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bug #1493: Make representation of HouseholderSequence consistent and working for complex numbers. Made corresponding unit test actually test that. Also simplify implementation of QR decompositions

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This commit is contained in:
Christoph Hertzberg
2018-04-15 10:15:28 +02:00
parent c9ecfff2e6
commit 42715533f1
9 changed files with 60 additions and 38 deletions
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29
test/householder.cpp
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@@ -49,6 +49,17 @@ template<typename MatrixType> void householder(const MatrixType& m)
v1.applyHouseholderOnTheLeft(essential,beta,tmp);
VERIFY_IS_APPROX(v1.norm(), v2.norm());
// reconstruct householder matrix:
SquareMatrixType id, H1, H2;
id.setIdentity(rows, rows);
H1 = H2 = id;
VectorType vv(rows);
vv << Scalar(1), essential;
H1.applyHouseholderOnTheLeft(essential, beta, tmp);
H2.applyHouseholderOnTheRight(essential, beta, tmp);
VERIFY_IS_APPROX(H1, H2);
VERIFY_IS_APPROX(H1, id - beta * vv*vv.adjoint());
MatrixType m1(rows, cols),
m2(rows, cols);
@@ -69,7 +80,7 @@ template<typename MatrixType> void householder(const MatrixType& m)
m3.rowwise() = v1.transpose();
m4 = m3;
m3.row(0).makeHouseholder(essential, beta, alpha);
m3.applyHouseholderOnTheRight(essential,beta,tmp);
m3.applyHouseholderOnTheRight(essential.conjugate(),beta,tmp);
VERIFY_IS_APPROX(m3.norm(), m4.norm());
if(rows>=2) VERIFY_IS_MUCH_SMALLER_THAN(m3.block(0,1,rows,rows-1).norm(), m3.norm());
VERIFY_IS_MUCH_SMALLER_THAN(numext::imag(m3(0,0)), numext::real(m3(0,0)));
@@ -104,14 +115,14 @@ template<typename MatrixType> void householder(const MatrixType& m)
VERIFY_IS_APPROX(hseq_mat.adjoint(), hseq_mat_adj);
VERIFY_IS_APPROX(hseq_mat.conjugate(), hseq_mat_conj);
VERIFY_IS_APPROX(hseq_mat.transpose(), hseq_mat_trans);
VERIFY_IS_APPROX(hseq_mat * m6, hseq_mat * m6);
VERIFY_IS_APPROX(hseq_mat.adjoint() * m6, hseq_mat_adj * m6);
VERIFY_IS_APPROX(hseq_mat.conjugate() * m6, hseq_mat_conj * m6);
VERIFY_IS_APPROX(hseq_mat.transpose() * m6, hseq_mat_trans * m6);
VERIFY_IS_APPROX(m6 * hseq_mat, m6 * hseq_mat);
VERIFY_IS_APPROX(m6 * hseq_mat.adjoint(), m6 * hseq_mat_adj);
VERIFY_IS_APPROX(m6 * hseq_mat.conjugate(), m6 * hseq_mat_conj);
VERIFY_IS_APPROX(m6 * hseq_mat.transpose(), m6 * hseq_mat_trans);
VERIFY_IS_APPROX(hseq * m6, hseq_mat * m6);
VERIFY_IS_APPROX(hseq.adjoint() * m6, hseq_mat_adj * m6);
VERIFY_IS_APPROX(hseq.conjugate() * m6, hseq_mat_conj * m6);
VERIFY_IS_APPROX(hseq.transpose() * m6, hseq_mat_trans * m6);
VERIFY_IS_APPROX(m6 * hseq, m6 * hseq_mat);
VERIFY_IS_APPROX(m6 * hseq.adjoint(), m6 * hseq_mat_adj);
VERIFY_IS_APPROX(m6 * hseq.conjugate(), m6 * hseq_mat_conj);
VERIFY_IS_APPROX(m6 * hseq.transpose(), m6 * hseq_mat_trans);
// test householder sequence on the right with a shift