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diagonalmatrices.cpp
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Thu, Feb 20, 22:50

diagonalmatrices.cpp
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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// 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 "main.h"
using namespace std;
template<typename MatrixType> void diagonalmatrices(const MatrixType& m)
{
typedef typename MatrixType::Scalar Scalar;
enum { Rows = MatrixType::RowsAtCompileTime, Cols = MatrixType::ColsAtCompileTime };
typedef Matrix<Scalar, Rows, 1> VectorType;
typedef Matrix<Scalar, 1, Cols> RowVectorType;
typedef Matrix<Scalar, Rows, Rows> SquareMatrixType;
typedef Matrix<Scalar, Dynamic, Dynamic> DynMatrixType;
typedef DiagonalMatrix<Scalar, Rows> LeftDiagonalMatrix;
typedef DiagonalMatrix<Scalar, Cols> RightDiagonalMatrix;
typedef Matrix<Scalar, Rows==Dynamic?Dynamic:2*Rows, Cols==Dynamic?Dynamic:2*Cols> BigMatrix;
Index rows = m.rows();
Index cols = m.cols();
MatrixType m1 = MatrixType::Random(rows, cols),
m2 = MatrixType::Random(rows, cols);
VectorType v1 = VectorType::Random(rows),
v2 = VectorType::Random(rows);
RowVectorType rv1 = RowVectorType::Random(cols),
rv2 = RowVectorType::Random(cols);
LeftDiagonalMatrix ldm1(v1), ldm2(v2);
RightDiagonalMatrix rdm1(rv1), rdm2(rv2);
Scalar s1 = internal::random<Scalar>();
SquareMatrixType sq_m1 (v1.asDiagonal());
VERIFY_IS_APPROX(sq_m1, v1.asDiagonal().toDenseMatrix());
sq_m1 = v1.asDiagonal();
VERIFY_IS_APPROX(sq_m1, v1.asDiagonal().toDenseMatrix());
SquareMatrixType sq_m2 = v1.asDiagonal();
VERIFY_IS_APPROX(sq_m1, sq_m2);
ldm1 = v1.asDiagonal();
LeftDiagonalMatrix ldm3(v1);
VERIFY_IS_APPROX(ldm1.diagonal(), ldm3.diagonal());
LeftDiagonalMatrix ldm4 = v1.asDiagonal();
VERIFY_IS_APPROX(ldm1.diagonal(), ldm4.diagonal());
sq_m1.block(0,0,rows,rows) = ldm1;
VERIFY_IS_APPROX(sq_m1, ldm1.toDenseMatrix());
sq_m1.transpose() = ldm1;
VERIFY_IS_APPROX(sq_m1, ldm1.toDenseMatrix());
Index i = internal::random<Index>(0, rows-1);
Index j = internal::random<Index>(0, cols-1);
VERIFY_IS_APPROX( ((ldm1 * m1)(i,j)) , ldm1.diagonal()(i) * m1(i,j) );
VERIFY_IS_APPROX( ((ldm1 * (m1+m2))(i,j)) , ldm1.diagonal()(i) * (m1+m2)(i,j) );
VERIFY_IS_APPROX( ((m1 * rdm1)(i,j)) , rdm1.diagonal()(j) * m1(i,j) );
VERIFY_IS_APPROX( ((v1.asDiagonal() * m1)(i,j)) , v1(i) * m1(i,j) );
VERIFY_IS_APPROX( ((m1 * rv1.asDiagonal())(i,j)) , rv1(j) * m1(i,j) );
VERIFY_IS_APPROX( (((v1+v2).asDiagonal() * m1)(i,j)) , (v1+v2)(i) * m1(i,j) );
VERIFY_IS_APPROX( (((v1+v2).asDiagonal() * (m1+m2))(i,j)) , (v1+v2)(i) * (m1+m2)(i,j) );
VERIFY_IS_APPROX( ((m1 * (rv1+rv2).asDiagonal())(i,j)) , (rv1+rv2)(j) * m1(i,j) );
VERIFY_IS_APPROX( (((m1+m2) * (rv1+rv2).asDiagonal())(i,j)) , (rv1+rv2)(j) * (m1+m2)(i,j) );
if(rows>1)
{
DynMatrixType tmp = m1.topRows(rows/2), res;
VERIFY_IS_APPROX( (res = m1.topRows(rows/2) * rv1.asDiagonal()), tmp * rv1.asDiagonal() );
VERIFY_IS_APPROX( (res = v1.head(rows/2).asDiagonal()*m1.topRows(rows/2)), v1.head(rows/2).asDiagonal()*tmp );
}
BigMatrix big;
big.setZero(2*rows, 2*cols);
big.block(i,j,rows,cols) = m1;
big.block(i,j,rows,cols) = v1.asDiagonal() * big.block(i,j,rows,cols);
VERIFY_IS_APPROX((big.block(i,j,rows,cols)) , v1.asDiagonal() * m1 );
big.block(i,j,rows,cols) = m1;
big.block(i,j,rows,cols) = big.block(i,j,rows,cols) * rv1.asDiagonal();
VERIFY_IS_APPROX((big.block(i,j,rows,cols)) , m1 * rv1.asDiagonal() );
// scalar multiple
VERIFY_IS_APPROX(LeftDiagonalMatrix(ldm1*s1).diagonal(), ldm1.diagonal() * s1);
VERIFY_IS_APPROX(LeftDiagonalMatrix(s1*ldm1).diagonal(), s1 * ldm1.diagonal());
VERIFY_IS_APPROX(m1 * (rdm1 * s1), (m1 * rdm1) * s1);
VERIFY_IS_APPROX(m1 * (s1 * rdm1), (m1 * rdm1) * s1);
// Diagonal to dense
sq_m1.setRandom();
sq_m2 = sq_m1;
VERIFY_IS_APPROX( (sq_m1 += (s1*v1).asDiagonal()), sq_m2 += (s1*v1).asDiagonal().toDenseMatrix() );
VERIFY_IS_APPROX( (sq_m1 -= (s1*v1).asDiagonal()), sq_m2 -= (s1*v1).asDiagonal().toDenseMatrix() );
VERIFY_IS_APPROX( (sq_m1 = (s1*v1).asDiagonal()), (s1*v1).asDiagonal().toDenseMatrix() );
sq_m1.setRandom();
sq_m2 = v1.asDiagonal();
sq_m2 = sq_m1 * sq_m2;
VERIFY_IS_APPROX( (sq_m1*v1.asDiagonal()).col(i), sq_m2.col(i) );
VERIFY_IS_APPROX( (sq_m1*v1.asDiagonal()).row(i), sq_m2.row(i) );
sq_m1 = v1.asDiagonal();
sq_m2 = v2.asDiagonal();
SquareMatrixType sq_m3 = v1.asDiagonal();
VERIFY_IS_APPROX( sq_m3 = v1.asDiagonal() + v2.asDiagonal(), sq_m1 + sq_m2);
VERIFY_IS_APPROX( sq_m3 = v1.asDiagonal() - v2.asDiagonal(), sq_m1 - sq_m2);
VERIFY_IS_APPROX( sq_m3 = v1.asDiagonal() - 2*v2.asDiagonal() + v1.asDiagonal(), sq_m1 - 2*sq_m2 + sq_m1);
}
template<typename MatrixType> void as_scalar_product(const MatrixType& m)
{
typedef typename MatrixType::Scalar Scalar;
typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> VectorType;
typedef Matrix<Scalar, Dynamic, Dynamic> DynMatrixType;
typedef Matrix<Scalar, Dynamic, 1> DynVectorType;
typedef Matrix<Scalar, 1, Dynamic> DynRowVectorType;
Index rows = m.rows();
Index depth = internal::random<Index>(1,EIGEN_TEST_MAX_SIZE);
VectorType v1 = VectorType::Random(rows);
DynVectorType dv1 = DynVectorType::Random(depth);
DynRowVectorType drv1 = DynRowVectorType::Random(depth);
DynMatrixType dm1 = dv1;
DynMatrixType drm1 = drv1;
Scalar s = v1(0);
VERIFY_IS_APPROX( v1.asDiagonal() * drv1, s*drv1 );
VERIFY_IS_APPROX( dv1 * v1.asDiagonal(), dv1*s );
VERIFY_IS_APPROX( v1.asDiagonal() * drm1, s*drm1 );
VERIFY_IS_APPROX( dm1 * v1.asDiagonal(), dm1*s );
}
template<int>
void bug987()
{
Matrix3Xd points = Matrix3Xd::Random(3, 3);
Vector2d diag = Vector2d::Random();
Matrix2Xd tmp1 = points.topRows<2>(), res1, res2;
VERIFY_IS_APPROX( res1 = diag.asDiagonal() * points.topRows<2>(), res2 = diag.asDiagonal() * tmp1 );
Matrix2d tmp2 = points.topLeftCorner<2,2>();
VERIFY_IS_APPROX(( res1 = points.topLeftCorner<2,2>()*diag.asDiagonal()) , res2 = tmp2*diag.asDiagonal() );
}
EIGEN_DECLARE_TEST(diagonalmatrices)
{
for(int i = 0; i < g_repeat; i++) {
CALL_SUBTEST_1( diagonalmatrices(Matrix<float, 1, 1>()) );
CALL_SUBTEST_1( as_scalar_product(Matrix<float, 1, 1>()) );
CALL_SUBTEST_2( diagonalmatrices(Matrix3f()) );
CALL_SUBTEST_3( diagonalmatrices(Matrix<double,3,3,RowMajor>()) );
CALL_SUBTEST_4( diagonalmatrices(Matrix4d()) );
CALL_SUBTEST_5( diagonalmatrices(Matrix<float,4,4,RowMajor>()) );
CALL_SUBTEST_6( diagonalmatrices(MatrixXcf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
CALL_SUBTEST_6( as_scalar_product(MatrixXcf(1,1)) );
CALL_SUBTEST_7( diagonalmatrices(MatrixXi(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
CALL_SUBTEST_8( diagonalmatrices(Matrix<double,Dynamic,Dynamic,RowMajor>(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
CALL_SUBTEST_9( diagonalmatrices(MatrixXf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
CALL_SUBTEST_9( diagonalmatrices(MatrixXf(1,1)) );
CALL_SUBTEST_9( as_scalar_product(MatrixXf(1,1)) );
}
CALL_SUBTEST_10( bug987<0>() );
}

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