aboutsummaryrefslogtreecommitdiffhomepage
diff options
context:
space:
mode:
Diffstat
-rw-r--r--test/jacobisvd.cpp413
-rw-r--r--test/svd_common.h454
-rw-r--r--unsupported/test/bdcsvd.cpp233
-rw-r--r--unsupported/test/jacobisvd.cpp198
-rw-r--r--unsupported/test/svd_common.h261
5 files changed, 540 insertions, 1019 deletions
diff --git a/test/jacobisvd.cpp b/test/jacobisvd.cpp
index cd04db5be..bfcadce95 100644
--- a/test/jacobisvd.cpp
+++ b/test/jacobisvd.cpp
@@ -1,7 +1,7 @@
// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
-// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2008-2014 Gael Guennebaud <gael.guennebaud@inria.fr>
// Copyright (C) 2009 Benoit Jacob <jacob.benoit.1@gmail.com>
//
// This Source Code Form is subject to the terms of the Mozilla
@@ -14,273 +14,47 @@
#include "main.h"
#include <Eigen/SVD>
-template<typename MatrixType, int QRPreconditioner>
-void jacobisvd_check_full(const MatrixType& m, const JacobiSVD<MatrixType, QRPreconditioner>& svd)
-{
- typedef typename MatrixType::Index Index;
- Index rows = m.rows();
- Index cols = m.cols();
-
- enum {
- RowsAtCompileTime = MatrixType::RowsAtCompileTime,
- ColsAtCompileTime = MatrixType::ColsAtCompileTime
- };
-
- typedef typename MatrixType::Scalar Scalar;
- typedef Matrix<Scalar, RowsAtCompileTime, RowsAtCompileTime> MatrixUType;
- typedef Matrix<Scalar, ColsAtCompileTime, ColsAtCompileTime> MatrixVType;
-
- MatrixType sigma = MatrixType::Zero(rows,cols);
- sigma.diagonal() = svd.singularValues().template cast<Scalar>();
- MatrixUType u = svd.matrixU();
- MatrixVType v = svd.matrixV();
-
- VERIFY_IS_APPROX(m, u * sigma * v.adjoint());
- VERIFY_IS_UNITARY(u);
- VERIFY_IS_UNITARY(v);
-}
-
-template<typename MatrixType, int QRPreconditioner>
-void jacobisvd_compare_to_full(const MatrixType& m,
- unsigned int computationOptions,
- const JacobiSVD<MatrixType, QRPreconditioner>& referenceSvd)
-{
- typedef typename MatrixType::Index Index;
- Index rows = m.rows();
- Index cols = m.cols();
- Index diagSize = (std::min)(rows, cols);
-
- JacobiSVD<MatrixType, QRPreconditioner> svd(m, computationOptions);
-
- VERIFY_IS_APPROX(svd.singularValues(), referenceSvd.singularValues());
- if(computationOptions & ComputeFullU)
- VERIFY_IS_APPROX(svd.matrixU(), referenceSvd.matrixU());
- if(computationOptions & ComputeThinU)
- VERIFY_IS_APPROX(svd.matrixU(), referenceSvd.matrixU().leftCols(diagSize));
- if(computationOptions & ComputeFullV)
- VERIFY_IS_APPROX(svd.matrixV(), referenceSvd.matrixV());
- if(computationOptions & ComputeThinV)
- VERIFY_IS_APPROX(svd.matrixV(), referenceSvd.matrixV().leftCols(diagSize));
-}
-
-template<typename MatrixType, int QRPreconditioner>
-void jacobisvd_solve(const MatrixType& m, unsigned int computationOptions)
-{
- typedef typename MatrixType::Scalar Scalar;
- typedef typename MatrixType::RealScalar RealScalar;
- typedef typename MatrixType::Index Index;
- Index rows = m.rows();
- Index cols = m.cols();
-
- enum {
- RowsAtCompileTime = MatrixType::RowsAtCompileTime,
- ColsAtCompileTime = MatrixType::ColsAtCompileTime
- };
-
- typedef Matrix<Scalar, RowsAtCompileTime, Dynamic> RhsType;
- typedef Matrix<Scalar, ColsAtCompileTime, Dynamic> SolutionType;
-
- RhsType rhs = RhsType::Random(rows, internal::random<Index>(1, cols));
- JacobiSVD<MatrixType, QRPreconditioner> svd(m, computationOptions);
-
- if(internal::is_same<RealScalar,double>::value) svd.setThreshold(1e-8);
- else if(internal::is_same<RealScalar,float>::value) svd.setThreshold(1e-4);
-
- SolutionType x = svd.solve(rhs);
-
- RealScalar residual = (m*x-rhs).norm();
- // Check that there is no significantly better solution in the neighborhood of x
- if(!test_isMuchSmallerThan(residual,rhs.norm()))
- {
- // If the residual is very small, then we have an exact solution, so we are already good.
- for(int k=0;k<x.rows();++k)
- {
- SolutionType y(x);
- y.row(k).array() += 2*NumTraits<RealScalar>::epsilon();
- RealScalar residual_y = (m*y-rhs).norm();
- VERIFY( test_isApprox(residual_y,residual) || residual < residual_y );
-
- y.row(k) = x.row(k).array() - 2*NumTraits<RealScalar>::epsilon();
- residual_y = (m*y-rhs).norm();
- VERIFY( test_isApprox(residual_y,residual) || residual < residual_y );
- }
- }
-
- // evaluate normal equation which works also for least-squares solutions
- if(internal::is_same<RealScalar,double>::value)
- {
- // This test is not stable with single precision.
- // This is probably because squaring m signicantly affects the precision.
- VERIFY_IS_APPROX(m.adjoint()*m*x,m.adjoint()*rhs);
- }
-
- // check minimal norm solutions
- {
- // generate a full-rank m x n problem with m<n
- enum {
- RankAtCompileTime2 = ColsAtCompileTime==Dynamic ? Dynamic : (ColsAtCompileTime)/2+1,
- RowsAtCompileTime3 = ColsAtCompileTime==Dynamic ? Dynamic : ColsAtCompileTime+1
- };
- typedef Matrix<Scalar, RankAtCompileTime2, ColsAtCompileTime> MatrixType2;
- typedef Matrix<Scalar, RankAtCompileTime2, 1> RhsType2;
- typedef Matrix<Scalar, ColsAtCompileTime, RankAtCompileTime2> MatrixType2T;
- Index rank = RankAtCompileTime2==Dynamic ? internal::random<Index>(1,cols) : Index(RankAtCompileTime2);
- MatrixType2 m2(rank,cols);
- int guard = 0;
- do {
- m2.setRandom();
- } while(m2.jacobiSvd().setThreshold(test_precision<Scalar>()).rank()!=rank && (++guard)<10);
- VERIFY(guard<10);
- RhsType2 rhs2 = RhsType2::Random(rank);
- // use QR to find a reference minimal norm solution
- HouseholderQR<MatrixType2T> qr(m2.adjoint());
- Matrix<Scalar,Dynamic,1> tmp = qr.matrixQR().topLeftCorner(rank,rank).template triangularView<Upper>().adjoint().solve(rhs2);
- tmp.conservativeResize(cols);
- tmp.tail(cols-rank).setZero();
- SolutionType x21 = qr.householderQ() * tmp;
- // now check with SVD
- JacobiSVD<MatrixType2, ColPivHouseholderQRPreconditioner> svd2(m2, computationOptions);
- SolutionType x22 = svd2.solve(rhs2);
- VERIFY_IS_APPROX(m2*x21, rhs2);
- VERIFY_IS_APPROX(m2*x22, rhs2);
- VERIFY_IS_APPROX(x21, x22);
-
- // Now check with a rank deficient matrix
- typedef Matrix<Scalar, RowsAtCompileTime3, ColsAtCompileTime> MatrixType3;
- typedef Matrix<Scalar, RowsAtCompileTime3, 1> RhsType3;
- Index rows3 = RowsAtCompileTime3==Dynamic ? internal::random<Index>(rank+1,2*cols) : Index(RowsAtCompileTime3);
- Matrix<Scalar,RowsAtCompileTime3,Dynamic> C = Matrix<Scalar,RowsAtCompileTime3,Dynamic>::Random(rows3,rank);
- MatrixType3 m3 = C * m2;
- RhsType3 rhs3 = C * rhs2;
- JacobiSVD<MatrixType3, ColPivHouseholderQRPreconditioner> svd3(m3, computationOptions);
- SolutionType x3 = svd3.solve(rhs3);
- VERIFY_IS_APPROX(m3*x3, rhs3);
- VERIFY_IS_APPROX(m3*x21, rhs3);
- VERIFY_IS_APPROX(m2*x3, rhs2);
-
- VERIFY_IS_APPROX(x21, x3);
- }
-}
-
-template<typename MatrixType, int QRPreconditioner>
-void jacobisvd_test_all_computation_options(const MatrixType& m)
-{
- if (QRPreconditioner == NoQRPreconditioner && m.rows() != m.cols())
- return;
- JacobiSVD<MatrixType, QRPreconditioner> fullSvd(m, ComputeFullU|ComputeFullV);
- CALL_SUBTEST(( jacobisvd_check_full(m, fullSvd) ));
- CALL_SUBTEST(( jacobisvd_solve<MatrixType, QRPreconditioner>(m, ComputeFullU | ComputeFullV) ));
-
- #if defined __INTEL_COMPILER
- // remark #111: statement is unreachable
- #pragma warning disable 111
- #endif
- if(QRPreconditioner == FullPivHouseholderQRPreconditioner)
- return;
-
- CALL_SUBTEST(( jacobisvd_compare_to_full(m, ComputeFullU, fullSvd) ));
- CALL_SUBTEST(( jacobisvd_compare_to_full(m, ComputeFullV, fullSvd) ));
- CALL_SUBTEST(( jacobisvd_compare_to_full(m, 0, fullSvd) ));
-
- if (MatrixType::ColsAtCompileTime == Dynamic) {
- // thin U/V are only available with dynamic number of columns
- CALL_SUBTEST(( jacobisvd_compare_to_full(m, ComputeFullU|ComputeThinV, fullSvd) ));
- CALL_SUBTEST(( jacobisvd_compare_to_full(m, ComputeThinV, fullSvd) ));
- CALL_SUBTEST(( jacobisvd_compare_to_full(m, ComputeThinU|ComputeFullV, fullSvd) ));
- CALL_SUBTEST(( jacobisvd_compare_to_full(m, ComputeThinU , fullSvd) ));
- CALL_SUBTEST(( jacobisvd_compare_to_full(m, ComputeThinU|ComputeThinV, fullSvd) ));
- CALL_SUBTEST(( jacobisvd_solve<MatrixType, QRPreconditioner>(m, ComputeFullU | ComputeThinV) ));
- CALL_SUBTEST(( jacobisvd_solve<MatrixType, QRPreconditioner>(m, ComputeThinU | ComputeFullV) ));
- CALL_SUBTEST(( jacobisvd_solve<MatrixType, QRPreconditioner>(m, ComputeThinU | ComputeThinV) ));
-
- // test reconstruction
- typedef typename MatrixType::Index Index;
- Index diagSize = (std::min)(m.rows(), m.cols());
- JacobiSVD<MatrixType, QRPreconditioner> svd(m, ComputeThinU | ComputeThinV);
- VERIFY_IS_APPROX(m, svd.matrixU().leftCols(diagSize) * svd.singularValues().asDiagonal() * svd.matrixV().leftCols(diagSize).adjoint());
- }
-}
+#define SVD_DEFAULT(M) JacobiSVD<M>
+#define SVD_FOR_MIN_NORM(M) JacobiSVD<M,ColPivHouseholderQRPreconditioner>
+#include "svd_common.h"
+// Check all variants of JacobiSVD
template<typename MatrixType>
void jacobisvd(const MatrixType& a = MatrixType(), bool pickrandom = true)
{
MatrixType m = a;
if(pickrandom)
- {
- typedef typename MatrixType::Scalar Scalar;
- typedef typename MatrixType::RealScalar RealScalar;
- typedef typename MatrixType::Index Index;
- Index diagSize = (std::min)(a.rows(), a.cols());
- RealScalar s = std::numeric_limits<RealScalar>::max_exponent10/4;
- s = internal::random<RealScalar>(1,s);
- Matrix<RealScalar,Dynamic,1> d = Matrix<RealScalar,Dynamic,1>::Random(diagSize);
- for(Index k=0; k<diagSize; ++k)
- d(k) = d(k)*std::pow(RealScalar(10),internal::random<RealScalar>(-s,s));
- m = Matrix<Scalar,Dynamic,Dynamic>::Random(a.rows(),diagSize) * d.asDiagonal() * Matrix<Scalar,Dynamic,Dynamic>::Random(diagSize,a.cols());
- // cancel some coeffs
- Index n = internal::random<Index>(0,m.size()-1);
- for(Index i=0; i<n; ++i)
- m(internal::random<Index>(0,m.rows()-1), internal::random<Index>(0,m.cols()-1)) = Scalar(0);
- }
+ svd_fill_random(m);
- CALL_SUBTEST(( jacobisvd_test_all_computation_options<MatrixType, FullPivHouseholderQRPreconditioner>(m) ));
- CALL_SUBTEST(( jacobisvd_test_all_computation_options<MatrixType, ColPivHouseholderQRPreconditioner>(m) ));
- CALL_SUBTEST(( jacobisvd_test_all_computation_options<MatrixType, HouseholderQRPreconditioner>(m) ));
- CALL_SUBTEST(( jacobisvd_test_all_computation_options<MatrixType, NoQRPreconditioner>(m) ));
+ CALL_SUBTEST(( svd_test_all_computation_options<JacobiSVD<MatrixType, FullPivHouseholderQRPreconditioner> >(m, true) )); // check full only
+ CALL_SUBTEST(( svd_test_all_computation_options<JacobiSVD<MatrixType, ColPivHouseholderQRPreconditioner> >(m, false) ));
+ CALL_SUBTEST(( svd_test_all_computation_options<JacobiSVD<MatrixType, HouseholderQRPreconditioner> >(m, false) ));
+ if(m.rows()==m.cols())
+ CALL_SUBTEST(( svd_test_all_computation_options<JacobiSVD<MatrixType, NoQRPreconditioner> >(m, false) ));
}
template<typename MatrixType> void jacobisvd_verify_assert(const MatrixType& m)
{
- typedef typename MatrixType::Scalar Scalar;
+ svd_verify_assert<JacobiSVD<MatrixType> >(m);
typedef typename MatrixType::Index Index;
Index rows = m.rows();
Index cols = m.cols();
enum {
- RowsAtCompileTime = MatrixType::RowsAtCompileTime,
ColsAtCompileTime = MatrixType::ColsAtCompileTime
};
- typedef Matrix<Scalar, RowsAtCompileTime, 1> RhsType;
-
- RhsType rhs(rows);
-
- JacobiSVD<MatrixType> svd;
- VERIFY_RAISES_ASSERT(svd.matrixU())
- VERIFY_RAISES_ASSERT(svd.singularValues())
- VERIFY_RAISES_ASSERT(svd.matrixV())
- VERIFY_RAISES_ASSERT(svd.solve(rhs))
MatrixType a = MatrixType::Zero(rows, cols);
a.setZero();
- svd.compute(a, 0);
- VERIFY_RAISES_ASSERT(svd.matrixU())
- VERIFY_RAISES_ASSERT(svd.matrixV())
- svd.singularValues();
- VERIFY_RAISES_ASSERT(svd.solve(rhs))
if (ColsAtCompileTime == Dynamic)
{
- svd.compute(a, ComputeThinU);
- svd.matrixU();
- VERIFY_RAISES_ASSERT(svd.matrixV())
- VERIFY_RAISES_ASSERT(svd.solve(rhs))
-
- svd.compute(a, ComputeThinV);
- svd.matrixV();
- VERIFY_RAISES_ASSERT(svd.matrixU())
- VERIFY_RAISES_ASSERT(svd.solve(rhs))
-
JacobiSVD<MatrixType, FullPivHouseholderQRPreconditioner> svd_fullqr;
VERIFY_RAISES_ASSERT(svd_fullqr.compute(a, ComputeFullU|ComputeThinV))
VERIFY_RAISES_ASSERT(svd_fullqr.compute(a, ComputeThinU|ComputeThinV))
VERIFY_RAISES_ASSERT(svd_fullqr.compute(a, ComputeThinU|ComputeFullV))
}
- else
- {
- VERIFY_RAISES_ASSERT(svd.compute(a, ComputeThinU))
- VERIFY_RAISES_ASSERT(svd.compute(a, ComputeThinV))
- }
}
template<typename MatrixType>
@@ -296,165 +70,17 @@ void jacobisvd_method()
VERIFY_IS_APPROX(m.jacobiSvd(ComputeFullU|ComputeFullV).solve(m), m);
}
-// work around stupid msvc error when constructing at compile time an expression that involves
-// a division by zero, even if the numeric type has floating point
-template<typename Scalar>
-EIGEN_DONT_INLINE Scalar zero() { return Scalar(0); }
-
-// workaround aggressive optimization in ICC
-template<typename T> EIGEN_DONT_INLINE T sub(T a, T b) { return a - b; }
-
-template<typename MatrixType>
-void jacobisvd_inf_nan()
-{
- // all this function does is verify we don't iterate infinitely on nan/inf values
-
- JacobiSVD<MatrixType> svd;
- typedef typename MatrixType::Scalar Scalar;
- Scalar some_inf = Scalar(1) / zero<Scalar>();
- VERIFY(sub(some_inf, some_inf) != sub(some_inf, some_inf));
- svd.compute(MatrixType::Constant(10,10,some_inf), ComputeFullU | ComputeFullV);
-
- Scalar nan = std::numeric_limits<Scalar>::quiet_NaN();
- VERIFY(nan != nan);
- svd.compute(MatrixType::Constant(10,10,nan), ComputeFullU | ComputeFullV);
-
- MatrixType m = MatrixType::Zero(10,10);
- m(internal::random<int>(0,9), internal::random<int>(0,9)) = some_inf;
- svd.compute(m, ComputeFullU | ComputeFullV);
-
- m = MatrixType::Zero(10,10);
- m(internal::random<int>(0,9), internal::random<int>(0,9)) = nan;
- svd.compute(m, ComputeFullU | ComputeFullV);
-
- // regression test for bug 791
- m.resize(3,3);
- m << 0, 2*NumTraits<Scalar>::epsilon(), 0.5,
- 0, -0.5, 0,
- nan, 0, 0;
- svd.compute(m, ComputeFullU | ComputeFullV);
-
- m.resize(4,4);
- m << 1, 0, 0, 0,
- 0, 3, 1, 2e-308,
- 1, 0, 1, nan,
- 0, nan, nan, 0;
- svd.compute(m, ComputeFullU | ComputeFullV);
-}
-
-// Regression test for bug 286: JacobiSVD loops indefinitely with some
-// matrices containing denormal numbers.
-void jacobisvd_underoverflow()
-{
-#if defined __INTEL_COMPILER
-// shut up warning #239: floating point underflow
-#pragma warning push
-#pragma warning disable 239
-#endif
- Matrix2d M;
- M << -7.90884e-313, -4.94e-324,
- 0, 5.60844e-313;
- JacobiSVD<Matrix2d> svd;
- svd.compute(M,ComputeFullU|ComputeFullV);
- jacobisvd_check_full(M,svd);
-
- VectorXd value_set(9);
- value_set << 0, 1, -1, 5.60844e-313, -5.60844e-313, 4.94e-324, -4.94e-324, -4.94e-223, 4.94e-223;
- Array4i id(0,0,0,0);
- int k = 0;
- do
- {
- M << value_set(id(0)), value_set(id(1)), value_set(id(2)), value_set(id(3));
- svd.compute(M,ComputeFullU|ComputeFullV);
- jacobisvd_check_full(M,svd);
-
- id(k)++;
- if(id(k)>=value_set.size())
- {
- while(k<3 && id(k)>=value_set.size()) id(++k)++;
- id.head(k).setZero();
- k=0;
- }
-
- } while((id<int(value_set.size())).all());
-
-#if defined __INTEL_COMPILER
-#pragma warning pop
-#endif
-
- // Check for overflow:
- Matrix3d M3;
- M3 << 4.4331978442502944e+307, -5.8585363752028680e+307, 6.4527017443412964e+307,
- 3.7841695601406358e+307, 2.4331702789740617e+306, -3.5235707140272905e+307,
- -8.7190887618028355e+307, -7.3453213709232193e+307, -2.4367363684472105e+307;
-
- JacobiSVD<Matrix3d> svd3;
- svd3.compute(M3,ComputeFullU|ComputeFullV); // just check we don't loop indefinitely
- jacobisvd_check_full(M3,svd3);
-}
-
-void jacobisvd_preallocate()
-{
- Vector3f v(3.f, 2.f, 1.f);
- MatrixXf m = v.asDiagonal();
-
- internal::set_is_malloc_allowed(false);
- VERIFY_RAISES_ASSERT(VectorXf tmp(10);)
- JacobiSVD<MatrixXf> svd;
- internal::set_is_malloc_allowed(true);
- svd.compute(m);
- VERIFY_IS_APPROX(svd.singularValues(), v);
-
- JacobiSVD<MatrixXf> svd2(3,3);
- internal::set_is_malloc_allowed(false);
- svd2.compute(m);
- internal::set_is_malloc_allowed(true);
- VERIFY_IS_APPROX(svd2.singularValues(), v);
- VERIFY_RAISES_ASSERT(svd2.matrixU());
- VERIFY_RAISES_ASSERT(svd2.matrixV());
- svd2.compute(m, ComputeFullU | ComputeFullV);
- VERIFY_IS_APPROX(svd2.matrixU(), Matrix3f::Identity());
- VERIFY_IS_APPROX(svd2.matrixV(), Matrix3f::Identity());
- internal::set_is_malloc_allowed(false);
- svd2.compute(m);
- internal::set_is_malloc_allowed(true);
-
- JacobiSVD<MatrixXf> svd3(3,3,ComputeFullU|ComputeFullV);
- internal::set_is_malloc_allowed(false);
- svd2.compute(m);
- internal::set_is_malloc_allowed(true);
- VERIFY_IS_APPROX(svd2.singularValues(), v);
- VERIFY_IS_APPROX(svd2.matrixU(), Matrix3f::Identity());
- VERIFY_IS_APPROX(svd2.matrixV(), Matrix3f::Identity());
- internal::set_is_malloc_allowed(false);
- svd2.compute(m, ComputeFullU|ComputeFullV);
- internal::set_is_malloc_allowed(true);
-}
-
void test_jacobisvd()
{
CALL_SUBTEST_3(( jacobisvd_verify_assert(Matrix3f()) ));
CALL_SUBTEST_4(( jacobisvd_verify_assert(Matrix4d()) ));
CALL_SUBTEST_7(( jacobisvd_verify_assert(MatrixXf(10,12)) ));
CALL_SUBTEST_8(( jacobisvd_verify_assert(MatrixXcd(7,5)) ));
+
+ svd_all_trivial_2x2(jacobisvd<Matrix2cd>);
+ svd_all_trivial_2x2(jacobisvd<Matrix2d>);
for(int i = 0; i < g_repeat; i++) {
- Matrix2cd m;
- m << 0, 1,
- 0, 1;
- CALL_SUBTEST_1(( jacobisvd(m, false) ));
- m << 1, 0,
- 1, 0;
- CALL_SUBTEST_1(( jacobisvd(m, false) ));
-
- Matrix2d n;
- n << 0, 0,
- 0, 0;
- CALL_SUBTEST_2(( jacobisvd(n, false) ));
- n << 0, 0,
- 0, 1;
- CALL_SUBTEST_2(( jacobisvd(n, false) ));
-
CALL_SUBTEST_3(( jacobisvd<Matrix3f>() ));
CALL_SUBTEST_4(( jacobisvd<Matrix4d>() ));
CALL_SUBTEST_5(( jacobisvd<Matrix<float,3,5> >() ));
@@ -473,8 +99,8 @@ void test_jacobisvd()
(void) c;
// Test on inf/nan matrix
- CALL_SUBTEST_7( jacobisvd_inf_nan<MatrixXf>() );
- CALL_SUBTEST_10( jacobisvd_inf_nan<MatrixXd>() );
+ CALL_SUBTEST_7( (svd_inf_nan<JacobiSVD<MatrixXf>, MatrixXf>()) );
+ CALL_SUBTEST_10( (svd_inf_nan<JacobiSVD<MatrixXd>, MatrixXd>()) );
}
CALL_SUBTEST_7(( jacobisvd<MatrixXf>(MatrixXf(internal::random<int>(EIGEN_TEST_MAX_SIZE/4, EIGEN_TEST_MAX_SIZE/2), internal::random<int>(EIGEN_TEST_MAX_SIZE/4, EIGEN_TEST_MAX_SIZE/2))) ));
@@ -488,8 +114,7 @@ void test_jacobisvd()
CALL_SUBTEST_7( JacobiSVD<MatrixXf>(10,10) );
// Check that preallocation avoids subsequent mallocs
- CALL_SUBTEST_9( jacobisvd_preallocate() );
+ CALL_SUBTEST_9( svd_preallocate() );
- // Regression check for bug 286
- CALL_SUBTEST_2( jacobisvd_underoverflow() );
+ CALL_SUBTEST_2( svd_underoverflow() );
}
diff --git a/test/svd_common.h b/test/svd_common.h
new file mode 100644
index 000000000..4631939e5
--- /dev/null
+++ b/test/svd_common.h
@@ -0,0 +1,454 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2014 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2009 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef SVD_DEFAULT
+#error a macro SVD_DEFAULT(MatrixType) must be defined prior to including svd_common.h
+#endif
+
+#ifndef SVD_FOR_MIN_NORM
+#error a macro SVD_FOR_MIN_NORM(MatrixType) must be defined prior to including svd_common.h
+#endif
+
+// Check that the matrix m is properly reconstructed and that the U and V factors are unitary
+// The SVD must have already been computed.
+template<typename SvdType, typename MatrixType>
+void svd_check_full(const MatrixType& m, const SvdType& svd)
+{
+ typedef typename MatrixType::Index Index;
+ Index rows = m.rows();
+ Index cols = m.cols();
+
+ enum {
+ RowsAtCompileTime = MatrixType::RowsAtCompileTime,
+ ColsAtCompileTime = MatrixType::ColsAtCompileTime
+ };
+
+ typedef typename MatrixType::Scalar Scalar;
+ typedef Matrix<Scalar, RowsAtCompileTime, RowsAtCompileTime> MatrixUType;
+ typedef Matrix<Scalar, ColsAtCompileTime, ColsAtCompileTime> MatrixVType;
+
+ MatrixType sigma = MatrixType::Zero(rows,cols);
+ sigma.diagonal() = svd.singularValues().template cast<Scalar>();
+ MatrixUType u = svd.matrixU();
+ MatrixVType v = svd.matrixV();
+
+ VERIFY_IS_APPROX(m, u * sigma * v.adjoint());
+ VERIFY_IS_UNITARY(u);
+ VERIFY_IS_UNITARY(v);
+}
+
+// Compare partial SVD defined by computationOptions to a full SVD referenceSvd
+template<typename SvdType, typename MatrixType>
+void svd_compare_to_full(const MatrixType& m,
+ unsigned int computationOptions,
+ const SvdType& referenceSvd)
+{
+ typedef typename MatrixType::Index Index;
+ Index rows = m.rows();
+ Index cols = m.cols();
+ Index diagSize = (std::min)(rows, cols);
+
+ SvdType svd(m, computationOptions);
+
+ VERIFY_IS_APPROX(svd.singularValues(), referenceSvd.singularValues());
+ if(computationOptions & ComputeFullU) VERIFY_IS_APPROX(svd.matrixU(), referenceSvd.matrixU());
+ if(computationOptions & ComputeThinU) VERIFY_IS_APPROX(svd.matrixU(), referenceSvd.matrixU().leftCols(diagSize));
+ if(computationOptions & ComputeFullV) VERIFY_IS_APPROX(svd.matrixV(), referenceSvd.matrixV());
+ if(computationOptions & ComputeThinV) VERIFY_IS_APPROX(svd.matrixV(), referenceSvd.matrixV().leftCols(diagSize));
+}
+
+//
+template<typename SvdType, typename MatrixType>
+void svd_least_square(const MatrixType& m, unsigned int computationOptions)
+{
+ typedef typename MatrixType::Scalar Scalar;
+ typedef typename MatrixType::RealScalar RealScalar;
+ typedef typename MatrixType::Index Index;
+ Index rows = m.rows();
+ Index cols = m.cols();
+
+ enum {
+ RowsAtCompileTime = MatrixType::RowsAtCompileTime,
+ ColsAtCompileTime = MatrixType::ColsAtCompileTime
+ };
+
+ typedef Matrix<Scalar, RowsAtCompileTime, Dynamic> RhsType;
+ typedef Matrix<Scalar, ColsAtCompileTime, Dynamic> SolutionType;
+
+ RhsType rhs = RhsType::Random(rows, internal::random<Index>(1, cols));
+ SvdType svd(m, computationOptions);
+
+ if(internal::is_same<RealScalar,double>::value) svd.setThreshold(1e-8);
+ else if(internal::is_same<RealScalar,float>::value) svd.setThreshold(1e-4);
+
+ SolutionType x = svd.solve(rhs);
+
+ RealScalar residual = (m*x-rhs).norm();
+ // Check that there is no significantly better solution in the neighborhood of x
+ if(!test_isMuchSmallerThan(residual,rhs.norm()))
+ {
+ // If the residual is very small, then we have an exact solution, so we are already good.
+ for(int k=0;k<x.rows();++k)
+ {
+ SolutionType y(x);
+ y.row(k).array() += 2*NumTraits<RealScalar>::epsilon();
+ RealScalar residual_y = (m*y-rhs).norm();
+ VERIFY( test_isApprox(residual_y,residual) || residual < residual_y );
+
+ y.row(k) = x.row(k).array() - 2*NumTraits<RealScalar>::epsilon();
+ residual_y = (m*y-rhs).norm();
+ VERIFY( test_isApprox(residual_y,residual) || residual < residual_y );
+ }
+ }
+
+ // evaluate normal equation which works also for least-squares solutions
+ if(internal::is_same<RealScalar,double>::value)
+ {
+ // This test is not stable with single precision.
+ // This is probably because squaring m signicantly affects the precision.
+ VERIFY_IS_APPROX(m.adjoint()*m*x,m.adjoint()*rhs);
+ }
+}
+
+// check minimal norm solutions, the inoput matrix m is only used to recover problem size
+template<typename MatrixType>
+void svd_min_norm(const MatrixType& m, unsigned int computationOptions)
+{
+ typedef typename MatrixType::Scalar Scalar;
+ typedef typename MatrixType::Index Index;
+ Index cols = m.cols();
+
+ enum {
+ ColsAtCompileTime = MatrixType::ColsAtCompileTime
+ };
+
+ typedef Matrix<Scalar, ColsAtCompileTime, Dynamic> SolutionType;
+
+ // generate a full-rank m x n problem with m<n
+ enum {
+ RankAtCompileTime2 = ColsAtCompileTime==Dynamic ? Dynamic : (ColsAtCompileTime)/2+1,
+ RowsAtCompileTime3 = ColsAtCompileTime==Dynamic ? Dynamic : ColsAtCompileTime+1
+ };
+ typedef Matrix<Scalar, RankAtCompileTime2, ColsAtCompileTime> MatrixType2;
+ typedef Matrix<Scalar, RankAtCompileTime2, 1> RhsType2;
+ typedef Matrix<Scalar, ColsAtCompileTime, RankAtCompileTime2> MatrixType2T;
+ Index rank = RankAtCompileTime2==Dynamic ? internal::random<Index>(1,cols) : Index(RankAtCompileTime2);
+ MatrixType2 m2(rank,cols);
+ int guard = 0;
+ do {
+ m2.setRandom();
+ } while(SVD_FOR_MIN_NORM(MatrixType2)(m2).setThreshold(test_precision<Scalar>()).rank()!=rank && (++guard)<10);
+ VERIFY(guard<10);
+ RhsType2 rhs2 = RhsType2::Random(rank);
+ // use QR to find a reference minimal norm solution
+ HouseholderQR<MatrixType2T> qr(m2.adjoint());
+ Matrix<Scalar,Dynamic,1> tmp = qr.matrixQR().topLeftCorner(rank,rank).template triangularView<Upper>().adjoint().solve(rhs2);
+ tmp.conservativeResize(cols);
+ tmp.tail(cols-rank).setZero();
+ SolutionType x21 = qr.householderQ() * tmp;
+ // now check with SVD
+ SVD_FOR_MIN_NORM(MatrixType2) svd2(m2, computationOptions);
+ SolutionType x22 = svd2.solve(rhs2);
+ VERIFY_IS_APPROX(m2*x21, rhs2);
+ VERIFY_IS_APPROX(m2*x22, rhs2);
+ VERIFY_IS_APPROX(x21, x22);
+
+ // Now check with a rank deficient matrix
+ typedef Matrix<Scalar, RowsAtCompileTime3, ColsAtCompileTime> MatrixType3;
+ typedef Matrix<Scalar, RowsAtCompileTime3, 1> RhsType3;
+ Index rows3 = RowsAtCompileTime3==Dynamic ? internal::random<Index>(rank+1,2*cols) : Index(RowsAtCompileTime3);
+ Matrix<Scalar,RowsAtCompileTime3,Dynamic> C = Matrix<Scalar,RowsAtCompileTime3,Dynamic>::Random(rows3,rank);
+ MatrixType3 m3 = C * m2;
+ RhsType3 rhs3 = C * rhs2;
+ SVD_FOR_MIN_NORM(MatrixType3) svd3(m3, computationOptions);
+ SolutionType x3 = svd3.solve(rhs3);
+ VERIFY_IS_APPROX(m3*x3, rhs3);
+ VERIFY_IS_APPROX(m3*x21, rhs3);
+ VERIFY_IS_APPROX(m2*x3, rhs2);
+
+ VERIFY_IS_APPROX(x21, x3);
+}
+
+// Check full, compare_to_full, least_square, and min_norm for all possible compute-options
+template<typename SvdType, typename MatrixType>
+void svd_test_all_computation_options(const MatrixType& m, bool full_only)
+{
+// if (QRPreconditioner == NoQRPreconditioner && m.rows() != m.cols())
+// return;
+ SvdType fullSvd(m, ComputeFullU|ComputeFullV);
+ CALL_SUBTEST(( svd_check_full(m, fullSvd) ));
+ CALL_SUBTEST(( svd_least_square<SvdType>(m, ComputeFullU | ComputeFullV) ));
+ CALL_SUBTEST(( svd_min_norm(m, ComputeFullU | ComputeFullV) ));
+
+ #if defined __INTEL_COMPILER
+ // remark #111: statement is unreachable
+ #pragma warning disable 111
+ #endif
+ if(full_only)
+ return;
+
+ CALL_SUBTEST(( svd_compare_to_full(m, ComputeFullU, fullSvd) ));
+ CALL_SUBTEST(( svd_compare_to_full(m, ComputeFullV, fullSvd) ));
+ CALL_SUBTEST(( svd_compare_to_full(m, 0, fullSvd) ));
+
+ if (MatrixType::ColsAtCompileTime == Dynamic) {
+ // thin U/V are only available with dynamic number of columns
+ CALL_SUBTEST(( svd_compare_to_full(m, ComputeFullU|ComputeThinV, fullSvd) ));
+ CALL_SUBTEST(( svd_compare_to_full(m, ComputeThinV, fullSvd) ));
+ CALL_SUBTEST(( svd_compare_to_full(m, ComputeThinU|ComputeFullV, fullSvd) ));
+ CALL_SUBTEST(( svd_compare_to_full(m, ComputeThinU , fullSvd) ));
+ CALL_SUBTEST(( svd_compare_to_full(m, ComputeThinU|ComputeThinV, fullSvd) ));
+
+ CALL_SUBTEST(( svd_least_square<SvdType>(m, ComputeFullU | ComputeThinV) ));
+ CALL_SUBTEST(( svd_least_square<SvdType>(m, ComputeThinU | ComputeFullV) ));
+ CALL_SUBTEST(( svd_least_square<SvdType>(m, ComputeThinU | ComputeThinV) ));
+
+ CALL_SUBTEST(( svd_min_norm(m, ComputeFullU | ComputeThinV) ));
+ CALL_SUBTEST(( svd_min_norm(m, ComputeThinU | ComputeFullV) ));
+ CALL_SUBTEST(( svd_min_norm(m, ComputeThinU | ComputeThinV) ));
+
+ // test reconstruction
+ typedef typename MatrixType::Index Index;
+ Index diagSize = (std::min)(m.rows(), m.cols());
+ SvdType svd(m, ComputeThinU | ComputeThinV);
+ VERIFY_IS_APPROX(m, svd.matrixU().leftCols(diagSize) * svd.singularValues().asDiagonal() * svd.matrixV().leftCols(diagSize).adjoint());
+ }
+}
+
+template<typename MatrixType>
+void svd_fill_random(MatrixType &m)
+{
+ typedef typename MatrixType::Scalar Scalar;
+ typedef typename MatrixType::RealScalar RealScalar;
+ typedef typename MatrixType::Index Index;
+ Index diagSize = (std::min)(m.rows(), m.cols());
+ RealScalar s = std::numeric_limits<RealScalar>::max_exponent10/4;
+ s = internal::random<RealScalar>(1,s);
+ Matrix<RealScalar,Dynamic,1> d = Matrix<RealScalar,Dynamic,1>::Random(diagSize);
+ for(Index k=0; k<diagSize; ++k)
+ d(k) = d(k)*std::pow(RealScalar(10),internal::random<RealScalar>(-s,s));
+ m = Matrix<Scalar,Dynamic,Dynamic>::Random(m.rows(),diagSize) * d.asDiagonal() * Matrix<Scalar,Dynamic,Dynamic>::Random(diagSize,m.cols());
+ // cancel some coeffs
+ Index n = internal::random<Index>(0,m.size()-1);
+ for(Index i=0; i<n; ++i)
+ m(internal::random<Index>(0,m.rows()-1), internal::random<Index>(0,m.cols()-1)) = Scalar(0);
+}
+
+
+// work around stupid msvc error when constructing at compile time an expression that involves
+// a division by zero, even if the numeric type has floating point
+template<typename Scalar>
+EIGEN_DONT_INLINE Scalar zero() { return Scalar(0); }
+
+// workaround aggressive optimization in ICC
+template<typename T> EIGEN_DONT_INLINE T sub(T a, T b) { return a - b; }
+
+// all this function does is verify we don't iterate infinitely on nan/inf values
+template<typename SvdType, typename MatrixType>
+void svd_inf_nan()
+{
+ SvdType svd;
+ typedef typename MatrixType::Scalar Scalar;
+ Scalar some_inf = Scalar(1) / zero<Scalar>();
+ VERIFY(sub(some_inf, some_inf) != sub(some_inf, some_inf));
+ svd.compute(MatrixType::Constant(10,10,some_inf), ComputeFullU | ComputeFullV);
+
+ Scalar nan = std::numeric_limits<Scalar>::quiet_NaN();
+ VERIFY(nan != nan);
+ svd.compute(MatrixType::Constant(10,10,nan), ComputeFullU | ComputeFullV);
+
+ MatrixType m = MatrixType::Zero(10,10);
+ m(internal::random<int>(0,9), internal::random<int>(0,9)) = some_inf;
+ svd.compute(m, ComputeFullU | ComputeFullV);
+
+ m = MatrixType::Zero(10,10);
+ m(internal::random<int>(0,9), internal::random<int>(0,9)) = nan;
+ svd.compute(m, ComputeFullU | ComputeFullV);
+
+ // regression test for bug 791
+ m.resize(3,3);
+ m << 0, 2*NumTraits<Scalar>::epsilon(), 0.5,
+ 0, -0.5, 0,
+ nan, 0, 0;
+ svd.compute(m, ComputeFullU | ComputeFullV);
+
+ m.resize(4,4);
+ m << 1, 0, 0, 0,
+ 0, 3, 1, 2e-308,
+ 1, 0, 1, nan,
+ 0, nan, nan, 0;
+ svd.compute(m, ComputeFullU | ComputeFullV);
+}
+
+// Regression test for bug 286: JacobiSVD loops indefinitely with some
+// matrices containing denormal numbers.
+void svd_underoverflow()
+{
+#if defined __INTEL_COMPILER
+// shut up warning #239: floating point underflow
+#pragma warning push
+#pragma warning disable 239
+#endif
+ Matrix2d M;
+ M << -7.90884e-313, -4.94e-324,
+ 0, 5.60844e-313;
+ SVD_DEFAULT(Matrix2d) svd;
+ svd.compute(M,ComputeFullU|ComputeFullV);
+ svd_check_full(M,svd);
+
+ // Check all 2x2 matrices made with the following coefficients:
+ VectorXd value_set(9);
+ value_set << 0, 1, -1, 5.60844e-313, -5.60844e-313, 4.94e-324, -4.94e-324, -4.94e-223, 4.94e-223;
+ Array4i id(0,0,0,0);
+ int k = 0;
+ do
+ {
+ M << value_set(id(0)), value_set(id(1)), value_set(id(2)), value_set(id(3));
+ svd.compute(M,ComputeFullU|ComputeFullV);
+ svd_check_full(M,svd);
+
+ id(k)++;
+ if(id(k)>=value_set.size())
+ {
+ while(k<3 && id(k)>=value_set.size()) id(++k)++;
+ id.head(k).setZero();
+ k=0;
+ }
+
+ } while((id<int(value_set.size())).all());
+
+#if defined __INTEL_COMPILER
+#pragma warning pop
+#endif
+
+ // Check for overflow:
+ Matrix3d M3;
+ M3 << 4.4331978442502944e+307, -5.8585363752028680e+307, 6.4527017443412964e+307,
+ 3.7841695601406358e+307, 2.4331702789740617e+306, -3.5235707140272905e+307,
+ -8.7190887618028355e+307, -7.3453213709232193e+307, -2.4367363684472105e+307;
+
+ SVD_DEFAULT(Matrix3d) svd3;
+ svd3.compute(M3,ComputeFullU|ComputeFullV); // just check we don't loop indefinitely
+ svd_check_full(M3,svd3);
+}
+
+// void jacobisvd(const MatrixType& a = MatrixType(), bool pickrandom = true)
+
+template<typename MatrixType>
+void svd_all_trivial_2x2( void (*cb)(const MatrixType&,bool) )
+{
+ MatrixType M;
+ VectorXd value_set(3);
+ value_set << 0, 1, -1;
+ Array4i id(0,0,0,0);
+ int k = 0;
+ do
+ {
+ M << value_set(id(0)), value_set(id(1)), value_set(id(2)), value_set(id(3));
+
+ cb(M,false);
+
+ id(k)++;
+ if(id(k)>=value_set.size())
+ {
+ while(k<3 && id(k)>=value_set.size()) id(++k)++;
+ id.head(k).setZero();
+ k=0;
+ }
+
+ } while((id<int(value_set.size())).all());
+}
+
+void svd_preallocate()
+{
+ Vector3f v(3.f, 2.f, 1.f);
+ MatrixXf m = v.asDiagonal();
+
+ internal::set_is_malloc_allowed(false);
+ VERIFY_RAISES_ASSERT(VectorXf tmp(10);)
+ SVD_DEFAULT(MatrixXf) svd;
+ internal::set_is_malloc_allowed(true);
+ svd.compute(m);
+ VERIFY_IS_APPROX(svd.singularValues(), v);
+
+ SVD_DEFAULT(MatrixXf) svd2(3,3);
+ internal::set_is_malloc_allowed(false);
+ svd2.compute(m);
+ internal::set_is_malloc_allowed(true);
+ VERIFY_IS_APPROX(svd2.singularValues(), v);
+ VERIFY_RAISES_ASSERT(svd2.matrixU());
+ VERIFY_RAISES_ASSERT(svd2.matrixV());
+ svd2.compute(m, ComputeFullU | ComputeFullV);
+ VERIFY_IS_APPROX(svd2.matrixU(), Matrix3f::Identity());
+ VERIFY_IS_APPROX(svd2.matrixV(), Matrix3f::Identity());
+ internal::set_is_malloc_allowed(false);
+ svd2.compute(m);
+ internal::set_is_malloc_allowed(true);
+
+ SVD_DEFAULT(MatrixXf) svd3(3,3,ComputeFullU|ComputeFullV);
+ internal::set_is_malloc_allowed(false);
+ svd2.compute(m);
+ internal::set_is_malloc_allowed(true);
+ VERIFY_IS_APPROX(svd2.singularValues(), v);
+ VERIFY_IS_APPROX(svd2.matrixU(), Matrix3f::Identity());
+ VERIFY_IS_APPROX(svd2.matrixV(), Matrix3f::Identity());
+ internal::set_is_malloc_allowed(false);
+ svd2.compute(m, ComputeFullU|ComputeFullV);
+ internal::set_is_malloc_allowed(true);
+}
+
+template<typename SvdType,typename MatrixType>
+void svd_verify_assert(const MatrixType& m)
+{
+ typedef typename MatrixType::Scalar Scalar;
+ typedef typename MatrixType::Index Index;
+ Index rows = m.rows();
+ Index cols = m.cols();
+
+ enum {
+ RowsAtCompileTime = MatrixType::RowsAtCompileTime,
+ ColsAtCompileTime = MatrixType::ColsAtCompileTime
+ };
+
+ typedef Matrix<Scalar, RowsAtCompileTime, 1> RhsType;
+ RhsType rhs(rows);
+ SvdType svd;
+ VERIFY_RAISES_ASSERT(svd.matrixU())
+ VERIFY_RAISES_ASSERT(svd.singularValues())
+ VERIFY_RAISES_ASSERT(svd.matrixV())
+ VERIFY_RAISES_ASSERT(svd.solve(rhs))
+ MatrixType a = MatrixType::Zero(rows, cols);
+ a.setZero();
+ svd.compute(a, 0);
+ VERIFY_RAISES_ASSERT(svd.matrixU())
+ VERIFY_RAISES_ASSERT(svd.matrixV())
+ svd.singularValues();
+ VERIFY_RAISES_ASSERT(svd.solve(rhs))
+
+ if (ColsAtCompileTime == Dynamic)
+ {
+ svd.compute(a, ComputeThinU);
+ svd.matrixU();
+ VERIFY_RAISES_ASSERT(svd.matrixV())
+ VERIFY_RAISES_ASSERT(svd.solve(rhs))
+ svd.compute(a, ComputeThinV);
+ svd.matrixV();
+ VERIFY_RAISES_ASSERT(svd.matrixU())
+ VERIFY_RAISES_ASSERT(svd.solve(rhs))
+ }
+ else
+ {
+ VERIFY_RAISES_ASSERT(svd.compute(a, ComputeThinU))
+ VERIFY_RAISES_ASSERT(svd.compute(a, ComputeThinV))
+ }
+}
+
+#undef SVD_DEFAULT
+#undef SVD_FOR_MIN_NORM
diff --git a/unsupported/test/bdcsvd.cpp b/unsupported/test/bdcsvd.cpp
index 115a649b0..4ad991522 100644
--- a/unsupported/test/bdcsvd.cpp
+++ b/unsupported/test/bdcsvd.cpp
@@ -10,204 +10,105 @@
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/
-#include "svd_common.h"
+// discard stack allocation as that too bypasses malloc
+#define EIGEN_STACK_ALLOCATION_LIMIT 0
+#define EIGEN_RUNTIME_NO_MALLOC
+
+#include "main.h"
+#include <unsupported/Eigen/BDCSVD>
#include <iostream>
#include <Eigen/LU>
-// check if "svd" is the good image of "m"
-template<typename MatrixType>
-void bdcsvd_check_full(const MatrixType& m, const BDCSVD<MatrixType>& svd)
-{
- svd_check_full< MatrixType, BDCSVD< MatrixType > >(m, svd);
-}
-
-// Compare to a reference value
-template<typename MatrixType>
-void bdcsvd_compare_to_full(const MatrixType& m,
- unsigned int computationOptions,
- const BDCSVD<MatrixType>& referenceSvd)
-{
- svd_compare_to_full< MatrixType, BDCSVD< MatrixType > >(m, computationOptions, referenceSvd);
-} // end bdcsvd_compare_to_full
+#define SVD_DEFAULT(M) BDCSVD<M>
+// #define SVD_FOR_MIN_NORM(M) BDCSVD<M>
+#define SVD_FOR_MIN_NORM(M) JacobiSVD<M,ColPivHouseholderQRPreconditioner>
+#include "../../test/svd_common.h"
-template<typename MatrixType>
-void bdcsvd_solve(const MatrixType& m, unsigned int computationOptions)
-{
- svd_solve< MatrixType, BDCSVD< MatrixType > >(m, computationOptions);
-} // end template bdcsvd_solve
-
-
-// test the computations options
-template<typename MatrixType>
-void bdcsvd_test_all_computation_options(const MatrixType& m)
-{
- BDCSVD<MatrixType> fullSvd(m, ComputeFullU|ComputeFullV);
- svd_test_computation_options_1< MatrixType, BDCSVD< MatrixType > >(m, fullSvd);
- svd_test_computation_options_2< MatrixType, BDCSVD< MatrixType > >(m, fullSvd);
-} // end bdcsvd_test_all_computation_options
-
-
-// Call a test with all the computations options
+// Check all variants of JacobiSVD
template<typename MatrixType>
void bdcsvd(const MatrixType& a = MatrixType(), bool pickrandom = true)
{
- MatrixType m = pickrandom ? MatrixType::Random(a.rows(), a.cols()) : a;
- bdcsvd_test_all_computation_options<MatrixType>(m);
-} // end template bdcsvd
-
-
-// verify assert
-template<typename MatrixType>
-void bdcsvd_verify_assert(const MatrixType& m)
-{
- svd_verify_assert< MatrixType, BDCSVD< MatrixType > >(m);
-}// end template bdcsvd_verify_assert
+ MatrixType m = a;
+ if(pickrandom)
+ svd_fill_random(m);
+ CALL_SUBTEST(( svd_test_all_computation_options<BDCSVD<MatrixType> >(m, false) ));
+}
-// test weird values
-template<typename MatrixType>
-void bdcsvd_inf_nan()
-{
- svd_inf_nan< MatrixType, BDCSVD< MatrixType > >();
-}// end template bdcsvd_inf_nan
-
-
-
-void bdcsvd_preallocate()
-{
- svd_preallocate< BDCSVD< MatrixXf > >();
-} // end bdcsvd_preallocate
-
+// template<typename MatrixType>
+// void bdcsvd_method()
+// {
+// enum { Size = MatrixType::RowsAtCompileTime };
+// typedef typename MatrixType::RealScalar RealScalar;
+// typedef Matrix<RealScalar, Size, 1> RealVecType;
+// MatrixType m = MatrixType::Identity();
+// VERIFY_IS_APPROX(m.bdcSvd().singularValues(), RealVecType::Ones());
+// VERIFY_RAISES_ASSERT(m.bdcSvd().matrixU());
+// VERIFY_RAISES_ASSERT(m.bdcSvd().matrixV());
+// VERIFY_IS_APPROX(m.bdcSvd(ComputeFullU|ComputeFullV).solve(m), m);
+// }
// compare the Singular values returned with Jacobi and Bdc
template<typename MatrixType>
void compare_bdc_jacobi(const MatrixType& a = MatrixType(), unsigned int computationOptions = 0)
{
- std::cout << "debut compare" << std::endl;
MatrixType m = MatrixType::Random(a.rows(), a.cols());
BDCSVD<MatrixType> bdc_svd(m);
JacobiSVD<MatrixType> jacobi_svd(m);
VERIFY_IS_APPROX(bdc_svd.singularValues(), jacobi_svd.singularValues());
- if(computationOptions & ComputeFullU)
- VERIFY_IS_APPROX(bdc_svd.matrixU(), jacobi_svd.matrixU());
- if(computationOptions & ComputeThinU)
- VERIFY_IS_APPROX(bdc_svd.matrixU(), jacobi_svd.matrixU());
- if(computationOptions & ComputeFullV)
- VERIFY_IS_APPROX(bdc_svd.matrixV(), jacobi_svd.matrixV());
- if(computationOptions & ComputeThinV)
- VERIFY_IS_APPROX(bdc_svd.matrixV(), jacobi_svd.matrixV());
- std::cout << "fin compare" << std::endl;
-} // end template compare_bdc_jacobi
-
-
-// call the tests
+ if(computationOptions & ComputeFullU) VERIFY_IS_APPROX(bdc_svd.matrixU(), jacobi_svd.matrixU());
+ if(computationOptions & ComputeThinU) VERIFY_IS_APPROX(bdc_svd.matrixU(), jacobi_svd.matrixU());
+ if(computationOptions & ComputeFullV) VERIFY_IS_APPROX(bdc_svd.matrixV(), jacobi_svd.matrixV());
+ if(computationOptions & ComputeThinV) VERIFY_IS_APPROX(bdc_svd.matrixV(), jacobi_svd.matrixV());
+}
+
void test_bdcsvd()
{
- // test of Dynamic defined Matrix (42, 42) of float
- CALL_SUBTEST_11(( bdcsvd_verify_assert<Matrix<float,Dynamic,Dynamic> >
- (Matrix<float,Dynamic,Dynamic>(42,42)) ));
- CALL_SUBTEST_11(( compare_bdc_jacobi<Matrix<float,Dynamic,Dynamic> >
- (Matrix<float,Dynamic,Dynamic>(42,42), 0) ));
- CALL_SUBTEST_11(( bdcsvd<Matrix<float,Dynamic,Dynamic> >
- (Matrix<float,Dynamic,Dynamic>(42,42)) ));
-
- // test of Dynamic defined Matrix (50, 50) of double
- CALL_SUBTEST_13(( bdcsvd_verify_assert<Matrix<double,Dynamic,Dynamic> >
- (Matrix<double,Dynamic,Dynamic>(50,50)) ));
- CALL_SUBTEST_13(( compare_bdc_jacobi<Matrix<double,Dynamic,Dynamic> >
- (Matrix<double,Dynamic,Dynamic>(50,50), 0) ));
- CALL_SUBTEST_13(( bdcsvd<Matrix<double,Dynamic,Dynamic> >
- (Matrix<double,Dynamic,Dynamic>(50, 50)) ));
-
- // test of Dynamic defined Matrix (22, 22) of complex double
- CALL_SUBTEST_14(( bdcsvd_verify_assert<Matrix<std::complex<double>,Dynamic,Dynamic> >
- (Matrix<std::complex<double>,Dynamic,Dynamic>(22,22)) ));
- CALL_SUBTEST_14(( compare_bdc_jacobi<Matrix<std::complex<double>,Dynamic,Dynamic> >
- (Matrix<std::complex<double>, Dynamic, Dynamic> (22,22), 0) ));
- CALL_SUBTEST_14(( bdcsvd<Matrix<std::complex<double>,Dynamic,Dynamic> >
- (Matrix<std::complex<double>,Dynamic,Dynamic>(22, 22)) ));
-
- // test of Dynamic defined Matrix (10, 10) of int
- //CALL_SUBTEST_15(( bdcsvd_verify_assert<Matrix<int,Dynamic,Dynamic> >
- // (Matrix<int,Dynamic,Dynamic>(10,10)) ));
- //CALL_SUBTEST_15(( compare_bdc_jacobi<Matrix<int,Dynamic,Dynamic> >
- // (Matrix<int,Dynamic,Dynamic>(10,10), 0) ));
- //CALL_SUBTEST_15(( bdcsvd<Matrix<int,Dynamic,Dynamic> >
- // (Matrix<int,Dynamic,Dynamic>(10, 10)) ));
+ CALL_SUBTEST_3(( svd_verify_assert<BDCSVD<Matrix3f> >(Matrix3f()) ));
+ CALL_SUBTEST_4(( svd_verify_assert<BDCSVD<Matrix4d> >(Matrix4d()) ));
+ CALL_SUBTEST_7(( svd_verify_assert<BDCSVD<MatrixXf> >(MatrixXf(10,12)) ));
+ CALL_SUBTEST_8(( svd_verify_assert<BDCSVD<MatrixXcd> >(MatrixXcd(7,5)) ));
+// svd_all_trivial_2x2(bdcsvd<Matrix2cd>);
+// svd_all_trivial_2x2(bdcsvd<Matrix2d>);
- // test of Dynamic defined Matrix (8, 6) of double
-
- CALL_SUBTEST_16(( bdcsvd_verify_assert<Matrix<double,Dynamic,Dynamic> >
- (Matrix<double,Dynamic,Dynamic>(8,6)) ));
- CALL_SUBTEST_16(( compare_bdc_jacobi<Matrix<double,Dynamic,Dynamic> >
- (Matrix<double,Dynamic,Dynamic>(8, 6), 0) ));
- CALL_SUBTEST_16(( bdcsvd<Matrix<double,Dynamic,Dynamic> >
- (Matrix<double,Dynamic,Dynamic>(8, 6)) ));
-
-
-
- // test of Dynamic defined Matrix (36, 12) of float
- CALL_SUBTEST_17(( compare_bdc_jacobi<Matrix<float,Dynamic,Dynamic> >
- (Matrix<float,Dynamic,Dynamic>(36, 12), 0) ));
- CALL_SUBTEST_17(( bdcsvd<Matrix<float,Dynamic,Dynamic> >
- (Matrix<float,Dynamic,Dynamic>(36, 12)) ));
-
- // test of Dynamic defined Matrix (5, 8) of double
- CALL_SUBTEST_18(( compare_bdc_jacobi<Matrix<double,Dynamic,Dynamic> >
- (Matrix<double,Dynamic,Dynamic>(5, 8), 0) ));
- CALL_SUBTEST_18(( bdcsvd<Matrix<double,Dynamic,Dynamic> >
- (Matrix<double,Dynamic,Dynamic>(5, 8)) ));
-
-
- // non regression tests
- CALL_SUBTEST_3(( bdcsvd_verify_assert(Matrix3f()) ));
- CALL_SUBTEST_4(( bdcsvd_verify_assert(Matrix4d()) ));
- CALL_SUBTEST_7(( bdcsvd_verify_assert(MatrixXf(10,12)) ));
- CALL_SUBTEST_8(( bdcsvd_verify_assert(MatrixXcd(7,5)) ));
-
- // SUBTESTS 1 and 2 on specifics matrix
for(int i = 0; i < g_repeat; i++) {
- Matrix2cd m;
- m << 0, 1,
- 0, 1;
- CALL_SUBTEST_1(( bdcsvd(m, false) ));
- m << 1, 0,
- 1, 0;
- CALL_SUBTEST_1(( bdcsvd(m, false) ));
-
- Matrix2d n;
- n << 0, 0,
- 0, 0;
- CALL_SUBTEST_2(( bdcsvd(n, false) ));
- n << 0, 0,
- 0, 1;
- CALL_SUBTEST_2(( bdcsvd(n, false) ));
+// CALL_SUBTEST_3(( bdcsvd<Matrix3f>() ));
+// CALL_SUBTEST_4(( bdcsvd<Matrix4d>() ));
+// CALL_SUBTEST_5(( bdcsvd<Matrix<float,3,5> >() ));
+
+ int r = internal::random<int>(1, EIGEN_TEST_MAX_SIZE/2),
+ c = internal::random<int>(1, EIGEN_TEST_MAX_SIZE/2);
- // Statics matrix don't work with BDSVD yet
- // bdc algo on a random 3x3 float matrix
- // CALL_SUBTEST_3(( bdcsvd<Matrix3f>() ));
- // bdc algo on a random 4x4 double matrix
- // CALL_SUBTEST_4(( bdcsvd<Matrix4d>() ));
- // bdc algo on a random 3x5 float matrix
- // CALL_SUBTEST_5(( bdcsvd<Matrix<float,3,5> >() ));
-
- int r = internal::random<int>(1, 30),
- c = internal::random<int>(1, 30);
- CALL_SUBTEST_7(( bdcsvd<MatrixXf>(MatrixXf(r,c)) ));
- CALL_SUBTEST_8(( bdcsvd<MatrixXcd>(MatrixXcd(r,c)) ));
+ TEST_SET_BUT_UNUSED_VARIABLE(r)
+ TEST_SET_BUT_UNUSED_VARIABLE(c)
+
+ CALL_SUBTEST_6(( bdcsvd(Matrix<double,Dynamic,2>(r,2)) ));
+ CALL_SUBTEST_7(( bdcsvd(MatrixXf(r,c)) ));
+ CALL_SUBTEST_7(( compare_bdc_jacobi(MatrixXf(r,c)) ));
+ CALL_SUBTEST_10(( bdcsvd(MatrixXd(r,c)) ));
+ CALL_SUBTEST_10(( compare_bdc_jacobi(MatrixXd(r,c)) ));
+ CALL_SUBTEST_8(( bdcsvd(MatrixXcd(r,c)) ));
+ CALL_SUBTEST_8(( compare_bdc_jacobi(MatrixXcd(r,c)) ));
(void) r;
(void) c;
// Test on inf/nan matrix
- CALL_SUBTEST_7( bdcsvd_inf_nan<MatrixXf>() );
+ CALL_SUBTEST_7( (svd_inf_nan<BDCSVD<MatrixXf>, MatrixXf>()) );
+ CALL_SUBTEST_10( (svd_inf_nan<BDCSVD<MatrixXd>, MatrixXd>()) );
}
- CALL_SUBTEST_7(( bdcsvd<MatrixXf>(MatrixXf(internal::random<int>(EIGEN_TEST_MAX_SIZE/4, EIGEN_TEST_MAX_SIZE/2), internal::random<int>(EIGEN_TEST_MAX_SIZE/4, EIGEN_TEST_MAX_SIZE/2))) ));
- CALL_SUBTEST_8(( bdcsvd<MatrixXcd>(MatrixXcd(internal::random<int>(EIGEN_TEST_MAX_SIZE/4, EIGEN_TEST_MAX_SIZE/3), internal::random<int>(EIGEN_TEST_MAX_SIZE/4, EIGEN_TEST_MAX_SIZE/3))) ));
+ // test matrixbase method
+// CALL_SUBTEST_1(( bdcsvd_method<Matrix2cd>() ));
+// CALL_SUBTEST_3(( bdcsvd_method<Matrix3f>() ));
// Test problem size constructors
CALL_SUBTEST_7( BDCSVD<MatrixXf>(10,10) );
-} // end test_bdcsvd
+ // Check that preallocation avoids subsequent mallocs
+ CALL_SUBTEST_9( svd_preallocate() );
+
+ CALL_SUBTEST_2( svd_underoverflow() );
+}
+
diff --git a/unsupported/test/jacobisvd.cpp b/unsupported/test/jacobisvd.cpp
deleted file mode 100644
index b4e884eee..000000000
--- a/unsupported/test/jacobisvd.cpp
+++ /dev/null
@@ -1,198 +0,0 @@
-// This file is part of Eigen, a lightweight C++ template library
-// for linear algebra.
-//
-// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
-// Copyright (C) 2009 Benoit Jacob <jacob.benoit.1@gmail.com>
-//
-// This Source Code Form is subject to the terms of the Mozilla
-// Public License v. 2.0. If a copy of the MPL was not distributed
-// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
-
-#include "svd_common.h"
-
-template<typename MatrixType, int QRPreconditioner>
-void jacobisvd_check_full(const MatrixType& m, const JacobiSVD<MatrixType, QRPreconditioner>& svd)
-{
- svd_check_full<MatrixType, JacobiSVD<MatrixType, QRPreconditioner > >(m, svd);
-}
-
-template<typename MatrixType, int QRPreconditioner>
-void jacobisvd_compare_to_full(const MatrixType& m,
- unsigned int computationOptions,
- const JacobiSVD<MatrixType, QRPreconditioner>& referenceSvd)
-{
- svd_compare_to_full<MatrixType, JacobiSVD<MatrixType, QRPreconditioner> >(m, computationOptions, referenceSvd);
-}
-
-
-template<typename MatrixType, int QRPreconditioner>
-void jacobisvd_solve(const MatrixType& m, unsigned int computationOptions)
-{
- svd_solve< MatrixType, JacobiSVD< MatrixType, QRPreconditioner > >(m, computationOptions);
-}
-
-
-
-template<typename MatrixType, int QRPreconditioner>
-void jacobisvd_test_all_computation_options(const MatrixType& m)
-{
-
- if (QRPreconditioner == NoQRPreconditioner && m.rows() != m.cols())
- return;
-
- JacobiSVD< MatrixType, QRPreconditioner > fullSvd(m, ComputeFullU|ComputeFullV);
- svd_test_computation_options_1< MatrixType, JacobiSVD< MatrixType, QRPreconditioner > >(m, fullSvd);
-
- if(QRPreconditioner == FullPivHouseholderQRPreconditioner)
- return;
- svd_test_computation_options_2< MatrixType, JacobiSVD< MatrixType, QRPreconditioner > >(m, fullSvd);
-
-}
-
-template<typename MatrixType>
-void jacobisvd(const MatrixType& a = MatrixType(), bool pickrandom = true)
-{
- MatrixType m = pickrandom ? MatrixType::Random(a.rows(), a.cols()) : a;
-
- jacobisvd_test_all_computation_options<MatrixType, FullPivHouseholderQRPreconditioner>(m);
- jacobisvd_test_all_computation_options<MatrixType, ColPivHouseholderQRPreconditioner>(m);
- jacobisvd_test_all_computation_options<MatrixType, HouseholderQRPreconditioner>(m);
- jacobisvd_test_all_computation_options<MatrixType, NoQRPreconditioner>(m);
-}
-
-
-template<typename MatrixType>
-void jacobisvd_verify_assert(const MatrixType& m)
-{
-
- svd_verify_assert<MatrixType, JacobiSVD< MatrixType > >(m);
-
- typedef typename MatrixType::Index Index;
- Index rows = m.rows();
- Index cols = m.cols();
-
- enum {
- RowsAtCompileTime = MatrixType::RowsAtCompileTime,
- ColsAtCompileTime = MatrixType::ColsAtCompileTime
- };
-
- MatrixType a = MatrixType::Zero(rows, cols);
- a.setZero();
-
- if (ColsAtCompileTime == Dynamic)
- {
- JacobiSVD<MatrixType, FullPivHouseholderQRPreconditioner> svd_fullqr;
- VERIFY_RAISES_ASSERT(svd_fullqr.compute(a, ComputeFullU|ComputeThinV))
- VERIFY_RAISES_ASSERT(svd_fullqr.compute(a, ComputeThinU|ComputeThinV))
- VERIFY_RAISES_ASSERT(svd_fullqr.compute(a, ComputeThinU|ComputeFullV))
- }
-}
-
-template<typename MatrixType>
-void jacobisvd_method()
-{
- enum { Size = MatrixType::RowsAtCompileTime };
- typedef typename MatrixType::RealScalar RealScalar;
- typedef Matrix<RealScalar, Size, 1> RealVecType;
- MatrixType m = MatrixType::Identity();
- VERIFY_IS_APPROX(m.jacobiSvd().singularValues(), RealVecType::Ones());
- VERIFY_RAISES_ASSERT(m.jacobiSvd().matrixU());
- VERIFY_RAISES_ASSERT(m.jacobiSvd().matrixV());
- VERIFY_IS_APPROX(m.jacobiSvd(ComputeFullU|ComputeFullV).solve(m), m);
-}
-
-
-
-template<typename MatrixType>
-void jacobisvd_inf_nan()
-{
- svd_inf_nan<MatrixType, JacobiSVD< MatrixType > >();
-}
-
-
-// Regression test for bug 286: JacobiSVD loops indefinitely with some
-// matrices containing denormal numbers.
-void jacobisvd_bug286()
-{
-#if defined __INTEL_COMPILER
-// shut up warning #239: floating point underflow
-#pragma warning push
-#pragma warning disable 239
-#endif
- Matrix2d M;
- M << -7.90884e-313, -4.94e-324,
- 0, 5.60844e-313;
-#if defined __INTEL_COMPILER
-#pragma warning pop
-#endif
- JacobiSVD<Matrix2d> svd;
- svd.compute(M); // just check we don't loop indefinitely
-}
-
-
-void jacobisvd_preallocate()
-{
- svd_preallocate< JacobiSVD <MatrixXf> >();
-}
-
-void test_jacobisvd()
-{
- CALL_SUBTEST_11(( jacobisvd<Matrix<double,Dynamic,Dynamic> >
- (Matrix<double,Dynamic,Dynamic>(16, 6)) ));
-
- CALL_SUBTEST_3(( jacobisvd_verify_assert(Matrix3f()) ));
- CALL_SUBTEST_4(( jacobisvd_verify_assert(Matrix4d()) ));
- CALL_SUBTEST_7(( jacobisvd_verify_assert(MatrixXf(10,12)) ));
- CALL_SUBTEST_8(( jacobisvd_verify_assert(MatrixXcd(7,5)) ));
-
- for(int i = 0; i < g_repeat; i++) {
- Matrix2cd m;
- m << 0, 1,
- 0, 1;
- CALL_SUBTEST_1(( jacobisvd(m, false) ));
- m << 1, 0,
- 1, 0;
- CALL_SUBTEST_1(( jacobisvd(m, false) ));
-
- Matrix2d n;
- n << 0, 0,
- 0, 0;
- CALL_SUBTEST_2(( jacobisvd(n, false) ));
- n << 0, 0,
- 0, 1;
- CALL_SUBTEST_2(( jacobisvd(n, false) ));
-
- CALL_SUBTEST_3(( jacobisvd<Matrix3f>() ));
- CALL_SUBTEST_4(( jacobisvd<Matrix4d>() ));
- CALL_SUBTEST_5(( jacobisvd<Matrix<float,3,5> >() ));
- CALL_SUBTEST_6(( jacobisvd<Matrix<double,Dynamic,2> >(Matrix<double,Dynamic,2>(10,2)) ));
-
- int r = internal::random<int>(1, 30),
- c = internal::random<int>(1, 30);
- CALL_SUBTEST_7(( jacobisvd<MatrixXf>(MatrixXf(r,c)) ));
- CALL_SUBTEST_8(( jacobisvd<MatrixXcd>(MatrixXcd(r,c)) ));
- (void) r;
- (void) c;
-
- // Test on inf/nan matrix
- CALL_SUBTEST_7( jacobisvd_inf_nan<MatrixXf>() );
- }
-
- CALL_SUBTEST_7(( jacobisvd<MatrixXf>(MatrixXf(internal::random<int>(EIGEN_TEST_MAX_SIZE/4, EIGEN_TEST_MAX_SIZE/2), internal::random<int>(EIGEN_TEST_MAX_SIZE/4, EIGEN_TEST_MAX_SIZE/2))) ));
- CALL_SUBTEST_8(( jacobisvd<MatrixXcd>(MatrixXcd(internal::random<int>(EIGEN_TEST_MAX_SIZE/4, EIGEN_TEST_MAX_SIZE/3), internal::random<int>(EIGEN_TEST_MAX_SIZE/4, EIGEN_TEST_MAX_SIZE/3))) ));
-
-
- // test matrixbase method
- CALL_SUBTEST_1(( jacobisvd_method<Matrix2cd>() ));
- CALL_SUBTEST_3(( jacobisvd_method<Matrix3f>() ));
-
-
- // Test problem size constructors
- CALL_SUBTEST_7( JacobiSVD<MatrixXf>(10,10) );
-
- // Check that preallocation avoids subsequent mallocs
- CALL_SUBTEST_9( jacobisvd_preallocate() );
-
- // Regression check for bug 286
- CALL_SUBTEST_2( jacobisvd_bug286() );
-}
diff --git a/unsupported/test/svd_common.h b/unsupported/test/svd_common.h
deleted file mode 100644
index 6a96e7c74..000000000
--- a/unsupported/test/svd_common.h
+++ /dev/null
@@ -1,261 +0,0 @@
-// This file is part of Eigen, a lightweight C++ template library
-// for linear algebra.
-//
-// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
-// Copyright (C) 2009 Benoit Jacob <jacob.benoit.1@gmail.com>
-//
-// Copyright (C) 2013 Gauthier Brun <brun.gauthier@gmail.com>
-// Copyright (C) 2013 Nicolas Carre <nicolas.carre@ensimag.fr>
-// Copyright (C) 2013 Jean Ceccato <jean.ceccato@ensimag.fr>
-// Copyright (C) 2013 Pierre Zoppitelli <pierre.zoppitelli@ensimag.fr>
-//
-// This Source Code Form is subject to the terms of the Mozilla
-// Public License v. 2.0. If a copy of the MPL was not distributed
-// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
-
-// discard stack allocation as that too bypasses malloc
-#define EIGEN_STACK_ALLOCATION_LIMIT 0
-#define EIGEN_RUNTIME_NO_MALLOC
-
-#include "main.h"
-#include <unsupported/Eigen/BDCSVD>
-#include <Eigen/LU>
-
-
-// check if "svd" is the good image of "m"
-template<typename MatrixType, typename SVD>
-void svd_check_full(const MatrixType& m, const SVD& svd)
-{
- typedef typename MatrixType::Index Index;
- Index rows = m.rows();
- Index cols = m.cols();
- enum {
- RowsAtCompileTime = MatrixType::RowsAtCompileTime,
- ColsAtCompileTime = MatrixType::ColsAtCompileTime
- };
-
- typedef typename MatrixType::Scalar Scalar;
- typedef Matrix<Scalar, RowsAtCompileTime, RowsAtCompileTime> MatrixUType;
- typedef Matrix<Scalar, ColsAtCompileTime, ColsAtCompileTime> MatrixVType;
-
-
- MatrixType sigma = MatrixType::Zero(rows, cols);
- sigma.diagonal() = svd.singularValues().template cast<Scalar>();
- MatrixUType u = svd.matrixU();
- MatrixVType v = svd.matrixV();
- VERIFY_IS_APPROX(m, u * sigma * v.adjoint());
- VERIFY_IS_UNITARY(u);
- VERIFY_IS_UNITARY(v);
-} // end svd_check_full
-
-
-
-// Compare to a reference value
-template<typename MatrixType, typename SVD>
-void svd_compare_to_full(const MatrixType& m,
- unsigned int computationOptions,
- const SVD& referenceSvd)
-{
- typedef typename MatrixType::Index Index;
- Index rows = m.rows();
- Index cols = m.cols();
- Index diagSize = (std::min)(rows, cols);
-
- SVD svd(m, computationOptions);
-
- VERIFY_IS_APPROX(svd.singularValues(), referenceSvd.singularValues());
- if(computationOptions & ComputeFullU)
- VERIFY_IS_APPROX(svd.matrixU(), referenceSvd.matrixU());
- if(computationOptions & ComputeThinU)
- VERIFY_IS_APPROX(svd.matrixU(), referenceSvd.matrixU().leftCols(diagSize));
- if(computationOptions & ComputeFullV)
- VERIFY_IS_APPROX(svd.matrixV(), referenceSvd.matrixV());
- if(computationOptions & ComputeThinV)
- VERIFY_IS_APPROX(svd.matrixV(), referenceSvd.matrixV().leftCols(diagSize));
-} // end svd_compare_to_full
-
-
-
-template<typename MatrixType, typename SVD>
-void svd_solve(const MatrixType& m, unsigned int computationOptions)
-{
- typedef typename MatrixType::Scalar Scalar;
- typedef typename MatrixType::Index Index;
- Index rows = m.rows();
- Index cols = m.cols();
-
- enum {
- RowsAtCompileTime = MatrixType::RowsAtCompileTime,
- ColsAtCompileTime = MatrixType::ColsAtCompileTime
- };
-
- typedef Matrix<Scalar, RowsAtCompileTime, Dynamic> RhsType;
- typedef Matrix<Scalar, ColsAtCompileTime, Dynamic> SolutionType;
-
- RhsType rhs = RhsType::Random(rows, internal::random<Index>(1, cols));
- SVD svd(m, computationOptions);
- SolutionType x = svd.solve(rhs);
- // evaluate normal equation which works also for least-squares solutions
- VERIFY_IS_APPROX(m.adjoint()*m*x,m.adjoint()*rhs);
-} // end svd_solve
-
-
-// test computations options
-// 2 functions because Jacobisvd can return before the second function
-template<typename MatrixType, typename SVD>
-void svd_test_computation_options_1(const MatrixType& m, const SVD& fullSvd)
-{
- svd_check_full< MatrixType, SVD >(m, fullSvd);
- svd_solve< MatrixType, SVD >(m, ComputeFullU | ComputeFullV);
-}
-
-
-template<typename MatrixType, typename SVD>
-void svd_test_computation_options_2(const MatrixType& m, const SVD& fullSvd)
-{
- svd_compare_to_full< MatrixType, SVD >(m, ComputeFullU, fullSvd);
- svd_compare_to_full< MatrixType, SVD >(m, ComputeFullV, fullSvd);
- svd_compare_to_full< MatrixType, SVD >(m, 0, fullSvd);
-
- if (MatrixType::ColsAtCompileTime == Dynamic) {
- // thin U/V are only available with dynamic number of columns
-
- svd_compare_to_full< MatrixType, SVD >(m, ComputeFullU|ComputeThinV, fullSvd);
- svd_compare_to_full< MatrixType, SVD >(m, ComputeThinV, fullSvd);
- svd_compare_to_full< MatrixType, SVD >(m, ComputeThinU|ComputeFullV, fullSvd);
- svd_compare_to_full< MatrixType, SVD >(m, ComputeThinU , fullSvd);
- svd_compare_to_full< MatrixType, SVD >(m, ComputeThinU|ComputeThinV, fullSvd);
- svd_solve<MatrixType, SVD>(m, ComputeFullU | ComputeThinV);
- svd_solve<MatrixType, SVD>(m, ComputeThinU | ComputeFullV);
- svd_solve<MatrixType, SVD>(m, ComputeThinU | ComputeThinV);
-
- typedef typename MatrixType::Index Index;
- Index diagSize = (std::min)(m.rows(), m.cols());
- SVD svd(m, ComputeThinU | ComputeThinV);
- VERIFY_IS_APPROX(m, svd.matrixU().leftCols(diagSize) * svd.singularValues().asDiagonal() * svd.matrixV().leftCols(diagSize).adjoint());
- }
-}
-
-template<typename MatrixType, typename SVD>
-void svd_verify_assert(const MatrixType& m)
-{
- typedef typename MatrixType::Scalar Scalar;
- typedef typename MatrixType::Index Index;
- Index rows = m.rows();
- Index cols = m.cols();
-
- enum {
- RowsAtCompileTime = MatrixType::RowsAtCompileTime,
- ColsAtCompileTime = MatrixType::ColsAtCompileTime
- };
-
- typedef Matrix<Scalar, RowsAtCompileTime, 1> RhsType;
- RhsType rhs(rows);
- SVD svd;
- VERIFY_RAISES_ASSERT(svd.matrixU())
- VERIFY_RAISES_ASSERT(svd.singularValues())
- VERIFY_RAISES_ASSERT(svd.matrixV())
- VERIFY_RAISES_ASSERT(svd.solve(rhs))
- MatrixType a = MatrixType::Zero(rows, cols);
- a.setZero();
- svd.compute(a, 0);
- VERIFY_RAISES_ASSERT(svd.matrixU())
- VERIFY_RAISES_ASSERT(svd.matrixV())
- svd.singularValues();
- VERIFY_RAISES_ASSERT(svd.solve(rhs))
-
- if (ColsAtCompileTime == Dynamic)
- {
- svd.compute(a, ComputeThinU);
- svd.matrixU();
- VERIFY_RAISES_ASSERT(svd.matrixV())
- VERIFY_RAISES_ASSERT(svd.solve(rhs))
- svd.compute(a, ComputeThinV);
- svd.matrixV();
- VERIFY_RAISES_ASSERT(svd.matrixU())
- VERIFY_RAISES_ASSERT(svd.solve(rhs))
- }
- else
- {
- VERIFY_RAISES_ASSERT(svd.compute(a, ComputeThinU))
- VERIFY_RAISES_ASSERT(svd.compute(a, ComputeThinV))
- }
-}
-
-// work around stupid msvc error when constructing at compile time an expression that involves
-// a division by zero, even if the numeric type has floating point
-template<typename Scalar>
-EIGEN_DONT_INLINE Scalar zero() { return Scalar(0); }
-
-// workaround aggressive optimization in ICC
-template<typename T> EIGEN_DONT_INLINE T sub(T a, T b) { return a - b; }
-
-
-template<typename MatrixType, typename SVD>
-void svd_inf_nan()
-{
- // all this function does is verify we don't iterate infinitely on nan/inf values
-
- SVD svd;
- typedef typename MatrixType::Scalar Scalar;
- Scalar some_inf = Scalar(1) / zero<Scalar>();
- VERIFY(sub(some_inf, some_inf) != sub(some_inf, some_inf));
- svd.compute(MatrixType::Constant(10,10,some_inf), ComputeFullU | ComputeFullV);
-
- Scalar some_nan = zero<Scalar> () / zero<Scalar> ();
- VERIFY(some_nan != some_nan);
- svd.compute(MatrixType::Constant(10,10,some_nan), ComputeFullU | ComputeFullV);
-
- MatrixType m = MatrixType::Zero(10,10);
- m(internal::random<int>(0,9), internal::random<int>(0,9)) = some_inf;
- svd.compute(m, ComputeFullU | ComputeFullV);
-
- m = MatrixType::Zero(10,10);
- m(internal::random<int>(0,9), internal::random<int>(0,9)) = some_nan;
- svd.compute(m, ComputeFullU | ComputeFullV);
-}
-
-
-template<typename SVD>
-void svd_preallocate()
-{
- Vector3f v(3.f, 2.f, 1.f);
- MatrixXf m = v.asDiagonal();
-
- internal::set_is_malloc_allowed(false);
- VERIFY_RAISES_ASSERT(VectorXf v(10);)
- SVD svd;
- internal::set_is_malloc_allowed(true);
- svd.compute(m);
- VERIFY_IS_APPROX(svd.singularValues(), v);
-
- SVD svd2(3,3);
- internal::set_is_malloc_allowed(false);
- svd2.compute(m);
- internal::set_is_malloc_allowed(true);
- VERIFY_IS_APPROX(svd2.singularValues(), v);
- VERIFY_RAISES_ASSERT(svd2.matrixU());
- VERIFY_RAISES_ASSERT(svd2.matrixV());
- svd2.compute(m, ComputeFullU | ComputeFullV);
- VERIFY_IS_APPROX(svd2.matrixU(), Matrix3f::Identity());
- VERIFY_IS_APPROX(svd2.matrixV(), Matrix3f::Identity());
- internal::set_is_malloc_allowed(false);
- svd2.compute(m);
- internal::set_is_malloc_allowed(true);
-
- SVD svd3(3,3,ComputeFullU|ComputeFullV);
- internal::set_is_malloc_allowed(false);
- svd2.compute(m);
- internal::set_is_malloc_allowed(true);
- VERIFY_IS_APPROX(svd2.singularValues(), v);
- VERIFY_IS_APPROX(svd2.matrixU(), Matrix3f::Identity());
- VERIFY_IS_APPROX(svd2.matrixV(), Matrix3f::Identity());
- internal::set_is_malloc_allowed(false);
- svd2.compute(m, ComputeFullU|ComputeFullV);
- internal::set_is_malloc_allowed(true);
-}
-
-
-
-
-
generated by cgit v1.2.3 (git 2.39.1) at 2024-05-29 11:45:20 +0000