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add a JacobiRotation class wrapping the cosine-sine pair with

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some convenient features (transpose, adjoint, product)
This commit is contained in:
Gael Guennebaud
2009-09-01 13:18:03 +02:00
parent 32f95ec267
commit 8392373d96
4 changed files with 123 additions and 77 deletions
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73
Eigen/src/SVD/JacobiSVD.h
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@@ -54,7 +54,7 @@ template<typename MatrixType, unsigned int Options> class JacobiSVD
MaxDiagSizeAtCompileTime = EIGEN_ENUM_MIN(MaxRowsAtCompileTime,MaxColsAtCompileTime),
MatrixOptions = MatrixType::Options
};
typedef Matrix<Scalar, Dynamic, Dynamic, MatrixOptions> DummyMatrixType;
typedef typename ei_meta_if<ComputeU,
Matrix<Scalar, RowsAtCompileTime, RowsAtCompileTime,
@@ -73,13 +73,13 @@ template<typename MatrixType, unsigned int Options> class JacobiSVD
JacobiSVD() : m_isInitialized(false) {}
JacobiSVD(const MatrixType& matrix) : m_isInitialized(false)
JacobiSVD(const MatrixType& matrix) : m_isInitialized(false)
{
compute(matrix);
}
JacobiSVD& compute(const MatrixType& matrix);
const MatrixUType& matrixU() const
{
ei_assert(m_isInitialized && "JacobiSVD is not initialized.");
@@ -103,7 +103,7 @@ template<typename MatrixType, unsigned int Options> class JacobiSVD
MatrixVType m_matrixV;
SingularValuesType m_singularValues;
bool m_isInitialized;
template<typename _MatrixType, unsigned int _Options, bool _IsComplex>
friend struct ei_svd_precondition_2x2_block_to_be_real;
};
@@ -120,11 +120,12 @@ struct ei_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;
enum { ComputeU = SVD::ComputeU, ComputeV = SVD::ComputeV };
static void run(MatrixType& work_matrix, JacobiSVD<MatrixType, Options>& svd, int p, int q)
{
Scalar c, s, z;
Scalar z;
JacobiRotation<Scalar> rot;
RealScalar n = ei_sqrt(ei_abs2(work_matrix.coeff(p,p)) + ei_abs2(work_matrix.coeff(q,p)));
if(n==0)
{
@@ -137,10 +138,10 @@ struct ei_svd_precondition_2x2_block_to_be_real<MatrixType, Options, true>
}
else
{
c = ei_conj(work_matrix.coeff(p,p)) / n;
s = work_matrix.coeff(q,p) / n;
work_matrix.applyJacobiOnTheLeft(p,q,c,s);
if(ComputeU) svd.m_matrixU.applyJacobiOnTheRight(p,q,ei_conj(c),-s);
rot.c() = ei_conj(work_matrix.coeff(p,p)) / n;
rot.s() = work_matrix.coeff(q,p) / n;
work_matrix.applyJacobiOnTheLeft(p,q,rot);
if(ComputeU) svd.m_matrixU.applyJacobiOnTheRight(p,q,rot.adjoint());
if(work_matrix.coeff(p,q) != Scalar(0))
{
Scalar z = ei_abs(work_matrix.coeff(p,q)) / work_matrix.coeff(p,q);
@@ -154,38 +155,34 @@ struct ei_svd_precondition_2x2_block_to_be_real<MatrixType, Options, true>
if(ComputeU) svd.m_matrixU.col(q) *= ei_conj(z);
}
}
}
}
};
template<typename MatrixType, typename RealScalar>
void ei_real_2x2_jacobi_svd(const MatrixType& matrix, int p, int q,
RealScalar *c_left, RealScalar *s_left,
RealScalar *c_right, RealScalar *s_right)
JacobiRotation<RealScalar> *j_left,
JacobiRotation<RealScalar> *j_right)
{
Matrix<RealScalar,2,2> m;
m << ei_real(matrix.coeff(p,p)), ei_real(matrix.coeff(p,q)),
ei_real(matrix.coeff(q,p)), ei_real(matrix.coeff(q,q));
RealScalar c1, s1;
ei_real(matrix.coeff(q,p)), ei_real(matrix.coeff(q,q));
JacobiRotation<RealScalar> rot1;
RealScalar t = m.coeff(0,0) + m.coeff(1,1);
RealScalar d = m.coeff(1,0) - m.coeff(0,1);
if(t == RealScalar(0))
{
c1 = 0;
s1 = d > 0 ? 1 : -1;
rot1.c() = 0;
rot1.s() = d > 0 ? 1 : -1;
}
else
{
RealScalar u = d / t;
c1 = RealScalar(1) / ei_sqrt(1 + ei_abs2(u));
s1 = c1 * u;
rot1.c() = RealScalar(1) / ei_sqrt(1 + ei_abs2(u));
rot1.s() = rot1.c() * u;
}
m.applyJacobiOnTheLeft(0,1,c1,s1);
RealScalar c2, s2;
m.makeJacobi(0,1,&c2,&s2);
*c_left = c1*c2 + s1*s2;
*s_left = s1*c2 - c1*s2;
*c_right = c2;
*s_right = s2;
m.applyJacobiOnTheLeft(0,1,rot1);
m.makeJacobi(0,1,j_right);
*j_left = rot1 * j_right->transpose();
}
template<typename MatrixType, unsigned int Options>
@@ -208,18 +205,18 @@ sweep_again:
{
ei_svd_precondition_2x2_block_to_be_real<MatrixType, Options>::run(work_matrix, *this, p, q);
RealScalar c_left, s_left, c_right, s_right;
ei_real_2x2_jacobi_svd(work_matrix, p, q, &c_left, &s_left, &c_right, &s_right);
work_matrix.applyJacobiOnTheLeft(p,q,c_left,s_left);
if(ComputeU) m_matrixU.applyJacobiOnTheRight(p,q,c_left,-s_left);
work_matrix.applyJacobiOnTheRight(p,q,c_right,s_right);
if(ComputeV) m_matrixV.applyJacobiOnTheRight(p,q,c_right,s_right);
JacobiRotation<RealScalar> j_left, j_right;
ei_real_2x2_jacobi_svd(work_matrix, p, q, &j_left, &j_right);
work_matrix.applyJacobiOnTheLeft(p,q,j_left);
if(ComputeU) m_matrixU.applyJacobiOnTheRight(p,q,j_left.transpose());
work_matrix.applyJacobiOnTheRight(p,q,j_right);
if(ComputeV) m_matrixV.applyJacobiOnTheRight(p,q,j_right);
}
}
}
RealScalar biggestOnDiag = work_matrix.diagonal().cwise().abs().maxCoeff();
RealScalar maxAllowedOffDiag = biggestOnDiag * precision;
for(int p = 0; p < size; ++p)
@@ -231,7 +228,7 @@ sweep_again:
if(ei_abs(work_matrix.coeff(p,q)) > maxAllowedOffDiag)
goto sweep_again;
}
for(int i = 0; i < size; ++i)
{
RealScalar a = ei_abs(work_matrix.coeff(i,i));
@@ -251,7 +248,7 @@ sweep_again:
if(ComputeV) m_matrixV.col(pos).swap(m_matrixV.col(i));
}
}
m_isInitialized = true;
return *this;
}