c++矩陣運算庫Eigen

Sub-matrices

Read-write access to acolumnor arowof a matrix (or array):

mat1.row(i) = mat2.col(j);mat1.col(j1).swap(mat1.col(j2));

Read-write access to sub-vectors:

Default versions	Optimized versions when the sizeis known at compile time
vec1.head(n)	vec1.head<n>()	the firstncoeffs
vec1.tail(n)	vec1.tail<n>()	the lastncoeffs
vec1.segment(pos,n)	vec1.segment<n>(pos)	thencoeffs in therange [pos:pos+n- 1]
Read-write access to sub-matrices:
mat1.block(i,j,rows,cols)(more)	mat1.block<rows,cols>(i,j)(more)	therowsxcolssub-matrixstarting from position (i,j)
mat1.topLeftCorner(rows,cols)mat1.topRightCorner(rows,cols)mat1.bottomLeftCorner(rows,cols)mat1.bottomRightCorner(rows,cols)	mat1.topLeftCorner<rows,cols>()mat1.topRightCorner<rows,cols>()mat1.bottomLeftCorner<rows,cols>()mat1.bottomRightCorner<rows,cols>()	therowsxcolssub-matrixtaken in one of the four corners
mat1.topRows(rows)mat1.bottomRows(rows)mat1.leftCols(cols)mat1.rightCols(cols)	mat1.topRows<rows>()mat1.bottomRows<rows>()mat1.leftCols<cols>()mat1.rightCols<cols>()	specialized versions of block()when the block fit two corners

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Miscellaneous operationsReverse

Vectors, rows, and/or columns of a matrix can be reversed (seeDenseBase::reverse(),DenseBase::reverseInPlace(),VectorwiseOp::reverse()).

vec.reverse() mat.colwise().reverse() mat.rowwise().reverse()vec.reverseInPlace()Replicate

Vectors, matrices, rows, and/or columns can be replicated in any direction (seeDenseBase::replicate(),VectorwiseOp::replicate())

vec.replicate(times) vec.replicate<Times>mat.replicate(vertical_times, horizontal_times) mat.replicate<VerticalTimes, HorizontalTimes>()mat.colwise().replicate(vertical_times, horizontal_times) mat.colwise().replicate<VerticalTimes, HorizontalTimes>()mat.rowwise().replicate(vertical_times, horizontal_times) mat.rowwise().replicate<VerticalTimes, HorizontalTimes>()

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Diagonal, Triangular, and Self-adjoint matrices

(matrix world*)

Diagonal matrices

Operation	Code
view a vectoras a diagonal matrix	mat1 = vec1.asDiagonal();
Declare a diagonal matrix	DiagonalMatrix<Scalar,SizeAtCompileTime> diag1(size);diag1.diagonal() = vector;
Access thediagonalandsuper/sub diagonalsof a matrix as a vector (read/write)	vec1 = mat1.diagonal(); mat1.diagonal() = vec1; // main diagonalvec1 = mat1.diagonal(+n); mat1.diagonal(+n) = vec1; // n-th super diagonalvec1 = mat1.diagonal(-n); mat1.diagonal(-n) = vec1; // n-th sub diagonalvec1 = mat1.diagonal<1>(); mat1.diagonal<1>() = vec1; // first super diagonalvec1 = mat1.diagonal<-2>(); mat1.diagonal<-2>() = vec1; // second sub diagonal
Optimized products and inverse	mat3 = scalar * diag1 * mat1;mat3 += scalar * mat1 * vec1.asDiagonal();mat3 = vec1.asDiagonal().inverse() * mat1mat3 = mat1 * diag1.inverse()

Triangular views

TriangularViewgives a view on a triangular part of a dense matrix and allows to perform optimized operations on it. The opposite triangular part is never referenced and can be used to store other information.

Note

The .triangularView() template member function requires thetemplatekeyword if it is used on an object of a type that depends on a template parameter; seeThe template and typename keywords in C++for details.

Operation	Code
Reference to a triangular with optionalunit or null diagonal (read/write):	m.triangularView<Xxx>()Xxx=Upper,Lower,StrictlyUpper,StrictlyLower,UnitUpper,UnitLower
Writing to a specific triangular part:(only the referenced triangular part is evaluated)	m1.triangularView<Eigen::Lower>() = m2 + m3
Conversion to a dense matrix setting the opposite triangular part to zero:	m2 = m1.triangularView<Eigen::UnitUpper>()
Products:	m3 += s1 * m1.adjoint().triangularView<Eigen::UnitUpper>() * m2m3 -= s1 * m2.conjugate() * m1.adjoint().triangularView<Eigen::Lower>()
Solving linear equations:	L1.triangularView<Eigen::UnitLower>().solveInPlace(M2)L1.triangularView<Eigen::Lower>().adjoint().solveInPlace(M3)U1.triangularView<Eigen::Upper>().solveInPlace<OnTheRight>(M4)

Symmetric/selfadjoint views

Just as for triangular matrix, you can reference any triangular part of a square matrix to see it as a selfadjoint matrix and perform special and optimized operations. Again the opposite triangular part is never referenced and can be used to store other information.

Note

The .selfadjointView() template member function requires thetemplatekeyword if it is used on an object of a type that depends on a template parameter; seeThe template and typename keywords in C++for details.

Operation	Code
Conversion to a dense matrix:	m2 = m.selfadjointView<Eigen::Lower>();
Product with another general matrix or vector:	m3 = s1 * m1.conjugate().selfadjointView<Eigen::Upper>() * m3;m3 -= s1 * m3.adjoint() * m1.selfadjointView<Eigen::Lower>();
Rank 1 and rank K update:	M1.selfadjointView<Eigen::Upper>().rankUpdate(M2,s1);M1.selfadjointView<Eigen::Lower>().rankUpdate(M2.adjoint(),-1);
Rank 2 update: ()	M.selfadjointView<Eigen::Upper>().rankUpdate(u,v,s);
Solving linear equations:()	// via a standard Cholesky factorizationm2 = m1.selfadjointView<Eigen::Upper>().llt().solve(m2);// via a Cholesky factorization with pivotingm2 = m1.selfadjointView<Eigen::Lower>().ldlt().solve(m2);

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