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RealSchur: Make sure zeros are really zero (cont'd); add default ctor, docs.

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This commit is contained in:
Jitse Niesen
2010-04-12 18:14:32 +01:00
parent 872df22ca4
commit 73d3a27667
4 changed files with 137 additions and 20 deletions
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24
test/schur_real.cpp
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@@ -29,23 +29,19 @@ template<typename MatrixType> void verifyIsQuasiTriangular(const MatrixType& T)
{
const int size = T.cols();
typedef typename MatrixType::Scalar Scalar;
typedef typename NumTraits<Scalar>::Real RealScalar;
// The "zeros" in the real Schur decomposition are only approximately zero
RealScalar norm = T.norm();
// Check T is lower Hessenberg
for(int row = 2; row < size; ++row) {
for(int col = 0; col < row - 1; ++col) {
VERIFY_IS_MUCH_SMALLER_THAN(T(row,col), norm);
VERIFY(T(row,col) == Scalar(0));
}
}
// Check that any non-zero on the subdiagonal is followed by a zero and is
// part of a 2x2 diagonal block with imaginary eigenvalues.
for(int row = 1; row < size; ++row) {
if (!test_ei_isMuchSmallerThan(T(row,row-1), norm)) {
VERIFY(row == size-1 || test_ei_isMuchSmallerThan(T(row+1,row), norm));
if (T(row,row-1) != Scalar(0)) {
VERIFY(row == size-1 || T(row+1,row) == 0);
Scalar tr = T(row-1,row-1) + T(row,row);
Scalar det = T(row-1,row-1) * T(row,row) - T(row-1,row) * T(row,row-1);
VERIFY(4 * det > tr * tr);
@@ -61,9 +57,23 @@ template<typename MatrixType> void schur(int size = MatrixType::ColsAtCompileTim
RealSchur<MatrixType> schurOfA(A);
MatrixType U = schurOfA.matrixU();
MatrixType T = schurOfA.matrixT();
std::cout << "T = \n" << T << "\n\n";
verifyIsQuasiTriangular(T);
VERIFY_IS_APPROX(A, U * T * U.transpose());
}
// Test asserts when not initialized
RealSchur<MatrixType> rsUninitialized;
VERIFY_RAISES_ASSERT(rsUninitialized.matrixT());
VERIFY_RAISES_ASSERT(rsUninitialized.matrixU());
// Test whether compute() and constructor returns same result
MatrixType A = MatrixType::Random(size, size);
RealSchur<MatrixType> rs1;
rs1.compute(A);
RealSchur<MatrixType> rs2(A);
VERIFY_IS_EQUAL(rs1.matrixT(), rs2.matrixT());
VERIFY_IS_EQUAL(rs1.matrixU(), rs2.matrixU());
}
void test_schur_real()