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Add an efficient rank2 update function (like the level2 blas xSYR2 routine).

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Note that it is already used in Tridiagonalization.
This commit is contained in:
Gael Guennebaud
2009-07-11 21:14:59 +02:00
parent b47dea8b7a
commit a2087cd7a3
11 changed files with 187 additions and 51 deletions
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4
test/eigensolver_selfadjoint.cpp
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@@ -119,8 +119,8 @@ void test_eigensolver_selfadjoint()
// very important to test a 3x3 matrix since we provide a special path for it
CALL_SUBTEST( selfadjointeigensolver(Matrix3f()) );
CALL_SUBTEST( selfadjointeigensolver(Matrix4d()) );
CALL_SUBTEST( selfadjointeigensolver(MatrixXf(7,7)) );
CALL_SUBTEST( selfadjointeigensolver(MatrixXcd(5,5)) );
CALL_SUBTEST( selfadjointeigensolver(MatrixXf(4,4)) );
CALL_SUBTEST( selfadjointeigensolver(MatrixXcd(7,7)) );
CALL_SUBTEST( selfadjointeigensolver(MatrixXd(19,19)) );
// some trivial but implementation-wise tricky cases

40
test/product_selfadjoint.cpp
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@@ -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@gmail.com>
// Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@gmail.com>
//
// Eigen is free software; you can redistribute it and/or
// modify it under the terms of the GNU Lesser General Public
@@ -29,20 +29,29 @@ template<typename MatrixType> void product_selfadjoint(const MatrixType& m)
typedef typename MatrixType::Scalar Scalar;
typedef typename NumTraits<Scalar>::Real RealScalar;
typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> VectorType;
typedef Matrix<Scalar, 1, MatrixType::RowsAtCompileTime> RowVectorType;
int rows = m.rows();
int cols = m.cols();
MatrixType m1 = MatrixType::Random(rows, cols),
m2 = MatrixType::Random(rows, cols);
m2 = MatrixType::Random(rows, cols),
m3;
VectorType v1 = VectorType::Random(rows),
v2 = VectorType::Random(rows);
RowVectorType r1 = RowVectorType::Random(rows),
r2 = RowVectorType::Random(rows);
Scalar s1 = ei_random<Scalar>(),
s2 = ei_random<Scalar>(),
s3 = ei_random<Scalar>();
m1 = m1.adjoint()*m1;
// lower
m2.setZero();
m2.template part<LowerTriangular>() = m1;
m2.template triangularView<LowerTriangular>() = m1;
ei_product_selfadjoint_vector<Scalar,MatrixType::Flags&RowMajorBit,LowerTriangularBit>
(cols,m2.data(),cols, v1.data(), v2.data());
VERIFY_IS_APPROX(v2, m1 * v1);
@@ -50,11 +59,30 @@ template<typename MatrixType> void product_selfadjoint(const MatrixType& m)
// upper
m2.setZero();
m2.template part<UpperTriangular>() = m1;
m2.template triangularView<UpperTriangular>() = m1;
ei_product_selfadjoint_vector<Scalar,MatrixType::Flags&RowMajorBit,UpperTriangularBit>(cols,m2.data(),cols, v1.data(), v2.data());
VERIFY_IS_APPROX(v2, m1 * v1);
VERIFY_IS_APPROX((m2.template selfadjointView<UpperTriangular>() * v1).eval(), m1 * v1);
// rank2 update
m2 = m1.template triangularView<LowerTriangular>();
m2.template selfadjointView<LowerTriangular>().rank2update(v1,v2);
VERIFY_IS_APPROX(m2, (m1 + v1 * v2.adjoint()+ v2 * v1.adjoint()).template triangularView<LowerTriangular>().toDense());
m2 = m1.template triangularView<UpperTriangular>();
m2.template selfadjointView<UpperTriangular>().rank2update(-v1,s2*v2,s3);
VERIFY_IS_APPROX(m2, (m1 + (-s2*s3) * (v1 * v2.adjoint()+ v2 * v1.adjoint())).template triangularView<UpperTriangular>().toDense());
m2 = m1.template triangularView<UpperTriangular>();
m2.template selfadjointView<UpperTriangular>().rank2update(-r1.adjoint(),r2.adjoint()*s3,s1);
VERIFY_IS_APPROX(m2, (m1 + (-s3*s1) * (r1.adjoint() * r2 + r2.adjoint() * r1)).template triangularView<UpperTriangular>().toDense());
m2 = m1.template triangularView<LowerTriangular>();
m2.block(1,1,rows-1,cols-1).template selfadjointView<LowerTriangular>().rank2update(v1.end(rows-1),v2.start(cols-1));
m3 = m1;
m3.block(1,1,rows-1,cols-1) += v1.end(rows-1) * v2.start(cols-1).adjoint()+ v2.start(cols-1) * v1.end(rows-1).adjoint();
VERIFY_IS_APPROX(m2, m3.template triangularView<LowerTriangular>().toDense());
}
void test_product_selfadjoint()
@@ -65,8 +93,8 @@ void test_product_selfadjoint()
CALL_SUBTEST( product_selfadjoint(Matrix3d()) );
CALL_SUBTEST( product_selfadjoint(MatrixXcf(4, 4)) );
CALL_SUBTEST( product_selfadjoint(MatrixXcd(21,21)) );
CALL_SUBTEST( product_selfadjoint(MatrixXd(17,17)) );
CALL_SUBTEST( product_selfadjoint(Matrix<float,Dynamic,Dynamic,RowMajor>(18,18)) );
CALL_SUBTEST( product_selfadjoint(MatrixXd(4,4)) );
CALL_SUBTEST( product_selfadjoint(Matrix<float,Dynamic,Dynamic,RowMajor>(17,17)) );
CALL_SUBTEST( product_selfadjoint(Matrix<std::complex<double>,Dynamic,Dynamic,RowMajor>(19, 19)) );
}
}