Base class for all dense matrices, vectors, and arrays. More...
Public Types | |
enum | { RowsAtCompileTime, ColsAtCompileTime, SizeAtCompileTime, MaxRowsAtCompileTime, MaxColsAtCompileTime, MaxSizeAtCompileTime, IsVectorAtCompileTime, Flags, IsRowMajor , CoeffReadCost } |
typedef internal::traits < Derived >::Index | Index |
The type of indices. |
Public Member Functions | |
bool | all (void) const |
bool | any (void) const |
Block< Derived > | block (Index startRow, Index startCol, Index blockRows, Index blockCols) |
const Block< const Derived > | block (Index startRow, Index startCol, Index blockRows, Index blockCols) const |
template<int BlockRows, int BlockCols> | |
Block< Derived, BlockRows, BlockCols > | block (Index startRow, Index startCol) |
template<int BlockRows, int BlockCols> | |
const Block< const Derived, BlockRows, BlockCols > | block (Index startRow, Index startCol) const |
Block< Derived > | bottomLeftCorner (Index cRows, Index cCols) |
const Block< const Derived > | bottomLeftCorner (Index cRows, Index cCols) const |
template<int CRows, int CCols> | |
Block< Derived, CRows, CCols > | bottomLeftCorner () |
template<int CRows, int CCols> | |
const Block< const Derived, CRows, CCols > | bottomLeftCorner () const |
Block< Derived > | bottomRightCorner (Index cRows, Index cCols) |
const Block< const Derived > | bottomRightCorner (Index cRows, Index cCols) const |
template<int CRows, int CCols> | |
Block< Derived, CRows, CCols > | bottomRightCorner () |
template<int CRows, int CCols> | |
const Block< const Derived, CRows, CCols > | bottomRightCorner () const |
RowsBlockXpr | bottomRows (Index n) |
ConstRowsBlockXpr | bottomRows (Index n) const |
template<int N> | |
NRowsBlockXpr< N >::Type | bottomRows () |
template<int N> | |
ConstNRowsBlockXpr< N >::Type | bottomRows () const |
ColXpr | col (Index i) |
ConstColXpr | col (Index i) const |
ConstColwiseReturnType | colwise () const |
ColwiseReturnType | colwise () |
Index | count () const |
const internal::eval< Derived > ::type | eval () const |
void | fill (const Scalar &value) |
template<unsigned int Added, unsigned int Removed> | |
const Flagged< Derived, Added, Removed > | flagged () const |
const WithFormat< Derived > | format (const IOFormat &fmt) const |
SegmentReturnType | head (Index size) |
DenseBase::ConstSegmentReturnType | head (Index size) const |
template<int Size> | |
FixedSegmentReturnType< Size > ::Type | head () |
template<int Size> | |
ConstFixedSegmentReturnType < Size >::Type | head () const |
Index | innerSize () const |
template<typename OtherDerived > | |
bool | isApprox (const DenseBase< OtherDerived > &other, RealScalar prec=NumTraits< Scalar >::dummy_precision()) const |
bool | isApproxToConstant (const Scalar &value, RealScalar prec=NumTraits< Scalar >::dummy_precision()) const |
bool | isConstant (const Scalar &value, RealScalar prec=NumTraits< Scalar >::dummy_precision()) const |
template<typename Derived > | |
bool | isMuchSmallerThan (const typename NumTraits< Scalar >::Real &other, RealScalar prec) const |
template<typename OtherDerived > | |
bool | isMuchSmallerThan (const DenseBase< OtherDerived > &other, RealScalar prec=NumTraits< Scalar >::dummy_precision()) const |
bool | isOnes (RealScalar prec=NumTraits< Scalar >::dummy_precision()) const |
bool | isZero (RealScalar prec=NumTraits< Scalar >::dummy_precision()) const |
ColsBlockXpr | leftCols (Index n) |
ConstColsBlockXpr | leftCols (Index n) const |
template<int N> | |
NColsBlockXpr< N >::Type | leftCols () |
template<int N> | |
ConstNColsBlockXpr< N >::Type | leftCols () const |
internal::traits< Derived >::Scalar | maxCoeff () const |
template<typename IndexType > | |
internal::traits< Derived >::Scalar | maxCoeff (IndexType *row, IndexType *col) const |
template<typename IndexType > | |
internal::traits< Derived >::Scalar | maxCoeff (IndexType *index) const |
Scalar | mean () const |
ColsBlockXpr | middleCols (Index startCol, Index numCols) |
ConstColsBlockXpr | middleCols (Index startCol, Index numCols) const |
template<int N> | |
NColsBlockXpr< N >::Type | middleCols (Index startCol) |
template<int N> | |
ConstNColsBlockXpr< N >::Type | middleCols (Index startCol) const |
RowsBlockXpr | middleRows (Index startRow, Index numRows) |
ConstRowsBlockXpr | middleRows (Index startRow, Index numRows) const |
template<int N> | |
NRowsBlockXpr< N >::Type | middleRows (Index startRow) |
template<int N> | |
ConstNRowsBlockXpr< N >::Type | middleRows (Index startRow) const |
internal::traits< Derived >::Scalar | minCoeff () const |
template<typename IndexType > | |
internal::traits< Derived >::Scalar | minCoeff (IndexType *row, IndexType *col) const |
template<typename IndexType > | |
internal::traits< Derived >::Scalar | minCoeff (IndexType *index) const |
const NestByValue< Derived > | nestByValue () const |
Index | nonZeros () const |
CommaInitializer< Derived > | operator<< (const Scalar &s) |
template<typename OtherDerived > | |
CommaInitializer< Derived > | operator<< (const DenseBase< OtherDerived > &other) |
template<typename OtherDerived > | |
Derived & | operator= (const DenseBase< OtherDerived > &other) |
Derived & | operator= (const DenseBase &other) |
template<typename OtherDerived > | |
Derived & | operator= (const EigenBase< OtherDerived > &other) |
Copies the generic expression other into *this. | |
Index | outerSize () const |
Scalar | prod () const |
template<typename Func > | |
internal::result_of< Func(typename internal::traits< Derived > ::Scalar)>::type | redux (const Func &func) const |
template<int RowFactor, int ColFactor> | |
const Replicate< Derived, RowFactor, ColFactor > | replicate () const |
const Replicate< Derived, Dynamic, Dynamic > | replicate (Index rowFacor, Index colFactor) const |
void | resize (Index size) |
void | resize (Index rows, Index cols) |
ReverseReturnType | reverse () |
ConstReverseReturnType | reverse () const |
void | reverseInPlace () |
ColsBlockXpr | rightCols (Index n) |
ConstColsBlockXpr | rightCols (Index n) const |
template<int N> | |
NColsBlockXpr< N >::Type | rightCols () |
template<int N> | |
ConstNColsBlockXpr< N >::Type | rightCols () const |
RowXpr | row (Index i) |
ConstRowXpr | row (Index i) const |
ConstRowwiseReturnType | rowwise () const |
RowwiseReturnType | rowwise () |
SegmentReturnType | segment (Index start, Index size) |
DenseBase::ConstSegmentReturnType | segment (Index start, Index size) const |
template<int Size> | |
FixedSegmentReturnType< Size > ::Type | segment (Index start) |
template<int Size> | |
ConstFixedSegmentReturnType < Size >::Type | segment (Index start) const |
template<typename ThenDerived , typename ElseDerived > | |
const Select< Derived, ThenDerived, ElseDerived > | select (const DenseBase< ThenDerived > &thenMatrix, const DenseBase< ElseDerived > &elseMatrix) const |
template<typename ThenDerived > | |
const Select< Derived, ThenDerived, typename ThenDerived::ConstantReturnType > | select (const DenseBase< ThenDerived > &thenMatrix, typename ThenDerived::Scalar elseScalar) const |
template<typename ElseDerived > | |
const Select< Derived, typename ElseDerived::ConstantReturnType, ElseDerived > | select (typename ElseDerived::Scalar thenScalar, const DenseBase< ElseDerived > &elseMatrix) const |
Derived & | setConstant (const Scalar &value) |
Derived & | setLinSpaced (Index size, const Scalar &low, const Scalar &high) |
Sets a linearly space vector. | |
Derived & | setOnes () |
Derived & | setRandom () |
Derived & | setZero () |
Scalar | sum () const |
template<typename OtherDerived > | |
void | swap (const DenseBase< OtherDerived > &other, int=OtherDerived::ThisConstantIsPrivateInPlainObjectBase) |
template<typename OtherDerived > | |
void | swap (PlainObjectBase< OtherDerived > &other) |
SegmentReturnType | tail (Index size) |
DenseBase::ConstSegmentReturnType | tail (Index size) const |
template<int Size> | |
FixedSegmentReturnType< Size > ::Type | tail () |
template<int Size> | |
ConstFixedSegmentReturnType < Size >::Type | tail () const |
Block< Derived > | topLeftCorner (Index cRows, Index cCols) |
const Block< const Derived > | topLeftCorner (Index cRows, Index cCols) const |
template<int CRows, int CCols> | |
Block< Derived, CRows, CCols > | topLeftCorner () |
template<int CRows, int CCols> | |
const Block< const Derived, CRows, CCols > | topLeftCorner () const |
Block< Derived > | topRightCorner (Index cRows, Index cCols) |
const Block< const Derived > | topRightCorner (Index cRows, Index cCols) const |
template<int CRows, int CCols> | |
Block< Derived, CRows, CCols > | topRightCorner () |
template<int CRows, int CCols> | |
const Block< const Derived, CRows, CCols > | topRightCorner () const |
RowsBlockXpr | topRows (Index n) |
ConstRowsBlockXpr | topRows (Index n) const |
template<int N> | |
NRowsBlockXpr< N >::Type | topRows () |
template<int N> | |
ConstNRowsBlockXpr< N >::Type | topRows () const |
Eigen::Transpose< Derived > | transpose () |
ConstTransposeReturnType | transpose () const |
void | transposeInPlace () |
CoeffReturnType | value () const |
template<typename Visitor > | |
void | visit (Visitor &func) const |
Static Public Member Functions | |
static const ConstantReturnType | Constant (Index rows, Index cols, const Scalar &value) |
static const ConstantReturnType | Constant (Index size, const Scalar &value) |
static const ConstantReturnType | Constant (const Scalar &value) |
static const SequentialLinSpacedReturnType | LinSpaced (Sequential_t, Index size, const Scalar &low, const Scalar &high) |
Sets a linearly space vector. | |
static const RandomAccessLinSpacedReturnType | LinSpaced (Index size, const Scalar &low, const Scalar &high) |
Sets a linearly space vector. | |
static const SequentialLinSpacedReturnType | LinSpaced (Sequential_t, const Scalar &low, const Scalar &high) |
Sets a linearly space vector. | |
static const RandomAccessLinSpacedReturnType | LinSpaced (const Scalar &low, const Scalar &high) |
Sets a linearly space vector. | |
template<typename CustomNullaryOp > | |
static const CwiseNullaryOp < CustomNullaryOp, Derived > | NullaryExpr (Index rows, Index cols, const CustomNullaryOp &func) |
template<typename CustomNullaryOp > | |
static const CwiseNullaryOp < CustomNullaryOp, Derived > | NullaryExpr (Index size, const CustomNullaryOp &func) |
template<typename CustomNullaryOp > | |
static const CwiseNullaryOp < CustomNullaryOp, Derived > | NullaryExpr (const CustomNullaryOp &func) |
static const ConstantReturnType | Ones (Index rows, Index cols) |
static const ConstantReturnType | Ones (Index size) |
static const ConstantReturnType | Ones () |
static const CwiseNullaryOp < internal::scalar_random_op < Scalar >, Derived > | Random (Index rows, Index cols) |
static const CwiseNullaryOp < internal::scalar_random_op < Scalar >, Derived > | Random (Index size) |
static const CwiseNullaryOp < internal::scalar_random_op < Scalar >, Derived > | Random () |
static const ConstantReturnType | Zero (Index rows, Index cols) |
static const ConstantReturnType | Zero (Index size) |
static const ConstantReturnType | Zero () |
Protected Member Functions | |
DenseBase () |
Related Functions | |
(Note that these are not member functions.) | |
template<typename Derived > | |
std::ostream & | operator<< (std::ostream &s, const DenseBase< Derived > &m) |
Base class for all dense matrices, vectors, and arrays.
This class is the base that is inherited by all dense objects (matrix, vector, arrays, and related expression types). The common Eigen API for dense objects is contained in this class.
Derived | is the derived type, e.g., a matrix type or an expression. |
This class can be extended with the help of the plugin mechanism described on the page Customizing/Extending Eigen by defining the preprocessor symbol EIGEN_DENSEBASE_PLUGIN
.
The type of indices.
To change this, #define
the preprocessor symbol EIGEN_DEFAULT_DENSE_INDEX_TYPE
.
anonymous enum |
RowsAtCompileTime |
The number of rows at compile-time. This is just a copy of the value provided by the Derived type. If a value is not known at compile-time, it is set to the Dynamic constant.
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ColsAtCompileTime |
The number of columns at compile-time. This is just a copy of the value provided by the Derived type. If a value is not known at compile-time, it is set to the Dynamic constant.
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SizeAtCompileTime |
This is equal to the number of coefficients, i.e. the number of rows times the number of columns, or to Dynamic if this is not known at compile-time.
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MaxRowsAtCompileTime |
This value is equal to the maximum possible number of rows that this expression might have. If this expression might have an arbitrarily high number of rows, this value is set to Dynamic. This value is useful to know when evaluating an expression, in order to determine whether it is possible to avoid doing a dynamic memory allocation. |
MaxColsAtCompileTime |
This value is equal to the maximum possible number of columns that this expression might have. If this expression might have an arbitrarily high number of columns, this value is set to Dynamic. This value is useful to know when evaluating an expression, in order to determine whether it is possible to avoid doing a dynamic memory allocation. |
MaxSizeAtCompileTime |
This value is equal to the maximum possible number of coefficients that this expression might have. If this expression might have an arbitrarily high number of coefficients, this value is set to Dynamic. This value is useful to know when evaluating an expression, in order to determine whether it is possible to avoid doing a dynamic memory allocation. |
IsVectorAtCompileTime |
This is set to true if either the number of rows or the number of columns is known at compile-time to be equal to 1. Indeed, in that case, we are dealing with a column-vector (if there is only one column) or with a row-vector (if there is only one row). |
Flags |
This stores expression Flags flags which may or may not be inherited by new expressions constructed from this one. See the list of flags. |
IsRowMajor |
True if this expression has row-major storage order. |
CoeffReadCost |
This is a rough measure of how expensive it is to read one coefficient from this expression. |
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inlineprotected |
Default constructor. Do nothing.
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inline |
Example:
Output:
Is ( 0.68 -0.211 0.566) inside the box: 0 Is (0.597 0.823 0.605) inside the box: 1
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inline |
startRow | the first row in the block |
startCol | the first column in the block |
blockRows | the number of rows in the block |
blockCols | the number of columns in the block |
Example:
Output:
Here is the matrix m: 7 9 -5 -3 -2 -6 1 0 6 -3 0 9 6 6 3 9 Here is m.block(1, 1, 2, 2): -6 1 -3 0 Now the matrix m is: 7 9 -5 -3 -2 0 0 0 6 0 0 9 6 6 3 9
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This is the const version of block(Index,Index,Index,Index).
The template parameters BlockRows and BlockCols are the number of rows and columns in the block.
startRow | the first row in the block |
startCol | the first column in the block |
Example:
Output:
Here is the matrix m: 7 9 -5 -3 -2 -6 1 0 6 -3 0 9 6 6 3 9 Here is m.block<2,2>(1,1): -6 1 -3 0 Now the matrix m is: 7 9 -5 -3 -2 0 0 0 6 0 0 9 6 6 3 9
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This is the const version of block<>(Index, Index).
cRows | the number of rows in the corner |
cCols | the number of columns in the corner |
Example:
Output:
Here is the matrix m: 7 9 -5 -3 -2 -6 1 0 6 -3 0 9 6 6 3 9 Here is m.bottomLeftCorner(2, 2): 6 -3 6 6 Now the matrix m is: 7 9 -5 -3 -2 -6 1 0 0 0 0 9 0 0 3 9
This is the const version of bottomLeftCorner(Index, Index).
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The template parameters CRows and CCols are the number of rows and columns in the corner.
Example:
Output:
Here is the matrix m: 7 9 -5 -3 -2 -6 1 0 6 -3 0 9 6 6 3 9 Here is m.bottomLeftCorner<2,2>(): 6 -3 6 6 Now the matrix m is: 7 9 -5 -3 -2 -6 1 0 0 0 0 9 0 0 3 9
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This is the const version of bottomLeftCorner<int, int>().
cRows | the number of rows in the corner |
cCols | the number of columns in the corner |
Example:
Output:
Here is the matrix m: 7 9 -5 -3 -2 -6 1 0 6 -3 0 9 6 6 3 9 Here is m.bottomRightCorner(2, 2): 0 9 3 9 Now the matrix m is: 7 9 -5 -3 -2 -6 1 0 6 -3 0 0 6 6 0 0
This is the const version of bottomRightCorner(Index, Index).
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The template parameters CRows and CCols are the number of rows and columns in the corner.
Example:
Output:
Here is the matrix m: 7 9 -5 -3 -2 -6 1 0 6 -3 0 9 6 6 3 9 Here is m.bottomRightCorner<2,2>(): 0 9 3 9 Now the matrix m is: 7 9 -5 -3 -2 -6 1 0 6 -3 0 0 6 6 0 0
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This is the const version of bottomRightCorner<int, int>().
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n | the number of rows in the block |
Example:
Output:
Here is the array a: 7 9 -5 -3 -2 -6 1 0 6 -3 0 9 6 6 3 9 Here is a.bottomRows(2): 6 -3 0 9 6 6 3 9 Now the array a is: 7 9 -5 -3 -2 -6 1 0 0 0 0 0 0 0 0 0
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This is the const version of bottomRows(Index).
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N | the number of rows in the block |
Example:
Output:
Here is the array a: 7 9 -5 -3 -2 -6 1 0 6 -3 0 9 6 6 3 9 Here is a.bottomRows<2>(): 6 -3 0 9 6 6 3 9 Now the array a is: 7 9 -5 -3 -2 -6 1 0 0 0 0 0 0 0 0 0
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This is the const version of bottomRows<int>().
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Example:
Output:
Here is the matrix m: 0.68 0.597 -0.33 -0.211 0.823 0.536 0.566 -0.605 -0.444 Here is the sum of each column: 1.04 0.815 -0.238 Here is the maximum absolute value of each column: 0.68 0.823 0.536
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inlinestatic |
The parameters rows and cols are the number of rows and of columns of the returned matrix. Must be compatible with this DenseBase type.
This variant is meant to be used for dynamic-size matrix types. For fixed-size types, it is redundant to pass rows and cols as arguments, so Zero() should be used instead.
The template parameter CustomNullaryOp is the type of the functor.
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inlinestatic |
The parameter size is the size of the returned vector. Must be compatible with this DenseBase type.
This is only for vectors (either row-vectors or column-vectors), i.e. matrices which are known at compile-time to have either one row or one column.
This variant is meant to be used for dynamic-size vector types. For fixed-size types, it is redundant to pass size as argument, so Zero() should be used instead.
The template parameter CustomNullaryOp is the type of the functor.
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inlinestatic |
This variant is only for fixed-size DenseBase types. For dynamic-size types, you need to use the variants taking size arguments.
The template parameter CustomNullaryOp is the type of the functor.
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inline |
Notice that in the case of a plain matrix or vector (not an expression) this function just returns a const reference, in order to avoid a useless copy.
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Alias for setConstant(): sets all coefficients in this expression to value.
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inline |
This is mostly for internal use.
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inline |
See class IOFormat for some examples.
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inline |
This is only for vectors (either row-vectors or column-vectors), i.e. matrices which are known at compile-time to have either one row or one column.
size | the number of coefficients in the block |
Example:
Output:
Here is the vector v: 7 -2 6 6 Here is v.head(2): 7 -2 Now the vector v is: 0 0 6 6
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This is the const version of head(Index).
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This is only for vectors (either row-vectors or column-vectors), i.e. matrices which are known at compile-time to have either one row or one column.
The template parameter Size is the number of coefficients in the block
Example:
Output:
Here is the vector v: 7 -2 6 6 Here is v.head(2): 7 -2 Now the vector v is: 0 0 6 6
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This is the const version of head<int>().
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bool isApprox | ( | const DenseBase< OtherDerived > & | other, |
RealScalar | prec = NumTraits<Scalar>::dummy_precision() |
||
) | const |
true
if *this
is approximately equal to other, within the precision determined by prec.
*this
is approximately equal to the zero matrix or vector. Indeed, isApprox(zero)
returns false unless *this
itself is exactly the zero matrix or vector. If you want to test whether *this
is zero, use internal::isMuchSmallerThan(const RealScalar&, RealScalar) instead.bool isApproxToConstant | ( | const Scalar & | value, |
RealScalar | prec = NumTraits<Scalar>::dummy_precision() |
||
) | const |
bool isConstant | ( | const Scalar & | value, |
RealScalar | prec = NumTraits<Scalar>::dummy_precision() |
||
) | const |
This is just an alias for isApproxToConstant().
bool isMuchSmallerThan | ( | const typename NumTraits< Scalar >::Real & | other, |
RealScalar | prec | ||
) | const |
true
if the norm of *this
is much smaller than other, within the precision determined by prec.
For matrices, the comparison is done using the Hilbert-Schmidt norm. For this reason, the value of the reference scalar other should come from the Hilbert-Schmidt norm of a reference matrix of same dimensions.
bool isMuchSmallerThan | ( | const DenseBase< OtherDerived > & | other, |
RealScalar | prec = NumTraits<Scalar>::dummy_precision() |
||
) | const |
true
if the norm of *this
is much smaller than the norm of other, within the precision determined by prec.
bool isOnes | ( | RealScalar | prec = NumTraits<Scalar>::dummy_precision() | ) | const |
Example:
Output:
Here's the matrix m: 1 1 1 1 1 1 1 1 1 m.isOnes() returns: 0 m.isOnes(1e-3) returns: 1
bool isZero | ( | RealScalar | prec = NumTraits<Scalar>::dummy_precision() | ) | const |
Example:
Output:
Here's the matrix m: 0 0 0.0001 0 0 0 0 0 0 m.isZero() returns: 0 m.isZero(1e-3) returns: 1
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inline |
n | the number of columns in the block |
Example:
Output:
Here is the array a: 7 9 -5 -3 -2 -6 1 0 6 -3 0 9 6 6 3 9 Here is a.leftCols(2): 7 9 -2 -6 6 -3 6 6 Now the array a is: 0 0 -5 -3 0 0 1 0 0 0 0 9 0 0 3 9
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This is the const version of leftCols(Index).
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N | the number of columns in the block |
Example:
Output:
Here is the array a: 7 9 -5 -3 -2 -6 1 0 6 -3 0 9 6 6 3 9 Here is a.leftCols<2>(): 7 9 -2 -6 6 -3 6 6 Now the array a is: 0 0 -5 -3 0 0 1 0 0 0 0 9 0 0 3 9
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inline |
This is the const version of leftCols<int>().
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inlinestatic |
Sets a linearly space vector.
The function generates 'size' equally spaced values in the closed interval [low,high]. This particular version of LinSpaced() uses sequential access, i.e. vector access is assumed to be a(0), a(1), ..., a(size). This assumption allows for better vectorization and yields faster code than the random access version.
This is only for vectors (either row-vectors or column-vectors), i.e. matrices which are known at compile-time to have either one row or one column.
Example:
Output:
7 8 9 10 0 0.25 0.5 0.75 1
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inlinestatic |
Sets a linearly space vector.
The function generates 'size' equally spaced values in the closed interval [low,high].
This is only for vectors (either row-vectors or column-vectors), i.e. matrices which are known at compile-time to have either one row or one column.
Example:
Output:
7 8 9 10 0 0.25 0.5 0.75 1
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inlinestatic |
Sets a linearly space vector.
The function generates 'size' equally spaced values in the closed interval [low,high]. This particular version of LinSpaced() uses sequential access, i.e. vector access is assumed to be a(0), a(1), ..., a(size). This assumption allows for better vectorization and yields faster code than the random access version.This is only for vectors (either row-vectors or column-vectors), i.e. matrices which are known at compile-time to have either one row or one column.Example:
Output:
7 8 9 10 0 0.25 0.5 0.75 1
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inlinestatic |
Sets a linearly space vector.
The function generates 'size' equally spaced values in the closed interval [low,high].This is only for vectors (either row-vectors or column-vectors), i.e. matrices which are known at compile-time to have either one row or one column.Example:
Output:
7 8 9 10 0 0.25 0.5 0.75 1
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inline |
internal::traits< Derived >::Scalar maxCoeff | ( | IndexType * | row, |
IndexType * | col | ||
) | const |
internal::traits< Derived >::Scalar maxCoeff | ( | IndexType * | index | ) | const |
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inline |
startCol | the index of the first column in the block |
numCols | the number of columns in the block |
Example:
Output:
A = 7 -6 0 9 -10 -2 -3 3 3 -5 6 6 -3 5 -8 6 -5 0 -8 6 9 1 9 2 -7 A(1..3,:) = -6 0 9 -3 3 3 6 -3 5 -5 0 -8 1 9 2
This is the const version of middleCols(Index,Index).
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inline |
N | the number of columns in the block |
startCol | the index of the first column in the block |
Example:
Output:
A = 7 -6 0 9 -10 -2 -3 3 3 -5 6 6 -3 5 -8 6 -5 0 -8 6 9 1 9 2 -7 A(:,1..3) = -6 0 9 -3 3 3 6 -3 5 -5 0 -8 1 9 2
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inline |
This is the const version of middleCols<int>().
startRow | the index of the first row in the block |
numRows | the number of rows in the block |
Example:
Output:
A = 7 -6 0 9 -10 -2 -3 3 3 -5 6 6 -3 5 -8 6 -5 0 -8 6 9 1 9 2 -7 A(2..3,:) = 6 6 -3 5 -8 6 -5 0 -8 6
This is the const version of middleRows(Index,Index).
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N | the number of rows in the block |
startRow | the index of the first row in the block |
Example:
Output:
A = 7 -6 0 9 -10 -2 -3 3 3 -5 6 6 -3 5 -8 6 -5 0 -8 6 9 1 9 2 -7 A(1..3,:) = -2 -3 3 3 -5 6 6 -3 5 -8 6 -5 0 -8 6
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This is the const version of middleRows<int>().
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internal::traits< Derived >::Scalar minCoeff | ( | IndexType * | row, |
IndexType * | col | ||
) | const |
internal::traits< Derived >::Scalar minCoeff | ( | IndexType * | index | ) | const |
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inline |
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inline |
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inlinestatic |
The parameters rows and cols are the number of rows and of columns of the returned matrix. Must be compatible with this MatrixBase type.
This variant is meant to be used for dynamic-size matrix types. For fixed-size types, it is redundant to pass rows and cols as arguments, so Zero() should be used instead.
The template parameter CustomNullaryOp is the type of the functor.
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The parameter size is the size of the returned vector. Must be compatible with this MatrixBase type.
This is only for vectors (either row-vectors or column-vectors), i.e. matrices which are known at compile-time to have either one row or one column.
This variant is meant to be used for dynamic-size vector types. For fixed-size types, it is redundant to pass size as argument, so Zero() should be used instead.
The template parameter CustomNullaryOp is the type of the functor.
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This variant is only for fixed-size DenseBase types. For dynamic-size types, you need to use the variants taking size arguments.
The template parameter CustomNullaryOp is the type of the functor.
The parameters rows and cols are the number of rows and of columns of the returned matrix. Must be compatible with this MatrixBase type.
This variant is meant to be used for dynamic-size matrix types. For fixed-size types, it is redundant to pass rows and cols as arguments, so Ones() should be used instead.
Example:
Output:
1 1 1 1 1 1
The parameter size is the size of the returned vector. Must be compatible with this MatrixBase type.
This is only for vectors (either row-vectors or column-vectors), i.e. matrices which are known at compile-time to have either one row or one column.
This variant is meant to be used for dynamic-size vector types. For fixed-size types, it is redundant to pass size as argument, so Ones() should be used instead.
Example:
Output:
6 6 6 6 1 1
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This variant is only for fixed-size MatrixBase types. For dynamic-size types, you need to use the variants taking size arguments.
Example:
Output:
1 1 1 1 6 6 6 6
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Convenient operator to set the coefficients of a matrix.
The coefficients must be provided in a row major order and exactly match the size of the matrix. Otherwise an assertion is raised.
Example:
Output:
1 2 3 4 5 6 7 8 9 10 11 0 12 13 0 0 0 1 14 15 16 14 5 6 15 8 9
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Derived& operator= | ( | const DenseBase< OtherDerived > & | other | ) |
Copies other into *this.
Reimplemented in MatrixBase< Derived >, MatrixBase< TriangularProduct< Mode, false, Lhs, true, Rhs, false > >, MatrixBase< DenseTimeSparseSelfAdjointProduct< Lhs, Rhs, UpLo > >, MatrixBase< ScaledProduct< NestedProduct > >, MatrixBase< SelfadjointProductMatrix< Lhs, LhsMode, false, Rhs, 0, true > >, MatrixBase< MatrixWrapper< ExpressionType > >, MatrixBase< SparseSelfAdjointTimeDenseProduct< Lhs, Rhs, UpLo > >, MatrixBase< GeneralProduct< Lhs, Rhs, OuterProduct > >, MatrixBase< Flagged< ExpressionType, Added, Removed > >, MatrixBase< SelfadjointProductMatrix< Lhs, LhsMode, false, Rhs, RhsMode, false > >, MatrixBase< GeneralProduct< Lhs, Rhs, GemmProduct > >, MatrixBase< TriangularProduct< Mode, LhsIsTriangular, Lhs, false, Rhs, false > >, MatrixBase< SelfadjointProductMatrix< Lhs, 0, true, Rhs, RhsMode, false > >, MatrixBase< Homogeneous< MatrixType, _Direction > >, MatrixBase< SparseTimeDenseProduct< Lhs, Rhs > >, MatrixBase< DenseTimeSparseProduct< Lhs, Rhs > >, MatrixBase< CoeffBasedProduct< LhsNested, RhsNested, NestingFlags > >, MatrixBase< Minor< MatrixType > >, MatrixBase< GeneralProduct< Lhs, Rhs, GemvProduct > >, MatrixBase< DiagonalProduct< MatrixType, DiagonalType, ProductOrder > >, and MatrixBase< TriangularProduct< Mode, true, Lhs, false, Rhs, true > >.
Derived& operator= | ( | const DenseBase< Derived > & | other | ) |
Special case of the template operator=, in order to prevent the compiler from generating a default operator= (issue hit with g++ 4.1)
Derived & operator= | ( | const EigenBase< OtherDerived > & | other | ) |
Copies the generic expression other into *this.
The expression must provide a (templated) evalTo(Derived& dst) const function which does the actual job. In practice, this allows any user to write its own special matrix without having to modify MatrixBase
Reimplemented in MatrixBase< Derived >, MatrixBase< TriangularProduct< Mode, false, Lhs, true, Rhs, false > >, MatrixBase< DenseTimeSparseSelfAdjointProduct< Lhs, Rhs, UpLo > >, MatrixBase< ScaledProduct< NestedProduct > >, MatrixBase< SelfadjointProductMatrix< Lhs, LhsMode, false, Rhs, 0, true > >, MatrixBase< MatrixWrapper< ExpressionType > >, MatrixBase< SparseSelfAdjointTimeDenseProduct< Lhs, Rhs, UpLo > >, MatrixBase< GeneralProduct< Lhs, Rhs, OuterProduct > >, MatrixBase< Flagged< ExpressionType, Added, Removed > >, MatrixBase< SelfadjointProductMatrix< Lhs, LhsMode, false, Rhs, RhsMode, false > >, MatrixBase< GeneralProduct< Lhs, Rhs, GemmProduct > >, MatrixBase< TriangularProduct< Mode, LhsIsTriangular, Lhs, false, Rhs, false > >, MatrixBase< SelfadjointProductMatrix< Lhs, 0, true, Rhs, RhsMode, false > >, MatrixBase< Homogeneous< MatrixType, _Direction > >, MatrixBase< SparseTimeDenseProduct< Lhs, Rhs > >, MatrixBase< DenseTimeSparseProduct< Lhs, Rhs > >, MatrixBase< CoeffBasedProduct< LhsNested, RhsNested, NestingFlags > >, MatrixBase< Minor< MatrixType > >, MatrixBase< GeneralProduct< Lhs, Rhs, GemvProduct > >, MatrixBase< DiagonalProduct< MatrixType, DiagonalType, ProductOrder > >, and MatrixBase< TriangularProduct< Mode, true, Lhs, false, Rhs, true > >.
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Example:
Output:
Here is the matrix m: 0.68 0.597 -0.33 -0.211 0.823 0.536 0.566 -0.605 -0.444 Here is the product of all the coefficients: 0.0019
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inlinestatic |
The parameters rows and cols are the number of rows and of columns of the returned matrix. Must be compatible with this MatrixBase type.
This variant is meant to be used for dynamic-size matrix types. For fixed-size types, it is redundant to pass rows and cols as arguments, so Random() should be used instead.
Example:
Output:
7 6 9 -2 6 -6
This expression has the "evaluate before nesting" flag so that it will be evaluated into a temporary matrix whenever it is nested in a larger expression. This prevents unexpected behavior with expressions involving random matrices.
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inlinestatic |
The parameter size is the size of the returned vector. Must be compatible with this MatrixBase type.
This is only for vectors (either row-vectors or column-vectors), i.e. matrices which are known at compile-time to have either one row or one column.
This variant is meant to be used for dynamic-size vector types. For fixed-size types, it is redundant to pass size as argument, so Random() should be used instead.
Example:
Output:
7 -2
This expression has the "evaluate before nesting" flag so that it will be evaluated into a temporary vector whenever it is nested in a larger expression. This prevents unexpected behavior with expressions involving random matrices.
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inlinestatic |
This variant is only for fixed-size MatrixBase types. For dynamic-size types, you need to use the variants taking size arguments.
Example:
Output:
700 600 -200 600
This expression has the "evaluate before nesting" flag so that it will be evaluated into a temporary matrix whenever it is nested in a larger expression. This prevents unexpected behavior with expressions involving random matrices.
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The template parameter BinaryOp is the type of the functor func which must be an associative operator. Both current STL and TR1 functor styles are handled.
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*this
Example:
Output:
Here is the matrix m: 7 6 9 -2 6 -6 m.replicate<3,2>() = ... 7 6 9 7 6 9 -2 6 -6 -2 6 -6 7 6 9 7 6 9 -2 6 -6 -2 6 -6 7 6 9 7 6 9 -2 6 -6 -2 6 -6
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*this
Example:
Output:
Here is the vector v: 7 -2 6 v.replicate(2,5) = ... 7 7 7 7 7 -2 -2 -2 -2 -2 6 6 6 6 6 7 7 7 7 7 -2 -2 -2 -2 -2 6 6 6 6 6
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Only plain matrices/arrays, not expressions, may be resized; therefore the only useful resize methods are Matrix::resize() and Array::resize(). The present method only asserts that the new size equals the old size, and does nothing else.
Only plain matrices/arrays, not expressions, may be resized; therefore the only useful resize methods are Matrix::resize() and Array::resize(). The present method only asserts that the new size equals the old size, and does nothing else.
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Example:
Output:
Here is the matrix m: 7 6 -3 1 -2 9 6 0 6 -6 -5 3 Here is the reverse of m: 3 -5 -6 6 0 6 9 -2 1 -3 6 7 Here is the coefficient (1,0) in the reverse of m: 0 Let us overwrite this coefficient with the value 4. Now the matrix m is: 7 6 -3 1 -2 9 6 4 6 -6 -5 3
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This is the const version of reverse().
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This is the "in place" version of reverse: it reverses *this
.
In most cases it is probably better to simply use the reversed expression of a matrix. However, when reversing the matrix data itself is really needed, then this "in-place" version is probably the right choice because it provides the following additional features:
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n | the number of columns in the block |
Example:
Output:
Here is the array a: 7 9 -5 -3 -2 -6 1 0 6 -3 0 9 6 6 3 9 Here is a.rightCols(2): -5 -3 1 0 0 9 3 9 Now the array a is: 7 9 0 0 -2 -6 0 0 6 -3 0 0 6 6 0 0
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This is the const version of rightCols(Index).
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N | the number of columns in the block |
Example:
Output:
Here is the array a: 7 9 -5 -3 -2 -6 1 0 6 -3 0 9 6 6 3 9 Here is a.rightCols<2>(): -5 -3 1 0 0 9 3 9 Now the array a is: 7 9 0 0 -2 -6 0 0 6 -3 0 0 6 6 0 0
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This is the const version of rightCols<int>().
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Example:
Output:
Here is the matrix m: 0.68 0.597 -0.33 -0.211 0.823 0.536 0.566 -0.605 -0.444 Here is the sum of each row: 0.948 1.15 -0.483 Here is the maximum absolute value of each row: 0.68 0.823 0.605
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This is only for vectors (either row-vectors or column-vectors), i.e. matrices which are known at compile-time to have either one row or one column.
start | the first coefficient in the segment |
size | the number of coefficients in the segment |
Example:
Output:
Here is the vector v: 7 -2 6 6 Here is v.segment(1, 2): -2 6 Now the vector v is: 7 0 0 6
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This is the const version of segment(Index,Index).
*this
This is only for vectors (either row-vectors or column-vectors), i.e. matrices which are known at compile-time to have either one row or one column.
The template parameter Size is the number of coefficients in the block
start | the index of the first element of the sub-vector |
Example:
Output:
Here is the vector v: 7 -2 6 6 Here is v.segment<2>(1): -2 6 Now the vector v is: 7 -2 0 0
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This is the const version of segment<int>(Index).
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Version of DenseBase::select(const DenseBase&, const DenseBase&) with the else expression being a scalar value.
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Version of DenseBase::select(const DenseBase&, const DenseBase&) with the then expression being a scalar value.
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Sets all coefficients in this expression to value.
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Sets a linearly space vector.
The function generates 'size' equally spaced values in the closed interval [low,high].
This is only for vectors (either row-vectors or column-vectors), i.e. matrices which are known at compile-time to have either one row or one column.
Example:
Output:
0.5 0.75 1 1.25 1.5
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Sets all coefficients in this expression to one.
Example:
Output:
7 9 -5 -3 1 1 1 1 6 -3 0 9 6 6 3 9
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Sets all coefficients in this expression to random values.
Example:
Output:
0 7 0 0 0 -2 0 0 0 6 0 0 0 6 0 0
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Sets all coefficients in this expression to zero.
Example:
Output:
7 9 -5 -3 0 0 0 0 6 -3 0 9 6 6 3 9
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swaps *this with the expression other.
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swaps *this with the matrix or array other.
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This is only for vectors (either row-vectors or column-vectors), i.e. matrices which are known at compile-time to have either one row or one column.
size | the number of coefficients in the block |
Example:
Output:
Here is the vector v: 7 -2 6 6 Here is v.tail(2): 6 6 Now the vector v is: 7 -2 0 0
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This is the const version of tail(Index).
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This is only for vectors (either row-vectors or column-vectors), i.e. matrices which are known at compile-time to have either one row or one column.
The template parameter Size is the number of coefficients in the block
Example:
Output:
Here is the vector v: 7 -2 6 6 Here is v.tail(2): 6 6 Now the vector v is: 7 -2 0 0
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This is the const version of tail<int>.
cRows | the number of rows in the corner |
cCols | the number of columns in the corner |
Example:
Output:
Here is the matrix m: 7 9 -5 -3 -2 -6 1 0 6 -3 0 9 6 6 3 9 Here is m.topLeftCorner(2, 2): 7 9 -2 -6 Now the matrix m is: 0 0 -5 -3 0 0 1 0 6 -3 0 9 6 6 3 9
This is the const version of topLeftCorner(Index, Index).
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The template parameters CRows and CCols are the number of rows and columns in the corner.
Example:
Output:
Here is the matrix m: 7 9 -5 -3 -2 -6 1 0 6 -3 0 9 6 6 3 9 Here is m.topLeftCorner<2,2>(): 7 9 -2 -6 Now the matrix m is: 0 0 -5 -3 0 0 1 0 6 -3 0 9 6 6 3 9
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This is the const version of topLeftCorner<int, int>().
cRows | the number of rows in the corner |
cCols | the number of columns in the corner |
Example:
Output:
Here is the matrix m: 7 9 -5 -3 -2 -6 1 0 6 -3 0 9 6 6 3 9 Here is m.topRightCorner(2, 2): -5 -3 1 0 Now the matrix m is: 7 9 0 0 -2 -6 0 0 6 -3 0 9 6 6 3 9
This is the const version of topRightCorner(Index, Index).
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The template parameters CRows and CCols are the number of rows and columns in the corner.
Example:
Output:
Here is the matrix m: 7 9 -5 -3 -2 -6 1 0 6 -3 0 9 6 6 3 9 Here is m.topRightCorner<2,2>(): -5 -3 1 0 Now the matrix m is: 7 9 0 0 -2 -6 0 0 6 -3 0 9 6 6 3 9
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This is the const version of topRightCorner<int, int>().
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n | the number of rows in the block |
Example:
Output:
Here is the array a: 7 9 -5 -3 -2 -6 1 0 6 -3 0 9 6 6 3 9 Here is a.topRows(2): 7 9 -5 -3 -2 -6 1 0 Now the array a is: 0 0 0 0 0 0 0 0 6 -3 0 9 6 6 3 9
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This is the const version of topRows(Index).
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N | the number of rows in the block |
Example:
Output:
Here is the array a: 7 9 -5 -3 -2 -6 1 0 6 -3 0 9 6 6 3 9 Here is a.topRows<2>(): 7 9 -5 -3 -2 -6 1 0 Now the array a is: 0 0 0 0 0 0 0 0 6 -3 0 9 6 6 3 9
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This is the const version of topRows<int>().
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Example:
Output:
Here is the matrix m: 7 6 -2 6 Here is the transpose of m: 7 -2 6 6 Here is the coefficient (1,0) in the transpose of m: 6 Let us overwrite this coefficient with the value 0. Now the matrix m is: 7 0 -2 6
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This is the const version of transpose().
Make sure you read the warning for transpose() !
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This is the "in place" version of transpose(): it replaces *this
by its own transpose. Thus, doing
has the same effect on m as doing
and is faster and also safer because in the latter line of code, forgetting the eval() results in a bug caused by aliasing.
Notice however that this method is only useful if you want to replace a matrix by its own transpose. If you just need the transpose of a matrix, use transpose().
*this
must be a resizable matrix.
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void visit | ( | Visitor & | visitor | ) | const |
Applies the visitor visitor to the whole coefficients of the matrix or vector.
The template parameter Visitor is the type of the visitor and provides the following interface:
The parameters rows and cols are the number of rows and of columns of the returned matrix. Must be compatible with this MatrixBase type.
This variant is meant to be used for dynamic-size matrix types. For fixed-size types, it is redundant to pass rows and cols as arguments, so Zero() should be used instead.
Example:
Output:
0 0 0 0 0 0
The parameter size is the size of the returned vector. Must be compatible with this MatrixBase type.
This is only for vectors (either row-vectors or column-vectors), i.e. matrices which are known at compile-time to have either one row or one column.
This variant is meant to be used for dynamic-size vector types. For fixed-size types, it is redundant to pass size as argument, so Zero() should be used instead.
Example:
Output:
0 0 0 0 0 0
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inlinestatic |
This variant is only for fixed-size MatrixBase types. For dynamic-size types, you need to use the variants taking size arguments.
Example:
Output:
0 0 0 0 0 0 0 0
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Outputs the matrix, to the given stream.
If you wish to print the matrix with a format different than the default, use DenseBase::format().
It is also possible to change the default format by defining EIGEN_DEFAULT_IO_FORMAT before including Eigen headers. If not defined, this will automatically be defined to Eigen::IOFormat(), that is the Eigen::IOFormat with default parameters.