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14 Commits
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d29654fb4e |
@@ -2,6 +2,7 @@
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#define EIGEN_SPARSECHOLESKY_MODULE_H
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#define EIGEN_SPARSECHOLESKY_MODULE_H
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#include "SparseCore"
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#include "SparseCore"
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#include "OrderingMethods"
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#include "src/Core/util/DisableStupidWarnings.h"
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#include "src/Core/util/DisableStupidWarnings.h"
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@@ -277,15 +277,13 @@ template<> struct ldlt_inplace<Lower>
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// are compared; if any diagonal is negligible compared
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// are compared; if any diagonal is negligible compared
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// to the largest overall, the algorithm bails.
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// to the largest overall, the algorithm bails.
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cutoff = abs(NumTraits<Scalar>::epsilon() * biggest_in_corner);
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cutoff = abs(NumTraits<Scalar>::epsilon() * biggest_in_corner);
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if(sign)
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*sign = real(mat.diagonal().coeff(index_of_biggest_in_corner)) > 0 ? 1 : -1;
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}
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}
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// Finish early if the matrix is not full rank.
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// Finish early if the matrix is not full rank.
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if(biggest_in_corner < cutoff)
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if(biggest_in_corner < cutoff)
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{
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{
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for(Index i = k; i < size; i++) transpositions.coeffRef(i) = i;
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for(Index i = k; i < size; i++) transpositions.coeffRef(i) = i;
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if(sign) *sign = 0;
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break;
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break;
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}
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}
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@@ -326,6 +324,16 @@ template<> struct ldlt_inplace<Lower>
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}
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}
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if((rs>0) && (abs(mat.coeffRef(k,k)) > cutoff))
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if((rs>0) && (abs(mat.coeffRef(k,k)) > cutoff))
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A21 /= mat.coeffRef(k,k);
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A21 /= mat.coeffRef(k,k);
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if(sign)
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{
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// LDLT is not guaranteed to work for indefinite matrices, but let's try to get the sign right
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int newSign = real(mat.diagonal().coeff(index_of_biggest_in_corner)) > 0;
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if(k == 0)
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*sign = newSign;
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else if(*sign != newSign)
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*sign = 0;
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}
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}
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}
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return true;
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return true;
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@@ -55,7 +55,7 @@ class ArrayWrapper : public ArrayBase<ArrayWrapper<ExpressionType> >
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inline Index outerStride() const { return m_expression.outerStride(); }
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inline Index outerStride() const { return m_expression.outerStride(); }
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inline Index innerStride() const { return m_expression.innerStride(); }
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inline Index innerStride() const { return m_expression.innerStride(); }
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inline ScalarWithConstIfNotLvalue* data() { return m_expression.data(); }
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inline ScalarWithConstIfNotLvalue* data() { return m_expression.const_cast_derived().data(); }
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inline const Scalar* data() const { return m_expression.data(); }
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inline const Scalar* data() const { return m_expression.data(); }
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inline CoeffReturnType coeff(Index row, Index col) const
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inline CoeffReturnType coeff(Index row, Index col) const
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@@ -175,7 +175,7 @@ class MatrixWrapper : public MatrixBase<MatrixWrapper<ExpressionType> >
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inline Index outerStride() const { return m_expression.outerStride(); }
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inline Index outerStride() const { return m_expression.outerStride(); }
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inline Index innerStride() const { return m_expression.innerStride(); }
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inline Index innerStride() const { return m_expression.innerStride(); }
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inline ScalarWithConstIfNotLvalue* data() { return m_expression.data(); }
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inline ScalarWithConstIfNotLvalue* data() { return m_expression.const_cast_derived().data(); }
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inline const Scalar* data() const { return m_expression.data(); }
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inline const Scalar* data() const { return m_expression.data(); }
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inline CoeffReturnType coeff(Index row, Index col) const
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inline CoeffReturnType coeff(Index row, Index col) const
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@@ -210,7 +210,7 @@ EIGEN_MKL_VML_DECLARE_UNARY_CALLS_LA(sqrt, Sqrt)
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EIGEN_MKL_VML_DECLARE_UNARY_CALLS_REAL(square, Sqr)
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EIGEN_MKL_VML_DECLARE_UNARY_CALLS_REAL(square, Sqr)
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// The vm*powx functions are not avaibale in the windows version of MKL.
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// The vm*powx functions are not avaibale in the windows version of MKL.
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#ifdef _WIN32
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#ifndef _WIN32
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EIGEN_MKL_VML_DECLARE_POW_CALL(pow, vmspowx_, float, float)
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EIGEN_MKL_VML_DECLARE_POW_CALL(pow, vmspowx_, float, float)
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EIGEN_MKL_VML_DECLARE_POW_CALL(pow, vmdpowx_, double, double)
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EIGEN_MKL_VML_DECLARE_POW_CALL(pow, vmdpowx_, double, double)
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EIGEN_MKL_VML_DECLARE_POW_CALL(pow, vmcpowx_, scomplex, MKL_Complex8)
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EIGEN_MKL_VML_DECLARE_POW_CALL(pow, vmcpowx_, scomplex, MKL_Complex8)
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@@ -56,8 +56,7 @@ template<typename ViewOp, typename MatrixType, typename StorageKind>
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class CwiseUnaryViewImpl;
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class CwiseUnaryViewImpl;
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template<typename ViewOp, typename MatrixType>
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template<typename ViewOp, typename MatrixType>
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class CwiseUnaryView : internal::no_assignment_operator,
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class CwiseUnaryView : public CwiseUnaryViewImpl<ViewOp, MatrixType, typename internal::traits<MatrixType>::StorageKind>
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public CwiseUnaryViewImpl<ViewOp, MatrixType, typename internal::traits<MatrixType>::StorageKind>
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{
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{
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public:
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public:
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@@ -99,6 +98,10 @@ class CwiseUnaryViewImpl<ViewOp,MatrixType,Dense>
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typedef typename internal::dense_xpr_base< CwiseUnaryView<ViewOp, MatrixType> >::type Base;
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typedef typename internal::dense_xpr_base< CwiseUnaryView<ViewOp, MatrixType> >::type Base;
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EIGEN_DENSE_PUBLIC_INTERFACE(Derived)
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EIGEN_DENSE_PUBLIC_INTERFACE(Derived)
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EIGEN_INHERIT_ASSIGNMENT_OPERATORS(CwiseUnaryViewImpl)
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inline Scalar* data() { return &coeffRef(0); }
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inline const Scalar* data() const { return &coeff(0); }
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inline Index innerStride() const
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inline Index innerStride() const
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{
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{
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@@ -104,6 +104,7 @@ template<typename MatrixType> class TransposeImpl<MatrixType,Dense>
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typedef typename internal::TransposeImpl_base<MatrixType>::type Base;
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typedef typename internal::TransposeImpl_base<MatrixType>::type Base;
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EIGEN_DENSE_PUBLIC_INTERFACE(Transpose<MatrixType>)
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EIGEN_DENSE_PUBLIC_INTERFACE(Transpose<MatrixType>)
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EIGEN_INHERIT_ASSIGNMENT_OPERATORS(TransposeImpl)
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inline Index innerStride() const { return derived().nestedExpression().innerStride(); }
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inline Index innerStride() const { return derived().nestedExpression().innerStride(); }
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inline Index outerStride() const { return derived().nestedExpression().outerStride(); }
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inline Index outerStride() const { return derived().nestedExpression().outerStride(); }
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@@ -252,7 +253,7 @@ struct inplace_transpose_selector;
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template<typename MatrixType>
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template<typename MatrixType>
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struct inplace_transpose_selector<MatrixType,true> { // square matrix
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struct inplace_transpose_selector<MatrixType,true> { // square matrix
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static void run(MatrixType& m) {
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static void run(MatrixType& m) {
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m.template triangularView<StrictlyUpper>().swap(m.transpose());
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m.matrix().template triangularView<StrictlyUpper>().swap(m.matrix().transpose());
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}
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}
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};
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};
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@@ -260,7 +261,7 @@ template<typename MatrixType>
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struct inplace_transpose_selector<MatrixType,false> { // non square matrix
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struct inplace_transpose_selector<MatrixType,false> { // non square matrix
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static void run(MatrixType& m) {
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static void run(MatrixType& m) {
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if (m.rows()==m.cols())
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if (m.rows()==m.cols())
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m.template triangularView<StrictlyUpper>().swap(m.transpose());
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m.matrix().template triangularView<StrictlyUpper>().swap(m.matrix().transpose());
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else
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else
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m = m.transpose().eval();
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m = m.transpose().eval();
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}
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}
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@@ -374,7 +374,7 @@ Packet4f psqrt<Packet4f>(const Packet4f& _x)
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Packet4f half = pmul(_x, pset1<Packet4f>(.5f));
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Packet4f half = pmul(_x, pset1<Packet4f>(.5f));
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/* select only the inverse sqrt of non-zero inputs */
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/* select only the inverse sqrt of non-zero inputs */
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Packet4f non_zero_mask = _mm_cmpgt_ps(_x, pset1<Packet4f>(std::numeric_limits<float>::epsilon()));
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Packet4f non_zero_mask = _mm_cmpgt_ps(_x, pset1<Packet4f>((std::numeric_limits<float>::min)()));
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Packet4f x = _mm_and_ps(non_zero_mask, _mm_rsqrt_ps(_x));
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Packet4f x = _mm_and_ps(non_zero_mask, _mm_rsqrt_ps(_x));
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x = pmul(x, psub(pset1<Packet4f>(1.5f), pmul(half, pmul(x,x))));
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x = pmul(x, psub(pset1<Packet4f>(1.5f), pmul(half, pmul(x,x))));
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@@ -13,7 +13,7 @@
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#define EIGEN_WORLD_VERSION 3
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#define EIGEN_WORLD_VERSION 3
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#define EIGEN_MAJOR_VERSION 1
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#define EIGEN_MAJOR_VERSION 1
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#define EIGEN_MINOR_VERSION 3
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#define EIGEN_MINOR_VERSION 4
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#define EIGEN_VERSION_AT_LEAST(x,y,z) (EIGEN_WORLD_VERSION>x || (EIGEN_WORLD_VERSION>=x && \
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#define EIGEN_VERSION_AT_LEAST(x,y,z) (EIGEN_WORLD_VERSION>x || (EIGEN_WORLD_VERSION>=x && \
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(EIGEN_MAJOR_VERSION>y || (EIGEN_MAJOR_VERSION>=y && \
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(EIGEN_MAJOR_VERSION>y || (EIGEN_MAJOR_VERSION>=y && \
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@@ -833,17 +833,13 @@ struct solve_retval<JacobiSVD<_MatrixType, QRPreconditioner>, Rhs>
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// A = U S V^*
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// A = U S V^*
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// So A^{-1} = V S^{-1} U^*
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// So A^{-1} = V S^{-1} U^*
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Matrix<Scalar, Dynamic, Rhs::ColsAtCompileTime, 0, _MatrixType::MaxRowsAtCompileTime, Rhs::MaxColsAtCompileTime> tmp;
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Index diagSize = (std::min)(dec().rows(), dec().cols());
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Index diagSize = (std::min)(dec().rows(), dec().cols());
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typename JacobiSVDType::SingularValuesType invertedSingVals(diagSize);
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Index nonzeroSingVals = dec().nonzeroSingularValues();
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Index nonzeroSingVals = dec().nonzeroSingularValues();
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invertedSingVals.head(nonzeroSingVals) = dec().singularValues().head(nonzeroSingVals).array().inverse();
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invertedSingVals.tail(diagSize - nonzeroSingVals).setZero();
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dst = dec().matrixV().leftCols(diagSize)
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tmp.noalias() = dec().matrixU().leftCols(nonzeroSingVals).adjoint() * rhs();
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* invertedSingVals.asDiagonal()
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tmp = dec().singularValues().head(nonzeroSingVals).asDiagonal().inverse() * tmp;
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* dec().matrixU().leftCols(diagSize).adjoint()
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dst = dec().matrixV().leftCols(nonzeroSingVals) * tmp;
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* rhs();
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}
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}
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};
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};
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} // end namespace internal
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} // end namespace internal
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@@ -98,8 +98,8 @@ Matrix3f a;
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MatrixXf b;
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MatrixXf b;
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\endcode
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\endcode
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Here,
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Here,
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\li \c a is a 3x3 matrix, with a static float[9] array of uninitialized coefficients,
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\li \c a is a 3-by-3 matrix, with a plain float[9] array of uninitialized coefficients,
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\li \c b is a dynamic-size matrix whose size is currently 0x0, and whose array of
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\li \c b is a dynamic-size matrix whose size is currently 0-by-0, and whose array of
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coefficients hasn't yet been allocated at all.
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coefficients hasn't yet been allocated at all.
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Constructors taking sizes are also available. For matrices, the number of rows is always passed first.
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Constructors taking sizes are also available. For matrices, the number of rows is always passed first.
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@@ -216,7 +216,7 @@ The simple answer is: use fixed
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sizes for very small sizes where you can, and use dynamic sizes for larger sizes or where you have to. For small sizes,
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sizes for very small sizes where you can, and use dynamic sizes for larger sizes or where you have to. For small sizes,
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especially for sizes smaller than (roughly) 16, using fixed sizes is hugely beneficial
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especially for sizes smaller than (roughly) 16, using fixed sizes is hugely beneficial
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to performance, as it allows Eigen to avoid dynamic memory allocation and to unroll
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to performance, as it allows Eigen to avoid dynamic memory allocation and to unroll
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loops. Internally, a fixed-size Eigen matrix is just a plain static array, i.e. doing
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loops. Internally, a fixed-size Eigen matrix is just a plain array, i.e. doing
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\code Matrix4f mymatrix; \endcode
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\code Matrix4f mymatrix; \endcode
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really amounts to just doing
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really amounts to just doing
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\code float mymatrix[16]; \endcode
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\code float mymatrix[16]; \endcode
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@@ -231,8 +231,9 @@ member variables.
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The limitation of using fixed sizes, of course, is that this is only possible
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The limitation of using fixed sizes, of course, is that this is only possible
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when you know the sizes at compile time. Also, for large enough sizes, say for sizes
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when you know the sizes at compile time. Also, for large enough sizes, say for sizes
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greater than (roughly) 32, the performance benefit of using fixed sizes becomes negligible.
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greater than (roughly) 32, the performance benefit of using fixed sizes becomes negligible.
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Worse, trying to create a very large matrix using fixed sizes could result in a stack overflow,
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Worse, trying to create a very large matrix using fixed sizes inside a function could result in a
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since Eigen will try to allocate the array as a static array, which by default goes on the stack.
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stack overflow, since Eigen will try to allocate the array automatically as a local variable, and
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this is normally done on the stack.
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Finally, depending on circumstances, Eigen can also be more aggressive trying to vectorize
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Finally, depending on circumstances, Eigen can also be more aggressive trying to vectorize
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(use SIMD instructions) when dynamic sizes are used, see \ref TopicVectorization "Vectorization".
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(use SIMD instructions) when dynamic sizes are used, see \ref TopicVectorization "Vectorization".
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@@ -130,7 +130,7 @@ Describing the \a buildProblem and \a save functions is out of the scope of this
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The SparseMatrix and SparseVector classes take three template arguments:
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The SparseMatrix and SparseVector classes take three template arguments:
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* the scalar type (e.g., double)
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* the scalar type (e.g., double)
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* the storage order (ColMajor or RowMajor, the default is RowMajor)
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* the storage order (ColMajor or RowMajor, the default is ColMajor)
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* the inner index type (default is \c int).
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* the inner index type (default is \c int).
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As for dense Matrix objects, constructors takes the size of the object.
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As for dense Matrix objects, constructors takes the size of the object.
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@@ -55,7 +55,7 @@ All combinations are allowed: you can have a matrix with a fixed number of rows
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Matrix<double, 6, Dynamic> // Dynamic number of columns (heap allocation)
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Matrix<double, 6, Dynamic> // Dynamic number of columns (heap allocation)
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Matrix<double, Dynamic, 2> // Dynamic number of rows (heap allocation)
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Matrix<double, Dynamic, 2> // Dynamic number of rows (heap allocation)
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Matrix<double, Dynamic, Dynamic, RowMajor> // Fully dynamic, row major (heap allocation)
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Matrix<double, Dynamic, Dynamic, RowMajor> // Fully dynamic, row major (heap allocation)
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Matrix<double, 13, 3> // Fully fixed (static allocation)
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Matrix<double, 13, 3> // Fully fixed (usually allocated on stack)
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\endcode
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\endcode
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In most cases, you can simply use one of the convenience typedefs for \ref matrixtypedefs "matrices" and \ref arraytypedefs "arrays". Some examples:
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In most cases, you can simply use one of the convenience typedefs for \ref matrixtypedefs "matrices" and \ref arraytypedefs "arrays". Some examples:
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Reference in New Issue
Block a user