basisDegrees = bspline.getBasisDegrees();
// Compute n value for each variable
// Total number of control points is ns(0)*...*ns(d-1)
std::vector<unsigned int> numBasisFunctions = bspline.getNumBasisFunctions();
// Get matrix of coefficients
DenseMatrix cps = controlPoints;
DenseMatrix coeffs = cps.block(bspline.getNumVariables(), 0, 1, cps.cols());
for (unsigned int d = 0; d < bspline.getNumVariables(); d++)
{
if (assertNear(xlb.at(d), xub.at(d)))
continue;
auto n = numBasisFunctions.at(d);
auto p = basisDegrees.at(d);
std::vector<double> knots = knotVectors.at(d);
assert(knots.size() == n+p+1);
// Tighten lower bound
unsigned int i = 1;
for (; i <= n; i++)
{
// Knot interval of interest: [t_0, t_i]
// Selection matrix
DenseMatrix S = DenseMatrix::Ones(1,1);
for (unsigned int d2 = 0; d2 < bspline.getNumVariables(); d2++)
{
DenseMatrix temp(S);
DenseMatrix Sd_full = DenseMatrix::Identity(numBasisFunctions.at(d2),numBasisFunctions.at(d2));
DenseMatrix Sd(Sd_full);
if (d == d2)
Sd = Sd_full.block(0,0,n,i);
S = kroneckerProduct(temp, Sd);
}
// Control points that have support in [t_0, t_i]
DenseMatrix selc = coeffs*S;
DenseVector minCP = selc.rowwise().minCoeff();
DenseVector maxCP = selc.rowwise().maxCoeff();
double minv = minCP(0);
double maxv = maxCP(0);
// Investigate feasibility
if (minv > upperBound || maxv < lowerBound)
continue; // infeasible
else
break; // feasible
}
// New valid lower bound on x(d) is knots(i-1)
if (i > 1)
{
if (!variables.at(d)->updateLowerBound(knots.at(i-1)))
return false;
}
// Tighten upper bound
i = 1;
for (; i <= n; i++)
{
// Knot interval of interest: [t_{n+p-i}, t_{n+p}]
// Selection matrix
DenseMatrix S = DenseMatrix::Ones(1,1);
for (unsigned int d2 = 0; d2 < bspline.getNumVariables(); d2++)
{
DenseMatrix temp(S);
DenseMatrix Sd_full = DenseMatrix::Identity(numBasisFunctions.at(d2),numBasisFunctions.at(d2));
DenseMatrix Sd(Sd_full);
if (d == d2)
Sd = Sd_full.block(0,n-i,n,i);
S = kroneckerProduct(temp, Sd);
}
// Control points that have support in [t_{n+p-i}, t_{n+p}]
DenseMatrix selc = coeffs*S;
DenseVector minCP = selc.rowwise().minCoeff();
DenseVector maxCP = selc.rowwise().maxCoeff();
double minv = minCP(0);
double maxv = maxCP(0);
// Investigate feasibility
if (minv > upperBound || maxv < lowerBound)
continue; // infeasible
else
break; // feasible
}
// New valid lower bound on x(d) is knots(n+p-(i-1))
if (i > 1)
{
if (!variables.at(d)->updateUpperBound(knots.at(n+p-(i-1))))
return false;
// NOTE: the upper bound seems to not be tight! can we use knots.at(n+p-i)?
}
}
return true;
}
void test_kronecker_product()
{
// DM = dense matrix; SM = sparse matrix
Matrix<double, 2, 3> DM_a;
SparseMatrix<double> SM_a(2,3);
SM_a.insert(0,0) = DM_a.coeffRef(0,0) = -0.4461540300782201;
SM_a.insert(0,1) = DM_a.coeffRef(0,1) = -0.8057364375283049;
SM_a.insert(0,2) = DM_a.coeffRef(0,2) = 0.3896572459516341;
SM_a.insert(1,0) = DM_a.coeffRef(1,0) = -0.9076572187376921;
SM_a.insert(1,1) = DM_a.coeffRef(1,1) = 0.6469156566545853;
SM_a.insert(1,2) = DM_a.coeffRef(1,2) = -0.3658010398782789;
MatrixXd DM_b(3,2);
SparseMatrix<double> SM_b(3,2);
SM_b.insert(0,0) = DM_b.coeffRef(0,0) = 0.9004440976767099;
SM_b.insert(0,1) = DM_b.coeffRef(0,1) = -0.2368830858139832;
SM_b.insert(1,0) = DM_b.coeffRef(1,0) = -0.9311078389941825;
SM_b.insert(1,1) = DM_b.coeffRef(1,1) = 0.5310335762980047;
SM_b.insert(2,0) = DM_b.coeffRef(2,0) = -0.1225112806872035;
SM_b.insert(2,1) = DM_b.coeffRef(2,1) = 0.5903998022741264;
SparseMatrix<double,RowMajor> SM_row_a(SM_a), SM_row_b(SM_b);
// test DM_fixedSize = kroneckerProduct(DM_block,DM)
Matrix<double, 6, 6> DM_fix_ab = kroneckerProduct(DM_a.topLeftCorner<2,3>(),DM_b);
CALL_SUBTEST(check_kronecker_product(DM_fix_ab));
CALL_SUBTEST(check_kronecker_product(kroneckerProduct(DM_a.topLeftCorner<2,3>(),DM_b)));
for(int i=0;i<DM_fix_ab.rows();++i)
for(int j=0;j<DM_fix_ab.cols();++j)
VERIFY_IS_APPROX(kroneckerProduct(DM_a,DM_b).coeff(i,j), DM_fix_ab(i,j));
// test DM_block = kroneckerProduct(DM,DM)
MatrixXd DM_block_ab(10,15);
DM_block_ab.block<6,6>(2,5) = kroneckerProduct(DM_a,DM_b);
CALL_SUBTEST(check_kronecker_product(DM_block_ab.block<6,6>(2,5)));
// test DM = kroneckerProduct(DM,DM)
MatrixXd DM_ab = kroneckerProduct(DM_a,DM_b);
CALL_SUBTEST(check_kronecker_product(DM_ab));
CALL_SUBTEST(check_kronecker_product(kroneckerProduct(DM_a,DM_b)));
// test SM = kroneckerProduct(SM,DM)
SparseMatrix<double> SM_ab = kroneckerProduct(SM_a,DM_b);
CALL_SUBTEST(check_kronecker_product(SM_ab));
SparseMatrix<double,RowMajor> SM_ab2 = kroneckerProduct(SM_a,DM_b);
CALL_SUBTEST(check_kronecker_product(SM_ab2));
CALL_SUBTEST(check_kronecker_product(kroneckerProduct(SM_a,DM_b)));
// test SM = kroneckerProduct(DM,SM)
SM_ab.setZero();
SM_ab.insert(0,0)=37.0;
SM_ab = kroneckerProduct(DM_a,SM_b);
CALL_SUBTEST(check_kronecker_product(SM_ab));
SM_ab2.setZero();
SM_ab2.insert(0,0)=37.0;
SM_ab2 = kroneckerProduct(DM_a,SM_b);
CALL_SUBTEST(check_kronecker_product(SM_ab2));
CALL_SUBTEST(check_kronecker_product(kroneckerProduct(DM_a,SM_b)));
// test SM = kroneckerProduct(SM,SM)
SM_ab.resize(2,33);
SM_ab.insert(0,0)=37.0;
SM_ab = kroneckerProduct(SM_a,SM_b);
CALL_SUBTEST(check_kronecker_product(SM_ab));
SM_ab2.resize(5,11);
SM_ab2.insert(0,0)=37.0;
SM_ab2 = kroneckerProduct(SM_a,SM_b);
CALL_SUBTEST(check_kronecker_product(SM_ab2));
CALL_SUBTEST(check_kronecker_product(kroneckerProduct(SM_a,SM_b)));
// test SM = kroneckerProduct(SM,SM) with sparse pattern
SM_a.resize(4,5);
SM_b.resize(3,2);
SM_a.resizeNonZeros(0);
SM_b.resizeNonZeros(0);
SM_a.insert(1,0) = -0.1;
SM_a.insert(0,3) = -0.2;
SM_a.insert(2,4) = 0.3;
SM_a.finalize();
SM_b.insert(0,0) = 0.4;
SM_b.insert(2,1) = -0.5;
SM_b.finalize();
SM_ab.resize(1,1);
SM_ab.insert(0,0)=37.0;
SM_ab = kroneckerProduct(SM_a,SM_b);
CALL_SUBTEST(check_sparse_kronecker_product(SM_ab));
// test dimension of result of DM = kroneckerProduct(DM,DM)
MatrixXd DM_a2(2,1);
MatrixXd DM_b2(5,4);
MatrixXd DM_ab2 = kroneckerProduct(DM_a2,DM_b2);
CALL_SUBTEST(check_dimension(DM_ab2,2*5,1*4));
DM_a2.resize(10,9);
DM_b2.resize(4,8);
DM_ab2 = kroneckerProduct(DM_a2,DM_b2);
CALL_SUBTEST(check_dimension(DM_ab2,10*4,9*8));
for(int i = 0; i < g_repeat; i++)
{
double density = Eigen::internal::random<double>(0.01,0.5);
int ra = Eigen::internal::random<int>(1,50);
int ca = Eigen::internal::random<int>(1,50);
int rb = Eigen::internal::random<int>(1,50);
int cb = Eigen::internal::random<int>(1,50);
SparseMatrix<float,ColMajor> sA(ra,ca), sB(rb,cb), sC;
SparseMatrix<float,RowMajor> sC2;
MatrixXf dA(ra,ca), dB(rb,cb), dC;
initSparse(density, dA, sA);
initSparse(density, dB, sB);
sC = kroneckerProduct(sA,sB);
dC = kroneckerProduct(dA,dB);
VERIFY_IS_APPROX(MatrixXf(sC),dC);
sC = kroneckerProduct(sA.transpose(),sB);
dC = kroneckerProduct(dA.transpose(),dB);
VERIFY_IS_APPROX(MatrixXf(sC),dC);
sC = kroneckerProduct(sA.transpose(),sB.transpose());
dC = kroneckerProduct(dA.transpose(),dB.transpose());
VERIFY_IS_APPROX(MatrixXf(sC),dC);
sC = kroneckerProduct(sA,sB.transpose());
dC = kroneckerProduct(dA,dB.transpose());
VERIFY_IS_APPROX(MatrixXf(sC),dC);
sC2 = kroneckerProduct(sA,sB);
dC = kroneckerProduct(dA,dB);
VERIFY_IS_APPROX(MatrixXf(sC2),dC);
}
}
