diff options
-rw-r--r-- | Eigen/src/LU/FullPivLU.h | 7 | ||||
-rw-r--r-- | test/inverse.cpp | 2 | ||||
-rw-r--r-- | test/lu.cpp | 65 | ||||
-rw-r--r-- | test/main.h | 12 | ||||
-rw-r--r-- | test/qr_colpivoting.cpp | 4 | ||||
-rw-r--r-- | test/qr_fullpivoting.cpp | 2 |
6 files changed, 42 insertions, 50 deletions
diff --git a/Eigen/src/LU/FullPivLU.h b/Eigen/src/LU/FullPivLU.h index ec551645b..0a305d52b 100644 --- a/Eigen/src/LU/FullPivLU.h +++ b/Eigen/src/LU/FullPivLU.h @@ -422,8 +422,11 @@ FullPivLU<MatrixType>& FullPivLU<MatrixType>::compute(const MatrixType& matrix) // when k==0, biggest_in_corner is the biggest coeff absolute value in the original matrix if(k == 0) cutoff = biggest_in_corner * NumTraits<Scalar>::epsilon(); - // if the pivot (hence the corner) is exactly zero, terminate to avoid generating nan/inf values - if(ei_abs(biggest_in_corner) < cutoff) + // if the pivot (hence the corner) is "zero", terminate to avoid generating nan/inf values. + // Notice that using an exact comparison (biggest_in_corner==0) here, as Golub-van Loan do in + // their pseudo-code, results in numerical instability! The cutoff here has been validated + // by running the unit test 'lu' with many repetitions. + if(biggest_in_corner < cutoff) { // before exiting, make sure to initialize the still uninitialized transpositions // in a sane state without destroying what we already have. diff --git a/test/inverse.cpp b/test/inverse.cpp index 3f6138e0c..1e567ad14 100644 --- a/test/inverse.cpp +++ b/test/inverse.cpp @@ -42,7 +42,7 @@ template<typename MatrixType> void inverse(const MatrixType& m) m2(rows, cols), mzero = MatrixType::Zero(rows, cols), identity = MatrixType::Identity(rows, rows); - createRandomProjectionOfRank(rows,rows,rows,m1); + createRandomPIMatrixOfRank(rows,rows,rows,m1); m2 = m1.inverse(); VERIFY_IS_APPROX(m1, m2.inverse() ); diff --git a/test/lu.cpp b/test/lu.cpp index 02f6ec805..442202a33 100644 --- a/test/lu.cpp +++ b/test/lu.cpp @@ -28,9 +28,6 @@ using namespace std; template<typename MatrixType> void lu_non_invertible() { - static int times_called = 0; - times_called++; - typedef typename MatrixType::Scalar Scalar; typedef typename MatrixType::RealScalar RealScalar; /* this test covers the following files: @@ -55,11 +52,16 @@ template<typename MatrixType> void lu_non_invertible() cols2 = cols = MatrixType::ColsAtCompileTime; } + enum { + RowsAtCompileTime = MatrixType::RowsAtCompileTime, + ColsAtCompileTime = MatrixType::ColsAtCompileTime + }; typedef typename ei_kernel_retval_base<FullPivLU<MatrixType> >::ReturnType KernelMatrixType; typedef typename ei_image_retval_base<FullPivLU<MatrixType> >::ReturnType ImageMatrixType; - typedef Matrix<typename MatrixType::Scalar, Dynamic, Dynamic> DynamicMatrixType; - typedef Matrix<typename MatrixType::Scalar, MatrixType::ColsAtCompileTime, MatrixType::ColsAtCompileTime> + typedef Matrix<typename MatrixType::Scalar, ColsAtCompileTime, ColsAtCompileTime> CMatrixType; + typedef Matrix<typename MatrixType::Scalar, RowsAtCompileTime, RowsAtCompileTime> + RMatrixType; int rank = ei_random<int>(1, std::min(rows, cols)-1); @@ -68,26 +70,21 @@ template<typename MatrixType> void lu_non_invertible() MatrixType m1(rows, cols), m3(rows, cols2); CMatrixType m2(cols, cols2); - createRandomProjectionOfRank(rank, rows, cols, m1); + createRandomPIMatrixOfRank(rank, rows, cols, m1); FullPivLU<MatrixType> lu; - // The special value 0.01 below works well in tests. Keep in mind that we're only computing the rank of projections. - // So it's not clear at all the epsilon should play any role there. + // The special value 0.01 below works well in tests. Keep in mind that we're only computing the rank + // of singular values are either 0 or 1. + // So it's not clear at all that the epsilon should play any role there. lu.setThreshold(RealScalar(0.01)); lu.compute(m1); - // FIXME need better way to construct trapezoid matrices. extend triangularView to support rectangular. - DynamicMatrixType u(rows,cols); - for(int i = 0; i < rows; i++) - for(int j = 0; j < cols; j++) - u(i,j) = i>j ? Scalar(0) : lu.matrixLU()(i,j); - DynamicMatrixType l(rows,rows); - for(int i = 0; i < rows; i++) - for(int j = 0; j < rows; j++) - l(i,j) = (i<j || j>=cols) ? Scalar(0) - : i==j ? Scalar(1) - : lu.matrixLU()(i,j); + MatrixType u(rows,cols); + u = lu.matrixLU().template triangularView<Upper>(); + RMatrixType l = RMatrixType::Identity(rows,rows); + l.block(0,0,rows,std::min(rows,cols)).template triangularView<StrictlyLower>() + = lu.matrixLU().block(0,0,rows,std::min(rows,cols)); VERIFY_IS_APPROX(lu.permutationP() * m1 * lu.permutationQ(), l*u); @@ -101,20 +98,8 @@ template<typename MatrixType> void lu_non_invertible() VERIFY(!lu.isSurjective()); VERIFY((m1 * m1kernel).isMuchSmallerThan(m1)); VERIFY(m1image.fullPivLu().rank() == rank); + VERIFY_IS_APPROX(m1 * m1.adjoint() * m1image, m1image); - // The following test is damn hard to get to succeed over a large number of repetitions. - // We're checking that the image is indeed the image, i.e. adding it as new columns doesn't increase the rank. - // Since we've already tested rank() above, the point here is not to test rank(), it is to test image(). - // Since image() is implemented in a very simple way that doesn't leave much room for choice, the occasional - // errors that we get here (one in 1e+4 repetitions roughly) are probably just a sign that it's a really - // hard test, so we just limit how many times it's run. - if(times_called < 100) - { - DynamicMatrixType sidebyside(m1.rows(), m1.cols() + m1image.cols()); - sidebyside << m1, m1image; - VERIFY(sidebyside.fullPivLu().rank() == rank); - } - m2 = CMatrixType::Random(cols,cols2); m3 = m1*m2; m2 = CMatrixType::Random(cols,cols2); @@ -128,20 +113,18 @@ template<typename MatrixType> void lu_invertible() /* this test covers the following files: LU.h */ + typedef typename MatrixType::Scalar Scalar; typedef typename NumTraits<typename MatrixType::Scalar>::Real RealScalar; int size = ei_random<int>(1,200); MatrixType m1(size, size), m2(size, size), m3(size, size); - m1 = MatrixType::Random(size,size); - - if (ei_is_same_type<RealScalar,float>::ret) - { - // let's build a matrix more stable to inverse - MatrixType a = MatrixType::Random(size,size*2); - m1 += a * a.adjoint(); - } + FullPivLU<MatrixType> lu; + lu.setThreshold(0.01); + do { + m1 = MatrixType::Random(size,size); + lu.compute(m1); + } while(!lu.isInvertible()); - FullPivLU<MatrixType> lu(m1); VERIFY(0 == lu.dimensionOfKernel()); VERIFY(lu.kernel().cols() == 1); // the kernel() should consist of a single (zero) column vector VERIFY(size == lu.rank()); diff --git a/test/main.h b/test/main.h index 6d296b2e3..96324de33 100644 --- a/test/main.h +++ b/test/main.h @@ -148,7 +148,7 @@ namespace Eigen #define EIGEN_INTERNAL_DEBUGGING #define EIGEN_NICE_RANDOM -#include <Eigen/QR> // required for createRandomProjectionOfRank +#include <Eigen/QR> // required for createRandomPIMatrixOfRank #define VERIFY(a) do { if (!(a)) { \ @@ -342,8 +342,13 @@ inline bool test_isUnitary(const MatrixBase<Derived>& m) return m.isUnitary(test_precision<typename ei_traits<Derived>::Scalar>()); } +/** Creates a random Partial Isometry matrix of given rank. + * + * A partial isometry is a matrix all of whose singular values are either 0 or 1. + * This is very useful to test rank-revealing algorithms. + */ template<typename MatrixType> -void createRandomProjectionOfRank(int desired_rank, int rows, int cols, MatrixType& m) +void createRandomPIMatrixOfRank(int desired_rank, int rows, int cols, MatrixType& m) { typedef typename ei_traits<MatrixType>::Scalar Scalar; enum { Rows = MatrixType::RowsAtCompileTime, Cols = MatrixType::ColsAtCompileTime }; @@ -360,7 +365,8 @@ void createRandomProjectionOfRank(int desired_rank, int rows, int cols, MatrixTy if(desired_rank == 1) { - m = VectorType::Random(rows) * VectorType::Random(cols).transpose(); + // here we normalize the vectors to get a partial isometry + m = VectorType::Random(rows).normalized() * VectorType::Random(cols).normalized().transpose(); return; } diff --git a/test/qr_colpivoting.cpp b/test/qr_colpivoting.cpp index abee32184..96cc66316 100644 --- a/test/qr_colpivoting.cpp +++ b/test/qr_colpivoting.cpp @@ -36,7 +36,7 @@ template<typename MatrixType> void qr() typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::RowsAtCompileTime> MatrixQType; typedef Matrix<Scalar, MatrixType::ColsAtCompileTime, 1> VectorType; MatrixType m1; - createRandomProjectionOfRank(rank,rows,cols,m1); + createRandomPIMatrixOfRank(rank,rows,cols,m1); ColPivHouseholderQR<MatrixType> qr(m1); VERIFY_IS_APPROX(rank, qr.rank()); VERIFY(cols - qr.rank() == qr.dimensionOfKernel()); @@ -64,7 +64,7 @@ template<typename MatrixType, int Cols2> void qr_fixedsize() typedef typename MatrixType::Scalar Scalar; int rank = ei_random<int>(1, std::min(int(Rows), int(Cols))-1); Matrix<Scalar,Rows,Cols> m1; - createRandomProjectionOfRank(rank,Rows,Cols,m1); + createRandomPIMatrixOfRank(rank,Rows,Cols,m1); ColPivHouseholderQR<Matrix<Scalar,Rows,Cols> > qr(m1); VERIFY_IS_APPROX(rank, qr.rank()); VERIFY(Cols - qr.rank() == qr.dimensionOfKernel()); diff --git a/test/qr_fullpivoting.cpp b/test/qr_fullpivoting.cpp index 60255f94c..7ad3af1fe 100644 --- a/test/qr_fullpivoting.cpp +++ b/test/qr_fullpivoting.cpp @@ -35,7 +35,7 @@ template<typename MatrixType> void qr() typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::RowsAtCompileTime> MatrixQType; typedef Matrix<Scalar, MatrixType::ColsAtCompileTime, 1> VectorType; MatrixType m1; - createRandomProjectionOfRank(rank,rows,cols,m1); + createRandomPIMatrixOfRank(rank,rows,cols,m1); FullPivHouseholderQR<MatrixType> qr(m1); VERIFY_IS_APPROX(rank, qr.rank()); VERIFY(cols - qr.rank() == qr.dimensionOfKernel()); |