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change the make householder algorithm so that the remaining coefficient

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is real, and make Tridiagonalization use it
This commit is contained in:
Gael Guennebaud
2009-08-17 17:04:32 +02:00
parent e125c199bb
commit ff0f005d4c
7 changed files with 75 additions and 105 deletions
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31
test/householder.cpp
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@@ -27,6 +27,8 @@
template<typename MatrixType> void householder(const MatrixType& m)
{
static bool even = true;
even = !even;
/* this test covers the following files:
Householder.h
*/
@@ -38,46 +40,55 @@ template<typename MatrixType> void householder(const MatrixType& m)
typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> VectorType;
typedef Matrix<Scalar, ei_decrement_size<MatrixType::RowsAtCompileTime>::ret, 1> EssentialVectorType;
typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::RowsAtCompileTime> SquareMatrixType;
Matrix<Scalar, EIGEN_ENUM_MAX(MatrixType::RowsAtCompileTime,MatrixType::ColsAtCompileTime), 1> _tmp(std::max(rows,cols));
Scalar* tmp = &_tmp.coeffRef(0,0);
RealScalar beta;
Scalar beta;
RealScalar alpha;
EssentialVectorType essential;
VectorType v1 = VectorType::Random(rows), v2;
v2 = v1;
v1.makeHouseholder(&essential, &beta);
v1.applyHouseholderOnTheLeft(essential,beta);
v1.makeHouseholder(&essential, &beta, &alpha);
v1.applyHouseholderOnTheLeft(essential,beta,tmp);
VERIFY_IS_APPROX(v1.norm(), v2.norm());
VERIFY_IS_MUCH_SMALLER_THAN(v1.end(rows-1).norm(), v1.norm());
v1 = VectorType::Random(rows);
v2 = v1;
v1.applyHouseholderOnTheLeft(essential,beta);
v1.applyHouseholderOnTheLeft(essential,beta,tmp);
VERIFY_IS_APPROX(v1.norm(), v2.norm());
MatrixType m1(rows, cols),
m2(rows, cols);
v1 = VectorType::Random(rows);
if(even) v1.end(rows-1).setZero();
m1.colwise() = v1;
m2 = m1;
m1.col(0).makeHouseholder(&essential, &beta);
m1.applyHouseholderOnTheLeft(essential,beta);
m1.col(0).makeHouseholder(&essential, &beta, &alpha);
m1.applyHouseholderOnTheLeft(essential,beta,tmp);
VERIFY_IS_APPROX(m1.norm(), m2.norm());
VERIFY_IS_MUCH_SMALLER_THAN(m1.block(1,0,rows-1,cols).norm(), m1.norm());
VERIFY_IS_MUCH_SMALLER_THAN(ei_imag(m1(0,0)), ei_real(m1(0,0)));
VERIFY_IS_APPROX(ei_real(m1(0,0)), alpha);
v1 = VectorType::Random(rows);
if(even) v1.end(rows-1).setZero();
SquareMatrixType m3(rows,rows), m4(rows,rows);
m3.rowwise() = v1.transpose();
m4 = m3;
m3.row(0).makeHouseholder(&essential, &beta);
m3.applyHouseholderOnTheRight(essential,beta);
m3.row(0).makeHouseholder(&essential, &beta, &alpha);
m3.applyHouseholderOnTheRight(essential,beta,tmp);
VERIFY_IS_APPROX(m3.norm(), m4.norm());
VERIFY_IS_MUCH_SMALLER_THAN(m3.block(0,1,rows,rows-1).norm(), m3.norm());
VERIFY_IS_MUCH_SMALLER_THAN(ei_imag(m3(0,0)), ei_real(m3(0,0)));
VERIFY_IS_APPROX(ei_real(m3(0,0)), alpha);
}
void test_householder()
{
for(int i = 0; i < g_repeat; i++) {
for(int i = 0; i < 2*g_repeat; i++) {
CALL_SUBTEST( householder(Matrix<double,2,2>()) );
CALL_SUBTEST( householder(Matrix<float,2,3>()) );
CALL_SUBTEST( householder(Matrix<double,3,5>()) );