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finally directly calling the low-level products is faster

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This commit is contained in:
Gael Guennebaud 2009-07-10 10:41:26 +02:00
parent 8885d56928
commit 1a1b2e9f27
12 changed files with 111 additions and 146 deletions
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10
Eigen/src/Core/GenericPacketMath.h
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@ -245,5 +245,15 @@ inline void ei_palign(PacketType& first, const PacketType& second)
ei_palign_impl<Offset,PacketType>::run(first,second);
}
/***************************************************************************
* Fast complex products (GCC generates a function call which is very slow)
***************************************************************************/
template<> inline std::complex<float> ei_pmul(const std::complex<float>& a, const std::complex<float>& b)
{ return std::complex<float>(ei_real(a)*ei_real(b) - ei_imag(a)*ei_imag(b), ei_imag(a)*ei_real(b) + ei_real(a)*ei_imag(b)); }
template<> inline std::complex<double> ei_pmul(const std::complex<double>& a, const std::complex<double>& b)
{ return std::complex<double>(ei_real(a)*ei_real(b) - ei_imag(a)*ei_imag(b), ei_imag(a)*ei_real(b) + ei_real(a)*ei_imag(b)); }
#endif // EIGEN_GENERIC_PACKET_MATH_H

3
Eigen/src/Core/Product.h
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@ -281,8 +281,7 @@ template<typename LhsNested, typename RhsNested, int ProductMode> class Product
*/
EIGEN_STRONG_INLINE bool _useCacheFriendlyProduct() const
{
#define EIGEN_CACHEFRIENDLY_PRODUCT_THRESHOLD 16
// TODO do something more accurate here
// TODO do something more accurate here (especially for mat-vec products)
return m_lhs.cols()>=EIGEN_CACHEFRIENDLY_PRODUCT_THRESHOLD
&& ( rows()>=EIGEN_CACHEFRIENDLY_PRODUCT_THRESHOLD
|| cols()>=EIGEN_CACHEFRIENDLY_PRODUCT_THRESHOLD);

81
Eigen/src/Core/SolveTriangular.h
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@ -27,7 +27,6 @@
template<typename Lhs, typename Rhs,
int Mode, // Upper/Lower | UnitDiag
// bool ConjugateLhs, bool ConjugateRhs,
int UpLo = (Mode & LowerTriangularBit)
? LowerTriangular
: (Mode & UpperTriangularBit)
@ -38,15 +37,20 @@ template<typename Lhs, typename Rhs,
struct ei_triangular_solver_selector;
// forward substitution, row-major
template<typename Lhs, typename Rhs, int Mode, /*bool ConjugateLhs, bool ConjugateRhs,*/ int UpLo>
struct ei_triangular_solver_selector<Lhs,Rhs,Mode,/*ConjugateLhs,ConjugateRhs,*/UpLo,RowMajor>
template<typename Lhs, typename Rhs, int Mode, int UpLo>
struct ei_triangular_solver_selector<Lhs,Rhs,Mode,UpLo,RowMajor>
{
typedef typename Rhs::Scalar Scalar;
typedef ei_product_factor_traits<Lhs> LhsProductTraits;
typedef typename LhsProductTraits::ActualXprType ActualLhsType;
enum {
IsLowerTriangular = (UpLo==LowerTriangular)
};
static void run(const Lhs& lhs, Rhs& other)
{//std::cerr << "row maj " << ConjugateLhs << " , " << ConjugateRhs
// << " " << typeid(Lhs).name() << "\n";
static const int PanelWidth = 40; // TODO make this a user definable constant
static const bool IsLowerTriangular = (UpLo==LowerTriangular);
{//std::cerr << "row maj " << LhsProductTraits::NeedToConjugate << "\n";
static const int PanelWidth = EIGEN_TUNE_TRSV_PANEL_WIDTH;
const ActualLhsType& actualLhs = LhsProductTraits::extract(lhs);
const int size = lhs.cols();
for(int c=0 ; c<other.cols() ; ++c)
{
@ -61,15 +65,12 @@ struct ei_triangular_solver_selector<Lhs,Rhs,Mode,/*ConjugateLhs,ConjugateRhs,*/
{
int startRow = IsLowerTriangular ? pi : pi-actualPanelWidth;
int startCol = IsLowerTriangular ? 0 : pi;
// Block<Rhs,Dynamic,1> target(other,startRow,c,actualPanelWidth,1);
// ei_cache_friendly_product_rowmajor_times_vector<ConjugateLhs,ConjugateRhs>(
// &(lhs.const_cast_derived().coeffRef(startRow,startCol)), lhs.stride(),
// &(other.coeffRef(startCol, c)), r,
// target, Scalar(-1));
other.col(c).segment(startRow,actualPanelWidth) -=
lhs.block(startRow,startCol,actualPanelWidth,r)
* other.col(c).segment(startCol,r);
Block<Rhs,Dynamic,1> target(other,startRow,c,actualPanelWidth,1);
ei_cache_friendly_product_rowmajor_times_vector<LhsProductTraits::NeedToConjugate,false>(
&(actualLhs.const_cast_derived().coeffRef(startRow,startCol)), actualLhs.stride(),
&(other.coeffRef(startCol, c)), r,
target, Scalar(-1));
}
for(int k=0; k<actualPanelWidth; ++k)
@ -83,7 +84,6 @@ struct ei_triangular_solver_selector<Lhs,Rhs,Mode,/*ConjugateLhs,ConjugateRhs,*/
if(!(Mode & UnitDiagBit))
other.coeffRef(i,c) /= lhs.coeff(i,i);
}
}
}
}
@ -94,17 +94,23 @@ struct ei_triangular_solver_selector<Lhs,Rhs,Mode,/*ConjugateLhs,ConjugateRhs,*/
// - inv(LowerTriangular,UnitDiag,ColMajor) * Column vector
// - inv(UpperTriangular, ColMajor) * Column vector
// - inv(UpperTriangular,UnitDiag,ColMajor) * Column vector
template<typename Lhs, typename Rhs, int Mode, /*bool ConjugateLhs, bool ConjugateRhs,*/ int UpLo>
struct ei_triangular_solver_selector<Lhs,Rhs,Mode,/*ConjugateLhs,ConjugateRhs,*/UpLo,ColMajor>
template<typename Lhs, typename Rhs, int Mode, int UpLo>
struct ei_triangular_solver_selector<Lhs,Rhs,Mode,UpLo,ColMajor>
{
typedef typename Rhs::Scalar Scalar;
typedef typename ei_packet_traits<Scalar>::type Packet;
enum { PacketSize = ei_packet_traits<Scalar>::size };
typedef ei_product_factor_traits<Lhs> LhsProductTraits;
typedef typename LhsProductTraits::ActualXprType ActualLhsType;
enum {
PacketSize = ei_packet_traits<Scalar>::size,
IsLowerTriangular = (UpLo==LowerTriangular)
};
static void run(const Lhs& lhs, Rhs& other)
{//std::cerr << "col maj " << ConjugateLhs << " , " << ConjugateRhs << "\n";
static const int PanelWidth = 4; // TODO make this a user definable constant
static const bool IsLowerTriangular = (UpLo==LowerTriangular);
{//std::cerr << "col maj " << LhsProductTraits::NeedToConjugate << "\n";
static const int PanelWidth = EIGEN_TUNE_TRSV_PANEL_WIDTH;
const ActualLhsType& actualLhs = LhsProductTraits::extract(lhs);
const int size = lhs.cols();
for(int c=0 ; c<other.cols() ; ++c)
{
@ -133,16 +139,15 @@ struct ei_triangular_solver_selector<Lhs,Rhs,Mode,/*ConjugateLhs,ConjugateRhs,*/
int r = IsLowerTriangular ? size - endBlock : startBlock; // remaining size
if (r > 0)
{
// ei_cache_friendly_product_colmajor_times_vector<ConjugateLhs,ConjugateRhs>(
// r,
// &(lhs.const_cast_derived().coeffRef(endBlock,startBlock)), lhs.stride(),
// other.col(c).segment(startBlock, actualPanelWidth),
// &(other.coeffRef(endBlock, c)),
// Scalar(-1));
other.col(c).segment(endBlock,r) -=
lhs.block(endBlock,startBlock,r,actualPanelWidth)
* other.col(c).segment(startBlock,actualPanelWidth);
// let's directly call this function because:
// 1 - it is faster to compile
// 2 - it is slighlty faster at runtime
ei_cache_friendly_product_colmajor_times_vector<LhsProductTraits::NeedToConjugate,false>(
r,
&(actualLhs.const_cast_derived().coeffRef(endBlock,startBlock)), actualLhs.stride(),
other.col(c).segment(startBlock, actualPanelWidth),
&(other.coeffRef(endBlock, c)),
Scalar(-1));
}
}
}
@ -168,21 +173,13 @@ void TriangularView<MatrixType,Mode>::solveInPlace(const MatrixBase<RhsDerived>&
ei_assert(!(Mode & ZeroDiagBit));
ei_assert(Mode & (UpperTriangularBit|LowerTriangularBit));
// typedef ei_product_factor_traits<MatrixType> LhsProductTraits;
// typedef ei_product_factor_traits<RhsDerived> RhsProductTraits;
// typedef typename LhsProductTraits::ActualXprType ActualLhsType;
// typedef typename RhsProductTraits::ActualXprType ActualRhsType;
// const ActualLhsType& actualLhs = LhsProductTraits::extract(_expression());
// ActualRhsType& actualRhs = const_cast<ActualRhsType&>(RhsProductTraits::extract(rhs));
enum { copy = ei_traits<RhsDerived>::Flags & RowMajorBit };
// std::cerr << typeid(MatrixType).name() << "\n";
typedef typename ei_meta_if<copy,
typename ei_plain_matrix_type_column_major<RhsDerived>::type, RhsDerived&>::ret RhsCopy;
RhsCopy rhsCopy(rhs);
ei_triangular_solver_selector<MatrixType, typename ei_unref<RhsCopy>::type,
Mode/*, LhsProductTraits::NeedToConjugate,RhsProductTraits::NeedToConjugate*/>::run(_expression(), rhsCopy);
Mode>::run(_expression(), rhsCopy);
if (copy)
rhs = rhsCopy;

2
Eigen/src/Core/arch/SSE/PacketMath.h
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@ -26,7 +26,7 @@
#define EIGEN_PACKET_MATH_SSE_H
#ifndef EIGEN_CACHEFRIENDLY_PRODUCT_THRESHOLD
#define EIGEN_CACHEFRIENDLY_PRODUCT_THRESHOLD 16
#define EIGEN_CACHEFRIENDLY_PRODUCT_THRESHOLD 8
#endif
typedef __m128 Packet4f;

6
Eigen/src/Core/products/GeneralMatrixMatrix.h
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@ -47,8 +47,7 @@ template<> struct ei_conj_helper<false,true>
{ return c + pmul(x,y); }
template<typename T> std::complex<T> pmul(const std::complex<T>& x, const std::complex<T>& y) const
//{ return std::complex<T>(ei_real(x)*ei_real(y) + ei_imag(x)*ei_imag(y), ei_imag(x)*ei_real(y) - ei_real(x)*ei_imag(y)); }
{ return x * ei_conj(y); }
{ return std::complex<T>(ei_real(x)*ei_real(y) + ei_imag(x)*ei_imag(y), ei_imag(x)*ei_real(y) - ei_real(x)*ei_imag(y)); }
};
template<> struct ei_conj_helper<true,false>
@ -68,8 +67,7 @@ template<> struct ei_conj_helper<true,true>
{ return c + pmul(x,y); }
template<typename T> std::complex<T> pmul(const std::complex<T>& x, const std::complex<T>& y) const
// { return std::complex<T>(ei_real(x)*ei_real(y) - ei_imag(x)*ei_imag(y), - ei_real(x)*ei_imag(y) - ei_imag(x)*ei_real(y)); }
{ return ei_conj(x) * ei_conj(y); }
{ return std::complex<T>(ei_real(x)*ei_real(y) - ei_imag(x)*ei_imag(y), - ei_real(x)*ei_imag(y) - ei_imag(x)*ei_real(y)); }
};
#ifndef EIGEN_EXTERN_INSTANTIATIONS

8
Eigen/src/Core/products/SelfadjointMatrixVector.h
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@ -25,14 +25,6 @@
#ifndef EIGEN_SELFADJOINT_MATRIX_VECTOR_H
#define EIGEN_SELFADJOINT_MATRIX_VECTOR_H
template<bool Conjugate> struct ei_conj_if {
template<typename Scalar> Scalar operator() (const Scalar& x) const { return ei_conj(x); }
};
template<> struct ei_conj_if<false> {
template<typename Scalar> Scalar& operator() (Scalar& x) const { return x; }
};
/* Optimized col-major selfadjoint matrix * vector product:
* This algorithm processes 2 columns at onces that allows to both reduce
* the number of load/stores of the result by a factor 2 and to reduce

7
Eigen/src/Core/util/Macros.h
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@ -94,6 +94,13 @@
#define EIGEN_TUNE_FOR_CPU_CACHE_SIZE (sizeof(float)*256*256)
#endif
/** Defines the maximal width of the blocks used in the triangular solver
* for vectors (level 2 blas xTRSV). The default is 8.
*/
#ifndef EIGEN_TUNE_TRSV_PANEL_WIDTH
#define EIGEN_TUNE_TRSV_PANEL_WIDTH 8
#endif
/** Allows to disable some optimizations which might affect the accuracy of the result.
* Such optimization are enabled by default, and set EIGEN_FAST_MATH to 0 to disable them.
* They currently include:

12
Eigen/src/Core/util/Meta.h
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@ -198,4 +198,16 @@ template<typename T> struct ei_is_diagonal<DiagonalWrapper<T> >
template<typename T, int S> struct ei_is_diagonal<DiagonalMatrix<T,S> >
{ enum { ret = true }; };
template<bool Conjugate> struct ei_conj_if;
template<> struct ei_conj_if<true> {
template<typename T>
inline T operator()(const T& x) { return ei_conj(x); }
};
template<> struct ei_conj_if<false> {
template<typename T>
inline const T& operator()(const T& x) { return x; }
};
#endif // EIGEN_META_H

20
test/cholesky.cpp
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@ -142,18 +142,18 @@ template<typename MatrixType> void cholesky_verify_assert()
void test_cholesky()
{
for(int i = 0; i < g_repeat; i++) {
// CALL_SUBTEST( cholesky(Matrix<double,1,1>()) );
// CALL_SUBTEST( cholesky(MatrixXd(1,1)) );
// CALL_SUBTEST( cholesky(Matrix2d()) );
// CALL_SUBTEST( cholesky(Matrix3f()) );
CALL_SUBTEST( cholesky(Matrix<double,1,1>()) );
CALL_SUBTEST( cholesky(MatrixXd(1,1)) );
CALL_SUBTEST( cholesky(Matrix2d()) );
CALL_SUBTEST( cholesky(Matrix3f()) );
CALL_SUBTEST( cholesky(Matrix4d()) );
CALL_SUBTEST( cholesky(MatrixXcd(7,7)) );
// CALL_SUBTEST( cholesky(MatrixXd(17,17)) );
// CALL_SUBTEST( cholesky(MatrixXf(200,200)) );
CALL_SUBTEST( cholesky(MatrixXd(17,17)) );
CALL_SUBTEST( cholesky(MatrixXf(200,200)) );
}
// CALL_SUBTEST( cholesky_verify_assert<Matrix3f>() );
// CALL_SUBTEST( cholesky_verify_assert<Matrix3d>() );
// CALL_SUBTEST( cholesky_verify_assert<MatrixXf>() );
// CALL_SUBTEST( cholesky_verify_assert<MatrixXd>() );
CALL_SUBTEST( cholesky_verify_assert<Matrix3f>() );
CALL_SUBTEST( cholesky_verify_assert<Matrix3d>() );
CALL_SUBTEST( cholesky_verify_assert<MatrixXf>() );
CALL_SUBTEST( cholesky_verify_assert<MatrixXd>() );
}

1
test/main.h
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@ -28,6 +28,7 @@
#include <iostream>
#include <string>
#include <vector>
#include <typeinfo>
#ifndef EIGEN_TEST_FUNC
#error EIGEN_TEST_FUNC must be defined

53
test/product_extra.cpp
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@ -47,8 +47,6 @@ template<typename MatrixType> void product_extra(const MatrixType& m)
square2 = MatrixType::Random(cols, cols),
res2 = MatrixType::Random(cols, cols);
RowVectorType v1 = RowVectorType::Random(rows), vrres(rows);
// v2 = RowVectorType::Random(rows),
// vzero = RowVectorType::Zero(rows);
ColVectorType vc2 = ColVectorType::Random(cols), vcres(cols);
OtherMajorMatrixType tm1 = m1;
@ -56,14 +54,14 @@ template<typename MatrixType> void product_extra(const MatrixType& m)
s2 = ei_random<Scalar>(),
s3 = ei_random<Scalar>();
int c0 = ei_random<int>(0,cols/2-1),
c1 = ei_random<int>(cols/2,cols),
r0 = ei_random<int>(0,rows/2-1),
r1 = ei_random<int>(rows/2,rows);
// int c0 = ei_random<int>(0,cols/2-1),
// c1 = ei_random<int>(cols/2,cols),
// r0 = ei_random<int>(0,rows/2-1),
// r1 = ei_random<int>(rows/2,rows);
// all the expressions in this test should be compiled as a single matrix product
// TODO: add internal checks to verify that
/*
VERIFY_IS_APPROX(m1 * m2.adjoint(), m1 * m2.adjoint().eval());
VERIFY_IS_APPROX(m1.adjoint() * square.adjoint(), m1.adjoint().eval() * square.adjoint().eval());
VERIFY_IS_APPROX(m1.adjoint() * m2, m1.adjoint().eval() * m2);
@ -111,49 +109,14 @@ template<typename MatrixType> void product_extra(const MatrixType& m)
VERIFY_IS_APPROX((-m1.adjoint() * s2) * (s1 * v1.adjoint()),
(-m1.adjoint()*s2).eval() * (s1 * v1.adjoint()).eval());
*/
// test with sub matrices
m2 = m1;
m3 = m1;
// std::cerr << (m1.block(r0,c0, r1-r0, c1-c0) * vc2.segment(c0,c1-c0)).rows() << " " << (m1.block(r0,c0, r1-r0, c1-c0) * vc2.segment(c0,c1-c0)).cols() << " == " << vrres.segment(r0,r1-r0).rows() << " " << vrres.segment(r0,r1-r0).cols() << "\n";
// m2.col(c0).segment(0,r1-r0) += (m1.block(r0,c0, r1-r0, c1-c0) * vc2.segment(c0,c1-c0)).lazy();
// m3.col(c0).segment(0,r1-r0) += (m1.block(r0,c0, r1-r0, c1-c0) * vc2.segment(c0,c1-c0)).eval();
Matrix<Scalar,Dynamic,1> a = m2.col(c0), b = a;
a.segment(5,r1-r0) += (m1.block(r0,c0, r1-r0, c1-c0) * vc2.segment(c0,c1-c0)).lazy();
b.segment(5,r1-r0) += (m1.block(r0,c0, r1-r0, c1-c0) * vc2.segment(c0,c1-c0)).eval();
// m2.col(c0).segment(0,r1-r0) += (m1.block(r0,c0, r1-r0, c1-c0) * vc2.segment(c0,c1-c0)).lazy();
// m3.col(c0).segment(0,r1-r0) += (m1.block(r0,c0, r1-r0, c1-c0) * vc2.segment(c0,c1-c0)).eval();
// if (!m2.isApprox(m3))
std::cerr << (a-b).cwise().abs().maxCoeff() << "\n";
VERIFY_IS_APPROX(a,b);
// VERIFY_IS_APPROX( vrres.segment(0,r1-r0).transpose().eval(),
// v1.segment(0,r1-r0).transpose() + m1.block(r0,c0, r1-r0, c1-c0).eval() * (vc2.segment(c0,c1-c0)).eval());
}
void test_product_extra()
{
for(int i = 0; i < g_repeat; i++) {
int rows = ei_random<int>(2,10);
int cols = ei_random<int>(2,10);
int c0 = ei_random<int>(0,cols/2-1),
c1 = ei_random<int>(cols/2,cols),
r0 = ei_random<int>(0,rows/2-1),
r1 = ei_random<int>(rows/2,rows);
MatrixXf m1 = MatrixXf::Random(rows,cols), m2 = m1;
Matrix<float,Dynamic,1> a = m2.col(c0), b = a;
Matrix<float,Dynamic,1> vc2 = Matrix<float,Dynamic,1>::Random(cols);
if (1+r1-r0<rows) {
a.segment(1,r1-r0) += (m1.block(r0,c0, r1-r0, c1-c0) * vc2.segment(c0,c1-c0)).lazy();
b.segment(1,r1-r0) += (m1.block(r0,c0, r1-r0, c1-c0) * vc2.segment(c0,c1-c0)).eval();
VERIFY_IS_APPROX(a,b);
}
// CALL_SUBTEST( product_extra(MatrixXf(ei_random<int>(1,320), ei_random<int>(1,320))) );
// CALL_SUBTEST( product_extra(MatrixXd(ei_random<int>(1,320), ei_random<int>(1,320))) );
// CALL_SUBTEST( product(MatrixXi(ei_random<int>(1,320), ei_random<int>(1,320))) );
// CALL_SUBTEST( product_extra(MatrixXcf(ei_random<int>(50,50), ei_random<int>(50,50))) );
// CALL_SUBTEST( product(Matrix<float,Dynamic,Dynamic,RowMajor>(ei_random<int>(1,320), ei_random<int>(1,320))) );
CALL_SUBTEST( product_extra(MatrixXf(ei_random<int>(1,320), ei_random<int>(1,320))) );
CALL_SUBTEST( product_extra(MatrixXcf(ei_random<int>(50,50), ei_random<int>(50,50))) );
CALL_SUBTEST( product_extra(Matrix<std::complex<double>,Dynamic,Dynamic,RowMajor>(ei_random<int>(1,50), ei_random<int>(1,50))) );
}
}

54
test/triangular.cpp
View File

@ -1,7 +1,7 @@
// This file is triangularView 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
@ -81,44 +81,35 @@ template<typename MatrixType> void triangular(const MatrixType& m)
m1.template triangularView<Eigen::LowerTriangular>() = (m2.transpose() * m2).lazy();
VERIFY_IS_APPROX(m3.template triangularView<Eigen::LowerTriangular>().toDense(), m1);
// VERIFY_IS_APPROX(m3.template triangularView<DiagonalBits>(), m3.diagonal().asDiagonal());
m1 = MatrixType::Random(rows, cols);
for (int i=0; i<rows; ++i)
while (ei_abs2(m1(i,i))<1e-3) m1(i,i) = ei_random<Scalar>();
Transpose<MatrixType> trm4(m4);
// test back and forward subsitution
m3 = m1.template triangularView<Eigen::UpperTriangular>();
VERIFY(m2.isApprox(m3.adjoint() * (m1.adjoint().template triangularView<Eigen::LowerTriangular>().solve(m2)), largerEps));
m3 = m1.template triangularView<Eigen::LowerTriangular>();
// VERIFY(m3.template triangularView<Eigen::LowerTriangular>().solve(m3).cwise().abs().isIdentity(test_precision<RealScalar>()));
// VERIFY(m3.transpose().template triangularView<Eigen::UpperTriangular>()
// .solve(m3.transpose()).cwise().abs().isIdentity(test_precision<RealScalar>()));
VERIFY(m2.isApprox(m3.transpose() * (m1.transpose().template triangularView<Eigen::UpperTriangular>().solve(m2)), largerEps));
m3 = m1.template triangularView<Eigen::UpperTriangular>();
VERIFY(m2.isApprox(m3 * (m1.template triangularView<Eigen::UpperTriangular>().solve(m2)), largerEps));
m3 = m1.template triangularView<Eigen::LowerTriangular>();
VERIFY(m2.isApprox(m3.conjugate() * (m1.conjugate().template triangularView<Eigen::LowerTriangular>().solve(m2)), largerEps));
// check M * inv(L) using in place API
m4 = m3;
m3.transpose().template triangularView<Eigen::UpperTriangular>().solveInPlace(trm4);
// VERIFY(m4.cwise().abs().isIdentity(test_precision<RealScalar>()));
VERIFY(m4.cwise().abs().isIdentity(test_precision<RealScalar>()));
// m3 = m1.template triangularView<Eigen::UpperTriangular>();
// VERIFY(m3.template triangularView<Eigen::UpperTriangular>().solve(m3).cwise().abs().isIdentity(test_precision<RealScalar>()));
// VERIFY(m3.transpose().template triangularView<Eigen::LowerTriangular>()
// .solve(m3.transpose()).cwise().abs().isIdentity(test_precision<RealScalar>()));
// // check M * inv(U) using in place API
// check M * inv(U) using in place API
m3 = m1.template triangularView<Eigen::UpperTriangular>();
m4 = m3;
m3.transpose().template triangularView<Eigen::LowerTriangular>().solveInPlace(trm4);
VERIFY(m4.cwise().abs().isIdentity(test_precision<RealScalar>()));
// m3 = m1.template triangularView<Eigen::UpperTriangular>();
// VERIFY(m2.isApprox(m3 * (m3.template triangularView<Eigen::UpperTriangular>().solve(m2)), largerEps));
// m3 = m1.template triangularView<Eigen::LowerTriangular>();
// std::cerr << (m2 -
// (m3 * (m3.template triangularView<Eigen::LowerTriangular>().solve(m2)))).cwise().abs() /*.maxCoeff()*/ << "\n\n";
// VERIFY(m2.isApprox(m3 * (m3.template triangularView<Eigen::LowerTriangular>().solve(m2)), largerEps));
// check solve with unit diagonal
// m3 = m1.template triangularView<Eigen::UnitUpperTriangular>();
// VERIFY(m2.isApprox(m3 * (m1.template triangularView<Eigen::UnitUpperTriangular>().solve(m2)), largerEps));
m3 = m1.template triangularView<Eigen::UnitUpperTriangular>();
VERIFY(m2.isApprox(m3 * (m1.template triangularView<Eigen::UnitUpperTriangular>().solve(m2)), largerEps));
// VERIFY(( m1.template triangularView<Eigen::UpperTriangular>()
// * m2.template triangularView<Eigen::UpperTriangular>()).isUpperTriangular());
@ -136,17 +127,12 @@ template<typename MatrixType> void triangular(const MatrixType& m)
void test_triangular()
{
for(int i = 0; i < g_repeat ; i++) {
// CALL_SUBTEST( triangular(Matrix<float, 1, 1>()) );
// CALL_SUBTEST( triangular(Matrix<float, 2, 2>()) );
// CALL_SUBTEST( triangular(Matrix3d()) );
// CALL_SUBTEST( triangular(MatrixXcf(4, 4)) );
// CALL_SUBTEST( triangular(Matrix<std::complex<float>,8, 8>()) );
// CALL_SUBTEST( triangular(MatrixXd(1,1)) );
// CALL_SUBTEST( triangular(MatrixXd(2,2)) );
// CALL_SUBTEST( triangular(MatrixXd(3,3)) );
// CALL_SUBTEST( triangular(MatrixXd(5,5)) );
// CALL_SUBTEST( triangular(MatrixXd(8,8)) );
CALL_SUBTEST( triangular(Matrix<float, 1, 1>()) );
CALL_SUBTEST( triangular(Matrix<float, 2, 2>()) );
CALL_SUBTEST( triangular(Matrix3d()) );
CALL_SUBTEST( triangular(MatrixXcf(4, 4)) );
CALL_SUBTEST( triangular(Matrix<std::complex<float>,8, 8>()) );
CALL_SUBTEST( triangular(MatrixXd(17,17)) );
// CALL_SUBTEST( triangular(Matrix<float,Dynamic,Dynamic,RowMajor>(5, 5)) );
CALL_SUBTEST( triangular(Matrix<float,Dynamic,Dynamic,RowMajor>(5, 5)) );
}
}