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Add true determinant to QR and it's variants

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sjusju
2022-07-29 18:24:14 +00:00
committed by Rasmus Munk Larsen
parent b7668c0371
commit ef4654bae7
7 changed files with 167 additions and 20 deletions
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11
test/qr.cpp
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@@ -75,15 +75,17 @@ template<typename MatrixType> void qr_invertible()
// now construct a matrix with prescribed determinant
m1.setZero();
for(int i = 0; i < size; i++) m1(i,i) = internal::random<Scalar>();
RealScalar absdet = abs(m1.diagonal().prod());
Scalar det = m1.diagonal().prod();
RealScalar absdet = abs(det);
m3 = qr.householderQ(); // get a unitary
m1 = m3 * m1 * m3;
m1 = m3 * m1 * m3.adjoint();
qr.compute(m1);
VERIFY_IS_APPROX(log(absdet), qr.logAbsDeterminant());
// This test is tricky if the determinant becomes too small.
// Since we generate random numbers with magnitude range [0,1], the average determinant is 0.5^size
VERIFY_IS_MUCH_SMALLER_THAN( abs(absdet-qr.absDeterminant()), numext::maxi(RealScalar(pow(0.5,size)),numext::maxi<RealScalar>(abs(absdet),abs(qr.absDeterminant()))) );
RealScalar tol = numext::maxi(RealScalar(pow(0.5,size)), numext::maxi<RealScalar>(abs(absdet), abs(qr.absDeterminant())));
VERIFY_IS_MUCH_SMALLER_THAN(abs(det - qr.determinant()), tol);
VERIFY_IS_MUCH_SMALLER_THAN(abs(absdet - qr.absDeterminant()), tol);
}
template<typename MatrixType> void qr_verify_assert()
@@ -96,6 +98,7 @@ template<typename MatrixType> void qr_verify_assert()
VERIFY_RAISES_ASSERT(qr.transpose().solve(tmp))
VERIFY_RAISES_ASSERT(qr.adjoint().solve(tmp))
VERIFY_RAISES_ASSERT(qr.householderQ())
VERIFY_RAISES_ASSERT(qr.determinant())
VERIFY_RAISES_ASSERT(qr.absDeterminant())
VERIFY_RAISES_ASSERT(qr.logAbsDeterminant())
}

8
test/qr_colpivoting.cpp
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@@ -273,10 +273,12 @@ template<typename MatrixType> void qr_invertible()
// now construct a matrix with prescribed determinant
m1.setZero();
for(int i = 0; i < size; i++) m1(i,i) = internal::random<Scalar>();
RealScalar absdet = abs(m1.diagonal().prod());
Scalar det = m1.diagonal().prod();
RealScalar absdet = abs(det);
m3 = qr.householderQ(); // get a unitary
m1 = m3 * m1 * m3;
m1 = m3 * m1 * m3.adjoint();
qr.compute(m1);
VERIFY_IS_APPROX(det, qr.determinant());
VERIFY_IS_APPROX(absdet, qr.absDeterminant());
VERIFY_IS_APPROX(log(absdet), qr.logAbsDeterminant());
}
@@ -296,6 +298,7 @@ template<typename MatrixType> void qr_verify_assert()
VERIFY_RAISES_ASSERT(qr.isSurjective())
VERIFY_RAISES_ASSERT(qr.isInvertible())
VERIFY_RAISES_ASSERT(qr.inverse())
VERIFY_RAISES_ASSERT(qr.determinant())
VERIFY_RAISES_ASSERT(qr.absDeterminant())
VERIFY_RAISES_ASSERT(qr.logAbsDeterminant())
}
@@ -315,6 +318,7 @@ template<typename MatrixType> void cod_verify_assert()
VERIFY_RAISES_ASSERT(cod.isSurjective())
VERIFY_RAISES_ASSERT(cod.isInvertible())
VERIFY_RAISES_ASSERT(cod.pseudoInverse())
VERIFY_RAISES_ASSERT(cod.determinant())
VERIFY_RAISES_ASSERT(cod.absDeterminant())
VERIFY_RAISES_ASSERT(cod.logAbsDeterminant())
}

7
test/qr_fullpivoting.cpp
View File

@@ -98,10 +98,12 @@ template<typename MatrixType> void qr_invertible()
// now construct a matrix with prescribed determinant
m1.setZero();
for(int i = 0; i < size; i++) m1(i,i) = internal::random<Scalar>();
RealScalar absdet = abs(m1.diagonal().prod());
Scalar det = m1.diagonal().prod();
RealScalar absdet = abs(det);
m3 = qr.matrixQ(); // get a unitary
m1 = m3 * m1 * m3;
m1 = m3 * m1 * m3.adjoint();
qr.compute(m1);
VERIFY_IS_APPROX(det, qr.determinant());
VERIFY_IS_APPROX(absdet, qr.absDeterminant());
VERIFY_IS_APPROX(log(absdet), qr.logAbsDeterminant());
}
@@ -121,6 +123,7 @@ template<typename MatrixType> void qr_verify_assert()
VERIFY_RAISES_ASSERT(qr.isSurjective())
VERIFY_RAISES_ASSERT(qr.isInvertible())
VERIFY_RAISES_ASSERT(qr.inverse())
VERIFY_RAISES_ASSERT(qr.determinant())
VERIFY_RAISES_ASSERT(qr.absDeterminant())
VERIFY_RAISES_ASSERT(qr.logAbsDeterminant())
}