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This commit is contained in:
Tobias Wood
2023-11-29 11:12:48 +00:00
parent 9ea520fc45
commit f38e16c193
534 changed files with 103368 additions and 116934 deletions
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872
Eigen/src/SVD/BDCSVD.h
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File diff suppressed because it is too large Load Diff

81
Eigen/src/SVD/BDCSVD_LAPACKE.h
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@@ -54,50 +54,58 @@ class BDCSVD_LAPACKE : public BDCSVD<MatrixType_, Options> {
typedef typename SVD::Scalar Scalar;
typedef typename SVD::RealScalar RealScalar;
public:
public:
// construct this by moving from a parent object
BDCSVD_LAPACKE(SVD&& svd) : SVD(std::move(svd)) {}
void compute_impl_lapacke(const MatrixType& matrix, unsigned int computationOptions) {
SVD::allocate(matrix.rows(), matrix.cols(), computationOptions);
SVD::m_nonzeroSingularValues = SVD::m_diagSize;
// prepare arguments to ?gesdd
const lapack_int matrix_order = lapack_storage_of(matrix);
const char jobz = (SVD::m_computeFullU || SVD::m_computeFullV) ? 'A' : (SVD::m_computeThinU || SVD::m_computeThinV) ? 'S' : 'N';
const char jobz = (SVD::m_computeFullU || SVD::m_computeFullV) ? 'A'
: (SVD::m_computeThinU || SVD::m_computeThinV) ? 'S'
: 'N';
const lapack_int u_cols = (jobz == 'A') ? to_lapack(SVD::rows()) : (jobz == 'S') ? to_lapack(SVD::diagSize()) : 1;
const lapack_int vt_rows = (jobz == 'A') ? to_lapack(SVD::cols()) : (jobz == 'S') ? to_lapack(SVD::diagSize()) : 1;
lapack_int ldu, ldvt;
Scalar *u, *vt, dummy;
MatrixType localU;
if (SVD::computeU() && !(SVD::m_computeThinU && SVD::m_computeFullV) ) {
ldu = to_lapack(SVD::m_matrixU.outerStride());
u = SVD::m_matrixU.data();
if (SVD::computeU() && !(SVD::m_computeThinU && SVD::m_computeFullV)) {
ldu = to_lapack(SVD::m_matrixU.outerStride());
u = SVD::m_matrixU.data();
} else if (SVD::computeV()) {
localU.resize(SVD::rows(), u_cols);
ldu = to_lapack(localU.outerStride());
u = localU.data();
} else { ldu=1; u=&dummy; }
ldu = to_lapack(localU.outerStride());
u = localU.data();
} else {
ldu = 1;
u = &dummy;
}
MatrixType localV;
if (SVD::computeU() || SVD::computeV()) {
localV.resize(vt_rows, SVD::cols());
ldvt = to_lapack(localV.outerStride());
vt = localV.data();
} else { ldvt=1; vt=&dummy; }
MatrixType temp; temp = matrix;
ldvt = to_lapack(localV.outerStride());
vt = localV.data();
} else {
ldvt = 1;
vt = &dummy;
}
MatrixType temp;
temp = matrix;
// actual call to ?gesdd
lapack_int info = gesdd( matrix_order, jobz, to_lapack(SVD::rows()), to_lapack(SVD::cols()),
to_lapack(temp.data()), to_lapack(temp.outerStride()), (RealScalar*)SVD::m_singularValues.data(),
to_lapack(u), ldu, to_lapack(vt), ldvt);
lapack_int info = gesdd(matrix_order, jobz, to_lapack(SVD::rows()), to_lapack(SVD::cols()), to_lapack(temp.data()),
to_lapack(temp.outerStride()), (RealScalar*)SVD::m_singularValues.data(), to_lapack(u), ldu,
to_lapack(vt), ldvt);
// Check the result of the LAPACK call
if (info < 0 || !SVD::m_singularValues.allFinite()) {
// this includes info == -4 => NaN entry in A
SVD::m_info = InvalidInput;
} else if (info > 0 ) {
} else if (info > 0) {
SVD::m_info = NoConvergence;
} else {
SVD::m_info = Success;
@@ -112,9 +120,9 @@ public:
}
};
template<typename MatrixType_, int Options>
BDCSVD<MatrixType_, Options>& BDCSVD_wrapper(BDCSVD<MatrixType_, Options>& svd, const MatrixType_& matrix, int computationOptions)
{
template <typename MatrixType_, int Options>
BDCSVD<MatrixType_, Options>& BDCSVD_wrapper(BDCSVD<MatrixType_, Options>& svd, const MatrixType_& matrix,
int computationOptions) {
// we need to move to the wrapper type and back
BDCSVD_LAPACKE<MatrixType_, Options> tmpSvd(std::move(svd));
tmpSvd.compute_impl_lapacke(matrix, computationOptions);
@@ -122,25 +130,26 @@ BDCSVD<MatrixType_, Options>& BDCSVD_wrapper(BDCSVD<MatrixType_, Options>& svd,
return svd;
}
} // end namespace lapacke_helpers
} // end namespace lapacke_helpers
} // end namespace internal
} // end namespace internal
#define EIGEN_LAPACKE_SDD(EIGTYPE, EIGCOLROW, OPTIONS) \
template<> inline \
BDCSVD<Matrix<EIGTYPE, Dynamic, Dynamic, EIGCOLROW, Dynamic, Dynamic>, OPTIONS>& \
BDCSVD<Matrix<EIGTYPE, Dynamic, Dynamic, EIGCOLROW, Dynamic, Dynamic>, OPTIONS>::compute_impl(const Matrix<EIGTYPE, Dynamic, Dynamic, EIGCOLROW, Dynamic, Dynamic>& matrix, unsigned int computationOptions) {\
return internal::lapacke_helpers::BDCSVD_wrapper(*this, matrix, computationOptions); \
}
#define EIGEN_LAPACKE_SDD(EIGTYPE, EIGCOLROW, OPTIONS) \
template <> \
inline BDCSVD<Matrix<EIGTYPE, Dynamic, Dynamic, EIGCOLROW, Dynamic, Dynamic>, OPTIONS>& \
BDCSVD<Matrix<EIGTYPE, Dynamic, Dynamic, EIGCOLROW, Dynamic, Dynamic>, OPTIONS>::compute_impl( \
const Matrix<EIGTYPE, Dynamic, Dynamic, EIGCOLROW, Dynamic, Dynamic>& matrix, unsigned int computationOptions) { \
return internal::lapacke_helpers::BDCSVD_wrapper(*this, matrix, computationOptions); \
}
#define EIGEN_LAPACK_SDD_OPTIONS(OPTIONS) \
EIGEN_LAPACKE_SDD(double, ColMajor, OPTIONS) \
EIGEN_LAPACKE_SDD(float, ColMajor, OPTIONS) \
#define EIGEN_LAPACK_SDD_OPTIONS(OPTIONS) \
EIGEN_LAPACKE_SDD(double, ColMajor, OPTIONS) \
EIGEN_LAPACKE_SDD(float, ColMajor, OPTIONS) \
EIGEN_LAPACKE_SDD(dcomplex, ColMajor, OPTIONS) \
EIGEN_LAPACKE_SDD(scomplex, ColMajor, OPTIONS) \
\
EIGEN_LAPACKE_SDD(double, RowMajor, OPTIONS) \
EIGEN_LAPACKE_SDD(float, RowMajor, OPTIONS) \
\
EIGEN_LAPACKE_SDD(double, RowMajor, OPTIONS) \
EIGEN_LAPACKE_SDD(float, RowMajor, OPTIONS) \
EIGEN_LAPACKE_SDD(dcomplex, RowMajor, OPTIONS) \
EIGEN_LAPACKE_SDD(scomplex, RowMajor, OPTIONS)
@@ -158,6 +167,6 @@ EIGEN_LAPACK_SDD_OPTIONS(ComputeFullU | ComputeThinV)
#undef EIGEN_LAPACKE_SDD
} // end namespace Eigen
} // end namespace Eigen
#endif // EIGEN_BDCSVD_LAPACKE_H
#endif // EIGEN_BDCSVD_LAPACKE_H

341
Eigen/src/SVD/JacobiSVD.h
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@@ -32,18 +32,15 @@ struct svd_precondition_2x2_block_to_be_real {};
enum { PreconditionIfMoreColsThanRows, PreconditionIfMoreRowsThanCols };
template<typename MatrixType, int QRPreconditioner, int Case>
struct qr_preconditioner_should_do_anything
{
enum { a = MatrixType::RowsAtCompileTime != Dynamic &&
MatrixType::ColsAtCompileTime != Dynamic &&
MatrixType::ColsAtCompileTime <= MatrixType::RowsAtCompileTime,
b = MatrixType::RowsAtCompileTime != Dynamic &&
MatrixType::ColsAtCompileTime != Dynamic &&
MatrixType::RowsAtCompileTime <= MatrixType::ColsAtCompileTime,
ret = !( (QRPreconditioner == NoQRPreconditioner) ||
(Case == PreconditionIfMoreColsThanRows && bool(a)) ||
(Case == PreconditionIfMoreRowsThanCols && bool(b)) )
template <typename MatrixType, int QRPreconditioner, int Case>
struct qr_preconditioner_should_do_anything {
enum {
a = MatrixType::RowsAtCompileTime != Dynamic && MatrixType::ColsAtCompileTime != Dynamic &&
MatrixType::ColsAtCompileTime <= MatrixType::RowsAtCompileTime,
b = MatrixType::RowsAtCompileTime != Dynamic && MatrixType::ColsAtCompileTime != Dynamic &&
MatrixType::RowsAtCompileTime <= MatrixType::ColsAtCompileTime,
ret = !((QRPreconditioner == NoQRPreconditioner) || (Case == PreconditionIfMoreColsThanRows && bool(a)) ||
(Case == PreconditionIfMoreRowsThanCols && bool(b)))
};
};
@@ -72,8 +69,7 @@ class qr_preconditioner_impl<MatrixType, Options, FullPivHouseholderQRPreconditi
typedef Matrix<Scalar, 1, WorkspaceSize, RowMajor, 1, MaxWorkspaceSize> WorkspaceType;
void allocate(const SVDType& svd) {
if (svd.rows() != m_qr.rows() || svd.cols() != m_qr.cols())
{
if (svd.rows() != m_qr.rows() || svd.cols() != m_qr.cols()) {
internal::destroy_at(&m_qr);
internal::construct_at(&m_qr, svd.rows(), svd.cols());
}
@@ -81,18 +77,17 @@ class qr_preconditioner_impl<MatrixType, Options, FullPivHouseholderQRPreconditi
}
bool run(SVDType& svd, const MatrixType& matrix) {
if(matrix.rows() > matrix.cols())
{
if (matrix.rows() > matrix.cols()) {
m_qr.compute(matrix);
svd.m_workMatrix = m_qr.matrixQR().block(0,0,matrix.cols(),matrix.cols()).template triangularView<Upper>();
if(svd.m_computeFullU) m_qr.matrixQ().evalTo(svd.m_matrixU, m_workspace);
if(svd.computeV()) svd.m_matrixV = m_qr.colsPermutation();
svd.m_workMatrix = m_qr.matrixQR().block(0, 0, matrix.cols(), matrix.cols()).template triangularView<Upper>();
if (svd.m_computeFullU) m_qr.matrixQ().evalTo(svd.m_matrixU, m_workspace);
if (svd.computeV()) svd.m_matrixV = m_qr.colsPermutation();
return true;
}
return false;
}
private:
private:
typedef FullPivHouseholderQR<MatrixType> QRType;
QRType m_qr;
WorkspaceType m_workspace;
@@ -118,8 +113,7 @@ class qr_preconditioner_impl<MatrixType, Options, FullPivHouseholderQRPreconditi
TransposeTypeWithSameStorageOrder;
void allocate(const SVDType& svd) {
if (svd.cols() != m_qr.rows() || svd.rows() != m_qr.cols())
{
if (svd.cols() != m_qr.rows() || svd.rows() != m_qr.cols()) {
internal::destroy_at(&m_qr);
internal::construct_at(&m_qr, svd.cols(), svd.rows());
}
@@ -128,19 +122,19 @@ class qr_preconditioner_impl<MatrixType, Options, FullPivHouseholderQRPreconditi
}
bool run(SVDType& svd, const MatrixType& matrix) {
if(matrix.cols() > matrix.rows())
{
if (matrix.cols() > matrix.rows()) {
m_adjoint = matrix.adjoint();
m_qr.compute(m_adjoint);
svd.m_workMatrix = m_qr.matrixQR().block(0,0,matrix.rows(),matrix.rows()).template triangularView<Upper>().adjoint();
if(svd.m_computeFullV) m_qr.matrixQ().evalTo(svd.m_matrixV, m_workspace);
if(svd.computeU()) svd.m_matrixU = m_qr.colsPermutation();
svd.m_workMatrix =
m_qr.matrixQR().block(0, 0, matrix.rows(), matrix.rows()).template triangularView<Upper>().adjoint();
if (svd.m_computeFullV) m_qr.matrixQ().evalTo(svd.m_matrixV, m_workspace);
if (svd.computeU()) svd.m_matrixU = m_qr.colsPermutation();
return true;
}
else return false;
} else
return false;
}
private:
private:
typedef FullPivHouseholderQR<TransposeTypeWithSameStorageOrder> QRType;
QRType m_qr;
TransposeTypeWithSameStorageOrder m_adjoint;
@@ -164,33 +158,33 @@ class qr_preconditioner_impl<MatrixType, Options, ColPivHouseholderQRPreconditio
typedef Matrix<Scalar, 1, WorkspaceSize, RowMajor, 1, MaxWorkspaceSize> WorkspaceType;
void allocate(const SVDType& svd) {
if (svd.rows() != m_qr.rows() || svd.cols() != m_qr.cols())
{
if (svd.rows() != m_qr.rows() || svd.cols() != m_qr.cols()) {
internal::destroy_at(&m_qr);
internal::construct_at(&m_qr, svd.rows(), svd.cols());
}
if (svd.m_computeFullU) m_workspace.resize(svd.rows());
else if (svd.m_computeThinU) m_workspace.resize(svd.cols());
if (svd.m_computeFullU)
m_workspace.resize(svd.rows());
else if (svd.m_computeThinU)
m_workspace.resize(svd.cols());
}
bool run(SVDType& svd, const MatrixType& matrix) {
if(matrix.rows() > matrix.cols())
{
if (matrix.rows() > matrix.cols()) {
m_qr.compute(matrix);
svd.m_workMatrix = m_qr.matrixQR().block(0,0,matrix.cols(),matrix.cols()).template triangularView<Upper>();
if(svd.m_computeFullU) m_qr.householderQ().evalTo(svd.m_matrixU, m_workspace);
else if(svd.m_computeThinU)
{
svd.m_workMatrix = m_qr.matrixQR().block(0, 0, matrix.cols(), matrix.cols()).template triangularView<Upper>();
if (svd.m_computeFullU)
m_qr.householderQ().evalTo(svd.m_matrixU, m_workspace);
else if (svd.m_computeThinU) {
svd.m_matrixU.setIdentity(matrix.rows(), matrix.cols());
m_qr.householderQ().applyThisOnTheLeft(svd.m_matrixU, m_workspace);
}
if(svd.computeV()) svd.m_matrixV = m_qr.colsPermutation();
if (svd.computeV()) svd.m_matrixV = m_qr.colsPermutation();
return true;
}
return false;
}
private:
private:
typedef ColPivHouseholderQR<MatrixType> QRType;
QRType m_qr;
WorkspaceType m_workspace;
@@ -220,36 +214,37 @@ class qr_preconditioner_impl<MatrixType, Options, ColPivHouseholderQRPreconditio
TransposeTypeWithSameStorageOrder;
void allocate(const SVDType& svd) {
if (svd.cols() != m_qr.rows() || svd.rows() != m_qr.cols())
{
if (svd.cols() != m_qr.rows() || svd.rows() != m_qr.cols()) {
internal::destroy_at(&m_qr);
internal::construct_at(&m_qr, svd.cols(), svd.rows());
}
if (svd.m_computeFullV) m_workspace.resize(svd.cols());
else if (svd.m_computeThinV) m_workspace.resize(svd.rows());
if (svd.m_computeFullV)
m_workspace.resize(svd.cols());
else if (svd.m_computeThinV)
m_workspace.resize(svd.rows());
m_adjoint.resize(svd.cols(), svd.rows());
}
bool run(SVDType& svd, const MatrixType& matrix) {
if(matrix.cols() > matrix.rows())
{
if (matrix.cols() > matrix.rows()) {
m_adjoint = matrix.adjoint();
m_qr.compute(m_adjoint);
svd.m_workMatrix = m_qr.matrixQR().block(0,0,matrix.rows(),matrix.rows()).template triangularView<Upper>().adjoint();
if(svd.m_computeFullV) m_qr.householderQ().evalTo(svd.m_matrixV, m_workspace);
else if(svd.m_computeThinV)
{
svd.m_workMatrix =
m_qr.matrixQR().block(0, 0, matrix.rows(), matrix.rows()).template triangularView<Upper>().adjoint();
if (svd.m_computeFullV)
m_qr.householderQ().evalTo(svd.m_matrixV, m_workspace);
else if (svd.m_computeThinV) {
svd.m_matrixV.setIdentity(matrix.cols(), matrix.rows());
m_qr.householderQ().applyThisOnTheLeft(svd.m_matrixV, m_workspace);
}
if(svd.computeU()) svd.m_matrixU = m_qr.colsPermutation();
if (svd.computeU()) svd.m_matrixU = m_qr.colsPermutation();
return true;
}
else return false;
} else
return false;
}
private:
private:
typedef ColPivHouseholderQR<TransposeTypeWithSameStorageOrder> QRType;
QRType m_qr;
TransposeTypeWithSameStorageOrder m_adjoint;
@@ -272,33 +267,33 @@ class qr_preconditioner_impl<MatrixType, Options, HouseholderQRPreconditioner, P
typedef Matrix<Scalar, 1, WorkspaceSize, RowMajor, 1, MaxWorkspaceSize> WorkspaceType;
void allocate(const SVDType& svd) {
if (svd.rows() != m_qr.rows() || svd.cols() != m_qr.cols())
{
if (svd.rows() != m_qr.rows() || svd.cols() != m_qr.cols()) {
internal::destroy_at(&m_qr);
internal::construct_at(&m_qr, svd.rows(), svd.cols());
}
if (svd.m_computeFullU) m_workspace.resize(svd.rows());
else if (svd.m_computeThinU) m_workspace.resize(svd.cols());
if (svd.m_computeFullU)
m_workspace.resize(svd.rows());
else if (svd.m_computeThinU)
m_workspace.resize(svd.cols());
}
bool run(SVDType& svd, const MatrixType& matrix) {
if(matrix.rows() > matrix.cols())
{
if (matrix.rows() > matrix.cols()) {
m_qr.compute(matrix);
svd.m_workMatrix = m_qr.matrixQR().block(0,0,matrix.cols(),matrix.cols()).template triangularView<Upper>();
if(svd.m_computeFullU) m_qr.householderQ().evalTo(svd.m_matrixU, m_workspace);
else if(svd.m_computeThinU)
{
svd.m_workMatrix = m_qr.matrixQR().block(0, 0, matrix.cols(), matrix.cols()).template triangularView<Upper>();
if (svd.m_computeFullU)
m_qr.householderQ().evalTo(svd.m_matrixU, m_workspace);
else if (svd.m_computeThinU) {
svd.m_matrixU.setIdentity(matrix.rows(), matrix.cols());
m_qr.householderQ().applyThisOnTheLeft(svd.m_matrixU, m_workspace);
}
if(svd.computeV()) svd.m_matrixV.setIdentity(matrix.cols(), matrix.cols());
if (svd.computeV()) svd.m_matrixV.setIdentity(matrix.cols(), matrix.cols());
return true;
}
return false;
}
private:
private:
typedef HouseholderQR<MatrixType> QRType;
QRType m_qr;
WorkspaceType m_workspace;
@@ -327,36 +322,37 @@ class qr_preconditioner_impl<MatrixType, Options, HouseholderQRPreconditioner, P
TransposeTypeWithSameStorageOrder;
void allocate(const SVDType& svd) {
if (svd.cols() != m_qr.rows() || svd.rows() != m_qr.cols())
{
if (svd.cols() != m_qr.rows() || svd.rows() != m_qr.cols()) {
internal::destroy_at(&m_qr);
internal::construct_at(&m_qr, svd.cols(), svd.rows());
}
if (svd.m_computeFullV) m_workspace.resize(svd.cols());
else if (svd.m_computeThinV) m_workspace.resize(svd.rows());
if (svd.m_computeFullV)
m_workspace.resize(svd.cols());
else if (svd.m_computeThinV)
m_workspace.resize(svd.rows());
m_adjoint.resize(svd.cols(), svd.rows());
}
bool run(SVDType& svd, const MatrixType& matrix) {
if(matrix.cols() > matrix.rows())
{
if (matrix.cols() > matrix.rows()) {
m_adjoint = matrix.adjoint();
m_qr.compute(m_adjoint);
svd.m_workMatrix = m_qr.matrixQR().block(0,0,matrix.rows(),matrix.rows()).template triangularView<Upper>().adjoint();
if(svd.m_computeFullV) m_qr.householderQ().evalTo(svd.m_matrixV, m_workspace);
else if(svd.m_computeThinV)
{
svd.m_workMatrix =
m_qr.matrixQR().block(0, 0, matrix.rows(), matrix.rows()).template triangularView<Upper>().adjoint();
if (svd.m_computeFullV)
m_qr.householderQ().evalTo(svd.m_matrixV, m_workspace);
else if (svd.m_computeThinV) {
svd.m_matrixV.setIdentity(matrix.cols(), matrix.rows());
m_qr.householderQ().applyThisOnTheLeft(svd.m_matrixV, m_workspace);
}
if(svd.computeU()) svd.m_matrixU.setIdentity(matrix.rows(), matrix.rows());
if (svd.computeU()) svd.m_matrixU.setIdentity(matrix.rows(), matrix.rows());
return true;
}
else return false;
} else
return false;
}
private:
private:
typedef HouseholderQR<TransposeTypeWithSameStorageOrder> QRType;
QRType m_qr;
TransposeTypeWithSameStorageOrder m_adjoint;
@@ -380,62 +376,56 @@ struct svd_precondition_2x2_block_to_be_real<MatrixType, Options, true> {
typedef JacobiSVD<MatrixType, Options> SVD;
typedef typename MatrixType::Scalar Scalar;
typedef typename MatrixType::RealScalar RealScalar;
static bool run(typename SVD::WorkMatrixType& work_matrix, SVD& svd, Index p, Index q, RealScalar& maxDiagEntry)
{
using std::sqrt;
static bool run(typename SVD::WorkMatrixType& work_matrix, SVD& svd, Index p, Index q, RealScalar& maxDiagEntry) {
using std::abs;
using std::sqrt;
Scalar z;
JacobiRotation<Scalar> rot;
RealScalar n = sqrt(numext::abs2(work_matrix.coeff(p,p)) + numext::abs2(work_matrix.coeff(q,p)));
RealScalar n = sqrt(numext::abs2(work_matrix.coeff(p, p)) + numext::abs2(work_matrix.coeff(q, p)));
const RealScalar considerAsZero = (std::numeric_limits<RealScalar>::min)();
const RealScalar precision = NumTraits<Scalar>::epsilon();
if(numext::is_exactly_zero(n))
{
if (numext::is_exactly_zero(n)) {
// make sure first column is zero
work_matrix.coeffRef(p,p) = work_matrix.coeffRef(q,p) = Scalar(0);
work_matrix.coeffRef(p, p) = work_matrix.coeffRef(q, p) = Scalar(0);
if(abs(numext::imag(work_matrix.coeff(p,q)))>considerAsZero)
{
// work_matrix.coeff(p,q) can be zero if work_matrix.coeff(q,p) is not zero but small enough to underflow when computing n
z = abs(work_matrix.coeff(p,q)) / work_matrix.coeff(p,q);
if (abs(numext::imag(work_matrix.coeff(p, q))) > considerAsZero) {
// work_matrix.coeff(p,q) can be zero if work_matrix.coeff(q,p) is not zero but small enough to underflow when
// computing n
z = abs(work_matrix.coeff(p, q)) / work_matrix.coeff(p, q);
work_matrix.row(p) *= z;
if(svd.computeU()) svd.m_matrixU.col(p) *= conj(z);
if (svd.computeU()) svd.m_matrixU.col(p) *= conj(z);
}
if(abs(numext::imag(work_matrix.coeff(q,q)))>considerAsZero)
{
z = abs(work_matrix.coeff(q,q)) / work_matrix.coeff(q,q);
if (abs(numext::imag(work_matrix.coeff(q, q))) > considerAsZero) {
z = abs(work_matrix.coeff(q, q)) / work_matrix.coeff(q, q);
work_matrix.row(q) *= z;
if(svd.computeU()) svd.m_matrixU.col(q) *= conj(z);
if (svd.computeU()) svd.m_matrixU.col(q) *= conj(z);
}
// otherwise the second row is already zero, so we have nothing to do.
}
else
{
rot.c() = conj(work_matrix.coeff(p,p)) / n;
rot.s() = work_matrix.coeff(q,p) / n;
work_matrix.applyOnTheLeft(p,q,rot);
if(svd.computeU()) svd.m_matrixU.applyOnTheRight(p,q,rot.adjoint());
if(abs(numext::imag(work_matrix.coeff(p,q)))>considerAsZero)
{
z = abs(work_matrix.coeff(p,q)) / work_matrix.coeff(p,q);
} else {
rot.c() = conj(work_matrix.coeff(p, p)) / n;
rot.s() = work_matrix.coeff(q, p) / n;
work_matrix.applyOnTheLeft(p, q, rot);
if (svd.computeU()) svd.m_matrixU.applyOnTheRight(p, q, rot.adjoint());
if (abs(numext::imag(work_matrix.coeff(p, q))) > considerAsZero) {
z = abs(work_matrix.coeff(p, q)) / work_matrix.coeff(p, q);
work_matrix.col(q) *= z;
if(svd.computeV()) svd.m_matrixV.col(q) *= z;
if (svd.computeV()) svd.m_matrixV.col(q) *= z;
}
if(abs(numext::imag(work_matrix.coeff(q,q)))>considerAsZero)
{
z = abs(work_matrix.coeff(q,q)) / work_matrix.coeff(q,q);
if (abs(numext::imag(work_matrix.coeff(q, q))) > considerAsZero) {
z = abs(work_matrix.coeff(q, q)) / work_matrix.coeff(q, q);
work_matrix.row(q) *= z;
if(svd.computeU()) svd.m_matrixU.col(q) *= conj(z);
if (svd.computeU()) svd.m_matrixU.col(q) *= conj(z);
}
}
// update largest diagonal entry
maxDiagEntry = numext::maxi<RealScalar>(maxDiagEntry,numext::maxi<RealScalar>(abs(work_matrix.coeff(p,p)), abs(work_matrix.coeff(q,q))));
maxDiagEntry = numext::maxi<RealScalar>(
maxDiagEntry, numext::maxi<RealScalar>(abs(work_matrix.coeff(p, p)), abs(work_matrix.coeff(q, q))));
// and check whether the 2x2 block is already diagonal
RealScalar threshold = numext::maxi<RealScalar>(considerAsZero, precision * maxDiagEntry);
return abs(work_matrix.coeff(p,q))>threshold || abs(work_matrix.coeff(q,p)) > threshold;
return abs(work_matrix.coeff(p, q)) > threshold || abs(work_matrix.coeff(q, p)) > threshold;
}
};
@@ -444,7 +434,7 @@ struct traits<JacobiSVD<MatrixType_, Options> > : svd_traits<MatrixType_, Option
typedef MatrixType_ MatrixType;
};
} // end namespace internal
} // end namespace internal
/** \ingroup SVD_Module
*
@@ -569,8 +559,7 @@ class JacobiSVD : public SVDBase<JacobiSVD<MatrixType_, Options_> > {
* \deprecated Will be removed in the next major Eigen version. Options should
* be specified in the \a Options template parameter.
*/
EIGEN_DEPRECATED
JacobiSVD(Index rows, Index cols, unsigned int computationOptions) {
EIGEN_DEPRECATED JacobiSVD(Index rows, Index cols, unsigned int computationOptions) {
internal::check_svd_options_assertions<MatrixType, Options>(computationOptions, rows, cols);
allocate(rows, cols, computationOptions);
}
@@ -612,22 +601,21 @@ class JacobiSVD : public SVDBase<JacobiSVD<MatrixType_, Options_> > {
*
* \param matrix the matrix to decompose
* \param computationOptions specify whether to compute Thin/Full unitaries U/V
*
*
* \deprecated Will be removed in the next major Eigen version. Options should
* be specified in the \a Options template parameter.
*/
EIGEN_DEPRECATED
JacobiSVD& compute(const MatrixType& matrix, unsigned int computationOptions) {
EIGEN_DEPRECATED JacobiSVD& compute(const MatrixType& matrix, unsigned int computationOptions) {
internal::check_svd_options_assertions<MatrixType, Options>(m_computationOptions, matrix.rows(), matrix.cols());
return compute_impl(matrix, computationOptions);
}
using Base::cols;
using Base::computeU;
using Base::computeV;
using Base::rows;
using Base::cols;
using Base::diagSize;
using Base::rank;
using Base::rows;
private:
void allocate(Index rows, Index cols, unsigned int computationOptions);
@@ -679,9 +667,9 @@ void JacobiSVD<MatrixType, Options>::allocate(Index rows_, Index cols_, unsigned
"Use the ColPivHouseholderQR preconditioner instead.");
m_workMatrix.resize(diagSize(), diagSize());
if(cols()>rows()) m_qr_precond_morecols.allocate(*this);
if(rows()>cols()) m_qr_precond_morerows.allocate(*this);
if(rows()!=cols()) m_scaledMatrix.resize(rows(),cols());
if (cols() > rows()) m_qr_precond_morecols.allocate(*this);
if (rows() > cols()) m_qr_precond_morerows.allocate(*this);
if (rows() != cols()) m_scaledMatrix.resize(rows(), cols());
}
template <typename MatrixType, int Options>
@@ -691,8 +679,8 @@ JacobiSVD<MatrixType, Options>& JacobiSVD<MatrixType, Options>::compute_impl(con
allocate(matrix.rows(), matrix.cols(), computationOptions);
// currently we stop when we reach precision 2*epsilon as the last bit of precision can require an unreasonable number of iterations,
// only worsening the precision of U and V as we accumulate more rotations
// currently we stop when we reach precision 2*epsilon as the last bit of precision can require an unreasonable number
// of iterations, only worsening the precision of U and V as we accumulate more rotations
const RealScalar precision = RealScalar(2) * NumTraits<Scalar>::epsilon();
// limit for denormal numbers to be considered zero in order to avoid infinite loops (see bug 286)
@@ -706,45 +694,39 @@ JacobiSVD<MatrixType, Options>& JacobiSVD<MatrixType, Options>::compute_impl(con
m_nonzeroSingularValues = 0;
return *this;
}
if(numext::is_exactly_zero(scale)) scale = RealScalar(1);
if (numext::is_exactly_zero(scale)) scale = RealScalar(1);
/*** step 1. The R-SVD step: we use a QR decomposition to reduce to the case of a square matrix */
if(rows() != cols())
{
if (rows() != cols()) {
m_scaledMatrix = matrix / scale;
m_qr_precond_morecols.run(*this, m_scaledMatrix);
m_qr_precond_morerows.run(*this, m_scaledMatrix);
}
else
{
m_workMatrix = matrix.template topLeftCorner<DiagSizeAtCompileTime,DiagSizeAtCompileTime>(diagSize(),diagSize()) / scale;
if(m_computeFullU) m_matrixU.setIdentity(rows(),rows());
if(m_computeThinU) m_matrixU.setIdentity(rows(),diagSize());
if(m_computeFullV) m_matrixV.setIdentity(cols(),cols());
if(m_computeThinV) m_matrixV.setIdentity(cols(),diagSize());
} else {
m_workMatrix =
matrix.template topLeftCorner<DiagSizeAtCompileTime, DiagSizeAtCompileTime>(diagSize(), diagSize()) / scale;
if (m_computeFullU) m_matrixU.setIdentity(rows(), rows());
if (m_computeThinU) m_matrixU.setIdentity(rows(), diagSize());
if (m_computeFullV) m_matrixV.setIdentity(cols(), cols());
if (m_computeThinV) m_matrixV.setIdentity(cols(), diagSize());
}
/*** step 2. The main Jacobi SVD iteration. ***/
RealScalar maxDiagEntry = m_workMatrix.cwiseAbs().diagonal().maxCoeff();
bool finished = false;
while(!finished)
{
while (!finished) {
finished = true;
// do a sweep: for all index pairs (p,q), perform SVD of the corresponding 2x2 sub-matrix
for(Index p = 1; p < diagSize(); ++p)
{
for(Index q = 0; q < p; ++q)
{
for (Index p = 1; p < diagSize(); ++p) {
for (Index q = 0; q < p; ++q) {
// if this 2x2 sub-matrix is not diagonal already...
// notice that this comparison will evaluate to false if any NaN is involved, ensuring that NaN's don't
// keep us iterating forever. Similarly, small denormal numbers are considered zero.
RealScalar threshold = numext::maxi<RealScalar>(considerAsZero, precision * maxDiagEntry);
if(abs(m_workMatrix.coeff(p,q))>threshold || abs(m_workMatrix.coeff(q,p)) > threshold)
{
if (abs(m_workMatrix.coeff(p, q)) > threshold || abs(m_workMatrix.coeff(q, p)) > threshold) {
finished = false;
// perform SVD decomposition of 2x2 sub-matrix corresponding to indices p,q to make it diagonal
// the complex to real operation returns true if the updated 2x2 block is not already diagonal
@@ -754,62 +736,57 @@ JacobiSVD<MatrixType, Options>& JacobiSVD<MatrixType, Options>::compute_impl(con
internal::real_2x2_jacobi_svd(m_workMatrix, p, q, &j_left, &j_right);
// accumulate resulting Jacobi rotations
m_workMatrix.applyOnTheLeft(p,q,j_left);
if(computeU()) m_matrixU.applyOnTheRight(p,q,j_left.transpose());
m_workMatrix.applyOnTheLeft(p, q, j_left);
if (computeU()) m_matrixU.applyOnTheRight(p, q, j_left.transpose());
m_workMatrix.applyOnTheRight(p,q,j_right);
if(computeV()) m_matrixV.applyOnTheRight(p,q,j_right);
m_workMatrix.applyOnTheRight(p, q, j_right);
if (computeV()) m_matrixV.applyOnTheRight(p, q, j_right);
// keep track of the largest diagonal coefficient
maxDiagEntry = numext::maxi<RealScalar>(maxDiagEntry,numext::maxi<RealScalar>(abs(m_workMatrix.coeff(p,p)), abs(m_workMatrix.coeff(q,q))));
maxDiagEntry = numext::maxi<RealScalar>(
maxDiagEntry, numext::maxi<RealScalar>(abs(m_workMatrix.coeff(p, p)), abs(m_workMatrix.coeff(q, q))));
}
}
}
}
}
/*** step 3. The work matrix is now diagonal, so ensure it's positive so its diagonal entries are the singular values ***/
/*** step 3. The work matrix is now diagonal, so ensure it's positive so its diagonal entries are the singular values
* ***/
for(Index i = 0; i < diagSize(); ++i)
{
for (Index i = 0; i < diagSize(); ++i) {
// For a complex matrix, some diagonal coefficients might note have been
// treated by svd_precondition_2x2_block_to_be_real, and the imaginary part
// of some diagonal entry might not be null.
if(NumTraits<Scalar>::IsComplex && abs(numext::imag(m_workMatrix.coeff(i,i)))>considerAsZero)
{
RealScalar a = abs(m_workMatrix.coeff(i,i));
if (NumTraits<Scalar>::IsComplex && abs(numext::imag(m_workMatrix.coeff(i, i))) > considerAsZero) {
RealScalar a = abs(m_workMatrix.coeff(i, i));
m_singularValues.coeffRef(i) = abs(a);
if(computeU()) m_matrixU.col(i) *= m_workMatrix.coeff(i,i)/a;
}
else
{
if (computeU()) m_matrixU.col(i) *= m_workMatrix.coeff(i, i) / a;
} else {
// m_workMatrix.coeff(i,i) is already real, no difficulty:
RealScalar a = numext::real(m_workMatrix.coeff(i,i));
RealScalar a = numext::real(m_workMatrix.coeff(i, i));
m_singularValues.coeffRef(i) = abs(a);
if(computeU() && (a<RealScalar(0))) m_matrixU.col(i) = -m_matrixU.col(i);
if (computeU() && (a < RealScalar(0))) m_matrixU.col(i) = -m_matrixU.col(i);
}
}
m_singularValues *= scale;
/*** step 4. Sort singular values in descending order and compute the number of nonzero singular values ***/
m_nonzeroSingularValues = diagSize();
for(Index i = 0; i < diagSize(); i++)
{
for (Index i = 0; i < diagSize(); i++) {
Index pos;
RealScalar maxRemainingSingularValue = m_singularValues.tail(diagSize()-i).maxCoeff(&pos);
if(numext::is_exactly_zero(maxRemainingSingularValue))
{
RealScalar maxRemainingSingularValue = m_singularValues.tail(diagSize() - i).maxCoeff(&pos);
if (numext::is_exactly_zero(maxRemainingSingularValue)) {
m_nonzeroSingularValues = i;
break;
}
if(pos)
{
if (pos) {
pos += i;
std::swap(m_singularValues.coeffRef(i), m_singularValues.coeffRef(pos));
if(computeU()) m_matrixU.col(pos).swap(m_matrixU.col(i));
if(computeV()) m_matrixV.col(pos).swap(m_matrixV.col(i));
if (computeU()) m_matrixU.col(pos).swap(m_matrixU.col(i));
if (computeV()) m_matrixV.col(pos).swap(m_matrixV.col(i));
}
}
@@ -818,12 +795,12 @@ JacobiSVD<MatrixType, Options>& JacobiSVD<MatrixType, Options>::compute_impl(con
}
/** \svd_module
*
* \return the singular value decomposition of \c *this computed by two-sided
* Jacobi transformations.
*
* \sa class JacobiSVD
*/
*
* \return the singular value decomposition of \c *this computed by two-sided
* Jacobi transformations.
*
* \sa class JacobiSVD
*/
template <typename Derived>
template <int Options>
JacobiSVD<typename MatrixBase<Derived>::PlainObject, Options> MatrixBase<Derived>::jacobiSvd() const {
@@ -839,4 +816,4 @@ JacobiSVD<typename MatrixBase<Derived>::PlainObject, Options> MatrixBase<Derived
} // end namespace Eigen
#endif // EIGEN_JACOBISVD_H
#endif // EIGEN_JACOBISVD_H

129
Eigen/src/SVD/JacobiSVD_LAPACKE.h
View File

@@ -36,68 +36,81 @@
// IWYU pragma: private
#include "./InternalHeaderCheck.h"
namespace Eigen {
namespace Eigen {
/** \internal Specialization for the data types supported by LAPACKe */
#define EIGEN_LAPACKE_SVD(EIGTYPE, LAPACKE_TYPE, LAPACKE_RTYPE, LAPACKE_PREFIX, EIGCOLROW, LAPACKE_COLROW, OPTIONS) \
template<> inline \
JacobiSVD<Matrix<EIGTYPE, Dynamic, Dynamic, EIGCOLROW, Dynamic, Dynamic>, OPTIONS>& \
JacobiSVD<Matrix<EIGTYPE, Dynamic, Dynamic, EIGCOLROW, Dynamic, Dynamic>, OPTIONS>::compute_impl(const Matrix<EIGTYPE, Dynamic, Dynamic, EIGCOLROW, Dynamic, Dynamic>& matrix, \
unsigned int computationOptions) \
{ \
typedef Matrix<EIGTYPE, Dynamic, Dynamic, EIGCOLROW, Dynamic, Dynamic> MatrixType; \
/*typedef MatrixType::Scalar Scalar;*/ \
/*typedef MatrixType::RealScalar RealScalar;*/ \
allocate(matrix.rows(), matrix.cols(), computationOptions); \
\
/*const RealScalar precision = RealScalar(2) * NumTraits<Scalar>::epsilon();*/ \
m_nonzeroSingularValues = diagSize(); \
\
lapack_int lda = internal::convert_index<lapack_int>(matrix.outerStride()), ldu, ldvt; \
lapack_int matrix_order = LAPACKE_COLROW; \
char jobu, jobvt; \
LAPACKE_TYPE *u, *vt, dummy; \
jobu = (m_computeFullU) ? 'A' : (m_computeThinU) ? 'S' : 'N'; \
jobvt = (m_computeFullV) ? 'A' : (m_computeThinV) ? 'S' : 'N'; \
if (computeU()) { \
ldu = internal::convert_index<lapack_int>(m_matrixU.outerStride()); \
u = (LAPACKE_TYPE*)m_matrixU.data(); \
} else { ldu=1; u=&dummy; }\
MatrixType localV; \
lapack_int vt_rows = (m_computeFullV) ? internal::convert_index<lapack_int>(cols()) : (m_computeThinV) ? internal::convert_index<lapack_int>(diagSize()) : 1; \
if (computeV()) { \
localV.resize(vt_rows, cols()); \
ldvt = internal::convert_index<lapack_int>(localV.outerStride()); \
vt = (LAPACKE_TYPE*)localV.data(); \
} else { ldvt=1; vt=&dummy; }\
Matrix<LAPACKE_RTYPE, Dynamic, Dynamic> superb; superb.resize(diagSize(), 1); \
MatrixType m_temp; m_temp = matrix; \
lapack_int info = LAPACKE_##LAPACKE_PREFIX##gesvd( matrix_order, jobu, jobvt, internal::convert_index<lapack_int>(rows()), internal::convert_index<lapack_int>(cols()), (LAPACKE_TYPE*)m_temp.data(), lda, (LAPACKE_RTYPE*)m_singularValues.data(), u, ldu, vt, ldvt, superb.data()); \
/* Check the result of the LAPACK call */ \
if (info < 0 || !m_singularValues.allFinite()) { \
m_info = InvalidInput; \
} else if (info > 0 ) { \
m_info = NoConvergence; \
} else { \
m_info = Success; \
if (computeV()) m_matrixV = localV.adjoint(); \
} \
/* for(int i=0;i<diagSize();i++) if (m_singularValues.coeffRef(i) < precision) { m_nonzeroSingularValues--; m_singularValues.coeffRef(i)=RealScalar(0);}*/ \
m_isInitialized = true; \
return *this; \
}
#define EIGEN_LAPACKE_SVD(EIGTYPE, LAPACKE_TYPE, LAPACKE_RTYPE, LAPACKE_PREFIX, EIGCOLROW, LAPACKE_COLROW, OPTIONS) \
template <> \
inline JacobiSVD<Matrix<EIGTYPE, Dynamic, Dynamic, EIGCOLROW, Dynamic, Dynamic>, OPTIONS>& \
JacobiSVD<Matrix<EIGTYPE, Dynamic, Dynamic, EIGCOLROW, Dynamic, Dynamic>, OPTIONS>::compute_impl( \
const Matrix<EIGTYPE, Dynamic, Dynamic, EIGCOLROW, Dynamic, Dynamic>& matrix, unsigned int computationOptions) { \
typedef Matrix<EIGTYPE, Dynamic, Dynamic, EIGCOLROW, Dynamic, Dynamic> MatrixType; \
/*typedef MatrixType::Scalar Scalar;*/ \
/*typedef MatrixType::RealScalar RealScalar;*/ \
allocate(matrix.rows(), matrix.cols(), computationOptions); \
\
/*const RealScalar precision = RealScalar(2) * NumTraits<Scalar>::epsilon();*/ \
m_nonzeroSingularValues = diagSize(); \
\
lapack_int lda = internal::convert_index<lapack_int>(matrix.outerStride()), ldu, ldvt; \
lapack_int matrix_order = LAPACKE_COLROW; \
char jobu, jobvt; \
LAPACKE_TYPE *u, *vt, dummy; \
jobu = (m_computeFullU) ? 'A' : (m_computeThinU) ? 'S' : 'N'; \
jobvt = (m_computeFullV) ? 'A' : (m_computeThinV) ? 'S' : 'N'; \
if (computeU()) { \
ldu = internal::convert_index<lapack_int>(m_matrixU.outerStride()); \
u = (LAPACKE_TYPE*)m_matrixU.data(); \
} else { \
ldu = 1; \
u = &dummy; \
} \
MatrixType localV; \
lapack_int vt_rows = (m_computeFullV) ? internal::convert_index<lapack_int>(cols()) \
: (m_computeThinV) ? internal::convert_index<lapack_int>(diagSize()) \
: 1; \
if (computeV()) { \
localV.resize(vt_rows, cols()); \
ldvt = internal::convert_index<lapack_int>(localV.outerStride()); \
vt = (LAPACKE_TYPE*)localV.data(); \
} else { \
ldvt = 1; \
vt = &dummy; \
} \
Matrix<LAPACKE_RTYPE, Dynamic, Dynamic> superb; \
superb.resize(diagSize(), 1); \
MatrixType m_temp; \
m_temp = matrix; \
lapack_int info = LAPACKE_##LAPACKE_PREFIX##gesvd( \
matrix_order, jobu, jobvt, internal::convert_index<lapack_int>(rows()), \
internal::convert_index<lapack_int>(cols()), (LAPACKE_TYPE*)m_temp.data(), lda, \
(LAPACKE_RTYPE*)m_singularValues.data(), u, ldu, vt, ldvt, superb.data()); \
/* Check the result of the LAPACK call */ \
if (info < 0 || !m_singularValues.allFinite()) { \
m_info = InvalidInput; \
} else if (info > 0) { \
m_info = NoConvergence; \
} else { \
m_info = Success; \
if (computeV()) m_matrixV = localV.adjoint(); \
} \
/* for(int i=0;i<diagSize();i++) if (m_singularValues.coeffRef(i) < precision) { m_nonzeroSingularValues--; \
* m_singularValues.coeffRef(i)=RealScalar(0);}*/ \
m_isInitialized = true; \
return *this; \
}
#define EIGEN_LAPACK_SVD_OPTIONS(OPTIONS) \
EIGEN_LAPACKE_SVD(double, double, double, d, ColMajor, LAPACK_COL_MAJOR, OPTIONS) \
EIGEN_LAPACKE_SVD(float, float, float , s, ColMajor, LAPACK_COL_MAJOR, OPTIONS) \
#define EIGEN_LAPACK_SVD_OPTIONS(OPTIONS) \
EIGEN_LAPACKE_SVD(double, double, double, d, ColMajor, LAPACK_COL_MAJOR, OPTIONS) \
EIGEN_LAPACKE_SVD(float, float, float, s, ColMajor, LAPACK_COL_MAJOR, OPTIONS) \
EIGEN_LAPACKE_SVD(dcomplex, lapack_complex_double, double, z, ColMajor, LAPACK_COL_MAJOR, OPTIONS) \
EIGEN_LAPACKE_SVD(scomplex, lapack_complex_float, float , c, ColMajor, LAPACK_COL_MAJOR, OPTIONS) \
\
EIGEN_LAPACKE_SVD(double, double, double, d, RowMajor, LAPACK_ROW_MAJOR, OPTIONS) \
EIGEN_LAPACKE_SVD(float, float, float , s, RowMajor, LAPACK_ROW_MAJOR, OPTIONS) \
EIGEN_LAPACKE_SVD(scomplex, lapack_complex_float, float, c, ColMajor, LAPACK_COL_MAJOR, OPTIONS) \
\
EIGEN_LAPACKE_SVD(double, double, double, d, RowMajor, LAPACK_ROW_MAJOR, OPTIONS) \
EIGEN_LAPACKE_SVD(float, float, float, s, RowMajor, LAPACK_ROW_MAJOR, OPTIONS) \
EIGEN_LAPACKE_SVD(dcomplex, lapack_complex_double, double, z, RowMajor, LAPACK_ROW_MAJOR, OPTIONS) \
EIGEN_LAPACKE_SVD(scomplex, lapack_complex_float, float , c, RowMajor, LAPACK_ROW_MAJOR, OPTIONS)
EIGEN_LAPACKE_SVD(scomplex, lapack_complex_float, float, c, RowMajor, LAPACK_ROW_MAJOR, OPTIONS)
EIGEN_LAPACK_SVD_OPTIONS(0)
EIGEN_LAPACK_SVD_OPTIONS(ComputeThinU)
@@ -109,6 +122,6 @@ EIGEN_LAPACK_SVD_OPTIONS(ComputeFullU | ComputeFullV)
EIGEN_LAPACK_SVD_OPTIONS(ComputeThinU | ComputeFullV)
EIGEN_LAPACK_SVD_OPTIONS(ComputeFullU | ComputeThinV)
} // end namespace Eigen
} // end namespace Eigen
#endif // EIGEN_JACOBISVD_LAPACKE_H
#endif // EIGEN_JACOBISVD_LAPACKE_H

285
Eigen/src/SVD/SVDBase.h
View File

@@ -38,24 +38,26 @@ constexpr bool should_svd_compute_full_u(int options) { return (options & Comput
constexpr bool should_svd_compute_thin_v(int options) { return (options & ComputeThinV) != 0; }
constexpr bool should_svd_compute_full_v(int options) { return (options & ComputeFullV) != 0; }
template<typename MatrixType, int Options>
template <typename MatrixType, int Options>
void check_svd_options_assertions(unsigned int computationOptions, Index rows, Index cols) {
EIGEN_STATIC_ASSERT((Options & ComputationOptionsBits) == 0,
"SVDBase: Cannot request U or V using both static and runtime options, even if they match. "
"Requesting unitaries at runtime is DEPRECATED: "
"Prefer requesting unitaries statically, using the Options template parameter.");
eigen_assert(!(should_svd_compute_thin_u(computationOptions) && cols < rows && MatrixType::RowsAtCompileTime != Dynamic) &&
!(should_svd_compute_thin_v(computationOptions) && rows < cols && MatrixType::ColsAtCompileTime != Dynamic) &&
"SVDBase: If thin U is requested at runtime, your matrix must have more rows than columns or a dynamic number of rows."
"Similarly, if thin V is requested at runtime, you matrix must have more columns than rows or a dynamic number of columns.");
eigen_assert(
!(should_svd_compute_thin_u(computationOptions) && cols < rows && MatrixType::RowsAtCompileTime != Dynamic) &&
!(should_svd_compute_thin_v(computationOptions) && rows < cols && MatrixType::ColsAtCompileTime != Dynamic) &&
"SVDBase: If thin U is requested at runtime, your matrix must have more rows than columns or a dynamic number of "
"rows."
"Similarly, if thin V is requested at runtime, you matrix must have more columns than rows or a dynamic number "
"of columns.");
(void)computationOptions;
(void)rows;
(void)cols;
}
template<typename Derived> struct traits<SVDBase<Derived> >
: traits<Derived>
{
template <typename Derived>
struct traits<SVDBase<Derived> > : traits<Derived> {
typedef MatrixXpr XprKind;
typedef SolverStorage StorageKind;
typedef int StorageIndex;
@@ -74,17 +76,13 @@ struct svd_traits : traits<MatrixType> {
internal::min_size_prefer_dynamic(MatrixType::RowsAtCompileTime, MatrixType::ColsAtCompileTime),
MaxDiagSizeAtCompileTime =
internal::min_size_prefer_dynamic(MatrixType::MaxRowsAtCompileTime, MatrixType::MaxColsAtCompileTime),
MatrixUColsAtCompileTime = ShouldComputeThinU ? DiagSizeAtCompileTime
: MatrixType::RowsAtCompileTime,
MatrixVColsAtCompileTime = ShouldComputeThinV ? DiagSizeAtCompileTime
: MatrixType::ColsAtCompileTime,
MatrixUMaxColsAtCompileTime = ShouldComputeThinU ? MaxDiagSizeAtCompileTime
: MatrixType::MaxRowsAtCompileTime,
MatrixVMaxColsAtCompileTime = ShouldComputeThinV ? MaxDiagSizeAtCompileTime
: MatrixType::MaxColsAtCompileTime
MatrixUColsAtCompileTime = ShouldComputeThinU ? DiagSizeAtCompileTime : MatrixType::RowsAtCompileTime,
MatrixVColsAtCompileTime = ShouldComputeThinV ? DiagSizeAtCompileTime : MatrixType::ColsAtCompileTime,
MatrixUMaxColsAtCompileTime = ShouldComputeThinU ? MaxDiagSizeAtCompileTime : MatrixType::MaxRowsAtCompileTime,
MatrixVMaxColsAtCompileTime = ShouldComputeThinV ? MaxDiagSizeAtCompileTime : MatrixType::MaxColsAtCompileTime
};
};
}
} // namespace internal
/** \ingroup SVD_Module
*
@@ -97,38 +95,37 @@ struct svd_traits : traits<MatrixType> {
*
* SVD decomposition consists in decomposing any n-by-p matrix \a A as a product
* \f[ A = U S V^* \f]
* where \a U is a n-by-n unitary, \a V is a p-by-p unitary, and \a S is a n-by-p real positive matrix which is zero outside of its main diagonal;
* the diagonal entries of S are known as the \em singular \em values of \a A and the columns of \a U and \a V are known as the left
* and right \em singular \em vectors of \a A respectively.
* where \a U is a n-by-n unitary, \a V is a p-by-p unitary, and \a S is a n-by-p real positive matrix which is zero
* outside of its main diagonal; the diagonal entries of S are known as the \em singular \em values of \a A and the
* columns of \a U and \a V are known as the left and right \em singular \em vectors of \a A respectively.
*
* Singular values are always sorted in decreasing order.
*
*
* You can ask for only \em thin \a U or \a V to be computed, meaning the following. In case of a rectangular n-by-p matrix, letting \a m be the
* smaller value among \a n and \a p, there are only \a m singular vectors; the remaining columns of \a U and \a V do not correspond to actual
* singular vectors. Asking for \em thin \a U or \a V means asking for only their \a m first columns to be formed. So \a U is then a n-by-m matrix,
* and \a V is then a p-by-m matrix. Notice that thin \a U and \a V are all you need for (least squares) solving.
*
* The status of the computation can be retrieved using the \a info() method. Unless \a info() returns \a Success, the results should be not
* considered well defined.
*
* If the input matrix has inf or nan coefficients, the result of the computation is undefined, and \a info() will return \a InvalidInput, but the computation is guaranteed to
* terminate in finite (and reasonable) time.
* \sa class BDCSVD, class JacobiSVD
*
* You can ask for only \em thin \a U or \a V to be computed, meaning the following. In case of a rectangular n-by-p
* matrix, letting \a m be the smaller value among \a n and \a p, there are only \a m singular vectors; the remaining
* columns of \a U and \a V do not correspond to actual singular vectors. Asking for \em thin \a U or \a V means asking
* for only their \a m first columns to be formed. So \a U is then a n-by-m matrix, and \a V is then a p-by-m matrix.
* Notice that thin \a U and \a V are all you need for (least squares) solving.
*
* The status of the computation can be retrieved using the \a info() method. Unless \a info() returns \a Success, the
* results should be not considered well defined.
*
* If the input matrix has inf or nan coefficients, the result of the computation is undefined, and \a info() will
* return \a InvalidInput, but the computation is guaranteed to terminate in finite (and reasonable) time. \sa class
* BDCSVD, class JacobiSVD
*/
template<typename Derived> class SVDBase
: public SolverBase<SVDBase<Derived> >
{
public:
template<typename Derived_>
template <typename Derived>
class SVDBase : public SolverBase<SVDBase<Derived> > {
public:
template <typename Derived_>
friend struct internal::solve_assertion;
typedef typename internal::traits<Derived>::MatrixType MatrixType;
typedef typename MatrixType::Scalar Scalar;
typedef typename NumTraits<typename MatrixType::Scalar>::Real RealScalar;
typedef typename Eigen::internal::traits<SVDBase>::StorageIndex StorageIndex;
typedef Eigen::Index Index; ///< \deprecated since Eigen 3.3
typedef Eigen::Index Index; ///< \deprecated since Eigen 3.3
static constexpr bool ShouldComputeFullU = internal::traits<Derived>::ShouldComputeFullU;
static constexpr bool ShouldComputeThinU = internal::traits<Derived>::ShouldComputeThinU;
@@ -167,14 +164,14 @@ public:
/** \returns the \a U matrix.
*
* For the SVD decomposition of a n-by-p matrix, letting \a m be the minimum of \a n and \a p,
* the U matrix is n-by-n if you asked for \link Eigen::ComputeFullU ComputeFullU \endlink, and is n-by-m if you asked for \link Eigen::ComputeThinU ComputeThinU \endlink.
* the U matrix is n-by-n if you asked for \link Eigen::ComputeFullU ComputeFullU \endlink, and is n-by-m if you asked
* for \link Eigen::ComputeThinU ComputeThinU \endlink.
*
* The \a m first columns of \a U are the left singular vectors of the matrix being decomposed.
*
* This method asserts that you asked for \a U to be computed.
*/
const MatrixUType& matrixU() const
{
const MatrixUType& matrixU() const {
_check_compute_assertions();
eigen_assert(computeU() && "This SVD decomposition didn't compute U. Did you ask for it?");
return m_matrixU;
@@ -183,14 +180,14 @@ public:
/** \returns the \a V matrix.
*
* For the SVD decomposition of a n-by-p matrix, letting \a m be the minimum of \a n and \a p,
* the V matrix is p-by-p if you asked for \link Eigen::ComputeFullV ComputeFullV \endlink, and is p-by-m if you asked for \link Eigen::ComputeThinV ComputeThinV \endlink.
* the V matrix is p-by-p if you asked for \link Eigen::ComputeFullV ComputeFullV \endlink, and is p-by-m if you asked
* for \link Eigen::ComputeThinV ComputeThinV \endlink.
*
* The \a m first columns of \a V are the right singular vectors of the matrix being decomposed.
*
* This method asserts that you asked for \a V to be computed.
*/
const MatrixVType& matrixV() const
{
const MatrixVType& matrixV() const {
_check_compute_assertions();
eigen_assert(computeV() && "This SVD decomposition didn't compute V. Did you ask for it?");
return m_matrixV;
@@ -201,82 +198,76 @@ public:
* For the SVD decomposition of a n-by-p matrix, letting \a m be the minimum of \a n and \a p, the
* returned vector has size \a m. Singular values are always sorted in decreasing order.
*/
const SingularValuesType& singularValues() const
{
const SingularValuesType& singularValues() const {
_check_compute_assertions();
return m_singularValues;
}
/** \returns the number of singular values that are not exactly 0 */
Index nonzeroSingularValues() const
{
Index nonzeroSingularValues() const {
_check_compute_assertions();
return m_nonzeroSingularValues;
}
/** \returns the rank of the matrix of which \c *this is the SVD.
*
* \note This method has to determine which singular values should be considered nonzero.
* For that, it uses the threshold value that you can control by calling
* setThreshold(const RealScalar&).
*/
inline Index rank() const
{
*
* \note This method has to determine which singular values should be considered nonzero.
* For that, it uses the threshold value that you can control by calling
* setThreshold(const RealScalar&).
*/
inline Index rank() const {
using std::abs;
_check_compute_assertions();
if(m_singularValues.size()==0) return 0;
RealScalar premultiplied_threshold = numext::maxi<RealScalar>(m_singularValues.coeff(0) * threshold(), (std::numeric_limits<RealScalar>::min)());
Index i = m_nonzeroSingularValues-1;
while(i>=0 && m_singularValues.coeff(i) < premultiplied_threshold) --i;
return i+1;
if (m_singularValues.size() == 0) return 0;
RealScalar premultiplied_threshold =
numext::maxi<RealScalar>(m_singularValues.coeff(0) * threshold(), (std::numeric_limits<RealScalar>::min)());
Index i = m_nonzeroSingularValues - 1;
while (i >= 0 && m_singularValues.coeff(i) < premultiplied_threshold) --i;
return i + 1;
}
/** Allows to prescribe a threshold to be used by certain methods, such as rank() and solve(),
* which need to determine when singular values are to be considered nonzero.
* This is not used for the SVD decomposition itself.
*
* When it needs to get the threshold value, Eigen calls threshold().
* The default is \c NumTraits<Scalar>::epsilon()
*
* \param threshold The new value to use as the threshold.
*
* A singular value will be considered nonzero if its value is strictly greater than
* \f$ \vert singular value \vert \leqslant threshold \times \vert max singular value \vert \f$.
*
* If you want to come back to the default behavior, call setThreshold(Default_t)
*/
Derived& setThreshold(const RealScalar& threshold)
{
* which need to determine when singular values are to be considered nonzero.
* This is not used for the SVD decomposition itself.
*
* When it needs to get the threshold value, Eigen calls threshold().
* The default is \c NumTraits<Scalar>::epsilon()
*
* \param threshold The new value to use as the threshold.
*
* A singular value will be considered nonzero if its value is strictly greater than
* \f$ \vert singular value \vert \leqslant threshold \times \vert max singular value \vert \f$.
*
* If you want to come back to the default behavior, call setThreshold(Default_t)
*/
Derived& setThreshold(const RealScalar& threshold) {
m_usePrescribedThreshold = true;
m_prescribedThreshold = threshold;
return derived();
}
/** Allows to come back to the default behavior, letting Eigen use its default formula for
* determining the threshold.
*
* You should pass the special object Eigen::Default as parameter here.
* \code svd.setThreshold(Eigen::Default); \endcode
*
* See the documentation of setThreshold(const RealScalar&).
*/
Derived& setThreshold(Default_t)
{
* determining the threshold.
*
* You should pass the special object Eigen::Default as parameter here.
* \code svd.setThreshold(Eigen::Default); \endcode
*
* See the documentation of setThreshold(const RealScalar&).
*/
Derived& setThreshold(Default_t) {
m_usePrescribedThreshold = false;
return derived();
}
/** Returns the threshold that will be used by certain methods such as rank().
*
* See the documentation of setThreshold(const RealScalar&).
*/
RealScalar threshold() const
{
*
* See the documentation of setThreshold(const RealScalar&).
*/
RealScalar threshold() const {
eigen_assert(m_isInitialized || m_usePrescribedThreshold);
// this temporary is needed to workaround a MSVC issue
Index diagSize = (std::max<Index>)(1,m_diagSize);
return m_usePrescribedThreshold ? m_prescribedThreshold
: RealScalar(diagSize)*NumTraits<Scalar>::epsilon();
Index diagSize = (std::max<Index>)(1, m_diagSize);
return m_usePrescribedThreshold ? m_prescribedThreshold : RealScalar(diagSize) * NumTraits<Scalar>::epsilon();
}
/** \returns true if \a U (full or thin) is asked for in this SVD decomposition */
@@ -287,56 +278,52 @@ public:
inline Index rows() const { return m_rows.value(); }
inline Index cols() const { return m_cols.value(); }
inline Index diagSize() const { return m_diagSize.value(); }
#ifdef EIGEN_PARSED_BY_DOXYGEN
/** \returns a (least squares) solution of \f$ A x = b \f$ using the current SVD decomposition of A.
*
* \param b the right-hand-side of the equation to solve.
*
* \note Solving requires both U and V to be computed. Thin U and V are enough, there is no need for full U or V.
*
* \note SVD solving is implicitly least-squares. Thus, this method serves both purposes of exact solving and least-squares solving.
* In other words, the returned solution is guaranteed to minimize the Euclidean norm \f$ \Vert A x - b \Vert \f$.
*/
template<typename Rhs>
inline const Solve<Derived, Rhs>
solve(const MatrixBase<Rhs>& b) const;
#endif
#ifdef EIGEN_PARSED_BY_DOXYGEN
/** \returns a (least squares) solution of \f$ A x = b \f$ using the current SVD decomposition of A.
*
* \param b the right-hand-side of the equation to solve.
*
* \note Solving requires both U and V to be computed. Thin U and V are enough, there is no need for full U or V.
*
* \note SVD solving is implicitly least-squares. Thus, this method serves both purposes of exact solving and
* least-squares solving. In other words, the returned solution is guaranteed to minimize the Euclidean norm \f$ \Vert
* A x - b \Vert \f$.
*/
template <typename Rhs>
inline const Solve<Derived, Rhs> solve(const MatrixBase<Rhs>& b) const;
#endif
/** \brief Reports whether previous computation was successful.
*
* \returns \c Success if computation was successful.
*/
EIGEN_DEVICE_FUNC
ComputationInfo info() const
{
EIGEN_DEVICE_FUNC ComputationInfo info() const {
eigen_assert(m_isInitialized && "SVD is not initialized.");
return m_info;
}
#ifndef EIGEN_PARSED_BY_DOXYGEN
template<typename RhsType, typename DstType>
void _solve_impl(const RhsType &rhs, DstType &dst) const;
#ifndef EIGEN_PARSED_BY_DOXYGEN
template <typename RhsType, typename DstType>
void _solve_impl(const RhsType& rhs, DstType& dst) const;
template<bool Conjugate, typename RhsType, typename DstType>
void _solve_impl_transposed(const RhsType &rhs, DstType &dst) const;
#endif
protected:
template <bool Conjugate, typename RhsType, typename DstType>
void _solve_impl_transposed(const RhsType& rhs, DstType& dst) const;
#endif
protected:
EIGEN_STATIC_ASSERT_NON_INTEGER(Scalar)
void _check_compute_assertions() const {
eigen_assert(m_isInitialized && "SVD is not initialized.");
}
void _check_compute_assertions() const { eigen_assert(m_isInitialized && "SVD is not initialized."); }
template<bool Transpose_, typename Rhs>
template <bool Transpose_, typename Rhs>
void _check_solve_assertion(const Rhs& b) const {
EIGEN_ONLY_USED_FOR_DEBUG(b);
_check_compute_assertions();
eigen_assert(computeU() && computeV() && "SVDBase::solve(): Both unitaries U and V are required to be computed (thin unitaries suffice).");
eigen_assert((Transpose_?cols():rows())==b.rows() && "SVDBase::solve(): invalid number of rows of the right hand side matrix b");
EIGEN_ONLY_USED_FOR_DEBUG(b);
_check_compute_assertions();
eigen_assert(computeU() && computeV() &&
"SVDBase::solve(): Both unitaries U and V are required to be computed (thin unitaries suffice).");
eigen_assert((Transpose_ ? cols() : rows()) == b.rows() &&
"SVDBase::solve(): invalid number of rows of the right hand side matrix b");
}
// return true if already allocated
@@ -381,31 +368,33 @@ protected:
};
#ifndef EIGEN_PARSED_BY_DOXYGEN
template<typename Derived>
template<typename RhsType, typename DstType>
void SVDBase<Derived>::_solve_impl(const RhsType &rhs, DstType &dst) const
{
template <typename Derived>
template <typename RhsType, typename DstType>
void SVDBase<Derived>::_solve_impl(const RhsType& rhs, DstType& dst) const {
// A = U S V^*
// So A^{-1} = V S^{-1} U^*
Matrix<typename RhsType::Scalar, Dynamic, RhsType::ColsAtCompileTime, 0, MatrixType::MaxRowsAtCompileTime, RhsType::MaxColsAtCompileTime> tmp;
Matrix<typename RhsType::Scalar, Dynamic, RhsType::ColsAtCompileTime, 0, MatrixType::MaxRowsAtCompileTime,
RhsType::MaxColsAtCompileTime>
tmp;
Index l_rank = rank();
tmp.noalias() = m_matrixU.leftCols(l_rank).adjoint() * rhs;
tmp.noalias() = m_matrixU.leftCols(l_rank).adjoint() * rhs;
tmp = m_singularValues.head(l_rank).asDiagonal().inverse() * tmp;
dst = m_matrixV.leftCols(l_rank) * tmp;
}
template<typename Derived>
template<bool Conjugate, typename RhsType, typename DstType>
void SVDBase<Derived>::_solve_impl_transposed(const RhsType &rhs, DstType &dst) const
{
template <typename Derived>
template <bool Conjugate, typename RhsType, typename DstType>
void SVDBase<Derived>::_solve_impl_transposed(const RhsType& rhs, DstType& dst) const {
// A = U S V^*
// So A^{-*} = U S^{-1} V^*
// And A^{-T} = U_conj S^{-1} V^T
Matrix<typename RhsType::Scalar, Dynamic, RhsType::ColsAtCompileTime, 0, MatrixType::MaxRowsAtCompileTime, RhsType::MaxColsAtCompileTime> tmp;
Matrix<typename RhsType::Scalar, Dynamic, RhsType::ColsAtCompileTime, 0, MatrixType::MaxRowsAtCompileTime,
RhsType::MaxColsAtCompileTime>
tmp;
Index l_rank = rank();
tmp.noalias() = m_matrixV.leftCols(l_rank).transpose().template conjugateIf<Conjugate>() * rhs;
tmp.noalias() = m_matrixV.leftCols(l_rank).transpose().template conjugateIf<Conjugate>() * rhs;
tmp = m_singularValues.head(l_rank).asDiagonal().inverse() * tmp;
dst = m_matrixU.template conjugateIf<!Conjugate>().leftCols(l_rank) * tmp;
}
@@ -415,11 +404,7 @@ template <typename Derived>
bool SVDBase<Derived>::allocate(Index rows, Index cols, unsigned int computationOptions) {
eigen_assert(rows >= 0 && cols >= 0);
if (m_isAllocated &&
rows == m_rows.value() &&
cols == m_cols.value() &&
computationOptions == m_computationOptions)
{
if (m_isAllocated && rows == m_rows.value() && cols == m_cols.value() && computationOptions == m_computationOptions) {
return true;
}
@@ -439,14 +424,14 @@ bool SVDBase<Derived>::allocate(Index rows, Index cols, unsigned int computation
m_diagSize.setValue(numext::mini(m_rows.value(), m_cols.value()));
m_singularValues.resize(m_diagSize.value());
if(RowsAtCompileTime==Dynamic)
if (RowsAtCompileTime == Dynamic)
m_matrixU.resize(m_rows.value(), m_computeFullU ? m_rows.value() : m_computeThinU ? m_diagSize.value() : 0);
if(ColsAtCompileTime==Dynamic)
if (ColsAtCompileTime == Dynamic)
m_matrixV.resize(m_cols.value(), m_computeFullV ? m_cols.value() : m_computeThinV ? m_diagSize.value() : 0);
return false;
}
}// end namespace
} // namespace Eigen
#endif // EIGEN_SVDBASE_H
#endif // EIGEN_SVDBASE_H

418
Eigen/src/SVD/UpperBidiagonalization.h
View File

@@ -14,219 +14,197 @@
// IWYU pragma: private
#include "./InternalHeaderCheck.h"
namespace Eigen {
namespace Eigen {
namespace internal {
// UpperBidiagonalization will probably be replaced by a Bidiagonalization class, don't want to make it stable API.
// At the same time, it's useful to keep for now as it's about the only thing that is testing the BandMatrix class.
template<typename MatrixType_> class UpperBidiagonalization
{
public:
template <typename MatrixType_>
class UpperBidiagonalization {
public:
typedef MatrixType_ MatrixType;
enum {
RowsAtCompileTime = MatrixType::RowsAtCompileTime,
ColsAtCompileTime = MatrixType::ColsAtCompileTime,
ColsAtCompileTimeMinusOne = internal::decrement_size<ColsAtCompileTime>::ret
};
typedef typename MatrixType::Scalar Scalar;
typedef typename MatrixType::RealScalar RealScalar;
typedef Eigen::Index Index; ///< \deprecated since Eigen 3.3
typedef Matrix<Scalar, 1, ColsAtCompileTime> RowVectorType;
typedef Matrix<Scalar, RowsAtCompileTime, 1> ColVectorType;
typedef BandMatrix<RealScalar, ColsAtCompileTime, ColsAtCompileTime, 1, 0, RowMajor> BidiagonalType;
typedef Matrix<Scalar, ColsAtCompileTime, 1> DiagVectorType;
typedef Matrix<Scalar, ColsAtCompileTimeMinusOne, 1> SuperDiagVectorType;
typedef HouseholderSequence<
const MatrixType, const internal::remove_all_t<typename Diagonal<const MatrixType, 0>::ConjugateReturnType> >
HouseholderUSequenceType;
typedef HouseholderSequence<const internal::remove_all_t<typename MatrixType::ConjugateReturnType>,
Diagonal<const MatrixType, 1>, OnTheRight>
HouseholderVSequenceType;
typedef MatrixType_ MatrixType;
enum {
RowsAtCompileTime = MatrixType::RowsAtCompileTime,
ColsAtCompileTime = MatrixType::ColsAtCompileTime,
ColsAtCompileTimeMinusOne = internal::decrement_size<ColsAtCompileTime>::ret
};
typedef typename MatrixType::Scalar Scalar;
typedef typename MatrixType::RealScalar RealScalar;
typedef Eigen::Index Index; ///< \deprecated since Eigen 3.3
typedef Matrix<Scalar, 1, ColsAtCompileTime> RowVectorType;
typedef Matrix<Scalar, RowsAtCompileTime, 1> ColVectorType;
typedef BandMatrix<RealScalar, ColsAtCompileTime, ColsAtCompileTime, 1, 0, RowMajor> BidiagonalType;
typedef Matrix<Scalar, ColsAtCompileTime, 1> DiagVectorType;
typedef Matrix<Scalar, ColsAtCompileTimeMinusOne, 1> SuperDiagVectorType;
typedef HouseholderSequence<
const MatrixType,
const internal::remove_all_t<typename Diagonal<const MatrixType,0>::ConjugateReturnType>
> HouseholderUSequenceType;
typedef HouseholderSequence<
const internal::remove_all_t<typename MatrixType::ConjugateReturnType>,
Diagonal<const MatrixType,1>,
OnTheRight
> HouseholderVSequenceType;
/**
* \brief Default Constructor.
*
* The default constructor is useful in cases in which the user intends to
* perform decompositions via Bidiagonalization::compute(const MatrixType&).
*/
UpperBidiagonalization() : m_householder(), m_bidiagonal(0, 0), m_isInitialized(false) {}
/**
* \brief Default Constructor.
*
* The default constructor is useful in cases in which the user intends to
* perform decompositions via Bidiagonalization::compute(const MatrixType&).
*/
UpperBidiagonalization() : m_householder(), m_bidiagonal(0, 0), m_isInitialized(false) {}
explicit UpperBidiagonalization(const MatrixType& matrix)
explicit UpperBidiagonalization(const MatrixType& matrix)
: m_householder(matrix.rows(), matrix.cols()),
m_bidiagonal(matrix.cols(), matrix.cols()),
m_isInitialized(false)
{
compute(matrix);
}
m_isInitialized(false) {
compute(matrix);
}
UpperBidiagonalization(Index rows, Index cols)
: m_householder(rows, cols),
m_bidiagonal(cols, cols),
m_isInitialized(false)
{}
UpperBidiagonalization(Index rows, Index cols)
: m_householder(rows, cols), m_bidiagonal(cols, cols), m_isInitialized(false) {}
UpperBidiagonalization& compute(const MatrixType& matrix);
UpperBidiagonalization& computeUnblocked(const MatrixType& matrix);
const MatrixType& householder() const { return m_householder; }
const BidiagonalType& bidiagonal() const { return m_bidiagonal; }
const HouseholderUSequenceType householderU() const
{
eigen_assert(m_isInitialized && "UpperBidiagonalization is not initialized.");
return HouseholderUSequenceType(m_householder, m_householder.diagonal().conjugate());
}
UpperBidiagonalization& compute(const MatrixType& matrix);
UpperBidiagonalization& computeUnblocked(const MatrixType& matrix);
const HouseholderVSequenceType householderV() // const here gives nasty errors and i'm lazy
{
eigen_assert(m_isInitialized && "UpperBidiagonalization is not initialized.");
return HouseholderVSequenceType(m_householder.conjugate(), m_householder.const_derived().template diagonal<1>())
.setLength(m_householder.cols()-1)
.setShift(1);
}
protected:
MatrixType m_householder;
BidiagonalType m_bidiagonal;
bool m_isInitialized;
const MatrixType& householder() const { return m_householder; }
const BidiagonalType& bidiagonal() const { return m_bidiagonal; }
const HouseholderUSequenceType householderU() const {
eigen_assert(m_isInitialized && "UpperBidiagonalization is not initialized.");
return HouseholderUSequenceType(m_householder, m_householder.diagonal().conjugate());
}
const HouseholderVSequenceType householderV() // const here gives nasty errors and i'm lazy
{
eigen_assert(m_isInitialized && "UpperBidiagonalization is not initialized.");
return HouseholderVSequenceType(m_householder.conjugate(), m_householder.const_derived().template diagonal<1>())
.setLength(m_householder.cols() - 1)
.setShift(1);
}
protected:
MatrixType m_householder;
BidiagonalType m_bidiagonal;
bool m_isInitialized;
};
// Standard upper bidiagonalization without fancy optimizations
// This version should be faster for small matrix size
template<typename MatrixType>
void upperbidiagonalization_inplace_unblocked(MatrixType& mat,
typename MatrixType::RealScalar *diagonal,
typename MatrixType::RealScalar *upper_diagonal,
typename MatrixType::Scalar* tempData = 0)
{
template <typename MatrixType>
void upperbidiagonalization_inplace_unblocked(MatrixType& mat, typename MatrixType::RealScalar* diagonal,
typename MatrixType::RealScalar* upper_diagonal,
typename MatrixType::Scalar* tempData = 0) {
typedef typename MatrixType::Scalar Scalar;
Index rows = mat.rows();
Index cols = mat.cols();
typedef Matrix<Scalar,Dynamic,1,ColMajor,MatrixType::MaxRowsAtCompileTime,1> TempType;
typedef Matrix<Scalar, Dynamic, 1, ColMajor, MatrixType::MaxRowsAtCompileTime, 1> TempType;
TempType tempVector;
if(tempData==0)
{
if (tempData == 0) {
tempVector.resize(rows);
tempData = tempVector.data();
}
for (Index k = 0; /* breaks at k==cols-1 below */ ; ++k)
{
for (Index k = 0; /* breaks at k==cols-1 below */; ++k) {
Index remainingRows = rows - k;
Index remainingCols = cols - k - 1;
// construct left householder transform in-place in A
mat.col(k).tail(remainingRows)
.makeHouseholderInPlace(mat.coeffRef(k,k), diagonal[k]);
mat.col(k).tail(remainingRows).makeHouseholderInPlace(mat.coeffRef(k, k), diagonal[k]);
// apply householder transform to remaining part of A on the left
mat.bottomRightCorner(remainingRows, remainingCols)
.applyHouseholderOnTheLeft(mat.col(k).tail(remainingRows-1), mat.coeff(k,k), tempData);
.applyHouseholderOnTheLeft(mat.col(k).tail(remainingRows - 1), mat.coeff(k, k), tempData);
if(k == cols-1) break;
if (k == cols - 1) break;
// construct right householder transform in-place in mat
mat.row(k).tail(remainingCols)
.makeHouseholderInPlace(mat.coeffRef(k,k+1), upper_diagonal[k]);
mat.row(k).tail(remainingCols).makeHouseholderInPlace(mat.coeffRef(k, k + 1), upper_diagonal[k]);
// apply householder transform to remaining part of mat on the left
mat.bottomRightCorner(remainingRows-1, remainingCols)
.applyHouseholderOnTheRight(mat.row(k).tail(remainingCols-1).adjoint(), mat.coeff(k,k+1), tempData);
mat.bottomRightCorner(remainingRows - 1, remainingCols)
.applyHouseholderOnTheRight(mat.row(k).tail(remainingCols - 1).adjoint(), mat.coeff(k, k + 1), tempData);
}
}
/** \internal
* Helper routine for the block reduction to upper bidiagonal form.
*
* Let's partition the matrix A:
*
* | A00 A01 |
* A = | |
* | A10 A11 |
*
* This function reduces to bidiagonal form the left \c rows x \a blockSize vertical panel [A00/A10]
* and the \a blockSize x \c cols horizontal panel [A00 A01] of the matrix \a A. The bottom-right block A11
* is updated using matrix-matrix products:
* A22 -= V * Y^T - X * U^T
* where V and U contains the left and right Householder vectors. U and V are stored in A10, and A01
* respectively, and the update matrices X and Y are computed during the reduction.
*
*/
template<typename MatrixType>
void upperbidiagonalization_blocked_helper(MatrixType& A,
typename MatrixType::RealScalar *diagonal,
typename MatrixType::RealScalar *upper_diagonal,
Index bs,
Ref<Matrix<typename MatrixType::Scalar, Dynamic, Dynamic,
traits<MatrixType>::Flags & RowMajorBit> > X,
Ref<Matrix<typename MatrixType::Scalar, Dynamic, Dynamic,
traits<MatrixType>::Flags & RowMajorBit> > Y)
{
* Helper routine for the block reduction to upper bidiagonal form.
*
* Let's partition the matrix A:
*
* | A00 A01 |
* A = | |
* | A10 A11 |
*
* This function reduces to bidiagonal form the left \c rows x \a blockSize vertical panel [A00/A10]
* and the \a blockSize x \c cols horizontal panel [A00 A01] of the matrix \a A. The bottom-right block A11
* is updated using matrix-matrix products:
* A22 -= V * Y^T - X * U^T
* where V and U contains the left and right Householder vectors. U and V are stored in A10, and A01
* respectively, and the update matrices X and Y are computed during the reduction.
*
*/
template <typename MatrixType>
void upperbidiagonalization_blocked_helper(
MatrixType& A, typename MatrixType::RealScalar* diagonal, typename MatrixType::RealScalar* upper_diagonal, Index bs,
Ref<Matrix<typename MatrixType::Scalar, Dynamic, Dynamic, traits<MatrixType>::Flags & RowMajorBit> > X,
Ref<Matrix<typename MatrixType::Scalar, Dynamic, Dynamic, traits<MatrixType>::Flags & RowMajorBit> > Y) {
typedef typename MatrixType::Scalar Scalar;
typedef typename MatrixType::RealScalar RealScalar;
typedef typename NumTraits<RealScalar>::Literal Literal;
static constexpr int StorageOrder = (traits<MatrixType>::Flags & RowMajorBit) ? RowMajor : ColMajor;
typedef InnerStride<StorageOrder == ColMajor ? 1 : Dynamic> ColInnerStride;
typedef InnerStride<StorageOrder == ColMajor ? Dynamic : 1> RowInnerStride;
typedef Ref<Matrix<Scalar, Dynamic, 1>, 0, ColInnerStride> SubColumnType;
typedef Ref<Matrix<Scalar, 1, Dynamic>, 0, RowInnerStride> SubRowType;
typedef Ref<Matrix<Scalar, Dynamic, Dynamic, StorageOrder > > SubMatType;
typedef Ref<Matrix<Scalar, Dynamic, 1>, 0, ColInnerStride> SubColumnType;
typedef Ref<Matrix<Scalar, 1, Dynamic>, 0, RowInnerStride> SubRowType;
typedef Ref<Matrix<Scalar, Dynamic, Dynamic, StorageOrder> > SubMatType;
Index brows = A.rows();
Index bcols = A.cols();
Scalar tau_u, tau_u_prev(0), tau_v;
for(Index k = 0; k < bs; ++k)
{
for (Index k = 0; k < bs; ++k) {
Index remainingRows = brows - k;
Index remainingCols = bcols - k - 1;
SubMatType X_k1( X.block(k,0, remainingRows,k) );
SubMatType V_k1( A.block(k,0, remainingRows,k) );
SubMatType X_k1(X.block(k, 0, remainingRows, k));
SubMatType V_k1(A.block(k, 0, remainingRows, k));
// 1 - update the k-th column of A
SubColumnType v_k = A.col(k).tail(remainingRows);
v_k -= V_k1 * Y.row(k).head(k).adjoint();
if(k) v_k -= X_k1 * A.col(k).head(k);
v_k -= V_k1 * Y.row(k).head(k).adjoint();
if (k) v_k -= X_k1 * A.col(k).head(k);
// 2 - construct left Householder transform in-place
v_k.makeHouseholderInPlace(tau_v, diagonal[k]);
if(k+1<bcols)
{
SubMatType Y_k ( Y.block(k+1,0, remainingCols, k+1) );
SubMatType U_k1 ( A.block(0,k+1, k,remainingCols) );
if (k + 1 < bcols) {
SubMatType Y_k(Y.block(k + 1, 0, remainingCols, k + 1));
SubMatType U_k1(A.block(0, k + 1, k, remainingCols));
// this eases the application of Householder transforAions
// A(k,k) will store tau_v later
A(k,k) = Scalar(1);
A(k, k) = Scalar(1);
// 3 - Compute y_k^T = tau_v * ( A^T*v_k - Y_k-1*V_k-1^T*v_k - U_k-1*X_k-1^T*v_k )
{
SubColumnType y_k( Y.col(k).tail(remainingCols) );
SubColumnType y_k(Y.col(k).tail(remainingCols));
// let's use the beginning of column k of Y as a temporary vector
SubColumnType tmp( Y.col(k).head(k) );
y_k.noalias() = A.block(k,k+1, remainingRows,remainingCols).adjoint() * v_k; // bottleneck
tmp.noalias() = V_k1.adjoint() * v_k;
SubColumnType tmp(Y.col(k).head(k));
y_k.noalias() = A.block(k, k + 1, remainingRows, remainingCols).adjoint() * v_k; // bottleneck
tmp.noalias() = V_k1.adjoint() * v_k;
y_k.noalias() -= Y_k.leftCols(k) * tmp;
tmp.noalias() = X_k1.adjoint() * v_k;
y_k.noalias() -= U_k1.adjoint() * tmp;
tmp.noalias() = X_k1.adjoint() * v_k;
y_k.noalias() -= U_k1.adjoint() * tmp;
y_k *= numext::conj(tau_v);
}
// 4 - update k-th row of A (it will become u_k)
SubRowType u_k( A.row(k).tail(remainingCols) );
SubRowType u_k(A.row(k).tail(remainingCols));
u_k = u_k.conjugate();
{
u_k -= Y_k * A.row(k).head(k+1).adjoint();
if(k) u_k -= U_k1.adjoint() * X.row(k).head(k).adjoint();
u_k -= Y_k * A.row(k).head(k + 1).adjoint();
if (k) u_k -= U_k1.adjoint() * X.row(k).head(k).adjoint();
}
// 5 - construct right Householder transform in-place
@@ -234,68 +212,61 @@ void upperbidiagonalization_blocked_helper(MatrixType& A,
// this eases the application of Householder transformations
// A(k,k+1) will store tau_u later
A(k,k+1) = Scalar(1);
A(k, k + 1) = Scalar(1);
// 6 - Compute x_k = tau_u * ( A*u_k - X_k-1*U_k-1^T*u_k - V_k*Y_k^T*u_k )
{
SubColumnType x_k ( X.col(k).tail(remainingRows-1) );
SubColumnType x_k(X.col(k).tail(remainingRows - 1));
// let's use the beginning of column k of X as a temporary vectors
// note that tmp0 and tmp1 overlaps
SubColumnType tmp0 ( X.col(k).head(k) ),
tmp1 ( X.col(k).head(k+1) );
x_k.noalias() = A.block(k+1,k+1, remainingRows-1,remainingCols) * u_k.transpose(); // bottleneck
tmp0.noalias() = U_k1 * u_k.transpose();
x_k.noalias() -= X_k1.bottomRows(remainingRows-1) * tmp0;
tmp1.noalias() = Y_k.adjoint() * u_k.transpose();
x_k.noalias() -= A.block(k+1,0, remainingRows-1,k+1) * tmp1;
SubColumnType tmp0(X.col(k).head(k)), tmp1(X.col(k).head(k + 1));
x_k.noalias() = A.block(k + 1, k + 1, remainingRows - 1, remainingCols) * u_k.transpose(); // bottleneck
tmp0.noalias() = U_k1 * u_k.transpose();
x_k.noalias() -= X_k1.bottomRows(remainingRows - 1) * tmp0;
tmp1.noalias() = Y_k.adjoint() * u_k.transpose();
x_k.noalias() -= A.block(k + 1, 0, remainingRows - 1, k + 1) * tmp1;
x_k *= numext::conj(tau_u);
tau_u = numext::conj(tau_u);
u_k = u_k.conjugate();
}
if(k>0) A.coeffRef(k-1,k) = tau_u_prev;
if (k > 0) A.coeffRef(k - 1, k) = tau_u_prev;
tau_u_prev = tau_u;
}
else
A.coeffRef(k-1,k) = tau_u_prev;
} else
A.coeffRef(k - 1, k) = tau_u_prev;
A.coeffRef(k,k) = tau_v;
A.coeffRef(k, k) = tau_v;
}
if(bs<bcols)
A.coeffRef(bs-1,bs) = tau_u_prev;
if (bs < bcols) A.coeffRef(bs - 1, bs) = tau_u_prev;
// update A22
if(bcols>bs && brows>bs)
{
SubMatType A11( A.bottomRightCorner(brows-bs,bcols-bs) );
SubMatType A10( A.block(bs,0, brows-bs,bs) );
SubMatType A01( A.block(0,bs, bs,bcols-bs) );
Scalar tmp = A01(bs-1,0);
A01(bs-1,0) = Literal(1);
A11.noalias() -= A10 * Y.topLeftCorner(bcols,bs).bottomRows(bcols-bs).adjoint();
A11.noalias() -= X.topLeftCorner(brows,bs).bottomRows(brows-bs) * A01;
A01(bs-1,0) = tmp;
if (bcols > bs && brows > bs) {
SubMatType A11(A.bottomRightCorner(brows - bs, bcols - bs));
SubMatType A10(A.block(bs, 0, brows - bs, bs));
SubMatType A01(A.block(0, bs, bs, bcols - bs));
Scalar tmp = A01(bs - 1, 0);
A01(bs - 1, 0) = Literal(1);
A11.noalias() -= A10 * Y.topLeftCorner(bcols, bs).bottomRows(bcols - bs).adjoint();
A11.noalias() -= X.topLeftCorner(brows, bs).bottomRows(brows - bs) * A01;
A01(bs - 1, 0) = tmp;
}
}
/** \internal
*
* Implementation of a block-bidiagonal reduction.
* It is based on the following paper:
* The Design of a Parallel Dense Linear Algebra Software Library: Reduction to Hessenberg, Tridiagonal, and Bidiagonal Form.
* by Jaeyoung Choi, Jack J. Dongarra, David W. Walker. (1995)
* section 3.3
*/
template<typename MatrixType, typename BidiagType>
void upperbidiagonalization_inplace_blocked(MatrixType& A, BidiagType& bidiagonal,
Index maxBlockSize=32,
typename MatrixType::Scalar* /*tempData*/ = 0)
{
*
* Implementation of a block-bidiagonal reduction.
* It is based on the following paper:
* The Design of a Parallel Dense Linear Algebra Software Library: Reduction to Hessenberg, Tridiagonal, and
* Bidiagonal Form. by Jaeyoung Choi, Jack J. Dongarra, David W. Walker. (1995) section 3.3
*/
template <typename MatrixType, typename BidiagType>
void upperbidiagonalization_inplace_blocked(MatrixType& A, BidiagType& bidiagonal, Index maxBlockSize = 32,
typename MatrixType::Scalar* /*tempData*/ = 0) {
typedef typename MatrixType::Scalar Scalar;
typedef Block<MatrixType,Dynamic,Dynamic> BlockType;
typedef Block<MatrixType, Dynamic, Dynamic> BlockType;
Index rows = A.rows();
Index cols = A.cols();
@@ -303,27 +274,20 @@ void upperbidiagonalization_inplace_blocked(MatrixType& A, BidiagType& bidiagona
// X and Y are work space
static constexpr int StorageOrder = (traits<MatrixType>::Flags & RowMajorBit) ? RowMajor : ColMajor;
Matrix<Scalar,
MatrixType::RowsAtCompileTime,
Dynamic,
StorageOrder,
MatrixType::MaxRowsAtCompileTime> X(rows,maxBlockSize);
Matrix<Scalar,
MatrixType::ColsAtCompileTime,
Dynamic,
StorageOrder,
MatrixType::MaxColsAtCompileTime> Y(cols,maxBlockSize);
Index blockSize = (std::min)(maxBlockSize,size);
Matrix<Scalar, MatrixType::RowsAtCompileTime, Dynamic, StorageOrder, MatrixType::MaxRowsAtCompileTime> X(
rows, maxBlockSize);
Matrix<Scalar, MatrixType::ColsAtCompileTime, Dynamic, StorageOrder, MatrixType::MaxColsAtCompileTime> Y(
cols, maxBlockSize);
Index blockSize = (std::min)(maxBlockSize, size);
Index k = 0;
for(k = 0; k < size; k += blockSize)
{
Index bs = (std::min)(size-k,blockSize); // actual size of the block
Index brows = rows - k; // rows of the block
Index bcols = cols - k; // columns of the block
for (k = 0; k < size; k += blockSize) {
Index bs = (std::min)(size - k, blockSize); // actual size of the block
Index brows = rows - k; // rows of the block
Index bcols = cols - k; // columns of the block
// partition the matrix A:
//
//
// | A00 A01 A02 |
// | |
// A = | A10 A11 A12 |
@@ -336,41 +300,32 @@ void upperbidiagonalization_inplace_blocked(MatrixType& A, BidiagType& bidiagona
// B = | |
// | A21 A22 |
BlockType B = A.block(k,k,brows,bcols);
BlockType B = A.block(k, k, brows, bcols);
// This stage performs the bidiagonalization of A11, A21, A12, and updating of A22.
// Finally, the algorithm continue on the updated A22.
//
// However, if B is too small, or A22 empty, then let's use an unblocked strategy
auto upper_diagonal = bidiagonal.template diagonal<1>();
typename MatrixType::RealScalar* upper_diagonal_ptr = upper_diagonal.size() > 0 ? &upper_diagonal.coeffRef(k) : nullptr;
typename MatrixType::RealScalar* upper_diagonal_ptr =
upper_diagonal.size() > 0 ? &upper_diagonal.coeffRef(k) : nullptr;
if(k+bs==cols || bcols<48) // somewhat arbitrary threshold
if (k + bs == cols || bcols < 48) // somewhat arbitrary threshold
{
upperbidiagonalization_inplace_unblocked(B,
&(bidiagonal.template diagonal<0>().coeffRef(k)),
upper_diagonal_ptr,
X.data()
);
break; // We're done
}
else
{
upperbidiagonalization_blocked_helper<BlockType>( B,
&(bidiagonal.template diagonal<0>().coeffRef(k)),
upper_diagonal_ptr,
bs,
X.topLeftCorner(brows,bs),
Y.topLeftCorner(bcols,bs)
);
upperbidiagonalization_inplace_unblocked(B, &(bidiagonal.template diagonal<0>().coeffRef(k)), upper_diagonal_ptr,
X.data());
break; // We're done
} else {
upperbidiagonalization_blocked_helper<BlockType>(B, &(bidiagonal.template diagonal<0>().coeffRef(k)),
upper_diagonal_ptr, bs, X.topLeftCorner(brows, bs),
Y.topLeftCorner(bcols, bs));
}
}
}
template<typename MatrixType_>
UpperBidiagonalization<MatrixType_>& UpperBidiagonalization<MatrixType_>::computeUnblocked(const MatrixType_& matrix)
{
template <typename MatrixType_>
UpperBidiagonalization<MatrixType_>& UpperBidiagonalization<MatrixType_>::computeUnblocked(const MatrixType_& matrix) {
Index rows = matrix.rows();
Index cols = matrix.cols();
EIGEN_ONLY_USED_FOR_DEBUG(cols);
@@ -381,18 +336,15 @@ UpperBidiagonalization<MatrixType_>& UpperBidiagonalization<MatrixType_>::comput
ColVectorType temp(rows);
upperbidiagonalization_inplace_unblocked(m_householder,
&(m_bidiagonal.template diagonal<0>().coeffRef(0)),
&(m_bidiagonal.template diagonal<1>().coeffRef(0)),
temp.data());
upperbidiagonalization_inplace_unblocked(m_householder, &(m_bidiagonal.template diagonal<0>().coeffRef(0)),
&(m_bidiagonal.template diagonal<1>().coeffRef(0)), temp.data());
m_isInitialized = true;
return *this;
}
template<typename MatrixType_>
UpperBidiagonalization<MatrixType_>& UpperBidiagonalization<MatrixType_>::compute(const MatrixType_& matrix)
{
template <typename MatrixType_>
UpperBidiagonalization<MatrixType_>& UpperBidiagonalization<MatrixType_>::compute(const MatrixType_& matrix) {
Index rows = matrix.rows();
Index cols = matrix.cols();
EIGEN_ONLY_USED_FOR_DEBUG(rows);
@@ -402,7 +354,7 @@ UpperBidiagonalization<MatrixType_>& UpperBidiagonalization<MatrixType_>::comput
m_householder = matrix;
upperbidiagonalization_inplace_blocked(m_householder, m_bidiagonal);
m_isInitialized = true;
return *this;
}
@@ -420,8 +372,8 @@ MatrixBase<Derived>::bidiagonalization() const
}
#endif
} // end namespace internal
} // end namespace internal
} // end namespace Eigen
} // end namespace Eigen
#endif // EIGEN_BIDIAGONALIZATION_H
#endif // EIGEN_BIDIAGONALIZATION_H